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+{"snippet": "\"It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way--in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only.\" -- Charles Dickens, A Tale of Two Cities. From Wikipedia. A comma splice is the use of a comma to join two independent clauses. For example: It is nearly half past five, we cannot reach town before dark. Although acceptable in some languages and compulsory in others (e.g., Bulgarian or French), comma splices are usually considered style errors in English. Would the sentence above be an example of an author making stylistic error on purpose? Thanks", "label": 1}
+{"snippet": "Normally Latex puts hyphens inside the text: ------------------------------------ Lorem ipsum dolor sit amet, consec- tetuer adipiscing elit. Aenean com- modo ligula eget dolor. Aenean mas- sa. Cum sociis natoque penatibus et magnis dis parturient montes, nasce- tur ridiculus mus. Donec quam felis, ultricies nec, pellentesque eu, pre- tium quis, sem. Nulla consequat mas- sa quis enim. Donec pede justo, fringilla vel, aliquet nec, vulputa- te eget, arcu. ------------------------------------ But I want to put it beside the text, because it is easier on the eyes and better for the reading flow: ------------------------------------ Lorem ipsum dolor sit amet, consecte- tuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridi- culus mus. Donec quam felis, ultrici- es nec, pellentesque eu, pretium quis, sem. Nulla consequat massa quis enim. Donec pede justo, fringil- la vel, aliquet nec, vulputate eget, arcu. ------------------------------------ I know that it is possible because I have seen it in some PDFs which were most likely created using Latex, but I did not find out how it is done.", "label": 1}
+{"snippet": "I am not a native English speaker, and I have just started to study physics in English. However, I came across the term heralded photon while I was reading a review article about optical quantum memory. I don't understand what it means. A dictionary explains herald as, \"to be a sign that something is going to happen,\" but it does not make any sense. Below is the excerpt from the article: If a single-photon detector is placed in one of the emission channels of non-degenerate spontaneous parametric down-conversion, a detection event indicates emission of a photon pair, and thus the presence of a single photon in the other channel. Such a heralded photon is emitted at an arbitrary time, however, making it unsuitable for many application. Would you help me understand this term?", "label": 1}
+{"snippet": "In the Cambridge Grammar of the English Language, Huddleston and Pullum use the term \"determinative\" for the lexical category of words like the, etc. And they use \"determiner\" for the grammatical function that is characteristically filled by determinatives (but which can also be filled by things such as genitive noun phrases). In an older generation of reference grammars, however, notably Quirk, et alia's Comprehensive Grammar of the English Language, the use of these terms is exactly reversed. That is, \"determiner\" is the lexical category and \"determinative\" is the grammatical function. The difference has been bugging me for a long time. Can anyone provide a principled explanation as to why we should prefer one over the other? I'm sure Huddleston and Pullum had a motivation to alter terminology that's been in use since Bloomfield's day, but I can't find any discussion in their work.", "label": 1}
+{"snippet": "I've been trying to determine an explanation for the falsity of a logical statement for some time now and I've had no luck in figuring out exactly how to go about it. The two part question goes as follows: Consider the arguments below. If the argument is valid, identify the rule of inference that establishes its validity. If not, explain why. a. If Robert understands the concepts correctly, he will be able to finish his assignment in two hours. Robert finished his assignment in more than two hours. Therefore, Robert did not understand the concepts correctly. b. If taxes increase, the housing market will decrease. Taxes are not increasing. Therefore, the housing market will not decrease. Perhaps I'm misunderstanding the way to determine the falsity of a logical statement? Any help is appreciated.", "label": 1}
+{"snippet": "I seem to remember hearing a medical term for the act of causing pain to one part of your body to relieve a chronic pain elsewhere in the body. For instance, someone who suffers from chronic back pain might break their finger so that they can stop focusing on their back pain. Or someone with a broken arm might intentionally drop something on their foot so the focus of pain transfers to their foot for a while. Is there such a term for this type of pain management technique? I was thinking this was called \"deferred pain\", but I cannot find anything on Google for that. Most of the search terms I've come up with lead me to \"referred pain,\" but that's not the term I'm looking for. That's completely different than what I'm talking about.", "label": 1}
+{"snippet": "I am trying to prove if f is continuous and closed (\"closed\" means the image of any closed subset of the domain is closed) then f(closure of X) equals the closure of f(X). I was able to prove that if f is continuous then f(closure of X) is a subset of closure of f(X). Now, I am trying to prove the other way around: closure of f(X) is a subset of f(closure of X). So here is my attempt: Let y be a point of the closure of f(X). Then y is either a point of f(X) or a limit point of f(X). I am wondering if f(X) is a subset of f(closure of X)? If this is true then in the former case, it is easy to conclude that y is also a point of f(closure of X) and in the latter case, I can show that y is also a limit point of f(closure of X). Since f is a closed mapping and the closure of X is closed, f(closure of X) is also closed, which implies y is a point of f(closure of X). Also, if you know how to prove that if f(closure of X) equals closure of f(X) then f is a continuous and closed mapping I would really appreciate it if you could give me some hints. Thanks a lot.", "label": 1}
+{"snippet": "I have a question regarding the usage of the words to and with in the sentence \"He lodged a complaint to/with the Authorities\". Which is correct? Note: Lodge in this context is \"to present (a complaint, appeal, claim, etc.) formally to the proper authorities\". I have been told that, in the said sentence, with is correct and not to. But, I am confused as to why with is correct and used more often than to, especially since the definition of with is \"accompanied by (another person or thing)\", while to is defined as \"identifying the recipient or intended recipient of something\". How could someone lodge a complaint with the Authorities? In my mind, with denotes that a person is lodging a complaint together with the Authorities. Could someone explain this to me?", "label": 1}
+{"snippet": "I am trying to prove the following statement regarding nowhere dense sets: \"In a metric space X, the frontier of an open set is the set of accumulation points of a discrete set.\" As far as my attempts go, I have gone back and looked at an earlier proof of Baire's Category Theorem and worked out the details (as to my understanding, it should be similar). However, I am still not seeing how to prove the above using said theorem. Does anyone have any hints or suggestions as to how to proceed? Note: I have already proven (as part of the above) that: a)In a metric space X without isolated points, the closure of a discrete set in X is nowhere dense in X. b) In any space X, the frontier of an open set is closed and nowhere dense. c) Every closed nowhere dense set is the frontier of an open set.", "label": 1}
+{"snippet": "My question concerns the usage of \"as if\" as an idiomatic interjection. The references I have consulted (etymonline, online dictionaries, etc.) seem to agree that \"as if\" is used in this context to convey incredulity or doubt. This is how I have always thought of it. The other day, I was with friends who used \"as if\" to express their surprise and joy about a wedding proposal. They weren't being sarcastic or incredulous; they were genuinely happy about the proposal. Here is a loosely paraphrased version of what they said: \"As if they're getting married!\" Is my friends' usage of \"as if\" standard? Is it a primarily regional distinction? (I am in Ontario, Canada right now.) The closest example we could come up with is someone says \"I can't believe that you won first prize!\" Of course, the person can and does believe it, so their words ought not to be taken literally. Is it the same idea with \"as if\"?", "label": 1}
+{"snippet": "A year ago, I took a statistics course at my university. The course was based on Rice's \"Mathematical Statistics and Data Analysis\". Apart from the fact that I did not find the book terribly good, I found that the lectures did not aid me a lot in understanding the material either. I did pass the course, but I didn't feel I really understood the material. Fast forward a year. I have now come to realise that statistics can be a very interesting and useful subject, but I haven't done any statistics ever since the course I just mentioned. I'm thinking of doing some statistics courses for my Master's degree, though. Question: do you know any good resources (video lectures, books, solved problems) which I can use to brush up my statistics knowledge? I like books that have a large number of solved problems and worked examples, so I can check whether I actually solved the problems correctly.", "label": 1}
+{"snippet": "I am fairly certain that there's an idiomatic phrase for this, referring to either the situation or the person. It's on the tip of my tongue. Scenario: Alice tells Bob to stop making a such a noise with his power tools. Bob replies that he had already stopped an hour ago and was anyway done for the day. How would you describe Alice, who instructed Bob to do something which he already did or was going to do? In other words, she gave him a redundant order that serves no purpose other than to reaffirm authority and stroke her own ego. Alternatively, she's making a show of strength by demanding that something that's already been done, be done. It's similar in concept to the French phrase \"faire la mouche du coche\" but not quite. It's along the lines of gadfly, backseat driver, busybody, or tooting one's own horn. EDIT: The closest matches so far are control freak and megalomaniac, but those still don't describe the post-facto aspect.", "label": 1}
+{"snippet": "The figure shows a circuit consisting of a battery, a switch, two identical lightbulbs, and a capacitor that is initially uncharged. a. Immediately after the switch is closed, are either or both bulbs glowing? Explain. b. If both bulbs are glowing, which is brighter? Or are they equally bright? Explain. c. For any bulb (A or B or both) that lights up immediately after the switch is closed, does its brightness increase with time, decrease with time, or remain unchanged? Explain. I really don't understand the concept of how a capacitor affects the flow of current in a circuit, and am having an incredibly hard time figuring out this question. At least an idea of where to start would be great. I had thought that for part A both light bulbs would begin glowing since the capacitor isn't charged, but i have no idea how to tell which one is brighter. I also think that for part C, the brightness of the bulbs would decrease over time after the capacitor is charged because once it's charged the voltage of the capacitor equals the voltage of the battery, hence there is no voltage potential and no current. Am I on the right track at all for this???", "label": 1}
+{"snippet": "Consider the following scenario: I get in a spaceship, and travel really close to the speed of light for a while, and then come back. A lot of time has passed on the Earth, but since I was traveling so fast, I only experienced a few years passing. So, my friends on Earth are dead, whereas I'm only a few years older. But what I'm having trouble wrapping my head around, is why is it them that's dead, and not me? After all, given what I understand about relativity, it's just as fair to say that my spaceship stayed still, and it was actually the Earth that traveled really fast and then came back to my ship. In that scenario though, the Earth being the fast-moving ship, and my ship being the stationary body, wouldn't it be that I am dead, and everyone on the Earth is just a few years older? If there really is no preferred frame of reference, then why does the ship-traveler live while the people on the Earth die?", "label": 1}
+{"snippet": "I often find myself putting excess commas and brackets (parentheses for all you US English speakers out there) into sentences, in hopes of rendering it more 'readable'. The trouble is, I am never sure just how much is too much and often need to seek the services of an adjudicator. However, this time no one could decide: how should the following phrase be punctuated? Like this, without commas? During the Great Depression the Nazi Party gained a lot of popularity because they promised to make Germany great again and there was nothing the German people as a whole wanted more. Or like this, with only one comma? During the Great Depression the Nazi Party gained a lot of popularity because they promised to make Germany great again, and there was nothing the German people as a whole wanted more. Or like this, with two commas? During the Great Depression, the Nazi Party gained a lot of popularity because they promised to make Germany great again, and there was nothing the German people as a whole wanted more. What option is the most grammatical and readable?", "label": 1}
+{"snippet": "I need someone to help me to define the meaning of the word \"en masse\" in the following context: the initial aim of internment during the later conflict was to identify and intern those who posed a particular threat to the safety or defence of the country. As the war progressed, however, this policy changed and Japanese residents were interned en masse \" Which of the following interpretations is correct? the initial aim of internment during the later conflict was to identify and intern those who posed a particular threat to the safety or defence of the country. As the war progressed, however, this policy changed and Japanese residents were interned together the initial aim of internment during the later conflict was to identify and intern those who posed a particular threat to the safety or defence of the country. As the war progressed, however, this policy changed and all Japanese residents were interned", "label": 1}
+{"snippet": "I came across the following thought experiment, and I would like to understand whether the controversy around it is justified. Imagine an experiment in which a mathematician is put to sleep with some kind of drug. He is located in a room that is designed in such a way as to keep him completely isolated from any kind of external information. The researchers have a sleep inducing drug that is able to put you to sleep and make you forget it was even administered. After the researchers have put the mathematician to sleep with this drug, they toss a fair coin. If it comes up heads they will wake the mathematician up once and administer the drug again. If it comes up tail they will wake him up twice, each time administering the drug again. Whenever the mathematician is awoken during the experiment, they will ask him for his best guess regarding the result of the coin toss. Eventually the experiment ends, and the researchers will awaken the mathematician a final time and tell him the experiment has ended. During the experiment, what answer should the mathematician give as his best guess for the result of the coin toss ? I think he should say that odds are the coin came up tail, but I am very curious what other people make of it, and whether there are any grounds for dissent at all.", "label": 1}
+{"snippet": "I'm looking for good book recommendations for preparing for the International Physics Olympiad. As stated on the IPhO syllabus, the topics covered are about the same as those in the first year or two of a physics degree: Mechanics: kinematics, dynamics, celestial mechanics, hydrodynamics Electromagnetism: Maxwell's equations, circuits, matter in EM fields Waves: damped/driven harmonic oscillators, waves, interference and diffraction, geometrical optics Modern: special relativity, matter waves, particle and nuclear physics Thermodynamics: laws of thermodynamics, heat engines, phase transitions However, there's less of an emphasis on complicated calculations, and more of an emphasis on problem solving and insight. For example, multivariable calculus is almost never used; instead many questions can be elegantly solved by symmetry. I'm looking for textbooks or problem books to bring me to this level, starting from the level of high school physics.", "label": 1}
+{"snippet": "I'm having trouble understanding the simple \"planetary\" model of the atom that I'm being taught in my basic chemistry course. In particular, I can't see how a negatively charged electron can stay in \"orbit\" around a positively charged nucleus. Even if the electron actually orbits the nucleus, wouldn't that orbit eventually decay? I can't reconcile the rapidly moving electrons required by the planetary model with the way atoms are described as forming bonds. If electrons are zooming around in orbits, how do they suddenly \"stop\" to form bonds. I understand that certain aspects of quantum mechanics were created to address these problems, and that there are other models of atoms. My question here is whether the planetary model itself addresses these concerns in some way (that I'm missing) and whether I'm right to be uncomfortable with it.", "label": 1}
+{"snippet": "I am interested in self-studying real analysis, and I was wondering which textbook I should pick up. I know all high school mathematics, I have read How to Prove It by Daniel J. Velleman (I did most of the exercises). I have completed a computational calculus course which covered everything up to and including integration by parts (including the substitution method and Riemann sums) I am currently considering: Principles of Mathematical Analysis by Walter Rudin From what I have heard this is not very well suited for self-study and that while the exercises are extremely difficult, if you take the time they are worth the effort. Calculus by Michael Spivak I have heard that while Spivak explains proofs in much more detail than Principles, it doesn't cover all of the material in the latter. Understanding Analysis by Stephen Abbott I don't know much about this. I have only seen some comments saying that it is an excellent introduction to analysis. Mathematical Analysis by Tom M. Apostol Extra clarification edit: I would prefer a book not to ''dumb down'' the material, something that would not hold my hand through every step, something that would force me to fill in the gaps myself instead of explaining every single step. That is why I am currently leaning towards Rudin, but before I decide I would still like some information on the book by Apostol.", "label": 1}
+{"snippet": "The answers to this related question suggest that to and in order to are pretty much interchangeable, the former being preferred in informal contexts. My question is about negative clauses. According to the answers to the linked questions, the following two sentences are fine and mean the same thing: We were speaking loudly to wake up Mr.Smith. We were speaking loudly in order to wake up Mr.Smith. Can the same be said about the following sentences? We were speaking quietly not to wake up Mr. Smith. We were speaking quietly in order not to wake up Mr. Smith. I am asking because when I used the first variant a friend of mine corrected me and said that I must use either in order or so as to make the sentence grammatical.", "label": 1}
+{"snippet": "I have taken a course in abstract algebra, which used Fraleigh's book. This semester I'm taking a course called Rings and Modules, which uses Bhattacharya's book, which is fine for the most part, but sometimes I can't understand the material. Today after the lecture I spoke to my professor, and he told me he thought some explanations and constructions in the book aren't very good. So I have Fraleigh, which is insufficient for the material I'm studying now, and I have Bhattacharya which sometimes confuses me. I've heard so much about Dummit and Foote, so I'm wondering if it's worth the cost of buying it now only to improve my understanding of certain topics? I'm also planning on taking Galois theory next semester, and if Dummit and Foote covers that as well, I suppose that's another reason to buy it because the Galois course at my university also uses Bhattacharya.", "label": 1}
+{"snippet": "I am wondering whether to use a restrictive relative clause such as: \"Multicopters belong to a family of aircraft called rotorcraft , which also includes helicopters, and although they appear to be similar, a multicopter's design is mechanically much simpler.\" or non-restrictive relative clause: \"Multicopters belong to a family of aircraft called rotorcraft that also includes helicopters, and although they appear to be similar, a multicopter's design is mechanically much simpler.\" I am leaning toward the latter because the second half of the complete sentence relies on the inclusion of the statement \"also includes helicopters\" for its meaning. However, the first part of the sentence (\"multicopters belong to a family of rotorcraft\") makes sense by itself (i.e. it could be a complete sentence), and the second part of the sentence is really another statement attached with \"and\". So I'm not sure. Would it be better as two separate sentences: \"Multicopters belong to a family of aircraft called rotorcraft, which also includes helicopters; although they appear to be similar, a multicopter's design is mechanically much simpler.\" Side-note: Now I'm going crazy, wondering whether it should be \"include\" or \"includes\". This is why it takes me so long to write anything. sigh", "label": 1}
+{"snippet": "There is a related question on this site here: Why glass is transparent? Which explains that glass is transparent because the atoms in glass have very large energy differences between energy levels and photons of visible light do not have enough energy to excite electrons from one energy level to another. Whereas, electrons in atoms of most other substances can be excited so the photon is absorbed. But my question is, why don't these excited electrons return to their original energy level and release a photon in the direction the original photon was travelling, hence allowing the light to pass through the object? Edit: I had not realised earlier that this exact same question had been asked before on this site here: Why aren't all objects transparent? So, I shall clarify my question a bit more. The answers to the linked question say that the energy of the excited electron is lost so the light is re emitted as waves with longer wavelengths which we cannot see. I'd like to know how exactly the electron loses this energy. One answer to the linked question states that the energy is lost to lattice vibrations, but I'd like to know how exactly an excited electron still bound to the atom can transfer its energy to lattice vibrations.", "label": 1}
+{"snippet": "I often hear the following, particularly during announcements when travelling by rail or air: On behalf of myself and the rest of the team, I would like to wish you a pleasant journey. I've always wondered whether this is grammatical. I found this question, which discusses how to form such a sentence, but it still seems unusual to me even if it is correct. Something closer to the following would seem more rational: On behalf of the whole team, I would like to wish you a pleasant journey. This is because the whole team is not speaking. Contrast this to the first example in which the speaker claims to be speaking on behalf of himself. Can either of these sentences be used to mean the same thing? Is one preferred over the other?", "label": 1}
+{"snippet": "Once again, y'all can blame my boss. Well, him or Captain Picard. He (my boss, not Picard) has the annoying habit of saying \"Make it sure that\", instead of \"Make sure that\". No matter how many times I correct him (usually via a post-it note thrust in his face while he's on the phone), he keeps making this mistake. Today, he clarified the root of his confusion: if there's an it in \"Make it so\" (he's a big ST:TNG fan), then why shouldn't there be an it in \"make sure that\", also? As a native speaker, the best I can come up with is \"because it sounds wrong\", and that's never enough to appease my boss. Help? How can I explain the difference to him? Is there logic behind it, or is it merely idiom?", "label": 1}
+{"snippet": "everyone. When referring to a person, are there any firm guidelines when it comes to the use of \"a\" or \"the\" after the comma that follows their name? To clarify: Recently, I was writing an article about Amy Winehouse, and I referred to her like this: \"Amy Winehouse, the troubled singer-songwriter who...\" A few weeks later, however, I was writing an article about a celebrated photographer, and it felt wrong to use \"the\" after the comma, so I wrote: \"Sebastiao Salgado, a celebrated Brazilian photographer who...\" As a result, I am now wondering if there are any solid guidelines? I realise that \"a\" is used when the subject is one of many, and that \"the\" is used when there is only one, but there have been times when I have followed these guidelines and the sentence has looked / felt wrong. Can anyone offer some guidance?", "label": 1}
+{"snippet": "In order for a body to move with uniform velocity in a circular path, there must exist some force towards the centre of curvature of the circular path. This is centripetal force. By Newton's Third Law, there must exist a reactive force that is equal in magnitude and opposite in direction. This is the reactive centrifugal force. My question is simple, and it is probably the result of lack of common sense but here it goes: In uniform circular motion, why don't these forces simply cancel each other out? If they did, how would we know they exist in that situation? When I swing a rock tied to a rope, I feel the centrifugal force, but not the centripetal force. In this situation how can the reactive force be greater than the force itself?", "label": 1}
+{"snippet": "This question refers to the paper Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures by Altland and Zirnbauer. In the paper the authors give a classification of Bogoliubov de Gennes Hamiltonians. More precisely the authors state that The aim of the current section is to classify systems according to their symmetries. Using the BdG formalism we will show that the presence or absence of time-reversal and/or spin-rotation invariance leads to four distinct symmetry classes. While I do understand their classifications I am wondering if it is sufficient to restrict oneself to time-reversal and spin-rotation invariance only? I am wondering why the authors seem to disregard important symmetries such as inversion symmetry of the underlying lattice or other point group symmetries? Hence I am wondering if the classification given in the paper is in fact complete? In particular the presence and absence of inversion symmetry plays a key role in the theoy of superconductivity (centrosymmetric vs. non-centrosymmetric superconductors) I would be very happy to hear thoughts and opinions on that.", "label": 1}
+{"snippet": "The number of points on a line is uncountably infinite. The number of lines on a plane is uncountably infinite. It seems like it follows that there would be an uncountably infinite number of points on a plane, too. But it seems unsatisfying to believe that these are both the same thing. Surely adding an entirely new dimension must in some way increase the cardinality of what we're talking about, right? Or if not, is there a convincing demonstration that it doesn't change anything? If they aren't, is there a way to show that they aren't? Are there mathematical ways of describing the distinction between the sizes of these sets, and if so, what are they called? (I'm having a lot of trouble searching for an answer because I'm not sure what words to use.)", "label": 1}
+{"snippet": "I'm looking for a good introductory text to analysis, or, more specifically, a text that puts calculus on a much more rigorous ground. I've just finished a year of calculus at my local university, and I feel a bit cheated by the course I took. In addition to having a poor teacher who focused on rote memorization, our text was abysmal. I ended up resorting to self study, which was a blessing in disguise because it led me to discover a love of logic, set theory, abstract algebra, and topology. I'm interested in becoming a math major when I graduate hs, and I'm comfortable with studying dense, more sophisticated texts as long as they are well written, comprehensive, and build the subject on the ground up. Online texts would be appreciated, as I'm spending the next few months travelling and wont be able to receive packages.", "label": 1}
+{"snippet": "Suppose we have a circular table. We have made a straight line groove in the table extending from the center to the circumference. Now we place a block at some distance from the center in the groove and start rotating the table. Suppose there is no friction between the walls of groove and the block. Result: The block finally moves out of the groove. If we consider the rotating frame of reference of the table, this motion can be easily explained with the help of centrifugal force which acts radially outward on the block. But when we consider the frame of reference of earth, I was not able to explain it. There are no radially outward forces on the block, just the normal reaction from the walls of the groove(which acts in a direction perpendicular to the groove) and the weight of the block(which acts downward). So how does the block eventually move out of the groove?", "label": 1}
+{"snippet": "I have just recently started learning some very basic thermodynamics and there is one question that has been driving me crazy: Why do we even need the Zeroth law of thermodynamics? The law states: If a body A, be in thermal equilibrium with two other bodies, B and C, then B and C are in thermal equilibrium with one another. (Wikipedia) This seems like the most obvious statement ever. How could B and C not be in thermal equilibrium? While looking for an answer I came across a Khan Academy video that deals with this exact question. The lecturer in the video says: \"...yeah our universe is like that but think about it a little harder, you could problably think of a universe where it might not be like that.\" (Video) This just confused me even more. If we follow that logic wouldn't we have to formulate something like Newtons Zeroth Law or Keplers Zeroth law too?", "label": 1}
+{"snippet": "I keep all my references in one huge BibTeX file, which happens to include the full journal name for each one. I'm currently preparing a manuscript that needs the journal names to be abbreviated. From the research I've done (including reading related questions on this site), it seems that (i) there is no standard automatic way to do this, but (ii) there are various tools such as biber and jabref that will allow me to pre-process my .bib file with a sort of global seach-and-replace for the journal names. However, since my manuscript only has a few references it would be easier to just manually type in the new journal name for each entry. Is there a way to do this? I'm looking for a quick-and-dirty LaTeX-only solution that won't require me to install anything that isn't already part of TeX Live, since I'm on a tight schedule. I know I could just edit the entries in my .bib file, but I don't want to do that, because I like to keep all my references in the same place. In case it's relevant, I maintain my .bib file using BibDesk on a Mac, I'm using the natbib package, and the bibliography style is apalike.", "label": 1}
+{"snippet": "This question related to the Grandfather Paradox. Assume that time travel to the past is a reality. What experiment/test could the time traveler perform in order to determine if he is in his own timeline or an alternate timeline/universe? If the time traveler was in his own timeline and kills his grandfather, that means he would have never been born -- and thus cannot travel back in time to kill his grandfather. If his grandfather was not killed, that means he would have been born -- and thus could travel back in time to kill his grandfather. And so on ... At the moment the time traveler kills his grandfather, what would happen if the time traveler was in his own timeline/universe? Would it be any different if the time traveler was in a different timeline/universe? How could the time traveler know for sure if he is in his own timeline/universe or not?", "label": 1}
+{"snippet": "English is not my native-tongue, so I always find it hard to grasp the concept of \"question tags\" and more importantly the way to answer to them. Let me explain with the help of this situation - I am supposed to complete my homework and I haven't. My mom suspects that I haven't and asks me the below question. I want to confess that I haven't. What should I answer? Mom : You didn't finish your homework, did you? Me : Yes, I haven't [OR] No, I haven't? I've always thought that it is \"Yes, I haven't\" because the questioner has already found out that I haven't and I should just assert it by saying 'Yes'. But a friend of mine says that it is \"No, I haven't\" because I am effectively answering the question \"did you?\". Which of us is correct?", "label": 1}
+{"snippet": "The latest Stack Exchange blog post contains the following section header: In which we stop being dumb I have never really understood what is going on in these \"in which...\" constructions at a grammatical level. Is it just an elision of something like \"this is a section in which...\"? Or, perhaps, is it an imitation of a famous quotation/title/etc. that has the same structure? I feel like I've only seen this construction on the internet, which suggests to me that it is either a piece of internet lingo that I've somehow missed or a very new construction that hasn't caught up to me yet. I am a native speaker of American English, but am relatively ignorant of other varieties, so perhaps this is just a feature of BrE that I'm unaware of or something. Note that I am not asking about constructions like: In which of these two fields should I write my name? These constructions are full sentences in which the preposition \"in\" has been hoisted to the beginning of the sentence, and I understand them perfectly well.", "label": 1}
+{"snippet": "I've been reading Lois Lowry's The Giver recently, and have questions regarding a sentence from her book. I know that some sentences in literature, like The Giver, do not always follow strict grammar rules and do not need to follow them, but I still can't understand the exact meaning of the sentence: They(Jonas and Gabriel) saw deer; and once, beside the road, looking at them curious and unafraid, a small reddish-brown creature with a thick tail, whose name Jonas did not know. In this excerpt, How does the adjective phrase, \"curious and unafraid,\" work in the sentence? Does it modify the verb \"looking at\"? To be grammatically correct, should it be changed to \"curiously and unafraidly\"? Where does \"a small reddish-brown creature with a thick tail, whose name Jonas did not know\" belong to? Why is the noun phrase placed at the end if it modifies the \"deer\" in the first clause? I absolutely don't consider it is wrong and this is not necessary to understand the whole story, but I can't help myself wondering how this sentence works. Could you help me parse this sentence?", "label": 1}
+{"snippet": "I am working on a document (using the scrbook class, if it is relevant) which will end up consisting of lots of text and a large number of tikz figures. Even when writing the very first chapter, I notice that running pdflatex, bibtex and makeindex takes a considerable amount of time. I expect this to become worse (i.e., even longer) when the amount of text and figures increases. I already structured my document into a number of files, since, during writing, I often make changes to only one part of the whole document (e.g., one chapter or one part of the appendix). Is there any way to reuse the files generated by pdflatex during the last run to get a preview of the updated document (without having to wait for the document to be rebuilt completely)? I would be fine with things like the TOC not being updated. My current toolchain and editor are set up on both, Windows (MiKTeX) and Linux (TeX Live), but I could live with being limited to one of the two platforms. My highest priority is to reduce the build times required for previewing.", "label": 1}
+{"snippet": "I'm very confused about how I should be using TexWorks on Ubuntu, and what the difference is between TexWorks, TexLive, and MikTex. So, I installed the TexLive package with sudo apt-get install texlive, because according to the website, this also installs TexWorks. However, after this installation, I could not find any reference to TexWorks on my machine. So, I then installed the TexWorks package with sudo apt-get install texworks. Now, I can open a .text file with TexWorks. But I am confused as to whether I am now using TexWorks, or TexLive (and what about MikTex?). Also, I am getting errors such as LaTeX Error: Filebbm.sty' not found.` This means I need to install this package. How can I do this? I am used to running TexWorks and MikTex in Windows, where packages were automatically installed on-the-fly as they were required, and ideally I would like something like this. Thanks!", "label": 1}
+{"snippet": "I'm not sure if my problem was asked before, but if so, a simple link to the answer would be appreciated. Basically I've recently seen videos about spud cannons that use compressed air and it got me thinking about the math behind it. Obviously for targeting purposes, one needs the final velocity at the end of the cannon barrel to substitute in newton's projectile motion equations and get the distance which is cool. Now to find the velocity at that point is where it gets really messy. Since the pressure of compressed air changes as it expands throughout the cannon barrel, the force it exerts on the projectile decreases and so does the acceleration. With the assumption of an isothermal expansion of the air in the barrel, how do you find the end velocity of the projectile at the end of the cannon barrel?", "label": 1}
+{"snippet": "I cannot understand why we cannot use \"even though\" instead of \"even so\" or vice versa. For example : I know her English isn't very good, but even so I can understand her. ( original sentence) If we can rewrite it with \"even though\", does it mean different thing? Even though her English isn't very good, I can understand her. (my sentence) Some other examples: The evidence was only circumstantial. Even so, he was convicted and spent ten years in prison for a crime that he perhaps did not commit. (original) Even though the evidence was only circumstantial, he was convicted and spent ten years in prison for a crime that he perhaps did not commit. She is loud and unfriendly. Even so, I like her. (original) Even though she is loud and unfriendly, I like her.", "label": 1}
+{"snippet": "One implication of general relativity is the concept of gravitational waves or gravitational radiation, ripples in spacetime thought to travel at speeds close to the speed of light. As far as I have researched, there is no direct evidence supporting their existence, but I have read many examples of indirect evidence. My question is regarding the nature of these proposed waves. I understand the motivation behind the idea of a gravitational wave, but I do not understand the reasoning behind how said wave is created. For instance, how is it possible for a wave to be created in spacetime, unless we make the assumption that spacetime (like a fabric) has some form of internal tension? When I attempt to visualize waves I tend to think back to sound waves and ocean waves...but these waves rely on internal forces between molecules in the medium to create the ripples. Do similar mechanics take place in a gravitational wave or is there some other explanation? Thank you for any help with this question.", "label": 1}
+{"snippet": "Let us define an inertial frame as a frame of reference where the laws of physics take their usual form, as opposed to non intertial frames where one has to introduce pseudo-forces. We can further define an equivalence class which contains other inertial frames as the class of frames of reference moving of constant velocity with respect to an initial inertial frame. Is it possible to show formally that there do not exist two inertial frames which cannot be put in the same equivalence class -- namely two inertial frames which are not moving at constant relative velocity one with respect to the other? I am aware of the fact that in a frame accelerated with respect to an inertial one there are pseudo forces, but I am concerned in particular in showing that there is no possible configuration in which they would all cancel out.", "label": 1}
+{"snippet": "Different authors seem to have different conventions when they define the term affine variety (similarly projective variety). For the purposes of this question let us stick with the affine case, and let us work over an algebraically closed field. For example: In Harris's Algebraic Geometry: A First Course, an affine variety is the zero set in the affine space, of a collection of polynomials. So, it is just a closed subset of the affine space under the Zariski topology. He calls an irreducible closed subset, an irreducible affine variety. (A similar convention is used in the book by Cox, Little and O'Shea) In Hartshorne's Algebraic Geometry, a closed subset of the affine space is called an affine algebraic set, and an irreducible closed subset is called an affine variety. In the recent book Algebraic Geometry I: Schemes With Examples by Goertz and Wedhorn, the authors use the terms affine algebraic set, and irreducible affine algebraic set for closed and irreducible closed subsets of the affine space respectively. They reserve the term affine variety for a space with functions that is isomorphic to a space with functions associated to an irreducible affine algebraic set (so, this is more in the spirit of Hartshorne). While it is usually clear from the context, what the authors of a particular book mean, when they use the terms above in bold, why are there different terminologies? Is there a consensus among mathematicians today, as to what they mean when they use the term affine algebraic variety?", "label": 1}
+{"snippet": "The five postulates (axioms) are: \"To draw a straight line from any point to any point.\" \"To produce [extend] a finite straight line continuously in a straight line.\" \"To describe a circle with any centre and distance [radius].\" \"That all right angles are equal to one another.\" \"That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.\" What's wrong with them? Which axiomatic system is being used nowadays? Hilbert's or SMSG (School Mathematics Study Group)? I believe in the case of SMSG the list of axioms contains some redundancy. Why do people say Euclid's axioms are 'far from being sound', even if they are all still (I guess) believed to be true? If there's something wrong with them, then maybe our better (Hilbert's or whatever) axiomatic system contains some false statements?", "label": 1}
+{"snippet": "I'm looking for a succinct way to describe what I believe is a semi-common situation, both in online discussions and sometimes in real life (e.g. with siblings during long car trips): when a discussion between two or more people turns sour, such that rather than discussing or debating the subject at hand, the people involved get sufficiently irritated with each other that they instead get drawn into a back-and-forth series of pointless/petty/passive-aggressive criticisms of each others' style, grammar, minor logical ambiguities, etc. I might call this \"hen-pecking\" (in reference to possibly-apocryphal reports that chickens packed into too-close proximity with each other will eventually start pecking each other to death, and must therefore either be given more space, or fitted with red contact lenses to calm them down), but I think there might be a better, more well-known phrase that describes the phenomenon. Can anyone supply such a phrase?", "label": 1}
+{"snippet": "In logic and computer programming, a conjunction of two logical statements is said to be true if and only if both statements are themselves true. For instance: \"The sky is blue\" and \"the grass is green\" is a conjunction of two logical statements. Note that a conjunction in this context is not the same as a grammatical conjunction. In product manuals, one often sees things like: \"These values are anded together\". However, \"anded\" doesn't seem like a proper English term, and it seems like there should be a verb for the act of combining two logical statements with a conjunction. Other logical operators like \"xor\" certainly use \"xored\" or \"xor'd\", but \"anded\" seems less acceptable somehow. Is there a nice English word for this operation? Some thoughts: \"conjoined\" doesn't seem sufficiently precise, because we're not just sticking the logical statements together, we're combining them with a particular operator (i.e. the clauses could still be conjoined with a disjunction operator instead). \"conjuncted\" might be appropriate, but I can't find anyone using it on the net, and I've never seen it used before in manuals and the like.", "label": 1}
+{"snippet": "The Poincare group has ten generators, which have the physical interpretation of energy, momentum, angular momentum, and the system center of mass, and which are of course conserved in any Poincare invariant system. Adding five more generators (of dilitation and the four special conformal transformations) extends the Poincare group to the conformal group. Do these five new quantities, which are conserved in any conformally invariant system, have any natural physical interpretation (something I can picture in my head)? Edit: To reiterate, I am familiar with the physical interpretation of the comformal symmetries. I am looking for a physical interpretation for the generators of the conformal symmetries. I'm not looking for the analog of \"momentum is the generator of spatial translations,\" I'm looking for the analog of \"conservation of momentum tells you that something moving in a straight line will continue to move in a straight line.\"", "label": 1}
+{"snippet": "I know there are a lot of reference requests for differential equations textbooks but none seem to be what I need. I'm looking for a book I can use for self study that isn't overly complicated and explains a lot (meaning it doesn't often say \"left as an exercise for the reader\" but instead proves all major results). I have taken mutlivariable calculus and am currently taking linear algebra so I also need a book that assumes no prior knowledge/experience with differential equations. If possible I'd prefer a book that explains the reasons for doing things and not just the methods. Thanks in advance. (If there is another question that I missed that asks for all these criteria please let me know and I'll see if those are what I'm looking for.)", "label": 1}
+{"snippet": "When someone says something unpleasant or rude, often the reply is \"Bite your tongue!\". But where did this come from? I can find a number of sources explaining that to bite one's tongue is to hold it between the teeth, preventing speech, and thus is a metaphor for not speaking; this makes sense, as I've seen \"I bit my tongue\" to mean \"I didn't say anything\". However, I can't find much about the usage as a response to something already said. Is it along the lines of \"You should have bit your tongue instead of saying that\"? Are the two usages actually related or just similar? For clarification: usage A of the phrase \"bite your tongue\" is a synonym for \"hold your tongue\", whereas the usage I'm interested in is used similarly to \"Wash out your mouth with soap\" (though that's usually used for swear words, whereas this can be used for any negatively-perceived statement, like saying something bad about a public figure who is well respected, or implying that a woman is over a certain age)", "label": 1}
+{"snippet": "You often hear it on the news. Some embarrassing nonsense goes down, and then some honcho steps in front of the cameras looking concerned and goes, \"I take full responsibility for what happened.\" What do they mean by that, exactly? Are they willing to be put on trial? Ready to pay a fine? Eager to resign? Do some community work for free? What? I believe I've heard the President, and some others in high positions, say it on a few occasions. What do they mean when they say it? Today I want to say this, as president and as Commander in Chief I take full responsibility for all of our counter terrorism operations including the one that inadvertently took the lives of Warren and Giovanni. President Obama from the White House (Here's the link)", "label": 1}
+{"snippet": "In this answer on Stack Overflow, the term \"several\" is used as an indeterminate number, the actual value of which is literally in the quintillions: Zero is one of several values that can be represented exactly. To my ear, this is an exceedingly strange use of \"several\", which led me to believe that the writer was confused. I realize that trying to truly pin down \"several\" is probably a hopeless task, but I'm curious if anyone else would use it for such an immensely vast quantity, and if there's regional variation in the usage. So: How many is \"several\"? Would anyone else use \"several\" for \"quintillions\"? This question addresses similar issues, but doesn't seem to have the answer I'm interested in (much of the discussion mentions lower bounds for \"several\", but not upper bounds).", "label": 1}
+{"snippet": "I'm relatively new to PDEs and ODEs. It seems that PDEs are generally more difficult to solve than ODEs, and so I intuitively have the feeling that one needs more information/knowledge/theorems in order to solve PDEs. I've seen many examples of going from from the ODE domain to the PDE domain, and vice versa. For example, I could set up an infinite series of ODEs that model an infinite line of masses connected by springs. Then one could, loosely speaking, get the wave equation (a PDE) when letting the mass go to density. Or, FEM approximates a PDE as a finite set of ODEs, but by letting each element go to zero size, one could regain the original PDE. Vice versa, the method of characteristics, or the method of separation of variables, allows one to rewrite a PDE as a (finite) set of ODEs. I'm wondering if there are general, perhaps hand-wavy, arguments for when it is possible to do such transformations? I feel that the PDE has to be sufficiently simple, or we need to know some additional information about the solution, in order to rewrite it to ODEs. Likewise I am guessing that only infinite sets of ODEs can be written as PDEs, but I am not sure if all infinite sets of ODEs are equivalent to a PDE.", "label": 1}
+{"snippet": "I'm a software developer, and as such I often use an IDE to fulfill my goals. For those who don't know: An integrated development environment (IDE) is a software application that provides comprehensive facilities to computer programmers for software development. Sometimes while programming I find myself making certain errors. One of them is creating a variable (A name that holds a certain value) that is never used. An IDE can show a certain message and underline the error for me so that I notice it quickly and fix it. I have been using multiple IDE's that have shown me the error shown above, but I just noticed something. In one IDE, the message is shown as \"Unused expression\", while the other says \"Useless expression\". Which IDE is saying it right? Is it supposed to be \"Useless\" or \"Unused\"?", "label": 1}
+{"snippet": "Can any noun ending in -ism describing some system or belief be changed for -ist to describe a member of that system? My question might be confusing, so I will run through a few examples: Nihilism => nihilist Feminism => feminist Racism => racist This seems to follow a pretty predictable pattern. So, when I learned a new word a while ago - misoneism (having a fear or hatred of innovation or change) - I was expecting to be able to call someone a misoneist, if it ever came to that. Unfortunately, while most dictionaries (online and paper) I have checked so far contain the word misoneism they do not contain the word misoneist. Were my assumptions correct that you can create any -ist noun from a root of -ism, or is this word in the dictionary because it really doesn't exist?", "label": 1}
+{"snippet": "I want to study Mumford's Abelian Varieties in the coming winter break. I tried to study it before, but I didn't find my self really understanding(or memorizing) too much. I guess a better and more solid way to learn something is to go over many exercises. So I'm asking for some exercises(or problems?) on abelian varieties, it would be nice if I can get them online. Thanks in advance. And about the exercises: I wish it would be kind of like the ones in Hartshorne, so that I can solve them if I understand the material well. And not too hard, I guess I'm not looking for some research level questions... Also I wish those exercises may focus more on the algebraic/arithmetic side. I know the description above might seem a little picky, I'd be very appreciated if anyone has any idea or source about this, thanks again in advance...", "label": 1}
+{"snippet": "I've been reading about how the conical shape of train wheels helps trains round turns without a differential. For those who are unfamiliar with the idea, the conical shape allows the wheels to shift and slide across the tracks, thus effectively varying their radii and allowing them to cover different distances while rotating at the same angular velocity. A cross-sectional view of the tracks and wheels generally looks something like: But what about a configuration like the following? I read in an online article that wheels in the second configuration may more easily slip and derail from the tracks (assuming there are no flanges to prevent them from doing so). But I can't convince myself using physics why that might be. Is one of these two configurations actually more reliable than the other?", "label": 1}
+{"snippet": "The following binary relation of the set {a, b, c, d, e} is given: R = { (a,b), (a,c), (b,c) } What I have to do is to find the smallest reflexive / symmetric / transitive / antisymmetric relation including R. I know what these relations are all about, but what I have trouble with is how to find them. For example, I see no reflexive relation in the set. Does \"including R\" mean that i can extend R with any element from the given set? So for example, if I am looking for a reflexion can I just add (a, a)? If I can extend the set, my solution would be: Reflexive: Add (a,a) Symmetric: Add (b,a) Transitive: Already satisfied Antisymmetric: Already satisfied? I am not sure about this one", "label": 1}
+{"snippet": "In the Wiki page A permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states. ..... A formal language is p-regular (also: a pure-group language) if it is accepted by a permutation automaton. The transition monoid of an automaton is the set of all functions on the set of states induced by input strings. See the page for more details. The transition monoid can be regarded as a monoid acting on the set of states. See this Wiki page for more details. In many literatures, an automaton is called strongly connected when the monoid action is transitive, i.e. there is always at least one transition (input string) from one state to another state. The transition monoid of a permutation automaton can be regarded as a permutation group acting on the set of states. If the action is transitive, then the transition monoid is a transitive permutation group. My question is What is the class of the languages accepted by DFAs whose transition monoids are transitive permutation groups? Is this class a proper subclass of p-regular language? Any literatures discussing this class of languages in details? I have searched many books and articles and found nothing helpful so far. I believe I don't have the appropriate key words yet. Thus I am seeking help. Any pointers/references will be appreciated very much. P.S. I asked a related question on CS.SE with more technical details toward computer science.", "label": 1}
+{"snippet": "Recently, two groups working on quantum computers published results on quantum error correction. The first was Rainer Blatt's group, who used trapped ions to perform a topologically encoded qubit using \"color code\": Quantum computations on a topologically encoded qubit (arxiv). The other one was John Martinis' group, who used superconducting qubits and performed a simplified version of a \"surface code\": State preservation by repetitive error detection in a superconducting quantum circuit (arxiv). Can anybody please explain to me, what is the difference between \"color code\" and \"surface code\"? What are the advantages and disadvantages of those? Why aren't the trapped-ion guys using the \"surface code\" or vice versa? The Martinis group has shown recently that they are above the threshold for surface-code QEC arxiv. Has any ion group (maybe by Blatt) shown similar quality of single- and two-qubit gates? Are there other groups who have the same level of control over their systems to perform multi-qubits quantum error-correction codes?", "label": 1}
+{"snippet": "Is there any easy (scriptable) way to convert a PDF with vector images into a PDF with raster images? In other words, I want to generate a PDF with the exact same text but with each vector image replaced with a rasterized version. I occasionally read PDFs of technical articles on my Kindle, and have found that reading a PDF directly is frustrating. Thankfully, Amazon's automatic conversion of PDFs to the Kindle format does a good job of reflowing the text portions of most of PDFs I have tried. However, while raster images seem to make it through the conversion process fine, vector images get horribly mangled. It would be great if I could easily convert a PDF so that all of its vector images were rasterized. I am interested in any possible solutions, but a Linux- or Windows-based one would be preferable. I can also get access to Adobe Acrobat if necessary.", "label": 1}
+{"snippet": "Looking at the nCatLab page on chain complexes, it is implicitly assumed at the start of the page that one is working in an additive category. However, the only structure required to define chain complexes is that one be working in a pointed category, so that the notion of a zero morphism makes sense. However, I have not been able to find any papers which consider chain complexes even in categories such as preadditive or semiadditive categories, much less arbitrary pointed categories. I understand that many of the results of homological algebra rely on an Abelian structure to work. Is it simply the case that non-additive categories don't have enough structure to yield any interesting results about these complexes? Or is there a concrete issue that prevents chain complexes from making sense at all in more general pointed categories? Do these issues still arise even when working in preadditive or semiadditive categories?", "label": 1}
+{"snippet": "Can someone please explain extraordinary optical transmission (EOT)? I'm hoping someone can describe the physical process by which light is transmitted through a periodic metal hole array which is optically thick (i.e. thickness > skin depth), for which the holes are sub-wavelength vs the incident light. I'm trying to visualise how this process works but I'm not having much luck. From what I understand, EOT is a mixture of surface plasmon polaritons (SPPs) being excited on the surface of the hole array and wave guided modes for the SPPs(?) to travel through to the opposite side of the array where they are decoupled into transmitted light. I guess it's the wave guided SPPs I'm having trouble with...i.e. why would there be a cut-off frequency due to the wave guide mode if SPPs travel along the metal surface? (Also, the position at which the SPPs would decouple has also been bugging me.) Any help would be great!", "label": 1}
+{"snippet": "I can't quite figure out which of the following expressions is more correct: He is the devil's advocate. He is a devil's advocate. He is playing devil's advocate. The combination of an article with the possessive is what confuses me. Exactly which word(s) does the article apply to? The first form seems to suggest either that he is an advocate of The Devil -- namely, Satan himself -- or even worse, that he is The Advocate of The Devil. (Kill him with fire!) The second form seems to suggest that he is an advocate of a devil (but not necessarily of The Devil, nor the only advocate out there.) This seems to fit better with the way this idiom is commonly used, but I haven't seen this idiom used very often with the indefinite article. It's usually used with the definite article. The third form suggests that he is playing a role named \"devil's advocate\", with no article attached to it. Similar examples: The King's speech, the Indian's prayer, the mother's room, etc.", "label": 1}
+{"snippet": "I've compiled a LaTeX document successfully by typing latex documentname.tex into terminal when in the correct working directory. The document successfully compiles. I'm using TexLive. I then make changes to the document. For some reason, when I type latex documentname.tex again, it compiles very quickly and gives me the previous version of the document out. I've tried deleting the output file and log file and typing latex documentname.tex yet again, but it still somehow outputs the old version of the document. Same for the pdflatex command - what is going wrong here? Is there some other command I should be using or extra arguments I can pass in? Even changing the filename of the document does not cause the new version to be compiled - I still get the old one out.", "label": 1}
+{"snippet": "Addiction is defined as \"the state of being enslaved to a habit or practice or to something that is psychologically or physically habit-forming, as narcotics, to such an extent that its cessation causes severe trauma.\" But sometimes a person will find something which they do not suffer any withdrawal from when the y stop doing it for a while, and they do not feel any great need to seek out on your own. Yet when they are actively engaged with it, they just do not want to stop and can find it very difficult to pull themselves away from. As an example, \"My son is addicted to MineCraft. Once he sits down at it he will play for hours, not even wanting to stop to eat or sleep even when all his friends have gone home. Yet unless one of his friends wants to play it with him to begin with he never touches it.\" I feel like \"addicted\" is the wrong word, because while the \"psychological enslavement\" part is correct, it does not seem to form a habit or exhibit withdrawal symptoms. It's almost like a temporary addiction that goes away whenever the stimuli is removed. Is there a word for this?", "label": 1}
+{"snippet": "As explained in the answers to this post, photons apparently exert a gravitational pull on other objects. It has also been explained on this site, that gravity propagates at the speed of light. I'm wondering, though, how do you reconcile these two facts? I'm trying to imagine the gravitational field made by a photon and it seems like there are some paradoxes. For example, how can gravity propagate ahead of the photon at the speed of light, if the photon is also travelling at the speed of light? My guess is the solution is probably found in relativity, but I certainly can't figure it out. Right now, the best I can do is to think about gravity as sound, and a photon as an object travelling at the speed of sound. Can anyone help me out?", "label": 1}
+{"snippet": "I would like to teach a little nonlinear PDE to an undergraduate who is taking a course in second-order linear boundary value problems. I have never taught nonlinear PDE before, although it is my research specialty. I have a decent book on solitons, but my research specialty is critical point theory in elliptic PDE. Several of my colleagues are experts on solitons. The critical point theory would probably require some Sobolev spaces, which I would like to avoid. I have Evans's great book on PDE, but I think it is too advanced for him. I would like to know if there are any free resources on the Web which I can use, to get readings for myself and the student, and exercises for the student. One more thing: I am interested in PDE that have explicit analytical solutions, or at least can be written as infinite sums of specific functions (I don't want to get into numerical methods for this project).", "label": 1}
+{"snippet": "I am not a physicist but I would really like to know what trained physicists think about this problem that came up in conversation the other day. I have been reading about the search for habitable planets for a little while and about the conditions it takes for a planet to be habitable. I understand that the right amount of heat is important for ideal conditions. Then I caught an interesting documentary on Oppenheimer, Heisenberg and the race for the atomic bomb in world war II. The documentary said something to the effect that a nuclear detonation or any nuclear reaction is very much like a small, very temporary star on earth. It got me thinking that nuclear reactors must also be analogous to mini-stars or suns so I started wondering what it would take to create a nuclear reactor that could make a planet (or moon) more habitable by allowing the heat produced to escape the reactor and warm the planet's surface. As an example, once the technology exists for a nuclear fusion reactor, could it possible to assemble one outside our atmosphere, send it into orbit around, for example, Jupiter's icy moon Europa in order to heat the surface and create more habitable conditions for life?", "label": 1}
+{"snippet": "We are going to establish a company in order to commercialize a stuttering treatment/therapy program. The treatment/therapy is really effective and backed by a lot of scientific research. In our recent discussions, some disagreement has come up whether to market it as the \"XYZ stuttering treatment\" or the \"XYZ stuttering therapy\". On one hand, calling our product the \"XYZ stuttering treatment\" might be advantageous, because in all the research literature it is referred to as such. On the other hand, calling it the \"XYZ stuttering therapy\" could be better, because all the competition markets/offers their programs as \"therapies\", and having the term \"therapy\" appears to be more serious and seems to imply effectiveness. Also, the word \"therapy\" appears to be more international, which could help if we offer the program abroad. I'm not a native speaker though, so I wanted to hear your opinion and feedback. What's really the difference between \"treatment\" and \"therapy\"? Would you rather recommend calling it the \"XYZ stuttering treatment\" or the \"XYZ stuttering therapy\"? Why?", "label": 1}
+{"snippet": "I don't understand how a vacuum, the absence of matter, can hold energy. How can it hold energy when Einstein proved that matter is energy? And a second related question; how does the energy in a vacuum allow the Universe to produce itself? And how does that account for why the Universe is expanding? I saw Krauss' lecture on YouTube called Universe from Nothing and only understood some of it, even though he was fantastic at putting things in layman's terms and making these concepts easy to visualize. However, he had a bunch of \"asides\", so it was a bit confusing. He mentioned that the curvature of the Universe was flat, but then also went on to say how that was the worst possible scenario. Why is a flat Universe such a bad thing?", "label": 1}
+{"snippet": "Often in my studies (economics) the assumption of a \"well-behaved\" function will be invoked. I don't exactly know what that entails (I think twice continuously differentiability is one of the requirements), nor do I know why this is necessary (though I imagine the why will depend on each case). Can someone explain it to me, and if there is an explanation of the why as well, I would be grateful. Thanks! EDIT: To give one example where the term appears, see this Wikipedia entry for utility functions, which says at one point: In order to simplify calculations, various assumptions have been made of utility functions. CES (constant elasticity of substitution, or isoelastic) utility Exponential utility Quasilinear utility Homothetic preferences Most utility functions used in modeling or theory are well-behaved. They are usually monotonic, quasi-concave, continuous and globally non-satiated. I might be wrong, but I don't think \"well-behaved\" means monotonic, quasi-concave, continuous and globally non-satiated. What about twice differentiable?", "label": 1}
+{"snippet": "I have always believed in keeping magnets and data storage devices far away from each other. Friends say I'm excessively cautious about it, but I seem to have a lot less data loss than they do! As cell phones have gained popularity, so have cell phone cases with magnetic clasps. Often these clasps are positioned near the center of the phone, in close proximity to where the microSD card is located in the phone. A friend has had two genuine Sandisk microSD cards (purchased at large brick and mortar retail stores) fail in their phone. They keep their phone in one of those cases with a magnetic clasp. Is it likely that the magnet is causing the loss of data, or are such magnets much too weak to result in affecting the data on a microSD card?", "label": 1}
+{"snippet": "I'll start with a disclaimer -- this is not a question about astrology itself, I'm neither trying to refute nor to defend astrology. I'm interested in purely technical things, which are mostly related to astronomy. Given a time and a place (usually related to the moment of birth of a person) one can create a horoscope -- kinda diagram, which represents the positions of planets, Sun and Moon, usually projected on ecliptic. The information about position is usually represented in a form of astrological \"houses\", which are related to the horizon position. I'm interested in a \"reverse\" process: given the horoscope with ecliptic coordinates of Sun and Moon and planets, and given those \"houses\" -- can one find the place and time for which the horoscope was constructed? I'm pretty sure that such kind of problems would be interesting for, say, historians -- maybe there are some research papers or literature describing techniques that allows one to do such things?", "label": 1}
+{"snippet": "First question: I have been reading English: An Essential Grammar by Gerald Nelson and it gives an example of the words 'hard' and 'fast' being used as both adjectives and adverbs: Adverb: John works hard. Peter drives fast. Adjective: John is used to hard work. Peter drives a fast car. I was wondering, can all adjectives be used as adverbs in this manner? E.g. Adjective: Small girl. Are these adverbs??? She is small. She was small. She looked small. Second question: Can present participle verbs be considered as adjectives? E.g. Are these adjectives or are they still considered as verbs? The singing lady. The growing crowd. The advancing army. Third question: Can all past participle verbs be considered adjectives? E.g. The written book. The cooked fish. The bitten apple. And lastly: Can all past participle verbs be considered as adverbs? E.g. The book was written in black ink. The fish seemed to be cooked.", "label": 1}
+{"snippet": "I'm trying to find out whether I should use a singular or plural verb when there are multiple gerunds as the subject of the sentence. For example: Running the correct course and keeping a steady pace are/is necessary in order to win. With either one of these by itself, \"is\" would be correct: Running the correct course is necessary in order to win. Keeping a steady pace is necessary in order to win. With both gerunds combined, I can't seem to figure out whether the verb should stay singular since each phrase is singular, or if it should become plural since there are two connected by \"and\". If we just treat the gerunds as regular nouns, then obviously it would become \"are\", but I'm not sure if gerunds have the exact same rules as regular nouns. I know that if the sentence was: Running the correct course and keeping a steady pace are both necessary. That \"are\" would be correct, but without the \"both\" it sounds incorrect to me. Does anyone know the official rule here?", "label": 1}
+{"snippet": "I am trying to solve six first order coupled ODE's, two of these are associated with a heat balance of a catalyst pellet, and four are mass balances. I have been trying to solve these equations using Orthogonal collocation (rather than using those algorithms used by NDSolve in Mathematica - my hope is to speed up the computation). I have found a lot of examples and lectures on using Orthogonal collocation to solve a single ordinary differential equation, however, I have not come across anything in the literature, as how to solve these equations when they are coupled. I therefore wanted to ask if anyone has experience with this, and could possibly point me toward some literature, and/or worked examples, or explain the twist on how to migrate from a single ODE to coupled ODE's. Best Regards", "label": 1}
+{"snippet": "So here's what I'm trying to do: Given a collection of lat/long coordinates that form a polygon like below, I want to be able to select a point inside the polygon and determine which side of the polygon it is closest to, and determine its distance to this closest edge. My problem is that I need to somehow get rid of the extra coordinates so I can do computation on them -- if, for instance, I only had four points that formed a four sided polygon (i.e. the west-most and east-most points on O'Farrell, and the west-most and east-most points on Ellis), I could do this computation. For instance, putting in the point for 'JINS' as input would return the edge that runs along O'Farrell St. We can assume that the polygon will not be smooth, and that each polygon represents a city square block, so they're relatively simple polygons. Can anyone think of a solution to this problem (whether that be getting rid of extra points or finding some other way to do this computation)? Thanks.", "label": 1}
+{"snippet": "I'm a student of Physics, however I usually study mathematics on texts aimed at mathematicians to gain a deeper understanding. Currently I'm studying differential geometry on Spivak's book and one of the main results I need is the relationship between vector fields and infinitesimal transformations, i.e.: the idea of infinitesimal generators. The only problem is that Spivak's way to get into this is a little more complex than what I need. Indeed he spends time with differential equations and topological properties of manifolds that are related to differential equations. These are interesting topics, but for now what I was really needing was this relationship of vectors and infinitesimal transformations and the understanding of where Lie Groups come into play. Is there a shorter path into these results without needing to go through all of that stuff on differential equations? Is there a more direct way to get into these topics? I ask that because perhaps Spivak just presented that way because he wanted to show how vector fields relates to differential equations in a more concrete way. Thanks very much in advance.", "label": 1}
+{"snippet": "I am having a discussion/conversation with a very close friend, and this conversation concerns me personally (you might even go as far as saying this is my best friend). At one point in our conversation he starts to \"spam\" (not literally, the messages have meaning and are well-formulated) me with many messages, but I really have nothing to say back (or anything useful to say back). I should clarify by saying that I completely understand what he is saying, and I somewhat agree with the things he said. He then proceeds to send me another text saying: \"Don't you have anything to comment?..\" How could I respond nicely with a proverb/saying of any kind that means \"silence is sometimes better than speaking when one doesn't have anything useful to say\"... I know some sayings like \"silence is gold\" or \"better to remain silent and be thought a fool than to speak and to remove all doubt\", but they don't really work for me in this scenario. I hope I was clear enough. Thanks", "label": 1}
+{"snippet": "I have been trying to find out what the definition of a noncommutative regular local ring is, but to no avail. In fact, how does one even begin to define Krull dimension for a noncommutative ring? Hence, I would appreciate it if someone could kindly provide definitions for the following, in the case when the ring under study is noncommutative: Regular. In the commutative case, the definition of regular involves localizing at prime ideals. However, in the noncommutative case, how do we do localization? Is Ore's Condition invoked somewhere? Regular local. In the commutative case, the definition of regular local involves Krull dimension. However, in the noncommutative case, do we have an analogue of Krull dimension? On a different note, in the commutative case, is it true that a local ring that is regular the same as a regular local ring? (This might seem to be a stupid question.)", "label": 1}
+{"snippet": "The use of the term sir as a form of address for men, especially those of higher rank or status, is discussed in several prior questions including this one. They all indicate that the term is reserved to males, and that there are a number of related terms for females, such as ma'am. A review of the first dozen online dictionaries at onelook.com confirms that sir is strictly reserved for male addressees. For example ODO defines it as used as a polite or respectful way of addressing a man, especially one in a position of authority: excuse me, sir On several recent television shows in the US, the term sir has been used by a police officer to address his or her supervisor who was female. In the context, the use was sincere and was not objected to by the superior. Has the use of sir when addressing a superior female in a military or quasi-military setting become acceptable, or is this merely literary license?", "label": 1}
+{"snippet": "Could you please recommend any good texts on algebraic geometry (just over the complex numbers rather than arbitrary fields) and on complex geometry including Kahler manifolds that could serve as an informal introduction to the subject for a theoretical physicist (having in mind the applications in physics, e.g. in the string theory)? What I want for a moment is to get some informal picture of the subject rather than being dug up into the gory details of the proofs and lost in higher and higher layers of abstraction of commutative algebra and category theory. The texts I have found so far are all rather dry and almost completely lack this informal streak, and all of them are geared towards pure mathematicians, so if there exists something like \"Algebraic geometry for physicists\" and \"Kahler manifolds for physicists\" (of course, they would probably have different titles :)), I would greatly appreciate the relevant references.", "label": 1}
+{"snippet": "How would I say that a phrase or word has \"lost it's meaning due to constant repetition.\" Take the word \"awesome\": \"Awesome\" used to denote a situation in which the speaker (or writer) was overwhelmed with \"awe.\" \"Awesome\" is now used as a measure of how \"interesting\" something is and isn't terribly high on that rating scale. How would I describe the loss of meaning due to the constant repetition of the word \"Awesome\"? Take George Santaya's words \"Those who cannot remember the past are condemned to repeat it\": People often say this phrase to try and instigate action but because of it's overuse, it no longer has any meaning. It's just something people say when they talk about The Holocaust, or the bad grades they got last semester in college. How would I describe the loss of meaning due to the constant repetition of the phrase \"Those who cannot remember the past are condemned to repeat it\"?", "label": 1}
+{"snippet": "Fat lot of good is a phrase that I grew up with and continue to use occasionally as in the following: He is working hard to fix the problem, but a fat lot of good it will do him without the proper tools. Which means that despite his best efforts, he is not likely to fix the problem until he starts using the proper tools. I've only heard the phrase used with a sarcastic tone as if the phrase is supposed to mean that it will do a lot of good. (Similar in tone to when someone says I could care less when they really mean I could not care less.) What is the origin of fat lot of good and was it ever in common usage with a positive meaning?", "label": 1}
+{"snippet": "I would not be able to put this into symbols, but I ask here because I think it's the correct place to ask. Would the chance of my parked car getting damaged (bumped or scraped) by other cars parking nearby increase over time? Gambler's fallacy says: if something happens less frequently than normal during some period, it will happen more frequently in the future. (wikipedia) For every time I leave my car parked, there is a chance it will get damaged. If I don't want to commit the gambler's fallacy, I should consider the chance of damage the same every time I park. But if I park at the same spot every day for many years, the chance that my car would have been damaged after all those years, would surely be greater than if I just parked there one day, right? How does this not contradict the gambler's fallacy? My insurance company asks a higher premium if I park on the street all year round, than in a garage, so somehow they must figure that the chance is higher than if I just park on the street one day. How does this not contradict the gambler's fallacy?", "label": 1}
+{"snippet": "The three laws are: First law: The velocity of a body remains constant unless the body is acted upon by an external force. Second law: The acceleration a of a body is parallel[disambiguation needed ] and directly proportional to the net force F and inversely proportional to the mass m, i.e., F = ma. Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear. The first law had already been formulated by some philosophers prior to Newton, Hobbes said in the Leviathan '...[the proposition] that when a thing is in motion it will eternally be in motion unless somewhat else stay it, though the reason be the same (namely that nothing can change itself)...', given his reasoning, I think it safe to mean constant speed and direction, otherwise change is occuring and he explicitly rules that out. I think the same proposition is mentioned in Lucretious's De Rerum Natura. Are there any antecedents for the second and third law?", "label": 1}
+{"snippet": "I was listening to The Infinite Monkey Cage on the BBC and they were talking about general relativity and gravity. They were saying that gravity is not a force as Newtonian laws describe and is at odds with your real world experience. They said that if you are sitting on a chair, you don't feel a force pulling you down onto the chair. You feel the chair pushing up onto your bottom - at least that's what it feels like when you sit down and try it. They seem to be saying that gravity is not a force pulling from the center of the Earth, it's me that's still and the chair pushing up against me due to acceleration. My question is if this description is accurate or have I misunderstood this? If you are sitting on a chair, is what we call gravity actually the chair accelerating up onto me due to the geometry of Space Time? Is there a better analogy for this?", "label": 1}
+{"snippet": "I'm having trouble completing a proof that for positive integers a and b, that the least common multiple of a and b is ab/gcd(a,b).This is how I've approached it so far: For s = lcm(a,b) we have the following definition: i) a|s and b|s ii) for any integer k where a|k and b|k, s|k Thus the proof comes down to proving that s satisfies these two properties. For i) let gcd(a,b) = d. Thus s = ab/d. Since gcd(a,b) = d, it follows that b/d is an integer so a|ab/d since ab/d = ta for t = b/d. The same conclusion can be made for b so i) is satisfied. Now comes the confusion. I'm not not sure how to prove that if a|k and b|k then ab/d|k. I tried using am = k and bn = k for integers m and n but it lead to no avail. Should I approach the problem som other way?", "label": 1}
+{"snippet": "I am teaching my students about the fairness criteria for voting system, working up towards arrow's impossibility theorem. One of the voting methods is called the pairwise comparison method: voters rank each of the candidates from most to least favourite. To tally the votes, talliers compare each pair of candidates. If candidate X is more often preferred than candidate Y, then X receives a point. (If they tie, they each get half a point.) At the end of the comparisons, the candidate with the most points is selected. We discuss criteria for a voting system to be fair. One criterion in particular is the \"irrelevant alternative criteria\" which states: If an election is held and a winner is declared, this winning candidate should remain the winner in any recalculation of votes as a result of one or more of the losing candidates dropping out. Can anyone think of an example of when the pairwise comparison method violates the irrelevant alternative criterion?", "label": 1}
+{"snippet": "I am trying to grasp some aspects of the quantum entanglement, but the existing resources (including some of the links here) seem a bit confusing. I am trying to find an answer to the following questions. If two particles are entangled and then separated, will affecting one of them affect the other (for example, the particle is placed in a field that would set some property of it in a specific direction), or will it disentangle the system? If affecting one particle affects the other, then how is it not possible to use this effect to transfer information (once; for example by affecting the spin of the first particle to be up the other particle would have its spin down)? Is affecting the particle equivalent to measuring the property affected (for example the spin)? When a property of the particle is measured, does the particle get entangled with the measuring apparatus? More precisely, does interaction imply entanglement of a sort? I apologize if the questions are trivial or nonsensical, but I am asking as a layman in the field.", "label": 1}
+{"snippet": "Here's what happens. I get stuck on some proof or some mathematical construction and I end up staring at the problem for hours, sometimes not making any progress. I do this because sometimes I think that I'm being lazy, I'm not thinking things through, or I'm just not thinking clearly. This approach is not practical because I only end up falling behind on other work. I don't like to look up solutions because I feel like, given enough time, I would be able to come up with the answer (or some good reasoning). But maybe I should start looking for answers after a shorter period of time. I don't know what the right thing to do is. Do you guys have similar problems? Should I feel bad because I have to look at solutions? Or is this just part of learning?", "label": 1}
+{"snippet": "I'm searching for some good reading material on multifractal analysis. Preferably something accessible that doesn't put the stress too much on mathematical proofs but rather on applications. As long as it gives a good review of the status of the field, the interesting results and applications, I would be happy. Also, if anything related to multifractal analysis and statistics or time series comes up, I'll take it as well. Books, papers, internetpages, videos, etc... accepted! EDIT: Since the question has been bumped, I decided to put a bounty on it. But I also want to make a bit more precise what I'm looking for. I have always had the impression when encountering the multifractal techniques that people are able to compute a whole bunch of numbers with some nice and fancy formulas. But I have always missed an \"understanding\" of what the numbers mean. Why is it useful to do a mutlifractal analysis of fluid flow? Of species abundance distributions? Etc... I feel like the technique is purely descriptive with little theory backing up the connection with some deeper underlying structures. But that may just be due to my limited understanding of the field and that is precisely why I ask for pointers to where I can look for this.", "label": 1}
+{"snippet": "Currently, I am attempting to learn noncommutative geometry. My interests mostly lie on the boundaries of pure mathematics and theoretical physics, so I am not only interested in the mathematical formulation of the theory, but also in the physical applications. I am familiar with differential/algebraic topology/particle physics and some basic notions of homological algebra, but am fairly weak in functional analysis. What books/references/review articles would one recommend as the best or easiest starting point to learning this subject? A book that is the most self-contained/pedagogical? (I am currently starting to read Basic Noncommutative Geometry by Khalkal, but was wondering if there were any books even more suitable for a beginner). As I want to get started with learning NCG as quickly as possible, are there any short review papers, notes, or specific chapters of texts where I can gain a bare minimum of prerequisites such as functional analysis to start reading a book on NCG instead of having to read an entire book on operator algebras before starting my study? Or some books that would be helpful that I could read concurrently? Thanks!", "label": 1}
+{"snippet": "Everyone knows how Schrodinger's Cat is set up, so the question becomes whether there's a quantum/classical boundary and what that boundary is. Some people say everything is quantum while some may think there's a line that separates quantum/classical. So the cat in the box would have to be a mixture of live/dead cat until one of two things happened. Decay occurred and poison gas is released that kills the cat or it doesn't occur and the experimenter opens the box and sees a live cat. Wouldn't the wave function be a quantum ensemble of these two states described in Hilbert space until one of these measurements occurred? What state is the cat in before one of these measurements occur? Doesn't it have to be in a quantum ensemble of both states until one of these measurements occur?", "label": 1}
+{"snippet": "Often it is said that Bell's theorem (and the observed violations thereof) rules out local hidden variable theories as the explanation for the seeming non-determinism found in quantum mechanics. I'm wondering if this extends also specifically to radioactive decay processes. So I guess this is really a question of whether the radioactive decay processes are currently understood to a level so that one can say that the seeming randomness boils down to some well-known quantum phenomena that would be covered by Bell's Theorem. Or, alternatively, that the decay processes are not understood to the extent that they are reducible to quantum phenomena and hence could have a different explanation. For example, one could imagine radioactive nuclei being a deterministic but chaotic system of interactions going through states, where sooner or later a state is reached where the decay occurs etc. The question is if such a view, where the individual decay is actually a deterministic phenomena (but appears as random since we dont know the current state of a particular atom) is compatible with current knowledge of radioactivity and quantum mechanics. The section https://en.wikipedia.org/wiki/Radioactive_decay#Theoretical_basis_of_decay_phenomena seems to leave the impression that the underlying mechanism of decay is not understood.", "label": 1}
+{"snippet": "Sometimes people make insincere arguments to justify an action (or inaction), based upon the impact to a particular group. For example, a person might say \"Building that sports arena near my house is irresponsible! Think of how many homeless people we could house with that money!\" In truth, the person does not want the arena near his or her house, and does not really care about whether homeless people are housed or not. What is the term used to describe the homeless people in this situation? Another example might be large industrial agriculture organizations defending government policies \"to protect the family farm\" when these organizations are not family farms and do not care about protecting family farms. What is the term used to describe family farms here? The best term I can think of is \"smokescreen\", as in \"Homeless people are being used as a smokescreen to hide other concerns about the sports arena\" but this seems informal, and there are probably better phrases (formal or informal). What are they?", "label": 1}
+{"snippet": "I'm building a website for a client in which customers can customise the shape of their board (curvature, length, width, thickness, and so forth) and the client has asked if we can calculate the volume of the board and display it in response to the user's customisations. This sounds like scary advanced calculus and/or differential geometry territory, but I said I'd try to find out the feasibility of doing so nonetheless. I'll mainly be using a set of bezier curves as a baseline to define the board shape and there will of course be curves in all dimensions. The nose will sometimes come to a point and other times be rounded off. The tail will come in a variety of shapes, including being rounded, coming to a point, or even having an inverted \"fish tail\" shape. Where would I even start with calculating the volume of a surfboard like this? I'd be looking to represent the volume in litres. Edit: I'm guessing I'd need to break the board down into chunks that minimise the number of simultaneous curves and calculate them individually. I'm thinking maybe it's also easier to calculate the volumes of each chunk relative to a uniform enclosing box and subtract each value from the total box volume to get the final volume...", "label": 1}
+{"snippet": "I'm trying to write a database schema for measurements in a variety of categories, and am having trouble coming up with names for some basic elements. Let's assume we are gathering heart rate and blood pressure measurements from a group of people. Each observation is composed of the individual being measured, the time the measurement was taken, and the amount of the measurement. What are each of these called? What is the name for the type of measurement being taken (heart rate or blood pressure in this example)? The collection of individuals is the sample, correct? If so, what is the term for the collection of observations? Please feel free to revise the question, as my lack of knowledge makes it hard to ask accurately. I can come up with names myself, but after failing to find anything in some statistical glossaries, I'm curious if there are canonical names for these basic elements.", "label": 1}
+{"snippet": "So this is my second query about the photovoltaic effect. I've looked into it more and understood it for the most part, but there's still something I don't completely get. After the electrons are excited into the conduction band, some sources say that they can't cross into the opposite material due to an electric field blocking their path and would need an external circuit, others say that some electrons do cross into the other material but their flow gets halted gradually into nothing by the formation of a depletion region, and would then need an external circuit to maintain a consistent flow. So which one is it? Another question is, what exactly causes the electrons to move in the first place? Their attraction to the holes in the opposite material? Simple as that? Much obliged, and thank you for your time. Bonus: If you could explain in a general context, rather than in relation to P-N junctions, you get extra brownie points.", "label": 1}
+{"snippet": "I've been reading up on nuclear reactors, and understand explanations of how it works, how water is heated to steam, which turns the turbines, etc.. I understand all of the safety features, and how control rods are used, and what they do with spent fuel. However, what I can't figure out (after lookin at many websites and videos) is where the reaction actually starts. The fuel rods contain Uranium pellets, and then they're put in the reactor, where the reaction starts and neutrons start hitting each other to create heat? So is this happening all over the reactor, or just in each fuel rod assembly? Also, you can hold a Uranium pellet in your hand (ideally wearing a glove) and it's not dangerous, so what starts a reaction? A lot of people say the reaction can start by itself, so why do uranium pellets not suddenly heat up and start spreading radiation by themselves? Is it because they haven't been enriched? What if you dropped a Uranium pellet on the floor?", "label": 1}
+{"snippet": "I'm not much informed about manifold but I should answer some questions about it. Based on the definition I have written an answer for the following question but I feel there is something wrong with it! Could you please help me? Q: Let M be a smooth manifold and suppose that we have an open cover for that. If S is a subset of M such that the intersection of each element of that cover and S is a submanifold, then S itself is a submanifold. A: Fix an arbitrary point p in M. This point belongs to an element of that cover and as we know the intersection of that element with S is a submanifold, so there exists a map around p such that satisfies the condition, so we are done!", "label": 1}
+{"snippet": "I hope it is appropriate to ask this type of question. I'm in my second year as an undergraduate right now. While my problem solving skills have improved tremendously, I almost never tried to actually remember what I learned. I always had the attitude: \"If I don't remember it, I will simply look it up.\" While this might be legitimate to a certain extent (especially when it comes down to definitions), I'm not sure where this leads to in terms of being able to see various connections much faster. Would you say that it is necessary to remember most of the things that you learnt so far? Of course it wouldn't do any damage at all, but one has always think about it in terms of efficiency, I guess. I mean, it's hard enough to learn mathematics itself - but remembering all of those things just to gain the ability of solving some problems faster? I'm not sure about that and would like to hear your opinion on it.", "label": 1}
+{"snippet": "Timothy Gowers asks What is so wrong with thinking of real numbers as infinite decimals? One of the early objectives of almost any university mathematics course is to teach people to stop thinking of the real numbers as infinite decimals and to regard them instead as elements of the unique complete ordered field, which can be shown to exist by means of Dedekind cuts, or Cauchy sequences of rationals. I would like to argue here that there is nothing wrong with thinking of them as infinite decimals: indeed, many of the traditional arguments of analysis become more intuitive when one does, even if they are less neat. Neatness is of course a great advantage, and I do not wish to suggest that universities should change the way they teach the real numbers. However, it is good to see how the conventional treatment is connected to, and grows out of, more `naive' ideas. and gives a short construction of the real numbers as infinite decimals, then using that to demonstrate the existence of square roots, and the intermediate value theorem. What are other reasons for or against thinking of real numbers as infinite decimals?", "label": 1}
+{"snippet": "In the last assignment given to me by my professor, there is a question which asks: In classical theory, it says that in presence of air friction, a pendulum continuously loses energy with time and its amplitude also decreases with time. However according to quantum theory, the pendulum loses energy only in discrete packets or quanta. This would lead to a decrease in the pendulum's energy in a step-wise manner. How can you show that there is no contradiction between quantum theory and the observed behavior of laboratory pendulums and springs? What I want to know now is: What exactly do I have to show mathematically to prove this result? I mean what kind of an equation will I have to derive or prove in order to answer this question? What will be the final equation after writing which I can say that \"So this concludes that there is no contradiction.\" I am completely clueless about what to do, right now. I don't want the complete answer or proof however. Thanks.", "label": 1}
+{"snippet": "In a laser interferometry experiment, we project a pattern of interference fringes onto a CCD sensor. For best results, we want good contrast between the bright and dark fringes, and we carefully compensate for various sources of noise - for example, by taking camera images with no fringes present, and with the laser turned off, and subtracting these images in the proper sequence. We'd expect therefore that the remaining signal should be highly linear, with the CCD signal at each pixel in direct proportion to the number of photons reaching it during the shutter time. What we actually find is that, as we vary the laser intensity and shutter time such that the average intensity across the image remains constant, with no pixels saturated, there is a definite \"sweet spot\" where the fringes are much more well-defined than at other settings. Either increasing or decreasing the laser intensity away from this point (with corresponding decreases or increases in shutter time) causes the fringe definition to deteriorate. I can't think of any reason why this should be. I know that in cases where the process generating the pattern has a time-constant (for example, using laser speckle interferometry to measure Brownian motion), there is an optimum exposure setting, but that shouldn't be the case in our system which is entirely static. So, what am I missing? I assume it's some property of the CCD sensor that I've overlooked.", "label": 1}
+{"snippet": "I was reading a physics book by some author and I got a little too confused with the explanation he stated about magnetic fields. A magnetic field is a field of force produced by current-carrying conductors or by permanent magnets. Correct me if I'm wrong: A magnetic field is basically a region / space where magnetic lines / flux lie. Thus, any magnetic objects inside the magnetic field will be attracted or repelled depending on its charges. Thus, this means that if a magnetic object is inside the magnetic field, the object should feel either a pulling or a pushing force acting on it. So, if the current-carrying conductors will produce a magnetic field, then this somehow means that I am inside a magnetic field produced by the current-carrying conductors (microchips and the wires inside the computer). And I believe I have enough metals around the computer, why don't my magnetic metals not experience any force acting on it?", "label": 1}
+{"snippet": "First of all, I'm genuinely sorry if this question isn't \"serious\" enough for this forum! A common cliche in movies and tv is that a very tough object (eg the villain) is frozen, and then hit with something, shattering into a million pieces. I've seen a demo of a flower being put into liquid nitrogen, then being crumbled, but a flower is a very delicate object to start off with. If I take a leg of lamb (for example) out of the freezer, I don't feel like it's in any danger of shattering into a million bits (unlike my foot if i were to drop it). So, is the whole \"cold = brittle\" thing just movie bullcrap? Or is there anything to it? Sticking with the leg of lamb example: is there a temperature to which a leg of lamb could be dropped that would make the leg of lamb prone to shattering? EDIT - i just realised that the question title could be read as \"Is there anything which is rendered extremely brittle by extreme cold?\". Obviously there are some things, eg flowers. Hence the title change.", "label": 1}
+{"snippet": "I'm sure his has a general form and welcome a link to a duplicate, but as I don't quite know what to search for, here goes. Whilst answering a question on the Mathematics Stack Exchange, I found myself needing to say the mid point of one diagonal of a rectangle is coincidental with the mid point of the other and that that point is the centre of the rectangle. So I said: \"The key is to prove that for all rectangles, the mid points of the diagonals are coincidental at the centre of the rectangle ...\" It suddenly struck me that the correct form might have been: \"The key is to prove that for all rectangles, the mid point of the diagonals are coincidental at the centre of the rectangle ...\" I suspect this is related to \"everyone took off his hat\". Could someone explain the reasoning behind the correct form.", "label": 1}
+{"snippet": "Possible Duplicate: What is the correct way to pluralize an acronym? I am helping a former intern ready their resume for distribution. The candidate used an abbreviation I was unfamiliar with: B.S.s in Physics, Computer Science, and Mathematics I am familiar with the student's educational background so after a moment of thought realized \"B.S.s\" was their attempt to indicate multiple bachelor of science degrees. That said I can see those unfamiliar with the student's background being confused. Unfortunately, I do not know how to provide the correct punctuation to indicate the correct grammatical number for multiple degrees in the same discipline. What is the correct plural form for multiple bachelor degrees? Additionally, are there variations for other degree levels: associates, masters, Ph.D, etc.? In addition to the abbreviation what's the correct way to indicate plurality for the unabbreviated form?", "label": 1}
+{"snippet": "I have only taken a basic quantum mechanics course (this book, so you know where I'm coming from), but I've been wondering about something. If we set up a quantum system in a known state and take a measurement of two incompatible observables, we will get two real numbers. If we repeat this experiment multiple times, then we will get two lists of real numbers (each list corresponding to the measurements of one of the observables). Quantum mechanics allows us to predict the average and standard deviation of these numbers, but it does not allow us to predict the individual numbers. If I understand correctly, this is a fundamental limit of the theory. The data is essentially random. Is it correct to say that most scientists believe that no theory will ever allow the prediction of these individual numbers? Why do they think that? And secondly, is there any other property of those numbers that quantum mechanics predicts that I am missing (other than mean and standard deviation)?", "label": 1}
+{"snippet": "I'm teaching a geometry course this semester, involving mainly Euclidean geometry and introducing non-Euclidean geometry. In discussing the importance of deductive proof, I'd like to present some examples of statements that may appear to be true (perhaps based on a common student misconception or over-generalisation), but are not. The aim would be to reinforce one of the reasons given for studying deductive proof: to properly determine the validity of statements claimed to be true. Can anyone offer interesting examples of such statements? An example would be that the circumcentre of a triangle lies inside the triangle. This is true for triangles without any obtuse angles - which seems to be the standard student (mis)conception of a triangle. However, I don't think that this is a particularly good example because the misconception is fairly easily revealed, as would statements that hold only for isoceles or right-angled triangles. I'd really like to have some statements whose lack of general validity is quite hard to tease out, or has some subtlety behind it. Of course the phrase 'may appear to be true' is subjective. The example quoted should be understood as indicating the level of thinking of the relevant students. Thanks.", "label": 1}
+{"snippet": "According to Wikipedia: For most radioactive nuclides, the half-life depends solely on nuclear properties and is essentially a constant. It is not affected by external factors such as temperature, pressure, chemical environment, or presence of a magnetic or electric field. Have any experiments been done to test what effect neutrinos have on decay rates? From what I understand, it might be difficult to isolate pretty much anything from the constant bombardment of neutrinos from the sun and other sources. So, how can we be sure decay rates are not effected in some way by neutrino collisions/interactions? Update \"The overwhelming majority [of neutrinos in the beam] will continue on past the lab, to infinity.\" This is from this article which describes how a beam is generated and detected at CERN. I need help understanding this: if the \"overwhelming majority\" of neutrinos cannot be stopped and the actual detection is considered an \"event,\" we can't possibly say that we know what decay rates would be in isolation since we can only stop an extremely tiny fraction of neutrinos from a beam. Neutrinos are naturally and constantly coming from all directions at all times. The best we have is test results of what happens when we beam extra neutrons at those substances (which I'd be interested in seeing the results of).", "label": 1}
+{"snippet": "About two years ago I watched some old Monty Python interviews. In one of them, Graham Chapman, a Brit, makes fun of Terry Gilliam (the only American) for his lack of vocabulary. He specifically cited a moment when the group flew over the great lakes and Gilliam said \"there's a bunch of water\". I found this amusing. But it's also stuck with me. And ever since, every American I meet with seems to have an affinity for saying \"a bunch\" to describe anything with a high quantitative value. This can be anything from purely literal (a bunch of parsley) -- though this doesn't bother me as much -- to the generally \"many\", such as \"a bunch of candies\" and almost sarcastically as in Gilliam's case (obviously several thousand cubic miles of water is a bit more than a \"bunch\"). But what is a solid alternative for these uses? Not that I'm looking for something to replace \"a bunch\" entirely. I find it can be useful and an endearing \"Americanism\". But I'd like to hear of some options. EDIT: Maybe I can make this more specific and ask this: What would an appropriate British expression be for the Gilliam scenario above? Maybe something like \"A Considerable Amount\"?", "label": 1}
+{"snippet": "In these forums and elsewhere it is routinely agreed that \"we do not have a theory of quantum gravity.\" My question is, how do we know that canonical quantum gravity is \"wrong\"? I understand that the theory is perturbatively nonrenormalizable, but doesn't that just mean that we can't apply perturbation theory to it? It seems the theory is nonperturbatively renormalizable. A theory being nonperturbative doesn't make it \"wrong\". My understanding is that in modern QFT nonrenormalizability is not anymore considered such a big deal, and that even the Standard Model is expected to be an effective theory modified by nonrenormalizable terms appearing at higher energies. So barring practical considerations, why is canonical quantum gravity considered \"not a theory of quantum gravity?\" EDIT: I am not sure that the term \"Canonical Quantum Gravity\" is correct. I am referring to what is called \"Quantum Einstein Gravity\" in this paper. If someone knows better please help me correct my terminology. I was not meaning to imply anything about LQG because I thought that LQG \"brought more to the table\" than just a nonperturbative approach to the same QFT, but I could be wrong about that.", "label": 1}
+{"snippet": "First let me introduce my terminology: A \"Mechanical theory\": A theory which describes time-evolution of a particle or a system of particles regardless of the fields affecting the particle/system. e.g. Classical mechanics, Quantum mechanics, etc. A \"Field theory\": A theory which describes time-evolution of a particle or a system of particles with taking the effect of fields on the particle/system into account and also a theory which describes time-evolution of the fields themselves. e.g. Classical gravitation, Classical electromagnetism, Quantum field theory, etc. But I am always confused that \"General relativity\" falls into which category. I know \"Special relativity\" just applies a modification to \"Classical kinematics\" to build \"Relativistic mechanics\". But \"General relativity\" is talking about \"Relativistic gravitational fields\" while also talking about \"Non-inertial frames of reference\". Now this is my question: Is \"General relativity\" a field theory or it's a mechanical theory? If it's a field theory is there any other way to study non-inertial frames in the context of \"Relativistic mechanics\" without bringing any special field into play?", "label": 1}
+{"snippet": "I'm a high school student and I'm trying to understand the concept of the Higgs boson. So I apologize ahead of time for any incoherence I may say. As per my understanding bosons are force carrying particle that are excitations of their respective fields. For example the photon is the boson of the electromagnetic field and an excitation of such. As per my understanding the Higgs boson is an excitation of the Higgs field, and also the Higgs boson is what directly interacts with other massless particles (quarks, leptons, etc). So in the attempt of trying to visualize it. Could it be said that the Higgs boson is like a wave made in the surface of a pool? Since the boson is an excitation in the Higgs field and a wave is an excitation in the water. Would this be a proper analogy? Additionally, how do this excitations in the Higgs field actually occur? How do Higgs bosons appear?", "label": 1}
+{"snippet": "I'm looking for an alternative way of saying \"You can't run before you can walk.\" This is equivalent to saying \"you can't take on higher level things before you have mastered the basics\". I am looking for either a rewording of the original phrase or a whole new phrase with the same meaning. I prefer that this not have any fancy words nor leave the reader scratching her or his head. I will use it in a semi-informal tutorial for future students of a programming class I am in. I use a short phrase at the beginning of each section which establishes the underlying theme in that section. This tutorial is meant to be something fun (and useful) to read, which is why I want something that catches the attention of the reader. For my purposes, there is nothing wrong with the original. I simply want something that is a bit more inclusive (some people can't walk or run). Thank you.", "label": 1}
+{"snippet": "I have a question related to already shortened words and their plural forms. As I have seen on this site and have found in the dictionary, words like mas and pas are the plural form of the shortened words ma and pa (as in mother and father). However, it occurs to me that were I to write this, in order to clarify the meaning of what I was trying to write (because if you are like me, you read mas and pas and did a double-take), I would write it as ma's and pa's. Some words like cuz have a similar issue, although the pluralization makes more sense: cuzzes. Perhaps cuz's? I know that in the pluralization of single letters there is some contention regarding whether there should or should not be an apostrophe (A's or a's versus As or as). \"I got a lot of A's this semester.\" just looks better to me, although I have no grammatical backing for this. I'm not sure if this is the same for these types of words as well. My question is this: Is there a precedent for using an apostrophe for words that are shortened to convey appropriate meaning, or is the convention simply to omit the apostrophe altogether and leave the word pluralized with an s?", "label": 1}
+{"snippet": "I'd like to know what franchise meas as a verb in the following sentence: Catering in this school has been franchised to the company. The native speakers I consulted, both American, don't seem very sure of its meaning. I know the verb typically means (of a large company like McDonald's) to permit an individual or a smaller company to sell products or offer services in its name. But in the example above, I can hardly imagine a large \"catering company\" sold the right to sell its products in a school to a smaller company. Perhaps this is because I haven't heard of catering companies in connection with franchise agreements in my country. Could it be that it means the authority of the school gave permission to a company to provide catering? Could 'outsource' be used in this context to replace 'franchise'?", "label": 1}
+{"snippet": "As an applied mathematics student coming from a small university, I have not had an adequate course in writing/formulating proofs for problems in advanced calculus/real analysis (my university has an advanced calculus course, not a real analysis course). In the fall I will take the first of a two part course in advanced calculus. I believe we will use Fitzpatrick's book, Advanced Calculus. So, in order to prepare for the rigor and proof writing that will be necessary in this course, is there a good book or pdf that will provide solutions to problems involving proofs? I've found plenty of books with tons of problems but finding solutions to check myself (or see if there is a more clever approach) has been difficult. I hope this isn't too broad of a question, maybe some of you coming from smaller universities will understand my dilemma.", "label": 1}
+{"snippet": "I'm trying to translate this text to Polish and everything seems pretty clear to me, apart from the usage of the words \"within\" and \"without\". I presume it's some kind of technical vocabulary referring to the subject of jousting. Could someone explain to me what these words mean? Here are three excerpts from the text: At those jousts the noble ladies and damsels will give the knight who jousts best of those without a horn garnished with gold, and they will give to the one who jousts best of those within a white greyhound with a collar of gold around its neck. And the noble ladies will give a circlet of gold to the one who jousts best of those without. And one within that jousts best will be given a golden belt. And there will be given in the same field to whoever jousts best of those without a noble courser, saddled and bridled. And whoever jousts best of those within will be given a fine chaplet well worked with silk.", "label": 1}
+{"snippet": "\"Crack The Whip\" is a game played on ice skating rinks where several individuals line up all facing the opposite end of the rink, and skate forward. When the group reaches the opposite end of the rink, the \"point man\" or the person on one end of the line stops, and everyone else pivots around him. Supposedly, the person on the opposite end swings around, and rockets forward at much greater speeds. However, I don't believe this is possible. Because the question remains, where would the extra speed come from? I was told that the momentum of all the people is transferred into the one person on the end. While there is a ponderous amount of outward force on the chain of people, I don't think it's possible to actually gain speed. And after watching my friends do it several times, I concluded the person on the end didn't seem to go any faster. Was it simply that the process was inefficient? Or is the theory even possible?", "label": 1}
+{"snippet": "Even though I don't work at Google, the Google Styleguides have been very helpful for me in adopting consistent, readable style conventions for my code. Unfortunately, there is no Google Styleguide for LaTeX. Q: For LaTeX, does anyone know of something equivalent to the Google Styleguides? Quick searches of the web for LaTeX styleguides have returned plenty of styleguides emphasizing how compiled LaTeX documents should appear. I couldn't find anything emphasizing how the uncompiled .tex document should appear. I suppose if there weren't anything equivalent to the Google Styleguides, a standard, very cleanly written and commented .tex template would suffice. UPDATE: Over at StackOverflow, I've found a similar post asking about Ruby coding style guidelines. There are a number of helpful links provided there. I'm looking for something kind of similar.", "label": 1}
+{"snippet": "I'm trying to figure out a kind of taxonomy of quantum phenomena. So far the categories I've come up with are (in historical order, with example phenomena): discrete quantities where continuous ones are expected (black-body spectrum, atomic spectra, Stern-Gerlach [spin spectra]), interference phenomena where trajectories are expected (double slit experiment), and long distance entanglement correlations (Bell's inequality phenomena). Am I missing anything major from this list? Did I incorrectly group something that should be in its own class? Can any of these classes be merged? As requested, how I would define classical phenomena: anything that behaves according to classical mechanics - objects that have (approximately enough) definite position and momentum that obey Newton's laws (even the relativistic versions), and waves that have infinitely variable amplitude, even when boundary conditions limit the frequency spectrum. Basically, I'm trying to get a clear picture of what the boundary between classical and quantum phenomena looks like.", "label": 1}
+{"snippet": "In the following statement, I am confused with the meaning of \"whether\" in the second sentence. Could you please advise which one is the meaning of this statement? a or b? The statement: \"For the grant of the permanent Partner visa, you can be either in or outside Australia. This is the case whether you lodged your original application in or outside Australia.\" The meaning: a) You can be either in or outside Australia for the grant of visa and it is not important where you have lodged your application. b) If you have lodged your application in Australia, you have to be in Australia for the grant of visa and if you have lodged your application outside Australia, you have to be outside Australia for the grant of visa. Many thanks, Kourosh", "label": 1}
+{"snippet": "An inertial frame of reference is described as being a frame of reference in which the first law of Newton (the law of inertia) holds. This means that all events as described with respect to this frame of reference must have a zero net force acting on it and therefore traces a straight line with a uniform non-translatory motion. But, I have read in some books, especially \"Introduction to Special Relativity\" by the well-known Robert Resnick, wherein his definition of an inertial frame of reference also refers to such a frame of reference as being an unaccelerated system. This is where I am confused. How can we describe a frame of reference as being unaccelerated if we occupy the frame of reference itself? No mechanical experiment conducted solely confined to a single frame of reference can determine the absolute motion of the frame of reference relative to another frame of reference. All that can be understood is that there is a certain uniform relative motion between frames of reference and no more. Is Robert Resnick saying that the inertial frame of reference is unaccelerated with reference to another frame of reference?", "label": 1}
+{"snippet": "I am currently a senior in high school, and I have been studying mathematics for about nine or ten years now in my personal time outside of school. I am not familiar with academia or in general higher education, but I do know that I want to continue studying mathematics or something in a related area. I am having a lot of trouble pinning down which universities I should consider going to, I don't think I am even ready to start comparing, so despite the 'softness' and vague nature of this question I feel I don't really have any where else to start then by asking which universities should I be looking into for mathematics? I have read many articles that rank schools according to some criteria, articles with titles like \"Top Universities for Mathematics\" or \"Best Mathematics Programs\", but I really want to get the opinions of people who study mathematics frequently. Any school suggestions would be greatly appreciated. I am trying to gather a list so don't hestiate. I live in California and am willing to go anywhere on the planet, so location is not a problem for me.", "label": 1}
+{"snippet": "What would be an idiom or word or name for someone that is an initial tester (like a beta tester). I am writing a speech for my younger brother's engagement and want to say how I have always been the first to try everything in my family--schooling, learning to drive, college applications, etc.--because I was the oldest son. My parents basically used me as a trial run to test the waters each step of the way in their parenting. They tweaked and refined the process with each of my two brothers. Now for his wedding, he's being sent out to scout for the proverbial mines for the first time. So I'm looking for a better term than beta tester to describe what I have been my entire life. I was kind of like a \"lab rat\", but that sounds horrible. Here's the line: \"Throughout our life, being the oldest, I was sent out as the front line to test the waters.\" I really hate that line. I hope having a better term for \"beta tester\" would make that line make more sense and sound better.", "label": 1}
+{"snippet": "Possible Duplicate: When is it okay to end a sentence in a preposition? So we've all heard the admonishments from our teachers not to end a clause with a preposition A plumber visits a wealthy estate to fix a clogged toilet. As the butler opens the door, the plumber barks out,\"I'm here to fix the toilet. Where's your bathroom at?\" \"Please try to speak with more discretion. We do not want to disturb our neighbors with the details of our plumbing issues. And we most certainly do not end our sentences with prepositions, sir. So the plumber lowers his tone and says more cordially, \"I'm here to fix the toilet. Where's your bathroom at, asshole.\" Anyway, back to the matter at hand. I have come under the impression that this is a rule of thumb to help the elementary student avoid mismatching case for the target of the preposition rather than a hard rule. For example by placing the preposition closer to its target, you avoid constructs like: \"Who did you give the invitation to?\" instead of the proper \"To whom did you give the invitation?\". Moving the preposition closer makes the incorrect case sound absurd. No one would ever say \"To who did you give the invitation?\" All of this introductory text leads up to this simple question: Is this phrase correct \"Whom did you give the invitation to?\" or is it still incorrect english even though we addressed the issue of case?", "label": 1}
+{"snippet": "Background: I am an upper level undergraduate physics student who just completed a course in classical mechanics, concluding with Lagrangian Mechanics and Hamilton's Variational Principle. My professor gave a lecture on the material, and his explanation struck me as a truism. Essentially, he argued that the difference between the Lagrangian evaluated along the parameters describing the true path and the Lagrangian evaluated along parameters corresponding to a mild perturbation of the parameters by a function an(x), where a is a scale factor, is zero. Where exactly is the profundity in this statement? I understood it as \"If we deviate the parameters away from the parameters that minimize the integral, and then take the limit as that deviation vanishes, the difference between the path described by these two sets of parameters is zero and the path must be the true path.\" Well of course this is true. What am I missing? Alternatively are there any decent texts that outline this principle at an undergraduate level?", "label": 1}
+{"snippet": "I am a high school senior and I am interested in doing a math research. I hope someone can recommend areas or topics of research that are challenging, rewarding, and yet do not exceed my capability. (I acknowledge this is quite hard) My math background: a. I have done competition math (Elementary number theory and combinatorics, Euclidean Geometry, and Algebraic manipulation) and I'm fairly comfortable with proofs. b. I had my first courses in Multivariable Calculus, Differential Equation, and Linear Algebra (Familiar with fundamental concepts, basic techniques and motivations) c. I have learned a portion of Abstract Algebra on my own and in summer programs including topics like Lagrange theorem, Vector spaces, Polynomial Rings, and Morphisms. d. I don't have a good background in statistics and probability e. I have been exposed to Knot theory and Chaos theory f. I do have basic programming skills in python and Mathematica, and I can work with LaTeX. I really appreciate your help!", "label": 1}
+{"snippet": "I am planning to take a graduate Geometry course next semester. The preliminary syllabus does not specify any textbook but has the following descriptions: Catalog Course Description: This course studies higher geometry including triangulations of polygons, Voronoi diagrams and Delaunay triangulation, algorithms in computational geometry, Euler characteristic of geometric objects, conics, elements of differential geometry of curves. Topics Covered: inequalities, Helly's theorem, power of a point, inversion, Voronoi diagrams and Delaunay triangulations, algorithms in computational geometry, Euler characteristic of geometric objects, conics and their affine and metric classification, elements of differential geometry of curves, polyhedra. I would like to study early taking advantage of my downtime. Is there any textbook that you would like to recommend for my self study? Thank you very much for your time and pointers.", "label": 1}
+{"snippet": "Fluid dynamical instabilities are present in many different everyday things. The famous tears in wine for example are a classical example of a Marangoni effect, where surface tension gradients due to evaporation cause an instability. I recently came across an instability that occurs when you have just emptied a glass with yoghurt drink and have only a film of the drink left on the walls of the glass. A tear-like pattern emerges over the time of about a minute that looks like shown below: I have been thinking what can cause this effect. It seems somewhat similar to a Marangoni effect, but given the ingredients of the yoghurt drink I think we can safely rule out evaporation on this timescale. Another potential effect explaining this would be viscous fingering, but for that to happen I believe the gas phase has to be driven, which it isn't here. Or perhaps it is a 'surface-version' of a Rayleigh-Taylor instability? Or maybe it is related to the non-newtonian nature of the yoghurt drink? To summarize: I don't know which instability I am looking at and I would love to know what causes this pattern on the glass with yoghurt drink! Does anyone know what is causing it?", "label": 1}
+{"snippet": "There's an old debate going on in the guitar community about how much does wood choice and body shape affect the sound of an electric guitar. No one denies that there's a difference acoustically (how the guitar sounds unplugged) because in this situation it's the wood and body shape that amplify the sound made by string vibrations, but when we're talking about the sound as it comes from the pickups, things get much more uncertain because there are a lot of variations even in supposedly identical guitar parts, and accounting for all of them for the purpose of doing an experiment where the only difference between two guitars is the wood is difficult (I certainly haven't heard of an experiment that was satisfying enough, but feel free to prove me wrong). I'm interested in a way to circumvent these practical difficulties using a theoretical explanation: Since the pickup only sees the string's vibrations, the question basically becomes \"does body shape and wood make enough difference in the way a string vibrates that it changes the sound in a noticeable way\", and this sounds like something that may be possible to figure out mathematically, or at the very least should be much easier to test because there are less variables involved. My question is: Is what I'm describing possible to calculate/test, and has this been done before?", "label": 1}
+{"snippet": "Let's say I am at the train station and I missed the train, I still see it driving off. I would naturally say to myself: 'Damn, that was the train I was hoping to get.' Would that be wrong? If not, why is the past progressive used here? I have been taught that you use the past progressive when you are either talking... about a longer action that was interrupted by a shorter action about actions that were happening at the same time about an action that was in process at a specific time in the past However, my sentence doesn't follow any of the rules above (at least I don't see that). Another sentence that I can't gramatically explain... Context: You told your friend David that Fred would not behave good when he is drunk before going to a party at which Fred gets drunk and then behaves bad. Later you say to David 'See? That's what I was talking about.' What's the grammatical explanation of this? Can anyone give me a rule why these sentences work? Thank you in advance!", "label": 1}
+{"snippet": "My friends and I were playing a game where you roll dice and you bet money on what picture it's going to land on and I began reasoning with myself that if I tallied up what pictures the dice landed on that the ones it has not landed on were more likely to come up in the next roll of the dice. So I began a process of observing two rounds and tallying up the results and then on the third round betting on the pictures that have not come up yet hoping that they would make their appearance on the next roll. Although I do not have any mathematical proof to verify this. Does anyone know what this phenomenon is called if it is even possible or if it is possible? Edit: I figured it out its called \"Gambler's fallacy\"", "label": 1}
+{"snippet": "Is \"family\" both plural and singular? or would I have to say families for the plural form? For example, which of these is the best option: \"A majority of those whose family were unaware of their sexuality...\" \"A majority of those whose families were unaware of their sexuality...\" \"A majority of those whose family was unaware of their sexuality...\" Edit: Here are some full sentences to give some context. Participants whose famil(ies) were aware of their sexuality were predominantly feminine and identified as gay, homosexual, drag queen, or a combination of these identities. All those who assumed their famil(ies) knew about their sexuality were gay identified and a majority identified as feminine. A majority of those whose famil(ies) were unaware were masculine and identified as non-gay, straight, down low or did not identify with any label.", "label": 1}
+{"snippet": "I'm reading Chris Hecker's third article on rigid body dynamics http://chrishecker.com/Rigid_body_dynamics Quoting... \"More importantly, if our collision detector supplies us with a 'normal vector' for the collision (denoted by n, and pointing toward body A by convention), we can define the 'relative normal velocity' as the component of the relative velocity in the direction of the collision normal.\" Which he defines as vAB . n where vab is the relative velocity of points A and B and n is the normal vector for the collision. I read Understanding Dot and Cross Product which explains that the dot product gives the length of one vector in the direction of another, which I think is what is being applied here, but I'm having a really hard time visualizing what is going on, specifically what the component is. Can anyone help explain what this component is and how using the dot product helps identify it?", "label": 1}
+{"snippet": "I would like to better understand how neutrino oscillations are consistent with conservation of momentum because I'm encountering some conceptual difficulties when thinking about it. I do have a background in standard QM but only rudimentary knowledge of particle physics. If the velocity expectation value of a neutrino in transit is constant, then it would appear to me that conservation of momentum could be violated when the flavor eigenstate at the location of the neutrino source is different from that at the location of the interaction, since they are associated with different masses. For this reason I would think that the velocity expectation value changes in transit (for instance, in such a way to keep the momentum expectation value constant as the neutrino oscillates), but then it seems to me that the neutrino is in effect \"accelerating\" without a \"force\" acting on it (of course, since the momentum expectation value is presumed constant, there may not be a real problem here, but it still seems strange). Any comments?", "label": 1}
+{"snippet": "I've recently learned about ultraproducts, but the source I learned from almost immediately after the definitions restricted to talking about countably incomplete ultrafilters. I know that the existence of countably complete ultrafilters is a large cardinal issue, but aside from this, is there a reason to focus on the countably incomplete case? Do ultraproducts (or even just ultrapowers) with a countably complete ultrafilter behave very differently from the countably incomplete ones? It would be great to have an example of the kinds of differences that happen, ideally in a fairly down-to-earth setting (maybe groups, or fields, or graphs?). The few places I've seen talk about countably complete ultrafilters all seem to be taking ultrapowers of models of ZFC, which is a bit much for me to grasp at this point. Since I just want to see the differences, it's fine with me if some set-theoretic hypotheses are needed to make the examples work.", "label": 1}
+{"snippet": "While my physics teacher was explaining pseudo forces to us he gave the following example : An elevator is accelerating upwards. In it there is a bob strung up by a rope. There are two observers, A in the elevator and B outside of the elevator, on the ground and not accelerating. Due to the action of gravity and the lift's acceleration the rope breaks and the bob falls. Does it do so at the same time for the two observers? The falling of the bob will be registered only when an observer sees a change in its position. This will happen earlier for observer A in the elevator compared with observer B outside. Question: At a particular time instant, is it possible for the rope (which holds the bob) to be both broken and taut for different observers?", "label": 1}
+{"snippet": "Is there a word to describe someone who uses complaints to indirectly brag about themselves? An example would be \"I hate going to concerts because people start singing and because I have perfect pitch it irritates me.\" Perhaps another example might be \"I don't like that video game. It's too easy and I get bored.\" The complaint would be in context, like the discussion is about concerts or the game in question, but the person uses it as an excuse to highlight something about which they want to brag. I don't think I'm looking for narcissism, as it's not necessarily that the person is trying to talk only about themselves, but rather that they specifically use a negative complaint to mask the fact that they are bragging. Is there such a word to describe this behavior?", "label": 1}
+{"snippet": "I think prejudice is too general. The definition Google gives me for prejudice is: \"preconceived opinion that is not based on reason or actual experience.\" - it doesn't specify that this preconceived opinion is due to membership in some group (or, more specifically, perceived membership in a group), although it seems to have that connotation, so maybe that is what I should go with. I think bigotry is too strong. For bigotry, we have (wikipedia): \"Bigotry is a state of mind where a person strongly and unfairly dislikes other people, ideas, etc. \" Bigotry sort of connotes hatred, not just bias. I want a way to describe the fact that a particular statement reveals an attitude that is unfairly biased against a culturally significant group, which may or may not be intentional or malicious.", "label": 1}
+{"snippet": "In one of the books on algebraic topology (I don't remember exactly which one) there was an exercise to build an example of two topological spaces having two continuous bijections between them which are not homotopy equivalent. To be honest, this exercise confuses me a little because, as I understand, each pair of homeomorphic spaces is homotopy equivalent by construction. On the other hand, the existence of bijective continuous mapping between spaces automatically provides their homeomorphism (correct me if I'm wrong). Thus, in this logic, if we have two continuous bijections between topological spaces this will inevitably lead to the homotopy equivalence between them. I guess, however, that there is a simple counterexample related to the discrete topologies which breaks such a reasoning (see, for example, this: Is a bijective homotopy equivalence with bijective homotopy inverse a homeomorphism?), but I have certain difficulties in discovering it. Is there any suggestion?", "label": 1}
+{"snippet": "One quality or trait that many employer looks for in a leader is the ability to not only perform well yourself but to also elevate the performance of others around you. For example, Steve Nash was an elite point guard and an all-star that made the people around him better. He made Shawn Marion and Amare Stoudemire all-stars and afterwards, when they were no longer teammates, they were not able to play at their all-star levels. You could say that Steve Nash is a great leader but it does not inherently imply that he also makes the people around him. Is there a specific word that describes this? A phrase to describe it would be, \"he brings the best out of others\", but I cannot think of a word to describe this ability/trait.", "label": 1}
+{"snippet": "I was driving to work this morning when this question occurred to me. I was going up a clover-leaf entrance ramp to the highway. The person in front of me was lazily floating the outside of the curve, whereas I always tend to hug the inside of the curve. Hugging the inside of the curve tends to lead to an apparently higher speed... and I soon had to apply the brakes to avoid hitting the floater in front of me. This made me wonder, why does hugging the inside of the turn yield an apparently faster speed? Is it simply because the inside is a shorter radius and thus you traverse it more quickly, thereby appearing to go faster (something I know track racers take advantage of, thus the expression \"he's got the inside track\")? Or, it occurred to me that it could be similar to the way a figure skater performing a pirouette speeds up as she pulls her arms and legs inwards. So as you continually pull your car inwards on the curve it actually does increase its velocity. Does the second concept actually come into play here, yielding an actual faster velocity? Or is it simply the first concept, yielding only an apparent faster velocity? (assuming our cars are identical weight, engine power, etc.)", "label": 1}
+{"snippet": "Given the equations of two spheres, how would I find the equation of any plane tangent to the two spheres? I tried something, but I realized that it failed, and I am not sure where to go from here. I have only basic knowledge of cross product, dot product, etc. and have not yet taken calculus. My attempt: I know the centers of the two spheres. I pick any point on the surface of the first sphere. I find the vector from the center of the first sphere to the point I selected. I then scale the center of the second sphere by the vector I just found divided by the radius of the first sphere and multiplied by the radius of the second sphere. Then, I construct the vector from the point I chose on the first sphere to the point I found on the second sphere. I take the cross product of this vector with the vector formed by the centers of the two spheres. I use this as the normal vector for my plane and plug in to get its equation. I noticed by experimentation that this does not work. Is there a way of solving this problem in a similar manner to what I tried above?", "label": 1}
+{"snippet": "Back when I studying the time independent perturbation theory of the Hamiltonian in quantum mechanics, I remember reading that there are only three problems in physics with exact solutions: the free particle, the harmonic oscillator and the hydrogen atom. It was further stated that any given problem (even a simple pendulum) could have its solution determined by applying a small perturbation to the exact solution of another similar problem, i.e., it would be an approximate solution. So I was left wondering: are the solutions to all [a] real life scenarios (where you don't go around neglecting friction, using symmetries, etc.) obtained through perturbation theory? That is, are they all approximations and not exact solutions? In that case, would it be fair to state that physics is inaccurate to a certain degree? [a] With the exception of the aforementioned ones.", "label": 1}
+{"snippet": "I'm a little out of my depth here... I'm trying to understand quasiparticle tunnelling in superconductor-insulator-superconductor junctions. Many books use the \"semiconductor model\" to explain this: (source: wikimedia.org) These diagrams show the available quasiparticle states (with a large band gap due to the formation of Cooper pairs), the filled states, and the empty states. My question with these diagrams is: shouldn't all the electrons exist as Cooper pairs? I assume that the lower band is filled with quasiparticles, since Cooper pairs would all be at the same energy level and quasiparticles obey Fermi-Dirac statistics, but I don't know where they're coming from. Also, why is there an energy gap in the quasiparticle energy states? I understand that this gap corresponds to the energy needed to break Cooper pairs, but I don't understand why would you need to break Cooper pairs to raise the energy of quasiparticles. Or is this \"semiconductor model\" not fully representative of the physics?", "label": 1}
+{"snippet": "I was working on a lab in class drawing Free Body Diagrams. The problem required we drew an FBD of a ball that is in the motion of being thrown. I drew a slightly diagonal line labelled Applied Force, a vertical line straight down labelled Gravity, and a line opposite of Gravity labelled Normal Force. I was told that there is no normal force at all in this situation, and that the only two forces are gravity and applied force. I was confused because I thought that the ball was being held up by the hand (acting as a surface) which provided a normal force while still being pushed by the hand in the positive direction resulting in an applied force. So in this situation, would the ball have any normal force at all acting on it?", "label": 1}
+{"snippet": "I'm a huge Pulp Fiction fan, and the following is one of my favorite scenes, but it also irks me. (source: IMDB) Jules: [Jules shoots the man on the couch] I'm sorry, did I break your concentration? I didn't mean to do that. Please, continue, you were saying something about best intentions. What's the matter? Oh, you were finished! Well, allow me to retort. What does Marsellus Wallace look like? Can a question be a retort to something? I see retort defined as (dictionary.reference.com): to reply to, usually in a sharp or retaliatory way; reply in kind to. to return (an accusation, epithet, etc.) upon the person uttering it. to answer (an argument or the like) by another to the contrary. All the above suggest some sort of a reply. But can a retort be a question, or even a counter-question ?", "label": 1}
+{"snippet": "Break comes to a close, and you, a renowned mathematics professor, step into a grand lecture hall to deliver the first lecture of the semester on topology. This is an introductory course. Half of the students cannot even pronounce homeomorphism. As you look around the room, a bead of sweat works its way across your brow. All you can think of is the possibility that the entire class will fail, and you will be mocked by the other professors. Then you take a sip of water and pull yourself together. You pick up a fresh (but not too fresh) piece of chalk, write your name across the board--effectively marking your territory--and address the class. How do you introduce a class of undergraduate students to the field of topology? I am looking for a creative, but precise explanation of the field and the most fundamental topological concepts. Diagrams and metaphors are welcome.", "label": 1}
+{"snippet": "Can a sentence like this: \"I don't know who the first man that made such and such thing in such and such place was,\" be grammatically correct if we don't put \"was\" at the end of the long phrase, that is, if we write: \"I don't know who was the first man that made such and such thing in such and such place\"? I can see in Google Books examples that in such cases the verb is often put after the wh-word, but I don't know if there is a grammar rule to support this. Some examples: \"We do not know who was the first man who ascended above a poor and humble people to become Egypt's first king ...\" \"... we do not know what was the ultimate judgment of the various members of the community ...\" \"I do not know who was the first to suggest a connection between the problem of free will and the breakdown ...\" \"I do not know what was the date of this change in me, nor of the train of ideas ...\" \"We do not know what was the primitive text from which Codex Bezae derived its Latin or its Greek ...\" \"We do not know what was the practice in the days of the monarchy, but the story of Athaliah shows ...\"", "label": 1}
+{"snippet": "I'm writing a paper about an algorithm that I have developed. Just for illustration, I will say that the method name is \"quicksort\". My question is about the usage of the in the following context: This paper proposes quicksort, a novel and fast algorithm. The advantage of quicksort is that... My question is whether I should use \"The advantage of the quicksort...\" or \"The advantage of quicksort\". I am also looking for resources explaining the usage of the in this context. [Meta] Usually, to check if a certain sentence is correct, I search Google using wildcards. However, in this case, the correct answer is depends on the context. I have also tried to find a answer in the following book but without success: Science Research Writing: A Guide for Non-Native Speakers of English.", "label": 1}
+{"snippet": "I'm entering my second year of undergrad (majoring in mathematics), and I've found that I am really bad at Linear Algebra, but very good at Calculus and Differential Equations. I'm hoping to venture onto Sci. Computing/Applied Maths, but I'm worried my inadequacy (as quite personally, unfortunate lack of interest) for Lin. Alg. will prevent me from being successful in topics such as Numerical Analysis, Algebra, as well as Scientific Computing. Does anyone in the applied maths field/experience with applied maths have any advice on what I should do? That is, what else is there like Calculus/DEs that will help me in this field? Or do i just need to buck up and get on my Lin. Alg. horse in order to get remotely close to where I want to go? I appreciate any and all input.", "label": 1}
+{"snippet": "I was looking for a synonym of spontaneous, and voluntary naturally came to my mind. In an attempt to understand the difference between them, I tried to google spontaneous vs voluntary. To my surprise, nothing really interesting popped up from search results. Then I decided to look them up respectively. As expected, voluntary is listed as a synonym of spontaneous according to many online resources, and vice versa. However, to my great shock, involuntary is also listed as a synonym of spontaneous by major online dictionaries. Although the fact does not necessarily imply voluntary and involuntary are synonyms, I continued to look further into voluntary vs involuntary due to confusion. I found that a voluntary action is something that is done voluntarily or with meaning to do so, while an involuntary action on the other hand is done automatically. Now I'm even more confused. The word automatically just reminds me of spontaneously, convincing me to believe involuntary is indeed a synonym of spontaneous while voluntary seems less so. Could someone please justify or explain the contradictions mentioned above? I'm totally lost.", "label": 1}
+{"snippet": "Suppose we have a contact process on a finite lattice. I'm asked to give a heuristic argument for the fact that the extinction time for the contact process is exponential in the size of the lattice when it is in the supercritical phase, and logarithmic in the size of the lattice when it is subcritical. The supercritical phase means that on the infinite lattice, the infection never goes extinct almost surely. I really don't know why this is the case. I get that the extinction time in the supercritical phase will grow rapidly, because if you make your lattice larger, the number of infected nodes grows. Because all these nodes are infected and they infect other nodes quickly (because of the supercritical phase), the other nodes will stay infected much longer. But is there any reason why this should be exponential (or logarithmic in the other case)?", "label": 1}
+{"snippet": "Motivation: If I start with the group axioms and drop the requirement that I have inverses, I get the monoid axioms. If I proceed to drop the requirement that I have an identity, I get the semigroup axioms. If I then drop the requirement of associativity, I get the magma axioms. If I drop the operation, I get the set axioms. A map preserving the monoid structure is a \"monoid homomorphism;\" a map preserving the semigroup structure is a \"semigroup homomorphism;\" etc. Question: Now suppose I start with the topological space axioms and start dropping conditions. Do the resulting sets of axioms have names? What about the maps preserving such structure -- do they have names? In particular, what about the smallest case of a sets equipped with some subset of their powersets, together with functions such that the preimage of a designated set is a designated set?", "label": 1}
+{"snippet": "There is a challenge involving a lemon floating in a jug of water which seems impossible to beat. I've noticed it in several pubs of Edinburgh. The challenge is as follows: There is a jug half filled with water. Floating in the water, there's a lemon. The lemon doesn't touch either the bottom nor the edges of the jug. The challenge is to successfully balance a coin on the lemon. Modifying, moving, or more generally touching the lemon are not allowed. Any attempt to balance a coin on the lemon seems to result in the lemon flipping over, and the coin to sink in the water. Why is it so hard to balance the coin while it's extremely easy to balance a coin on a lemon set on a table? How do you beat the lemon challenge?", "label": 1}
+{"snippet": "I've been using OpenOffice and/or MS Word to do my college assignments, but since I started this new discrete math course, I'm finding myself very annoyed with the math formula options in those programs. I learned about LaTeX and figured it would be my best option. Since I really just want to get my college assignments done with it and not use it for printing books I've written or anything, I decided to go with LyX. It has a quick and easy preview option, and isn't so different from what I'm used to. I still can't find a way to make the fancy, cursive script \"U\" that represents universe or universe of discourse that is used in set theory. Is there a specific package I need, or did I just miss it somehow. Also, if I do need a new package, how is that even done with LyX. Anyone with assistance has my gratitude.", "label": 1}
+{"snippet": "My wife was discussing pudding consistency this morning and used a sentence along the lines of, \"I only like the pudding you make\". I blinked and asked if she really liked the pudding I make and she replied, \"No, I mean the pudding you make, you know, like if I were to make some pudding\". She was using the \"you\" in a sense of a hypothetical person, I guess, like saying, \"That's what you do in a crisis\" when commenting on a riot scene in the news. You're not using \"you\" to refer to the person you're speaking to, but rather a form of general humanity. Anyhow, is there a term for such a usage such that you might be able to answer, \"Oh, sorry, I was using 'you' in the [term] context, not referring to you specifically\"?", "label": 1}
+{"snippet": "I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the lecturer just drew a picture of a solid wall with two slits and then showed pictures of the interference patterns generated by shooting a single electron at the slits. Fine enough, the electron interferes itself, which is beautifully explained by the wave function. However, aren't the atoms in the wall with the slits also described by a wave function? I mean, can we even meaningfully draw a picture of a 'slit' if it is roughly at the scale of an electron? Aren't we supposed to be dealing with a wave function there too? Looks to me the wall with the slits is treated as a 'classical' object (you can touch it, feel it, smell it) while electron is treated as a quantum object. But that simply cannot be the case. Question: how does the wave function that describes the atoms around the slit 'know' to interact with the wave function of the electron? Does it collapse? The reason I ask this is because when the electron does not make it through the slit, it must have collided with one of the atoms: but wouldn't collision imply that two particles were at the same place at the same time? Doesn't that require wave function collapse? I'm confused ...", "label": 1}
+{"snippet": "I'm trying to understand the connection between the wave model and the particle model for light. It's understood that the energy of a photon is given by E=hf, but from my understanding of fourier analysis, the only kind of wave that has a precise frequency is a plane wave. The plane wave is an idealization, since no real wave permeates all of space and time. So imagining a more realistic EM pulse, the frequency spectrum will have some kind of spread depending on the shape of the pulse. Is the pulse a single photon? Or is it a collection of photons, each with different frequencies? In the photoelectric effect, it's usually described as a single photon with sufficient energy being absorbed, kicking the electron out of its orbit. Let's imagine the pulse is symmetrically centred around the frequency with energy exactly equal to the metal's work function. What exactly happens to such a pulse? Will the whole pulse be absorbed, since its average frequency has energy of the work function? Or will the half of the pulse that has the higher frequency be absorbed, leaving the rest to reflect or what-not?", "label": 1}
+{"snippet": "Whenever I add milk to my morning coffee I often enjoy watching the patterns which are created. These patterns have a striking resemblance to certain fractals and my question is, \"Why?\" Oh dear, that is never a good question, so let's try \"Why shouldn't they?\" The obvious observations are that the water is very hot when the milk is added, so we expect the \"coffee particles\" (non-milk part) to have a higher velocity relative to the \"milk particles\". Secondly, the coffee part, having been recently stirred, is often still rotating (clockwise in my case). Finally, the image we observe is a projection of some distinct portion of a \"top layer\" of the milk and coffee mixture. Add diffusion into the mix and it really seems like some crazy stuff should go down! But I'm afraid I'm not satisfied. Why physics.SE... why?", "label": 1}
+{"snippet": "I read about this law / property a couple of months back, but I've forgotten what it's name was and I can't seem to find it by Googling. I was hoping someone could give me the name for this property. If I recall correctly, it was named after same famous mathematician like Gauss or something... More detail: This site was basically describing how you can make a long piece of metal, paper, etc. stronger by bending it along its long axis. This way, it is less likely to collapse along its length when upright. An example of this property was grass blades, which are able to stay upright due to the fold / bend along their long axis. If someone knows the exact name of this property, please do tell me!!", "label": 1}
+{"snippet": "I am familiar with basic quantum mechanics and I know that there is no concept of 'force' in quantum mechanics, unlike in classical mechanics. Problems in quantum mechanics are solved by writing down the Hamiltonian for a system, and trying to solve for the various eigenvalues. Some of the first problems that are taught to students learning Quantum Mechanics are the harmonic oscillator problem, and the Hydrogen atom problem, where the Hamiltonian takes the same form as a classical system. Since moving over to quantum mechanics requires one to lose several ideas that have been built up while learning classical mechanics, why is the potential found in quantum mechanics problem of the same form as classical mechanics? The potential for the hydrogen atom, for example, is classical in origin and is derived from the Coulomb force. How is this direct usage of the potential, which is purely classical in origin, justified by the theory?", "label": 1}
+{"snippet": "I'm in doubt in the application of Gauss' Law to find electric fields when the charge distribution is symmetric. Well, first of all: I know how to find the magnitude of the field - we just enclose the charge distribution with a gaussian surface on which the electric field will not change it's magnitude, and then using Gauss's Law we can write it in terms of the total charge inside and the area of the gaussian surface. My problem is: how do I find the direction of the field? I mean, in a spherical symmetric distribution it's easy, because we know what's the vector that points radially outwards (it's simply one of the unit vectors from spherical coordinates). But what about a cylindrical symmetric distribution ? Would I need to use the unit position vector of cylindric coordinates ? In the general case I would need to switch to more appropriate coordinates to write the field ? Is there a general way of treating this ? Sorry if this question is to silly or too basic. I'm just trying to understand how to use properly this law.", "label": 1}
+{"snippet": "Good afternoon, I'm trying to learn about Fuzzy alone, I was using some texts on the Internet about it, but it was very difficult to learn. I want to learn about Fuzzy set as shaper of uncertainty. Operations with fuzzy sets. Characterization and properties of fuzzy sets. The Zadeh extension principle. Fuzzy numbers. Fuzzy relationships. Fuzzy relational equations. Systems based on fuzzy rules and the Mamdani inference method. Fuzzy controller and an application. Compositional rule of inference. Inference method of Takagi-Sugeno-Kang. Approximation properties of fuzzy systems. Measures and fuzzy integrals. Introduction to fuzzy dynamic systems. I found these books on web -Fuzzy Mathematics: An Introduction for Engineers and Scientists, John N. Mordeson, Premchand S. Nair -Fuzzy logic with engineering applications, Timothy J Ross -Fuzzy sets and fuzzy logic, George J Klir Does anyone know any of these books? I am totally beginner in this matter, and unfortunately none of these books has available solutions. If anyone knows of any video material on this topic I'm grateful too.", "label": 1}
+{"snippet": "After spending almost one year on this site, I've realized that my knowledge of mathematics is not deep enough. I love mathematics, i mean I am obsessed with it. I have a masters degree in mathematics from a reputed university in India and now I want to pursue PhD in this subject. It's been one year since completion of masters degree and I am unable to find a place in any university for PhD (I failed at couple of entrances). So my question is, is my love and passion for this subject will help me to do research or to do research in mathematics one need an unusual brain? By unusual I mean who can instantly catch the logic and solves a problem, which I can't. I am slow. So I need some advice on this? How should I prepare myself? Thanks. Edit: By this question, I am not asking about which career I should choose. I know I want to do PhD. What I am asking is, \"How one should prepare before starting a PhD?\" What are the basic points I should be working on? Simply just reading many things would not help I guess. So if this question can be reopened and some one give me a pointer then it would be helpful.", "label": 1}
+{"snippet": "I'm writing a paper about classes of formal languages, and I'd like to have a diagram showing their heirarchy. Something similar to this (from Wikipedia:) Is there a LaTeX package which, I can give the relationship between the classes to, and have automatically generate and lay-out a venn-diagram for me? The idea is that I would give it the list of classes, and some relations between them, i.e. which were contained in each other, which were disjoint, which were incomparable but not disjoint. Containment is assumed to be transitive (i.e. if A is in B, B is in C, then A is in C). Is there a way to do this programatically, or a package to do it automatically? The idea is that I'm continually adding new classes to the diagram, and would love if it would automatically update itself every time I discovered a new relation.", "label": 1}
+{"snippet": "This sounds like a daft question, but I'm serious. Translation and rotation are clearly different -- the symmetry between them is broken by Newton's Laws. But in the Lagrangian/Hamiltonian frameworks, they look extremely similar! The Lagrangians for free rotation and free translation are exactly the same, up to the replacement of some letters. Working entirely with the Lagrangian framework, it's unclear when and where the symmetry breaking happens. Despite this, there are many clear asymmetries between translation and rotation: There is absolute rotation, but not absolute translation. (At least, I believe this is the orthodox position.) In space, starting with zero linear and angular momentum, it's possible to change your angular position but not your translational position (you can turn yourself around, but can't move your center of mass). In quantum mechanics, free particles can have continuous values of linear momentum but have quantized angular momentum. I know why the third point holds: localization causes quantization, and the set of possible angular positions is compact, while the set of possible positions is not. In fact, I feel like this is the only difference, a priori, between translation and rotation. In layman's terms, if you keep rotating, you'll get back to where you started, but if you keep translating, you won't. Is it possible to use this reasoning to extract the first and second bullet points above? If not, what exactly is the difference between translation and rotation?", "label": 1}
+{"snippet": "It's my first time to write latex with Mac os (or in fact, using Mac os in general) and unlike with Windows I'm having some trouble viewing my output files. I'm using texmaker. I would like to have either dvi or pdf viewer constantly open and auto-refreshing when I save changes or convert them to latex. I was told that Skim application should do the job, but I always have to close the dvi/pdf and re-open it for Skim to refresh my changes. Any suggestions or advices how to handle this properly? This might seem like a small problem, but when I save and view my changes constantly it is really painful (and time consuming) to always close the pdf/dvi viewer, re-open it and then scroll to the correct location. Thanks for all the help in advance.", "label": 1}
+{"snippet": "Basic books dealing with the interaction of X-rays with matter ussually don't mention anything about the polarisation, but I read somewhere that X-rays scattered in matter are linearly polarized, specially those scattered at right angles of the incident rays. If I remember well, the reason was discussed considering the unpolarized X-rays as a mix of classical electromagnetic waves polarized in all the possible directions: each polarized wave produces electrons oscillations in the direction of the polarization, and this oscillation leads to the emission of (scattered) waves with the same polarization but with maximum intensity in the plane perpendicular to the polarization. But we know that X-rays are not classical waves but quantum entities and they can be scattered by different mechanism: Rayleigh scattering, Compton efect...so, is the statement about the polarisation of the X-rays true? Is it valid for both types of interaction (Rayleigh and Compton)?", "label": 1}
+{"snippet": "This was explained to me many years ago, by a physics teacher, with the following analogy: \"If someone on the beach wants to reach someone else that is in the water, they will try to travel as much as they can on the beach and as little as possible on the water, because this way they will get there faster.\" I'm paraphrasing of course, but this is as accurate as I recall it. This explanation makes no sense to me. Was he telling me the light knows where it is going? It wants to get there faster? It chooses a different direction? (No need to answer these questions, this was just me trying to understand the analogy.) My attempts to clarify the issue were without success and many years later I still don't know. Why does light change direction when it travels through glass?", "label": 1}
+{"snippet": "I am attempting to write a program that will compute the average amount of a particular product produced when randomness is involved. Let's say that I am trying to produce some widget. Whenever the production process for this widget is started, it is not guaranteed that the process will be successful. So let's say that the probability of successfully producing a widget is P(s). However, you only start with M number of materials, and whenever a widget is successfully created, then C materials are used up. Similarly, whenever a widget fails to be prodeced L materials are used up. So we know the following: P(s) = probability that production process will yield a widget. M = Amount of starting materials C = Amount of materials used if widget successfully created. L = Amount of materials lost if failure to make widget.</code> The problem I am having is in trying to compute the average number of widgets created (and similarly, the average number of failed widgets) given different values for P(s), M, C, and L. How can I come up with an equation that gives me the average successes and failures to create widgets?", "label": 1}
+{"snippet": "Starting from tomorrow, I will be tutoring some undergraduate students following a course in general topology. I am looking for examples motivating the importance of topology in mathematics which can be explained without too much difficulty using concepts of other areas of mathematics (or physics) they have already treated (those areas would be mainly analysis, complex analysis, linear algebra, a little graph theory, some numerical methods for maths, and classical mechanics, electromagnetism, special relativity, some QM and a little statistical physics for physics). I have tried looking around, but I have found little that would motivate me to follow such a course. Do anybody have some nice example? Note: I will of course explain to them that without topology they'll be able to do very little advanced mathematics (e.g. functional analysis, differential geometry, ...) EDIT: Ok, I gave as examples Tychonoff's theorem, Brower's fixed point theorem and the Jordan curve theorem. I would like to keep this question alive, for personal interest. What are interesting (not too hard) applications of topology in other areas of mathematics?", "label": 1}
+{"snippet": "I have this sentence: I strongly believe that the first step in making the most efficient solution for any problem is analyzing it well. Would it be better to use either of the following? I strongly believe that the first step on making the most efficient solution for any problem is analyzing it well. I strongly believe that the first step at making the most efficient solution for any problem is analyzing it well. The context is as follows: First of all, I concentrate on understanding the big picture of any problem. I always try to recognize all the factors that have caused the problem. Then, I start planning the solution at a very high level in order to create long-term benefits. I strongly believe that the first step in making the most efficient solution to any problem is analyzing it well. In my opinion, \"What to do\" is much more important than \"How to do\".", "label": 1}
+{"snippet": "I was watching a show on the science channel about gas giants; there is something I do not understand. I am not a scientist, so this may be obvious to some. I learned that there a three states of an given physical object; solid, liquid, and gas depending on how cold or hot the object is. An easy example is ice, water and steam from coldest to hottest. So the theory is that Jupiter has a super-heated solid and very dense core that is made up of hydrogen. How does a gas like hydrogen become a solid while being super-heated? Is it that the pressure is so much that the gas is compressed into a solid? If so how much pressure does it take to compress hydrogen into a solid? How does the heat play into the equation?", "label": 1}
+{"snippet": "I've recently discovered that the following theorems require the axiom of choice to be proven: every surjective function has a right inverse. a real-valued function that is sequentially continuous at a point is necessarily continuous in the neighbourhood sense at that point. every vector space has a basis. When I revisited the proofs I was taught in first year, I was surprised that my lecturers had used the axiom of choice without declaring so. It seems strange that so much effort was dedicated to establishing that mathematics is a rigorous subject [indeed much time was spent on learning the field axioms, well-ordering axioms, Archimedean principle and (later) the completeness principle] but to ignore the axiom of choice. I am interested if there are reasons for omitting to mention the axiom of choice. Are there pedagogical reasons? Is it deemed too complicated? Is it more contentious than the other axioms? Question also asked at Mathematics Educators S.E.", "label": 1}
+{"snippet": "I've used 'extraterrestrial' twice in a paragraph already, so it's starting to get repetitive... Edit: The sentence I'm hoping to prove is 'Humans have reached [insert word] scales', referring to the furthest we've went in the universe. By reaching I mean actual physical human presence, which excludes anything discovered or photographed by probes, and limits us to the Moon. Hence, the question is to find a word describing Earth-Moon scales. In response to the numerous suggestions below: Unearthly or cosmic scales is too grand and fails to convey what I'm gunning for - a sense of humility and a slight disappointment at the lack of human achievement in interplanetary matters ever since the completion of the Apollo program. Alien scales just sounds plain silly. Extrasolar, interstellar, or intergalactic scales are factually incorrect. So far, off-planet seems to suit my purpose the best for now.", "label": 1}
+{"snippet": "I am trying to describe the evolution of a motion which is composed of smooth parts called \"free flights\" and instantaneous impacts. For example, consider a bouncing ball: its motion is a succession of free flights, separated with impacts (when the ball touches the ground). I would like to refer to two time-related quantities: the duration of free flights, and the dates of impacts. The word \"time\" can refer to a length of time, or an instant (a date). To raise the ambiguity, I have chosen the following terminology: \"free-flight durations\" describes a length of time between two impacts; \"impact times\" describes the date of impact. Is this correct and would \"impact instants\" or \"impact dates\" be better? I am open to other suggestions too, but I want to avoid \"period\" which I am already using to qualify repetitiveness.", "label": 1}
+{"snippet": "Based on the following example: Local Area Network (LAN) You can say that LAN is the short form and the Local Area Network is the long form. What is the another word for \"short form\"? (Is 'acronym' a better word for replacing 'short term'? or 'abbreviation' would be a better choice?) What is the another word for \"long form\"? (Would 'backronym' a better word choice to replace 'long form'?) I am open for other word choice to replace 'short form' and 'long form'. Appreciate any help offer. Update I have create a table as follows: |------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | Acronym | ??? | Meaning (?) | |------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | LAN | Local Area Network | supplies networking capability to a group of computers in close proximity to each other such as in an office building, a school, or a home. | |------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| What would be the header name to replace the \"???\"? And also, would the header name \"Meaning\" be suitable?", "label": 1}
+{"snippet": "I was wondering if the cardinality of a set is a well defined function, more specifically, does it have a well defined domain and range? One would say you could assign a number to every finite set, and a cardinality for an infinite set. So the range would be clear, the set of cardinal numbers. But what about the domain, here we get a few problems. This should be the set of all sets, yet this concept isn't allowed in mathematics as it leads to paradoxes like Russell's paradox. So how do we formalize the notion of 'cardinality'? It seems to behave like a function that maps sets into cardinal numbers, but you can't define it this way as that definition would be based on a paradoxical notion. Even if we only restrict ourselves to finite sets the problem pops up, as we could define the set {A} for every set, thereby showing a one-to-one correspondence between 'the set of all sets' (that doesn't exist) and the 'set of all sets with one element'. So how should one look at the concept of cardinality? You can't reasonably call it a function. Formalizing this concept without getting into paradoxes seems very hard indeed.", "label": 1}
+{"snippet": "I'm struggling to find the words to convey the concept even now, but perhaps it would make more sense to illustrate by example. Certain communities like Reddit and Quora tend to be liberal-leaning and have other attitudes and opinions not entirely reflective of the population as a whole, in large part simply because they are populated by the kind of people who can find these communities. Your average computer engineer is much more likely to be familiar with Reddit and use it regularly than your average janitor or priest, and especially more than someone without reliable Internet access. Similarly, Wikipedia articles or tumblr blogs are unlikely to be written by your grandparents, and thus reflect a certain subset of content and attitudes by virtue of the people who use them most. I thought about implicit bias, but it doesn't seem to quite reflect the unintentional barrier of entry in these cases, although it's the closest I could find off-hand.", "label": 1}
+{"snippet": "Suppose someone (like a boss, friend, cousin,.., to whom you can not say \"no\" easily) has a personal request for you which you find difficult to decline, but you cannot bring yourself to say no, because you feel embarrassed or too shy to say no (i.e. you do not feel free to say no), or just simply don't like them to feel offended or hurt. What is the expression or idiom that would convey this meaning: \"to accept a request in this situation, unwillingly but under your own moral pressure or just out of shyness\". I have found this idiom: \"to put somebody on the spot\", can I use it in this situation? For example: My mother-in-law asked me to accompany her to the market, and I was actually put on the spot by her request so I went shopping with her despite having a severe headache.", "label": 1}
+{"snippet": "I'm a software developer (although math isn't my strong point). I've developed a device to monitor/control my clothes dryer by monitoring the intake air's humidity & temperature, and the exhaust's humidity and temperature. The plan was to compare the exhaust air's humidity against the intake air. Once the humidity in both was around the same, it would mean that no more moisture is evaporating from the clothes, ie: they're dry. Unfortunately its not that straight forward. the air coming out of the dryer is much hotter, and because the sensor is giving me relative humidity values, I cannot compare it to the intake humidity (which is room temperature). I'm looking for a formula that will allow me to compare the two humidities, taking their temperature into account. An \"absolute\" humidity I guess, or literally the amount of moisture in the air. I've tried a couple of formulas I've found online but I'm not getting readings that look valid. Note that the value doesn't need to be an official, absolute humidity value, it simply needs to allow me to compare the intake and exhaust humidities, at different temperatures (but everything else, such as air pressure, etc... being equal). (Please feel free to suggest a more appropriate tag)", "label": 1}
+{"snippet": "My school requires that dissertations follow a set of sometimes odd formatting requirements. We have a latex class file which does a reasonable job at bringing documents into compliance with their requirements. There is, however, one requirement that I have't got a clue how to make happen: Footnote are supposed to be at the bottom of each page which can be accomplished by using footmisc. However, on the last page of a chapter the footnotes are supposed to be directly after the actual chapter text ends not at the bottom of the page. Now I can solve individual cases by adding vspace, or simply not putting footnotes at the end of my chapters. However, I'm wondering if there is a way to modify the class file to make this happen automatically.", "label": 1}
+{"snippet": "On a chat channel today I was reading two people talk about some of the more popular movie formats and movie players available. One of the interlocutors said something that got me thinking. I will cut quick to my question. Is there a semantic difference between the following two phrases: ... the last movie I played ... and ... the movie I played last ... To my non-native English ears and eyes, I fail to see a difference. But reading these two phrases again and again makes me uneasy. The more I read them, the more I feel that the first phrase gives off a whiff that would suggest that the speaker/writer does not watch movies very often, while the latter would identify someone who watches movies all the time. What do you folks think?", "label": 1}
+{"snippet": "Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about that same line. Now, Euler's Theorem simply says that any rigid body displacement can be decomposed into a rotation plus translation. This is easy to visualize. But what Chasles' Theorem says is something much stronger. Unfortunately, I am just not able to visualize it. Perhaps, I am comprehending it wrong. I mean how is it possible to have the axis of rotation and translation the same (or parallel) for the most general displacement. I mean, think of this case: A body is given a finite rotation about the X-axis and then a finite translation about the Z-axis. How can we find that \"screw\" axis along which both of them can be described?", "label": 1}
+{"snippet": "Lets say I have the following sentences... Cake is really bad for you. It contains a large amount of sugar. It contains common allergens. It looks silly. Additionally, lets say I wanted to connect all three of these thoughts together in a similar manner... Cake is really bad for you. It contains a large amount of sugar. It contains common allergens. And, it looks silly. Now, I know that using an \"And\" at the beginning of the sentence is poor grammar. I also realize this is more of a paragraph structure, so I could do some word-smithing to make it work that way. However, this feels a lot like a series of items, and I would really love to treat it as such... Cake is really bad for you: it contains a large amount of sugar; it contains common allergens; and it looks silly. Is there a structure in the English language that provides for this? Is the above the proper usage? Thanks!", "label": 1}
+{"snippet": "I'm taking a very computational course in partial differential equations. Because of this emphasis, I'm feeling very underwhelmed by the course, and have a lot of questions that really aren't answerable in the current state of affairs. My professor basically tells me to take an advanced course in real analysis for a rigorous treatment, but that's a long way away for me (at least two years), I was hoping that someone could answer this question here. In the course, we have only looked at three equations and some minor generalizations on them - the heat, wave, and potential equations. I understand these to be characteristic of larger classes of PDEs, but I don't know anything at all about them except sometimes I can separate variables. For each of them, the method has been identical. Separate variables, solve two (or sometimes even three) ODEs. Then by superposition, sum them up. Determine coefficients with Fourier sums or integrals. Wash, rinse, repeat. The question is this: How do I know that that is all the solutions? There is no existence/uniqueness theorem for PDEs. How can I know that without some more advanced technique for solving PDEs that I couldn't find others? Does it follow from existence/uniqueness of ODEs? What about for those larger classes of PDEs?", "label": 1}
+{"snippet": "When using the interrogative pronoun, 'who', what would the possessive form be? 'Who checks X letterbox every day?'. I feel it ought to be 'his' but some people I know claim it should be 'their', which to me seems to contradict the singular form of the verb 'check'. 'Who checks his letterbox every day?' is what I would say naturally. 'Who checks their letterbox every day?' sounds a bit off to me. Looking on the internet doesn't really return anything useful, only the use of 'their' as a singular pronoun, which seems to be somewhat popular a topic. Note, this is specifically regarding the interrogative pronoun; I understand the debate about his/her/their/ones in other circumstances but I want to know whether the same can apply to 'who' or 'whom'.", "label": 1}
+{"snippet": "I would be tempted to rephrase my question as : why do people seem to care only about the curvature of a connection on fiber bundles ? Indeed, the curvature gives the vertical part of the commutator of horizontal fields (the horizontal part is the lift of base commutator), while the commutator of vertical fields has nothing to do with the connection. So it remains, for me, aside from the curvature, to understand the commutator of a horizontal and a vertical field. In the case of principal bundles and principal (=invariant) connections, I understand it well, since we can use the action of the group. But what happens then in general for fiber bundles? Doesn't it give information on how the horizontal distribution vary in one fiber ? Thanks, Amin", "label": 1}
+{"snippet": "My understanding right now is that an example of conditional independence would be: If two people live in the same city, the probability that person A gets home in time for dinner, and the probability that person B gets home in time for dinner are independent; that is, we wouldn't expect one to have an effect on the other. But if a snow storm hits the city and introduces a probability C that traffic will be at a stand still, you would expect that the probability of both A getting home in time for dinner and B getting home in time for dinner, would change. If this is a correct understanding, I guess I still don't understand what exactly conditional independence is, or what it does for us (why does it have a separate name, as opposed to just compounded probabilities), and if this isn't a correct understanding, could someone please provide an example with an explanation?", "label": 1}
+{"snippet": "In Afrikaans, it is considered very disrespectful to use \"you\" ( \"jy\") when referring to someone who is above the level of a peer. Instead, it is expected that you use \"u\", which is a very respectful form of \"you\". Also you can talk in the third person \"How is ma'am today\" would be the equivalent. I cringe internally when I say \"How are you\" to someone older than me, because in Afrikaans it would be very rude. I was bought up to only ever refer to my parents in the third person. \"how is mom today\", \"what is dad doing\" when speaking in Afrikaans. The lack of English equivalent feels very wrong and disrespectful. What is the best way to convey this in English? I have been reassured that saying \"you\" to a parent isn't rude, and I understand that this can be cultural, but I'm particularly looking for what options English offers in this regard, as far as existing vocabulary, that convey respect. I'm in South Africa.", "label": 1}
+{"snippet": "In a modern nuclear reactor for example a PWR there are multiple containment systems which prevent the release of radioactive material into the environment and shield the environment from the radiation. Here is a quote from the wikipedia article about this: The reactor vessel is the first layer of shielding around the nuclear fuel and usually is designed to trap most of the radiation released during a nuclear reaction. The reactor vessel is also designed to withstand high pressures. I think that the radiation in this part is shielded partially by the walls of the pressure vessel and partially by the water it contains. However how much percent of the radiation is shielded by the water alone and how much by the walls? I.e. how do the shielding effects of the walls and the water compare to each other (roughly) and why?", "label": 1}
+{"snippet": "My brain immediately suggested the non-word \"promisand\", but I doubt I would be understood if I said that. What's a good word (or failing that, phrase) for the action or thing that was promised? This reminds me of Latin expressions like Carthaginem esse delendam (Carthage must be destroyed, lit., 'Carthage is a thing-which-is-to-be-destroyed') or perhaps that once-common mathematical expression QED quod erat demonstrandum ('that was a thing-which-is-to-be-proven'). Circumlocution or other forms are often possible: \"He gave me the promised widget\" or \"He did what he promised he would\". But sometimes it's useful to have a word that stands on its own. More generally, is there a good way to express the construction 'thing-which-is-to-be-X'? In Latin this is a gerundive, though it seems in my brief searches that the term means different things in English and other languages.", "label": 1}
+{"snippet": "\"One way mirrors\" are used in interrogation rooms etc. The wikipedia article states that: A true one way mirror does not, and cannot, exist. Light always passes exactly equally in both directions. However, when one side is brightly lit and the other kept dark, the darker side becomes difficult to see from the brightly lit side because it is masked by the much brighter reflection of the lit side. Which I think I understand. What I find strange is that this surely can't be any deep principle of physics, as it's easily \"violated\"; you could just place a camera on one side and a TV on the other side, and it would be perfectly \"see-through\" from one side but not the other. Couldn't you imagine a sort of microscopic version of the above \"violation\"?", "label": 1}
+{"snippet": "I am typing up formal invitations, and I want to say that transportation will be provided from Point A to Point B (but also from Point B back to Point A). In order to clear up the to-from/from-to confusion, I tried to use 'between' as follows: Transportation will be provided between Point A and Point B. Is it grammatically correct to use between in this manner? Transportation is really FROM Point A TO Point B -- although the car may travel between the two locations (i.e. not at either end point but in the middle), the transportation itself is to/from specific locations. Another option is to say Transportation will be provided to and from Point A and Point B. I am trying to find the most appropriate choice of preposition to accurately convey the meaning, and I was unsuccessful in determining this after searching myself.", "label": 1}
+{"snippet": "In a sentence where we have two listed words that are hyphenated, we can omit the latter part of the first compound and still be grammatically correct: I don't believe we will ever find helium-based or hydrogen-based life forms. I don't believe we will ever find helium- or hydrogen-based life forms. However, if we have two (related) words which both end in the same suffix, can we still apply this notation? I've seen this used before, but I'm not sure it's proper: It doesn't matter whether the character is a protagonist or antagonist. It doesn't matter whether the character is a pro- or antagonist. More often than in writing, I hear this in spoken conversation, usually with an emphasis on the prefixes (i.e. \"... a pro- or antagonist ...\"), as though there is actually a hyphen in both words. I've read up a small bit on conjugation reduction here (thanks to search actually finding that term for me), but it doesn't seem to answer this particular question. Is the reduction of non-hyphenated words allowed within English grammatical rules?", "label": 1}
+{"snippet": "I'm currently a PhD student in mathematics at a decent sized graduate school, but I've been questioning my desire to continue on and finish my doctorate after I achieve my master's, which will occur within the next year. I've been thinking about trying the actuarial exams so I might have a route to leave academia. I've never taken financial math, but I have taken a Calculus-based probability theory class, a mathematical statistics class, and two measure theory based probability classes. I've gotten at least an A- in all four classes. I've never taken a financial mathematics class, but I have taken a wide range of both applied and pure math classes. Based on the experiences of some people that have passed these two exams, given my background does studying for and passing both exams seem like a possibility for me? Thanks for any advice!", "label": 1}
+{"snippet": "I am writing tourist information for a city that has areas known for similar shops (fabric, jewelry, musical instruments), similar services (spas, funeral, automotive), and similar industries (textile, software, manufacturing). I am currently referring to all of these areas as districts (e.g. the fabric district, the funeral district, the manufacturing district). Unfortunately, this usage could potentially cause confusion because this city also has a number of governmental districts (similar to \"boroughs\" in NYC). Also, there is some ambiguity between places where things are made and where they are sold. For example, the fabric district could be easily confused with the textile district. Two questions: Is there a better general term than districts for areas that known for similar things? Are there better specific terms in the case that those areas are known for stores, services, or industries?", "label": 1}
+{"snippet": "I have this combinatorial assignment problem: K candidates apply for a job. There are R referees available to review their resumes and make a recommendation. Suppose that we would like M referees to review each candidate (M < R). How would you assign candidates to referees (or, conversely, referees to candidates)? There are two important cases: (a) K > (R choose M) and (b) K < (R chooses M). Case (a) actually reduces to case (b), so we only have to consider case (b). Of course, there are some constraints that make the assignment a bit challenging. We would like to have an even distribution of the number of candidates reviewed by each referee. We would also like to have some randomness or \"mixing\" in the assignment such that it is probable for any candidate to be assigned to any M-plet of referees. Is this an instance of a well known problem in combinatorics? Any hints or references to algorithms is appreciated.", "label": 1}
+{"snippet": "Quite a few times now, a waiter or shop assistant has asked me: Will that be fine? I've noticed that I've only ever heard Indian English speakers use this turn of phrase. To my (British) ear, it sounds unidiomatic: I would always ask Will that be OK? expecting the answer Yes, that's fine. I'm intrigued to know what's going on here. Am I right in my assumption, from my own experience, that this is common in Indian English but not British English or (I think) American English? I've been trying to analyse it to work out why there would be a difference, and I'm wondering whether it's something to do with stereotypical British reserve. The British question/answer would go something like this: Q: Will that be OK? [Subtext: of course, I wouldn't dream of suggesting that my poor efforts could ever be positively fine: mere acceptability is all a worm such as I can hope for.] A: Yes, that's fine. [Subtext: I wouldn't want to be so rude as to confirm his suspicion that it's merely acceptable. I'd better make it clear that his efforts are unrelentingly fantastic.] This seems a plausible enough reconstruction to explain why Brits like me are so unassuming, but it wouldn't really explain why Will that be fine? isn't also idiomatic in American English. Is this prevalent only in Indian English? If so, can anyone explain why?", "label": 1}
+{"snippet": "Like many programming books, there are mathematics books which do not provide exercises. Although similar in theory, how can I come up with exercises that will help illuminate a subject? The difference here is that when I pick up a programming book, I generally have an application in mind for whatever subject it is. This is not necessarily true when I pick up a mathematics book because I am not sure what type of questions I should ask. For example, when I first saw the definition of a measure space, I was not sure what kind of questions I should ask myself so that I can get more intuition about the subject. It was not until I saw multiple examples and solved many exercises that I learned what sort of questions were investigated in the book I read. Gaining such a skill where I could take a definition and extrapolate meaning is something I strongly desire. Is this sort of skill something that everyone learns as they gain more mathematical maturity, in a natural fashion, or is this something that has to be sought out?", "label": 1}
+{"snippet": "What does the word cousin mean when used as a verb? By context I take it to mean that someone is putting someone else on or being difficult with someone else. For example, in The Dark Tower (Stephen King) series Wizard and Glass, a character, Eddie, is pressuring another character, Roland, to tell a story of his youth and of the troubling things that happened to him. Roland has been reluctant to do this until now. When Eddie reminds him of his promise to tell them, he responds thusly: \"Would you think that I was cousining\", he said, \"if I asked for one more day to think of these things?\" In other examples I have taken it to mean lying or being decietful. Spoilers below: Later in Wolves of the Calla, Eddie shoots the \"eyes\" of a robot named Andy, effectively blinding him. Andy beings frantically yelling for help, interspersed with \"You cousining bastard!\". Eddie previously had lied and tricked Andy into entering a confined space where he would be easier to deal with. Regardless of instances, the word appears to have a pretty negative connotation of falsity or deceit. I would really like to know a more accepted definition, although I suspect that this use of the word is wholly Stephen Kings doing.", "label": 1}
+{"snippet": "I have a general question when it comes to deciding if an infinite series is convergent or divergent. The tests im familiar with are ; Ratio test, Direct comparison test, Limit comparison test, Root test and the Integral test. My question is if there is any way to tell what test is appropriate to start with just by looking at the series. At the moment I usually follow my own pattern and systematically try different tests. What I do is: Divergence test to see if the series is divergent. If its unsuccessful Ratio test, if unsuccessful Limit comparison test etc Which has been working fine, my concern is that it may be very time consuming if the first tests are unsuccessful, and might not be very efficient during exams. So basically: Is there a way to determine what tests are appropriate by just looking at the series? ( I have found nothing like this in my textbook, all the examples simply jump straight into the \"correct\" test).", "label": 1}
+{"snippet": "I recently read an article in the NY Times called A Black Hole Mystery Wrapped in a Firewall Paradox. I really liked the article, but reading one quote immediately made me think of asking Physics.SE a question: From the material in the smoke and flames of a burning book, for example, one could figure out whether it was the Bible or the Kama Sutra; the same should be true of the fizz and pop of black holes, these physicists argued. So, Physics.SE, theoretically, how would you figure out what book was burned from the smoke and flames? I do not intend for this to be a silly question. If the idea of \"information loss\" inside of a black hole is so difficult for some physicists to come to terms with, I figure those same physicists should have a perfectly good answer to my question.", "label": 1}
+{"snippet": "To me (an American), \"what to study in college\" sounds acceptable. Meanwhile, \"what to study in university\" sounds wrong. This suggests that these words have different grammatical attributes. This is shown somewhat in the example sentences on m-w.com: http://www.merriam-webster.com/dictionary/university I applied to several public universities. He lives near the university. http://www.merriam-webster.com/dictionary/college She teaches art at a local college. He graduated from one of the country's best colleges. She attended a business college. He attended college for several years, but didn't graduate. She dropped out of college. I went to Mount Holyoke College. When I was a junior in college, I spent a semester in Spain. the Edinburgh College of Art the London College of Fashion She is attending fashion college. Replacing the non-proper noun 'college' examples with 'university' doesn't sound right in many cases. He attended university for several years, but didn't graduate. She dropped out of university. When I was a junior in university, I spent a semester in Spain. Placing an article in front of 'university' does make it sound better. He attended a university for several years, but didn't graduate. She dropped out of the university. Meaning aside, what is the difference between 'college' and 'university' that suggest a different sentence structure to make it sound \"better\". While, Difference between \"college\" and \"university\" looks at the difference between the meanings, the question doesn't ask nor do the answers address the perceived grammatical difference.", "label": 1}
+{"snippet": "The answer to the question \"Could it be that Goldbach conjecture is undecidable?\" claims that it is possible for something such as the Goldbach conjecture to be undecidable, meaning that assuming that it is true and assuming that it is false would both lead to no contradiction. But if it is undecidable, then, if we assume that it is false, it would mean that exists an even number that cannot be written as the sum of two primes. If a natural number exists, then it can be written down using a finite number of digits (any natural number is definable). This means that that number exists whether or not the conjecture is true, so if we assumed that it was true, there would be a contradiction, so it therefore can't be undecidable. What is the flaw in what I just said?", "label": 1}
+{"snippet": "Because of English's lack of a gender neutral third person singular possessive pronoun, whenever the need for such a referent presents itself in the course of writing, we seem to be left with alternatives that are either cumbersome or otherwise awkward. There is the informal gender neutral \"himself\", and the informal singular \"themself\", and of course there is the more formal \"himself or herself\" which is both grammatically and politically correct but has the disadvantage of being incredibly annoying to write very quickly. Are there any other ways to truncate this expression, particularly (but not limited to) ways that stay within the bounds of standard correct English usage and grammar? For example, I thought of shortening it to \"his or herself\", but upon second thought this feels akin to what mathematicians would call can abuse of notation.", "label": 1}
+{"snippet": "When calculating the ideal class group of a number field, it is common to start with the Minkowski bound, followed by decomposing finitely many prime ideals of norm less than that bound, and finding relations between these primes. Is there a way of avoiding the use of Minkowski bound in the computation of the ideal class groups? For example, could we use some exact-sequence (say) to show some isomorphism of the ideal class group with some other familiar group? Or maybe the Artin reciprocity isomorphism can aid us in this direction? Or even, per chance we can avail of some suitable resolutions for the computation of some cohomology groups? As to why one wants to avoid the use of Minkowski bound at all, I just think that the idea of this bound is quite analytical, and there might be a way of algebraically calculating the ideal class group. I googled and searched this site, but didn't find anything useful. The site I found that talks about the computation of the ideal class groups, either views the Minkowski bound as a fundamental ingredient of its arguments, or uses the class number formula for imaginary quadratic fields, which I would like to avoid as well. Any hints, references, or ideas are welcomed, thanks in advance. P.S. This it not to say that I want to avoid all results of the geometry or analysis, just that I want to know if there are any results in this direction.", "label": 1}
+{"snippet": "This is a data sufficiency question - Q - How is A related to B? Statement I. B is the only son of D who is the daughter of A's father. Statement II. B is the father of C and is the only son of A's mother. A - I. If statement I alone is sufficient to answer the question. II If statement II alone is sufficient to answer the question. III If the data either in statement I or statement II alone is sufficient to answer the question. IV If both the statement together is not sufficient to answer the question. V If both the statement together is necessary to answer the question. MY ATTEMPT I think the answer will be Option I. From statement I, I got A is the uncle of B From statement II, I got A is the sister or the brother of B But I am not sure if I am right. Please help me solve this question.", "label": 1}
+{"snippet": "I have a question related to this: Projective modules I'm trying to understand the \"philosophy\" of the statement, because it seems too similar to the statement \"a module is free iff every element can be written uniquely as a finite linear combination of elements of a basis\". Is this \"projective basis\" property saying this: a module P is projective iff every element in P can be written as a finite linear combination of some elements of P? We lose uniqueness in the expression as a sum: in the elements of P, in the elements of R, and in the number of terms (so the concept of \"rank\" wouldn't make sense). Is this all, or am I misunderstanding the statement? Any other intuition related to that property is also appreciated.", "label": 1}
+{"snippet": "I learnt about an experiment to show that acceleration is proportional to force. It was done by placing a trolley (like a toy car) on a smooth track. At the end of the smooth horizontal track was a pulley connected to the trolley by a string which hung masses over the edge of the table. So the trolley experienced acceleration due to the weight from the masses. My problem is in what my textbook says to do next. They say you have to take a mass being hung over the edge, which results in less force applied to the trolley. But then they tell you to put the mass onto the trolley, to ensure constant mass in the system. The problem is in placing the mass onto the trolley. Surely the trolley's mass should stay constant throughout, since that is what we are measuring the acceleration, and not the system as a whole? I hope you can explain this to me, or if my book is incorrect. I'll expand on the experiment if you find my description confusing.", "label": 1}
+{"snippet": "Once again, a problem encountered while marking German pupils' exams. We teach them the following rules: A present participle can be used to shorten an active relative clause: The boy who was driving the car didn't stop = The boy driving the red car didn't stop A past participle can be used to shorten a passive relative clause: Strawberries which are grown in California are delicious = Strawberries grown in California are delicious. While marking, I encountered several problems. For example, why does this not work: The girl who has black hair is in the corner NOT The girl having black hair is in the corner or That's the man who is happy to be here NOT That's the man being happy to be here Does this all have to do with: the verbs have and be? (But \"The girl, being happy, phoned her friend\") the continuous and simple forms? (But \"We help people who live in ghettos = we help people living in ghettos\") the tenses? Or what? I'm totally stumped by this problem and do not know how to explain the pupils' mistakes to them. The problem seems to occur mostly with the use of the present participle. Who can help with some explanations or even better, specific rules!", "label": 1}
+{"snippet": "I recently stumbled upon an interesting quirk regarding words that are both nouns and verbs. They seem to all follow the same stress pattern. Here are a few examples: NOUNS I have a really long address. There is a huge contrast between winter and spring. Not a single object is blue. I'm not very good at creating produce. VERBS Make sure you address him properly. I try to contrast the two twins in my head. He will object to any change you propose. Produce the paper right this instant! Why do the nouns have stresses on the first syllable and the verbs have stresses on the last syllable? Is there a good reason for this, or is it just coincidence? These are just the examples I thought of - I'm sure there are more. There are also some \"noun/verb\"s that have the same stress: That was a huge surprise! Next time I'll surprise you! But I've yet to find a counterexample - one where the noun has an ending stress and the verb has a starting stress.", "label": 1}
+{"snippet": "Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom. Entanglement with this \"apparatus\" takes care of the decoherence. It is often said (I can provide references upon request) that the remaining problem is the one of \"selection\", and this is the point where one invariably invokes something philosophically radical, like many-worlds interpretation. In the above (pretty standard) context, I am trying to make sense of the following observation. Looking at the measuring system from a statistical mechanics point of view, it seems that triggering a particular macroscopic outcome requires spontaneous symmetry breaking via a (thermodynamically) irreversible transition of the \"apparatus\" from a metastable to a higher entropy final state. My attitude is that \"statistical mechanics point of view\" is not far from \"decoherent large quantum system\". So, the question is: Is it fair to say that statistical irreversibility (\"the second law\") and quantum measurement irreversibility (the \"wave-function collapse\") are necessarily linked? Can this link be made more concrete (e.g., traced in details in a particular model)? Can you give references to approaches to the measurement problem that explore this connection?", "label": 1}
+{"snippet": "I am studying for the AP BC Calculus Exam and I know about the free response questions from AP Central, and the Multiple Choice Collection. I was wondering if anyone here knew of where to obtain more problems? At least a collection of problems similar to those that appear on the BC Exam. I realize this is not a question about an actual math question, but I don't feel very confident in my math ability so I want more problems to solve. Ps. I don't have alot of cash, so I can't afford to buy barron's books or any test prep books. The local libaray doesn't have any -someone check the book out but never returned it, and the book store doesn't like it when you just sit there working out problems and you don't buy the book.", "label": 1}
+{"snippet": "From what I understand, in simple terms, The definition of iteration : The act of repeating a process The definition of recursion : The act of repeating smaller process of the same problem It these definitions aren't too far fetched, it looks to me that a recursion is a type of iteration. But I am yet to find a reliable source to confirm it. So my question is, is recursion is a type of iteration or I am comparing apple and orange? The premise : In the process of learning computer programming, a book is introducing me to recursion. I understand the basics and I know how it works from a programmers perspective. But I don't understand why they aren't introducing recursion as a type of iteration. They are introducing iteration and recursion as two different concepts. Why so? (I've scoured through math.stackexchange and stackoverflow, but yet to find a clear explanation to my question.)", "label": 1}
+{"snippet": "I don't want to re-invent the wheel here, and I know that there are a lot of good math libraries out there for all sorts of things; what I'm wondering is if there's one that generates its answers in LaTex? (Could be any sort of TeX; I'm not really familiar with which ones are used for what) Well, it could look like anything (just linear algebra, just calculus, just physics or chemistry, etc.) but it would be nice if it were an application with its own GUI that generates copy-and-paste LaTex code from different inputs and a whole set of operations at the user's disposal. It doesn't have to be that great, though. I wouldn't mind coding this myself, but before I embark, I'd like to see what my options are so that I know where to start.", "label": 1}
+{"snippet": "I'm going to start self-studying General Relativity from Sean Caroll's Spacetime and Geometry: An Introduction to General Relativity. I'd like to have a textbook on Differential Geometry/Calculus on Manifolds for me on the side. I do like mathematical rigor, and I'd like a textbook whose focus caters to my need. Having said that, I don't want a exchaustive mathematics textbook (although I'd appreciate one) that'll hinder me from going back to the physics in a timely manner. I looked for example at Lee's textbook but it seemed too advanced. I have done courses on Single and Multivariable Calculus, Linear Algebra, Analysis I and II and Topology but I'm not sure what book would be the most useful for me given that I have a knack of seeing all results formally. P.S: I'm a student of physics with a mathematical leaning.", "label": 1}
+{"snippet": "Four suspects were assembled in the director's office, having been accused of a devious crime: turning off the light switch during Mr. Buehler's business presentation. It was known that only one of the four turned off the switch. All four were friends, and the director's secretary overheard them plotting before they were brought into the director's office. They all agreed to tell the same number of false statements, although the secretary did not hear the agreed-upon number. Their statements are below. Who turned off the light switch? Joe: -Frank didn't do it. -I went to college with Felipe -I didn't do it Felipe: -I didnt do it -Joe didnt go to college with me -John didnt do it John: -We all agreed to tell one false statement -i didnt do it -Felipe did it Frank: -We all agreed to tell two false statements. -Felipe didnt do it - i didnt do it", "label": 1}
+{"snippet": "I would like to know if there is any physical significance associated with the derivative of a quantity with respect to proper time or is it just a mathematical trick. Since proper time is measured in its \"rest\" frame of a moving particle, it seems to me that particle is not going through any dynamics and therefore time derivatives should be zero in the rest frame. I understand that we use derivatives with respect to proper time to keep things Lorentz invariant....but that sounds more like a mathematical requirement rather than something of physical significance. Example: what is the physical significance of four-velocity. I know four velocity is tangent to the worldline but I find it hard to remember through physical intuition. I always have to go through a book to find its definition. Kindly excuse my ignorance.", "label": 1}
+{"snippet": "I am looking for a word that describes audio that does not contain words. For instance: John William's piece Duel of the Fates would be this, since they are just vocables for their musical effect, similar to the way any other instrument is used in that context. A recording of machine gun fire would be this, since there is no linguistic meaning. A song where someone is singing would not be this, because there are words with actual meaning. A book recording would not be this. Speaking in Tongues by the Talking Heads, and the main theme of Close Encounters of the Third Kind are sort of borderline, I'm really not sure which side they would fall on. Does anyone know of a word or phrase that would describe this category of sound?", "label": 1}
+{"snippet": "I know that string theory is still under heavy development, and as such it still can't make predictions (or not that many predictions anyways). On the other hand, it is clear from the number of years this theory has been under development and from the large number of theoretical physicists studying it, that it is considered a good and viable candidate as a quantum gravity theory. So, what is the evidence that this is true? Why is it considered such a good candidate as the correct quantum gravity theory? Without wanting to sound inflammatory in the least, it has been under heavy development for a very long time and it's still not able to make predictions, for example, or still makes outlandish statements (like extra dimensions) that would require a high amount of experimental evidence to be accepted. So - if so many people believe it is the way to go, there have to be good reasons, right? What are they?", "label": 1}
+{"snippet": "We've learnt that friction is the opposition of motion and that friction appears the instant a force is applied on an object i.e when an object is at rest (with no force acting on it) then there is no frictional force. The moment a small amount of force is applied, friction becomes a factor. Therefore, friction is just the \"equal and opposite\" force between two bodies. Now, let an object be accelerated to a velocity 'v'. Then, let the acceleration cease. Ideally, the object will come to a stand still. However, if the acceleration is zero, doesn't that mean that there is no force => there will be no \"equal and opposite\" force i.e frictional force. And, only if there is an opposing force will there be retardation. Obviously, my reasoning is flawed, if not then an object that has been accelerated to a velocity will continue to move at a constant velocity. However, I don't get where my reasoning is flawed. Please do help...", "label": 1}
+{"snippet": "I probably have seen this happen at various times in movies set in eras where people were very obsequious to royalty. The action I am trying to find the word for is a motion of the hand in a kind of circular motion or spiral (generally towards and away from oneself) while bowing towards someone, often while slowly moving backwards. My first thought was \"genuflect\" although to me that invokes the image of someone making the sign of the cross (although the dictionary doesn't seem to mention this, or in fact any hand movement - it seems to be closer to bowing then the hand movement) and I am looking for a word without any religious connotations. My second thought was \"flourish\" as that seems to be technically correct to some degree in the sense of \"a bold or extravagant gesture or action, made esp. to attract the attention of others\", but this word seems to have too many meanings that might confuse, and I am not sure anybody would recognize what I was talking about unless I put a lot of context into the sentence with it, or maybe even if I did!", "label": 1}
+{"snippet": "I'm attempting a novel approach to some tough integration problems. I'm using the idea of series expansions to help integrate. In other words, I will attempt to approximate integration by integrating the series expansion of an integrand, rather than direct integration or standard numerical methods. I believe I can approximate integration of a series very easily, compared to the other methods. However, there's a catch. I will use at least two different series expansions. One for the lower limit of integration, and one for the upper limit. Now, when I attempt to integrate these expansions, the constant of integration comes into play, and it's not obvious what it is. Since I am using at least two different series expansions, the constant of integration may differ for each expansion. So I'm wondering if there is an easy way to get the constants of integration without much more work. Any help, ideas, or suggestions are welcome. EDIT A few additional notes... I know ahead of time that the series will converge. I consider that I could integrate in sections, like quadrature, while still using the series to aid in integration. However, I am considering the idea of only using only the endpoints, with two different series. So the constants of integration would be different for each series. If I could somehow find them or find how they differ relative to one another, that would save me the trouble of breaking the integral into sections and using something akin to conventional numerical methods.", "label": 1}
+{"snippet": "In an earlier post - Phonetic understanding of tongue twisters - a comment was made that \"hyphens ...(are) ...not needed in speech, so they must be extraneous\". The phrase prompting this assertion was 'state of the art'. What does it mean to say that hyphens are not needed in speech? No one would say state hyphen of hyphen the hyphen art, of course. But when I say \"This is a state of the art paper on tongue twisters\" I make a point of saying the words 'state of the art' as a group and slightly apart from the run of the words on either side. If I didn't, and spoke the words in the same rhythm as the rest of the phrase, the meaning can easily be lost (and the sentence is certainly harder to read meaningfully at first sight). There is good reason to use hyphens, or some other notational device, in such cases, isn't there ? This is a state-of-the-art paper on tongue twisters This is a 'state of the art' paper on tongue twisters This is a state of the art paper on tongue twisters", "label": 1}
+{"snippet": "In my Computer Science class, we were introduced to the Average Salary problem, where a group of people want to determine their average salary, but they don't want anyone to be able to determine the salary of anyone else. I proposed a solution which I later looked up and found to be a fairly common one, wherein everyone writes down several numbers on separate pieces of paper that add up to their salary. The papers are then collected in a hat, totaled, and divided by the number of people. My professor said that he was looking for a solution that only involved direct communication as to avoid the use of \"trusted hardware\". However, he also told me that my solution was flawed because some information is unnecessarily revealed, and, I must assume for the sole purpose of tormenting me, he said we would go over it later when he revealed the solution to the rest of the class. He also told me my solution was still inadequate when I said that the numbers could be both positive and negative, and everyone was to submit an arbitrary amount of numbers. My question is not what is the ultimate solution to this problem, but rather, what is wrong with mine? What information could be revealed from arbitrary numbers that when added up equal the total salary?", "label": 1}
+{"snippet": "I am still trying to get a good grasp on the motivations behind various concepts in Differential Geometry. But I am struggling to come to terms with how certain concepts have this added attribute of being coordinate independent? How does one identify such objects, be it a tangent space or a covariant derivative. How does one go about trying to prove that a certain geometric object is coordinate independent? How is coordinate independence a part of the \"geometry\" of a given surface or is it? P.S.: Actually is the concept of a coordinate system part of the intrinsic or extrinsic geometry? I think its the former, but sometimes embedded spaces tend to make me think twice. Edit: I would appreciate if the covariant derivative could be used as an example.", "label": 1}
+{"snippet": "I am going through the chapter on compactness and completeness from Sternberg's Advanced Calculus and trying to build an intuition for what many of this topological properties mean, and which imply which. The book defines these concepts in the setting of metric spaces, but most of what I found online is in the about topology, and from what I see (correct me if I am wrong) it doesn't change the general picture much. I've made this diagram to see whats the relationship of the different concepts and have examples of each. I don't know if it is correct. For example, Is it true that a bounded complete metric (sub)space is compact (and therefore totally bounded)? Then why bother defining total boundedness? If you don't think anything else I wrote is a valid question stick to answering that, although pointing out any misconceptions I might have is appreciated. For intuition about compactness I've found this posts really helpful. It helps me to think that there are (at least) two different kinds of infinity: one in the sense of largeness (of which boundedness is the opposite), and another in the sense of denseness (of which discreteness is the opposite).", "label": 1}
+{"snippet": "My question concerns the theory proposed in this classic paper by Misner and Wheeler. In the paper, the authors propose the idea of \"charge without charge\"--namely, that positive and negative particles might really be the ends of a wormhole, with field lines going into a mouth interpreted as a \"negative\" particle and the outgoing field lines at the other end as the \"positive\" particle. However, I noticed that the paper didn't mention whether or not the wormholes were traversable. If the wormhole was not traversable by an external material source (i.e., they have unstable inner horizons, have curvature singularities, etc.), then could the field lines technically travel through the wormhole's neck, or would they, too, be blocked? I know that the \"charge without charge\" idea isn't probable due to the tiny wormhole tunnels collapsing to form black holes, but my question also concerns larger wormholes as well. Thus, could field lines travel through a macroscopic non-traversable wormhole?", "label": 1}
+{"snippet": "I am wondering what some applications of POVMs are in mathematics (or mathematical physics)? I am going through Berberian's 'Notes on Spectral Theory', which shows how we can write a normal operator as an integral over a spectral measure. Because it is not that much extra work, he treats operator valued integrals in generality, allowing for integration over a POVM. As it is however, I can't find any examples or motivations for integrating over POVMs. In quantum mechanics I have come across using POVMs to represent the most general form of measurement, but in that case a POVM is defined as a series of positive operators which sum to the identity. I suppose if you allow for a continuous range of results then this sum would become an integral, but is there anything else to it?", "label": 1}
+{"snippet": "I'm having a bit of trouble explaining to a friend whether or not there's a big difference between the three modifiers in the title. Same and very on their own are different enough, but when combined, I find it difficult to draw a proper line on their meanings. Consider the following: I lived in the same house you're talking about. I lived in the very house you're talking about. I lived in the very same house you're talking about. Here, I understand there is a nuance in sentences one and two, though I have trouble explaining just what it is. \"The very same\" sounds like \"the exact one\", but wouldn't that be what \"same\" means anyway? Plus, that last sentence truly boggles the mind. How do you explain the grade of intensity expressed in sentence three? How do you explain each modifier?", "label": 1}
+{"snippet": "I'm trying to translate a video on TED into my native language (Latvian). At the very start there is an expression I'm unfamiliar with - \"animal warmth\". I think I kind of understand the idea intuitively, but I can't think of any similar expressions in my native tongue (short of direct translation). It would be nice if someone could explain the concept to me, or give some more examples of usage. Here's the context: ... Because in my family, reading was the primary group activity. And this might sound antisocial to you, but for us it was really just a different way of being social. You have the animal warmth of your family sitting right next to you, but you are also free to go roaming around the adventureland inside your own mind.", "label": 1}
+{"snippet": "Is there a single word, or commonly-used term, to describe the act of baiting another person into calling bullshit, when in fact you're not bullshitting? Conceptually, this either a sub-type, or the direct opposite, of bluffing, which is the act of pretending you have better cards than you actually hold, in order to scare your opponent into folding. The word I'm looking for will describe (metaphorically) the act of pretending you have worse cards than you actually hold, in order to bait your opponent into calling you. I'm looking for a word which implies \"actively misleading\" (as in lying); examples might be a basketball player faking left (in order to make his guard shift left, so he can go around to the right) or generally faking out. This is not restricted to gambling (just as \"bluffing\" is not restricted to poker), I'm only using gambling terminology to make my meaning clear.", "label": 1}
+{"snippet": "About two years ago, I absolutely fell in love with mathematics. Since then, I have studied math almost religiously, absorbing everything I can about every subject I can. I have now established what I would call an understanding of most undergraduate topics, up to intermediate complex analysis, some abstract algebra, multivariate calculus, etc. I really want to get into a good college for mathematics - specifically MIT. As a middle schooler, I have plenty of time before I have to submit an application, and I really want to make the most of that time. You can't exactly put down \"was pretty good at math in middle school\" on a college application, so I was wondering what things I can do now to get a leg up in the future, that I could put down in a college essay or in my application. So far I've started a mathematical blog, and I am working really hard to get published by the time I finish high school. My question is - what else can I learn/do/create to give myself a head start in college and in employment as a mathematician?", "label": 1}
+{"snippet": "I recently came across the following problem from Paul Zeitz's book The Art and Craft of Problem Solving. Given the image below, can you find a way to connect corresponding blocks (i.e. A to A, B to B, C to C), without having any of the connecting lines intersect one another? The question was an interesting one for me, because for the longest time I was convinced that it was impossible, and when I finally became acquainted with the solution, it took me quite a while to \"accept\" it. Granted, I am not the sharpest tool in the shed, but upon introspection I also wonder if I am being hindered by the \"intuition\" I have come to develop, and implicitly \"accept\". I wonder if it would be a helpful exercise to perhaps go through experiences that help me dismantle this intuition. The most accessible way I can think of of undergoing such a process would be by reading helpful books, given my limited resources. While I think problem solving books such as the one I am reading right now is good for this purpose as a side-effect of its initial intention (\"teaching how to problem solve\"), I wonder if there are books that are geared specifically towards deconstructing and examining \"intution\"? Prospective answerers, please attempt to answer this refinement of the question instead.", "label": 1}
+{"snippet": "I am writing an essay on a book that I read where many of the characters are not human and have artificial intelligence instead. When I try to describe these characters, though, I find myself using \"android\", \"machine\", and \"robot,\" none of which seems correct. The characters are not humanoid, so I am not sure if android is the correct word for them (although I think it was used in the book). I also tried using \"inhuman\" and \"nonhuman\", but I feel like those may be too vague. I feel as if calling the characters \"machines\" sounds too insensitive since they express many traits that humans do and my essay is about how they are very similar to humans despite not being human. Does anyone have good synonyms for \"android\" or \"robot\" for me to describe these characters?", "label": 1}
+{"snippet": "I'm trying to do Young's double slit experiment at home. Note that I don't have a laser, only a torch. I could get a bulb or use a candle though, if it helps I built the slits by cutting into a black chart paper with a knife. I tried to build a setup by placing a single slit, double slits and a screen one after the other, and shine a torch through the single slit. I tried varying distance between single-slit/double-slit and double-slit/screen which did not help. I did not observe any interference pattern. All I got was two parallel bright fringes instead, like the ones you would get by shining a torch through two very thick slits. I think that is precisely the problem, that the slits are pretty thick. What is the optimal slit width I should have to observe an interference pattern? How do I build that with a chart paper? I have seen videos of this experiment online, where people use pencil leads and hair(!!), but they both use a laser. I don't want to use a laser(just because I don't have one, and I'm probably too lazy to go and get one!). Note that you may suggest using any other materials that might be easily available at home.", "label": 1}
+{"snippet": "I'm going to be a teaching assistant and I'm currently looking for books/reviewed articles/journals written by mathematicians or people who taught mathematics (at a university level) about pedagogy and/or their experience of teaching mathematics. I know that these readings can't replace the experience of teaching but I think sharing experiences can't be bad for my future students. To be more precise about what I'm looking for, I consider the following questions very interesting : What mathematical concepts are difficult for most students and why ? What are the basic errors of a new teacher ? What is a good course in mathematics ? What is a good exercise session ? I know that there are plenty of different answers of this question and I'm looking for different opinions to build mine. Thank you PS : References in French or English only.", "label": 1}
+{"snippet": "As written in the title, there's a specific word that is not too common in English that's used to describe the feeling you can get when you finally resolve your long-term disdain for someone, or reaching some sort of civility between you and them. I can't remember it but I would know it if I saw it. Example: He attained [a feeling of] ____ after talking to his estranged father after many years. I'm not looking for synonyms of peace or closure, and nothing on Thesaurus.com has helped me. It is a very specific, unique word. It's like closure, peace of mind, or inner peace, but I've only seen it used in the context of sunsetting a toxic, detached relationship. Edit: The actual meaning of the word I was looking for was peace of mind for any period of negativity. It's not necessarily unique to interpersonal relationships.", "label": 1}
+{"snippet": "I'm a physics undergraduate student who always enjoyed math, and briefly studied it at a university but for various reasons (laziness, youth) gave up and changed 'majors'. But I always wanted to go through an undergraduate math course in my own time, unconstrained by class, etc. Now that I've passed all my exams I was thinking of doing something over the summer. I had a look at Terry Tao's free lecture notes from an analysis course he taught and I was absolutely shocked at how good they are. I love the verbosity and how he motivates every bit of information. From what I read, he wrote an Analysis textbook which I intend to get. My question is, are there any other similar (in the sense of their exposition) textbooks for subjects such as Topology, Algebra (Linear and Abstract - from my brief studies I've come to believe that I'm an absolute algebra antitalent, but I'm hoping it's because I didn't have anything else than fairly dry lecture notes to study from, and let's be honest, I didn't study very much) and of course more advanced Analysis, Probability and Statistics?", "label": 1}
+{"snippet": "Some actions (such as generating the Table of Contents) require two passes of the TeX compiler: during the first pass, some data get written to an auxiliary file, only to be retrieved during the second pass. Here are a few TeX.SE questions that require two-pass solutions: Highlight referenced equation number Backreferences for equations (To be completed... feel free to edit if you come across such a question) Two-pass stuff has piqued my interest; I have a few questions: Can I write (append) custom data to an existing auxiliary file (e.g. .aux)? Is that even a good idea? If not, can I generate my own auxiliary file (with a custom extension) to store/retrieve some data? What are good sources for learning the basics of writing to & reading from auxiliary files?", "label": 1}
+{"snippet": "In answering Do these matrix rings have non-zero elements that are neither units nor zero divisors? I was surprised how hard it was to find anything on the Web about the generalization of the following fact to commutative rings: A square matrix over a field has trivial kernel if and only if its determinant is non-zero. As Bill demonstrated in the above question, a related fact about fields generalizes directly to commutative rings: A square matrix over a commutative ring is invertible if and only if its determinant is invertible. However, the kernel being trivial and the matrix being invertible are not equivalent for general rings, so the question arises what the proper generalization of the first fact is. Since it took me quite a lot of searching to find the answer to this rather basic question, and it's excplicitly encouraged to write a question and answer it to document something that might be useful to others, I thought I'd write this up here in an accessible form. So my questions are: What is the relationship between the determinant of a square matrix over a commutative ring and the triviality of its kernel? Can the simple relationship that holds for fields be generalized? And (generalizing with a view to the answer) what is a necessary and sufficient condition for a (not necessarily square) matrix over a commutative ring to have trivial kernel?", "label": 1}
+{"snippet": "People use the phrase \"x strikes a chord with me\" to address enthusiasm or personal movement. I know there is another question that addresses what this idiomatic phrase means, but I'm very curious as to where this came from and when? I've searched a number of English dictionaries in hopes that a definition of the idiom or simply the word chord would be affixed with the origin; I started with the Cambridge English dictionary and proceeded from there. I also tried many fruitless Google queries. If someone could point me towards a reliable resource, I'd have no problem doing further research. I know music is a very emotional endeavor, so I could see the connection there--considering chords are a significant component of music--but this is purely a personal inference. Does anyone know this idiom's origin?", "label": 1}
+{"snippet": "They had cooks and drivers, and guards who occupied a gatehouse, armed with machetes. Seeing as I had regularly petitioned my parents for an electric fence, the business with the guards strikes me as the last word in quiet sophistication. - David Sedaris, Me Talk Pretty One Day I have three questions about this sentence. First, I think \"Seeing as\" in the sentence is working as a conjunction, but I only get the meaning vaguely. Are there other alternative conjunctions for it? Second, the context is that the author is envying his boy friend's family [\"They\"] for having had servants such as cooks, drivers, and guards. My question is, what does \"the business\" mean here? I think it is more like \"the story about the guards\". Is that correct? Third, I do not understand what \"in quiet sophistication\" means. I looked up the dictionary for the word \"sophistication\", but I think the words put together make a new meaning or something.", "label": 1}
+{"snippet": "I'm writing up my Teaching Statement for an Assistant Professor position in the sciences. Because all I do is read and write science, I have no elegance in my writing at all! I'm trying to make the last sentence sound better: I have been fortunate enough to work with some great mentors in my life journey thus far. Integrity, compassion, and selfless care for students were role-modeled for me on a day-to-day basis, teaching me things far beyond academics. It has been a life-long goal to attempt to replicate them. I'm trying to express that it has been a life-long goal of mine to pass-on what great mentors in my life have done for me to future students. They took me under their wings and provided important role-modeling, perspective, and guidance in my life when I was a drifting early-twenty-something male. Is there a nice and succinct way of writing this? Is there a phrase or an expression that has the same meaning as the highlighted text in the provided context? Is there a word that could replace \"attempt to replicate them\" to make it more concise?", "label": 1}
+{"snippet": "I was considering honorifics and I realized that sometimes we include and sometimes we omit a possessive in front of them. I was wondering if there was a formal rule for such? For example: Your highness, the French delegation has arrived. vs. Highness, the French delegation has arrived. Obviously, the your has been omitted here (or perhaps elided). But, there are other honorifics where this is never done. For example: when addressing the mayor or a judge (in AmE), you might say \"Your Honor\", but you'd never say, \"Honor\". Rather, you'd say Mr. Mayor or Judge in those cases. Is there a rule to this, or is merely that your has been elided in the above example, and it should have been written with an apostrophe: 'Highness, the French delegation has arrived. Note: I'm deliberately ignoring the honorifics that never carry a possessive: Mr., Mrs., Dr., etc.", "label": 1}
+{"snippet": "It is uncanny how many books will insist that neither 'many' nor 'much' can be used in positive sentences. Have you got many pens? / Have you got much money? --> correct I haven't got many pens. / I haven't got much money. --> correct I have got many pens. / I have got much money. --> INCORRECT And yet, those same books will invariably have a text where - lo and behold - 'many' is used in a positive sentence! I can only guess that proper grammar rules are as dictated, but every day use has drifted considerably from the said rule. So I ask you: what is the real usage of 'many'. Has it become common in any type of sentence? Or are there situations when 'many' can be used in positive sentences and situations when it can't? Because I really don't know what to say when the students point at a text and say it isn't following the rule they are supposed to follow.", "label": 1}
+{"snippet": "I'm interested in others' suggestions/recommendations for resources to help me acquire reading proficiency (of current math literature, as well as classic math texts) in German. I realize that German has evolved as a language, so ideally, the resource(s) I'm looking for take that into account, or else perhaps I'll need a number of resources to accomplish such proficiency. I suspect I'll need to include multiple resources (in multiple forms) in my efforts to acquire the level of reading proficiency I'd like to have. I do like \"hard copy\" material, at least in part, from which to study. But I'm also very open to suggested websites, multimedia packages, etc. In part, I'd like to acquire reading proficiency in German to meet a degree requirement, but as a native English speaker, I would also like to be able to study directly from significant original German sources. Finally, there's no doubt that a sound/solid reference/translation dictionary (or two or three!) will be indispensable, as well. Any recommendations for such will be greatly appreciated, keeping in mind that my aim is to be proficient in reading mathematically-oriented German literature (though I've no objections to expanding from this base!).", "label": 1}
+{"snippet": "My current background in analysis is approximately the material in Folland's Real Analysis. I've also read the Analysis text by Lieb and Loss and I also took a graduate level class on complex analysis, which went up to Big Picard and some Nevanlinna theory. For my own amusement I've thought about furthering my knowledge of general analysis. I've heard wonderful things about Stein's book on Singular integrals and his Fourier analysis on Euclidean spaces. Would these be an interesting next step? I'm especially interested in learning more about harmonic analysis and especially learning enough to understand the modern language of these fields. EDIT: Here's maybe a more concise way of phrasing this questions: What's the core knowledge that every graduate student in analysis, regardless of specialization, at a top school is expected to know? What would be a reading list?", "label": 1}
+{"snippet": "When you're taking a mathematics class, you usually know exactly what sections of a book you need to know, and you can focus your time on these important sections. However, when studying by myself, even when I'm trying to study the book as thoroughly as possible, I often feel tempted to skip sections of material (maybe a subsection of a chapter, a proof, or an exercise set). Yet at the same time, I don't want to skip it, fearing that what I want to skip might be something really important. Some reasons you might want to skip are: You might feel that you already know it well enough The proof or the exercises might be too difficult or boring The section might seem not very important For instance, when self-studying from Apostol's Calculus, I felt the need to skip the section on calculating errors of the taylor series for the log function because it seemed unimportant, and the 'rigorous' proof of the FTC which seemed completely unmotivated. What are your strategies for studying material in a thorough, complete way? When is it best to skip -- and how should you determine if the material you're skipping is important or not?", "label": 1}
+{"snippet": "I want to refer to parties that are hosted for players. Which of the following phrases is grammatically correct? \"Player Parties\" \"Players Parties\" \"Players' Parties\" \"Player's Parties\" A sentence where I might use this phrase is as follows: \"We host [...]\" Intended usage: I want to use the phrase in a promotional clip alongside a party that is taking place. The clip will show the party happening, and the phrase will appear over the video to describe the event taking place in the clip. The parties are put on for players to provide an opportunity for them to socialize, meet other players and relax. This reference cites the two main uses of the apostrophe that we are all familiar with (the possessive and to indicate omitted letters). In the context I have used the phrase, do the parties belong to the players? Which of the four above phrases would best match my intended meaning? This is most certainly not a duplicate of the question related by Edwin, I am referring to the specific case I have outlined above, which is dependent on the correct meaning to be ascribed to this phrase, as per my intended usage.", "label": 1}
+{"snippet": "First of all, I want to make clear what I'm NOT asking. I'm not hoping to do a rehash of the implications of nonstandard analysis on calculus. Rather, I'm interested in its use in \"harder\" math. I'm currently reading through Goldblatt's Lectures on the Hyperreals and working on the later sections, wherein he discusses ways of rephrasing other areas of math in nonstandard language (e.g. Loeb measures). I'm trying to understand what the purpose of this is. I understand that nonstandard doesn't get us new results, that is there's nothing we can prove in a nonstandard framework that we can't prove over old-fashioned ZFC. I also understand that generally nonstandard allows us to see the spaces we work in \"more intuitively\", e.g. Loeb measures allow us to see Lebesgue measure in a more finitary light, but I don't have much of a sense for what this more intuition looks like when we're actually trying to prove statements. So what is the use of nonstandard analysis in its broadest sense? To those of y'all who study/use/teach it, what do you see it as buying you over \"standard\" analysis?", "label": 1}
+{"snippet": "First time I've asked on this Stack; I hope this is on-topic. I'm laying out a control panel. One of its functions involves an alarm, but under certain circumstances the alarm might be triggered repeatedly, which is annoying. So there's a button which prevents the alarm happening for a while, which is labelled \"[problem] Alarm Silence\" - not entirely grammatical, but I'm happy with it in context. The alarm warns of a potentially expensive mistake, so you don't want to accidentally leave it silenced. So you should manually press this button again when silencing is no longer really necessary, and the control system will also do that for you if it notices you leaving the specific situation that causes multiple alarms. And in any case after a certain length of time. Underneath the button is an explanatory note which currently says: Silenced when lit. Press to re-enable. Also re-enables automatically. I think that's clear, but I don't really like the word \"re-enable\". Can anyone suggest a good alternative, bearing in mind the limited space available on the physical panel? All the replacements I can think of - \"activate\", for example - imply that they will immediately sound the alarm. That's not what happens; re-enabling just allows the alarm to go off if it wants to, it doesn't actively cause it to sound.", "label": 1}
+{"snippet": "I recently started to study problems with prolate spheroidal geometries, for which prolate spheroidal coordinates are most suited. In particular I have the advantage that the problem is axisymmetric around the spheroid major axis. While I'm used to Spherical Harmonics expansions and also to solutions of Laplace equation in terms of Spherical Harmonics I'm not used to spheroidal coordinates and spheroidal harmonics. Specifically i'm looking for some reference on spheroidal harmonics, and how to expand scalar functions in terms of spheroidal harmonics. Do you have any reading to suggest me? Perhaps a book? I couldn't find anything useful with a (rather) quick search on google. PS I am an engineer so I don't want to go deep into the geometry and mathematical details of spheroidal coordinates and harmonics, i only need a way to solve a biharmonic scalar equation in these coordinates Thanks in advance.", "label": 1}
+{"snippet": "In my physics lessons, my teachers have always been keen to tell my class that Jupiter is considered a 'failed star' by scientists. Is this true? In my own effort I wondered if maybe this could just be being regurgitated from an outdated physics syllabus that still considers the Solar System to have nine planets. From that thought onward, through my research on the Internet, I haven't found people referring to Jupiter as such and people always call it a planet rather than a brown dwarf. Furthermore, it's my understanding that brown dwarfs possess more mass than Jupiter suggesting to me that Jupiter possesses too little mass for fusion to even be plausible. So am I correct in thinking that Jupiter is 'only' a planet, or are my physics teachers correct in saying it is a failed star (and if so, why)?", "label": 1}
+{"snippet": "I have read this text about a man who has spent a terrible holiday (in the island of Thassos) due to the disorganisation of the travel company. In fact the text consists in the complaint letter that he wrote to the bloke of the company... I report the passage that I can't understand: Over the years I have been on many holidays to Greece and I can safely say that, until this year, all of those holidays were wonderful. For example, I once spent six weeks on Crete. I loved that holiday so much that I have returned every spring for the last four years. Could you please tell me based on which rule is it necessary to use the present perfect (that I have put in bold) instead of the simple past?", "label": 1}
+{"snippet": "I remember sitting in on a conference talk by a person (possibly Rainer Blatt) doing research with trapped ions (or single atoms strongly coupled to light in an optical cavity), and the person showed a photo of the trap with dots of light from the fluorescence of the single atoms/ions. I thought the person mentioned you could see this with the naked eye b/c the optical coupling to the ion in the trap was so strong, but thinking about it now I'm not sure if this can be true and I can't seem to find any (obvious) reference to this in the literature. So my question: Is it possible to see light from a strongly coupled single atom or ion with the naked eye? If so can you point me to a reference (and hopefully an image of this as well)? Note: The best I can find is the image below from the Blatt research group taken with a CCD (details here). However it is not at all obvious that this would be visible to the naked eye, or if the exposure was just set very high on the camera.", "label": 1}
+{"snippet": "I am standing on the surface of some planet. Gravity is described via General Relativity with some static metric (e.g. the Schwarzschild metric, so static means no time dependence, but the metric may vary from place to place). I send a blue photon up to my friend, who is x meters above me in some tower (we are both at rest relative to each other). He measures the photon and finds out it is red. We both conclude that a gravitational redshift occured. However, where did the energy go? In GR there is no gravitational energy so the photon did not trade \"light energy\" with potential energy. I found several threads about this, but often they viewed this topic from a cosmological point of view where the metric does depend on time and thus Noether does not work to argue for a conservation of energy. Arguments without cosmology used the explanation via potential energy (which is not a thing in GR, as far as I know). So, since the metric is still time independent the energy should be conserved according to Noether. What is going on? Edit: On the Einstein thought-experiment in the linked question: This does not explain why energy is not conserved from a mathematical or physical point of view. This could also be viewed as a reason why you can not turn photons into matter (and vice versa) without losing energy.", "label": 1}
+{"snippet": "Trying to name things in a computer data model. People have a variety of name roles, such as legal name, maiden name, etc. \"The Sultan of Swat\" is a nickname or pseudonym of George Ruth. It seems to stand alone. You don't often see him called \"The Sultan of Swat\" Ruth. \"Babe\" is also his nickname, but is often used together with other parts of his name, as in \"Babe Ruth\". It's more like the \"Bobby\" in Robert \"Bobby\" Kennedy. I've seen \"diminutive\" as well as \"appellation\" used. Are the two kinds of nicknames actually different? And if so, what terms to use? Update. A few more examples for clarification: Is Malcolm X a sobriquet, pseudonym, or just his preferred name? If an Asian student at a western college takes a more western name is that a sobriquet or preferred name?", "label": 1}
+{"snippet": "I find it hard to comprehend the law of conservation of energy. Allow me to explain my confusion. I understand that the law of conservation of energy states that energy is neither created nor destroyed. However, it has to come to a point in time where the origin of that energy is magically 'created'. How do we explain that? For example, you can say that the energy in a falling ball comes from a human lifting and dropping it. Of course, that energy comes from food that we eat, and so on, all the way to the Sun. I know that some of you may be able to explain how the sun gets the energy, etc., but you get my point. I can go all the way back until a single point where you can no long go back.", "label": 1}
+{"snippet": "I was copy-editing a report at work and came across the following sentence: While sustainability in the transport sector was rated relatively high, the sustainability of the power sector was found to be weak. The grammar nerd in me says this should be: While sustainability in the financial and transport sector projects was rated relatively highly, the sustainability of the power sector was found to be weak. Because after all, it feels more natural to say \"The project was rated highly\", rather than \"The project was rated high.\" But for some reason, I would feel more at ease saying \"The project was rated relatively high.\" and not \"The project was rated relatively highly.\". What is it about adding a \"relatively\" to this sentence that makes it different, when the fundamental syntax structure does not change? Adding one adverb in front of another doesn't automatically turn the former into an adjective does it? So why do I feel like it does here? Is \"relatively\" somehow unique relative to other adverbs? (see what I did there!)", "label": 1}
+{"snippet": "To be clear on this, I know what is the definition of an inner product space and some properties and theorems about them. What I am asking for is an intuition for this definition in the complex case. In the real case, the intuition (or at least one of them) is geometric: The inner product of two vectors is the length of the projection of the first to the second scaled by the norms of both vectors so that it is symmetric (modulo some details). In particular I (and everybody else) think of \"inner product zero\" as geometric orthogonality and of orthonormal bases as, well, orthonormal bases and so on. The question is, what should I think about when working with complex (or should I say hermitian?) inner product spaces? what is the \"meaning\" of the complex number associated to two vectors called their inner product? I will be happy to hear all kinds of answers. For example, what physical phenomena does it model or in what mathematical situations does in \"naturally\" appear. Answers that stress the \"nice structure\" resulting are also welcome, yet I feel that by itself it is a bit unsatisfying.", "label": 1}
+{"snippet": "Sometimes, I got really confused by the use of the Present Perfect tense. Given the fact, that we don't have this structure in Russian, all we can is to base our knowledge on grammar rules. The rules are quite simple: Experience: I have been to London twice. Unfinished actions: I have lived in Moscow since I was born. Close connection to the present situation: I have just cooked dinner. However, when it comes to simple questions, all that grammar rules are not so obvious. For example, if I am not sure and want to re-ask, could I say something like Have you meant? or Did you mean? Another case: I've sent you the letter and I sent you the letter. Does the first mean that I have just done it and the second that it was some time ago? How do you use it?", "label": 1}
+{"snippet": "I am modeling a closed natural circulation loop, filled with water. Some parts of the loop are heated, some are cooled and other are assumed adiabatic. As an effect of heating and cooling the density of water changes and so does the total pressure in the loop. My question is as follows: Is there a way to calculate the total pressure of the system in terms of, for example, mean density, mean temperature and total volume of the system? For air, the ideal gas equation should be a nice approximation, but it is not applicable for liquids. The problem becomes more complex when the water starts to boil at some point, then it is a two-phase fluid. I have seen answer to this question What equation of state is needed for liquid states? but it does not help in my case.", "label": 1}
+{"snippet": "I am trying to the calculate the link budget for link between a ground station on Earth (with a particular latitude and longitude) and a rover at a particular location on the surface of Mars, either directly or through a satellite on Mars. Now, if I need to determine the link availability between the rover and the ground station, the first step is to determine weather I have a line of sight between the ground station and the rover. For this, the first step is to determine whether Mars is above our horizon or not and if so, for how long. This can be easily done using packages such as PyEphem or Novas. The next step would be to determine if the rover is actually facing Earth or is on the other side of Mars. It is this second step that I need to determine with reasonable accuracy, but have not been able to figure out how to so far. Later on I would need to include the satellites in the link path as well, but for now, I need to determine if I can get a straight line of sight communication between the rover on Mars and ground station on Earth. Any sort of help will be appreciated.", "label": 1}
+{"snippet": "I can find good explanations of how the disjoint union topology is constructed, but I am confused about how things such as complements, boundaries, limit points, etc. are to be understood in this context. For example, suppose we have two spaces, P and M and create their disjoint Union X with the disjoint union topology. It would seem that subsets of P and M must then be subsets of X that are disjoint. However, do they need to be separate as well or could a subset of P have limit points in a subset of M? With what open sets would the limit points be defined? How about the closure or boundary of unions of subsets of P and M? It seems from what I have been able to find that you could not define an open set in X that did not already exist in P or M, so I am confused. Any clarification or a pointer to a relevant treatment would be greatly appreciated. Ernie", "label": 1}
+{"snippet": "A nice little oddity which I thought I'd ask about. I stumbled across the delightful word 'Boustrophedon' in relation to the scanning actions of some printers (inkjet/dot matrix). I believe that this roughly derives from the notion of 'As the ox ploughs the field'. I mentioned this to a colleague who had a farming background. He stated that in older times, this isn't actually how an ox would have ploughed the field, owing to the direction the plough would have turned the earth. Apparently, the field would have been ploughed in spiral pattern to ensure that meeting edges of the plough lines would have their earth turned in the same direction, or 'like the spider builds its web'. Which got me thinking. Is there a colourful noun of some sort that describes this sort of pattern/action?", "label": 1}
+{"snippet": "I just graduated and a mate moved into a flat (none of us are physicists by the way). So, were graduates, we got a new flat, and were broke. So, were now having a debate on how to keep a fridge cool... well, cooler. I suggest that a fridge full of water will keep the food colder, as objects get cooler when water evaporates, (like when we sweat). He says that the fridge just has to do extra work to keep the water cool, but I said it doesn't matter as it's already colder when it enters the fridge, and it's properties should mean that the overall effect, is a colder fridge. Another conundrum, if I AM right, is it more effective to store the water at the bottom, middle, or top shelves? Also, what size/shape should the water be in, should it be stored in glasses, bowls, or in the form of cloths, where the surface area can be distributed, a lot more widely.", "label": 1}
+{"snippet": "Let's imagine standing on a shore, and dropping rocks into a lake. Each rock causes ripples to travel outwards. Now let's imagine there is a monstrous whirl pool somewhere out there in the lake gobbling up waves.. It's quite complex to picture, but In my imagination I could envision a clever enough person analyzing the waves coming back to the shore and deducing things about waves that \"got lost\" so to speak. Now I understand there was some great debate between Stephen Hawking and Leonard Susskind about information theory and black holes. I don't remember who won that debate, but my understanding is that either way black holes are supposed to do a pretty bang up job of destroying information. So either my simplistic universe is flawed, or maybe I'm over estimating how clever the rock guy could be.. but I don't think so. Let's picture one single rock throw. The outgoing waves at some point get destroyed and you have something like this: and then at some point the wave pieces that didn't get destroyed reflect back and I can't draw that good and it get's all messy, but surely a lot of information comes back to the shore guy right?", "label": 1}
+{"snippet": "A hollow metal sphere is electrically neutral (no excess charge). A small amount of negative charge is suddenly placed at one point P on this metal sphere. If we check on this excess negative charge a few seconds later we will find one of the following possibilities: (a) All of the excess charge remains right around P. (b) The excess charge has distributed itself evenly over the outside surface of the sphere. (c) The excess charge is evenly distributed over the inside and outside surface. (d) Most of the charge is still at point P, but some will have spread over the sphere. (e) There will be no excess charge left. Which one is correct and why? I guess it is some kind of electrostatic induction - phenomena going on. Am I right? I understand that excess charge is distributed over hollow sphere and that negative and positive charges are distributed opposite sides, but don't know which one positive or negative go to inside surface.", "label": 1}
+{"snippet": "The following paragraph has been extracted from the Wikipedia (Atomic orbitals): Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot, however, show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of finding the electron (almost) anywhere in space. Is the statement by Wikipedia correct? Since, there is a probability of finding electron at any distance from the nucleus, when the electron comes far from the nucleus, I will block it, so that it won't return to its parent atom. Am I not stealing the electron? I can steal even the electron of your body being in India, be careful! That's what we layman think from those statements. What's the actual meaning of the wikipedia statement?", "label": 1}
+{"snippet": "I was watching \"Cold Opening: Homeland Security - Saturday Night Live\". I am supposed to translate the entire sketch for my next classes, but I really don't know what is the joke here. I only know that magenta is a color and that is all. Can someone explain to me what is funny about this? I really need that. Here is a part of the transcript where the joke is used: \"Before we begin today's briefing, I wish to announce that, on the basis of change in the nature of Al-Qaeda chatter, we are changing the current threat level to Magenta. Let me repeat: the threat level is now.. Magenta. What is Magenta? It's a darker maroon. It's not quite an ox blood. It's more plum color than.. say.. a crimson. How serious is it? [ sighs ] I honestly don't have an answer for that.\"", "label": 1}
+{"snippet": "This question is sort of in the spirit of this xkcd: The light we get from stars was emitted many years in the past, but the distances to stars which are bright enough to be visible to the naked eye are not that great, so the light we received likely wasn't emitted long enough ago that the stars would have undertaken significant changes. On the other hand, some bright stars are red giants, which are very bright, very far away, and pretty close to the end of their lives, so there is a higher chance that they have collapsed in the meantime. So: what numerical fraction of stars which are visible by naked eye are likely to have undertaken significant steps in their stellar evolution? Here I'm interested both in main-sequence stars evolving into red giants, giants undergoing collapse, and similar events. Similarly, how does this answer change if you increase the range to stars that are visible using a reasonable pair of binoculars? In case special relativistic effects are important, for the purposes of this thread, both the current frame of reference of the solar system and the rest frame of the galaxy are interesting.", "label": 1}
+{"snippet": "This popular question about \"whether an AC circuit with one end grounded to Earth and the other end grounded to Mars would work (ignoring resistance/inductance of the wire)\" was recently asked on the Electronics SE. (Picture edited from the one in the above link) Though I respect the AC/DC experts there, I think (with the exception of the top answer) they are all wrong. My issue is that they all assume that AC requires a complete circuit in order to function. However, my understanding is that a complete circuit is necessary for DC, but not AC. My intuitive understanding is that AC is similar to two gas-filled rooms with a pump between them - the pump couldn't indefinitely pump gas from one room to another without a complete circuit (DC), but it could pump the gas back and forth indefinitely (AC). In the latter case, not having a complete circuit just offers more resistance to the pump (with smaller rooms causing a larger resistance). Is my understanding correct - can AC circuits really function without a complete loop? More importantly, what are the equations that govern this? If larger isolated conductors really offer less AC-resistance than smaller AC conductors, how is this resistance computed/quantified? Would its \"cause\" be considered inductance, or something else?", "label": 1}
+{"snippet": "I'd like to learn formal math. Preferably, though not necessarily, starting with predicate logic/first order logic rather than higher order logic. I am trying to find resources (papers, books etc.) for doing this, but I haven't found anything I really like. There are lots of resources for predicate and first order logic, but most do not approach the topics in a very formal way. For example, many text don't seem to try to define what they mean by \"variables\" or mention substitution as an important concept. Tries to explicitly describe as many of the rules of the game as it can. Many texts bring up \"truth tables\" without having formal rules for what you're allowed to do with those tables. Does anyone have resources that fit these criteria? Edit: many of the answers are good and helpful, but I feel like I should add some clarifying remarks: Many texts mention that you can view math as merely manipulation of symbols. I don't doubt that this can be done, but I would like to see it done. A resource that explains the process of producing proofs explicitly in terms of manipulating symbols rather than in terms of functions, statements etc (at least without first defining these terms) would be helpful. I'd like to be able to pretend I was a person who didn't know any math and was just acting as a human computer, producing proofs. I'd like a resource that explains producing proofs like I was such a computer (not necessarily ONLY like that).", "label": 1}
+{"snippet": "I understand that photons, even when traveling at the speed of light, cannot escape the event horizon of a black hole. Are gravitons and other virtual particles traveling at the speed of light also confined by event horizons? If so, it seems that the gravitational field created by the black hole would result only from the mass of the black hole beyond the event horizon, where gravitons are capable of escaping. As a result, would there would be a disparity between the apparent mass of the black hole due to its gravitational field on other celestial bodies and the total amount of matter contained within the black hole? Also, I was reading this question: Nature of gravity: gravitons, curvature of space-time or both?, which suggests that gravitons and curved space may be indistinguishable. However, if gravitons are bound by the event horizon it seems that a black hole would act differently based on whether gravity results from gravitons or curved space-time. The existence of bound gravitons would negate the gravitational field of mass within the event horizon, resulting in a significantly lower gravitational field outside of the black hole. Would this occur, or am I neglecting some effect of relativity upon the gravitational field?", "label": 1}
+{"snippet": "I was teaching my young nephew some math the other day, and from discussing the typical sort of word problems he's encountering in class, I noticed that the \"-th\" suffix adds a distinct meaning to adjectives. For example: If a ship is long, it has length. If a woman is wide, she has width. If a person is strong, he possesses strength. If what I say is true, I'm speaking truth. A lumbering panda moving slow is full of sloth. Now, I've learned some linguistics from English L&U, and I'm guessing this \"-th\" suffix is an affix that changes adjectives into nouns. My questions are: What exactly is this \"-th\" suffix adding to the meaning? Secondly, does the \"-th\" originate from a separate word in Old English? Lastly, is there something to say about the vowel shifts that seems to be occurring in some of the transformations (e.g., strong going to strength) that somehow fits in with the ablaut system of strong verbs/weak verbs, that I learned of from the excellent responses to my previous question?", "label": 1}
+{"snippet": "Consider a lone photon. As its frequency increases, its energy increases. Taken to the limit, a sufficiently-high-frequency photon could be a black hole unto itself. But the frequency of a photon is dependent on the inertial frame of the observer. Two observers could each observe this photon to be either above or below this critical frequency. Or, I could accelerate to \"catch up\" to this photon, red-shifting it until it is no longer energetic enough to be a black hole. So couldn't I at one moment observe a particle to disappear beyond the event horizon, accelerate until the event horizon no longer exists, and hence observe what happened to the particle after crossing that threshold? Is this in-principle possible? If not, why not? EDIT: to clarify, I am not asking how much energy-due-to-photon-momentum is required to create a black hole, I am asking: given that threshold energy, how does the event horizon appear to different inertial frames which observe the photon to be above/below this threshold?", "label": 1}
+{"snippet": "Does an object possess specificity to or for another object? Every time I go to express this concept in writing, I struggle over which preposition is the more appropriate and more precise. This is dilemma is encountered all the time in technical scientific writing, for example in biology where one speaks of enzymes with specificity to/for a particular substrate. I can't find much of a consensus there: I'm just as likely to see one form as the other in articles and published papers. My trusty Google consensus search isn't of much help either: the phrase \"specificity to\" occurs just about as often as the phrase \"specificity for\" does. Although all of the examples I can think of at the time are biological in nature, I'm certain that there are others, so I'm asking this as a more general grammatical usage question. Do they mean something subtly different? Should one form always be preferred over the other? Of course, it may be that either is entirely correct. Given that preposition usage is highly idiomatic in all languages (and English especially), there may not be a rule that definitively resolves this question.", "label": 1}
+{"snippet": "It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it \"appears\" to be experiencing gravitational acceleration. Do we also say along with it, that the object flying past in reality exeriences NO attraction force towards the massive object? Is it just following the spacetime geodesic curve while experiencing NO attractive force? Now come to the other issue: Supposing two objects are at rest relative to each other, ie they are not following any spacetime geodesic. Then why will they experience gravitational attraction towards each other? E.g. why will an apple fall to earth? Why won't it sit there in its original position high above the earth? How does the curvature of spacetime cause it to experience an attraction force towards the earth, and why would we need to exert a force in reverse direction to prevent it from falling? How does the curvature of spacetime cause this? When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve. So we cannot just say that it fell to earth because its geodesic curve passed through the earth. Why did the spacetime curvature cause it to start moving in the first place?", "label": 1}
+{"snippet": "Which is correct? There are no comments. There is no comment. Which would you use for a web application, i.e. what to display when a blog post or an article has no comment attached? Actually, I am trying to fix an application that says: \"There is no comments\"! Would that ever be right? More generally speaking, it feels wrong to have a plural after the negative no/none or with the preposition without (see my previous question \"Without reason\" or \"Without reasons\"?). Those words imply zero, i.e. less than one, while plural is two or more. Yet, I know that phrases like \"There are no comments\" or \"He is without friends\" are common. It seems illogical to me. Are the majority of people making a grammar mistake when using such expressions, or else can you explain why this is correct?", "label": 1}
+{"snippet": "The word \"complete\" seems to be used in several distinct ways. Perhaps my confusion is as much linguistic as mathematical? A basis, by definition, spans the space; some books call this \"complete\" -- though then the phrase \"complete basis\" is redundant. In physics/engineering, \"complete\" seems to be reserved for orthogonal/orthonormal bases -- which necessarily means not merely a vector space, but specifically an inner product space. A complete basis in this QM sense does more than merely span the space: the concept of orthogonality allows for Parseval's relation, non-overlapping projections, Gram-Schmidt, etc. Is it even possible to have a complete basis (in this QM sense) that is NOT orthogonal? Though complete in the sense of Hilbert space and Cauchy sequences seems to be a different use of the term, the convergence of sequences within the space seems not so far afield, conceptually, from Parseval. So is it really so different?", "label": 1}
+{"snippet": "I was recently asked the question \"How do you know when you've become a better mathematician/better at mathematics?,\" and I realized that at that moment I did not have a valid answer, since I have been using my performance on tests to make that judgement. After putting some thought into it, I would say that one could at the very least use the following criteria: Learning material of similar difficulty at a faster pace with the same level of retention and understanding. Ability to bring together a larger number of theorems/lemmas/etc to use in showing a result (as opposed to doing problems that almost follow directly from the theorems). While those might encompass a good amount of information that would indicate whether you have been improving, I know that at my level there is still a lot more for me to experience and learn. So I would like to pose this question to everyone here, how do you know when you have become better at mathematics?", "label": 1}
+{"snippet": "If I have a normal distribution, the posterior for the variance is the inverse Chi-square distribution assuming the same is used as a conjugate prior. But what if my data has extra noise added so that the observed sample variance is the sum of the population variance and my extra noise variance? But then the poisterior for the variance is different. Is there a name for that distribution? You can't just subtract the noise term because you can end up with negative values. It is similar to the Skellam distribution of the difference of two Poisson variables in this way. I am really interested in this from a Gibbs sampler point of view. I would like to draw the variance from the conditional posterior if possible. If that isn't easy I can fall back on Metropolis Hastings, I suppose.", "label": 1}
+{"snippet": "I own a company called Find My Bus Ltd that brands itself as Find My Bus. Yesterday we sat down and had a discussion regarding the name and all came to the agreement that it didn't represent the company as we originally wanted it to. Seeing three separate words in a name that when thought of without any context sounds quite funky, we decided it would be better to merge the words into one name. We aren't the first to do this, in fact it is becoming a trend to merge words into one name. For example: DigitalOcean, StatusCake. In my opinion both of those names look fine because they consist of two words. However, when you do this with Find My Bus you see: FindMyBus. Is it just me, or does it look wrong having three words merged and capitalized? Would it be better to use Findmybus or perhaps FindmyBus? Apologies if this seems like I'm running a poll, I'm not, I just simply would like to ask users with experience in the English language which looks the most appropriate for a company name.", "label": 1}
+{"snippet": "Quantum numbers are supposed to denote every individual orbital. But if orbital shells are probability functions, then orbitals can't be definite, solid things. So in that case, there can be variation in the amount of energy given off when an electron drops between shells - it might, say, give off a tiny little bit more energy and drop to just below the orbital shell. Isn't this possible since orbitals are just probability functions - like \"Here's where the electron probably is\"? Not entirely sure where I was going with this, but I think the final question is, how come quantum numbers are only ever integers? Edit: My question is about why quantum numbers as taught in schools are always integers. \"Orbitals\" as predicted by the Bohr model are in fact clouds of electrons, probability functions about where an electron probably is rather than a definite statement about where it definitely is. That means there's got to be wiggle room about how far an electron can be from the nucleus. So does that mean that quantum numbers are an oversimplification, or just averages? Or am I just misunderstanding the whole \"orbitals are just probability clouds\" thing? Edit: Ugh. Right. I'm an idiot. I forgot to mention that I'm only talking about the principal quantum number, n, the one telling which orbital the electron's in.", "label": 1}
+{"snippet": "How do issues of naturalness arise when regularizing QFT using dimensional regularization? I can only recall ever seeing naturalness arguments (hierarchy problem, cosmological constant problem, etc.) phrased in terms regularizing with a cutoff, where naturalness issues arise when physical quantities are quadratically divergent in the cutoff scale. Is it hard to see how the same naturalness issues are addressed using dimensional regularization? Are there some hidden assumptions involved in using dimensional regularization? Do you reach the same conclusions as you do using a cutoff, but only after also using the RG equations? I recall being told that when dimensional regularization is used to remove power law divergences there is additionally some optimistic assumption being made about the UV physics, but I don't know if that's correct or relevant to this problem.", "label": 1}
+{"snippet": "Well let's start off with that I'm not a physicist but I'd like some thoughts on something I came across in my hometown. This guy: Is it possible that due to the electrical charge of magnets this guy can make the illusion that he can float ? Or is this probably a cheap trick that fools the eye ? I was standing there for quite some time watching the guy and he keep moving his feet. The resistance that he appeared to have was from a magnet force keeping him afloat. So after I passed this guy I did some physics searches on the web and the first thing that caught my eye was the electrical charge of magnets. So the question is : Is this related to the electrical charge of a magnet or a cheap trick ?", "label": 1}
+{"snippet": "I am trying to understand the meanings of \"covariant transformation\" and \"contravariant transformation\" and how they are related. I have read the related Wikipedia article and still feel I cannot state, with mathematical precision, the definition of these terms. The Wikipedia article states that a covariant transformation, in the context of a vector space, is one that \"describes new basis vectors in terms of old basis vectors\". This is not a satisfactory definition unless, of course, no other transformations can be described as \"covariant\". I have seen however the word \"covariant\" being used to describe other sorts of transformations as \"covariant\". Namely, the \"physicists\" definition of co/contravariant transformations where components transform as such-and-such (which makes absolutely zero mathematical sense to me). This leads one to believe that co/contravariant transformations are always defined in terms of derivatives of coordinate changes and I don't believe this is the case. I understand what co/contra-variant tensors are, at least from a mathematical perspective, so this is not a question about the meanings of \"contravariant tensor\" or \"covariant tensor\"; indeed, These concepts have been well-explained here. My question then, in summary, What are lucid, self-contained and mathematically precise definitions of \"covariant transformation\" and \"contravariant transformation\"? A reference to such definitions would also work wonderfully.", "label": 1}
+{"snippet": "I had the idea of, what if you ground up some magnets into a fine powder, what would happen with the powered, and how would it act? After some google searches, it seems that this isn't done very often, and that not much would come of the powder as the poles will mostly be misaligned. So my next question was, what (if anything) would happen if you ran some electricity through some magnetic powder? Would the poles align? Could the powder be manipulated? Could it's magnetism be manipulated? i.e If you made a magnetic powder trail in a small amplitude sine wave shape, and applied some current to it. Would the powder be able to move into a straight line, or possible break the connection (or even move at all)? I haven't been able to find much information on this topic (of electricity WITH magnets) and I am trying to learn more on this topic.", "label": 1}
+{"snippet": "Prompted by comments to this question on English Learners (about \"That's you done\"), I've been searching Google Books for similar constructions of the general form that's [pro]noun adjective (for this context, I classify past-tense verb forms such as done, fucked, finished as adjectives). What I seem to be finding is that using \"That's\" in this way (not referencing anything in particular, just \"whatever came before/caused the current situation\") is a relatively recent phenomenon. I'm also getting the impression it's more common in BrE than Ame. So by implication, if the boss says to his secretary... \"Just get those letters off in the post, and that's you done for the day.\" ...I should assume the boss is probably British, rather than American. Would my assumption be right? Can anyone shed more light on the usage? Is it the same as... \"Here's me doing all the work while you just sit around waiting to be fed.\" (said by, for example, hard-pressed mother to idle teenage offspring)", "label": 1}
+{"snippet": "The question is written like this: Is it possible to find an infinite set of points in the plane, not all on the same straight line, such that the distance between EVERY pair of points is rational? This would be so easy if these points could be on the same straight line, but I couldn't get any idea to solve the question above(not all points on the same straight line). I believe there must be a kind of concatenation between the points but I couldn't figure it out. What I tried is totally mess. I tried to draw some triangles and to connect some points from one triangle to another, but in vain. Note: I want to see a real example of such an infinite set of points in the plane that can be an answer for the question. A graph for these points would be helpful.", "label": 1}
+{"snippet": "Recent observations of the accelerating expansion of the universe have been quantified and for the time being given a name as to the cause: Dark Energy. And from what I've read from other, similar questions is that Dark Matter is a pressure that is causing this expansion, although we don't know the details of the mechanism yet behind this pressure. But is there anything in our present theories of physics or observations that rules out gravity itself as the cause of this expansion? I'm thinking along the lines of an analogy: the nature of the strong nuclear force which, at close distance, tends to bind together nucleons, but at even closer distances repels them. Couldn't this repulsive force we observe, this dark energy, just be the effects of the gravitational force on a larger scale of space?", "label": 1}
+{"snippet": "I have a subtle doubt about the physical interpretation of the mathematical definition of vector field as a derivation. In basic physics we understand a vector quantity as a quantity that needs more than magnitude to be fully specified, in other words, quantities with the notion of direction. This goes very well with the also basic mathematical definition that a vector is an equivalence class of oriented line segments. However, when we go to the study of manifolds, we see that a better definition of vector is to say that a vector at a point is a derivation on the algebra of smooth functions on that point. But then, we represent forces for instance with vectors, what's the interpretation of representing one force acting on a point by a derivation on the smooth functions on the point? I imagine that there must be some interpretation for that, but I didn't find what's it. Sorry if this question seems silly. I'm just trying to bring together those concepts. And thanks you all in advance.", "label": 1}
+{"snippet": "I have a question about the appropriate usage the possessive personal pronoun \"mine\" over the possessive determiner \"my\". I have done some research and understood the differences between them, but my questions isn't quite about that. One of the main purposes of pronouns is to eliminate repetitions, yet I cannot be sure whether to use it or not if there isn't a possessive determiner such as my, your, her, their etc that establishes the noun being referred to. For example, I thought of the sentence below: Your dog attacked mine! ('Mine' used as a substitute for 'my dog', as 'your dog' established the noun in question) The above is no doubt a better construction than: Your dog attacked my dog! Which sounds somewhat awkward in comparison. However, if there isn't a possessive determiner preceding it in a sentence: A wild dog attack mine! It sounds jarring and not as natural as: A wild dog attack my dog or My dog was attacked by a wild one. I don't know if there is a grammar rule that would explain my question, but fellow memebers, is it still correct to use the possessive personal pronoun (such as mine) in the case above, or can it only be used if a possessive determiner (such as your) is used before it? Many thanks!", "label": 1}
+{"snippet": "When I used to play video games, \"all in\" meant that you were devoting your army to a \"do or die\" effort. In other words, you were either going to win or lose in the next battle. The \"all in\" meant that you typically brought all of your soldiers to fight, holding none back. But years ago I was doing the Daily Jumble, and the hint was something like \"After running a marathon he was _ __\". This was before the web, so I had nothing to fall back on. It turns out the answer was \"ALL IN\" meaning \"tired\". I asked a friend and he said \"that's a usage from the eastern U.S.\" I certainly hadn't heard it before then and I still haven't since. Is this a common meaning? Maybe some easterners can chime in?", "label": 1}
+{"snippet": "In this sentence, would you use \"to inform\" or \"for informing\"? These findings are critical ______ future research Likewise, would you use \"to understand\" or \"for understanding\" in the following? These results provide a powerful framework _____ existing patterns. This is a question that comes up a lot in science writing: when do you use the \"to\" vs. the \"for\" version of a verb? Is there a word for these two different uses? And is there a rule for deciding which one is correct? They often get used interchangeably, but I can't find any hard rules for deciding between the two. People often use the \"to\" version because it sounds less passive, but I find it more ambiguous and a bit clunky, but I can't find any actual sources to say which is correct.", "label": 1}
+{"snippet": "I don't get this joke: It smells like up dog in here, What's up dog? Nuuthin dog, what's up with you? (source) I understand that the person asking \"What's up dog\" is tricked into asking a question they didn't intend to ask. I also understand the meaning of the \"What's up?\" question. I don't understand why this exact question has been chosen. If anything, it sounds demeaning to the person who's making the joke and is referred to as dog by the receiver of the joke. If I were to make a similar joke, I'd replace dog with something like master, so that it'd sound like the receiver of the joke respects the person making the joke more than it might be in reality. Does the word dog in this context have some alternative meaning, perhaps? Or is this joke funny simply because the receiver of the joke asks a funny question, no matter what the question is?", "label": 1}
+{"snippet": "How common is it for native English speakers to actively replace the past tense 'did' with the past participle 'done'? I used to think it was only really done in rather vulgar dialects, but I have increasingly heard this usage now by people who speak otherwise normal Received Pronunciation, or Standard American English: I done the report. You done it yesterday. He done it already. I can't help but interpret this replacement of 'did' as sounding somehow uneducated, but is it becoming a standard in some dialects? Is the word 'did' dying out? And do these speakers use the 'done' replacement when switching the word order around in a question; for example, would they say: Done you do it today? ... or even: Done you it today? ... instead of: Did you do it today?", "label": 1}
+{"snippet": "In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with. First of all, the S-matrix is a scattering matrix which comes from scattering processes. In the context of quantum mechanics and quantum field theory, we often compute the S-matrix, and we use well-known formulas, i.e, the LSZ reduction formula On Wikipedia, they describe a R-matrix, as related with the Yang-Baxter equation (governing equation for integrability), and they add some comments that it is related with resonance. My questions are, then: Can you give me a clear definition and a governing equation for a R-matrix? How are S-matrix and R-matrix related to each other? Why is the R-matrix important in integrability (Yang-Baxter equation)?", "label": 1}
+{"snippet": "I am confused about the usage of the words like and unlike in sentences. Like and unlike make me confused because I see them being used everywhere almost interchangeably, and to make matters worse I even saw commas making difference in meaning. Which of the following sentences is most correct, and least ambiguous? Unlike Xbox, Playstation can't play Halo. Playstation can't play Halo unlike Xbox can. Playstation can't play Halo, unlike Xbox can. Like Xbox, Playstation can't play Halo. Playstation can't play Halo like Xbox can. Playstation can't play Halo, like Xbox can. Playstation can't play Halo unlike Xbox. Playstation can't play Halo, unlike Xbox. Playstation can't play Halo like Xbox. Playstation can't play Halo, like Xbox. In case you don't know what I actually wanted to say in those sentences: I'm trying to say that Playstation can't run the Halo video game and Xbox can run that game. I probably should have tried sentences with no brands but I can't imagine any meaningful sentences at this moment which contains like/unlike.", "label": 1}
+{"snippet": "I'm new to finite fields - I have been watching various lectures and reading about them, but I'm missing a step. I can understand what a group, ring field and prime field is, no problem. But when we have a prime extension field, suddenly the elements are no longer numbers, they are polynomials. I'm sure there is some great mathematical tricks which show that we can (or must?) use polynomials to be able to satisfy the rules of a field within a prime extension field, but I haven't been able to find a coherent explanation of this step. People I have asked in person don't seen to know either, it's just assumed that that is the way it is. So I have two questions: What is a clear explanation of \"why polynomials?\". Has anyone tried using constructs other than polynomials to satisfy the same field rules? Thanks in advance.", "label": 1}
+{"snippet": "There are many books, written by highly decorated academics, which feature proofs that I can hardly comprehend in an acceptable amount of time. Roughly each week, it happens that I find myself having spent around three hours to convince myself of a single proof - usually, the proofs are from textbooks for undergraduates. Sometimes, I am horribly slow at finding detailed arguments which connect the presented conclusions (and which are necessary to convince myself that the conclusions are beyond question). Then, I feel that the authors take steps that are not small enough for me; and I wonder whether I should digest every proof (or merely use the theorems). I am not particularly gifted. Still, I strive to improve myself. Do you think that one can learn or train to understand proofs faster?", "label": 1}
+{"snippet": "I want to typeset diagrams describing functions which take multiple inputs and return multiple outputs. These should look like boxes with labels in them like \"f\" or \"g\" and with some input wires coming in and some output wires going out. The diagrams I'd like to typeset will involve several such boxes with some output wires connected to some input wires. I can draw some examples of what I want if this description is unclear. I would prefer to be able to do this in xy-pic, for example using xy-graph somehow. Is this a good idea, or should I just learn how to do this in TikZ? Or is there an even better way? Edit: To be more specific, here are the diagrams I want (although their orientation is negotiable, e.g. if you show me how to do this with the diagrams going to the right instead of down that's great). I should have mentioned that I also want to label the wires.", "label": 1}
+{"snippet": "Suppose I was standing in the sea, and touched an electric fence; I would receive an electric shock, because both my body and the sea are conductors, and create a path for the electricity to flow. The sea is so big that it has the capacity to draw and dissipate a great quantity of charge. However, if the sea was drained away, and I was standing on some rocks, would I still receive an electric shock, even though rock is not a conductor? And if I did receive a shock, where would this electricity even flow to? Would it just be dissipated amongst the rocks / soil / sand beneath my feet (even though they are insulators)? My question comes from me wondering why we receive electric shocks at all, when there is usually some form of insulator between you and the charged object, such as your shoes, the carpet, several layers of bricks, and indeed the entire composition of soil and rocks beneath the building that make up the \"Earth\".", "label": 1}
+{"snippet": "I will be writing a report in which I analyse the performance of a piece of software. I would like to show my data using PGFPlot. My plan of attack is to schedule a script to run on the machine I am using, which will run the program a number of time with a variety of parameters (the main one being the number of processors I use) and dump all the data in to a .dat file. Can PGFPlot this? Can I ask it to average all the tests with the same parameters? I will be plotting a line graph with the average time, but I would also like to plot the standard deviation of the results. Is PGFPlot the tool for this? Or should I be using LibreOffice to generate the relevant data, and only use PGFPlot at the end? Thank you", "label": 1}
+{"snippet": "I dont get why a forward gear allows sliding a car backwards. Any ideas? So this is a car with an automatic transmission. The transmission is in the drive mode (move forward). Car is at the slope facing the hill up. I am in the car pushing the gas pedal very gently. The car is supposed to move forward going up the hill. Instead it moves backwards down the hill, because I am not pushing the gas pedal hard enough. I haven't switched it to reverse. This is where I don't get it, because it turns out that the wheels are spinning in the opposite direction of what the transmission gears tell them to spin. How can this be possible? Or, to put it in a different way, how can a car move backwards when it is in \"drive\" mode (supposed to go forward)?", "label": 1}
+{"snippet": "I am simultaneously taking courses in functional analysis and commutative algebra. In doing so, I found that there is, at least heuristically, some similarity between the notion of an algebraic variety (essentially, the zero locus of a family of polynomials) and the annihilator of a subspace of a Banach space (the collection of continuous functionals that \"kill\" the subspace). In doing some reading, I came upon the Banach-Stone theorem, which implies that the algebra of scalars is an analogue of the structure sheaf of a ring, and is evidently an essential ingredient in non-commutative geometry (thank you, Wikipedia). One finds a one-to-one correspondence between finitely generated nilpotent free k-algebras and affine varieties by first asking what algebraic structure (finitely generated nilpotent free k-algebra) corresponds to the geometric object (affine variety). Then, inspecting what sort of geometric object gives the correspondence with the more general commutative rings, we find schemes. This analogue of a structure sheaf makes me think that there might be analogous sort of correspondence in the Banach algebra setting. Is this the case? If so, can anybody provide some references, interesting papers, etc?", "label": 1}
+{"snippet": "The following is a GRE sentence completion question. The most striking thing about the politician is how often his politics have been (i)_____rather than ideological, as he adapts his political positions at any particular moment to the political realities that constrain him. He does not, however, piously (ii)_____political principles only to betray them in practice. Rather, he attempts in subtle ways to balance his political self-interest with a (iii)_____, viewing himself as an instrument of some unchanging higher purpose. Options: a. quixotic, brandish, thoroughgoing pragmatism b. strategic, brandish, deeply felt moral code (correct answer) c. self-righteous, flout, deeply felt moral code d. self-righteous, brandish, profound cynicism e. strategic, follow, profound cynicism I am able to get how strategic and deeply felt moral code fits in the first and third blank but confused about the second blank. What is the intention behind choosing brandish? Why not follow or flout?", "label": 1}
+{"snippet": "While studying Faraday rotation (linear magneto-optic rotation) I came across a fact that Faraday rotation can be enhanced. Verdet constant which depends on the wavelength can be enhanced as change in refractive index with change in wavelength is maximum near resonant light. Now if the incident light frequency is resonant with the atomic transition frequency then light will get absorbed in the medium and we'll get very less light at the output for observation. It is my understanding that optical pumping is done to make medium transparent to the resonant light, as when majority of electrons will be trapped in dark state we'll get considerable light at the output to measure change in the plane of polarization. Is my understanding accurate or is there anything that i have missed? Does optical pumping enhance faraday rotation in some other way also?", "label": 1}
+{"snippet": "I had previously asked about how useful everyday solar physics data is to other astronomers ... But about a year from now, we will have another Venus transit, where Venus will pass between the sun and the earth ... I was just in a meeting with some EPO (education and public outreach) folks about trying to prepare something for the event, and we can do the basic 'make a pinhole camera' kids activities, and use it for awareness of our field ... But is there any novel science that we could use the event for? We're especially interested in trying to find something 'Citizen Science', where we could try to organize people to contribute some data from across the world that might help advance our knowledge of something. (it doesn't even have to be astronomy ... We had an idea of trying to get people to take pictures of the transit, and send the images, and we could try to use it to estimate how the quality of seeing varies, but we weren't sure if there were liability issues if someone managed to ruin a camera or their eyes in the process)", "label": 1}
+{"snippet": "(Please note: I've seen some other questions asked like the one I myself am asking, I realize that I am indeed late to the party, but I am genuinely curious and none of the previous answers have satiated me as of yet. Note that this is a highly hypothetical question, asked by somebody who isn't even a college student studying the idea of physics at this point in time, so go easy on me here. Sorry if this isn't worded well, but I still haven't studied much on the subject, nor am I used to typing up thesis papers. Excuse me please.) Theoretically, it is stated that if you were to travel through a Kerr Black Hole- a Black Hole with a rotating ring singularity- it would allow you to go back to an earlier point in time. Another says you can travel through time using a Wormhole and exotic matter. What I'm curious about is whether or not time travel is hypothetically feasible were one of these true, as in whether or not the sheer force would crush a human by attempting to use one of these routes.", "label": 1}
+{"snippet": "A BibTeX question (using BibDesk). I am having trouble working out how to make BibTeX handle the new Digital Library of Mathematical Functions (DLMF) web page. No authors or editors are listed. DLMF itself suggests (http://dlmf.nist.gov/help/cite) When referring to the web site from a print publication, it is recommended to use the following format. Digital Library of Mathematical Functions. Release date. National Institute of Standards and Technology from http://dlmf.nist.gov/. where the Release date can be found at the bottom of all DLMF pages. None of book, webpage, url, ... does it like this. Also, if I put NIST or DLMF in the author field, with or without braces, I get \"NIST, \" in the refernce list, i.e., it is expecting a first initial. This is going to be a very highly cited web page. It is the replacement for the venerable Abramowitz & Stegun and will be the standard reference for mathematical functions.", "label": 1}
+{"snippet": "Sometimes I see something like \"a mapping preserves the structures of its domain and of its codomain\". From Wiki about morphisms in category theory: a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory, group homomorphisms; in topology, continuous functions, and so on. I was wondering why the structure-preserving mappings between two topological/measurable spaces are defined by the \"inverse\" of the mapping, while the structure-preserving mappings between two groups/vector spaces are not? Why are the structure-preserving mappings between two topological spaces chosen to be continuous mappings instead of open mappings? I also see that \"a mapping preserves some property of subsets, points or whatever\". Such as Continuous linear mappings between topological vector spaces preserve boundedness. According to Brian's reply to my earlier question, this quote should be understood as \"under a continuous linear mapping, the image of any bounded domain subset is also a bounded codomain subset\", not as \"under a continuous linear mapping, the inverse image of any bounded codomain subset is also a bounded domain subset\". I wonder why? It seems at first to me like how continuous mappings preserve topologies, but it is actually in the same way as how group homomorphisms preserve group structures. Thanks and regards!", "label": 1}
+{"snippet": "We tried my electrolyzer with a friend today, we filled a small bottle with HHO gas, and set it on fire. It was loud but not a big deal, like a firecracker. Then we added some soapy water and created HHO bubbles instead of filling the bottle with HHO underwater. Then we lit the bubbles and it exploded so loud that for a while all we heard was just ringing. It was way too louder than when before, same gas same bottle, we even tried it twice with same result. Im wondering why is it so unbelievably louder. I thought that maybe the sound just traveled in a different way, because the bottle was turned in the opposite way (towards the ceiling instead of towards the floor), but im not sure.", "label": 1}
+{"snippet": "Sometimes in quantum cosmology, when we are thinking about 'wave functions of the universe' we have in mind some sort of formal path integral, where we include not just the variations in the dynamical fields (metric and so forth), but also possibly some sort of prescription for summing over all possible topologies. At least, that seems to be some sort of heurestic guess often encountered in the literature (Hawking et al). Now, in String theory, admittedly a different context but there is a rather well defined notion of how this works (basically as a generalization of Feynman graphs over Riemann surfaces). However I don't understand exactly how this is supposed to work in quantum cosmology exactly (say in the Wheeler-De Witt context). First of all there seems to be a massive amount of overcounting already at the metric level (where presumably one needs to mod out by all the diffeomorphisms), but how exactly does one deal with the topologies? Do they only include connected topologies? Is there even a mathematical formalism on how to even approach this problem? Any good papers that deal with this in a comprehensive way?", "label": 1}
+{"snippet": "When I'm pushing a tall, cylindrical object stood on its end (like a Pringles can) I can push it near its bottom, and it will slide forwards, or push it near the top, and it will topple over. So, there must obviously be a point somewhere on the side of the cylinder where it stops moving forwards and begins falling forwards. My question is, how can I calculate where this point occurs? It might be something fairly obvious, like: \"above the center of mass\" or something like that, but I'm guessing that it's something more complicated, taking into account friction, etc. This knowledge will be very useful in my life, as the next time someone asks me to \"slide along the beer\" I can whip out my pocket calculator, my ruler and measuring instruments, and finally stop being such an embarrassment. I swear, it falls over every single time.", "label": 1}
+{"snippet": "This image from Wikipedia shows how a black hole would look like: A black circle that acts as a gravitational lens for light rays coming from behind. How would a rotating black hole look like? How would it look like when viewed from side and when viewed from the top (along its axis of rotation)? If I understand it correctly, withing the ergosphere photons are dragged in the direction of the rotation, and just outside it photons would be still heavily influenced by the rotation. Also this video descibes in detail how would it be to descend into a black hole. What would be different when descending into a rotating one? In particular, what would we see inside the ergosphere? And how would it be different below the event horizon?", "label": 1}
+{"snippet": "I've began learning LaTeX for the expressive purpose of eventually creating a resume template of my own. A business school friend of mine showed a very professionally-looking resume he created from a workshop, and I would like to turn it into a LaTeX template. I know there are already many existing resume templates, but I would like to create my own. I also know that there are many tutorials and guides for LaTeX, but I would like to know if there are any that can lead me towards creating templates, specifically something in resume/cv form. I know that it will be a long and arduous task to learn how to create templates, much less a template for a stylized resume, but I would like to make that my goal for learning the language. Would it be simpler to just modify or tweak a preexisting template?", "label": 1}
+{"snippet": "I am currently a math major in college and my main problem is that it feels directionless. My college offers little in term of variety in undergraduate math so I moved on into taking graduate courses and I am actually loving it. But at this point I am just randomly taking courses that looks interesting and was wondering if there was specific directions to take within math. And even past that where will it lead. Thanks EDIT After reading the comments I decided to add extra info. On the courses that I like, I have taken Abstract Algebra and Linear Algebra and really enjoyed them and also Number theory. I have also taken the typical three semester Calculus courses, Differential Equations, Discrete Math, Probability, Numerical Analysis and Real Analysis. On these courses I like them though I am not as enthusiastic about them as I am for the other courses I have mentioned. Though I find their applications very interesting. And more specifically on the question it is on what paths are there to take in school and also what paths are there to take after graduation.", "label": 1}
+{"snippet": "When creating a presentation, I sometimes create extra slides that contain additional information, a more thorough explanation, or an extra plot pertaining to certain parts of my talk. These extra slides are usually in a separate PDF and the document is usually only opened if an audience member asks a question or requests information and one of my extra slides supplements my response nicely. I am wondering if it's possible to insert these slides into my presentation with the two following options: The extra slides are skipped when progressing through the presentation unless... I click on a hyperlink placed somewhere on the slide. If clicked, we traverse to the extra slide. From this slide, continuing to the 'next' slide would send us back to the slide that got us here originally. The above can be accomplished with two (or more) PDFs (one with the presentation, one -- or more -- with the supplemental slides) via hyperref but ideally I would like to only have one document. I am not familiar enough with ifthen to know if it can be done with that package. Any help would be much appreciated.", "label": 1}
+{"snippet": "Some time ago I learned the difference between a present participle and a gerund, so today I decided to pass any online test to make sure I understand it. I passed it having made only one mistake, which asked the difference between the two in this sentence: Nobody was surprised at John being absent. One needed to choose between present participle and gerund in reference to the word being. I chose present participle because the word being here plays a role of an adjective apart from a verb. I thought that if it had read John's being, then the word would have been a participle because it would be a noun in a form of a verb. I know, this question is a duplicate and I agree that it should be closed, but I just would like to find out whether it was me who made a mistake or whether it was the website that diddo.", "label": 1}
+{"snippet": "Background: I was cooking eggs (very difficult) with a plastic spatula which was not very good, so when I set it on the border of the pan it began melting. In order to keep cooking, I reached for a wooden spoon which can touch the pan without melting. This led me to wonder about the behaviors of the materials. For example, if I had left the plastic spatula it would have melted, but if I had turned up the temperature enough it would have actually ignited and caught a flame. If I had done the same with the wooden spoon, it wouldn't melt as I turned up the temperature but it would ignite eventually. So why is it that certain materials (plastic in this case) will go through the process of melting, then igniting, but wood just seems to skip the melting and go straight into ignition? My only guess is that somehow wood has a melting point higher than its ignition point, but I am not even sure if that makes physical sense. A Google search led me to a strange-looking forum with disappointing answers. My understanding of thermodynamics is only as far as the math goes, but I am conceptually blind in this area. Maybe someone can shed some more light.", "label": 1}
+{"snippet": "I think everyone should have seen a bowl of hot water moving by itself on a flat surface such as glass(seems like it is moving by itself but maybe there are some external force applied to it when it moves). What is the explanation of this phenomenon? Hypotheses : Since the bowl is heavy, for it to move the friction between the bowl and the surface must be very very low. I have heard that water may form a thin layer between the bowl and the surface, but l'm not sure whether it is the case or not. I think the bowl can move by itself because heat makes the air below the bowl expand. Edit : I will re-experiment those again and update the question in few days. Maybe I will take a video clip too. and I am not talking about a magic trick whatsoever.", "label": 1}
+{"snippet": "For the absolute life of me, I cannot seem to wrap my head around the proofs given in my number theory and cryptography class. Maybe it's the teacher, or the textbook, both or neither, but this is causing me great concern for two reasons. First is obvious, since I hate solving math without a full comprehensive understanding of the concepts. Second, I have the feeling I'll be asked to prove concepts in my exams. So how do I go about this? Does anyone have any textbooks or something (or anything) that could help me grasp all this better? To clarify, the main concepts covered in class are GCDs, Euclidean algorithm, concepts of coprimes, Euler-Fermat theorem etc. Then these bleed into solving cryptosystems such as RSA, Chinese Remainder Theorem and others. Thanks!", "label": 1}
+{"snippet": "\"It is also my favorite quotation. \" Does this sentence mean that this is my favorite quotation in addition to other quotations which are my favorites, or does it mean that I am a person who has this quotation as a favorite, in addition to the persons who have this quotation as a favorite? Does \"also\" indicate the presence of more (favorite) quotations, or more persons who have this quotation as a favorite? If it is the former, how what is the correct way express the later? I mean if a person says, \"This is my favorite quotation\", how should I express that I also have it in the list of my favorites? Should I say, \"It is also my favorite.\"? I want it to be more formal than \"Mine too\". A side question which arose while asking the question above: Is the following sentence correct from the perspective of punctuation? I mean if a person says, \"This is my favorite quotation\", how should I express that I also have it in the list of my favorites?", "label": 1}
+{"snippet": "I am trying to prepare a paper for submission to a journal that is not an AAS publication, but I would still like to use the AASTeX package for the tools it provides and stylistic reasons. The journal does not have its own LaTeX package, so I can use the AASTeX package as long as I make sure to conform to the few given guidelines. One of the guidelines I need to follow is using the in-text citation format of [n] where n is a positive integer. Each reference in the references section should be labeled with a corresponding number. If I were not using the AASTeX package, thebibliography environment would use this format. The modified version in AASTeX package forces you to use AAS format. How can I use LaTeX's default thebibliography with the AASTeX package? EDIT: In order to make this question more specific, I want to know what I can comment out of the class file (or add) in order for the default thebibliography to be used. Alternatively, what options can I add to a blank tex file to get a similar look and feel to AASTeX style without the AASTeX thebibliography? Alternative packages that are already made that are similar in style would otherwise be appreciated if I'm asking for too much.", "label": 1}
+{"snippet": "This question actually came about from a discussion of another question posed here The neutron is known to be comprised of an electron and a proton, and there are observations that the neutron can be created by these particles or alternately decay into these particles. Furthermore the stability of the neutron is vastly improved if it remains bound within the nucleus. So presumably the nuclear force helps to maintain the neutron's stability. Once outside the nucleus the neutron has a much harder time keeping itself together, and once again becomes a proton and electron. And just to keep matters, and this post more simple and shorter, I'm neglecting the additional fact that the electron antineutrino is also produced in the decay. Now getting to my question, I'm wondering why we have to consider the neutron as a separate particle within itself rather than a proton-electron \"system\" of particles? Is there an experiment that refutes this way of looking at things? (note I'm asking for an experiment or set of experiments, not just theories)?", "label": 1}
+{"snippet": "I have been performing an experiment at school in which I test the force on an iron surface from the magnetic field of an electromagnet. The electromagnet has a rectangular iron core. The theory predicts that the force increases linear with the surface area of the iron plate. This is because the volume between the plate and the magnet contains a certain amount of energy, which is equal to the force exerted on the plate times the distance between the plate and the magnet. I found that the force does not increase linear with the surface. This is because of the divergence of the magnetic field of a bar magnet, which is what the core of the electromagnet essentially is. Researching the magnetic field of a bar magnet, I discovered that there is a higher density of field lines at the edges of the poles, and thus a stronger force on the plate. There are some images on this website, such as the one below. I am curious as to why the field is stronger here. I know that the electric field is stronger at edges and corners because the electrons repel and end up at a higher concentration there, is it the same concept for magnetic fields?", "label": 1}
+{"snippet": "I would like some help with what the word it in the paragraph below (with emphasis added; the word is not emphasized in this way in the original). Does it refer to the TV or the antenna outlet? The passage is taken from Haruki Murakami's TV People. Everything gets removed from the sideboard to make room for the television. The TV people plug it into a wall socket, then switch it on. Then there is a tinkling noise, and the screen lights up. A moment later, the picture floats into view. They change the channels by remote control. But all the channels are blank---probably, I think, because they haven't connected the set to an antenna. There has to be antenna outlet somewhere in the apartment. I seem to remember the superintendent telling us where it was when we moved into this condominium. All you had to do was connect it. But I can't remember where it is. We don't own a television, so I've completely forgotten.", "label": 1}
+{"snippet": "I was finding the are the of hypocycloids. Then it struck me that apart from integration, there could be another method of finding the area of the hypocycloid with different curves. But the problem is I am not getting my answer right. So could somebody please help me tell if my logic is wrong altogether or if I am doing some other mistake. Here is the another method I am talking about:- Take case of a deltoid - we can make a deltoid by taking an equilateral triangle, and on all three of its vertices drawing circles whose radius is half the side of the triangle. Now the figure left in the middle is a deltoid. Similarly, we could use n number of sides in the regular polygon to draw hypocycloids with n cusps. (see the pictures below - the red coloured drawing in the middle is the hypocycloid) Is this idea wrong? Thank you so much :)", "label": 1}
+{"snippet": "Materials in quantum information often emphasize that one and two bit classical reversible gates cannot achieve universality for the classical reversible computation, whereas universal quantum computing can be achieved only using one or two qubits gates. I want to understand why classical reversible computing cannot be achieved with only one and two bits classical reversible gates. I consulted with some of the materials, but all the materials I consulted with only 'illustrated' why it was difficult or seemed to be impossible to simulate some kinds of classical reversible gates only using one and two bits classical reversible gates, never giving a satisfactory clear mathematical proof as to that impossibility. Specifically, I wonder if there is any mathematically clear proof for the claim that Toffoli gate cannot be achieved only using one and two bits classical reversible gates. Thanks in advance.", "label": 1}
+{"snippet": "If you make a straight cut through a square, one part can always be made to cover the other. (This is true by symmetry if the cut goes through the centre, and if it doesn't, you can shift it to the centre while taking from one part and giving to the other.) However, if you cut an equilateral triangle, it may or may not be the case that one part can be made to cover the other. In some cases it may depend on whether we're allowed to flip the parts; I'll leave that to you in case one or the other version has a more elegant solution. How can the cuts that allow one part to cover the other best be characterized? What is the probability that a random cut will allow one part to cover the other? Of course we need to specify a distribution for the cuts, and again I'll leave you to choose between two plausible distributions in case one yields a nicer result: Either Jaynes' solution to the Bertrand \"paradox\" (i.e. random straws thrown from afar, with uniformly distributed directions and uniformly distributed coordinates perpendicular to their direction), or a cut defined by two independently uniformly distributed points on two different sides of the triangle. Update: I've posted the case without flipping as a separate question.", "label": 1}
+{"snippet": "I'm looking for an adjective that describes an object that, rather than is just the outside, is instead just the inside. Searching for antonyms of hollow, I have only found the word solid, which suggests both the inside and outside of an object. I really need a way to describe something as being just the inside of something. I can only think of words like core or heart to describe what I'm looking for, but those are nouns. When a tree has only its exterior, the tree is hollow. It is a hollow tree. When a tree has only its interior, the tree is _____. It is a _____ tree. Perhaps tree was a bad example, it was the only object I could think of at the time that made sense to be a hollow object. Any object where that description could apply is a reasonable substitute, it does not have to be specifically about a tree.", "label": 1}
+{"snippet": "I've long wondered about the future of our species. Taking the long view, I find it very amusing to consider the challenges that humans will face and (hopefully) overcome on our journey to the end of time. The most vexing problem is the apparently insurmountable issue of Proton Decay and how this could put a premature halt to our species and in fact any complex baryonic structures. I know that Proton Decay has not been observed in practice, but the timescales involved for the effects to become appreciable have not and will not for a great long while elapse(d). The only possible solution I've been able to come up with is Anthropo-nucleosynthesis (this is the only term I could think of meaning \"human caused matter generation\" but maybe there already is a word/phrase for it that I am unaware of). That would only be effective if these newly forged protons/neutrons would have the same lifespan as those that were created from Big Bang nucleosynthesis. Anyways, I know this was a very long winded intro question/statement, but I'm curious as to your thoughts, solutions, refinements, or problems with anything I've laid out here. What do you think?", "label": 1}
+{"snippet": "My aim is to produce an html-file with the same text as the pdf produced by LaTeX- The html shall represent the pagination and line-break structure of the pdf: When there is a linebreak in the pdf I want to produce a <br> in html, when there is a paragraph I want to produce a <p> in html, when there is a newpage in the pdf I want to produce a horizontal line in html. Handling of the paragraphs is easy since they are defined in the input file. But line-breaking and pagination depends on the font and on the width and height of the document (and maybe on some other things I cannot even imagine yet). Is there a way of getting LaTex to tell me where it broke the lines and where it started a new page?", "label": 1}
+{"snippet": "I've been searching the internet all day for this particular case and can't find a single word on the subject - whether that's my poor searching or the subject is obscure, I do not know. I am also not particularly fluent with mathematical jargon, so forgive my fumbling explanation. Hopefully one of you may re-phrase my problem after I present it. This Tangent Chord Angle diagram is the closest visual representation I can find for describing my dilemma. I'll be referring to points from this diagram, although it doesn't demonstrate the problem itself, only the starting conditions of my problem. I have been trying to write a program that will rotate a vector TP from a point T tangent to circle O until that vector essentially describes a chord on the circle (possibly TA if the magnitude of A equals the magnitude of P). I know: T, the initial tangent point TP, the initial vector from T O, the circle on which T lies The radius of circle O I have no clue what to do to get that vector to \"fit\" inside the circle. I understand there are two possible chords depending on the direction of rotation - I'll be using whichever angle is closer to the vector's original angle. Again, forgive my inability. I'm afraid it would take considerably longer for me just to learn how to more appropriately describe the problem.", "label": 1}
+{"snippet": "I have long found the Simulation Hypothesis to be better-able to answer questions that I have regarding the universe than the string theory and the quantum field theory. What I believe is that the notion of our universe being a simulation, especially in the last few years, has developed to the point where it should be seriously considered as a candidate for A Theory of Everything. Work on it, by the likes of Nick Bostrom (who proposed the Simulation Argument in his groundbreaking paper), has been cohesive and it has time and time again been proven to be just as plausible as any theory out there. Remember that a theory is just that, a theory. And as a theory, the Simulation Argument gives fitting answers to a lot of questions that physicists have found hard to answer for decades. Much to the dismay of pragmatists, the results yielded by the Double-Slit Experiment have been particularly insightful. The Simulation Hypothesis has much less irregularities than the other theories. It pays just as much heed to the laws of physics and mathematics, even being better able to address issues of epistemology and metaphysics. Then why is it that we don't even see it as a contender for A Theory of Everything?", "label": 1}
+{"snippet": "An off-topic question posed at Mathoverflow by Andrew Stacey, but one which fits here: One thing that came out of Terry Tao's recent blog posts on this matter (first post and follow up) is that it's hard to get an overview of all the different ways of getting one's amazing mathematics onto the web. I thought it'd be useful to gather together a list of such. This meant to be a list of ways to do it, not examples of where it's already being done. Standard community wiki rules: one thing per answer and feel free to edit other's answers. Additional rules: it'd be useful to have a little more than just links. A brief description, pros and cons (be objective), platforms (does it only work on Linux, sort of thing) - things that might help someone decide which things to examine further.", "label": 1}
+{"snippet": "To move charge from one point to another in an electric field, the force which we must apply is equal and opposite to the force due to the field. (Quoted from Engineering Electromagnetics by Hayt.) Here is my concern: To move a charge, shouldn't the force that we must apply be just a little higher than the force exrted on the charge by the field? I know that electric field intensity is the amount of 'kick' a test charge feels when placed in that electric field. Now if I apply the SAME amount of force against the force due to E field, the charge, according to my understanding, will just stay there and won't move. If I apply a force just a little higher than force due to E field, only then the charge should move. Why does the text say that to MOVE charge in E field, we should apply force EQUAL to that of the force experienced by charge because of E field.", "label": 1}
+{"snippet": "I've come across a book that has this general questions about lines and planes. I can't agree with some of the answers it presents, for the reasons that I'll state below: True or False: Three distinct points form a plane - BOOK ANSWER: True - MY ANSWER: False, they cannot belong to the same line Two intersecting lines form a plane - BOOK ANSWER: True - MY ANSWER: False, they can be parallel and coincident lines. Two lines that don't belong to a same plane are skew - BOOK ANSWER: True - MY ANSWER: True If three lines are parallel, there is a plane that contains them - BOOK ANSWER: True - MY ANSWER: False, they can be parallel and coincident lines. If three distinct lines are intersecting two by two, then they form only one plane - For this last one there's no answer and I'm not sure about the conclusion. If you could help me, I appreciate it. Thank you.", "label": 1}
+{"snippet": "This question concerns the residual heat (if any) contained within the Earth's moon. At the time of the Apollo moon landings, it was widely reported that the boot marks left by the astronauts would last \"forever\", as there is no atmosphere to disturb them and because the moon was geologically \"dead.\" Ignoring cosmic dust, moon quakes (which have since been confirmed) and the blast created by the Eagle lander top section as it left the moon, is this idea of extremely long term preservation of the boot prints really valid? Do we know if the moon is capable of creating convection cells, carrying heat to the surface and gradually erasing the boot prints and tracks left by the astronauts by stirring the dust particles surrounding them? Does the Earth create gravitational forces within the interior of the moon, even though I appreciate they may be a low order compared to the extreme example of Jupiter on Io?", "label": 1}
+{"snippet": "As you know the active noise cancellation technology used in many application such as protection of aircraft cabins and car interiors to reduce engine noise also some headphones use this feature to reduce unwanted ambient sounds. Actually I don't know the details of how this feature works, but I do know that it has input (microphone) that receives noise waves, control unit that invert the incoming noise waves and output (speakers) to emit inverted noise waves and therefore they will cancel each other. What I'm not understanding is that If we considered the sound waves are traveling in air, then the inverted noise waves emitted from the speaker will reach the listener before they combine with the original noise waves so they cancel each other while the inverted noise waves are traveling in a solid-media (components of the microphone, speaker, etc.) faster than the original noise waves traveling in air. I'm I missing something or there is another feature they use to adjust the speed of sound in the active noise cancellation?", "label": 1}
+{"snippet": "I am an undergraduate CS student but I love mathematics and spend most of my time doing and reading math books. I realize that it's important to get into the habit of reading papers and journals so it will be easier to think of ideas for projects and research. I'd like to know how I should start reading papers and what papers are good for beginners? The areas of mathematics I really like are Discrete Mathematics, Combinatorics, Number Theory, Mathematical Induction, Problem Solving, etc. I like things like Calculus too but I feel papers on Calculus would be too difficult to understand. Also, are there any particular efficient methodologies for reading papers? Is knowledge better gotten from books or from papers? Note: I want to say that there are already threads asking which papers every mathematician should read, and which every computer scientist should read. The purpose of this thread is slightly different. It isn't asking which standard papers everyone should know. It's asking which papers allow for an incisive entry into deeper knowledge of the subject. P.S. : For the benefit of anyone who sees this thread later, I did find a wonderful journal called Crux Mathematicorum'' dedicated solely to problem solving! They allow free access to their back issues on their website. Other good journals I found wereParabola'' and ``Pi in The Sky,'' both of which may be read online for free.", "label": 1}
+{"snippet": "I am trying to make a computer game, which involve radioactive hazard. The game is still in its early stage, and I want to add mechanisms which are as realistic and as fun as possible. So I'm trying to understand how radioactivity is \"absorbed\" in the air. For example (please excuse any physic mistake), if you have some alpha radioactivity, it will be absorbed by a very thin material, like a sheet of paper. For Beta, it's more like an aluminium sheet, and for gamma you're dead already. But how does the radioactivity weaken in the air ? Is it absorbed by random elements and the energy is lost in them ? I guess the explanation is similar to why Wifi just doesn't work at great distance, but then I'm not sure how it happens. Feel free to give any text explanation, however I'm open (even if a bit afraid) of mathematical explanation. I'm pretty sure there is a theorem or something about this, this would be even better (although explanation won't hurt).", "label": 1}
+{"snippet": "I have a basic enough question. Assume that one has one of those ideal see saws, i.e. the teeter-totter pivots on point source, the balance is of uniform mass etc. Now assume that one places an object of mass m on one end. This will force the balance to tilt on side. Now suppose that one adds another mass of m on the other side. What happens? It seems that everyone agrees that the the balance would move to the stable equilibrium, that is the middle. What I don't understand is, what is the Force that moves the teeter-totter to the middle position? Once the second mass has been placed on the other side, the two net forces acting on the pivot is the same. And since the distance is the same, the torque is the same. So what force is it that moves the balance to the middle? And if no such force exists then every position of the balance is valid if the two weights are equal, then how do those mass balances work?", "label": 1}
+{"snippet": "In a previous question, I learned that in order to detect an object in space, what matters is how much electromagnetic radiation it is giving off, and what sources of EM radiation the sensor can pick up. Given that the sensitivity of the sensor over the spectrum is a parameter for detectability, I would like to learn if some wavelengths of EM radiation are more difficult to detect than others, over increasingly longer distances in space. From my experience in biology, I know that longer wavelengths of lights from a source can be \"pierce\" deeper into tissue than shorter wavelengths (a bit counter-intuitive!). In fact, that's the premise of \"two-photon microscopy\" -- using wavelengths of light with such low energy that fluorescent dyes need to absorb two low energy photons in order to be excited. So, the probability of that happening is lower, but there are many benefits, including the fact that longer wavelength light can penetrate deeper into tissue. Does the physics behind such concerns at the microscale also affect detectability at astronomical scales? Is some EM radiation easier to detect than EM radiation with other energies? Can EM radiation of certain energies \"travel\" longer distances through imperfect, real space?", "label": 1}
+{"snippet": "Good evening, I'm writing my thesis in Latex, with which I already had the pleasure to work for some other projects, but I'm now facing a problem I don't know how to solve. I'll try to get to the point as straight as possible: let's say I have a chapter of simulation results, which includes a huge set of images. This chapter is subdivided itself in some sections, among which the images are distributed. Now, what I would like to have is a way to have all the images related to section A inseted before section B starts and so on. I don't mean I want to precisely insert them where I want (the most of them are set of subfigures, difficult to be fit anywhere), it would be enough to be able to tell the compiler to put them all before the next section starts. Do someone of you have any suggestion on the matter ? Thanks a lot in advance Michele", "label": 1}
+{"snippet": "This is kind of a big squooshy question (or series of questions), which I will try to cast in a more precise form. Apologies if I don't succeed. Context: I'm an amateur set theory/category theory enthusiast with special interest in stratified set theories. My knowledge is substantial in odd spots, but not very well rounded. Because of the ubiquity of talk of models in the literature, it seemed like a thing I should learn, but I'm having a difficult time because I feel like I don't grasp certain informal aspects of \"model theory in practice\", even though I technically understand about the first half of David Marker's \"Model Theory: An Introduction\", for instance. Questions: What are the big questions one wants to answer with models that would either be unapproachable or extremely painful without it? I gather questions of consistency are important ones, but are there other main ones? When does one want to know about the second order properties of elementarily equivalent models, and why? Are there even general answers to these questions, or am I asking things I would have to ask, say, another set theorist about to get anything informative? I hope this isn't too poor a question; I'm flailing a bit to articulate beyond \"it's cool, but WHY???\"", "label": 1}
+{"snippet": "Looking at Cohen's success at proving independence of the Axiom of Choice and the Continuum Hypothesis, I was wondering if it was possible to mechanize forcing techniques for the purpose of proving independence (and hence undecidability) of conjectures. It would seem to be useful to test any sentence you're trying to prove or disprove with an automated theorem prover for independence. I'm imagining some automated forcing technique that constructs a model of ZFC plus the conjecture and its negation to prove it isn't a theorem of ZFC (or whatever foundation being used) rather than spinning forever on an undecidable statement, since the incompleteness theorems indicate that any statement in a sufficiently strong formal system can be undecidable. Its not obvious to me how to automate such a method, as its probably quite a bit more complicated than just implementing resolution, but it would be nice to have automated reasoning go down three paths of searching for proof of a conjecture, proof of its negation, and proof of its independence.", "label": 1}
+{"snippet": "If I write My car can go pretty far and it gets good mileage I have combined two independent clauses to create a compound sentence. I might just as easily write My car can go pretty far. And it gets good mileage. But if I write Surprisingly, my car can go pretty far and it gets good mileage, meaning that it is a surprise my car has both of these attributes, then the independence of each clause seems diminished, because one without the other is not surprising. In other words, I cannot write Surprisingly, my car can go pretty far. And it gets good mileage. Is there a way to describe this difference? Is there an overriding term for two or more independent clauses that actually do not mean the same thing when not joined?", "label": 1}
+{"snippet": "I was watching a BBC sitcom. The scene is set in a wedding ceremony. In the opening of the speech of the father of the bride, he tends to be humorous, and thus he says: \"Welcome to the wedding of Laura and Paul, whether you're friends, family or freeloaders, loved ones or loathed ones, people we like or people we had to invite, and whether you're here for a free meal or a free drink, people who wouldn't have missed this special day for the world or people who had nothing better to do. You are all welcome.\" I am baffled by his using \"wouldn't have missed.\" According to the context, I reckon what he means is more or less \"people who wouldn't like to miss this special day for the world.\" But if he means exactly like that, why does he use the perplexing \"wouldn't have missed?\" Alright, he might be trying to be witty, implying \"people who thought if they came to the wedding, they wouldn't have missed this special day after the wedding.\" Is my interpretation right? Even the the implication is like that, I was still wondering how it sounds like in a native speaker's ears? For me, a non-native speaker, all I received was only full of confusion. Not humorous at all. If I were in that wedding, I would get lost and stuck in this \"wouldn't have missed\" and miss out a bunch of the rest of the speech.", "label": 1}
+{"snippet": "If a conformal mapping, e.g., a Schwarz-Christoffel mapping, maps the real line (from left to right) to a polygon, which is traced out from left to right, why is the upper half plane mapped to the interior of the polygon? Is it a preservation of orientation argument? I.e., since the upper half plane was to the \"left\" of the moving point in the z-plane (moving along the real axis), then the image of the upper half plane will again be to the left of the curve, which is also going from left to right, until it closes at the final vertex to form the polygon. I know that one can use a test point and then make a connectedness argument, but if the integral (or any tricky conformal mapping) were hard to evaluate, such as an elliptic integral, I don't feel that this is a wise move to make, and that there could possibly be a better way to argue why the image of the UHP is inside the polygon. Thanks,", "label": 1}
+{"snippet": "So, I know that this question may be tough to answer, but I am asking this question in all seriousness, and I don't consider myself a newbie... Lately, I am trying to find a way to \"generalize\" my approach classical mechanics. Specifically, I need a system that can always guarantee a solution to any problem. In a sense, just like mathematicians like to generalize stuff. For example, if you get a system of linear equations, you can always solve it by using the Gauss method of substitution... I often have the problem of seeing why the solution provided by the textbook is right, but I don't see why my solution is wrong... I'm guessing this is the motivation behind my quest. I know a field as big as mechanics is hard to cover with one or two principles, but I need something to always help me set the correct system up, the rest being \"just math\". So is there a method that yields a uniform system? I have heard that Lagrangian mechanics can provide something like this, but I'm not sure whether to take it up... Can anyone post their experiences with that? Lastly, I would add that I am no stranger to advanced math topics. I like linear algebra and multivariable calculus... from my experience learning new math has always enhanced and deepened my understanding of physics. Don't hesitate if you have to offer something... maybe a book or similar resource...", "label": 1}
+{"snippet": "Today my laptop battery died while I was finishing off a sticky note and so naturally I just went 'Oh, bollocks!'. After all, it didn't warrant one of the \"big six\"; it was more a \"damn\" moment. So I opted for \"bollocks\". I didn't think it was rude; it was just fun to say. I was around a colleague at the time and they gave me a bit of a look (and, frankly, an 'Excuse me?!'). They told me that it's just another way of saying \"bullshit\", yet based on their response, obviously not a euphemism. (I'm sceptical though. I know the dictionary says \"balls\", but it didn't say anything about \"bullshit\".) I've always thought that \"bollocks\" is just one of those great British words that are relatively harmless but fun to say, like \"bugger\" or \"sugarbush\". So, is it actually rude? Or is it just rude to some people? (If it's relevant, I live in Australia.)", "label": 1}
+{"snippet": "I understand the phrase when it is used literally in this example. He's ill and doesn't know what he's saying. I perceive it to mean that a person is struggling with an illness that prevents him from thinking clearly and understanding his words. However, there have been times where the usage seems more vague to me, particularly when it is directed at an able-minded or sound-minded person. He doesn't know what he's saying. I don't think you know what you're saying. Okay. I think there are some possibilities. A person uses the phrase as a personal attack on the other person's intellect. A person uses the phrase to discredit the other person. A person is implying that the target person is oblivious to a connotation or perception of the target person has said. A person uses the phrase to expose evidence that the target person is a dilettante. Perhaps, the phrase means each one in different contexts, or perhaps, it means a combination of them?", "label": 1}
+{"snippet": "Nearly four years ago, upon hearing of the observation of time dilation in two optical atomic clocks at an elevation one metre apart, due to acceleration towards earths centre of gravity by Chou, C. W.; Hume, D. B.; Rosenband, T.; Wineland, D. J. I wondered where the point would be, at which time dilation caused by acceleration toward the earth gives way to time dilation caused by acceleration around the earth, via orbital velocity. (I mean the point at which the two effects are at equilibrium with each other.) I asked a friend who is a physicist, he got back to me almost immediately, fascinated by his back of an envelope calculations that this point is the Clarke orbit, or the geosynchronous orbit. If for instance the rotation velocity of earth were a slightly different speed, the result would be different, and no relationship apparent. I think there may be a very interesting relationship waiting to be revealed. Is there a physical or mathematical relationship? And if so, what is it? Not being a mathematician (I'm an artist) I'm not capable of doing the math, but this has fascinated me ever since.", "label": 1}
+{"snippet": "While studying for my thesis (in dynamical systems) I've encountered multiple times with the concept of nuclear operators and nuclear spaces, often linked with the works of Grothendieck. For example, when studying the generalized transfer operator (or Ruelle operator) for the Gauss Map, Dieter Mayer points out that this operator is in fact nuclear (On the thermodynamic formalism for the Gauss map). While I can understand the definition of a nuclear operator, I still cannot get the real importance of being nuclear of order zero. Usually I'm interested in spectral gap properties for transfer operators, but is there any implication of the nuclear property? Also, any reference for nuclear operators and Fredholm kernels would be appreciated, since trying to learn directly from Grothendieck's works has been really difficult for me. Thanks in advance.", "label": 1}
+{"snippet": "I don't really understand the reason why wave theory of light fails to explain the blackbody radiation. My textbook says the Planck's quantum theory explains blackbody radiation. It says \"If we assume, he said, that radiation is emitted in packets of energy instead of continuously as in a wave, then we can explain the black body spectrum.\" So, the problem in the wave theory is that energy is absorbed or emitted continuously, not in multiple quanta. But why is continuous emission or absorption a problem when we deal with black body radiation? I was taught in class (or maybe I interpreted it this way) that if energy would be continuously radiated, then the intensity of radiation must increase on heating the black body and wavelength of light would stay same. But from experiment, wavelength changes. Hence it fails to explain it. But assuming that what I wrote above is correct, why can't the wavelength change? And even in Planck's theory, why can't simply the number of quanta emitted increase and frequency be constant, so it gives radiation of same wavelength? Please note that I have tried my best to look this up on the Internet, but all I see is explanations for back body radiations in terms of Planck's theory. If you find this question not framed well/not acceptable in its current form, please leave a comment so that I can edit it, before downvoting it to close it.", "label": 1}
+{"snippet": "Not all questions start with Wh- words, so why don't we start a question with a question mark to make it more obvious that it is actually a question? For instance, when I'm reading a book which has a long interrogative sentence at the bottom of the right-hand page, it often isn't until I turn to the next page that I realize it is a question. Not that this represents too much of a problem, but from a beginner's perspective it must make it harder to interpret the words of the sentence in the correct context. Similarly, why don't we start exclamatory sentences with an exclamation mark? I know this is a trivial question, but I'm wondering whether some kind of historical or colonial/imperial decision might explain the absence of these marks in the situations I describe. P.S. I am a student programmer, so pardon my ignorance / funniness", "label": 1}
+{"snippet": "We are regularly taught in high-schools and universities that, according to General Relativity (GR), gravity is nothing but a manifestation of space-time curvature (which, in its turn, is caused by matter and energy). However, GR is still only a model, which hasn't been challenged by experimental evidence/precision thus far. E.g., in wiki one might find a lot of alternatives to GR, some of which agree with observations not worse than GR (e.g., Brans-Dicke theory). There are theories which describe gravity not in terms of curvature, but in terms of torsion - but in reality gravity cannot be both at the same time! Besides, as far as I understand, curved space might be described as a curved surface in non-curved space of a higher dimension. So my question is: do I miss something and there are strong model-independent reasons to believe that gravity is geometry, or is it just that authors in most textbooks and articles imply that this is a model-dependent interpretation, without saying it explicitly?", "label": 1}
+{"snippet": "Suppose the big bang did create equal portions of matter and antimatter and they exist right over top of each other, such that there is a constant inversion going on. Since a matter and antimatter universe would be identical, we wouldn't know whether we're living in one or the other; therefore, isn't it possible that at any given time we could be in one or the other, or oscillating between the two at a very high frequency, perhaps even at the smallest possible unit of time? Could such frequent inversions be responsible for what we call \"inertia\", since disturbances could cause a slinky-like reaction where the matter and antimatter pair are annihilating and recreating each other or swinging around each other in a tandem dance across space? Could such a phenomenon be responsible for quantum phenomena such as particles having no definite location, since they would be constantly coming into and out of existence in slightly different locations, with fairly regular offsets giving rise to an apparent quantum field? Wouldn't that explain entanglement as well? And if such a thing is occurring throughout the universe everywhere, perhaps it explains inflation as well, since it wouldn't be an expansion of space, so much as a shrinking of the size of every single particle in existence as the constant oscillation between matter and antimatter loses energy somehow...", "label": 1}
+{"snippet": "My daughter is in high school and is working on a science project. She has really enjoyed writing the paper in LaTeX. Now, she has to make a tri-fold presentation of the major points. In the past, that has meant PowerPoint printed onto letter-size paper then pasting those pages (one slide per page) onto the board. How can we resize beamer to have at least the same aspect ratio as letter-size paper? Ideally, we would have the same dimensions, also, but that is not so important as we can scale at print time. I have used beamerposter in the past, but that generates just one page, I think. Any suggestions are appreciated. The default is to simply use beamer as-is and scale to as close to letter size as possible when printing.", "label": 1}
+{"snippet": "There are a few tools that will automatically retrieve BibTeX-formatted references from MathSciNet. BibDesk is offered with TeXShop, but only works on a Mac. Are there similar tools that work for Unix/Linux or for Windows? There are a few applications written as stand-alones that get the job done: mscget (requires python), bibupdate, bibget (a shell script). JabRef can retrieve references from a number of archives, but MathSciNet is not listed among these resources. Some potential tools are mentioned in this answer to What are good sites to find citations in BibTex format?, listed under \"Reference managers that allow BibTeX export/import\". MathSciNet is not included among the archives covered, although it is mentioned as a resource from which BibTeX-formatted references can be downloaded manually. Note: I work for Mathematical Reviews / MathSciNet.", "label": 1}
+{"snippet": "I have previously done a course on group theory and now I am doing a reading course on category theory. So as an interesting exercise I have been asked to write an exposition of group theory for someone who already knows category theory but doesn't know any group theory. I have been given the liberty to decide how I build the theory. I already have a vague idea of what is to be done. However, I would like to hear ideas about what should be done. So I solicit advice on things I should emphasize, the ways I can exploit the given familiarity with category theory for a more economic presentation and/or a exposition through \"the path of least resistance\". And please feel free to also mention any tips or precautions. Please refer me to material along this line. Thanks!", "label": 1}
+{"snippet": "I often have problems with article words referencing to its correct referent. In the following statement for example: The touching scenes in the film leaves the audience a heavy feeling, encouraging them to consider charitable acts and the role it plays in our society. My intention is to have the word \"them\" linked to the audience, and the word \"it\" linked to the charitable acts. I am quite confident that the word \"them\" does link to the audience. But I am worry that the word \"it\" may not link to the charitable acts. I find that there is possibility the reader may confuse \"it\" referring to the touching scenes in the film instead of the charitable acts. Are the article words in the sentence that I have constructed above correctly linked to its referents? In general, is there a rule to watch out when identifying references in long and complex sentences?", "label": 1}
+{"snippet": "I am currently studying English and as such enjoy reading English books from time to time; for instance I have recently been reading the fifth book of A Song of Ice and Fire since the French version was not to be released anytime soon. As I read it I often came across a grammatical form I had never encountered previously, this form being the usage of \"for\" to introduce propositions as per this example: \"We must learn english, for it is one of the most widely-spoken language.\" My question if the following: is this form correct (I do think it is), and if it is then is it still used today? I really like this usage of the \"for\" preposition but still, I'd like to be sure it can be used before actually using it (in class or elsewhere). Thanks! EDIT: Upon further searches, now knowing that \"for\" is in that case a conjunction, I found out that this form is perfectly correct - though it is more of a literary form.", "label": 1}
+{"snippet": "I am discussing with a friend (over email) the pros and cons of various interview styles. At some point in the email I write: \"Ideally the candidate will demonstrate X.\" Then in the next sentence I want to describe, by comparison, what action by the candidate would not be ideal. I was initially tempted to write: \"What would be bad would be if the candidate did Y\" but the bold-text \"would be\" sounds wrong as used here. Instead, I feel I should write something like: What would be bad is if the candidate did Y\" because I'm saying that [the action that would be bad] = Y, as opposed to [the action that would be bad] would be Y. In other words, I know that the action Y would be bad. Neither phrase sounds perfect though. I would appreciate any explanation of a 'correct' phrasing! Also I am from the UK, but living in the US, so I am interested in usage in each place (if there is a difference). Finally, I apologize if I have mis-tagged this question - it seems to me to be a question about use of either the conditional tense or the subjunctive mood, but this could be wrong.", "label": 1}
+{"snippet": "My question is basically this, if I am only able to measure the total electric field and the magnetic field at a few discrete points in space and time, is it possible to separate the convective and the inductive electric field? Here is the background. Consider the geomagnetosphere. There is a background geomagnetic field. There is a convective background electric field. Now picture a bunch of charged particles in addition with various energies and velocities so they are guided by the fields and in return modify the fields and so on. There are also other oscillations in both fields introduced from outside. So now we have an induced electric field. I then throw a satellite in there which reports the total magnetic field vector and the total electric field vector but these are only discrete values in space and in time and I have a very small sample of the entire magnetosphere. Is this even theoretically possible? It seems like at least some theoretical work must have been done on this. If someone can nudge me in the right direction or point to some references, it will be a great help.", "label": 1}
+{"snippet": "The Boltzman approach to statistical mechanics explains the fact that systems equilibriate by the idea that the equillibrium macrostate is associated with an overwhelming number of microstates, so that, given sufficiently ergotic dynamics, the system is overwhelmingly likely to move into a microstate associated with equilibrium. To what extent is it possible to extend the story to nonequilibrium dynamics? Can I make concrete predictions about the approach to equilibrium as passing from less likely macrostates to more likely macrostates? (Wouldn't this require us to say something about the geometric positioning of macrostate regions in phase space, rather then just measuring their area? Otherwise you'd think the system would immediately equilibriate rather than passing through intermediate states.) Can the fluctuation-dissipation theorem be explained in this way? Edit: Upon a bit more poking around, it looks like the fluctuation-dissipation theorem cannot be explained in this way. The reason is that this theorem discusses the time-independent distribution of fluctuations in some macroscopic parameter (e.g. energy of a subsystem) but, as far as I understand, it does not describe the time dependence of such a parameter. In particular, I'd really like to understand is if it's possible to explain things like Fourier's Law of thermal conduction (that the rate of heat transfer through a material is proportional to the negative temperature gradient and to the cross-sectional area) with a Boltzman story. According to these slides, it's surprisingly hard.", "label": 1}
+{"snippet": "After having switched computer I had to reinstall TeXLive and TeXMaker on my Mac OS X Yosemite, however, after having done this I whenever I try to compile with (pdflatex) TeXMaker I get the error: log file not found. I am aware that this means that TeXMaker is not able to find my TeX distribution, but what baffles me is that if I compile manually via the terminal with pdflatex test everything works like a charm. I have tried to reset the settings (even though they should be after a clean install), without luck. If I first compile via the terminal and afterwards via TeXMaker, I do not get an error, but it does not compile either. Any suggestions? EDIT: I tried to remove the installation and install it using macTeX in stead of the general installer for Unix systems. Of some reason this helped, even though it have installed the same version in the same location on my harddrive.", "label": 1}
+{"snippet": "I am searching for the \"most natural\" definition of a (geometrical/space) point as an element of \"something\" in mathematics (I am trying to design a small computational geometry library on strong mathematical basis). For example, for a vector, it's easy: a vector is an element of a vector space, end of story. Same for a tensor: a tensor is an element of the tensor product of vector spaces. But how to define a point in the same way? Can a point be defined as an element of an affine space or as an element of a topological space? If both are true, what are the difference between the two types of points, and what would be the most natural (it's subjective) approach to define a point in geometry? Moreover, do other approaches exist (a point is an element of XXXX)? EDIT: I know that a point is an axiom/primitive notion but to design the library I need to make a choice. And I want to know the best option...", "label": 1}
+{"snippet": "This is a question I have been wondering about the last few days, and I'm still not sure if it should be posted here on in the music section, so please excuse me if it's misposted. Hatsune Miku is a world-wide popstar, taking news and filling concert halls. What makes her unique is that she is not a human person. She is a VOCALOID, a program. While browsing the interwebs I started to realize I was in conflict with myself. What would be the correct way refering to Miku: \"What is Hatsune Miku?\" or \"Who is Hatsune Miku?\" From my perspective I see it as \"What\" defines an object while \"Who\" defines a living persona, an identity, person you can refer to. Miku efficiently takes both spots as she is originally only a created persona, but have also performed live on concert. Thanks in advance.", "label": 1}
+{"snippet": "It'd be nice to be able to style words or sentences or subsections based on arbitrary metrics. For example, it might be useful to highlight words based on their length - bolder highlighting for longer words, so that you can zoom out of the document, and get a quick picture of where it is getting complex. Another example along the same lines might be to highlight paragraphs based on their readability score. For the last example, this might involve something like converting the paragraph to plain text, calculating the score (externally?), mapping the score to a colour, then applying the color to the paragraph. Is it possible to do something like this on a document-wide basis? ie. not having to add a command around every paragraph? Can the length of a word/sentence/paragraph be easily calculated within tex, or should this be done externally?", "label": 1}
+{"snippet": "I've read questions like this one, this one, and this one which ask why we use complex numbers instead of real numbers, and that's one half of the question, but the other half, which I've never seen conclusively explained, is why we use complex numbers as a wrapper at all. From what I understand, there's nothing special about complex numbers in this case; they're simply a container (a struct, for those familiar with programming) for a pair of numbers which describe magnitude an phase. Is there a mathematical or convenience reason why, traditionally, FFT uses complex number systems for this purpose? Is there a historical aspect to it? Is there any reason why we shouldn't just describe the magnitude and phase as a vector or some other similar structure?", "label": 1}
+{"snippet": "Reading this explanation, I've understood that the divergence in computation of Casimir force on two parallel conducting plates is because of an unphysical model of ideal conductor, which makes EM field vanish on its boundaries. This looks much like unphysical model of rigid body in relativistic mechanics. Still, zeta regularization appears to somehow correctly remove the divergence and give sensible results. This must mean that effectively, it replaces our \"too ideal\" conductor with a \"moderately ideal\" one. So, the boundary conditions for EM field are no longer as simple as zero. So, my question is now: what boundary conditions does zeta-regularization implicitly impose on the EM field instead of the original ones? Does such change of boundary conditions in fact mean that the force will depend on which conductor the plates are made of?", "label": 1}
+{"snippet": "Why isn't this possible? I've seen the ducted fans, it works (even if it is very rough). I've also seen the magnetic boards that hover above a special magnetic-reactive surface. But that isn't true hovering in the sense of usability as you cannot leave that surface and you cannot surely expect a proper surface to be everywhere so your hoverboard is quite ineffective as the ATV that we've always wanted in a device like this. So my question is this: why can't a device with a strong powerplant charge electromagnets that are facing eachother to repel, hover? I have had this idea since I was a child but no one really can tell me why or why it won't work. I do not understand physics that well and I am sure there is an obvious answer. It makes no sense to me why it won't work.", "label": 1}
+{"snippet": "If I have an X amount of randomly generated positive numbers, what type of algorithm could I run to find the following: Precisely where the largest difference exists between two of the numbers? How much is that difference? Where does the smallest gap exist? How much is that difference? Generate a list of all differences and how many occurrences there are of each difference It has been a while since I have taken any sort of math class, so pardon the potentially inaccurate tags. Ideally I'm looking for a way to generate a list of all the differences, and then place those differences into a descending order. Once the list of all the differences into a descending order is created, we still need to be able to identify where in the original set of numbers, each particular difference takes place.", "label": 1}
+{"snippet": "I am writing a story with a character who was a prince born albino in a very superstitious country. His Uncle intensely feared killing him, as he believed it would release a demon inside of him. This myth becomes the only thing that saves his life when his kingdom is overthrown as a child. He learned that having people falsely fear him keeps him safer than trying to dispel the rumors. I need a term for someone who encourages his own awful reputation, so that he can win through fear without having to actually be fearsome. Think of Captain Shakespeare from Stardust as being a good example. The word in a sentence may be used much like the words illusion or facade. I am not necessarily looking for a noun or an adjective in particular; just a word, or perhaps a short collection of words to explain or describe the concept. Several example sentences include: \"He was known to ____\" \"His ____ was falling to pieces\".", "label": 1}
+{"snippet": "I am in a bind, trying to wrap up my thesis in two weeks time. My university requires me to use their citation style, which they only provide for endnote or zotero. Since all my citations are in bibtex (which I know, and I have no time to experiment with other bibliographic formats or programs, trying to make them collaborate with latex) I wonder if there is any possible way to convert a citation style language (csl) style file into a bst file that I can use. That would make life so much easier. I have googled and searched the forums that I know of, but all answers I have seen are discouraging. They are however not up to date. If someone knows of a procedure to accomplish csl->bst style file I would be highly indebted.", "label": 1}
+{"snippet": "I am just going to give an example of what I mean using Skolem's Paradox. I don't want to get into Skolem;s Paradox itself or its \"resolution.\" Skolem's showed that in first-order formulations of ZFC, whether some set A is countable depends on what is in the model. For example, take a model M of ZFC (assuming there is one). Let M satisfy the statement \"S | S is countable.\" This means there exists a bijection from S to {naturals} in M (i.e. there is a particular set of ordered pairs in M). Now, remove all and only those bijections from M and call this new model M'. Assume M' is still a model of ZFC. Is S still countable? No. Countability is relative to the elements of M's domain. How how does a mathematical object, e.g. a countable set, relate to the real world? Is it in the real world? Is is instantiated in the real world? What is meant when mathematicians say (e.g. as Cantor's Theorem says) that uncountable sets exist? That is, what is the relation of math-objects to the real world?", "label": 1}
+{"snippet": "I decided to study Euclid for fun. I have Oliver Bryne's edition. I also want, as much as possible, to construct the figures myself, to get a deeper understanding. How did people traditionally do this? I have a compass, and a ruler. So far I've constructed the first three propositions from book one. However, it's not clear to me how I ought to draw the fourth proposition, or whether it's only meant to be understood. The later propositions use the earlier propositions where equal line lengths were drawn using circles. If I want to use those same deductions to construct later propositions, should I simply copy the line length with a ruler? Surprisingly, google didn't turn up much guidance for this project. I'm assuming earlier generations of pupils would have drawn Euclid, no?", "label": 1}
+{"snippet": "From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is grueling. However I'm certain that there are things that one could do to prepare in advance for the rigours of such a degree. What i'd like to know is what foundations must be in place so that the experience of learning mathematics at university is an enjoyable one. Enjoyable in the sense that if you're exposed to a new topic you aren't floundering and you can dive straight in and enjoy the exposition and the process of learning, without having to go backwards plugging in numerous gaps and addressing other deficiencies in your knowledge. I'm certain that a good grounding in pre-calculus mathematics and calculus are a prerequisite but aren't all that's needed. What are the things that must one know in order to have a solid grounding in mathematics, with the aim of studying mathematics at a higher level? Edit: Let's assume it's a quite a demanding degree programme: MIT, Harvard, Cambridge, etc.", "label": 1}
+{"snippet": "I was thinking deeply about figurative language today, and I read a sentence that must be an example of a specific type of figurative language, but I didn't remember learning about it and couldn't find it on a reference I use. The sentence, from Street Love by Walter Dean Myers, is: Could it even withstand the voltage of / His mother's shock? Myers builds the metaphor of voltage off of one definition of the word shock, while also calling the other to mind, since the mother would be surprised/upset at this event. It seems to me that there ought to be a word for this! Any ideas? I found a similar example, too. It was used as an example of parallelism on the site I was referencing: She liked sneaking up to Ted and putting the ice cream down his back, because he was so cool about it. It ins't a metaphor, but it similarly uses both meanings of the word (cool, in this case). I thought it might be helpful as a clarifying example.", "label": 1}
+{"snippet": "As I understand it, there is a large contingent of physicists who believe that the measurement problem is \"solved\" by decoherence, without, for example, needing to postulate the existence of \"many worlds.\" Yet at the same time my understanding is that in the decoherence picture there is only unitary evolution of the wave function, and that while the appearance of collapse is explained, the global superposition of states still in fact exists, and whether or not multiple states within the universal wave function observe the same appearance of collapse (but to different eigenvalues) is a question that is left completely unaddressed. Therefore my reading of the decoherence picture is that it is virtually identical to an Everettian approach, except that it purposefully ignores an obvious interpretational consequence of its description. Is this true, or do decoherence-based approaches somehow argue that there really is only a unique observer within the universal wave function that observes a collapse to unique eigenvalues, and that there is some form of symmetry breaking that allows this to happen at the expense of all the other potentially conscious components of the universal wave function?", "label": 1}
+{"snippet": "My colleague and I are working on our style used in communications, and we have a question around whether it's acceptable to use \"you're\" or if we should always write \"you are\". Our style guide says: Our tone is conversational, honest, thoughtful, but never familiar or using slang terms The specific example we're looking at would be in an email from an IT department of a company to employees with instructions on installing a new system. We want a sub-heading at the end to conclude the message. And so the heading would read either: You're ready to use [product name]! You are ready to use [product name]! Which better meets the requirements of our style guide? Is you're too familiar? Slangy? Is you are too stilted to be conversational? Does it convey thoughtfulness? Could one form be more appropriate than another in different circumstances? There has been discussion on using contractions in formal writing (of which this question has been tagged as a duplicate), but I feel our style guideline is more nuanced than just \"formal\".", "label": 1}
+{"snippet": "I cannot hear the distinction between certain sets of vowel sounds. Normally the words in each of these sets (and of several others) all sound identical to me: Don, Dawn; marry, merry, Mary; ah, awe; cot, caught; ferry, fairy. If the speaker's accent heightens the differences between them I might be able to tell them apart, but cannot tell which word is intended by which of the different pronunciations. I can do that only from context. This may not be uncommon in American English; maps of regional variations in pronunciation suggest that about half of the country pronounce Don and Dawn the same way. This would explain why I hear those names the same way, but only if I lived in that part of the country. What is this trait called? I wish I knew.", "label": 1}
+{"snippet": "In any sizable system, the number of equilibrium states are much, much greater then the number of non-equilibrium states. Since each accessible micro state is equally probably, it is overwhelmingly likely that we will find the system in an equilibrium state. However, for a closed system, one that does not interact with any external system, the number of micro states is fixed. Therefore the entropy is fixed. At any given time, the system will be in one of its micro states. Even if the system is in a micro state that does not look like equilibrium from a macroscopic point of view, its entropy will remain the same, since entropy is a property of all the micro states, not just a given micro state. So, are the number of accessible micro states (and hence entropy) of an isolated system constant?", "label": 1}
+{"snippet": "There is a mother, Ann, who has a stereotypical 'good' personality: she is religious, a teacher, and a very generous lady. Her daughter, Emily, isn't the nicest lady: she whines a lot, insults people, and is ignorant to her family history. My professor asked to mention in my essay that Emily's personality was an 'un-improvement', as compared to her mother's. I can't find a way to say this without sounding awkward. What I have so far is: \"Emily's personality shows a degraded structure as the generations of her family trickle down.\" I already know that I do not want to use that sentence: it sounds awful and confusing, in my opinion (I can bet that you had to read it twice before understanding what I was trying to say). Can anyone else think of a way I could say this?", "label": 1}
+{"snippet": "When I've attended math competition discussions, I've often heard people remark \"oh, this is a famous problem\" or say that it's similar to one. Most of them I've actually never heard of before. Competition books tend to have a vast list of past problems, and I haven't been able to sift through and tell which ones are supposedly well known and which ones aren't. Contest math isn't especially a priority for me, but it would be nice to at least know of certain problems I should be familiar with. Could someone give a list of some problems and technique that are part of the \"folklore\", so to speak? I'm interested in any competition topic, but to narrow the discussion, let's try to emphasize competition problems in calculus/analysis (sequences, series, integrals, etc.)", "label": 1}
+{"snippet": "I was wondering if there are some general definitions for direct product and for direct sum, for example in category theory or in set theory, so that the concepts for vector spaces, Abelian groups, rings can be unified, or in other words, the common features of those specific concepts can be abstracted? In particular, the following quotes from Wikipedia (direct sum and direct product) seem to make attempts to reveal their relation to Cartesian product in set theory and (co)product in category theory, but also say that the relation is not always true. one can often define a direct product of objects already known, giving a new one. This is generally the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one talks about the product in category theory, which formalizes these notions. one can often define a direct sum of objects already known, giving a new one. This is generally the Cartesian product of the underlying sets (or some subset of it), together with a suitably defined structure. More abstractly, the direct sum is often, but not always, the coproduct in the category in question. Thanks and regards!", "label": 1}
+{"snippet": "I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest bid, and an ask that was slightly lower than the current lowest ask. Whenever anyone bought or sold, that would mean that I would always be one of the people they bought/sold from/to. This would allow me to make a profit equal to the gap between the two. The problem I'm having is in calculating the risks. As far as I can tell the variables involved are: Variables out of my control Gap between highest bid and ask offered by others Average price paid for \"pot\" of BTC that I'm trading with Some measure of the volatility of prices over the preceding period (Risk) How much volume would move the market by a given amount higher or lower Variables within my control Maximum exposure in terms of money Maximum difference in ratio between GBP reserve and BTC reserve Size of the gap between my bid/ask prices (out from the exact centre as percentage of total gap) I'm struggling to figure out how to model this effectively though. I studied Computer Science and have a basic grasp of probability theory, but this is a bit beyond me. Any help, or pointers to the \"proper\" formula to model this would be greatly appreciated.", "label": 1}
+{"snippet": "Of course a lot of people misunderstand the primary meaning of the adjective \"moot\" -- \"open to question\" or \"argued about but not possible to prove\" -- using the word only in the expression \"moot point\", which rightly or wrongly is often taken to mean \"not worth debating\". As a result the word is apt to cause confusion, even when properly used. So is there a better word to use for the minor meaning of \"moot\" -- \"not worth talking about\" or \"no longer important or worth discussing\"? A term which might be used in the sentence \"The question of what color to paint the ceiling is _____ since we won't be adding on after all\"? (One advantage of \"moot\" in this sense is that it's short and abrupt, which serves to enhance the meaning. Except that the wrong meaning may still be \"heard\".)", "label": 1}
+{"snippet": "This might appear to be a bad question to some but i can't figure out the answer. While reading about an electric circuit, i found this on the web: Over the course of time, one could think of positive charges moving from the positive plate through the charge pipe (wire) to the negative plate. That is, positive charge would naturally move in the direction of the electric field that had been created by the arrangement of the two oppositely charged plates. As a positive charge leaves the upper plate, the plate would become less positively charged as illustrated in the animation at the right. As a positive charge reaches the negative plate, that plate would become less negatively charged. So my question is that why does only the positive charge flow? Since positive and negative charges attract each other, it seems to me that the negative charge can also move towards positive charge. Am, I wrong at some point? If the question is unclear, ask me to edit it in the comment.", "label": 1}
+{"snippet": "Very soft question I admit, but it's something that's been bothering me for a while. I've been thinking that being self taught has the problem of accreditation. You can't evaluate a mathematician in a vacuum. You need an accredited mathematician to decide whether or not someone else is also a mathematician worthy of accreditation. Well, who evaluated the other mathematician? Other accredited mathematicians. It's sort of like becoming a member of an exclusive club. We put the job of accreditation on our universities. But what if some person was discovered, off-the-grid so to speak, who had taught themselves mathematics from library textbooks. How could such a person evaluate themselves? How do you know if you're making progress when you study? It's tricky. It's like language learning. Do I speak German more fluently now than I did yesterday? I've no idea. Who can say? It's like playing with Lego. How do you know if you're getting better with Legos? You build more complicated things. But who's to say one person's Lego helicopter is better than another's Lego Enterprise? What's the goal with Legos? Is there one? Should there be one? I know already that this question will be deleted almost immediately, but I think these are important questions and many people visiting this site are in fact self-taught and I'm sure these questions show up as massive roadblocks. Thanks for reading.", "label": 1}
+{"snippet": "In English, a vector is said to have two properties: a length and a direction. The possible directions correspond to half-lines out of the origin (so that, eg, up and down are different directions). In many other languages, a vector is said to have three properties: directions correspond to lines (so that a vector pointing up and one pointing down have the same up-down direction), and a third property determines which way the vector is pointing along that line (up or down in our example). This may seem strange at first, but it's actually very useful to separate these concepts in mathematics. In fact, I need to do it in something I'm writing right now, but I can't find the right English words for it. Firstly, I need a word to indicate that third property. Is there any accepted term for it? In the wikipedia article on vectors, there is a picture where it is labeled as \"sense\", although the term does not occur anywhere in the article itself. Secondly, I might need a clear way to indicate which sense of the word \"direction\" I'm using (line or half-line). This does not need to be a single word, but it should be as clear and unambiguous as possible. It would be even better if any official references for this usage could be found. This problem is bound to have come up before in the translation of foreign scientific literature.", "label": 1}
+{"snippet": "I saw on wikipedia that the shape of a raindrop is explained by using Laplace pressure. But why? Since the drop is in motion, we shouldn't be able to use an hydrostatic law, am I wrong? The bigger a drop of mercury is, the lesser spherical its shape is. Ideally, if we consider only the surface tension, the drop should be spherical. What energy should you take into account in order to understand the problem? I know the surface tension tends to minimise the fluid surface. I also know it will tend to minimise the potential energy of the drop. So we should take into account the gravitational potential energy. But how can we take the minimum of two different constraints (fluid surface and gravitational potential energy)? Is there a potential linked to the surface tension?", "label": 1}
+{"snippet": "I was pondering about EM Waves and fields and felt that there is an inconsistency in the physical picture of EM waves that I have in my mind. For example let us consider a charge at rest . Now lets say we want to test the electric field due to this charge Q at a point P. So to do this we need to place another charge at that point and find if we can feel any force due to that charge. Now I think for Q to exert a force on test charge or an electric field to be established at that point there must be EM waves propagating from the charge Q to the test charge. However there are no accelerating charges which are the prerequisites for EM waves to be generated . So this brings in an inconsistency in the physical picture of EM waves I have in my mind. I believe that there is some misconception I am having and I am positively looking forward to replies to clear it out.", "label": 1}
+{"snippet": "After a period in a .tex file, within a paragraph, should I use a space or a new line? I.e. like this: Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec rhoncus vestibulum metus ut suscipit. Sed suscipit sem ligula, iaculis dignissim turpis ultricies vitae. Curabitur interdum lorem fermentum tellus blandit venenatis et et nisi. Ut elementum interdum nulla, at dapibus urna consequat ut. Nulla sodales in nulla et semper. Proin et consequat lacus. Nam faucibus, dui sit amet sodales cursus, nunc neque mattis eros, a pharetra purus elit quis tortor. Or like this: Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec rhoncus vestibulum metus ut suscipit. Sed suscipit sem ligula, iaculis dignissim turpis ultricies vitae. Curabitur interdum lorem fermentum tellus blandit venenatis et et nisi. Ut elementum interdum nulla, at dapibus urna consequat ut. Nulla sodales in nulla et semper. Proin et consequat lacus. Nam faucibus, dui sit amet sodales cursus, nunc neque mattis eros, a pharetra purus elit quis tortor.", "label": 1}
+{"snippet": "'George hasn't turned up,' said Nick. 'A nuisance his having to go back to Plymouth last night. He'll get over this evening sometime or other, I expect. In time for the dance anyway. I've got a man for Maggie. Presentable, if not passionately interesting.' A faint roaring sound drifted in through the window. 'Oh! curse that speedboat,' said Lazarus. 'I get so tired of it.' 'That's not the speedboat,' said Nick. 'That's a sea-plane.' 'I believe you're right.' 'Of course I'm right. The sound's quite different.' 'When are you going to get your Moth, Nick?' 'When I can raise the money,' laughed Nick. 'And then, I suppose you'll be off to Australia like that girl-what's her name?' 'I'd love to-' 'I admire her enormously,' said Mrs. Rice, in her tired voice. 'What marvelous nerve! All by herself too.' 'I admire all these flying people,' said Lazarus. 'If Michael Seton had succeeded in his flight round the world he'd have been the hero of the day-and rightly so. A thousand pities he's come to grief. He's the kind of man England can't afford to lose.' (Peril at End House, Agatha Christie) I suppose Moth here refers to an expensive brand/thing but can't figure out exactly what. The phrase in question is bolded.", "label": 1}
+{"snippet": "Can anyone explain the essential difference between situations where nouns are used in a general sense and where they are used to indicate a specific type or instance of something? Specifically, I want to understand when to use a definite article and when to use no article at all. Murphy (fourth edition) give as an example of the specific type: When was the telephone invented? and as an example of the general type: Doctors are usually paid more than teachers. In some instances, i get a sense of why the noun is treated as it is, but not always. Moreover, in the above examples, it isn't obvious to me that the author means \"telephone\" exactly as a type of communication, and \"doctors\" may be defined as a particular profession (not in general, but rather precisely this class of workers who are paid better than others).", "label": 1}
+{"snippet": "I've just gone through every google search I can think of without success. Is there an archive, database, list, or other compilation of LaTeX style files? I've found plenty of style files specific to certain journals or conferences, but are there any 'generic' themes out there? I'd like to make my document look a little different from whatever the out-of-the-box LaTex default, and more than just changing the font... I'm no pro, and don't have the expertise, time, or motivation to write my own style file. Also, I assume there are plenty of style files out there, analagous to the different 'Themes' or 'templates' used by microsoft products. Ideally there would be an image/example so that i could see what the style made the document look like. Where are they?", "label": 1}
+{"snippet": "This is a phonetics question. I am teaching English as a Second Language. In phonetics, we all know the \"i\" in \"think\" is a \"short i\" sound. Additionally, the \"i\" in \"bit\" is a \"short i\" sound. However, when many of my students pronounce \"think\", \"link\", \"stink\", and so on - they pronounce the \"i\" in those words in an unnatural fashion (as if they are taking the \"i\" directly from other \"short i\" words and putting it into these words). To my ear, and my pronunciation, the \"i\" in \"think\" is far different from the \"i\" in \"bit\", even if it is short. In the same way, the \"i\" in \"-ing\" is different from the \"i\" in \"bit\" (or \"sit\", \"grit\", \"fit\", etc.). I believe this has a lot to do with the \"n\", but I'd like some technical explanation regarding the nuances of the system and how I can explain different pronunciations of a \"short i\" sound (instead of just having them listen and repeat).", "label": 1}
+{"snippet": "We know that neutrino eigenstates are not mass eigenstate and this therefore produces neutrino oscillations. This is, however, deduced from the fact that the neutrino of one flavor produces the corresponding partner lepton of the same flavor (electron neutrino only produces electrons, etc.). My question is : how do we know that this is indeed the case experimentally? I know that the standard model predicts that it is the case, but how can we verify that, if the only way to tell that there was a neutrino of a given flavor is to detect the corresponding partner ? EDIT : To give some precision about the kind of answer I'd like : Saying : we know the flavor of a neutrino by the lepton it produces is not enough. In that case, we could imagine that a lepton does not always produces the corresponding neutrino (say, an \"electronic neutrino\" is by definition a neutrino that creates electrons when it interacts with a nucleon, but we could imagine that an electron could produce half of the time a \"muonic neutrino\" (always producing muons) and half of the time an \"electronic neutrino\"). I know that's not what predicts the standard model, but has it been verified experimentally ? If so, how can we do that, as we don't know what is produced before detecting it... I ask that because we could imagine that it could be another way to \"explain\" at least part of the neutrino oscillations physics.", "label": 1}
+{"snippet": "\"You just won the lottery? Chapeau!\" This is the first time I have seen such usage in English. Literally 'Chapeau' means 'hat', but the intention (that I get from the internet) is something like 'My hat is off to you' or 'Hats off!' or 'Congratulations!' or 'Mad props!' or 'Good for you' or 'Cheers'. The primary question is: What is the provenance of this in English. And secondary questions: - at what point did it enter English? Is it direct to British English from across the channel? Or is it North American only, borrowed from French-Canadian? - And what is the feel of it? Is it mostly ironic (as 'good for you' often is)? - Is there a difference in English usage between the French singular 'chapeau!' and the plural 'chapeaux!' (or is it meaningless distinction in English). I've seen both usages.", "label": 1}
+{"snippet": "A different question about truly spherical objects in nature (Do spheres exist in nature?) made me think of a lecture I had been at where, as I recall, it was mentioned that the most perfectly spherical object in nature is in fact (the event horizon of) a black hole. In the comments of the aforementioned question, I was informed that any deviations from a spherical shape of such an event horizon would be damped out within a very short time, related to the characteristic timescale of the system. So I was wondering what order of timescales exactly we're talking about here, I would appreciate some elaboration on this. And something I thought of just now: would it be possible for some wave (periodic) phenomenon to occur in this horizon, periodically distorting the spherical shape?", "label": 1}
+{"snippet": "Does speed of pressurized gas escaping through a narrow nozzle into vacuum depend on the pressure? I've asked a question on Space.SE regarding utilizing gas at extreme pressures for propulsion. My idea was that the higher the pressure of the gas, the higher specific impulse would be achieved, because it would increase speed of the escaping particles. An answer cites the Choked Flow article, claiming The exhaust speed of a rocket is limited by the speed of sound. The answer was criticized as the linked article only gives the case of atmospheric pressure on one side and vacuum on the other as where this would apply, and my question was about way higher pressures. I'm finding this answer difficult to accept too, because speed of sound should be relative to the medium; a co-pilot of a supersonic plane can still communicate with the pilot, because the air enclosed in the cockpit moves with them. So, in a long pipe, speed of sound in decompressing gas should be relative to the local speed of the gas. Still, I don't have any solid background or source to back it up - thus the question. Is the speed still limited to speed of sound in case of very high pressures? If so, what effect limits it?", "label": 1}
+{"snippet": "Heat can be evolved or absorbed when two dissimilar liquids are mixed together at constant temperature and pressure. This is called the heat of mixing of the mixture. I'm trying to understand the molecular \"picture\" associated with this process. Here is my current attempt: Initially, there are two pure substances each with its own \"like-like\" intermolecular forces. During mixing, these forces have to be overcome in order to \"break-up\" the similar molecules to \"make way\" for the dissimilar molecules. This requires energy and so is endothermic for both pure substances, correct? It would be like boiling the liquid (energy input) to achieve an ideal gas (no interactions) of each pure substance. The second component of the net energy change is the release of energy when forming the mixture. Now, we have to accomodate both the \"like-like\" interaction forces (presumably at different intermolecular distances than the pure substance) and the \"like-unlike\" interaction forces. Overall, this direction is exothermic since formation of the solution with interaction forces is lower energy overall than the non-interacting ideal gas mixture, right? So I have two offsetting directions in the two components of energy change associated with mixing. The net effect (endo or exothermic) obviously will depend on the quantitative forces associated with the each component of the process. Do I have the basic molecular picture correct?", "label": 1}
+{"snippet": "If we have a perfect Schwarzschild black hole (uncharged and stationary), and we \"perturb\" the black hole by dropping in a some small object. For simplicity \"dropping\" means sending the object on straight inward trajectory near the speed of light. Clearly the falling object will cause some small (time dependent) curvature of space due to its mass and trajectory, and in particular, once it passes the even horizon, the object will cause some perturbation to the null surface (horizon) surrounding the singularity (intuitively I would think they would resemble waves or ripples). Analogously to how a pebble dropped in a pond causes ripples along the surface. Is there any way to calculate (i.e. approximate numerically) the effect of such a perturbation of the metric surrounding the black hole?, and specifically to calculate the \"wobbling\" of the null surface as a result of the perturbation,maybe something analogous to quantum perturbation theory? Or more broadly, does anyone know of any papers or relevant articles about a problem such as this?", "label": 1}
+{"snippet": "Recently I was told of a job offer to analyse astronomical data. The job offer states that they want somebody with knowledge of astronomical data analysis software and it will be a plus somebody who has experience with programming languages, giving as examples: IDL and Fortran. My first question is: Is Matlab a good programming language? I mean, to treat astronomical data and any other things that they might want? From what I see IDL is comparable to Matlab, both have pros and cons but basically they both do the job. For my second question, and I'm sorry if I should post this on a different post but are very closely related, the selection for this job will be made by analysing data from some surveys on the optic, millimeter and infrared frequencies from the Hubble, Spitzer, Herschel and Apex telescopes. My other question is: what kind of data is this and what kind of treatment I may have to do? If somebody could indicate me somewhere online where free data is available I would be deeply thankful. My experience on this kind of job is, clearly, limited, but I believe I have all the theoretical knowledge to tackle the problem, I just need to know what to study and train.", "label": 1}
+{"snippet": "As an example of someone who has discovered maths at a later point in my life than average, and who has (perhaps unusually?) proven the point that it is perfectly possible to study undergraduate mathematics with almost no prerequisites, I am now having to accept that fluency in mathematical techniques is in the end extremely important in the long run. I am curious about the extent to which having a rich exposure to elementary maths techniques must influence creativity in research later on? At the moment I have taken on a full-time programming job, and I am looking for optimal methods for improving fluency in elementary maths, that could work in such a limited time frame. Any suggestions? Could it be feasible to multi-task- say, for example, practice methods of mental arithmetic at the same time as doing something else?", "label": 1}
+{"snippet": "Consider these two sentences, one with a contraction, one without: I didn't check my voicemail. I did not check my voicemail. didn't is expanded to did not. Now consider: Why didn't you check your voicemail? If you want to write this without a contraction, you must write it as: Why did you not check your voicemail? The word you comes in between did and not when didn't is expanded. This: Why did not you check your voicemail? is probably not correct at all. I've never heard anyone speak like that, and never seen that written, even though didn't is expanded directly into did not. This came up during discussion the other day, and I was wondering if there was a term for this situation where a contraction cannot be expanded into what might seem the most obvious form.", "label": 1}
+{"snippet": "So I was trying to figure out the reason why my old (and probably sufficiently damaged) needle on my phonograph (turntable) was not working like it was a little while ago. With my headphones on, I was playing around with it and happened to touch two of the leads on the underbody of the needle. All of a sudden, a man's voice was speaking to me in a muffled, mid-pass tone, slightly audible but definitely discernible (talking about the \"nightmares of the Obama regime\" or something odd like that). The voices only occurred when I was in contact with both leads. Why is this? Did I turn myself into a giant watery antenna? I know phonographs have some interesting physics to them, but this is a new one. Why is it so clear? I can hardly get old analog radios to focus cleanly, let alone my own body. Is there a natural resonance that caused such a clear audio frequency to be heard?", "label": 1}
+{"snippet": "In Texmaker, I like using the shortcut to enter math mode. This shortcut creates two dollar signs, and allows you to immediately type text in between the two. My problem is that I would like to be able to continue typing outside of this block immediately upon finishing with my math text. I would like to, say, hit \"tab\" and be able to start typing outside the math block, one space after the latter dollar sign. How do I do this? Is there a shortcut for this? If not, can I create one? Alternatiely: Can I edit the Math shortcuts that come with Texmaker? I don't mean that I want to edit the keys I press to obtain the code -- rather, I would like to change the code that is available from the Math menu.", "label": 1}
+{"snippet": "Let's suppose you go to Ikea to buy a wardrobe, but you have to make sure it fits in your room. You find two that are really nice and since you like them so much you decide to buy both of them. So you measure their length, width and height (just to be sure they fit in your room). For the width you have no problem: They could be thicker or narrower and would still fit. However the first wardrobe length is not good. It's too long so you write in comments: Please provide a shorter one. The second wardrobe length is good but its height is not. This one is too tall so you write in comments: Please provide a shorter one. Wardrobe A is too large so it must be shorter. Wardrobe B is too tall so it must be shorter. Because shorter has two meanings you end up receiving both wardrobes with incorrect sizes. Now the question: Is there a pair of words for length and height that avoid using the same word to mean less magnitude?", "label": 1}
+{"snippet": "According to the current Big Bang with inflation cosmological model? I was under the mistaken impression that there was very low volume, very high temperature/pressure, very low entropy and the Big Bang (perhaps prompted by the high pressure) resulted in an expansion of volume where energy didn't change much so temperature went down and entropy went up. Now I've learned about inflation and how there is no conservation of energy at cosmological scales and that the universe gained an exponential amount of energy during the inflationary period. How did this happen with a decrease in temperature? Inflation was a period of supercooled expansion, was it not? Why was positive pressure not enough to cause inflation such that we need a negative pressure in the form of the inflaton field (or later dark energy) to explain the expansion of the universe? Thanks for your time", "label": 1}
+{"snippet": "You can obviously move a solid at a different speed along the surface of another solid, so how come the velocity of the fluid at the fluid-solid interface must be equal to that of the solid? What physical property dictates that the no-slip is valid for fluids but not solids? The Wikipedia page has the following: Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance brings down the fluid velocity to zero. which didn't make sense to me since I'm not sure how they prove that this is true for any fluid-solid interface.", "label": 1}
+{"snippet": "A long time ago I was thinking about how the Imperial system of measurements is arbitrary and annoying, and I decided to design the best system of units ever (I wasn't very old then). I worked on this idea occasionally for years without making any progress. When I finally got serious about it, I discovered Planck Units and that seemed to settle the issue. Now my problem is that Planck Units are so small that they can't be used for \"normal\" things without huge exponents, most of these being very different depending on the quantity being measured. Solving human-scale equations with these units by computer would thus either be very inaccurate due to floating-point errors (for numbers that are even within range) or very slow due to the need for extended precision. They also go \"up\" but not \"down\", which renders almost half of the possibile signed floating-point values as useless. I considered the idea of creating a new system by raising each Planck Unit with a standard exponent or multiplier, but I think this would bring some into an acceptable range but not others. So what I want to know is whether a system of natural units exists that uses units that are appropriate for work with technology that humans can interact with, or can be made appropriate without introducing too many arbitrary elements.", "label": 1}
+{"snippet": "My friend has a tendency to wear mismatched socks, because he \"Can't be bothered wasting time matching them, so he just pairs them up at random\". One day I noticed he was wearing matching socks, which was apparently not on purpose. This got me thinking, if you have N different pairs of socks and you start matching them at random, what is the probability of putting together at least one correct pair? What first came to my mind was the famous Hat-checking problem, which I cannot generalize to answer this question. I tried programming the problem though and noticed that the chance of getting a correct pair becomes significantly lower with large inputs. It does seem to converge though, but I'm not sure how to find the limit analytically.", "label": 1}
+{"snippet": "I'm currently writing a simulation in python with scipy and matplotlib to reproduce an one dimensional driven diffusive system described in this paper from M.R. Evans et al. The system consists of positive, negative and hole particles. On the left side of the system the positive (negative) particles are produced on the left (right) side with a possibility a and destroyed at the right (left) side with the possibility b. In some cases the system should show a flip between positive and negative high density states and I'm trying to reproduce this behaviour with my simulation. But all I can see is an increasing current within my simulation and I can't find any problems in my code explaining such behaviour. Does anyone here have some experience simulation such or similar systems? Cheers, Florian", "label": 1}
+{"snippet": "Sorry if this question is naive. It is just a curiosity that I have. Are there theoretical or experimental reasons why gravity should not be an emergent property of nature? Assume a standard model view of the world in the very small. Is it possible that gravity only applies to systems with a scale large enough to encompass very large numbers of particles as an emergent property? After all: the standard model works very well without gravity; general relativity (and gravity in general) has only been measured at distances on the millimeter scale. How could gravity emerge? For example, it could be that space-time only gets curved by systems which have measurable properties, or only gets curved by average values. In other words that the stress-energy tensor has a minimum scale by which it varies. Edit to explain a bit better what I'm thinking of. We would not have a proper quantum gravity as such. I.e. no unified theory that contains QM and GR at the same time. We could have a \"small\" (possibly semi-classical) glue theory that only needs to explain how the two theories cross over: the conditions and mechanism of wave packet reduction (or the other corresponding phenomena in other QM interpretations, like universe branching or decoherence or whatnot) how this is correlated to curvature - how GM phenomena arise at this transition point. Are there theoretical or experimental reasons why such a reasoning is fundamentally incorrect?", "label": 1}
+{"snippet": "Reading about intellectual history and the history of natural science, I have very often come across the expression to come-to-be as a synonym for to come into being, to start to exist, to originate, and so on. I also see commonly used such verbal expressions as to come to know (for to learn, to acquire knowledge of) or to come to see (for to realize), and so on. My question now is twofold: If one is allowed to write to come-to-be and to come-to-know and to come-to-see, is there some definite end to this or am I allowed also to write to come-to-converge, to come-to-acquire, to come-to-X? If I am allowed also to use other combinations, then what about the dashes/hyphens in these expressions. I usually see come-to-be with dashes, but the to come to know without (I think). Why is that so? Should one be consistent? Or has to come-to-be become a lexical entity that warrants a particular use of dashes, whereas the other expressions are simply compound verbs that do not warrant an equal use of dashes? What about \"to-come-to-converge` and other less usual instances of such combinations?", "label": 1}
+{"snippet": "Feynman Path Integrals are a way of calculating the wave function of quantum mechanics. It usually integrates every possible path through all of space. I wonder if there is any study of Feynman path integrals through a space with holes in it - with regions of space excluded from the integration process. More specifically, I'm wondering about points or regions of space where the amplitude must be zero. I assume that a point or region that is exclude from the path integral means that the amplitude will be zero there. I've heard described elsewhere that a space with holes in it can result in curvature in that space. And I wonder if the classical limit of a particle path will become curved due to nearby holes. This might result in the curvature of general relativity. So I wonder if there has been any study on this.", "label": 1}
+{"snippet": "I think the wave function of a free electron is nonzero almost everywhere. In particular there are regions of space arbitrarily far away where the electron has positive probability of being found. If I prepare an electron in a particular position, then wait a small amount of time and then check to see if it has appeared in a region that is too far away for it to reach even if it traveled at the speed of light, there is a positive probability that I (or my assistant, who is coordinating with me) will find it there. What have I missed? This seems a lot like spooky action at a distance, but with spooky action no matter/information actually moves faster than light, wheras in this situation the electron actually moves a greater distance than light could in a given amount of time.", "label": 1}
+{"snippet": "I'm working on ray tracing and I'm trying to understand the impact of the angle at which a light-path intersects the surface of a light source on the amount of light that source delivers to the path (per unit time, of course). My assumption for an ideal diffuse light source is that light rays leaving a particular point on the surface of the light source are uniformly distributed, in which case the angle of the path is irrelevant. I think that in essence, this assumption models each point on the diffuse surface of the light as an individual point-light source. Is that a fair assumption for something like a frosted light bulb, where I'm modeling the light as coming directly from the surface of the bulb, not the filament? Or alternatively, if I wanted to actually model the filament itself, would the same assumption be relatively valid? Are there any light sources for which this assumption would not work? I'm assuming lasers would not work this way, with most of the light leaving in one particular direction, but I'm not really worried about modeling laser light. For spot lights, I believe this is still just an ordinary \"diffuse\" light source which uses mirrors, an aperture, and lenses to direct the light once it has already left the light source so I could model it this way (though I suppose a more efficient model would encapsulate all of this and take the angle of the path into account).", "label": 1}
+{"snippet": "Is there a game which is perfect, that is: always provides a decisive victor, and involves no component of luck Possible games which would be perfect or near-perfect might involve the pie rule. https://en.wikipedia.org/wiki/Pie_rule For the purposes of this question, a 'decisive victor' means that there is no tie, draw or stalemate- the game always ends with one player winning and another losing. 'Luck' includes any arbitrary decision outside the strategy of the players, such as deciding who gets to go first by flipping a coin. In other words, what I'm asking is: is there a strategy game in which neither player has an advantage due to luck, but one of them must win. It seems to me that there cannot be, because otherwise if two 'perfect' players played against each other, what could be the result?", "label": 1}
+{"snippet": "In an electric circuit, how does the excitation of the free electrons to higher energy levels translate into net forward motion of the electrons to the positive terminal? My concept of electrons being excited by the electric field is that they have a higher orbital but they are still localized around the nucleus of a few atoms (especially in a more resistive element). But I know there must be a small net forward motion for there to be current. I need to marry the classical model of the colliding electrons and atoms of the medium with the Quantum principles involving the excitation of charges to higher energy bands and emission of photons. Also, a second question is what causes the electric field in the conductor to be practically zero (compared to that in the resistor) in a non - electrostatic model (i.e., when there is a current). Thank you so much for your help. I have scoured the internet for insight but I have not found a site that marries the classical to modern theory clearly for me.", "label": 1}
+{"snippet": "For class I'm supposed to create a PDA state diagram that is capable of generating an infinite language with no state q such that q is reachable from the start state, there is no cycle within the diagram that starts at q and ends at q, and there is not path from q to and end state. Essentially, I'm trying to prove that a PDA does not need looping states to create an infinite language but I do not know the first place to start. I know that a PDA can make use of lambda transitions which could possibly be to my benefit, and I know that there can be multiple paths resulting from the same transition but I cannot wrap my head around an infinite number of possibilities without any sort of loop. I suppose I'm not looking for a definitive answer, more so something to get me pointing in the right direction. Thanks!", "label": 1}
+{"snippet": "I have the following question, and given few proofs (provided by friends, professors, and my myself) which seem to work, I suspect the answer is yes: But I am still not completely sure. The question is: (A): \"For any given value x, are there uncountably many (countably infinite) binary sequences (ones and zeroes) whose limiting relative frequency is x\" Is this an open question? I ask this because all of those whom I've asked, had either not thought about the question nor knew the answer until they came up with their own proof. So has (A) been proven in the literature, and if so where? I am interested because if the answer to (A) is no, it can be easily shown that the Kolmogorov formalization/calculus of probability is undermined. This holds because the Kolmogorov calculus seems to require that (A) is true. That the Kolmogorov calculus requires (A) can be easily shown given its axiom of countable additivity, and its theorem: the strong law of large numbers (ie, simply consider that any infinite sequence of independent and identical random variables/trails has probability zero, if the individual outcome probabilities on each trial is less than one). Even if non-standard analysis is applied (so that infinite sequences composed of individual independent and identical random variable with non zero probability are assigned infinitesimal probability values, rather then zero probability values), it appears that this result (ie (A)) is demanded by the Kolmogorov calculus", "label": 1}
+{"snippet": "I am struggling with the concept of tension in a rope. Below specific questions. I am understanding tension to be an elastic force between rope molecules. If so, is it fair to say the net tension on each rope molecule is zero (if rope is in rest) but there is a net tension for the rope whose direction is opposite to applied force? What is the direction of the tension. I am reading conflicting answers for it. If a mass attached to rope is hanging. I think tension in rope is equal and opposite of weight. is that true? Kleppner seems to mention that tension has no direction which is confusing me. Also, does the tension vary. Mass attached to rope and hanging. does value of tension vary throughout the rope?", "label": 1}
+{"snippet": "Here is an old but interesting task from a math book, but I'm completely clueless: A teacher stands at the chalkboard and draws a line, starting from the left side of the board, towards the right. The line is ten centimeters long. Then he draws, without interruption, a second line with half of the length of the first line towards the right. Then a third, with a third of the length of the first. Then a fourth with a quarter of the length, and so on and so forth. The teacher works very carefully. With pointed chalk, he adds a new line per second. The chalkboard is one meter and ninety centimeters wide. How long the teacher needs, to arrive at the right side of the chalkboard? As the teacher finished, he constructed a square on each line. The side length of the squares corresponds to the length of the respective lines. How big is the surface area of all the squares together, approximately? Can't even tell if it is about a convergent respectively divergent series. Can you help? Thank you!", "label": 1}
+{"snippet": "I'm using LyX for writing my article. And I want to add a bibtex library to add references for it. I can do that and then add citations from that library without a problem. But the thing is, I'm writing the article and adding references as I write. I don't have a ready-made library of references beforehand. On every paragraph I would like to add a citation that was not there before. But as far as it works in LyX, you add the bibtex library to your file and then add its citations to your article. So by every new reference I want to add, I have to remove my bib library and reload it for the new citation to be added and this is a bit tiresome because I'm going to have a lot of references. So I was wondering if there's something I don't know or is there another way of doing that. Would appreciate it.", "label": 1}
+{"snippet": "I know how to use LaTeX (not an expert, but still quite some experience - wrote couple of papers and my thesis, can make TikZ pictures etc.), but I don't have the slightest idea, what XeTeX, LuaTeX, etc. are. For an invitation card I'd like to design I found this beautiful font named zapfino. But it's for XeTeX or LuaTex. This website has a nice example: http://nitens.org/taraborelli/latex#glyph I downloaded that tex code, but I can't compile the code on my ubuntu machine (with texlive) - neither using LaTeX (no surprise there), nor xetex, nor luatex, nor xelatex. I always have issues. Best works xelatex, it only complains about the font not being found before it exits. I downloaded the font from <removed> and put the .otf file into /usr/local/share/texmf (where the TEXMFLOCAL variable points to), but that does not change anything. What do I do wrong? Is there a possibility to make zapfino work with latex? and if not, how can I compile that small example on my machine, what do I have to do? Furthermore - is there a way of combining XeTeX (for the font) with LaTeX (for TikZ-tricks)?", "label": 1}
+{"snippet": "Let A and B be linearly independent subsets of a finite dimensional vector space. I want to show that if |A|>|B| then there exists an x in A s.t. B union {x} is linearly independent. My proof is ' Let |A|=n and |B|=r. Suppose B union {x} is linearly dependent for all x in A then span A is in span B. Since |B|=r , vector space spanned by B has dimension at most r. And vector space spanned by A has dimension at most r , since span A is in span B. But then it is contradict to A is linearly independent , since |A|=n > r implies A is linearly dependent. Therefore our assumption is false ' Is that right? And, someone have another proof? I want to prove it by using linearly independent but dimension of vector space.", "label": 1}
+{"snippet": "There're other previous questions about using a color background with fancyhdr so that you get a colored header and/or footer. However, they discuss either using a different color box for each part of the header, or working with a single part header (i.e: a header with just the center part, for example). But what if I have a complete header with three parts (left, center, and right), and I want all the three parts inside a single colored box? Ideally, the colored box should have no margins, but the three header parts should keep their original margins, so I guess I cannot use the fancyhdr margin parameters for that. I really need to use fancyhdr for the header. I can add more packages if necessary, but the header must still be created with fancyhdr.", "label": 1}
+{"snippet": "In short, I'm hoping for some reading recommendations. I'm starting to do some work with Calabi-Yau manifolds, though my prerequisites are fairly minimal in differential geometry. I've taken a relaxed reading course on differential geometry, hopping around Spivak, and I'm taking a full course this semester. I've also taken a reading course on elliptic curves and a full course in algebraic geometry, building up to Riemann-Roch, in case there are some reads that build from that angle. So, does anyone have any recommendations for good reading material for my situation? Mostly I'm asking because I've been informed I have to read papers and present (relaxed) talks on the material, and I'd like to not fall flat on my face on the very first talk! Thanks! (Also, any recommendations on presenting material you very not familiar with is welcome.)", "label": 1}
+{"snippet": "Please note that I am posting this question because I'm still not sure if I understand the difference although I did a comprehensive study of a great number of answers to the \"for versus to\" questions. This issue turns out to be much more complicated than I expected. I chose to pick this among many and different questions still to be made. (A) It is important FOR me to speak proper English. (B) It is important TO me to speak proper English. (A) It is important FOR me to speak proper English. Could this imply that he or she is an English learner and wants to improve his or her English very much, making it possible to rephrase it as \"it is important that I speak proper English?\" (B) It is important TO me to speak proper English. Could this imply that he or she, presumably a native English speaker, expects English to be spoken properly no matter who the speaker is, making it possible to rephrase it as \"it is important to me that English be spoken properly\" or \"speaking proper English is important to me?\" My guess is that they wouldn't be interchangeable and could have different meanings as above. I would appreciate any advice, hopefully including any rule of thumb.", "label": 1}
+{"snippet": "Consider the following sentence: I have a lot to talk about with John about his project. Since I can swap the position of the first about to make it 'I have a lot to talk with John about', then I would end up with: I have a lot to talk with John about about his project. My question is, can I consolidate the two instances of about, giving me: I have a lot to talk with John about his project. Or do I have to keep two prepositions there, but change the second about to something else in order to make it sound less-awkward, as in: I have a lot to talk with John about regarding his project. Related question (now that I'm thinking more...er...about this): is the first about really an adverb, in which case, of course, I cannot ever consolidate the two?", "label": 1}
+{"snippet": "I'm studying the first chapter of Hartshorne's Algebraic Geometry by myself and I found this book really hard for a beginner like me, but my advisor said to me that I had to study Algebraic Geometry by this book during my vacations. Then any part of the Hartshorne's book which I find very dry or superficial I search the same subject in another books or notes available online which are easier to read and have more examples. So my question is if there is some book or pdf to accompany Hartshorne's book? I mean the same contents but more detailed, if there isn't such book, it can be a book for each section of the first chapter. In this way, the first chapter of Hartshorne's book for me would be more a route to follow for an introduction of algebraic geometry, than a book to study. Remark: I know there are a lot of posts asking requests of books in algebraic geometry on this site, my question is more specific, I'm only asking this because I couldn't find any good resources with I need. Any suggestions would be really appreciated. Thanks in advance", "label": 1}
+{"snippet": "Notes for context: I am a native BrEng speaker. I have read \"Each of these is\" vs. \"each of these are\", How does \"each\" change \"are\" to \"is\"?, and What should I use between \"triple\" vs. \"all\"? and I understand the general concept of \"Each of them is\" and how \"each\" always takes the singular. Reading my daughter's bedtime story this evening, I came across the phrase \"They each have a bag of equipment\". It made me wonder why the following seems naturally (to me at least) to be true: (Correct) Each of them has an X (Correct) They each have an X (Correct) Each of them is a Y (Incorrect?) They each are a Y I would never say (to use the examples from one of the posts I linked) \"I have three pens. They each are green.\", but \"I have three pens. They each have a lid.\" is fine. Is \"to have\" different from \"to be\" when it comes to using it with \"each\"?", "label": 1}
+{"snippet": "The other day I saw this life-hack: And I was wondering how true it is. First of all, I always thought(listening to weather forecasts) that low-pressure atmosphere is what correlates with rain; although I never learned the argument behind it. Anyway, even if low atmospheric pressure correlates with storms and rain; how much(and in what sense) does this affect the bubbles in my morning coffee(if any)? My initial guess is that there should be a threshold pressure that will differentiate whether the bubbles will stick to an edge or suspend in the middle. Since this is an everyday-life question, I should say that experimental answers are welcome as well as rigorous theoretical ones. Also, I am wondering if we can make a barometer based on the bubbles in a mug of coffee? If so, how sensitive it would be?", "label": 1}
+{"snippet": "Consider the following exchange: Alice: Did Charlotte send you that email? Bob: No, but I'm sure she'll send it eventually. In this case, there's no upper bound on the period of time in which Charlotte can send the email to Bob for his expectation to be met. Suppose I want it to be limited by some point in the past or in the future: Alice: Did Charlotte send you that email last month? Bob: No, but I'm sure she sent it eventually. Can Bob say that? What about: Alice: Did Charlotte send you that email last month? Bob: No, but I'm sure she sent it eventually-by-one-week-ago. And what about: Alice: Did Charlotte send you that email last month? Bob: No, but I'm sure she has sent/did send/will send it eventually-by-one-month-from-now. How can Bob express his certainty that the email was sent, or will be sent, at some point in time between the day Alice mentioned and the limit time Bob is referring to?", "label": 1}
+{"snippet": "Here's the situation: You and your spouse are talking with a third person who is of the opposite gender as yourself. e.g., my wife and I are talking with a woman named - let's call her Joan. If I'm talking to Joan about my firstborn son, I don't want to say \"my son\" because it may imply that he is not also my wife's son. I also don't necessarily want to say \"our son\" because it may imply that Joan is the co-parent, even though everyone present knows that's not the case (it could be even more awkward with a couple talking to a man, and the wife is talking, because there might be a little more doubt about the biological parentage in that circumstance). Of course, I could gesture at my wife while saying \"our son,\" but is there a verbal way of indicating the child belongs to myself and my wife without saying something long and awkward like \"the son of my wife and myself\" or \"I and my wife's son\" or \"me and my wife's son\" etc.? UPDATE The comments make sense; I guess I should have presented the scenario as my wife not being there; if in the course of the conversation I mentioned my wife, and then later my son, but said that (\"my son\" -- or \"our son\") those expressions would seem even awkwarder to me (without my wife present). But the commenter is probably right that I'm overthinking it.", "label": 1}
+{"snippet": "The OpenStreetMap Sign Up page advises new users on its password policy: With OpenID a password is not required, but some extra tools or server [sic] may still need one. I've added [sic] immediately after the error in the middle of the sentence. When I read the sentence, I immediately thought \"Which extra tools or servers need a password?\" How do I express this while quoting the original text, so that I may bring attention to the error? Do I put [sic] inside the quote like this: Which \"extra tools or server [sic]\" need a password? Or put it outside the quote like this: Which \"extra tools or server\" [sic] need a password? Or do something else? (Would it be petty to call out a small error in this way?)", "label": 1}
+{"snippet": "I was curious earlier about the use of various pronouns / possessives in English (primarily first person), so I chose a selection of them and was surprised to discover that, among other oddities, \"I\" has apparently undergone a rather drastic shift in use over the last century. I was wondering whether any further statistical analysis of usage had been done to describe these trends. Specifically, whether there's any statistical (so, not anecdotal or simply convincing-sounding) explanation for what patterns of use of the word might be responsible? What constructions fell out of use so markedly? What constructions have been revived, and which new ones are most responsible? P.S: This may be too broad a question, but since (as per the help center) it does appear to fall under the site's remit, I thought I might as well ask. Plus, my own research was getting me nowhere; somewhat unsurprisingly, adding the most common words in the language to a search string doesn't really narrow down results significantly.", "label": 1}
+{"snippet": "Temperature is just an indication of a combined property of the masses of the molecules and their random motion. In principle, we can explain \"no effective energy transfer between two conducting solid bodies in contact\" via a condition in terms of the masses of the molecules and their speeds such that due to the collisions of molecules of two bodies, net energy transfer between two bodies is zero. But it would be a complex calculative work to derive this condition analytically so we use the temperature scale just as a phenomenological parameter to easily determine the condition of \"no net energy transfer between conducting solids\" for practical purposes. But it does not denote any fundamentally new property of the body separate from the already known mechanical properties of the same. Then why do we call it a fundamental quantity, e.g. in the SI list of fundamental quantities?", "label": 1}
+{"snippet": "I always notice this weird thing and try to overcome it but cant. As shown in the image when I ride the bike by just one hand and pull the handle back say from the right side so as commonly the handle should rotate towards right and the bike should turn to right. But that doesn't happen. No matter what I do the handle turns to left and the bike always go to left. And when I try to push it forward so that it turns to left then the handle turns to right and so the bike also turns to right. As from how much I know about laws of motion I don't know why it happens. Please explain as it is too much weird and interesting for me.", "label": 1}
+{"snippet": "What benchmarks or useful signs can be found to declassify neologisms? Obviously, inclusion in a dictionary is as likely as anything to declare a neologism a word but what happens just before that point? Note that I am not asking how long it takes to convert a neologism. I am asking if there are there any good indications of neologisms about to phase into the lexicon. The flip side is also interesting: When is it safe to say that a neologism is not likely to catch on without some drastic intervention? For instance, kipple is an interesting word with a distinct meaning but it seems so far outside of the cultural sphere that it seems safe to claim it will never become a recognized word. I suspect that answers to the first part (what makes a neologism stick) are likely to answer the second part via absence. As in, if a certain thing is a good sign for a neologism, its absence is evidence against the neologism.", "label": 1}
+{"snippet": "I have never really found a way to comfortably comprehend the idea of time shift even though I know its not the hard part of relativity theory. In that light, can someone point out what is wrong or right about the following logic I'm thinking of here: The scenario is: There are four things in my universe: a wallclock, a flashlight, my wrist watch and myself. I shine the flashlight at my wrist which is in the same line of sight as the wallclock and see they two clocks are synchronized. Now my wristwatch, my flashlight and myself begin traveling away from the wallclock along the line of sight. It seems to me that logically the light I'm running away from will take longer to reach my eye, so that means I would see the wall clock run slower, no? But according to what I think I know, when a minute passes for me, more than a minute passes for the wall clock. I just feel like I must be looking at it wrong. Any pointers are appreciated. This is just recreational thinking...", "label": 1}
+{"snippet": "So a company has n available projects and k employees on the bench. Each project has a \"number of hours\" associated with it. Each employee has an hourly rate that the parent company gets paid gets paid if he is on a project. Not all employees can be assigned to any project i.e. each employee has a subset of the n projects he can work on. I want to assign the employees to projects so that I can maximize what the company makes from the assignment. Each project can be assigned to only one employee. I am thinking of using dynamic programming but am unable to reach a recursion which I can use to fill a table. I am thinking along the lines of: Max_profit= max(For each employee -> {assign him to each of the projects on his available list and recurse with the remaining projects on the remaining employees or do not assign him to any project and recurse}. Any help will be appreciated!", "label": 1}
+{"snippet": "Imagine a situation where one sees a woman without being aware of her surroundings and concludes wrongly something about her and the group she is a part of. For example, the person sees the writings on woman's face and proceeds to conclude that the she is part of a protest group, but is soon told otherwise. Now the person sees the bigger picture and learns that it was actually a football match. What may he respond? I'm looking for the right response. \"Sorry, I was ... by that woman\" \"The woman ... me\" maybe: \"Sorry, I was misled by that woman\" \"That girl tricked me (into thinking it was a protest)\" \"I was deceived by that woman\" There must be a more fitting word. I'm looking for a verb which describes the woman's unintentional misleading of a person into concluding wrongly. She was the reason why the person came to the wrong conclusion, because women rarely attend football matches so one concluded it was something more plausible. As if the person was tricked into believing something based on a single characteristics which turned out to be the one which can't represent the entire group.", "label": 1}
+{"snippet": "My problem concerns a finite set of points in a space, for example (A,B,C,D,E). The information I have on the points is the distances of separations between the points and it comes in two sets. The distance of A from all of (B,C,D,E) and the distance of B from all of (A,C,D,E). The values of these distances are impossible if the points were to lie in a two dimensional space. To determine the minimum dimension that these points could lie in it has been suggested to me to try running an algorithm by the name of Multidimensional Scaling, MDS for short, that maps points in high dimensional space to lower dimensions. This algorithm that takes as input the pairwise distances between all of the points has a \"stress\" function can be evaluated to see how well these distances are maintained when mapped to the lower dimension. Therefore one possible way of solving my problem could be to to run the algorithm and start from the second dimension and increment upwards until the stress function approaches zero closely enough at which point I will have the answer for what dimension the points lie in. However the pairwise distance data I have is not complete and plugging in zeros for the missing data does not make sense because we believe the all of the points in question to be distinct.", "label": 1}
+{"snippet": "In Russell's famous paradox (\"Does the set of all sets which do not contain themselves contain itself?\") he obviously makes the assumption that a set can contain itself. I do not understand how this should be possible and therefore my answer to Russell's question would simply be \"No, because a set cannot contain itself in the first place.\" How can a set be exactly the same set as the one that contains it? To me it seems unavoidable that the containing set will always have one more additional level of depth compared to all the sets which it contains, just like those russian matryoshka-dolls where every doll contains at least one more doll than all the dolls inside it. Of course one can define something like \"the set of all sets with at least one element\" which of course would include a lot of sets and therefore by definition should also include itself, but does it necessarily need to include itself just because its definition demands so? To me this only seems to prove that it's possible to define something that cannot exist beyond its pure definition.", "label": 1}
+{"snippet": "During my teenage years I got into arts and slowly but surely I continue to pursue different art forms (poetry, music, painting, photography, etc) but it was just recently that I got interested in mathematics. I used to hate it in high school, mostly because it was thought as formulas to memorize and the results were only right or wrong with no room to understand why. I was reading about mysticism & occultism which turned me on to numerology, and from there found myself mesmerized by pure mathematics. I'm not interested in applied mathematics, I just find it mundane and trivial while pure math is eternal, abstract and creative. Right now I'm reviewing my high school topics so I can go into more complex ones. Being using a college algebra textbook I found in a public library and reading Basic Mathematics by Serge Lang. I'm really a beginner still so if anyone can give me some tips or suggestions to grow into this divine pursuit of abstraction I'll appreciate it. Which topics would I need to have a good foundation to build my studies in pure, theoretical math?", "label": 1}
+{"snippet": "I understand that water boils at lower temperatures at lower pressures, but I want to know what happens when external heat is supplied to a body of water at low pressure. Suppose I have a hot object in an enclosed chamber. I then cover the hot object with water, then vacuum the air out so the pressure drops. I know that with out the help of any additional heat the water can boil at low temperature because i have dropped the pressure, but what happens when I introduce the hot object? Does the water boil even faster because of the exchange of heat between the water and the hot object? What is the boiling point of the water at low pressure and the help of additional heat VS. the boiling point at just vacuum pressure?", "label": 1}
+{"snippet": "When a person is employed by a company, they are normally issued some sort of equipment or tools that they are supposed to use in a regular course of their work. If they decide to quit the job or they are laid off they will have to return the tools or equipment in proper and working condition. The tools will be inspected, their number and condition, and in case anything is missing or broken that person will have to bear the cost of replacing that tool or instrument. But what word or phrase could I use to say that someone who is quitting his job is required to account for the condition of a larger, immovable piece of machinery that he worked on. Clearly I can't say that he was \"issued with the machine\" or that he \"returned the machine\", but he's still responsible that the machine is in proper and working condition. For example, there must not be missing parts, or defects due to his negligence or anything like that, for which he could be held responsible, and would need to pay for. How can I say that he was \"put in charge of the machine\" when he started working for the company and also that, on quitting the job, and inspection of the machine he is \"relieved of the responsibility for it\".", "label": 1}
+{"snippet": "I am a casual TeX user. Mostly I have used it to type up some reports/homeworks for class in my graduate engineering work. In the past I have used document type \"article\". And then kept all the defaults. I need to self publish something online. At the highest level I would like to know: How do you setup a TeX document to self publish a book online? Some more low level questions: Is there a document type for \"book\" and what is its name? I am looking at Amazon Createspace. Amazon Createspace's requirements are: filetype=pdf, trim size, margins (gutter and outside margins). All of these various trim size, margins gutter/outside can be adjusted in the Tex document? Has anyone seen any good TeX templates for Amazon Createspace? If you could demonstrate how to tweak a specific \"book\" document type that would be very helpful also. Other than the above questions, please feel free to offer any other sort of help since I am completely new to this process (advice, links to good tutorials, links to wikibooks).", "label": 1}
+{"snippet": "In the definition of an algebra over a field in the wiki entry , it states that an algebra over a field is a vector space equipped with a bilinear product. Question: Does anyone know how a bilinear product is defined? Then a unital associative algebra is defined: An algebra such that the product is associative and has an identity is therefore a ring that is also a vector space, and this equipped with a field of scalars. Such an algebra is called here a unital associative algebra. Question: It is stated that the associativity of the product and identity makes it a ring that is also a vector space. What about the left and right distributivity of multiplication over addition which is required for a ring? How is that guaranteed to be satisfied?", "label": 1}
+{"snippet": "In ZFC, a cardinal is an isomorphism class of sets. However ZFC doesn't explicitly have classes; NBG, which is a conservative extension of ZFC does. There is no largest cardinal by Cantors Theorem There is no set of all sets - it is in fact a class. Classes do not have cardinalities, as these have been only defined for sets - but if one could define a cardinality for classes - wouldn't this, in some sense be a 'limit' of all cardinals in Set, including all large cardinal axioms? Thus, is it possible to extend the notion of cardinality in any significant way to classes? Apologies for the loose phrasing of this question. It was originally going to be a posting on Philosophy.SE, but I thought I would get better answers here.", "label": 1}
+{"snippet": "Before I proceed, let me first say I have done research and understand the general idea between the two: summed up crudely reversible happens in a slower continuous manner while irreversible happens immediately due to a sudden change in conditions. Or mathematically, I suppose you could say the irreversible change isn't continuous and therefore the entropy formula is not integratabtle. But I was given an example of a box with a partition and gas in only one chamber. The removal of the partition and the expansion of the gas is a form of irreversible entropy because the gas fills the chamber almost instantaneously. So I'm left with the question: what if the partition doesn't disappear but is simply disconnected from the walls and the gas is able to push the wall as if the gas was doing work on a piston. This would then be seen as reversible correct? As you would be able to see the partition move in a continuous path across the box. If I am correct in my beliefs up to this point, then... What if the partition is made the size of an atom, wouldn't work still be done on the atom? Wouldn't it still take a continuous path across the box? So is this reversible or irreversible?", "label": 1}
+{"snippet": "Suppose we are considering some fluid. As I currently understand, viscosity exists because of the following: supposing we draw one infinitesimal surface on the fluid, then the fluid parcels on either side have different momentum. Since a fluid parcel is made up of a large number of molecules and its velocity is the average velocity of those molecules if some molecules cross the surface into the other fluid parcel they will change the average velocity of the fluid parcel they migrated into. In that case, this will change the momentum of the fluid parcels and since change of momentum is related to force this will give rise to one kind of force which will be the viscosity force. Is that understanding right? I thought at first there was something to do with the collisions of molecules but what I said above is what I understood when I read about it on the book. If it's not like that, how we should think about viscosity qualitatively?", "label": 1}
+{"snippet": "Not sure where else to put this as I did not see a StackExchange for legal questions. Will gladly remove if someone can suggest a more appropriate place. We are submitting a proposal in response to a government RFP. My client thinks that any and all uses of ensure, assure, or insure, (unless specifically about insurance) in any document (not just the specific proposal we are doing today) should be avoided as it exposes them to legal liability. So on a resume we can't say, \"Mr. Jones utilized cutting edge technology to ensure optimal placement of gizmos\". It is true that if we represent that we can do the work and then fail we will have some legal liability. But I don't believe the liability attaches in our proposal, it would be when we sign a contract. ETA: The done thing here is to use \"make sure\" in place of these words. Which would be legally identical, wouldn't it? Is it plausible that one could avoid liability by using \"make sure\" instead of \"ensure\"?", "label": 1}
+{"snippet": "When a horse is being registered with the country's official registry, a clerk arrives to the stable to file the necessary paperwork. This process involves writing down the owner's data, the horse's parentage, measuring height at withers, and noting down locations of the special \"fingerprinting features\" that are unique to individual horse and remain constant through its whole life - the fur pattern along the mane. Specifically, the locations where the fur converges forming a small tip, diverges revealing a little skin, or forms a small whirl, clockwise or anticlockwise These are noted down with respective symbols on a chart of horse's neck, filed with the registry, and allow to uniquely identify the horse, say, in case of theft and dispute of ownership. What are these \"features\" called in English?", "label": 1}
+{"snippet": "Apologies to all if this has been asked before, I searched but was unable to find one similar. This is a question that has been bugging me for a while that i haven't really been able to find a suitable answer for. I am aware that the space between an atoms nucleus and its electron cloud is teeming with virtual particles that allow the exchange of energy that give electrons an assigned energy level or 'shell' but what bugs me is about the space in between atoms. What is in between atoms? is it classifiable as a vacuum where nothing at all exists? I would find it hard to believe that atoms are pushed right up against each other at all times due to repulsive charges on the nucleus acting upon any other. I accept that the gap is unbelievably small but on the scale of atoms and electrons, how small are we talking? Is there even a gap at all? Do we know what is in between or is it unknown? is it a similar process to the virtual particles between nucleus and electrons? It is to my limited understanding that when particles \"collide\" there is no physical interaction, rather an exchange of energy through virtual photons. Is that what exists in all of these gaps? a constant exchange of virtual energy that acts as a consistent repulsion between all atoms?", "label": 1}
+{"snippet": "This question is about how the ground state is chosen in a spontaneous symmetry breaking process. Say we have a Mexican Hat potential (e.g. the one for the Higgs field) and are sitting at the unstable equilibrium in the middle. My lecturer said that then the \"state would decay into\" a random one of the stable equilibria that are located on a circle around the origin. My question is now how exactly this \"random\" direction the symmetry is broken into is determined. To illustrate my problem: For the equivalent process in a superconductor I understand at least conceptually how that could happen. We have some thermal motion that is a statistical process, so the random choice of the direction of symmetry breaking really just comes from the chaotic dependence on the thermal initial conditions. What I don't understand is where such a random process could come from in the case of particle physics since I thought of the fields as fundamental. But maybe I am completely misunderstanding and such a decay from an unstable equilibrium to a Ground State never actually happens. EDIT From the comments knzhou seems to think that the breaking is an actual process while seeking_infinity says that it is just that you have to \"expand your Taylor series\" about a minimum. The latter would resolve the problem completely, but is it true that this only matters when we do perturbation theory?", "label": 1}
+{"snippet": "I am performing a simulation involving growth of bacteria. This is an agent-based simulation where the solutes (glucose, oxygen etc.) are represented as a concentration field discretised over space, and the bacteria are discrete objects in a continuous space (spherical blobs with a size, mass and position). The concentration fields diffuse throughout space, and the bacteria provide the reaction by taking up (or releasing) these solutes. The rate of uptake at any position in space is proportional to the amount of biomass at that position. Hence this becomes a reaction-diffusion problem. The simulation is time discretised such that in one time step: concentration fields are solved to steady state by numerical integration of a reaction-diffusion equation for the current amount of biomass bacteria grow (biomass in the system changes) with respect to the updated concentration fields I want to know, how valid is this approximation? I have always justified it that diffusion happens on a much smaller timescale than growth of the bacteria. Is it worth creating a transient solver where the reaction-diffusion equation is solved over a finite length of time and the bugs are grown for the same amount of time in a leapfrog-like scheme?", "label": 1}
+{"snippet": "I am trying to calculate an instantaneous merger of two rotating spheres into one. Two spheres each rotating around their own axis of rotation (which are generally not aligned) and moving relative to each other. Imagine two entirely inelastically colliding planets. While I can calculate their individual spin angular momentum and the orbital angular momentum, it is unclear to me how to combine this into one (spin) angular momentum for the resulting sphere. It seems to me I cannot simply add the four vectors together... or can I? After merging the two into a single body maintaining the initial momentum, can I calculate the released energy (in the inelastic collision) simply as the difference in kinetic energy, using the same reference frame? I realize this should be pretty trivial, but I have thus far not been able to neither derive nor locate and answer.", "label": 1}
+{"snippet": "My professor of algebraic function fields class gave me a paper to make a project (give the proof details, fill some gaps, etc). As my previous question here suggests, the paper he gave me is hard for me. He says if I know another paper to work, it's ok. He is very busy and he doesn't care about me and leaves me to find another one. My background: I finished Fulton's algebraic curves book. I finished the third chapter of Stichtenoth's Algebraic function fields and codes. I've heard that if we finish the third chapter of Stichtenoth's book we're prepared to make some research in the area. However, as I said my ambition is much lower, is there some paper which I can read by myself with ONLY this background? I need some suggestions. I don't know if I have many choices, so ANY paper following these criteria not so old, it would be great, really. I hope not asking so much, I really need help, you're my last chance. Thanks very much in advance", "label": 1}
+{"snippet": "I came across this question on Yahoo! Answers: Should M-theory read, M-hypothesis? It being limited evidence for further investigation, perhaps not yet a theory. I responded thus: (I realise the words \"use\" and \"usage\" are.. ahem.. overused. Please disregard this stylistic concern.) I believe this use of the word \"theory\" reflects an overlap in mathematics and theoretical physics. In mathematics, the word \"theory\" is used informally to refer to \"a self-consistent body of definitions, axioms, theorems, examples, and so on\" (reference). Examples of this usage include \"field theory\" and \"group theory\". This differs from the scientific use of the word \"theory\" to mean \"an extensively tested hypothesis\". I believe the use of the word \"theory\" here is a purposeful reference to the fact that the inventors were interested in laying a mathematical foundation for their model. Note that \"string theory\" has the exact same usage. In fact, the usage seems to be quite rampant throughout theoretical physics. However, that's quite possibly just a way to rationalise what is actually carelessness on the part of scientists using the terms. It may not even fit with the facts; my knowledge of theoretical physics is admittedly slim. Can anyone give any support for or against my explanation? I found this blog entry wherein commenter James Reed chalks it up to a combination of carelessness and an alternate definition of \"theory\" as \"a model being developed by a theorist\" (which is similar to the informal mathematical definition, I think).", "label": 1}
+{"snippet": "If you're at the wrong place at the wrong time, is this actually a bad thing? Don't the two negatives words result in a positive meaning? For instance, being at the wrong place at the right time wouldn't be good, and being at the right place at the wrong time, that too would have a negative result. As I see it, being at the wrong place, at the wrong time, could result in the second negative cancelling out the first negative and therefore the phrase doesn't necessarily have a negative meaning, am I correct? As an example, take a sales appointment. You go to the right place at the right time, that's good, you've got there OK. However you go the right place at the wrong time, and that's not good as you aren't expected, and if you go the wrong place at the right time, well, you've missed your appointment. Go the wrong place at the right time, doesn't mean you've missed the appointment though does it? It doesn't mean that you didn't get to the appointment. Is this correct? Although it's generally seen as a negative phrase, it could be used positively? What would be the full implication of this, as all definitions I've seen give this phrase a completely negative meaning and don't take this into account.", "label": 1}
+{"snippet": "What does it mean when a denomination or theological tradition is described to be \"pietistic\"? The definitions of Merriam-Webster for \"pietistic\" mean: of or relating to Pietism a : of or relating to religious devotion or devout persons b : marked by overly sentimental or emotional devotion to religion : RELIGIOSE I do not think the second definition is the one that is used when someone describes a theological tradition as pietistic, because that one seems to connote general piety or being a very pious person. I think the first definition is close, because it merely uses the adjectival form of Pietism. I have also done some reading in The A to Z of Lutheranism, looking for the entry on Pietism, and it characterizes Pietism as: ecumenical, emotional, lay-focused, and interested in institutions only if they are voluntary associations focus on the regeneration or conversion of the believer, and on living, active, heartfelt faith opposition toward [Lutheran] Orthodoxy for its overattention to the will and the intellect, seeing it as encouraging a barren and arid assent rather than living faith Later, Pietism opposed its own child, Enlightenment rationalism, for its overattention to reason, seeing it as setting skepticism above faith. I am aware that Pietism has greatly influenced other Christian denominations, but I am still not sure what it means essentially for a Christian denomination to be described as pietistic. Do all the definitions sum up to some sort of anti-intellectualism or something more?", "label": 1}
+{"snippet": "This is what I'm trying to express [Foo] can be simplifiedly characterised as [bar]. However I am unable to find references for such as word as simplifiedly. What I want to say is that the following characterisation as [bar] is to be understood as being simplified for the sake of explaining [Foo] in the first place. How would you phrase it? I would prefer if the structure of the sentence would remain unchanged. But if there is no such word maybe this can be restructured without being too verbose. Edit: It's not a question of rhythm or aesthetics, it's a question of meaning. I'm not trying to say that the characterisation I'm making is simple to derive, I'm trying to say that I'm making a characterisation that is simplifying the matter of [Foo], which is in fact a bit more general/complicated than its representation as [bar] might suggest. For me \"simply\" has the taste of what I'm not trying to say (according to the above paragraph). Regarding the suggested \"more simply\", I have no gut feeling and will have to trust you as experts.", "label": 1}
+{"snippet": "I am looking for a word or term that means something like: you are using previous results outside boundaries of the original experiment/observation earlier experience/results does not apply in all other cases you are extrapolating findings beyond original context those specific test results don't apply to every case there is no evidence that previous observations apply in all other cases those findings cannot be applied here it does not follow that... For example - someone has measured some attribute and concluded it increases efficiency (ignoring correlation and causality) - then extrapolate to claim that all other cases would benefit from increasing this attribute. I want to say that is not true, because the original observation applied to specific situation and it's faulty logic or extrapolating too much to assume the same thing works everywhere. I Found a list of fallacies on Wikipedia- the ones that I think are most appropriate are: Faulty Generalization, Hasty Generalization, Fallacy of Composition and Inductive Fallacy", "label": 1}
+{"snippet": "There are a couple of idioms whose meaning is from time to time or occasionally. Every so often (Every) once in a while (Every) now and then/again Every actually is a determiner (or, broadly speaking, an adjective) specifying a noun or noun phrase and means that everybody or everything of the referred group is addressed, as in every day, every man, or every student. Obviously, every is also used when referring to a period or range of time, e.g., every thirty minutes or every week but, again, the time frame is given as a noun. I was looking at the entry in Etymology Online, as well at Merriam-Webster and Oxford dictionaries to get further information. Etymology Online doesn't address the matter at all. While the dictionaries at least define these phrases and list a couple of examples, they do not give any clue to answer my questions: what part of role is every playing in these expressions (from both a grammatical and logical point of view) and where did this usage come from.", "label": 1}
+{"snippet": "I have a list of events. A few of them may be cancelled or they may be \"moved\" to another date. The latter are usually postponed but not necessarily. For cancelled events I add the state \"Cancelled\". What is the best word (or short phrase) to describe a date change of an event? Is it \"Rescheduled\"? I saw some answers here, but they referred to full sentences. Edit: As it has been asked for clarification. In the German sources usually only \"verschoben\" is used. In this case this can mean \"date of event will be changed\" but also \"previous date of event has already been set to a new date\". Im looking for such a word. But now I'm also thinking about introducing a new state in my data model to express the distinction between the state \"to be rescheduled\" and \"rescheduled to/postponed to\".", "label": 1}
+{"snippet": "I am writing a dissertation and I have a two collections of data from my research which I would like to compare using graphs. I have the values for abscissa and ordinate and I am looking for some sort of tool into which I can input the values I have and which will plot and trace the graph so I can show the variations in both samples. Just something simple nothing very complicated. I have been searching the Internet for something like this for hours and I can't seem to find one. What I have found so far are tools which take a function before drawing the graph, but what I need is something which can take the values directly in order to draw the graph connecting them. I don't know whether my search terms are not accurate enough to describe what I need so I hope someone here may be able to help me out. Please, does anyone know a simple tool which I can use to achieve this? (Windows or - eventually - Linux would be highly appreciated)", "label": 1}
+{"snippet": "I have always thought that colons were used to clarify, expand, provide evidence for the preceding sentence, or show an example. I have heard that this is not true. (Truly, it is a shame if it is so: colons are my favorite punctuation.) Which of the following sentences uses the colon correctly: There are three children in my class: two boys and one girl. There are three children in my class: Jack, Larry, and Susan. He is undoubtedly a true man: his beard is long and his hands are strong. It was a big fireplace: not one of those ornamental dainties you find in the houses of snobs, but a real fireplace that had a utility surpassed only by the greatest furnaces. She was a promiscuous fiend: she had seduced every guest who had dared to pass her threshold with her fiery eyes and her wealth. This is the problem with your stubbornness: if you happen to be wrong, it will be all the more embarassing. Never in my life have I been homesick: perhaps I am emotionally stronger than others, or perhaps they have a better home than I.", "label": 1}
+{"snippet": "I am a user of LaTeX for about two years and I can see that almost every package which exists for TeX is free and these packages are maintained perfectly; packages are updated regularly and new packages or classes are developed when needed. Why people do such volunteer work? How do they benefit from the time they spend on creating and maintaining things related to TeX, LaTeX and friends? Do they do these just to have fun, fill their leisure time and learn something during the time they do not work or does working on these help people to develop their own business and work? I know that every person may have his own reason to work on open source/free softwares, but how should I answer this question and convince somebody asking such question and thinks that it is just waste of time spending time on something which has not any financial benefit? I personally really love TeX and LaTeX and spend some of my time learning about it but once somebody asked similar question and I had no answer to him.", "label": 1}
+{"snippet": "As space-time is distorted in a gravitational field, relativistic effects such as time dilation and length contraction take effect. Time dilation is explained simply enough: closer to the source of gravity, slower the time passage. However, space contraction gives no such clear answer. for example, a single thread on the matter contains the following: gravitational field would produce a transverse expansion of distances gravitational fields produce increased distances in the direction perpendicular to the field [gravitational fields] produce decreased distances in the radial direction So, to pose the question as bluntly and directly as I can: Ignoring all other effects (relativistic or otherwise), which is shorter: a measuring stick closer to the source of gravity or a farther one? If the orientation of the stick plays a part, try to answer for both the case where it's pointing towards the source of gravity, as well as perpendicular. Similarly, if the position of the observer relative to source of gravity plays a part try to take that into account (but it doesn't seem to in the case of time dilation so I don't expect it here either)", "label": 1}
+{"snippet": "Will a machine or a technique ever be possible that allows artificial gravity in interplanetary space? And I ask out of pure curiosity. I know there is the \"Vomit Comet\" that allows for a non-gravity 'simulation' (for lack of a better word) on Earth, and I was thinking about if there would be a way to reverse that and rather have gravity in space. edit: Say I was building a space shuttle because I'm dying to go to the moon (true story). Unlimited budget, the smartest people you can fathom helping me build my space shuttle. I get motion sickness and the whole \"anti-gravity\" thing wouldn't really work for me. Would there be a way to have gravity on my space shuttle? Perhaps by using a type of machine or magnets or something of the like?", "label": 1}
+{"snippet": "I found some theoretical questions in an old test of my school, and would like some help with the ones I cant answer: It is said that the electric field is an intermediary of the electric interaction. What does this mean? Why the participation of this intermediate is necessary and can not establish direct interaction between charges ( as supposed by Coulomb ) ? Electrostatic field lines are open. How can you establish a relation between this and the fact that electric force is conservative? If a charge is placed inside a non-uniform electrostatic field, will it move alongside the field lines? (I think this is true, because the electric field is parallel to the electric force which is what causes the movement state variation, but I'm not sure...)", "label": 1}
+{"snippet": "I realised, reading another Phys.SE question about balloons moving forwards in an accelerating car that I don't really understand how buoyancy works. Particularly concerning, for a SCUBA diver. The top answers to that question seem to claim that balloons get their \"sense of down\" from a pressure differential. They continue: when a car accelerates, the air at the back of the car becomes more dense, and at the front less dense, changing the plane of the pressure differential and so also, the balloon's sense of up. I find that extremely hard to credit. However, I realised that I don't really know why less dense things float in more dense things. I'm fairly sure it's something to do with displacement of heavier things by lighter things, and I think pressure acting on the lighter thing's surface has something to do with it, but that's about it.", "label": 1}
+{"snippet": "I have a LaTeX document that works fine, but it does give a warning message every time I compile it. Here is the text of the warning message: LaTeX Warning: Label `' multiply defined. The name of the label that is multiply defined appears to be an empty string. I am confused about this, but I have had trouble searching for it online because the key element is the empty string, which does not make for a good search term. Does anyone know what this warning message could mean? I can post details of the document in question as needed, but at this point I have no idea what parts could be important. Got it. I guess I didn't realize that bibliography items counted as labels - since I never had any intention of referring to them anywhere, I left all of their labels blank initially.", "label": 1}
+{"snippet": "I was reading Surtees' Young Tom Hall the other day, and came across this... Sir Thomas, whose father had been a great army tailor, was a Dublin Castle knight, but, like all truly great men, condescending withal - and no feast or fete, or wedding, or christening, in Fleecyborough, or within a radius of three miles, was considered perfect without Sir Thomas Thimbleton of Thimbleton Park (so he called his villa and twenty acres of land). Does anyone know what a Dublin Castle knight is? It doesn't sound terribly complimentary. Farmer & Henley, Partridge and Green have Dublin dissector, Dublin packet, Dublin trick and Dublin rules, but no knight. A search of the internet produces thousands of references to a song, whose lyrics I have perused but which doesn't appear to be relevant.", "label": 1}
+{"snippet": "In the U.S. when someone orders a 'well drink' they are typically intending to order a drink (i.e. \"vodka tonic, well\") with the cheapest of the liquor the bar has available Where did the \"well\" come from? It is distinct from what is called a \"call drink\", which is when the customer specifies the brand (i.e. Stoli tonic). Since well liquor is also distinguished in contrast to middle- and top-shelf liquors, is \"well\" perhaps being used as a reference of altitude (e.g., a well is a subterranean water hole)? Is it coincidence or is it etymologically pertinent that the Hebrew word \"be'er\" means \"well\" in the sense of shaft/recepticle? To emphasize, this question is asking for information on the origin of the word \"well\" in its sense and usage behind a bar. Where does this usage of \"well\" derive from and how was it adopted for bar usage?", "label": 1}
+{"snippet": "There are a few other topics I found that explore this idea from a different perspective: Is randomness deterministic? Can randomness exist? Is the universe fundamentally deterministic? My question is on similar lines but from the perspective of complexity and within the framework of classical mechanics. It would seem to me that what we typically describe as \"random\", for example in probability theory, refers to the unpredictability within a complex system. A coin flip has many different initial conditions: the size and shape of the coin, the way the hand moves when it flips it, the material of the surface the coin lands on, the movement of molecules in the air etc. It also has many many interacting parts, many of which exist on the atomic scale, and whose relationship with other parts change dynamically. Probability is a mathematical model that allows us to tell what possible average outputs the system can produce given all the internal variables that are unknown to us. Is this a fair characterization? However, if we were, in theory, to know all the initial conditions and had a way of describing all of the interactions of all variables in this dynamic system once it has begun, could we not predict the outcome (assuming theoretical computational power)? My main question: Is there any kind of dynamic system in classical mechanics in which the outcome would not be predictable and, if so, why not?", "label": 1}
+{"snippet": "Consider these sentences: If you haven't got a fresh chicken, I'll take a frozen. If you haven't got a fresh chicken, I'll take the frozen. If you haven't got fresh cream, I'll take canned. If you haven't got (any) fresh cream, I'll take some canned. If you haven't got fresh cream, I'll take the canned. As you see, frozen and canned are adjectives that are used attributively but their accompanying nouns are left out. Is it grammatical to do so? Under what conditions? Does the phrase remain a noun phrase? Of course, the problem can be detoured by adding back the omitted nouns (frozen chicken/one, canned cream), but the question is, cannot the adjectives do alone? You can also share your native impression and tell us (preferably in the comment section) which of the sentences above you find acceptable and which unnatural.", "label": 1}
+{"snippet": "I am writing a document which will contain many small (approximately a page) snippets of text, potentially organized in sections or subsections. To each such section, I would like to attach several \"tags\" from a predefined list. At a different place in the document, I would like to make a list of all tags and the sections which are associated with each. I have an idea how to make a very primitive tagging system if the tags list occurs in the end of the document (e.g. I can successively redefine a command adding text to it; later I can place this command to list the contents). Does anyone know a better solution? Ideally I would like to organize my tags in the beginning of the document, after the table of contents. I feel there might be a package which does this but I haven't been able to find one.", "label": 1}
+{"snippet": "Suppose, sometime in the future I develop an experimental superweapon capable of blowing up the entire Moon. If I used it to break the Moon into multiple pieces of varying sizes, we would then have giant chunks of Moon rocks floating around. We all know the Moon is drifting away from us at a constant rate. But now, rather than there being a single concentrated mass we have multiple masses. If I understand Newtonian Gravitation correctly, the bigger the object the more gravitational pull it has. For example, if I landed on Phobos (if that is possible) and jumped, it would take a longer time for me to fall down than it would, say if I jumped while on Earth's Moon. After being broken up into smaller pieces, which of the following would happen to the Earth's Moon? A) The Moon remnants keep drifting away from us, regardless of the fact that the pieces are now smaller. B) The Moon now does not have the \"power\" to counter Earth's gravity due to not being the massive object it used to be, so the pieces all fall to the Earth and that ends everything. C) The Moon gets close to Earth but does not fall down on the surface. The pieces form an asteroid belt made of lunar remains much like the Jovian planets, which will never get away or closer to us and remain in a relatively perfect ellipse?", "label": 1}
+{"snippet": "I am always surprised by the subtleties that are embedded in the wave/particle dualism. That is why I read again and again the paragraph in the Dirac's classical text dealing with the single photon interference. Here, it is clearly stated that any measurement of the kick-off of a mirror would cause the photon wave function to collapse, then completely spoiling the quantum interference of the probability distribution. So I wonder if here some ad hoc definiton of measurement is assumed, since in general terms, no matter how I chose to support the mirror, that support will experience a momentum transfer (or radiation pressure) therefore its kick-off will be definitely measured. To be precise, I found no reason to assume that, provided I have a sensitive enough device, I could not measure the single photon radiation pressure (gravitational wave interferometers actually can do that). So the point is that I could, but I don't do it? Subsequent inspections of the Dirac's text unfortunately did not improve my understanding.", "label": 1}
+{"snippet": "First of all, English is my foreign language. I've never thought of this until the release of the film Dr. Strange the supreme sorcerer. My co-worker argued that Dr. means Doctor (as a job), while I translate it to Dr (as a title, like Master, bachelor, doctor). I think Dr is, of course, short for Doctor, which can be both a title or a job. However, I'm not so sure if they have the same meaning (when using as a prefix). The question is: Does Dr. as a prefix could mean both as a job and a title or only one? If it has only one meaning, how do I distinguish those two? How do I know if it's being used as a job or as a title? P/S: Also, does Dr. as a title has anything relate to those in {Master, Doctor, Bachelor}?", "label": 1}
+{"snippet": "The class of words called 'words of comparison' includes words such as 'higher' and 'highest'. The words 'higher' and 'highest' express comparative height. The term for the class of words that includes 'higher' is 'the comparative'. The term for the class of words that includes 'highest' is 'the superlative'. Is there a linguistic term that denotes the class of properties that words of comparison compare? I'd appreciate whatever answers people can offer, but I'd prefer answers that include a completion one of these two similes. The word 'higher' and the word 'highest' are to the word 'height' as the phrase 'the comparative' and the phrase 'the superlative' are to '_____'. The word 'higher' and the word 'highest' are to the property called 'height' as the phrase 'the comparative' and the phrase 'the superlative' are to _____. Thank you, -Hal", "label": 1}
+{"snippet": "Is there an adjective that can express the concept of a law that supersedes other laws? I would prefer a single adjective that has legal connotations, although a present participle will suffice. The phrases supreme law and overruling law approximate this concept, but supreme merely seems to indicate significance, and overruling implies direct contradiction, rather than \"displacement in favor of another\" as supersedure indicates (the laws do not run completely contrary to one another, but one is more appropriate and takes precedent). Also, the phrases the law which has primacy over other laws and the law which supersedes other laws are too wordy and awkward for my intended usage in a paper about a certain contentious Supreme Court decision. Is there an adjectival form of \"primacy\" or \"supersedure\", or another adjective which accurately describes this legal usage? Here is the sort of context in which I intend to use such an adjective: The ruling demonstrated disregard for the ________ constitution/law/legal right.", "label": 1}
+{"snippet": "I want to fill the holes in my knowledge and get to a masterful level at undergraduate material, so I am looking for books to help me with that. I recently took the GRE Math Subject test and I focused on calculus problems. I am not sure how I did and I will be happy getting into just one graduate school, but what I really want to do is get better. I do not have much to do for the next few months, so I want to become expertly proficient in calculus, linear algebra, ODE, abstract algebra, number theory, and any other core subject. I have taken classes on these subjects so I am looking for books that do the following: Cover material in a concise and complete manner Have advanced questions that help me prepare for future learning Have answers to the questions Thanks!", "label": 1}
+{"snippet": "Tchrist's comment here on my answer to an etymology question brought the following to mind: Ox (from Old English oxa) maintains the same vowel in the plural oxen that it has in the singular. But child has a different vowel (an English short vowel) in the plural. Brethren, an archaic or specialized form of the plural of brother, is a similar case; it changes its vowel in the plural as well, through i-mutation. (Yet brothers does not.) I've looked at http://etymonline.com to find these two words, as well as looking briefly in an introduction to Old English published by the Medieval Institute at Western Michigan University, and discovered that child has an older plural, which might be childer in Modern English. But I'm still not entirely clear on its history; and I'm confused about what the text says about brother. Why do these two words with (standard, archaic, or alternative) plurals ending in -en have vowel changes in the plural, when ox does not?", "label": 1}
+{"snippet": "I just had a conversation where the sentence 'The system is broken because it's fixed!' was correctly spoken under the pretense where fixed means that it's rigged. Assuming that context of rigged matches as a weak synonym for broken, the question came up - what's the word for a pair of words that are simultaneously synonyms and antonyms? I am not asking about autoantonyms. I am not even looking for a single word. I am trying to find a term to describe the relationship of two different words, where one is an autoantonym and where one of its definitions is synonymous with the second word, causing the two words to be synonyms and antonyms at the same time. In my example: fixed = rigged: fixed and rigged are synonyms fixed = repaired: fixed and rigged are antonyms What is the label given to the relationship between fixed and rigged?", "label": 1}
+{"snippet": "In the Hindi language there is an equivalent phrase which is widely used when a common man who is trying to suggest an idea to a person in power or some higher authority respectfully without challenging the latter's incompetency to 'not see the flaw' in the system. Example: A head of the police department being addressed by a common man (person of a lower stratum) giving an intellectual suggestion. I have translated a suggestion which was originally in Hindi. Common man: Small mouth big words but Sir, wouldn't it be a better idea to install wireless communication systems in police station too? Is this phrase used in a similar fashion in English too? The only phrase I have seen is 'in my humble opinion' used at the start of sentence in such cases. Another phrase I know is 'Small mouth, big talk' but I haven't seen it used as a prefix in sentences. Any other appropriate suggestions are also welcome.", "label": 1}
+{"snippet": "I am a physics undergrad, wishing to pursue a PhD in Math. I am mostly self taught in the typical math undergrad curriculum. I am looking for more input, in ways I can improve my mathematical thinking. So, my question is once you read a proof of a particular theorem, what should be the important things that you are looking for in the proof. How should you approach it? So, one of the things I have learnt to do is to look at every hypothesis of the theorem, and see its effect on the proof, or how do the subsections of the proof correspond to parts of the hypothesis, and how they fit together. However, what I find difficult is to recognize how the proof fits together in the general scheme of things. What should I ask or explore after the proof? How can I learn to solve problems more quickly and effectively through proof - reading? I am very slow are problem solving and wish to improve that. Lastly, I am terrible at coming up with new examples, and I don't even seem to remember examples beyond very typical ones. How can I improve this ability through reading of proofs? I hope this question is welcome here. Otherwise, please feel free to close it. I understand this is a vague and difficult question, but any kind of input (however small) will be highly appreciated.", "label": 1}
+{"snippet": "I've learned that there is no authoritative dictionary for English. I wonder on what juristic basis students are corrected when making mistakes in an English class. How can someone say that whatever the student did wrong is not considered correct English by other people. In German schools, students may only be \"punished\" (by getting a bad mark) when they had the chance to know better. For example when they have violated a rule in the official German dictionary. That is impossible when there is no official dictionary. How do schools in Britain or the US handle that issue? Note: There is no official reference of the German language either. However, authorities in Germany are advised to use the German language as specified in a dictionary called \"Duden\". Pupils in Germany are graded using the \"Duden\" dictionary. Other German-speaking countries may use other dictionary.", "label": 1}
+{"snippet": "On our sister site a user recently used the term \"tags\" in relation to taxis in China. I thought it might mean some kind of official authorization to operate a taxi. But upon clarification I was told \"tags\" actually means \"License plates and stickers that show the registration is currently valid\". I'm a native speaker of Australian English and I've travelled in almost every English speaking country and didn't know this use of \"tags\", though I guess this is not a topic that's come up in conversation in my travels often either. In which countries would this sense be known? Just USA? USA and it's neighbours in Canada and Belize? All English speaking countries other than Australia? Even in Australia and I somehow remained ignorant of it despite having classic cars as a hobby for a number of years?", "label": 1}
+{"snippet": "I am working on a Project and one of the major part of it is a GAS Detector, The GAS Detector detects the large number of flammable gases, but in order to test the Detector I am required to release certain gases in a room from the GAS cylinder with different flammable gases. There is no such thing in a room which could cause ignition, still i wonder if the Static electricity produces in a room somehow, can it cause the fire or some harm due to this gases ?? Is there even the slightest possiblity that it could be harmful ? I just want to know if it may cause so that I could tell my Professors why I am testing the GAS sensor with the Hydrogen gas present in air.", "label": 1}
+{"snippet": "Let us assume that we want to describe the full process of photon emission by electron A and absorption by electron B. Therefore electron B must be on the forward lightcone of electron A. In the normal forwards in time description a virtual photon propagates from A to B depositing a certain amount of energy and momentum onto electron B. But does this process alone also describe the recoil of electron A? Should one also include the backwards-in-time virtual photon which propagates from B to A depositing an equal amount of negative energy and momentum back onto electron A? Between measurements no-one is \"looking\" at a quantum system so in the spirit of \"what isn't prohibited is compulsory\" maybe it evolves both forwards and backwards in time. One could say that the product of the forward-in-time and backward-in-time propagators give the full probability of photon emission by A and absorption by B. Is this where the Born rule comes from (as in John Cramer's TIQM)?", "label": 1}
+{"snippet": "Let q be a generalized coordinate with a conjugate momentum p and a potential resulting in a periodic motion of q. What is the meaning of the Fourier transform of q(t) over its period? Can this be interpreted as the distribution of momenta? I know this is the case in QM but what happens in the Classical case? For instance for a particle in a box (classical) with an initial velocity of p/m, the motion is a triangle wave. The Fourier transform is a squared sinc function. As the triangle wave gets smaller, the F transform spreads out and vice versa. Very nice but the only two momenta for the particle are p and -p as the particle either moves up with constant speed or moved down at constant speed.", "label": 1}
+{"snippet": "Complex analysis, and in particular contour integrals and the residue theory have proved a very powerful tool in computing a large class of real function integrals which would be quite troublesome to compute if only within the scope of real calculus. There are a great many techniques designed for this purpose, for instance, both the choice of the complex variable function and the choice of an appropriate contour is critical to our success of computation. I want to study these techniques systematically, so I want recommendations for tutorials that cover them in a systematical way, the more inclusive the better. In a word, I want to learn as many those techniques as possible, so I think such a tutorial is a must. Any advice is welcome. Thanks! Ps: the tutorial I currently have at hand is Stein's Complex Analysis, it is good but covers too few exercises about such techniques.", "label": 1}
+{"snippet": "S.E friends, Due to my genuine interest to Goldbach's conjecture, I decided to self-study the subject of additive number theory on this upcoming Fall. Before jumping to such fascinating field of mathematics, I decided to self-study \"introductory\" number theory as I never took a number-theory course in past. While browsing through websites and libraries, I found books like Ireland/Rosen, Apostol, Nathanson,Hardy/Wright, Sierpinski, and Niven/Zuckerman/Montogomery. I really like them but I am not sure what book would be best for my plan to study additive number theory. Ireland/Rosen looks like it emphasizes algebraic aspect and assumes familiarity with elementary number theory from readers, Hardy/Wright and Apostol looks like an introduction to analytic number theory (which I am doubting if it is better idea to just start with additive number theory), etc. Currently, I fear that choosing wrong book might kill my curiosity to the number theory. What books do you recommend to prepare for analytic number theory?", "label": 1}
+{"snippet": "I hope this is the right word to use. To me, these forces seem kind of fanciful (except for General Relativity and Gravity, which have a geometric interpretation). For example, how do two charged particles know that they are to move apart from each other? Do they communicate with each other somehow through some means? I've heard some people tell me that they bounce together messenger photons. So does one electron receive a messenger photon, go, \"Oh hey, I should move in the direction opposite of where this came from, due to the data in it\", and then move? Aren't photons also associated with energy, as well? Does this type of mediation imply that electrons give off energy in order to exert force on other electrons? Every electron is repelled by every other electron in the universe, right? How does it know where to send its force mediators? Does it just know what direction to point it in? Does it simply send it in all directions in a continuum? Does that mean it's always giving off photons/energy? I'm just not sure how to view \"how\" it is that electrons know they are to move away from each other. These questions have always bugged me when studying forces. I'm sure the Standard Model has something to shed some light on it.", "label": 1}
+{"snippet": "Is it possible to let LaTeX manage minipage placement similar to how LaTeX manages figures and tables to be placed? This question comes from my previous question. I could move the minipages around manual for the best use of space but this becomes a hassle as the number of minipages increases. If possible, it would convenient for LaTeX to handle this task. Can this be done? Note: I want management like a float environment but not a float. As I stated in the linked post, I want to place minipages that butt up against each other across three columns. I dont want wasted white space (like a float would induce). I do want the the minipages to be able to rearrange themselves for the best use of the page without me going in and placing them higher or lower in the document.", "label": 1}
+{"snippet": "In case of a charged particle which is travelling at a uniform velocity, the electric field due to it at a given point doesn't change instantaneously . The reason for this delay in change of electric field , physically , can be explained as the time the electric field needs to propagate to that point, or, let's say, the change in electric field takes some time to propagate . I would like to know what exactly does it mean by a propagating electric field, and how exactly does it propagate ? What can we put forth as a reason to explain this propagation at a speed equal to the speed of EM radiations ? (I hope the coming up answers would comprise an important part explaining this physically. ) I guess we can derive the speed of EM radiation from Maxwell's equation ; can we show that this propagation too has the same speed ?", "label": 1}
+{"snippet": "Mass and energy are interchangeable. Does that mean time and space are interchangeable too? Reason for question: The only difference I can comprehend between matter and energy is that energy has no duration; a photon does not age (even if the universe does). Matter has endurance, and travels through time. Close to a black hole (in regions of high gravitational fields), time slows, and the speed of light (as measured externally) would seem slower (would give doppler-like transformations); effectively time is converted into space; a photon may \"appear\" to take a year to travel a few yards (again, as seen from outside). But from the inside (the photon's-eye view) a light year is still a light year. So, can an area of space a few feet across (externally) be a light-year wide (internally) (TARDIS sort of thing)?", "label": 1}
+{"snippet": "I've asked a question about olfactory's relation to observational and it got me thinking about other senses as well. There are five (or six if you're supernaturally believing), so, what are the exact term to fill out the blanks in the following? It's the bold parts that are interesting and I wonder if the already filled out ones are correct. Visual the beauty is in the eye of the beholder Audial the euphony is in the ear of the listener(?) Olfactious the fragrance is in the nostril of the inhaler Flavorous(?) the taste(?) is in the bud of the eater/taster(?) Touchy/sensefull(?) the feeling is in the hand of the caresser Supernatural the spookiness(?) is in the mind(?) of the medium(?) Kindly, please note that I've no intention to start using these expression outside when interacting with average people. I'm just curious about the linguistic translation between senses and my mathematical mind craves completeness. I know how to express all six sentences in English. I just don't know how to express those while \"following the suit\", so to speak. It's a purely and strictly academic curiosity.", "label": 1}
+{"snippet": "Take a look at the image below. At the point B a motor is spinning really fast in anticlockwise direction. The motor should be connected to a propeller (I didnt draw it) that will pull the bar upwards but let's suppose the propeller is not connected and the motor is just spinning really fast at X rpm. A person is holding the bar at position A. What torque or force will the person at A feel? The bar has length L. I know if I connect the propeller the bar will be pulled upwards (you dont need to tell me about this) but I am pretty sure it's gonna generate a \"reaction torque\" in the bar that will be transmited to the person holding at A. I would like to know the formula to understand the force/toque that A will feel.", "label": 1}
+{"snippet": "This part of the book says that, because the two liquids have the same pressure at the same height (that's true), then if a liquid has a higher height, the liquid would have more pressure at a horizontal line, and then the liquid would tend to flow to the weaker side. However, it isn't really pressure that drives the liquid, it is force (or acceleration). So the flow of a liquid shouldn't depend of the pressure, but the force at that line. And the force, depends of the diameter of the tube, because force is dependente of pressure. So in this case, the two tubes have diferente diameters, therefore the acceleration that drives the liquid from one place to another would depend of the diameter. Then we couldn't just say that the liquids tend to equate.", "label": 1}
+{"snippet": "So I have often read that, at least in e.g. northern Europe, in the colder seasons, there is not enough UV (-B) light arriving from the sun, so many people have not enough vitamin-D from that. At first I thought it was simply due to the sun \"shining\" for only a much shorter period of time in winter compared to summer and hence less possible exposure (not to mention that most of the skin area is covered then). But I just had a thought coming to my mind, thinking about that in the mornings and evenings, we mostly see red light here, the higher end of the visible spectrum not getting through. I am not familiar with the physics behind that phenomenon, but thought that the higher-end of the spectrum like the invisible UV light may not be getting through here for even longer parts of the day towards and away from high noon, and that in winter, the part of the day where UV gets through is maybe very narrow and that's why it's said not to be enough. Is that correct? And how exactly does this work physically?", "label": 1}
+{"snippet": "Background: In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets. \"Measurement\" takes place when a screen is placed on one end, blocking one of the states. The final measurement we perform (spin state of particles exiting) is heavily dependent on whether we perform a measurement or not, whether by blocking particles exiting the device or by blocking particles by setting up a screen within a modified SG device The interaction between the particles and magnets should also exert a force on the magnets, causing them to move slightly. The motion of these magnets seems to not affect the outcome of the experiment significantly, yet that would imply that the motion of the magnets could be measured without affecting the outcome of the experiment. This seems at odds with Heisenberg's uncertainty principle, that we are getting information for free. My Professor tells me that the force exerted on the magnets by the particles is so minuscule that it cannot be measured (I assume it is similar to how we can't measure particles' momentum and position simultaneously, because any photons we shoot at the particle will end up imparting change?) What's going on here? I wanted to double check here and see where I went wrong with my assumptions.", "label": 1}
+{"snippet": "How are Superposition and Entanglement related? I don't know much of Quantum Mechanics. I am CSE student and got started with this Quantum Computing. It is interesting! If anybody can help me on this, without digging deep into mathematical details. \"The principle of quantum superposition refers to pure states of a quantum system. One considers a primary beam of quantal entities that passes into a primary beam splitter or quantum analyser that has multiple output channels. A beam has a pure state when every one of its quantal entities passes into one and the same output channel. A primary beam with a pure state is passed into another, different, secondary beam splitter or quantum analyser. Then the emerging quanta are probabilistically in its several output channels. These several emergent, intermediate, beams are respectively pure with respect to the secondary analyser. They are then passed to respective copies of the secondary analyser, arranged so as to bring them together into a single reconstituted beam. That beam is then passed to a copy of the primary analyser. In general, it will be probabilistically split into the several output channels.\" - Wikipedia I did not get that! Any help is appreciated.", "label": 1}
+{"snippet": "There are lots of ways to apply the mean field method to deal with the Ising model whose ground state is a ferromagnetic state. Hence, it is easy to find the order parameter named magnetization to describe the mean behavior of spin-spin interaction. But, in the antiferromagnetic Ising model, the ground state is an antiferromagnetic state, and I realize it is difficult to find a parameter which effectively describes the mean interaction. If I choose magnetization similar to what we did in Ising model, then, I find it is zero, the mean field is always zero. I get nothing from this mean field. I cannot find a direct physical parameter describing the system to replace the spin-spin interaction. Does this imply that the mean behavior of spin-spin interaction is always zero? Is there a mean field method to deal with the antiferromagnetic Ising model? I hope you can help me, thanks!", "label": 1}
+{"snippet": "My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an equation, but that's about it. Similarly, I can follow arguments that pseudovectors behave differently in \"mirrors\" than vectors. But my response to this is always: Okay, so what? When would I ever \"do physics\" in a mirror? The usefulness eludes me. I'd like to gain a better understanding of the importance of this difference. When is it useful for an experimental physicist to distinguish between the two? When is it useful for a theoretical physicist to distinguish between the two? I believe symmetry is important to at least one of these, but would appreciate a practical rather than abstract argument of when one has to be careful about the distinction.", "label": 1}
+{"snippet": "We are two partners about to launch a product that is currently called \"Coralline\". We are inspired from the animal and its habitat in underwater. Since this will be an international product I am having second thoughts about this word because it is hard to pronounce and transcribe for non-native English speakers. Also I believe it is not a commonly used word in English so even native English speakers will not grasp the meaning at first glance. I am looking for a word that resembles Coralline or coral reefs, like \"seaweed\" etc. My criteria are: Unique Easy to remember Easy to spell Any help would be much appreciated. Additional information: We ended up with Coralline through a research on fractals. That might be a cue for any suggestion. We are going with underwater/reef theme some words related to that can also help.", "label": 1}
+{"snippet": "I can understand the causative form (quite less frequently, we simply say causal verb) with make and get but when used with have/has, it sometimes makes me think differently. Of course, I can understand the construction like the following. I had a barber cut my hair yesterday. In its passive form, it can be written as I had my hair cut yesterday (by a barber). I can also understand that the preceding sentence (passive construction) cannot be rewritten as follows. I had cut my hair yesterday. If it's modified in this way then both the sentences have a significant difference in meaning that I can understand. The thing I don't understand properly when a bare infinitive is replaced with an infinitive in such kind of constructions, such as. He has his wife cook dinner for him. What happens, if the bare infinitive i.e cook is replaced with an infinitive like the following. He has his wife to cook dinner for him. At a glance, you will be able to understand the difference between them but for me, it's not English but it's my native language in which as far as I know there is no difference between these two sentences and even the causative construction is simply made by just using some suffixes to the main verb in a sentence. So please take it easy. Could you please expose the important difference between these preceding two sentences?", "label": 1}
+{"snippet": "Referencing Stephen Hawking's recent paper Information Preservation and Weather Forecasting for Black Holes and this question. I understand concept of holding the information on the apparent horizon of a black hole for later release in the form of garbled radiation, but how is it that this differs ( if at all ) from the Hawking Radiation generated by the Unruh effect near the horizon? My, possibly flawed, train of thought is that the aforementioned black hole sucks in everything in matter in it's immediate surroundings, and due to the Feynman diagram that corresponds to particle-antiparticle pairs spontaneously popping into existence with one particle on the other side of the horizon, the energy from the matter sucked in, is imparted to which ever particle is outside of the event horizon to repay the energy debt to the Universe.", "label": 1}
+{"snippet": "I'd like to know why in a parallel loop, the voltage, along with the current, isn't divided. e.g. in this image from a youtube video the voltage in parallel loop is the same across both resistors, for some reason this seems counter-intuitive to me. Also later on in the video, the resistance was proportional to the voltage. I talked about this in class today, there was some debate on whether the voltage is inversely or directly proportional to the resistance. My argument was that because the resistance is higher, there must be less voltage going through at that point. So as resistance increases, voltage drops, showing an inverse proportion, but then someone in the class brought up the equation V=IR, in the circuits we've looked at, the current is seen to be the same throughout, in series, so it can be simplified to V=(K)R, V(proportion sign)R which would mean as Voltage went up, so would the resistance. Then we were talking about this in parallel, and things got more confusing, he spoke about the current not being the same across both resistors therefore we cant use the above rule, which I understood, but he didn't explain what actually happens. I'm getting confused writing this question.. perhaps I should do a few practice questions. My teacher was worryingly also unsure. I Hope this question doesn't come across too ambiguously.", "label": 1}
+{"snippet": "I have joined a grammar MOOC starting with an introduction to English tenses. One of the practice questions left me confused. The question is as follows: Do these two sentences have similar meaning or different meaning? Julie has studied French for two years. Julie has been studying French for two years. I'm not sure how similar is similar, but having a questionable sense of the language I think I should follow the rules. Grammar books state that Continuous tenses are designed to emphasise duration. If an author finds relevant to emphasise the duration, this semantic or emotional meaning is relevant to the reader. Both of the sentences deliver information about the duration. I'm not sure if there exists any difference in connotation or the second sentence is an example of 'grammatical tautology'.", "label": 1}
+{"snippet": "(Too) Long ago, I had some problems with some equation. I wanted them to look like this (this is how they looked in LyX), but when compiled they looked like this: . What botheres me compared to how it looks in LyX is that way too much spacing between the columns is used in the compiled version. there isn't a space after the \"=\" the last column is aligned to the right (not to the left, as I wanted it to be). Because only now I found time, to post this question here, I unfortunately don't remember the name of the environment used for this (I only kept the screenshots). But I remember that I tried out all of the AMS environments( align, alignat etc.) as well as the eqnarray environment and not a single one provided me with an output that looks like the one in LyX. Has anyone an idea how I could get LaTeX make these (test)equations look like the LyX screenshot ?", "label": 1}
+{"snippet": "Personally I learned Physics in high-school and found it very interesting, I read up a lot about physics in my free time. Personally I am also a programmer which I think is also good when it comes to Physics. Now I want to start studying in a university and my dilemma right is mainly between Math/Computer Science/Physics. It's possible to do a degree in just one or combine two of them. Currently, the subjects that I find most interesting in Physics are the most advanced ones: Relativity and most of all Quantum Mechanics. I've always been fascinated with materials, what they are formed of at the most elementary level. Now for the real question. From what I usually read it's very hard to get into physics research, of course it's not impossible but still I'd like to ask: Are there careers that are related to quantum mechanics or relativity that are not as a researcher? If so, what are they? can you give examples?", "label": 1}
+{"snippet": "Why does the definition of an irreducible element require us to be in an integral domain? Why can we not define an irreducible element exactly the same in a commutative ring that is not an integral domain? We have that an element is irreducible if it cannot be written as a product of two non-unit elements. Unit elements are well defined and unique in a commutative ring that is not an integral domain, so I cannot see that being the problem. I've proven a proposition of my own design (probably well known and elementary, an definitely trivial). I used irreducible elements, but otherwise nothing that requires me to move from a commutative ring to an integral domain. Do irreducible elements really require me to be in an integral domain?", "label": 1}
+{"snippet": "I am not sure whether the sun originally emits everything in the electromagnetic spectrum, (whatever the relative strengths of each portion might be), but I do read that many waves, including gamma / x-ray, and UVC, are filtered or 'converted' to heat after travelling through solar plasma and atmospheric layers like ozone. But what I am interested in is the lower end of the spectrum (frequency-wise) - like those we ourselves harness for communication. Does the sun emit low frequency radiation (below infrared), in the first place, and if so, how much of it - if any - actually reaches us on Earth within that same range? I am guessing it is either none, or only a very small amount as otherwise I assume it would interrupt severely with our own radio communication here on Earth.", "label": 1}
+{"snippet": "When a nuclear device is detonated at ground level, we see the familiar mushroom cloud, which is undoubtedly caused by the weight of the atmosphere suppressing the upward thrust, causing the debris and dust to be curved down back towards the Earth. The horizontally propelled mass again does not travel very far from the point of detonation. One would expect the nuclear explosion to escape from the atmosphere, after all Gravity is thought to be the weakest force? But in reality, gravity is the only force and both nuclear and magnetic forces would not be present without gravity. So are we in error comparing like for like, when in reality we are comparing what are currently thought to be separate forces? Gravity is responsible for holding all particles, from sub atomic to planets and suns together and the nuclear explosion merely illustrates it perfectly?", "label": 1}
+{"snippet": "While googling about whether \"atheist\" should be capitalized, and skimming past posts by people blogging about atheism rather than about English grammar, I came across http://uwf.edu/writelab/reviews/capitalization/ It says [Capitalize] Religions and religious terms Examples: Catholicism, Hinduism, Buddha, the Bible, Christian, the Ten Commandments, Baptist church, Mt. Zion Methodist Church NOTE: Do not capitalize the following: Examples: church, communion, atheist, agnostic, spirituality but I don't recall hearing of such a prescription before. Wouldn't most of the examples listed be capitalized because they're proper nouns? Are there good examples of words being capitalized solely because they're religious terms? I'm mainly interested in modern English, rather than days of past where a lot more words were capitalized than they are nowadays. Somewhat related: When should the word \"God\" be capitalized? - use \"God\" when referring to the name of the god of Judaism and Christianity (a proper noun), but \"god\" when referring to the general concept of a deity (common noun).", "label": 1}
+{"snippet": "Say you have an author who has a lot of random personal stories from their life, all interesting, but don't stand on their own to be an interesting, single story. The author decides, \"why not combine them all into one story?\" Well, that sort of becomes an autobiography, I guess, if you actually tell the story in a more chronological way that follows the timeline of their life. What if the author decides not to do everything chronologically? Basically, taking these non-fictional stories, reordering them a little, and placing them all into a fictional character's life, somewhat shortening the timespan in the process? Basically, the story itself and the character would be fictional, but each separate story within the fictional story is non-fictional. Does the fictional part of the story trump the non-fictional parts of the story and just classify the entire thing as fiction, or a novel? Or is there any special word or perhaps genre that would be used to better identify something like this? Ultimately, is there a word to identify a fictional story made up of non-fictional stories? I've seen this similar question, but it talks about historical settings in a novel, mainly the non-fictional location a book is set in. I can't imagine that's really the same thing, as the situation I'm outlining is kind of the opposite. The stories themselves are non-fictional, but the setting, location, characters, etc are all fictional.", "label": 1}
+{"snippet": "I am looking for a figurative or graphic expression to describe the minimal luggage content, fast to pack, or that you always have with you, without which you would feel less safe when travelling. The expression should be concise too. When I take a plane, and since luggage in the cargo area can get lost, I generally have a toothbrush and underwear. With those, I am not afraid of spending an unplanned night in an hotel in a unknown town. I would say in my language that I have my \"pants and brush\", as a short for \"a second pair of underpants, socks and a toothbrush\", but this does not seem colloquial in English. In other words, is there a colloquial figurative expression for what one carries when travelling light?", "label": 1}
+{"snippet": "I'm taking the curl of the deviatoric stress tensor in index notation, and I've ran across something that I can't seem to be able to simplify. The issue is shown in the following portion of the curl operation: The first two terms on the right hand side should be zero because the curl of a scalar and the curl of a gradient of a scalar are zero. The last term will then be given by: Since U has a subscript m on that last term on the RHS, then I can't just define it as the gradient of the vorticity like I did on the first term on the RHS. Is there any further way to simplify it or does that just have to be the curl of the gradient of velocity?", "label": 1}
+{"snippet": "The setting: Imagine the scenario where I am searching for something and once I find it I identify it, then afterwards when I no longer need it I discard it. If at some point I need to identify it again I perform the search again and will succeed since it's still there. The problem: The noun for the process of identifying something would most likely be \"identification\". I'm pretty sure the word \"discardation\" is not an actual word, and \"discard\" or \"discardure\" just leaves me wanting for something less overlapping and more commonly used. The Question: What would be a nice noun to describe the process of \"discarding\" something temporarily. Looking at the thesaurus words like: remove, reject, cancel, reject, relinquish and the like come into play but I feel like those words have a more dramatic impact imposed behind them than I would like to portray. Something similar to dislocate perhaps, with an intention to remove. Disconnect seems like a good option yet I feel like I would have to change identify to connect if I choose to do so.", "label": 1}
+{"snippet": "Although I know the clear meaning of commonly used prepositions in English, sometimes, I'm a little confused with them and cannot understand the difference between them. A week or so ago, I asked a question on StackOverflow which was titled by me as follows. Varargs in method overloading in Java. In this simple question title, Java is a programming language as everybody knows, \"Varargs\" (abbreviated to variable arguments, specifically variable number of arguments) and \"method overloading\" are two concepts used in the Java programming language. Before I asked the question, I was not sure at all whether the question title should have been as it is mentioned above or it should have been modified as follows. Varargs with method overloading in Java. Which one is grammatically correct, both or none of them?", "label": 1}
+{"snippet": "Many of the books I use are parts of series. biblatex gives you more fields to add bibliographic information to than BibTeX does, but it has no fields appropriate for the editor of a series. If I use the EDITOR field, the bibliography will (by default) print edited by, which doesn't give the right impression of what the role of the series editor is. I'm wondering if there is any easy way to add a new field SERIESEDITOR, which will make biblatex by default print its content preceded by Series edited by or make sure that whatever is in SERIESEDITOR gets printed directly after the name of the series, such that is says something like [Name of series], edited by [series editor]. In other words, is there any way I can do this in the preamble of my document, without having to venture into writing new bibliography styles?", "label": 1}
+{"snippet": "Pardon my ignorance, but I am really interested in understanding the quantum mechanics and it's interesting implications, but clearly I don't, since I keep coming up with violations to many physics theorems. In particular, the delayed choice quantum eraser experiment is of interest. Consider the wikipedia diagram, In this experiment, there is random chance for the path that will be taken in the lower part of the diagram. Hence, one must wait till the end of the experiment and then (using the coincidence counter) filter the information of each photon's path. Hence, the patterns one sees are only known after the experiment. The Quantum entanglement is only verified after the experiment is completed. But instead of allowing random chance, what if you forced all photons to go to a particular path. To my understanding, if PS was modified (see the following diagrams) into a switch that forced either \"separate slit\" detection or \"interference\" then would that allow \"faster than light\" communication?", "label": 1}
+{"snippet": "On this site, people ask questions and then answers and proofs for those answers come from readers. Readers mark the best answer and then people focus on the next interesting topic. Sometimes, a question will have many answers with proofs from different points of view and people commenting on whether the proofs are valid or not. My question is this, \"given a statement, how many valid proofs are there for that statement?\" For example, if one is interested in the irrationality of root two there are many proofs available, all equally valid, some longer than others, some requiring basic math skills, others requiring in-depth knowledge. We have a proof for Fermat's last theorem, but how many other proofs are there? Is it possible to look at a statement and know that it has a finite number of proofs or an unlimited number?", "label": 1}
+{"snippet": "I would like to make the bubbles in my soda drink last longer. For example, one good thing to do is to keep the bottle shut when you don't drink. But what else I can do? Should I try to minimize the surface between the drink and the air from the bottle? How about the surface of contact with the bottle? The bottle should be made of glass, or plastic? Does the temperature matter? Should I keep the bottle in a vertical position, to ensure more pressure at least for a part of it? Other, less realistic methods, are to keep it under pressure all the time, use a carbonating device, or drink it on the ocean floor. Or never open the bottle :), but assume that I want to open and drink from time to time.", "label": 1}
+{"snippet": "I'm trying to understand where energy is located in a quantum field world. For force fields, there are conserved properties that (in my mind's eye) are always stuck in that field. These arise from symmetries in the fields, by Noether's Theorem. As such, I imagine that properties such as charge can move around in the field but never leave or appear. Noether's Theorem also explains conservation of energy as related to a symmetry, the invariance of the laws of nature at any point in time. It seems fair, then, to say that energy is a property of the field that makes up spacetime itself. When a charge is carried by a particle, that particle can have different masses with equal charge. I am not sure how I should picture the difference in the fields. A muon, for instance, has both mass and charge. My question is then, which fields contain the muon's properties? Is it all in the muon field? And does this mean that both charges and energy can transfer between fields? Or is a muon a sympathetic coupling between the muon field, EM field (charge) and spacetime curvature (energy)?", "label": 1}
+{"snippet": "Theoretically, a change in either electric or magnetic field will cause a current to flow , I am already familiar to Faraday's law of electromagnetic induction, so I tried to search about producing a current using a varying electric field, didn't find anything, I found an interesting apparatus though: Tesla's electrostatic induction apparatus. My question here is about Lenz's law, will this law be applicable here? I know the law is in case of magnets , but I tried to imagine what will happen if we tried the coil magnet situation where approaching coil to the coil a resisting force will develop , but if we replaced the magnet with an electret (electrostatic equivalent of permanent magnet), as it approaches the loop the side near the electret will obtain a partial charge opposing to charge of the electret causing it to approach faster (the opposite of what happens with a magnet). In the end of the article Tesla wrote The output of such an apparatus is very small, but some of the effects peculiar to alternating currents of short periods may be observed. The effects, however, cannot be compared with those obtainable with an induction coil which is operated by an alternate current machine of high frequency, some of which were described by me a short while ago. Why was the output of such an apparatus small? Does an electric field have a smaller influence on electrons than a magnetic field?", "label": 1}
+{"snippet": "I just met with a very basic question. (Might even sound silly!) My textbook kinda says(not exactly), 'Whatever flows is a fluid'. That got me wondering because we are creating a whole category of matter just because they flow! So there must be some significance to 'flowing'. That further led me to ask why in the first place should we say liquids and gases \"flow\" and not \"move\"?! It seems to tell me that there should be a major difference between the physics of flow and movement. What is it? PS:- I don't want the difference in meaning from a dictionary but a scientific difference. Please don't get too mathematical. I haven't acquired good mathematical skills YET. Edit:- Okay. Since a comment below says \"Movement is actually seldom defined very rigorously\", I suppose I must refine my question here. Consider someone is saying that a box moves on a table as you applied a force on it. Now why is that person saying it 'moved' rather than it 'flowed', here? What is the difference between flow and movement in this case and how can we generalize the idea?", "label": 1}
+{"snippet": "I have a hard time understand the statement that When you only look at the classical limit or classical physics, string theory exactly agrees with general relativity Because from what I know, String Theory assumes a fixed space time background (ie, all the strings and membranes interact in a fix background, and their interaction gives rise to fundamental particles that we observe), but General Relativity assumes that the space time background is influenced by what is in it and the interaction between them. Given that both have very different assumptions, what do string theorists mean when they say string theory agrees with general relativity in a classical limit? Or more specifically, how does string theory--a fix spacetime background theory-- reconciles with the general relativity on dynamic spacetime background part? I can understand a fix, static spacetime in the context of changing, dynamic spacetime background, but I cannot understand a chanding, dynamic spacetime in the context of a fix, static spacetime background.", "label": 1}
+{"snippet": "What are the rules for typesetting superscript, subscript and fractions (as in a/b but with an horizontal fraction bar)? I am centring the subscript on the baseline, the superscript on the cap height and the fraction bar on the x height. Latex appears to be doing that as well. What I haven't figured out is how to position the numerators and denominators relative to the fraction bar. I know the bounding box of the numerator and denominator, but how much spacing should there be with the fraction bar? I can access all the regular metrics of the font (ascender, descender, leading, cap-height, x-height). Edit: (based on appendix g) As far as I can tell, the distance between the fraction bar and the numerator/denominator box is three times the fraction bar thickness. It seems to me that this would not produce a symmetrical output if the font descent value is different from the ascent value minus the cap height value. I mean the apparent distance between the fraction bar and the bottom of the numerator text, and, the distance between the fraction bar and the top of the denominator text. Visually either the numerator or denominator would appear further away from the fraction bar even if both contain the same text.", "label": 1}
+{"snippet": "The idea is that the difficulty of the game of chess is derived primarily from the asymmetry between the king and queen. all other chess pieces are arranged symmetrically and can move symmetrically, then, if there were two queens (or two kings) instead of a king and queen for each player, the game would be exactly symmetrical. The idea is that, in this case, if the second player repeats symmetrically the moves of the first, the outcome should be a draw. But I'm not able to prove this (and perhaps it is not true) but it seems that the symmetry should introduce a simplification in the game who may moreover allow to define a strategy. My knowledge of game theory is very poor, but I'd like to know if there are any studies on this symmetrical variant of the chess game.", "label": 1}
+{"snippet": "I have gone through a lot of seemingly similar questions/issue but have not find a solution. Since we are working as a group there are some that prefer to write using MS Word-EndNote. I have all references in BibTeX and these are updated from time to time (when something moves from pre-print to actual publication with addition of issue/page etc, minor corrections in citations in the main database, etc). I have no problem importing my automatically generated BibTeX file into EndNote. However, this BibTeX file gets updated from time to time and I would like to keep the EndNote database up to date as well. Re-importing the new BibTeX file into EndNote makes the process unnecessarily difficult, since you would end up doing deduplication of the results. Does anyone have a solution? There is a willingness to change to Zotero, so if you have a solution using Zotero, I'm also quite interested. Simply put: .bib file that is updated from time to time, is there a way to keep my EndNote/Zotero database updated based on this .bib file?", "label": 1}
+{"snippet": "I am writing a technical research article. I have an experiment where precision can be easily determined (bid-ask spreads for the economists). Calculating some formula twice based on the precise observation of the upper bound and the lower bound does change the results (obviously) and is not negligible, but it does not negate the theory that is underlying. That is, the effect of the measurement error is clearly visible, but in general the theory can still be accepted. How do i express this in a concise way? Thanks. edit: Per request, more details. I can observe market values, but with limited precision. I only observe two values, bid and ask, and the true value lies between those. Calculating measurements using bid-values gives me different results than using ask-values. Both results confirm the theory I'm testing. The difference exists, but it does not fundamentally change the conclusion that the theory itself can be confirmed. Is there a concise expression for 'confirms, but not as strongly' or 'doesn't negate, but differences are considerable'? I guess it is obvious why I need a concise expression...", "label": 1}
+{"snippet": "John Rennie's answer to this question got me thinking about the water supply in a house. I know that water supplies are normally operated at an over-pressure with respect to atmospheric pressure to make sure that if you open the tap the water will flow out due to the lower pressure at the exit of the tap (including a correction for pressure losses due to the plumbing and potential height differences). What I am wondering is how adjusting the tap results in an adjustment of the flow rate from that tap if the water pressure in the main supply is a constant (probably by approximation)? Because in that case the pressure upstream is fixed, the pressure downstream (atmosphere) is fixed so pinching or opening a valve should not change the flow rate. Obviously it does change the flow rate so there must be something else going on. The only thing I can think of is that the water supply somehow acts as if there are parallel connected (hydraulic) resistances as illustrated in the schematic below which makes sure that the distribution at the flow split can be adjusted. Is that the right thinking or is there a different argument why the flow is adjustable? (The dashed line indicates some way of rerouting the water back to the mains, although that cannot be a direct connection because that would allow a pressure drop over this section)", "label": 1}
+{"snippet": "Wikipedia mentions that: Some languages flexibly integrate onomatopoeic words into their structure. This may evolve into a new word, up to the point that it is no longer recognized as onomatopoeia. One example is English \"bleat\" for the sheep noise: in medieval times it was pronounced approximately as \"blairt\" (but without an R-component), or \"blet\" with the vowel drawled, which is much more accurate as onomatopoeia than the modern pronunciation. Did bleat really lose its onomatopoeic character? Is \"baa\" used instead in all situations? Furthermore from the book \"A Grammar of Iconism\" By Earl R. Anderson: According to the passage above: When onomatopoeic words are used as verbs, do they lose their onomatopoeic character? ( not all of them but some of them in time? or depends on the context?) Can we still say that shiver, growl and bleat are onomatopoeic words? Or did they inherit their onomatopoeic label from their more mimetic versions: brr, grr and baa?", "label": 1}
+{"snippet": "When using the method of action variation to establish GR field equation in one of the steps we use Stock's theorem on an arbitrary manifold to show that one of the terms contributes nothing to the variation wrt the inverse metric. See for example the Wikipedia entry on Einstein-Hilbert action. Most texts that I read, without writing the actual steps of calculations, simply say that variation at infinity vanishes and hence the above mentioned term vanishes. Can someone please do the actual calculation involving the application of Stoke's theorem for an arbitrary manifold here, which I do no see in textbooks, as I am confused, in particular, are we assuming the variation of the inverse metric or its covariant derivative to be zero at infinite timelike or spacelike coordinates?", "label": 1}
+{"snippet": "In this question the issue came up as to whether there's any difference in the level of politeness/correctness involved in I'd rather not say as opposed to I'd prefer not to say. My own gut feeling is the prefer form is a bit more \"formal\" (and thus arguably more correct/polite). This NGram shows that I'd rather occurs far more often than I'd prefer. Partly that's just because the rather form is more common, but the difference is far less marked with the more formal I would rather/prefer. I take this to mean rather is more suited to casual use/conversation when used with this meaning. It could be lots of verbs besides say, and I don't think the not is necessarily relevant here either. But usages vary for certain alternatives - for example, go blind only seems to work with rather. That's just my opinion. Does anyone have arguments/evidence/sources to either back up or refute the proposition that I'd prefer not to say is more formal than I'd rather not say?", "label": 1}
+{"snippet": "I'm about to dive into LaTeX in preparation for writing a (technical) Master's Thesis. Since I'm kind of disappointed with the disregard to typography that is sometimes shown in such works I want to do it better, and just picked up The Elements of Typographic Style by Robert Bringhurst. Thanks to LaTeX and clever templates there are of course many things I no longer need to worry so much about, but there were interesting notions such as using small caps for acronyms and text figures (\"old-style\" small numbers), which I'll likely use rather frequently. I've found the syntax for these two, but I fear there are other aspects that I should also know right from the beginning so that I correctly set the markup right away and don't later need to go through the document for all that stuff. So long story short: Does someone know a nice guide on using LaTeX in regards of good typography, rather than all the technical aspects of constructing and structuring a document for which there's plenty of reference?", "label": 1}
+{"snippet": "This is a soft question. It's extremely commonplace for mathematician's to refer to work as \"elegant,\" \"beautiful,\" and I've seen many compare the process of doing mathematics to painting, or playing music. I think that for the most part, I can understand how certain theorems, formula, or general theory can be evocative, surprising, or maybe just confounding. However, what is less clear is how far the analogy of art can be extended. Art, as much as it makes one elated or excited, also has the capacity to elicit feelings of sadness or melancholy (or any further scope.) I was wondering if this is the case for mathematics as well. I know certainly some people have cited the proof for the four-color theorem as \"disappointing,\" (although I don't have a suitable background to have a stake in this) but this doesn't seem to have quite the same flavor as a musical masterpiece that makes one feel negatively. I cannot think of such an experience that I have had, and I'm curious to see if maybe there are some examples that others feel strongly about. Here are some non-examples: Freshman's Dream: I'm not really interested in the feeling of something you'd hope works, but winds up being false because of an error Math that's too difficult for you to understand. edit: I was surprised to see such a decidedly negative response to my question. Maybe I have it all wrong, in which case, I'd also like to be corrected with a convincing argument.", "label": 1}
+{"snippet": "I think this is a genuine math problem. And it's somehow related to knot energy but not directly solved by the latter. Why can't I tie a hard knot on a rope of infinite length? By infinity I mean you never pull back either ends of the rope. And I attentively add a constraint to the rope that the rope is smooth thus no friction. So the problem is only about the topology (not exactly) of that rope. I cannot think of a better word than topology since the topology of the rope should never change. But apparently I don't know a better one. In my preliminary thoughts, there should be a solution that performs a integration involving the direction and twist of the rope along the infinite length. And the sign of the integration determines whether it's a hard knot or not. And the fact that you cannot pull back the end means you cannot change that sign.", "label": 1}
+{"snippet": "I was soldering an LED when accidentally the soldering wire touched the LED's other Pin while the soldering iron was touching the other and the LED lit up, not bright but bright enough to be seen. I did it again to see did it actually light up, and it did. I noticed my bare feet were touching the ground so I raised it to observe, the LED got dim. Another thing I observed was that no matter what pin (cathode or anode) touched what (soldering iron or soldering wire), it lit up. Why did it lit up? I know that heat causes particles (electrons in this case) to move (kinetic molecular theory), but does it move enough to make an LED light up? As a diode it has a voltage value after it allows current to flow, was the heat enough to make it past that limiting voltage? (I don't remember the actual term). Why did the polarity not matter? I have no clue about this. LED like any other diode is biased means allowing current flow in one direction, than why does this happen? Does the electron movement not matter in this case?", "label": 1}
+{"snippet": "Sometimes I hate classes for mathematicians. It is not their precision and formality in building the concepts, but they never give a motivation. So in the course my professor started right with the definition of vector space, assuming I suppose that everybody knows what he is talking about. Well, reading some books for beginners like me I've realized that vector spaces are actually a generalization of working with the properties of Euclidean spaces. Now the topic is about linear transformations. I understand the definition, they are special cases of mappings. Well, the thing is that I don't know why the definition has to be so, what is the real motivation for such a definition?. what is behind the meaning of 'linear'? My first impression is that maybe it has something to do with just preserving the operations of vectors, though I don't know why. What makes linear transformations to be special compared with those that are not linear? Sorry for this question, maybe it is too naive but it's really important to me.", "label": 1}
+{"snippet": "I had an interesting conversation with CuriousOne the other day about the question Experiment that demonstrates the wave-particle duality of electrons. I thought that wave-particle duality existed, CuriousOne thought it didn't (whether CuriousOne thought this wasn't true for both light and matter, or just matter I'm not really sure). Some of the comments were really interesting, and I wanted to know what some of the physicists here thought. The comments on the question are just below the main question, and are just below my answer to the question (now moved to chat). Please don't close this with \"not enough research\" as the reason, I did look into it, but some of CuriousOne's comments left me kind of confused. In terms of people thinking this is a duplicate: I am asking whether there is experimental evidence for electrons having a wave-particle duality (this duality being like the one light has) and whether the double-slit experiment is an example of experimental evidence for this. Question: Was de Broglie's hypothesis that electrons (and other matter) have wave-particle duality correct? Does the double-slit experiment prove this, or have anything to do with this? What is some experimental evidence for de Broglie's hypothesis? Thanks!", "label": 1}
+{"snippet": "In elementary school, I was taught the rhyme: \"i\" before \"e\" except after \"c\", and in words like \"neighbor\" and \"weigh\" Obviously this means that \"ei\" is used in \"deceive\" (it comes after \"c\") and \"sleigh\" (\"gh\" follows it). The word \"weird\" does not follow this rule, and I have always thought that to be weird (please pardon the pun). It has neither a \"c\" nor \"gh\", so why does it have this \"ei\" vowel combination instead of \"ie\"? While writing this post, I noticed that \"neither\" also disobeys the rule, just like \"weird\". At first, I thought that maybe the \"English gods\" thought it would be a funny meta-joke to let \"weird\" have a weird spelling (like how \"awkward\" awkwardly has a \"k\" surrounded by two \"w\"s), but apparently there are other words as well!", "label": 1}
+{"snippet": "To start with, I have almost no any experience in the theory of finitely additive (f.a.) measures, but I work a bit with countably additive (c.a.) ones and find the theory in the latter case amazingly beautiful. My concern is that at the moment measures have been introduced as an extension of such notions as area and volume, I can understand that the additivity property came alone naturally. However, I believe, that at that moment the choice f.a. vs. c.a. might not have any strong arguments. Later, it appeared that in many cases the space of c.a. (but not f.a.) measures is the dual of a corresponding space of all bounded continuous functions. Since the latter is a pretty \"natural\" object, I would say that its dual is \"natural\" as well. Would it be right to say that c.a. measures are more \"natural\" than f.a. ones, or that it appeared to be more successful/useful, and if so - why do we need the f.a. measures? I hope, that a bit loose formulation of the question still allows for an answer.", "label": 1}
+{"snippet": "I recently started reading the book Multiple View Geometry by Hartley and Zisserman. In the first chapter, I came across the following concepts. Projective geometry is an extension of Euclidean geometry with two lines always meeting at a point. In perspective, geometry parallelism does not exist. Then he goes on to explain how the points at infinity in the world like the points at the horizon appear as a line in the image of the world taken by a camera. Then he says a line which I cannot relate is the following.. The geometry of the projective plane and a distinguished line is known as Affine Geometry and any projective transformation that maps the distinguished line in one space to the distinguished line of the other space is known as an Affine transform. I have the following questions Is the camera plane the projective space of the real world? Is the line which is the image of the horizon the distinguished line? Whenever we do an Affine transform do we need to look out for a distinguished line? Why does just a distinction of the geometry a line in the perspective plane make the geometry an Affine geometry?", "label": 1}
+{"snippet": "I've landed in a physics debate amongst bike mechanics. In a typical bicycle hub you have a simple bearing; the cups are set in the hub, the race (cone) threads onto the axel and there are just loose ball bearings in between (no ball retainer). When properly adjusted, there is no play in the system, and the axel turns smoothly. I imagine this is an elementary question, but when you put weight on the axel (rider on the bike) is the force concentrated on the bottom of the cone, or is it evenly distributed to all of the balls around the cone? What forces are at work in a bicycle hub? I made this image for the sake of convenience if anyone feels so inclined to be awesome and use it to make a diagram/illustration: Exceptionally illustrated answers will be worthy of additional bounty (more up-votes means more bounty to give :) I will offer a bounty of everything I have for an exemplary answer to this question).", "label": 1}
+{"snippet": "Is it correct, and safe to say, that -- generally speaking -- verbal constructions with \"with' are to a certain extent more widely and commonly used in AE than in BE and other varieties of English ? E. g. Speak/talk with (as opposed to the shared speak/talk to); visit with (=chat/converse with); meet (up) with (originally chiefly AE); get back with someone (as opposed to the shared \"get back to\"); stick with (as opposed to the shared \"stick to\"); check back with (as opposed to \"check back to\"); compare with (as opposed to the shared \"compare to\"); correspond with something (as opposed to the shared \"correspond to\"); interview with someone (as opposed to the shared \"interview someone\"); consult with someone (as opposed to the shared \"consult someone\"); conform with (as opposed to the shared \"conform to\");(...)", "label": 1}
+{"snippet": "Before starting algebraic geometry, I got some understanding of Compact Riemann Surfaces which is more or less rigorous; and then I attended a couple of lectures on analytic geometry. I did not quite fully grasp the analytic geometry rigorously; but it stuck in my mind and this previous experiences helped me greatly when learning algebraic geometry. However I am not able to imagine what would be the precise analogue of Cartan's Theorem A for algebraic varieties over a field. There is the wikipedia article: http://en.wikipedia.org/wiki/Cartan's_theorems_A_and_B which tells me the precise analogue of Cartan Theorem B in the book of Hartshorne. And indeed it is really analogous. But it does not mention Theorem A. Note that here I am restricting the situation to varieties out of fear of any pathologies schemes might have.", "label": 1}
+{"snippet": "I have been trying to read about the energetics of observed supernovae for some time. And while the observed core-collapse supernovae have many scientific papers about them trying to estimate the energy released in different evemts like this one, I couldn't find similar reports for Type Ia SNe telling how much energy was actually released. All I could find about energy estimates for Type Ia SNe were different model of detonation and they are very close in the numbers they compute. So, is this lack of Type Ia SNe energetics because they are essentially the same and only one model can be applied to all of them ? I know Type Ia SN is the result of a thermonuclear runaway in a WD with a Chandrasekhar mass limit, so they should actually produce the same amount of kinetic energy for the ejecta. So is it true that all Type Ia supernovae observed share have similar released energy ? PS : I am concerned about kinetic energy more than optical and light curves, so the mass of the Ni produced and the luminosity is not important for me here.", "label": 1}
+{"snippet": "I was wondering if there has been any category theoretic advancements in the study of the Riemann Hypothesis and the theory surrounding it? This question is meant in the same vein as these questions, but specifically for category theory. These other two questions do not have any answers related specifically to category theory. EDIT: Just to be clear, and because Zhen Lin brought up a good point about category theory being mostly a language for mathematics: I understand that category theory is a language like thing, but it can still be useful in mathematics. I had in mind maybe an advancement in one of the fields related to the RH, in which category theory plays an important or central role. Or perhaps a category theoretic equivalent statement or something similar.", "label": 1}
+{"snippet": "One of my friend who stopped studying maths in high school told me once You study maths, can you help me fill my tax forms? In her mind, advancing in maths studies implied manipulating an increasing amount of numbers. The reality I faced was the contrary: I dropped numbers for some more abstract notions (i.e. letters and symbols). I wonder if a (putative) link between abstraction and use of numbers has been investigated. For instance, can we say that one area of mathematics is more abstract than another one just because it uses less numbers in its formulation? Or, is this particular domain of maths became more complex as it uses less numbers? One possible metric I think of would be the number of numbers per \"mathematical\" line. This question may not be within the scope of math.stackexchange, but I didn't find a more suitable site. Thanks!", "label": 1}
+{"snippet": "I have a ... pdf file, which contains figures of plots such as the following: Now the second plot isn't too hard to draw on TikZ (I assume... I hope? I don't have any experience apart from drawing circuits!), but it's figures like the first picture that I'm more worried about. I want to re-draw them in code (like in TikZ or any package really) so that they appear in higher quality than if I were to just take a screenshot and post that in my LaTeX doc. Are there any tools that can automatically convert images like these into code? It doesn't have to be perfect, I can tweak it as necessary, I would just like at least the basic code done so that I don't have to start new with every single one. Even examples found online don't really match up to something like the first picture, and I'd rather not go through mountains of examples/pdfs/how-tos to draw something relatively simple. So how can I tackle something like the first drawing in code easily, i.e. convert it to compilable code? Any help would be appreciated!", "label": 1}
+{"snippet": "I'm reading a Mathematical Logic book (A course in mathematical logic, Bell.M ) and the author is saying that the symbols of a formal language don't have a well-defined shape, he's claiming that they are abstract entities. I think he is saying that even though symbols are usually defined by its shape, the symbols of a formal language have 'abstract' shapes. He goes on explaining that we couldn't possible be able to define an exact shape in a formal language because that wouldn't be reproduceble in all metalanguages studying the symbols of that objective language ( the formal language ). He proposes them, that when we are studying a formal language ( objective language ) by means of a meta-language, and we want to reference the objects of the formal language ( its symbols ), we use as name, metalinguistic symbols. By doing this, we don't have to worry with the \"shape\" of the symbols in the objective languaeg when we are changing the meta-language that is studying the formal language, because the shape is not well-defined, they are allowed to vary with the meta-language. All in all, i think he is claiming that the symbols, lexicon or alphabet of a formal language, and hence the syntax is independent of its visual representation. I'm curious if this approach is worth to make and also if people are worried to make such distinction ( or is it only him ) ? Also, i would like to be corrected if i misunderstood the point.", "label": 1}
+{"snippet": "The thought experiment goes like this: Say there is some circuit which turns a lamp on/off with just a flick of a switch. Say its off; you flick it, it turns on; flick it again it turns off, and so on. So say you are conducting the experiment for two minutes. When the remaining time halves, you flick the switch; and when that remaining time halves, you flick again...This process goes on infinitely, until two minutes is reached. Mathematics says that the sum of all those remaining half-times will eventually tend to two minutes. And the outcome i.e. the final state is always unpredictable. We can't really know if its on/off. Lets not concern about the final state. What would we actually observe towards the end, few micro seconds towards the two minute mark? Wouldn't the lamp appear turned on? What would happen if the time between two flicks tend to zero?", "label": 1}
+{"snippet": "Imagine the following gedankenexperiment. Observer Alice is right here on Earth. Observer Bob is at say Alpha Centauri. A pair of maximally entangled qubits is formed with one qubit handed over to Observer Alice and the other sealed in a box on Pluto shielded from decoherence. It takes a few years for any signal to reach Observer Bob. Observer Alice measures her qubit and \"collapses\" it. To her, the pair of qubits is no longer entangled. However, for a few years, will Observer Bob think there is an entanglement? We have to be careful here. Once the qubit on Earth has been measured by Earthlings, the entanglement is \"shared\". By the well known monogamy of entanglement theorem, any correlation between both qubits by themselves will have become classical. However, Observer Bob, who has a very good working knowledge of quantum mechanics and relativity, knows that for a few hours, until light signals can reach Pluto, the system consisting of an expanding bubble around Earth and the Pluto qubit are in an entangled state. Alice, who lives inside this bubble, will beg to differ. Is quantum entanglement an objective or subjective property? Closely related to Wigner's friend and intersubjectivity in quantum mechanics and Given entanglement, why is it permissible to consider the quantum state of subsystems?.", "label": 1}
+{"snippet": "Many dictionaries use a semicolon in a meaning for a word. For instance for the word impertinent I have seen: \"outside the bounds of proper speech or behaviour; impudent; insolent; saucy\" Then there is a synonym explanation of connotations for impertinent, impudent, insolent, and saucy. My question is: Does the semicolon introduce synonyms always? Does it mean that the word following a semicolon SHARES the meaning of the main entry word you are looking up; that is, the sense preceding the first semicolon in the meaning? I know that insolent cannot be substituted for impertinent, but maybe impertinent can be substituted for insolent with a loss of connotation. Just what the heck are these guys who write dictionaries trying to convey with the semicolon in the meaning of a word?", "label": 1}
+{"snippet": "A question that has been bugging me for quite a while was raised by some communication between my employer and a partner organisation based in Dubai. It turned out that more than once, it's been noticed that this other party tend to use a particular tone of address in letters and emails. Whereas they will address male members of staff as 'Mr Bloggs' - which is quite acceptable and polite, even somewhat deferential given that it's quite uncommon and most other third parties tend to address you by first name after it's been quoted at least once in the exchange - they rigorously insist on referring to female colleagues as Miss Helen, and so on. That is, declining to use the individual's (known) surname, and presuming unless corrected that she is unmarried. Is this due to some antiquated perception of propriety in English correspondence, or is it a custom originating from the culture of the people involved? I would lean toward guessing the latter; since in parts of the Middle East having women in the workplace is less common and perhaps one might presume that a female employee is unmarried, unless it is determined otherwise. Is it thought by the demographic that we are talking to that using the maiden name of a woman known in a professional capacity is in some way vulgar?", "label": 1}
+{"snippet": "I'm reading Yelizaveta Bam of Daniil Kharms (tr. Neil Cornwell) and stumbled upon the following dialogue: Ivan I.: But who then lights the lamp? Pyotr N.: No one, it burns by itself. Ivan I.:But that surely cannot be! Pyotr N.: Empty, stupid words! There is an infinite movement, the breathing of the lighter elements, planetary motion, the earth's rotation, the crazed alternation of day and night, the combination of remote nature, the anger and strength of remote nature, anger and strength of untamed beasts and the laws of light and wave. (I emulated the formatting used in the book) What does \"the breathing of the lighter elements\" mean here (or in general)? Since it is supposed to be an \"infinite movement\" I cannot relate it to the breathing of a living thing.", "label": 1}
+{"snippet": "First of all: I was not able to compile a MWE, since the error seems to be connected to one of my documents, all of which are classified. I'm experiencing (for the first time) the following error: When opening a file in Acrobat Reader and then trying to print, I receive the errors The document could not be printed There were no pages selected to print My file is structured as follows: A beamer-file created in LuaLatex In the beamer-file, several other PDFs are included. Either created by AutoCAD or - and this seems to be the problem - by Latex (pdflatex). Some of the other PDF-files are included inside a tikz-environment (if that matters). All PDF pages are included as images using the graphics-package. By trying to include different PDFs and varying the amount of PDFs I discovered that the problem seems to be that different pages are included in different tikz-environments (it could be a completely different reason as well, this is just a feeling). I've created several other presentations using beamer all of which included multiple PDFs - but those PDFs were NOT Latex-created files. These other presentations work (and print) like a charm. Using a different PDF viewer solves the problem. However, as the created presentation will be sent off to customers, using a different PDF viewer is no valid solution. Also, the problem seems to be connected to some printers. E.g. using CutePDF causes the error, while (sometimes) using the network HP printer works.", "label": 1}
+{"snippet": "I am looking for a method to save the lecture materials, and examples without hand copying from the boards during the lectures. Unfortunately some courses don't have the material available, and sometimes you want to copy a specific example. EDIT: The reason I would like to avoid copying by hand is that it is sometimes very distracting, especially when the example is complex. I would like to focus on the material itself and devote less time and effort to handwriting it. So far I thought of using a tablet with an application such as Camscanner to take photos of the board during the lectures. However sometimes I would want to add a hand note or an notation on the photo itself using a stylus pen (or similar). UPDATE: Camscanner will auto recognize the board boundaries for you and fix the perspective. Also once you took one photo you automatically add subsequent photos to the same document, i.e. same lecture. Very handful feature is that you can add hand notes on the image right after taking it, making notations easy. Any advice on an effective method or an application designed for that?", "label": 1}
+{"snippet": "I was writing a market research report the other day and listed the challenges my company faced in the market in question, then I created a new section header for the... uhh... easy bits? That's when I realized I could think of no reasonable antonym for challenge in the noun form. I can certainly describe it -- characteristics of the market that will be of benefit to our entry \"Advantages\" is close to the mark but doesn't quite capture the idea because I feel that is in reference to our company, rather than in reference to the market itself. To give an example: Challenges > customer purchasing power is low > public perception of our manufacturing location is negative (Easy Bits / Cakewalks / Happy Things / etc.) > no competitive product on the market > strong transportation network with low logistical costs \"Incentives\" also seems close, but not quite there. Any ideas?", "label": 1}
+{"snippet": "When speaking with my mother a couple of days ago, I read to her a message I was sending to my cousin on her behalf ending with: \"... the birthday of your youngest.\" [implying her child] She immediately leapt on this and said that as my cousin only had two children, the use of the superlative was not permitted and the comparative must be used instead: \"... the birthday of your younger child.\" She was adamant that this was a solid grammatical rule that she was taught throughout her education. As a younger Briton, I have relatively little formal grammatical education to older people who were better taught in this regard, so I usually defer to her on grammatical rule knowledge. Is she right? Are superlatives not permitted when the domain of the object is only two? To me it seems bizarre. The minimum or maximum of any set does not only exist when there are different minima and maxima, or indeed something which is neither.", "label": 1}
+{"snippet": "English or any other language could be written or spoken in both the forms, either the user could use simple words or he could use some technical words, my question regarding English is which has more impact on listener, Simplicity in language? or Complexity by using technical words? and is it dependent of whether you are speaking or writing? Simplicity, i.e, using simple words in your language can be effective as it helps the listener understand you better. The brain of listener can easily understand what you meant to say, whereas Complexity brings elegance. A speech or text with some technical words used in it looks more promising and can express much more than the same text written in a simple language. So ultimately, which is better? PS : By Complexity, I didn't meant to say English which could not be understood, I just meant the use of more complicated and technical words in the language.", "label": 1}
+{"snippet": "Unlike the use of \"no problem\" as an alternative to \"you're welcome\" or \"my pleasure,\" neither of which bothers me much in common speech, its use as a reply to an instruction or directive to put right what the respondent has done wrong, particularly if at great expense or at substantial loss of available time, tests my patience and my temper. To my Boomer-generation ear, it says the respondent somehow feels that s/he is doing me a favor by setting things right rather than accepting responsibility for them, and somehow cannot see that a problem truly is involved. Is this a generational shift that I should get used to, or is the use of \"no problem\" in this context an erroneous use of this expression? (For now, at least.)", "label": 1}
+{"snippet": "Here is a sentence from Chapter Seventeen of Huckleberry Finn. The sentence appears in a grammar worksheet: When I got to the three log doorsteps I heard them unlocking and unbarring and unbolting. My English teacher stated that \"them\" was an indirect object, and unlocking and unbolting was a direct object, as that is what was being directly heard. She states that indirect objects can answer the questions \"by whom\", referring to the direct object. (The doing could be done by the indirect object.) This doesn't really make sense to me. My first impression was that them was the direct object and the participles unlocking and unbolting were modifying them. So, can an indirect object in a sense do the action of a gerund direct object? Any help is welcome!", "label": 1}
+{"snippet": "I've always been able to manipulate equations found in school homework easily. But when tackling more challenging questions from puzzle books - where I might need three quarters of a page to manipulate the equation into the ideal form - I find myself easily making mistakes. The obvious solution is more practice. But I can't find a suitable landfill of questions where the focus is on manipulating tediously long/complicated algebraic equations instead of practicing some kind of technique or problem. Has anyone had the same problem as me and found a felicitous way to overcome it? (Other than the obvious advice to be more careful, which you have to sacrifice speed for unless you've already had lots of practice) P.S. I'm not sure if this question belongs here; if it does not, I'll be glad to remove it.", "label": 1}
+{"snippet": "I am currently an undergraduate and thinking about applying to graduate school for math. The problem is that I don't know what field I want to go. Taking graduate classes even more confuse me because the more I learn the less I know what specifically I want to do. My question is to where to find an information about different fields of mathematics? Maybe you can recommend me some good journals about math with overview of top areas of math or popular fields. I already spoke with my professors, asked graduate students about their history but I think that my knowledge about math in a broad sense grows slower than I want it. Maybe there is some good website with people chatting about different fields of research? What about conferences: is there a conference available for undergrad about top-trands in mathematics? All sources and all answers are welcome. I am mostly interested in pure math, but I also like applied math.", "label": 1}
+{"snippet": "I have searched for some time for the \"insider scoop\" on how academics operate when it comes to mathematical research (theoretical physics research would also be interesting, but mostly interested about math research).I read \"Letters to a young mathematician\" which was a nice book but didn't talk much about the research process. If I google \"Research process\", or \"How is research done\", I mainly get recommendations of steps of how to do independent research. These step include brainstorming, choosing a research subject and looking through background information and articles. But how are these done in an academic setting and in a group setting? I understand usually while doing a PhD you would have an advisor which would help you with these things but you would mostly do them independently. But I mean people who are employed as mathematics professors at a university, how do they go about it? Do they do just this independent process? Do they cooperate together on the same research? Mostly what is interesting to me is how a group of people can research something together, and if this is even attempted.", "label": 1}
+{"snippet": "TikZ provides the two keys execute at end picture={<code>} and execute at end scope={<code>} which can be used to execute any code at the end of the picture and of the current scope, respectively. I now like to execute some code at the end of the picture if a TikZ key defined by me is used outside a scope environment, i.e. in the optional argument of tikzpicture or at the end of the scope if it is used inside the scope, i.e. in its optional argument. I also like to access the bounding box of that area, i.e. the complete one or only the one of the scope, respectively. Is there am easy way to do this? Cascaded scopes should also be supported. I don't see a possibility to detect if I'm inside a scope or not. In theory the whole tikzpicture is a scope by itself and execute at end scope seems to work but the manual explicitly states it should only be used in the optional argument of a scope environment. I know about 'local bounding box' but then I would have to use it for every scope with a different name to avoid collisions.", "label": 1}
+{"snippet": "I'm trying to submit a journal paper through ScholarOne Manuscript (an outdated automatic build system some scientific journals use). The issue is that I'm using biblatex. I tried with both backends, biber and bibtex, and I couldn't get it through. Has any of you managed to make a successful submission to ScholarOne with biblatex? Update: They use some build tool which forcefully calls bibtex. After many unsuccessful attempts to make it work with biblatex (also with backend=bibtex), I decided to convert everything to bibtex. The main issue is their referencing style: a mix of author-numeric(superscript) which I was not able to replicate easily without biblatex and I had to hardcode some citations: If you have a better idea regarding the citation style let me know although maybe I should open a new question for that.", "label": 1}
+{"snippet": "Frequently I hear Americans (admittedly mainly in TV/movies) say \"personal\" and \"regular\" in the following contexts: \"Don't take it personal.\" \"I like that he treats me regular.\" Both of these are horribly incorrect to my British ear - I have never heard either here, it would be \"personally\" and \"regularly\", ignoring the fact that the second sentence is slightly awkward anyway (we would probably say \"like a regular person\"). My question is, do Americans 'know' this is incorrect, i.e. would John hear Jane speaking in this manner and think \"her English isn't great\" or whatever, or would it sound perfectly normal - is this an accepted use, that all Americans would use? I could easily believe it would be the latter, since 'momentarily' for example has a totally different meaning in AE. ('in a moment for undisclosed amount of time' vs. 'for a moment at an disclosed time').", "label": 1}
+{"snippet": "I think I kind of understand this process but I would like someone to explain it more completely. For those who aren't aware here is the scenario I'm talking about: As terrain maintenance at my local ski slope we often use salt to firm the snow around jumps on warm slushy days. Throwing down a even layer of salt causes the snow to become firm and icy on its top layer (thus causing jumps to hold up better during heavy use). My best guess to this phenomena is that the latent heat of vaporization in the melting of some of the snow causes the snow below to become colder. As the snow on top melts it sinks down leaving an icy layer on top. Am I on the right track? or is something else going on?", "label": 1}
+{"snippet": "I am a native German speaker and in German it is considered very bad style to use a word more than once in a sentence or even in close proximity. So you usually have a big list of synonyms in your head and you always cycle though these words while writing or even change complete sentences so you will not have to use the same words. I always automatically assumed that this is also the case in English. Now someone told me that this is actually nothing you have to be concerned about. (This sentence is actually a good example for this. I could have written: \"Now someone told me that this is actually not the case in English.\" but I already used \"the case in English\" in the sentence before that and such repetitions are considered to be extremely clumsy writing in German.) Could someone please comment on this?", "label": 1}
+{"snippet": "I want to tell that something reminds/hint us of another thing. For example, in an application, a sorting method used in it has similarities to bubble sort but not completely the same. In this case, when reading about the sorting method used in the application reminds or hints me of, or brings to mind the idea of bubble sort. So, I tried to put this idea into a sentence this way: The sorting method used in the application reminisces bubble sort. But in this sentence, is the word reminisces used appropriately? So I thought of phrasing it the other way: The sorting method used in the application is a reminiscent of bubble sort. I seldom hear the word reminiscent being used in this context and it sounds weird when I use it this way. Is it correct? Since it also feels like a hint, I thought maybe I could use the word \"allude\": The sorting method used in the application alludes bubble sort. Here, again, alludes doesn't sound like a right word to use. What word or way of phrasing should I use to get this idea across clearly?", "label": 1}
+{"snippet": "With the following definition: To lower in quality or character. Synonyms found: corrupt, pervert, subvert, demoralize, demoralise, debauch, debase, profane, vitiate, deprave, misdirect However all of those have a very \"intentionally evil\" connotation. I would say more along the lines of \"messed up\", but it needs to portray that it's somewhat intentional, just not with the evil slant. Intentionally done, but unintentionally wrong, is what I'm looking for. Perfect Example: My nick name on here is Aequitarum Custos, which is a \"bastardized\" Latin, it should have been Aequitatis Custos (the correct way to say what I wanted). I intentionally created my nick like that, but had no intention to make it wrong. Reason for desiring a synonym is due to the perceived obscenity of the word bastard by some people.", "label": 1}
+{"snippet": "What is the formal definition of an event? According to Wikipedia, \"an event is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it.\" This definition seems too large because it includes even points where no identifiable process is happening. On the other hand, what about particle-fields interaction: a comet passing through the gravitation field of the Sun a collision between two particles where one particle is entering the field of another particle and then bouncing off in a parabolic worldline (deceleration & acceleration). In both cases a field is continuously acting on an object, thus the event itself seems to be somewhat continuous. Can someone provide a formal definition which is taking into account particle-fields interaction? Do continuous events exist? Edit: The Wikipedia definition (which also might be found in textbooks) is inacceptable for a particular reason: Events (such as a particle collision) have somewhat observer-independent character, i.e.all observers agree on the fact that an event happened, even if they disagree on the time & the simultaneity of the event. In contrast, we cannot say that observers agree on any \"point in spacetime\". => A sufficient answer would be a good reference for what @By Symmetry wrote.", "label": 1}
+{"snippet": "There's an experiment demonstrating the properties of super-fluid Helium compared to normal fluid Helium, in which the Helium is put in a jar who's bottom is porous. The super-fluid can pass through the small capillaries, while the normal fluid can not. Another experiment uses a fine grained powder (implying the same holds for percolation through porous medium as wall as though the capillaries) The video of this experiment can be seen here My question is: Is the permeability threshold determined only by the viscosity of the fluid? Doesn't surface tension also play a role in determining whether the liquid will percolate? Or do they implicitly assume there's no difference in surface tension between the two phases? Mercury has similar viscosity as water, with a much higher surface tension - and it will not get absorbed in fine sand, while water will - isn't it because water wets the send, while mercury does not?", "label": 1}
+{"snippet": "In some posts in this forum I've read that sign convention in optics is useful for making formula memorizing easier, and that we have to use sign convention again while applying the formulae to neutralize the effect of taking sign convention... I tried to use geometry and saw that indeed without sign convention we get two formulae for lens maker's formula and so on... so in that way sign convention is useful... But i could not derive the formula for linear magnification by geometry - without sign convention the derivation does not match the formula given in the text books (which says m must be negative for convex lens when image is real). Can somebody please explain how to get it, and if not why don't we get it? The Sign Convention used is: The direction of the incident ray is positive. Incident ray is always incident from the left side on the refracting surface. Perpendicular distance of an object is positive when measured upwards from principal axis. Distance is always taken FROM the pole of the refracting surface.", "label": 1}
+{"snippet": "From Planetmath A meager or Baire first category set in a topological space is one which is a countable union of nowhere dense sets. A Baire second category set is one which contains a countable union of open and dense sets. From Wikipedia: A subset of a topological space X is called nowhere dense in X if the interior of its closure is empty of first category or meagre in X if it is a union of countably many nowhere dense subsets of second category or nonmeagre in X if it is not of first category in X I was wondering according to Wikipedia's definition, is any subset of a topological space either of first category or of second category? are the definitions for second category set in Planetmath and Wikipedia consistent with each other? Wikipedia says these definitions are used for \"historical definition\" of Baire space. I was wondering if they are archaic i.e. no longer in use? Thanks and regards!", "label": 1}
+{"snippet": "This is the law of stable equilibrium, according to Hatsopoulos and Keenan: A system having specified allowed states and an upper bound in volume can reach from any given state one and only one stable state and leave no net effect on its environment. Consider the following system: two sealed containers of gas. Container A contains a weight on a raised platform. Container B contains a flywheel. A string-pulley system connects the flywheel to container A. Let our system be both containers combined. Here are two options to reach stable equilibrium We slide the weight in A off the platform; it crashes to the bottom, raising the temperature of A. Instead, we slide the weight onto the string's hook, such that, as the weight gently falls, the flywheel spins and raises the temperature of B. It seems we have reached two different stable states despite making no effect on the environment, contrary to the law. What am I missing here?", "label": 1}
+{"snippet": "Is it correct to say: Would you like to start a cooperation (with us)? Or should it be: Would you like to cooperate (with us)? I feel like the first sentence is wrong, as it sounds to much like saying would you like to start a corporation (with us)? (with a dutch accent) but the second sentence suggests more aggressive style of asking for someone to cooperate with you. Maybe there is a better way to ask this question? edit I should also state I am referring to a international business venture / collaboration. Where for example we would like to sell electronics on our website from his/her company for a small commission or put your vacation house up for rent on our website for a small commission. You would eventually sign a contact to do this(of course). So what I'm asking is: is it correct to ask the above stated questions? or is there a better way? Note: It should not sound like you would want to 'hook up' with the person your talking to e.g. partnering relationship", "label": 1}
+{"snippet": "Colon or semicolon when because is omitted from a sentence e.g., I am sorry I disturbed you (;) (:) (because) it looked like you were having a lot of fun there. Because explains and clarifies a preceding clause so would it be correct to use a colon preceding the explanatory clause if because is omitted? Alternatively, because can be replaced by for, which is a coordinating conjunction and would correctly be punctuated with a semicolon. I am sorry I disturbed you, for it looked like you were having a lot of fun there. I am sorry I disturbed you; it looked like you were having a lot of fun there. For is of course reasonably archaic but is useful sometimes for grammatical clarity. And if anyone wants to comment on the that omission and comma replacement, I'd be very happy. I am sorry (that)(,) I disturbed you because it looked like you were having a lot of fun there.", "label": 1}
+{"snippet": "Im taking a class in graduate probability. My background is in engineering (very used to math in an applied sense). I am also taking an undergraduate class in real analysis along side (should have taken it before, but I couldn't) I have a couple of questions: We're spending time looking at measurable functions on measurable sets. The definition of a \"measurable set\" is one who lies in a sigma algebra. My conceptual understanding of a sigma algebra (I know the technical def: countable additivity, etc.) is the resolution with which we understand a certain space - the sets that can be measured - even more simply: the sets we can actually use. We say a sigma algebra is the \"domain\" of our measure. In other words, a (prob) measure can't measure just any old arbitrary set/sets of set. We define a sigma algebra to handle this, and say our measure operates over this sigma algebra. However, the power set is actually a sigma algebra (the largest one, according to our definition), and yet not every element of the power set is measurable? I'm having a little trouble reconciling my conceptual understanding of a sigma algebra (the behave good-measurable sets) with its actual def (which gives us the power set dilemma). How does the Borel Sigma Algebra fit into this conceptual understanding? How about non measurable sets? Is there a concept of the largest sigma algebra of only measurable sets, which is a subset of the power set?", "label": 1}
+{"snippet": "The hyperreal number system adds infinities and infinitesimals, allowing Calculus to be done using these things instead of limits (sort of like when calculus was originally invented, but with rigor).This got me thinking, could this be done with topology to create hypertopology (an equivalent but perhaps more intuitive way of doing topology)? It should be able to translate, since hyperreals can be represented as ultrafilters of reals. Hypertopology would involve ultrafilters of the points of the topology presumably. To define the topology, I presume you would define when two points of the hypertopology are infinitesimally close. To convert a metric space into a topology, you would simply define two hypertopology points as close whenever their distance is infinitesimal (again, ultrafilters can be applied point wise.) Has this ever been studied? What axioms would hypertopology \"closeness\" need to follow to be equivalent to regular topology? Is there an axiomatic approach (not requiring the ultrafilters (the hyperreals have an axiomatic basis))?", "label": 1}
+{"snippet": "Imagine a cat jumping off a roof onto a sledge on ice. Model this as simply as possible, e.g. no resistive forces, perfectly rigid cat, sledge and floor. Moreover, the cat and sledge move in a straight line. The cat will have a vertical component to its momentum when it lands, but the sledge will - more or less - move off horizontally. What happens to the vertical component of momentum? Should we consider the Earth as a third body in the collision, and conclude that the Earth moves away with an immersurably small velocity? When performing calculations, can we simply ignore the vertical component post-landing? In reality, roughly what factor of the vertical motion's kinetic energy goes into heat, sound, vibrations, etc? (I don't mean list them one-by-one, just what is \"non-Earth moving\"?)", "label": 1}
+{"snippet": "I got confirmed from a graduate school starting from next year and I will major algebraic geometry. Until now, I have never thought that I study little things than others with my age. However, I heard that some of my colleagues already studied Hartshorne at least once and quite a few of them have read Rudin's RCA when they were undergaduates. It's kinda unbelievable to me, but it seems like if they really did study and understood, then they will write absolutely a better Ph.D thesis than mine. So I'm now very worrying myself. I want to know whether this situation is general. Is it recommenable to study graduate subjects as early as possible? Or are there people here who experienced the same thing too? Was that beneficial? Between \"studying each thing deep and slow\" and \"skimming many subjects as fast as possible\", which one is better?", "label": 1}
+{"snippet": "While researching about lasers (it's my hobby), it suddenly hit me: there are lasers for every color of the visible spectrum, but there are no brown lasers. Brown isn't even on the rainbow. How is it possible that we can see it? Even stranger, brown as a color is produced with red and green, but when you mix red and green light, it makes yellow. Now this is where it gets VERY interesting: There are forbidden colors, colors that cannot be perceived by the human eye though they are a mix of perceivable colors. They are caused because the cones devoted to complimentary colors will cancel each other out. Red-green is one. Blue-yellow another. The highly interesting thing is, brown absorbs all other colors but reflects red and green. I don't think it's a coincidence that while brown is, for some unknown reason, not on the visible spectrum but still perceivable, it reflect out red and green, components of a forbidden color. I also don't think that it's a coincidence that magenta does not lie on the rainbow, is nevertheless perceivable, and that it reflects...blue-yellow?", "label": 1}
+{"snippet": "I am already fluent in portuguese and english, and I can also read spanish well. I have to read a text which is in french, and I'm having some difficulties. Knowing that there are a lot of people out there in the field of mathematics that are able readers of several languages, I would like to get the opinions of more experient professionals about their own experiences with different languages and from which ones they get/got more benefits from. I intent to use these opinions as a guide to choose the next language I will learn how to read, if not everything, at least mathematical texts. My initial belief is that I will get the most beneficial experience by learning french and then german, but I'm not sure; I never had experience to acknowledge mathematical texts in more strange languages (although once I started trying to learn korean - gave up some weeks later for lack of time). Opinions?", "label": 1}
+{"snippet": "In my notes I wrote that Rutherford's model of the atom could not explain spectral lines, because that is what my textbook says. I'm not really sure about the details of spectral lines though. I know that when electrons interact with photons of specific frequency, they transition between energy levels (ie they could increase and become excited). After they become excited, they 'de-excite'. This allows them to release a photon and jump back to a lower orbit after they release a photon. This photon has frequency that corresponds between the difference in transition. This frequency correlates to a particular colour. So how then does this colour produce spectral lines, and therefore balmer series? (is that the right word usage?). How does Bohr's model not explain spectral lines (does it not talk about electron transitions, electron orbits etc and thus cannot deduce further?). What current model explains this?", "label": 1}
+{"snippet": "After working on my oral skills in English for a couple of years, I know more interested in learning written English, specially by reading. I have been reading a couple of books over the last months (Game of Thrones, the whole Sherlock Holmes, Lord of the Rings, some Stephen King...) and articles (the Guardian, the New York Times, the Atlantic, mostly). But although I've felt some improvements in my understanding, and learned lots of words, I'm still not enjoying reading English as much as I do enjoy reading French (which is my natural language), and I'm not even what you could call a literary (checking my other stackexchange affiliations would prove you that...). When reading English I just follow the plot, but I'm really totally insensitive in the style of writing, in the choice of words, ... I hardly realized that when reading a few pages of French the other day, it's even way easier to focus on what I read when it is French than English. Fellow who learned English as a second (or third, or more...) language, have already felt that? Have you been through that? How long did it take? Or is it just a never ending job in progress but I'll never reach the ease I have with French?", "label": 1}
+{"snippet": "I know this might not be an easy question, I've already read the wikipedia page, and there is an interesting view: Therefore, the main difference between chaotic systems and complex systems is their history. Chaotic systems do not rely on their history as complex ones do. Chaotic behaviour pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'. On the other hand, complex systems evolve far from equilibrium at the edge of chaos. However, I want to know a little bit more of their differences and intersections. If I'm not (terribly) mistaken, according to how the development of chaotic systems started, the emphasis was put on deterministic systems (should that part be of dynamic systems?), but now, with complex systems, according to what I understood of what Prigogine said, the emphasis should be put in other types of systems more close to reality. So what can you guys tell me about these two?", "label": 1}
+{"snippet": "Generally speaking, by the well-known BCS theory, the more carrier density( density of state at Fermi surface) leads to higher critical temperature. However, in many researches, people fond that the relation between critical temperature and carrier density is not simple. There is a superconducting dome in phase diagram, no matter what carriers are electrons or holes. There exist a critical carrier density which gives the maximum critical temperature. Why is there a superconducting dome? What reduces the critical temperature when carrier density is higher than the critical carrier density? What is the physical reason? By the way, I don't think it can be simply explained by inducing disorder or impurity when doping. It is usually happen in chemical doping. However, there are many electrostatic doping researching on this topic, and usually it would only induce high carrier density without impurity or disorder, but also show similar nature of superconducting dome.", "label": 1}
+{"snippet": "Consider the sentence: While this assumption, on its own, is relatively innocuous, if implausible, in practice, it is supplemented by assumptions... The 'if' here really means something more like 'but perhaps also'. Another sentence: He appeared very happy, if not exuberant, at her arrival. 'if not' here means something like 'and perhaps even', as if the latter statement should be a more extreme version of the former. But it also feels like an exclusive disjunction. That is, it is one or maybe the other, but not both. On the other hand, 'if' by itself feels like both statements could be true. I can conjure up many examples where both 'if' and 'if not' violate my above descriptions and many more which just seem malformed and awkward but fit them, e.g., 'He seems happy, if not a little confused'. or 'The proof appeared correct, if sloppily constructed,'... Adding further confusion, if I make a small change to the previous example: 'The proof appeared correct, if a little sloppy, .., it feels correctly formed although the semantics or grammar have not changed substantially (although I could be wrong as I am thoroughly confused now). So my questions are: are there any concise descriptions of how to use 'if' and 'if not'? Does this grammar usage have a name? When are they interchangeable and when not? Thanks", "label": 1}
+{"snippet": "I'm facing a difficulty about referring to previously mentioned words. It's something that bothers me a lot about the English language. Please consider Mathematicians can use these theorems to their advantage. versus Mathematicians can, to their advantage, use these theorems. Which is more correct? The first sounds more natural and most people would probably say it's correct. However, I would think that technically the first is wrong and the second is correct, even though the second is a bit more unnatural. Why? Because in the first, their is referring to the last thing mentioned, namely these theorems, which is absurd. In the second, their actually refers to the mathematicians, as it should. What do you think? If the first is (also) correct, my question is simply this: Since when can sentences be counted as being correct just because they happen to make sense from the context?", "label": 1}
+{"snippet": "I was suggested to use the term bullet-proofed by a colleague. Someone else now pointed out that bullet-proofed might not even exist, because we can't build the past tense of an adjective. Part one of the question is: can to bullet-proof be a verb which describes \"making something bullet-proof\"? And in consequence bullet-proofed then means \"having made something bullet-proof\"? So far, that's just for me, learning about it. I actually have decided to replace the word by something else. The word is intended to be used like \"a bullet-proofed solution\", which is close to foolproof or stable or tested. However, I would not use foolproof as a term here, because it might sound offending in the business context it is used. Can you think of the correct term my colleague might have had in mind when suggesting bullet-proofed? Note that we're both non-native English speakers. Update: @skymninge hit the definition. The intended use is like \"not subject to correction, alteration, or modification\", so I am looking for a synonym of that.", "label": 1}
+{"snippet": "I am not an expert on figure exports and, although I have been searching around quite a lot, I can't find the answer to my problem. During the writing of a journal article, I had the idea of using psfrag to replace text on my .eps figures generated with Matlab. That works fine, as long as the main text .tex file is compiled as a whole. The problems start when one tries to generate the figures separately (since almost all journals require the figures to be uploaded as separate files). I have been trying to find a way to compile each figure into an .eps file with the psfrag labels added, so that I can submit these files separately. Maybe my problem is ill-posed to begin with (for example, even if one manages to compile a single eps file with the psfrag substitutions, how can one control the relative sizes of figure and text?). If this is the case, I would appreciate if someone could provide a correct workflow for ending up with .eps figures whose text has the same font with the article. Note: the only solution that I have managed to find and seems to be what I want, is the fragmaster.pl script, which however I do not how to operate in windows.", "label": 1}
+{"snippet": "I'm trying to fill out a survey that asks me about features that should or should not be included in a smartphone app. The actual questions are confidential, but it's in the style of a sentence like this: \"You can control the temperature of the room you're in\" followed by these options (of which you can choose one) Assuming I'd choose \"I would like it\" for the second row. Does that mean find it positive that the feature is not part of the app, or rather that if it's not a part, I'd like it to become one? Similar with the \"expect\" answer. Would I expect the feature not to be part of the app, or would I expect it to be and miss it if it's not a feature? I was sent the link by a \"noreply@foo.bar\" mail, so I don't know whom to ask. I'm passionate about the topic, though, and would like to answer this as precise as possible.", "label": 1}
+{"snippet": "A video shows two spherical objects (made up of particles) collide. The title refers to them as two planets colliding. When the objects are indeed as large is planets (however large that might be), the video seems sped up. What if the objects are smaller than that, like the size of marbles? Would they still move as slowly (relatively to each other) as if they were planets? So, to put it differently, when scaling such a situation down, would they move faster relative to each other? Could the video be showing 'real-time' progression when they would be marbles? Updated question If there are two situations that both have two spherical objects in them that have the exact shape etc. (so both situations only differ in proportion), and you would look at both situations at the same time, would one be progressing quicker than the other? Disclaimer: I have limited physics knowledge. Please help me improve this question if it is unclear or hard to understand.", "label": 1}
+{"snippet": "I'm spending too much time thinking about this problem : I need to show that the shrinking wedge of circles which is path connected, locally path connected ,doesn't have a simply connected covering space . hatcher gives a condition for a space to be semi locally connected it's about the induced injection between the fundamental group of a neighborhood U and the fundamental group of our space (here we need the opposite of that) . I've asked my doctor about it and he told me that I can't use it since our space is \"locally path connected \" and not semi locally ..Can anyone help me prove that this X : shrinking wedge of circles does't have a simply connected covering space ? I supposed it had , then i took a loop in my space X ,I lifted it up to a loop in the simply connected covering space , this loop would be homotopic to the constant loop, my intuition is to project it down , and prove that since my space is not simply connected this loop can't be trivial but I'm feeling there's something missing or wrong .. Any help is appreciated.", "label": 1}
+{"snippet": "This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at hand where the chemical potential is negative. (why?) For fermions, isn't the sign of the chemical potential a matter of definition? The way we normally write our equations for the Fermi-Dirac distribution the chemical potential happens to that value of energy at which the corresponding state has a occupation probability of half. And within this definition the holes in a semiconductor have a negative chemical potential. It would be helpful if someone can help make a statement about the chemical potential which is independent of any convention. {Like one argues that negative temperature is a sign of instability of the system.} Also isn't it possible for fermions in an interacting theory to have a negative chemical potential? Also if there is a \"physical argument\" as to why bosons can't have a positive chemical potential? (Again, can an interacting theory of bosons make a difference to the scenario?) And how do these issues change when thinking in the framework of QFT? (No one draws the QCD phase diagram with the chemical potential on the negative X-axis!) In QFT does the chemical potential get some intrinsic meaning since relativistically there is a finite lower bound of the energy of any particle given by its rest mass?", "label": 1}
+{"snippet": "Is there a way to selectively disable a specific ligature in XeLaTex? I cannot see how. The selnolig package seems to do what I need but I don't even know how to use Lualatex with my Texshop setup on Mac. Specifics: I am using XeLaTex, new to it and trying to figure my way around and set up some standard templates for my own use, e.g. academic papers. I am mostly using Linux Libertine O. I have the same issue with Adobe Caslon Pro. Why: The \"Th\" ligature bothers me, particularly in titles. I never see it used in print. See, for example, the New Yorker magazine which uses Caslon, most ligatures are set but never Th. I never see it in books either. (I know this is picky).", "label": 1}
+{"snippet": "If a body becomes charged by losing electrons for example, it will experience a braking force when it is accelerated due to radiation called Bremsstrahlung radiation. Part of the energy used to accelerate the charged body will be emitted as radiation. It should therefore take more energy to accelerate the charged mass than the energy required to accelerate the body without the charge. The Larmor formula calculates the non-relativistic power radiated by the acceleration. There is also a relativistic derivation. The charged body will appear to be more massive due to this effect. It can be explained by the fact that part of the energy is going to kinetic energy and part to radiation. Nevertheless, F=ma should imply a higher mass so are we dealing with a more massive body?", "label": 1}
+{"snippet": "Why can't you create energy out of nowhere For me it's not enough that a smart guy for hundreds of years said so. Some scientists and religious people said that the earth was flat - untill someone said it wasn't. And we know that it isn't flat, we can prove it. I can prove it. Do we just say we can't create energy out of nowhere because Newton said so? Is that our argument - and that no one has proven wrong yet? I think you know some kind of mathemagic that proof that Newton is correct; could you please explain it to me? What about Vacuum Quantum Fluctuations and the Casimir Effect? Is that just a mathematical estimation? Or where do the energy come from? In my (non scientist) eyes it comes like - from nowhere. Is a Zero Point Energy Module possible? I have found this article. Actually all my questions are based on this article. It would be nice if you take a look on the article and try to explain against it. In this article on a no-name-blog there is the claim, that a lot of scientists (phds, professors and so on from well known universities) say that such a \"free energy generator\" is possible, and that it was build. But because companies would lose money, it will never come to society. There is a lot of fancy words in it, a lot of PhD and other titles and sources on like Nature.", "label": 1}
+{"snippet": "Below is a review by music critic Robert Christgau of a Flaming Lips album. I've pasted the entire review, but my focus is on the first two sentences. Primarily, is it idiomatic to use \"couldn't\" here? Because unless I'm wrong, isn't the point of what he's saying that you don't have to hate Sgt. Pepper to think it \"could\" do with a little ribbing, etc.? You don't have to hate Sgt. Pepper to think it couldn't do with a little ribbing, travesty, desecration. In fact, you could love it as much as I do and think that. As hilarious sobersides from multiple generations charge indignantly that the Lips and their various beards fail to \"interpret\" the songs, all three modes of deconstruction are in play on this grand hoot of a fore-to-aft remake. Highlights for me include a theme statement that gains meanings it never had from its attendant distortions, a creaky \"When I'm Sixty-Four,\" Miley Cyrus so sweet on \"Lucy in the Sky,\" and Julianna Barwick adding just what \"She's Leaving Home\" cries out for--a female voice. Only \"Fixing a Hole\" truly fizzles. As for \"A Day in the Life,\" yeah--the original rocks. A-", "label": 1}
+{"snippet": "M-W has the following definition for mixed metaphor: a figure of speech combining inconsistent or incongruous metaphors Hence a requirement is that a 'mixed metaphor' contains more than one metaphor. Eric Lippert comments in another thread: \"mixed metaphor\" is more commonly used to describe the result of accidentally combining two metaphors in a way that does not make sense as a whole. \"For me it was stormy in the great sea of life, but then I came to a crossroads.\" He does not claim that this is a necessary condition, and I'd agree. I've just written in another thread: ' \"John is a real tiger\" works, but \"That lion is a real tiger\" is best avoided.' Each of these two statements contains a single metaphor. Does any definition of 'mixed metaphor' apply to the inappropriate (incongruous juxtaposing of tenor and obviously related vehicle) metaphor in the second sentence?", "label": 1}
+{"snippet": "Else-site, I got into a discussion with a member where the thread turned accusatory and defensive because I said a programming language had tricky details that you learned over time. I did not mean that it was a bad thing, only that there were features less traveled that really enhance the effectiveness of code. One of the Definitions of 'tricky' given by M-W is \"requiring skill or caution\" and the other two are even more negative. Even \"difficult to do or deal with\" leans negative into the \"It shouldn't be that difficult\" realm. Yet difficult is not always bad. Sometimes it just is, mastery of any topic is difficult, and sometimes just knowing the subtle features is enough, it's a sign of a skilled practitioner to leverage these subtleties, and it's those I call tricky. Am I off on my usage, and what resources exist to try to divine these usage subtleties? I'm a native speaker, yet I can't always explain why I shade word meaning a certain direction that is not supported by a dictionary.", "label": 1}
+{"snippet": "I came across a question where i was asked to find the force exerted by the walls of a frustum shaped bucket on a liquid inside it . I found the force exerted by the liquid on the walls of the bucket by concepts of hydrostatic force and thought that by newton's third law both the forces will be equal and opposite . But the answer was totally different . I checked the solution in that simple force dynamics (newton's second law) was used considering the weight of the liquid , the normal force by the floor of the bucket, the atmospheric pressure and the force by the walls. Then since the liquid was at equilibrium all the forces were vetorially equated with each other . I am convinced with this solution but i also don't see any problem with my approach . So how should it be ?", "label": 1}
+{"snippet": "How do you see non-academic mathematics? I have an impression that the academy has still a quite significant prestige and is thought to be the safe-guard for \"real science\". That is, to verify that those that have the most experience in science, can produce science and have the \"blessing\" of the academy, in order to deviate from informal publications made outside of academia, whose content cannot be guaranteed and that do not necessarily go through peer-review. However, esp. in mathematics, there's no real reason why mathematics cannot be produced anywhere. I.e. academy does not add much to the process of doing mathematics. Social connections to like-minded people perhaps. Then there's the internet, which makes all information pretty accessible. So do you think there's a place for \"open source, non-academic mathematics\"?", "label": 1}
+{"snippet": "So basically, I was trying to find a good answer to the question of how light interacts matter. Namely on the quantum level what causes matter to appear transparent, reflective, opaque, etc I came upon the answer with respect to transparency here, but I feel that the concept isn't fully explored here and that something is missing (particularly in the coloured light talk). The jist is that light passes through some matter because the energy gap between the matter's electron's low and excited state exceeds the energy of the photon, and thus the light is not absorbed and the photon passes through the matter. Could someone provide more detailed information about transparency, and information about reflection etc. So I guess for the purposes of forming this into a question I'll simply ask why some materials reflect light and look like mirrors while other materials reflect light with less precision? (thought I get the feeling it has similarly to do with basic mechanics and the regularity of the electron distribution)", "label": 1}
+{"snippet": "I live by Internet, as both a user and a developer. This dual role gives me a chance to observe. Every time I try to ask something in communities like StackOverflow, I always pick words carefully and provide sufficient information, hoping that my questions will be answered in a short time. But even so, sometimes my questions still get ignored. Maybe StackOverflow, or even the whole Internet, is too big a world, filled by floods of information. Small people try to fit in, but end up being swallowed by Twitter and Facebook, without even a sound. So, enough of complaining, I just want to know: Is there a word or a phrase to describe this phenomenon where people find themselves lost in the the great Information Age, ignored by others?", "label": 1}
+{"snippet": "I've been reading the book \"Geometric Mechancis\" by Darryl Holm and the in the first chapter he treats geometric optics. There the author talks about light rays and those light rays looks like trajectories as of particles as we consider in Classical Mechanics. The first thing that the author state is Fermat's principle that seems to define one action and then determine the path that light follows (i.e. the light ray) being the one which extremizes the action. In all of that discussion, it seemed to me that geometric optics is then all about treating light not as a wave, but rather as a collection of particles. Is that it? In geometric optics we should think of light as a collection of particles? In that setting, a light ray is just the path followed by one such particle, or is it composed by many particles?", "label": 1}
+{"snippet": "This question stems from a disagreement between me and my girlfriend. During the hot summer months, we like to open up the windows during the early morning to cool down our flat a bit. One of us thinks that every window should be opened fully, since that will ensure maximum airflow, the oter swears that the actual area of open window is not a huge factor. We both agree though, that at least in most situations, opening the windows fully is the best option; the question is rather. All other things being equal, how will doubling the area of one open window affect the airflow in a flat? If it helps at all, we typically also have a fan or two running in the flat and we have windows at opposite ends of the flat, which are all open.", "label": 1}
+{"snippet": "Let imagine a tunnel that connect two distant places at the globe (eastern-western or north-south) There are a lot of posible \"distances\" or metrics, defined by maps, routes, \"as the crow flies\", etc.. but none of those distance can be shorter than the distance of the tunel. So if two trains travels at same speed, one inside the tunnel and other above in the surface, the one on the tunnel will reach first. If this is possible, then perhaps it's possible to have differents coexisting metrics with differents dispositions or topologies, within the same system. Of course that if we describe a space-time metric surrounding a sphere, then \"holes\" in it would change the metric (just because it's not a sphere anymore). But it's strange for me that making a hole we could change in some way the space-time shape. In an extreme case. Could be an euclidian space of same dimension be build within a non-euclidian space? I would like to have a view from people familiar with general theory of relativity, thanks", "label": 1}
+{"snippet": "The hippopede is historically famous because Eudoxus used its properties in the first mathematical model of planetary motion. He nested concentric spheres rotating at different inclinations to each other, and had the motion transfer from outer ones inward, the planet was attached to the equator of the innermost sphere. With three or more spheres he achieved trajectories with backward loops (\"retrogradations\") similar to those observed for the planets. But with just two (see animations here and here) the trajectory is the figure eight shaped curve obtained by intersecting a sphere with a cylinder touching it from the inside (see interactive graphic illustrating that it really is the same curve). Clearly, under any composition of rotations a moving point has to stay on a sphere, but why is it also confined to an off-centered cylinder?", "label": 1}
+{"snippet": "I was reading G.I.Taylor's Single - Photon Double Slit experiment. Now, at a time only a single photon gets emitted. What is the probability of it at a certain point of the screen to hit? The answer is written rather abruptly: Although the photon can hit anywhere, the probability is more, where the brightness(bright fringes) i.e. Intensity is more. Now, this means intensity existed before photon actually hit the wall? How can it be possible? When photon hits the screen, the energy gets transferred to the screen. So, after photon collides, intensity does come in discussion. But if we accept the answer, it is like saying that energy came somehow on the screen before the photon; after that photons would strike there where the intensity of the energy is more. So, who is actually transferring the energy: photon or the waves? If it is wave that transfers energy as being evident from the above quoted argument, then what photons are doing actually ?? What are they meant for if they are not responsible for transferring energy??", "label": 1}
+{"snippet": "Let's define a \"hand-incalculable problem\" as a mathematical problem that can not be solved by available human calculation power (using only writing materials and utensils) at a specific date and geography, during lifetime of the person who posed the problem. Given a specific date and problem can we strictly label the problem as \"hand-incalculable\"? Edit: We assume that algorithm to verify the solution is known. Edit: I am looking for a general classification similar to P/NP/NP-Complete which is used in computation theory. I wonder if we could define such classes for mathematical problems as HC(hand-calculable)/HI(hand-incalculable)/HI-Complete at any specific date. Even an absolute classification based on available human FLOPS and not related to a specific date, would be nice. Edit: HC: Hand-calculable at a specific date. HI: Hand-Incalculable at a specific date. HI-Complete: Hand-incalculable no matter how far mathematics will advance in future; consider a dynamic programming problem that needs millions of FLOPS of calculation power to be solved in reasonable time (during lifetime of the person who posed the problem).", "label": 1}
+{"snippet": "I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. Taking into account Newton equations for the electron and the proton and Maxwell equations for the electromagnetic field produced by these charges one obtains a higly non-linear set of coupled equations. In such a nonlinear system could some feedback effects between proton and electron take place so to make possible a stable dynamics (or at least a dynamics unstable on such long time scales longer that we can consider hydrogen to be stable)? In this way the system's stability already obtained through quantum mechanics could be reproduced by a full classical approach! P.s.: Please, as I know of the great successes that quantum theory has had since its birth, try not to answer the question telling how quantum mechanics wonderfully solves the problem. P.p.s.: I'm also aware of the fact that electron should lose energy and that this should cause it to fall on the proton in a very short time, so please try to avoid also this argument. I asked this question to understand if the oversymplifing hypothesis', which are fundamental in solving this problem (neglect proton's motion and, as a consequence, magnetic effects) and are quiet ubiquitous in physics, wouldn't mask the potential richness that could arise from mathematical complexity.", "label": 1}
+{"snippet": "He was born and brought up in this village, but after staying and studying abroad his childhood friends seem backwards to him; he _ this place now. Or He had lived in this city all his life but whenever he gets a chance he starts counting the flaws. He thanklessly _ his homeland. It might even apply to a situation like say you party every weekend but if somebody else does the same you criticize them. Note: Read title: act of crticizing one's own homeland/city/country I can use words like criticize, betray or badmouth in my sentences, but I am looking for more like an idiom or phrase or even a proverb, that may or may not fit into my sentences but explains the intent. The intent here is being a hypocrite to an extent, yes but there's an addition of viewing one's own homeland or people as backwards(where I don't think that person has changed, they are just trying to show off). In hindi there's a saying \"jis thali me khaya usme ched kiya\" which means destroying the plate in which you are served. I'm kinda looking for an english analog for this proverb. I thought \"don't shit where you eat\" would be the close but it was hilarious to find out it's meaning and of course that it's nowhere close.", "label": 1}
+{"snippet": "Whenever I write TeX/LaTeX documents, I always find that annoying because I can't really focus on the content, It's not that I don't like TeX or what it does for me, it's just the fact that the document quickly becomes something way too verbose. I was thinking about adopting an intermediate syntax, something more \"dry\", that can help me focusing on the content and only use LaTeX later on in the process to create the last pieces of the layout and the paging. So far I was able to identify rst ( reStructuredText ) and docbook, needless to say I have no experience with neither of the two, but I have a few requirements while asking for your help: support for math formulas support for include external resources like snippets of code or images (vector images for the most part) The kind of documents that I would like to write while adopting this \"dry\" solution are small books and articles for the most part, so often times I need to separate things into chapters or paragraphs and I would like to have a solution that is modular and flexible.", "label": 1}
+{"snippet": "First and foremost I want to say that by no means am I a physics guru, but I still ponder this question. While I can understand from my current understanding of physics that a perpetual machine is yet,by current understanding, unattainable, does that mean that there is no hope for a free source of energy? Confined to the forces of the Earth we are bound by gravity, a constant form of energy acting on all, but what is the reasoning for not attempting such a feat in the midst of space where the levels of interference with the generation of energy(again from my current understanding) is so minimal? I understand that there would technically be friction on a molecular scale with particles bouncing and colliding with each other, and other potential space debris. However, other than that what is stopping us from achieving the goal of this, or am I simply missing information?", "label": 1}
+{"snippet": "So I decide to self-study the real analysis (measure theory, Banach space, etc.). Surprisingly, I found that Rudin-RCA is quite readable; it is less terse than his PMA. Although the required text for my introductory analysis course was PMA, I mostly studied from Hairer/Wanner's Analysis by Its History (I did not like PMA at all). Although I said readable, I do not know if I actually understand whole materials as I am middle of first chapter, and I already have topology background from Singer/Thorpe and Engelking. I actually like Rudin-RCA, but I am not sure if I am taking great risk as many experience people seem to not liking Rudin for learning... Is Rudin-RCA suitable for a first introduction to the real analysis? Is it outdated? What should I know if I decide to study Rudin-RCA. I am not planning to read the chapters in complex analysis as I am reading Barry Simon's excellent books in the complex analysis.", "label": 1}
+{"snippet": "I have the following sentence: Increase your rating as you develop your coding skills while you evaluate the skills of other developers. However, I now realize that this sentence is a bit off since it doesn't communicate properly. Some feel that this sentence sounds challenging since some imply that you're competing and working with other programmers. I am trying to make it feel more inviting and feel less like a challenge but an opportunity to not only give back to the community but also improve your own skills. I am trying to remove the potential stress that goes into evaluating someone or letting x number of people evaluate you since you're already judged by your manager. I was thinking that maybe changing the tone of this sentence to be less a declaration but more of an open suggestion. Any help would be greatly appreciated.", "label": 1}
+{"snippet": "If an angle is the measure of distance between to points (Edit: Ok, admittedly bad phrasing. A measure of rotation between two intersecting lines, or points, etc.), is there such a thing as a zero degree angle? I asked a math nerd friend about this years ago and he still hates me for it but couldn't prove it either way at the time. Is this merely pedantic or delusional thoughts regarding definition of \"angle\" (Edit: based on answer below regarding Euclidian geometry, this all now seems very likely a colossal misunderstanding) or am I missing something? I do not think zero degree angles exist. Is there proof of this either way? Edit: A better question would be why Euclidian zero degree angles were thought to not exist, or why he avoided them?", "label": 1}
+{"snippet": "Suppose someone comes up with a great original idea. Some time later, someone else comes up with exactly the same idea without knowing that idea been conceived already and even without being influenced in any way by the other person's thought. In other words, both of them make the discovery totally independently and not at the same time. For example, Leibniz and Newton invented Calculus this way; Cook and Levin established NP-Complete theory this way. The idea from the very first inventor is no doubt considered original. But what about the same idea independently conceived by others later in time? I have no problem calling the latter original, although it seems less original than the very original one. Would there be a word or phrase that can readily convey the state of being \"less\" original?", "label": 1}
+{"snippet": "Specifically, I am referring to the traditional gesture some female service staff members seem to do, when demonstrating their work or their readiness to receive orders. Also, this is the gesture Alice Cullen performs in Twilight movies on several occasions (if I remember correctly). I could not find a photo with this exact gesture. It is similar to the one shown in the first photo, but the hands are held higher with demonstrativeness, tension, sharpness of movement and gesture itself (possibly with emotion and a smile), and military-like demeanor. The main difference with with the second photo is that in the gesture I refer to, the hands are held in the front and not in the back; also, the way the hands are interlocked is different (more like in the first picture).", "label": 1}
+{"snippet": "I have a circle moving on a spherical surface. If the camera angle is fixed, is there a way to calculate the original circle's offset from the centre given the distorted ellipse formed when the circle moves to the edge of the sphere(as seen from the camera)? I've looked into Listing's plane and the Tissot directrix(because I'm working with eyeball rotation), but neither seems to provide a clear solution to this. I've also looked papers regarding eyeball roation but they seem to focus on the physiological aspects rather than the math of the movement. In other words: In the picture above, given one of the outer nine images as well as the middle one, I want to calculate how much the circle(i.e. iris) has moved/rotated from its position in the middle picture. I assume it has to do with comparing the distorted ellipse with the circle, but I can't seem to find out how. Is there some formula for this?", "label": 1}
+{"snippet": "Reading the wikipedia article about the particle in the box, there is this image: Animations from B to F show wave function of a particle in a box starting from ground state up to excited states. The animation C shows wave function behavior in the first excited state and at the middle point both real part (blue) and imaginary part (red) of the wavefunctions are zero all the time. Does it mean that particle will never ever be found at that point? Similarly, for second excited state in the picture D we have two points where this happens, so does that mean that there are two points in space where particle will never ever be found? I can't really tell from the picture if this continues for higher excited states. Is there some law that says for the n-th excited state there will be n points in space where probability of finding particle is zero?", "label": 1}
+{"snippet": "I've seen nice graph showing relative activity of each isotope in Chernobyl fallout: Could anyone suggest similar graph or raw data but for absolute isotope activity for the case of nuclear explosion fallout? (for some boosted fission bomb) So that one could see how much gamma, beta and alpha-active particles one should expect over time, and particle energy. PS. This graph is for damaged nuclear plant fallout, but I want absolute graph for nuclear explosion fallout. Explosions have different isotope content due to much shorter duration. Update: I see that graph might be hard to find. Maybe someone have isotope content i.e. how much % of each isotope? Or at least how it is supposed to be different from Chernobyl fallout. Then I might be able to simulate decay by myself.", "label": 1}
+{"snippet": "What's a word that can be used to describe an author's portrayal of a scene as normal even though the content of what is described is innately disturbing/unnatural? He cut open the dog's underbelly and we all took turns examining its insides, which were just as we had expected them to be. To get over the disappointment it was suggested we head out for drinks later, which I was forced to decline... The writer's description of the scene is word. The writer words the scene. This disgusting scene is worded by the writer. Earlier I was able to think specifically of the word, but now I can't even remember whether it was an adjective/verb, so sorry for being so open in my example usages, but hopefully this contains enough information for someone to propose something.", "label": 1}
+{"snippet": "I have a question about a Quantum Mechanics machine that should interact with the past, I can't find any flaws with it, but I just want to make sure. The machine has a lot of facts about history, some true and some false, and the machine knows which one each fact is. It measures the spin of an electron, and if it has an up spin, it tells a true 'fact' and then a false 'fact', but if it has a down spin, it tells the a false 'fact' and then a true 'fact'. It does this several times so it will probably have both at least once. So until you check which one, the past is in a sense, in a quantum state of being one thing or another. If this all stems from incredible stupidity, I'm really sorry, but if it doesn't, thanks in advance. EDIT: To specify, the part where it 'interacts' with the past, is when you check which spin it is, so you can use a coin to do the same thing. In other words: each fact is true and false at the same time, so checking collapses and 'changes' the past.", "label": 1}
+{"snippet": "in Dire Straits \"Sultans of Swing\" what is the meaning of these two lines: In the first verse: You get a shiver in the dark It's been raining in the park but meantime South of the river you stop and you hold everything A band is blowing Dixie double four time You feel all right when you hear that music ring As I understand blowing Dixie means something like fooling around. But what is double four time? And then later: And Harry doesn't mind if he doesn't make the scene. He's got a daytime job, he's doing alright. He can play the honky tonk like anything, Savin' it up for Friday night. What does it mean? Is he playing really good but saving it up or doesn't do it very well? Thanks.", "label": 1}
+{"snippet": "As is the case with most students (I suppose), I seem to have lost touch with the do doing some \"basic\" math -- calculating integrals, playing around with matrices and doing some linear algebra etc. -- as I have proceeded through my undergraduate program. To be honest, I didn't practice a whole lost of questions when I took these introductory courses, so I presume that's one source from where this issue stems. I'm a student of physics with a mathematical leaning. Ideally, I don't want to go through a mathematical methods textbooks for physicists/engineers since they're pretty superficial (at times) and are more like \"here's-a-result-now-go-solve-problems.\" At the same time, I don't think I have the time to sit through very long textbooks, such as James Stewart's Calculus. Any suggestions of textbooks, given my aforementioned concerns, where one can \"practice\" calculus, linear algebra, complex analysis etc. to stay in touch with the practice of being able to solve in questions in closed form.", "label": 1}
+{"snippet": "Is there a way to tell TeX to avoid breaking the page after the first word of a sentence? ... ... He was quite dead. Apparently his neck had been broken. The lightning flashed for a third time, and his face leaped upon me. I sprang to my feet. It (text continues on next page) And then you have to turn the page for the rest of the sentence. It's not in a line on it's own so it can't be penalized like an orphan line. Can TeX be told, to resolve these by, say, breaking the page before that first word? Note: Although the answers given below are very informative, the general consensus had been that the best practice is to leave this for the proofreaders to spot, and then fix manually.", "label": 1}
+{"snippet": "I got a question about the usage of generalization of collocations. There is a word such as \"bird of prey\" to refer to birds eating animal flesh. And one way to generalize reference of a noun is to put \"the\" in front of the word, especially for animals, plants, recent inventions; the lion is the king of the animal world of Africa / the smartphone is nowadays a required item. Then my question is whether this kind of expression below is also okay to show generalization; The bird of prey is a bird that eats animal flesh. For other nouns, such as \"man of steel,\" when someone says \"the man of steel,\" a native English speaker would think some particular or specific man of steel since there are several possible possibilities; Stalin, or the Superman in the recent movie, etc.", "label": 1}
+{"snippet": "I am not very familiar with the quirkiness of relativity, and I was wondering how to explain this situation. If a beam of light is shining at some object at some distance from the origin of the beam, does relativity imply that photons in the beam lack time flow and, thereby, never actually experience contact with the object? Wouldn't the photon observe no time passing in the surroundings, immediately at the source of the beam? Could it tell it was moving? However, we see it make contact, so does that mean that what is observed might never actually ever happen in another reference frame? Also, when we see the beam of light traveling at c, how can we record the beam's movement? Shouldn't the beam's photons appear to be in some timeless state?", "label": 1}
+{"snippet": "The closest description I can think of is a \"drama queen/king\", except that tends to describe people who like being in a drama. Instead, I want a phrase describing people who like to pick up on stories such as the following: questionable decisions of others controversies immoral acts and then they get on their soapbox and passionately rant, uttering phrases like \"it's disgusting\", \"it's a joke\", \"anyone who agrees with them should be ashamed\". Perhaps the descriptive term for that person might need to include that they are often immune to reason on subjective topics, and that the rants cause displeasure in the listeners, since frequent rants can wear listeners down, as the tone is loud, highly opinionated and of a very negative nature. The reason I ask is I want search terms to Google to find techniques for dealing with such a person, and protecting one's self from their effects. Edit: it is not really about whether someone finds faults in others, but the manner in which they frequently rant about issues, either in others, or institutions, or the nature of things.", "label": 1}
+{"snippet": "The area/arc-length is given by an integral or the integral defines the area/arc-length is one the first things we learn in Calculus, but that is done in the Cartesian coordinates, next one moves to polar coordinates and the area is transformed/redefined by a new integral using the Jacobian. My question is : Since area and arc length are invariant of coordinate system, is there a way to define them other than in Cartesian coordinates and transform them from coordinate system to coordinate system with the help of Jacobian? In other words is there a way that area/arc-length is defined independet of coordinate system and then according to the structure of coordinate system it's integral form is reached, without tranforming between coordinate systems, but for a given coordinate system it is derived. (and without the use of Jacobian to move between coordinate systems)", "label": 1}
+{"snippet": "I have a pair of shoes, which seem to isolate me from the ground. In effect I'm gathering static charge and every time i grab an aluminum door handle, that current discharges and that hurts. Ouch. I invented a way to workaround that: when I'm going to touch door handle, first I take my Skeletool (a stainless steel multitool) and touch the door handle with it. Sometimes I even see the small spark and hear the discharge and then I can touch the handle myself unharmed. But what interests me is: why discharging through the multitool does not hurt? This is an electrical current flow what hurts and the current flows the same way even if I hold the tool in my hand. Tool has surely less resistance than human body, so it shouldn't change anything. But it does not hurt :) Why?", "label": 1}
+{"snippet": "Please refer to the figure attached. Consider a normal force is acting on the top of sphere. A constant coefficient of friction causes frictional force throughout the sliding. I want to know after this sphere slides (pure sliding no rolling) for sometime and assuming that it wears as it slides, what should be the shape of sphere after sliding? The one shown in (a) or (b)? In short, I want to know whether the worn side of sphere will be a straight line or a curved one? What will happen if a sphere slides against a sphere? Also, I will highly appreciate if someone can refer to some good papers / books about this. Edit: Additional assumptions Lets assume that hardness of both surfaces is the same. Also assume that material is removed but is not attached to any of the surfaces (no adhesive wear). The phenomenon under consideration is abrasive wear (but no accumulation of wear debris). If a lubricant is in circulation, it is easy to realize this kind of wear", "label": 1}
+{"snippet": "This question pertains to programing but is really a math question. I am building an application that draws a line graph, similar to a stock line graph. The problem is I am not starting with a known set of numbers. The values will come in based on an altitude value. So, when I start the graph I have no idea what the max and min values of my data set will be, because they max might not come along for some time. Like I mentioned, these values will be added to the graph when I receive and elevation value but I don't know these until they are received from my device (iPhone). Is there a formula used to calculate a line graph for unknown values? How can I know what x and y values to use for each new value received? And how can I calculate the min and max of the graph?", "label": 1}
+{"snippet": "I want to discuss with my boss a part of this code - so I need a name for it. items = array.map(function(item){ return item.item; }); I want to say \"This usage of the same identifier twice is _______________ and confusing.\" They might respond \"No this is _________ which is fine\". Is tautology an accurate word to use there? the saying of the same thing twice over in different words, generally considered to be a fault of style The use of item in the function call e.g., function(item) could be named anything you want, so instead you could have: items = array.map(function(data){ return data.item; }); What is this called if not tautology? Edit: A non-programming example, would be naming a street Road Street, or worse naming an area in London, London (perhaps New York New York would also work).", "label": 1}
+{"snippet": "In several articles and books, I have read that \"the magnetic force on or due to a small element of a circuit is equivalent to two or more of its component elements, provided that the current remains same\". i.e. the magnetic force on or due to AB(in red) is the same as the magnetic force on or due to its component current elements (in black) However this doesn't make sense to me because in a closed circuit, the vector addition of current elements is zero. It means the resultant current element of a closed circuit is zero. Hence the force on or due to a closed circuit is zero. However this is not the case (a closed circuit experiences and exerts magnetic force). Then how can \"law of vector addition of current elements\" be valid?", "label": 1}
+{"snippet": "I don't know why, but since recently my Emacs is behaving strangely. As usual I compiled using C-c C-c to call LaTeX, then there were errors and it asked me to type (as usual) C-c '. but when I did it just commented out the whole paragraph, which is the same effect as C-c %. C-c % still works the same and typing ' produces the same letter, i.e., '. so I somehow have my doubts that it is related to the keyboard, but not out of the question, of course. I can't recall having done any setting changes or changes to my setup since the last time it worked perfectly, but i am not completely sure. I'm running Emacs under Ubuntu, Latex/MP Fly Ref are the automatically hooked modes. Does anyone have an idea?", "label": 1}
+{"snippet": "Dictionary definitions of `bonny' admit to chiefly British (or even Scots), but give no further hint of the possible tinges of this word. Bonny (adj.) means attractive, fair; fine, excellent [M-W]. Perhaps I perceive it as slightly archaic, hence this post. Is this word (still) functioning in the meaning given, and what are the caveats of its usage? Is it the teensiest bit pretentious, or otherwise out of the ordinary? If not, what might be typical usage? (I know about bonny, bonny banks of Loch Lomond. I know about blithe and bonny ladies. I know about one wife or another being `very bonny, thank you'. These, and a perhaps a few other titbits I acquired somewhere, more or less defined the word for me, and I'm finding it difficult to shift away.)", "label": 1}
+{"snippet": "I am creating a program but facing problem with proper language for comment string in program. My program performs some operation. This operation typically always generates some data. (meaningful data if operation went as expected or error data if operation didn't go well). Now this program returns these two things to user: data, True - if operation generates meaningful data data, False - if operation generates error data I want a comment string at the start of program which mentions what this program is returning to user, and I am not able to come up with a single word which will define True/False nature of this data. Things I have on mind for comment string: \"Returns data and True/False based on result of operation\" (UGLY) \"Returns data and success nature of operation\" (WUT?) \"Returns data and boolean result of operation\" (Not good) \"Returns data and .....\" (I am not good at this really)", "label": 1}
+{"snippet": "I got into a discussion with my physics teacher about the speed of light and I asked What if an object with mass was to lose mass as it gained speed-- would that allow for an object to eventually reach the speed of light or surpass it if possible through that thinking? My teacher didn't really have an answer to that and I was wondering if there was any law of science that prevented an object with mass to become mass-less. Because I know this may be simple minded in thinking but if an object with mass must have infinite energy to reach the speed of light and at that point will have infinite mass, what if an object was to reduce its mass until it had none? Would it then not need infinite energy and be able to move at or past the speed of light in theory?", "label": 1}
+{"snippet": "What cases can \"y'all\" work in? A prior question asks about the 'proper' usage of \"y'all\", but it and its answers only address nominative case (all examples are nominative). I think that there are some cases where \"y'all\" doesn't work as is. For example, nominative: \"Y'all come back now, ya hear?\" accusative: \"I'll ring y'all up tomorrow after the fish fry.\" possessive: \"Bring y'all's swimsuits. The pool will be open.\" (or \"y'allses\". yes, I find this is questionable usage) vocative: \"Hey y'all! Where's the keg?\" but instrumental/dative/indirect object?: nothing sounds right. ? I'll bring the BBQ over to y'all. ? This party is all for y'all. These don't sound right to me. The alternatives that sound right to me would be: I'll bring the BBQ over to you all. This party is all for you all. Can anyone confirm my usage? Has there been a study/paper on this? I ask because most pronouns in English have forms for different cases, so it is not given that \"y'all\", though a synonym for \"you\" which only has a different form in possessive case, would or would not have a different form.", "label": 1}
+{"snippet": "What word best describes the experience of starting something, and ending up, before you know it, far deeper into it than you had ever intended, or far more embroiled, involved, or even having finished or done it irreversibly. An example might be, say, opening a book out of curiosity, and finding yourself, the next thing you know, dumbfounded to have finished the whole book, almost as if it had happened by some driving involuntary osmosis or in a blackout. Example sentence with blank for desired word: Having opened the tome with the intent of reading only the first paragraph, she found herself, in what seemed like hardly an hour, staring at it's back cover almost as an alcoholic might awaken from a blackout to an empty liquor cabinet, and wondering at the _________ way some deeds are done in life, almost as if they are done to you.", "label": 1}
+{"snippet": "I watched this video: popped water balloons And as you see when the needle pops the balloons the water stays in the same shape as the balloon for a few fragments of a second. The force impacting the water after the balloon has been popped must be gravity, and since the water stays in the same shape for a while must mean that the water \"doesn't know\" that it's gravity it should \"listen\" to now during that time. What does this say about the speed of gravity? How slow/fast is it and what happens with larger/smaller objects? One thing holding the water together could be air pressure, but what happens with if you do the exact same thing in vaccuum? Will it stay in the same shape for a few moment or will it dissolve at the \"speed of gravity\"? Let's say it stays the same, what would that mean for earth if the sun disappeared? Would we feel the gravitational reaction way after the light went out?", "label": 1}
+{"snippet": "I've just got wondering if this sentence is grammatically correct: You are who I love. This is what I am thinking: Let's focus on the who clause, then you can find that the missing element from this clause is actually an object after the verb love. Therefore, who should be changed to whom, which is an object relative pronoun. You are whom I love. Now, the whom clause has no problem, but you can see that whom clause works as an object. However, there is the place at which a subject complement should be. So, I should either change the whom clause back to a who clause or make you into an object. You is whom I love. It's you whom I love. Whom I love is you. After all that, I came this far with these three sentences and I think the most appropriate sentence is the second one, but I'm not sure if my assumption is right; the way I fixed the sentence, is it right?", "label": 1}
+{"snippet": "I will greatly appreciate your help with this question. I use beamerposter and want all the blocks (across various columns) to be of the same height (= max height of among all other blocks). I came across your solution here: How to modify columns/column environments so they resize automatically to the largest column ? However, in case of beamerposter, blocks can be located in different columns. And this trick of placing blocks inside columns and count the height does not work here. I need somehow to fetch all blocks of all columns of the poster and compute max height (and set each block height to this value, maybe a certain parameter for blocks ?). I imagine there should be a way to re-use a solution from here: How to modify columns/column environments so they resize automatically to the largest column ? by nesting blocks into special dummy columns to count them and to adjust their height. I tried to play around this idea but failed in my tryings. Can you please suggest a solution here? I will greatly appreciate your help with this question. Thank you / John", "label": 1}
+{"snippet": "i have problem to determine if the word bake is transitive or intransitive verb from the Phrase \"Samantha can bake at any time of the day.\" i am reading from a book called English grammar understanding the basic it say Action verbs that act upon something are called transitive verbs. Action verbs that do not act upon something are called intransitive verbs. If a verb (in any of its forms) can be put in one of the following slots, it is transitive: (a) What did you_____? (b) Who did you______ ? If a verb cannot be put in one of these slots, it is intransitive. If a verb (in one of its forms) can be put in one of the following slots, it is transitive: (a) He _____ something. (b) He____ someone. If a verb (in one of its forms) can be put in the following slot, it is intransitive: He____ by following the grammar i can say \"he bake something\" or \"what did you bake\" it look transitive for me", "label": 1}
+{"snippet": "Since we have working models for forces \"combining\" or being describable via a single framework at higher energies (such as the \"electroweak\" force and the aim of GUTs), does electromagnetism split into an \"electric\" force and a \"magnetic\" force at lower energies, or is this simply a misnomer in the English language born of the order in which the behaviors where discovered and related? As an aside, the main reason I ask is because I have heard \"spin\" (the quantum number; which I might add in hindsight was badly named if considering the laymen such as myself) described as a \"magnetic moment\", and something entirely disconnected from \"electric charge\" (another quantum number); to my limited knowledge, there is no known meaningful correlation between the two properties (though obviously I might have just not read about/understood such). I'm a confused layman, and any answers will be much appreciated!", "label": 1}
+{"snippet": "Looking around trying to find questions concerning the intuition behind discrete/indiscrete topologies, I haven't found much towards the essence of what these particular topologies imply about the space (and why it is meaningful). I realize that in a discrete topology, every set is both closed and open, as is the case with the indiscrete topology, however that the topologies are disconnected and connected respectively. That this somehow tells us about distinguishability between points; in the case of the discrete topology we have that every set of points can be at least disconnected from other sets of points, and that in the indiscrete topology, this is not the case. Now the difference between the neighborhoods then would be then that for the Indiscrete topology, all the neighborhoods include all other points, but that in the discrete topology each point has a neighborhood which doesn't include the other points. Am I correct so far? But I know there is much more, could someone expound on the intuition what is going on, maybe even including things such as levels of \"seperated-ness\", and perhaps what happens in between the Indiscrete and Discrete Topologies? Thanks, Brian", "label": 1}
+{"snippet": "If I fill a plastic ziploc-shaped bag with water, the cross section profile should be sort of teardrop shaped (assuming we ignore the edge effects of the bag being sealed on the sides as well as the top and bottom). The bag should \"sag\"/get wider until to get the center of gravity as low as possible. Initially, getting wider will let more water towards the bottom but eventually this is offset by the bottom of the bag moving up (because the sides are fixed length). Is there a common function that describes the shape the cross-section of the bag makes? I would guess the bottom is a parabola, since gravity likes to make parabolas. Then I would guess the top is linear because its under tension. But I have no idea what the transition region might look like and whether you could put those two together into a nice function.", "label": 1}
+{"snippet": "Are the slang usages of \"bud\" (mainly meaning cannabis, and occasionally clitoris, from what I understood) prevalent enough that I should avoid using them in a product intended for international availability? Example sentences which could be printed: \"John has created a bud here!\" \"Share this bud!\" (ouch) \"Create bud\" I would appreciate very much if you could state which part of the world you're from when answering this question. Some context: The lexical field surrounding a service I'm designing revolves around trees, plants, and nature in general. My team and I are in the process of selecting names for the various parts of the service, and we are struggling with one: It should depict something with potential, which is not yet fully developed, but holds the bases for future interactions. Seed would not be relevant, as this part of the service is sprouting from something we called a Tree, and I feel it would generate confusion about which one generates the other. Bud came to mind, and seems a good choice. it fits wery well with the rest of our service part's names. However, it does not seem to be a very commonly used word (much less than \"tree\", \"branches\", \"leaves\", \"roots\" and so on), and I'm afraid this could heighten the chances of it to be read in an alternate meaning. This item could be named a Leaf as well, which conveys a less accurate meaning, but possibly avoids this problem.", "label": 1}
+{"snippet": "Is there a logical story behind this phrase? Because when looked at from a naive perspective, giving somebody their own medicine sounds like a kind thing to do as it would only treat their illness. The phrase only makes sense in the context of someone who knowingly sells poison as medicine, which is a rather rare thing (or was it common in the old times?). The most popular origin story I could find about \"dose/taste of one's own medicine\" is a tale where a cheat sells a medicine that does nothing, then gets sick and people give him his own medicine. And even with this background, it makes little sense, as the medicine doesn't sound like it harms him. Does anybody know the name of this story? Perhaps there's more depth to it.", "label": 1}
+{"snippet": "The smallest possible cardinality of a base is called the weight of the topological space. I was wondering if all minimal bases have the same cardinality, and if every base contains a subset whose cardinality is the weight of the topological space? What aspects are common between a (smallest) base of a topology and a base of a vector space, besides the following similarity (open subset <-> vector, union <-> linear combination): every open subset is the union of some members in the base; every vector is the linear combination of some members in the base. Note that a base in a vector space is also a base in the linear matroid. Not sure if we can have some nice structure like matroid for a topological space to understand its (smallest) bases. Thanks and regards!", "label": 1}
+{"snippet": "My daughter said to me this morning (the context is irrelevant): Er, it's all wet! The interjection I have written here as Er was synonymous with Yuck. Its wetness did not cause great happiness. But what's the right way to write it? The problem with the way I've formulated it above is that it looks like the Er of (genuine or mock) hesitation, synonymous with Um. In fact I think that would be as natural a reading of the sentence as the Yuck reading. This would significantly change the overall understanding, and change the response from disgust to something like confusion. I could try Err, but I don't think that's any less ambiguous. And of course I could write Yuck, which would convey the right sense, but direct quotation ought to respect the original wording. (I have a feeling that this is a British expression, so I'm tentatively tagging as BrE, but I'm uncertain about this. It's supported by noting that the answers to this question don't mention Er at all.)", "label": 1}
+{"snippet": "Let us suppose I am running on a street. When my eyes are open, I can see many things moving backward, and thus it gives me an idea that I am moving wrt those things. Not even this, even if I close my eyes during the run, I can really feel that I am moving. Now assume that I reach a world where there is absolutely nothing except my own body, and my eyes are closed. I am still feeling that I am running. The question is I am running wrt to what? Even if I open my eyes I would feel that I am still running, may be very fast. But visually I would not able to perceive my movement. Does it mean that my movement in space is an illusion? If not, then I am moving w.r.t what? There is absolutely nothing around me!", "label": 1}
+{"snippet": "Or, I guess it could be worded, since when and why was it counted as part of a formal writing style to capitalize many general nouns? (After all, it's not German ...) This is also a trend in legal documents, however, I believe, attributable to the fact that certain terms (e.g. \"Company\") can have very specific definitions. Here is the second paragraph of the Declaration of Independence. We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.--Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.", "label": 1}
+{"snippet": "One formulation of Dilworth's theorem(for finite partially ordered sets) states that : There exists an antichain A, and a partition of the order into a family P of chains, such that the number of chains in the partition equals the cardinality of A. The above is an extract from this wiki page. However, I don't understand how the above statement is equivalent to the following formulation of the theorem. In any finite partially ordered set, the maximum number of elements in any antichain equals the minimum number of chains in any partition of the set into chains. The wiki article does try to explain this. Here is their explanation: Dilworth's theorem states that there exists an antichain A, and a partition of the order into a family P of chains, such that the number of chains in the partition equals the cardinality of A. When this occurs, A must be the largest antichain in the order, for any antichain can have at most one element from each member of P. Similarly, P must be the smallest family of chains into which the order can be partitioned, for any partition into chains must have at least one chain per element of A. I don't get why the statements \"...for any antichain can have at most one element from each member of P\" and \"....for any partition into chains must have at least one chain per element of A\" together imply the maximality of the antichain and the minimality of the number of chains. Any help in understanding why these are equivalent formulations will be appreciated. Background: I am mostly a problem solver. I am learning order theory because of its connections to Hall's marriage lemma and because it seems very interesting. I am not following any book, but am trying to learn some order theory online. So I am a total beginner in this area.", "label": 1}
+{"snippet": "I'm looking for the name of the logical fallacy where intent or agency is assumed when in fact there is none. It's a common fallacy in my experience, but I can't seem to find it described specifically on any site that discusses logical fallacies. It seems to be a special case of apophenia, but Wikipedia and Google turn up nothing specific to an \"apophenia of intent\" or any related phrase. The best I've been able to find is this rather obscure blog post that names it the \"agency fallacy,\" but I haven't been able to find any other sites that use that phrase. Does this fallacy even have a name? Here are a few examples: A child, playing with magnets, finds that they repel when held one way and attract when held another way. Seeing this, the child thinks \"oh, those ends want to be together, but the other ends want to be apart.\" They have (unconsciously) read intent into a deterministic physical process. A picnicker gets rained on and thinks \"Darn it, rain! You just couldn't resist ruining a nice day, could you?\" Again, they have (unconsciously) attributed agency to a mindless natural process. Two people pass each other in a crowded hall. One trips and stumbles into the other. The other thinks \"What a jerk! Why'd they do that to me?\" They have mistakenly attributed intent (specifically, malice) to an action that was accidental. This is the case of the fallacy that Hanlon's Razor warns against. A socialist on a soapbox shouts \"Capitalism is the source of all the world's evil! It's stealing our jobs and lining the pockets of bureaucrats!\" Although the use of metaphor is more deliberate here than with the child or the picnicker, it is still misleading: capitalism can't do anything on its own, only the people who participate in it can.", "label": 1}
+{"snippet": "I was given the following question for comprehension pasted below: What does John mean when he says that he would only win his own money? And I answered that John meant that Marry won't be betting any money, so he will be winning only his own money. Professor marked it incorrect. Can you please what exactly is the problem? I have marked the relevant information in bold letters in the comprehension passage. \"Hullo,\" said John, \"it's raining again. What a nuisance I Now we shan't be able to play tennis this afternoon.\" \"No,\" said Mary, \"I suppose we shan't. Let's stay at home and stick some photographs in our book, shall we?\" \"Do you really want to?\" said John rather doubt. fully. \"I thought you said you didn't like doing it because it was so messy.\" \"Oh,' replied Mary, \"I'll just watch you sticking them in.\" \"Oh, no, you won't,\" said John. \"You've done that to me before. You'll have to do your share, my girl I \" \"All right. Then what about playing cards? You're keen enough on doing that with your friends at the club.\" \"But you don't know how to play,\" protested John. \"That's all right. You can teach me, can't you? You taught me to drive a car.\" \"Well, it's not much fun teaching someone to play cards. The whole point of playing cards is the chance of winning.\" \"You'd be sure to win if you played with me, because I don't know how to play. Surely that would be better than playing with your friends, because you sometimes lose there.\" \"But if I did win when I was playing against you, I would only win my own money.\" Mary laughed. Then she said. \"All right, I think we'll just have to go to the cinema. There's a good film on at the Grand, isn't there?\" \"Not the Grand,\" said John. \"The Splendid.\" \"Oh, yes,\" said Mary. \"I keep on getting them mixed up. The Grand's the one down by the river, isn't it?\" \"Yes,\" answered John. \"After we've been here a few more weeks we'll know everything there is to know about this town: it's small enough. Well, we'd better go, or we'll be too late for the matinee. Have you got your umbrella back from Jane yet, or will you have to go on sharing mine?\" \"No, I got mine back. I came across Jane in a shop this morning. She was carrying my umbrella, but she put it down for a moment while she looked in her handbag for some money. So I picked the umbrella up and started to walk out. The shopkeeper was horrified. He said, 'Madam, that umbrella belongs to this lady!' 'No, it doesn't,' I answered, 'it belongs to me.' 'That's right,' said Jane. 'It does.' You should have seen the shopkeeper's face! He didn't know whether to believe his eyes or his ears-especially as Jane pretended never to have seen me before: you know how she loves a joke!\"", "label": 1}
+{"snippet": "What are some good ways to motivate the material on infinite series that appears at the end of a typical American Calculus II course? My students in this course are generally from biochemistry, computer science, economics, business, and physics (with a few humanities folks taking the course for fun) - not just math majors. I have struggled some in the past to motivate the infinite series material to these students. For one, it doesn't fit with the rest of Calc II, which is on the integral. Over the years I have \"converged\" on telling them that the main point of the unit is Taylor series and that the rest of the material is there primarily so that we have the tools we need in order to understand Taylor series. Then I illustrate some of the many uses of Taylor series (mainly function approximation, at this level). This approach works better than anything I've come up with thus far with respect to getting my students to care about infinite series, but I feel a little like I'm selling the rest of the material short by subordinating it to Taylor series. Does anyone have other ways of motivating infinite series that they would like to share? (Again, only a small percentage of the students in my class are math majors.) Background: The material in this unit typically consists of sequences, basic series (like geometric and telescoping ones), a slew of tests for convergence (e.g., integral test, ratio test, root test), an introduction to power series, Taylor and Maclaurin series, and maybe binomial series.", "label": 1}
+{"snippet": "I am a pre-engineering student currently taking a Single Variable Calculus course at a community college. I recognize that my future success (or not so much) as an engineer will be based, in large part, on my capabilities with and understanding of Calculus. Therefore, I really, really want to master it like I've never mastered any subject before. I'm doing well in my class, and my instructor is great, but I am under the impression that this course and it's textbook (Calculus, Early Transcendentals by Stewart) do not delve quite as deeply into Calculus as I would like. Also, the textbook frequently introduces new techniques and concepts with little to no explanation. (Incidentally, I'm a self-taught software developer, so I am adept at learning new topics on my own. Learning Mathematics is, IMHO, quite similar to learning a new programming language.) So I'm hoping to find some really excellent Calculus textbooks that will give me deep insight into the topics of differentiation and integration (and any other topics my course may be missing). I've used Google and my school's library to search extensively, and I've found no shortage of Calculus textbooks. My problem is that, since I'm just now learning the basics, I have no way to know just how in-depth an advanced or in-depth book should go, or what important information my current textbook may be missing. I own a copy of The Calculus Lifesaver, by Adrian Banner, which is absolutely outstanding. If anyone reading this happens to be struggling with Calculus, this is the book to turn to. I also have been taking advantage of the Calculus courses in MIT's OpenCourseware. Calculus Revisited, with Herbert Gross, has been very helpful. His way of explaining the concepts just really \"clicks\" with me. So, with that said, I'm just hoping the experts in the community here can recommend some great resources (e.g. books, free online courses, or other media) to help me optimize my knowledge of Calculus. Thanks in advance!", "label": 1}
+{"snippet": "I am new to the world of stochastic processes and Brownian motion, and am having a hard time finding easily digestible reference material (especially ones with well-worked out examples). So, in a way this question is more of a request for sources/references than a specific answer. To give a little context to where I am approaching this from, it is specifically from the class of statistics referred to as \"group sequential testing\" (though there are several similar or analagous names, such as \"interm analyses\", \"conditional power calculations\", \"futility analyses\", etc.). I am posting this here rather than on CrossValidated simply because cursory searches reveal that people here are more familiar with the basics of stochastic processes than seems to be the case over on the stats-specific StackExchange, so I feel that I will get more helpful advice/answers here. Anyway, the primary textbook for this field of statistical analyses is Statistical Monitoring of Clinical Trials: A Unified Approach, by Proschan, Lan, and Wittes. The basic mathematical framework for much of the book is Brownian motion; that is, the theory behind many of the group sequential tests outlined in the book is founded on the fact that standardized test statistics evaluated over time can be seen to satisfy the properties of Brownian motion. What I am trying to do is prove whether or not certain classes of non-parametric statistics (specifically the Wilcoxon rank-sum) satisfy these properties, and thus allow one to use this broader framework in that context. So, what I am looking for are sources or references with examples of demonstrating how some arbitrary process can be shown to satisfy the properties of Brownian motion. When I search this site or Google, I can find dozens of examples, but none of them are quite that helpful, since the are generally all based on proving that some function of a Weiner process is itself a Weiner process (e.g. this question or this one). These aren't terribly illustrative to me, since the proofs all rely on the fact that some element of the process under consideration is already given to satisfy the properties of Brownian motion, rather than \"starting from scratch\", so to speak. Now, I do know the basic steps for proving a process is Brownian motion (this question has them delineated rather nicely). However, I am having a difficult time finding any worked examples of these steps being applied to a process \"from scratch\" (which is especially critical since I am unfamiliar with a lot of the notations used in stochastic processes, which are often subtly different than those taught to us statisticians). Can anybody point me in the direction of some nice examples or references that would be helpful, here?", "label": 1}
+{"snippet": "There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you move the molecules from cell to adjacent cell at random, the large-scale results are in many ways a good simulation of gas behavior. In particular, even though molecules are individually moving in only the four cardinal directions, at a large scale the simulation does not show any bias to these four directions. If you start with a large square lump of material, it will rapidly diffuse into a circle. This property of the simulation is called isotropy. Long ago when I was involved in research in this area I was told that this worked fine for gas flow simulations, but not for incompressible fluids. If one wanted to make an isotropic two-dimensional simulation of incompressible fluid flow, I was told, one had to use a hexagonal lattice instead of a square lattice. I was told that one could deduce from the Navier-Stokes equations that that any simulation of incompressible fluid on a square lattice would necessarily be anisotropic. Is this correct? If so, how does the proof go? If the argument is complex, is it possible to get an intuitive idea of why compressible and incompressible fluids are different in this regard? What is a reference that would include the full proof? Addendum: Despite the answer I posted below, I still don't understand any of the details. I would be glad to award the bounty to someone who could explain it.", "label": 1}
+{"snippet": "British English often employs mass nouns where American English would only employ count nouns. Count nouns are nouns which take pluralization and numerical quantifiers like 'many'. Mass nouns can't be pluralized and take volume quantifiers like 'a bit of'. For example: I like sport. I like drink. I pay tax. I've got toothache/earache/stomachache/backache. I eat mashed potato/scrambled egg. I play with lego. In American English, we would render these: I like sports. I like to drink / I like to have drinks. I pay taxes. I've got a toothache/earache/stomachache/backache. I eat mashed potatoes/scrambled eggs. I play with legos. These facts are documented here, here and here. But this difference is not mentioned on the Wikipedia page comparing British English to American English. My question is simply what other nouns which are standardly count in AmE are often mass in BrE? Further, are there any broad categories of nouns (for example, food nouns) that tend to be count in AmE but tend to be mass in BrE? Or does the difference only exist for particular and isolated lexical items? (The first link I provided says that many foods are not conventionally massified in BrE, for example 'refried bean'). Here are two final caveats: First, I know that any count noun can be turned into a mass noun by simply putting it in the syntactic position of a mass noun. That's why \"I ate (a bit of) chicken\" is acceptable in both AmE and BrE. But I am asking about the obvious differences between AmE and BrE regards their conventional uses of nouns as mass and count. Second, I know these types of list questions are hard for single users to answer, and sometimes generate controversy on EL&U (for example, this one on kennings generated some controvery). Still, I'll upvote any responses that make a novel contribution.", "label": 1}
+{"snippet": "An elementary fact that people learn about mirrors is the law of reflection, that the angle of incidence of a light beam striking the mirror (as measured with respect to a normal) equals the angle of reflection. Does this law also hold for a mirror that is moving? Consider a square mirror that is moving at speed v in a direction perpendicular to the mirror. (You can think of the mirror as starting in the xy-plane and moving in the positive z direction of a Cartesian coordinate system.) As the mirror approaches a certain observation point, another person shines a laser beam of frequency w at the mirror so that the beam makes an angle A with the normal to the mirror. (You can think of the beam as lying in the yz-plane.) What angle and frequency will you measure for the reflected light beam? Does the law of reflection still hold? Do your conclusions change if the mirror moves parallel, rather than perpendicular, to its plane (say in the y direction if it starts in the xy-plane)? Note: The large mirror of the Hubble space telescope is an example of a mirror in motion as it orbits the earth. From your analysis, do you think the users of the Hubble have to take into account the motion of the mirror when measuring properties of its images? I know that this question could be according to the .SE standards be too broad. But I request you not to close this question, I would really appreciate people if this question is answered rather than flagged or closed.", "label": 1}
+{"snippet": "\"You do research in mathematics! Can you explain your research to me?\" If you're a research mathematician, and you have any contact with people outside of the mathematics community, I'm sure you've been asked this question many times. For years now, I've struggled to find a satisfying answer. I think an ideal answer to this question should: be accessible to someone who hasn't studied math since high school build intrigue and wonder honestly, albeit vaguely reflect your research only require a few sentences (Of course, these guidelines will change depending on the audience and venue. For example, speaking with an engineer over a meal allows more time and technical language than would speaking with a stranger on a bus.) I study the representation theory of algebraic groups and Lie algebras over fields of positive characteristic, so I usually say something along the following lines: I work with two algebraic objects that are closely related called algebraic groups and Lie algebras. These objects can act on spaces (like three-dimensional space) by transforming them in a nice way, and I study these actions. One aspect of my work that is especially challenging is that I use number systems in which a chosen prime number is equal to zero. Honestly, based on my guidelines above, I think this response is poor, but with so much to communicate in such limited terms with such limited time, the task seems nearly impossible. Using my guidelines, how would you describe your own field of research? Or, if my guidelines are too strict, how would you deal with this question?", "label": 1}
+{"snippet": "So I am reading the essay \"On Some Verses of Virgil\" by Michel de Montaigne (translation by Donald M. Frame) and I came across this particular sentence. Is there any ugliness in doing wrong that can dispense us from the duty of confessing it? The choice of vocabulary here is, honestly, quite confusing to me. Here is the sentence again with the preceding paragraph for context: The diseases of the body become clearer as they increase. We find that what we were calling a cold or a sprain is the gout. The diseases of the soul grow more obscure as they grow stronger; the sickest man is least sensible of them. That is why they must be handled often in the light of day, with a pitiless hand, be opened up and torn from the hollow of our breast. As in the matter of good deeds, so in the matter of evil deeds, mere confession is sometimes reparation. Is there any ugliness in doing wrong that can dispense us from the duty of confessing it? It's been a long time sense I've had this much difficulty understanding the exact conclusion a sentence was trying to reach. My first instinct is to assume that the sentence is somewhat synonymous with: Is there any ugliness in doing wrong that can [spare] us from the [ordeal] of confessing it? But then a friend of mine offered an interpretation more to the effect of: Is there any [wrongdoing so exceptional] that [it will] [render our confession truly unprecedented in the context of humanity]? Meanwhile, another translation (found on Project Gutenberg) renders the sentence thus: Is there any deformity in doing amiss, that can excuse us from confessing ourselves? I don't have much confidence in either his or my interpretation, and this other translation isn't clearing things up for me much at all. What is Michel de Montaigne saying?", "label": 1}
+{"snippet": "I am writing a formal document. It is a petition to appeal an administrative law decision. The decision is jam-packed full of sloppy mistakes of every kind imaginable. (The guy who wrote it couldn't even manage to spell the name of my town correctly in the title of the document.) I list all the errors and inaccuracies in my appeal petition, with specific references to pages in the hearing transcript and exhibits. But I want to preface the list with something that means the following: A number of the problems noted might seem rather insignificant, but I will list them all, to show the review officer how incredibly sloppy the decision is. OR: what a slapdash job the hearing officer did in analyzing the case and writing up the decision. Only I can't say \"incredibly sloppy\", I need more formal language. I need a more subtle way of saying sloppy. I don't mind making adjustments in my sample sentence to accommodate a different part of speech or whatever. Note, the following question is somewhat related but doesn't. A word for not paying attention to detail, causing sloppiness. One idea: A number of the problems noted might seem rather insignificant, but I will list them all, to show the review officer the shocking lack of care taken in analyzing the case and documenting the decision. Another idea: The hearing officer's slapdash [or: haphazard] analysis and write-up resulted in erroneous references and errors of fact that are too numerous to list in the space allowed. I will only be able to provide corrections for a portion.", "label": 1}
+{"snippet": "I have used classical Lagrangian mechanics for quite a while, and what I like about it is that everything can be derived from a very small number of geometric principles. There are just three things you need to \"take on faith\": That configuration space should be endowed with a Riemannian metric given by mass; That forces arise from scalar potentials on configuration space; Hamilton's principle of extremal action. The last is perhaps most objectionable: why should the universe want to evolve in a way that minimizes the action? I have no idea, and my understanding is that nobody else does either. But if I assume these hypotheses, everything else follows mechanically: equations of motion, Noether's theorem, etc. What I would like to do is to learn quantum mechanics, starting from similar geometric principles. For example, I might take as a key principle that configurations should be probability distributions over configuration space, rather than single points, but this doesn't lead to quantum mechanics; I also need (for some reason?) to instead take configurations to be complex-valued functions over configuration space. But even then I don't see how to get anything like Schroedinger's equation from a (modification of) Hamilton's principle. I did some searching and I've found that there is indeed some variational foundation for quantum mechanics (and Feynman seemed to have championed this formulation) but the articles I've seen so far assume I already understand quantum mechanics. My question: Is there a good reference that builds quantum mechanics from scratch, based on variational and geometric principles? If it's easier to instead start with a more general theory (e.g. quantum field theory) let me know as well.", "label": 1}
+{"snippet": "For instance, \"A politician must be able to think quickly on the spot. He or she must also have no qualms about lying.\" I know some people who use \"they\", but as that both sounds and is ungrammatical, I'm wondering if there is any other concise and non-awkward alternative. Edit: Apparently many do consider \"they\" as correct. This surprised me, because I know someone who actually wrote a grammar book, who told me in no uncertain terms that \"they\" could not be used (in fact, I'd asked them - ha! - this question before I posted it here). And a quick look online found legitimate sources advocating both positions. I suppose it's one of those issues, such as whether the previous sentence was incorrect for beginning with a conjunction, where it really just depends who you ask. Regardless, to me personally, \"they\" in the above example sounds clunky at best and incorrect at worst. So I suppose my question can be rephrased as, 'is there any alternative to 'he or she', other than 'they'?\" Secondly, to whoever tagged this as \"politically-correct\": acknowledging the existence of genderqueer or transgender people isn't a political issue at all, until those made uncomfortable by people unlike them make it one. Trying to avoid excluding and thus unconsciously discriminating against a group of people in your writing isn't born out of a need to be 'politically correct' - it's born out of basic human decency. Finally, yes, in the example above, I could use a comma and avoid the need for a pronoun at all - but the question I'm asking applies to instances where one may not want to do so (i.e. the sentences are long and stringy enough as it is).", "label": 1}
+{"snippet": "I'm writing some copy for a marketing campaign that promotes the use of a software testing tool by demonstrating how the results of the tool provide you with a greater wealth of information on which to make business decisions. In relation to this, I'm using the term \"informed decisions\" and my initial wording included the phrase \"help you make more informed decisions\". The phrase \"more informed decisions\" is one that is common to me and from a Google search appears to be common in the context in which I am using it, that is to denote that with additional evidence a decision can be more informed than without. I considered whether this phrase runs the risk of being misinterpreted or being confusing due to a slight ambiguity. The phrase \"more informed decisions\" could be interpreted as meaning decisions that are more greatly informed, or it could be interpreted as a greater number of informed decisions (e.g. here is one informed decision, here are more informed decisions). I then considered the phrase \"better informed decisions\". I feel this has the same intended meaning but removes the above ambiguity. It could refer to decisions that are better informed or it could refer to informed decisions that are better. Both are on subject and would be fine to me. A quick Google search suggested that the phrase \"more informed decisions\" is significantly more commonly used than \"better informed decisions\". I have a feeling that \"better informed\" is more grammatically-correct than \"more informed\" although I have no formal basis for this. Out of the phases \"more informed decisions\" and \"better informed decisions\", is there a more correct form?", "label": 1}
+{"snippet": "I was reading this interpretation from this site, where these lines are noteworthy enough to talk for the fact that this interpretation doesn't actually talk about many-worlds: These are the \"many worlds\" in question, although it should be clear that the label is somewhat misleading. People sometimes raise the objection to the many-worlds interpretation that it's simply too extravagant to be taken seriously--all those different \"parallel realities,\" infinite in number, just so that we don't have to believe in wave function collapse. That's silly. Before we made an observation, the universe was described by a single wave function, which assigned a particular amplitude to every possible observational outcome; after the observation, the universe is described by a single wave function, which assigns a particular amplitude to every possible observational outcome. Before and after, the wave function of the universe is just a particular point in the space of states describing the universe, and that space of states didn't get any bigger or smaller. No new \"worlds\" have really been created; the wave function still contains the same amount of information (after all, in this interpretation its evolution is reversible). It has simply evolved in such a way that there are now a greater number of distinct subsets of the wave function describing individual conscious beings such as ourselves. The many-worlds interpretation of quantum mechanics may or may not be right; but to object to it on the grounds that \"Gee, that's a lot of worlds,\" is wrong-headed. I'm not really understanding the reason \"It has simply evolved in such a way that there are now a greater number of distinct subsets of the wave function describing individual conscious beings such as ourselves.\" What is it saying? Can anyone explain me?", "label": 1}
+{"snippet": "Firstly I'm not saying that I don't believe in Cantor's diagonalization arguments, I know that there is a deficiency in my knowledge so I'm asking this question to patch those gaps in my understanding. From my understanding of Cantor's Diagonalization argument, if you apply diagonalization to a mapping from one set of numbers to another, you will always obtain a number that is not in the mapping. So this works to prove that the reals aren't countable because if you have a mapping from the naturals to the reals then you can use diagonalization to obtain a number that's not in the mapping, and this number is a real obviously, so the mapping isn't a surjection. We're not allowed to assume that the mapping from the naturals to the reals is a bijection to begin with. But when people explain why the diagonalization process doesn't produce a rational from a mapping from naturals to rationals we are allowed to assume that the mapping is a bijection to begin with? In the questions asked here: Why does Cantor's diagonal argument not work for rational numbers? The answers says: To be precise, the procedure does not let you guarantee that the number you obtain has a periodic decimal expansion (that is, that it is a rational number), and so you are unable to show that the \"diagonal number\" is a rational that was not in the original list. In fact, if your original list is given explicitly by some bijection, then one is able to show just as explicitly that the number you obtain is not a rational. Why are we allowed to assume that the original list is a bijection? Is there some way to prove that the mapping from the naturals to the rationals is a bijection that is not susceptible to diagonalization? If we can assume that the mapping from naturals to rationals is an undiagonalizable bijection why can't we do the same for the mapping from naturals to reals?", "label": 1}
+{"snippet": "According to path integral theory, it can be assumed that a particle travelling from a point A to B (in an experiment that has not been designed to detect the path) takes all the possible paths from A to B. (Please note that I use the words 'can be assumed' because I know that there is a debate whether the particle really takes all the paths that are considered in path integral or not.) Now, energy of a particle is closely related to its momentum in quantum mechanics. So, in a double slit experiment, we can setup the detector at the interference screen so that it not only detects the position of the individual particles, but also their energy. This will not violate uncertainty principle because we will still not have the knowledge of the direction of the velocity of the particle, but only the magnitude of energy. Now, being able to detect the energy of particles in a double slit experiment will be interesting because then we will be able to find out whether the energy of the detected particle is equal to that of the input particle or not. If it is equal, then it would mean that the energy is conserved during the path. Yet, according to the path integral, the particle can be assumed to take all the possible paths. Since we know the initial and final energy of the particle, this means that we can only consider those paths in path integral where the energy fluctuates only in the middle of the path! So, is it theoretically possible to detect the energy of the individual particles at the detectors in the double slit experiment. If yes, then theoretically, is the energy conserved at the start and the end of the path. And most importantly, do you know of any experiment that has been done to detect the energy of the individual particles at the interference screen. Please give me the links to the paper discussing this.", "label": 1}
+{"snippet": "I was looking up how to find relationships between Sobolev spaces and I came across this post on MO in which the first comment talks about a scaling procedure for understanding the relationships: To find the right values of k,p,r,a, I was taught to use scaling arguments. Take a nice enough singularity for the function inside the domain, and make it worse and worse, and compare how the norms change. This usually lets you solve for the appropriate parameter (and if it doesn't it tells you there is something special about that embedding). For unbounded domains you can do the same thing, and this often shows why certain embeddings cannot exist (handling singularities both inside and at infinity is hard). Other answers also mentioned this scaling approach, which I have never heard of, with one comment saying: Comparing the behavior of the different Sobolev norms for a compactly supported family of functions converging to a Dirac delta function is indeed the simplest way to figure out these inclusions. In general, understanding how things behave under rescalings is extremely useful but, as far as I know, rarely mentioned in print. It seems that you have to learn about it by word of mouth or stumble onto it yourself. Physicists and chemists also use this often and call it \"unit analysis\". So does anyone here know of this scaling approach? If so could you give a worked example for some specific function, so somebody (like myself) who is new to Sobolev spaces can learn how to apply it and gain a better understanding of these spaces?", "label": 1}
+{"snippet": "In all textbooks the magnetic field around a wire carrying a current is found from Ampere's Law. However, I would like to know what the expression for the magnetic field is, using the full time-dependent Maxwell's equations (and how to get there): Hopefully this will give me some insight into how the field is set up via EM waves. Note that I am specifically interested in how the field according to Ampere's Law is actually set up in a time-dependent fashion via EM waves. For simplicity let's say I'm interested in the magnetic field created by a wire attached to the electrodes of a battery. When you turn the battery on, the magnetic field around the wire is rapidly created. How can I get a time-dependent solution for this? Feel free to suggest how the battery could be treated, how the electrons in the wire respond etc. (I suppose all of these things must be part of the model). Also feel free to treat a simplified problem, eg. we could do the equivalent problem for the magnetic field around an infinite slab of material if that makes the geometry easier. My primary interest is in how the field is propagated into the vacuum around the wire - I would like to see how the solution eventually tends toward Ampere's Law. EDIT: I will try to make the question easier to understand: We are often taught the magnetic field around a wire arises from Ampere's Law. This applies to a steady state situation only - i.e. it does not occur instantaneously. It does not tell you how the signal (whether that be voltage or current) originating in the wire actually gets out to the vacuum around the wire, as the current starts at zero and ramps up to some constant value. Presumably this happens via the generation of EM waves, because of course Ampere's Law is not valid on very short timescales. I would like to know what the solution is for the magnetic field around a wire when you are not in the steady state, which should reveal how the magnetic field propagates into the vacuum. Obviously the solution would have to correspond to Ampere's Law in the long time limit. I do not mind so much what device you use to get the current flowing in the wire in the first place. For example if you want to use a battery connected by a switch to the wire then fine. Or an AC generator slowly ramped up with some assumed time-profile would also be fine. In other words, if you would like to answer this question, you could choose whatever model you think best describes the scenario in which a wire is connected to a battery by a switch and the switch is turned on (or, as I mentioned some other, similar process). The wire can be any shape you choose. I just choose a \"wire\" because it's the most commonly used simple conductor, but if you would prefer to use for example a slab of conductor, that is fine, because my interest is in how the time-dependent fields converge to Ampere's Law.", "label": 1}
+{"snippet": "I am a computer science student that is struggling with a problem of mathematical nature. Thus far I have only studied calculus, discrete mathematics and linear algebra, but cannot figure out how to approach this problem. I tried Stack Exchange, but due to the mathematical nature they suggested me to ask here, so here goes: I am trying to create shopping lists from a collection of products, where the returned shopping list should be optimized for cost as well as to meet another condition. For example, let's say that I want to create shopping lists based on the energy content of the products. When the user enters a total sum, the returned shopping list should try to max out the kcal content while keeping the total sum at or around the sum specified by the user. I've gotten so far as to create the collection of products, and all products are stored as objects with fields holding nutritional values and price etc. The kcal-value is also stored as a member variable in each product's object. At first I considered looping through all combinations of products, sort out those that are way out of the price interval, and then return the one with the highest kcal content. But as the numbers of products available increases this soon becomes a non-viable option I think. I now wonder if there is any algorithm to solve this problem, if not, is there any way to easily implement this? I've understood that this is a problem of linear type, (discrete?, diophantine?), but that's about all.", "label": 1}
+{"snippet": "As far as I understand it, quantum mechanics requires that a particle's position to be not specifically determined in space, but rather be 'spread' out through space, in the sense that we can only know the probability a particle is at a particular location. This can be visualised through the wavefunction. When we then try to measure the particle's position, (say by firing a high energy photon at it), the particle will turn out to be at some particular location, which corresponds to the wave function collapsing (I'm not too sure if this is the right use of the term). The particle could however be found in a large range of positions. Consider an air particle, which has an initial wavefunction (in black), which we then fire a photon at to determine the position of. The air particle could then be found at position A or found at position B, with roughly equal probability. The two circumstances however cause a slight disturbance, which 'propagates' through space. What I mean by this is this air particle's position and momentum will affect the air particles near it, which will affect the air particles near those, and so on and so forth. Through chaos theory, a small change in initial conditions will result in a very different outcome, so this single misplaced air molecule has the potential to change everything about Earth. In the above diagram, air particles are depicted by dashes, with their velocities depicted by the length of the dash. As can be seen, the two situations A and B lead to a 'propagation of disturbance' (the area in which the air particles are different between situation A and situation B) which is depicted by the black circle. What I'm interested in is how quickly the circle grown in size. At first, I thought that it should propagate at the speed of light. Imagine that our air particle is situated at the North Pole. An air particle situated at the south pole will have a wavefunction that is VERY NEARLY zero at the north pole, but it will still be finite(I think). For this reason, a small disturbance of the air particle at the north pole will result in a disturbance at the South Pole directly, at the speed of light. Another voice in my head however said that this was rather silly. The disturbance should propagate rather slowly, and should only propagate through the collision of air particles. Through the atmosphere it would travel at roughly the average speed of air particles in the atmosphere, and through the solid ground it would travel very slowly. Which of the two, if either, is correct?", "label": 1}
+{"snippet": "I am by no means an expert in the realm of physics. I do from time to time, try to understand the concepts of modern physics and their applications. I came across this video that I am currently watching, and in the beginning it explains what would happen to someone if they crossed over the event horizon of a black hole. From my understanding, the time dilation is so great near a black hole, that if you were to cross over the event horizon someone viewing you from further away would never actually see you cross and you would appear frozen forever at the edge of the event horizon due to this time dilation near great mass. If this is true, in the sense that the entire existence of the universe outside the black hole would unfold while you were stuck at the edge of the event horizon due to time dilation (Please fact check me here, I would love to know if time does actually stop for you if you cross the event horizon of a black hole), wouldn't it be true that you would actually spend no time at all inside the black hole due to hawking radiation and it's effect on the evaporation of black holes? What I mean by this is that, apparently from what I've read, a black hole will evaporate and cease to exist at the end of some finite period of time in the universe due to it giving off hawking radiation. If this is true, and if the fact that you appear to be forever frozen at the event horizon due to time dilation is also true, wouldn't it seem from the perspective of the person crossing the event horizon that the black hole ceases to exist? I am very intrigued by this possible paradox that I was questioning and I would love to know more about it's ramifications, if there are any, from many of you whom are more advanced that I. Thank you in advance.", "label": 1}
+{"snippet": "What determines whether something is a \"noun adjunct\" or just a garden-variety adjective? Does it matter in any meaningful way? Here is my hypothesis, but I can't find any authoritative source to back it up. I'm hoping someone here can weigh in more definitively. Classification of noun adjuncts is based subjectively on whether the word is in \"common usage\" as a noun. \"Book\" and \"chicken\" are commonly nouns and would be considered noun adjuncts in \"book collector\" and \"chicken soup\"; \"yellow\", not so much. Noun adjuncts may share some common qualities that differentiate them from other adjectives (like not being able to be inflected into superlative forms... one can't be a \"book-est collector\"). But they are still fundamentally adjectives and may even appear in the dictionary as such if the adjectival usage is common enough. What I've found so far... Wikipedia defines a \"noun adjunct\" as: an optional noun that modifies another noun; it is a noun functioning as an adjective. But English words are not decreed to be nouns or adjectives by some higher authority. So it seems strange that one can prescriptively conclude that something \"is a noun\" in the first place, let alone extrapolate that it \"is a noun functioning as an adjective\". The wiki article cites \"chicken soup\" as an example of a noun adjunct, but at least one dictionary gives a definition for \"chicken\" as: adj. (of food) containing, made from, or having the flavor of chicken So it seems that there are some differing points of view on how to categorize these words. This question was spawned from some discussion in this question, this question and this other question.", "label": 1}
+{"snippet": "The past few months I have been studying astronomy and Integral Field Spectroscopy (IFS). What I want to do is to fit a galaxy kinematic model to data (ie: estimate the model parameters that give the best fit result). At the moment I extract the velocity and velocity dispersion maps from an IFS datacube but I am not sure how to deal with the Point Spread Function (PSF). What is more correct: Deconvolve the data with the PSF and then fit the model to the deconvolved data? Or convolve the model with the PSF and then fit the PSF-convolved model to the data? The first approach sounds computationally faster to me because only one deconvolution is involved, but at the same time it won't give the best result because deconvolution is ill-posed even if the PSF is known. Is that right? The second solution sounds computationally slower because I will have to convolve the PSF with the model for every single model evaluation, but it will give better results because the convolution result/solution is well defined. Is that right? The data sources I use for my experiments are products of some data reduction pipeline. Why the deconvolution of the PSF is not part of the data-reduction step? Is it because of what I mentioned above? ie: The deconvolution is an ill-posed procedure and it may affect (in a bad way) the data. I am not very familiar with the deconvolution procedure but so far I have found that the Richardson-Lucy technique is a method for deconvolving with a known PSF. Are there other better techniques that are proven to give better results?", "label": 1}
+{"snippet": "Before getting into the question, here are some remarks: Given a single point charge, the value of electric field at the position of the charge is singular/undefined, which makes sense, since a particle cannot interact with itself. Given a discrete charge distribution, the value of the field at an empty point(i.e. no particles reside at that point), is the field contribution from all the charges. However, if the point of interest contains a point-charge, then the value of the field is the field contribution from all the charges except the charge that resides at that point. Now here's my inquiry: In the case of discrete charge distribution, it makes sense to speak of the value of the electric field at a given point, whether that point contains a point-charge or not. What about continuous distributions? My intuition says yes, we can; since one can think of continuous distributions as an extension of discrete ones, with the difference being that the former contains uncountably infinite charges. Therefore, to calculate the field value at any given point on the continuous charge distribution, one has to consider the field contributions from all the charges except the one residing at that point. Example: The value of the electric field at any point on an infinite sheet (plane) of charges should be zero. Since at any given point on the sheet, one can think of that point as being surrounded by infinite concentric rings, where the field contribution from each ring (by symmetry) is zero. So does it make sense to speak of the value of electric field on continuous charge distribution? Or is it not defined?", "label": 1}
+{"snippet": "A rather simple question for liquids specialists I guess but I have hard time finding information about this. Here is my problem. I understand the ideal gas theory and the Maxwell's speed distribution. I see an ideal gas as small balls (mostly surrounded by void) moving around very fast and colliding elasticly with each others. If you want to be more precise, you use an interatomic potential such as the Lennard Jones potential that takes into account Van der Waals attractive interactions as well as the repulsive ones. You can define a kinetic (positive) pressure, kinetic temperature and molecular (negative) pressure with such a simple model. I think I understand that pretty well for now. On the other side, I think I understand cristals fine as well. I see them as atoms bounded together by springs in which waves can flow and each atom oscillates around an minimal potential energy position. I have seen how you can calculate cristal's thermal capacity using Debye's model. So for now I think I have an idea of how a solid behaves at the molecular scale. But what about liquids? I have read very interesting posts here about molecules velocity in liquids and I would be glad to have a more general view of what a liquid is from a molecular perspective. As I understood it, molecules in liquids also oscillate around a minimal potential energy position but they can also swap positions with each other. Is that correct? Are there any tabulated values of molecules swapping speed in liquids ? Concerning pressure. Should I represent pressure in liquids as a sum of a (positive) kinetic pressure due to molecules collision and a (negative) molecular pressure due to attractive interactions between molecules? Is this a good way of representing myself a liquid at a molecular scale? Is there a model explaining the relation between viscosity and molecules attractive interactions ? -----------EDIT--------- I got the answer about swapping molecules. Now this brings me to my question about pressure in liquids from a molecular perspective. Concerning ideal gases, pressure is due to molecules collisions. Does this still stand for liquids or is it more a question of \"weight\" exerted by molecules on each others? Does any one know a molecular pressure model for liquids? Thank you", "label": 1}
+{"snippet": "We can speak of \"microbes\" or \"micro-organisms,\" and I used to think that these terms clearly included viruses. And they are used this way by at least some other people; here's a website that refers to viruses as a category of microbe. However, I recently discovered that these terms are usually defined as referring to microscopic \"life,\" and the definition of \"life\" with regards to viruses is a contentious topic. When dealing with disease-causing agents, we can use the word \"pathogen.\" However, not all bacteria and viruses are pathogenic. All viruses must infect living cells to reproduce, so it is appropriate to refer to all viruses as \"infectious agents\" (this is what the Wikipedia article on viruses uses in its introduction). However, not all bacteria are necessarily infectious. The informal terms \"bug\" and \"germ\" do exist. While these don't seem strictly limited to pathogens, that seems to be their most typical use. But for a technical audience, does any term exist for which there is a consensus that it refers to both all bacteria and all viruses? If no single word exists, a short two-word phrase along the lines of \"biological entity\" would also be OK. (This phrase also comes from the \"virus\" Wikipedia article, and seems to be the best fit I've found so far. I can also think of a few others along these lines, like \"microbial entity\" which could be seen as a shorter equivalent to \"microscopic biological entity.\") Here are the most important criteria I'll consider when deciding whether to accept an answer: technical correctness: The term must be acceptable regardless of whether one considers viruses to be living or non-living, organisms or not organisms. \"Micro-organism\" does not meet this criterion because some people do not consider viruses to be organisms. positive scope: It must include all viruses and all bacteria. \"Pathogen\" does not meet this criterion because not all viruses or bacteria are pathogenic. negative scope: It should not include inorganic objects, whether microscopic or macroscopic. E.g. rock particles. It's OK if it includes protists or multi-cellular organisms, or prions and other \"pro-life,\" or some combination of any of these. Other important criteria for me: established terminology: I'd prefer a term that is already in use to a neologism. If a neologism seems to be necessary, I'd like it to be linguistically well-formed and etymologically transparent. length: all else equal, I'd prefer a shorter term. grammatical number: I'd prefer a term that can be used in the singular to refer to a single species of viruses or bacteria, as opposed to an always-plural word or a singular mass noun.", "label": 1}
+{"snippet": "I recently had an argument with a friend around the question \"have you ever thought about something?\" The question was asked in the context of exploring some life possibilities, such as buying a sports car or moving to a different country. The disagreement was around whether an affirmative answer to the question bears the hidden meaning that the something being considered is something that the person answering actively wants. To give an example: when asked \"have you ever thought about moving to Sweden?\", if a person answers in the affirmative, which of the following two meanings best describes their answer? They consider moving to Sweden a practical possibility, and they actually want to do so in the future. The thought has crossed their mind, but nothing can be inferred about whether they want or plan to move to Sweden in the future. Assume the subject is not currently living in Sweden :) Question update: Some of you answered that the meaning depends on other factors, such as tone of voice, body language, context, etc. As I said in a comment, to the purposes of this question, ignore such secondary conversational artifacts. They can always extend the range of meaning of any sentence or word, from the \"proper\" sense, to the complete opposite, such as when being sarcastic (e.g. \"Would you like to go to Sweden?\" \"Yeah, right...\") Consequently, the disclaimer \"it depends on the tone of voice\" can probably be applied to most answers on this site. To put it another way: assume you read the text, with minimal context. What's the meaning then?", "label": 1}
+{"snippet": "Ok so I'm a programmer, I'm not a mathematician, I've got a minor in math but I didn't even do particularly well at it so please bear with some possibly really stupid thoughts. Just please try to explain to me why what I'm asking is stupid so that I don't keep making a fool of myself. I recently found myself thinking along the following lines: If you take the stand that it's solipsism to talk about anything that cannot be put to use in predicting an outcome then cannot you apply the same axiom to basic mathematical operations? For example does addition really have any meaning outside of the context of placing two objects in a box and predicting how many are inside? Yeah, I realize that's a dangerous question to ask a board full of mathematicians but I imagine you can ask this question about any axiom. The problem is that in reality if you put one thing and then another into a box it does not mean that there will be two things in the box. There will likely be two things of course but if the objects are point particles like electrons there's a chance there will be one or three, or a million electrons there. Heck, the same is even possible with apples, just incredibly unlikely. I don't have the mathematical wherewithal to think through what this would mean but intuitively it would seem that this might not have many implications for addition, but might for subtraction (unless you could somehow have negative amounts of particles which I won't rule out), and certainly for things like integration and derivation. I would assume that someone's done work along these lines before? Has anyone actually created a system around it? Was it useful? Are there any accessible books or articles about it? Just interested", "label": 1}
+{"snippet": "This question was actually asked by Alan Munn in a comment to How do I create a LCM tree diagram?. I repeat (and self-answer) it here because the answer is too long to fit the margin :-) qtree is a well-known and heavily used package for drawing trees using the so-called bracket notation. (The bracket notation is especially familiar to linguists.) forest is my own, recent package for the same job. Due to the awesome power of pgf/tikz (in particular, the pgfkeys utility), which it is based on, forest is an extremely flexible package. ---From the feedback I got so far, including feedback from this site, I don't seem to be the only one who believes so. Which makes me happy. :-) Although both qtree and forest encode trees using the bracket notation, the exact syntax is somewhat different. While forest requires that each node (including its children) be enclosed in square brackets (like this: [node [child node] ... [child node]]), qtree relaxes this requirement in the case of terminal nodes (leaves): they can be separated simply by whitespace, like this: [.node leaf ... leaf ]. Furthermore, the packages differ in the encoding of node labels: as showh above, in qtree a bracketed (usually non-terminal) node's label must be preceded by a dot (.). (forest uses the same syntax as synttree; another package that uses (and extends) qtree's syntax is (obviously) tikz-qtree. As I mentioned in a comment in the above-mentioned question, I have decided for synttree-like syntax purely out of personal taste. I guess I found it more consistent.) As Alan pointed out, the difference in the syntax makes the potential transition from qtree to forest harder: nobody wants to throw away tons of trees (s)he has painstakingly drawn. Thus Alan's question: would it be possible for forest to support both syntactic dialects?", "label": 1}
+{"snippet": "My good friend is from Pittsburgh and frequently uses the word whenever to mean the word when. I am aware this is a regional dialect and really wish to respect that, but it is causing numerous problems in our spoken communication. (I am also a native English speaker but am not accustomed to this usage of \"when\" and \"whenever\".) I have expressed my concerns to him and asked him to use a neutral dialect to improve communication, but he argues it is valid English, he doesn't understand the difference between the two anyway, he \"doesn't have problems with anyone else understanding [him]\", and that my misunderstandings are because I \"have Asperger's and understand [his] speech literally\". (I would guess if no one else has an issue with his speech, it's because he speaks English primarily with people who have the same regional dialect and non-native English-speakers and uses French and German for work. That said, perhaps everyone else does understand what he means without any confusion. When I ask for clarification, he gets irritated.) What should I do? Examples of such misunderstandings are below: Example: Whenever my aunt was about to die, she called me into the room and told me she loved me. I understood this as his aunt periodically became ill to the point where she was close to dying and called him into the room to say she loved him. (My background in healthcare makes this seem like a very plausible situation.) I responded to him in a way that reflected my understanding of the habitual nature of this. He was annoyed and said it was obvious that the aunt was about to die one time and that, as such, this calling-into-the-room was a one-time occurrence. Example: Whenever my sister was born, my dad fainted. It is obvious to me that his sister was born one time. In this instance, although I believe the better word choice is when, I can understand that his father fainted when his sister was born. Example: Whenever I moved to Germany, I lived in Berlin. I knew he had moved to Germany once for a (temporary, location-based) job. However, his statement surprised me, and I thought maybe I was wrong (and as a friend I wanted to learn more if he had actually moved numerous times), so I asked how many times he'd moved to/lived in Germany. He was equally surprised by my question, responded he'd moved to Germany once, and could not understand how there could be any confusion in the statement.", "label": 1}
+{"snippet": "I have an object with incident light rays traveling away from this object. Some of these rays are traveling from the left-hand side through a simple lens (say, a double-convex converging lens). As these rays enter the lens, they are partially refracted, reflected, and absorbed. As these rays leave the lens, they are refracted even further, and eventually the light rays converge to a point (on a film screen or something). Since the light rays are partially reflected and absorbed, wouldn't the light rays that entered the lens at the edges (where the lens is thinner) be less reflected/absorbed than the light rays that entered the lens near the center (where the lens is thicker)? If the light rays converged onto a film screen, would the differences in the intensity of light caused by these reflections/absorption (which can be traced back to differing thicknesses of the lens at different points) cause any issues with the images? Would this ever need to be taken into an account by a scientist or student conducting an experiment involving data obtained from a camera? Also, for a given convex lens (made of a particular material, and with a specific curvature), can the intensity of light as it reaches the focus point be thought of as a function of \"vertical\" distance from the center of the lens? This thought comes from the fact that this vertical distance would determine how much lens-material the light travels through. Are there examples of such functions, or is there a way of coming up with one for a simple lens?", "label": 1}
+{"snippet": "Recently I was asked to explain the difference between reflection and total internal reflection from a purely conceptual standpoint (no math). Let me explain what I already know. Reflection and refraction at the quantum level are the same thing. Light is a photon. A photon is a discrete particle that has wave characteristics (a finite wave traveling like a bullet). As the photon travels it collides with electrons in the matter of the medium it is traveling in. Depending on the energy of the photon and the allowed energy bands of the medium the photon cause the electron to jump up a level. If the photon is absorbed then the medium will increase its motion (at the macro scale increasing its temperature). If the photon is not absorbed it will be re-emitted (really as a new photon). I have read and watched Feynman's QED lectures and book and have a pretty good understanding of his process for determining how all these paths come together to give the net path of the photon. The general rule of thumb is that the photon wants to take the path which requires the least amount of time. I understand how this principle goes to explain refraction and reflection. What I don't seem to understand is why does one material seem to cause a higher percentage of refraction compared to another (metal vs. glass). What about the electron configuration of a the medium changes the net effect of the absorption and re-emissions of the photons? Is there a change in the probability of the photon being re-emitted in a reverse direction? Is there a farther distance the photon can travel before being incident onto an electron? This is the part where my understand breaks down. When you have hit the critical angle in a medium that refracts and the light completely reflects, are the photons moving is the same manner as they would be in a material that always reflects? How does this connect to the question in the previous paragraph? I know I have a bunch of mini questions embedded in answering this one larger question. Any help on any of the parts would be greatly appreciated?", "label": 1}
+{"snippet": "A few months ago I was telling high school students about Fermat's principle. You can use it to show that light reflects off a surface at equal angles. To set it up, you put in boundary conditions, like \"the light starts at A and ends at B\". But these conditions by themselves are insufficient to determine what the path is, because there's an extra irrelevant stationary time path, which is the light going directly from A to B without ever bouncing off the surface. We get rid of this by adding in another boundary condition, i.e. that we only care about paths that actually do bounce. Then the solution is unique. Of course the second I finished saying this one of the students asked \"what if you're inside an elliptical mirror, and A and B are the two foci?\" In this case, you can impose the condition \"we only care about paths that hit the mirror\", but this doesn't nail down the path at all because any path that consists of a straight line from A to the mirror, followed by a straight line to B, will take equal time! So in this case the principle tells us nothing at all. The fact that we can get no information whatsoever from an action principle feels disturbing. I thought the standard model was based on one of those! My questions are Is this anything more than a mathematical curiosity? Does this come up as a problem/obstacle in higher physics? Is there a nicer, mathematically natural way to state the \"only count bouncing paths\" condition? Also, is there a \"nice\" condition that specifies a path in the ellipse case? What should I have told that student?", "label": 1}
+{"snippet": "I have a long-term goal of acquiring graduate-level knowledge in Analysis, Algebra and Geometry/Topology. Once that is achieved, I am interested in applying this knowledge to both pure and applied mathematics. In particular, I am interested in various aspects of smooth manifolds, co/homology and mathematical physics. I have acquired a smattering of knowledge in all of these areas but feel that I need to become more focused to make make coherent progress. I have a very bad habit of picking up a book, reading a bit, working out a few details, and then moving on to other random topics in other random books. In doing this, I don't really feel like I accomplish much. To rectify this admittedly undisciplined approach, I have decided to select core source material from each of the three major areas listed above and focus on it until I have assimilated all the information in that material. For analysis, I have selected Amann and Eschers' Analysis, volumes I, II, and III. I made this choice because out of the analysis texts I have surveyed, theirs seems to be the most comprehensive and treats elementary and advanced analysis as a unified discipline. My basic strategy is to treat each theorem, example, etc. as a problem and give a fair amount of effort to proving before consulting the text. I think this is probably the best way to approach the material for maximum understanding but it requires a considerable amount of time. There are probably thousands of these sorts of \"problems\" among the three volumes. Ulitimately, I would like to end up with a notebook (which would probably number in the thousands of pages) that contains all of the details to all of the theorems completely worked out, as much as possible, with my own thoughts. Again, this seems like it will take forever and my time on this earth is unfortunately finite. I'm reasonably confident though that the production of such a set of notes would lead to at least a fair level of mastery of the material in question. Can anyone suggest an alternate strategy that might be more effective in terms of time but that would lead to a comparable level of mastery? It is also a problem that I might actually prove a fact completely on my own but then, a month later, might not be able to recall it in a time of need. What strategies are helpful for best ingraining this material (other than the obvious \"Work lots of problems\" approach)? Would appreciate any tips or pointers.", "label": 1}
+{"snippet": "On StackOverflow.com I often find that people ask questions about problems that arise due to poor design choices (typically due to a lack of knowledge about the particular programming language). For example, the OP will make a choice at point A that is wrong, then in order to correct follow-up errors goes on to B, C, D ... and at point X (s)he gets stuck, and thus asks a question about X, when the solution to the problem is actually to fix A. Note that this is not limited to programming, but can be any project. Earlier, I came up with The Underwater House problem to describe a similar situation: Q: \"I have this underwater house. I am having big problems with leaks and water damage. What is the best way to stop a leak?\" To which the answer of course is: \"The best way is to not build a house under water.\" When faced with such a question, I often feel the urge to name it, or create some classification, to let the OP know right away what the mistake is. The best way to state this that I have come up with is: \"You are asking The Wrong Question.\" However, I feel that this is inadequate, and requires further explanation. Is there a more self-explanatory way to state this? Some simile, saying or phrase? Update: I felt that no answer really fits the bill better than \"The Wrong Question\", though \"treating the symptom\" was arguably the best answer. The amalgam \"you're treating the symptom of a design problem\", while dead on the money, is not as clear, concise and pithy as one would like. And sometimes not correct.", "label": 1}
+{"snippet": "Related: How would a black hole power plant work? I have put a bit of commentary enumerating my confusions in parentheses I read in Black Holes and Time Warps (Kip Thorne), that quasars can generate their jets from four different processes. These all involved the accretion disk, but there was one which doesn't make quite as much sense. It was called the Blandford-Znajek process, and it involved magnetic field lines carrying current. The process was visualized in two ways. A black hole, with magnetic field lines, is spinning. In the first visualisation (viewpoint actually), the magnetic field lines 'spin' along with the black hole, and nearby plasma is anchored onto the field lines by electrical forces (where did the electrical fields come from?). The plasma can slide along the field lines but not across them (why?). Since the field lines are spinning, centrifugal forces will fling them up and down the field lines, forming jets. The other viewpoint is this, and it makes even less sense (to me that is, I haven't had a formal education in GR): The magnetic fields and the swirl of space generate a voltage difference across the field lines (Why? How?). The voltage carries current across the magnetic field lines (why are the field lines behaving like wires?). This current travels across plasma, which accelerates it, creating the jets. Now the main thing that doesn't make sense, is that magnetic field lines are behaving like wires. Why would they? I suspect the answer lies hidden somewhere in the equivalence of EM waves in different frames, but I can't think up any convincing argument from that side. If the answer involves GR equations, you don't need to solve it here (wouldn't make sense to me), but if you have to, just refer to the equation and what you did to it, along with the final result. Thanks!", "label": 1}
+{"snippet": "I can't seem to find a specific answer to this anywhere. I understand that in a rocket there is a chemical reaction that causes gas particles to leave the rocket at high velocity. By Newton's third law, and the conservation of momentum, this caused the rocket to be propelled. What is missing is a physical explaination of what exactly causes this force on the rocket, as most answers annoyingly miss this final bit! People often use a skateboard-bowling ball analogy. However, in this analogy the person throws the ball and the ball provides an equal and opposite force on the person as it is thrown. The problem is, rocket doesn't 'throw' the exhaust out as it directly doesn't accelerate the particles - this is a result of a reaction. So what exactly causes the force on the rocket itself? Is it the case that in the explosion some gas particles collide with the rocket base, and the nossle is designed as to maximise collisions that will provide an upward force? I have seen people say this is wrong, or suggest it is right. Wikipedia says: 'About half of the rocket engine's thrust comes from the unbalanced pressures inside the combustion chamber, and the rest comes from the pressures acting against the inside of the nozzle' I want to be able to understand this in terms of particle collisions. I know there is a force due to the physical laws but people don't seem interested in the mechanics of the force itself. Back to the analogy: if someone where to throw a bowling ball over your skateboard, you wouldn't move, just as particles leaving a rocket, without collision of any kind, wouldn't cause the rocket to move (I know that's not possible, but hopefully makes my point). Hope this question makes sense.", "label": 1}
+{"snippet": "Here is a traditional derivation of time dilation: There's a train with a lamp in the ceiling, moving at velocity v with respect to an observer. In the frame of the observer, the path taken by the light from the lamp straight down to the ground is actually diagonal because the train has moved forwards by the time the light hits the ground. Since the speed of light is constant, the time it took for the light to reach the ground must have been GREATER, because the distance traveled was the hypotenuse of a triangle whose side is the height of the lamp and whose base is the distance traveled by the train in the time it took the light to travel. That's the essence of it, math not included because it's not relevant to my question: This derivation works for light, yes, but it's based on the fact that the speed of light is identical in all frames, so applying the same procedure to a ball, say, would not work. In short: We calculated that light travel time has been dilated. How does this argument extend for ALL objects, not just light? Also: I have heard of answers involving light clocks (devices which measure time based on how long it takes light to move some distance), using the following arguments: Measuring time with a light clock shows that time clearly dilates. counter-argument: how do you know that the light clock is accurate then? Maybe other clocks would disagree, and time only dilates for light? If one uses both a light clock AND a variety of other clocks: The argument is that if you used both clock types and only the light clock went out-of-sync, you could tell that YOU were the one moving, so this violates the postulate of relativity (all inertial frames are equally valid; none are \"THE\" rest frame). counter-argument: this is okay with me if the person observing a difference is in the clock frame. But if they are not, relativity seems satisfied with the condition that, if a train observer and a \"stationary\" observer both have both types of clocks, each person sees the other person's clocks as out-of-sync with the other person's light clocks (nobody looks at their own clocks). I am aware of the experimental evidence that particle decays follow time dilation. I'd just like some evidence that it applies to all phenomena, rather than just the set which we have experimentally verified. Best would be a theoretical argument from Einstein's postulates. I am an undergraduate in my senior year, who has not yet taken General Relativity, so I would appreciate it if that were kept in mind in any explanation!", "label": 1}
+{"snippet": "Context: I prepare my scientific documents using LaTeX and compile to a PDF. I often need to seek comments on drafts from collaborators who do not use LaTeX. Most of these collaborators use Windows OS. Assume also that the collaborator does not need to edit the document. They only need to be able to add comments to the document. Most would be familiar with the commenting system in MS Word, for example. I'd like to be able to give the collaborator some clear instructions about what software and system they should use to comment on the draft. This should involve free software and an easy to use interface. Question: What is a good strategy for getting comments on draft documents when the collaborator does not know LaTeX? Initial thoughts: I know Adobe professional allows you to add comments to a PDF. However, some collaborators don't have this software and it costs money. I could send the raw LaTeX to the collaborator. However, given all the markup, the collaborator may find LaTeX source a bit mysterious. UPDATE: After posting I noticed Andrew Stacey's answer to a similar question. Along with a number of other good tips (such as printing and getting paper comments), he mentions jarnal, xournal, and gournal as free cross-platform PDF annotators. I'd be curious to know whether experts have found them adequate for the above mentioned purpose and whether any of them are to be preferred. Others mention FoXIt. And yet others discuss the option of exporting to MS Word or Open Office and using the reviewing system within these programs.", "label": 1}
+{"snippet": "I read everywhere the famous, but offhand statement that \"the universe began from a single point\" and this bugs me because that surely isn't true. My understanding has always been that this was an oversimplification for the sake of explaining it to children when it fact the universe is - and always has been - infinite. The observable universe has a size, but surely no one is seriously suggesting that the observable universe is all there is? That's just the farthest we can see, what with space expanding faster than light and what not. But surely the truth of it is that the universe goes on forever in every direction and has no \"centre\". Then it seems to me that the concept of everything start from a \"point\" is just silly. Infinite density, yes. But surely it still had infinite size? I had always thought it quite obvious that the universe \"started\" as an infinitely dense, infinitely sized, \"clump\" of energy which gradually expanded and cooled as the energy was distributed over a larger space (because space itself is expanding, not because the \"point\" expands). Am I at odds with the scientific community on this? Do people honestly believe everything start from a literal singularity? A single point? Or is that just the result of only talking about the observable universe which has a definite size? But the universe as a whole is infinite, surely, so how it possibly have come from a single point? I understand that if you assume the observable universe is all there is then when you extrapolate backwards in time you end up with a singularity, but the observable universe is just a bubble in an infinite universe.", "label": 1}
+{"snippet": "The famous Riemann rearrangement theorem states that for a conditionally convergent real number series, we can rearrange the order of summation to make it converge to any prescribed number in the extended real line. In particular, this result sheds much light on the significance of absolute convergence, without which it would be quite dangerous to manipulate a convergent series. For improper (Riemann) integrals, we can also distinguish conditionally convergent integrals from absolutely convergent ones using analogous definitions. I'm wondering, however, if there also exists an analogous \"rearrangement theorem\" for improper integrals which reveals the essential difference (like eligibility for rearrangement, in the case of numerical series) between the two kinds of convergent integrals? Indeed, can we even define an integral version of \"rearrangement\"? Of course, one distinction I'm already aware of is that absolutely convergent integrals are also integrable in the Lebesgue sense while conditionally convergent ones fail to be. But this is not what I want, since it doesn't appear nearly as striking as what is exhibited in the series version. PS: as far as I can tell, one probable way to see why eligibility for rearrangement matters is how we define a valid expectation for a numerical random variable. We require expectations (numerical series for discrete random variables, and integrals for continuous ones) to be absolutely convergent, for if they were not, then they would undesirably depend on the \"chronological order\" in which we observe events, violating our basic principle that expectations should be stable and inherent in the random variable itself, rather than affected by how each event chronologically arises.", "label": 1}
+{"snippet": "My questions concerns that classic train paradox, wherein there is a train and a tunnel of equal length, and the train is traveling and some fraction of the speed of light towards the tunnel. According to the Special Theory of Relativity, an observer outside the tunnel will see the train length contracted (Lorentz Contraction), whereas an observer inside will see the tunnel contracted. Additionally, suppose that there were doors at the ends of the tunnel and that the observer outside the tunnel closed both doors instantaneously when he/she saw that the train was completely inside the tunnel. The classic resolution of this paradox invokes the non-simultaneity of events, explaining that the observer in the train sees the far door close first, and then, once the train has begun to exit the tunnel, looks back to see the door at the beginning close. Thus, both observers agree that the train does not touch the door when they are closed for an instant. Now my questions. Why is it that the observer on the train sees the far door close first? It seems to me that the information coming from the far door would reach the observer on the train only after the information from the other door is reach. Under this interpretation, the observer on the train would observe the train getting hit by the doors. What if, by some means, this event can be explained in terms of a stationary observer too? Everyone always concludes that the train remains untouched by the doors, but really the only condition that needs to be met is that both observers must agree. Why can't they both agree that the train was hit? So, to summarize. Why is the door that is farther away from the train observed to close first? Why can't the other possible conclusion (both see a hit train) be observed?", "label": 1}
+{"snippet": "I was reading on wavelets and it seems that its hard to find a precise mathematical definition of what this concept is. My confusion first arose due to Gilbert Stang's linear algebra book. In particular consider the following extract: It talks about how to change a vector from one basis to another but it never rigorously defines what a wavelet is (by the way, I did understand that extract I included, just not the concept of \"wavelet\"). From my understanding, some special basis are called wavelets (for some special reason). But which basis are we allowed to call wavelets? I would assume that they have something to do with linear algebra and oscillation/sinusoidal functions but I don't really see what the relation between the two is. To look for an alternative explanation I went to wikipedia and the initial paragraph starts as follows: A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. It can typically be visualized as a \"brief oscillation\" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have specific properties that make them useful for signal processing. Wavelets can be combined, using a \"reverse, shift, multiply and integrate\" technique called convolution, with portions of a known signal to extract information from the unknown signal. With that description it makes me feel that wavelets are actually functions. However, I've had difficulty understanding this precisely, specially when trying to relate it to linear algebra. I guess I am having a hard time connecting the three, wavelets, linear algebra and their relations to sinusoidal functions (if there is any relation to them).", "label": 1}
+{"snippet": "I have confused myself about the following variant of Maxwell's demon and I can't seem to find out where the energy went. Consider this: You have a chain (one dimension) of spins (up/down) with a nearest-neighbor coupling. Energy is minimized if spins are aligned. Let us say the energy difference between alignment and not-alignment is E. The zero temperature state is either all up or all down. If we heat the state up to a temperature T, some of the spins will flip with a probability given by the Bolzmann-factor, depending on the ratio T/E. So far so good. Now the finite temperature state has energy because the states aren't all aligned, but the distribution is thermal and it's no useful (free) energy. However, if you knew which spins are misaligned, you could selectively flip them. Let us say the system is such that you can flip them by shooting a photon with energy E at the spin. Eg, you shoot at the middle spin in a series of three. If it's up,up,up then the photon will be absorbed and you end up with up, down, up. If it's up, down, up, the photon stimulates emission and you get up, up, up plus two photons of energy E. If you have up, down, down, the photon doesn't change anything about the total energy. The same happens if you exchange all ups with downs. Now the thing is this: If you do not know which spins you have to flip, your chances of gaining or losing energy by shooting photons at the chain are the same. You just convert one thermal state into the other. But if you knew which spins to flip, you could topple them over selectively and get energy out of the system. Essentially, you extract it from the thermal bath that did heat up the chain. That's possible (I think) because you are using information to reduce the entropy of the system. My question is this: How do I see that the energy needed to measure the spin orientations in the chain is at least as large as the energy I can gain by flipping them selective once I have measured? It isn't clear to me why it should not be possible to measure them with some very low-energetic probe, eg measuring the local magnetic field with the Hall effect.", "label": 1}
+{"snippet": "Consider an American actor who is tasked with mastering British Received Pronunciation for an upcoming role. If he has a talent for vocal mimicry, as many actors do, he should have no trouble picking up the \"rules\" of RP just from listening to people speak it: the non-rhotacism of the dialect, the aspiration of intervocalic t, the characteristic intonation patterns and prosody of RP, and so on. For the most part, he should have no trouble speaking RP like a native. Yet he would never in a million years figure out on his own that lieutenant should be pronounced \"leftenant,\" for example, or that controversy is often pronounced with the accent on the second syllable, unless he hears those specific words pronounced. To my knowledge, there are no general characteristics of RP that account for the mysterious appearance of an f in lieutenant (or, if you prefer, there are no general characteristics of General American that account for its absence). You just have to know how those specific words should be pronounced, because you'll never figure it out on your own. Do linguists recognize a distinction between the \"rules\" of a dialect on the one hand and its individual pronunciation \"quirks\" on the other? Is there a term for this phenomenon? Is it considered merely a variation on regional preferences for certain words over their synonyms (e.g., rubbish vs. garbage), or is there something else at play here? (Disclaimer: I take no position on whether the BE or AE pronunciation of any of these words should be considered the \"quirky\" one; I simply note that one couldn't easily intuit one pronunciation just from knowing the other.)", "label": 1}
+{"snippet": "Suppose I am conducting the Quantum Eraser experiment. The results of this experiment are easy to understand with the traditional quantum mechanical interpretation of a pair of entangled photons. Specifically, suppose that I am performing the \"eraser\" part of the experiment in which one photon is diagonally polarized so that when the entangled partner passes through the circular polarizers of the double-slit apparatus it cannot be determined through which slit it passed (thus reproducing an interference pattern). Now suppose (It's like supposition Inception! Supposings inside supposings inside supposings.) that I Lorentz boost into a reference frame in which the particle passing through the double-slit apparatus is received at the detector (and consequently has its polarization measured) before its entangled partner gets diagonally polarized. It appears that there are two possible outcomes: either (a) I disagree with the results recorded by an observer in the commoving frame of the experiment (i.e. I see no interference pattern.) or (b) I must conclude that the future polarization of the entangled partner somehow reached back in time and changed the outcome of my measurement. So which is it? Do I get different results or do I need to embrace a further layer of quantum non-locality? This is a tough one for me to understand because of its complementary experiment: Imagine putting the polarizer much farther away than the double slit apparatus so that there is no interference pattern created (because the entangled partner does not get diagonally polarized until after the measurement has already occurred). In that case, I could boost into a frame where an interference pattern should occur because the partner gets polarized first. (Or am I missing something? Will there be - or not be - an interference pattern regardless?) If the answer is that I get the same results as the commoving measurement, then why is the commoving frame preferred? Why is it its results that are maintained in all reference frames and not the (expected) results from my boosted frame (which should be just as valid)? Also, I think that this version of the experiment is fundamentally different from the Delayed-Choice Quantum Eraser experiment and Wheeler's thought experiment since both of those experiments are easily explained by representing the particle in a different eigenbasis (namely, as being in a superposition of the interfering and the non-interfering states - instead of being in a \"collapsed\" state of another observable). However, I am also interested to know whether I am wrong in this estimation. Are these experiments basically the same? Can conclusions about or explanations of one of them be generalized to the others? Edit: Because of the question in the comments, I've added a little additional explanation for why I think the experiments are basically different. Primarily, the difference comes from the fact that both Wheeler's thought experiment and the Delayed-Choice Quantum Eraser can be explained in such a way that apparent \"cause\" always precedes \"effect.\" Causality is still violated, but at least its not giving us information about the future. For instance, if we didn't know whether or not the entangled partner beam would get polarized a year from now (in the quantum eraser experiment), we could predict whether it does or not today by determining whether or not there was an interference pattern at the double-slits. If there exists any boosted frame in which the beam gets polarized first, then that result must carry over to the frames where it gets polarized after. So \"future-telling\" can happen in the relativistic quantum eraser, but not in the other two experiments. For example, in the Wheeler experiment, we polarize the photon and then after the fact decide at random whether to measure its polarization or not. If we measure the polarization, we get no interference; if we don't measure the polarization, we do get interference. Often this is ascribed to a sort of \"predictive\" non-locality, but just as easily, we could say that the polarized state of the photon is actually a superposition of states (namely, interfering and non-interfering) and when we measure its polarization we collapse it into the non-interfering state (and if we don't, we collapse it into interference). Likewise for the delayed-choice quantum eraser: instead of thinking that the beam-splitter in the future decided the interference in the past, you could just as easily conclude that the interference (or not) in the past decided the outcome of the beam-split in the future.", "label": 1}
+{"snippet": "In a previous Phys.SE question, Does a spaceship travelling at near lightspeed see the universe aging slow or fast?, the answer (which was followed by a proof involving co-moving reference frames) was given as The short answer is that yes, an astronaut moving relative to the cosmic microwave background would measure a shorter time since the Big Bang than an observer stationary wrt to the CMB. However, an observer in such a spaceship will consider the time of any object which is at the CMBR co-moving reference frame to be moving slower than itself. Is this not a conflicting result? For example, let's say the spaceship and a CMBR Earth communicate as they pass by each other. Each would have an estimate of the age of the universe, and each would have an estimate of the measured age of universe that the other would give, based on their own measurement of the age and the time dilation that they assume the other would experience. Here are the results The CMBR observer is fine - both his estimate of the universe's age that the spaceship would give and the estimate actually given by the spaceship match and are less than his own estimate of the universe's age. However, the spaceship expects the CMBR observer to have a lower estimate of the age of the universe because their clock is (according to spaceship observer) ticking slower than his own. What the spaceship observer does not expect is that the CMBR observer's estimate is larger than his own estimate of the age of the universe, yet that is what happens. How is this resolved without implying a preferred reference frame?", "label": 1}
+{"snippet": "I tried to make rain with a bottle and a balloon but it failed. The bottle was small, only a couple inches wide and the threaded part that I had the balloon on was less than an inch. In particular it was the size of this hydrogen peroxide bottle: It was originally a hydrogen peroxide bottle but all the hydrogen peroxide was out of it when I did this experiment. I stretched the balloon a little bit and put it over the threaded part of the bottle. But right before that I put hot water in the bottle. I knew that some water was evaporating. Also there was regular air(including dust particles) inside the balloon(I did this outside during a dry spell during the summer). This gives plenty of opportunities for the water to condense to form a cloud in the balloon and eventually, rain. However I left it out there for several days and nothing happened. The balloon didn't inflate from the water vapor bouncing off of the balloon. The water didn't condense enough to be noticeable. Rain didn't form. I thought that maybe there was too little water and too little air so I went to a much bigger bottle(about a gallon in size). The balloon started to separate. I also had a control of an open bottle in the same conditions while doing this experiment. The water level did not change in the open bottle even when the humidity was low. So why didn't the balloon inflate if the fact that both the water and the air were hot should have increased the vapor pressure, thus causing the balloon to inflate? Why didn't the water condense into a cloud that I could see through the latex of the balloon if it were inflated? Why didn't the water get to the critical size for raindrops if there were plenty of dust particles in there for the water to condense on to form water droplets and eventually raindrops? Why didn't the water level in the open bottle change? Is there anything I can do to improve this rain in a balloon experiment besides having a source of heat underneath the water?", "label": 1}
+{"snippet": "The principle conservation of energy is often taken as an obvious fact, or law of nature. But it seems to me the definition of energy is far from obvious, or natural: http://en.wikipedia.org/wiki/Energy lists lots of different types of energy. So if I want to apply this principle in some concrete experiment, I have to go through all the forms of energy and consider whether this form of energy is applicable to each particular entity in my experiment. This seems like a rather cookbook-oriented approach (and the wiki list doesn't even claim to be complete!). Now I wonder: ---> to what extent can these different energies be derived from some single simpler definition? For example, if my model is that everything is made up of atoms (I don't want to consider anything at a smaller scale, I fear that would muddle the discussion and miss the main point. Also, I'm considering only classical mechanics.) which are determined by their position, momentum, charge and mass (?), is there a clear and exhaustive definition of the energy of a such a system? EDIT: In light of comments and answers, I think I need to clarify my question a bit. Is it true that the electric potential and gravitation potential (for atoms, say) will explain all instances of conservation of 'energy' occurring in classical mechanics? If no, is there some modification of \"electric potential and gravitation potential\" above which will yield yes? My question is not really about mathematics - Noether's theorem for example is a purely mathematical statement about mathematical objects. Of course mathematics and my question are related since they both involve similar kinds of reasoning, but I'm ultimately after a physical or intuitive explanation (which is not possible using only mathematics since this involves choice of a model, which needs to be explained intuitively) or assertion that all these energies (chemical, elastic, magenetic et.c. (possibly not including nuclear energy - let's assume we're in the times when we did not know about the inner workings of atoms)) come from some simple energy defined for atoms (for example).", "label": 1}
+{"snippet": "I'm nearing the end of the semester of an introductory-level complex variables class. (Very introductory -- it's the version of the class that's only required for engineering and physics majors, as it doesn't require two semesters of undergrad analysis that are prerequisite to the complex variables class for math majors, at my school.) One of the many fascinating things I've seen this semester has been, speaking in broad terms, the behavior of analytic function, and the way that a harmonic function and its conjugate 'synchronize' (for lack of a better word) to create analyticity. Despite the examples I've seen of harmonic functions being steady-state solutions to heat problems and showing up in descriptions of electric fields and whatnot, I feel like I lack any sense of what the 'harmonicity' of harmonic functions is all about. On a side note: I do recall one day, however, where I was working through an example having to do with the level curves of a harmonic function and its conjugate, where I believe the significance what they points of intersection where always orthogonal. This 'mesh' notion created, for me, a visual image of how the the two functions work together to give an analytic function its synchronized, predictable nature. (But, as with most things, I could be mistaken in my understanding of this; these weren't points being stressed in the book, and it was in a chapter later in the book than what we'll cover in the class.) So, my question is that of how one ought finish this statement:\"I was considering a problem, and I intuitively knew the solution would need to be a harmonic function because the problem had the property...\" I stress the word 'intuitively,' by the way. If you feel this misses the point of harmonic functions and how I should think of them, then by all means please answer however you feel is appropriate.", "label": 1}
+{"snippet": "I'm quite perplexed by the notion of 'observation' in regards to the collapse of a particle's probability wave. Does a particle's wave only collapse when it is involved in a strong interaction (such as a collision with another particle, like bouncing a photon off another particle to determine the other particle's position) or does any interaction with another particle or field also cause this collapse? For example, I presume traditional detectors such as those mentioned when talking about the double slit experiment are devices that do exactly as I stated above and (in the case of the double slit) have a stream of photons (like a curtain) going from the top of the slit to the bottom which the electron (or particle being shot at the slits) has to pass through and therefore get smashed into by the photons. So given an environment where there was no other gravitational or electromagnetic influence, or where the effects of such have been taken into account, what would happen if you had a region of space within which a massive neutral particle 'is' (ie, it's probability wave fills this volume), and then shot a beam of photons across the bow of this region (so as to pass nearby, but not intersect), and then have a photo-sensitive plate on the other side to see if the photons passed straight by, or were pulled towards one direction slightly by the warping of spacetime caused by the massive neutral particle (gravitational lensing on a mini scale)? Does this even make sense? And if the photons were being pulled slightly towards the massive neutral particle, would the waveform collapse at this point, since if the mass of the neutral particle was known, the amount by which the photons path had been bent could confirm it's position couldn't it? Or perhaps take the above and use an electromagnetically positive particle as the target and an electromagnetically negative particle as the beam you shoot by it to see if it is effected by the electromagnetic field caused by the target particle if that makes more sense. I might be making some silly errors or assumptions here, I'm only a layman with no formal education or in depth knowledge, so be gentle :)", "label": 1}
+{"snippet": "First I will have to explain my question. Look at the image below. This shows doppler shift when an object is moving horizontally to the direction of the wave. Keep the word 'horizontally' in mind. Now this happens because: I will quote Jim from his answer for Redshifting of light from a moving light source We all know that light is a wave, when you turn on your headlights and drive in reverse, the light is doppler shifted because of the motion of source. When not moving, each cycle of the light wave is emitted from the same position; it has a specific set of wavelengths. The distance between one crest of a wave and the next crest is equal to the speed of light, c, times the period of the light (which is determined by the oscillations in your headlights and won't change when you are in motion). When you drive backwards, the distance between one crest and the next becomes the period times c plus the period times your backwards velocity (approximately); the second crest is not emitted at the same location as the first, so it extends the wavelength. From your perspective, the emitted wave would not be red-shifted at all, but from a stationary observer's perspective it is. So now my question is, imagine a car which has a torch attached to one of its windows. The torch is switched on and the car begins to move. When the car moves, its movement is in the opposite axis from the propagation of the wave. So each crest will be released from a different location while the first crest is already on its way in a straight line. I will try to represent this graphically. The representation is very estimate. It just shows how would the light bend as each crest is released from a different location. Please explain this to me. Will the light actually bend? Why or Why not? Edit What I have concluded from the answers is that first a photon is emitted and then it continues as a wave and is in no way attached to other photons. Is this right? If I got this then I got the answer for my question.", "label": 1}
+{"snippet": "I'm a math student, starting a PhD in the near future. My field of research will be mostly in the field of applied mathematics / numerics. Topics will deal with Kinetic Theory, Moment Equations, Fractional Diffusion, Spetral Methods. I think I have a solid background in numerical computing, especially for PDEs. Now for my Masterthesis I've dealt with numerical methods for fractional diffusion equations. Since (fractional) diffusion is related to Brownian motion / CTRWs, a lot of authors named mathematical finance as a field that is impacted by their research. The problem is, that I have absolutely no background in finance / econ whatsoever, but I would really like to get into this topic. I think it would open me a lot of opportunities to gain a little expertise in that field. I started to read some mathematical finance papers, referenced in the papers I encountered and noticed quite quickly, that I lack the non-mathematical background. The goal of this question is maybe a bit ambition. I would like to get to know the field of mathematical finance over the next three years. Start with the basics and then move quickly to mathematical finance with a focus on computing / simulation. Since I will do this on top of my work, I would also appreciate books that I can pick up every other day/evening and just read a little. What interests me espacially are processes that are related to Stochastic DEs, Brownian Motion, Ramdom processes. Especially topics that might rely on the same basics as diffusive processes / kinetic theory. For example, some buzzwords I encountered where stylized facts, options, derivatives (in finance). Maybe you could split up your recommendations in the categories finance/econ, general mathematical finance and random processes / SDEs in finance. If you have general remarks regarding my proceedings please feel free to contribute (for example, what do you think about visiting certain lectures offered at my university, broadening my mathematical background, relating my research to the field of finance, software I should get to know like R, etc.) Thank you very much!", "label": 1}
+{"snippet": "Suppose I have plotted the body angles of a flying aeroplane.I have two such plots. One of a normal plane, and the other plot in which a primary sensor of the aeroplane is removed. So with the absence of a sensor you are expected to see an instability in their flight. Below are the two graphs--- The first one is the control flight, and the second one is the experimental (sensor removed.) Lets look at the second graph --- you can see that the roll of the flight is sinusoidal. Even the pitch is slightly. But the sinusoid fluctuation of the roll is more prominent. And I see this fluctuation in all my experimental graphs (sensor-removed) that I have obtained, and none in the control (normal) graphs. Now, I would like to quantify this fluctuation. One way of quantifying it would be to plot the mean and standard deviation of roll in both cases and show that the standard deviation is very high in the second case. But this is not correct because, the standard deviation might also be very high in the first case ---- this can happen when the flight rolls a lot, but does not necessarily fluctuate. It could roll in one direction, maintain that for some time, then roll in the opposite direction or the same one. Its not fluctuating, but standard deviation will be high. So, I am looking for another parameter, to quantify this fluctuation in the graph, something like a fourier transform perhaps. Something that would accentuate the instability bit. Suggestions people?", "label": 1}
+{"snippet": "During an episode of Archer, he criticized a journalist's grammar for her misuse of the word 'child-murderer'. She meant one who murders children, and Archer argued in using the hyphenated form, she implied the accused man is a child who murders. Is this correct? I searched \"child-murder\" and \"child-murderer\", only to find columns eschewing the hyphen in nearly all cases. Instead, the columnists, relied on context as to whether they are referring to a child who murders or one who murders children. I, however, am purely interested in the proper use of the hyphen in this situation, as it could possibly extend to other situations as well. The trouble seems to arise from child not having an adjective or descriptive form. With 'teen', one does not run into this problem: Teenage murderer vs teen murderer However, if one uses 'adolescent murderer', it becomes unclear as to whether one means an adolescent who murders or... you get the picture. This problem arises from adolescent being both an adjective and noun; a hyphen can resolve the ambiguity. But once again, how should the hyphen be used? I found a similar question: What is the plural of 'only child'? I err on the side of only-children, in the event that 'only children' reads as 'just/simply/merely children'. Some suggested entirely new phrasing, while others say that the context is sufficient. I don't believe one should change his entire sentence when proper use of the hyphen can get his meaning across just fine, and even when context is suitable, proper grammar is still rule of law.", "label": 1}
+{"snippet": "I'll try my best to explain my question with examples because I don't have much knowledge on the theory. So say that I had a block of water in air, a cube of water, that is dropping. If the cube wasn't too big, I believe that as it will drop, then the air from underneath it will rush to either side of it, as the water displaces the air on it's way down. Now lets change the situation. Say I had the cube of water, but now its suspended in the air in a tank (like a fish tank), as shown in the picture. Here, I believe that there is the weight force of the water acting evenly downwards, but the air pressure may be different, as the whole system is bounded by the walls. Logically, I believe that the air would then rush through the center of the water cube, forming a bubble, allowing the water to rush down to the bottom. Though this may be completely wrong, I'm not sure. So my question is, is that is there any possible shape for the water to be originally in, so that all the forces sort of balance so that there is no distortions in the shape, and that then the air will be compressed under the force? I understand that perhaps at the microscopic level, if we take into account the random motion of molecules, and other factors, that there will inevitably be some sort of inbalance, but macroscopically what would be the perfect shape? I'm not even sure if any of this makes any sense. Thanks for any help understanding.", "label": 1}
+{"snippet": "Saw a question about faster than light travel... I still have the same question though none of the answers offered any resolution for me. It is so summarily assumed by all physicists and commentaries that exceeding the speed of light would turn back the clock. I can't see the relation. Doubling the amount of any speed halves the time taken to travel a given distance. Keep doubling the speed and that time is halved (or otherwise divided). Divide any quantity (time in this case) and you always end up with a fraction of it but never zero and certainly never a negative amount as would be the case for the causality conflict. So it seems to me that whatever speed one attains, there is always a positive time element in the travel no matter how tiny!! The speed of light is only unique to me in that it is the fastest observed speed but is otherwise just another speed quantity set by nature (just like the speed of sound etc) could it be that other elements in nature are travelling faster than light but we lack the means to detect or measure them (like the rebellious neutrino)? I also don't understand time as an independent element that can be slowed sped up etc. It seems to me that time is simply a relative measure of the ever-changing state of matter relative to other states of matter. If every thing in the universe stopped- that is all state of matter everywhere frozen, all electrons frozen in place etc wouldn't we observe that time had stopped? Isn't it therefore our observation of the changing state of matter around us that gives the perception (perhaps illusion) of time? I can therefore only understand time as a subjective sense of changing states relative to an observer! It should be the rate of change of these states that slow down or speed up (in relation to the observer or instrument) and not the universal rate of change or universal time that changes! It would also debunk any notion of time travel, as it would involve the manipulation of every particle in the universe to a previous of future state... Disclaimer.. I hate calculations, stink at them and have no idea what mathematical formulas are used to arrive at the accepted conclusions so I'm not trying to dispute any findings etc by the experts, just trying to align my lay understanding to their conclusions.", "label": 1}
+{"snippet": "Everyone does know that the surface of a conductor is at equipotential during equilibrium. I was reading Feynman's lectures where I found this (bold)line: Suppose that we have a situation in which a total charge Q is placed on an arbitrary conductor. Now we will not be able to say exactly where the charges are. They will spread out in some way on the surface. How can we know how the charges have distributed themselves on the surface? They must distribute themselves so that the potential of the surface is constant. If the surface were not an equipotential, there would be an electric field inside the conductor, and the charges would keep moving until it became zero. This is a much good reasoning for the surface to be an equipotential one; if there were any region to be in higher potential, charges would flow towards them to neutralize and again make the surface equipotential. To understand his explanation, I thought of a positively charged surface that is not in equipotential status; so there would be an electric field which would prompt the free electrons inside the conductor to go there & nullify the field to make the surface equipotential, right? But what about the positive charges that are now inside the conductor? Okay, they would by repulsion move towards the surface. But what is the GUARANTEE that they would form the equipotential surface? What really happens when they go on the surface that compels them to make an equipotential surface?? [After all, you can't say:\" since you are studying electrostatics, there must be equipotential region on the surface no matter what happens; that's it\"-this is what my school-teacher said when I asked him.]", "label": 1}
+{"snippet": "I'm thinking of writing a short story set on a version of Earth that is tidally locked to the Sun. I'm not exactly sure how to research the topic. Here's a number of questions about what would happen: How hot would the light side get? Are we talking ocean-boiling levels? I imagine that life would eventually flourish, given the massive constant energy source. Is this accurate? On that note, I imagine massive thunderstorms along all the coasts due to increased evaporation. How bad would they get? Would the ground ever see the Sun, or only rainfall? How cold would the dark side get? Is it conceivable that any life could still exist there? (Life has proven itself quite versitile in the past, i.e. life at the bottom of the ocean.) What wind speed would the twilight zone experience? I imagine the atmosphere would transfer heat from one side to the other, but would the wind speeds be bearable? In what direction would air flow? I hear that the oceans would recede into disjoint northern and southern oceans if the world stopped spinning. Would this also happen if the Earth became tidally locked? Would the Sun create a 'tidal' bulge in the ocean at the apex of the light side? Would this or the above dominate ocean behavior? Would we completely lose the magnetic field? Would life be able to survive without such shielding from magnetic radiation? Would the Moon eventually unlock the Earth? What state would the Moon have to be in for there to be both a locking between the Sun and the Earth as well as the Earth and the Moon? What other radical differences would exist between our Earth and a tidally locked alternative?", "label": 1}
+{"snippet": "I was asking the other day how to find certain fonts of a document. Well at last it was easy. I came to the Mathematical Pi LT Std font and ITC New Baskerville Std results and for that part, I was pleased because I finally managed to get those fonts. So far, I have only used LaTeX for my documents and papers for the University and own projects and as most of us know, there are very few pleasant Math Fonts to use (at least for me). I have tried XeLaTeX and mathspec package to set the digits and latin to Baskerville and Greek to Mathematical Pi, but it turns out to be very clumsy when it comes to spacing and that stuff... and I ended up not liking the result. I have been checking the glyphs of Mathematical Pi and it contains a lot more than Greek Letters (obviously) but I don't know how to tell XeLaTeX to use for example the integral sign, relation signs, sums and everything else. I would like to know if there is any way to use Mathematical Pi font at full with any of the TeX systems and if that is not the case how to use that font other way, because I have been trying to use it in MS Word with its equation editor but I have not been successfull nor finding how to do it. Can anyone help me with this?, I'm sure there has to be a way since I have found that font in many books. Thank you all in advance.", "label": 1}
+{"snippet": "It's not really clear to me how does QM attacks determinism. It sure attacks computability, which is a component of newtonian, naive determinism, but it's often claimed to destroy determinism itself (which says that we can't compute events, but they are determined anyway). A photon is both a particle and a wave; a particle doesn't have both speed and momentum defined values at the same time; some things are not a in a state, but in a superposition, until they are measured. It's cool, I get it. But aren't there a lot of macroscopical objects that can be described this way as well? A just published book is both a best-seller and a failure, until enough people buy it. It would be impossible to compute which state it is until the state itself 'happens'. I'm not sure I'm just referring to hidden variables. Where is the problem with observation exactly? It is obvious that the fact that a scientist decides to observe the particle as a wave is due to the fact that he's doing that experiment. And he's doing that experiment because he likes science, because it's written in his DNA or in his education. He's working because he needs to eat, because chemistry of his body tells him so, and so on. The impossibility to compute in advance which state is correct is due to the free will of the observer, in the exact same way in which the book is a best-seller or not (the decision of people to buy it). But it's just because it's too difficult to know everything: a God-like creature could perfectly know how many people would buy the book and also if the scientist decides to measure the photon as particle or as a wave at a given time. Is this just superdeterminism? (https://en.wikipedia.org/wiki/Superdeterminism) Looks like a pretty logical observation to me. What I am missing?", "label": 1}
+{"snippet": "I have recently been studying continuous dynamical systems whose phase space can be divided into a number of regions. Inside each of these the flow is smooth, but there is a discrete jump in the flow just at the boundaries. In the mathematical description, the right hand side of the differential equation is different for different regions of the phase space of the dynamical variables. Note: I don't mean something trivial like systems which exhibit smoothness in different regions of physical space separated by boundaries, like differently heated gases in partitions, or water in contact with vapour etc. The different regions I mention are regions in the phase space of the dynamical systems. So imagine a set of continuous-time differential equations defining a flow which is segregated in its phase space into regions in which the evolution of the equations is piecewise smooth. I also don't mean phase transition. There is no variation of order parameter or bifurcations here. The piecewise smoothness exists in the dynamical phase space for a fixed value of the system parameters. I have been studying them in an engineering context of a mechanical device in which there is a sudden change in the velocity of a moving part when it hits something. But it struck me that such piecewise smooth systems should be found in many scenarios, from other areas of physics, maybe certain quantum phenomena, to biological systems that can be studied with the theory of dynamical systems. Some examples of the kind of systems I am looking for are: Quantum mechanics: the Muffin-Tin potential is a quantum model where the potential (the right side of the differential equation) is approximated to be piecewise defined. Classical mechanics: the hard impacting oscillator (oscillator with a rigid wall at an end restricting the amplitude, like the devices I was studying). Theoretical computer science: Hybrid automata and reachability problems which are further piecewise linear. I am curious to apply my understanding of the mechanical system to such systems. So, what are other dynamical systems in nature which exhibit piecewise smooth behaviour?", "label": 1}
+{"snippet": "I posed a closely related question here but it received a tumbleweeds award. So I thought I would post it from a different angle to see if I can illicit at least some thoughtful comments if not answers. The modeling of many physical systems utilize the mathematical tools of calculus, by writing the relationship of physical quantities in the form of differential equations. Considering time dependent operations of integration and differentiation, the dynamics of a physical system may be expressed in terms of one form or the other. A good example are the Maxwell Equations which are often written in both differential and integral forms. Integral forms tend to express where the system has been up to where the system is at present while differential forms tend to express where a system is now and where it will be in the near future. So the two forms tend to imply a sense of causality. So this brings me to my question. Since we tend to observe a causal universe (at least at a macroscopic level) are integral forms a more natural approach to modeling systems? I'm using the word 'natural' in the sense that the nature of the universe tends to work one way vs another. In this case I'm saying nature tends to integrate rather than differentiate to propagate change. We can write our equations in differential form, solve them and predict, and they are useful tools. But isn't mother nature's path one of integration? I tend to believe this is so by my experience in simulating systems. Simulating systems in an integral form rather than differential form always seems to lead to better results.", "label": 1}
+{"snippet": "Right now I'm writing an essay on Death in Venice, and I'm having trouble finding the right word or phrase to express how Aschenbach is parallel to the old man on the boat to Venice (both dress up to fit in with youth, some repetition of specific phrases in descriptions, youth from Pola vs youth from Poland, etc.). The closest word I can find to describe what is a \"parallel\". I see this word used a lot on the internet to describe (usually in TV shows) when something that one character did in a past episode is similar to something that a character (usually different, but I've also seen it used to point out character development via slight differences in the parallel). It kind of describes two completely separate scenes that have a much more powerful meaning when juxtaposed (usually very blatant mirroring, etc. to point this out to viewer/reader). In my case, it would be the scene with Aschenbach observing the man on the boat and the scene where Aschenbach applies makeup for Tadzio. Specifically, the man on the boat foreshadows the \"endgame\" for Aschenbach. In my essay, I've referred to it mostly as foreshadowing, but I think the depth of the connection that Mann makes warrants something a little stronger. The word foil came to mind, in terms of the intensity and how it's character specific, but obviously, it has the opposite meaning of what I'm going for. I did think about just using the word \"parallel\", but I when I looked it up, the definition for the word parallelism came up, and as a literary term it seemed from this definition, it seems that this word as a literary device refers to parallel syntax and a not to a broader similarity. I've come up with \"symmetry\" and \"mirror\" to describe individual aspects, but I was wondering if there is a proper term that encompasses the broad connection between the two characters.", "label": 1}
+{"snippet": "I was looking at this question on SE and the answers seemed to say that the reason why matter doesn't expand along with space is because of forces like gravity, electromagnetism, etc. However, i feel like this has to mean the fields themselves don't \"expand\" along with space. Let me explain... From my understanding, the expansion of space is about the expansion of space itself, not about distances within space changing. For example it's about the space taken up by one meter increasing, not about the distance between entities increasing from one meter to two. If these assumptions are off please let me know. Keeping that in mind, look at redshifted light for example- This happens when the distance between crests of the light wave increases, changing the light's frequency. However, if space expansion doesn't increase distances within space, there should be no change of frequency, because there is no change in distance between crests. We do however see that the frequency does change with metric expansion. The only way i can think of to resolve this issue is to say that the expansion of space itself affects the wave. The only way for the expansion of space to affect the wave, is for the wave's field to not expand with space. The EM field \"density\" has to stay constant relative to the density of space (sorry for all the informal wording). Or in the case of gravity- if space expands, the distance (and therefore gravitational influence) between objects should remain unchanged. However, for gravity to keep mass from expanding along with the expansion of space, it would have to exert a force that isn't proportional to changes in space density. The behavior of gravity (relative to the distances that determine it's influence) changes based on the density of space. This would have to mean, like EM, the gravitational field does not expand with space. That's how we're able to deduce expansion, because the fields themselves are our reference points. This isn't about waves/excitations of a field, it's about the field itself, if that makes any sense. If this is true, how do we reconcile the expansion of space with fields remaining constant?", "label": 1}
+{"snippet": "I play the flute as a hobby, and I've noticed that when playing middle D or E flat, one can interrupt the air column by releasing a certain key (which is near the middle of the air column), and yet have no effect on the pitch (though the quality changes for the better). I'll be putting a few diagrams here, since it is hard describing the situation in words. The black portions of the diagrams represent closed holes--basically \"air cannot escape from here\". The gray represents holes which are closed due to lever action, but need not be. Here's a diagram without coloring (all diagrams are click-to-enlarge): The mouthpiece is attached on the left, as marked in the diagram. The second key is just a ghost key connected to the first (and has no hole underneath it), so I'll just remove it from the diagrams: A few examples Alright. Normally, when playing consecutive notes, you make the air column shorter by releasing a key. For example, this is F: This is F#: And this is G: One can easily see the physics behind this, an unbroken air column is formed from the mouthpiece. The weird stuff Now, let's look at middle D and E flat: D: E flat: Here, the air column is broken in between. I feel that both should play the same note, that is C#: But they don't. I can close the hole, creating an unbroken air column in both cases, but the sound quality diminishes. A bit more experimentation (aka \"what have you tried?\") Reading this section is strictly optional, but will probably help I did a lot of experimenting with this key, turning up some interesting results. Hereafter, I'm calling the key \"the red key\", and marking it as such in the diagrams. When the red key is \"closed\", no air can escape and it forms part of the air column. If I play low D/E flat, I only get a clear note when the red key is closed. With it open, I get a note which has extremely bad quality, as well as being off-pitch. This is markedly opposite with what happens on middle D/E flat (mentioned above), there there is no change in pitch, and the difference in quality is reversed. Pictured: Low E flat (for low D extend the RHS of the black portion a bit more). Note that the fingering, save the red key, is the same for middle D/E flat Actually, this seems to be happening for all of the low notes--each one is affected drastically when the red key is lifted. Going on to the notes immediately after E flat For E, quality is drastically reduced when the red key is open. The harmonic (second fundamental) of E, which is B, is more prominent than the note itself. One can make the E more prominent by blowing faster, but this reduces quality. Red key closed gives a clear note, as it should. For F, a similar thing happens as with E. With the red key closed, it plays normally. With it open, you hear a medium-quality C (first harmonic of F), and no F at all. Blowing faster just gives a high C. The notes immediately below D have a fingering starting from no keys pressed (has to happen every octave, obviously). For the first few notes here, lifting the red key gives you C#, as expected. (I'm not explicitly marking the key red here, otherwise it'll get confusing what the correct fingering is) In C#, pressing the red key will obviously change the note ....to C: Obviously, lifting the red key here will get you back to C# One (half) step lower, we have B, which again goes to C# when the red key is lifted It gets interesting again when we play B flat. Lifting the red key here gives a note between C# and C And if we go down to A, lifting the red key gives us a C And a bit of experimentation with the trill keys (the actual holes are on the other side of the flute). Whereas messing with the red key for D and E flat produces no change of pitch, messing with the trill keys (which are the same size as the red key and are furthermore pretty near it) does. Hitting the second trill key while playing D gives E flat. One should note that this second trill key opens the hole closest to the mouthpiece. Note the visual similarity between this and the situation in the \"the weird stuff\" section Hitting the first trill key while playing D gives a note between D and E (the two trill keys are close to each other, you may have to see the enlarged version to get the difference) Hitting the second trill key while playing E flat gives a note between E and F Hitting the first trill key while playing E flat gives E flat (No diagram here, these two are the same as the last two, except that the far right edge of the black portion is closer) The Question Now, the red key(and the trill keys) are about half the diameter of the other keys. I suspect that this is quite significant here, but I can't explain it myself. My main question is, why does disturbing the air column as shown in the section \"the weird stuff\" not change the pitch? One has added an escape route for air, the column should then vibrate as if the remaining keys were open--that is C#. I suspect that the underlying principle is the same, so I have a few other related questions (optional): Why does the red key not change the pitch on D/E flat, but makes it go into the second fundamental/harmonic for E and above? Why does the red key change the pitch to notes which are not harmonics, instead close to C#(one of them isn't even part of the chromatic scale--it is between two notes) for B flat and A? The red key is pretty similar to the trill keys with respect to size and general location. Yet, using a trill key on D changes the pitch, whereas using the red key doesn't. Why is this so?", "label": 1}
+{"snippet": "Having been an avid lover of Mathematics, it is my dream to become a mathematician one day. I have been learning some \"Advanced Mathematics\" (Real Analysis and some Abstract Algebra mostly, and a little bit of Linear Algebra). The first thing that anyone jumping from High School Math to proof based, rigorous math, should notice is how different they are from each other. Math that I am learning now is definitely not like the Math that I now do at school. This is the fist thing I realized when I started doing Real Analysis a few months back. Advanced Math, I noticed, is exceptionally beautiful and at times it is like art, utterly elegant and aesthetically pleasing. I don't know if others share this same feeling with me. I used to enjoy Math then, for sure, but nothing compared to the enjoyment I am having now. Because of the enjoyment I get while doing Math, I am pretty much sure that I would like to major in math someday and if possible go to a graduate school in mathematics. But this being said, I do have a small concern. Because Higher Math is so very different from grade-school math, I fear that as I dive in deeper and deeper into mathematics, I might realize that the Math I do then has changed so much that it was nowhere close to the Math that appealed me. How substantial is this fear? Is it legitimate? Because this community is full of Mathematicians, I figured this would be the best place to ask If you guys experienced such a feeling too? How and in what ways did you find math different from fairly lower level math that I am currently into. Any help is much appreciated!", "label": 1}
+{"snippet": "I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical constructs, operations, entities, and even the basic terminology (which I have come to understand is incredibly elegant, precise, and deliberate) to real world, physical, even visible phenomena. I think under the pretense that the things I do in the mathematical world represent real, fundamental structures in this Universe. For example, the fact that terms can 'cancel' out in an equation has profound implications on the workings of the Universe and should be heeded and studied as such. In other words, I try to make sense of the things I learn in math classes by finding their analogs in the real word, because I assume they must have at least one. Thinking with this frame of mind has led me to appreciate mathematics in a deeply profound and beautiful way, and it's the mindset that I try to share with other people when explaining why mathematics should be studied and why people describe it as beautiful. When I learn something new in a math class, I try to understand and remember that these are not simply tedious equations and formulas that mean nothing and come from nowhere, but that they have real physical and, mostly, intuitive meaning. All that being said, I'm taking my first liner algebra course this term, and it's becoming harder to utilize this mentality, not simply because linear algebra deals with such things as infinite dimensionality which we obviously have no intuitive way of grasping or visualizing, but really just because the class seems more about computation and calculation than concept and philosophy. I worry that my thinking has led me astray, primarily because it becomes hard to focus on just doing sheer, brute force calculation without wondering and worrying about what these constructs really mean. This leads me to fall behind in lecture, take hours longer than is probably necessary on the homework, and add to an overall level of frustration that has been building for some time now because of it, which only clouds my understanding even more. My question is really more of a plea for advice. Should I abandon my way of thinking about mathematics as though it will become increasingly unhelpful in future courses and topics, or is linear algebra truly more about numerical gymnastics than tangible interpretation? Should I focus, currently, on simply learning the algorithms for computation now assuming that the philosophical groundwork will be exposed later on, after which the conceptual work that I'm looking for will yield itself? I'd really appreciate responses from the people that frequent this site. I've been nothing but overwhelmed at the level of quality, thought, and sincerity in the answers I've read here and throughout the conversations I've eavesdropped so far. Also, please direct me to similar questions if you know of any, and help me with the tagging of this question, as it is the first one I've ever asked on this site.", "label": 1}
+{"snippet": "There's a poem in bahasa indonesia, titled \"Aku Ingin (I want)\" by Sapardi Djoko Damono, translated to english by John H. McGlynn. This is the english version: I want I want to love you simply, in words not spoken: tinder to the flame which transforms it to ash I want to love you simply, in signs not expressed: clouds to the rain which make them evanesce source What I want to ask lies on the last line, especially the word \"make\". This was originally being questioned in a blog post (in bahasa indonesia). The OP caught that make usage, and his post caught my attention, thus I asked it here to get more understanding of it. Seems like for Indonesian who reads the poem in bahasa indonesia, the last line interpreted as \"rain that makes the clouds vanish\". Just like the first verse interpreted as \"fire that burns tinder to ashes\". Thus, the word make on the last line should have be used by rain, that would make it makes. But in the poem's english version, make stayed make, make it looks like it's used by the clouds. Meanwhile on the first verse, both tinder and flame are singular, thus hard to know to which transforms is used. My question is, why is it make, without s? Is it a different interpretation, or is there some kind of poetic usage on that word, or is it a common usage for english poem (by english poem, I mean poem using english language)? Sorry for broken english, and in case I asked in a wrong place, please tell me where should I had asked.", "label": 1}
+{"snippet": "I have never understood what measuring process (if any) is supposed to be continuously polling the quantum state of an unstable bound system subjected to decay via quantum tunnelling. The reason I reckon some kind of polling process should exist in the first place is the following: According to the QM postulates, the unitary evolution of such a system should by definition keep it reversible, so it is only when measured that a decay can be observed or not. But this would make the decay rate dependent on the measurement rate, while we well know that the decay probability is constant, and the decay deemed \"spontaneaous\". What am I missing? Edit: From the discussion in the comment section I gather I have not been clear about what I am asking here exactly. Let me try to reformulate the question. It is about how quantum tunnelling is supposed to explain the exponential dynamics of a decay process. I am not asking about the Zeno effect; quite the opposite, actually: why, in the absence of any measurement, do we have an exponential decay at all? I just do not understand at what point in the unitary evolution of the unstable system the tunnelling effect is spontaneously happening. The polling process I imagined is just a way to ask \"why does the tunnelling effect manifest iself ?\" because I cannot see how it can manifest without a measurement. Please do not infer that I am making up my pet theory here. I am only looking for a way to picture the situation, which at this time I don't get at all.", "label": 1}
+{"snippet": "We have statements, and we have questions. A request made in the form of a statement has a question equivalent. But is that question equivalent implicit, or is it simply a rewording of the statement form? Take the following: \"Please tell me why I sound like a sissy.\" This has the question form of: \"Why do I sound like a sissy?\" Is that question form implied within the statement form? I would argue it is not. http://www.merriam-webster.com/ defines imply as: \"to express (something) in an indirect way : to suggest (something) without saying or showing it plainly\" This definition can be interpreted to mean: Something implied must be identified with knowledge outside of what is only directly stated but based on what is stated - one must add context to what is stated. That may be stretching it a bit, but if one does not use any logic or outside knowledge to examine the meaning of provided information, other than that needed to identify the direct meaning directly present, one cannot identify anything that is implied. Here's an example: in the statement form of the quote I provided, one could say that it is implied that the individual requesting the information wants to know said information. It is implied because it is not directly stated in any of the words that the individual requesting actually wants to know; it is suggested, but not directly stated. For all we know, the individual is requesting for someone else. The reason I say that the question form is not implied is because we need no more information (other than the \"why do\", but that is simply part of forming a question) than what is presented in the statement. We have all the information needed to form a question out of what is provided, but we do not have enough information to state with absolute certainty that the individual requesting the information is the one who actually wants to know said information. Based on this, I would say that the question form of a statement is not implicit. Am I correct?", "label": 1}
+{"snippet": "Recently I became very much intrigued by algebraic topology and am spending quite some time learning it. My reasons are three-fold: it's a beautiful theory; it gives geometric justification to (or perhaps rather an application of) many purely algebraic structures; and it has fascinating applications in quantum field theory and condensed matter theory. Nevertheless, what I am familiar with currently are just basics: various homology and cohomology theories, homotopy theory and some standard applications (Brouwer, Borsuk-Ulam, etc., etc.). While these are of course interesting of and by themselves (and I expect spending a great amount of time on understanding all of this properly), I guess it is more or less understood for some fifty years now, so supposedly people work on topics far more advanced than this (or at the very least they use far more advanced tools to understand standard but hard problems). So, I'd also like to know what the field is about from the modern perspective (some interesting problems and research topics, advanced tools, etc.) so that I can see a little where will the study of the subject lead me in the long run. Sorry if the question is too broad but I am not sure where else to look (I've more or less browsed through all general articles on AT at wikipedia and tried to search MO too). I've heard few magic words like K-theory, sheaf cohomology, various spectral sequences, etc. but I don't understand these at all yet; more importantly my motivation to learn these things is lacking since I have no idea how or when these magic words are used (although I am pretty sure they are used a lot).", "label": 1}
+{"snippet": "I have been inspired by some sci-fi cannons that seem to operate by initially spinning up a projectile inside the cannon, and then suddenly firing the projectile out at high speed. Now, I am wondering whether it is possible for such a cannon to perform practically. So, from an energy point of view, it appears that this hypothetical cannon is able to do work on this projectile by spinning it up using a torque, and this work increases the rotational KE. Then, there is some unknown process that cause the transfer of rotational KE into translative KE, causing the projectile to fly off with a particular velocity. It would be appear that the spinning-up function of the cannon would be an interesting way of having the KE of the cannonball stored up and ready for firing. However, even though translative KE and rotational KE are both KE, the same type of energy, it looks like extra work needs to be done to transfer between both types of KE. To do this, by applying the principle of superposition, it looks like you would need to combine the effects of undoing the spin with a reversed torque, and then applying a force, in the direction of the cannon firing, in a short space of time. Does this apparent backtracking of doing work not seem inefficient, making the spinning-up of the projectile a waste of resources? Are there any real, practical mechanisms that work especially well in converting rotational KE into translative KE? In short, can there be any practicality in a cannon that initially spins up it's projectiles?", "label": 1}
+{"snippet": "So, to make it abundantly clear what I am asking for, here is an example picture edited (poorly) in a drawing software: At left, you can see my current TexStudio look: the are where real text is indeed entered had its colors properly customized with a .txsprofile object. However, the menu toolbar, the tabs area and so on are still colored in light-gray, while I would like them to have a darker look (as in the image to the right). Is it possible to achieve that somehow? I am aware that plenty of questions have been asked here and elsewhere on the topic of TexStudio's colors. For example: How do I change the colors of the application interface in TexStudio? Dark theme for Texstudio How can I set a dark theme in TeXstudio? How do I change color settings in TeXStudio? However, none of them really addressed the main point at hand: how to customize the colors of TexStudio's menus, toolbars, etc (not the colors of the text-editor part of TexStudio). The colors of the text-editor of TexStudio can be modified directly at the Syntax Highlighting options in the Tools>Configurations menu. However, rarely something is said about the other parts of TexStudio. When a question pops up about this, it gets either no answers or very low-detailed reactions. For instance: How do I change the colors of the application interface in TexStudio? Change background colour of toolbars in TeXstudio I realize that what TexStudio is doing is probably just retrieving the operational system color for it's menus, tool-bars and such. My question is whether there is anyway to bypass that and customize such colors.", "label": 1}
+{"snippet": "So I've recently seen a few people use the word \"sufferer\" to describe themselves having a certain mental disorder. I know that a person thinking that they are suffering a certain disorder may be quite subjective, but their usage is still questionable. The best exhibit I have for this question is somebody calling themself a \"sufferer\" of the mental disorder \"misophonia\". To save you a Google search, basically it means that you become pretty annoyed or even enraged at noises like people chewing ice, people chewing food loudly in general, and et cetera. I too have this disorder (if you can call it that) and I did not relate to the word \"sufferer\" at all, so I disagreed with the usage (not verbally; I didn't want to start an argument). To elaborate even more, I will include another example. I have seen people call themselves a \"sufferer\" of a disorder called \"visual snow\". Basically, this disorder causes static to cover one's vision in a way almost relatable to TV static (not really). It's very hard to explain and it is rare, but I suggest you Google it because it is interesting. Once again, I too have this disorder and have had it for my entire life. Seeing people describe their experience as \"suffering\" almost baffle me. I only notice my static if I am in a situation that has solid color (like pitch black or looking at a whiteboard) or if I purposefully pay attention to the static. It never obtrudes life in any way and many who tolerate this disorder will agree that it is not obtrusive. With all of this I do not understand why one would say they are suffering from a disorder that does not inflict physical, mental, and/or social harm. Each side of health is arguable, as neither of these technically cause harm on either end (referring to a commenter, you becoming enraged and punching a wall is not direct pain from the disorder \"misophonia). So my main question is, after seeing that Google defines the \"dated\" usage of the word as a \"tolerator\", would the word \"sufferer\" be acceptable in cases in which one does not necessarily \"suffer\" anything? I'll apologize that this question is really subjective and may not have any answer, but really I am just trying to get a consensus. Thank you in advance!", "label": 1}
+{"snippet": "This question isn't answered here: Differentiate between past and present just by pronunciation when word is followed by d- or similiar sound That question asks about what happens when the following word begins with a consonant in general. This one is asking about the various possibilities for an intervocalic tap if a following word is an unstressed function word beginning with /t/. It's also asking whether there's any possibility for regressive assimilation here. I read this in American accent book. I quote the text exactly how it is written in the book: The suffix -ed is not pronounced precisely when it is linked to another consonant. For example, mailed the sounds very much like mail the in the following sentences: I already mailed the letter. I will mail the letter. The suffix -ed is not heard at all when it is linked to /t/ or /d/. For example talked to sounds identical to talk to in the following sentences: I talked to her yesterday. I talk to her every day. Okay but then my question is, how do Americans distinguish between these two sentences: I try to call you. I tried to call you. In the first sentence the /t/ will be realised by a voiced tap because it occurs between two vowels. In the second will we get a regular [t] and then a voiced tap? Will we get a double tap or a double length tap? Or will we just get a single tap? Or maybe here we will just get two regular /t/s? Do native speakers differentiate between \"I tried to call you\" and \"I try to call you\" from the context?", "label": 1}
+{"snippet": "For the sake of time, is it bad to just accept some fast paced class's theorem's (such as MIT's algebra class) as true even if you don't completely understand the proof or can't remember the proof off top of your head (after a while has passed?). I often find myself wasting too much time trying to memorize proofs when that's not the point of the class (and I can actually wait to memorize the proof later). Sometimes, I get caught up in one detail of the proof for hours and end up not having time to learn how to actually use the theorem and do the homework. Also, is it bad to gain a complete and working understanding of something after you take the class. I am not mentally capable of fully absorbing both what the class want's us to get and thinking about it enough to have a complete and sufficiently deep understanding of the subject all in one semester. However, I feel bad if I wait to think deeply about the class material until after the course is done, but I simply don't have enough time to fully understand some things during the semester. I always hear this advice on making sure you understand everything when you are studying to practice/do mathematics, but that seems not practical if you are taking four or more classes and struggling to make sure you understand what you need to for your other classes have other obligations to attend to.(and also if English is not your first language). I feel like a lot of the advice I hear is for native English speakers (I came to the U.S. when I was four, so I'm practically a native English speaker, but not when it comes to understanding things well the first time through in math, or at least making the understand be thorough by a native English speaker's standards.) The reason I ask this is because I can't say I fully understand something in English unless I can explain the proof verbally/descriptively to someone.", "label": 1}
+{"snippet": "We make an important distinction between the topological insulators (which are essentially uncorrelated band insulators, \"with a twist\") and topological order (which covers a variety of exotic properties in certain quantum many-body ground states). The topological insulators are clearly \"topological\" in the sense of the connectedness of the single particle Hilbert space for one electron; however they are not \"robust\" in the same way as topologically ordered matter. My question is this: Topological order is certainly the more general and intriguing situation, but the notion of \"topology\" seems actually less explicit than in the topological insulators. Is there an easy way to reconcile this? Perhaps a starting point might be, can we imagine a \"topological insulator in Fock space\"? Would such a beast have \"long range entanglement\" and \"topological order\"? Edit: While this has received very nice answers, I should maybe clarify what I'm looking for a bit; I'm aware of the \"standard definitions\" of (symmetry protected) topological insulators and topological order and why they are very different phenomena. However, if I'm talking to nonexperts, I can describe topological insulators as, more or less, \"Berry phases can give rise to a nontrivial 'band geometry,' and analogous to Gauss-Bonnet there is a nice quantity calculable from this that characterizes instead the 'band topology' and this quantity is also physically measurable\" and they seem quite happy with this. On the other hand, while the connection to something like Gauss-Bonnet might be clear for topological order in \"TQFTs\" or in the ground state degeneracy, these seem a bit formal. I think my favorite answer is the adiabatic continuity (or lack thereof) that Everett pointed out, but now that I'm thinking about it perhaps what I should have asked for is -- What are the geometric properties of states with topological order from which we could deduce the topological order with some kind of Chern number (but without starting from a Chern-Simons field theory and putting in the right one by hand ;) ). Is there anything like this?", "label": 1}
+{"snippet": "I've been thinking about infrared radiation and noticing more and more how the human skin seems actually pretty sensitive to it. You can easily feel a bonfire from several meters away, far away from where any convection would heat your skin. When you open the hood of your car you can feel the heat from the engine even standing back a step or two (away from the updraft of hot air). Now try this: hold the palms of your hands against eachother a couple of inches apart and keep them like that for a couple of seconds. Then slowly (to avoid wind cooling) lift the other palm so they no longer face eachother. Do you feel it? For me there's a noticeable difference in warmth. Is that the skin detecting black body radiation from other skin? This could be easily blind-tested with a friend; you hold your palm out and look the other way, then see if you can correctly tell when your friend's palm is near you palm and when its not. Maybe the human skin is even able to detect black body radiation from another human standing behind her? Kind of like a sixth sense. Could explain the sensation of \"i knew someone was there\". I've noticed also that when you stand close to a concrete wall that was heated by the sun, but the sun has just set, you can tell which direction the wall is just from the heat on your body. Is this all placebo or does it actually work that way?", "label": 1}
+{"snippet": "Has anyone actually developed a Program Synthesis system for creating computer programs automatically from a non-procedural specification that is taken from a fairly robust system of specifications? For example, I might say \"Check if X is a factor of Y.\" or \"List all prime numbers between X and Y.\" and out pops a program or two written in PHP that does just that. I would actually pay money for an example that shows that the answer is yes. Let's say you have relations for less than and multiplication, and you give a wff of logic. So it can be (exists A)MUL(A,X,Y) where MUL(A,B,C) iff A x B = C, for the first specification above. For the second specification with output of a number (the prime numbers) instead of TRUE or FALSE, we could say variable N means output all values of N such that the wff is TRUE. I have heard the claim that the answer is yes, but articles give no real examples of its being used. Either there is no example, or what they call an example merely displays a program and claims that it was or can be generated by some system that is imagined or even described in detail, but the example lacks any details at all. Can someone give a complete example of a system, a specification, the resulting program(s) and step-by-step exactly how that program is automatically constructed? And if an example is given, could it be a simple program with only a few steps to create, rather than dozens of pages of formulas that would take months to go through and is suspect of being obfuscation hiding the fact that it is not genuine?", "label": 1}
+{"snippet": "I was recently in an argument with a friend who - equipped with an apparent understanding of the etymology of the words lend and borrow - insisted that to lend an object required not just the temporary exchange of its possession, but also a geographical displacement. He compared the words lend and borrow to take and bring which involve a transition to/from one's locus, which are apparently linked (though I can't independently verify) to our subject words grammatically. I argued that to so strongly stipulate (as he did) that an exchange was not a lending because the relocation was not significant (ie; it did not leave his personally defined location), is foolish given the complete generality / ambiguity of the word location. He insisted he could not lend me the salt-shaker as it traveled from his hand to mine because we were both common to the location 'this house', though I remarked that we sat in different locations; our respective chairs. After much debate, we concluded that to require lending to constitute a relocation is a poor definition, since there are (according to him) obvious stipulations as to the definition of the location. So... is any of this actually correct? Does lending actually have any requirement for a displacement of the lent object? If so, what exactly are these conditions (or rather, if they are as contextually defined as we both probably expect, what is a more appropriate word than 'relocation'?)? (I finally remarked that language is defined by the understanding of its speakers, and that I'd personally never heard a relocation was required in the lending of something. I also think the phrase \"lend me your ears\" doesn't beckon for their displacement...)", "label": 1}
+{"snippet": "Rational numbers, rational functions, and Gaussian rationals are examples of fields of fractions. In each of those cases, one knows what the quotients are long before one hears of the idea of constructing the field of fractions of an integral domain. One case where one (typically??) does not know of such a thing in advance is the field of \"convolution quotients\"---the field of fractions of a ring of functions of a real variable in which the \"multiplication\" is convolution. But convolution quotients will not be appreciated by students who just finished a first-semester calculus course last week. Is there some example one could mention to such students where they wouldn't think they already know what is meant by division of the objects in question? Later edit suggested by answers and comments posted so far: I had in mind two or three purposes. One was that I wanted to mention this topic a bit obliquely in something the students are to read, and that had to be really terse, so I can't do anything really involved. Less than an hour after I posted the question, this ended up being a parenthetical comment on the course web site that said: \"(for example, why is it that one can `divide' one divergent series by another?)\". Here I had in mind the ring of formal power series suggested by Chris Eagle, but of course I needed to ruthlessly avoid mentioning power series. A second purpose concerned possible future uses. Not only in courses: if we get some good examples here, I'd like to add them to Wikipedia's article titled \"field of fractions\". A possible third purpose was just the satisfaction of knowing more than one decent example (since the only one mentioned above that's \"decent\" in the relevant sense is convolution quotients).", "label": 1}
+{"snippet": "Assuming that antimatter is matter with time arrow reversed, would it be right to say that matter beyond black hole event horizon then would become antimatter because of space and time axes exchanged? Would not black hole then appear like a nice universe consisting from antimatter that slowly expands as matter falls into it? I do not claim anything just want to find out how wrong the idea is. Although, it is not really related to the question but I would like shortly explain where from my crazy idea that matter can indeed move to the opposite time direction is coming. I think that there was no Big Bang but initially was space filled with matter fluctuating back and forth in time (field fluctuating between matter and antimatter). Since there was no real matter - matter and antimatter fluctuated from vacuum and annihilated chaotically and hence there were no state transitions (movement) which we perceive as time - there was no time, in fact there was no matter either - just vacuum. But at some random event indicated as 'shortly after Big Bang', CP-symmetry got broken, which caused antimatter to disappear and gave rise to the time which we since perceive as going forward (if by some other event antimatter had won our time would go into opposite direction - but this does not mean 'back in time'). CP-violation caused universe expansion, but there was no initial rapid expansion, since universe did not arise from a singularity, but from a homogeneous space, which is in sync with recent Cosmic background radiation observations.", "label": 1}
+{"snippet": "One only needs to search MMA.SE, math journals, wikipedia, or god-forbid, n-cat lab, for keywords listed in the title, which can be extended with: uniform-, regular-, complete-, local-, partial-, non- (see below) &c&c, to be convinced that modified concepts are replete across maths, proliferating, and their diversity is likely accelerating. Shafarevich: \"it is the destiny of mathematics to expand in all directions.\" This trend, coupled with the lack of standardized terminology, can make it difficult to compare results or in same cases even definitions. It seems clear that in general a modifier term doesn't categorically reveal whether the modified concept is a specialization or generalization of the underlying concept (eg, subset versus superset, or subcategory versus supercategory). In some cases the modified concept might not bear a sub/super relation to the underlying, for exmaple, co- and op- in category theory and universal algebra (what's the relationship of universal co-algebra to algebra or co-induction to induction?). So it appears we must be content with enumerating cases to discern the relation and then compare to see if a big picture emerges. Basic examples: Semigroups are generalizations of groups but inverse semigroups are specializations of semigroups. (Quasicrystals are crystals - this got the Nobel - but their symmetries don't satisfy the crystal restriction theorem, eg, translation invariance, so are not groups, but might be modeled by inverse semigroups [ML]). Quasimetrics are generalizations of metrics, but ultrametrics are specializations of the latter[VS] . Noncommutative geometry, Connes stresses, includes commutative geometry so it is a generalization. In the absence of an online OEIS-like database, would it be possible to crowd-source many more examples of mathematical concepts or categories noting sub/super (or other) relation to the underlying?", "label": 1}
+{"snippet": "I think physicists can deal with this question best. I answered a question about \"immortality\" when some guy claimed I got it wrong that neurons die (I argued that even if you live a billion years you die slowly many times over because all your cells incl. nervous cells will have to be replaced, meaning you will regularly - but never suddenly - become a new person; also: continuous learning, and information storage is physical, and our brain has very limited capacity so memories will change), immortal means they are immortal. That got me thinking: Is it actually possible to have repair systems in each cell, or isn't it better to have a repair system on a much higher macro level and cell-level immortality is actually impossible? Background: The smaller the scale, the more events like quantum effects and Boltzman (energy) distribution (e.g. random atom movements, crystal structure defects, breaking bonds) dominate. Meaning small systems WILL break in unpredictable ways, so only large systems can live long and have reliable repair systems because the larger the system the less important those effects become. Summary: It is much better (or even possible) to have big long-living systems than small ones, because the inevitable repair system cannot be too small because it will be subject to random events of the micro-world. An \"immortal\" human would have a body-level repair system that repairs by letting broken cells die (we have that already) and build a new one, instead of having a repair system on the cell-level that would make cells immortal (too unreliable, won't work). Or in other words: The smaller the system the less likely a long life can be achieved. Note that I'm asking about complex dynamic systems, not static objects or information. Like living organisms or (complicated) machines, and about their chance to \"live long\".", "label": 1}
+{"snippet": "There's a list of \"New York\" words and phrases that's been surfacing on the Web periodically for quite a few years. Not all New Yorkers speak like that, I assure you. Only barely-above-the-gutter white New Yorkers with Brooklyn roots, plus lower-middle-class Jews from Borough Park and wanna-be Italian mafiosi from Bensonhurst. I know one Italian limo driver who still says \"youse\" because (get this! ...) he wishes to preserve that particular brand of Brooklyn dialect. Here's the list: Filayda: A single phrase made out of two English words. As in, \"I don't want this for now but I'll take it 'filayda.'\" [I don't remember ever using the expression myself, but I do hear it often. Ricky V.]. Wawda: That which if not inhaled directly from the faucet is, if from a classier social set, sipped out of a glass. Naydivs: Local types born and reared in \"Bronzvle.\" Tooner Samwidge: Luncheon staple. Mellid Cheese Samwidge: A menu choice if the luncheonette is out of tooner. [Somewhat archaic, both of them, since the disappearance of the luncheonette as a concept. R. V.] Kawfy: What washes down Mellid Cheese. Berle: Not Milton's last name but the method by which an egg is often cooked. Earl: What French fries lay in. Goil: The way people who say \"berle\" and \"earl\" pronounce \"girl.\" Buzz: Large lumbering public vehicle usually located all in a clump or, if you're in a rush to be transported crosstown, at sporadic intervals. [An exaggeration, actually. R.V.]. Gazz: That which goes into the buzz. Fiff: The major avenue which separates Manhattan's East Side from the West. Sixt: The major avenue one block from Fiff. Ate. The major avenue one block from Seventh. [Despite the numerous moronic efforts to rename Sixt to \"Avenue of the Americas\" (eww); despite the fact that the ... uh ... official ... name appears on anything and everything that's mailed to or from Sixt, it's Sixt, and will still be Sixt a thousand years from now, one would hope] Ey: A manner of summoning those whom you would alternatively greet with \"Whassup?\" Bronnix: One of the land masses the Triboro connex. [The Bronx, actually: a neighborhood named after the Swedish immigrant Jonas Bronck and his family, the Broncks. The Triboro is the Triborough Bridge, built by the infernal Robert Moses. It was an automobile-only bridge back then; it has been (reluctantly) changed to automobile-and-bicycle and renamed (idiotically) Robert F. Kennedy Bridge, since. R.V.]. Lirracher: Stuff like what Dostoyevsky wrote. [Personally I don't know what this obsession with Dostoyevsky is. There have been infinitely better writers, including Russian writers. R.V.] Liberry: Where one goes to immerse in lirracher. Purdy: The view outside the Empire State Building. [This isn't specific to New Yorkers. R.V.]. Awfissa: Policeman. Cop. Patrolman. Sergeant. Dude in blue on horseback. Downashaw: Where Rockaway is. [Rockaway and Far Rockaway, actually, commonly known as the Rockways; the latter is the last stop on the \"A\" train; never take it if you can help it. R.V.] Ackrost: From here to there. [An exaggeration. R.V.] Monicker: Miss Lewinsky. Lannick: As opposed to Pacific. Fewcha: Follows the present. Ahkinsore: Clinton territory. Winda: What is always broken and what in the hot weather never rolls down in a cab. Payment. What one walks on so one doesn't get hit by a car. Innerestin: What this particular column should be unless you're somebody who demands quality. Youse: Second person singular. Yiz: Second person plural. Yizzle: A contraction to be used in the sense of, \"Yizzle call me.\" Now most of this is very familiar to me as a New Yorker; I am, however, puzzled by a couple of things here. Specifically, I can't figure out what the original list's author had in mind when he wrote \"Earl.\" I mean, yes, I get it, it's \"oil.\" But ... hmm ... either I've never heard a New Yorker say it like that or I have a problem seeing the forest for the very familiar-looking trees ingrained in my psyche. Before you start pondering on this, let me remind you that the New York brand of English is unapologetically rhotic. Agressively rhotic. Defiantly rhotic. \"Earl\"? Really? Rhyming with \"girl\"? I don't get it. What am I missing? Bonus question: While I hear \"youse\" all the time, as Damon Runyon did nearly a century ago, I've yet to encounter \"yiz.\" I don't get the joke. Care to explain?", "label": 1}
+{"snippet": "This question related to Why are magnetic lines of force invisible? and is motivated by a comment of @BlackbodyBlacklight, based on that, the illustrating example may depend on that linked question as context to be clearly understandable. A remote magnetic field, in the sense that it is not at the location of measurement, could influence the location of measurement in some (possibly indirect) way that allows to derive information about it's structure. This is comparable to deriving information about a remote temperature profile based on properties of the local electromagnetic field, like when using a camera, or just seeing something glow. It might well turn out that it is fundamentally impossible to derive information about a remote magnetic field, (given some sensible constraints). In this case, an Answer should ideally explain why that is the case. What is described above is roughly comparable to human perception, which was the context where the question came up originally. Therefore, I will illustrate my initial ideas in that context in the section below: Establishing the context for the question (The biological aspects referred to are part of the illustration, not directly related to the question): The motivating idea was: \"We can not see magnetic fields, but that may be because it was not important during evolution to acquire this capability.\" Could it be possible, in principle, to \"see\" magnetic fields? Now, if it would have been helpful during evolution - what kind of perception is possible purely from the physical side of the question - assuming \"perfect evolution\". The linked question asks about seeing magnetic field lines - so could something like eyes for seeing field lines have evolved? I assume not, so we do not need to go into details whether to see them on surfaces, as lines at a fixed distance, etc. (Feel free to make creative assumptions as needed regarding how to \"see\") What did evolve, in some birds and bacteria, is perception of the field of Earth in terms of direction of the local(!) field lines - something like \"feeling north and south\". The actual question, related to physics of magnetic fields, in comparison to phenomena for which human perception exists: What are the physical constraints? Seeing a magnetic field like a fourth base color would not work - there is no radiation. Something similar to spacial sound perception? Which would mean to measure from a finite set of \"local\" reference points to collect measurements on a given remote locatioin. Anything better than measuring a local field vector is certainly interesting.", "label": 1}
+{"snippet": "I have a question about adjoint operator. I have known that bounded linear operator on Hilbert space has a unique adjoint operator, but I am wondering whether there is similar existence result about bounded linear operator on Banach space? Thank you.", "label": 1}
+{"snippet": "I am learning measure theory this semester. The definition for sigma-algebra is \"a collection of sets that is closed under complements and countable unions and intersections.\" I wonder what does it mean by \"closed under complements and countable unions and intersections.\" Thank you so much for your help!", "label": 1}
+{"snippet": "I know that \"callipygian\" means \"having beautiful buttocks\"... so I was wondering if there is an English word that means \"having beautiful hair\". I tried googling this but couldn't find anything so far.", "label": 1}
+{"snippet": "I'm preparing for an exam and I can't seem to figure out the reasoning behind the answer to this question. Why do they use a chi-squared test? Can someone walk me through their explanation? Thanks.", "label": 1}
+{"snippet": "I'm looking for a good textbook for an introduction to Stochastic Analysis, preferably one that focuses on rigour. I am familiar with measure theory and basic probability theory. The direction I am mostly interested in is stochastic differential equations.", "label": 1}
+{"snippet": "I'm terribly confused on the concept of \"rank of a linear transformation\". My book keeps using it, but it doesn't clarify what it means (or at least I haven't been able to find it). Is it the same as the rank of the matrix? For example, if A is a mxn matrix, what would be the rank(A)?", "label": 1}
+{"snippet": "I've recently been working through a lot of physics problems and a lot of them say to assume that the mass of the string used in a problem involving a pulley, for example, is negligible. Why is this important? What would happen if the mass of the string wasn't negligible?", "label": 1}
+{"snippet": "How do I properly punctuate this sentence: \"I prepared, packaged, and priced beef, pork, chicken, and seafood.\" I am trying to say that I did those three actions to those four kinds of meat, but I am unsure of what to do. Should there be a colon or semi-colon between priced and beef?", "label": 1}
+{"snippet": "I'm not a native English speaker, and I don't understand the meaning of the phrase \"in your general direction.\" I have found its use in the line from Monty Python and the Holy Grail: I fart in your general direction.", "label": 1}
+{"snippet": "This problem is taken from the book Mathematical Circles by Dmitri Fomin, et al., translated by Mark Saul and published by the American Mathematical Society. Can anyone describe what the question actually means?", "label": 1}
+{"snippet": "I'm reading a book on probabilistic robotics and it mentions that \"this probability density function is quadratic in x.\" I haven't heard of the phrase \"quadratic in x\" before. Can someone explain what it means? Does it mean that the graph has a quadratic shape?", "label": 1}
+{"snippet": "I don't want subsections to appear in the table of contents of my Lyx document. How do I turn them off? I went to Tools -> Settings -> Numbering & TOC, but it won't let me modify anything. What should I do?", "label": 1}
+{"snippet": "I just read this interesting interview with Frank Wilczek and he talks a couple of times about gate symmetry, without ever defining the term. This isn't a term I've come across, and google throws up a blank. What is gate symmetry, and are there any good references?", "label": 1}
+{"snippet": "I have a LaTeX document that contains proprietary information. I need to print a version of the document that has a box around the text with a disclaimer (something to the effect of \"Proprietary information of company XYZ, do not redistribute without express consent'). How can I do this? If it matters, I'm using MacTex.", "label": 1}
+{"snippet": "Density Functional Theory (DFT) is formulated to obtain ground state properties of atoms, molecules and condensed matter. However, why is DFT not able to predict the exact band gaps of semiconductors and insulators? Does it mean that the band gaps of semiconductors and insulators are not the ground states?", "label": 1}
+{"snippet": "I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost. Is there a way to explain how the Higgs field works, in a way that people like me might have a hope of understanding?", "label": 1}
+{"snippet": "Is it possible to establish that the lines joining the mid points of opposite sides of a quadrilateral bisect each other. I attempted using mid point theorem of triangles but I couldn't prove it", "label": 1}
+{"snippet": "I am trying to find an English translation of Camille Jordan's work \"Cours D'analyse\". Only the French edition is on Amazon, so since this is a somewhat specialized topic, I thought perhaps someone in this forum might know. TIA, Matt", "label": 1}
+{"snippet": "I am currently studying Electrical & Electronic Engineering. I wish to pursue Quantum Mechanics or Quantum Computing as my research subject. Is it possible for me to do my M.Tech. and then pursue my research subject? What are the prerequisites for studying these subjects? I would be grateful if you could help me.", "label": 1}
+{"snippet": "Prove that if the real part of an entire function is bounded so is the imaginary part, without using Liouville's theorem. In particular, is there a way to prove this using the Cauchy-Riemann equations?", "label": 1}
+{"snippet": "I'm sorry if I ask this question at the wrong place, but I don't know a better one. I am a Master's student and I am really interested in analysis, but I also want to get into AI. Does anyone know a natural way to combine these two interests? Thanks in advance.", "label": 1}
+{"snippet": "The title basically states the whole question..I was trying to invoke the Mean Value Theorem on it but it hasn't worked..I was wondering if I'm supposed to solve it some other way. I just need hints, please. Thank you.", "label": 1}
+{"snippet": "This has been bugging me. Why is the lower case letter \"a\" used to spell \"abelian group\" when upper case letters are used to spell the terms, \"Gaussian Integral\", \"Cantor set\" or \"Cauchy sequence\"? Don't know where else to ask.", "label": 1}
+{"snippet": "As far as I can tell, if a function is holomorphic on its domain, then it's also meromorphic and vice versa. Can someone tell me what the difference between these two properties are (if any)? A counter-example and an explanation of why it's a counter-example would be nice.", "label": 1}
+{"snippet": "I'm reading \"The Portrait of a Lady\" by Henry James, and I found the following two sentences. \"I suppose that after a girl has refused an English lord she may do anything,\" her aunt rejoined. \"After that one needn't stand on trifles.\" What does \"one needn't stand on trifles\" mean?", "label": 1}
+{"snippet": "I am making a piece of software which has the ability to send out Emails and SMS messages. My boss has asked for both facilities to go under the same heading in a dropdown menu. But I can't think of a suitable work that encapsulates both. Any suggestions?", "label": 1}
+{"snippet": "We've all seen that label on our passenger side mirrors that says, \"Objects in mirror are closer than they appear.\" Why is this? Further, why does it only apply to the passenger side mirror, and not the driver-side or rear-view mirrors?", "label": 1}
+{"snippet": "Show that Lebesgue measure can be expressed as a countable sum of probability measures. I'm trying to do something with the countable additivity property in order to show this, but so far nothing is working. I don't think this is supposed to be difficult, but I'm not seeing it, so any help you could give would be most appreciated!", "label": 1}
+{"snippet": "I'm trying to compile a LaTeX template to a PDF, but it's not working. The template is available in this link (on the right side in Article Templates). I'm using TeXnic Center. Can anyone please try to compile this and let me know if it's working.", "label": 1}
+{"snippet": "I am trying to use Egorov's Theorem in a proof. However, I only have convergence in measure of f_k to f and uniform integrability of f_k. How can I combine these two to get convergence point wise so that I can use Egorov? Thank you so much for your help!", "label": 1}
+{"snippet": "Is the following sentence grammatically correct? \"Symptoms of lactic acid build up in muscles include cramps, spasms, fatigue and sensitivity.\" Does \"sensitivity\" need to be qualified, as in \"sensitivity to touch\"? Can someone point out the \"rules\" that come into play here?", "label": 1}
+{"snippet": "As a student in a highschool physics class, my teacher has repeatedly told me that photons are massless. Yet, I have also heard from other sources that photons have momentum. If photons were to have momementum, that would mean that they have mass as according to p = mv. Do photons really have mass? Also, how would this mass be calculated?", "label": 1}
+{"snippet": "I heard somewhere that the capacitance of a superconductor is much higher than regular conductors, but I haven't heard or seen anything yet proving or disproving such. So whats the truth? And why?", "label": 1}
+{"snippet": "A colleague asked me this question, and I couldn't come up with an answer that satisfied him, so I'm wondering if anyone can help: Why does a man with a short temper become a short-tempered man? In other words, why do you need the -ed at the end? Are there any special rules for this?", "label": 1}
+{"snippet": "Is there a path connected topological space such that its fundamental group is non-trivial, but its first homology group is trivial? Since the first homology group of a space is the abelianization of the fundamental group, we are looking for a non-trivial group whose abelianization is trivial. Is there such a group?", "label": 1}
+{"snippet": "I got edited on Stack Overflow because I used \"I'm\", \"you're\" and \"I'd\" instead of \"I am\" etc. Is it considered rude to use contractions like that in informal conversations on the internet? I would not use them in papers but, I thought on Stack Overflow it was okay.", "label": 1}
+{"snippet": "This is probably a stupid question but I will have to ask it. If you had a set of N correlated random variables and knew the correlation matrix, can one compute the joint probability distribution of all variables? Does it make a difference if the correlation matrix was built using Pearson's rho or Kendall's Tau for example? Thanks, Bogdan.", "label": 1}
+{"snippet": "My book says all extensions of finite fields are cyclic, but I could not find a proof (maybe I haven't looked hard enough). If it's straightforward, can you tell me why it's true? Thanks :)", "label": 1}
+{"snippet": "I'm trying to solve this question: I didn't understand why the hint is true and how to apply it. I really need help, because it's my first question on this subject and my experience on this field is zero. I need some help. Thanks a lot", "label": 1}
+{"snippet": "I do know Schreier's theorem, which states that a finite index subgroup of a finitely generated group is finitely generated. Other than this, I have no reason to suspect a positive answer to my question, other than it would be nice.", "label": 1}
+{"snippet": "Could someone tell me if I've worked this out right? I'm unsure of the process, especially the final parts where I convert it to a sinc function. Please let me know if I've made mistakes anywhere else too.", "label": 1}
+{"snippet": "The Shannon-Hartley theorem gives an expression for the capacity of a bandwidth and power limited channel. How would one formulate this theorem mathematically (rigorously)? I understand the formula given, but not how to formulate the assumptions made mathematically.", "label": 1}
+{"snippet": "What is the standard way in latex to display certain objects (e.g. pictures, tables, etc.) side by side, instead of one below the other? I thought about using the tabular environment for this, but I'm not sure if there isn't a better way.", "label": 1}
+{"snippet": "I am reading the book \"Lebesgue Measure and Integration: An Introduction\" by Frank Burk, and it says the following: If the Lebesuge outer measure is finitiely additive, then it is countably additive. How can I prove this?", "label": 1}
+{"snippet": "Hello everyone, I'm trying to solve this problem, but I'm stuck... i don't quite understand the definition of the norm, If you guys can give me a better explanation, I would appreciate it, Thanks", "label": 1}
+{"snippet": "It is well known that a local ring is a ring containing only one maximal ideal. I was wondering if there is a characterization (or any information) of the commutative rings such that all their non-trivial ideals are maximal. Thanks.", "label": 1}
+{"snippet": "I am an undergraduate student doing a project on rooted trees. I was wondering if anyone would know any easy to understand references that explains Grossman and Larson's Hopf Algebra on rooted trees? In particular, I want to know how the comultiplication, counit, and antipode are defined. Maybe if there is anything that explains their paper 'Hopf-algebraic structures of families of trees'.", "label": 1}
+{"snippet": "I've seen in a documentary that when a star collapses and becomes a black hole, it starts to eat the planets around. But it has the same mass, so how does its gravitational field strength increase?", "label": 1}
+{"snippet": "Which one is correct? Centuries ago, people weren't aware that the planets revolved around the sun. Centuries ago, people weren't aware that the planets revolve around the sun. In my grammar book it has mentioned the first one as \"grammatical correct sentence\", but it has not done such a comparison.", "label": 1}
+{"snippet": "What lessons do we have from string theory regarding the fate of singularities in general relativity? What happens to black hole singularities? What happens to cosmological singularities? Which points of view on string theory yielded results in this respect? String field theory? AdS/CFT? Matrix theory? I suppose perturbative string theory is not applicable in the vicinity of singularities.", "label": 1}
+{"snippet": "I've always thought \"to slumber\" meant to sleep deeply or for a long period of time. Several colloquial but less reputable dictionaries agree with me (http://www.urbandictionary.com/define.php?term=slumber, http://www.yourdictionary.com/slumber) but Merriam-Webster and the OED disagree, defining slumber as \"to sleep lightly\" and \"to sleep, esp. to sleep lightly; to doze or drowse,\" respectively. Which is correct in modern usage?", "label": 1}
+{"snippet": "Question: Which of the following graphs correctly describes the variation of kinetic energy with time of a block when it slides down a smooth inclined plane from rest? The answer is C but I do not understand why. How do we know if the velocity increases as it slides down the inclined plane?", "label": 1}
+{"snippet": "Why must a symmetric positive definite matrix must be invertible? I'm reading a proof of the Levi-Civita theorem in differential geometry but the author states this without proof and I haven't been able to prove it.", "label": 1}
+{"snippet": "I was wondering if it's possible to produce the anarchy symbol (the circled 'A') in LaTeX. I tried googling \"latex anarchist\" and got nothing but merchandise and porn, and while I'm not complaining, I also wanted the anarchy symbol.", "label": 1}
+{"snippet": "Is there a way to increase the font size in the source window of TeXworks? I guess I'm showing my age, but for me it is almost unusable. It's kind of annoying having to put my face so close to the screen to get any work done.", "label": 1}
+{"snippet": "I'm trying to make a figure environment that can select between multiple images. I am not trying to do multiple subfigures but rather a single figure environment that can cycle through multiple images like a slideshow. At this point I don't have any particular format in mind. I am just looking to see if Latex has the ability to do this. Thanks in advance.", "label": 1}
+{"snippet": "I read the following sentence in the book Options, Futures, and Other Derivatives: Treasury bond prices in the United States are quoted in dollars and thirty-seconds of a dollar. Here is my question: How should I understand the phrase in bold, namely, \"thirty-seconds of a dollar\"? I think the plural form \"thirty-seconds\" means several thirty-seconds of a dollar. Does it make sense?", "label": 1}
+{"snippet": "noob question here. I'm interested in reading The Elegant Universe by Brian Greene, but I've read some reviews that say the science has been discredited. I'm a total layman, has the science been discredited?", "label": 1}
+{"snippet": "I have a strong mathematical background and I am interested in the relationship between mathematics and music. I have found some introductory material on the web. Do you know any good books that will broaden my perspective of this subject?", "label": 1}
+{"snippet": "While looking for something on this site I accidentally found a document class which is perfect for a scientific report with two columns layout. Unfortunately I forgot its name. Could someone point me out the document classes which implements two column layout without using multicol packages?", "label": 1}
+{"snippet": "If the universe is undergoing inflation, and there is a minimum scale that things can exist at (the Planck length), does that mean that new Planck-sized domains have to be continuously popping into existence? If not, does that mean that the Planck length is constantly changing?", "label": 1}
+{"snippet": "What do they mean? How should I use them? Which one is more appropriate to what context? I was talking to a colleague of mine and we couldn't get to a consensus about what should we say when referring to drinks, for example: A lemonade is made of lemons. or A lemonade is made with lemons.", "label": 1}
+{"snippet": "If the title of a song ends a sentence, whether a statement or interrogative, where does the period or question mark go? For example, is it: The Beatles sang \"She Loves You.\" or The Beatles sang \"She Loves You\". Is it: Did The Beatles sing \"She Loves You?\" or Did The Beatles sing \"She Loves You\"?", "label": 1}
+{"snippet": "I'm having some trouble understanding the concept of negative work. For example, my book says that if I lower a box to the ground, the box does positive work on my hands and my hands do negative work on the box. So, if work occurs when a force causes displacement, how does negative work happen? Are my hands displacing anything?", "label": 1}
+{"snippet": "How to prove Ampere's Circuital Law in case of any conductor. My text gives the proof of only the special case when the conductor is long and straight. I am trying to prove it, but haven't been successful. Any hints would be welcome.", "label": 1}
+{"snippet": "I've recently come across the following sentence: Round the corner walked Hannah, and nearly bumped into Louise. The first clause sounds clumsy to me. I think the example above should be written like this: Hannah walked round the corner, and nearly bumped into Louise. Is it ever right to put the subject at the end of a clause?", "label": 1}
+{"snippet": "When I was much younger, I remember the press always referred to the U.S. president using the title of the office: \"President Nixon\" was followed by \"President Ford\" then \"President Carter\". Now that seems to have fallen out of favor and the common reference is: \"Mr. Obama\". My question is: when and why did that change happen? Was it associated with a particular president?", "label": 1}
+{"snippet": "Is there a sequential criterion for differentiability,just like there is one for continuity ? If not then,why so ? I'm studying undergraduate real analysis and haven't really come across one. Thanks in advance !", "label": 1}
+{"snippet": "What does \"sit in the back of the bus\" in the following sentence mean? It has been taken from Harvey Milk's \"The Hope Speech.\" The first gay people we elect must be strong. They must not be content to sit in the back of the bus. They must not be content to accept pablum.", "label": 1}
+{"snippet": "The Ricci tensor is defined as the contraction of the Riemann tensor in its upper and the second lower index. I was wondering why it is defined this way. What happens if the Ricci tensor is defined as a different contraction of the Riemann tensor? Would it satisfy Einstein equations? Does the usual definition have any physical or geometrical meaning?", "label": 1}
+{"snippet": "What is it called when the subject of a sentence is the same as the object of the previous sentence? For example: I'm going to Freddy's house. Freddy lives down the block. The block is paved with gravel. The gravel is jagged.", "label": 1}
+{"snippet": "I am unable to comprehend why ammeter is connected in series and voltmeter in parallel in a circuit. My book doesn't give any explanation about it nor am I able to understand it from the internet. Can someone please explain this to me (a beginner).", "label": 1}
+{"snippet": "Helium is a scarce resource, as it escapes the atmosphere over time. If we run out of Helium deposits, will it be possible to manufacture more helium through nuclear fusion or another nuclear process? If so, how much energy will be required?", "label": 1}
+{"snippet": "Is it more correct to say 'The picture hung crooked on the wall' or 'The picture hung crookedly on the wall'? My instinct is that the first one sounds better to me as a native speaker, but someone else I was talking to was convinced that only the second is correct. What's better here?", "label": 1}
+{"snippet": "Possible Duplicate: Should I put a comma before the last item in a list? What is the difference between tomato puree, paste, and sauce? OR What is the difference between tomato puree, paste and sauce? Do we need a comma before and in this case?", "label": 1}
+{"snippet": "A Lie group is a group which is a smooth manifold such that the multiplication and inversion are smooth. When does a Lie group become simple? What is the difference between simple and semi-simple Lie group? Just want a quick answer here. Thanks", "label": 1}
+{"snippet": "I'm working on an engineering project, and I'd like to be able to input an equation into my CAD software, rather than drawing a spline. The spline is pretty simple - a gentle curve which begins and ends horizontal. Is there a simple equation for this curve? Or perhaps two equations, one for each half? I can also work with parametric equations, if necessary.", "label": 1}
+{"snippet": "How can I center the titles of the chapters in the frontmatter and the backmatter of a document written using memoir? Keep in mind that the mainmatter chapters should not be affected at all.", "label": 1}
+{"snippet": "I keep coming across the term pseudocubic unit cell while reading about orthorhombic perovskite structures. No clear explanation is given in papers. Can someone please tell me how these structures are generated and what exactly is meant by them?", "label": 1}
+{"snippet": "What does \"sanding a doorstep\" mean? Does it mean polishing the doorstep? Or filling it in with sand? I read this expression in Charles Dickens' book, The Haunted House where it says, I found the landlord of the little inn sanding his doorstep.", "label": 1}
+{"snippet": "A person who makes desserts is called a pastry chef, but is there a name for the action itself of making desserts? \"Cooking\" is too general, and \"baking\" implies bread, cakes, etc. which is not quite what I mean. Any ideas?", "label": 1}
+{"snippet": "What are the differences between \"unto\" and \"to\"? It seems that in many contexts where the word \"unto\" is used, \"to\" could be substituted and would be perfectly correct. It reminds me of flammable/inflammable, where \"flammable\" came into use because the \"in\" in \"inflammable\" caused people to think that it meant not inflammable. Is this a similar situation?", "label": 1}
+{"snippet": "Is it possible that the universe is infinitely large and contains an infinite amount of mass that is distributed in such a way that gravitational force is never infinite? If so, is it possible that the infinite amount of mass that is outside of our light cone could affect us with gravitational force?", "label": 1}
+{"snippet": "Which one is correct? I am a new graduate and have been teaching German for a few weeks now. I am a newly graduate and ... I can't decide whether to use \"new\" or \"newly\".", "label": 1}
+{"snippet": "I have noticed the appearance of the phrase \"not so much\" in the language recently. It strikes me as both grammatically incorrect and humorous when used. For example,\"Jim is very smart; his brother, not so much.\" Or,\"That girl has a beautiful face; her figure, not so much.\" Has anyone else noticed this new colloquialism?", "label": 1}
+{"snippet": "I'm having trouble understanding how to find an invariant to check if it's preserved, and generally how induction is used in proving the correctness of algorithms (binary search primarily, but others as well).", "label": 1}
+{"snippet": "I'm doing a science project, and we're wondering if it is possible to compress pure carbon (C) to the point where it becomes diamonds? What would the process have to be and how much energy would this take? Has this been done and is this feasible?", "label": 1}
+{"snippet": "Prove that any graph that can be obtained from the Petersen graph by adding one extra edge has a Hamiltonian cycle. So I've found that removing any vertex yields a Hamiltonian cycle -- I'm not sure if that's relevant or helpful, as I wasn't able to link that to the main question above. I thought I'd include that in case though.", "label": 1}
+{"snippet": "Are both \"an hour and a half\" and \"one and a half hours\" correct? If so, is either more appropriate in different contexts? Example context: \"The Superbowl starts in less than one and a half hours.\" \"The Superbowl starts in less than an hour and a half.\"", "label": 1}
+{"snippet": "Does anyone have a link to Hilbert's Original Proof of the Nullstellensatz, or know a book where it's printed? I'd be interested to see what it was like. I only really know the Noether normalisation and Zariski proofs. While these are both good, it would be nice to have it 'from the horse's mouth'! Many thanks in advance.", "label": 1}
+{"snippet": "The term \"ginger\" is often used as a slang term for someone with bright red hair. But ginger (the spice) is actually a bright yellow in color. Where does this term come from, then?", "label": 1}
+{"snippet": "I have been trying to understand clearly the concept of non locality, hidden variables, quantum measurement etc through research papers. I also read Quantum Theory and measurment by Wheeler and Zurek but I feel I've got nothing into my head. Please recommend some introductory books on above mentioned topics for beginners.", "label": 1}
+{"snippet": "I have been trying to learn some basics of topology on my own, I have learnt the basic definitions. I have not been able to understand the proof provided in the text. Could anyone provide a clearer proof, or kindly explain me the outline of the proof provided here?", "label": 1}
+{"snippet": "In a commutative ring (with unity), is it true that (a) any maximal ideal is a prime ideal? (b) any prime ideal is a maximal ideal? (b) is almost certainly false, because a maximal ideal is a stronger concept than a prime ideal, but I don't know of any example to give. And I'm not sure about (a).", "label": 1}
+{"snippet": "An orthogonal matrix necessarily has orthonormal columns, and orthonormal columns necessarily give an orthogonal matrix. Also, orthonormal columns imply orthonormal rows. But how about the converse of the last statement? Meaning, do orthonormal rows necessarily imply orthonormal columns? Thanks", "label": 1}
+{"snippet": "I wanted to know what is the typical strength of the magnetic field generated by the tip of a magnetic screwdriver, but couldn't find it anywhere on the manufacturers' webpages. So I was wondering, is it possible to estimate it from the sort of objects that a magnetic screwdriver can pick up?", "label": 1}
+{"snippet": "I just want to confirm that I am right about these expressions. The \"foot of the stairs\" is the bottom of the staircase, and the \"head of the stairs\" is the top, correct? Are these expressions commonly used? Or is there a better alternative?", "label": 1}
+{"snippet": "The speed of light in a medium is independent of motion of source relative to medium but it depends on the motion of observer relative to the medium. I don't understand why it is so.", "label": 1}
+{"snippet": "I'm working on an app which displays status messages, like: \"XY is now available\" \"XY is now offline\" I'm wondering which of the followings is correct: \"XY is now idle\" \"XY is now idling\"", "label": 1}
+{"snippet": "Is there a word or phrase to describe someone who is willing to do extra work in the short term to avoid work in the long run? I have seen \"lazy\" used for this, but I'd like to know if there's a more precise term.", "label": 1}
+{"snippet": "In our daily life a lot of photons of visible light, infrared and radio etc move around us. We know that light is an electromagnetic radiation. So why doesn't that electromagnetic radiation affect a magnetic compass?", "label": 1}
+{"snippet": "Is there a word or expression describing a phone call when the caller doesn't hang up, but also doesn't say anything (or at least nothing can be heard)? I'm specifically looking for a term describing such call made to scare someone (with the caller breath being heard). My initial thought was that it's called silent call, but according to Wikipedia it means something different.", "label": 1}
+{"snippet": "\"If matrices B and AB have the same rank, prove that they must have the same null spaces.\" I have absolutely NO idea how to prove this one, been stuck for hours now. Even if you don't know the answer, any help is greatly appreciated.", "label": 1}
+{"snippet": "I am an absolute newcomer when it comes to quantum physics. So kindly suggest me a book which covers all the fundamental ideas, equations and all such stuff related to qp, so that i can master the basics and then move on to the advanced stuff.Thank you.", "label": 1}
+{"snippet": "I have recently read the proof that the Brownian Motion and Fractional Brownian motion are almost surely Holder Continuous. I was wondering if this can be extended to a higher class of continuous stochastic process, is there a characterisation of such class? Is this class much bigger than the Brownian Motion/ Fractional Brownian motion? Maybe even the whole set of continuous stochastic processes?", "label": 1}
+{"snippet": "I am studying finite element method.While studying i am confuse with numerical integration and interpolation.Is this two methods are same or different?. If they are different then is there any relation between them?.", "label": 1}
+{"snippet": "I need some help understanding Gaussian mixture models. In particular, I am trying to find the relationship between GMMs and K means. What is the basic algorithm for GMM? I am not sure where the \"clustering\" comes in. Can someone give me a basic example as to how this actually works?", "label": 1}
+{"snippet": "I'm currently prepping for some high school math competitions soon, and I was wondering if anyone knows any resources that are out there with an abundance of contest-math-related geometry problems. Geometry is definitely my weak point in contest math, and any input would be appreciated. Thanks!", "label": 1}
+{"snippet": "How come the following sentences have the same meaning when they have different voices? I can be substituted for John. (Passive) I can substitute for John. (Active) They both mean \"I can replace John.\"", "label": 1}
+{"snippet": "I am studying a function whose Fourier transform is zero on a set of strictly positive Lebesgue measure and I need to know this: If a set has a strictly positive Lebesgue measure can we prove that it contains an interval? Help is much appreciated", "label": 1}
+{"snippet": "Please describe how a vacuum flask/thermos works. How does the vacuum prevent convection/conduction/radiation? How does the lid with the curvy lines prevent either of the aforementioned heat transfers? If there are any other parts that may prevent heat transfer, please also list them.", "label": 1}
+{"snippet": "I'm trying to show that the quotient of the Heisenberg group with it's own center, H/Z(H), is abelian. I'm not entirely sure what makes up this quotient group in the first place though... and I'm a little confused as to what quotients of matrix groups with multiplicative operators look like. Help, thanks", "label": 1}
+{"snippet": "There has been a similar question before: How to convert a hexadecimal number to an octal number? But, in my case I need an Algorithm to directly convert a number from Octal to Hexadecimal and back without converting it to binary/decimal as an intermediate step. Is it possible?", "label": 1}
+{"snippet": "Gentlemen, thought my practice in solving Gauss Jordan elimination questions, I faced this question and I got stuck in it for quite long time, and I couldn't figure out the answer. Could you lend me a hand in solving this question. Thank you!", "label": 1}
+{"snippet": "Someone recently pointed out to me that most English-speakers will say \"I saw a big brown spider,\" rather than \"I saw a brown big spider\". However, the second sentence has the same literal meaning as the first. Are there instances in which adjectives are non-commutative, so that permuting the order of the adjectives changes the literal meaning of what's being said?", "label": 1}
+{"snippet": "I've read that attraction and repulsion between particles is caused by the exchange of virtual photons, and that virtual photons carry information. I don't understand how a virtual photon actually causes any attraction or repulsion, and how does it carry information anyway if it's \"virtual\"? Aren't photons an excitation of the electromagnetic field?", "label": 1}
+{"snippet": "Why is the standard for implementations of the AES algorithm called \"Rijndael\"? Is it simply a name? Or has it some kind of meaning? I tried googling this one, but without any helpful results.", "label": 1}
+{"snippet": "From the linear algebra books that I've encountered, they either discuss exclusively about finite-dimensional vector spaces, or assume that the reader already knows about infinite-dimensional vector space, Hamel basis, etc. What books explain the concept of infinite-dimensional vector space and its structures?", "label": 1}
+{"snippet": "In Dutch we use it to refer to (the airtime of) tv-shows that start around dinner. Is there an equivalent to it? I suppose it's sort of an idiom, but probably too specific to be considered so.", "label": 1}
+{"snippet": "I would like to measure the energies of particles emitted from a variety of ionizing radiation sources (alpha and beta), and then convert these energies to velocities. However, I am not too sure about how I might go about measuring these energies. Would this even be feasible? If so, how could it be done? How are these energies measured by professionals?", "label": 1}
+{"snippet": "Are there any integral domains in which no nonzero prime ideal is finitely generated? (Other than fields, of course, where the condition is vacuously satisfied.) I asked a similar question the other day, but the solution there relied on using zero-divisors and that didn't really help clear up the situation I was considering.", "label": 1}
+{"snippet": "If I have an ordered set X = {a, b, c} and another ordered set Y = {a, b}, I know that that Y is a subset of X but I also want to convey that Y is the prefix of X if that makes sense. Is there a name for that?", "label": 1}
+{"snippet": "The Great Dark Spot is an anti-cyclone in Neptune. But unlike the Great Red Spot of Jupiter which lasts for more than hundred years, the Great Dark Spot exists for only one year or so. Why is it so??", "label": 1}
+{"snippet": "I was attending my college re-union and a speaker just said that \"Having an ebook reader is status quo\". Apparently, it means that it is in vogue or in fashion. I do not think it is the correct usage. But I am a bit confused. Can someone clarify?", "label": 1}
+{"snippet": "I know from reading about the gravitational waves detected by Ligo, that when an object has angular acceleration, it produces gravitational waves. I'm wondering if an object creates gravitational waves when only accelerating in one direction, however? I'm also curious as to how the nature of the waves would differ in this case.", "label": 1}
+{"snippet": "Possible Duplicate: What is the correct way to pluralize an acronym? How would you make the plural form of an acronym? For example, if you have two of Nintendo's game console, the DS. Would you say, \"I have two DSes,\" \"I have two DSs,\" or something else?", "label": 1}
+{"snippet": "I am going to send a email to a secretary of a CEO thanking her for scheduling a meeting. What would be a good phrase for the opening of email? Should I write: Thank you for scheduling the meeting or would it be more appropriate to write: Thank you for accommodating our request", "label": 1}
+{"snippet": "Recently, I am interested in the Hecke algebras, but I'm not very familiar with it. Who can provide me some meterials about the history and the development of the Hecke algebras? Is there any good books or papers about Hecke algebras? Any help will be appreciated.", "label": 1}
+{"snippet": "When you get an error in LaTeX, the message \"Undefined control sequence\" is printed. Why is it called \"control sequence\" and not \"command\", for example? How does the sequence work? Is this a TeX or LaTeX thing?", "label": 1}
+{"snippet": "I'm an Android programmer and am working on a graphing calculator. I have been looking for a formula for sine and cosine to put in there. I have a decent understanding of mathematics but can not seem to find this formula. Any help would be great, thanks.", "label": 1}
+{"snippet": "I am having difficulty in understanding about weighted linear least squares. Could anybody explain me instead of minimizing the residual sum of squares why we need to minimize the weighted sum of squares? Further, I want to know about the term weighted? Although I have gone through some wiki notes but I am not able to understand. Thank you very much for the help.", "label": 1}
+{"snippet": "I just downloaded and installed MikTex and TexMaker today, and was wondering if you have any advice. I'm starting to read through various wikipedia tutorials, and other guides, but videos would be an immense help!", "label": 1}
+{"snippet": "A and B worked together to complete a certain task in three hours. If A works alone, he can complete the task in five hours. If B works alone, how much longer will it take him to complete the task? I have the answer to this question, but I just don't get how that works. Please help me out.", "label": 1}
+{"snippet": "Most important theorems in measure theory do not assume the completeness of measure spaces. Monotone convergence theorem, Dominated convergence theorem, and Fubini's theorem, to name a few. So I wonder if the completion of a measure space is necessary. In particular do we need to consider Lebesgue measurable sets which are not Borel sets?", "label": 1}
+{"snippet": "When i put a pencil in the middle of a paper and rotate it very fast, whatsoever is written on it, will appear in concentric circles. What is the reason behind this phenomenon and what is it called?", "label": 1}
+{"snippet": "The variational method, as it pertains to quantum mechanics, is used to approximate the energies of a particular system. Is it possible to use the same variational method to approximate the eigenvalues of other observables?", "label": 1}
+{"snippet": "I have been searching in vain for statistics about the runtime of pdfTeX, LuaTeX and XeTeX. My impression is that (ordering by increasing runtime), LuaTeX > XeTeX > pdfTeX, but exactly how big is this difference?", "label": 1}
+{"snippet": "In referring to a particular femme fatale, I described her \"femme fataleness.\" That is \"ungrammatical\" (I believe) but got the point across. Is there a correct term for this particular attribute? If so, what is it?", "label": 1}
+{"snippet": "I'm struggling to understand how to define multiplication and addition, now that I've been told that multiplication is not just repeated addition. It seems that the axioms for the two are identical, save that multiplication is said to not have an inverse for the additive identity. Doesn't this imply that multiplication cannot be defined without an addition?", "label": 1}
+{"snippet": "I know that any Riemann integrable functions have at most countably many discontinuities, and similarly, any bounded functions with countable number of discontinuities are Lebesgue integrable. But is it necessarily true that any Riemann integrable functions have at most countably many discontinuities? Thanks", "label": 1}
+{"snippet": "I see that you can use a Stern-Gerlach apparatus for massive particles that can be deflected, but that doesn't work for photons. What would you do instead to measure photon spin in a lab?", "label": 1}
+{"snippet": "I would appreciate it if you could explain to me the difference between implementing and executing in the context of the following sentence: The implementing agency(ies) for this project is UNEP and the national executing agency is the Department of Environment.", "label": 1}
+{"snippet": "Can you please clarify for me which is the correct answer to the following question: Do you often have visitors? a. Yes, pretty much every day b. Yes, quite often c. Not very often.", "label": 1}
+{"snippet": "As the title says it, I want to know how people find the work function of a metal without knowing the threshold frequency. Yes I've already searched on Google but I didn't find anything really relevant. I just found how to calculate Work function with threshold frequency.", "label": 1}
+{"snippet": "I was given a piecewise function, which happens to be continuous on some interval. It asks me to prove that it's Riemann integrable. I know that continuous functions are Riemann integrable, but is there a way to prove it for some specific function (without using that theorem that continuous functions are Riemann integrable)?", "label": 1}
+{"snippet": "For any graph G, prove that the line graph L(G) is claw-free. I have a fairly good intuition for this one but it's hard to put into words. I really need help with this one! I feel that I should use the pigeonhole principle...", "label": 1}
+{"snippet": "This integral comes from a physics book when calculating a field of an uniformly charged sphere (without Gauss' Law). It says that it can be done by partial fractions, but I cannot imagine how.", "label": 1}
+{"snippet": "Question: Prove that at any given moment, there exists a pair of diametrically opposed points on the equator of the Earth that have the same temperature. Use the Intermediate Value Theorem. Now I've been kinda struggling with how to deal with the Intermediate Value Theorem and I have no idea where to even start on this one.", "label": 1}
+{"snippet": "You can visualize a first-order Markov chain as a graph with nodes corresponding to states and edges corresponding to transitions. Are there any known strategies to visualize a second-order Markov chain, i.e. where transitions have two past elements and one future element?", "label": 1}
+{"snippet": "In graph theory, what is the difference between a cycle and a simple cycle? My impression is that a simple cycle is the same as a cycle except that you cannot repeat vertices. Is this correct?", "label": 1}
+{"snippet": "I have been searching in the literature, with no results, for the (Zero Field) Magnetic Susceptibility of BiSCCO, but I cannot find any article regarding that. Does someone have a reference that might be useful to me? Thanks a lot.", "label": 1}
+{"snippet": "Consider a recursive Mergesort implementation that calls Insertion Sort on sublists smaller than some threshold. If there are n calls to Mergesort, how many calls will there be to Insertion Sort? Why? Wouldn't this depend on the threshold, or is there another way to look at this?", "label": 1}
+{"snippet": "Does \"feel committed to\" require an infinitive or gerund complement? For example, which of the following is grammatical? I feel committed to following up on that. I feel committed to follow up on that.", "label": 1}
+{"snippet": "Even if Lebesgue measure and integration can be defined without using the extended reals, it might not be a very helpful formulation. My motivation for asking this question is that I'm curious about in which ways Lebesgue integration is an extension of Riemann integration, which doesn't necessarily use extended reals.", "label": 1}
+{"snippet": "The Cayley table tells us whether a group is abelian. Because the group operation of an abelian group is commutative, a group is abelian if and only if its Cayley table is symmetric along its diagonal axis. Sorry, but why is this true?", "label": 1}
+{"snippet": "What is the difference between pull over and pull away? I am still trying to get used to American English. It seems like if I do not understand the driving vocabulary I am going to fail in the driving test.", "label": 1}
+{"snippet": "What's the difference in the usage of these two adverbs continuously and continually? Here are some examples: a) She was told off for continually being late. b) It rained continuously for three hours this morning. c) The firemen worked continuously through the night. d) I'm afraid you continually make the same mistakes.", "label": 1}
+{"snippet": "Does adding the word \"ok\" to the end of a statement imply a choice instead of a command or order? Example: \"Wash the dishes now\". as opposed to \"Wash the dishes now, ok?\" Does this weaken your statement?", "label": 1}
+{"snippet": "The four major cities in the Netherlands, i.e. Amsterdam, Rotterdam, The Hague and Utrecht belong to the Randstad. What is the English translation for the Dutch word Randstad? I have found downtown but I wonder whether this is the correct translation.", "label": 1}
+{"snippet": "I was wondering about discrete metric space. Is it a proper metric space? I am trying to find some example of non proper metric space. I am not sure whether discrete metric space is proper or not.", "label": 1}
+{"snippet": "Possible Duplicate: Why is matter drawn into a black hole not condensed into a single point within the singularity? When we speak of black holes and their associated singularity, why is matter drawn into a black hole condensed into a single point within the singularity?", "label": 1}
+{"snippet": "I've heard a lot about the CJK package, so I want to give that a try. There is, however, no documentation for that package (see the link), nor do the available documentation files at CJK's website tell me anything about how to use the package. So how do I figure out how to use this package?", "label": 1}
+{"snippet": "In my physics textbook it describes the events at the beginning of the Universe. I'm confused about the order at a certain point. It says that at some point primordial helium is created, then it says that later atoms are formed. Isn't primordial helium made of atoms? Thank you :)", "label": 1}
+{"snippet": "Will we ever come up with non-gender specific pronouns and possessive pronouns for the English language? It seems that there are many new words in the English language every year, so why not gender-neutral pronouns? This would solve many problems, in literature and in everyday life.", "label": 1}
+{"snippet": "Which would be better to say? He reminds me of Dill from To Kill a Mockingbird. He reminds me of Dill in To Kill a Mockingbird. He reminds me of Dill of To Kill a Mockingbird. Also, which is more appropriate in a formal context?", "label": 1}
+{"snippet": "Possible Duplicate: What are your favorite English language tools? I have a question regarding the English language that is too general for this site according to the faq. OTOH, I don't know where to look for the answer. Is there a list of sites, books, etc. that are commonly used to answer questions?", "label": 1}
+{"snippet": "While playing around with cyclotomic fields, I started to wonder about taking the roots of unity in higher dimensional analogues of the complex plane. Are the roots of unity well defined in the quaternions, octonions, and other hypercomplex algebras? Are there higher dimensional cyclotomic fields, and if so do they have any interesting properties like unique factorization or interesting morphisms?", "label": 1}
+{"snippet": "Do the Law of Sines and the Law of Cosines apply to all triangles? Particularly, could you use these laws on right triangles? That is, could you use these laws instead of the Sine=opposite/hypotenuse, Cosine=adjacent/hypotenuse, and Tangent=opposite/adjacent rules to solve right triangles? I can't find this stated in any of my textbooks, nor has my instructor said anything about it, which I find odd.", "label": 1}
+{"snippet": "Is there any difference between the following two statements: I have to pay bills I have bills to pay Could you please tell us the difference between the above two statements and when to use them?", "label": 1}
+{"snippet": "I've always found it irksome when people form sentences such as \"I'm done my homework.\" It is of my understanding that you are never done something, but rather you are done with something. Am I right to be bothered by this?", "label": 1}
+{"snippet": "I'm told at school that the Electromotive Force (e.m.f) of a battery equals the potential difference between the terminals of the battery when there is no current. How is that possible? How can there be a potential difference with no charge flowing?", "label": 1}
+{"snippet": "How do you exactly define what is and isn't a dimension? I heard somewhere that it is \"anything you can move through\" but if that is right, why wasn't time and space considered a dimension before Einstein?", "label": 1}
+{"snippet": "Connes's non-commutative geometry program includes an approach to the Standard Model that employs a non-commutative extension of Riemannian metric. In recent years I've heard physicists say that this approach does not hold significant interest in the physics community. Is this, in fact, the case? If so, why? I do not mean for this question to be argumentative, but instead would like clarification.", "label": 1}
+{"snippet": "We were taught at school that if we want to make something plural, we should add \"s\" at the end. Later on, I learned that there are uncountable nouns. Not so much familiar with it. Can you please give some examples?", "label": 1}
+{"snippet": "I learned how to use bibtex from the LaTeX wikibook, found here. They say that to compile a LaTeX file that uses bibtex, you need to call pdflatex once, followed by bibtex, followed by two more calls to pdflatex. I'm wondering: what's actually going on at each of these steps? Why do I need to run pdflatex and bibtex in that order?", "label": 1}
+{"snippet": "If physics is the study of the physical universe, wouldn't that mean chemistry, biology, neuroscience, zoology, history, economics, sociology, etc, wouldn't they all be subfields of physics? I believe they are. If anyone can convince me otherwise with a good argument, the answer will be accepted.", "label": 1}
+{"snippet": "I need to figure out this property of Hermitian / Orthogonal projections \"A is a Hermitian projection if and only if it is an orthogonal projection\" Your assistance will be highly appreciated. Thank You", "label": 1}
+{"snippet": "Photons travel at the speed of light. Is there a known explanation of this phenomenon, and if yes, what is it? Edit: To be clearer, my question is why do photons travel at all. Why do they have a speed?", "label": 1}
+{"snippet": "I'm having some problems determining which of the following is more grammatically correct: The season that I like the best is Winter or Winter is the season that I like the best I know that both are technically correct, but when would you use one over the other?", "label": 1}
+{"snippet": "One of the requirements of my English final includes removing all prepositions from a previously written essay. I'm having trouble getting rid of prepositions like \"to\", \"in\", \"of\", and other common preposition that seem like a requirement in writing. Could someone point me in the right direction? Thanks.", "label": 1}
+{"snippet": "I recently came across this proposition that the eigenvalues of a product of square matrices are invariant under cyclic permutation of the product order. Is there perhaps some group theoretic way of proving this proposition? I've tried a few cases and it seems to be true, but a direct proof has proven elusive. Or is a proof not so simple?", "label": 1}
+{"snippet": "I've read that the characteristic function of a probability distribution always exists because it's bounded. However, the characteristic function is still Taylor expanded in terms of the moments of a given probability distribution. Given the the moments don't necessarily exist, why is it that the characteristic function still exists?", "label": 1}
+{"snippet": "I'm trying to wrap my mind around the semantic differences between the words \"Register\" and \"Apply\". For example, are there any real differences between these two sentences: \"I will apply for this event.\" \"I will register for this event.\" What is the best way to think about the meanings between the two words?", "label": 1}
+{"snippet": "From my experience, it seems that although unstable is more commonly used, instable is often preferred in engineering and scientific contexts, e.g. \"aircraft instability\", \"instable algorithm\". Are there any differences in the implied meaning of the two terms? Should unstable be preferred?", "label": 1}
+{"snippet": "I saw a few groups on the web. A group's name is \"Non alcohol ~\" and another one is \"Alcohol free ~\". But I don't know the difference between \"non alcohol\" and \"alcohol free\". I think that \"non alcohol\" and \"alcohol free\" have the same meaning. Am I right?", "label": 1}
+{"snippet": "In fluid mechanics the terms 'pure straining flow' and 'pure rotational flow' are often thrown around (see e.g. here). I have tried looking for a formal definition of these two but have not been able to find one (or in fact anything you might call a definition). So how can we formally define these two terms?", "label": 1}
+{"snippet": "In the spin Hall effect, electrons with different spins accumulate in opposite directions without any external magnetic field. Broadly, the reason behind this is the spin-orbit interaction. But, the question is how? How does the spin-orbit interaction leads to this. A physical explanation will suffice.", "label": 1}
+{"snippet": "Is there any connection between fluctuation dissipation theorem and Kramers-Kronig relations? They are often described together under linear response theory but I do not see any exact connection (like one being special case of another).", "label": 1}
+{"snippet": "The force of gravity is constantly being applied to an orbiting object. And therefore the object is constantly accelerating. Why doesn't gravity eventually \"win\" over the object's momentum, like a force such as friction eventually slows down a car that runs out of gas? I understand (I think) how relativity explains it, but how does Newtonian mechanics explain it?", "label": 1}
+{"snippet": "I am trying to find the equation for the form that is in the picture. Basically it is an infinitely extending roller coaster loop. I just can not find the magic words in Google. Any suggestions? What is it called? What is the equation?", "label": 1}
+{"snippet": "When referring to a U.S. state in a formal document, is it correct to capitalize \"State,\" or should it remain uncapitalized? For example: This school is accredited by the State of Maryland OR This school is accredited by the state of Maryland", "label": 1}
+{"snippet": "I have a doubt about the Hermite Spline. Is it the interpolation with the minimum value of curvature among the possible interpolative functions between two points? Is it possible to demonstrate it? Thank you very much!", "label": 1}
+{"snippet": "Dirac delta function can be defined in several ways. I know two definitions. One is as a distribution and the other is as a measure. I found many materials on the derivatives of delta function as a distribution. However, I couldn't find materials dealing derivatives of delta function as a measure. Could someone point me at any materials or explain it?", "label": 1}
+{"snippet": "Would you please tell me which of these four sentences is correct one? I am so confused with them :( Action movies are three times as popular as comedies for men. Action movies are three times more popular than comedies for men. Men watch action movies three times as many as comedies. Three times as many men watch action movies than comedies.", "label": 1}
+{"snippet": "I'm aware that the Milky Way has a dark matter 'halo' around it, presumably a spherically symmetric distribution. But I'm completely ignorant regarding the theories explaining dark matter... Is there any reason to not expect a star-sized object to also be made of dark matter? I know they'll be extremely difficult to detect, but I'm wondering if it's even physically possible to exist.", "label": 1}
+{"snippet": "How many triangles in this picture: I know that I can just count the triangles to solve this specific problem. I would be interested to know if there is a systematic approach to doing this that can be generalized to larger diagrams of the same type.", "label": 1}
+{"snippet": "I'm having trouble obtaining the answer for this practice-test problem. I'm taking the volume of the whole cylinder as if it weren't cut then subtract the portion cut off. But I'm not getting any of the answers below. Any hints will be greatly appreciated. Thank you all.", "label": 1}
+{"snippet": "After listening of some lectures of Leonard Susskind about black holes, he mentioned that conservation of information is one of the foundations of physics. After searching the web I cannot seem to find how we came up with this theory. Could someone explain how we know this is true and/or how did we come to this conclusion?", "label": 1}
+{"snippet": "According to a book I'm reading, the Fourier transform is widely used in quantum mechanics (QM). That came as a huge surprise to me. (Unfortunately, the book doesn't go on to give any simple examples of how it's used!) So can someone provide one please?", "label": 1}
+{"snippet": "I want to know if I can determine the time where the sun's azimuth is at a given value. In other words, I want a function that takes the sun azimuth along with longitude or time zone and outputs the time. Is there anything like this?", "label": 1}
+{"snippet": "After reading definitions of universal and k-universal (or k-independent) hash function families, I can't get the difference between them. Also, I couldn't find any examples of hash function families being universal, but not k-universal (it's written, that k-universality is stronger, so they must exist). Could you please clarify the subject to me, or give a good piece of literature/articles to read about it?", "label": 1}
+{"snippet": "A recent arXiv article measures the variation of gravitational potential in a local region around the solar system, and from that it tries to infer the mass density. Are there any valid counterarguments to their conclusion, i.e: that there is no dark matter near our vicinity?", "label": 1}
+{"snippet": "I rarely need the ancillary files TeX produces when compiling a document (.aux, .log, .out, .synctex.gz). In fact, I've only ever had to read the .log, and that's only a few times. Is there a way to write them to a separate directory, so that my working directory only contains .tex and .pdf files?", "label": 1}
+{"snippet": "I'm looking for a package in which you can create nice bar and/or line charts in LaTeX. Currently I'm plotting the charts in Calc (OpenOffice), export it to a PDF document, crop it and then including it as graphics. I reckon there should be some more efficient way of doing this, preferably entirely in LaTeX.", "label": 1}
+{"snippet": "In special relativity, when two observers move in respect to each other, each observes the other's clock tick slower. An observer floating in space far from gravitational fields, observes earth clock ticking slower; at what rate is the clock of the floating observer ticking as observed from earth?", "label": 1}
+{"snippet": "Where does the word \"crack\" originate from in the phrase \"Give me another crack at that\"? Curious to know if it's in reference to driving horses? Perhaps a derivative of \"craic\" in Irish? Or in a structural metaphor about material splitting? Cheers.", "label": 1}
+{"snippet": "Do you use a question mark when a sentence starts as a question but then turns into a statement? For example, \"Can you explain this to me, because I don't understand the second part.\" \"What did he just say, because I couldn't hear him over the noise of the television.\" I usually use a period but don't know if that is correct.", "label": 1}
+{"snippet": "I'm trying to use different distance metrics like Euclidean, Manhattan, cosine, chebyshev among other distance metrics in my k-means algorithm to calculate distances between the data points and the centers. In what situation would one distance metric be more useful over the other in a clustering scenario? [Comparing all the above mentioned distance metrics]", "label": 1}
+{"snippet": "Let I be an open interval that contains the point c and let f be a function that is defined on I except possibly at the point c. Suppose that lim |f(x)| as x->c exists. Give an example to show that lim f(x) as x->c may not exist. Not really sure of an example for this?", "label": 1}
+{"snippet": "I'm modeling the flight trajectory of a golf ball, and using angular velocity to calculate the Magnus force. Currently, I'm assuming angular velocity to be fixed throughout the ball's flight. How accurate will this be? How much will the angular velocity of the ball be affected by air resistance?", "label": 1}
+{"snippet": "I got really confused about the graph of the relationship between wavelength and intensity of black body radiation. What does the peak stand for? And what does the graph tell us? How can we analyze it?", "label": 1}
+{"snippet": "How would I go about computing the volume of an ellipsoid with spherical caps removed and a cylindrical hole through it? I'm thinking about finding dV of a cross section (the ellipsoid has a circular horizontal cross section). Would this be the best way to go? I need to find if the volume is dependent on the radius of the sphere.", "label": 1}
+{"snippet": "I'm looking for a proper English word to say \"conversational partner\". Is \"interlocutor\" a word an average person would understand? Are there any other words or shorter expressions which could describe a person you are having a conversation with, but who is not your friend and is basically unknown to you?", "label": 1}
+{"snippet": "Is there a polynomial time algorithm that gives the extreme point as output for which objective function is minimized/maximized ? I am not looking for any solution that minimizes/maximizes the objective function, but an extreme point of the feasible region for which objective function is minimized/maximized.", "label": 1}
+{"snippet": "I have read that in projectile motion both vertical and horizontal components are independent of each other but i don't get it that how it is possible i think that they are dependent. If they are not could someone explain with a mathematical relation.", "label": 1}
+{"snippet": "On a yoghurt advert, the voiceover claimed that you have infinite combinations with it. However, given that there is a finite amount of matter, is it possible to have infinite combinations with the yoghurt or just a very large number of combinations?", "label": 1}
+{"snippet": "In the Lagrangian path-integral formulation of QFT, an anomalous symmetry is defined to be a symmetry of the action which is not a symmetry of the measure of the path integral, and therefore not a symmetry of the partition function. How do we define an anomalous symmetry in the Hamiltonian formulation of QFT, where this is no path integral or partition function?", "label": 1}
+{"snippet": "Speaker A: We want to ask you some questions. If you don't mind, of course. Speaker B: [He opens the door of his house] Sure, be my guests. Is the idiom being used correctly? If not, what would be a better alternative?", "label": 1}
+{"snippet": "He missed out several important facts. He omitted several important facts. I think these two sentences are the same meaning. Is there a slight difference? A few days ago, an American native speaker explained to me that \"omit\" means intentionally take out whereas \"miss out\" means mistakenly take out. Is it true? Could anyone clarify the difference to me?", "label": 1}
+{"snippet": "There are several PR firms, lobbying groups who specialize in mud slinging, making wild allegations on behalf of their clients. Is there a word that describes such a person whose job is to make allegations against others?", "label": 1}
+{"snippet": "I looked all over but could not find anything. Is there a package out there that has a symbol/dingbat of a calculator? I know there probably isn't, but I've seen much stranger stuff out there before...", "label": 1}
+{"snippet": "Suppose there are two light beams. One is red while the other is violet. The energy of both is the same. Which one of these beams has a larger number of photons, or is the number of photons relevant?", "label": 1}
+{"snippet": "I am sure there has to be a more precise word to describe a person that is not giving up on her beliefs no matter what other says. You could say consistent in her beliefs, but I am looking for something more elaborate. An example of such a person might be Margaret Thatcher. Thanks", "label": 1}
+{"snippet": "What is the origin of the idiomatic expression rub someone the wrong way? Is it correct to use the idiom in reverse, i.e. rub someone the right way, possibly meaning to calm or to please?", "label": 1}
+{"snippet": "I know of at least three equivalent formulations of QM: The \"normal/standard\" one, dealing with Hilbert spaces and state vectors. The Feynman path-integral formulation. The Wigner-Weyl phase space formulation. My question is: what is the usual name given to the first, \"normal\" formulation that everyone learns as an undergraduate?", "label": 1}
+{"snippet": "I know the differences in the meaning of word \"trash\" and \"garbage\" but how about \"take out the trash\" vs. \"take out the garbage\"? Can both these expressions be used interchangeably? What is the difference in meaning if any?", "label": 1}
+{"snippet": "My textbook states that \"Laser communication is much faster than microwave communication.\" But, how can that be? Both are electromagnetic waves with different frequencies but, how can the speed be different? Or Is the statement referring to any kind of processing speeds involved?", "label": 1}
+{"snippet": "I might be mistaken, but I feel odd calling the following \"wooden handrails\", since handrails are supposed to be made of metal. Is it OK to call it \"handrail\", \"guard rail\", or a \"wooden handrail\"? Or is there a better term for it?", "label": 1}
+{"snippet": "Today, my teacher proved to our class that every convergent sequence is a Cauchy sequence and said that the opposite is not true, i.e. Not every Cauchy sequence is a convergent sequence. However he didn't prove the second statement. Is there an example or a proof where Cauchy sequence is not convergent?", "label": 1}
+{"snippet": "Is there any good word/phrase/idiom for that feeling of scorn when you're accepted by someone/something after getting rejected the first time? I remember a phrase being quoted by Nathan Fillion in Castle when Richard Castle's daughter is rejected to Stanford and later gets in. Still can't remember the lines, just the situation.", "label": 1}
+{"snippet": "I'm fairly well-versed in calculus but I would like to explore beyond calculus. I have looked into the basics of some topics in higher mathematics such as group theory and abstract algebra and they intrigue me. I am wondering if there are any recommended methods or resources I should use to learn more about these topics. And is there any recommended starting point?", "label": 1}
+{"snippet": "I'm a complete beginner at LaTeX, and I'm trying to typeset a complex layout. How should I go about building a page like the one shown below. Edit I was able to replicate the layout using minipages with the multicols package. The images were embedded using the graphicx package.", "label": 1}
+{"snippet": "I came across several forums and articles saying that criteria is plural and criterion is singular. Some gave me the impression that criterion is used to denote a set of rules. What is the correct use of these two words?", "label": 1}
+{"snippet": "I have somehow managed to lose all my document classes and hence cannot compile anything. I have tried re-configuring and re-installing to no avail. I am on a university computer and cannot edit the program files.", "label": 1}
+{"snippet": "\"If they would have been painted this afternoon, the walls would be completely dry by tomorrow evening.\" The quoted sentence is ungrammatical. I believe it has something to do with tense, but I do not believe that the 'if...would be' structure requires parallelism. So what is wrong with this sentence? Thank you.", "label": 1}
+{"snippet": "Is solving problems quickly an important trait for a mathematician to have? Is solving textbook/olympiad style problems quickly necessary to succeed in math? To make an analogy, is it better to be a sprinter or a marathon runner in mathematics?", "label": 1}
+{"snippet": "I have had real difficulty with permutation/combination questions in probability and statistics texts. What I have real difficulty with is transforming word problems into mathematical form to solve. Are there any recommendations for a good text that might help me to do this? Or any suggestions for how to tackle these sorts of problems. Thanks", "label": 1}
+{"snippet": "Is there a word that works as a milder version of strenuous? Strenuous is defined by Oxford as something \"requiring or using great effort or exertion.\" I'm looking for a word with a similar definition except for the \"great\" part.", "label": 1}
+{"snippet": "I am confused on how to properly describe an all expense paid vacation. Is it an all expenses paid vacation or an all expense paid vacation, and are there any hyphens between all, expense or expenses, and paid? I ask because it seems to be all over the place on google search.", "label": 1}
+{"snippet": "What exactly is meant by Lorentz invariance? Is it just an experimental observation, or is there a theory that postulates it? What quantities do we expect to be Lorentz invariant? Charge? Charge densities? Forces? Lagrangians?", "label": 1}
+{"snippet": "I've heard many people use the term \"goose bumps\"; in my family, they were \"goose pimples,\" but I don't know if this was peculiar to us, or if others also use it. My wife's family's saying for this was \"Chilly bumps.\" Are there others? Is one considered the \"most correct\"?", "label": 1}
+{"snippet": "I've read a few different explanations of how hovercrafts hover, and they all mention a low-pressure cushion of air. This confuses me though: If there is low pressure under the hovercraft, why doesn't it get sucked to the ground? Also, if air is being forced into the space under the craft, why is this air cushion not high-pressure?", "label": 1}
+{"snippet": "It is known that in general, a mixed state can have multiple pure state decompositions. However, it has a unique eigendecomposition in the absence of degenerate eigenvalues. What is the special significance of this eigendecomposition over other pure state decompositions for the same density matrix?", "label": 1}
+{"snippet": "As the title suggests, Can the effects of a person's mass upon the local gravitational field be detected and measured remotely? I am aware any mass produces and effects gravity but couldn't find anything in my searching if it is possible or theoretically possible to detect this effect remotely.", "label": 1}
+{"snippet": "I used to pronounce 'detail' as ['di:teil] with accent on the first syllable. However, these days I hear people (and on the radio) say [di'teil] with accent on the second syllable. Is my pronunciation incorrect? Is there a regional preference for this?", "label": 1}
+{"snippet": "I'm a high school teacher and someone asked me this in my class, and to be honest I'm quite stumped! I haven't done any high level math in such a long time, and I'm really not sure how to approach this. Is the solution even approachable to a highschool student? Thanks for the help.", "label": 1}
+{"snippet": "I am going to learn some math about functionALs (like functional derivative, functional integration, functional Fourier transform) and calculus of variation. Just looking forward to any good introductory text for this topic. Any idea will be appreciated.", "label": 1}
+{"snippet": "That would not have happened if John had completed his work. That would have not happened if John had completed his work. The former seems correct. The latter doesn't seem incorrect. Are there any cases where one ought to use the latter instead of the former?", "label": 1}
+{"snippet": "For example I've written: \"I have an interest in rock climbing and am a member of the mountaineers Society.\" My friend thinks it has to be: \"I have an interest in rock climbing and I am a member of the mountaineers Society.\" which I think sounds bad. Which is right?", "label": 1}
+{"snippet": "What is the past perfect of \"have\"? Is it \"have\", \"had\", or \"had had\"? And if it is \"had had\", doesn't it sound weird and awkward? when and how do I use it? Thanks.", "label": 1}
+{"snippet": "I have a problem that I need to prove using induction. Prove that a surjective function has at least as many members in its domain as it does in its codomain. Do I begin by using the axiom of choice? Thanks.", "label": 1}
+{"snippet": "In Arabic, the expression \"Summer cloud\" is usually used to mean that \"this is not going to last for a long time\" or \"it won't last as long as you think it will\". Is there an equivalent phrase in English?", "label": 1}
+{"snippet": "So I'm essentially trying to find an explicit description of the smallest subfield generated by a subset of the field. I know that if s is an element of the subset, we must also have its additive and multiplicative inverse. Is there a succint way of describing the subfield set-theoretically? Again, the intuition seems clear, but I'm struggling with a formal description...", "label": 1}
+{"snippet": "This morning I heard the word \"constitutionality\" being used by a journalist with regard to the debate over the legality of health care reforms here in the US. This grates on my British ears as I would simply use 'constitutional' in this context. Does 'constitutionality' have a different meaning? Is this a recent Americanism?", "label": 1}
+{"snippet": "When measuring blood viscosity, the literature claims that we generally use a cone-and-plate viscometer. Why is this; is there any way to explain this mathematically in terms of the shear rate, etc? Does it have to do with the fact that the shear rate is constant in this device? Why won't it work with a parallel-plate viscometer?", "label": 1}
+{"snippet": "What does the phrase \"begging the question\" really mean? And does it even matter if I use it correctly? Almost everyone just uses it as a synonym for \"posing the question\" these days.", "label": 1}
+{"snippet": "Is there a good template for software release notes? I typically cover new features, bug fixes, and enhancements. I'm currently using HTML but its ugly and not easy to distribute. Ultimately, I'd like to produce a single PDF.", "label": 1}
+{"snippet": "I've been going over the algebraic topology part of Munkres and this question has stumped me. If we have a complete metric space that is not compact, must it be simply-connected (path-connected plus trivial fundamental group)? My intuition tells me no, but I can't come up with an example.", "label": 1}
+{"snippet": "This may be trivial, but I want to be sure I understand correctly: Is it true that the interior of a simple polygon is always a simply-connected subset of the plane? I.e, is it eligible for the Riemann mapping theorem?", "label": 1}
+{"snippet": "I am wondering if there's an English expression for making someone fall in love with you. In Hungarian there is a term that could be translated into something like \"fooling someone into yourself\" - meaning you make the person fall deep in love with you, and it is implied that it's thanks to some deceitful or dishonest behavior.", "label": 1}
+{"snippet": "I'm trying to get some intuition, I think it almost makes sense, since you can think of the area of a square is length multiplied by height. The volume of a cube is length multiplied by height, multiplied by depth. I don't understand how to find the volume of the hypercube. What's the correct intuition?", "label": 1}
+{"snippet": "I recently became interested in the solution to Hilbert's tenth problem, in reading about the succession of results that lead up to the proof I came across the notion of recursive sets and recursively enumerable sets. The distinction between the two sets is very subtle. I need some help in answering the question in the title. Thank you in advance.", "label": 1}
+{"snippet": "What is it called when a character knows something the audience doesn't? For example, if the character was stating something obvious like \"today is your birthday\", saying it only to inform the audience, what is that called?", "label": 1}
+{"snippet": "I know that the game which is called football in Europe is called soccer in the U.S. But I wonder to what extent this differentiation is strict. What do people from England call their favorite game in conversations with Americans? Is there a misunderstanding in this case?", "label": 1}
+{"snippet": "When reading certain books I will encounter names of places or people that have been abbreviated. An example is in Catherine Hutter's translation of Goethe's \"The Sorrows of Young Werther\": A few days ago I met a man called V., an ingenuous fellow with a very pleasant face. Why is this done?", "label": 1}
+{"snippet": "Let's say I'm trying to describe two things that change. The first changes often and the second changes less often. Is there a better word than \"volatility\" to use in the following scenario? Is it even proper in this use? The first thing has \"high volatility\" The second thing has \"low volatility\"", "label": 1}
+{"snippet": "I feel like when two conjectures are inconsistent with one another, it's a clear sign of our misunderstanding of deeper mathematics. I was wondering if anyone knew of a comprehensive list of conjectures that contradict other conjectures.", "label": 1}
+{"snippet": "An ice cream shop sells ice creams in five possible flavours. How many combinations of three scoop cones are possibles?[Note:The repetition of flavours is allowed but the order in which the flavours are chosen does not matter.]", "label": 1}
+{"snippet": "Consider the following sentences: If I had my own place, I could do whatever I want. If I had my own place, I could do whatever I wanted. She said I could do whatever I want. She said I could do whatever I wanted. Which ones are correct and why? Is the answer different in a conditional, or does that not matter?", "label": 1}
+{"snippet": "I am using sharelatex (great tool) but I haven't been able to find a way to show the ruler (blue numbers on the sides of the paper) that comes with the CVPR template. I was wondering if someone has had the same problem and how did they solve it.", "label": 1}
+{"snippet": "\"It's precisely in contrast to the ordinary that the resurrection stands out.\" Could someone explain what the author meant by \"in contrast to the ordinary\"? Could I replace \"in contrast\" in this case with \"opposite\"?", "label": 1}
+{"snippet": "I'm fascinated by the fundamental questions raised by the Double Slit Experiment at the quantum level. I found this \"Dr Quantum\" video clip which seems like a great explanation. But is it scientifically accurate?", "label": 1}
+{"snippet": "I'm following my first course in field theory and the professor began, like many books do, by introducing the scalar field. However, I am a bit hesitant about the physical idea of fields. My question is: what is the physical meaning of the fields? Why they are introduced? I read the introduction of the books of Peskin and Weinberg but I'm not satisfied.", "label": 1}
+{"snippet": "I have an electric stove, and when I turn it on and turn off the lights, I notice the stove glowing. However, as I turn down the temperature, it eventually goes away completely. Is there a cut-off point for glowing? What actually is giving off the light? Does the heat itself give off the light, or the metal?", "label": 1}
+{"snippet": "In Flemish we have a saying \"Vijgen na pasen\". Translated: \"figs after Easter\". It means a solution comes too late to be of any use. What is the English equivalent for this? Some googling gives me \"Closing the barn door when the cow has bolted\", but the explanation seems to point more towards the wrong solution for a problem.", "label": 1}
+{"snippet": "I am an undergraduate physics student, and I wanted to study about interacting particle systems. I have studied probability theory, linear algebra, and statistical mechanics. I know basic measure theory and stochastic processes, but have very little knowledge of algebra. What more do I have to know to study interacting particle systems? (Please give names to some reference books if possible)", "label": 1}
+{"snippet": "I know that the zeros of analytic function (with one variable) over complex plane are isolated. However, I am not aware about the structure of the zeros set of analytic functions over complex plane with several variables. My question is: How I can understood this structure.", "label": 1}
+{"snippet": "According to this Fritinancy entry, the demonym for Norfolk, England is \"North Anglian,\" rather than \"Norfolker\" or \"Norfolkite,\" for historical reasons. What about Norfolk, Virginia, in the United States? I suppose you could argue for the same historical reasons, since it was named after Norfolk in England, but that just feels wrong to me.", "label": 1}
+{"snippet": "I am using sidewaysfigure for many of my figures. When I print out my document, for reasons I don't understand, the figure captions are on the inside and not the outside. Is there a quick way to flip all the sideways figures without affecting anything else?", "label": 1}
+{"snippet": "Does the current acceleration of the universe imply that our universe is open? If the universe is closed, from the Friedmann equations, the acceleration of the universe wouldn't be possible, would it? (Of course, except for the very early inflation era.)", "label": 1}
+{"snippet": "I know how to use a .bib file to add BibTex and use that in the main document. Is there a way I can include the bib-file in my latex document and not use an external bib-file?", "label": 1}
+{"snippet": "Do magnets (permanent) become weaker as they are exposed to para-magnetic objects? I was thinking about this after seeing this. I am buying a magnet and wish to know if a magnet (permanent) loses its magnetic domain structure or alignment when exposed to para magnetic materials.", "label": 1}
+{"snippet": "If I understand correctly, scientists were able to find strong evidence for the existence of quarks by using deep inelastic scattering. If quarks (hypothetically) are composed of preons, could we use similar methods to detect the preons? If so, how would we have to modify the scattering experiments used to detect quarks?", "label": 1}
+{"snippet": "I have a funnel and I notice when I try to pour powdered sugar through it, it blocks up unless I tap it. If I put sand in the funnel, it goes through. Is there a theory of funnels that can predict what materials will pass through a funnel of given dimensions?", "label": 1}
+{"snippet": "If I project a circle over the Z-axis, I'll get a cilinder. If I project a square over the Z-axis, I'll get a parallelepiped. If I project an ellipse over the Z-axis, I'll get a... whatsitsname? I can't find the name of this object, and I can't believe it doesn't have one to begin with.", "label": 1}
+{"snippet": "If I write a paper, is it acceptable for me to use a title like \"analysis of PDEs related to blah blah blah\" instead of \"analysis of partial differential equations related to blah blah blah\"? I intend on using in the abstract the words partial differential equations and writing (PDE) in brackets next to it. Is this reasonable? Thanks.", "label": 1}
+{"snippet": "In my high school and college math classes, I've always seen graphs drawn with either no arrows on the ends of the axes or with arrows on both ends. A colleague recently argued with me that this was crazy and arrows are always placed on one side of each axis to indicate the positive direction. Like so: Which style is more prevalent?", "label": 1}
+{"snippet": "In a normal double slit experiment, I'm told that sunlight doesn't produce a visible interference pattern because there is no stable phase relationship between the two slits. However, sunlight bouncing off a CD does produce interference-based rainbows, so sunlight can interfere if the slits are close enough. How close do the slits need to be to see interference when direct sunlight falls on them?", "label": 1}
+{"snippet": "I'm sorry if this was asked before but with all the stars and dark matter and all the other stuff, curently in the Universe, what's the avarage temperature of the Universe? Is it like extremely high or extremely low?", "label": 1}
+{"snippet": "Let's say we have a given wavefunction and we want to find a particle that will fulfill the properties for that wavefunction. How can we do that? Is it possible? I was thinking of using Schrodinger's equation.. would that work? (please tell me if there is anything wrong with this question so I can fix it!)", "label": 1}
+{"snippet": "I need to find a word which means \"the town or city in which one lives\". Words like \"residence\" or \"domicile\" appear to have this meaning, but because \"residence\" and \"domicile\" can also mean \"the home in which one lives\", my readers will be confused. Is there a word which only refers to the geographic location?", "label": 1}
+{"snippet": "The standard Bernoulli Equation has three terms on each side, a kinetic energy term, a potential energy term and a pressure term. I've never seen an extension of this to also include a rotational kinetic energy term. Do things get too crazy when fluids rotate for a simple extension to the equation?", "label": 1}
+{"snippet": "I don't know why, but despite having read the definition over too many times to count, its one of those words that just doesn't click. I see it being used in sentences and have never been able to fully understand it either. Could someone help explain it, and use it in a sentence? Thanks!", "label": 1}
+{"snippet": "I think I should use broke because it is in past tense. Am I correct? If incorrect, can you explain to me briefly which case is correct? I was thinking about punching him and breaking his teeth. I was thinking about punching him and broke his teeth.", "label": 1}
+{"snippet": "I would like to get into a career that uses alot of applied math. I took a numerical analysis course in undergrad and liked it, so I plan to self-learn numerical methods for PDEs. Other than the MIT OCW, are there any good textbooks or lectures notes that can be viewed online? Particularly those that are geared towards engineers/scientists, since I'm not into theorems/proofs", "label": 1}
+{"snippet": "I read here that a major ingredient in Whitney's strong embedding theorem and later Smale's celebrated h-cobordism theorem is the Whitney trick. Can someone give an intuitive description of the trick? To be more specific, I would be happy to know why and where the trick was applied ? Thanks.", "label": 1}
+{"snippet": "So I am learning LaTeX and I find it slow to test changes. So I'd edit the .tex file, then go to command line, and run pdflatex, wait for it to complete, and then open total commander, and then open the .pdf file. Does anyone know a faster way to test changes? (WYSIWYG?)", "label": 1}
+{"snippet": "I'm looking for a word to describe the final flight of an aircraft (or other vessels if there is no direct equivalent) such as the final flight of the space shuttle. Does anyone know if a word like this exists? Thanks!", "label": 1}
+{"snippet": "We have a project at school to develop an idea about how we can generate electricity. My question is: do collisions between matter and antimatter particles generate heat, so that one could harvest it using turbines?", "label": 1}
+{"snippet": "I want to show that the domain of any partially defined recursive function is equal to the range of some ( totally defined ) recursive function. I haven't understood which is the difference between a partially defined recursive function and a totally defined recursive function? Could you explain it to me?", "label": 1}
+{"snippet": "Why are measurable functions called \"measurable\"? What exactly is being \"measured\"? For measurable sets, I can intuitively understand that the measure of the set \"measures\" how large is the set. Thanks for any help!", "label": 1}
+{"snippet": "I have recently falled into an error because I didn't use % when I was supposed to. My question is now: When do I have to use % at the end of the line and when should I leave it out?", "label": 1}
+{"snippet": "Can we add an uncountable number of positive elements, and can this sum be finite? I always have trouble understanding mathematical operations when dealing with an uncountable number of elements. Any help would be great.", "label": 1}
+{"snippet": "I have seen this phrase do not pass go a couple of times reading Internet forums, but I don't remember figuring it out in context, as I've never played the game Monopoly. What does it mean?", "label": 1}
+{"snippet": "Under normal lens operation, a beam is sent through the centre of the lens along the optical axis (ie perpendicular to the lens's plane). What happens when a beam is sent through a lens at an angle to the optical axis? Does it simply exit the lens at the same angle?", "label": 1}
+{"snippet": "You get taught about matrices and how they work but nobody ever tells you WHY they work in the way that they do. What was the idea that sparked the creation of matrices?", "label": 1}
+{"snippet": "In crystallography, we always speak about the direct and reciprocal lattice spaces. One property about these spaces in mentioned here, as follows: Each point (hkl) in the reciprocal lattice corresponds to a set of lattice planes (hkl) in the real space lattice. Can anyone give a proof for this statement?", "label": 1}
+{"snippet": "What I am asking is this: Why can't a body be solid, then solid-ish, then solid-like, then liquid-like, then liquid-ish, then liquid, then vapor-like and then vapor? Why is there a rigid temperature boundaries between solid, liquid and vapor? Why doesn't water simply change \"states\" in a continuous manner?", "label": 1}
+{"snippet": "I was wondering what is the difference between I wasn't knowing and I didn't know? If I say, I wasn't knowing, I am talking about something unknown in past, the act of not knowing is finished, it means that I know it now, but before it was unknown to me.", "label": 1}
+{"snippet": "Suppose I have a graph and I calculate the eigenvalues of the adjacency matrix and find that there are some number of zero eigenvalues. Do zero eigenvalues have any significance? Also is there a good way to interpret the inverse (when it exists)? In some cases the inverse is called the Green's function. Thanks!", "label": 1}
+{"snippet": "Verbs can be conjugated to past/future tenses. Nouns can be pluralized. Adjectives also have comparative and superlative forms. For example fast, faster, and fastest. What is the word that describes converting between the base form and the comparative and superlative forms?", "label": 1}
+{"snippet": "I was wondering where the noun punk stems from. Obviously, it's used for members of a certain subculture, but has the word been in use before the invention of said subculture and been adapted for it, or has it been made up specifically for it?", "label": 1}
+{"snippet": "Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating about an axis which is perpendicular to the force and which goes through the center of mass. What is the proof of this?", "label": 1}
+{"snippet": "I've been doing some maths work using the rate of flow of liquids. I've used various models for the flow and various methods to integrate these models. The one thing that is confusing me is the difference between constants of proportionality, and constants of integration?", "label": 1}
+{"snippet": "With today's computers having several gigabytes of memory, why does TeX still have such limited capacity, and why are modern TeX installations not adjusted for higher capacity by default? Why is adjusting TeX capacity only recommended as a last resort?", "label": 1}
+{"snippet": "State the domain and range of the following graphs. Express each domain using interval notation and express each range using set-builder notation. I think I'm beginning to understand using interval notation and set builder notation, but I'm still having trouble with the endpoints.", "label": 1}
+{"snippet": "British English makes the distinction between 'practise' (verb) and 'practice' (noun). Based on this, I would judge the following sentence as incorrect: In practise, computers often crash. Nevertheless, I see it frequently. Could 'practise' possibly be a verb in this phrase?", "label": 1}
+{"snippet": "I read the definition of a hereditarily compact space in topospaces.subwiki.org, it says: A topological space is termed hereditarily compact if every subset of it is compact in the subspace topology. I don't understand how this is any different from saying: every subset is compact. Can someone explain the difference?", "label": 1}
+{"snippet": "Excerpt: In developed countries, running water is available everywhere and air-conditioning is expected not just in our homes but in our cars. We don't realize that these are luxuries. My sentence: The author mentions \"running water\" and \"air-conditioning\" as examples of things we take for granted. Are the quotation marks required?", "label": 1}
+{"snippet": "Imagine a body in a tub which is in a lift. When the lift is stationary, the body is floating. If the lift accelerates upwards with a constant acceleration, what will happen to the buoyancy? Will its value change or not? I do not think it shouldn't. But my friend says it will. But why?", "label": 1}
+{"snippet": "I have researched a little on loop quantum gravity (LQG), but all I got were very ambiguous explanations about loops and nodes that all end with mathematical equations. If someone could give me a non-mathematical, clear idea of LQG, I would really appreciate it.", "label": 1}
+{"snippet": "Is it possible to formulate classical electrodynamics (in the sense of deriving Maxwell's equations) from a least-action principle, without the use of potentials? That is, is there a lagrangian which depends only on the electric and magnetic fields and which will have Maxwell's equations as its Euler-Lagrange equations?", "label": 1}
+{"snippet": "I have seen the phrase used in this form or as a template for other rhetorical questions - e.g., \"what's an honest economist to do?\"; \"what's an honest business owner to do?\";\"what's an honest Nigerian to do?\" I cannot find any reference to its original use in literature, but was asked recently \"who said that?\" - and didn't have an answer.", "label": 1}
+{"snippet": "I have tried to find this out through google and searching this site with no luck. Basically, are the terms 'law' and 'identity' interchangeable in Mathematics? What is described as 'logarithmic identities' in one place is referred to as 'log laws' elsewhere. Similiarly, 'index laws' and 'exponential identities'.", "label": 1}
+{"snippet": "I'd like to create a custom design for my beamer presentations. How could I achieve this? I have neither found any resources for that nor does the official beamer documentation talk about it. Are there any good resources to start with?", "label": 1}
+{"snippet": "What's a word for an inaccurate artistic representation that doesn't retain all the qualities or features of the original subject? For example: There is a painting of a king but it doesn't have the expected semblance. It looks like him but there are oddities, like an elongated nose, or bigger eyes and ears.", "label": 1}
+{"snippet": "The energy required to remove an electron from the surface of a metal is less than that required to remove an electron from a free atom. Why?The electron is bound to the nucleus in an atom by electrostatic forces. How is an electron 'free' on a metal surface?", "label": 1}
+{"snippet": "What is the difference between the following sentences? Even in those days he played golf on Wednesday. Even in those days he played golf on every Wednesday. Even in those days he played golf every Wednesday. In a non-progressive sentence, which adverb phrase (in those days, or every Wednesday) is used to refer a serial state (habitual)?", "label": 1}
+{"snippet": "I've long been familiar with crenulated edges, but until today I wasn't aware of crenelated. Looking at the definitions, they seem to describe the same kind of feature, that of notches on an edge that are more rounded in contrast to, say, serrated. What are the differences in nuances? When would be a \"wrong\" time to use one over the other?", "label": 1}
+{"snippet": "Each shop in a town has an odd number of customers and each pair of shops shares an even number of customers. Prove that there are at least as many customers as there are shops. Any hints are appreciated.", "label": 1}
+{"snippet": "Can someone summarize why an ambient space isn't needed to measure curvature when parallel transporting tangent vectors or vector fields along a curve on a Riemannian manifold? How do we define the vector's direction and magnitude without one?", "label": 1}
+{"snippet": "Is it possible to say that the directional derivatives of a function f at a exists but f is not differentiable at a? If so, why? I cannot get the intuition about it. Could someone please elaborate on this point a little bit? I am self studying mostly, so I need to discuss these trivial matters with someone :) Thanks in advance!", "label": 1}
+{"snippet": "I am really bummed out to find that the term \"strict monomorphism\" is already used to mean something else. Can anybody console me with the knowledge that there is another name I can use for a monomorphism that is not an isomorphism?", "label": 1}
+{"snippet": "I'm searching for the word for someone who believes in the preservation of other people's cultures. Does anyone know of a good word for this? I don't think \"anthropologist\" is a good word, as that indicates the study of the cultures, but people can have this belief without studying them.", "label": 1}
+{"snippet": "Nowadays, the \"white\" in \"decent white folk\" can refer to race. But did it always refer to race, or did it have another meaning? I tried looking at Google NGrams, but it has very few hits.", "label": 1}
+{"snippet": "The majorant criterion says if a series in a Banach space has a convergent majorant, then it converges absolutely. My question is, what if a series in a Banach space has a convergent minorant, does it converges? Or, what if a series in a Banach space has a divergent majorant, does it diverges? Thank you for help.", "label": 1}
+{"snippet": "I would like to combine the words \"event\" and \"explorer\" to \"eventexplorer\". But I am actually not sure if that works. Can I use this combination to describe something like \"people who discover new events\"? English is not my mother language, therefore the question.", "label": 1}
+{"snippet": "Possible Duplicate: Continuous footnote numbering How can I achieve that footnotes have a global numbering scheme, and not a per chapter numbering? I am using the book class from the koma-script. I am also using the footmisc package.", "label": 1}
+{"snippet": "The following is a multiple choice question in an English test: The employers prepared, with all due _______, for a conference with the Trade Union. A. caution B. concern C. certainty D. consideration I feel A (\"with all due caution\") is ok, but I am not sure.", "label": 1}
+{"snippet": "Is there a common phrase for the opposite of reaching a settlement in a lawsuit? That is, is there a common phrase for going to court and having a judge reach a decision?", "label": 1}
+{"snippet": "Seeing how infinite the universe appears and out of all of those stars, planets, galaxies, there must be other life forms. Mathematically, the odds are very good. Is there a mathematical equation to determine the chances of other life forms in the universe?", "label": 1}
+{"snippet": "I'm looking for a geometric interpretation of this theorem: My book doesn't give any kind of explanation of it. Again, I'm not looking for a proof - I'm looking for a geometric interpretation. Thanks.", "label": 1}
+{"snippet": "I don't know whether this even makes any sense, but if 'observation' can be considered as 'recieving and reading information', can an act of observation (of a system) change (increase or decrease) its entropy?", "label": 1}
+{"snippet": "Many books on plasma physics (Chen, Goldston, Lieberman) say that quasineutrality must be satisfied for the matter in question to be a plasma. Yet, we know that non-neutral plasmas exist. So why do so many books make this claim?", "label": 1}
+{"snippet": "Some verbs are followed by ing, e.g. I enjoy swimming. We can't say I enjoy to swim. Likewise, some verbs are followed by to, e.g. I decided to make a plan. Which particular verbs are followed by ing and to? Can you please provide a list for that? Moreover, which verbs can be followed by both without having the meaning changed?", "label": 1}
+{"snippet": "Consider the vector space V=Fun(X,F) where F is a field. Where Fun(x,F) is the set of all functions X->F. How do you show that there is a zero element in V? And how would you describe the additive inverse?", "label": 1}
+{"snippet": "I know that if the second and third row can somehow be manipulated to zero, then the matrix will have a single pivot. However, I'm not so sure about a matrix having no pivots, because that just means the entire matrix is filled with zero. Thank you!", "label": 1}
+{"snippet": "This question actually has two parts: a. Prove that every subspace of a topological space with the discrete topology has the discrete topology. b. Prove that every subspace of a topological space with the trivial topology has the trivial topology. If I can do part a, part b will be easy. What do I need to demonstrate, exactly, to show that a is true?", "label": 1}
+{"snippet": "I am looking for a book that explains Linear Algebra, where it is build from axioms to higher level of Linear Algebra. It does not have to be a book on elementary level. As example from other fields, Tao's Analysis would be perfect example. Do you know if there is a book which is in similar manner as Tao's Analysis? Thanks", "label": 1}
+{"snippet": "We all know that the universe is governed by four Fundamental Forces which are The strong force , The weak force , The electromagnetic force and The gravitational force . Now, is there any relationship between Electromagnetism and gravity?", "label": 1}
+{"snippet": "I am trying to figure out which bibliography style this is: I am using the natbib package with the apalike bibliography style, which is what I want for the right column, but I am missing the left column (author year). I think this is a nice addition for easier reference.", "label": 1}
+{"snippet": "I have been asked to construct this plot in maple for an analysis assignment. I have been given no other instructions on how to do this. I am not familiar at all with defining or plotting these kinds of functions in maple. Any help would be greatly appreciated as I have been struggling with this for a few days now. Thank you!", "label": 1}
+{"snippet": "In the bible, \"he\" and \"his\" are capitalized when they are used to refer to God. Is this grammatically correct? If so, what rule do we have that allows these words to be capitalized?", "label": 1}
+{"snippet": "From what I understand, superposition is when two states exist in all of their possible forms simultaneously until the moment of wave function collapse, when they essentially reduce into a single state. I'm having trouble demonstrating what a superposition state is using bra-ket notation (a simple example), and I don't really understand where the probabilities for collapse come from?", "label": 1}
+{"snippet": "In the following sentence, what is the function of \"not, as one might assume, in English\"? For example, is it some type of clause that modifies \"wrote\"? The Irish author Samuel Beckett originally wrote his most famous play, Waiting for Godot, in French, not, as one might assume, in English.", "label": 1}
+{"snippet": "A metal ring is placed in a magnetic field. The ring has a gap in it though. As it falls through the magnetic field, is it true that it still experiences an induced emf and eddy currents but not a proper current?", "label": 1}
+{"snippet": "Recently a program gave me this text in a dialog box: \"All purchases have been downloaded for this account.\" While I understand its meaning, splitting the subject (the noun and its attributive phrase) makes it awkward in my mind. \"All purchases for this account have been downloaded\" seems clearer to me. Is there a grammar rule to cover this?", "label": 1}
+{"snippet": "One can easily prove that every covariance matrix is positive semi-definite. I come across many claims that the converse is also true; that is, Every symmetric positive semi-definite matrix is a covariance marix of some multivariate distribution. Is it true? If it is, how can we prove it?", "label": 1}
+{"snippet": "Is it correct to end adjacent words in 's to show possession? For example \"My neighbour's dog's ball is always in my yard\", or should it be \"My neighbour dogs ball is always in my yard\" or \"My neighbour dog's ball is always in my yard\"?", "label": 1}
+{"snippet": "I am trying to craft the following sentence in a way that sounds a lot less cliche. Any ideas? \"The ability to write has been a gift that has gotten me through the hills and the valleys of my life\"", "label": 1}
+{"snippet": "I'm planning to do an internship and I usually address my supervisor as Mr. X, however, he signs his emails with his first name is that means I can address him with his first name ? Note: I haven't met him yet.(if that's makes a difference)", "label": 1}
+{"snippet": "recently I sat for an exam where I was asked this question - Concurrence means all of the following except: A. Agreement B. Accord C. Consensus D. Coincidence E. Harmony What could be the correct answer ? I opted for D. Coincidence. Was I right ?", "label": 1}
+{"snippet": "Does anyone know anything about how the meaning of \"just about\" came to have opposite meanings in the UK and North America. For example, in the UK, The team just about won. means that the team won, but it was close (ie The team barely won.). However, in North America, it means that the team almost won.", "label": 1}
+{"snippet": "I have found some information on Wikipedia concerned with XeTeX and the unicode-math package. My question is, if I include the unicode-math package in my document, is it enough to have LaTeX installed and run the Unix latex command on my file, or do I need to have XeLaTeX installed as well in order to transform my source file into a .dvi/.ps/.pdf file? Thanks.", "label": 1}
+{"snippet": "I am relatively new to TeX/LaTeX and so far learnt all about it using online documentation or question-and-answer websites like this one. Should I consider buying a LaTeX guide book though? What would be your advices for doing so?", "label": 1}
+{"snippet": "I'm trying to prove the Arrow's Theorem is not true when there are two candidates, however I'm having trouble trying to prove that there is no dictator. I have suggested that in a majority rules voting system, unanimity and IIA are satisfied but I have no idea how to prove that it isn't a dictatorship.", "label": 1}
+{"snippet": "The phrase \"Fire Away\", meaning \"Ask me questions\", appears to be a metaphor stemming from an old military term involving discharging firearms (source). However, \"Away\" is generally a directional term, yet in the phrase \"Fire away\" it seems to mean \"at will\" or \"with abandon\". How did it get such an unusual meaning? Was this a sarcastic instruction perhaps?", "label": 1}
+{"snippet": "I have MathML that I need to render in my LaTeX document. Is there a recommended way of doing so? So far, from googling, I've found MathParser - a Java converter. But I was hoping there might be a better way to do it.", "label": 1}
+{"snippet": "It is well known that the running time of the simplex algorithm depends on the diameter of the polytope induced by the constraints. Is there any non-linear optimization technique that also has this property ?", "label": 1}
+{"snippet": "I used TeXstudio last year and I had a lot of trouble with referencing and producing a bibliography. Reading around online, this is a widespread problem. Which Latex editor is best to use to make it easier to produce a bibliography?", "label": 1}
+{"snippet": "So far, I've come across several examples of frieze groups, but I've not yet come across an understandable definition of what they are. I've also been asked questions that ask me to state the isometries preserving said frieze groups and I don't really understand how I should know what these are either. Could someone please explain this to me? Many thanks.", "label": 1}
+{"snippet": "I am looking for a generic word for a person who is being visited. The opposite of visitor according to thesaurus.com is host. That's not what I'm looking for. A couple examples: an employee being visited by a guest; a student being visited by their parent at school. I can't think of anything except \"visitee\" and I couldn't find it officially used anywhere.", "label": 1}
+{"snippet": "I'm having trouble finding typical quantities in fiber optic communication. In particular, what kind of powers are generally used (or what is the minimum that fiber optics receivers can detect effectively)? What frequencies of light are generally used, and what are typical sampling rates?", "label": 1}
+{"snippet": "Recently a colleague of mine said to me that the \"Guys who are switched on really annoy me?\". Since I am not a native speaker, I do not know what he meant by \"switched on\". Can you fine folks shed some light on this? Thanks!", "label": 1}
+{"snippet": "The quantum fields are operator valued distributions. In some sloppy books like Peskin and Schroeder the Euler-Lagrange equation are used to get the equations of motion. What does it mean to take a derivative with respect to some operator?", "label": 1}
+{"snippet": "Which is correct? I would like to request you to refrain from shouting. I would like to request of you to refrain from shouting. I would like to request from you to refrain from shouting. Something else?", "label": 1}
+{"snippet": "Somewhere on the internet I've read about a guy ordering a coffee in the name of \"Bueller\". Apparently, the cashier called out that name repeatedly. I've looked up the term but it gave me no clue as to why it's so hilarious. Is that a cultural reference or a linguistic one?!", "label": 1}
+{"snippet": "Almost all of the orbits of planets and other celestial bodies are elliptical, not circular. Is this due to gravitational pull by other nearby massive bodies? If this was the case a two body system should always have a circular orbit. Is that true?", "label": 1}
+{"snippet": "I heard that, at the Quantum level, events can happen out of order making causality invalid. Thus the future can happen in the present and the present in the future. Is this true?", "label": 1}
+{"snippet": "I know the Schwarzschild event horizon is a null surface generated by null geodesics. But what does that actually mean in terms of the path of a light ray that reaches it? Does that mean the geodesic trajectory of light on the surface will be along the surface? Which way will the light ray go? And what equation shows this?", "label": 1}
+{"snippet": "So I'm guessing it has to do with temperature of surface water, temperature of surrounding, surface area, humidity,... I always wondered if there was an equation to describe evaporation, never learned one in high school.", "label": 1}
+{"snippet": "From: Moduli space we see that moduli of curves is a very algebro-geometric topic. It is easy to understand its relevance and importance in algebraic geometry. But the mind boggles when we try to imagine how on earth such a topic from pure and abstruse mathematics is relevant in physics. I will be thankful if somebody can give some explanation.", "label": 1}
+{"snippet": "I'd like to ask about parity of baryon. When I search a parity section of textbook, it only explain about parity of meson, not baryon. And I can't find experimental method for parity determination of baryons. Am I missing something? Or is there special reason for baryon?", "label": 1}
+{"snippet": "Why is the inner product of a character with an irreducible character a non-negative integer? I can see that by properties of the inner product it will be non-negative but I cannot see why it would be an integer?", "label": 1}
+{"snippet": "I have to find the curvature and torsion of a curve (parametrised by arc length), given only the Binormal vector. Whilst I understand how to find these if I have the curve, I cannot for the life of me work out how to go in this direction. Any help would be appreciated", "label": 1}
+{"snippet": "Hi there I was wondering if someone could please help me? I understand the solution of this until it gets to the Polynomial Estimation Lemma part. What is the Polynomial Estimation Lemma and how can it be applied? Many thanks in advance.", "label": 1}
+{"snippet": "Does anyone know what the chromatic number of a graph chosen randomly on n vertices is, as n tends to infinity? I mean, almost all graphs have chromatic number greater than any fixed k. But in terms of estimates, is O(n), O(log n), O(sqrt(n)) a good estimate for the chromatic number of large random graphs?", "label": 1}
+{"snippet": "Possible Duplicate: How to superimpose LaTeX on a picture? Take this image for example: How can I add labels to an image as done above without manually drawing a line and adding text at the end of the line?", "label": 1}
+{"snippet": "I am looking for a nice compact book in abstract algebra (especially group theory) which develops the material by asking questions the reader must answer. An example of what I'm looking for is Combinatorics through guided discovery.", "label": 1}
+{"snippet": "I am trying to understand the following sentence from a legal document. Can anyone explain me what 'commutation' means? Immovable property presently sold is free and clear of all seigniorial dues having commuted and the price of commutation has been paid.", "label": 1}
+{"snippet": "The two-slit experiment is a classic example of how measurements can affect the behavior of particles. This seems reasonable because, to my knowledge, the measurement is \"active\" in that it adds energy to the system. But how is this reconciled with macroscopic observations (such as looking at Schroedinger's cat) that are \"passive\" in that they are collecting information already there without affecting the system?", "label": 1}
+{"snippet": "I have heard that the verb go used to be wend in olden days. I am curious if there is any historical or other explanation why the past form of wend, i.e. went, is still in use while the simple present and past participle forms are gone. Any idea or link to some resources which deal with this fact?", "label": 1}
+{"snippet": "Are there specific rules / conventions at play when creating demonyms? Or are they merely formed organically over time - the most popular winning out? There are many suffixes to choose from, but I cannot find concrete guidelines as to which is proper to use in which instance.", "label": 1}
+{"snippet": "Ok, so I got the answer to part i), but however, I'm not so sure how to get the answer to part ii). The answers say its an ellipse and they specified the equation, but I can't understand how they came to that conclusion. Can anyone help me out, please :)", "label": 1}
+{"snippet": "The Oxford Dictionary of Difficult Words defines vindictive as follows: having or showing a strong or unreasoning desire for revenge. What is a word for a having desire to be destructive or to break something?", "label": 1}
+{"snippet": "I want to turn off printing of DOIs in my BibTex bibliography in Lyx. When I try to add the option doi=false under Document settings -> Bibliography -> Bibliography generation -> Options the bibliography is not generated anymore (i.e. question mark for citation and empty bibliography). How can I set this option via Lyx ?", "label": 1}
+{"snippet": "How can we know that North Korea and Iran (to name a few) are exploding nuclear weapons if no inspectors have ever been granted access to suspected nuclear sites in these countries? How can we passively detect a secret detonation of a nuclear warhead? What are the telltale signs of a nuclear detonation?", "label": 1}
+{"snippet": "I know that Edmond's Blossom algorithm can be used to find a minimum weight perfect matching for a given graph. However, is there an efficient algorithm known that can find all the minimum weight matchings. Or one that can sample uniformly from them all?", "label": 1}
+{"snippet": "I've been reading Lee Smolin's Life of the Cosmos. Great book and it makes a lot of sense that the conditions in black holes are the same as conditions at the big bang. Question is, has his theory about Cosmological Natural Selection been disproved as the wikipedia article states?", "label": 1}
+{"snippet": "Loosely defined, sabermetrics is the study/usage/development of baseball statistics. I get the \"metrics\" part of the word, and I know what a saber is. But, what do sabers have to do with baseball? My only idea is that the baseball bat is kind of like a saber, but that seems to be a stretch.", "label": 1}
+{"snippet": "I just finished reading the Wikipedia article on the Cauchy condensation test. I understand the trapezoidal view, but apparently \"the 'condensation' of terms is analogous to a substitution of an exponential function\". Can anyone explain what is meant by this?", "label": 1}
+{"snippet": "How would you describe someone who fritters away money on inexpensive, trivial things, like coffee, but refuses to spend money on expensive, necessary things, like a decent new laptop (buying a lousy one instead)? Is there an expression? I want to say \"penny foolish and pound wise\", except that \"pound wise\" is inappropriate here, as skimping on the large outlay is a false economy.", "label": 1}
+{"snippet": "I have heard of the \"Big Rip\" as one theory for the eventual end of the universe. If the speed at which the universe is expanding, and all the matter inside it is moving away from all other matter at an increasing rate, would the matter eventually have to move at the speed of light? Or would it have to slow down?", "label": 1}
+{"snippet": "People often refer to the country US as America and to the people from the US as Americans. As far as I know, that's the only case in the world where a continent's name is used for a country's name (let me know if I'm wrong). Why does that happen?", "label": 1}
+{"snippet": "I'm looking for the proof of that: d(x,y) = d (y,x). I know that I have to use the \"non-negativity\" and \"triangle inequality\" but I don't know how to combine them to get the result.", "label": 1}
+{"snippet": "In discussing Doppler effect, we use the word \"apparent frequency\". Does it mean that the frequency of the sound is still that of the source and it is some physiological phenomenon in the listener's ears that give rise to the Doppler effect?", "label": 1}
+{"snippet": "Could you please let me know if the following excerpt of a sentence is grammatically correct (specifically the preposition after \"effort\"): \"Should there be anything that you feel we are missing, your insight would be invaluable to our effort in improving our products(...)\" An explanation on why it is/isn't correct would also be highly appreciated. Prepositions are tough. :(", "label": 1}
+{"snippet": "I am having trouble reducing the footer space. I have a list of contents that is printing below the page number appearing in the footer. How do I solve this issue? I tried setting the footskip length but it didn't work.", "label": 1}
+{"snippet": "Is there an English equivalent to this familiar saying used in India: Don't speak unless you can improve silence. The saying loosely means it is better to be silent than prattle on about something.", "label": 1}
+{"snippet": "I read that the canonical commutation relation between momentum and position can be seen as the Lie Algebra of the Heisenberg group. While I get why the commutation relations of momentum and momentum, momentum and angular momentum and so on arise from the Lorentz group, I don't quite get where the physical symmetry of the Heisenberg group stems from. Any suggestions?", "label": 1}
+{"snippet": "This question may be redundant and I apologize in advance but I am really having a hard time to digest the notion of proportional to in mathematics. Kindly, can someone simplify the idea of it and when we can say proportional to something. Thank you for your help.", "label": 1}
+{"snippet": "I am currently studying Multivariate Calculus (Larson and Edwards book). I want to do a project in computer science to see some nice applications of things I am learning. Any specific source of papers/journals/books? thanks", "label": 1}
+{"snippet": "Since I am reading some stuff about weak convergence of probability measures, I started to wonder what is the dual space of the space consisting of all the finite (signed) measures (which is well known to be a Banach space with the norm being total variation). Is there any characterization of it? We may impose extra assumptions on the underlying space if necessary.", "label": 1}
+{"snippet": "I see many people using \"Dear\" while addressing people in email. But, I feel \"Dear\" is more intimate word in English and should be used with only relations. How does the word \"Dear\" is used at all places irrespective of relationships?", "label": 1}
+{"snippet": "I'd like to customize verbose biblatex citations to exclude URLs (and DOIs) while keeping them in the bibliography. Is there a simple way to accomplish this? While I'm at it, I'd like to get rid of the \"In: \" that the verbose styles use (in both the bibliography and citations), and put the URLs and DOIs on separate lines in the bibliography.", "label": 1}
+{"snippet": "According to Feynman in this youtube video the photons that are released when a tree burns are sort of those that were trapped during photosynthesis. Are these the exact same photons produced by the Sun or do photons get destroyed / created somehow?", "label": 1}
+{"snippet": "If I drag an object across a surface and a force due to friction acts on the object which is equal and opposite to the force I apply, the net work done on the object is zero. So where does the energy come from to heat up the object and it's surface?", "label": 1}
+{"snippet": "Given the standard topology, is there any relationship between dense, uncountable sets and isolated points? For example, the set of irrationals is both dense and uncountable and contains no isolated points. Just something I've been wondering working my way through real analysis.", "label": 1}
+{"snippet": "I am trying to build something like the two following pictures, using TikZ (I am still learning): The pictures are just an illustration and there is no need of the shading. Anybody can help me?", "label": 1}
+{"snippet": "I'm British. I am editing a document, and I was going to correct a use of \"all together\" where the author clearly meant \"altogether\" (as in \"entirely\"). But then I realised this might just be a British distinction... is it? Do Americans accept \"all together\" as a valid alternative to \"altogether\", i.e. \"entirely\"? (The document is for an international audience.)", "label": 1}
+{"snippet": "Possible Duplicate: A word for two very different things juxtaposed? What is the word to describe when two ideas (often contrasting) are placed next to each other to enhance the situation or idea being presented? I believe it could describe the placement of two words or ideas in a poem, or two melodies in a song, or two objects in a piece of art.", "label": 1}
+{"snippet": "Since baryons (e.g. protons, neutrons) are composite particles it should be possible to split them apart. If so, is it then possible to extract useable energy out of the splitting of baryons in analogy to nuclear fission?", "label": 1}
+{"snippet": "I've been having an argument with a colleague about this sentence, could you please let me know which one of us is correct: There are no shortage of applications for our product in this space. She is convinced that are should be replaced by is, and I think it should stand as it is. Thanks for your help!", "label": 1}
+{"snippet": "A pendulum clock ticks slower on top of a mountain and ticks faster at ground level, but an atomic clock ticks faster on top of a mountain and ticks slower at ground level. Gravity affects pendulum clocks in the exact opposite way to atomic clocks. Which clock is giving us the correct time? Are they both wrong?", "label": 1}
+{"snippet": "It's the wall that a suspect stands in front of when a mug shot is taken. I don't know what to call it so it's hard for me to find information about the wall itself.", "label": 1}
+{"snippet": "Most references that I have come across refer to the Schottky Barrier in the setting of Metal and Semiconductor Interface. Would it be correct to use the term Schottky Barrier to refer to the mismatch in energy levels in other settings (e.g. semiconductor-seminconductor)?", "label": 1}
+{"snippet": "I'm studying for an exam and came across this problem in the book. Any ideas how one would go about solving this problem? Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and final demand vector d. Round production levels to the nearest whole number.", "label": 1}
+{"snippet": "By Godel's second incompleteness theorem, a consistent theory (to which the theorem applies) cannot prove itself consistent. I learned that it's also impossible to have a pair of consistent theories each proving the consistency of the other. But I can't see how this follows from the second theorem. Or is there something more involved?", "label": 1}
+{"snippet": "If you have a set of points on a hemisphere, how do you find a point on that hemisphere that has the minimum total great circle distance to the points in the set.", "label": 1}
+{"snippet": "I was boiling penne and rigatoni pasta in the same pot (both are hollow cylindrical pasta of approximately the same length, but rigatoni has a noticeably larger diameter) and almost all of the penne pasta managed to find its way inside one of the pieces of rigatoni. Why does this happen? Below is a picture of my dinner showing an example of this.", "label": 1}
+{"snippet": "I don't understand the concept of asymptotic variance. Given the mle of a probability function, the likelihood function and the random variables how do I find asymptotic variance? What exactly is asymptotic variance? I'm finding this concept very confusing.", "label": 1}
+{"snippet": "I had thought that Jew was gender-neutral, until I heard somebody who was asked if their mother was a Jew and responded, \"of course not; she's a Jewess\". Is Jew a gender-neutral form, or does one need to distinguish between Jew and Jewess?", "label": 1}
+{"snippet": "I noticed that the Kelly Criterion resembles a ratio between the mean and variance in a continuous probability distribution. Now the mean and variance are important values in portfolio optimization (Modern Portfolio Theory). Is there some relationship between the two since both seek to maximize returns and minimize risk?", "label": 1}
+{"snippet": "The wild flowers looked like a soft orange blanket ______________ the desert. A. covering B. covered C. cover D. to cover I chose C. I thought that 'looked' is a past participle and 'cover' would be the predicate. Why is 'looked like' the main verb and not a past participle?", "label": 1}
+{"snippet": "When asking how someone wants their tea, they reply: \"lots of milk and sugar\". Is that to be interpreted as \"Lots of milk and sugar\" or \"lots of milk and (lots) of sugar\" according to the rules of English?", "label": 1}
+{"snippet": "I want to prove this in the infinite dimensional Hilbert space case. What is the easiest way to go about this (What do I need to know, what theorems do I need,etc). My aim is to show every normal operator admits invariant subspaces.", "label": 1}
+{"snippet": "Let R be a Commutative ring with unity, such that R[x] is UFD. If R[x] is a PID then it is a Eucledian Domain? Is the last statement about being eucledian domain correct?", "label": 1}
+{"snippet": "There is no other harsher critic than yourself. I'm really stumped on this one. The more I read it the less correct it sounds. I think the word harsher is making the sentence sound fairly off putting. Other variations include: There is no harsher critic other than yourself. Any help would be greatly appreciated!", "label": 1}
+{"snippet": "I'm looking for a word that could describe a person who is very gullible and easily trusts people. My specific example is Fortunato from Edgar Allen Poe's story: The Cask of Amontillado Edit: the character's name is Fortunato.", "label": 1}
+{"snippet": "I'm making several assumptions, not sure if any are correct: there is a black hole at the center of a galaxy the black hole is eating the galaxy Eventually the galaxy will be gone, right? Has this been observed? Do we know what happens afterwards? Posting here since astronomy got merged into physics", "label": 1}
+{"snippet": "https://en.wikipedia.org/wiki/File:Hopf-bif.gif Does anyone know how this animation was produced? I could make it by stitching together snapshots (what I'm doing) but this seems primitive, especially for how nice this animation looks. Any ideas?", "label": 1}
+{"snippet": "I haven't been able to find a proof of this result online. Is there any proof that is relatively simple to understand? In particular, I want to also show that the upper triangle matrix that is similar to the complex one has diagonal values that are the eigenvalues of the complex one.", "label": 1}
+{"snippet": "I was looking to apply a color gradient to some text (i.e. Chapter / section headings) and I searched through the Internet but was unable to find a minimum working example. Is it something that can be done in XeLaTeX? I decided to ask here, thinking someone in the community might have already done similar to that.", "label": 1}
+{"snippet": "Suppose I have a sphere. Inside the sphere I have an inscribed cube. What I am interested in is finding out what is the latitude and longitude (or coordinates) of a point on the sphere which will be projected on a cube's face given the coodinate of a point on one of the cube's faces. Does anyone have any equations for this?", "label": 1}
+{"snippet": "I understand that rectifying antenna (rectenna) is supposed to convert electromagnetic energy to electric current however I do not understand how it's really working. I do get that it's kind of like how transformer works, but beyond that I am clueless. Could someone explain this to me?", "label": 1}
+{"snippet": "What does \"characteristic wave\" mean in the context of plasma waves? For example, when propagating parallel to the plasma magnetic field, the characteristic wave is circularly polarized. Does this mean that only a circularly polarized wave can propagate in this direction? Could an elliptically polarized wave travel in this direction instead?", "label": 1}
+{"snippet": "Is there a word for days you don't work? In portuguese you have the term \"dias de folga\" that means the days that you would normally work but will not because the company gave you those days to rest. One is said in portugues to be in \"folga\". Is there a correspondent word or term in english?", "label": 1}
+{"snippet": "Is there an overview available for Arabic fonts in LaTeX / XeTeX? Ideally with output examples, so that it becomes clear how they compare. So far, I'm aware of Geeza Pro, Amiri (and its variants), Sheherazade and, Al Nile. But I assume there is much more out there.", "label": 1}
+{"snippet": "Well, since the electron is going around the nucleus, it must have an angular momentum (plus its spin). And since it is charged it must create an electric field. If I have understood it correctly it is the interaction with this field that is causing the so-called Anomalous Zeeman effect? Is this correct? And does does this have any other consequences?", "label": 1}
+{"snippet": "According to Wikipedia, an open formula is a WFF without quantifiers. I have read that a propositional function is the same as open formula. Are both of these statements correct? Is it true that one can't have a propositional function with quantifiers?", "label": 1}
+{"snippet": "Of course we can always say \"the sun is up\", but is it acceptable to say \"the sun is risen\" just as we use verb \"to be\" before other past participles like \"she is gone\"? Or should we say \"the sun has risen\"? Does it make any difference?", "label": 1}
+{"snippet": "Why the current is the same at all of the positions in a series circuit? although there are different voltages at different positions of the circuit. What i know is that as the electron passes one resistor, the force of attraction from the negative terminal is less. Doesn't this affect the current?", "label": 1}
+{"snippet": "What's the difference in spirit between \"gallimaufry\" and \"farrago\"? Are there any sentences where using one or the other would lead to a subtly different meaning? Both are defined in dictionaries as \"a confused mixture\", or a synonym of \"hotchpotch\". I'm afraid they're too close to just be able to compare their dictionary definitions.", "label": 1}
+{"snippet": "I am interested in applications problems of Linear Algebra. If somebody can recommend me an interesting book, or papers about, I will appreciate this. Thanks. (I need this for a course of Linear Algebra for Engineering where I am the lecturer).", "label": 1}
+{"snippet": "Does anyone know the font style used in Kato's Perturbation Theory for Linear Operators? Better yet, does anyone know of a TeX package or style file that replicates the layout and style used throughout Kato's book?", "label": 1}
+{"snippet": "One of Twitter's error messages reads: Something is technically wrong. Of course I understand what they mean, but am I wrong to interpret this as \"strictly speaking, there is something wrong\" instead of the intended \"there is a technical issue\"? What would be the ideal, succinct way to phrase this, maintaining simplicity and clarity?", "label": 1}
+{"snippet": "This is a very simple question but I wasn't able to find a question like it and I wasn't a math major. Did tangent originate in trigonometry, geometry, or calculus? I remember using tangent lines in geometry, trig, and calculus but I'm curious which came first. http://www.mathopenref.com/tangentline.html", "label": 1}
+{"snippet": "G is a planar graph. E is an arbitrary edge of G. \"There exists a planar drawing of G where E is on the unbounded face of the drawing.\" Why is the above statement true? Any help is appreciated.", "label": 1}
+{"snippet": "I am reading Wilkie Collins' The Moonstone, and a prominent character in the story has the name of Betteredge. My question is (since I like to imagine the dialogue in a British-English book as if spoken with a British accent), would \"Betteredge\" sound more like \"Better edge\", more like \"Bedderitch\", or is it pronounced completely differently?", "label": 1}
+{"snippet": "Does \"so that\" and \"for ... to\" have the same usage? For example: I bought this sweater so (that) you can wear it. and: I bought this sweater for you to wear it. Is there any difference between the two expressions or do they have the same meaning?", "label": 1}
+{"snippet": "Can anyone give a specific example of a diffeomorphism and also of composing a function with a diffeomorphism and how this helps mathematics as a whole? In other words, how does this fit into the grand scheme of mathematics? Thanks", "label": 1}
+{"snippet": "In the context of \"Which station should I get off?\" (asked when you're on the train), what would be another way to say this, without using \"get off\" (which has other connotations) and still colloquial (either American or British English)? I thought about \"exit\" or \"alight\". Are there other, better ways to say this? Thank you.", "label": 1}
+{"snippet": "I'm familiar with the concepts of group isomorphism, ring isomorphism, and graph isomorphism, but it's never been presented to me what an isomorphism is in general: given any X, what is an X isomorphism? Informally, I understand isomorphism as \"preservation of structure\", where \"preservation\" is domain specific. Is there a formal definition?", "label": 1}
+{"snippet": "I'm using the align package for multiple-row equations. Some rows the equations are just a bit longer than the textwidth (I'm using double column). I only want to reduce the fontsize of those particular rows, not the whole align environment. How do I do that?", "label": 1}
+{"snippet": "I don't need to list all the proper divisors; I just want to compute their sum. While checking and summing up all proper divisors isn't an issue for small numbers, it becomes significantly slower for larger numbers. Any suggestions? Thanks!", "label": 1}
+{"snippet": "While trying to locate the etymology of the Tamil slang, OB, I ran across the following claim: This entirely Tamilian term, strangely enough, has its origins in the term \"off-beat\" used in the British Army to refer to retired officers or soldiers. I'd like to know if there's any truth to the claim that \"off-beat\" was a British Army term for retired officers.", "label": 1}
+{"snippet": "In graph theory what is the difference between isomerism and isomorphism? I found a post somewhat similar to it but couldn't understand my problem from that. So I asked again specifically asking my question.", "label": 1}
+{"snippet": "The following is an excerpt from Chern's Lectures on Differential Geometry: I don't see how the proof shows the other direction of the set inclusion. Would anybody explain the logic in the \"furthermore\" part of the proof? The following are definitions of the notations:", "label": 1}
+{"snippet": "I use it all the time since I work with databases, but every time I write it somewhere with spell check I get the squiggly line below it. I've seen other people spell it with an \"s\" instead of a \"z\" but neither have an entry in the Merriam Webster dictionary. http://www.merriam-webster.com/dictionary/denormalized http://www.merriam-webster.com/dictionary/denormalised Is this just technical jargon or am I misspelling it?", "label": 1}
+{"snippet": "I think the both answer is \"yes\". How can I prove that Schwartz space is closed under multiplication ? Because if I know that, it is easy to see that being closed under convolution is satisfied. Help me please. Thanks", "label": 1}
+{"snippet": "I am creating a poster using beamerposter, and I would like to include Feynman diagrams generated using feynmp. However, the native scaling of feynmp is indented for letter-size documents, and is far too small for a poster. Is there a way to scale the diagram to poster-size while keeping its features properly proportioned?", "label": 1}
+{"snippet": "I am starting a chapter on divisibility in commutative rings, and I was wondering if there was a way to translate theorems about gcd to lcm and vice versa. I know the concepts are considered \"dual\" in some sense, so perhaps the theorems relating to them are also dual.", "label": 1}
+{"snippet": "I am unable to see the correctness of this statement. It seems the author has considered this statement trivial and hence has not given any proof of this statement. But I am unable to prove it.", "label": 1}
+{"snippet": "I've seen a lot of work on homomorphisms of modules, but is it possible to construct a homomorphism as a module itself? For example, how would you define a specific module structure on a set of homomorphisms, for example, a dual space.", "label": 1}
+{"snippet": "Which of the three articles (a/an/the) would the blanks in the following sentence take? It is not unusual for ____ editor to tamper with _____ writer's manuscript. I think it should be 'an' and 'the' in the first and second blank respectively, but my colleagues think otherwise. Please suggest.", "label": 1}
+{"snippet": "I would like to know whether it is correct or not to use the word \"scope\" to refer to a book's section, subsection or paragraph. For instance We will address these matters in the next scope.", "label": 1}
+{"snippet": "A very common type of convergence in probability theory is 'almost sure convergence'. I don't understand why this type is used at all. In principle, we should always be able to substitute it by a uniform convergence almost sure due to Egorov's theorem. So why do people in probability theory refer to this weaker concept? If anything is unclear, please let me know.", "label": 1}
+{"snippet": "I'm kind of confused as to how I should punctuate the following sentence: A land as old as time and whose history defies any simple description. The author added a comma before \"and\", but i'm not convinced. Can \"whose history defies any simple description.\" stand on its own as a sentence?", "label": 1}
+{"snippet": "I've seen the following (e.g. here): I've learned a bit about groups and I could give examples of groups, but when reading the given table, I couldn't imagine of what a magma would be. It has no associativity, no identity, no divisibility and no commutativity. I can't imagine what such a thing would be. Can you give a concrete example of a magma?", "label": 1}
+{"snippet": "I saw a passage \"this doesn't mean to get riches and honors.\" 'rich' is an adjective but 'riches' is a plural noun according to the dictionary. Are there any other examples where an adjective becomes a noun by adding suffix '-s' or '-es'? or 'riches' is the only case?", "label": 1}
+{"snippet": "I wrote a text about our company's services and added that we also can offer products tailored to the needs of our clients. One of my colleagues insisted that the expression was wrong and I should say that we offered tailor-made products. Is there actually a difference between the two expressions generally or in the context I described?", "label": 1}
+{"snippet": "I have found many places that list the various rules on using hyphens in math, but nothing to explain why we have the rule. I have some students who are asking and I would like to be able to give them an answer instead of saying it is just the rule.", "label": 1}
+{"snippet": "I'm teaching a class with a very gentle introduction to Markov chains (the class is an alternative to taking calculus). I'm not a probabilist, so I haven't spent any time thinking about these objects. Does anyone know of any very compelling non-mathematical examples of Markov chains, or, at least, of non-mathematical things that can be well approximated by Markov chains?", "label": 1}
+{"snippet": "Adherent (\"a person who follows or upholds a leader, cause, etc.; supporter; follower\") is the word I am considering. For example, would a group of people who support and fight for freedom be called adherents (ignoring the obvious \"freedom fighter\")?", "label": 1}
+{"snippet": "Assume a scenario in which you talk with someone and then he puts your integrity/reliability \"in doubt\". Meaning: He doubts that you are truly reliable/innocent/trustworthy. So you want to say to him a phrase that means \"Do you really put my integrity in doubt?\" or something similar. I'm quite certain that this kind of phrase exists, but I don't remember what it is.", "label": 1}
+{"snippet": "For example if a student wishes for a storm because he wants his classes to be suspended. His main intention is to have no school but not necessarily to have a storm. Not sure if this makes any sense. I'm pretty sure there's no word for it but I don't know because English is not my first language.", "label": 1}
+{"snippet": "A student in my class mentioned his approach to proving isomorphism via the rank-nullity theorem rather than showing an inverse's existence. I didn't quite understand how, but perhaps someone here might be able to explain...", "label": 1}
+{"snippet": "When creating an unconstrained optimization problem from an equality constrained one, the usual way to build the Lagrangian, is by adding a term consisting of a multiplier, multiplied by the equality constraint. Are there problem instances, where it makes better sense to square the equality constraint and then use that in the unconstrained problem?", "label": 1}
+{"snippet": "I use LaTeX and want to create a bookmark which opens a file but I want to specify the page no. I have looked at texdoc bookmark but cannot get it to work. Anyone any ideas?", "label": 1}
+{"snippet": "It seems, to me at least, that most Statistics textbooks focus on the Statistical methods and techniques, or on the mathematics behind them. Would you recommend me some textbooks (or any online source) that discuss the \"logical\" reasoning behind the techniques? Thanks in advance!", "label": 1}
+{"snippet": "I have been introduced to algorithms, computability and computational complexity (as part of my minor in CS). What are some mathematical topics that I can tackle with the new perspectives I acquired from these ideas of computer science? Could you suggest some reference books (preferably self-contained and accessible to an undergraduate)?", "label": 1}
+{"snippet": "Fourier says that any periodic function can be represented like a infinite sum of sine functions with their appropriate periods,amplitudes and phases. My question is: is it possible to represent the periodic function like a sum of other periodic functions like a square wave function or some other shape, or they must be the sine functions?", "label": 1}
+{"snippet": "What experiments prove that heat can be \"trapped\" by a layer of material with suitable optical properties, such as carbon dioxide? I've read a little on Wikipedia but I've got only some names, not the experiments.", "label": 1}
+{"snippet": "What is the difference between ago and before when they are both used as adverbs in the following sentences: I saw him seven days ago. and I had seen him seven days before.", "label": 1}
+{"snippet": "Could somebody please provide a sketch of a proof of the fact that the Tor functor commutes with direct limits? I have been trying to show that the Tor of a module with the direct limit of a family of modules satisfies the required universal property, but it seems too complex.", "label": 1}
+{"snippet": "Sometimes when I speak with my fellows at work, I start my sentences with \"so\" or \"um\". I don't know if this a bad behavior in business speak or not? If so, how can I get rid of those filler words?", "label": 1}
+{"snippet": "From what I can glean, it'll and I've exist as standard contractions, but I am unsure of whether it'll've either exists or is acceptable. \"It will have\" should be able to be reduced to \"it'll've\", shouldn't it?", "label": 1}
+{"snippet": "We say that if any particles from outside fall into the black hole, they eventually hit singularity. Then why not particles already inside the black hole are at singularity? Or are they? If yes, then why does a black hole have a finite size?", "label": 1}
+{"snippet": "What is the meaning of the phrase \"new strands of research\" in the following sentence: The last two decades have also seen the emergence of new strands of research on multilingualism which have incorporated critical and poststructuralist perspective from social theory and embraced new epistemologies and research methods. Is there any synonym for this phrase or for the word strand in this context?", "label": 1}
+{"snippet": "Given any figure with four vertices and four straight edges, prove that one can construct a perfect parallelogram by connecting the midpoints of such figure. This to me is a very fundamental and interesting geometry problem. How would I begin to prove this?", "label": 1}
+{"snippet": "What actually causes a rocket to move? Is it the pressure in the rocket engine or the amount and velocity of mass that is being ejected out. The reason I am asking is, I found these two explanations for a rocket motion. Are they same or different. If same, is there any correlation between them?", "label": 1}
+{"snippet": "I have a long definition for Picard groups, but it is too abstract for me to really understand and apply. Could someone give an example or two on how to calculate the Picard group for a quadratic integer ring? Also the relevance of the exact sequence?", "label": 1}
+{"snippet": "I am comfortable with the way physicists use differentials as elements of area/volume. I know the (algebraic) formal definition of differential forms, but it makes no intuitive sense, especially since it is not immediately compatible (to me) with the physicist POV. How do the two fit in?", "label": 1}
+{"snippet": "I know what anti-matter is and how when it collides with matter both are annihilated. However, what about anti-photons? Are there such things as anti-photons? I initially thought the idea preposterous. However I am curious because, if anti-photons don't exist, then anti-matter could theoretically transfer its energy to normal matter - through the mechanism of light. Is it right?", "label": 1}
+{"snippet": "I am taking a course in Mathematical Physics Junior Level (Undergraduate). We are working from Arfken's \"Mathematical Methods for physicists\", but i am finding trouble with it specially in the determinants and matrices chapter, since it is not detailed enough. any suggestions for a more detailed book?", "label": 1}
+{"snippet": "Which one should I use: Are you going somewhere nice on holiday this year? or Are you going anywhere nice on holiday this year? The presence of the word \"nice\" bothers me a bit and deters me from using \"anywhere\".", "label": 1}
+{"snippet": "I'm trying to calculate an integral with respect to a complex value. I just want to know if I can estimate the integral using the residue theorem separately for the real and imaginary parts of the mentioned value or I cannot at all use this method here.", "label": 1}
+{"snippet": "By Cantor's intersection theorem I know that a sequence of nonempty compact sets which are nested has nonempty intersection. But how can I use that to prove that arbitrary intersection of compact sets is compact?", "label": 1}
+{"snippet": "Let's say I am having a telephone conference with rest of the team, and somebody asks me \"Dude, are you there?\" How should I reply? Yes, dude, I am there. or Yes, I am here? It is difficult for me to see the difference.", "label": 1}
+{"snippet": "To what branch of mathematics does the Hodge conjecture belong? I'm aware that it's very advanced, but what kind of prerequisites would one need to understand those problems? Can you suggest some good texts for a senior undergraduate/beginning graduate?", "label": 1}
+{"snippet": "I'd like to write a program that uses the exact (down to the second) amount of time from one new moon (or full moon) to the next. Yet, I am told that this period is irregular. Yet, it seems to be predicted in a number of places (ie, by the navy). How do they do this? http://aa.usno.navy.mil/data/docs/MoonPhase.php", "label": 1}
+{"snippet": "For example a situation where you are on the phone with a friend and he is with a person that you know. You would ask him to say hi for you. The french equivalent would be \"Passer le bonjour\" I am looking for formal and informal ways to say that.", "label": 1}
+{"snippet": "I'd like to label my nodes with text that has a 'halo' around it of a different colour. Is this possible? The reason is that my label text covers different parts of my diagram with different background colours, so no single colour will make the label legible. I'd ideally like the text to be black, with a white halo.", "label": 1}
+{"snippet": "Each (finite-dimensional) Lie algebra has exactly one simply connected Lie group associated to it (up to isomorphism). What can we say about all other connected groups with the same Lie algebra ? Thank you in advance", "label": 1}
+{"snippet": "When a car is traveling round a banked track as fast as possible, it has a tendency to slip up the slope. Opposite in the case when the car travels slowly and has a tendency to slip down. Can someone please give me an intuitive reason as to why this \"tendency to slip up or down\" occurs.", "label": 1}
+{"snippet": "Possible Duplicate: What word means what many people think 'ironic' means? While irony actually means 'the opposite of what is expected', it is often misused in a context to make it mean 'an unexpected and amusing coincidence or similarity'. Is there any word that does actually mean this?", "label": 1}
+{"snippet": "Given a parallelogram with congruent diagonals, you are asked to prove that the parallelogram is a rectangle. Would saying: A parallelogram must be a rectangle if the diagonals are congruent. be a valid proof for this question?", "label": 1}
+{"snippet": "I'm developing a web based application that allows people to send email to many customers, for advertisement purposes. What's the correct name for that? newsletter or mailshot? EDIT: to avoid unnecessary answers like \"spam\" please note that customers subscribe to the service first.", "label": 1}
+{"snippet": "We know that if the infinite sum of a multiplicative function is absolute convergent, then the sum can be expressed as infinite product and the infinite product is absolutely convergent. Does there exists a multiplicative function such that the infinite sum is divergent, yet its Euler product is still absolute convergent? Thanks a lot", "label": 1}
+{"snippet": "I know that a smooth manifold is a topological manifold whose transition maps are smooth. Must the coordinate maps also be smooth? Must they be diffeomorphisms? MathWorld seems to think so, but I do not understand why it follows from the definition that this must be the case.", "label": 1}
+{"snippet": "Since strings are extended objects, is all angular momentum in string theory essentially \"orbital\" angular momentum? Or is there still a kind of intrinsic angular momentum assigned to a string? Either way, is there anything that prevents the \"intrinsic spin\" of a particle represented by a string from being arbitrarily large?", "label": 1}
+{"snippet": "Say I had a parameterization of a surface and I wanted to determine if the surface was closed, to determine the applicability of divergence theorem. My math professor said a surface is closed if it does not have a \"boundary\", such as the sphere or the torus. How would I determine this mathematically? Is there a specific property that is satisfied?", "label": 1}
+{"snippet": "I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus. I was thinking of trying abstract algebra. I would appreciate any book recommendations. Thanks in advance. Andrew", "label": 1}
+{"snippet": "I am using chapters. I want to include one section (a page or two) that does not have a chapter number, and that does not increment the chapter counter. I've tried includeing it, without using chapter, and the section didn't show up at all. How can I include a chapter-less section in a chaptered document?", "label": 1}
+{"snippet": "A very quick question: Is it correct to say \"In case I won't be able to watch that\"? If it's acceptable to say that, what type of sentence is it? UPDATE: As a clarification, I want to say \"Can you give me that in case I won't be able to have it later\". Probably, it's more a supposition than a conditional.", "label": 1}
+{"snippet": "I'm trying to better understand the meaning of the phrase in the Skyy Vodka ad (\"Vodka so filtered we even took the Russia out of it\"). AFAIK the name Russia is never used with a definitive article, but I also doubt that Skyy promoters are uneducated. Can someone please explain why \"the Russia\"?", "label": 1}
+{"snippet": "What I'm looking for isn't quite the same as a Pyrrhic victory, as the action isn't necessarily done to obtain victory. Rather, it is any action that will ultimately result in the person taking said action to pay great (preferably terrible) cost either along the way or afterward, whether or not they realize it in advance.", "label": 1}
+{"snippet": "I am going to be participating in the high school division of the Purple Comet Math Meet. Since computers are allowed to be used on the competition, I was wondering if anyone can recommend software/programs that I can use to solve these types of questions. Thanks!", "label": 1}
+{"snippet": "Which of these is correct: I didn't realize how much clothes you had on the floor I didn't realize how much clothing you had on the floor Any additional explanation about clothes versus clothing would be helpful. This other question discusses the meaning of the two words, but doesn't help with the grammar problem above:What is the difference between \"clothes\" and \"clothing\"?", "label": 1}
+{"snippet": "In the following two sentences \"did\" and \"were\" seem to be conveying the same meaning. If that's the case, what is the difference between the two and which one is more preferred? If you studied, you would pass the exam. If you were to study, you would pass the exam.", "label": 1}
+{"snippet": "Where does the word \"bravo\" come from? In Spanish, it can be related to bravery but I fail to see the connection with the congratulatory mode it's used today in spectacles and related activities.", "label": 1}
+{"snippet": "I believe there is also a computing or physics theory that contains this word. (i.e. \"Something Theory\") It's definitely at least two syllables long and I'm pretty sure there's at least one 'b' somewhere in the word. Thank you!", "label": 1}
+{"snippet": "In some physics theories like string theory we have notion of spatially extended quantum objects - strings, membranes etc. Assuming that such objects exist, how would they appear in experiments ? More precisely are there any thought experiments for determining whether a quantum thing being observed has spatial extension or not, and if it has spatial extension then what is its dimension, topology etc.", "label": 1}
+{"snippet": "I have seem one proof here. However it involves concepts like exterior algebra. For positive definite matrix there is a proof for Sylvester's criterion by induction. I am wondering if there is any simpler proof for positive semi-definite matrix. Thanks!", "label": 1}
+{"snippet": "I'm really tired of going through tons of wikipedia pages. Wikipedia is a good thing, but at one point one who wants to go deeper needs an ordered, comprehensive and formal treatment. Me at least. Therefore, I would like some recommendations for detailed and comprehensive books on plane geometry.", "label": 1}
+{"snippet": "I'm looking for a word that would describe something like a modern phone that retains a rotary dial. The dial's design was originally functional, but phone's function doesn't rely on the dial any more - it's just an aesthetic choice.", "label": 1}
+{"snippet": "I got these graphs from Wolfram Alpha. Can anyone please explain why the result differs by the order of operations for square roots? I thought the rule only applied to division, multiplication and subraction algorithms. Thanks.", "label": 1}
+{"snippet": "What's a non-judgmental way to say a person or group of people are \"red necks\" in the sense they may hold some very conservative or old fashioned beliefs. For example, someone who doesn't believe autism is a real medical condition? I realize any phrase for it may cause offense, but I'm aiming for the least possible.", "label": 1}
+{"snippet": "I want to separate my book into different volumes, I searched this site and there is no satisfactory solution. I tried to work around with a package called volumes http://mirrors.ctan.org/macros/latex/contrib/volumes/volumes.pdf However, after reading the manual, I still have no idea about how to use it, so can anyone just give me a concrete and compilable example.", "label": 1}
+{"snippet": "How do you describe in a phrase the movement of something that you may see through the corner of your eye ? Like a slight movement that the corner of your eye may catch ?", "label": 1}
+{"snippet": "My math professor has said that it would be useful to start with complex analysis before learning fourier series in the signals and systems course(I'm an undergrad EE). Do you agree with that and why ?! (I'm planning to learn complex variables from Brown/Churchil)", "label": 1}
+{"snippet": "If there are two spheres (hollow and solid) with equal mass and radius and we want to find the hollow sphere without using any equipment. What's the best way(s) to recognize the hollow sphere and solid sphere?", "label": 1}
+{"snippet": "Possible Duplicate: Impurity scattering temperature dependence Is there any temperature dependence of relaxation time in impurity scattering of conducting electrons? It seems to me that there is none. But, some people claim that there is. So if you could explain, how temperature dependence comes into play?", "label": 1}
+{"snippet": "When working in a professional setting, especially in administration or technical fields, common words/phrases/acronyms get used quite frequently. I've noticed that the more they are used daily, the faster they are physically spoken and the more relaxed the syllables become in the word, often making it sound completely different than when first used/spoken. Is there a term for this phenomena?", "label": 1}
+{"snippet": "Gravitational waves are continuously stretching and squeezing the shape of Earth. Using this fact, LIGO is detecting it by interference of light. But the Sun and Moon's tidal effects are also trying to stretch the Earth. Does this affect the detection of gravitational waves? If so, then how do they eliminate these effects?", "label": 1}
+{"snippet": "We will have a lot of skills, but certainly, we also have limitations. I don't know whether it's right or wrong to place \"but\" and \"certainly\" together. Since \"but\" is conjunction, while \"certainly\" is adverb here. Should i change it into: We will have a lot of skills, but, certainly, we also have limitations. Can you give me some help?", "label": 1}
+{"snippet": "What would the Heisenberg uncertainty principle and De Broglie wavelength be for a baseball that is not moving (i.e has zero velocity)? Also, since macroscopic objects like baseballs have extremely small wavelengths, would this mean a high frequency? If so, would this frequency not be dangerous as it would greater than gamma and X-rays?", "label": 1}
+{"snippet": "The Airy disk intensity formula is given in the mathematical details section of the Wikipedia Airy disk article in terms of the Bessel function of the first kind. I am interested in the asymptotic behavior of the tail of this function. Is it exponential or powerlaw? If powerlaw, what power? Can you give a Taylor series expansion? TIA.", "label": 1}
+{"snippet": "I know how this formula works and it is quite interesting actually but how would you prove this relationship? Through induction (seems difficult since there's no equation for prime numbers), but I'm not sure if there is any other way to show this equation. Any ideas?", "label": 1}
+{"snippet": "I am wondering if I can use the word \"compensate\" to mean \"adjust to correct\" something in a document for a programming/mechanic related subject? E.g. Can \"position compensation of target objects\" mean \"position correction of target objects\"? Thank you in advance.", "label": 1}
+{"snippet": "For every graph G, prove that (vertex cover of G) is less than or equal to (twice it's matching). I tried a couple of examples and it works but I can't follow a trend to build my proof. Does anybody know how to prove it?", "label": 1}
+{"snippet": "I noticed that when I throw salt into a cooking pot and then mix, the salt collects in the center. As salt is denser than water, I would have expected it to go towards the border of the pot, and not in the middle. What is going on exactly there?", "label": 1}
+{"snippet": "Today I realized that the word \"Real\" in \"Real Estate\" might be about \"royalty\" instead of \"reality\". English is a foreign language to me, so I don't really know the literal meaning and origin of the term \"Real Estate\". Might \"Real\" be an alternative term for \"Royal\"?", "label": 1}
+{"snippet": "Consider the example: I am happy to wait. In some publications, the function of the infinitive is called 'adverb'. In others, it is 'complement of adjective'. Is there a difference in the naming of the function? I've always learnt that adverbs do modify adjectives, and I'm wondering why the name of this particular function is not the same everywhere.", "label": 1}
+{"snippet": "I don't know how this phenomenon is called. Simply put, I can either put the noun to the end and place it's properties before, or I can use \"of\". What is the difference, is some form more formal and suitable for academic writing?", "label": 1}
+{"snippet": "A is a closed convex set with non-empty interior. Does A must equal to the convex hull of its boundary? I know this is false when A is half space. But what about other sets?", "label": 1}
+{"snippet": "All the games of the Fallout franchise start their intro with the phrase War. War never changes... I was wondering if this was an original phrase or was it from literature or some speech?", "label": 1}
+{"snippet": "I'm reviewing for a math test this Tuesday and just want to make sure I'm doing things right. If someone could check my work that would be great. Here's the question (work below): Here's my work: Thank you in advance!", "label": 1}
+{"snippet": "I want to know if this function is unif.conv. or not... Actually it is one of the my mid-exem problems. I got zero score for it.... What did I wrong in this problem? and What is the easiest way to see whether it is unif.conv. or not?", "label": 1}
+{"snippet": "Why is it common in English to address animals as \"it\"? It's not an inanimate or abstract object, they have a gender and they're alive. A chair, idea, tree, rock, etc are an \"it\", but why does English speakers address a dog, cat, bird, fish, etc as \"it\"? Isn't male the \"default gender\" in English?", "label": 1}
+{"snippet": "I have no idea what a good title for this question should be. I'm asking a database guy about a problem with our data. I'm considering phrasing it this way: Is there any other field or fields that have this property? Is \"have\" correct?", "label": 1}
+{"snippet": "So I've stumbled upon this question in Grimmett and Stirzaker's text. I have their solutions manual, which starts off like this: The line above, where the statement is expanded into sums, is where I'm stuck. Would be glad if someone could elucidate it.", "label": 1}
+{"snippet": "Possible Duplicate: Can a word be contracted twice (e.g. \"I'ven't\")? What is the correct way to contract \"should not have\", if there is one? \"Should have\" becomes \"should've\", \"should not\" becomes \"shouldn't\". Is \"shouldn't've correct? It seems very strange to have two apostrophes in one word, but it also seems incorrect to skip an apostrophe where letters are omitted.", "label": 1}
+{"snippet": "Suppose we created a vacuum and spinned a turbine inside it with some amount of force. According to newton's second law it will keep spinning as there is no air resistance, so why can we not make electricity out of it?", "label": 1}
+{"snippet": "I'm not a native speaker so it might just be me finding this strange, but why is the auto in grand theft auto at the end? Shouldn't it be grand auto theft or something like this? I thought the expression described the crime of stealing cars?", "label": 1}
+{"snippet": "This question about alien species and planets brought up something I've been thinking about on and off for years. We capitalize names of alien races like Vulcan, Timelord, Cylon (well, maybe not alien), Krell, Nox, Minbari, and so on, but we never capitalize human. So how did we end up capitalizing names for sentient species when we don't do that for our own race?", "label": 1}
+{"snippet": "I am new to Latex. I have to write thesis for my MS. For that I search latex templates and find one template at http://web.mit.edu/thesis/tex/ I edit the template accordingly but not able to change the institute name. Can anyone help me changing the name. Thanks in advance.", "label": 1}
+{"snippet": "Telescopes have angular diffraction limit depending on the observed wavelength and aperture diameter. I've read that it's possible to go beyond the limit for microscopes. But is it possible to do the same for telescopes too?", "label": 1}
+{"snippet": "I have a memoir document, with custom settings for margins, headers and footers, etc. I just found out it is being printed single-sided instead of double-sided, and I was wondering if there is a simple command to treat all pages as odd pages. How can I tell memoir to format the even pages exactly as it would the odd pages?", "label": 1}
+{"snippet": "Which mathematical results has Lewis Carroll, the author of Alice's Adventures in Wonderland, produced? Wikipedia is very vague with regard to this topic and gives us little more than a matrix identity connected with his name. I would be especially interested in his most important theorems on mathematical logic.", "label": 1}
+{"snippet": "Keep on: \"to continue doing something, or to do something many times.\" Go on: \"a) to continue doing something or being in a situation. b) to continue without stopping\". From Longman Dictionary of Contemporary English", "label": 1}
+{"snippet": "I'm looking for the most colloquial synonym for the term 'first class', in the meaning of 'first gathering of a course'. My reason for looking for an alternative is that 'first class' is too easily read as 'first-class', as in 'top-notch'. Would 'opening class' be correct and normal-sounding? Thanks in advance.", "label": 1}
+{"snippet": "Possible Duplicate: Preposition usage: on, in, and at I guess the difference is that when you say \"I work on a project\", it shows that your are the owner of the project, whereas \"in a project\" shows that you are the member of a project. Is my guess correct?", "label": 1}
+{"snippet": "In the movie As Good As It Gets, there is this dialogue: Simon Bishop: Thank you, Melvin. You... overwhelm me. [pauses] Simon Bishop: I love you. Melvin Udall: I tell you, buddy... I'd be the luckiest guy alive if that did it for me. What does I'd be the luckiest guy alive if that did it for me mean ?", "label": 1}
+{"snippet": "I am very familiar to the congruences in modular arithemtic, But sometimes I can see questions related to supercongruences but I couldn't find any information about it on google. Can someone explain what it is? and what is the difference with a classic congruence?", "label": 1}
+{"snippet": "In geometry, the set of points within a circle is called a disk (open disk if it excludes the boundary, closed disk if it includes it). Is there a similar notion for squares or rectangles? \"A filled rectangle that includes the boundary is called a closed _______.\" \"A filled square that excludes the boundary is called an open ________.\"", "label": 1}
+{"snippet": "The Hertzsprung-Russell diagram that categorizes star types uses the letter codes O, B, A, F, G, K, and M to indicate a star's temperature/color. Hottest (blue) is O and coolest (red) is M. What do the letters themselves relate to? For example, why is \"O\" used for hottest/blue?", "label": 1}
+{"snippet": "Does anyone know of any sources that talk about (or know what topics I can start looking at that relate to) the mathematics behind poetry, e.g., ratios of syllables, equations for meter, frequency of different sounds made in the English language etc.?", "label": 1}
+{"snippet": "There are several ways/methods to perform factoring. I am revising factoring at KhanAcademy, there are factoring by grouping, factoring special product and factoring difference of squares. Although, I can work on the exercise, but I do not really understand when to apply factoring by grouping.", "label": 1}
+{"snippet": "I am very confused with a question I have found in relation to Excel. I am hoping someone can help me do this or at-least give me direction in which I can figure out how to do this. So far I don't even know where to get started.", "label": 1}
+{"snippet": "we know that in a group G, if H,K be subgroups such that H is normal, then the product HK is also a subgroup. does the converse hold? i.e. if H is a subgroup of a group G such that for any subgroup K of G, the product HK is a subgroup, can we conclude that H must be a normal subgroup?", "label": 1}
+{"snippet": "What is a verb for illusion? I want to use it in a sentence like the following: The optical effect [illudes] my perception of its real shape. But illude does not exist. But I cannot find illude in my Dictionary (OS X Dictionary.app). I want to find a verb that is somewhere between deceive and confuse.", "label": 1}
+{"snippet": "In the fourth episode of Sons of Anarchy's second season, there is a scene where Bobby is wearing chaps and all the guys are making fun of him. Then he says: Cowhide can take the man-hide. I can't figure what it means! I would appreciate it if someone would explain the meaning.", "label": 1}
+{"snippet": "If you have a sequence of real analytic functions that converge on every compact subset in your domain, do their derivatives necessarily converge to the derivatives of the function that they converge to?", "label": 1}
+{"snippet": "Suppose you drop an object which has two ends, of which one is heavy and the other is pretty light. Will the object fall with its heavier end downward or with the lighter one? Why does it happen?", "label": 1}
+{"snippet": "The expression \"It's all up hill from here!\" and \"It's all down hill from here!\" mean that things will only get better or things will only get worst. Metaphorically going uphill can provide for a better position, while going down hill is easier. Which expression represents which way?", "label": 1}
+{"snippet": "Theoretically, if a black hole grew to a huge scale such that the effect of dark energy was large, could the black hole become 'normal' space again (i.e. no horizon or singularity)? What I'm trying to understand is, does dark energy 'uncurve' space-time?", "label": 1}
+{"snippet": "An electron and a proton are moving on straight parallel path with same velocity. They enter a region of semi infinite magnetic field perpendicular to velocity. What will happen there? Will both of them never come out of the field? Or they come out with same velocity at same time?", "label": 1}
+{"snippet": "How to determine the ground state of a classical field, for example an electromagnetic field? What is the difference between the the ground state of a classical field and that of a quantum field?", "label": 1}
+{"snippet": "What is the opposite of \"abbreviation\"? For example, if \"ELL\" is an abbreviation for \"English Language Learners\", then \"English Language Learners\" is a(n) _______________ for \"ELL\". I'm looking for a word that will work for all abbreviations, not just acronyms, so another example would be: if \"abbr.\" is an abbreviation for \"abbreviation\", then \"abbreviation\" is a(n) _______________ for \"abbr.\"", "label": 1}
+{"snippet": "This question was asked by one of my Professor during the class. I'm getting intuition that these functions should be one-one (I'm wrong maybe). But, I'm unable to classify all such functions. Please help in this!!", "label": 1}
+{"snippet": "As I understand, we do not have yet a unified theory covering at once both general relativity and quantum mechanics. However, do we have a theoretical framework completely covering both classical Newtonian gravitation (i.e. without space-time curvature or for not so massive gravitational sources) and quantum mechanics? Is there any reference on this question?", "label": 1}
+{"snippet": "Silly thought. A transducer, by definition, is a device that converts variations in one form of energy to another. An electric lamp converts electricity into visible light - the brightness may vary depending upon the electric potential applied. Is it correct to state an Electric Lamp is a transducer?", "label": 1}
+{"snippet": "This is part of a CNN news article I need to translate. I am not quite sure about what situation the phrase describes. Here is the part the expression comes from: \"When did the light switch go off for you to say, oh, my goodness, things have really drastically changed and I'm in trouble if I don't change with them?\"", "label": 1}
+{"snippet": "How to tell if a particular EPS figure has a TIFF preview and how to remove this preview? For some reason the Journal of Mathematical Physics don't want these preview to be there when uploading files.", "label": 1}
+{"snippet": "In Mathematics, often a theory becomes popular because it tells us something new or gives different proof for already established facts. For example, I have read that algebraic number theory is helpful because it helped us to solve some diaphontine equations (most notably, Fermat's last theorem). I want to know what kind of questions are answered by Galois Representations.", "label": 1}
+{"snippet": "I know most primality tests are probabilistic, but doesn't that pose a major problem to security like RSA that depend on the prime numbers always having no smaller factors? And if you can repeat the tests enough times to ensure that the number is prime, then would it be correct to say it's not probabilistic anymore?", "label": 1}
+{"snippet": "I heard the saying, \"life of Riley\" when someone was talking about my cat, and I wondered what the origin of the expression is. The only thing I can think of is that it comes from the name of someone who was pampered and lazy, a king for example.", "label": 1}
+{"snippet": "For example an electron radiates when accelerated. So does a positron. But is the radiation emitted by accelerated positronium the sum of the radiation emitted by each separately? If not, why not? If so, does this provide a way of testing whether a given neutral particle is composite? For example, does a neutron bremsstrahlung when decelerated?", "label": 1}
+{"snippet": "It's always puzzled me how objects with properties like rest mass and charge (and color) could really be geometric points. Is this just a fiction needed for the math to work? Could quantum field theory work with spherical electrons and quarks?", "label": 1}
+{"snippet": "Which of the following is grammatical? He wants to remain a cool kid for the rest of his life. He wants to remain as a cool kid for the rest of his life.", "label": 1}
+{"snippet": "I know how to calculate mean and variance of some given numbers but I have trouble computing them for probability distributions especially when it is a continuous probability distribution. For example, can you show me how to calculate mean and variance of Gaussian distribution?", "label": 1}
+{"snippet": "Can somebody provide an example of a network with a high clustering coefficient and a large average path length? A visual representation of such a network would be great. No reason for asking, besides that I think it would be interesting.", "label": 1}
+{"snippet": "Why do we need a weak convergence for the sequence in a Hilbert space to be convergent? A Hilbert space is a complete pre-Hilbert space, so, every sequence converges in a given space. Where is my confusion? Many thanks.", "label": 1}
+{"snippet": "I'm looking to find the width and height of a rectangle without rotation within a rotated bounding rectangle. I have rotation in degrees and the width and height of the bounding rectangle. Basically I'm looking to find the largest ( largest area ) un-rotated rectangle that will fit inside a rotated rectangle of any given size.", "label": 1}
+{"snippet": "I am looking for an example (with proof) of two norms defined on the same vector space, such that the norms on the two spaces are NOT equivalent, but such that one norm dominates the other...", "label": 1}
+{"snippet": "I am coming across the term: non-convex optimization problem. What exactly is this non-convex structure, and how do I know by only looking at the structure of the problem, I could tell it is non-convex and thus difficult to solve?", "label": 1}
+{"snippet": "Is there a word for the situation when someone takes something said in the most negative possible way, basically stretching what is said to fit the negative meaning that they desire it to mean. Example: \"Maybe we shouldn't hang out.\" to mean: \"I never want to talk to you again, you are cut from my life.\"", "label": 1}
+{"snippet": "when the sound barrier is broken, a series of concentric waves of sound is produced.Does it mean when the speed of light barrier is broken, a ripple of photons are created in the space-time fabric?", "label": 1}
+{"snippet": "This is purely a curiosity, but I'm fascinated by mid-word pluralization, even if the word in question is a compound word. For example, passersby or standersby. No others have occurred to me. Can you provide other examples, or a link to a resource that enumerates them? I'm particularly interested in compounds that do not include spaces or hyphens.", "label": 1}
+{"snippet": "After six months of looking for jobs, she got a reply from a job application she posted online from Macy's asking her to come to a interview. The sentence does not sound right to me, what would be the correct way to say this?", "label": 1}
+{"snippet": "I am trying to figure out how to solve the questions above for the given PDF but im not sure how to do the steps. I'm not looking for answers here as I want to know how to do it, just looking for the equations and steps for each part. I know the standard deviation is the square root of the variance correct?", "label": 1}
+{"snippet": "An essential part of a guitar is its hollow body. Without it, the strings wouldn't be very loud; as far as I know, the purpose of the body is to set up some sort of resonance and make the sound louder. How does this work? How can an isolated system amplify sound? Where is the energy coming from?", "label": 1}
+{"snippet": "For programming purpose, I'd like to compare the entropy of two Poisson distributions to the entropy of a single Skellam distribution. The entropy of a Poisson distribution is given in this wiki article. What is the entropy of a Skellam distribution?", "label": 1}
+{"snippet": "I am writing a sentence like so: \"I bought the Dell laptop because not only did I find the price appealing but I also liked the the fact that the laptop had an integrated webcam.\" Is my use of \".. not only .. but also ...\" appropriate? Is there a better way to phrase such a sentence?", "label": 1}
+{"snippet": "I know that 'Jutland', a part of Denmark, comes from the Danish 'Jylland', which describes the same region. But was that name just invented at random, or does it come from the verb 'jut', as the land juts out into the ocean?", "label": 1}
+{"snippet": "I have read that accelerating or oscillating electron emits photons. But why and how does it so? And why only photons? There are other bosons like gluons, W and Z bosons, so why does electron emit only photons? And what is the mechanism ?", "label": 1}
+{"snippet": "When we write a business email and want some information from the mail recipient, then which is the most professional way to ask for information? Does using \"please\" in a sentence make it look bad?", "label": 1}
+{"snippet": "I recently went through some important numbers like the Stirling and Bell number for calculation of partitions /equivalence relations. I was wondering if someone can help me get a list of important numbers and their applications in Combinatorics ; like Catalan , Fibonacci , Stirling etc.???", "label": 1}
+{"snippet": "For example, the word \"jihad.\" Translated, the word means \"struggle\" or \"strive\" and I am sure there are others. The word \"jihad,\" is just taking the pronunciation of the word in the native tongue, and spelling it phonetically in English. Is there a specific word for that?", "label": 1}
+{"snippet": "Why do some pressure cookers initially leak steam from the sides and after a while settle down and don't leak? Is it a positive feedback mechanism from the building steam which makes the sealing tighter and vice versa?", "label": 1}
+{"snippet": "I have a distance matrix M and have used multidimensional scaling and it gives me some eigenvalues. How should I interpret such eigenvalues? Do they show some sort of variability or what? More practically, I really cannot understand the real meaning of eigenvalue. For example I can understand |M|, but I have no sense about the eigenvalue.", "label": 1}
+{"snippet": "I heard that If we travel for long distances in the direction of the rotation of the earth, we can gain some extra hours in the journey. Is it true? What if we travel in the opposite direction?", "label": 1}
+{"snippet": "The multline environment does exactly what I want in splitting a long formula between lines by utilizing the horizontal space to the fullest. (I don't want the alignment features of the align environment.) The problem is, I want to vertically center the equation number, as opposed to making it appear on the second line (as it does by default). How do I do this?", "label": 1}
+{"snippet": "Is it possible to create a head-mounted optical device that allows the user to see the wind, by means of thermal imaging / infrared detection, variations in the light's refractive index, or something similar?", "label": 1}
+{"snippet": "I wanted to ask about the exact meaning of pathology. Is it just for disease or can we use it for other things? I mean, for example, if I want to talk about the determination of harms in culture or technology, can I use the term \"technology pathology\" or \"culture pathology\"?", "label": 1}
+{"snippet": "I am writing a paper on a dystopia and how the leader came to be. I need a term to describe how he wasn't elected into power but he just assumed the role of instigator and no one questioned him.", "label": 1}
+{"snippet": "Caroline wondered whether there were coffee shops and restaurants in other galaxies. She imagined them installed on floating asteroids, or in the rest area of cosmic highways. Since the universe was so infinitely large, how couldn't there be at least one or two? Is installed a good term to use in this case? If not, are there other better options?", "label": 1}
+{"snippet": "Why in adiabatic compression and expansion small volumetric change occurs while in isothermic compression or expansion very small pressure is applied and volume changes very significantly i am referring to PV diagram of Carnot engine?", "label": 1}
+{"snippet": "This question is about font in Tex. I want to make my Tex output have the font as in this book https://www.math.wisc.edu/~boston/ddt.pdf but I do not know how. I have no idea where to begin. I appreciate your help!", "label": 1}
+{"snippet": "Both the Laplace transform and the Fourier transform in some sense decode the \"spectrum\" of a function. The Laplace transform gives a power-series decomposition whereas the Fourier transform gives a harmonic (or loop-based) decomposition. Are there deep connections between these two transforms? The formulaic connection is clear, but is there something deeper? (Maybe the answer will involve spectral theory?)", "label": 1}
+{"snippet": "How does our sun create positrons? And does the sun emit said positrons after their creation? I read that the sun creates positrons at it's center but I couldn't find how they form. Is it a byproduct of fusion or does it occur as our sun stars to die?", "label": 1}
+{"snippet": "I read that the following is ungrammatical: Because of the accident, he arrived at the dock an hour late. As such, he missed the boat and forfeited his deposit. Why? What is the correct usage of as such?", "label": 1}
+{"snippet": "Refraction: light changes direction of propagation when entering a material with a different refractive index. Does the direction of propagation of light change sharply and almost instantaneously (as shown in the diagram) or smoothly?", "label": 1}
+{"snippet": "I'm not a native English speaker, but sometimes I get the feeling that the pronunciation of English words is random. Why is \"Yosemite\" is pronounced as \"Yoh-Sem-Ee-Tee\" and written as \"Yosemite\" and not as \"Yosemitee\"?", "label": 1}
+{"snippet": "It is well known that any conformal mapping of the unit disk onto itself extends to the unit cirle. However, is there an homeomorphism of the unit disk onto itself which does not extend to a continuous function on the closed unit disk? If yes, can you give an explicit one? Thank you, Malik", "label": 1}
+{"snippet": "If I issued a payment to a company, and I wanted them to notify me when receiving the payment, could I say 'please acknowledge the payment when receiving it?' Is the word 'acknowledge' alright to be used here?", "label": 1}
+{"snippet": "Which of the following, if any, is correct? You answered the same questions as me. You answered the same questions as I did. You answered the same questions as I have. How can you tell? I tried Googling it, but I only get Breaking Bad references. I also saw this, but I don't know how it would apply in this context.", "label": 1}
+{"snippet": "I have this fragment: ... the experience and knowledge gained will be helpful in my career as a neuropathologist. Is the \"as\" here okay? It somehow does not sound right to me. Obviously I want to say that it will be helpful to me, during my career in neuropathology.", "label": 1}
+{"snippet": "Here are a few attributes that a text may have: \"name\", \"length\", \"quality\", etc. What's the name of the text attribute that refers to the text itself? Would that be the text's \"content\", the text's \"body\" or something else?", "label": 1}
+{"snippet": "Is there a way to convince LaTeX to automatically add tildes in front of one- and two-letter words, numbers and such simple things (in normal mode, not in math mode)? I know there are preprocessors for that, but manually launching them is tedious. What's the best way to achieve it automatically?", "label": 1}
+{"snippet": "I came across this sentence as I was reading a book: My clothes disintegrated, victims of the sea. I think saying: My clothes, victims of the sea, disintegrated. would be correct. Which one is the right one?", "label": 1}
+{"snippet": "When an object is heated a lot and then brutally cooled down or vice-versa, it can crack or even break spectacularly. What happens inside that makes it do that? Is it only because the hot core swells when the cold surface shrinks, which causes internal stresses? Bonus: Are certain materials more sensitive to thermal shocks (high CTE?)?", "label": 1}
+{"snippet": "I am working on a project involving the motion of rigid body. From the literatures, I found two main tools, namely the dual-quaternions and screw theory. May I ask what are the major differences between them? It is appreciated that if some documents can be suggested for beginners.", "label": 1}
+{"snippet": "I'm using the memoir class, and would like new chapters to begin on the left-hand page, unless the chapters in question are only one page long. Neither openleft nor openany give this behavior. I am not opposed to using another class, or using sections instead of chapters, if I can get this behavior by doing so.", "label": 1}
+{"snippet": "What is the third order term in the Taylor Series Expansion? I know it will just be third order partial derivatives but I want to know how is it expressed in a compact Matrix notation. For instance Jacobian for first order, Hessian for second order partial derivatives. In other words, what is the third order term in the equation below? Thanks for your help!", "label": 1}
+{"snippet": "I used \"It's not fair\", but someone told me \"fair\" is the \"F\" word, and they don't like it in their house. Should I avoid using it? ps: sorry if my question offended someone, I didn't mean to it.", "label": 1}
+{"snippet": "I need a prove that pumping lemma can't be used to prove regular language. Pumping lemma is only used for proving non-regular language, but I need to show that how it can't be used to prove regular languages?", "label": 1}
+{"snippet": "Are there any interesting theorems outside of set theory that use ordinals in their proofs? The only example I know of is Goodstein's theorem, and I haven't been able to find anything else. In other (more vague) words, what is the use of ordinals? (Other than Goodstein.) Theorems that use the word \"ordinals\" in their statement don't count; Goodstein is a good example.", "label": 1}
+{"snippet": "I remember there is a theorem that states that if you have more polynomials than the number of variables, there must be an algebraic relation between them, but I forget what the theorem is called. (I'd also appreciate if I could be directed to a proof of it.) Thanks.", "label": 1}
+{"snippet": "Are the finite dimensional comodules the compact objects in the category of comodules over a Hopf algebra? If yes, is there a reference? If no, which are the compact objects? Here by compact I mean that the Hom functor from the compact object preserves filtered colimits. Thank you!", "label": 1}
+{"snippet": "I have to build a simple electromotor in the following way: I attach a permanent magnet to a battery, connect some metal supports to the terminals of the battery, and place a coil of wire on the supports, suspended above the magnet. My question is, will it still work just as well (or at all) if the wire is insulated? Thanks!", "label": 1}
+{"snippet": "I tend to think of data structures of type Structure.Field.Subfield as analogous to file directories. I.e that Structure is a folder and Field is a folder inside the folder.. etc. Is this a good way to think about it?", "label": 1}
+{"snippet": "I'm having a brain cramp: if cookies should be avoided, and carrots are preferable instead, is it correct to say: Avoid cookies in favor of carrots. or if not, what's the correct way to phrase?", "label": 1}
+{"snippet": "I understand the mathematical definition of Uniform Continuity. But I was wondering that if there is a intuitive explanation for this concept similar to Continuity where we sometimes say that if I draw the graph of a continuous function I do not need to lift the chalk from the board.", "label": 1}
+{"snippet": "For the sake of argument, assume the LHC was able to accelerate / focus / collide neutron beams, with the same energy levels it runs at for p-p collision. Would the collisions produce any major differences vs the p-p collisions?", "label": 1}
+{"snippet": "Is there a simple, elegant solution to add footnotes in a table (tabular)? Preferably, the solution can also support the cleveref package. EDIT: My intended effect is that, the footnotes should be displayed at the bottom of the page, just as regular footnotes are. However, I've checked out ctable package but found no such feature. Am I missing something?", "label": 1}
+{"snippet": "We are given the lengths of all sides of a polygon. We need to determine if the given polygon is convex or concave. How can this be done? What is the propery applied to determine this?", "label": 1}
+{"snippet": "I'm starting to read Baby Rudin (Principles of mathematical analysis) now and I wonder whether you know of any companions to it. Another supplementary book would do too. I tried Silvia's notes, but I found them a bit too \"logical\" so to say. Are they good? What else do you recommend?", "label": 1}
+{"snippet": "I've exhausted the usual High School curriculum for Mathematics and i need some recommendations. I want to start a serious course in Mathematics at a local college, but that's simply too long to wait, i'd like to get started now. So right now i'm just looking for some fantastic books and some fantastic tips, any recommendations are appreciated.", "label": 1}
+{"snippet": "Consider the following examples: \"And it is a bottle, too.\" \"And it is a bottle too.\" Is there a semantic difference between these two sentences? Or do they mean the same thing, with or without the comma before \"too\"? If not, what is the correct usage of the comma in context of \"too\"?", "label": 1}
+{"snippet": "I have learned that the classical measurement of the speed of light with a rotating mirror does not work with a laser (as opposed to, say, a mercury-vapor lamp). Can you tell me if and how coherency of light is necessary/contraindicated for the success of this experiment?", "label": 1}
+{"snippet": "If we consider a balloon full of air submerged in water then we all know that it will rise rapidly. I am having trouble understanding this at the level of individual molecules of air and water. What is a molecular/microscopic explanation for this phenomenon?", "label": 1}
+{"snippet": "Is it correct to use \"But\" at the start of a sentence like this? You can afford it. But think twice before buying it. Won't using \"But\" instead of \"However\" mark me as a non-native speaker?", "label": 1}
+{"snippet": "I have read that the electric energy flows from the battery into the circuit through electric field created outside the wires into the light bulb (or any other resistor). I have also read that the friction caused in the movement of electrons cause light bulb to heat up. So which is the correct explanation?", "label": 1}
+{"snippet": "I am preparing my CV with moderncv and chose the casual style. Now, I would like to omit the icons for phone, email etc. How do I do this? Thank you very much in advance!", "label": 1}
+{"snippet": "I am trying to understand a statement of a problem. Wondering how can a striaght lines in three different planes meeting at one point. Does not it imply that all the three planes are also intersecting at some line?. Can three lines in parallel planes meet at some point?.", "label": 1}
+{"snippet": "I am compiling my document in Persian using XeLaTeX, but the references are all in English and I'm appending them using BibTeX. At the end of the document, the references are all unknown characters, how could I handle this problem?", "label": 1}
+{"snippet": "I want to simulate an impact between two bodies according to gravity, and eventually considering other forces to stick matter together. I'd like to use python to do this, but I am open to alternatives. What kind of tools or libraries can I use to perform this task ?", "label": 1}
+{"snippet": "The nebulae we see in the night sky are forming new stars. The stars are eating up the nebulae and there is no obvious process in which those nebulae are being created to compensate for that. Shouldn't the universe have run out of those nebulae a long time ago?", "label": 1}
+{"snippet": "Often when I want to say that something became clear, I may instead say that the thing \"became lucid\" or that the thing is \"becoming lucid\" is there a single word that I can substitute for this?", "label": 1}
+{"snippet": "Consider the following excerpt of the Liouville's theorem proof taken from \"Arnold - mathematical methods of classical mechanics\": In changing the variables in the integral, I don't understand why there is not the absolute value of the Jacobian determinant. Why the determinant of the Jacobian of the flow is positive?", "label": 1}
+{"snippet": "If one pays for transportation of oneself a fare has been paid. What is paid if the transportation is of a non-person object (a parcel, a letter, a vegetable, a box of rocks)?", "label": 1}
+{"snippet": "Why do people use \"skies\" instead of \"sky\" (when, indeed, we only have one sky)? Reach for the sky/skies! and I'm glad to finally see some blue skies. I'm glad to finally see a blue sky.", "label": 1}
+{"snippet": "So, I came to naming a variable in my PHP today. The variable was to contain information about the state of a switch, E.g - on and off. However, I couldn't, for the life of me, think of what to name it. I ended up settling for State. But for arguments sake, what other words could I have substituted for State?", "label": 1}
+{"snippet": "According to the Oxford English Dictionary, a diatribe is defined as a forceful and bitter verbal attack against someone or something. I had previously understood it to mean something more along the lines of drawn out, longer than it needs to be, impassioned persuasion. For example, in a friendly letter, My [diatribe] begins here. Any alternatives?", "label": 1}
+{"snippet": "I'm gluing the edges of a square together with the caveat that there's a \"fold\" down the middle. I think this produces sort of a sphere with four \"pinches\". I'm wondering if my intuition is correct and if someone could provide a more rigorous foundation for what I'm trying to do and elaborate on the nature of the singularities.", "label": 1}
+{"snippet": "There are n studio apartments in a building. Some of the apartments are connected with each other by direct phone line. Prove that it is possible to assign to each apartment a female or a male in such way that each person has direct connection with at least as many people of the opposite sex as he/she has with people the same sex.", "label": 1}
+{"snippet": "So the sentience is \"It's hard to find a good path to taking this mission on\", I wonder why it is \"to taking it on\" not \"to take it on\", is \"taking\" using as a gerund? Can I say \"It's hard to find a good path to take this mission on\"? What's the difference?", "label": 1}
+{"snippet": "I really like the nLab and its collaborative style of writing. Are there any other websites which follow the same philosophy, but on different topics, or with different points of view? For example, is there one more on the metric aspects of Riemannian Geometry, Geometric Analysis, Harmonic Analysis and the like?", "label": 1}
+{"snippet": "Intuitively to me it seems likes increasing compression ratio would require more work to compress the gasses before ignition, so you'd just end up getting back what you put in - like a spring. What am I missing?", "label": 1}
+{"snippet": "If yes, why don't they fill up with water, and can you breathe the air there? Like, it's not exactly atmosphere there, but an underwater cave with higher ceiling. P.S. Possible that it has a different name than air pocket, but due to my limited knowledge of English, I have no idea. Thanks in advance!", "label": 1}
+{"snippet": "Possible Duplicate: Calculating prime numbers The question is in the title. Is there a number that is divisible only by numbers greater than its square root? If not, why? I need this because it can speed up a calculation algorithm significantly if the answer is no.", "label": 1}
+{"snippet": "We often use \"cool water\". But can we use \"cool water\" or \"cold water\"? Which is correct? Examples: I drink cool water only. People always like cool water. In the above examples, instead of the word cool, can we use cold?", "label": 1}
+{"snippet": "If you want to fly a spaceship with human passengers as close to the Sun as possible, then what effects would the spaceship have to be designed to counteract in order to keep the passengers alive and how close to the Sun could you get before there would be no way to counteract the effects ?", "label": 1}
+{"snippet": "There is a book titled Running for Mortals. I didn't recognize word mortal. Then I looked up it and get the meaning as below. mortal N - A human being I wonder, is mortal widely used as human being or it is used only for special areas like sports, medical, etc?", "label": 1}
+{"snippet": "What is an uncommon synonym for the noun \"motion\" (movement)? I'm looking for cool sounding words like \"twitter\" that are synonyms or somehow relate to motion, the noun that means movement. Example: \"I bought a motion detector to alert my household of criminals.\"", "label": 1}
+{"snippet": "There are many documentaries, forums, blogs and more dedicated to Dark Matter. I have been frantically searching for an answer to my question however none of my sources have clarity to the matter of hand. I would really love a clear explanation to: What exactly is Dark Matter? Please help me to have a clear understanding.", "label": 1}
+{"snippet": "I was wondering what happens to the electron after it leaves it's valence shell and strikes a stable valence shell; in an insulating material? I realize that the energy from the strike, is absorbed by the atom that was struck and that these electrons do not 'break free'...so what happens to the electron that struck them?", "label": 1}
+{"snippet": "I hold him in high regard. The court holds him responsible/liable. She held it dear. We hold these truths to be self evident. This construction only seems to work with certain adjectives. Are these examples all set phrases or can it be used freely? Can I say \"I hold that crazy\" and make sense?", "label": 1}
+{"snippet": "I have a question like how can we mathematically prove that for a general matrix Conjugate Gradient method will always converge within n steps in exact arithmetic ? where n is the size of the matrix.", "label": 1}
+{"snippet": "I'm writing a presentation using the Singapore theme. The dots in the navigation bar are appearing vertically (one below the other) rather than horizontally. This is consuming a lot of space of my frames and is even not looking good presentation wise. I have seen presentations using this theme where the dots appear horizontally. How can I do this?", "label": 1}
+{"snippet": "I have a maximum number of pixels that I can process in my app at one time. The user must be able to open any image and if it's bigger than the maximum number of pixels it should be scaled down to fit the maximum resolution size. Keeping the rectangle ratio. How can I calculate the new rectangle?", "label": 1}
+{"snippet": "I can't find the precise definition of what is the orientation of a GaAs lattice. Being the superposition of two fcc lattices (one of Ga, the other of As), I would think that it is the direction of the closest Ga atom to any As atom of the structure. Is it right?", "label": 1}
+{"snippet": "I am writing a chapter in a book and I want to say that \"I believe that this researcher is right ....\", in a more formal way. Can I say \"The present author believes .....\"", "label": 1}
+{"snippet": "In statistics one often hears the phrases \"log likelihood\" and \"log error\". Why is it natural to consider the logarithm of these guys? My wild guess is that the Gaussian is a pretty \"normal\" distribution, and it's natural to take the log of such a thing. But this is pretty sketchy. A pointer to a reference would be great.", "label": 1}
+{"snippet": "I wrote \"How is conditions being unfair not an issue?\" instead of \"How are conditions being unfair not an issue?\" as I believe the subject of the sentence is 'conditions being unfair' rather than 'conditions'. However, I'm not quite sure. Which is it?", "label": 1}
+{"snippet": "So I understand that the an inner product space basically uses pythagorean theorem because it is similar to a distance formula. I'm still having trouble with this proof. I am a bit confused about where to start. It could be notation that is throwing me off, so any breakdown would be great.", "label": 1}
+{"snippet": "I always find it very difficult to understand the notion of chemical potential physically/intuitively unlike pressure and temperature in statistical mechanics. Can some one suggest some nice references or briefly discuss about it intuitively. Actually I came across it again in the context of AdS/CFT. It will be really helpful if it is discussed in holographic context.", "label": 1}
+{"snippet": "There's a Polaroid photo in the album, and I want to ask the owner about the person in it. Can I ask him: \"Who's that man in the snapshot (shot)?, or I should ask \"Who's that man in the picture (photo)?\" Thanks in advance, Victor.", "label": 1}
+{"snippet": "Is there a name for this manner of purposely speaking in double negatives, e.g. I wouldn't say no to a cup of tea! I've noticed it as a habit of some people, perhaps often going along with a particular type of sense of humour and British understatement.", "label": 1}
+{"snippet": "in a company bylaws document, I'm trying to describe situations in which a the term of a company director can be ended. These include death, as well as \"going insane\" or \"losing his mind\" - but I'm looking for a more \"PC\" or \"legalese\" way of saying this. Any ideas?", "label": 1}
+{"snippet": "Lady Macbeth has plotted this out carefully and diligently. Can I use the word \"plot\" in such a way? I know most people would want to replace that with \"planned\", but I don't want to keep using that word.", "label": 1}
+{"snippet": "Is there a more casual way to say \"send me an email\"? I'm going to put this at the bottom of the \"contact\" section of a website. \"Pop me an email\" is the only one I've managed to come up with.", "label": 1}
+{"snippet": "I'm wondering if an ordinary power series expansion of the floor function is possible, and what it is if it's possible. Additionally, I'm wondering what some of the most common uses of the floor function are in practice. Additionally, I'd like to know what use a series expansion of a floor function may be. So, again, what's the series expansion of the floor function?", "label": 1}
+{"snippet": "I'd like to say: The calm, balmy evening air showed no sign of the carnage that would ensue. My question is: should it be \"no sign of\" or \"no signs of\"? Obviously the word \"sign\" is countable noun in this context. One sign. Two signs. But NO SIGN means zero sign. Should I use sign in singular form \"sign\" or plural form \"signs\" here?", "label": 1}
+{"snippet": "According to wolfram a function is monotonic if its derivative never changes sign, but the derivative doesn't have to be continuous. So I feel the answer is Yes, tangent is monotonically increasing. Maybe not?", "label": 1}
+{"snippet": "We're a bunch of friends building an RC boat, this may sound stupid but I had an argument with a friend where he insisted that his design will work. Basically, he's saying that by putting a powerfull fan and a piece of tissue as a sail, when the fan will blow air into it, the boat will move. What do you think?", "label": 1}
+{"snippet": "I came across this line in a site: Can u make sth effective for a sports betting related product? I can't understand what is meant by sth effective here. I tried to google it but was unable to understand. Can anybody explain to me what is meant by this word? Is it an English word or is it from another language?", "label": 1}
+{"snippet": "Is there a word that describes a discussion that never gets to the core of the issue, but continuously lingers on the periphery? I was hoping to fit it into a sentence such as : \"He derided his retainers for their _____.\"", "label": 1}
+{"snippet": "We know that multiplicity of least eigenvalue of laplacian matrix of graph gives us number of connected components in graph.What is intuition behind this theorem? How do we know that this works in reality?Is there any proof of that sort?", "label": 1}
+{"snippet": "I'm quite confused about this actually! In fact, I had always thought current flows from a region of higher potential to a lower one. Does it have anything to do with the fact that it's a source of emf instead? What significance does that have?", "label": 1}
+{"snippet": "So I'm trying to prove the validity of this formula and I am a bit lost, not sure how to start. I know generally speaking a valid formula is one where if all the premises are true, then the conclusion can not be false, but I don't know how to prove this really. any help is appreciated https://i.stack.imgur.com/Opmck.jpg", "label": 1}
+{"snippet": "I was writing an email, and I started off with I am writing to inform you of certain errors... However, is this use outdated or awkward in emails (assuming that I don't know the recipient)? What about formal correspondence (e.g. letters)?", "label": 1}
+{"snippet": "Are they two different phenomena or same phenomena having different properties in different situations? In what scenario should we consider induced emf and in what scenario should we consider motional emf? And which of the following does faraday's law and lenz law mention about? Are both caused due to induced electric field?", "label": 1}
+{"snippet": "I'm trying to represent some string conditions in terms of regex. One of those conditions I find hard to transform is that the string must have at least three different characters. So is there any plausible regex for that condition? Suppose the alphabet only contains English characters (a-z A-Z). Thank you,", "label": 1}
+{"snippet": "What's the exact term used to describe the \"why\" in some people's spoken English (somewhat rural or archaic by now, I suppose) as in \"When I saw how much it cost, why, I knew I couldn't afford it\".....or \"When our family car broke down, why, we'd just walk, until we could fix it\", etc....anybody recognize these? If so, why the \"why\"?", "label": 1}
+{"snippet": "I am doing documentation for a web application issue and I'm not sure how best to word what I'm trying to say: \"This appears to work no longer in any web browser.\" \"This appears no longer to work in any web browser.\" \"This appears not to work any longer in any web browser.\" Which is most correct, or are they all equally correct?", "label": 1}
+{"snippet": "Sometimes, my supervisor writes emails to ask whether we can cancel or reschedule our meetings, or request me other things. The way he writes emails is very polite. And I usually reply him by: Yes, sure! Yes, it's fine! I wonder if these responses are considered polite? How do I politely (but not really formally) respond to my Professors' requests? Thank you very much!", "label": 1}
+{"snippet": "I am designing an algorithm that generates shapes of bezier curves. Each output are control points for a single curve. In some cases, it should return a circle. Which control points does the algorithm have to output for the shape to become a circle?", "label": 1}
+{"snippet": "It's an exercise of the book Linear Algebra Done Right. I'm not clear about how to prove these problems, would you please offer me some suggestion about how to improve this kind of ability, thanks a lot.", "label": 1}
+{"snippet": "A scammer got a hollow gold bar and fills it with a combination of lead and air, with the same average density as gold. What's the simplest way of discovering the fraud? I know that x-rays will see it, but are there simple means for analyzing it? (without destroying it)", "label": 1}
+{"snippet": "I'd like to have output an equals sign that has a small question mark over the top of it. (I'm proving an equation, but it is not obvious until the final step that the equation is true.) Do I need to create a special symbol myself (via a macro, etc.), or is there already one defined?", "label": 1}
+{"snippet": "If I have a friend that spreads their interests too thin, gathering a large body of superficial knowledge related to many topics, I'd probably use the phrase \"jack of all trades, master of none\" to describe them. Are there any phrases or idioms to describe the opposite? Someone suffering from an extreme overspecialisation, who is so singular in their expertise it perhaps damages effectiveness?", "label": 1}
+{"snippet": "Title says it all, I'm looking for the formula to get the bearing from one point to another on a number plane. I have found examples of this for lat/lon around the earth but that's not exactly what i need. Thanks", "label": 1}
+{"snippet": "Besides SVO, which are the word orders that can be found in English? Are there any that are peculiar to dialects such as Singlish or Indian English? Please provide an example sentence for each order along with pertinent information such as tense, mood, voice, etc.", "label": 1}
+{"snippet": "Question: Is it possible to start a grammatically-correct English sentence with the word \"Than\"? If no, what other English words share this property? Background: Trevor claimed that it is impossible. This is an attempt to verify or repudiate Trevor's claim.", "label": 1}
+{"snippet": "Example: \"So,\" I said, after deciding on a topic of conversation, \"do you like karaoke?\" \"So,\" I said, after having decided on a topic of conversation, \"do you like karaoke?\" What's the difference? Is having decided an uncommon usage?", "label": 1}
+{"snippet": "Suppose I have a weighted connected graph which is traversable (each vertex has even degree) and I wish to walk over all edges. Clearly any Eulerian path minimizes the total weight. What can be said about the case of non-traversable (weighted connected) graphs? Can a minimum-weight path still be found in polynomial time?", "label": 1}
+{"snippet": "Is there any word or phrase to describe a person who always feels rthat he has forgotten something even if he hasn't forgotten something really, while going out from somewhere? Example :- Peter is a xxx as he always feels that he has forgotten something, whenever he goes out of his house. What can be the replacement of xxx?", "label": 1}
+{"snippet": "The plural form of leaf is leaves, although according to Merriam-Webster leafs is also correct. Dwarf can be pluralized as either dwarfs or dwarves. Conversely, the words roof and safe are pluralized as roofs and safes. Is there any logic underpinning these variations? Is there a historical trend where words that were previously pluralized as -ves are now being increasingly pluralized as -fs?", "label": 1}
+{"snippet": "If the question state: A connected and undirected graph, then does this graph allow loop or multiple edges? I searched over the internet, but some allow, some don't. It's so confusing. Any idea? Thank you.", "label": 1}
+{"snippet": "I am doing Spivak's Calculus, and I find it EXTREMELY difficult. I usually ask questions here because I cannot do the problems on my own. How long should it take to do a Spivak problem? Is it preparatory for contest problems such as Putnam? Thanks!", "label": 1}
+{"snippet": "For a long time I was wondering why there is I win instead of I won. I met such usage in a lot of games and movies. For me, it's logical to say I won, because this winning action is done already. I win for me seems like I'm winning right now. Can anyone clarify this for me?", "label": 1}
+{"snippet": "Palindromes are words, sentences, numbers that are the same forwards and backwards. Is there a term for words that are one word forwards but a different word backwards? For example, star backwards is rats, or god is dog.", "label": 1}
+{"snippet": "Are there any good books on musical theory from a mathematical standpoint? Is \"Music theory and mathematics : chords, collections, and transformations\", edited by Jack Douthett, Martha M. Hyde, and Charles J. Smith, one on them?", "label": 1}
+{"snippet": "As far as I know, it is valid to say \"they can produce music on their own terms\" when you want to say that a group can produce music without having to answer to anybody but themselves. Is it also valid to say \"they can produce music in their own terms\"? Does this convey the same thing? If not, what does it really mean?", "label": 1}
+{"snippet": "I've recently discovered a guy named Gary Vaynerchuk. At his Youtube channel he named himself as garyvee. Besides his last inital is V (spoken vee), does the double ee has any meaning ?", "label": 1}
+{"snippet": "The proof featured at http://planetmath.org/newtonsmethodworksforconvexrealfunctions shows that, roughly speaking, Newton's method is unconditionally convergent for convex/concave functions. I am looking for a textbook or paper reference of this fact. I have found part of it in Michael Spivak's Calculus:", "label": 1}
+{"snippet": "What is it called when a letter is within another letter? For example, the letter O within the letter L: Edit: Or the first C in the Coca-Cola logo: Does this arrangement of type have a name?", "label": 1}
+{"snippet": "I am aware that the plural of metropolis is metropolises, but to me it sounds stilted and to be honest I cannot recall ever hearing it used. Is there an irregular plural of metropolis that would be in a less formal register. Any common mistaken pluralizations?", "label": 1}
+{"snippet": "I have bought many books about vocabulary. Most of them by Cambridge Press. However, I don't know if it is the right way to learn vocabulary from a book like those or is it better to pick new words while reading! Any studies around this?", "label": 1}
+{"snippet": "In LyX I accidentally clicked 'Version Control' -> 'Revert to Repository Version' as it's just below 'Check In changes' option. This resulted in loss of all work since last check in, and using 'redo' is not possible. Is it possible to undo a revert like this?", "label": 1}
+{"snippet": "I'm in the process of purchasing a house and reading through the contract, I can't find a single instance of the comma. (As if legalese wasn't hard enough to read already!) This includes the segregation of sentence clauses, separating lists, following certain leading adverbs (however, therefore, etc.), etc. Are commas considered superfluous in legal documents? Perhaps just property documents?", "label": 1}
+{"snippet": "The usual mantra of a quantum field theory is that real particles (as opposed to virtual ones) are excitations of a field. Is this a necessary property of all (operator-valued) quantum field theories? Are there any theories currently in existence whose fields do not or cannot produce real particles?", "label": 1}
+{"snippet": "What do we mean when we talk about a topological space or a metric space? I see some people calling metric topologies metric spaces and I wonder if there is some synonymity between a topology and a space? What is it that the word means, and if there are multiple meanings how can one distinguish them?", "label": 1}
+{"snippet": "Should it be \"find your company's zen\" or \"find your companys' zen\"? Or perhaps another? I am convinced it should be \"find your company's zen\" as it suggests ownership of said zen, but I want to be sure. What should it be?", "label": 1}
+{"snippet": "I'm creating an application that has a checkbox to assist colorblind users. I'm not so fond of the term because it isn't accurate, but at the same time I don't want to seem overtly politically correct. A couple of options I'm juggling right now: Colorblind assistance Reduced color perception assistance Color perception assistance Problems perceiving colors?", "label": 1}
+{"snippet": "Can someone help me understand what's going on here? This is for a problem involving moment generating functions, which is related to statistics and probability, but I figured it was more of a math questions. The whole expansion is below:", "label": 1}
+{"snippet": "My first question here..sorry if I'm not very specific but I try to be. A T-tetromino has three connected blocks in a line and another one above the middle block. How many ways can one be painted on the grid if orientation matters? What about if it doesn't?", "label": 1}
+{"snippet": "I thought that Empty was the word, that besides its original meaning, could be used when you refer to some abstract idea, like \"I feel like my soul is empty today\". However, recently I've encountered the word Vacuous in the same abstract contaxt \"That idea is vacuous\". So what's the difference between those two?", "label": 1}
+{"snippet": "Does anyone have any suggestions as to what is a good topic for a short talk on theoretical physics to a bunch of Math and Physics undergrads that might make them \"embrace\" theoretical physics? Thanks. (Brain storm: String theory, quantum tunneling, etc...?) Also it would be great if someone could suggest some resources.", "label": 1}
+{"snippet": "While the moon is certainly not a good reflector of solar radiation, surely the radiation it reflects back heats the Earth (even if it is a terribly small amount). How would one go about calculating (or estimating) this heating contribution on a night with a Full Moon?", "label": 1}
+{"snippet": "I need to rewrite my article to fit in the format of Hindawi Special Issue Cloud-Oriented Data Center Networking. After searching their site, I can't really find any useful information about formatting, they only mention that pdfs and docs are accepted, nothing more, any LaTeX template is given. What should I do?", "label": 1}
+{"snippet": "How would you say \"I'd like to get off the medication\" not using the colloquial phrasal verb \"get off\"? I.e., something that you'd hear someone well-versed in the English language say. For example, can someone fill in a word or phrase to complete the following sentence: I'd like to be ___ medication by next month.", "label": 1}
+{"snippet": "I had a question on LCDs after noticing something interesting about its color. LCDs are black when they aren't used. But when we observe LCDs closely, we see they are made up of red, green, and blue dots. Therefore, since they reflect red, green, and blue, collectively, an LCD screen should look white. So why does it look black?", "label": 1}
+{"snippet": "How can I create a blind footnote such as the one in the picture below? By blind I mean that there is no number in the text, or in the footnote. I would like to have this footnote on the bottom of the first page of my document and all the other footnotes in the document should be unaltered.", "label": 1}
+{"snippet": "What is an example of a prevariety in which the intersection of some two open affines is not an open affine? My examples of prevarieties that are not varieties does not extend beyond the affine line with the origin doubled. My guess is that the plane with four origins might give an example but I don't see how. Thanks.", "label": 1}
+{"snippet": "I used to read the term \"pure energy\" in the context of matter-antimatter annihilation. Is the \"pure energy\" spoken of photons? Is it some form of heat? Some kind of particles with mass? Basically, what does \"pure energy\" in the context of matter-antimatter annihilation refer to?", "label": 1}
+{"snippet": "One thing I love about English is that verbs can be easily created just by adding the suffix \"-ing\" and adjectives by adding \"-ly\". How would you call this phenomenon? Examples: Googling, Youtubing Pants-shittingly", "label": 1}
+{"snippet": "We have a scalene trapezoid. We know AB and CD bases and the diagonal AC. Be P the point of intersection of the two diagonals. Is it possible to find the general expression for AP? I would like to know the formula for AP, if it exists, depending on AB, CD, AC", "label": 1}
+{"snippet": "I have a circular area, and I need to distribute a certain number of points in this circle in a Poisson Distribution. Functionally, how would I be able to distribute the points in a Poisson distribution? If I were to just place the points as 'randomly' as possible, would that be good enough?", "label": 1}
+{"snippet": "Are there any simple \"experiments\" that can be done in a high school science lab that could demonstrate some sort of basic principals of wormholes or spacetime? Or sort of proving how long something would take to get through a wormhole or why you wouldn't be able to travel through them etc.", "label": 1}
+{"snippet": "I'm not sure I understand the question. As far as I understand it when it says vector space of dimension n, it signifies that there will be n amount of vectors; right? So basically it wants you to prove that a set of two vectors can't span a set of three vectors?", "label": 1}
+{"snippet": "If we have a smooth football in the shape of an ellipsoid, and that water runs down on its sides, can we trace the path of a water drop on it? For a sphere it seems easy because the force tangential to the surface is perpendicular to the radial vector whereas in the case of an ellipsoid it isn't. Any help?", "label": 1}
+{"snippet": "Is it possible to create a picture that would look like this? I have solved a problem that also asks to draw a similar picture. Don't want to ruin my document by inserting a picture of the drawing by hand (see below). Any insight is greatly appreciated.", "label": 1}
+{"snippet": "I downloaded both TeXnicCenter and MiKTeX on a new PC. When compiling a file (which was made on another pc), I get the error ctable.sty not found. Then I get the suggestion to download the correct package from the internet, but it does not work. How do I choose the correct \"remote package repository\" in the given list? Thanks for your help", "label": 1}
+{"snippet": "I am not a native English speaker and there are some grammar mistakes I do a lot, especially have/has in conjunction with each/every, and so on. Q: Is there some way to highlight all occurrences of some words (from a list I specify) in a document automatically?", "label": 1}
+{"snippet": "Can we reconstruct a polynomial with only Y values? What if the number of Y values are far more than the degree of the polynomial? Also can we obtain the root of this polynomial with this Y's value without interpolating?(i.e. without knowing the coefficients of the polynomial)", "label": 1}
+{"snippet": "The potential for the Higgs field is a quartic one (Mexican hat). Is this done for simplicity or are there fundamental reasons for this choice? I can imagine further contributions to this potential without altering the essentials, which may lead to differences in the derived particle masses.", "label": 1}
+{"snippet": "If photons don't interact directly, how can electromagnetic waves interfere? I know that photons can scatter via higher order mechanisms, but not directly. Does those mechanisms explain the classical phenomenon of wave interference?", "label": 1}
+{"snippet": "Where do the formulas for reciprocal lattice vectors come from? I recently began studying tensors and the same formula's appeared yet again, this time called dual basis vectors! This reignited my interest in a derivation of the reciprocal lattice. Can someone provide some insight into this?", "label": 1}
+{"snippet": "This question presumes that vanilla texlive is superior and thus deserves to be installed despite the troubles over Ubuntu apt-get. What exactly are these benefits? I'm considering going back to texlive via apt-get due to some issues in Rstudio and knitr, but want to fully understand the trade-offs.", "label": 1}
+{"snippet": "We have the following graph: whose every line is colored either red or green. Prove that in every possible coloration there exists one red or/and one green triangle. This problem was introduced in reference to the Dirichlet's box principle.", "label": 1}
+{"snippet": "I came across the word \"cable\" very often in http://www.guardian.co.uk. Like: WikiLeaks cables: Drive to tackle Islamists made 'little progress' US embassy cables: How the Guardian protects sources WikiLeaks embassy cables: the key points at a glance I know what a cable is, but what does \"cable\" here mean?", "label": 1}
+{"snippet": "Is this what 'No good deed goes unpunished' means? No matter how good you are or how many good deeds you do (or favors you do) for someone, s/he will always find fault with (bitch about) them and will not be truly appreciative. Could someone please cite an example of this idiom's usage, please? Thank you.", "label": 1}
+{"snippet": "I'm a postgraduate student in physics, but I have achieved interesting results in Cauchy equation. I found a reason why Adams method for solving differential equations gives rise to divergent solutions. I explained this phenomena and provided a new improved integration schema. Could anybody help me to choose a good mathematical journal where I can publish my results?", "label": 1}
+{"snippet": "Is the minimal polynomial of a linear transformation equal to that of its matrix representation on some basis? One of my textbooks on linear algebra defines eigenvalues and eigenvectors in terms of minimal polynomials, while the other textbooks define them in terms of characteristic polynomials. What is good about defining them in terms of minimal polynomials? Why are minimal polynomials important?", "label": 1}
+{"snippet": "I want to get a list of bib-keys from my .bib file which I don't actually use in my document. I have found \"Unused bibliography entries - how to check which entries were not used?\" but since I'm using biblatex I don't have the information in the .aux files, so I can't use checkcites. Is there a biblatex way to get such a list?", "label": 1}
+{"snippet": "Are the odds of predicting that someone would win the lottery the same as just some random person winning the lottery, or are they different probabilities? Because to me, if I read that someone had won the lottery, I wouldn't be that amazed, but if someone predicted that a particular person would win and that prediction came true, I'd think that's far more far-fetch.", "label": 1}
+{"snippet": "Question:Find the number of arrangements of all the letters in TALLAHASSEE. How many of these arrangements have no adjacent A's? I want to know why it is a combination prob and not permutation.", "label": 1}
+{"snippet": "Why is polarized light used in microscopy for the analysis of rocks(for example)? Why not use unpolarized light? What is it with polarized light that makes the analysis of rocks better? Edit: please refer to the actual physics behind your answer", "label": 1}
+{"snippet": "I make figures in powerpoint, export them as pngs, and include them in my document. I sometimes get strange borders around them, sometimes around indivual elements of the ppt file, like this (black boxes are just censoring): It doesn't print, but looks bad on the screen. Any tips to get rid of it?", "label": 1}
+{"snippet": "In the dictionary, the words \"convert\" and \"transform\" both have the meaning of changing the form of something. So how should I distinguish them? In what situation they are of the same meaning, and in what situation they are different?", "label": 1}
+{"snippet": "Do I need a comma before \"particularly\" in the case below? Thank you very much for your help! Vitamin D has properties against metabolic, neoplastic, and immune disorders particularly breast cancer, osteoporosis, and cardiovascular disease.", "label": 1}
+{"snippet": "Recently I came across the word substantional. What's its definition, and how can it be used in a sentence? Are there any common synonyms? Where did this word come from? I suspect it's related to substantial, but it's not entirely clear. This was used in a context looking for reference back to an authority of some kind, but I'm unsure if this is relevant.", "label": 1}
+{"snippet": "I read this term shave cream in NY Times today. According to the results in COCA (Corpus of Contemporary American English), shaving cream (I also found this word in the dictionary) is far more common than shave cream in American English. I would like to know if there's any difference between these two terms.", "label": 1}
+{"snippet": "I was criticized the other day for using this word. It never occurred to me that it was offensive, but Wikipedia says it \"may\" be derogatory. Given Vancouver's hockey team, I tend to think it's benign, but I wouldn't want to get William Shatner angry. Please help me oot.", "label": 1}
+{"snippet": "In a sentence beginning, \"The head officer[,] or his designee[,] shall...\" are the bracketed commas appropriate? If so, could you explain the formal grammar rule that would require them? I'm a legal proofreader; if I suggest commas, it must be ascribed to a formal grammar rule, rather than personal choice. (And as a bonus question, is the comma I placed before \"rather\" necessary?)", "label": 1}
+{"snippet": "Is there a word to concisely say 'an unavoidable sin'? Or maybe just a better way to say it. This is in the context for example of someone who habitually does some particular activity and then regrets it afterwards.", "label": 1}
+{"snippet": "In Mormon missionary culture, they use the word \"trunky\" to describe the feeling at the end of their two-year mission when they are tired, ready to go home, and are mentally packing their trunks to go home. They have mentally checked out from their mission at hand. I'm looking for a commonly used word or phrase that means generally the same thing as \"trunky\".", "label": 1}
+{"snippet": "What's the word to describe someone who acts arrogantly and always disagrees with others unreasonably in order to upset people around him/her? [I'm not looking for adjectives like unpleasant, annoying, unfriendly, rude, I'm looking for a more specific term like opinionated, didactic, loquacious, gregarious ] I think I'd come across it before but I've forgotten what it is..", "label": 1}
+{"snippet": "Which is your most favourite subject in school ? What is your most favourite subject in school ? Which one is acceptable? If both are acceptable, do they have any difference in meaning?", "label": 1}
+{"snippet": "What is the exact meaning of the sentence below? We can't try to get away with something in an academic paper that we would abhor in a political debate (or worse yet, in a political advertisement). The sentence is from the first paragraph of the article 'Being Logical'. Especially, where does the something belong initially? In an academic paper or in a political debate?", "label": 1}
+{"snippet": "I have existing .tex file and want to create similar one. I am doing this by saving the file with another name, I just click \"save as\", but it won't be saved as a .tex file. Instead it creates .bak file or something else that cannot be compiled any more. What is the problem and what I'm doing wrong?", "label": 1}
+{"snippet": "I'm curious as to how to construct an infinite variable polynomial. Is there an nice formulation of such a thing? I've attempted using functions and functionals to construct one, but that didn't lead anywhere. I need it to find a separatrix for a functional-differential system of equations. I'm very appreciative of any help.", "label": 1}
+{"snippet": "All I have to do is run the plastic comb through my hair and hover it over small pieces of paper, right? The comb should then be charged and attract the pieces of paper... but that doesn't seem to work. I've used the tiniest bits of paper too. What's happening?", "label": 1}
+{"snippet": "How many elements are there in a total ordering T of a set A with |A| = n? I have no clue on how to do this problem. If someone could let me know how to start the problem, it would be much appreciated.thanks", "label": 1}
+{"snippet": "Is there a way to construct lists by multiple instances of a field instead of using and or comma, respectively? E.g., instead of @article{FooBar, ... author = {John Doe and Richard Roe}, keywords={foo, bar}, ... } I would like to get the same result in the reference by @article{FooBar, ... author = {John Doe}, author = {Richard Roe}, keyword={foo}, keyword={bar}, ... }", "label": 1}
+{"snippet": "I am using the tcolorbox package, and I want to use a gradient ellipse title box with border on the titlepage. It is possible somehow or I have to use another package to manage this?", "label": 1}
+{"snippet": "I have heard someone say \"As a consultant, Dave can charge orbital fees, so we would rather have you do it.\" I tried to look up \"orbital\" but did not find what I was expecting.", "label": 1}
+{"snippet": "I am not a native speaker and yesterday someone told me that \"She got her first child\" would be misunderstood and \"She had her first child\" is correct. Now I wonder if this is a 'local' thing here in Wales or a general 'rule'.", "label": 1}
+{"snippet": "The following is taken from a website: Sir, do you realize your wife fell out of the car several miles back? The expression fell out here, as I checked in the dictionary, doesn't make any sense. Does it mean fell off?", "label": 1}
+{"snippet": "When a Force is applied on a body at rest, it produces Acceleration which is equal to change in Velocity. But due to the Force, we see that the Velocity is increasing consequently. So why don't we take both of them proportional to each other rather than Force and Acceleration?", "label": 1}
+{"snippet": "I wanted to use a header which looks like the image attached below. At first I tried using a fbox with a parbox but I had issues with the right widths because the text wasn't properly aligned at all. What would be your attempt at mimicking the style of the first three lines in the sample?", "label": 1}
+{"snippet": "I want to apolagize in advance if the questions are too easy but I tried on my own and apparently I didn't make it, so please help.Also write down every single step in the solutions without omitting anything that you may consider as obvious. First task:", "label": 1}
+{"snippet": "I have two questions. The first question: What are the differences in meaning and grammar between \"until you listen to me\" and \"until you start listening to me\"? I'm hoping that someone can help me here. But there is another question: What are the differences between 'I'm hoping' and 'I hope'?", "label": 1}
+{"snippet": "Would it be considered a malapropism to substitute a word or portion of a word in a phrase with another word or portion of a word, generally rhyming with the original word, and generally considered an offensive replacement? For example, the term \"Election Day\" substituted with \"Erection Day\" or the company name \"Pizza Hut\" to \"Pizza Slut\"?", "label": 1}
+{"snippet": "Here, in the place where I am being hosted, almost every evening there is an event usually called \"burlesque\". Is \"burlesque\" normally used by Americans? How is the word used generally? In what context do we refer to this word?", "label": 1}
+{"snippet": "If a function has countably infinite number of discontinuities, can it still be called piecewise continuous [say greatest integer function]? I read that a piecewise continuous has finitely many discontinuities. Thanks for the help in advance.", "label": 1}
+{"snippet": "I have found increasingly that I am accidentally typing ctrl-d instead of ctrl-f only to silently comment out an entire paragraph I am working on. Is there a way to disable ctrl-d ? Ideally I would still like to be able to comment out paragraphs so if it can be mapped to some other keyboard shortcut that would be even better.", "label": 1}
+{"snippet": "Imagine the 'Bishop' chess piece. The four directions that it can move can be called 'diagonal'. Similarly the 'Castle' moves in the horizontal and vertical directions. Is there a single word that describes this movement?", "label": 1}
+{"snippet": "Can you please tell me if my comma in the following statement is correct? Should there be a comma after \"questions\" as it is below? Should you have any questions, please feel free to contact me at the number below.", "label": 1}
+{"snippet": "The only meaning of \"ass\" I knew until today was the fleshy body part. But what I read today on a shopping receipt shocked me. One of the items mentioned there was Other ass. Surely that shop doesn't sell body parts. So does this word have some other meaning or is it just a spelling mistake?", "label": 1}
+{"snippet": "I would like to know whether there are mathematical models for the processes of melting (like an ice-cream melting on the biscuit rather than snow) and weaving (or interweaving). If so, of what kind? If you need more specification, please tell me. Thanks in advance.", "label": 1}
+{"snippet": "From the common English grammar lesson, the past perfect tense with had is usually followed by dependent clause. For example: He had studied English before he moved to New York. Now, if I want to say something like this: Yes, I had turned off the lamp. or I had made two mistakes: ... ... Is it allowed in English grammar?", "label": 1}
+{"snippet": "Is it true that the number of arbitrary constants in the solution (if solutions exist) always equal to the order of an ordinary differential equation? If yes, how to \"prove\" such a statement, if it can be proved at all? If no, what are typical counterexamples?", "label": 1}
+{"snippet": "A haven is a place that is safe. So, \"safe haven\" is redundant. Shockingly, several state legislatures have even passed laws for dropping off babies with no penalty; these laws are usually referred to as \"safe haven\" laws.", "label": 1}
+{"snippet": "There are lots of good apps for teaching mathematics to children but I would like to learn about apps for undergraduate/graduate/research levels. Helper questions Any algebra system (like Maple, Sage)? Interactive geometry (like GeoGebra, Cabri, etc)? What else?", "label": 1}
+{"snippet": "I'd like to put am image in a certain position on the title page in beamer. I also don't want it to interrupt the text flow, i.. I want the image to appear \"behind\" the text. Any ideas?", "label": 1}
+{"snippet": "\"There is no man outside the house\" \"There is not a man outside the house\" \"There was no solution to the problem\" \"There was not a solution to the problem\" Can I use both of them? Are the sentences equivalent? Which one is more idiomatic?", "label": 1}
+{"snippet": "Is it possible to have a clickable \"copy to clipboard\" feature in a PDF document generated by LaTeX? Ideally in the form of a macro that also allows for graphical elements to be embedded inside it (to make, say, a custom button that, when clicked, copies something to the clipboard). Edit: An Acrobat only solution will work too.", "label": 1}
+{"snippet": "I am looking for a phrase that compares two characters that share very similar attributes and characteristics. Prufrock and Hamlet truly are [ ... ] I don't want something like \"very much alike\" or \"similar\"or anything like that. Rather, I'm looking for a distinct phrase to describe this.", "label": 1}
+{"snippet": "I know we use normal linear regression for modeling functions on datasets, but can someone explain how neural networks help in approximating more complex functions, especially when they are nonlinear? Intuitively, what does each layer adds to the whole process of approximation? What I am looking for is an explanation of how neural networks approximate functions, and not a comparison with the biological neurons.", "label": 1}
+{"snippet": "We know the values of the coordinates (Xa,Ya), (Xb,Yb), and (Xc,Yc). We also know the lengths of A, B, and C. Is there a way (equation) to figure out the exact coordinates where the three lines A, B, and C intersect (the x? and y?). I assume you could rotate all three of the lines until eventually they matched up.", "label": 1}
+{"snippet": "Deal all, I am looking for a gentle introduction to algebraic invariant theory (for a Bachelor project) with some simple (but interesting) applications in representation theory (of finite groups, of Lie algebras). Thanks for your help!", "label": 1}
+{"snippet": "Is there a single word or a couple single words that would describe the situation of not being able to fully express/explain your feelings or emotions to someone so that you can get them to understand your situation or point of view? This doesn't quite include feelings.", "label": 1}
+{"snippet": "I am looking for a word or an idiom about showing respect to someone superior in work because you are afraid of him. I'm not talking about real respect or showing respect to him or his works, just getting scared by his ruthless actions. Is there a word or an idiom for respecting someone because you are afraid of him?", "label": 1}
+{"snippet": "There is a sentence: I am grateful to Mr. White for A and B[,] and to Mr. Black for C and D. Should I put a comma before \"and to Mr. Black\" or not?", "label": 1}
+{"snippet": "Has anyone proved or disproved that there are a finite number of minor-closed graph families? If not, what is the general belief in the math community? Alternately, is there another approach (not using minors) to classifying undirected graphs?", "label": 1}
+{"snippet": "I've just learned about removable discontinuities. So, when we have such a function we redefine it, making a new function that is defined at the point the first isn't. What is the point of this? What advantages do we get? Wouldn't making it continuous cause problems when we use it instead of the old one?", "label": 1}
+{"snippet": "We all know that we can see anything because of Light Absorption and all. We can hear things because of caused vibrations. But what makes an object smell? I read somewhere about the presence of odorous chemical compounds in the objects which makes them smell. Then, What gives smell to those odorous chemical compounds?", "label": 1}
+{"snippet": "If a hypothetical cylinder was infinitely long, could it vibrate at any frequency, since any frequency would be a harmonic of it? And (less hypothetically) if a cylinder was only really long, would it have a similar effect? I'm talking specifically about sound waves (and more specifically, trumpets).", "label": 1}
+{"snippet": "Is it possible to use the character set available in the \"Webdings\" OpenType font which is installed on my PC using XeLaTeX? Other non-symbol fonts seem to work fine, but I just get boxes for every character I try in this font, and other symbol fonts like Wingdings etc.", "label": 1}
+{"snippet": "When are two natural transformations between two functors considered the same? When are two morphisms in a category considered the same? Do we have such a notion like we have in Set theory? Thanks", "label": 1}
+{"snippet": "Does the adjective Machiavellian always have a capital letter? For example: The Machiavellian Iago manipulates Othello into believing his wife, Desdemona, had an affair. Not sure if this is anything to go by but, Microsoft Word corrects the word to have a capital. I am not sure if this is also the case when it is an adjective.", "label": 1}
+{"snippet": "Does a diagonal matrix commute with every other matrix of the same size? I'm stuck on one line of a proof that I am writing, and I would like to switch order between a non-diagonal and a diagonal matrix. Thanks,", "label": 1}
+{"snippet": "I'm trying to find a simple and easy to understand example of a free module that has bases of differing sizes. We were told about the existence of them in class but no example was given.", "label": 1}
+{"snippet": "The name of our research center is Southeastern Transportation Center, STC is the acronym, of course. In writing, I use STC, not 'the STC' but our director says 'the' is needed so that it reads well. For example, I write: STC supports graduate education.; director says it should be The STC supports graduate education. Ruling?", "label": 1}
+{"snippet": "I'm confused by this sentence: \"Lakesha hopes to win the approval of her mother by switching her major from fine arts to med.\" I think that in this case hope is intransitive, and I think the part \"to win....mother\" is working as an adverbial infinitive phrase. Is it the object?", "label": 1}
+{"snippet": "I can't clearly get this phrase. Is it related to the \"kick out the jams\"? Or \"jam\" means the song/jazz improvisation, so what does \"kick out\" mean in that case? The context is \"they are kicking out the last jam of their set\".", "label": 1}
+{"snippet": "Okay, so everywhere I've read, I hear the main difference is the requirement of a medium. But for example, if you take the case of heat 'radiating' from a red-hot iron, isn't that actually convection and not radiation? I mean, isn't the temperature difference between the surrounding air and the iron causing the air to gain heat?", "label": 1}
+{"snippet": "I'd like to use tikz to shade an isosceles triangle with points A B C and length of AB and AC are equal. Shading should go from AB (red) to AC (green) where the color on a line through A always stays the same. I have found such a shading for circles but unfortunately not yet for triangles... Thanks in advance Jan", "label": 1}
+{"snippet": "My teacher gave me an error identification question, which is : \"An itch resulting when a nerve that can carry pain is only slightly stimulated\". I have a feeling the word \"resulting\" is a fault but don't know how to use it properly or if it needs change. Please help me.", "label": 1}
+{"snippet": "Is it possible to use the phrase: \"We are meeting at last\" when two people meet for the first time? For example, in a movie one person said: \"We meet at last\". Why did he use the present simple instead of present continuous? I mean, this was an action, which was happening at the moment of speaking.", "label": 1}
+{"snippet": "What is the physical meaning of the fractional integral and fractional derivative? And many researchers deal with the fractional boundary value problems, and what is the physical background? What is the applications of the fractional boundary value problem?", "label": 1}
+{"snippet": "The question and my attempt can be found here: https://i.stack.imgur.com/WSkbv.jpg I don't quite understand what i'm suppose to do. It says to prove the inequality with whatever so I tried to substitute and then factor and I thought it would just work out, but it didn't. Thanks", "label": 1}
+{"snippet": "Speaking of probability distribution, Can someone kindly tell how and when I use binomial distribution and uniform distribution in real life situations? I understand their mathematical formulas but I want to be able to choose the right one to perform when a certain problem is given to me to analyze. Thank you in advance.", "label": 1}
+{"snippet": "I have seen lots of answers proving this theorem via induction. However, I'd like to know how to prove that every digraph such as all vertices have in degree equal to its out degree is Eulerian, using the concept of maximum trail. Does anyone have a clue?", "label": 1}
+{"snippet": "I have a question in my text book that asks me to simplify the above expression. I reached the solution: However, the textbook gives the answer as: I appreciate that the value of these two expressions is the same. However, I am unsure as to how and why the answer above was reached instead of my answer.", "label": 1}
+{"snippet": "I'd like to draw a partial arrow (i.e. with only \"half\" of the tip) but with a triangular tip shape (e.g. using >=latex), instead of the standard single line you get with \"left to\", \"right to\", etc. The result should be something like the following image: How can I achieve this? I haven't seen any such tip in the TikZ/PGF manual.", "label": 1}
+{"snippet": "I would like to find a suitable word, that summarises data like different body parts' circumferences. What I could think of is 'Body Information', but it sounds bad at least for my non-native ears, and I don't know whether there is something better.", "label": 1}
+{"snippet": "CERN recently stated that antimatter may be repelled by matter, much like the opposite effect of Gravity. So is it possible that antimatter is actually repelled to the edges of the Universe to create a sort of outer-shell, something that allows the expansion of the Universe into nothingness.", "label": 1}
+{"snippet": "I am interested in having a local change to the default theme of beamer. I want every title in the beginning of a slide to be boldfaced, black (instead of purplish, black) with a horizontal line that stretches below it, with some margin between the line and the end points of the slide. Is that possible to do with beamer?", "label": 1}
+{"snippet": "Dictionary.com lists plagiarist as the noun form of plagiarism and lists plagiarizer as the noun form of plagiarize. I do not see the distinction of the separate entries and expected both words to be listed as noun forms.", "label": 1}
+{"snippet": "I was studying a photoelectric simulation (http://phet.colorado.edu/en/simulation/photoelectric) and I observed a really unusual thing. When I held intensity and potential at a constant value and then varied the frequency I observed that there was peak in photocurrent. That is, it first increased when moving towards ultraviolet and then decreased. Please try it yourself and explain.", "label": 1}
+{"snippet": "I am a graduate student. I wanted to do computation on heat transfer problem mainly heat convection. I am working on turbulent regime. Can you kindly suggest some good books so that I can get introduced and then use a few as references for my research from a physics perspective.", "label": 1}
+{"snippet": "How flexible is the measurement \"a dozen\"? If there are nine hundred and ninety-nine thousand people at a rally it is acceptable to say one million people attended, but if eleven people are arrested is it acceptable to round up to a dozen?", "label": 1}
+{"snippet": "Offhand, I'd say it's a variation of the bouffant with a bun on top. It transcends generations. Here's a fairly famous painting by John Sloan: And, almost a hundred years later, here's Captain Janeway:", "label": 1}
+{"snippet": "I am writing a paper on terrorism throughout social media, yet I cannot find a way to phrase the state of horror within a country. My sentence is as follows, \"Terrorist attacks are detrimental to the families of its victims as well as the (state of horror/fear) within the country.\"", "label": 1}
+{"snippet": "If I had bought insurance for the trip, I would have got a refund after I got sick and had to cancel. OR If I had bought insurance for the trip, I would have got a refund after I had got sick and (had) had to cancel. ?", "label": 1}
+{"snippet": "Obviously experiment is the end-all-be-all of any science, but I'm curious if there's any a priori reason to model space as Euclidean three-space (from a pre-relativity viewpoint, of course; I'm ignoring the fact that space is only locally Euclidean). I'm comfortable with differential geometry if it's necessary.", "label": 1}
+{"snippet": "Note this question is not a duplicate of this question because that question does not address the use of \"far more\". It sounds strange to me but it's probably perfectly fine. \"Many more\" or \"far more people\" sounds better. The example sentence: Much more people came to the party last time.", "label": 1}
+{"snippet": "The situation is as shown above. Now, to explain why the bottom disk rises, I applied Bernoulli's Equation at a point just below and just above the disk.The pressure difference hence obtained should push the disk up. Even though this is definitely incorrect, as these two points are not on a streamline, I have no clue as to the correct explanation.", "label": 1}
+{"snippet": "A line from William Golding's The Lord of the Flies: All round him the long scar smashed into the jungle was a bath of heat. Is it just me or does the sentence seem grammatically off?", "label": 1}
+{"snippet": "Several species of fish have names that are both singular and plural form. These include cod, flounder, salmon, and trout, they are used to describe one fish or ten. Does this stem from fish being both singular and plural? Was the irregular plural form passed along to the species of fish?", "label": 1}
+{"snippet": "According to OED, the most common use of \"terse\" is: Freed from verbal redundancy; neatly concise; compact and pithy in style or language. I've see some usage of terse conciseness, or terse brevity, or similar constructions. To me that seems redundant, even ironic. Am I wrong?", "label": 1}
+{"snippet": "from my understanding,every set has at least two subsets; the null set and the original set itself. My question is, what is the power set of the null set? Shouldn't it be just itself?", "label": 1}
+{"snippet": "Can I somehow use natbib with beamer now? When I try to load the natbib package the file does not compile. There is some old evidence that there is a conflict here: Beamer and Natbib. But maybe this is now rectified?", "label": 1}
+{"snippet": "I am currently spending some time creating a (partial) Liferay translation for the Greek language, and I came upon this original English message text: Your request processed successfully. Can the verb \"process\" be used intransitively in this manner? Or would this be the correct form? Your request was processed successfully.", "label": 1}
+{"snippet": "John Von Neumann once said to Felix Smith, \"Young man, in mathematics you don't understand things. You just get used to them.\" This was a response to Smith's fear about the method of characteristics. Did he mean that with experience and practice, one obtains understanding?", "label": 1}
+{"snippet": "What is the word to describe the phenomenon where at first nobody has the intension to clap (after a performance, lecture, etc). But suddenly one person starts clapping loudly, breaking the silence, and there goes the applause! Everyone starts clapping!", "label": 1}
+{"snippet": "I vaguely remember there is a notion of numbers rich in divisors, i.e. (number of divisors of N)/N is comparatively large. What's their name? Given a number M, how could I find such a number in its neighbourhood?", "label": 1}
+{"snippet": "What does the following sentence mean? This menu will be shown to all users but John. Does it mean that the menu will be shown to all users except John or only to John?", "label": 1}
+{"snippet": "\"I gave him two dollars.\" This tacitly means \"to him\". Are there exceptions to the rule that an indirect object in English always means \"to\" or \"for\"? In English, \"I stole him two dollars\" does not mean \"I stole two dollars from him\", and one does not say \"I withheld him that information\" (either of those usages would be valid in German).", "label": 1}
+{"snippet": "What is the word for the action of telling the horse you are on to move forward, turn left, turn right, or the like? I assume \"driving\" would be the easiest to understand, but it sounds like it does not fit a living thing like a horse. The word \"controlling\" seems most accurate, yet controlling an animal gives negative connotations, does it not?", "label": 1}
+{"snippet": "I am not looking for a good book but an appropriate book that is suitable for my logic course. Currently the professor only offers lectures. (Not sure why, perhaps there is no universal approach to logic, so no suitable book?) Ideally, the book contains question similar to the question I asked here. Any suggestions would be very welcomed.", "label": 1}
+{"snippet": "Is there a way to add a hyperlink to a reference from a bibliography (bib/bbl) in an image (created using IPE)? I want to create an image with text that when clicked directs to a reference in the bibliography in the document.", "label": 1}
+{"snippet": "How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, for the photon Green function, for the phonon Green function)? Explanations and references for actual constructions would be greatly appreciated. What is the use of skeleton diagrams in qft and in many-body physics?", "label": 1}
+{"snippet": "I guess the answer is NO, for polynomials. I know that there are more than one series expansion for every function. But I am talking about power series here. All Ideas are appreciated", "label": 1}
+{"snippet": "What, if any, is the difference between the two? My best guess is that a 'roundel' is the traffic island or structure that you drive around, while the 'roundabout' also includes the road you're driving on.", "label": 1}
+{"snippet": "Which one sounds better or is correct? I managed a number of challenging projects, such as / which included (...) designing new electronic devices (...) the design of new electronic devices (...) new electronic devices design", "label": 1}
+{"snippet": "What can be said about the determinant of a matrix when its rows (or similarly, columns) are unit vectors? Do such determinants have a geometric interpretation? For example, in the two-dimensional case, the determinant of two unit length vectors is the sinus between them.", "label": 1}
+{"snippet": "What insights does category theory offer in terms of grand unified theories? Any references to books or papers that give categorical descriptions of any of the common grand unified theories would be helpful.", "label": 1}
+{"snippet": "I was told by a fellow student that sometimes one cannot represent certain functions by a taylor series. I was also told that sometimes using a taylor series in a proof is invalid. Is any of this true? When is it invalid to use taylor series expansion? Edit: By certain functions, I mean well behaved functions with nice properties, entire, countinuous, etc.", "label": 1}
+{"snippet": "I was wondering how to get in my acronym list \":\" (colon) after the short abbreviation, for example: I want to get UV: Ultra Violet but I keep getting UV Ultra Violet without the colon.", "label": 1}
+{"snippet": "Two circles intersect in points B and A. Through the point A is drawn a line that intersects the circles in points C and D. Prove that the measure of angle CBD is a constant value for any line that is drawn through the point A. Thanks a lot for your possible help!", "label": 1}
+{"snippet": "Is there a more formal synonym for \"doing one's best\"? For example, as a formal document title: \"Is the government [doing its best] to...\" Or is it suitable (i.e., sufficiently formal) as it is?", "label": 1}
+{"snippet": "One which is influenced and steered by pressures from a government which itself is corrupt. Doesn't sound too unfamiliar today, does it? Anyway, it is to help me translate a German word \"die Systempresse\".", "label": 1}
+{"snippet": "It's widely known that the name \"JavaScript\" is trademarked by Oracle (formerly a trademark of Sun, formerly a trademark of Netscape). What was formerly a trademark of Netscape? Sun? Oracle? JavaScript? How would one recast the sentence to unambiguously give each of the alternate meanings? [EDIT] The sentence is merely an example. The question relates to correctly structuring a sentence for clarity.", "label": 1}
+{"snippet": "(ignoring the air resistance that causes the bottle to take positions in mid air. Let's say it is dropped in a vacuum with earth's gravity accelerating it downwards) I just cannot catch what happens with the bubble with my bare eye, and I thought I should better ask some experts :)", "label": 1}
+{"snippet": "What is a formal word/phrase that describes a person who always searches to benefit from other people? It is hard to recall the word in my own language to translate. So I decided to give it a try and ask here. I prefer adjective", "label": 1}
+{"snippet": "I understand that torque is defined as the cross product of the difference vector between the point of impact and the center of mass and the force vector, but what happens when the impact is over an area? Do I just find the center of the area and use that as the impact point?", "label": 1}
+{"snippet": "When would you use \"expert in\" and when would you use \"expert on\"? A quick google search yields about the same for both, but I have a feeling \"expert in\" can occur in sentences somehow with a different meaning altogether.", "label": 1}
+{"snippet": "Given an acute triangle ABC with altitudes AH, BK. Let M be the midpoint of AB. The line through CM intersect HK at D. Draw AL perpendicular to BD at L. Prove that the circle containing C, K and L is tangent to the line going through BC", "label": 1}
+{"snippet": "Is there a word that references someone's \"humanness\"? Something that one would posses, that would characterise them as human. I wouldn't say \"human\" in terms of morals, but \"human\" in the most literal sense. I'll give an example: \"He demonstrates extreme physical ability, to the point where I question his __\". What would be the most appropriate way to express this?", "label": 1}
+{"snippet": "I don't have any knowledge of statistics beyond high school common sense. Why is the standard deviation usually seen in combinatorics textbooks, and why is the standard deviation defined intentionally? What is its purpose? Thanks in advance. I have checked in Wikipedia and many other websites to see what this is, but they are not very concise and clear.", "label": 1}
+{"snippet": "Possible Duplicate: Proof that Pi is constant (the same for all circles), without using limits How can you prove that the ratio of the circumference to the radius is a constant (regardless of what the constant is) using elementary geometry. Thank you", "label": 1}
+{"snippet": "Is the concatenation of two arbitrary alphabets is considered an alphabet ? Also Is the set of all Java reserved words is considered an alphabet ? I am inclined to say yes. We could take a string and consider it a symbol. What do you think ?", "label": 1}
+{"snippet": "This might be too general question, but still, I think this may be some useful question. So, what math branches are there generally? (for example, one branch would be abstract algebra, differential geometry etc.) Or what math branches are recognized in undergraduate math programmes?", "label": 1}
+{"snippet": "I have been trying to find a quick answer of this, but my google searches didn't get me anywhere. I'm confused about using in or on in the following sentence. We will return your call in the following business Day or We will return your call on the following business Day Thank you", "label": 1}
+{"snippet": "I can't find a reference for a set of generating vectors for the Tetrahedral-octahedral honeycomb lattice. I would like to know the \"canonical\" set and if possible a more general set described by angles (I think it would take three angles to completely describe it but I'm not sure on this either.)", "label": 1}
+{"snippet": "Is there a word that describes a concept which loses its power when put into words? EDIT: For example, the context could be a philosophical (or pseudo-philosophical) idea like \"zen\" attitude. When a monk can not tell his pupil directly how to achieve enlightenment because the idea is _____.", "label": 1}
+{"snippet": "I used VerbTeX app in my Android phone. But this app does not support XeLaTeX and requires an internet connection to be used. Is there any distribution of TeX for Android? How I can install TeX on my Android phone?", "label": 1}
+{"snippet": "Can anyone show me or direct me to a (free, online reference of a) FULL proof of Green's and Stokes' Theorems? I have been looking and all the proofs I've read prove the theorems for a certain class/type of surfaces/regions...but does anyone know of a general, complete proof?", "label": 1}
+{"snippet": "I mean I will continue to work for this company for maybe some months or some years, so can I use \"for some time\" as I mentioned in the title. What would a native speaker say? Thanks in advance.", "label": 1}
+{"snippet": "In The Econometrics of Financial Markets by Campbell, Lo and MacKinlay -- a beautifully typeset book -- I have found gorgeous cross correlation matrices of the style below. What is an elegant way to typeset these labels for the rows and columns in LaTeX (ideally in conjunction with the amsmath matrices)?", "label": 1}
+{"snippet": "Is the concept of a field just a mathematical construct? Is there any way to realize its existence? For instance, the fact that moving a charge affects other charges in the surrounding not instantaneously is explained in terms of the existence of an electric field. Is there no other approach to this problem?", "label": 1}
+{"snippet": "For example, If this van's a-rockin', don't come a-knockin' Here We Come A-caroling (song title) Come on-a My House (song title) I have a few related questions: What is the \"a-\" or \"-a\" called? Is there a function beyond a rhythmic one? Why is \"a-\" attached to a word at all -- and why attach to a word at all?", "label": 1}
+{"snippet": "Shade-off and halo effect introduce distortion to phase contrast images. I am trying to utilize these features to write a program which could identify spherical cells from (positive) phase contrast images. Since cells are not necessarily of the same diameter, I want to figure out the theoretical intensity distribution. Could anybody give me some hints?", "label": 1}
+{"snippet": "Say a rotating ball or neutron star gets completely annhilated to energy by meeting its anti-matter counterpart (also rotating in the same direction), what happens to the angular momentum? It cannot disappear due to conservation laws.", "label": 1}
+{"snippet": "A polar coordinate function f(x) can be rotated around the axis by h with the shift f(x - h). However, this rotates the graph. Is there a way to shift a polar coordinate function by x and y measurements? If so, what is it? Can it be done for all functions or only a subset?", "label": 1}
+{"snippet": "In what ways did the points made by the writer in the introduction contradicts her conclusion? (In the question listed above, shouldn't \"contradicts\" be written as \"contradict\" - since we are referring to the \"points\" made by the writer?)", "label": 1}
+{"snippet": "Any idea how can I automatically invoke Mathtype from texstudio using macro (javascript) and put the formula back onto texstudio automatically. It can be done manually, but I want to know is it possible to do this in an automated manner like when invoking mathtype from word.", "label": 1}
+{"snippet": "Usually, when we see two letters put together it is to define the pronunciation or to differentiate synonyms or just its foreign origins. But some words don't seem to have any reason to double up. Why does vacuum have two of the letter U? Why does aardvark have two of the letter A? Why does llama have two of the letter L?", "label": 1}
+{"snippet": "In the following sentence, should I use 'who' or 'whom?: An Open Letter To Those [Who/Whom] I Have Hurt I googled the usage and it said to test by replacing with He/She or Him/Her representing Who and Whom respectively. I don't think that applies in this situation.", "label": 1}
+{"snippet": "What is the difference between gain optimization and gains optimization in a financial context? I want to know in particular if one of those terms is better English, or if they have different meanings.", "label": 1}
+{"snippet": "I've come across the phrase \"take tea\" in some sentences, and reckoned it is used as an idiom and not meant literally. For instance, \"Children to compete for chance to take tea with the Mad Hatter.\" That sounds like an interesting pun. What does it mean, and what are its origins?", "label": 1}
+{"snippet": "I'm considering two books to learn vector calculus at a level beyond that presented in standard calculus textbooks such as Thomas' or Stewart's, and more applied than a very rigorous text like Munkre's manifolds. Which one covers more advanced topics? Which one is more rigorous? Which one is more applied? Marsden's or Colley's Vector Calculus?", "label": 1}
+{"snippet": "A person belongs to a different country than the one she is currently in. She is clearly a foreigner/alien. But what is the single word for the discrimination faced by her when the natives of this country constantly call her a foreigner in order to point out that she does not belong here? In other words, what's the word for domicile based discrimination?", "label": 1}
+{"snippet": "Is there a derivation of the magnetic field from the electric field of a charge q moving with speed v? (I know that there are some online, but my limited knowledge in multivariable calculus does not help in understanding such derivations.) I understand conceptually how a changing electric field can produce a magnetic field but I do not understand it mathematically.", "label": 1}
+{"snippet": "Call a set finite if there is a bijection of the set with some natural number, and call a set infinite if there is an injection of the set of natural numbers into that set. How do you prove that sets which are not finite are infinite? Does it require using the Axiom of Choice?", "label": 1}
+{"snippet": "For example, if I wanted to know what the product/coproduct is in a certain category, I could find it on that site. I commonly come across websites (such as wikipedia) that give a few examples of some categorical concept. I would like a site with a large database which is constantly updated.", "label": 1}
+{"snippet": "So I always hear that you can't disturb quantum computers because this will ruin the particles superstate. Well, how do we know WHEN to retrieve the result from the calculation? How can we determine when the calculation is finished, without observing it?", "label": 1}
+{"snippet": "You go to a store and buy a product that sounds like it's the best deal. But then you get it home, and it doesn't deliver. What does deliver mean here? Does it mean It doesn't work as you expected?", "label": 1}
+{"snippet": "Thanks for reading my question. I'm wonder why a symplectic form should be closed. I found many different answers in the internet, but it sounds like a technical requirement (if we omit this requisit, we obtain almost symplectic structures, insteresting as well). Why do yo think? I just want to have a fresh perspective. Thank you in advance.", "label": 1}
+{"snippet": "I recently came across the term encampment. Although I could understand that the word must be very close related to camp, it bugs me that I don't understand why such a long word for the same thing exists. Is encampment a more sophisticated word than camp? The translation for both words refer to the same words in my mother tongue (german).", "label": 1}
+{"snippet": "I'm self-studying now and I've found an exercise. Matt ... while we were having dinner. The correct answer is phoned. But I couldn't figure out why was phoning is not a right choice. There is some logic in this answer because Matt is doing a continuous action. Maybe there is something in usage of while I don't know yet?", "label": 1}
+{"snippet": "Wolfram isn't helping me much so I am curious if there are other programs out there. I don't know what degree it is, but I have a series of numbers and I'd like to determine the linear recurrence function/coefficients so I can find any value I want via matrix exponentiation. Are there such programs for interpolating, and how would I do it?", "label": 1}
+{"snippet": "According to reputable sources, sideburns is a corruption of burnsides, a reference to the Civil War General Ambrose E. Burnside. What was this style of facial hair called before that? I'm referring to side whiskers and a mustache with a clean-shaven chin. Also, is there any difference between the original sideburns and friendly mutton chops?", "label": 1}
+{"snippet": "We know function and its inverse are mirror image about the line y=x and also that their composition is identity function (y=x again) So I was wondering if there is a link? I tried to look up for graphical interpretation of composition of functions but I couldn't fund any.", "label": 1}
+{"snippet": "According to Wikipedia: In the form of a screw jack it is commonly used to lift moderately heavy weights, such as vehicles. More commonly it is used as an adjustable support for heavy loads, such as the foundations of houses, or large vehicles. These can support a heavy load, but not lift it. Insights into its mechanism is greatly appreciated .", "label": 1}
+{"snippet": "Consider the task of extracting a cylindrical rod held by friction in a tightly fitting shaft. Instinctively one would tend to twist the rod around its axis while pulling. The question is, what is the physical basis for this? Does applying a torque reduce the axial force required?", "label": 1}
+{"snippet": "I received an email suggesting that we do something: \"next week, when we would have been\" doing something else. Would you call this an example of future subjunctive? If not, then what? Perhaps it's a present perfect subjunctive? I have been searching for an answer and have found few sites with any reference to a counterfactual statement set in the future.", "label": 1}
+{"snippet": "Let us say I have a single (converging lens) could I use the Abbe diffraction limit (for a microscope) to find its resolution or do I have to use the Rayleigh criterion. (i.e. Is the Abbe diffraction limit strictly for a microscope with more then one lens, or can it be used with only one lens?)", "label": 1}
+{"snippet": "I want to make a cardboard lamp, but i want it to look like half a sphere. Given a cardboard thickness of x, and a circle width of y, how many elements do I need and what radius do the elements need to be? Anyone got a formula for that? thanks alot!", "label": 1}
+{"snippet": "I'm looking for a synonym for the word \"time card\" or \"clock card\". I try to find a word for a card with which you can track your work times on a certain device your employe installs for its workers. I used the expression clock card but a native friend from uk said it is not a common expression. Can u help me?", "label": 1}
+{"snippet": "What I wrote is: \"However, just as any other data carrier, images not only contain important data, but also such of lesser significance to us. \" I want to say that images not only contain important data, but they also contain data of lesser significance. How can I write it without repeating \"contain\" and make the whole sentence sound more natural?", "label": 1}
+{"snippet": "The majority of definitions give the same meaning - \"Pandora's box\" is a synonym for \"a source of extensive but unforeseen troubles or problems.\" Are there any other metaphors or phrases with the same meaning?", "label": 1}
+{"snippet": "A book divided in several chapters/topics, can also be considered to be divided in categories (or have categories)? Not sure if category can be used in this case, or if it should only be used in the context of category theory.", "label": 1}
+{"snippet": "I need a very much physical explanation for the phenomenon of Resonance associated with forced oscillations (damped). I have gone through HRW and Concepts of Physics by H C Verma, but that wasn't of much use for me. I got some mathematical idea of the thing, but still I'm not confident.", "label": 1}
+{"snippet": "If tidal power plants are slowing down Earth's rotation then is it theoretically possible to build a power plant that would drain energy from Earth's angular momentum (thus slowing down it's rotation)? What would such machine look like?", "label": 1}
+{"snippet": "What's the word for the condition in which you have a unusually high body temperature after being exposed to harmful winds without proper clothing protection? It's as if the winds somehow got through your pores and made you sick.", "label": 1}
+{"snippet": "When I spin a penny, I spin it on its \"edge\" (circumference). So why is it that when the penny inevitably stops spinning, it never comes to rest on its edge, instead falling onto one of its faces? It is not a problem with the \"thinness\" of the penny; its possible to balance a penny on its edge in a couple of seconds.", "label": 1}
+{"snippet": "So I was writing a lab report for Physics I, where I was describing projectile motion. I had written Since gravity on Earth does not have a horizontal force, the object will not lose horizontal velocity (velocity in the x direction). Then this made me think, is there any gravitational force found in nature that has both vertical and horizontal components?", "label": 1}
+{"snippet": "Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in the sense that if a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system).", "label": 1}
+{"snippet": "It is known that there are no diproton or dineutron nuclei. Does this mean that two protons or neutrons are not actually attracted to each other? Even if the attraction was weak, wouldn't it cause bound states anyway? Related: What do we know about the interactions between the protons and neutrons in a nucleus?", "label": 1}
+{"snippet": "I have recently heard the term \"Acme developer of IPhone.\" I was just wondering what it stands for? I think I know the meaning: Is it when a developer goes to a client and presents his/her ideas for the app?", "label": 1}
+{"snippet": "Anthony Martin, assistant accountant, PwC, and associate editor, Washington Post. The commas above look a little too much. Are they technically all correct? Which would you recommend removed? I was thinking of removing the one before \"and\" since it looks the most clunky, but feel that comma is necessary here.", "label": 1}
+{"snippet": "Like charges repel. What keeps an electron's charge from repelling itself? This problem would come up if an electron was divisible and its parts had fractional charge. A related question is, what keeps an electron from being divisible?", "label": 1}
+{"snippet": "I got that words from novel. I've been looking for the meaning but still can't get what it means. Is that kind of slang? \"Hi, Mr.Tushman! I see you're running a little behind today! Did your car get rear-ended again? What a bum rap!\"", "label": 1}
+{"snippet": "I have gps trackings that I know they fall into a certain pattern - a line with a known angle. How do I find the line that minimizes the distances of the points from it but is in the correct angle? Unfortunately, I can't post an image for example.", "label": 1}
+{"snippet": "I have a question about the following: Texas is only one of the states that still have sizable wheat production. Texas is the only one of states that still has sizable wheat production. I want to know whether the above construction is true. If so, what is the rule?", "label": 1}
+{"snippet": "Can guilty be used as a noun? For example, as in the title of Chase's novel: The guilty are afraid. Is it that people or folks is understood after guilty and in effect an ellipsis? I do not find guilty marked as a noun in Webster or Wikitionary.", "label": 1}
+{"snippet": "I know you can draw a protractor with TikZ. The problem is that my students use the triangular shaped one like this. So in order to make it a little bit more familiar to them, I am wondering if there is also a predefined one like this one?", "label": 1}
+{"snippet": "Is there a particular word for a joke or a humorous story which has a moral to it? In a way, something that is similar to a fable, but with the humour implied.", "label": 1}
+{"snippet": "I have read several explanations of standard deviation and z-score, I know how to it calculate them but I am not sure what is differences betwen them. Can someone explain it to me? When is suitable to use stdev and when z-score?", "label": 1}
+{"snippet": "I want to have an answer with that question above for my physics lesson. I really don't have an idea about it, so, I ask help from you guys and hope that someone can help me with it.", "label": 1}
+{"snippet": "I would like a way to convert a document from HTML to LaTeX, on a Windows platform. A main motivation of mine is for ways to display books from Project Gutenberg. such as, Wells' The Invisible Man. What is my best option?", "label": 1}
+{"snippet": "I am trying draw a line of distinction between these three events. As I understand it: Ritual is somewhat related to a religion. Festival is associated with a group of people and that brings happiness. Ceremony is something that is followed by a group of individuals before performing a task. Can someone please tell me if I am wrong, and also provide some examples?", "label": 1}
+{"snippet": "In one of his lectures Richard Feynman, a great genius and a 'naughty Bronx kid', refers to to the Coulomb force, electricity as \"the screwing force\". Apart from the obvious joke and double entendre, can you explain that original definition and in what way it is different from other forces or from an EM wave?", "label": 1}
+{"snippet": "Could somebody suggest a single word for 'I think it is right but not exactly sure about it'. I can say 'I am almost sure' but wondering if a word exists with same meaning.", "label": 1}
+{"snippet": "Does present perfect in conditional only mean future situations? Can it be used for hypothetical future? When I went to Africa, I thought as if I have already been there. If you have studied, you would pass the exam.", "label": 1}
+{"snippet": "I was wondering why you would say \"There is people coming\" as you can hear in the last trailer of Game of Thrones. English is not my native language but I'd think that you have to use plural in this sentence such as \"There are people coming\". Is this \"urban\"-talk or am I missing something?", "label": 1}
+{"snippet": "I am not very good at speaking and listening English. Can someone please suggest some songs, which have clear pronunciation of English words, to listen and understand the songs too and also I can use them to improve my vocabulary. Actually very fast music, especially those with too many and loud musical instruments never helped me understanding the lyrics.", "label": 1}
+{"snippet": "What is the physics behind welding iron? It is obviously the electricity that causes the two metal parts to fuse but what is the role of the welding rod and why is it said to damage your eyes when you look at the spark. Is it just the brightness, or does it radiate a specific wavelength that is more damaging, such as UV rays?", "label": 1}
+{"snippet": "The universe is believed to have originated from absolutely nothing, and we know it is still expanding. Physics says \"something can arise from nothing\". I understand how mass and energy are related and one can take the form of other. But, how can everything arise from absolutely nothing?", "label": 1}
+{"snippet": "I am pretty new to Turing Machines and I am trying to understand the basic things first...so my question is , would this machine accept all words ending in 'a' ? if that's the case would the REJECT state be all string without 'a' and ending with 'b' ?", "label": 1}
+{"snippet": "Is this sentence correct? She will grow up hating what she sees in the mirror. Or should it be: She will grow up hating what she will see in the mirror. I think first one is correct, I just want to know why and the rule.", "label": 1}
+{"snippet": "\"packet\" and \"package\" are synonyms when we refer to mailings, but does the same apply to \"network packet\"? My co-worker frequently says: \"network package\". It's like nails on a chalkboard to me, but is it correct?", "label": 1}
+{"snippet": "Which one is more proper to use: 'allocable' or 'allocatable'? Sources say the former is derived from the original Latin word 'allocare', while the latter is a part-of-speech-variant of the English word 'allocate'. Also, is there a standard rule in English to form able-ending adjective of words terminating in 'ate'? Thank you.", "label": 1}
+{"snippet": "I need to find uses and interesting questions by using jacobian matrix for a project work ,can any one help me. I found jacobian matrix is used in dynamical systems, but i didn't understand it.Is there is any question in dynamical systems which is connected to jacobian matrix", "label": 1}
+{"snippet": "I have the same problem like here: How to create custom section titles with a \"<title> <number>\" format in ConTeXt? But I would like to solve it in LaTeX. Is there a simple way to adapt code from the @phg's answer?", "label": 1}
+{"snippet": "If I tell you the real and imaginary parts of the index of refraction for all frequencies, name a property that can't be predicted based on that information. If you're assuming this is a gas, specify your answers to properties measured in gases. Likewise for solid, etc. edit: I see my question is not a good fit for this site: https://physics.stackexchange.com/help/dont-ask My apologies!", "label": 1}
+{"snippet": "I am making a small book and I want to put a phrase in both pages like the picture above, I want to keep the chapter title and page numbers. Could you give me a hand on this?", "label": 1}
+{"snippet": "Well, our professor in class posed a question to all of us: Is frequency a scalar quantity? The obvious answer, of course, is yes, it is, because it does not have a direction associated with it. But then, a scalar is defined as a coordinate invariant quantity. In the case of frequency this obviously fails (the Doppler shift). So how do we classify it?", "label": 1}
+{"snippet": "Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc): For any given set, the intersection with the empty set results in the empty set. For any real number, multiplication with zero results in zero.", "label": 1}
+{"snippet": "I have a question that is short and sweet: Are spectra (both fluorescence and absorbance) of any molecule dependent on temperature? In particular, is the spectral lineshape function of any molecule dependent on the temperature (so, kinetic energy) of the surroundings and possibly itself?", "label": 1}
+{"snippet": "Why is this a wrong Triangulation ? I have to say, we had triangulation at the end of the topology course, so not in details. And the professor only mentioned the basic rules for the triangulation, but in this case, idon't know why it fails.", "label": 1}
+{"snippet": "I was reading the book \"Theories of Integration\" by Douglas Kurtz, and I have a question about the following proof from the book. Specifically, would it be valid to replace the argument that follows \"It remains to show that A satisfies the Definition [of Riemann Integral]\" by: Thanks!", "label": 1}
+{"snippet": "If it's infinite, is it countable or uncountable infinite? I am a newbie to this topic... I don't know what modular arithmetic for polynomials means. Can someone please give me a link where I can learn?", "label": 1}
+{"snippet": "I have problem with sentences structures. I have sentences: I specialize in design wireless and wired network infrastructure, configure devices company's Cisco Systems and MikroTik, and security and techniques used successfully to protect IT resources. Additionally, I have knowledge of voice over IP (VoIP) technology. I am not sure, is this sentence grammatically correct? Thank you in advance for your help.", "label": 1}
+{"snippet": "If one rotates a function such as the sine function about the origin, is there a general method to find the taylor series for the rotated function? Assuming of course that the rotated function is still a single valued function.", "label": 1}
+{"snippet": "I would like to find a mathematical function like the one I sketched below. My first idea was to rotate a sin function, but now I don't think that would work because I would like the function to be well-defined so that for one x, there is only one y.", "label": 1}
+{"snippet": "I understand that the quadratic equation can solve any second order polynomial. Furthermore, equations exist for polynomials up to fourth order. However, without a graduate level degree and a deep understanding of mathematics, is there an explanation of how we can prove that the equations for solutions to a fifth order and above don't exist? Thanks in advance.", "label": 1}
+{"snippet": "Suppose you met a famous person, and you were shy and anxious and almost overwhelmed by them. Is there a word for describing that? Similar to getting stage fright, or \"choking\", except in this case for a person? When he said hello to me, I couldn't respond. I (was) __________.", "label": 1}
+{"snippet": "When two nouns come together like taxi driver, the role of the first noun is noun adjunct. Now the question is what is the second noun's role. I mean the role of driver in taxi driver. Thanks", "label": 1}
+{"snippet": "I feel like it could mean either \"what you are capable of doing,\" or \"what you are willing to do.\" Do one of those better represent the meaning of this phrase or are they both right?", "label": 1}
+{"snippet": "I've been trying to look at stopping times and continuous time change in martingales but have trouble understanding without some concrete examples. Anyone knows of any good references that might be helpful? Thanks!", "label": 1}
+{"snippet": "A wire has cylindrical symmetry, therefore we should consider the possibility of the induced by field in the p,phi and z directions. I know from the right hand rule that we only get a field in the phi direction but I'm not sure how we show that there is no field radially or along the length of the wire.", "label": 1}
+{"snippet": "I wrote the following sentences: Eyed closed, he imagined the moment disintegrating, returning to the stars, and continue existing there for eternity. Eyed closed, he imagined the moment disintegrating, and returning to the stars to continue existing there for eternity. Now, I'm not sure if I should say continue existing there or continuing existing there.", "label": 1}
+{"snippet": "Suppose I somehow know propagator for a given quantum mechanical system but I don't happen to know either the Lagrangian or Hamiltonian. (For simplicity, assume that this is non-relativistic.) Is there a procedure by which I can recover the original Lagrangian?", "label": 1}
+{"snippet": "I used to say cleats but found it uncommon for some people, though I had no trouble with soccer shoes. I have always lived in a Spanish-speaking country (Nicaragua) so I find it hard to know why that is. Are cleats only used in some places? Wikipedia also mentions football boots.", "label": 1}
+{"snippet": "Which is a good book to refresh discrete maths fundamentals for a grad student? It would be great if the book has short and terse explanations of concepts with lots of worked out examples(/to be worked out exercises) to set the brain rolling. Can someone suggest a similar refresher for graduate level algorithms?", "label": 1}
+{"snippet": "Given two latitude and longitude points, the bearing with respect to north of a great-circle path starting at each point, and the distance between the two points, how can I calculate the latitude and longitude of the intersection of the two paths if it exists?", "label": 1}
+{"snippet": "Can anything be stated about the distribution of the digits of Pi, i.e., if I were to sample n digits of Pi, can anything be said about the probability to observe certain digits, or is there any reason to assume that they would not be evenly distributed? This is purely a curiosity question.", "label": 1}
+{"snippet": "Recently I have considered the following question: for a sequence of i.i.d. random variables(maybe normal distribution), the expectation of the maximum of n such kind of variables is dependent on n, so if n goes to infinity, will the expectation of the maximum of infinite i.i.d random variables be infinite? What is the upper bound of it?", "label": 1}
+{"snippet": "What is a polite way to describe a person as \"white-washed\", i.e. a person of visible color who acts and talks and cultured the way a white Western person is. Or is white-washed OK ?", "label": 1}
+{"snippet": "So I am filling out a CV and answering about my education, when it comes up 'year obtained' I have never come across this on a CV before and if I have it hasn't been worded this way. Could someone help me? I am confused about whether it asking me the year I started or left, Thank you.", "label": 1}
+{"snippet": "What would be a good term for the subject of a requirement? If one has a requirement applied to them, they would be the [word] of that requirement. I'm looking for something more descriptive than subject or target. Constrained seems like a good fit, but it feels a bit unwieldy?", "label": 1}
+{"snippet": "Is there a non-collective noun for an \"instance\" of publicity? In other words, a restaurant receives publicity every time a local newspaper publishes a review or an article about it. Each of those articles or reviews are examples of a [blank] for the restaurant?", "label": 1}
+{"snippet": "We know that the ring of analytic function on a connected open set is a Bezout domain. Do we know what happens if we remove the hypothesis of connectedness? It is no longer a domain, but does the ring share the same nice properties like: every finitely generated ideal is principal?", "label": 1}
+{"snippet": "The other day I was talking to a friend about when to use \"middle\" or \"center\". I was using it in the context of top, middle, bottom, as a listing, and he suggested it should be top, center, bottom. I want to know whether it should be middle or center.", "label": 1}
+{"snippet": "I have a feeling that this usage - which I personally find highly irritating, because it suggests either that the initiator of a conversation is helping a person who is in dire straits or that they themselves are in trouble and seeking help from a lifeguard figure - became popular in California, but is that correct?", "label": 1}
+{"snippet": "Recently, I am studying Chinese Zodiac Compatibility. They said \"Snake (one born in Snake year) and Rat (one born in Rat year) are a volatile pair\". I am not sure what \"volatile pair\" mean? like each person can go to different direction in their life or something like that? or they just do not like to each other See the website here http://www.travelchinaguide.com/intro/social_customs/zodiac/compatibility.htm", "label": 1}
+{"snippet": "What are the Ishibashi states and Cardy states in CFTs? I am familiar with conformal field theory language. It would be great if someone can discuss about the basic idea of these states and their applications.", "label": 1}
+{"snippet": "If a rubber ball is red, I know that it is absorbing all colours except for red, which it is reflecting. So there is not actually a part of the object that contains any red. But what tells an object to reflect the light that it does? Is it something in the surface that does not let that wavelength enter it? Thanks.", "label": 1}
+{"snippet": "I have always wondered and once I even got it, but then completely forgot. I understand that gravity causes high and low tides in oceans, but why does it occur on the other side of Earth?", "label": 1}
+{"snippet": "Which of the following is correct when addressing an audience or more than one person? Or are both equally valid? I hope you have all had wonderful summers! OR I hope you have all had a wonderful summer!", "label": 1}
+{"snippet": "Please forgive my stupidity. So many years after my undergraduate study and so many years after dealing with various concrete ODEs and PDEs, I still cannot tell the essential difference between them. What specific belongs to PDEs but not to ODEs? What conclusion for ODEs cannot be generalized to PDEs? At the moment, my understanding is simply that PDEs have more than one variables.", "label": 1}
+{"snippet": "Is it okay to use ain't in formal conversation? I know ain't can be used for am not, is not, are not, have not, has not. So if I can use it in day-to-day life, it will be easier for me I guess.", "label": 1}
+{"snippet": "As an ESL I'm not sure if I can use the following sentences: You can take no other directions. I'm using it on giving indications to a foreigner. Should I use instead: You can't take other directions. Which one do you think it is the most natural/idiomatic?", "label": 1}
+{"snippet": "Can someone give me some information about this area? PDEs on non-cylindrical domains I take to mean parabolic (let's fixed parabolic) PDEs on domains which evolve in time. What is the state of the art on this topic? What kind of problems do people consider? What tools are used for existence and uniqueness? Any recommended papers?", "label": 1}
+{"snippet": "Sometimes I feel uncomfortable to say \"How do you spell xxx ?\". It sounds like asking his or her own way of spelling a word implicating that I am not necessarily expecting the correct answer. Is \"How do you ... ?\" a polite question to ask the right way to do things ?", "label": 1}
+{"snippet": "I'll take the sky diver example. Right when a sky diver jumps out of the plane the net force of the diver is greatest. Then the diver begins to reach terminal velocity where the force of resistance = the force of gravity. So while the force of air resistance increases to equal the force of gravity is the sky diver decelerating?", "label": 1}
+{"snippet": "I am looking for exact or perturbative solution realistic lotka-volterra (the one with logistic term in one of the equations) equations in population dynamics. Any reference where they have done it will be useful.", "label": 1}
+{"snippet": "I'd like to know whether the phrase \"where I be\" is grammatically incorrect or whether it is correct if in the subjunctive mood. If it is in the subjunctive mood, what exactly would it mean? The entire example sentence is: I look for a place where I be free.", "label": 1}
+{"snippet": "Idiomatically we do say \"a strong will\". But can we say \"strong wills\"? The context is The optimism and (the) strong will(s) of the handicapped children touched me deeply. Also, do I need a \"the\" before \"strong will(s)\" in this sentence? Thanks.", "label": 1}
+{"snippet": "Does a direct limit of projective need to be projective? And is the inverse limit of injectives injective? I guess they need not, but I can't find an example. Can you help please?", "label": 1}
+{"snippet": "Is this sentence grammatically correct? [This method] binds a handler to one or more events to be executed once for each matched element. source Is it just a contraction of the following sentence? This method binds a handler to one or more events, that is (supposed) to be executed once for each matched element.", "label": 1}
+{"snippet": "Did Feyman suggest even though Q.M. has great predictive power no one will ever really understand it ? Some people have said there may be hidden variables that explain underlying principles of Q.M. but has this been ruled out? Has Q.M. been put in an axiomatic framework?", "label": 1}
+{"snippet": "I have difficulties in using each. Which would be correct in the following sentences? They are each connected to a hydrogen atom/hydrogen atoms. They each are connected to a hydrogen atom/hydrogen atoms. They are connected to each hydrogen atom/atoms. [Assuming that each of them is connected to one H atom.] We each have our own car/cars. [Assuming that each of us has one car.]", "label": 1}
+{"snippet": "After reading the Wikipedia article about procuration, I'm still confused. Here's what I want to know: What does the author mean by \"the phrase per procurationem is ambiguous if used with undeclinable English names\"? If I sign a letter on behalf of someone, is this protocol acceptable? Sincerely, Secretary's Signature p.p. Account Owner's Name The author implies this method is debatable. What's the debate?", "label": 1}
+{"snippet": "How is the meaning of a sentences affected by chosing one of those words? For instance, what's the different between The screech cicadas reverberated through the forest. and The screech cicadas reverberated throughout the forest.", "label": 1}
+{"snippet": "This is the word problem. If they work together, John and Vince can finish their project in Biology in two days. If they worked individually, it will take John three days longer than Vince to complete the task. How long will it take each to do the job alone? Thanks in advance ;)", "label": 1}
+{"snippet": "In soccer, if a player waits for another player to get into a proper position before passing the ball to him then can I say \"That was a nicely waited pass\" or would that be grammatically correct?", "label": 1}
+{"snippet": "I see the British normally use plural form of the verbs associated with collective nouns. An example, \"The team have fired its coach\" versus \"The team has fired its coach\". I have been told this is slang that has become mainstream. Any idea as to its real origin?", "label": 1}
+{"snippet": "I understand the nature of light can be complex and has extensive theories/experimental data. We hear light can be both a wave and particle, so why can't it be both, a wave of particles?", "label": 1}
+{"snippet": "By this, I mean someone who is not extremely religious, but, in a time of crisis, will turn to religion for hope. An example would be a mother who prays if her daughter is kidnapped, but does not pray on a daily basis. Is there a word for this?", "label": 1}
+{"snippet": "Here are two sentences patterns: Have you ever been to the opera when you lived in Milan? and Did you ever go to the opera when you lived in Milan? What is the difference between them? How can we say, which is right sentence?", "label": 1}
+{"snippet": "My native language has a word for that process hence I am curious to find out if English has one. I searched for it on the Internet without success. Apart from \"removing stem\", I found \"removing leaves\" from cilantro.", "label": 1}
+{"snippet": "Assuming inter-universal (see here) travel is possible, can a perfectly mathematically describable universe exist inside a multiverse? If it could, would that mean that the multiverse is mathematically describable as well? (A perfectly mathematically describable universe would be perfectly predictable as well. Can one predict the future of such a universe when inter-universal travel is possible and the multiverse is not perfectly mathematically describable?)", "label": 1}
+{"snippet": "And if so, then why does everybody keep asserting nothing can go faster than light speed (I'm implicitly assuming there could be something which we do not observe, which goes faster than light)?", "label": 1}
+{"snippet": "Consider a solid yogurt. Can we assign a specific state of matter to it? I mean, it behaves like solid. However, if we \"mix\" it with a spoon, it becomes liquid, or at least in the usual sense. It is also quite plastic, which complicates. My current guess is that it is either a glass or a gel, but I'm quite unsure about it.", "label": 1}
+{"snippet": "Is open mapping theorem true for a analytic function in several variable ? I've encountered a problem, which can be solved easily if that's true. But I couldn't find that after doing some Googling", "label": 1}
+{"snippet": "I am looking for a expression, phrase or word that describes a person or behavior that pretends a mistake made was intentionally done so as to save face. There is a phrase in my language saying \"To pretend that the fall was a technique/stunt\". I am looking for an equivalent for this in English.", "label": 1}
+{"snippet": "And you may not really expect an answer or want/need an answer. Not quite rhetorical. For example you may be talking about something that happened and wondering who did it and everyone knows who did it including yourself but you ask, 'I wonder who that was.'", "label": 1}
+{"snippet": "Sorry for the daft question, but, is the following a correct thing to say? \"The preimage of a function f is a function iff for any element b in the range, there exists exactly one a in the domain such that f(a) = b\" \"A function is injective iff its pre-image is a function.\" Thank you.", "label": 1}
+{"snippet": "While showing my work to my adviser, he uttered a sentence, \"You could do it better!\". Is it analogous to: You could have done better OR You can do it better (so improve it)? It seems to me this sentence can mean both of these.", "label": 1}
+{"snippet": "Is it possible to create a certain design of a conductor to reduce eddy currents greatly? So that the magnetic \"breaking\" can be reduced? Is it even possible for the force generated by the eddy currents to become negligible?", "label": 1}
+{"snippet": "I know that when some of the previously unsolved problems were solved they created new fields in mathematics. May someone explain to me what would be the result of a major problem like the Hodge Conjecture being solved vs a \"smaller\" problem like \"Do quasiperfect numbers exist?\" in today's society. Thank you in advance.", "label": 1}
+{"snippet": "What exactly does a phrase 'we need to take contingency on them' mean? This is an expression I heard from a project manager so I presume it has to do smth with risk mitigation. However, I'd rather not guess. Thanks.", "label": 1}
+{"snippet": "I know there're various types of rhyme in English, such as slant rhyme. There're also things called assonance and consonance. I plan to rhyme \"pan\" with \"screen\". Essentially two monosyllabic words ending with \"n\". Obviously this is imperfect rhyme at best. Is there a linguistic term to describe this type of pairing? If so, what is it called? Thank you.", "label": 1}
+{"snippet": "How would I indicate, for example, that I am going to use \"toms\" to mean \"tomatoes\". Something like: Tomatoes (toms) are red. This is false as some toms are green. I like toms.", "label": 1}
+{"snippet": "Is the usage of \"though\" in the following sentence correct? It's said that it is a picture of a rabbit, but I'm sure enough that what I see is, though, a fish. Don't mind the contents. What I want to ask is whether I can use \"though\" that way or not. If not, why?", "label": 1}
+{"snippet": "\"Small initial discrepancies may not be seen as meet for a federal case, particularly when the employee, trying to succeed in a nontraditional environment, is averse to making waves.\" Is there a legalistic meaning for meet or did the author mean to use the word meat in the text quoted above?", "label": 1}
+{"snippet": "I dont think so, because then the rays will intersect and the image will be real. Please let me know if you know a case in which a virtual image is formed in front of the mirror.", "label": 1}
+{"snippet": "I ask a question about \"What is a wavefront?\" which follows the question \"What makes the radiation behind a slit coherent\". For the wavefront it was answered, that \"In electromagnetics ...(that are) the points that are at the same height.\" Now I'm wondering, are the wavefronts moving?", "label": 1}
+{"snippet": "A lemma in my lecture notes claims, as in the title, given a surjective ring homoromorphism from R to S, ideals in S are the R submodules of S (in the first paragraph - picture attached), but I can't see why this is true. Note that we are assuming all rings are commutative. . Any help very much appreciated", "label": 1}
+{"snippet": "What is (if any) the name of the operation of changing the root of a rooted tree? Picking a vertex which is not the root, then reorienting the edges in such a way that the vertex becomes the root?", "label": 1}
+{"snippet": "I know that through the Abel Ruffini Theorem the general solution to a polynomial of degree five or more cannot be found explicitly. But are there are any other ways to find the roots of such a polynomial besides exhaustive methods like Newton's Method? The question of finding such roots arose when trying to find the the y maximum of the unit lemniscate.", "label": 1}
+{"snippet": "What would you call a triangular object with two sloping, concave sides? See the following image. Consider object A, object B and the entire structure as a whole; object C. What do we call object C? It is related to architecture. I'm trying to describe the structure of an opera house design proposal.", "label": 1}
+{"snippet": "Is it the same as the space of all possible descriptions of a single electron? If not, how do they differ? Please give the mathematical name or specification of this space or these spaces.", "label": 1}
+{"snippet": "What I want to know is: the preimage of an integer by a valuation map is an open set? Otherwise: Can we cover a valuation field by open sets with elements with fixed valuation?", "label": 1}
+{"snippet": "When you say \"I had it coming\", does it always mean \"I caused it to happen to me\"? Can it also mean in an appropriate context \"it just happened to me\"? Also, does it always have to be \"coming\" and not base form \"come\" like \"I had it come\"?", "label": 1}
+{"snippet": "It is preferred to use ipad to create and edit TeX files and use LaTeX. I know some applications to use TeX but they need Internet and are not complete. Is it possible to use texlive on Ipad (IOS)?", "label": 1}
+{"snippet": "A. \"John gave the slogan\". Make it an interrogative sentence with WH-word. Which one is correct? Who did give the slogan? Who gave the slogan? B. \"Grandfather came to meet John\". Make it an interrogative sentence with WH-word. Which one is correct? Who came to meet John? Who did come to meet John?", "label": 1}
+{"snippet": "I found this sentence in Collins COBUILD English Grammar. \"Was the Colonel waved his paper yet?\" I have no clue about what it could mean. Grammar-wise, it looks totally messed up. Is it me not getting something here or might that be an odd sort of error on the publisher's side?", "label": 1}
+{"snippet": "Possible Duplicate: Differences among words describing someone who is expert in many things I just wondered, what could we call a person with deep knowledge in various fields? For example, computers, music, sports, etc. I think I could use sage, but it wouldn't be appropriate if someone is experienced in multiple fields.", "label": 1}
+{"snippet": "Is it the case that for a harmonic function on a graph any value of the interior point is the weighted average of the boundary points? I know that for a harmonic function each point is the weighted average of its adjacent neighbors, but can you extend that to the boundary points?", "label": 1}
+{"snippet": "I'm very curious about how light is created. I'm trying to get back to some type of real understanding about why everything on the sub-atomic level vibrates and the implications for the preservation of both the conservation of energy and conservation of momentum. How is light created at the atomic level?", "label": 1}
+{"snippet": "My primary and most common example is to read something and say (or write) that it \"sounds familiar\". Text has no sound. I'm sure there is a technical term for this practice or phenomenon. What is it?", "label": 1}
+{"snippet": "I'm doing a small research project into these but their Wiki page and other pages I've looked at just detail what they are, and their properties. Does anyone know of any real world applications or some interesting facts besides their properties?", "label": 1}
+{"snippet": "What is the equivalent word for a person who doesn't want to hear/listen others' personal feelings/information. If not, the equivalent word for a person who are stubborn in listening to others' feelings/information. Opposite to the meaning of the word reticent.", "label": 1}
+{"snippet": "Actually, I was seeking for top universities, which has mathematics depart, in Pakistan and I found one, namely Quaid-i-Azam University. Which is known for its Education in \"Natural Science\". Then I apprehend what is Natural Science. So, I started to read the article on Wikipedia about it but I didn't find mathematics in their context. Is not mathematics a branch of \"Natural Science\"?", "label": 1}
+{"snippet": "I'm wanting to make a logic tree using forest that looks something like the picture below: I'm struggling to list the premises of the argument at the first node of the tree in the way that is done in the picture. Any help would be much appreciated!", "label": 1}
+{"snippet": "I understand how spinning tops don't tip over, cf. e.g. this and this Phys.SE questions. What I'm more interested is in identifying the factors that determine the direction the spinning top moves to?", "label": 1}
+{"snippet": "In the same way as when they surround a nucleus? How about when electrons go through wires or are ejected as beta particles? Do they still only have probabilities of being somewhere, or...?", "label": 1}
+{"snippet": "My student wrote in his essay it gives her face a peculiar charm? I tried all the dictionaries at hand (hard-copy and electronic ones) but did not find a definite answer whether this phrase sounds English. Could you please help me?", "label": 1}
+{"snippet": "I am reading about zeta function from book by Ingham. In that book the following theorem is given. I am unable to understand what does he mean by finite part of plane in the statement.", "label": 1}
+{"snippet": "As I decided to use LaTeX to make a presentation and I'm a newbie, I would like a not-very-long tutorial that introduces all features of the beamer class package one can use along with its output. Is there any other package which is preferred over beamer?", "label": 1}
+{"snippet": "Can anyone please help me understand the symmetries of G, where G is the group of the symmetries of the circle. Prove that G has elements of order n for all positive n integers, as as elements of infinitive order. Thank you", "label": 1}
+{"snippet": "I would like to know which fields in physics have seen growth or benefited by applying QFT? I know that approaches to quantum gravity such as string theory use QFT, HEP and also some branches of condensed matter physics. Where is it applied in condensed matter physics exactly? And in what other areas of theoretical physics, has QFT been applied?", "label": 1}
+{"snippet": "In constructing the trace space on a subset of a measurable space, it seems one has to assume that the subset is an element of the original measure space's sigma algebra, i.e., measurable in the original measure space. This is not explicitly given in the problem statement. I have not found a list of errata for this book anywhere.", "label": 1}
+{"snippet": "I've heard in many places, educated people saying \"but nevertheless...\". I think both but and nevertheless have the play the same role. Is their combination, as to emphasize that what follows is opposes to the previous statement(s), allowed? Is it considered redundant or uneducated?", "label": 1}
+{"snippet": "When we put a little pin on the surface of water, it floats; is this because of surface tension or buoyancy? Can somebody also draw a force diagram for me to explain how surface tension of water supports an object. And anybody has any advise for me that I can do any simple experiment to demonstrate water-surface tension?", "label": 1}
+{"snippet": "I'd like to include in my LaTeX code some form of indication that certain words are keywords, or that a phrase is a quote, or that another phrase is an example, etc. Where can I find a list of inbuilt semantic indications like these?", "label": 1}
+{"snippet": "In my search for the definition for the poetry term \"doggerel,\" which I still do not understand, I came across the term \"irregular rhyme.\" Can someone explain the definition of these terms, and how they are used in the literary sense?", "label": 1}
+{"snippet": "I found something called \"Cervantex\" here on this plattform. I tried to Google it, but I have one problem - I don't speak Spanish. So are there anyone who please could tell me, what Cervantex is, and what it could be used to? Thank you in advance.", "label": 1}
+{"snippet": "On Wikipedia we read: dirty money: (idiomatic) Money that is illegally gained, illegally transferred or illegally utilized. Especially money gained through forgery, bribery, or thievery. Is there a precise origin of the idiom \"dirty money\"? Why has the word \"dirty\" replaced \"illegal\"? (perhaps because an author has used it an important novel?)", "label": 1}
+{"snippet": "what does it mean \"to be in receipt of something\"? I have checked the meaning but have not figured it out fully, since I am a translator I need a literal translation for me to build out a meaningful, usable sentence in my own language. Thanks in advance", "label": 1}
+{"snippet": "what will be happen if we put asynchronous generator in vacuum chamber & run it above its synchronous speed. After reaching its over synchronous speed we will cut off electrical supply. Can it run continuously? Can we generate electricity from it?", "label": 1}
+{"snippet": "Blogs and websites typically provide an index page of entries where they show an excerpt of the post. Excerpts usually include title, author, post date, and a blurb. What is the term for these sorts of excerpt?", "label": 1}
+{"snippet": "The text I am studying from seems to suggest that the rank of a quadratic form q on a vector space V is equal to n=dim(V), and I'm confused as to why this is the case.", "label": 1}
+{"snippet": "Is there single word that means \"all seeing\"? From what I can tell, omniscient is often used to cover this, but that more accurately means \"all knowing\". It likely stems from a presumption that if you can see all, you know all. Nevertheless, I'm looking for a word that means specifically \"all seeing\". Would it be something like omnivisient?", "label": 1}
+{"snippet": "QUESTION: Compare and contrast the following distributions giving examples Geometric and Negative Binomial distributions Exponential and Gamma distributions I don't understand how I would answer this had it come in an exam... Do I derive one distribution from the other? Or simply state in the simplest of terms what makes each pair of distributions similar...?", "label": 1}
+{"snippet": "I am about to collect information from multiple sources and transform them into one language/terminology. I wonder what would be the correct term for this process? Maybe a different word would fit even better? Thanks!", "label": 1}
+{"snippet": "Why does each individual photon have such a low amount of energy? I am hit by photons all day and I find it amazing that I am not vaporized. Am I simply too physically big for the photons to harm me much, or perhaps the Earth's magnetic field filters out enough harmful causes such as gamma rays?", "label": 1}
+{"snippet": "I understand the meaning of this word in general, but there's just one question. Here are two examples: We painted even the floor. AND We even painted the floor. Are they correct and if so, do they have the same meaning?", "label": 1}
+{"snippet": "Consider the name John J Doe Jr. If John is the first name, J is the middle initial, & Doe is the last name, what is Jr.? I checked with Webster years ago and they could not find a specific name.", "label": 1}
+{"snippet": "Why each sphere admits an orientation reversing diffeomorphism onto itself? (For even dimensional ones can we take conjugation map?) And why complex projective spaces do not admit? Is there a geometric way to see this without using characteristic classes?", "label": 1}
+{"snippet": "I would like to be able to draw a box that shows up on in the PDF but does not print, just like the boxes around links that are made using the hyperref package. I would like to put a minipage environment with multiple paragraphs inside the box.", "label": 1}
+{"snippet": "I know that we now have telescopes which can capture the images of the stars and galaxies millions of light-years away from us. Does the telescope capture the past image of the star, i.e. the light which it emitted centuries ago? What guarantee is there that the star is still alive? What basis do organizations like NASA plan missions for evading such stars?", "label": 1}
+{"snippet": "If a civilization could build a strong , lightweight tube, hundreds of thousands of kilometers long , could theoretically use it to communicate faster than light, simply by rotating it at one end , the other rotates at the same time , or not ?", "label": 1}
+{"snippet": "Of triangle ABC, I am given the coordinates of two points (A and B) and the angles between the side AB and each of the two other sides. How can I get the coordinates of point C?", "label": 1}
+{"snippet": "I'm writing a project and I am stuck on the last part which I have to explain the usage of mixed and scalar product of vectors, where are they useful, what could be done with them in the future and so on. Where can I find information about this?", "label": 1}
+{"snippet": "From Wikipedia, \"In Norwegian and Swedish, Kraken is the definite form of krake.\" Since \"Kraken\" is already the definite form, why do we add a \"the\" prior to \"Kraken\"? Or \"Kraken\" is a word taken from another language, therefore its grammatical property was dropped?", "label": 1}
+{"snippet": "From etymonline, ingenious, ingenuous, indigenous all share the same roots: in- and indu- mean \"in\", and \"gen\" means \"produce\". But the meanings of the words are not the same. So do you have some ways to remember the differences between their meanings?", "label": 1}
+{"snippet": "We are looking to use this text, as a headline on our sustainability page, on our website. As coworker asked if \"sustainably\" was grammatically correct. I am unsure. TCS believes that thinking sustainably will make our future stronger, to think globally and act locally through a variety of green initiatives Is the word sustainable used correctly, is it even a word?", "label": 1}
+{"snippet": "If you take a look at WolframAlpha, or other computer algebraic system, you will find that it is able to do symbolic manipulation like real humans. For example, if you type in an integral, it can show you step by step on how to solve the integration. What are the algorithms behind all this?", "label": 1}
+{"snippet": "In the textbooks that I read (namely Ashcroft/Mermin , Marder, etc.) it seems that a distinction is made between the correlations in electron gas and a Couloumb interaction between the electrons. What is exactly meant by the concept of correlations? How is that connected to the interactions in electron gas, and how does the screening enters the picture?", "label": 1}
+{"snippet": "Albert Einstein is often considered the most original scientist of the modern age. Even he, though, acknowledged his reliance on the work of others, such Emmy Noether. I have trouble understanding why is it correct to have \"though\" in this sentence.", "label": 1}
+{"snippet": "Want to know if there is a collective word to describe these kind of words that change their meanings in an opposite way (rather than irrelevantly) when a single letter is added/removed/changed so that I can look them up. Otherwise can you provide some examples here? e.g. appeal <> appal", "label": 1}
+{"snippet": "I often read sentences where the idea is \"I would say\" but it starts with \"I guess\". For example: I would say he is not coming. I guess he is not coming. Do both have the same meaning?", "label": 1}
+{"snippet": "Are proton, antiproton, electron, positron the only subatomic particles that can freely exist (i.e. I don't want particles that only exist in bound state as constituents such as quarks) and don't decay, i.e. are stable? What about muons? Are there other particles/hadrons that can exist freely (i.e. not in some bound states) and don't decay?", "label": 1}
+{"snippet": "i want to ask what's the difference between these sentences. Because Can't is present tense and happened is past tense. Could anyone explain it to me thank you! She Can't believe what happened to her. She Couldn't believe what happened to her.", "label": 1}
+{"snippet": "I'd like to have some boxes colored differently from others in a baposter. It seems like a natural way to do this is to allow a specification of some parameters (boxColorOne, borderColor, etc) in the options for headerbox, but I don't know how to make this happen.", "label": 1}
+{"snippet": "A: do you have any questions? B: None so far. Is \"none so far\" a strange English and was it correct to use it in the dialogue above?.I was told by a native speaker that it is strange to use it this way in the dialogue.", "label": 1}
+{"snippet": "What is the origin or history of using \"skin\" to refer to \"money?\" For example, a golf competition called a \"skins game\" or, referring to an investor who, \"has some skin in the game.\"", "label": 1}
+{"snippet": "The arrow of time is usually defined by the direction in which entropy increases. In a closed system, if there's a max entropy that the system can reach, does that mean time stops or at least become undefined at the max entropy state? See also: For an isolated system, can the entropy decrease or increase?", "label": 1}
+{"snippet": "A graph, a chart, and a plot can all refer to the same thing. Is there any even somewhat consistent distinction in these three words? (I mean, in this particular sense of the words; it is not relevant that a chart is also a nautical map, a plot is also a scheme, and a graph is also an unrelated mathematical object.)", "label": 1}
+{"snippet": "I have zero idea what this construction is called. Here are a few examples that I've just whipped up: He was fired, and his friend punished. He was robbed, and his brother kidnapped. The idea is that the second part of the sentence takes the same verb as the first. Kind of like continuity of the sentence.", "label": 1}
+{"snippet": "A Hamilton circuit (or path) is a path that visits each vertex exactly once (except the start/end point) and ends at the starting point. I've stared at this for quite a while and cannot find a Hamilton circuit yet my guide says that one exists. Where is the path?", "label": 1}
+{"snippet": "I need to cite as an endnote (with the endnotes package) twice in the same chapter of a document. How do I do it without introducing twice the reference? That is, how do I refer to the same endnote in different parts of the chapter? Thanks", "label": 1}
+{"snippet": "In how many ways can you break a off a rectangular piece of chocolate from a chocolate bar with m x n squares. [We must respect the structure of the chocolate bar, that is break only along horizontal or vertical lines.", "label": 1}
+{"snippet": "What is an example of a situation where AB is not subgroup of G, when A, B are subgroups of G? My first instinct is always to go for some dihedral group or other...But I could not find an example of a case when the above is true. Maybe I am doing it wrong...", "label": 1}
+{"snippet": "Which of the following is correct: Supplier of tile, stone, tools and equipment or Supplier of tiles, stones, tools and equipment If you could provide an English rule to know that would also be very much appreciated. Thanks!", "label": 1}
+{"snippet": "Is it possible to determine a triangle given its three perpendicular bisectors (meeting at a point which will be the circumcenter) and, say, a point of an edge, or any condition that can make the solution unique, using compass and straightedge? Of course I could put a system of equations, but I'm looking for a graphical procedure.", "label": 1}
+{"snippet": "I came across this symbol on page xix of the book Universal Artificial Intelligence by Hutter: (link to full text of book) It is used for the Solomonoff-Levin universal semi-measure. I've never seen it before, and wondering if anyone can help me understand. Thanks.", "label": 1}
+{"snippet": "I'd like to design a chapter heading similar to the one in the picture below. I like to put a line between the number and the chapter name and also align the the chapter name to the left. I'm using the document class book. Any ideas how to do it?", "label": 1}
+{"snippet": "Is there a word that means \"outdated name\"? For example: Record, although very little music is on vinyl Film, although most movies are digital Horsepower, although no one uses horses as a metric anymore Phone, although it's mostly used to access the web and so on.", "label": 1}
+{"snippet": "In a quad. ABCD with AB=CD, P and Q are mid points of diagonals AC and BD.P and Q joined and extended hits both sides AB and CD at S and T respectively. How can I prove that angle AST=angle DTS?", "label": 1}
+{"snippet": "What are the prerequisites to prove the central limit theorem? In my statistics textbook it is stated without a complete proof, so I guess I need more than calculus. However, do I need more than undergraduate real and complex analysis? In what book can I find a complete proof of the central limit theorem?", "label": 1}
+{"snippet": "I'm at university and I learned linear algebra, set theory, logic, and other kind of mathematics that use functions a lot. Now, I know that function is very important and useful in mathematics but I never asked why we need to define the domain and co-domain of a function? How is it useful? Thank you in advance.", "label": 1}
+{"snippet": "I have this written down in my notes, but cannot seem to find verification of it. How can I see this fact? I believe there is a theorem, something along the lines of if a group G is isomorphic to H then, H is a group. Can anybody verify this or point me to the direction I am looking for? Thanks.", "label": 1}
+{"snippet": "I've been learning homology (and hence Category Theory) and have been interested in groupoids for some time. I've gotten to localization in categories, and that has sparked the following question: Is the localization of a category a groupoid? So going further, isn't localization a functor from Cat (the category of categories) to groupoids (which can be seen as a sub-category of Cat)?", "label": 1}
+{"snippet": "Here is the question: and here is the solution: Can someone please explain it to me - the second line in particular. I don't understand where the limits for the series' come from.", "label": 1}
+{"snippet": "What is the adjectival form of Plato? \"Platonistic\"? For example, in the following sentence: He made the Platonistic statement that there are truths, but there is also the Truth. Or is it incorrect to turn a proper noun into an adjective?", "label": 1}
+{"snippet": "Can anybody explain for me how this structure \"is at its highest level\" is correct. Example : Confidence in the British economy is at its highest level since the Coalition came to power amid signs the recovery is gathering pace", "label": 1}
+{"snippet": "Speaker A: \"You lived in Hawaii? Cool! How was it? Tell me, tell me. Speaker B: \"Haha, it wasn't as interesting as you/you'd think. What's the correct option in this case? Or should I have written as you might think instead?", "label": 1}
+{"snippet": "When did the word 'want' stop meaning \"in need of\" or 'lacking' and begin to refer to desire? (Evidence old phrases with the original meaning like: \"want for nothing\" or \"waste not, want not\".)", "label": 1}
+{"snippet": "How much of a difference would it make if every roof, road and vehicle were painted white? This would certainly reduce the urban heat island effect but how much of a difference would it make to total scattered insolation? Apologies in advance for this the bizarre question.", "label": 1}
+{"snippet": "I'd like to ask if these following sentences have the same meaning ? Hong Kong had been ruled at the whim of its colonial overlords. Hong Kong had been ruled by arbitrary colonial overlords. And what should we infer from the sentences, ruler changes often and randomly or the way of their rule changes often and randomly?", "label": 1}
+{"snippet": "How would I prove that a span of certain vectors is equal to the span of their scalar multiples. The proof would include proving both sets are subsets of one another? Span{x,y,z} = Span{ax,by,cx} where x,y,z are vectors and a,b,c are non-zero scalars.", "label": 1}
+{"snippet": "I use colour diagrams (saved as pdf files) which I include in my LaTeX file. Is there any options in pdflatex to create a gray scale document or a pdf viewer where you can view the document in gray scale? Enabling you to view the document and fix any problems before it gets printed on a non-colour printer.", "label": 1}
+{"snippet": "What are the ways electrostatic charged objects leak charge in humid conditions? Can airborne particles pick up charge by contact, then be repelled hence removing charge? If so would it be a significant factor?", "label": 1}
+{"snippet": "I always get the doubt about this. I know that a bike measures its speed based on the motion of its front wheel. So what is the case with train? Is it same principle? Then what about an airplane? Is it by radars?", "label": 1}
+{"snippet": "In the novel A Day Among The Liars by Edward Page Mitchell, there is this sentence: \"My rod creaked and bent double,\" a stout, red-faced gentleman was saying, \"and the birch spun like a testotum.\" Please can anyone explain the meaning of \"birch spun like a testotum\"?", "label": 1}
+{"snippet": "Have we as of yet been able to calculate the space-time curvature around a galactic (or idealized) disk? I have not heard of or been able to find this. Is it even possible to calculate anything meaningful, either analytically or numerically? What I'm curious about is the shape near the disk itself, either ignoring dark matter or including some halo configuration", "label": 1}
+{"snippet": "What is good dictionary software? I am asking about the ones that can be downloaded and used on Windows machines, and not online websites. I thought Word Web is a good one, but are there any advanced and good dictionaries?", "label": 1}
+{"snippet": "When somebody talks in a way where they swallow parts of a word, talk very fast or talk in a way that is difficult for most listeners to comprehend, what do you call the way this person speaks? I'm looking for an adverb that conveys the meaning \"unclearly\", \"mangled\" or just \"ununderstandbly\" (yeah I know it's not a word).", "label": 1}
+{"snippet": "Which degree of 'less' is correct in the following sentence - \"Seats in this room are much less/lesser in comparison to the adjacent one.\" Also please state any general rule of English if it is being applied here. Thanks.", "label": 1}
+{"snippet": "Is the phrase ... because of my current educational and residential situation a correct way to refer to where and why I study what I do and why I live where I do? Or should it be \"education and residence situation\"?", "label": 1}
+{"snippet": "Recently, I was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the idea was silly. But I then googled it and found this article. Is this idea really compatible with other theories as the article mentions? Is there any chance of this proposition being true?", "label": 1}
+{"snippet": "Does anyone have suggestions for books, or lecture notes, (or videos) for studying pullback rings? I know definition; and a few facts about it (for example when it is Noetherian). Now I want to start for learning it. I'm not good at category theory, so please consider this in your answer. I've read Bruns-Herzog's book an I'm familiar with homological algebra. Thanks a lot!", "label": 1}
+{"snippet": "Is the comma used correctly in these two sentences? In order to sign and return the documents to us with EchoSign, the two initial boxes marked in red will require your initials. In any case, there are two initial boxes marked in red which will require initials, in order to sign and return the documents to us with EchoSign.", "label": 1}
+{"snippet": "Write the best verb-form for the blank. A: Who have you worked with? B: I ________ with people from all over the world. The intended answer is 'have worked'. One of my students answered, 'have been working'. Of course it makes sense. But do you think 'have been working' can be called the best form for that blank above?", "label": 1}
+{"snippet": "I almost hesitate to ask this, because it is hard to believe no one else asked it; but it isn't showing up in the \"similar titles\" list. What is special about 'C' that switches the 'IE' immediately following it?", "label": 1}
+{"snippet": "When two systems are in thermal equilibrium, this means that there is no heat flow between them. What is the analogous definition for mechanical equilibrium? (I know that in mechanical equilibrium the pressure of the two systems must be the same, like temperature in thermal equilibrium, and this is not the definition I am after)", "label": 1}
+{"snippet": "Let's imagine, I'm speaking about someone's three specific cars, which are over there, there, and there. Now I'm saying that I have installed a new sound system in all of them. Which is right: [...] I have installed a new sound system in all the three cars. [...] I have installed a new sound system in all three cars.", "label": 1}
+{"snippet": "There is well known gravitational redshift of real photons. What about gravitational redshift of virtual photons of charged neutron star? Is electrostatic force become weaker while mass of charged neutron star is growing? How can electrostatic field of a charged particle swallowed by a black hole escape from the event horizon? How can charged black holes exist at all?", "label": 1}
+{"snippet": "Here I have some basic questions about max-plus algebra. How this is useful? Why we need to define a different algebra? What aspects are highlighted in this which were untouched in conventional algebra?", "label": 1}
+{"snippet": "The computational algebra system MAGMA has a function called Order. What it does is find the multiplicative order of its argument, which must be a nonzero element of a field. This question is asking about how this order is calculated. Can anyone point me to a reference explaining that or explain that to me in an answer?", "label": 1}
+{"snippet": "When light passes from a more dense to a less dense substance, (for example passing from water into air), the light is refracted (or bent) away from the normal. My question, is there any theory that i can say precisely why light go away from normal or get closed to the normal.", "label": 1}
+{"snippet": "I want to draw Hermite-Gaussian modes using tikz, all that is really needed is a blurred circle and blurred lines that overlay splitting it into different sections as shown in this picture: I am not even able to find a proper way of doing the first one, since all blurring options i have found so far are not smooth enough.", "label": 1}
+{"snippet": "I am having trouble coming up with an example of spaces where there exists a weak homotopy equivalence in one direction but not the other. Any hints or references are greatly appreciated! Note: This is an instance of stagnating autodidactic studying, hence no home-work tag.", "label": 1}
+{"snippet": "I'm writing a story for my English class. Does the following sentence effectively mean that she had a good figure behind her dress? She hid quite a figure behind the Wardrobe. Does it apply to both male and female?", "label": 1}
+{"snippet": "I wanted to convey that a university degree is true and valid, but I am not sure if the word \"established\" can be used for the degree itself. Any suggestions on which words I can use to convey that same meaning for a \"degree\"? Can I check if it is the word \"established\" can be used for an educational program?", "label": 1}
+{"snippet": "I am trying to write a class based on the book class (a thesis class for my department). My question is: is it bad for some reason (or, is it considered bad) to use packages in the class files instead of more primitive TeX / LaTeX commands? For example, should I use the geometry package or the relevant primitive commands?", "label": 1}
+{"snippet": "I understand that playing a square wave from speakers cannot produce a PERFECTLY sharp division between compression and rarefaction. But it's sharp enough to sound distinctly different from a sine wave. As it travels, does the wave \"smoosh out\" even further as it travels, changing from a square wave into something closer to a sine wave?", "label": 1}
+{"snippet": "Is rate of change of velocity wrt distance and rate of change of velocity wrt time the same thing?If both are same can we define acceleration in the former way? Please explain using calculus.", "label": 1}
+{"snippet": "I want to know the difference between already and yet in this example: I was surprised that they had __ to decide what to do. My answer on this question was already and my teacher marked it as a wrong answer in the test. What's the difference between already and yet in that sentence?", "label": 1}
+{"snippet": "Can you help me explain the meaning of the phrase \"ascend to rule the heavens on\" in the sentence below? Myth was born in Thebes of Geb and Nut who ascended to rule the heavens on their death.", "label": 1}
+{"snippet": "Usually from books, Rayleigh scattering only refers to the light scattering by neutral atoms or molecules. For example if I want to measure temperature or number density in combustion using Rayleigh scattering, and a lot of combustion intermediate species are not really neutral, do I have to take care of the scattering signal from ions? Same question to plasma measurement because of ionization. Thanks.", "label": 1}
+{"snippet": "I thought during this transition only the potential energy increases as energy is used to weaken the van Der Waal forces between the molecules. And that the internal energy is only dependent on the change in kinetic energy . So why does internal energy increase? Thankyou for the help.", "label": 1}
+{"snippet": "Ex. He threw the grenade, but it blew off part of his leg. He wasn't expecting any case of _______ damage, but that's what you get when you're reckless. Is it \"collateral\" damage?", "label": 1}
+{"snippet": "The diagonal entries of a triangular matrix are the Eigen values of the matrix as per the theorm. My question is why not convert the given ordinary matrix into a triangular one by row reducing it and now the diagonal entries will be the Eigen values of the matrix", "label": 1}
+{"snippet": "These words are all more or less interchangeable, but I'm wondering which is most distinguished. If I have a group of representatives, but some are the leaders of their groups and others are just regular members of their groups, or some are from influential groups and some are from uninfluential groups, which terms would I use to hint at who is most important?", "label": 1}
+{"snippet": "Are there any significant differences in meaning or usage between \"everyone\" and \"everybody\", or \"anybody\" and \"anyone\"? As far as I know, there are some grammatical points involving \"everyone\" and \"everybody\", or \"anybody\" and \"anyone\", but books/internet/professors cannot identify any differences of meaning or usage between these two pronouns.", "label": 1}
+{"snippet": "Impossible to automatically generate BibTex keys using Ctrl-G as I did it with the previous version of JabRef. It seems that there is a bug in this issue of Jabref. Please help me...", "label": 1}
+{"snippet": "I am reading some lecture notes (completed with exercises and competition-like problems) provided by my college professor, but I would like to study probability from a proper book. Can you suggest one with good problems and clear rigorous style?", "label": 1}
+{"snippet": "Is there a non-gendered term for manning a station, as in manning the desk? The only ideas I can come up with are \"stationed at\" the desk or other clunky things. Finding the right gerund would make my day.", "label": 1}
+{"snippet": "I have a vague idea of the three words kill, murder and slay, but I am not sure exactly what makes the verbs different (as well as the nouns killer, murderer and slayer). When do we use each of them?", "label": 1}
+{"snippet": "Possible Duplicate: Typesetting algorithms in LaTeX like Knuth Does anyone know if there is a style that mimics Knuth's The Art of Computer Programming? Baring that, would anyone know how to customize the memoir class to get an analogous result?", "label": 1}
+{"snippet": "Using natbib, how can I obtain a full reference inline in the body of a document? I need to include the full reference, not just the citation, at the beginning of a chapter.", "label": 1}
+{"snippet": "I know that there is a noun for cancer as an area of medicine: oncology. But is there a word for things under the umbrella of the art and science of cancer treatment? I was thinking of something other than \"cancer therapy.\" Something like \"oncologics\", although that's not actually a word.", "label": 1}
+{"snippet": "Are there contra variant and covariant vectors or are there only contra variant and covariant basis for vectors and these basis transform into further contra variant and covariant basis respectively according to certain co-ordinate transformation laws, keeping the vector as it is, which can be viewed as an arrow ?", "label": 1}
+{"snippet": "I have a beamer template provided by my university. I want to edit it such that there is a table of content in all slides at the left side. For simplicity, we can consider a plain template and if anyone helps me on this template, I can build it according to my template. Thanks in advance.", "label": 1}
+{"snippet": "While reading one of the technical books I encountered \"the remainder of the text will explore how the .NET framework...\". From the context I understood it means \"the remaining text of the book will explore ...\". Is there any difference between them or why is one used over the other?", "label": 1}
+{"snippet": "I recently heard an American presenter using the phrase \"discover what it is that is important to you.\" What is the linguistic difference between saying \"what it is that is,\" rather than \"what is\"?", "label": 1}
+{"snippet": "Given that the atmosphere of Titan is mostly methane, and from a comment on this TED talk... Would it blow up from a lighted match-stick? Seems like it's at least plausible. But, wouldn't the lack of oxygen hinder this event? Or perhaps I'm confusing the blow up with combustion?", "label": 1}
+{"snippet": "Shall I use do or make together with statistical inference? Refering to this site, do is used \"when someone performs an action, activity or task\" and make for \"constructing, building or creating\". In my understanding of \"statistical inference\" it can be both: the action of drawing conclusions and the results of this process. So which one shall I use?", "label": 1}
+{"snippet": "I want to refer to a report available on a particular site. Although some human being must have compiled the report, but there isn't any reference to any specific name. Which BibTeX attribute should I choose for such citing.", "label": 1}
+{"snippet": "In the song Tonight Again, there's a line going They may be right but only maybe I understand that \"maybe\" is an adverb, while \"may be\" is a combination of the verbs \"may\" and \"be\", as mentioned in this question. However, is there any difference in the degree of certainty between the two, as might be suggested by the \"but only\"?", "label": 1}
+{"snippet": "I'm looking for a way of creating glossaries, with the help of glossaries package, per chapter or section. In a particular glossary for section should be only the terms used in this section. If term is used in multiple section - appear in correspondent glossaries. Example (done with the help of description environment, just for an example): How can I achieve this?", "label": 1}
+{"snippet": "I'm looking for the word that means certain words when placed together sound bad. Example: Mary is sad because she had bad luck. Better wording: Sadness engulfed Mary after she experienced misfortune. What is the word that means example numer one SOUNDS awkward?", "label": 1}
+{"snippet": "As you probably know, electrical current and magnetic fields are close friends. In an iPhone there is a compass, however there are also lots of cables and in all of them, or at least in most of them passes a current. How come the current doesn't drive the compass away (and far) from the real north?", "label": 1}
+{"snippet": "For people who go an extra mile to make others comfortable, be it friends, family, etc. I need an adjective or a noun, most probably one word, that can describe people who always keep others above or ahead of themselves.", "label": 1}
+{"snippet": "Given these two versions of a sentence: For many people, dogs are the best friends. To many people, dogs are the best friends. I have following questions: What is the difference between using for and using to for this sentence? Are both versions grammatical? If not, which one should be used and why?", "label": 1}
+{"snippet": "I want to create epub document, but I only have a tex file (unfortunately, mathematical formulas, and drawing diagrams). I tried pandoc: tex to html, tex to xhtml, to xml, but nothing works properly. I use tikz. You can do the epub file with png or svg? Some ideas?", "label": 1}
+{"snippet": "We have an idea to post short ads like \"our company is hiring\" in company blog posts. The company develops software and one of duties of people we want to hire will be finding, locating and fixing bugs in programs. Can we refer to such people as \"bug assassins\"? Won't \"assassin\" word have some negative meaning?", "label": 1}
+{"snippet": "I have a general question about the applications of mathematics. What are some applications of mathematics that are not scientific, perhaps maybe literary or philosophical, or political. I am basically asking for the scope of mathematics, and looking for concrete examples.", "label": 1}
+{"snippet": "How are the external magnetic field intensity H, magnetisation M and the entropy related to each other? i.e. if I change the magnetic field intensity by dH what will be the change in entropy dS in terms of M.", "label": 1}
+{"snippet": "If repeatedly picking a random element from a set, what is the expected number of times I'd have to pick before seeing all the elements of the set? Edit: when picking an element, it is simply counted and not removed from the set, so it can be picked again.", "label": 1}
+{"snippet": "After the spontaneous breakdown of local symmetry in presence of gauge fields (Higgs Mechanism), we can always choose a gauge where the Goldstone bosons are eaten up by the gauge field (also called unitary gauge). Which Lagrangian should be used for physical calculations-(i) the one in which goldstone excitations are present or (ii) the one in which they disappear?", "label": 1}
+{"snippet": "I'm working on an optics project that I'm using Fresnel Equation for Intensity. but I've got a question, is copper a non-magnetic ? You know because in Fresnel Equation, for non-magnetic materials which their refractive index is a real number, the formula is more simple. Thanks in advance", "label": 1}
+{"snippet": "What is the perfect word for the clicking sound which happens when you stretch your bones? When chiropractors try to do adjustments, we can hear a clicking sound on the bones. What is that sound called?", "label": 1}
+{"snippet": "I'm writing a CV and in one section I'd like to enumerate the activities I did. Should I write I proved ... I participated ... I mentored ... ... or Proved ... Participated ... Mentored ... ... or Prove ... Participate ... Mentor ... ... or any other better form for the verbs?", "label": 1}
+{"snippet": "I've solved a bi-objective optimization problem by means of NOMAD solver from OPTI Toolbox and as a result I've obtained a Pareto frontier: How to interpret the visible \"gap\" in the Pareto frontier?", "label": 1}
+{"snippet": "I am looking for a proof of the next theorem: \"If the higher order time derivative Lagrangian is non-degenerate, there is at least one linear instability in the Hamiltonian of this system.\" Where Non-degeneracy means that the highest time derivative term can be expressed in terms of canonical variables.", "label": 1}
+{"snippet": "Every source I look at online says something vague about Church's notion being equivalent to Turing's, but what exactly is the Church-Turing thesis? As I understand, it attempts to precisely define the term \"algorithm,\" but my understanding is not very strong of this concept.", "label": 1}
+{"snippet": "What do you call nature words ending in -land? For example, moorland, wetland, marshland, woodland...You get the picture. Is there a name for such things? And is there one for a place that is surrounded by water/made up of shores of lakes/rivers/streams besides wetland?", "label": 1}
+{"snippet": "What is the difference between prevention and avoidance? Can you give generic examples? The reason for my question is, that I want to know the difference between preventing and avoiding a threat against a (technical) system.", "label": 1}
+{"snippet": "I often say What is an idiom? When I read Longman Pocket Idioms Dictionary Cased, I saw the sentence What are idioms? Are there any differences between the two forms? Which one is preferred?", "label": 1}
+{"snippet": "I'm aware of this question, where most answers point out how to externalise the TikZ parts in some way. I want to know which journals actually accept TikZ in submissions, and possibly which versions.", "label": 1}
+{"snippet": "If a body A needs to be charged by a charged body B by process of induction, then why it's necessary that A must be a conducting body or must have a free electron. Also what is major difference between Induction & Polarization of a body. Experts please explain me it in detail.", "label": 1}
+{"snippet": "Where in the analytic hierarchy is the theory of all true sentences in ZFC? In higher-order ZFC? In ZFC plus large cardinal axioms? Edit: It seems that this is ill-defined. Why is this ill-defined for ZFC, but true for weaker theories like Peano arithmetic and higher-order arithmetic?", "label": 1}
+{"snippet": "I had read that light does slow down in glass because photons interact with atoms in glass. They are absorbed and re-emitted and during this phenomenon it's speed decreases. See also this and this Phys.SE post and links therein. But then why does it bend? It has confused me a lot! Furthermore i have very little knowledge of Optics or Physics as a whole.", "label": 1}
+{"snippet": "I need a word to say to the person that apologizes for something that they didn't do but feel responsible for. The word word mean: \"I accept your apology, but it is not needed. (you, are entirely fine!)\"", "label": 1}
+{"snippet": "My significant other tells me that I'm not \"going to go\" to the shops, I'm \"going to\" the shops, and beats me mercilessly when I say that. Is this not correct? I might not be going to the shops until later, is my point!", "label": 1}
+{"snippet": "Derive the MLE for Bernoulli distribution? Just need help studying for a test tomorrow and this is a question on the practice exam. I think I will get a question on this just with a different distribution so can someone help me?", "label": 1}
+{"snippet": "The defining property of the A series paper is that when a sheet of paper (represented by a rectangle) is cut in half, both of the resulting rectangles are similar to the original one. Are there any other shapes or solids that have this property? Google is silent.", "label": 1}
+{"snippet": "This famously known fractal has infinitely many circles, however I find it hard to find a rigid proof that confirms how or why this fractal is composed of infinitely many circles (and only circles). What if, at one point inside the circle, there comes a point where no proper circle that is tangential to the other circles in the fractal can be constructed?", "label": 1}
+{"snippet": "Is it \"superior of\" or \"superior to\"? In a sentence: We conclude that our proposed model is superior to the base case. or We conclude that our proposed model is superior of the base case.", "label": 1}
+{"snippet": "Yes, we can easily explain to all intelligent adults why the Earth looks flat, when it is actually round. But my question is, how can we explain this fact, that the Earth is round, to those people who will not accept new data, which contradicts their knowledge, by providing them with some proper facts?", "label": 1}
+{"snippet": "Is there an adjective meaning attainable through aural practice? As in \"This language skill is more easily attainable through aural practice.\" That is, the more you listen, the more that skill develops. Is there a single word you could put in the blank in \"This is a/an ...... skill\"", "label": 1}
+{"snippet": "If time moves more slowly on Earth (due to our proximity to a gravitational body) than for someone orbiting Earth in a spaceship, yet the opposite occurs in the frequently cited \"twin paradox\" of the earth-bound twin vs. the twin in the fast-moving spacecraft, then my question would be this--is the slowing of \"time\" the same as the slowing of molecular/atomic motion?", "label": 1}
+{"snippet": "If gravity is this \"unexplainable force\" that pulls everything to the center of a planet or stellar remnant you stand upon, why doesn't gravity pull itself? If gravity affects anything with energy, why doesn't gravity affect itself? Gravity is energy, right?", "label": 1}
+{"snippet": "Wikipedia give this answer \"Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples (\"models\") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes \"the theory of groups\" as an object of study.\" Can someone please explain the difference in more specific terms.", "label": 1}
+{"snippet": "What does a rotating hoop, with each point moving at a velocity close to the speed of light, appear like with respect from a stationary observers perspective. For example how does the shape of the hoop change? (Note, I'm not intending to ask about optical effects, but rather what physically happens, analogous to length contraction of a moving train.)", "label": 1}
+{"snippet": "I am doing homework and I got confused about this phrase when I was writing. I am not a native English speaker. (...) and the only way to do this was taking control of everything and being authoritarian towards the people who/that could not do anything about it. I would be grateful if you help me clarify which word should I use.", "label": 1}
+{"snippet": "I would like to know if there is any global command that would prevent any page-breaks inside sections. All my sections are short enough. I read some solutions, such as Absolutely, definitely, preventing page break, but I would like an automatic solution.", "label": 1}
+{"snippet": "I was at an Model UN conference and often notes like the following get passed. As I'm not a native speaker, I assume that this has to do with some pronunciational issue. Can you please explain what's so funny about this sentence? (Djibouti seemed to be often used in such context.) If Bangkok invaded Djibouti would Greece help?", "label": 1}
+{"snippet": "This is an exercise following a discussion of fibrations. preceding that there was a discussion of cofibrations and the long exact sequence of homotopy groups of a pair. Any hints would be greatly appreciated. Thanks for your time.", "label": 1}
+{"snippet": "Is there a simple term for the question this one was closed as a dupe of other than \"the question this one was closed as a dupe of\", because \"the question this one was closed as a dupe of\" is pretty long and unwieldy and much in need of a simpler term than \"the question this one was closed as a dupe of\".", "label": 1}
+{"snippet": "For an event, I would like to add next to the name of some participants, that they \"will be there\". For example, Mr. AAA Mr. BBB (will be there) Ms. CCC Can any one suggest a better, professional replacement for \"will be there\". Thanks in advance.", "label": 1}
+{"snippet": "I need to copy (with small editions) the shown definition in my own document. I don't have the source code of this pdf, so I don't have any idea which environment/package/etc. should be used to create the definition in same style.", "label": 1}
+{"snippet": "Can we write down a generic expression for propagator for any arbitrary spin? At the least, about the ultraviolet behavior of these propagator. Especially, I would like to know whether there is a specific dependence on spin of the field.", "label": 1}
+{"snippet": "What is the idiom for a guy/situation who/where has his own lacking but still mocks others? Like you are poor but you laugh at a rich man who has just become bankrupt. For example, suppose like this \"A drainer mocks at a needle\". Explanation: A drainer has hundreds of pores, but he is mocking at needle's only one hole.", "label": 1}
+{"snippet": "At the temperature range of ordinary fire or maybe even ordinary boiling water, is the Coulomb potential between light atomic nuclei occasionally overcome to give way to fusion? Basically, how are the nuclear fusion cross sections calculated and are they a function of temperature?", "label": 1}
+{"snippet": "When am I supposed to use the terminology of EM \"wavenumber\", instead of \"wavelength\" (or frequency)? The concepts of wavelength and frequency are no problem for me, but wavenumber (number of wavelengths per unit length) seems redundant to me as a student engineer and proto-physicist. And then there's use of energy levels at higher frequencies.", "label": 1}
+{"snippet": "There is a nine digit number . If you delete the digit at its unit place the remaining number would be divisible by nine, if you delete the digit at its tenth place the remaining number would be divisible by eight and the process continues. all the digits of the number are unique...what is the required number?", "label": 1}
+{"snippet": "LatexDraw is a PSTricks code generator for Latex. LatexDraw generates PSTricks codes of any fugure are drawn. Are there any such tools that will generate pgf-tikz code of any figure for latex? If yes please suggest me. Thank you in advance.", "label": 1}
+{"snippet": "I considered 'self-proclaimed' but that, I believe, suggests an element of self-promotion (the proclamation aspect) whereas soi-disant, at least as I think of it, is more about self-presentation and in some contexts self-deceit.", "label": 1}
+{"snippet": "I'm writing a document where I had to change all instances of the variable i to x and the document is already considerably long. Is there a editor that will allow me to do this, or in general, replace text inside math environments?", "label": 1}
+{"snippet": "This is a follow-up to Do Lipschitz/Hurwitz quaternions satisfy the Ore condition? Jyrki Lahtonen answered the question in the positive by noticing that every right principal ideal in either ring has a non-empty intersection with the center. Does this property have a name? Has it been studied? Are there Ore domains without it? Are there cancellative Ore monoids that don't have this property?", "label": 1}
+{"snippet": "Backlog/noun an accumulation of uncompleted work waiting for you when you return from vacation . It's a pity that we don't have \"forelog\" as a word for work that is done to clear one's desk before a vacation. What are the some alternatives to define all the work that is done to clear one's desk before a vacation?", "label": 1}
+{"snippet": "I keep hearing about big bang, but there are no white holes and no black hole has been observed exploding. So is there a point in which a black hole reaches critical mass?", "label": 1}
+{"snippet": "I'm writing my PhD thesis in latex and learned a lot from this forum. However, I could not find an answer to the question how do I put an decorative hook before the chapter title. I think that it looks rather nice to have this but thats personal.", "label": 1}
+{"snippet": "What is the covariance matrix of the product of a random scalar and a random vector in general (if any) and in all special cases, in terms of the variance of the scalar and the covariance matrix of the vector?", "label": 1}
+{"snippet": "What is the currect research status of solving Navier-Stokes Equation, any up-to-date review/good paper on this topic? Or direct numerical simulation is still the best way to understand the complexity of turbulence? Thanks", "label": 1}
+{"snippet": "\"I touched their forehead[s] with my fingertip.\" I'm not certaint whether or not forehead in this example should be singular or plural. There's a group of people, so obviously, multiple foreheads are being touched. However each individual person only has one forehead.", "label": 1}
+{"snippet": "Wikipedia says: Having an eigenvalue is an accidental property of a real matrix (since it may fail to have an eigenvalue), but every complex matrix has an eigenvalue. Yet, IMO, real matrices are subclass of complex ones. So, even without having any mathematical degree I see that this cannot be true.", "label": 1}
+{"snippet": "(I'm new to latex and don't know the right keywords to search.) I would like to put a header and footer lines to my figures (floats), instead a framebox, since they sometimes takes longer than a whole page. Any suggestions? I want the result to look like:", "label": 1}
+{"snippet": "The pulley is with a finite mass. The two blocks, hence, have different tensions exerted on the rope. My question is do the two blocks have the same acceleration ? I would like a reason for the same.", "label": 1}
+{"snippet": "In a recent question, it was stated that particles in high pressure air always flow to lower pressure. In a pipe with a constriction, fluid flows from from low to high pressure after the constriction. (From here.) How are these concepts related?", "label": 1}
+{"snippet": "let f:R->R What is the range of the function f I think it is(-infinity to infinity). But i am confused because p/q is in their lowest term. Can Someone please help me, Thanks in advance", "label": 1}
+{"snippet": "I'm looking for a word that means: bigotry against, or disdain for, uncouth people. ('Misanthropy' is too general, I think.) This would sort of be the converse of anti-intellectualism. By 'uncouth people', I mean people who (example) might casually toss litter into the street and not give it a second thought, etc.", "label": 1}
+{"snippet": "I asked a similar question about bubbles making less friction on a mass moving through water, now I'm wondering of sound waves could do the same thing as supercavitation or possibly create it's own propulsion with the right combination of frequencies.", "label": 1}
+{"snippet": "I was working in products of structures and I am trying to find a counterexample to the following: \"the product of totally ordered sets is a totally ordered set.\" Unfortunately I could not find one. Can someone provide me with a counterexample?", "label": 1}
+{"snippet": "Should I use You are granted the choice to either be my friend or my enemy. or You are granted the choice of either being my friend or my enemy. ? It's for my poem and I want to double-check.", "label": 1}
+{"snippet": "I think the expectation is a function of random variables. I also know that a function of a random variable is a random variable. So the expectation is a random variable? But I also know the expectation is a constant. I am confused about this.", "label": 1}
+{"snippet": "Do all the planets in our solar system have the same angular speed? Physics teacher says yes, my research is not crystal clear. I want to make sure I have the right information for future reference.", "label": 1}
+{"snippet": "To explain the matter-antimatter assymmetry, CP should be violated according to Sakharov conditions. Charge conjugation is required as matter and antimatter have opposite charges but why Parity Violation? Is it because they have opposite chirality as well? Isn't it model dependent?", "label": 1}
+{"snippet": "Is there a term for a person who by local standards is normal in his/her behaviour? I mean a person who tends to like the same sports, same teams, same music, and same hobbies. Because in El Salvador people are like that, and I call them (in my mind) very generic, trivial, and boring.", "label": 1}
+{"snippet": "Let M be a surface M, i am concerned with Abelian covers. These are the covering spaces for which the deck group is Abelian. The largest such cover corresponds to the commutator subgroup of the fundamental group , in which case the deck group is the homology group. I would like to know how to construct it for a genus two surface.", "label": 1}
+{"snippet": "For as long as I can remember, I've only used the word 'delete' in a technological context. I'm fairly certain, most kids--or the generation before them--know exactly what the word means. Did this word get much use in other literary works?", "label": 1}
+{"snippet": "Is there an idiom or word for describing the moment or situation when governments blame some unknown power(s) for bad results caused by their own actions? These governments try to acquit themselves by blaming these nonexistent, external powers.", "label": 1}
+{"snippet": "I'm not sure, but I'm being asked to describe the set of points that are in this neighborhood of a circle with radius r. here is the only thing I can think of ...which is the equation of a circle with epsilons added to the y...It seems incorrect.", "label": 1}
+{"snippet": "In the context of the following sentence: \"This report gives an overview of x, which took place between the second and final year of my degree from xmonth to ymonth.\" Should I be using the word year or years? I'm inclined to choose the latter, as I am referring to two years and not one.", "label": 1}
+{"snippet": "Why does \"used to\" mean \"accustomed to\"? Why is \"used to\" used to indicate a recurring past event? In I used to be used to using it. there are three meanings of \"use\". I ask about the etymologies of the two bolded meanings.", "label": 1}
+{"snippet": "What's that word meaning 'thus more strongly'? As in X applies to Y, and thus even more strongly to Z. E.g.: The body's immune system needs warmth, so adequate heating is good for you (and [this conclusion follows with even more force] for sick people) I seem to remember that there is such a word, and it's Latin, though I could be wrong.", "label": 1}
+{"snippet": "The Wikipedia article describing the electromagnetic stress energy tensor seems to suggest that this tensor can only be defined in flat space-time. How is it possible to define an electromagnetic stress energy tensor this way since any available electromagnetic energy/momentum must render the space-time curvature nonzero? How in practice would someone extract useful information with this stress energy tensor?", "label": 1}
+{"snippet": "What is the negation of this statement ? \"The equation has real distinct roots\" Is it \"The equation has no real distinct roots \" or \"The equation has no real roots \" or Is it \"The equation has no real roots, but it can have real repeated roots\"", "label": 1}
+{"snippet": "When I write something like this: I am a man that is doing these things. Is it correct to shorten it like this? I am a man doing these things. And does it require commas?", "label": 1}
+{"snippet": "So while I was solving this, I marked the correct answer as D, though the correct answer is claimed to be C. What I have read from different books is do not assume anything from the figures. So the solution assumes that the triangle formed would be a right-angled triangle, but it would be wrong to assume that, right?", "label": 1}
+{"snippet": "If you are applying to a school you are an \"applicant\". What is the word for the thing you're applying to? Similar to the sentence \"the stalker stalks the stalkee\", what would be in the blank in the sentence The applicant applies to the ______?", "label": 1}
+{"snippet": "I read this question in the sample questions section. It hasn't been asked yet, now I'd like to know. I have heard that regional dialects of English are often more closely related to provincial dialects because the comparatively well-to-do Londoner did not need or want to move to a strange new land and instead people from the countryside went abroad.", "label": 1}
+{"snippet": "I have to purchase some items. We have to tell how many ways are there to select N items of K types. However, the constraint here is we need to have at least one item of each type. How many ways exist?", "label": 1}
+{"snippet": "I know that a cone isn't a regular surface because I can't construct a chart with cts partial derivatives at its tip. But can anyone show me this last step rigorously? Why would any chart for the tip have a discontinuous partial derivative?", "label": 1}
+{"snippet": "Possible Duplicate: Put legend (pgfplots) below the plot I'm trying to set correctly the right position of the legend of my plot. I would have the legend just bottom right of my plot. Any idea? Using this code I got error legend style={ cells={anchor=south}, legend pos=outer south east, },", "label": 1}
+{"snippet": "Is is acceptable to use \"different\" as a preposition, as you would use \"unlike\" or \"in contrast to\", like in the following example? Thus, different from previous work, we aim to answer those questions.", "label": 1}
+{"snippet": "Hurry up and get ready for school. Don't be a slowcoach! Be a ______ ! What fits in the _____ ? Hopefully something other than fastcoach! I found some old discussion but nothing there seem to fit. Slowcoach (BrE) = Slowpoke (US).", "label": 1}
+{"snippet": "I'm going blank here, so forgive me for what should be simple. The search engines weren't helpful. I tried to search. Example: The finicky felines finished their food. I'm drawing a serious blank here, so go easy on me.", "label": 1}
+{"snippet": "I'm currently struggling which of the following two versions (I anononymized them) is the correct grammatical form for the title of a publication: Evaluating Safety, Cleverness and Fastness of Masking Systems Evaluating the Safety, Cleverness and Fastness of Masking Systems We are currently using the first version. Is it missing \"the\"?", "label": 1}
+{"snippet": "I'm doing some maintenance work on some software - whose original developers are unknown. There is a report called the \"All Zingo Report\", which basically dumps all the data for the primary \"entity\" in the database (the primary entity represents a person that has been referred to a government-associated medical program). Why would the word \"zingo\" be used to describe such a report?", "label": 1}
+{"snippet": "As far as I understand Everett's Many-Worlds Interpretation, he makes the case for a realist theory of QM at the enormous cost of many-worlds. Are there any arguments in favour of Everett's interpretation that makes the case for his theory one a purely instrumental or operational view - in that certain calculation look easier or more 'elegant'?", "label": 1}
+{"snippet": "OK, this is an attempt: I remained there, gazing at the sea. Its color was light green in the part closest to the shore, turned slightly darker in the middle, then abruptly changed to dark blue in deeper waters. Are those words commonly used? Or is there a better and simpler terminology to describe them?", "label": 1}
+{"snippet": "Why doesn't the volume of water in a nuclear fuel pool become irradiated? Why wouldn't the water around the pool become radioactive and circulate around making the whole thing deadly? My question spawned from this cartoon from XKCD. The Spent Fuel Pool", "label": 1}
+{"snippet": "I have some problem with \"at the cost of\" here. Does \"light reveals itself at the expense of obscuring something else\" mean: light reveals itself by lighting other things (because light itself has no physical presence and so is defined with its effects)? or light reveals itself by obscuring other things?", "label": 1}
+{"snippet": "What can we say about the quantum state from the number of zero and non-zero eigenvalues of the corresponding density matrix? Anything related to entanglement or any other properties? Does they vary with the nature of states such as it is pure or mixed? Please add some references.", "label": 1}
+{"snippet": "If one brings a fluorescent bulb close to a plasma ball, why does the touch of a finger cause the bulb to become brighter when touched? Why, when you hold the metal portion of the bulb, as opposed to the glass, does it NOT turn on at all?", "label": 1}
+{"snippet": "I was recently looking at automatic differentiation. Does something like automatic differentiation exist for integration? Would the integral be equivalent to something like Euler's method? (or am I thinking about it wrong?) edit: I am looking at some inherited code that includes https://projects.coin-or.org/ADOL-C as a black box.", "label": 1}
+{"snippet": "I want to use brackets similar to lceil, rceil and lfoor, rfloor, but with the vertical lines on both sides at an angle. Does anything like this already exist? If not, would it be difficult to create them?", "label": 1}
+{"snippet": "In manifolds and complex geometry there is this thing called the pullback. Usually when I see it, its going backwards on maps that are going forwards. I've been told that it is just a composition of functions. I just need help understanding this concept.", "label": 1}
+{"snippet": "Could you give examples where one is better suited than the other one? Or are they completely synonymous? (I'm not a native speaker.) Update: I'm writing a piece software documentation and I wonder if it's better to use choose or opt: ... Note that these components can receive input themselves (although they may opt/choose not to). ...", "label": 1}
+{"snippet": "I am writing my M.Sc. thesis in biochemistry, which has mathematics. I am new to latex, but I am greatly interested in it. I am watching/reading tutorials but was wondering if the community could recommend a good set of video lectures/pdf to write a document such as a thesis? Thank you very much for your time!", "label": 1}
+{"snippet": "I used the code from here to get text to wrap around images, but whenever I have a long image near the end of the page, it runs off the page and gets cut off. How do I fix this?", "label": 1}
+{"snippet": "My navigation bar at the top of each slide (that links to each section) has too many sections. I would like to keep the bar and keep each section but I would like to wrap it i.e. have it on two lines. Is that possible? I am using compress and I am using progressbar as a theme.", "label": 1}
+{"snippet": "The moon shone on his face as he spoke, and the girl was pleased to watch it, it seemed to breathe such an innocent and old-world kindness of disposition, yet with something high too, as of a well-founded self-content. What does this \"as of\" mean here? I would need a sentence structure explanation.", "label": 1}
+{"snippet": "Someone just told me that writing \"it makes me happy\" is incorrect in its sense not in grammatical aspect because \"it\" is \"not human\" please help me, is it okay to write \"it\" with \"happy\"? I am learning English so please help me.", "label": 1}
+{"snippet": "I am looking for a similar solution as here Description list with aligned descriptions except that I want to use it with beamer. If I use enumitem with beamer, inner theme is replaced by enumitem. I do not want to use enumitem because of this problem. Is there any alternative package or solution which works only with description? Kindly suggest.", "label": 1}
+{"snippet": "during a lab experiment, i noticed that a metal ball has a much harder time rolling on metal rails when their is a current passing through it and the rails. I was wondering why and if there was a name for this force. Does the fact that a current passes \"pull \" the balls towards the rails and increases friction? Thanks", "label": 1}
+{"snippet": "this may look like a duplicate question to this one and many, but really I had a hardtime in finding the desired solution. The breaklines=true didn't work as it breaks the long command. Hence simple copy and paste doesn't work, because when the code is pasted in terminal it gets split over many lines with preceding angle brackets > .", "label": 1}
+{"snippet": "I've read anything getting close to a regular black hole would experience spaghettification but not when you get close to super-massive black hole. Is there a point of \"peak spaghettification\" where the mass of the black hole exerts the greatest tidal force? Or, have I misunderstood something along the way?", "label": 1}
+{"snippet": "Do quantum probability and free probability mean the same thing - that is, they deal with noncommutative random variables? What about quantum measure theory? Is quantum measure theory the foundation of quantum probability (kind of like measure theory is the foundation of the classical probability theory)?", "label": 1}
+{"snippet": "A father's age is now five times that of his first born son. Six year from now, the old man's age will be only three times that his first born son. Find age of each.", "label": 1}
+{"snippet": "This is my sentence, and I was hoping to make it sound more academic: The aim is to ascertain whether or not the actors from the two films analysed can be considered to be heroes Is there a better, more academic way of saying 'whether or not'?", "label": 1}
+{"snippet": "Imagine that you would like to write down your passwords or other critical information into a sheet of paper. Could an algorithms without using a computer be so good as to avoid people of cracking it? There seems to exists some secret code messages that weren't discovered for centuries. So, theoretically it sound plausible, but how would I proceed?", "label": 1}
+{"snippet": "It is remarked by some text book that according to definition of absolutely continuous functions if the finite sums in the definition are replaced by the sums of (infinite) countable items, the assertion still holds. But I don't know why, even I understand that the number of the finite items is arbitrary. Any comments are welcomed. S.C.Liu", "label": 1}
+{"snippet": "let say that we can detect the wavelength and frequency of radio wave then can we detect that from where these radio waves are coming or from how much distance these waves are coming?", "label": 1}
+{"snippet": "If I am given the position vector of a particle at any time, how can I know if the particle spins clockwise or counterclockwise? UPDATE: Maybe I should have said that the particle is moving in cirlces.", "label": 1}
+{"snippet": "Would a switch of the word 'assistant' and 'manager' cause differences in a universal corporate context? In my opinion, assistant manager is just a rank below a manager. This seems to apply to manager assistant.", "label": 1}
+{"snippet": "The name of the city of Sodom is the etymon of sodomy. Question: Are there words in English for which Gomorrah is an etymon? According to Online Etymology Dictionary the unit omer is related to Gomorrah. Beyond this I haven't found other words that are, at least, related. It would be interesting to know.", "label": 1}
+{"snippet": "This is the only similar spelling mix-up in English that gets me every freakin' time. I can never remember which is which. One is a mathematical notion; the other is a nice thing to say. Does anyone know of any clever mnemonics for complement / compliment to get this one straight?", "label": 1}
+{"snippet": "Compact Linear Operator is defined such that the operator will map any bounded set into a relatively compact set. Why is this property so special that it can be named as \"compact\"? Does it share some similar properties as compact sets? What is the motivation to define and study such a set?", "label": 1}
+{"snippet": "Just saw the definition of word miss from some web dictionary, which says \"to fail to hit, catch, etc something.\" I suppose this could be written as \"to fail to hit, catch, or do something alike something.\" Does that etc mean, technically, \"or many other things alike\"? How? Doesn't et mean \"and\" in Latin?", "label": 1}
+{"snippet": "So the way I understand FG-modules is that it is analogous to a vector space defined over a field F with G a basis. However, I encountered a problem given the hypothesis that V is a possibly infinite dimensional FG-module where G is a finite group. I am confused how you can have a FG-module when your \"basis\" G is finite?", "label": 1}
+{"snippet": "Hounds tend to \"bay\" rather than \"bark\". When a dog barks, you can say \"he let out a loud bark\". In a similar construction emphasizing the hound-ness of the creature, can you say \"he emitted a loud bay that echoed through the chamber\"? Or would it be a bark regardless?", "label": 1}
+{"snippet": "Just a book problem I need help on: A letter is picked at random from the alphabet. Find the probability that the letter is contained in the word \"house\" or in the word \"phone\". I know this problem has something to do with mutually inclusive?? Would be great if someone could explain this to me Thanks!", "label": 1}
+{"snippet": "There are quite a few modern sans-serif humanist fonts, slab-serif fonts and other interesting Google web fonts. How do we typeset in LaTeX/PDFTeX/LuaTeX/XeTeX using them? Is there a way in TeX to call fonts like the Google fonts directly from their CDN URI? Are there any packages like Michael Sharpe's package that covers these modern fonts?", "label": 1}
+{"snippet": "Why do we feel tired while running as during running we are increasing our kinetic energy. I understand that the energy inside us(from food or something else) is being converted to KE while running but when we stop to which form is this KE converted???", "label": 1}
+{"snippet": "I understand how to use the theorem environment in LaTex and would like to know if there is a similar environment for postulates or how I can make an environment for postulates on my own.", "label": 1}
+{"snippet": "The title basically explains everything. The OP is an independent learner, who in the current stage sets S.S.Chern's proof of the generalised Gauss-Bonnet theorem as the goal. But what is the prerequisite knowledge of reading his two papers? I'm afraid basic Riemannian geometry would not suffice.", "label": 1}
+{"snippet": "Show by a counterexample that the following \"converse\" of Theorem(A subgroup of a cyclic group is cyclic) is not a theorem : \"If a group G is such that every proper subgroup is cyclic, then G is cyclic.\"", "label": 1}
+{"snippet": "In a standard poker game (no wild cards), suppose you are dealt five cards and your hand contains exactly one pair. You trade in the three worthless cards for new ones. What is the probability that your hand improves? meaning that there is a substantive transformation from one \"kind\" of hand into another", "label": 1}
+{"snippet": "Is it hard to calculate the coordinates and zoom factor that was used to generate a fractal image of, say, the Mandelbrot set? If you know the rest of the parameters, like how many iterations where used, in generating the image.", "label": 1}
+{"snippet": "I'm reading Srednicki's QFT textbook. I'd like to do some projects that put the content learned into actual use. Is there any good project topic? I don't mind if it's already worked out some where. I just want to experience the process of actually putting QFT into use, or simply relating the textbook knowledge to more problem-oriented situation. The textbook problems are smaller drills.", "label": 1}
+{"snippet": "I am a beginner of Fourier analysis, but my major is economics, I have not much of idea about frequency domain. My question is, since we have whole set of theory to work on time domain, such as time series analysis and stochastic process, why we need frequency domain.", "label": 1}
+{"snippet": "Earlier I wrote a sentence that happened to end with a plural possessive. Is this OK to have? For example, \"I got the guys' costumes, but not the girls'.\" looks odd to me. It would be easy to reword or simply add costumes at the end, but is it grammatically correct?", "label": 1}
+{"snippet": "As we know, the Ky Fan norm is convex, and so is the Ky Fan k-norm. My question is, does this imply that the difference between them is a non-convex function, since it results from \"difference between two convex\" functions ?", "label": 1}
+{"snippet": "We see Rainbows many times, but we always see them Horizontally or from Sideways. Why can't we see it from under it?/From the point where it starts or ends(end points)? I also want to stress on that, I am asking on viewing part and not about the formation, reason, causes of a rainbow.", "label": 1}
+{"snippet": "Finite groups and finitely generated groups are intensively studied, but are there interesting investigations on non finitely generated groups? I already know some references for abelian groups, so I am rather interested by nonabelian groups; are they nice enough to hope general results? Maybe are there interesting links with set theory?", "label": 1}
+{"snippet": "I have a current waveform from my circuit which goes up and down the x-axis. x-axis represents time and my y axis represents current. How should I calculate total area under the curve? Should I take the absolute for negative part of current or just waveform integral will work?", "label": 1}
+{"snippet": "If you consider them as laws, then there must be independent definitions of force and mass but I don't think there's such definitions. If you consider them as definitions, then why are they still called laws?", "label": 1}
+{"snippet": "Can someone please show me how this works, i'm going out of my mind I know the truth tables for the individual AND, OR AND NOT but when it comes to them being combined my understanding is shattered into pieces =/", "label": 1}
+{"snippet": "Is there any group with the non-trivial frattini subgroup such that the intersection of the Frattini subgroup and the commutator subgroup is trivial? Expect the groups can be constructed by the direct product of two groups; an abelian group with the non-trivial Frattini subgroup and a group with the trivial Fratini subgroup?", "label": 1}
+{"snippet": "With literary or historical references, what phrase would an English-speaking monarch have used to indicate to either their attendants or to their court that they were in need of using the toilet facilities?", "label": 1}
+{"snippet": "Do these three words mean the same thing? From my understanding, discordant means not agreeing or out of tune. This is similar to non-concurring (as concurring would mean agreeing on something). Also, controversial means something which gives rise to disagreement. How do I understand the subtle difference in meaning when the wors are so similar?", "label": 1}
+{"snippet": "Given this sentence: I look forward to learning new subjects and contributing to teaching them, (to?) facing new and diverse challenges, and (to?) producing outstanding work. My instinct is that I can omit the second and third to, but can someone please confirm and explain?", "label": 1}
+{"snippet": "Which sentence is grammatically accurate or they both acceptable? \"The main ingredient is blueberries\" sounds better to me. \"The main ingredient\" is indicative of one type of ingredient, so does that mean that it doesn't matter if \"blueberry\" is in plural or singular form?", "label": 1}
+{"snippet": "The sentence I am unsure about is: A rigid adherence to the doctrine of precedent would have resulted in a country where segregation was lawful but minimum wages were not. I'm confused by the subjunctive, and in particular the proper usages of 'was' and 'were'. Are they used properly above?", "label": 1}
+{"snippet": "I am transferring a professor's .doc files to LaTeX so that we can do more sophisticated formatting and I ran across a problem. I would like to recreate this number line in LaTeX. Help with which package to use and which commands to study would be a great help.", "label": 1}
+{"snippet": "Is there a word that names the sequence events were written about or described in, as opposed to the word chronologically? Example: Did you want us to present the events in the story chronologically or (in the sequence they were written)?", "label": 1}
+{"snippet": "Is QFT being applied to quantum computing and control theory? I took yesteryear a basic course on quantum computing and if I remember correctly we didn't touch on any QFT (though I think that if it were a course with prequisites of QFT, not a lot of people would have attended the course).", "label": 1}
+{"snippet": "im trying to find some sort of formula to calculate lines within a circle. I need to find the length of the various lines within the circle from which I only know the diameter. Is there some sort of formula that uses the dropoff of a circles side from the center? Thanks, Martijn", "label": 1}
+{"snippet": "Are there simple alternative of these font sizes in ConTeXt? Or one needs to use some special module? I looked at this page here. It seems to be a lot of boilerplate of such a simple task.", "label": 1}
+{"snippet": "Can I always find a Hamiltonian for any given Dynamical System such that the Hamiltons' equations are satisfied? The hamiltonian may be an extremely complicated function (Possibly containing complex terms) but in principle, is it always possible to find the hamiltonian for a given Dynamical System?", "label": 1}
+{"snippet": "Given the principal directions (max and min), principal curvatures, and normal of a surface at point n, how would you go about looking for a point on the surface at a given vector distance from n? I'm trying to create a Solidworks Addin to map a spline to a surface and have limited mathematical knowledge (up to diff eq).", "label": 1}
+{"snippet": "If I conduct an experiment and get results, and I can then relate those to real life in a way, what is the verb that this link to is doing? My first thought was validate, but that isn't correct.", "label": 1}
+{"snippet": "With certain electronic devices if you make a mistake you can brick (used as a verb) the device, so that it ends up in a defunct state. So the device ends up being bricked. What is the correct term to recover from this bricked state? On the web one can find the terms debrick and unbrick, but which one is correct?", "label": 1}
+{"snippet": "Possible Duplicate: Include < and > symbol Why when I create pdf in texlive with pdflatex, the characters < and > are displayed as inverted ! and ?, respectively. However, when I copy/past them, they are OK. What is the problem with PDF display. It's like the system does not have appropriate font, but aren't they common characters?", "label": 1}
+{"snippet": "I'm not super solid on my linear algebra, so I am getting lost in the discussions of halfspaces. Can someone give me an intuitive explanation (possibly with a concrete toy problem) of Blackwell's Approachability Theorem, and the algorithm its proof constructs?", "label": 1}
+{"snippet": "Is there any other word which can be used instead of something and some stuff, and how can the use of something and some stuff be avoided. For example: He saw her dwelling on something; it seemed more like she was trying to recall something. can it be written differently, without using something and/or some stuff?", "label": 1}
+{"snippet": "I want to express that the sleeping time has no much relationship with the activity and ... But the following sentence looks very strange. Please help me paraphrase this one: No absolute relationship between sleep time and the activity, entertainment, and learning time.", "label": 1}
+{"snippet": "How can I generate in xelatex a QR code with any given image inside, like so or better like this, using either pstricks or the new qrcode package? Note that the QR-code must still work after including the image.", "label": 1}
+{"snippet": "I have a question on comparisons. I said no error first, and that was wrong. I don't see an error with B or D or A. Is it C \"being\"? Should it be switched to be?", "label": 1}
+{"snippet": "Can someone illustrate the idea of \"forcing\" in set theory through some simple examples? The article on forcing on wikipedia goes straight to axiom of choice and continuum hypothesis, I wonder if there are simpler application that illustrates this so called technique.", "label": 1}
+{"snippet": "What is entropy of the universe? What is the change in entropy of our universe? Is this change increases or decreases? If the entropy of universe keeps on increasing then what are the consequences? Is there any limiting factor to this increase? One practical application of entropy where it is applied in day to day life?", "label": 1}
+{"snippet": "Now i doing the home work about Residue Integration and i doubt that \"Can the direction of Contour Integral be affect to the result of integration?\" I mean with the same shape of contour but direction of contour changes from clockwise to counterclockwise or counterclockwise to clockwise.", "label": 1}
+{"snippet": "In Ion Optics, an immersion lens is composed of two planar apertured electrodes. My question is why it is called an 'Immersion\" lens? I know that an Einzel lense has three or more electrodes. But physically for the ion optics, what is the difference between Immersion and Einzel lens? Or what is the advantage of Einzel over immersion lens?", "label": 1}
+{"snippet": "I read Griffiths EM today and it says something very interesting but a little bothering to me. It states for an atom, the position of center of mass of an electron cloud lies in the center of the proton. But my question is why? What will happen if this is not true?", "label": 1}
+{"snippet": "Are coproducts left exact or right exact functors in general? Let k be a commutative ring (unital assosiative). Specifically in the category of k-algebras is the tensor exact. (This is not the case in the category of k-modules, but then again the tensor is not a coproduct therein).", "label": 1}
+{"snippet": "I have heard that phrase recently on this YouTube video \"Why We Row (Inspirational)\" and I can assume what it means, but I just don't understand it on the context of the speech. ... don't be suprised if someone decides to flip the script and take a pass on yelling uncle, and then suddenly as the old saying goes, we got ourselves a game.", "label": 1}
+{"snippet": "For a transformation such as this, how does one determine the form of the kernel? Is it simply making the right side equal to zero, solving for each individual variable, and then creating a matrix with these 'new' a,b,c,d values?", "label": 1}
+{"snippet": "I am often asked to prove properties of regular bipartite graphs, and beyond the two parts having equal size nothing seems obvious. Are these graphs more intuitive than they first seem? In particular, right now I can't work out why an r-regular bipartite graph is r-edge-colourable. Thanks", "label": 1}
+{"snippet": "Where I can find a proof of self similarity of Grigorchuk group. I read it somewhere that Grig group follows this interesting property so I read about it but could not find a proof anywhere. It was not so trivial to me, so may be someone has any reference on it which one can provide. Thanks.", "label": 1}
+{"snippet": "I know that -tight switch arranges the image size to include all the ink on the page. For this instance, however, I want to give a width of my choice and crop only in the vertical direction. Furthermore I only want to crop the space below the image. Is this possible without modifying the dvipng source code?", "label": 1}
+{"snippet": "If you had a powerful electromagnet in the shape of a hollow sphere in which the top and bottom halves are the opposing poles, what can the magnetic filed at the center of the sphere be used for?", "label": 1}
+{"snippet": "When reading grammar, I find the names of the tenses kind of weird to me; Present simple and not simple present past simple and not simple past present continuous and not continuous present etc Does this contradict with the \"adjective noun\" ordering rule or is it an exception (or something else)?", "label": 1}
+{"snippet": "I know one should never use The reason is because, but does the same apply to The reason is so? It would make sense, because when someone asks you \"Why (insert question here)?\" , it's common to reply, \"So that (reason here).\" I'm not certain about this though and have not found anything online.", "label": 1}
+{"snippet": "I'm using different fonts in XeLaTex. However, there are some fonts installed in the same name in my system. How can I change the name of the fonts to distinguish them in Linux System?", "label": 1}
+{"snippet": "In the metatype FAQ, there's a section called \"I have Metafont sources of some font. How could I convert it to TrueType using Metatype?\" In that, he lays out a dozen steps that really should be scripted. Does anyone know of such a script? (I understand the result won't look very good at low font sizes.)", "label": 1}
+{"snippet": "I was wondering if interchange and exchange are equivalent and can be used interchangeably or exchangeably (okay this is an example already)? What are the differences between their prefixes, inter- and ex-? It is common for XML to be used in interchanging data over the Internet.", "label": 1}
+{"snippet": "I do not have a clue on how to solve out this type of question, and how to deal with integration with a combination of brownian motion and linear function. Can anyone help me out please?", "label": 1}
+{"snippet": "I'm going to be studying this result for a dissertation this year, and I wondered what there were in the way of higher-dimensional analogues? Also, what are some standing research questions on this theme? I think the interplay of the different theories is fascinating.", "label": 1}
+{"snippet": "I have learnt that a fraction with a surd in its most simplest form should have the surd in the numerator and not the denominator? Why is it convention not to leave the surd on the denominator? Is it just arbitrary convention or does it have an actual purpose?", "label": 1}
+{"snippet": "If I toss a coin an infinite amount of times, can I be sure to get an infinite amount of heads? Is it possible for it to be tails every flip meaning I get no heads at all?", "label": 1}
+{"snippet": "five friends including Bilyana and Bojana are sitting in a row in a theatre determine the probability that they are not sitting together. This is part of a homework assignment. I don't even know where to start with this.", "label": 1}
+{"snippet": "To pluralise is to make plural, dog becomes dogs, conversely singularise. What is the generic term for such actions? The number of a verb is its singularity or plurality, so perhaps numberise? Is there a word for the concept or process of pluralisation and singularisation?", "label": 1}
+{"snippet": "Lighter nuclei liberate energy when undergoing fusion, heavier nuclei when undergoing fission. What is it about the nucleus of an Iron atom that makes it so stable? Alternatively: Iron has the greatest nuclear binding energy - but why?", "label": 1}
+{"snippet": "I'm looking for a word with the meaning that 'rapidise' sounds like it ought to have. The sentence: to make the process more rapid would be replaced with: to rapidise [sic] the process I have considered accelerate quicken or hasten expedite which work, but are not quite right for me. I'll use 'accelerate' in the absence of anything else, though.", "label": 1}
+{"snippet": "In the quote, \"He is to resist the vulgar prosperity that retrogrades ever to barbarism\" What does resist mean? to tolerate to protest What does vulgar prosperity mean? obscene prosperity ill mannered prosperity What does ever mean? always occasionally What does retrogrades mean?", "label": 1}
+{"snippet": "If I had a list of awards and wanted to organise that list by the organizations that gave out those awards, what would be a good word to use? I can only think of by awarder which doesn't sound great.", "label": 1}
+{"snippet": "Something less roguish than \"imp\" or \"wag.\" I'm thinking about a person who is perhaps a bit sullen or in need of some levity. The word or phrase would be better if it expressed how this person feels rather than labelling the type of person they are. Maybe a type of sentiment.", "label": 1}
+{"snippet": "I hope I am not being pedantic; however, I could not come up with an answer on the internet. I wonder which is the letter which can be discriminated from the alphabet system on the basis of its myriad uses. Any suggestions?", "label": 1}
+{"snippet": "I am using krantz-single.sty in which the environments example and theorem are already defined with its own fonts, numbering (according to chapter) etc. I would like to number examples and theorems consecutively. So, I cannot use amsthm.sty to define Example as a newtheorem. I need only the counter for numbering to change. How to do it?", "label": 1}
+{"snippet": "In your opinion, what is the most cosmological or physics argument that may favor the existence of something like a god to produce a universe like ours and what is the most counter argument for that. Please don't drag this discussion into theology.", "label": 1}
+{"snippet": "I want to write a sentence something like this - > I like to meet people of my native origin(country, city, town and so on). How can i write the things that are in bold in one word - > I like to meet ____", "label": 1}
+{"snippet": "Can anyone show detailed proof of why radius of convergence of perturbation series in quantum electrodynamics is zero? And how is perturbation series constructed? So, as this argument requires imaginary electric charge of bispinor field (negative coupling constant), how is this argument considered valid?", "label": 1}
+{"snippet": "W is the complex-valued transformation of the original signals x and y without selection of the window length with respect to time t. W is the complex-valued transformation of the original signals x and y without a selection of the window length with respect to time t. Which is correct?", "label": 1}
+{"snippet": "I want to combine the following sentence: Relationship between son and mother, and relationship between daughter and mother Into one sentence for title of an article: Relationship between son, daughter and mother Is grammar and meaning correct?", "label": 1}
+{"snippet": "Nouns can be used as adjectives modifying other nouns, like: The discussion was about supplier local content development. Can we rephrase the above to: The discussion was about local content development of supplier. In general, can we rephrase nouns acting as adjectives to \"of\" clause like the example cited above?", "label": 1}
+{"snippet": "Assume that a charged particle accelerates/vibrates at a certain frequency and as a result produces e.g. red light. If every frequency has just a single wavelength associated with it, then the charge can never be a source of white light. So how do we get white light? What is the equation that relates the vibration frequency of a charge with the wavelength emitted?", "label": 1}
+{"snippet": "i've just found out that EM stress energy tensor along with gravitational stress energy contribute to the curvature of space. So, does the electroweak field also contribute to the curvature of space? And what about another field like the higgs field? Sorry if my question is to speculative since i really curious with this kind of stuff", "label": 1}
+{"snippet": "I think its something to do with acceleration but can't put my finger on it. Something about the most power needed as the greatest acceleration, as water flows up to full rate the accel and thus power decreases. Does that make sense?", "label": 1}
+{"snippet": "I am not too sure just by reading the manual as to the subtle differences between the .initial and .default PGF key types. Can someone explain and demonstrate the differences with a minimal example?", "label": 1}
+{"snippet": "Many spherical harmonics derivations start from finding a solution to Laplace's equation and the results are in fact what are called spherical harmonics. However, how's Laplace's equation really related to spheres? Particularly, Wikipedia says spherical harmonics being defined \"on the surface of a sphere\".", "label": 1}
+{"snippet": "Say I have three kinds of items that I call A, B, and C. Now, I want to ask someone to create one. Which form is the correct one? Create an item A. or Create an A item. ?", "label": 1}
+{"snippet": "My magnet seems to work independently of, and unaffected by, the Earth's magnetic field, yet the magnetic field of my magnet changes as I introduce some other similar magnets of varied sizes into its field. How would the magnetic field of this magnet differ at different locations on, orbiting around, and anywhere between, Earth and our other planets?", "label": 1}
+{"snippet": "In my business communication over Internet text messengers, for example Google Talk or Skype, I see that many people often use shorten words like u instead of you, r instead of are and the like. How appropriate is usage of such words in contemporary communication? Is it used in emails also? Should we avoid it as much as possible?", "label": 1}
+{"snippet": "I would like to contact my recruiter (via email) asking for updates on my application. What should I put in the title so it is informative, but also at the same time does not sound like I am too impatient? (I also would like to provide additional information about my accomplishments in the email) Thanks", "label": 1}
+{"snippet": "If I'm attempting to be booked to do an event, and I'm saying: \"we're now booking dates for such and such\". Is that proper usage of booking? Or should I say, \"we are being booked for dates in such and such\"?", "label": 1}
+{"snippet": "The Dold-Thom construction on a space is its free commutative monoid. Its homotopy groups are isomorphic to the integral homology groups of the original space. What are the integral homology groups of the Dold-Thom construction?", "label": 1}
+{"snippet": "I have read that a wire contracts side ways on stretching it . But why? What happens at the atomic level when a string is stretched? When there is no force applied in the side ways direction, why does the wire contract sideways decreasing its cross section?", "label": 1}
+{"snippet": "Let us pretend the 'one who hates his own image' is a 'selfie-loather'. If so, a sentence incorporating the term could be He always said he hated mirrors and I had assumed he was a 'selfie-loather' so I was shocked when I saw him apparently admiring his face in the glass!", "label": 1}
+{"snippet": "I have read that pseudocapacitors are combined of a carbon electrode and a metal oxide one. On the carbon electrode simply a double layer is built up and on the other some chemical actions(redox) happens. I was wondering how the chemical reaction happens and how this is possible when we have just on electrode in the reaction?", "label": 1}
+{"snippet": "We know Cauchy Residue theorem from the Complex analysis. however I wonder if there is a kind of Generalization of Cauchy integral and Residue theorem to the complex multidimensional holomorphic function too ? if such theorem exists, please mention any possible application of this theorem too. Can this theorem help in Iterative elimination of roots of a polynomial equations system ?", "label": 1}
+{"snippet": "Is the difference purely stylistic, or is there a slight change of meaning in using one form of over the other? \"It is the god-given given that must be accepted because it cannot be changed,\" as opposed to: \"It is the god-given given that must be accepted: it cannot be changed.\"", "label": 1}
+{"snippet": "I'll take one day leave for my family affair. I'll take one day leave for my family stuff. What's the different exactly? Or what situation is the best to use \"affair\", and \"stuff\" ?", "label": 1}
+{"snippet": "we know that if R as a ring is left artinian then ring R has a minimal left ideal and left socle of R is nonempty. now i wanna know can we prove this: if R is left artinian ring then right socle of R is nonempty. how can i find a relation between them? tank you for your help", "label": 1}
+{"snippet": "As the title says, does a polynomial with an infinite number of terms define algebraic numbers as roots? An algebraic number is defined as a solution to a polynomial with rational coefficients, but it is not usually specified whether this polynomial can have infinite terms.", "label": 1}
+{"snippet": "If I remember correctly you cannot compress a liquid, but I know you can compress a gas. (usually to the point it becomes a liquid then no further) What happens if I were to compress soda water? A liquid with a gas trapped in it. Would the gas escape the liquid, then compress? Or compress within the liquid?", "label": 1}
+{"snippet": "I have found this list of densities here: http://wiki.chemprime.chemeddl.org/index.php/Density_of_Black_Holes and I am looking for the density of quarks but I have not found it. I was wondering if Black Holes could be some kind of quark plasma (QGP). Is this possible?", "label": 1}
+{"snippet": "Why does the second requirement of a basis, i.e. that a point in two sets must also be contained in a third set contained in the intersection of the two set, make sense? Why is that what we should think of as a basis?", "label": 1}
+{"snippet": "There are people who keep their things in a prim and proper manner. They take good care of their stuff and use it with care. Is there a single word to describe them?", "label": 1}
+{"snippet": "How does one correctly use the word \"allegory\" in a sentence? For example: This story is an allegory [for|of] pride. I have seen examples of both: the long poem is an allegory of love and jealousy [Merriam-Webster] To that extent, are his experiences an allegory for life? [Your Dictionary]", "label": 1}
+{"snippet": "I am using pgfplots to create charts. How can I adjust the width of images of legend entries? I have adjusted plot coordinates in legend image code in the line legend style, but this not worked truely. Is there any way to do this?", "label": 1}
+{"snippet": "I would like to define a maximum height and a maximum width for an image at same time. I suppose there must be a package to do this, but actually I'm unable to find it...", "label": 1}
+{"snippet": "I am writing a research paper on quantum shuffle multiplication, and there is just one piece that I'm missing: I want to give one or several examples of its applications, and so far I have not been able to find any by searching online.", "label": 1}
+{"snippet": "Please consider the following image: Now I'm just trying to understand how exactly this thing is rotated...I'm looking at it exactly like on the image of the car...So the normal force is slightly bent because of the angle, but the angle seems to be on the opposite side from where it should be, I'd think it would be the lower corner, not the upper.", "label": 1}
+{"snippet": "\"Indeed, whoever buys this needs to want a tablet and laptop in more or less equal measure.\" \"Needs to want\"? Isn't it a kind of unnecessary way around saying: \"I think that people buy this if they want a tablet and laptop in more or less equal measure.\"? Or am I missing something?", "label": 1}
+{"snippet": "Using a truth table I had no problems to proof, that this equation is correct. But how can I transform the first part to get to the second? I tried using de morgan but I never made it. Can anyone give me advice?", "label": 1}
+{"snippet": "I want to change position of tufte-book(twoside) class in my thesis. In normal mode, margins for odd pages is on the right side and for evens, is on the left side of page. I want to change the position of margins. Normal: Reverse:", "label": 1}
+{"snippet": "Are there meridians that effect cloud movement? While observing radar images of moisture bearing cloud movements (at my location in Florida), I've noticed a splitting of the cloud formations a majority of the time. It has become apparent and predictable.", "label": 1}
+{"snippet": "Question is said in title.Suppose X is a separable topological space and S is a dense subspace of X,to prove S is separable or give a counter-example,and we may add what conditions to make this statement true?", "label": 1}
+{"snippet": "If you have an asteroid for example and a planet, isolated from all other gravitational influence and initially at rest with respect to each other, how would you find a position vs time function for the asteroid and the planet falling toward each other?", "label": 1}
+{"snippet": "I know this is true if F is infinite but don't know how to prove it. And is this still true if F is finite? I think The Primitive Element Theorem is the keypoint to prove this statement. Primitive Element Theorem: Let K/F be a finite extension of fields, if F(K/F) is finite, then there exists q in K such that K=F(q).", "label": 1}
+{"snippet": "What's the most general way of obtaining the mean field theory of a microscopic Hamiltonian/action ? Is the Hubbard-Stratonovich transformation the only systematic method? If the answer is yes then what does necessitate our mean field parameter to be a Bosonic quantity ? Is the reason that all of directly physical observable quantities should commute?", "label": 1}
+{"snippet": "Could be there material that begins melting/softening when it's temperature is lowered? I would say no, but I've seen enough physics to know that not always life is so easy. Moreover I think I've heard something about it, but can't remember a thing.", "label": 1}
+{"snippet": "When a lamp or other luminous object is very bright, we cannot see clearly the things close to it. What we see is a whitish region that surrounds it. What do we call this? (Is it a perception or a phenomenon?) This picture features a lamp in the centre; half the image consists of the white region surrounding the lamp.", "label": 1}
+{"snippet": "Which of the following questions are correct according to the grammar, and why? When will be the results declared? When will the results be declared? Does this hold to all future perfect tenses?", "label": 1}
+{"snippet": "\"Welcome to our store!\" \"We have the best hamburgers in the market which we have been cooking for generation after generation with no equal!\" \"The best prices around for such a complete piece of work\" et cetra. Is there a good expression for such words?", "label": 1}
+{"snippet": "How can we say Mike has an apple, and Jane has an apple in a single clause? Can I say Both Mike and Jane have an apple or Mike and Jane each have an apple? They sound fine to me but I am not sure. Is there any alternative? Each of Mike and Jane has an apple might sound too complicated.", "label": 1}
+{"snippet": "Could you help me find the one-sided exact binomial test formula? I use this statistical test in R-language, but I can't find the formula for it. Eng Wikipedia (https://en.wikipedia.org/wiki/Binomial_test) and RLang help gives me only examples without needed math description. Thank you!", "label": 1}
+{"snippet": "I'm using LyX and need to have the chapters to start soon after the end of the previous chapter. A LyX solution will be most appreciated. Document class report and I am not to change the document class.", "label": 1}
+{"snippet": "I don't even know how to title my request. I am also not including any code, because I have absolutely no starting point. I'm writing a technical document and once in a while I need to put a notice/warning into the text. What I want to do is best described by seeing what I've done in Word: I'd be so grateful for any help!", "label": 1}
+{"snippet": "I search all over the Internet for a proof of Descartes's rule of sign. Found a pdf file which has page-long proof that a high schooler has to no way to understand. Can somebody talented here give me a proof of the rule, in geometry preferably, or if impossible to be done in geometry in simple algebra or trigonometry.", "label": 1}
+{"snippet": "I am reading a book that states the hero \"knew himself to be among the dead\". Does this means that he considered himself as good as dead, or that he understood that all the people around him were dead? Generally, what does \"among the dead\" means?", "label": 1}
+{"snippet": "Can anyone describe to me one change to the electric field and one change to the magnetic field that MUST take place as particles gains energy in a synchrotron accelerator? This could also just be an in general question about particles gaining energy.", "label": 1}
+{"snippet": "In Chinese, when we want to express the idea of \"change A which is erroneous to B which is correct\", we usually say \"correct A to B\"; very concise, right? But is it the proper way to express that meaning? If so, please cite a web page containing that expression; if not, present the correct way please and cite a web page too.", "label": 1}
+{"snippet": "Water waves are dispersive ( longer wavelengths travel faster ) but sound waves in air are not, otherwise we would listen first the high frequencies and the low frequencies after. What decides if a wave will be dispersive or not? This question has been asked again. I am looking for an answer or a comment that explains the physical reasons behind the mathematics.", "label": 1}
+{"snippet": "Most people know the classic committe style problems. I read this solution to one of the basic version of the committe problem and was impressed, but not sure why it works. I was hoping someone could explain why does it work.", "label": 1}
+{"snippet": "Rolling implies rotation and translation. Cranking implies the motion people used to do before power windows and Sliding is what actually happens to the window. When and why did people start using the expression \"roll the windows down,\" instead of something more descriptive?", "label": 1}
+{"snippet": "If I form a sentence like: I could read the book if I hadn't wasted my time. Would it be considered a past perfect sentence with the part I could read the book being in simple past for context in the sentence or does it only show a possibility?", "label": 1}
+{"snippet": "Is there a formula for generating a set of Coprime integers that every element of this set is coprime to the other elements in this set? I want to create a collection of this formulas!", "label": 1}
+{"snippet": "I am new. I have a question about the icons in the texstudio IDE for tex: the icons in both the tool bar and in the left panel are pretty small. Is there a way to enlarge them a little bit? Thanks very much.", "label": 1}
+{"snippet": "What is correct between \"bests\" & \"best\", when used in the context as per title. To clarify, there is no noun after this term. i.e. it's not \"one of the best [XYZ]s\". Example: I had been to that restaurant. It's indeed one of the best/bests (?)\"", "label": 1}
+{"snippet": "I'd like to create a new style in TikZ for nodes with transparent background, rounded corners, with labels oriented vertically on their left on a opaque fill (similar to a tabbed paper). A sample sketch is given below. The \"Label\" will be given to the style as parameter.", "label": 1}
+{"snippet": "I know how to work from a chemical equation to an ODE, as described here: http://brunel.ac.uk/~cspgoop/uploads/ode_chemical_network.pdf How do I go the other way? I want to convert the Lotka-Volterra ODE system to chemical equations so I can use it in a cell simulation program.", "label": 1}
+{"snippet": "I would like to create B-Lymphocyte picture (antigen) and i would like to know if someone could give me a start point (e.g. online examples, etc.). Here are some examples of what i would like to create: Regards", "label": 1}
+{"snippet": "Which is the correct form when adding the -ify suffix to member? memberify membrify I know it's not a regular word, I want to use it in a context for something like \"make me a member\".", "label": 1}
+{"snippet": "Are there any books specifically on collision processes between atoms and molecules and collision probability? I would like to get an overview of the factors that determine collision probability between particles, like number density, relative velocity, particle size and such.", "label": 1}
+{"snippet": "I am in favour of compromises and I am glad that Gabriel also is. Is it okay here to end the sentence with \"also is\"? Is there a better/more proper way to express this?", "label": 1}
+{"snippet": "I would like to ask a question about an abbreviation about for weighing silk and goatswool in a commercial manuscript. The abbreviation using like on the photos. Can you please help me what is the meaning of these abbreviations. Any suggestions are welcome.", "label": 1}
+{"snippet": "If we place a small magnet between two wires carrying current in opposite direction separated by some distance r, will the magnet move or not? And if the magnet will move then in what direction will it move and how?", "label": 1}
+{"snippet": "I am a bit lost how to proceed this integration (I got a recommendation to use substitution here) with goniometric functions in here. I know the correct result, but still can't determine it.", "label": 1}
+{"snippet": "If I place a compass over a wire(such that the wire is positioned north-south) with charge flowing through it, and it points northeast, how can I determine the direction of the electron current flowing through the wire?", "label": 1}
+{"snippet": "Sometimes we read books rather quickly and don't give them much (or any) thought, so the action 'reading' does not necessarily imply that we have given enough thoughts to any book we read. Is there a word that describes reading a book with great care; usually but necessarily slowly over a long period of time.", "label": 1}
+{"snippet": "Usually a two-body nuclear problem is exactly solvable through quantum mechanics e.g. the deuteron nucleus having two particles a neutron and proton. As one goes over to three particle systems, say a triton or a neutron described as composed of three quarks, the equations get coupled. Is there a simple way out to get to calculate the ground state of three particle systems?", "label": 1}
+{"snippet": "In this derivation is it necessary to write the triple integral, as I thought that if we are dealing with one fluid particle it only contains one \"point\" and hence we do not have to take a sum?", "label": 1}
+{"snippet": "I am not understanding why gradient will show the direction in which the function value rises most quickly. It is just the vector of partial derivatives of the function. And why its magnitude will determine how fast the temperature rises in that direction.", "label": 1}
+{"snippet": "I'm looking for a references / short book which discusses what is going on LHC collider - specific experiments, collision processes, analysis of data, how exactly the facility is operating (not professional level but for a high-energy Phd level). I would love to hear your recommendations.", "label": 1}
+{"snippet": "How to visualise solenoidal vector field;I am thinking it as a solenoid going in a circular fashion with propagation in the z direction. I was solving a problem to check that field is solenoidal or not ?", "label": 1}
+{"snippet": "Online resources describe a function as a correlation between domain and range values, while a sequence is just a bunch of numbers correlated with the term. Isn't this the same thing if you consider the term to be the domain and the sequence value at that term to be the range? What's the difference between a sequence and function?", "label": 1}
+{"snippet": "I am interested in good integer approximation from below and from above for binary Log(N!). The question and the question provides only a general idea but not exact values. In other words I need integers A and B so that A <= Log(N!) <= B", "label": 1}
+{"snippet": "I have done some integration in the past, but came across the following question: The question is simple, calculate the integral and give the final answer. I am really not sure what to do and how I fill in the infinite values. Could somebody give me some more insight in how to solve this question.", "label": 1}
+{"snippet": "I want to use taint in a positive context, something along the lines of: I will have the opportunity to taint my life with the culture and experiences of others. What would be a better word for this purpose?", "label": 1}
+{"snippet": "I want to use well-connected in the context of The James family was a well-connected family in ... Can someone suggest better ways to say it? I want it to mean that that particular family was well known in the area, was well respected, and had clout.", "label": 1}
+{"snippet": "In ZF classes are used informally to resolve Russells Paradox, that is the collection of all sets that do not contain themselves does not form a set but a proper class. But doesn't the same paradox manifest itself when discussing the class of all classes that do not contain themselves?", "label": 1}
+{"snippet": "In the latest South Park episode, I noticed a line: We have so many abandoned babies and not enough people like yourself who care. Which kinda struck me, because I'd expect it to be people like you. Is the original quote broken, or are both correct, representing a different meaning?", "label": 1}
+{"snippet": "Is it important for a physicist to be good at math? Should he be on par with a mathematician? According to me physics and math are like English and biology we study them in the same language but they are not same.", "label": 1}
+{"snippet": "What does \"uncancellable\" mean? Does it mean that something may be uncancelled, or that something may not be cancelled? [Edit:] How would one express each of those ideas? For bonus points, is there a way to be indicate that something may be not uncancelled? In-uncancellable?", "label": 1}
+{"snippet": "Which of the following is grammatical? He had lollies be they red or blue? He had lollies be them red or blue? It seems as if it could be them as an object of be.", "label": 1}
+{"snippet": "When I first see the following, it is the best theme that I've seen. I want to get theme like this. How can I use theme like this? Bayesian Nonparametrics Part II, Peter Orbanz", "label": 1}
+{"snippet": "I was looking for a free PDF from which I can review MV calculus. Specifically: MV Limits, Continuity, Differentiation. Differentiation of vector and scalar fields Surface/Multiple Integrals A succinct book would be great, (coherent) course notes and presentations would do as well. I ran google searches with filetype:pdf but I couldn't find one which fits all my requirements.", "label": 1}
+{"snippet": "Does anyone know which Latex environments that are supported in pandoc when converting Markdown to html? I have tested equation, align, alignat which seams to work, so is there e.g. a family/kind of environments that are supported, so I don't need to test by trial and error?", "label": 1}
+{"snippet": "There are many problems involving, proving numbers are irrational or not an integer and so forth (e.g roots of polynomials, size of an angle) What are some general techniques/tricks that I can use in these types of olympiad problems?", "label": 1}
+{"snippet": "Is there some well known and useful measures of non-linearity for functions? I know this is rather broad question (more precisely two questions), but I'm stuck with my problem and interested in all answers in hopes it will unlock my thinking process.", "label": 1}
+{"snippet": "The nation and the world would be better off if Congress took a break from partisanship and finally debated a legal framework for the American military action .... Republican lawmakers prefer to simply blame President Obama rather than earn their paychecks.", "label": 1}
+{"snippet": "I've noticed that during British lightning storms, I have only ever seen sheet lightning However, on holiday in other countries, I frequently see Forked Lightning Q) Is this just caused by cloud, or is it two distinct forms of lightning? Q) Is there a reason Britain only seems to get the sheet kind?", "label": 1}
+{"snippet": "As the title states. Is there a way to insert a background picture for a beamercolorbox. I mean I can make two of them overlap or something, but can I insert a background picture somehow? Thanks.", "label": 1}
+{"snippet": "I have seen a nice looking table of contents in a Beamer presentation. There were some formulas, pictures, graphs situated across the frame in a shadow background. Any idea how to do this?", "label": 1}
+{"snippet": "? She cracked an egg into the frying pan. In this sentence, should cracked be replaced with broke? I take that to crack means to break, but without causing a complete separation of the parts. The windshield of this car was cracked.", "label": 1}
+{"snippet": "I have two magnetic bars and when they are brought close sideway the two bars join where the two South poles are adjacent to each other, and so does the two North poles. If the magnetic field goes from South to North and repel when is the same pole, why doesn't the magnetic bar rotate and align itself to NSNS?", "label": 1}
+{"snippet": "What is the difference between a) By then, you will have shown what you meant to do since the beginning. b) By then, you will show what you meant to do since the beginning.(Is this grammatically correct at all?) Thank you.", "label": 1}
+{"snippet": "I m writing one article in which i need to write a paragraph full of medical terms. How can i wrap a text in a line without using line break (or hyphen)? Regards", "label": 1}
+{"snippet": "I am having trouble coming up with a noun that is almost like an Easter egg. Is there any word that could be something someone intentionally leaves for another person to find at a later time?", "label": 1}
+{"snippet": "There are commercial software that create the look of an analog page flipping effect from a PDF document. Is there a similar animation in TeX? (Not to be confused with flippdf package which gives a mirror image for printing machines.)", "label": 1}
+{"snippet": "I am uncertain on how to approach this proof. For most everything I've encountered concerning symmetry, it has involved taking the transpose in order to show some property. Here, I'm not certain if and how that would be effective.", "label": 1}
+{"snippet": "In a cylindrical chamber with a high diameter-to-height ratio; a fluid is tangentially injected. there is an axial exit to the cylinder. how do I determine if the vortex so formed is laminar or turbulent? what parameter will indicate this? (this is a simulation; so I can measure whichever velocity/turbulent KE that is needed.)", "label": 1}
+{"snippet": "Can of course be used in technical writing? I heard that it is used typically in informal writing. I am not sure though. For example, The existing scheduling techniques work well on a mix of single threaded workloads where half of the threads are memory-intensive and half are CPU-intensive. Of course, these are not designed for scheduling multithreaded programs.", "label": 1}
+{"snippet": "If airport security scanners of any kind (xray, thermal, whatever else they use) looked at two items: A printed paper textbook The same printed paper textbook into which we have inserted a regular folded US letter-sized paper with something written on it with a pencil, pen, marker, etc. Could the security be able to detect the difference between the two?", "label": 1}
+{"snippet": "Two diagonal matrices each other's entries rearranged (same eigenvalues and multiplicities), are they similar? This seems like such a simple question, but I can't quite see a connection. I want to say that the two diagonal matrices can commute with each other, and this gives us the algebraic edge to show their similarity, but I'm generally bad with abstract algebra proofs.", "label": 1}
+{"snippet": "If a group is finitely generated, then it is a quotient of the free group on the set of generators. Further if a subgroup of a group has some finite presentation, does it mean that it is normal, intuitively a presentation corresponds to idenitifying certain element (or words), so it might be in some sense a quotient, and therefore normal. Is this right?", "label": 1}
+{"snippet": "I look for an advanced linear algebra (A complete book but wich deals indiferently with infinite/finite vector space). To give an idea i expect a book that (for exemple) would prove the existence of a base in any vector space by Zorn Lemma. Thanks PS: I found Bourbaki's book but the level is quite hard", "label": 1}
+{"snippet": "Is the following conjecture true ? I am trying to collect some properties about box topology and product topology in order to study for topology exam. is the product of connected compact space connected in the box topology?", "label": 1}
+{"snippet": "I don't know whether a semicolon or a comma should be used. For example: Now that GoT is done for the season what will James complain about besides Disney movies?Find out on a new episode of Off Time Radio; if he ever texts me back.", "label": 1}
+{"snippet": "The designer prefers using mathptmx font for the book, but I really dislike its greek characters. They are larger and bolder than non-greek characters. Do you have any suggestion how to please both the designer and myself? :-) Maybe you could suggest another font that looks like Times (New) Roman and does not have this \"problem\" with greek characters'? Math support is essential.", "label": 1}
+{"snippet": "When diagramming the sentence, \"Simon, would you please sing now?\", should I diagram Simon or you as the subject? Would you be diagrammed as pronoun and please as an interjection? I am trying to help my son diagram real-life sentences and am getting stuck myself.", "label": 1}
+{"snippet": "I wanna ask why sequence is important in general topology. As far as i know, many theorem can be proved without using sequence. Does sequence make some proof easier than other way? or is there any other reason? If yes, can you give some example for references?", "label": 1}
+{"snippet": "Similar to the Newton Raphson algorithm that has a (global) convergence property when we minimize a (strictly) convex function over Euclidean space (based on the second order Taylor serise expansion with a geometric or any other property), can we say that it also has a convergence property by replacing Euclidean space with a convex cone?", "label": 1}
+{"snippet": "How can you add vertical space between the word \"Proof\" and the actual start of the proof? This question shows how to start the proof on a new line, but I can't add space properly.", "label": 1}
+{"snippet": "I've heard that the cat which there may not be enough room to swing actually refers to a type of whip. Is that true? What is the actual origin of the phrase not/barely enough room to swing a cat?", "label": 1}
+{"snippet": "I am digitizing a book and there is only a single page which has page border as shown in the attached image. How can I create border to a single page? Is there a library where I can choose a border from?", "label": 1}
+{"snippet": "Is the Riemann sphere anything more than a simple visual tool to help students understand the complex planes, or the behavior of complex valued functions at infinity, limit points etc? Or is there a practical use in calculations of complex valued functions using the topology or geometry of the the sphere itself?", "label": 1}
+{"snippet": "What are the conditions to be met by a LP that allows to infer that its optimum solution will be integral? Is total unimodularity a necessary and/or sufficient condition? What if all variables are binary?", "label": 1}
+{"snippet": "I recently used a sentence similar to the following: Curiously, do you prefer black? Some people found it grammatically incorrect. That was a surprise, for I thought it was perfectly okay. Someone even came with an alternative: Out of curiosity, do you prefer black? Is the second sentence actually better? Is there a real difference (bar the number of characters)?", "label": 1}
+{"snippet": "I have seen many popular accounts of simple magic squares but I would like to find a proper mathematical background to understanding magic squares. What background knowledge do I need. I am a retired senior school maths teacher.", "label": 1}
+{"snippet": "The condition to get an interference pattern we must need coherent sources. After superposition, they produce interference. If we select a random photon in the superposition states, can I know the source it came from?", "label": 1}
+{"snippet": "When there is a phrase like \"the page of the book,\" is it correct to put both the in the sentence? What are the rules in general? What if we had more OF in the sentence? e.g. \"the room of the department of the organization\"", "label": 1}
+{"snippet": "Is hydrostatic pressure independent of temperature? Why only the weight of overlaying liquid is taken into account for calculating hydrostatic pressure and not the collision forces due to temperature? In space (if temperature is not zero),will the liquid pressure on walls be zero?", "label": 1}
+{"snippet": "Does anyone know how to make relatively simple diagrams like the images below? Is there a some sort of \"template\" I could use perhaps? I'd like to code my Calculus notes but I'm not sure how to make the diagrams. It's Left approximation, right approximation, and middle approximation, respectively. Alas...", "label": 1}
+{"snippet": "I am looking for a singular word that categorizes this set of words: {forewords, preface, prologue, chapter, author's note, etc} The best I can come up with right now is Section Heading which is obviously not one word.", "label": 1}
+{"snippet": "I am using latex editor LyX. I write a book with many authors. I want to list each author name in each chapter in table of content. How can I list author name in table of content?", "label": 1}
+{"snippet": "That chair was very sturdy, or so I thought. \"Or so I thought\" means the previous phrase is wrong after a while of consideration. (or something similar) Is there any term/words that can replace \"or so I thought\" in the same/similar context? (Rephrasing is fine, but not just purely replacing the words, ie. \"or so I presumed\")", "label": 1}
+{"snippet": "I sent my CV to get a job into one company. But they rejected it. The reason was: \"Please do not send your CV without a cover note.\" English is not my native language and it is hard for me to understand what cover note means. What is it?", "label": 1}
+{"snippet": "There are several question in this site comparing different basis functions including Schauder basis and others, but I could not connect the difference between the Schauder basis and Eigenbasis clearly. Would someone please point the best way to contrast between the two?", "label": 1}
+{"snippet": "What is a word or concept that describes a situation where one person puts forth a point of view, and another person does not directly address the position, but instead responds with an obvious, basic fact whose implications cast doubt on the correctness or strength of the point of view? This is intended to belittle the point of view.", "label": 1}
+{"snippet": "We recently had a discussion whether \"Pay for play\" or \"Play for pay\" is the correct term to describe that you get money when you play. Which one is correct to point out that you get paid for playing?", "label": 1}
+{"snippet": "is there any function whose zero is singular point of function ? i.e. construct a complex valued function such that there is zero of function at which it fails to be analytic f: D to C is a function where D is subset of C", "label": 1}
+{"snippet": "Graduation day is coming; when trying to send a card to a friend I have a difficulty to decide which preposition to use in this simple phrase. \"Good luck with/in/on your journey!\" My first thought is to use \"on\". However; a google search shows the three prepositions are often used. Thanks!", "label": 1}
+{"snippet": "I want to understand the proof of how to estimate variance from the Normal distr, using the method of moments. It boils down to simple algebra. I can't understand why I tried to prove it like this but get an error in the end.", "label": 1}
+{"snippet": "I'm writing a text and am confused about a word I knew before. The definition is : to Take away the property of someone (by government or bank or a legal institution). I have found seize or take over, but I know there is better word for it which I had used in my translations before. Can any one suggest a better word?", "label": 1}
+{"snippet": "In describing electron states in hydrogen, we have a very \"simple\" picture, at least in intro-quantum. But this only has one electron! As we permit more electrons, we also have things like the exclusion principle, which comes from the spin-statistics theorem, but that relies on the electrons having some kind of coupled wave functions, right? Why do electrons always come in pairs?", "label": 1}
+{"snippet": "We assume that distribution of electrons follows Fermi-Dirac distribution / statistics in semiconductor model which will help to find the concentrations of electron and holes and the relationship between them. Why is it that we use this distribution? Why in particular is this distribution used in such models?", "label": 1}
+{"snippet": "What is the literary device used for the following quote from The Fellowship of the Ring : By light of moon and ray of star I think that it is an idiom.... I may be wrong!", "label": 1}
+{"snippet": "I have a URL in my bibliography which line-breaks in an unpleasant way. The URL breaks as follows: http://www.mathworks.se/help/matlab/matlab_oop/(break) implementing-operators-for-your-class.html I want to allow breaks at \"-\" so that the URL would look something like: http://www.mathworks.se/help/matlab/matlab_oop/implementing-operators-(break) for-your-class.html I'm using a customized plainnat.bst file in order to get surnames first if that makes some difference.", "label": 1}
+{"snippet": "After conferring with each other concerning the foregoing matters, if the parties do not reach an agreement upon any such matter, Petitioner shall have the descretion to make the decision and the provision hereinafter set forth concerning resolution of disputes shall not apply to her decision.", "label": 1}
+{"snippet": "Right now I am taking an algorithms class. However my university does not provide a discrete math course. To make matters a little rougher, proofs and induction had barely been touched by any of my computer science courses. If possible, could you provide a few links to learn this concept from?", "label": 1}
+{"snippet": "What is the coefficient of mass gained/lost by a star in its first phase transitioning into a blackhole. Does the blackhole have more or less mass than the star it was made from? Thank you Regards", "label": 1}
+{"snippet": "How is Base emitter junction and collector emitter junction biased? How do we determine the value of potential difference between emitter and collector required to be maintained in order to determine input characteristic of transistor? Explanations covering nitty gritty are most welcome.", "label": 1}
+{"snippet": "AFAIK the limit of a term does not exist if that term does not converge, but I haven't found a suiting question here yet. This probably is a double of a similar question.", "label": 1}
+{"snippet": "Kuvio (Finnish for 'pattern') seems to be a very general tool for diagram making. Which are the major disadvantages? Why isn't it used more often (only one Q/A on the site seems to mention it)? Can it be used in papers sent to mathematical journals? About Kuvio and other packages on diagrams", "label": 1}
+{"snippet": "\"Do you think the children enjoyed their meal?\" As you can see, this question started with the \"Present Tense's auxiliary verb\" which was \"Do\". Why can we still use Past Tense's verb (enjoyed) then? By the way, I'm a newbie. Named \"David\"", "label": 1}
+{"snippet": "from the Wapshot Chronicle by John Cheever: For with his maturity, Moses had found in himself a taste for the grain and hair of life. The context doesn't really help so much in understanding.", "label": 1}
+{"snippet": "I have the following sentence: I am a developer, thinker, and a strong advocate on micro-services, architecture and development of blah blah I am a strong advocate ON Or should it be: I am a strong advocate OF", "label": 1}
+{"snippet": "How can we use a reduction to prove non membership of a class. Can we say if A is reducible to B they are in same class or if we can't reduce A to B. B is not same class as A. Regards,", "label": 1}
+{"snippet": "We know that magnetic field arises due to relative velocity of charged particle . Electrons in wire move at very slow drift velocity but relativistic variation of magnetic field doesn't seem to apply on them because if observer also travels with drift velocity , magnetic forces on wire should vanish if its in external magnetic field but it doesn't ?", "label": 1}
+{"snippet": "According to my teacher, an electron is point sized and it does not absorb or release energy. Moreover, my teacher says their orbital absorbs energy rather than the electron. If that is the case, then what about the photoelectric effect, in which electrons release energy after excitement?", "label": 1}
+{"snippet": "A closed group in Facebook bash me for asking them if there's such word as \"UNSWAPPING\" I reached Google and Dictionaries of which I failed to find this word. Yes, there's an adjective \"unswapped\" but I never found \"UNSWAPPING\" please help me. I want to know the precise answer. Thank you!", "label": 1}
+{"snippet": "I am writing my master's thesis now, and I got a small question on the two terms in the title. You probably noticed, my English sucks... I have a sentence like: \"this model is needed\", but I want to change the to sentence to \"this model is in need\". Is that correct?", "label": 1}
+{"snippet": "Electromagnetic induction sounds quite analogous to inertia to me. Just like inertia it opposes the 'change'. So is this phenomenon has something to do with what we call inertia for macroscopic objects. And do electron has some inertia like property to create this phenomenon.", "label": 1}
+{"snippet": "Take a video camera and crank up the frames per second rate. Disregarding current technological advancements, could a camera's FPS go so fast that any two captured images be identical? Would accomplishing this defy \"time\"?", "label": 1}
+{"snippet": "It is tempting to switch to unicode-math. But there is (at least) one point that I still don't like. That are the double stroke characters. They look simply terrible in XITS Math. Just compare: with Are there any better options with unicode-math? At least they should be serif!", "label": 1}
+{"snippet": "I have several full names in my rather large bibiography. Since I do not want to change all these I'd like to have the forename shortened to an initial. So \"Lieschen Mueller\" should get \"Mueller L.\". I use the standard authoryear style.", "label": 1}
+{"snippet": "I'm trying to write a paper about US Invasion in Iraq is unjust morally, militarily, and legally. I can't think of words to explain when I'm trying to explain that I have moral \"evidence\" or ideas from the book that will help to support my moral argument. It is technically not evidence, but what word should I use to accurately explain it like evidence?", "label": 1}
+{"snippet": "Often I read about \"under-appreciated\" books. Being an author myself, I am putting together my resume in English and I am unsure what word to use to describe a book that has had positive reviews and apparently was sucessful. Should I say \"appreciated book dealing with..\"? Also do I need to use articles? Title of the book (An) appreciated book dealing ..", "label": 1}
+{"snippet": "Possible Duplicates: What is the correct possessive for nouns ending in s? Pronouncing possessive words that already end in s How do I pronounce possessives that end with the awkward \"s's\" and \"'s\"? Examples: I found the mistress's attitude ridiculous These are the eggs' shells. Which coat is Amos'?", "label": 1}
+{"snippet": "Suppose in this moment the universe stopped expanding, how long would if take and how would we register the change? Since the bodies are still and it is space that is expanding in between, we wouldn't notice the change even if the expansion would completely stop in a short time?", "label": 1}
+{"snippet": "I want to extend the implementations of the examples here to represent graphs with vertices simply represented as text as shown in the figure . I wasn't able to find similar templates/examples in the tikz manual. Could someone point me to a MWE?", "label": 1}
+{"snippet": "A nurse is telling: There was a girl who was driving inside a tunnel and something just fell on her car and she died. That messes me up more than thinking about patients who are sick. I have a hard time understanding what is the meaning of the phrasal verb in the context.", "label": 1}
+{"snippet": "I have Ellipse's center-points, minor-radius and major-radius. I can find, how to check if given point(x, y) exists in Ellipse or not. Now, I want to find given point(x,y) exists at which angle in Ellipse. Thanks in advance Vikram", "label": 1}
+{"snippet": "If we have a solid conducting sphere with charges around it, then the electric field inside the sphere is zero, otherwise the electrons of the sphere would not be in equilibrium as there would be a net force acting on it. However, if its a hollow sphere, then why does the electric field inside the hollow sphere have to be zero?", "label": 1}
+{"snippet": "In this sentence: \"We would also accept an international transfer, but in that case we would ask you to pay your bank's charges at the time of the instruction to ensure that we received the full amount\" is it correct to use \"received\" or should it be in present tense?", "label": 1}
+{"snippet": "When must an edge for a connected simple graph appear in every spanning tree for this graph? I would have thought it was the midpoint of the longest simple path in the graph. However, there would then be another way to connect the graph, so location of vertices doesn't matter.", "label": 1}
+{"snippet": "I'm editing a post that has the sentence: How much larger should it be to be secure? I've come across other situations where there are repetitions in a sentence (such as that that) and am hoping for a word to describe this occurrence and a generalized approach to rethink it so the sentence becomes clearer.", "label": 1}
+{"snippet": "A question for \"real\" mathematicians who have become better acculturated to math-speak than this philosopher! If you read a phrase like ... the natural numbers equipped with the evens-before-odds order ... just what do you understand by equipped? [I have my suspicions, of course, but I won't prejudice the comments/answers by saying ...!]", "label": 1}
+{"snippet": "I can't get this right, but I'm not sure which is the correct statement: We do not tolerate against pornography images. or is it We do not tolerate with pornography images. Which is the correct way of not agreeing with pornography images?", "label": 1}
+{"snippet": "I approached this exam question the wrong way apparently, help please? Consider the word \"mathematics\". In how many ways can you rearrange all the letters so that the vowels are paired and always apart?", "label": 1}
+{"snippet": "My desktop background rotates through a bunch of space and nature scenes, and this one came up. What would be the effect on people walking around down here, if another earth was looming overhead instead of our moon.", "label": 1}
+{"snippet": "I have attempting to solve this using the infinite ramsey theorem, with colouring based on whether the sum of two vertices has an even or odd number of distinct prime factors. This is leading to an infinite recursion. Is this ok? At the end of all time I will be done.", "label": 1}
+{"snippet": "Can we prove or disprove that : There exists for any given closed figure, a point which is equidistant from all of its vertices? Any closed figure means literally any closed figure? I am gonna instinctively say no, but How!?", "label": 1}
+{"snippet": "The mainland counties of England form a graph with counties as vertices and edges as touching borders. Is there a Hamiltonian path one can take? This is not homework, I just have an idea for a holiday around England where I visit every county only once!", "label": 1}
+{"snippet": "Say I have a laser. If I spin the laser so that the beam sweeps in an arc along a very distant object, could that dot travel faster than the speed of light? In Diagram form:", "label": 1}
+{"snippet": "Question is as clear as stated in title. What is the maximum energy that can be stored in a gluon field flux tube without production of an quark anti-quark pair? And how much it usually store in a meson?", "label": 1}
+{"snippet": "It would be [adjective] to dismiss president's new policy, as purely politic playing, it appears he has genuine intentions to improve the well being of the poor. What adjective would be correct to mean that things were dismissed too quickly?", "label": 1}
+{"snippet": "This is a question just out of interest to know the power of integration by parts. There are various level of integration by parts. What are some of the most general form of integration by parts? I have encountered it very often in PDE's. I look forward to gaining more insights on it. Thank you for your ideas, help and discussions.", "label": 1}
+{"snippet": "Is there any undergraduate textbook on graph theory using linear algebra? A request is a beginning with graph matrices that explain most concepts in graph theory? P.s. This thread has more specific requests than this thread What are good books to learn graph theory?.", "label": 1}
+{"snippet": "Is there a package to produce syntax-colored blocks of source code in plain TeX ? A listings equivalent ? Or (maybe) some macro to produce a colored tex input for some given source code ? Is it possible to achieve something through LuaTeX ?", "label": 1}
+{"snippet": "I am looking for a correct expression for an activity when a person is injured or in a bad leath condition for any reason and is doing special exercises to feel better. Is it reeducate? Rehabilitate? Vindicate? Thank you.", "label": 1}
+{"snippet": "Is there a rule, which states that one must or must not use comma before \"then\" in a sentence like this: If you can read this, then you might want to answer this question.", "label": 1}
+{"snippet": "I use the method described in this link for getting hyperlinks from different PDF files: Can you have hyperlinks to locations in different PDFs? I would like to remain with two open PDF files, source and destination. When I use the described method, the source PDF is replaced by the target PDF. Can I control how to display the PDF files?", "label": 1}
+{"snippet": "are there any concrete rules that say wich words(parts of speech) in a title should start with a capital ? what would be a correct capitalization for the title of this question ?", "label": 1}
+{"snippet": "He is not satisfied with her praise. He is rather satisfied with my praise. I am sure this \"rather\" modifies \"with my praise.\" But the position of it doesn't have to be in front of \"with?\" Like only, as in \"You only clean your room when it gets helplessly untidy.\"", "label": 1}
+{"snippet": "I think there must be a good word for this, but can't think of what it might be. Harmony and Melody are pieces of it, beat seems simplistic, Instrumentation seems too scientific and dull. Any Ideas?", "label": 1}
+{"snippet": "I know that you can construct a square root of a given segment through a certain construction, and I know that construction. What is the proof that this construction works to construct a square root?", "label": 1}
+{"snippet": "What is the meaning and the accurate use of the word \"Aura\"? Does it mean literally \" Atmosphere\"? consider this example: \" Heavy snow,, thunders... strong wind. What a lovely aura! \" P.S: I meant by aura not the weather itself but the general atmosphere around me that i feel at that moment.. My feeling. Thanks in advance!", "label": 1}
+{"snippet": "What are the different kinds of relations one can obtain between the elements of a finite Geometric progression other than the fact that one element upon the previous element gives the common ratio?", "label": 1}
+{"snippet": "I would like to ask this question; A word that is used to describe someone who is very kind and likes most to help other people with their problems? (I need both a noun and an adjective; if they are all applied)", "label": 1}
+{"snippet": "I liked the bar of the first answer in this question: Progress bar for latex-beamer so my question is if there is a way to put this progress bar in the right/left side of the slides. Thanks.", "label": 1}
+{"snippet": "What is the type (adjective, noun, etc.) of the word atom in hydrogen atom? I think that atom here does not qualify hydrogen in any way and we can use it or not, and the meaning of the word hydrogen will not change. So, hydrogen atom and hydrogen are equivalent.", "label": 1}
+{"snippet": "I use LyX. When I use the \"Title\" environment under article(hebrew), it uses very big spacings between it and the rest of the document. How do I control the spacing and make it use a compact title so my resume will all fit in one page?", "label": 1}
+{"snippet": "I need to reply to an email and I wanted to clarify to the other person that: I understand exactly what needs to be done on the technical side but I'm not familiarized with the red tape involved in the process. Would that be, somehow, offensive?", "label": 1}
+{"snippet": "If C is a collection of connected subsets of M, all having a point in common, prove that union of C is connected. I know a set is connected if it is not disconnected. Also, from the above, I know the intersection of all subsets C is nonempty. I am not sure where to go from there.", "label": 1}
+{"snippet": "When two words are put together as in \"heads up\", \"put down\", \"build out\"... are they considered a phrase? And if so, do the term for these are \"adjectival phrases\" as they mention on this question: Is \"put together\" an adjectival phrase?.", "label": 1}
+{"snippet": "Which is better? The protocol was signed last week after all punch list items were fixed up. or The protocol was signed last week after all punch list items had been fixed up.", "label": 1}
+{"snippet": "I am using white colored font on black page and somehow I am losing my page numbers. I suppose the page number is still in black color. So How do we set the color of page number? And while on the topic, how about color of page runners etc.", "label": 1}
+{"snippet": "I need sections included in the TOC, but not in the body text for a PDF output; so when I click the section at TOC, it will jump to the related page [where section header/title is not displayed]. How do I do this?", "label": 1}
+{"snippet": "Is there any approach or mathematical formula using which we can predict the interarrival times for a Poisson distribution (not the expected interarrival time as it comes out to be same dependent only the rate parameter) ? Do we need require to know the probability distribution for finding the time interval for a a particular number of events to occur ?", "label": 1}
+{"snippet": "Many resources state that light skin/pale skin absorbs more UV than dark-colour skin. Doesn't black absorb maximum radiation? For an example, see this article: Natural selection therefore favored a genetic solution to that problem by evolving to a pale skin that absorbs UV more efficiently.", "label": 1}
+{"snippet": "You have a large house. Negative question= Don't you have a large house? Saying ''Haven't you a large house?'' is wrong am i correct? But is ''Haven't you got a large house?'' correct or wrong?", "label": 1}
+{"snippet": "I found that net charge density in the interior of a conductor is zero.The charge resides only on the surface.Then can we say that there is no volume charge density of any uniformly charge conductor?", "label": 1}
+{"snippet": "I will provide definitions for which I can't think of the word: as though not trying one's best having the appearance of little effort The word is used to describe something that you look at and think, \"They're not really trying.\" I remember thinking this is a good vocab word, and darn it, I forgot it. This has been driving me crazy all day.", "label": 1}
+{"snippet": "Now, shadows dawn as the twilight comes. Dawn has the meaning \"come into existence\". Does it work that way almost every time with words like, for example, shadows? Or, are there quite limited types of word that can be used with dawn? And, the sentence above, does it sound awkward to you?", "label": 1}
+{"snippet": "Can a virtual image created by a concave lens create any image by the convex lens oriented parallel (at the same direction of refracted rays of the concave one) with the concave one? If not, can any other orientation of the convex lens can do the work? What is the effectiveness of a high powered convex lens to do the stuff?", "label": 1}
+{"snippet": "Is it correct to say: At the time, circumstances arose such that I had to leave the city. in the meaning that situation got such that the speaker could not stay in the city anymore? Particularly, I am curious if one can say arise about circumstances or situation.", "label": 1}
+{"snippet": "When I walked on the road, I happened to pass a pool of mud. Somebody had already set some blocks of stones and bricks on the mud from one end to other end in order to pass it. I could pass it by treading on the blocks of stones. What do you call such a temporary arrangement to walk on?", "label": 1}
+{"snippet": "I recently encountered: vernal adj. of, in, or appropriate to spring And I truly wonder if there is also equivalents for the other seasons (summer, autumn, and winter). EDIT: I just found aestival n. relating to summer. Please feel free to contribute words that have the similar/same meaning to spring and summer even though I have found those.", "label": 1}
+{"snippet": "What does the prefix atta mean? What is it trying to abbreviate? What a? Wiktionary claims that it stands for that's a or that's the, but I do not see the resemblance to atta.", "label": 1}
+{"snippet": "On Wikipedia, I read, \"A box can be thought of 'small boxes' infinitely repeating in all three dimensional directions\" I don't understand what does Wikipedia wants to say with a box containing infinite numbers of similar small boxes. Why would it be infinite. I can have any integer however. Can any one explain it to me?", "label": 1}
+{"snippet": "What actually elementary proof means ? If there is an elementary proof for a conjecture , then is it a theorem ? I saw papers on some conjectures proving stating as elementary proof. Then it means the conjecture is proved ? Is there any site that correctly tells about status of a conjecture ? thanks in advance .", "label": 1}
+{"snippet": "I remember that there was one technique of English writing that writes down every single word what one thinks. I forgot what this type of writing is called, does anyone knows the word? \"umm, I think yesterday was raining, eh.. but oh wait, no, It's incorrect. It was cloudy.......\"", "label": 1}
+{"snippet": "I see commutivity used in contexts where the meaning appears to be the same as commutativity. Here are an example from physics and another example. Is commutivity incorrect? Does it differ from commutativity?", "label": 1}
+{"snippet": "I have to take a talk of an hour and I have to talk about blow-up of toric varieties. Can you suggest me some interesting examples that I can present? How can I find a good reference for the theory needed? I'd like to do a talk rich of images and interesting examples. Thank you!", "label": 1}
+{"snippet": "In case of identical particles we multiply the individual wave functions of the particles to get the system wave funtion. But why are we not adding? Or performing any other operation to get the system wave function. Can anyone show the math that what physics will be violated if i simply add the individual particle's wave function?", "label": 1}
+{"snippet": "I found this phrase in The Adventures of Sherlock Holmes book; this is the full paragraph, with my emphasis: You will remember that I remarked the other day, just before we went into the very simple problem presented by Miss Mary Sutherland, that for strange effects and extraordinary combinations we must go to life itself, which is always far more daring than any effort of the imagination. Does it mean something like \"more daring than we thought\"?", "label": 1}
+{"snippet": "Here's the quote (from The Tragedy of Macbeth, by William Shakespeare): This supernatural soliciting Cannot be ill, cannot be good. If ill, Why hath it given me earnest of success, Commencing in a truth? I am thane of Cawdor. If good, why do I yield to that suggestion Whose horrid image doth unfix my hair And make my seated heart knock at my ribs, Against the use of nature? The connotations may have changed since it was written, but doesn't the word \"seated\" evoke the image of the object under discussion being, to all intents, still? As in pretty much motionless? What am I missing?", "label": 1}
+{"snippet": "Google defines paradox in three ways, the first two being: a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory. a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true. These are almost opposite definitions. My English book defined it as the second, but I've always understood it to mean the first. Which is the most common usage?", "label": 1}
+{"snippet": "What happens to the energy when waves completely cancel each other out via destructive interference? It seems like the energy just disappears, but that would violate the law of energy conservation. My guess is that the kinetic energy is transformed into potential energy. Or maybe what happens to the energy depends on the specific interference scenario? Can someone elaborate on that or correct me if I'm wrong?", "label": 1}
+{"snippet": "I'm studying Complex Analysis and everything up to this point has been pretty straightforward to visualise, but I can't get my head around residues, especially as they seem to have two very different definitions (as a Laurent series coefficient and as an expression involving an integral on a closed path) that I can't understand why they equate. Can anyone give a fairly simple explanation of residues? Thanks!", "label": 1}
+{"snippet": "A paracompact space is a space in which every open cover has a locally finite refinement. A compact space is a space in which every open cover has a finite subcover. Why must the product of a compact and a paracompact space be paracompact? I really have very little intuition about how to go about this question, so any hints or a proof would be greatly appreciated.", "label": 1}
+{"snippet": "Is there a word that is similar to \"marketing\" that doesn't imply the idea of commercialization or profit? For example, a non-profit that assists domestic abuse victims may run a campaign where they advertise their services. They may put up posters, buy billboard space, and so forth. While this is marketing, people in that industry may be very reluctant to call it a \"marketing campaign\". This is because marketing tends to carry the connotation of trying to sell something. Is there a more neutral word?", "label": 1}
+{"snippet": "I'm currently working on an English project and I have chosen to rewrite a story (Heart of Darkness by Joseph Conrad) in a biblical, King James style. I have done a large amount of reading but I do sometimes get confused, especially on certain sentence structures. Do you have any tips on grammar, vocabulary, or sentence structure that will help me make my writing seem more authentic?", "label": 1}
+{"snippet": "Can someone please explain why the van der Waals force is attractive instead of repulsive? My understanding is that is has to do with the electron cloud creating a dipole, but I can't seem to understand why the force isn't repulsive (since like charges repel.) Since the electron cloud is moving, I would think it would cause a force that is attractive sometimes and repulsive sometimes, with the average effect being more repulsive. Obviously I am missing something!", "label": 1}
+{"snippet": "I'm really sorry if this question has been asked before, I looked but couldn't find anything. I'm going through an elementary number theory book and in the first chapter it introduces the least integer principle. There is no proof accompanied with it, it just states: \"a nonempty set of integers that is bounded below contains a smallest element.\" Is the reason the book doesn't give a proof because we take this as an axiom? Or is the proof so trivial that it need not be written? Thanks!", "label": 1}
+{"snippet": "I've been reading a Real Analysis textbook that my friend loaned to me. I have come across a proposition that says that a totally bounded set is bounded, but a bounded set is not always totally bounded. This makes sense, however I am having trouble thinking of an example of a set that is bounded but not totally bounded. Could anyone shed some light on this? Thanks!", "label": 1}
+{"snippet": "I am working on some optimization problems, and I am aware of the method of proving that the \"angle of incidence equals the angle of reflection\" using Fermat's principle and calculus. However, my textbook suggests that there is a simple way to prove this without calculus, but I'm a little unsure about how to do this. I would appreciate any advice on how to proceed.", "label": 1}
+{"snippet": "Here are the definitions of the two words: Hypocrisy: the practice of claiming to have moral standards or beliefs to which one's own behavior does not conform; pretense. Affectation: behavior, speech, or writing that is artificial and designed to impress. However, I'm not sure about the difference between the usage/connotation of these two words? Is there any example where you would use hypocrisy instead of affectation or the other way round?", "label": 1}
+{"snippet": "Wikipedia says: In particle physics, supersymmetry (often abbreviated SUSY) is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners. In a theory with unbroken supersymmetry, for every type of boson there exists a corresponding type of fermion with the same mass and internal quantum numbers (other than spin), and vice-versa. There is only indirect evidence for the existence of supersymmetry [...] I want a mathematical explanation of SUSY.", "label": 1}
+{"snippet": "I know that when I'm solving a linear equation of the form ax = b (mod n), the gcd(a,n) tells me how many solutions there are. I don't really understand why this is. More than a proof, I'm interested in an explanation that will help me understand the relation between the gcd and number of solutions. Also, why does the gcd need to divide b for there to exist solutions? Thanks", "label": 1}
+{"snippet": "I'm trying to wrap my head around function spaces. I get that you can define the inner product as the integral the multiplication of two functions over the entire domain because it satisfies the properties of the inner product. What I don't understand is what makes this a complete space? I don't understand the concept how a complete space works with functions. Any insight would be appreciated.", "label": 1}
+{"snippet": "When is it appropriate to use the terms Dear Sir or Madam and To whom it may concern? The rules I was taught state that Dear Sir or Madam should be used when you're writing a letter to a person about something that person has direct involvement in (e.g. returning a defective product to a customer service department). By the same rules, To whom it may concern would be used for situations in which the recipient is a third party to the topic of the letter (e.g. regarding a letter of reference or recommendation). Was I taught correctly? Is the rule actually something else? Or is this one of those situations where many people have an opinion but there is no real rule?", "label": 1}
+{"snippet": "I've been trying to determine an explanation for the falsity of a logical statement for some time now and I've had no luck in figuring out exactly how to go about it. The statement in question goes as follows: Explain why the statement for any integers a, b, c, if ab = ac, then b = c is false. Perhaps I'm misunderstanding the way to determine the falsity of a logical statement? Any help is appreciated.", "label": 1}
+{"snippet": "What is the difference between positive definite kernels and positive definite functions? As I understand it, a positive definite kernel is a positive definite function if it is translation invariant. Is this correct? If not, what is the actual relationship between these concepts? I'm reading Learning with Kernels and using this text, Wikipedia, and Google, haven't been able to find a good answer to this question. References are appreciated!", "label": 1}
+{"snippet": "Often, I'll be driving down the road on a summer day, and as I look ahead toward the horizon, I notice that the road looks like there's a puddle of water on it, or that it was somehow wet. Of course, as I get closer, the effect disappears. I know that it is some kind of atmospheric effect. What is it called, and how does it work?", "label": 1}
+{"snippet": "Just as there is a difference in meaning between \"likely\" and \"liable\" in terms of a desirable or undesirable outcome, is there any subtle diference between \"apt\" and \"likely\" ? Does the use of \"apt to\" and \"likely to\" in the following sentences convey the same degree of expectation ? \"John is apt to call on us on Wednesday afternoon.\" \"John is likely to call on us on Wednesday afternoon.\" My dog is apt to run away if I don't close the gate. My dog is likely to run away if I don't close the gate.", "label": 1}
+{"snippet": "I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect. As I found them very interesting, I would appreciate if anyone could provide me with some good sources(books, internet links etc) to learn more about them. Please keep in mind that I am only an undergraduate student, so difficult graduate stuff might not be of very use to me.", "label": 1}
+{"snippet": "I'm currently learning about local extrema in serveral variables and have come across the second derivative test for classifying critical points of multivariable functions. I have read and understood the test (see link below), however I don't understand the idea behind it. Why is the critical point of a function a minimum if the eigenvalues of the Hessian matrix are all positive? I understand the idea behind the single variable case, however I am confused about the role of eigenvalues in the case of several variables. http://en.wikipedia.org/wiki/Second_partial_derivative_test Any insight into this would be much appreciated. Thanks.", "label": 1}
+{"snippet": "Wikipedia's page for Imperial Units does not list Fahrenheit. The corresponding page for SI Units lists Kelvin as an SI unit, and Celsius as a derived SI unit. This leads me to believe that Fahrenheit does not belong to the Imperial System. Fahrenheit is listed as a page belonging to the Imperial Units category, also on Wikipedia. I know that the US mostly uses the Imperial system and also uses Fahrenheit for temperature. Meanwhile, the UK mostly uses the metric system and also uses Celsius for temperature. Is this just a coincidence, or is Fahrenheit actually a part of the Imperial system?", "label": 1}
+{"snippet": "I'd like to use \"digitally challenged\" to refer to someone who is missing part or all of a finger, but it sounds like I'm talking about someone who doesn't know how to use computers. Are there any phrases, ideally somewhat humorous in nature, that I can use to refer to people who are missing part or all of a finger? Example usage: Steer clear of that izakaya. I've heard some of the patrons are [alternative to \"digitally challenged\"].", "label": 1}
+{"snippet": "I'm preparing some marketing materials for my boss, and one section contains the phrase \"Here are a few examples:\". The list that follows contains two items, which strikes me as being incorrect, though I can't find much evidence of this. Is it semantically correct to refer to two items as \"a few\"? Is there a solid rule for this, or is it just personal preference? Edit - As Armen correctly pointed out, this question is about semantics rather than grammar. I changed my phrasing to reflect this.", "label": 1}
+{"snippet": "At the moment I am following a course on variational methods for mathematicians. Last week we derived the Euler-Lagrange equations for a functional under a constraint. In this derivation we found that the Lagrange multiplier may depend on time. However, I could not remember having ever seen an example of a Lagrange multiplier dependent on time during my physics courses. Does anyone have a nice (mechanical) example?", "label": 1}
+{"snippet": "I know that it is technically impossible to reach the speed of light in vacuum since the mass of the object travelling would reach infinity. However in a medium, would there be some sort of theoretical equivalent to a sonic boom that would occur? Since sonic booms are formed when sound waves can't catch up with an object, could the same happen with light waves? Would it look like an immense burst of light in the sky?", "label": 1}
+{"snippet": "I'm writing an essay for medical school applications. Both my parents were physicians, so it is what I was familiar with growing up. Instead of pursuing medicine in college, I decided to pursue something else and try a few different careers after college. Now I'm back on the medicine path and I'm trying to explain why I needed to try other stuff first. I'm hesitant to use the word \"comfort zone\" because I think it implies that medicine would be the comfortable (i.e., easy) path, when that is not the case. Any other phrases come to mind that explain this sentiment?", "label": 1}
+{"snippet": "I have been learning more about Hilbert spaces in an effort to better understand quantum mechanics. Most of the properties of Hilbert spaces seem useful (e.g. vector space, inner product, complex numbers, etc), but I don't understand why we need the inner product space to form a complete metric space. My Questions: Why do we need the inner product space to form a metric space? Why does it have to be a complete metric space?", "label": 1}
+{"snippet": "I've been studying random walks as part of a finance course and I'm starting to become really interested, and I'd like to start a study of them from a mathematics (i.e. more formal/rigorous) point of view. However, my knowledge of mathematics is quite limited (calculus, basic linear algebra and probability, a bit of (stochastic) differential equations). So I was wondering what fields I need to familiarise myself with before I can effectively study random walks. Maybe there's even a good self-contained book on random walks for beginners?", "label": 1}
+{"snippet": "In Mendelson's book (\"Introduction to mathematical logic\") he defines truth values for sentences in the propositional calculus using truth tables. However, it seems to me he assumes implicitly that every well-formed sentence (what he calls \"statement form\") has a unique parsing; i.e. it is impossible for the same statement form to arise in two different ways. This is of course correct, but it requires a proof. The omission of such proof (or even mentioning it is needed) is somewhat surprising for me as Mendelson's book is otherwise very explicit about everything. Am I missing something?", "label": 1}
+{"snippet": "I have been trying to work this problem out for a bit and am stuck. Does anybody have any ideas how to proceed or solve this? I think this has something to do with rings and fields but I can't seem to find the connection. EDIT: I know the other proof listed as a duplicate here, but it uses Cauchy's Theorem and we are not allowed to use that because we skipped that chapter.", "label": 1}
+{"snippet": "Does it sound right to say \"be successful\" instead of \"good luck\" as a quick reply? For instance: A : I have a tough exam tomorrow. B : I hope you'll be successful in your exam. I suppose using \"be successful\" as a part of a sentence sounds right, but isn't it kind of awkward or unnatural to say \"be successful\" as a short reply instead of \"good luck\"?", "label": 1}
+{"snippet": "Apologies if this question has been posted somewhere else, but I have not managed to find an answer that works for me. I am trying to create a bibliography using Harvard style, using BibDesk to create the .bib file, and Biber and BibLatex. However, the bibliography contains the DOI, the URL, the ISSN, a further e-print URL - all things I do not want. My question is: is there a way to delete these fields in BibDesk, so that they are absent in the .bib file?", "label": 1}
+{"snippet": "I came across this problem in my textbook, and I don't understand why the answer is 'as' and not 'that'. \"We are attracted to people who have a sense of humor, who can laugh at the same things ____ we laugh at.\" In the sentence above, the word that goes in the blank is 'as' according to the textbook. Could someone explain why? Thank you in advance.", "label": 1}
+{"snippet": "I want to apply the Biot-Savart law to calculate the magnetic field at a point created by current flowing through a square/rectangular conductor. More specifically, a trace on a printed circuit board. To me, a trace on a circuit board is the summation of many infinitesimal rectangular conductors. I have seen lots of examples for a wire (circular conductor), but not rectangular. How should I go about getting started with this problem?", "label": 1}
+{"snippet": "I just came across the following sentence in the book \"The theory of everything\": If one keeps traveling in a certain direction on the surface of the Earth, one never comes up against an impassable barrier or falls over the edge, but eventually comes back to where one started. Using multiple \"one\"s repeatedly in a sentence sounds odd to me. Since I found it in a reputable book, I am wondering whether it sounds good to the ears of a native English speaker. Wouldn't it be better to replace the second and third \"one\" with \"he\", \"she\" or \"they\"?", "label": 1}
+{"snippet": "Definition: dilemma a situation in which a difficult choice has to be made between two or more alternatives, especially ones that are equally undesirable. a difficult situation or problem. Source: Google. Example sentence: The dilemma of modern life: trying to find an outlet outside of your house. I guess this sentence fits the second definition. So is it correct? (Or should I use another word instead?)", "label": 1}
+{"snippet": "When someone has unreasonable expectations and feels that he is owed by others, this trait is described as a \"sense of entitlement\". But how do you refer to the person who has this trait other than calling him \"a person with a sense of entitlement\"? If there is no single word to describe this kind of character, can you suggest a few equivalent phrases for \"a person with a sense of entitlement\"?", "label": 1}
+{"snippet": "Let's say I want to describe a habit in the past (something that happened many times over and over again) in the form of a conditional statement. Is the following sentence grammatically correct? If I forgot to do my homework, I would pretend the dog ate it. Or is it If I had forgotten to do my homework, I would pretend the dog ate it. Or is there another, more correct form?", "label": 1}
+{"snippet": "I have been trying to understand the notion of parallel transport and covariant derivative. I am unable to see why the change in a vector when it is parallel transported from one point to another shouldn't be a vector. If it is, why isn't the Levi-Cevita connection not a tensor ? Hence my questions are : What is a connection geometrically ? What is parallel transport in a particular coordinate system geometrically ?", "label": 1}
+{"snippet": "I need some help with the following question: In the game of \"odd man out\" each player tosses a fair coin. If all the coins turn up the same except for one, the player tossing the different coin is declared the odd man out and is eliminated from the contest. Suppose that three people are playing. What is the probability that someone will be eliminated on the first round? Hint: use the complement.", "label": 1}
+{"snippet": "I've just switched from mac to windows and have just started using TeXworks. I like it, but I find that the default pdf viewer is difficult to use. For example, there doesn't seem to be a key command for going to the bottom or top of the current page; I can't view pages continuously; spacebar does nothing for navigation; and trackpad functionality appears to be broken (scrolling with the trackpad causes the pages to jump around in a seemingly random fashion). Is there a list of key commands somewhere? Or is there a way of using a different default pdf viewer?", "label": 1}
+{"snippet": "What are the advantages and disadvantages of piecewise linear interpolation, cubic interpolation, and cubic spline interpolation? I know that piecewise linear interpolation is not smooth and may not be accurate for nonlinear functions. The other two are smooth. But I think my understanding is a little superficial. Especially the difference between the cubic interpolation and cubic spline though I know how to compute them. Could someone help me understanding the advantages and disadvantages of these three? Thanks so much!", "label": 1}
+{"snippet": "While reading my copy of \"Resnick and Halliday\", I noticed that the book has made a distinction b/w the terms \" degree celsius\" and \"celsius degree\". When I googled this, I was able to find only one matching hit(on the first page), which stated that while degree celsius is the unit for the measured temperature, celsius degree is the unit of the difference in temperature. Is this correct? Please share your knowledge and help me.", "label": 1}
+{"snippet": "A single toss of a fair coin cannot be predicted. But if we observe a large number of tosses, we can prove mathematically the law that roughly half of them will show up heads. The movements of individual molecules in a gas cannot be predicted and can be assumed to be random. But if we observe some macroscopic phenomena such as temperature or pressure, we can prove mathematically that some laws are satisfied. Individual quantum events are random. But if we observe a large number of such events, we discover experimentally that they satisfy the laws of quantum mechanics. Could the laws of quantum mechanics be proved mathematically as in the examples above?", "label": 1}
+{"snippet": "Here's what I know about dark matter: Astrophysicists realized the movements of galaxies and other astronomical bodies cannot be explained by the gravitational effects of matter known to be there, so either there is a lot of matter missing that doesn't react with light or general relativity needs to be fixed. For the purpose of this question, assume the former. I've read that this \"dark matter\" can't be composed of baryons (quarks and leptons). My question is how do we know that it can't be baryonic? After all, air is invisible. Maybe that's a bad analogy, but you get my point: Why can't there be matter that is invisible, yet composed of baryons?", "label": 1}
+{"snippet": "So, I have been solving a number of exercises involving contraction mapping. However, I am struggling to understand what exactly contraction mapping is at its most basic. All I really understand from the concept is that if we have two sets, then one specific point on the set is being mapped closer to another - I'm not sure if I have the right definition. Can somebody please explain this to me in the most layman way possible?", "label": 1}
+{"snippet": "I was trying to understand the undecidable nature of the continuum hypothesis and came up with the following question: The set of circles with a rational diameter is countably infinite (with cardinality equal to the cardinality of integers). The set of circles with a rational circumference is countably infinite (with cardinality equal to the cardinality of integers). The cardinality of the union of these sets is clearly smaller than the uncountable set of irrational numbers, but why isn't it larger than the set of countable integers?", "label": 1}
+{"snippet": "I often hear about string theory and its complicated mathematical structure as a physical theory, but I can't say that I've ever actually seen any of the related math. In general, I'm curious as to what the mathematics of string theory look like, can anyone point me to some references? In specific, I want to know if there is a fundamental equation in string theory that is assumed as a starting point for most problems, something comparable to Newton's second law in mechanics or the Schrodinger equation in QM?", "label": 1}
+{"snippet": "Recently, I am studying the online course Effective Field Theory provided by MIT OCW. Prof. Stewart gives a nice picture to summarize the effective theories: As a newbie in this field (I only have a knowledge of QFT on the level of Peskin & Schroeder's book), I am quite confused with so many terminologies. What do they stand for and Why do we need these different theories? Could someone explain this picture in depth (especially on their advantages and limitations)? Any help will be greatly appreciated.", "label": 1}
+{"snippet": "When a solid object moves in the atmosphere (e.g. a plane), in which direction does air fill up the \"empty space\" left by the translation of the object? Does this depends on the direction of movement of the object? (e.g. if the plane is moving horizontally, or is landing, or taking off) PS: I am aware of this question and I think this is not a duplicate of that one.", "label": 1}
+{"snippet": "Here in Pittsburgh, we have lots of \"Let's go Steelers!\" (and some diehards who also say \"Let's go Bucs!\", but they're dying out). What does that phrase even imply? I assume it's similar to \"Go Steelers\", which I'm also not sure of the implications. \"Go Steelers... to victory!\" is a very strange way to phrase the sentence. Does anyone know where this phrase comes from?", "label": 1}
+{"snippet": "I was trying to describe my friend as being someone who gets upset in the absence of immediate gratification, but couldn't think of a good word. A good example would be someone who comes back from the gym and takes off their shirt expecting to look fit after one session. Is there a word to describe someone that does this? The closest I could think of was \"impatient\", but that doesn't quite pin down the meaning.", "label": 1}
+{"snippet": "I was wondering how this phrase sounds in English: She is a little bit shy. In my country the people say \"a little bit\" a lot, and sometimes they use it wrong. I have the impression that in US (or even in other countries where English is spoken), people prefer to be more specific saying \"She is shy\". Anyway, I don't want to be misunderstood, can you tell me if the above phrase sounds awkward, and in which situations I can use \"a little bit\" without problem.", "label": 1}
+{"snippet": "I know that Galois Theory can be used to answer the following question: Why is there no formula for the roots of a fifth (or higher) degree polynomial equation in terms of the coefficients of the polynomial, using only the usual algebraic operations (addition, subtraction, multiplication, division) and application of radicals (square roots, cube roots, etc)? Can real analysis be used also to answer this question (e.g using the intermediate value theorem, etc..)? Is there some sort of connection between real analysis and galois theory?", "label": 1}
+{"snippet": "My sentence is as follows: I lodged a complaint with Acme Corporation, a private entity. Does it need to be changed into: I lodged a complaint with Acme Corporation, which was a private entity. I appreciate the meaning between the two sentences is slightly different. I would just like to know if the first sentence is grammatically correct. It looks correct to me but I have been told that only the second version is grammatically correct. Is there a 'rule' governing this situation that I can reference?", "label": 1}
+{"snippet": "Does one need to invoke quantum mechanics to explain Casimir or van der Waals forces? I see that textbooks show derivations of van der Waal forces with no QM but the Casimir force is typically described within QM. Additional questions I have are: Is there a difference between van der Waals and Casimir forces? Are there distinct examples of these two forces in real life? Is there a way to prove a given force is van der Waal and not Casimir or vice versa?", "label": 1}
+{"snippet": "This question on a different SE site asks the question of what the etymology of the word \"Xenomorph\" is, and the consensus, from the comments at least, is that it has none - that it was purely invented for that movie. My question is, is this true? Did this word purely exist as a creation of the movies, as a portmanteau of two separate words? Or is there an origint that dates back to before the creation of these movies? I realize this is the ELU stack exchange, so I don't expect a detailed explanation of the etymological origins movie-side, I'm simply curious if there is any evidence that this word existed prior to the Alien franchise.", "label": 1}
+{"snippet": "I looked up the definition of a Joke on Dictionary.com which gave me this \"Something said or done to provoke laughter or cause amusement, as a witticism, a short and amusing anecdote, or a prankish act.\" If someone had the intention to make a joke but failed to provoke laughter is it still a Joke, and if someone did not have the intention to make a joke yet it provoked laughter, does it count as a Joke.", "label": 1}
+{"snippet": "I proved the following statement: The composition factors of every finite solvable group are isomorphic to cylic groups of prime order. I want to use this result to prove that every two finite solvable groups of the same order have the same composition factors. If I knew that for every prime number in the decomposition of the order of the groups there is a composition factor that is cyclic of that order I would obviously be finished. However, I'm not even sure if this statement is true and I don't have a good idea on how to proceed in case the statement isn't true. Help will be appreciated! :)", "label": 1}
+{"snippet": "A recent paper authored by Niayesh Afshordi and Joao Magueijo is in the news claiming to challenge Einstein's theory on constancy of light speed. It says light might have travelled with a faster pace during the initial stages of Big bang which apparently sets aside the inflation hypothesis. My question is whether it actually invalidates Einstein's relativity - which depends on constancy of speed of light. Or is it only applicable to the very early universe?", "label": 1}
+{"snippet": "I'm writing a thesis in a scientific area, and in a draft I wrote that it was \"not possible to tell which set of data is more accurate\", meaning that it was not possible to tell which was closer to the true values of the thing being measured. One of my supervisors objected to this language, claiming that either one is accurate or one is not - that it's no more possible to be more or less accurate than it is to be more or less pregnant. For the purposes of this thesis I will simply avoid this phrasing, but out of curiosity: is he right?", "label": 1}
+{"snippet": "I have been reading up on the correct use of 'which' and 'that' but I am still struggling. I am unsure if 'must be taken regularly' is restrictive or not. Both 'which' and 'that' sound correct to me. Can someone please tell me which word is correct to use in the following sentence: Arava is a strongly recommended medication, which must be taken regularly. Arava is a strongly recommended medication that must be taken regularly. Thank you.", "label": 1}
+{"snippet": "I am looking for a word that describes a personality/person (not in a negative but neutral/positive way) that doesn't care abut anything, has a neutral opinion about most things, is very care free/laxed, etc. The closest I could think of is narcissist but it's not quite right. Is there such a word? I guess an example would be like \"Dave doesn't care if we have a salad, a burger, or a soup for lunch, he is a/very ________.\" Thanks.", "label": 1}
+{"snippet": "Given a finite dimensional algebra, what is the exact relation between the indecomposable projective modules, and a general indecomposable module? In the case of an oriented quiver without cycles for example, it is easy to find the simples, and the indecomposable projectives. What does this tell us about a general indecomposable module? I guess the main question is, to understand the complete representation theory of a finite dimensional algebra (or let's say a quiver), what else do we need besides the simples and the projective indecomposables?", "label": 1}
+{"snippet": "I'm looking for an online coupled oscillation simulation. The best I have got so far is this --- https://phet.colorado.edu/sims/normal-modes/normal-modes_en.html But I'm looking for something which has more options like changing the mass of the objects, changing the spring constants, cutting off the springs. Please suggest if you have come across better simulations. PS : I apologize if this question does not belong here. I need a coupled oscillation simulator for my work.", "label": 1}
+{"snippet": "Are there other usages of the expression \"don't ask don't tell\" besides the one from its Wikipedia page? Don't ask, don't tell (DADT) is the term commonly used for the policy restricting United States military personnel from efforts to discriminate or harass closeted homosexual or bisexual service members or applicants, while barring those who are openly gay, lesbian, or bisexual from military service. Or is the expression also used in contexts not related to homosexualism in the military?", "label": 1}
+{"snippet": "As part of a promotion a toy is put in each packet of crisps sold. There are eight different toys available. Each toy is equally likely to be found in any packet of crisps. David buys four packets of crisps. a. Find the probability that the four toys in these packets are all different. b. Of the eight toys in the packets, his favourites are the yo-yo and the gyroscope. Find the probability that he finds at least one of his favourite toys in these four packets. I'm stumped on b. Can someone explain how to do part b to me please?", "label": 1}
+{"snippet": "A Group is an algebraic structure consisting of a set of elements together with an operation that combines any two elements to form a third element. The operation satisfies four conditions Closure Associativity Existence of Identity Existence of Inverse Intuitively I understand the purpose of Closure and Associativity Property. But I'm not getting the intuition behind Identity and Inverse. Whats the purpose of having these elements in a group. I searched everywhere and find only common definition which are straight forward. But nobody discuss why it's important. Can anybody explain it to me.", "label": 1}
+{"snippet": "I recently saw a question today pertaining to Russian mathematics and I have a similar question but of a slightly different flavor. I've always heard that the Soviet Union had a history of producing influential mathematicians in geometry/topology and I'm curious if anybody knows of any worthwhile Russian texts on these subjects. I can speak Russian fluently and I'm interested in pursuing these fields and learning the perspectives of some of the old Soviet mathematicians. Would anybody know of such texts? Thank you.", "label": 1}
+{"snippet": "What is the trajectory of a particle in a string or a rope that goes under the effect of a wave pulse. The illustration in this image is not what I am asking about, I just attached it in order to give you an idea of the case I mean. If you give me a picture of the trajectory, I'd be grateful. Thanks in advance.", "label": 1}
+{"snippet": "I find typing `a word' and ``a word'' quite inconvenient, because I find it rather annoying to type ` and `` all the time. Instead, I'd prefer typing 'a word' and \"a word\" (which I often do when I don't pay attention, causing wrong displays). I was hoping the inputenc package would make this possible, but apparently it doesn't. Is there a solution for this?", "label": 1}
+{"snippet": "It is well-known that in a Noetherian UFD, every height one prime ideal is principal. I was wondering whether this statement holds if one replaces 'UFD' with 'locally factorial domain'. I am aware of the fact that 'locally factorial' in general does not imply 'factorial', i.e., 'unique factorization' (though have never come accross locally factorial domains that are not UFDs), so I believe that there is a counterexample to this. However I cannot come up with any.", "label": 1}
+{"snippet": "Can anyone tell the difference between these two phrasal verbs above? A soldier took the flag down from the flagpole. A soldier got the flag down from the flagpole. My father took the electric fan from the wall. My father got the electric fan from the wall. To me, these four sentences look exactly similar in meaning. In Merriam-Webster Dictionary, the phrasal verb \"take down\" is used as \"disassemble\" or \"pull to pieces\" :Take down the building, take a rifle down. Is it possible for the phrasal verb \"get down\" to be used as \"disassemble\"?", "label": 1}
+{"snippet": "I've been told that HJB equations can be solved numerically. I know very little about the subject, could someone provide a couple of comments or a reference (ideally, one that is accessible for a layman) on: What are the main numerical methods used and, roughly, how do they work? What are the limitations of the methods? For example, does the complexity scale badly with dimension?", "label": 1}
+{"snippet": "I'm doing some research for a book I'm writing, and, as the title implies, I'm looking to understand what happens when a supersonic jet sustains in-flight damage. Specifically, what happens to the occupants if the cockpit is breached? (I assume that this is why jet pilots wear masks?) Could a jet maintain super sonic speeds (for at least a short time) with such a breach? What would happen to a person in the cockpit without a mask if there was a cockpit breach at those speeds? Just how weird do things get at super-sonic speeds? Could a conventional airliner ever reach mach one in extreme circumstances? Many thanks!", "label": 1}
+{"snippet": "First of all, how exactly do you entangle two atoms? I've heard about how they entangled atoms in quantum Teleportation experiments, but I don't get how they did it. I've heard that the atoms must \"interact\", but what exactly does that mean? Do they have to touch? Do they have to be within a certain distance - like a foot or an inch - from each other?", "label": 1}
+{"snippet": "After spending some time researching about the centrifugal force, I now understand that it is needed in a non-inertial reference frame for Newton's Laws to hold true. However, I don't understand why we only feel the centrifugal force when moving in a circular path. For example, if you imagine yourself being spun around in a circle, then in your frame of reference you would feel yourself being pushed outwards. But since in your frame of reference you are stationary, the outwards force must be balanced by an inward pull (for you to remain stationary). So why would you only feel the outwards force but not the inwards force?", "label": 1}
+{"snippet": "I am studying elementary particle physics and I am wondering what a parton level Feynman diagram is? My understanding is that partons are representations of the quark and gluon substructure of hadrons, and so I am assuming that any diagram that has a quark or gluon qualifies as a parton-level diagram, but I cannot find any reference to it in my notes or online. Could anyone explain (with examples preferably), what a parton-level Feynman diagram is?", "label": 1}
+{"snippet": "There are many 'rules' on the net saying that a comma should be placed before the relative pronoun 'which' in a non-restrictive clause. (http://www.oxforddictionaries.com/words/relative-clauses) But would the sentence have the same meaning without the comma before the relative pronoun? Does omitting a comma before a relative pronoun change a nonrestrictive clause into a restrictive clause? For example: 'We ate the pizza, which was nice.' 'We ate the pizza which was nice.' If so does the same apply to relative pronouns other than 'which'?", "label": 1}
+{"snippet": "I am wondering whether there are countably many or uncountably many spanning trees of the integer lattice rooted at a particular vertex, say the origin. In a spanning tree rooted at the origin there is a unique path from each vertex to the origin. There are countably many paths to the origin for each vertex, and each spanning tree is uniquely determined by the paths for each vertex in the integer lattice. There are uncountably many ways to choose a path for each vertex, but not every choice of paths will correspond to a spanning tree, so this doesn't help in determining whether there are countably many or uncountably many. Any help would be appreciated.", "label": 1}
+{"snippet": "I'm taking an intro to proof via number theory class and I'm trying to prove that if a|b and b|c then a|c. So you write down there exist integers k and m such that ka = b and mb = c. Then you substitute ka in for b in the second equation and write (mk)a = c (by associative property). We know (mk) is an integer by the Closure property and so a|c. My question is, how do we know substitution is allowed (or is it not)? Is this something that can be proven from the Axioms of the Integers or something inherent in equivalence relations? Any insight would be awesome thank you!", "label": 1}
+{"snippet": "The reason I ask this is because I was trying to draw multiple lines in pgfplots (I was trying to make a drawing showing how Riemann sums and integrals are connected). And after unsuccessfully trying to use a for loop for an hour or so, I found this solution, which was pretty unsatisfying since it's just a workaround for this particular case. And I thought that it would have been much easier with the power of Python. So, my question is: What do I lose by switching to matplotlib?", "label": 1}
+{"snippet": "The difference between rational and irrational numbers is always stated as: rational numbers can be written as the ratio of two integers, and irrational numbers can't. However, why do mathematicians make a distinction between these two types of numbers? Why are integers special anyway, other than being historically significant? Is there any property that sets rational or irrational numbers apart, other than the way they are written in our number system?", "label": 1}
+{"snippet": "I am interested in learning about duality in convex optimization. I am looking for something to read which is: Reasonably short. Fairly self-contained (if it is a chapter in a textbook, I would like to be able to read it without having first to read the preceeding chapters). Mathematically rigorous: everything is proved. Well-written, i.e., does not take ages to parse. The first one is particularly important for me - I am looking for something I can learn in a few days. The best I have found so far is the chapter on duality in Boyd & Vandenberghe. Does anyone have any other recommendations?", "label": 1}
+{"snippet": "My recent assignment was to write an essay using a template my teacher had given me. The essay was supposed to begin with a phrase like 'It is common knowledge that' or 'there is no denying that', but I wanted to be more original and wrote the phrase 'It is no secret that', which I had heard used many times, instead. Later, my teacher told me the phrase was kind of obscure and most likely informal and that I shouldn't use it. So I want to find out if it is actually applicable and acceptable in an essay. P.S. I'm not a native speaker, so please don't judge me if I'm being stupid.", "label": 1}
+{"snippet": "I have three sentences of which I'm not sure which one is grammatical, and why. It refers to the Eiffel Tower. It is used as the symbol of Paris and of France for over a century. It was used as the symbol of Paris and of France for over a century. It has been used as the symbol of Paris and of France for over a century.", "label": 1}
+{"snippet": "After watching a movie in which levitating water was used as an illusion, I was curious to discover how it works. Unfortunately I cannot find any great explanations of the science behind the effect, only that strobe lights are what cause it. I want to know why strobe lights cause this effect. Here is a video of the illusion. It is my assumption that there is a steady stream of water, and the strobe lights are flickering on and off at a certain rate. Why then do I not see the entire stream of water being lit up, rather than individual droplets? What causes the droplets to appear to \"move?\" And why are there dark spaces between the droplets when there is apparently water there?", "label": 1}
+{"snippet": "I'm wondering if there is a name for graphs such that if there is an edge between vertices A and B and a second edge between vertices B and C then there must be an edge between vertices A and C. My understanding is that this means that the graph is composed entirely of cliques. The graph need not be connected so it may contain multiple cliques, but there cannot be any edges between cliques. Is there a particular name for this structure? Thanks!", "label": 1}
+{"snippet": "I am not a native speaker of the English language but have been living in United Kingdom for last couple of years. Once I was with my friend who was an Irish and I said \"Its cold outside\" and he said that I was wrong and should have said \"Its cool outside\". I am still not sure why I was wrong? Could someone really differentiate the use of word \"cool\" and \"cold\" in that case?", "label": 1}
+{"snippet": "Is there a word that names an excuse made so as to not look stupid? Here is an example that actually happened: A guy walks up to a girl and starts talking to her. After talking for some time, the girl asks the guy to give her a kiss, but the guy refuses. So to this, the girl said, \"I just wanted to test you if you are a good guy or a bad one.\"", "label": 1}
+{"snippet": "This is probably a stupid question, but what makes the three magical elementary row operations, as taught in elementary linear algebra courses, special? In other words, in what way are they \"natural\" (as opposed to \"arbitrary\")? It seems that they're always presented in a somewhat haphazard manner (\"these are the three legendary elementary row operations, don't ask why, they just are\"). From what I understand, they satisfy some nice properties, such as the inverse of each being an operation of the same type, etc. But is there something that characterizes them, i.e. is there some definition of what constitutes \"elementary\" that's only satisfied by the three types of elementary matrices, and no other matrix?", "label": 1}
+{"snippet": "There is a single obscure word whose very definition is when one says \"I'm sorry for saying this, but\" or \"I hate to tell you this, but\", and then proceeds to do the very opposite and attacks or lambasts the person they're talking to. For the life of me I can't find it and I've searched high and low. Can someone please help me? Many thanks and cheers!", "label": 1}
+{"snippet": "I can't find anywhere the advantages of using Ridder's method over any other numerical method. My professor said that it specializes in solving a unique set of functions, but I can't find anything about it anywhere. When is Ridder's method more useful than something else and why? I realize it may sound like a silly question but I have to answer it for a project. Thanks!", "label": 1}
+{"snippet": "Consider the set of words {one, two, three, four, five, six, seven, eight, nine, ten}. I want to write the associated partitions of this set under the relation R where two words are equivalent if they have the same number of letters. It's obvious one, two, six, and ten are all equivalent but I'm not exactly how to write the partitions with the curly brackets... Would it be {{one, two, six, ten}, {four, five, nine}, {three, seven, eight}}? Or would I write these partitions separately like {{one},{two},{six},{ten}}, {{four},{five},{nine}}, and {{three},{seven},{eight}}? What do the curly brackets actually say and what's the difference between the two ways I just wrote them?", "label": 1}
+{"snippet": "As far as I know, the classical approach to special relativity is to take Einstein's postulates as the starting point of the logical sequence, then to derive the Lorentz transformations from them, and finally to derive the invariance of the interval and other consequences from the latter. I'm curious to know if it would be sufficient to take the frame-independence of the interval alone as the initial hypothesis to derive the other results (including the Lorentz transformations and the postulates). Is this possible, or do we have to prove that the interval is Lorentz-invariant first? If this approach is consistent, would it offer any technical advantage w/r/t the classical one?", "label": 1}
+{"snippet": "Question: In Functional Analysis we can note things like: every closed subspace of a Banach space is Banach. In this case, what does \"closed subspace\" mean? Does this mean closed under the norm topology? Or does this mean closed in the sense that multiplication of scalars and addition of vectors is closed? Or does this mean closed with respect to limits? I'm reviewing this material and I realized that even though I have this in my notes a number of times I am unsure of what this actually is. I thought it was the second statement above, but the third statement makes the \"every closed subspace of a banach space is banach\" statement easy to prove.", "label": 1}
+{"snippet": "Is the use of two or more successive relative clauses common or grammarically accepted in English? As in \"The man who is sitting in the wheelchair and who has a broken leg. Or \"The man who is sitting in the wheelchair and whose leg is broken.\" I know, of course, there are ways to shorten them, but I just want to know if it sounds grammatical to native speakers of English to use successive relative clauses, whether in spoken or written language.", "label": 1}
+{"snippet": "My professor asked us a few questions in class and asked us to think about them. He's going to reveal the solutions on Thursday, but I want to understand it before he talks about it on Thursday in greater detail. If anyone could explain any of the things below, it would be appreciated. Thanks in advance. (and if you can't, don't worry- I can ask the professor after class on Thursday)", "label": 1}
+{"snippet": "Suppose I have the sentence: \"All apples are green.\" Although it is not a true statement, clearly it is a declarative sentence. Can any declarative sentence like this be made into an interrogative sentence (a question) merely by replacing the period with a question mark? The reason I ask is because the typical word order for such a question would be: \"Are all apples green?\" Notice that the verb has been moved to the beginning of the sentence. This is the way most of us would word the sentence when phrasing it as a question.", "label": 1}
+{"snippet": "I was wondering if there is a non-geometric interpretation of the dot product (or the inner product more generally). That is, an interpretation that has no concept of length and angle. My motivation for asking this lies in how, in quantum mechanics, the inner product between the bra and ket vectors are often taken. However, these vectors do not represent spatial concepts, but are rather, a vector containing probabilities (which isn't a spatial concept). Thanks for any help!", "label": 1}
+{"snippet": "What is the way to say that something \"should be done\" in the past? I know there is a \"should have\" structure, but it is used for situations, when something was to be done in the past, but it wasn't. E.g. \"You should have called me yesterday. Why didn't you?\" So, would it be correct to say \"It should have been done\" in a situation when something was to be done and in fact it WAS DONE?", "label": 1}
+{"snippet": "I was explaining it's vs. its to someone the other day, and I said \"None of the pronouns (his, hers, theirs, yours, its, whose, ...) has an apostrophe.\" Later I got to wondering whether that was really true, and sure enough fairly quickly found one that does: one's, as in \"One's memory isn't what it used to be.\" Are there other pronouns that use an apostrophe?", "label": 1}
+{"snippet": "It seems to me that \"optical\" relates more to the mechanics of light and vision, whereas \"visual\" is a much broader term. For example, hallucinations are classed as \"visual\" or \"auditory\", rather than \"optical\" or \"acoustic\". Other examples are visual puns, visual cliches, visual metaphors, etc. I notice on the Wikipedia page on optical illusions uses the terms interchangeably. Is there a semantic reason why the term \"optical illusion\" is used instead of visual?", "label": 1}
+{"snippet": "The sentence I wrote is as follows: The idea behind this technique was that the human eye could not differentiate between the individual colors of each point, thereby causing the eye to blend the colors together to form a more complete image. My professor said that the \"thereby\" in that sentence should have a semicolon behind it and a comma in front, but as far as I know, a semicolon separates two independent clauses. I don't think \"causing the eye to blend colors together ...\" is a complete sentence, but she said it should be written as \";thereby,\". Is she correct?", "label": 1}
+{"snippet": "I'm having trouble putting the pieces together. In SM, neutral kaon oscillation is heavily constrained. This means, roughly, that the squark mass matrices have to be diagonal. And this is called universality of soft parameters. What exactly is universality and why do we have universality in this situation? Furthermore, is having diagonal squark mass matrices sufficient? In a lot of SUSY theories, they go one step further and assume the scalar masses are the same for the first and second generations (pMSSM for instance). Why is this additional step necessary?", "label": 1}
+{"snippet": "Since it's Friday and others are playing games, here's another one to take us into the weekend. Everyone knows about those Russian nesting dolls (called matryoshka dolls, I believe). A small doll nests inside a larger, which itself is inside a larger doll, and so on. This game does the same with words. You start with a three-letter word, add a letter to make another word, and so on. Longest word wins. The catch? Each additional letter has to form a legitimate word. Here's one to start you off: bur burr burro burrow burrows Good luck.", "label": 1}
+{"snippet": "Is there a word that describes a person who tries to get as much information as possible when making a decision for fear of committing a mistake that might affect both him and others in a negative fashion? The only word I could think of was indecisive, but it has a connotation that suggests hesitation and irresolution when making decisions, which is not what I'm going for, since I want a sense of absolute commitment when making the decision.", "label": 1}
+{"snippet": "Which of the following books is better to prepare for a mathematical competition at the undergraduate level? The art and craft of problem solving (ACoPS) or Problem solving through problems (PSTP). I think that ACoPS doesn't have an abstract algebra chapter and PSTP doesn't have a combinatorics chapter, so, which one would you recommend me to use and why (I can't use both right now)? Thanks in advance!", "label": 1}
+{"snippet": "I'm not sure how to phrase this question. I'm sure I could write it in terms of operators between Frechet spaces, or something like that. Let me apologies to any analysts in advance for my lack of rigor. I'm basically interested in \"how many\" elementary functions have elementary anti-derivatives. I realize that I ought to impose some conditions on the functions, e.g. differentiable, and on the domains of definition. It would be great if someone could give an answer which puts this question in to the correct language, provide sufficient restrictions and then state any known results. Sorry to be so wishy-washy!", "label": 1}
+{"snippet": "Occasionally, I write letters that I actually print out and send by snail mail :). I'd like them to look as formal as possible. Archaic (pre-typewriter) Dutch customs require the sender's address to be in the top left corner and the recipient's in the top right. The place and date should be aligned with the recipient's address. The sign off (\"Yours truly\") should also be aligned with that. Of course there are also specific rules for the amount of vertical whitespace. Does anyone know of a good package that lets me customize all this stuff, preferably in a .sty file or something that I can include, so I don't have to do it again for every letter?", "label": 1}
+{"snippet": "Are the following two statements written in correct grammar? What do they mean? Can they be written in more easily understandable manner? If yes, how should they be re-written? The student's pass will be issued no earlier than one month from the course commencement date. This letter will be valid for two months or till the course commencement date as indicated above, whichever is later.", "label": 1}
+{"snippet": "In a formal letter addressed to one or more unknown recipients, \"Dear Sir or Madam\" is the customary salutation. As a German native speaker, who is used to \"Sehr geehrte Damen und Herren\", writing \"Sir\" before \"Madam\" sounds impolite to my ear and I feel the urge to change the order. I know that I must never directly carry over conventional expressions from one language to another, but it makes me wonder: Are there any differences between \"Dear Sir or Madam\" and \"Dear Madam or Sir\"? In particular, would the latter sound more polite or rather come across as outlandish?", "label": 1}
+{"snippet": "Ok, so here is an example sentence. \"I hoped to lose the race so I wouldn't have to run against him.\" Here's my dilemma. I was questioning whether a comma was necessary after \"race\" to separate the two independent clauses connected by \"so,\" the coordinating conjunction, but then it occurred to me: Is \"I wouldn't have to run against him\" an independent clause, or is it dependent? If it were standing on its own, would it be considered a fragment? Can someone please explain?", "label": 1}
+{"snippet": "I have been googling around, searching for the origins of the phrasal verb \"to fall asleep\" but so far I have found no references. I was wondering specifically why we use the verb \"to fall\" to characterize the process of going to sleep and my conjecture is that it somehow links in with the connotations of tiredness and fatigue that the verb \"to fall\" bears.", "label": 1}
+{"snippet": "The Feynman Lectures on Physics probably constitute the most famous introductory physics textbook ever written. The level of intuition it provides is hard to beat; I first started reading it in middle school, and a decade later I'm still finding new insights in it. Yet when I recommend it to others, they often have sticker-shock. It is a three-volume book, after all. So is there any legal way to read the Feynman Lectures for free, on the Internet?", "label": 1}
+{"snippet": "When passing someone in the hall, you might say \"How are you?\" as a greeting, but not meaning it literally, as you don't really require an answer. Is \"How are you?\" (or \"How's it going?\", etc.) an idiom when used this way? \"Idiom\" doesn't seem appropriate because that combination of words generally has the literal meaning. Is there another word for this? Sorry if I am not making this clear. If I can clarify in some way, please ask. Edit: Could someone explain why this question might have been voted down? Not complaining, just trying to learn.", "label": 1}
+{"snippet": "I want to know which of the following would be the correct way to phrase my sentence, pasted below. I've come across this problem several times in my writing and want to settle this for good so that I don't always second guess myself: \"When he learned of the sins he had committed, Oedipus blinded himself as punishment\" or \"When Oedipus learned of the sins he had committed, he blinded himself as punishment\" Is one of these more grammatically correct than the other, or are they essentially the same? Is there a general rule for phrasing such sentences?", "label": 1}
+{"snippet": "In Australian English there has always been a distinction between \"pissed\" (intoxicated) and \"pissed off\" (angry, irritated). I've noticed a trend towards the American usage where \"he was really pissed\" is now much more likely to mean the latter. I'm aware of the futility of resisting the natural evolution of language, particulary the juggernaut of American language imperialism via films and TV, but it seems a shame that \"I did it because I was pissed\" is now ambiguous. Is this a trend in other English speaking countries where the Australian usage was common?", "label": 1}
+{"snippet": "I often try to distinguish between immediate-feedback communication, such as talking in person, on the phone, or by instant message, and delayed-feedback communication, such as email. (Or at least, delayed in the sense that it's socially acceptable to not respond right away.) I usually would say something like, \"I'd prefer to discuss this in real-time,\" which usually gets the point across, but I'm wondering if there is a better way to describe this concept. (\"Can we talk about this using an immediate-feedback medium?\" sounds a little awkward.)", "label": 1}
+{"snippet": "\"What does {holding nose} P.U. mean?\" my son asked me tonight. I told him I didn't know, and he laughed and said \"It means stinky, Mommy!\" Very funny and well said, but it left me wondering. A search of Wikipedia and Etymology Online came up wanting and my etymological dictionaries are packed in boxes. What does this abbreviation stand for and why does it mean stinky?", "label": 1}
+{"snippet": "There is a term orbit insertion which means a maneuver performed by a spacecraft flying by a celestial body in order to become an artificial satellite. What word or phrase would you use to describe the result of this process? And from the following sentences, which are correct? The probe entered the orbit of Mars. The probe inserted into the orbit of Mars. The probe was inserted into the orbit of Mars.", "label": 1}
+{"snippet": "What are some simple proofs that the points on an elliptic curve form an abelian group under addition? I am mostly looking for proofs of closure and associativity, since the other three requirements follow immediately from the definitions. Note that I am specifically looking for simpler proofs, since I am only still in high-school, so I have not learned about homomorphisms and isomorphisms and matrices yet. An intuitive 'proof' will also suffice (since again, it's only high-school level). Also, are elliptic curve points always an abelian group under addition? Or only over the rational numbers or over some finite prime field (and not over the reals)? I'm trying to write a paper/essay on elliptic curve cryptography, but I can't get these proofs to work.", "label": 1}
+{"snippet": "Possible Duplicate: An idiom for deriving pleasure from another's suffering We often experience the following: We feel happy when our fellow classmates get a bad grade and not necessarily when we ourselves get a good grade. We feel excited when our opposing team plays really awful and not necessarily when we our team plays well. We feel pleased when one person we hate experiences some kind of misfortune and not necessarily when we ourselves get good luck. What is a word or phrase to describe the phenomenon above?", "label": 1}
+{"snippet": "My highschool textbook states that Zener diodes are a special type of diode which is made of highly doped p and n junctions, and which can survive reverse bias - unlike normal diodes, which get damaged due to the excess heat produced in that mode. How can heavy doping help Zener diodes avoid damage in reverse bias? Is it that it somehow gets rid of the excess heat produced in the diode? How does it do it?", "label": 1}
+{"snippet": "My textbook doesn't explain this very well, so what I want to know is: What is the purpose of parametric equations? What is a parameter? What is the advantage of these equations over a function y=f(x)? What do they essentially enable you to do? I find this topic to be impenetrable so a thorough explanation in simple terms would be very much appreciated. Thank you.", "label": 1}
+{"snippet": "This question may sound dumb, (it will to me, hopefully, in a day or two!), but does the term phase difference apply only for sinusoidal waves? Wikipedia defines 'phase' as the following: Phase in sinusoidal functions or in waves has two different, but closely related, meanings. One is the initial angle of a sinusoidal function at its origin and is sometimes called phase offset or phase difference. Another usage is the fraction of the wave cycle that has elapsed relative to the origin. I'm confused about this specific part: Another usage is the fraction of the wave cycle that has elapsed relative to the origin Can this definition apply for any wave function, or just sinusoidal ones?", "label": 1}
+{"snippet": "Is there a single word that denotes the belief that women are or should be inferior to men? For example, That ideology advocates murder, rape, slavery, homophobia, xenophobia and [insert the requested word here]. The word patriarchy comes to mind but I am not sure if it fits in the sentence above. I am also thinking of sexism, but it denotes prejudice based on sex, which, although in practice usually against women, can work both ways. Any suggestions?", "label": 1}
+{"snippet": "I am reading about the going-up and going-down theorems in Atiyah & Macdonald's commutative algebra book. I'm wondering if anyone could give me some basic facts/examples to help me understand why these two theorems are so important. Neither of these theorems are actually used in Atiyah & Macdonald, and yet I don't find the statements to be so obviously remarkable that they should deserve a special name.", "label": 1}
+{"snippet": "While I was writing a status update today on social media I decided to do some grammar-learning. The status update was \"Happy Labor Day everyone!\" and I am now wondering if I should place a comma between \"Day\" and \"everyone?\" My grammar skills aren't great, and this may be staring me right in the face as I'm thinking about it, but researching on the web and Stack Exchange hasn't brought up the case yet. Help would be much appreciated.", "label": 1}
+{"snippet": "I noticed the following sentence, taken from Mark Twain's \"The Awful German Language:\" Fifthly, I would do away with those long compounded words; or require the speaker to deliver them in sections, with intermissions for refreshments. What is the grammatical function of the semicolon here? I would have expected a comma to be appropriate here, as to me it coordinates a dependent clause, and that would be solely under the jurisdiction of a comma, as I understood. I thought semicolons were for replacing conjunctions between independent clauses or avoiding confusion with commas when writing a list that requires commas for one of the points within. Thank you!", "label": 1}
+{"snippet": "Find the volume of the solid that remains after a circular hole of radius a is bored through the center of a solid sphere of radius r > a. So in the picture it looks like a circle with a cylinder cut out of the middle. I am not even sure where to start with this. I know this has to do with integrals but I am not sure how to set this up to even get an integral. Any help would be greatly appreciated.", "label": 1}
+{"snippet": "I was reading about different variations of nim game and I'm trying to find the winning strategy in one of them: there are n empty places on the circle. Two players are placing their coins on empty places. They can put their coin only on empty places which aren't next to a coin of the opponent. In one turn each player can place only one coin. The player who can't move loses. Who's got the winning strategy for each n? I think that for even n the second player will win, because he can always place his coins symmetrically to the first player's. But what about for odd n?", "label": 1}
+{"snippet": "I would like to have a definition for non-modular lattices which clearly sets them appart from their modular counterparts, thereby focusing on their main distinctive feature. Besides, I would be very grateful to you if you could provide me with an explanation about orto-modularity, which Birkhoff and von Neumann allegedly considered to be the basis of quantum logic, as opposed to modular logics. Is there any correlation between the two types of lattices and this issue of orto-modularity? Thanks in advance.", "label": 1}
+{"snippet": "Is a Topological Space an Algebraic Structure? I am referring to the Wikipedia definition: algebraic structure generally refers to a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms. Examples of algebraic structures include groups, rings, fields, and lattices. More complex structures can be defined by introducing multiple operations, different underlying sets, or by altering the defining axioms. Examples of more complex algebraic structures include vector spaces, modules, and algebras.", "label": 1}
+{"snippet": "This is an exercise from Alhfors Complex Analysis book- to show that an analytic function with a nonessential singularity at infinity must be a polynomial. It seems like it should probably be pretty straight forward, but I must be missing something. If it has a removable singularity at infinity then it extends to an analytic function on the Riemann sphere, and so must be constant by Liouville's theorem. What if there is a pole at infinity though? This was homework some time ago, and I never finished it :/ but have been thinking about it again recently. Thanks :)", "label": 1}
+{"snippet": "What is the word for \"stealing things during natural disasters\"? For example, two guys are listening to the news and hear that there will be a huge typhoon tomorrow, and that there will also be no electricity. So, these two guys decide to steal things from a shop on the day of the disaster. Is there any single word for \"stealing things during natural disasters\"?", "label": 1}
+{"snippet": "I'm looking for a reference for something I thought was easy and well known. There are (at least) two definitions of expander graphs. There is a combinatorial definition via edge expansion, and an algebraic definition using the spectral gap. Neither of these definitions require the graph to be regular. Now, I always thought that the Cheeger inequalities implied that these definitions were equivalent up to the constants. However, when I looked up the Cheeger inequalities it seems that they only talk about regular graphs. Is there a version of Cheeger's inequalities for nonregular graphs as well? In general, is it true that a family of (not necessarily regular) graphs is a family of expanders in the first sense iff they are expanders in the second sense?", "label": 1}
+{"snippet": "I am using graphicx to typeset the figures for my PhD thesis. I have large files in .eps format. However, whenever I try to typeset the file (using pdfTeX), the console says \"LaTeX error: File 'Figure' not found\" It is in the same directory as my .tex file, and the file will typeset if I create it as a .dvi and then convert it to .pdf. I would rather not do this though, because I want to use hyperref.", "label": 1}
+{"snippet": "Light as an electromagnetic wave can be polarized in different ways, e.g. linear or circular. As far as I understand it currently this can be compared to the spin direction of a propagation electron (spin angular momentum of light). Now I have learned that an electromagnetic wave can also have an orbital angular momentum, which is described for example in Wikipedia as a kind of shifted wavefront. While trying to get my head around these phenomena I was thinking about other wave-like objects in physics besides photons. Do all particles and/or excitations (e.g. a spin wave) exhibit orbital angular momentum and what are the physical consequences?", "label": 1}
+{"snippet": "I'm writing an essay right now and I'm deliberating whether or not I should use Pagan gods instead of Greek gods (to provide variation in the essay). I've looked up the word pagan in the dictionary and it mentioned it was a derogatory term. Would it be acceptable to use it though in an essay or would it be inconsiderate for me to use that term?", "label": 1}
+{"snippet": "I'm trying to phrase a sentence in which I'm wishing that something goes easily for someone, but can't get the wording to sound right, and not awkward. For example, someone may be studying for a test and I wish that their studying goes easy. These are the phrases I could come up with. I hope it goes easy for you. I hope the studying goes easy for you. I wish you the best in studying. I'm hoping the studying goes easily for you. Good luck studying. (I don't really like this one since it's a bit vague) Any other suggestions?", "label": 1}
+{"snippet": "Does anybody know the source of this idiom or have an explanation of how it originated? I know it means that the speaker does not trust the person in question, but I want to know the etymology of the idiom. How did it mutate from something literal into this? Obviously trust is not measured in the same way as distance, so I want to understand the correlation in this context.", "label": 1}
+{"snippet": "Is there any good reference for Poisson geometry/Poisson manifolds out there? I would like to give a deep look to the subject, but all I seem to be able to find are short chapters or interludes in text about symplectic geometry. Looking a bit around on the web, the only thing I found is this book. Has anybody read it? And if so, is it good or is there something better? For those left wondering: the book in the link above seems a good introduction. A more advanced text is given by the book Poisson Geometry, Deformation Quantisation and Group Representations (Cambridge University Press).", "label": 1}
+{"snippet": "I'm not a mathematician, but I'm teaching a bit of algebra to some budding logicians, and introducing them to/reminding them of the notions of isomorphism, homomorphism, etc. I'd like to give them an example of an endomorphism which isn't an automorphism, so that they can see the point of there being a name for these separate concepts. I'd also like the example to be as simple as possible, ideally just with some infinite group. But it's proving to be harder than I expected to do this. Every candidate I've come up with turns out to be either an automorphism or not really a homomorphism in the first place. Suggestions, please? EDIT: Should have said explicitly from the beginning, I'm hoping for an example where the homomorphism is surjective.", "label": 1}
+{"snippet": "Is the probability space associated with a compact group with Haar probability always a standard probability space? I recall seeing somewhere the fact that if the topology generating the Borel sigma algebra is not metrizable then the probability space is not standard, or something along these lines. If so then any non-metrizable compact group would show the answer to the above question to be negative, but I am unable to find any firm reference for the above fact. Any help with answering the above question would be much appreciated.", "label": 1}
+{"snippet": "Please help me determine whether or not to include a comma at the end of the third sentence: \"I won't be talking to my ex at the party tonight.\" -\"But what if she talks to you?\" \"I won't be listening to her either.\" -or- \"I won't be talking to my ex at the party tonight.\" -\"But what if she talks to you?\" \"I won't be listening to her, either.\" Thanks!", "label": 1}
+{"snippet": "Can anyone provide a word which describes a person who shows a lot of enthusiasm in the beginning but gets bored gradually and eventually leaves the task uncompleted? I looked at jaded, but it doesn't fulfill the criteria. Jaded seems to describe more of an overworked fellow, whereas the word I'm looking for would describe the nature of person. The word I'm looking for would describe a person who always exhibits this behavior.", "label": 1}
+{"snippet": "I have a few questions about simple situations. What should I say to another person right after falling? a) I fell b) I have fallen What should I say to another person right after throwing a ball? a) I threw the ball b) I have thrown the ball What should I say to another person right after taking something? a) I took b) I have taken Please provide explanations for your answers.", "label": 1}
+{"snippet": "I live in Thailand and we pronounce \"w\" and \"v\" the same. When I spoke to American people they told me that the \"v\" sound was different from \"w\". They told me to move my lower lip to the upper teeth, then say \"v\", but I don't get it. I want to know how to pronounce \"v\" in English. If you can suggest me how to practice it, that would be great!", "label": 1}
+{"snippet": "I was looking at the ice formed in my refrigerator and found out there were a lot of air bubbles inside it. The shape of the air pockets seemed strange to me. There were many small spherical ones and the bigger ones were in the shape of vertical ellipses. I am not able to understand what's the cause of these different shapes of bubbles. can anyone explain?", "label": 1}
+{"snippet": "The following is from the MIT-Harvard Tournament: You are trapped in ancient Japan, and a giant enemy crab is approaching! You must defeat it by cutting off its two claws and six legs and attacking its weak point for massive damage. You cannot cut off any of its claws until you cut off at least three of its legs, and you cannot attack its weak point until you have cut off all of its claws and legs. In how many ways can you defeat the giant enemy crab? (Note that the legs are distinguishable, as are the claws.)", "label": 1}
+{"snippet": "I am a physics undergrad interested in stuff like dynamical systems, chaos theory etc. Is there ongoing research in these fields? I am talking about pure research and not applications to things like weather etc? I hope this question is appropriate for Physics SE. I asked this question, because I browsed through the websites of the physics departments of a few renowned universities (MIT, Princeton, Caltech) etc, but nowhere it mentioned research in these areas.", "label": 1}
+{"snippet": "I picked up a copy of G.H. Hardy's 'Divergent Series' a few days ago. So far I love it, as I love the ideas associated with sequences and series, but I am finding it a bit difficult to understand. I assumed I knew everything I would need to understand it(Calculus I/II, etc.), but perhaps not. What would the possible prerequisites for understanding this book be? Also, does anyone have any tactics for getting the best comprehension/understanding of the concepts in this book? Thanks!", "label": 1}
+{"snippet": "I know that the proper way to use \"not too long ago\" is: \"Not too long ago, contractors used to build houses and sell them to dealers. It was the responsibility of the dealers to provide financing to potential home buyers.\" Instead of these two sentences, can I use: \"If not too long ago, contractors used to build houses and sell them to dealers, who were responsible for providing financing to potential home buyers, today most builders also offer financing alternatives.\"? My question is whether \"if not too long ago\" is correct or not. If it's not correct, I would highly appreciate it if someone could explain why. Thank you, Maria", "label": 1}
+{"snippet": "I created a table and it starts from the left and goes all the way to right, which looks really skewed. So I want to center align the whole table but couldn't figure out how to do it. I'm new to latex so I don't know how to use other plugin or macros, but I suppose there's a command for this basic functionality. Can anyone tell me?", "label": 1}
+{"snippet": "I am working with certain input-output maps that can be thought of as large RLC-networks. I thought maybe this might be a place to get some thoughts/ideas/answers. My basic question is, given some large connected RLC network (all linear and ideal elements) and two ports in the network, say 'a' and 'b', can the transfer-function between the ports have non-minimum phase zeros? More generally, is it true that every transfer function representing an RLC-circuit network is minimum phase? I suspect the answer is true, but I am having a hard time proving it. Thanks!", "label": 1}
+{"snippet": "After taking an introductions to proofs course and abstract algebra, I have been trying to study from Rudin's Principles of Mathematical Analysis. Unfortunately, I still find it very very difficult to read through Rudin let alone do the exercises. Sometimes I spend an entire week trying to understand a proof but get nowhere. At this point, would it be advisible to read a more introductory text in analysis or continue to work through Rudin? Or try reading some more abstract algebra?", "label": 1}
+{"snippet": "I am studying English and I have a question. I found it in my text book written by some teacher who is not a native speaker. \"Those who came first and in greatest numbers to make their homes on the eastern coast of North America were mostly from England.\" I do understand the meaning of this sentence, but I cannot understand why the word 'greatest', Superlative adjective, is not accompanied by the word \"the\". Is there any specific reason for that?", "label": 1}
+{"snippet": "How do you parse the following sentence? The lamp by which she read the book grew dimmer. My friend says that \"by which she read the book\" qualifies \"the lamp\". So, it would basically mean \"The lamp that she was using to read grew dimmer.\" For some reason, I comprehend the sentence as \"The lamp that she was near while reading the book grew dimmer.\" Can it go both ways, or...? Also, about the usage of \"grew dimmer\" there, should it be \"dimmed\" instead? Thanks.", "label": 1}
+{"snippet": "Look at the endings of the following words: blight, bought, breadth, brought, caught, delight, depth, fifth, fought, fourth, fright, freight, height, light, plight, taught, thought, width, ... As you may have already noticed, some of the words in that list end in ht, whereas the rest of them end in th. I have some questions regarding those endings: I. Do all words of the English language that end with ht end, actually, with ght? II. Is there any rule of thumb out there that helps one to recall (or determine) when the ending of a given word is th and not ht (or the other way around)? Thanks in advance for your insightful replies!", "label": 1}
+{"snippet": "I'm well aware that bulwark refers to something used as a fortification or a defense. However, I was wondering if the word bulwarker is an acceptable word to use in English. I know it's possible to be a bulwark (\"He built a bulwark upon the hill.\"), and I know you can bulwark something from something else (\"I will do whatever I can to bulwark the attack.\"). However, I'm unsure if it is possible to be a bulwarker.", "label": 1}
+{"snippet": "I am entering an interesting team based math contest called the purple comet, and quite a lot of questions on this contest involve Diophantine equations. For this contest, you are given a computer, and I was thinking of making a program that solved a linear Diophantine equation. The issue with this is that I can barely solve one by hand, much less make a rigorous algorithm to solve one. I am aware of Euclid's algorithm, but when the numbers get big, this method gets pretty inefficient, not to mention that it would be kind of a nasty thing to program. Are there any other smart algorithms out there for solving a linear Diophantine equation?", "label": 1}
+{"snippet": "I was writing an essay when Word picked up an error in my writing; specifically, it wanted to replace \"vast majority\" with \"clear majority.\" So my question is: is \"clear majority\" better, more eloquent, or clearer than \"vast majority?\" If so, how? A similar post here talks about the differences between similar expressions, but I want to know about the difference between \"vast majority\" and \"clear majority.\"", "label": 1}
+{"snippet": "When speaking about turbulence in fluid mechanics many times authors speak about \"premultiplied energy spectra\" but they never explain what really it is. I have searched for a definition but I did not manage to find it. I guess that is something related about the real energy contained in a region of scales when using a logarithm scale representation but I am not sure. So, what are these \"premultiplied energy spectra\"?", "label": 1}
+{"snippet": "I have been looking around to find an answer to my question, but I was unable to find one that addressed my specific problem. I want to create the following sentence, but I'm not sure whether it's correct. \"Not only the world has changed during this time but also we have in particular.\" I apologize in advance if I have overlooked an easy solution to this.", "label": 1}
+{"snippet": "I'm looking for a term to accurately describe a person who can only read but cannot write. While I'm primarily concerned with people who have never learned to write, I would also be interested in any additional terms used to represent people who have lost the ability to write as a result of disuse. Both illiterate and unlettered imply an inability to read as well as to write.", "label": 1}
+{"snippet": "I'm a bit confused. QFT is claimed to incorporate both Quantum Mechanics and Special Relativity. Therefore it should address the problem of non-locality caused by entanglement. However when I search for an answer on the Internet, I found nothing. I'm not complaining. But it seems that most people only use QFT to do some fancy particle stuff and forgot we should care more about the more fundamental stuff.", "label": 1}
+{"snippet": "I've noticed that, when I'm driving and it's raining, the faster I go the more rain I get on the windshield and the faster I have to run the wipers to compensate. When I'm stopped at a red light I can just about turn the wipers off, but once we get moving again I have to turn them up so I can see clearly. Intuitively I would think that, assuming a statistically even distribution of rainfall throughout the local area, speed should not matter because for every raindrop I move into the path of, I'm moving out from under another one at the same time. But this is definitely not what I observe in actual driving conditions, so what's going on?", "label": 1}
+{"snippet": "I am studying Linear Algebra. I have faced a problem to understand Symmetric Matrix with spectral decomposition. After I studied spectral decomposition, the next page in my book talks about a positive definite matrix and quadratic form. I am kind of lost what relationships are there between symmetric decomposition, a positive definite matrix, and quadratic form. Hope I can have some explanations. Thank you in advance.", "label": 1}
+{"snippet": "According to Collins English Dictionary, and of course as everyone knows, a doula is a woman who is trained to provide support to women and their families during pregnancy, childbirth, and the period of time following the birth However, the definition in wiktionary says: A support person, usually female, who may not have medical or midwifery training, who provides emotional assistance to a mother or pregnant couple before, during or after childbirth. Is pregnant couple actually an acceptable term for referring to an expectant couple?", "label": 1}
+{"snippet": "I'm about to wrap a course in partial differential equations. We've discussed the heat/wave equations and introductory Fourier Analysis. I'd like to do some reading into the field of thermodynamics. Would it be best to start with an introductory text given to most lower-division under graduates or should I begin with something with a little more meat on the bones? By meat on the bones, I mean a bit more rigor and explanation for the fundamental theorems and applications. If this is not clear enough please ask for clarification, I'll be glad to provide it.", "label": 1}
+{"snippet": "I know that air pressure and temperature are inversely proportional. Now I saw in a book that \"Atmospheric pressure decreases as we go higher and higher.\" But at greater heights the temperature becomes low, and so the air pressure would be high. But it is given atmospheric pressure decreases with altitude. I understand that air pressure and atmospheric pressure are different. But I can't understand how they are different.", "label": 1}
+{"snippet": "Given two (or more) loans of different balances and interest rates and a single amount of funds available per payment period, is there a way to calculate the best way to split the available funds to minimize the amount of money repaid? I'm not really sure where to start to look into this type of question so if someone could point me in the right direction or provide an answer that would be great!", "label": 1}
+{"snippet": "In my physics classes, I remember it being repeated a few times that gravity is a much weaker force than the other three fundamental forces, and being told this is an open problem in physics. However, I don't understand why this is a problem. I see no intrinsic reason why the four fundamental forces should have similar strengths in the first place. So why then is the fact that gravity is many orders of magnitude weaker than the other fundamental forces a problem? Note: I've attempted to read the Wikipedia article on the Hierarchy problem, but it is far too technical for me.", "label": 1}
+{"snippet": "I'm reading a paper titled \"Luminescence spectra of quantum dots in microcavities II Fermions\" (link). In section III, the authors introduce so-called closing operators. I don't have enough background knowledge to understand the technique there. So it's natural for me to look for other literature or books on the topic. But it turns out the \"closing operator\" is defined only by these authors and I couldn't find any literature on this. Could you give me any key words which can lead me to related literature? Or you can point me directly to a literature.", "label": 1}
+{"snippet": "Generally speaking when we say \"our friend\" we are referring to someone who is a friend of ours. However, I have noticed that at times these words are used sarcastically to refer to someone who is actually not a friend but an enemy/adversary. So with respect to the sentence below, is the term our friend used as a form of irony? Our friends the Saudis, who never persecute women, gays and other religious minority groups, have somehow managed to lead the UN Human Rights Council", "label": 1}
+{"snippet": "I'm starting my last year of high school, and I will have to do an all year research on a mathematical topic. I'm a really passionate learner and I'm very involved in computer science. I am stuck on finding an idea that will both be challenging and fun. I would also really love to integrate computer science in it, since that's what I want to study afterwards. Thank you in advance.", "label": 1}
+{"snippet": "Some dictionaries define a scalar as follows: A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction. -- The Free Dictionary However, it is my impression that in many contexts scalars can be signed, in which case their magnitude (their absolute value) does not specify its value. This definition is even used on a test question here. Is it true that this definition is inaccurate?", "label": 1}
+{"snippet": "I'm currently taking a numerical analysis course. We are covering linear algebra topics, the gist of the first chapter of the course being solving systems of linear equations. The lecturer has introduced SVD decomposition, condition number of a matrix, LU decomposition and QR decomposition (using Householder decomposition). In the past I've been used to very rigorous, thorough and well-organized math courses. But I feel like what I'm learning here is shallow since there are very few proofs. So my question is Can you recommend rigorous textbooks or detailed lecture notes that cover the topics I mentioned above ?", "label": 1}
+{"snippet": "So I'm trying to prove that the set of polynomials in C([a,b],R) is not open. I understand the definition of an open set, but I'm wondering how to find a point that is not contained in the interior if it's the set of polynomials. Also, Can a subset of a metric space ever be both open and dense? I'm thinking it can, only if the interior is empty. ? Would love help with these! Thanks in advance!", "label": 1}
+{"snippet": "Why is a homogeneous function called homogeneous? When I ask this, I don't mean, \"Show me how to algebraically manipulate a function whose input has been multiplied by a constant to get the original function multiplied by the same constant.\" I mean--why do we use the word \"homogeneous\"? That word in particular must have been chosen for a reason; what is it meant to communicate in this context?", "label": 1}
+{"snippet": "I know how to solve linear homogeneous ordinary differential equations with constant coefficients using the differential operator D, by using this method. Is it possible to use a similar method (using the differential operator) to solve more advanced ODEs? I'm thinking of both more advanced linear ODEs, such as Euler-Cauchy differential equations, as well as non-linear ODEs. Are there any articles on the web on this topic, or even textbooks that use this method to solve ODEs?", "label": 1}
+{"snippet": "One oddity I notice is that if a random or quasi-random data series such as price data is plotted, it is similar to a random walk, but if the same data series is plotted using candlesticks (open-close, high-low), there appears to be in many cases an undulating pattern. I assume that this is caused by some kind of aliasing. Is there a mathematical explanation for it?", "label": 1}
+{"snippet": "I am an mechanical engineering student so I'm kind of ashamed to ask this question but I have a weak math background and am digging into some of my knowledge gaps. So my question is where are all of the constants of integration and why are they generally ignored? Is it simply because they are usually treated to be zero? I guess what I'm looking for is an intuition in regards to integration constants...i.e. how do I wrap my mind around why the integration constant is/was ignored, and how can I truly understand what is going on when these constants are ignored. Any insights or conversation is greatly appreciated. Thanks in advance!", "label": 1}
+{"snippet": "I don't know where I've heard such expression. I try to explain (for sales) what our software tool does and I use this sentence: \"It helps you to deploy apps in a very simple fashion\". And then I describe the steps of how it works. I googled this expression and I found only one reddit post. Is it a widely used expression in the US? Will native speakers understand me? What about non-native speakers like EU folks, will they? Can I rephrase it as \"in the simplest possible fashion\"? Thanks!", "label": 1}
+{"snippet": "My background : I'm currently in my junior year in college majoring in astrophysics. I have taken GR, and some intro cosmology here and there, but nothing in great depth. I had my heart set on taking a full physical cosmology class this spring. As luck would have it, I can't take the physical cosmology class due to scheduling conflict ! I intend to proceed to graduate school in astrophysics, so I would have to take the graduate level cosmology then, but in the mean time, I was thinking of teaching myself undergrad cosmology out of Barbara Ryden's book. My question is : any advise for undergrads teaching themselves this subject matter ? Are there any \"go to\" resources? is Ryden a good choice?", "label": 1}
+{"snippet": "I was wondering if it's possible to construct a table in LaTeX which has a fixed header so when we scroll down the page of the output PDF, we can still read the column names and keep track of what the numbers in the table represent. I have seen in a post here at stackoverflow about how to do this with HTML and someone had linked to this example: http://www.mustafaozcan.net/en/demo/fixedtableheader/jquery-fixedtableheader-demo-en.html I would like to be able to do that in a PDF produced by LaTeX. Is that possible?", "label": 1}
+{"snippet": "I was doing some calculations in MATLAB, and noticed a pattern that may be obvious to stats experts, but I didn't notice it before. If I have a time-series, and I remove a linear trend / detrend it, I find that the mean of the detrended data is zero, as expected. However, I was surprised to find out that the standard deviation of both the detrended data and original data is roughly the same. Is this what one should expect? Thanks!", "label": 1}
+{"snippet": "I am just beginning to read about the use of \"Concave Programming\" methods and use of the Karush-Kuhn-Tucker conditions to identify the maximum value of a non-linear objective function subject to inequality constraints. The examples I have seen in the text I have at hand, all involve only linear constraints. Is this method equally applicable to situations where not only are there multiple constraints, but where one or more of those constraints are non-linear ?", "label": 1}
+{"snippet": "Wikipedia has the following quote on John von Neumann: Stan Ulam, who knew von Neumann well, described his mastery of mathematics this way: \"Most mathematicians know one method. For example, Norbert Wiener had mastered Fourier transforms. Some mathematicians have mastered two methods and might really impress someone who knows only one of them. John von Neumann had mastered three methods.\" He went on to explain that the three methods were: A facility with the symbolic manipulation of linear operators; An intuitive feeling for the logical structure of any new mathematical theory; An intuitive feeling for the combinatorial superstructure of new theories. And I am wondering what do 'logical structure' and 'combinatorial superstructure' mean in this context? Please explain these methods. https://en.wikipedia.org/wiki/John_von_Neumann#Mastery_of_mathematics", "label": 1}
+{"snippet": "I am studying client's request arrival patterns on web and application servers. About web server's request arrival pattern I read that \"The request arrival rate on web server follows Poisson distribution\". And about application server I read the sentence \"The request arrival rate on application server follows exponential distribution. Now kindly explain \" is there any difference between Poisson and exponential distribution in the context of client's request arrival pattern on server\". Is there any difference between poisson and exponential distributions?", "label": 1}
+{"snippet": "I'm working on a project right now and part of the introduction is about energy, and I'm trying to introduce the notion of energy in an unconventional way. Right now, I am looking for examples of situations in physics and chemistry where energy plays a key role. Another way of putting it is: I am looking for questions where the answer is energy. I'm basically trying to motivate the concept of energy and demonstrate why it is important. Does anybody have ideas of seemingly fundamental occurrences where a true answer is provided by the notion of energy? Thanks!", "label": 1}
+{"snippet": "When used as an expletive, the name Jesus Christ often gets an H inserted into the middle of it for some reason. I've heard lots of guesses about what the H stands for, the most popular one being Henry, but no one seems to actually know, and I've never gotten any good explanation of where it came from or why it became popular to insert it. Is there any documentation of when Jesus H. Christ as opposed to simply Jesus Christ came into currency as an expletive? Is there any authoritative explanation of what, if anything, the H was originally supposed to stand for?", "label": 1}
+{"snippet": "In high school a while ago, I learned a bunch of random terms for words and phrases: synecdoche, antonym, oxymoron, palindrome, etc. There's one term that escapes me but I can give examples of it. I don't love my wife because she is beautiful but she is beautiful because I love her. We travel not to escape life, but for life not to escape us. What is the name of this term? Thanks in advance, it's killing me not being able to remember.", "label": 1}
+{"snippet": "D-branes, as I currently understand them, are submanifolds of spacetime on which open strings can end with Dirichlet boundary conditions. On the other hand, type II string theory is a theory of oriented closed strings - the difference between IIA and IIB coming from the choice of GSO projection. Based on these observations, I have the following questions: If type II string theory is built from closed strings, why are D-branes considered in the theory? If open strings are included in type II, does the GSO projection act on the open strings? If so, how?", "label": 1}
+{"snippet": "Trying to show that if a sequence converges, it either has a maximum, a minimum or both, I reached a dead-end. Assuming it is not constant, it is still bounded and its supremum and infimum aren't equal. Then I assumed that the supremum and infimum are not in the sequence. I want to show that there are two subsequences that converge to each of them but for that to happen I have to show they are accumulation points. I tried to use definition but failed. I know logically that following my assumption they have to be accumulation points but I can't derive it from the definitions. Any help?", "label": 1}
+{"snippet": "I'm working on finding whether sequences converge or diverge. If it converges, I need to find where it converges to. From my understanding, to find whether a sequence converges, I simply have to find the limit of the function. I'm having trouble getting started on this one (as well as one more, but I'll stick to one at a time). I would appreciate if someone could explain how I should start this one.", "label": 1}
+{"snippet": "This may not be the correct place to ask such a question. I have read a mathematical paper on multiclass total variation clustering. I wish to use the algorithm in the contents to compare with another clustering result. My question is: Is there a proper etiquette for asking the author(s) of the paper for their code? Is it rude to do so? Should I just try to figure it out on my own? Or is this something that is common? One reason why I want to ask is because I am short on time and may not be able to figure it out by my deadline. Any comments would be greatly appreciated.", "label": 1}
+{"snippet": "When writing a book on popular culture, I'm using italics to introduce a film title into my paragraph. In the next paragraph I refer to the film title again. Should I use italics on the second occasion, or stick with normal text? I'm tempted to go for the latter - as over-use of italics would spoil the flow of the text, and the title has already been introduced to the reader. Thoughts?", "label": 1}
+{"snippet": "This question may sound naive but still I haven't seen it being discussed in any book. Why do we parametrize surfaces with two variables as opposed to curves? Initially I thought that it is not possible to fill enough points in the space with one variable but there are space filling curves so it is certainly not the reason. Is it because we need to move in two directions?", "label": 1}
+{"snippet": "So I've modeled the interactions between the sun and all the planets (and the interactions between the planets) using Verlet integration. I've used data from Wikipedia for masses, distance from the sun etc. I initialized the initial velocities of the planets via the critical velocity equation. This produces nice stable velocities. I'm unsure of how to calculate the initial velocity of the moon so that it stays in orbit around the earth.", "label": 1}
+{"snippet": "I just learned from Wikipedia that coproduct of two (commutative) rings is given by tensor product over integers, and that coproduct of a family of rings is given by a \"construction analogous to the free product of groups.\" Can the tensor product approach be generalized to an arbitrary family of rings? (Infinite tensor product?) I'm a little surprised that coproduct of commutative rings requires noncommutative structure (free group). Does someone have a reference which explicitly constructs the coproduct?", "label": 1}
+{"snippet": "If I have a binary number W bits wide, initially all set to zero, and I repeatedly pick a random bit and toggle it from zero to one or vice versa, how many times would I need to do this to achieve maximum entropy? I hope I am using the term \"maximum entropy\" correctly -- what I mean is a point where the distribution of ones and zeros is as random as possible, and no amount of continued toggling will make the distribution any more random.", "label": 1}
+{"snippet": "Any given square is always a rectangle, but a rectangle isn't necessarily a square, so squares and rectangles have a _ relationship. I've been noticing this sort of thing everywhere ever since I noticed that I didn't know a good word for it. I've been calling it a container relationship because one class of things is contained within a larger class of things. However, a \"container\" relationship doesn't sound very good and doesn't really convey the meaning on its own. A more elegant word would be helpful. Edit: A specific definition would be something like: a is always b. b is sometimes a.", "label": 1}
+{"snippet": "I'm not a physicist, but I'm really interested in Nanotechnology. I've a question, and I hope that I can be provided by an answer. I was reading some articles about the one-dimensional CdSe nanostructures. My question is why it's called one-dimensional? Is it because of their geometrical shapes or something else? I truly appreciate any hint or a resource could lead to the answer. Thanks.", "label": 1}
+{"snippet": "Let's say I have an isolated, adiabatic chamber which is divided into two parts with a massless, frictionless piston. One part has vacuum, while the other has a gas. In the beginning, they are at equilibrium. I release the piston, and the gas expands, thereby pushing the piston towards the end of the box. Since the process is a free expansion, there is no work done by the gas. One could thus say, that the gas applied no force whatsoever, on the piston. Then why did the piston move in the first place?", "label": 1}
+{"snippet": "What does the expression \"eat shit\" represent in the following sentences? Eat shit, I'm not going to do your dirty work. Is this similar to \"I dislike doing your dirty work\"? Or does it mean \"Go to hell.\"? Eat shit, I am not going to follow you. I found many different interpretations of this expression on Urban Dictionary, so I am quite confused. Please could someone clarify.", "label": 1}
+{"snippet": "What I want to ask is what would happen if you split a single light ray (a photon) into two using a half silvered mirror? Would the emerging light rays have half the amplitude as the original one or half the frequency of the original wave? Basically will the frequency get distributed or the amplitude? EDIT I specifically mean a \"Single\" photon or a single light ray. For those who think a single photon cannot be split, you are wrong. A photon has been split by using special crystals. It is called Parametric down conversion.", "label": 1}
+{"snippet": "If the text I am quoting is italicised or bold, does my quote need to include this special font treatment? If I want to emphasise something in the quote, can I make words italic? For example, suppose that the text I'm quoting is: I love apples. I really love them! Can I quote that as \"I love apples. I really love them!\"? Also, can I quote the beginning as \"I love apples,\"? Thanks!", "label": 1}
+{"snippet": "I don't understand how to solve problems of conditional probability.Here's a problem which I fail to understand.\"Consider all families with two children and assume that each child is equally likely to be a boy or a girl.If such a family is chosen at random and found to have a boy,then what is the probability that it has another boy.\"Please help me to solve this problem.", "label": 1}
+{"snippet": "I have question which I'm unsure of whether or not I am thinking about it right. If an object is sliding down frictionless incline and it then comes to the \"foot\" of the incline where it encounters friction, how far would it travel. The foot of the incline is horizontal. The only information given was height of the incline and the coefficient of kinetic friction. I used conservation of energy to find the velocity at the foot of the incline. After, I solved for horizontal displacement using kinetic energy = displacement x mass x gravitational acceleration x coefficient of kinetic friction. Can anyone offer some insight into whether or not this is a good approach? Thank you.", "label": 1}
+{"snippet": "The following true/false question was posed: An isomorphism between to vector spaces can always be represented by a square singular matrix. This is not true. I know that in the case of finite dimensional vector spaces: A map is an isomorphism iff it can be represented by a square non-singular matrix. I would like to know whether it is possible to prove this in general (i.e for all vector spaces)?", "label": 1}
+{"snippet": "Initially, when the current starts flowing the temperature of the filament is less and thus resistance is less. So, more current flows through the bulb and the power delivered to the bulb is more. As, time passes and the filament starts glowing at a steady rate its temperature has increased which in turn has increased its resistance. So, less current flows through it and thus less power is delivered. Is this the case? Please help me understand the situation.", "label": 1}
+{"snippet": "I'm a programmer and I'm looking for a single word that works for the following scenario: I have a list of basic information about people, I call this list the 'user repository'. I need a word for \"to view and change more detailed information about a person\". I've thought of using words like refine and elaborate, but they don't seem to quite fit the idea that the data can be viewed and changed.", "label": 1}
+{"snippet": "Suppose that a person buys a packet of sugar. On the way home, the packet falls off his hands and the sugar scatters on the ground. Nobody is expected to gather the sugar again, but that person does so; of course not for his own use anymore, but to donate it to the poor! Obviously, if the packet hadn't fallen down, he wouldn't have decided to donate it. It goes without saying that this kind of donation and charity is morally worthless and not considered a good deed. Is there any English idiom to describe this kind of charity or donation? Thanks in advance.", "label": 1}
+{"snippet": "I tutor student in SAT Reading. One of the SAT tests has the following sentence: \"With their dark dungeons and damp living quarters, medieval castles offered few of the comforts to be found in royal palaces.\" The student thought this must be wrong as \"to be\" seemed superfluous. To me, there's a subtle difference in meaning if the sentence was changed to \"few of the comforts found in royal palaces.\" The only way I could describe it was that \"to be\" adds a more theoretical and abstract quality to the sentence. Is there a clearer way to put all this and the change \"to be\" makes? Thx in advance, J", "label": 1}
+{"snippet": "This is something that crops up on the BBC a lot and irks me. For example, from a story today: One woman is critically ill and three others have been injured after they were stabbed near a supermarket car park in west London. To me, you are ill (or sick) if you have, for example, contracted a disease and using it in the sense of someone being injured is wrong. Google gives the definition of ill as \"suffering from an illness or disease or feeling unwell.\" and I'm sure that a car crash or stabbing would certainly make you feel unwell, but I still don't think it's right. Is it?", "label": 1}
+{"snippet": "So i am currently learning about double integrals and to be honest i am not really understanding how we compute the volume over general regions. Here is the proof provided in my text book. It all makes sense until the last part. Since we use Fubini's theorem we can change the order in which we integrate. Since that is true wouldn't that mean that the Fubinis Theorem applies to all double integrals? Since this is obviously not true can you point out what am i doing wrong? IF you need any more clarification/photos please comment.", "label": 1}
+{"snippet": "I am applying for a new job; I currently work in my family-owned F&B firm. Now, in the job portal, there is a column where I have to mention my current company. I don't want to give the name of my firm as it is not well-known and also, it is not in the same domain as the job I am applying for. I have currently put down \"Own F&B establishment\" in the column. But the \"own\" part seems kind of odd to me. Is there any other word or phrase that I can use instead, which would indicate I am not just working there, but am a stakeholder.", "label": 1}
+{"snippet": "It is right on the tip of my tongue, and I have searched the online thesauruses but I can't come up with it. What's the word that could fill in the blank: He came to the ___ conclusion that you must be willing to serve if you want to truly lead. The best I could come up with is \"non-intuitive\", but that just doesn't sound right. I know there's a better one. I want a word that means \"this is not what you would expect\", \"this goes against your intuition\". Something that approaches \"nonsensical\" or \"irrational\" but without the disparaging overtones, yet more forceful than \"surprising\".", "label": 1}
+{"snippet": "I am struggling on this one question, where it is asking to define an XOR automata which is defined as an NFA and it is defined as the following: N accepts the string x if the number of distinct accepting states that can be reached by a path labeled with x is odd. I'm supposed to prove that any languages accepted by the XOR automata is regular and that any regular language can be accepted by the XOR automata. Can anyone explain to me how I may be able to go about starting this proof? Thanks.", "label": 1}
+{"snippet": "My question is simple. I'm an undergraduate student taking Partial Differential Equations. I'm looking for a problem book with solutions. My intent is to just do problem after problem to practice for my final and our assigned PDE book doesn't have the answers, so there's no way of checking. Would anyone happen to know of a good PDE book that has problems and answers (or if possible a solution manual) that I can find online? The book we're currently using is: Basic Partial Differential Equations by David Bleecker and George Csordas. Thank you", "label": 1}
+{"snippet": "I'm looking for an adjective that describes the fact that a ship is sailing at sea. Much as \"afoot\" describes a person being in the state of walking. I was hoping \"asail\" would be a word, but can't find it from Google. The word would replace the square brackets in the following example: In Plato's ship of state metaphor, a ship is [sailing at sea], helmed by a captain ...", "label": 1}
+{"snippet": "The Large Hadron Collider (LHC) \"remains one of the largest and most complex experimental facilities ever built\" (Wikipedia); it may even be the most complex project in humankind's history (?). Such projects usually have impact beyond their original target and boost science and technology in a non-trivial way. I wonder, then, what kind of impact it has or might have on other science and technology fields, in particular on mathematics (if any), and what specific impact has mathematics had (or might have) on the LHC project (if any)? Cross-post on mathoverflow: Impact of LHC on math.", "label": 1}
+{"snippet": "I realize that \"kinda\" is an informal form of \"kind of\". However, would \"kinda\" be appropriate in fiction or dialogue? Or would it be more acceptable to stick to \"kind of\"? This is for a fiction novel from first person view. Additionally, I found that when I write, I tend to use \"kinda\" for more informal sentences (\"it was kinda freaky\") and \"kind of\" for more serious sentences, I would use \"kind of\" (\"I kind of knew how they felt\"). Is this acceptable or would it be preferable to use \"kinda\" or \"kind of\" consistently?", "label": 1}
+{"snippet": "We know that a Hilbert space is separable if and only if it has a countable orthonormal basis. What I want to ask is If a Hilbert space has an uncountable orthonormal basis, does it mean that it is not separable? Or equivalently, does it imply that the Hilbert space does not have a countable basis? I know that if a vector space has infinite number of linearly independent vectors then it cannot have a finite (Hamel) basis. But here we do not deal with Hamel basis but with a complete orthonormal set, do I cannot apply the usual techniques. Any ideas?", "label": 1}
+{"snippet": "I am having lots of trouble with this series. I will upload a picture of what I did. According to Wolfram, the series converges by the ratio test. I also don't know how I would use a different test for such a series. Two of the limits weren't difficult, but obviously I have to do something else, since I am not getting the right answer. We haven't covered Stirling approximation if it applies here, so I'd like some help without using it. Thank you so much.", "label": 1}
+{"snippet": "In chemistry we learned about the penetrating power of three common types of radiation: alpha, beta, and gamma. Alpha can be stopped by paper, beta is stopped by a sheet of metal (I think) and gamma is stopped by lead. In the same unit, we talked a lot about nuclear weapons, but not once discussed the neutron radiation that causes the chain reaction in nuclear weapons. What kind of penetrating power does neutron radiation have in comparison to the other three we learned about?", "label": 1}
+{"snippet": "I only have a basic, mostly classical understanding of physics and am just starting to learn about photons. Am I correct in saying that, as a photon moves through space, the strength of its electric field varies? If I am correct, what is the qualitative nature of this field? Is it positive (would repel a nearby proton it was passing by) or negative (would attract a nearby proton it was passing by)? Does it switch between positive and negative? Or would it have no effect on a proton it was passing by (the field is neither positive or negative)? If the field is neither, how is it even possible for an electric field to exist without being positive or negative? What would such a field even mean?", "label": 1}
+{"snippet": "I know what \"begging the question\" originally means, but I just can't make any sense of the idiom. The phrase really seems to have nothing to do with its own meaning. The original Latin phrase, petitio principii, is often translated as \"assuming the initial point,\" which quite simply explains the practice. Does the phrase \"begging the question\" carry any meaning (related to what it's used for)?", "label": 1}
+{"snippet": "I was wondering why it is almost impossible to find a geometrical explanation of why adding two linear equations helps us to find a solution of a system of linear equations? Am I right that adding two linear equations will result in an equation of a line which will pass through a point where two linear equations intersect? If it is right then I completely don't understand why such a crucial point in understanding how to solve systems of equations is never properly taught even at a university level.", "label": 1}
+{"snippet": "According to the Bernoulli's equation, if velocity decreases, then pressure increases. I am trying to understand the Bernoulli's effect based on a situation. Suppose we have a stream of water. Let's assume it is an ideal fluid. Imagine the water flows out from a wider pipe to a narrower pipe. Since the area decreases, according to the Continuity equation, velocity of water molecules increase. This causes an decrease in pressure. I don't understand the last part. If water molecules' velocity increase, then their kinetic energy also increases. Wouldn't this causes more collision between pipe's wall and water molecules, thus giving higher pressure?", "label": 1}
+{"snippet": "I hope this isn't an inappropriate question here! I'd like to ask the following (perhaps slightly ill-posed) question: why do we study prime ideals in general (commutative or non-commutative) rings? The situation is somewhat clear to me in some nice cases such as Dedekind rings, but even in slightly more general settings (e.g. general commutative Noetherian rings) the theory becomes rather horrible. What benefit do we gain from an understanding of the prime ideals of a ring? Thank you!", "label": 1}
+{"snippet": "The following quote from Anthony Burgess has a comma after it: There is, in fact, not much point in writing a novel unless you can show the possibility of moral transformation, or an increase in wisdom, operating in your chief character or characters. But this quote from William S. Burroughs doesn't: There is in fact something obscene and sinister about photography, a desire to imprison, to incorporate, a sexual intensity of pursuit. When should you use a comma after \"there is in fact\"? Is it necessary to put a comma after \"there is in fact\"?", "label": 1}
+{"snippet": "While learning about shock waves in an introductory Gas Dynamics course, it was revealed that normal shocks are unstable if formed in a converging channel. Even if the local conditions ostensibly require the presence of a shock in the converging section, the flow instead chooses to reinvent itself, moving the shock wave to a diverging section while simultaneously altering the upstream conditions. I can verify that this is a genuine phenomenon, but is there any formal explanation in terms of the underlying flow physics?", "label": 1}
+{"snippet": "We are struggling to find the correct word(s) that describes a list of all messages in the system that are sorted by recency. Trending does not work because what we are displaying is not what is popular in the system, only the most recent. Recent does not work because it implies there is a limit to the number of messages we display. All does not work because it does not imply that they are sorted by recency. Any hints or suggestions are welcome. Thanks!", "label": 1}
+{"snippet": "In an electron gun, the heating filament heats the cathode, releasing electrons by thermionic emission. I've read that \"electrons are negatively charged particles and the positively charged cylindrical anode develops a strong electric field that exerts a force on the electrons, accelerating them along the tube\". However, I don't think that this explanation is very clear, and I was wondering specifically how the \"strong electric field\" inside the cylindrical anode is able to accelerate the electrons?", "label": 1}
+{"snippet": "My understanding is that in quantum mechanics the wavefunction may be expressed as a function or as a ket vector (composed of many orthogonal ket vectors). I'm not too sure about the further differences between these two approaches. For example, I am familiar with operating on the wavefunction as a function with the hamiltonian operator, but when you use ket vectors can you use the hamiltonian operator in the same way or do you have to find matrix representations of the operators? I would also be grateful for any links to websites or books explaining the different approaches.", "label": 1}
+{"snippet": "What is the English word for \"collecting money for a special event from a group of people\"? For example, say some friends are planing a party. Each one has to contribute some amount of money to the event. What is the word or phrase that can be used to explain this kind of activity? I have found \"fund raising\" to have a similar meaning, but I feel it's more along the lines of \"collecting money for some charity event\". Is that right, and is there a better word I can use?", "label": 1}
+{"snippet": "I'm trying to write a tagline for my live blogging service, and this is what I've come up with: Live blogs that are a breeze to write, a pleasure to read and are actually updated in real-time. Is that correct grammar or should it be Live blogs that are a breeze to write, a pleasure to read and actually updated in real-time. The completions 'a breeze to write' and 'a pleasure to read' both follow '... that are'. So why does 'are actually...' sound better to me? Doesn't that repeat the 'are'?", "label": 1}
+{"snippet": "Given any problem, how do I know whether it is solvable using Dynamic Programming? For example: consider the rod cutting problem. Now, how do I know whether dynamic programming will give me an optimal answer? Basically my question is: how do I check if a problem follows the \"Principle of Optimality\" - that optimal solution of every problem involves the optimal solution of a sub problem. And are there any problems that don't follow this principle? (If there aren't, my original question becomes redundant, of course!)", "label": 1}
+{"snippet": "In mathematics we often have statements like a x <= b, where a and b are constants and x is a variable. Now there may be variables satisfying the inequality (that is the statement is true) as well as variables violating it (in which case it's false). However I don't have any words in my vocabulary to express stricter statements: Is there a word to describe that the variable x satisfies the equality a x = b? What about the case that a x < b? I remember having read \"x is a root of the inequality\" meaning a x = b somewhere, but I can't remember where.", "label": 1}
+{"snippet": "Let's say me and a colleague are going to a meeting and I want to make sure his responses to the questions raised are similar to mine, that we are in agreement and we will responde in a similar manner. Can I say: \"Let's make sure our responses are aligned\" or, \"Please let me know your views cause I want my responses to be aligned with yours.\"", "label": 1}
+{"snippet": "The words \"opportunism\" and \"opportunist\" suggest the ability to take advantage of situations -- but they assume that one is doing so for one's own benefit, which makes the terms pejorative. What is a non-pejorative word in English that means \"have the skill and wisdom to recognize and seize opportunities that lead to broad gains\"? I am looking for something that is part of the \"art\" of diplomacy and politics, for example. \"Clever\" is a somewhat helpful adjective, but there is no such thing as a \"cleverist.\" \"Entrepreneur\" means is a person who is willing to take on risk and innovate, but lacks the sense of seizing opportunities as they emerge. It seems like an important concept that has no word. Any suggestions?", "label": 1}
+{"snippet": "This image from NASA illustrates drag coefficients for several shapes: It is generally accepted that some variation of the teardrop/airfoil shape has the lowest drag coefficient. I was wondering what shape has the highest drag coefficient. The image suggests that it is a flat plate, and that would seem to be an intuitively correct answer, but is that correct? Is there some other shape (perhaps with a concave front or back relative to motion) that has an even higher drag coefficient?", "label": 1}
+{"snippet": "Clouds are made out of tiny droplets of water. These droplets, to my understanding, act like tiny prisms (which is why there are rainbows after rain). From my line of thinking, if we had a room with a bunch of prisms randomly placed about and had a light enter from one side, the walls would be quite colorful. Why, then are clouds white (and then darker shades of gray as they become filled with more rain)? Edit: I understand that white is all the colors together, but if that logic applies to clouds, then why not rainbows?", "label": 1}
+{"snippet": "Question: Which of the following affect the frequency of a tuning fork? Tine stiffness Tine length The force with which it's struck Density of the surrounding air Temperature of the surrounding air Answer Attempt: Based on the formula for the frequency, I know that tine stiffness (or density) affects it, and so does the tine length. I believe the temperature and density of air can have a slight affect as well. What about the force with which it's struck?", "label": 1}
+{"snippet": "We're releasing a website in which the users can submit and join video game competitions. The game can be League of Legends, FIFA, Counter Strike and so forth. We're not native english speakers so we're not sure whether we should use \"tournament\", \"championship\" or simply \"game\" to characterize an instance of these competitions. What is the difference between these terms? Which of them would be more suitable for one single instance of an eletronic sport competition?", "label": 1}
+{"snippet": "This is possibly a silly question but when we derive the equations of motion of a particle using the principle of least action. We must assume that there is a single minimum (for a fixed choice of boundary conditions), right? What happens if we have two minimums? How do we decide what trajectory that particle took? Is it just a case of never creating a Lagrangian with that form?", "label": 1}
+{"snippet": "I am documenting a piece of software that will be transferred to a customer. The customer will run the software continuously. They may choose to update and improve it, but this is optional. To keep the software running smoothly, there is a minimum set of upkeep tasks that must be done periodically. Things like checking error logs, testing server uptime, making backups, and so on. For the document, I want a recognizable term to describe this set of activities. Here are words I thought of so far, which I feel are inadequate: Minimum upkeep tasks Maintenance mode Life support activities Bare-bones operation", "label": 1}
+{"snippet": "I am working on a barn door tracker for taking astro photos. My drive train has a small periodic error that I'm trying to eliminate and I was hoping someone might be able to suggest a formula that would approximate what is shown in the attached image. The image shows three cycles of the error. It appears to me to be similar to a sine wave but with the upper half stretched out. It doesn't need to be exact, just something so when I subtract it out, I'll get close to a straight line. I hope that makes sense. Any assistance would be greatly appreciated.", "label": 1}
+{"snippet": "I am currently completing a maths project that aims to approximate the roots of functions using MATLAB. The two root finding methods that I have used are inverse quadratic interpolation and the secant method. I have written scripts for both methods and have obtained approximations to the roots of different functions. I was wondering if it was possible to graphically illustrate the various iterations for a specific function, on the same graph, to show the method converging to the actual root value? If this is possible I would like to be able to complete it on MATLAB if not then excel? Does anyone know if this is possible or even how to go about completing it? Thank you!!", "label": 1}
+{"snippet": "Wikipedia gives the following definition of a formal proof: A formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language) each of which is an axiom, as assumption, or follows from the preceding sentences in the sequence by a rule of inference. Given this definition, a sequence whose final term is an axiom could qualify as being a formal proof. What would it be a proof of? The idea that an axiom can have a formal proof, seems anti-intuitive. I haven't been able to find a definition of 'formal proof' sufficiently detailed as to unequivocally answer the question posed within the title of this post.", "label": 1}
+{"snippet": "I have heard of impulsive differential equations being used in some epidemiological models of infectious disease. I haven't heard of them before in my math education, and I was wondering how they might work. I presume there is some mechanism to introduce a step-wise/impulse discontinuity, but I'm not sure what a simple model might look light, or how it behaves. Any help would be appreciated.", "label": 1}
+{"snippet": "In the foreword for a knitting book there's this passage: Knitting has become as ubiquitous as the humble sheep. Which is followed by a couple more sentences on how great it would be to learn how to knit etc. I've googled \"the humble sheep\", and haven't had any success. Is the phrase roughly equivalent to \"Wool is everywhere nowadays, and wherever there's wool, there's knitting\"?", "label": 1}
+{"snippet": "I'm using the word subscription with the following meaning: subscription: an arrangement to receive something, typically a publication, regularly by paying in advance. (Definition taken from Google, I'm not sure how to link to the source) Basically, I'm looking for a word that is an arrangement to send something. Does anyone have any good suggestions for what that might be? I have thought about Producer & Publication, but they seem a little off to me. A 'Producer' can produce the something to send, but doesn't necessarily have to send them and a Publication seems like the something that is being sent.", "label": 1}
+{"snippet": "Our company occasionally has to write letters to a third-party in response to a complaint. There are times when we only know the complainant's last name (usually with first initial). Typically, we would write something like \"Mr. Jones signed up for service on...\" or \"Mrs. Smith contacted us on...\". If we do not know the person's gender, what is the appropriate way to refer to the customer? Would we just use \"complainant\" or should we ensure that we use the customer's name? EX: \"The complainant contacted us on...\" vs. \"J. Smith (the Complainant) contacted us on...\"?", "label": 1}
+{"snippet": "A Ponzi scheme is a fraudster uses money from new investors to pay old investors, so that it looks like he is doing something profitable. At some point, when all the investors want their money, he doesn't have it (because he took some of it). A key part of the definition of Ponzi scheme is fraud (the fraudster said he was making money when he wasn't). What's the word for a \"Ponzi scheme\", happening by accident. For example, a bunch of people may invest in a stock causing a bubble, and then the price crashes. This is like a Ponzi scheme because those who sold first got a profit at the expense of everyone else, but there wasn't any fraud since it happened by accident.", "label": 1}
+{"snippet": "I am using Tikz externalize for the figures in a manuscript. The original files containing the Tikz/pgfplots code have been deleted (but will be regenerated in several hours when my simulations finish running). In the meantime, I would like to make a few changes to the text and give it to someone else to review. I still have the output files from the previous Tikz compilation. Is there a way to prevent Tikz from trying to rebuild these files and instead use them as is?", "label": 1}
+{"snippet": "I'm wondering if there's a word or term for a person who looks for an opportunity to insult and berate other people. I'm sure you've all been there; you're using an online public forum, like Facebook, to voice an opinion. There's always that one person who gets completely offended, or they take things completely out of context. They then proceed to publicly scold and shame you - excessively, it seems. It makes you wonder if maybe they're just looking for something to complain about, or if they enjoy being abusive? Maybe they just get a kick out of making you look bad, and want everyone else to dislike you? \"Troll\" and \"butthurt\" seem to fit fairly well, but I was hoping to find a more traditional English equivalent.", "label": 1}
+{"snippet": "First of all, I ain't a native speaker. And one of the most confusing sentences to me is I ain't going to this place no more. Ain't in this sentence basically means am not, so it translates to I am not going to this place no more. What exactly does no more in this sentence mean? Does it have the same meaning as any more?", "label": 1}
+{"snippet": "I am facing an example that I am not able to understand at all. It says the the limit of a pointwise convergent sequence of positive semi-definite metrices is positive semi-definite. Basically, I do not understand how to use the pointwise convergence for a matrix, that is, I do not know a definition that is general enough to be applied to that case, and I was not able to find it anywhere. Can someone help me?", "label": 1}
+{"snippet": "Here is the full question: Prove that every continuous function on a closed interval is Riemann integrable. Give an example of a continuous function on an open interval which is not integrable. I think he might be Riemann integrable for the second question because I'm pretty sure that every continuous function on an open interval is integrable just by definition. If that's not true, does anyone have any ideas for the answer?", "label": 1}
+{"snippet": "I am brand new to lattices/partitions. Given that the set of all partitions of a finite set is a poset ordered by refinement, how does one prove that it is a lattice? I know you have to prove that the join and meet exist, but how does one construct them in this case? In other words, what are the join and meet of two partitions?", "label": 1}
+{"snippet": "I have been reading about Jupiter as of late and reason I am asking is if Jupiter has strong enough gravity to pull hydrogen to itself then it should be only matter of time when it will acquire enough mass to ignite itself and become a star, same would apply to any other planet that is big enough to hold hydrogen (In other words if planet gains more matter than it looses it will become a star eventually). Or am I missing something here?", "label": 1}
+{"snippet": "As I understand it (and admittedly it's a weak grasp), a computer processes information irreversibly (AND gates, for example), and therefore has some minimum entropy increase associated with its computations. The true entropy increase is much greater, and comes from the conversion of electrical energy to heat. How efficient is a typical desktop computer when viewed in this light? Make any assumptions you find useful about the energy use, computations per second, temperature of the room, etc.", "label": 1}
+{"snippet": "In my mathematical writing in grad school there used to be sentences like \"Whenever x is a fish, then x is an animal.\" (Yes, that's what my dissertation was on!) I am a native speaker of English and this seemed fine to me. My adviser (who is not a native speaker of English, though it's not entirely relevant) insisted that this was incorrect, so I stopped using it because he was pretty much the only one reading what I wrote. He suggested replacing \"then\" with \"we must have that\" (which I did). I still wonder, though...is it really incorrect?", "label": 1}
+{"snippet": "I notice that a lot of researchers tend to have crappy-looking websites, often because they aren't willing to put in the time it takes to learn HTML, CSS, and design principles--they'd rather do research. I'm assuming that said researchers know LaTeX, as it's pretty much the standard for academic typesetting. So why not leverage that knowledge to make a kick-ass homepage? Are there any LaTeX packages or tools that are designed with the easy creation of a nice-looking website in mind? And, no, I don't mean just haphazardly turning a topology paper into a Web page.", "label": 1}
+{"snippet": "I once asked some English people the following question: \"At what time do you go to sleep?\" They gave me a blank stare. You see, I tried to avoid the standard expression \"At what time do you go to bed?\" because it is ambiguous. I may get into my bed but may not fall asleep right away. I may be reading or emailing on my iPad or watch TV.", "label": 1}
+{"snippet": "I'm looking for a mathematical treatment of mass action kinetics under the assumption of detailed balance. In particular, I'm interested in the proof that the free energy is a global Lyapunov function. There are many papers that prove this for the more general case of \"complex balance\". However, I'm not particularly interested in that generalisation, because I'm interested in applications to chemistry, which means making different generalisations that are not compatible with it. So my questions are: What is a nice, simple proof that assumes detailed balance and shows that the free energy is a global Lyapunov function? Is there a good overview paper that gives a concise mathematical treatment of the subject without making generalisations beyond what can be observed in a real (closed) chemical system?", "label": 1}
+{"snippet": "This has been bugging me for a while, does anyone know what this word is? Maybe I imagined it. I thought it might have been \"superfluous\", but I don't think that is it, then I thought it might have been \"hyperbole\" but I do not think that is it either. Any thoughts? Here is some context. Person A: If a billion people view my web site, my server will crash. Person B: That is a ___ example. The difference between the word that I am looking for and \"hyperbolic\" is that a hyperbole is not meant to be taken literally and this is. Hope that helps.", "label": 1}
+{"snippet": "Is there a term for the word that describes where a person is from or what nationality they are? For example, someone from America is an American, and someone from Finland is a Finn. Is there are term for the words American and Finn that denotes that they mean \"someone from a particular place\"? I could have sworn I stumbled upon such a word years ago, but I cannot for the life of me remember it.", "label": 1}
+{"snippet": "To me \"I must help her\" sounds wrong. I feel that I would rarely say this. On one website they say that 'must' is more for personal obligations (e.g. I must help my mother.) and that 'have to' is for external obligations (e.g. my boss says I have to finish the report.) Is it that simple (and vague)? Or does anyone have a better explanation?", "label": 1}
+{"snippet": "Is the sentence: \"We felt we had let our coach down because we hadn't won the match\" correct? I read a sentence \"We felt we had let our coach down because we didn't win the match\" in an English textbook. I wonder that, when we compare the happening time of the three things: A \"feel\" B \"let our coach down\" and C \"did not win the match\" it will be C> B> A. So is it possible to say: \"We felt we had let our coach down because we hadn't won the match\" also? If it is ok, too, are there any differences between the two sentences? Thank you very much in advance.", "label": 1}
+{"snippet": "I'm interested in knowing the structure of a CNOT gate, in quantum computing. THe problem with that is, that I've read how the structure of a nuclear quantum computer works, but I still don't understand how that can be implemented to create a quantum CNOT gate. I've read the article of the original proposal of Cirac-Zoller, but it wasn't explained very good, I guess, so I want to ask, if someone has a link to some publication where it's explained better than there, possibly with more pictures rather then formulas. Thanks.", "label": 1}
+{"snippet": "A: I can't understand why my parents keep me from buying fast food. B: Me, too. It's delicious. Does B's answer sound natural? In Korea, we usually teach that we should use 'me, neither' in a negative sentence, 'me, too' in a positive sentence. But I am not sure if this is always true. I think that 'me, too' is a valid response in this particular case, but one of my students said that 'me, too' is grammatically incorrect, so it is unnatural. Who is right?", "label": 1}
+{"snippet": "While reading about linear algebra for math olympiads in these notes, I came across the following assertion: Remark. The set of invertible matrices form a Zariski (dense) open subset, and hence to verify a polynomial identity, it suffices to verify it on this dense subset. Could someone provide an explanation of what it means to be a \"Zariski (dense) open subset\"? A proof of this result is sketched in the notes, but I feel there is some deeper theory going on underneath. In case anyone is interested, the author has a similar set of notes here.", "label": 1}
+{"snippet": "I'm in the process of learning about Matroid Theory (I'm reading Oxley's book). I came to this from combinatorics and topology. Now, I just read of connections between matroids and combinatorial optimization. Yet the only example I've seen so far is that of the greedy algorithm. So, I'm wondering if there is some astounding application of matroids to optimization. By that I mean either something that can be solved with matroids and for which no matroids-free solution is known, or something that can be solved much more easily using matroids.", "label": 1}
+{"snippet": "The Free Dictionary defines it as \"to start to accept and deal with a difficult situation,\" but I don't know what accept means in this expression. Does accept mean to welcome the difficult situation? That can't be right, as I've heard \"come to terms with\" pertain to one whose friend or family member died, and I doubt anyone would welcome that. Does accept mean tolerate, as in to allow the difficult thing to happen? That wouldn't work either, as going back to the death example, there's nothing one can do to make the dead individual stop being dead (for now, at least). So, I'd like some help understanding \"come to terms with\" given my trouble with the definition I've seen.", "label": 1}
+{"snippet": "I was excited to learn that XeLaTeX finally has microtype support (I had asked about that earlier). However, after adding microtype to my document, I noticed that line breaks at hyphens now go wrong. Previously, the word foo-bar would be hyphenated as: foo- bar But with microtype enabled, I now get foo-bar and that runs over the right margin. Is this a known problem, and are there tuning parameters to fix this?", "label": 1}
+{"snippet": "I'm working through Mumford's Red Book, and after introducing the definition of a sheaf, he says \"Sheaves are almost standard nowadays, and we will not develop their properties in detail.\" So I guess I need another source to read about sheafs from. Does anybody know of any expository papers that cover them? I'd prefer to not have to dig deep into a separate textbook if possible.", "label": 1}
+{"snippet": "As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates due to gravity. It can reach a point where its velocity is high enough to keep falling but also keep missing the object it is falling towards. What keeps it from accelerating (because of gravity) and eventually reaching escape velocity? I feel like I'm either looking at things the wrong way or I have the entire thing wrong.", "label": 1}
+{"snippet": "I have a circle with a known center and radius. I have an arc with a known radius and two points on its edge, where one end is at the same position as the circle's center. Is there a way to find their point of intersection that's simpler than turning this into two circles and intersecting those (and somehow figuring out which of the two points of intersection to use)? In other words, the green bits of this diagram are known, and I'm trying to find the red:", "label": 1}
+{"snippet": "I'm having trouble deciding whether the word 'name' can be used possessively. Currently I'm thinking it's correct to say: Patients' names have been altered to provide anonymity However it just doesn't look right to me. Is the above correct for a group of patients or would any of the following be better: Patients names have been altered to provide anonymity Patient names have been altered to provide anonymity", "label": 1}
+{"snippet": "What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a convincing proof that it can be done at the level of path integral. How do we know for sure that Minkowski action and Euclidean action lead to the equivalent physical result? Is there an example where they differ by e.g. a contribution from a pole not taken into account while performing Wick rotation?", "label": 1}
+{"snippet": "I have been studying the concept of transcedental numbers. Till now, I had taken it for granted that all important numbers like pi and e were transcedental. I have no reason for assuming this or for clustering them together. It's just my intuition had placed numbers like pi, e and the golden ratio together and for some reason assumed they are all transcedental. This was before I was aware of a rigorous definition of a transcedental number. I just remembered that the golden ratio is one less than it's square. So, it does satisfy an algebraic equation. Does this mean that the golden ratio is not a transcedental number?", "label": 1}
+{"snippet": "I have a problem analysing this sentence from the point of finite/nonfinite clauses, clause elements and their functions: He does not want to destroy his parents' dream of him achieving a Cambridge degree. I am especially interested in the: dream of him achieving a Cambridge degree. I know that 'achieving a Cambridge degree' is a non-finite -ing participle clause. However what is its function? And what is the function of 'of him'? Is it a postmodification?", "label": 1}
+{"snippet": "In a one dimensional lattice system with periodic boundary conditions, in which the last and the first site of the lattice are the same site, momentum is conserved modulo a vector of the reciprocal lattice. My question is if for a system with open boundary conditions, in which the single particle wave functions vanish in the two extremes of the chain, momentum or quasi-momentum is conserved. In principle, there is no discrete (nor continuous) translation symmetry, so momentum shouldn't be conserved. However, I wonder if momentum conservation is completely lost or if there are some remains.", "label": 1}
+{"snippet": "When you put chopsticks (or any other object) in a glass cup of water, why do the chopsticks seem curved or bent? Is it because of the shape of the cup, the water, or the chopsticks itself? Note: I'm sorry I currently don't have an image of it. You can try this at home. Just put a pair of chopsticks in a glass of water. If you have an image, please edit this question and put an image in.", "label": 1}
+{"snippet": "I am a first year student at varsity and I am new to Astronomy. A question came up in my tut asking about the Hubble constant and cosmological time. I couldn't answer it because I have not understood the relationship between the two. What I've heard is that H is constant for space(although I don't understand what that implies), and is not for time. What does this all mean?! Please help...and please keep things simple.", "label": 1}
+{"snippet": "Consider the quote from \"What is a Grantor Trust\" article. This trust is revocable, which simply means it can be altered, modified, and otherwise changed or even terminated during the life of the grantor, provided that the grantor has full mental capacity. As far as I could figure out from other forums words \"alter\" and \"modified\" mean \"to change slightly\", and \"change\" is more generic word and may also mean \"replace\" or \"exchange for something else\". The text in bold sounds to me like \"it can be slightly changed, slightly changed, and otherwise changed\". Are there some differences in meaning between \"alter\" and \"modify\" in this context or in general? Are they generally interchangeable?", "label": 1}
+{"snippet": "In the most basic sense, what is abstract algebra about? Wolfram Mathworld has the following definition: \"Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields.\" I find this, however, to say the least, not very informative. What do they mean by abstract algebraic structures? Along these lines, what are groups, rings, and fields then? I've been told by a friend that groups, essentially, are sets of objects, although, this still leaves me wondering what he means by objects (explicitly). I don't need anything rigorous. Just some intuitive definitions to give me some direction. Thanks!", "label": 1}
+{"snippet": "I'm a programmer and like to name my variables as accurately as possible (who knows who will be reading my code in a few years' time?) I've been thinking about sports video games recently, and have thought about the idea of a generic sports game engine. Most sports games have an arena, crowds, a playing surface and players. They also have a puck, ball, discus, javelin, etc. and this has me wondering: What is a generic term for this object? Something that could transcend all sports. Edit: Since it seems there may be no exact term for this type of object, I'd gladly settle for some sort of analog.", "label": 1}
+{"snippet": "I think to answer this question we would have to fully understand the nature of black holes. It seems to me that the smaller black hole could have a lower density than the larger one. In this case the smaller black hole might be effected by the tidal forces of the larger black hole. But if the densities of the two black holes were the same, wouldn't the smaller black hole be immune to spaghettification?", "label": 1}
+{"snippet": "Is it somehow possible to extend TexStudio to use dictionary words in autocompletion? For example, when I type \"som\", I want the autocompletion list to show me all words from the dictionary starting with \"som\". I know TexStudio uses autocompletion for words that already appear in the same document. I've tried to create a .CWL file, but apparently it is only for commands and plain words are not supported.", "label": 1}
+{"snippet": "I'm trying to create my own ultrasonic humidifier. I ordered the misting part which works great but it only functions correctly in shallow water. So I'd like to feed from a large water reservoir to a smaller one. My question is how can I fill the smaller reservoir to a desired water level? Will I have to use a closing/opening valve or is there a simpler way? (I was thinking a small balloon hooked up to a pulley that opens and closes a latch much like a toilet but I am trying to avoid complexity.)", "label": 1}
+{"snippet": "My assignment asks us to prove or provide a counter example for If R is symmetric, then Rc is symmetric. I know that if R is symmetric, then (x,y) and (y,x) are both in R, but what I do not understand is what is R^c, what does R^c do to the relation? I believe that complement basically means \"not\", so does that mean the complement of R is NOT symmetric? I can't seem to wrap my head around this concept, any help would be appreciated. Thanks", "label": 1}
+{"snippet": "The metaphor of a surface (typically a pool table or a trampoline) distorted by a massive object is commonly used as a metaphor for illustrating gravitationally induced space-time curvature. But as has been pointed out here and elsewhere, this explanation seems (to a layman like me, at least), to be \"hopelessly circular\", and in the end contributes little to an understanding of how modern theories of gravitation work. Are there other (or additional) metaphors that might be helpful in illustrating to lay readers (a) what motivates modern gravitational theory and (b) why it has greater explanatory power than Newtonian gravitation?", "label": 1}
+{"snippet": "A field F is algebraically closed if every non constant polynomial in F[x] has a root in F. Is this the right definition? I am wondering if only one root in F and the rest of the roots not in F can also be considered 'algebraically closed'? I remember reading somewhere that if a root is in F then all roots are in F. Is this a special case of something? If so, could someone enlighten me on what it is? Thank you", "label": 1}
+{"snippet": "Assuming an object is moving in a straight line propelled by a force. How much energy would that force have to exert so that there are no known forces or objects that could stop it from moving in that straight line? I'd guess limits like the speed of light might come into play here, but it would be interesting to know what the values would be if those limits weren't there.", "label": 1}
+{"snippet": "I am in sales and when I make a cold call I typically begin the conversation with, \"I just wanted to...\" Some common phrases are, \"I just wanted to see if you might be interested...\" or \"I just wanted to follow up with you...\" I hate this phrase as it shows a lack of confidence and it's not truthful. I want more than JUST to do something, I want to engage in a conversation so I feel disingenuous starting the conversation with this statement. Does anyone have any alternative ways of beginning these statements? Thanks!", "label": 1}
+{"snippet": "I am a newbie to Mac OS X. I installed TeXmaker and found that the Chinese characters in the interface are garbled completely (see figure below). I tried a lot to fix this but nothing worked. Finally I realized that this is related to the \"Interface fonts\". However, on my mac there's no such setting option!!! (Previously I used ArchLinux and there was indeed such a button) Does someone happen to know how to modify \"interface fonts\" for mac TeXmaker? Many thanks in advance!", "label": 1}
+{"snippet": "Sorry for the elementary question, but I am confused. Suppose I am telling someone about a conversation I had with a friend the previous day. Which would be correct? \"I asked him if he were well\" \"I asked him if he is well\" \"I asked him if he was well\" Am I right in saying that the third sentence would be \"double past tense\", as in referring to a previous conversation where I asked my friend if he was well at an even earlier point in time?", "label": 1}
+{"snippet": "Apart from Cantor's diagonalization argument, there are a number of ways to show that cardinality of R is greater than that of N (eg: Baire Category theorem, path connectedness of R and so on). Are there any arguments outside Set Theory which naturally lead us to sets of higher cardinality than R ? In other words, if Set Theory never existed, would we be happy to conclude that there are only three types of cardinality - finite, countably infinite and uncountably infinite - or would we have gone beyond ?", "label": 1}
+{"snippet": "In prime numbers, one has the sieve of Eratosthenes, which is a method of computing the next prime, once you have all previous primes: You just cross out the multiples of the previous primes on the number line, and the first remaining number is the next prime. I wonder whether there is such a method for prime gaps. Of course, one could add up the prime gaps and then apply the sieve of Eratosthenes, get the next prime, and then compute the next prime gap from it, but I wonder whether there is a more \"direct\" way.", "label": 1}
+{"snippet": "I have a problem in Texmaker. I have divided a document into a number of subfiles. I would like to compile the whole document from the current subfile without running the master file. I tried to define the current file as a master file by changing the status of the current subfile to a master file in Options menu. However, I receive errors after running the subfile. Can you please give me some pieces of advice in this respect?", "label": 1}
+{"snippet": "Let's look at an internal combustion engine (more precisely a standard gasoline car engine) as a black box (so without going too much into details about internal processes). The inputs of this system are throttle (gas pedal position), moment of inertia it sees and possibly external torque? And the outputs are torque and angular velocity. Can you provide me with a simple model of these relations? Or in other words, how do I know how throttle affects the movement of the car?", "label": 1}
+{"snippet": "Could anyone briefly explain, or point me towards a resource explaining, the main differences between the main integration theories, namely: Riemann Integration Riemann-Stieltjes Integration Lebesgue Integration Lebesgue-Stieltjes Integration I understand that this a question with a potentially very long answer, since integration is no small theory. I can find information on these integrals separately, but I would really be interested in a comparison of these integrals with one another.", "label": 1}
+{"snippet": "Recently, I have lost a great amount of work on a project in LaTeX because of unwittingly saving changes when cutting out a large chunk of text and copying the remaining part. I was wondering if there was any way to bring back a version of a LaTeX document from a previous time to this incident. I know such a function is available on Google Docs, but is it available here? If so, how? Thanks!", "label": 1}
+{"snippet": "I'd like to ask how verbs 'to be riddled with something' (idiom) and 'to teem with something' (phrasal verb) overlap each other and can we replace with one another in the same sentence? For example: ...the judiciary are riddled with prejudices and the judicial system is filled with flaws, and innocent people will be executed. His body was riddled with cancer. Her typing was slow and riddled with mistakes. The woods are riddled with rabbit holes. The streets were teeming with tourists. A river teeming with fish ( The sentences were excerpted from Oxford Dictionary Online)", "label": 1}
+{"snippet": "I am writing a large Sweave document that will be broken up into many chapters with the final output being a large pdf of everything and an individual pdf for each chapter (with the same page and caption numbering as in the large pdf). I found some great answers about working with multiple files but haven't seen how to also create the individual chapter pdfs with proper pagination. Is there a way to do that?", "label": 1}
+{"snippet": "I am not a native English Speaker, but I work with English speakers on a daily basis and they have always troubles pronouncing my surname, so they will often ask me to tell them how they can pronounce it. My surname is Sulce. I also tried a pronouncing service and they said \"Sorry, we can't pronounce that.\" So, I would like to ask native speakers to help on defining the most correct way to pronounce it. What's the first pronunciation that comes to your mind for the word Sulce?", "label": 1}
+{"snippet": "I've read in books that one can't put one's hand through a table because the table offers a \"Normal Reaction\" to the hand. And it is also stated that this force is electromagnetic in nature. But what is this force? Can it be explained using classical electromagnetism \"in terms of something I'm more familiar with\"? Moreover, if it is this force that stops my hand from going through the table, why is it that certain other solid substances, like sand, don't produce the same result? Also, is there any limit to this Normal reaction? I mean on pushing too hard my hand might go through the table. Is there any upper limit to this force?", "label": 1}
+{"snippet": "A location, A, is said to be equidistant from two other locations, B and C, if the distance from A to B is the same as the distance from A to C. What is the equivalent word to use in the context of time? That is, suppose that the distance from A to B is different from the distance from A to C, but it takes the same amount of time to get from A to B as it does from A to C.", "label": 1}
+{"snippet": "i'm having a problem with the definition of open, closed and clopen sets. I have understood the basic definitions, but then the teacher today in class said that the normed space is limitless. A colleague of mine said then that the normed space is clopen, but i can't really see why. To me, a normed space, since it has no limits, it is impossible to find a ball that has points not belonging to the normed space, so it can't be a closed set, right? Then, it must be an open set. Or am I mixing everything up? Thanks in advance!", "label": 1}
+{"snippet": "I'm looking for a word that describes the act of doing something without a real logical reason but just because they can. A example of what I'm talking about would be like this: The boy hacked the Pentagon just because he could. He didn't steal anything and he didn't want the attention; he just wanted to proclaim his own self-dignity. What would you call someone like that or the act of doing something like that?", "label": 1}
+{"snippet": "I was looking at reviews for Sakurai's Quantum Mechanics textbook, and some mentioned it being outdated, specifically mentioning his use of imaginary time. Is this idea deliberately avoided in modern treatments? I can't see why a simple parameter change t->it, would be or not be an outdated concept. It doesn't make things significantly prettier, but it doesn't hurt anything either. With that said I've never before heard the specific phrase imaginary time so maybe it is outdated.", "label": 1}
+{"snippet": "I am looking for a word or phrase regarding something that is \"impossible\". I can't seem to put my finger on it, but I am trying to think of the word to describe something that is the top of the top, and thus impossible to achieve? The only two words I have come up with are elusive and formidable, neither of which really mean what I want them to mean. I want something more clever to put it plainly.", "label": 1}
+{"snippet": "According to Biber's Longman Student Grammar of Spoken and Written English, insterts are one of the three families of words (apart from lexical and functional words). At some point, the author explains that inserts generally carry emotional and discoursal meanings, such as oh, ah, wow, used to express a speaker's emotional response to a situation, or yeah, no, okay used to signal a response to what has just been said. Could someone,please, explain in simple words, what does the 'discoursal meaning' mean?", "label": 1}
+{"snippet": "I believe the answer to this question is yes. I was hoping someone would critique my logic. Let X be a separable and metrizable space. Then it has a countable dense subset A. Let B be a basis for X. For every a in A, choose a basis element U in B such that a is in U (if such exists). This forms a countable collection V. Suppose, for a contradiction, there is an element x that is in no element of V. Then x is in a basis element U. U must contain an element of A since A is dense. But this U is not in our collection V, a contradiction.", "label": 1}
+{"snippet": "I'm running into an issue with my dissertation. I'm using a template created to format my dissertation according to the University's guidelines. When I format it using the twoside argument for the class, I get my list of figures and List of Tables pages each with an extra page afterward saying List of Figures - Continued, but there is nothing else on the page. This only happens with the twoside argument.", "label": 1}
+{"snippet": "For example, if I take a slap shot on a hockey puck, from what I understand, the forces acting on the puck are friction, the normal force, and the puck's weight. And, since I'm not constantly either pushing the puck, or pulling the puck there are no other forces acting on the puck, because me shooting the puck was just a one time force. Am I thinking about this correctly?", "label": 1}
+{"snippet": "Which is the appropriate word to be used in the sentence: The system we were testing was determined to be insecure/unsecure. The usage is in the context of security, specifically a lack thereof. I've always said insecure, because I didn't believe unsecure was a word (although unsecured is). Even as I type this, I'm getting a spell check complaint about it. However, I was laughed at once when I called a particular device \"insecure.\"", "label": 1}
+{"snippet": "With reference to Black holes in particular, how can you approximate the luminosity of an accretion disk? It is possible to quantify the temperature at a given point, but as the disk is not a black body, and this temperature is at a specific point, I am unsure how to equate this to luminosity - surely you could not do so using the Stefan-Boltzmann constant?", "label": 1}
+{"snippet": "I happened upon the following sentence in a textbook: 'An increase in the number and size of islets is characteristic of infants born to diabetic mothers. I get that, as the sentence is presented, the singular noun 'increase' is governing the singular verb 'is', but aren't two different 'increases' being described, one in size and one in number? On another note, I would probably see nothing wrong with 'The love of money and power was his undoing'. I'd imagine a single 'love' that embraces both 'money' and 'power'. So, what's the rule in matters like this?", "label": 1}
+{"snippet": "The person at the desk next to me is writing his Ph.D. thesis, and is trying to decide how to lay out some tables. He has too much data for one table, but is not a fan of rotated tables. So we were talking and had the idea that he could make two tables, and place them on adjacent pages so you could see them at once. However, you'd have to make sure they didn't wind up on the front/back of a single page. Is there a way to do that, or is this sheer madness?", "label": 1}
+{"snippet": "The sentence, \"he took my toy away\" can be rewritten as, \"he took away my toy.\" However, \"he took me away\" cannot be rewitten as \"he took away me.\" The second sentence sounds awkward at the very least, and I do not think it is grammatically correct, but I do not know any exact rule stating so. Is the last sentence valid, and if not, why?", "label": 1}
+{"snippet": "I recently found myself in a situation where I wanted to use a line that went something like this: \"...we must examine the effects these ideas had on their respective creators...\" and I just couldn't find the right word in place of \"creators\". Something feels off about \"creators\". We don't create thoughts we have thoughts or we think thoughts. \"Owners\" doesn't really work as no one can \"own\" a thought, and \"thinkers\" sounds too childish. What other words are there that describe \"the person who came up with an idea\"?", "label": 1}
+{"snippet": "In the book The Road to Reality by Roger Penrose, projective geometry as developed during the Renaissance is framed as (eventually) playing a pivotal role in quantum mechanics. (In fact, Penrose seems enamored with the idea that there is some connection between painting and physics, particularly where twistor theory is concerned. The book's epilogue is the most blatant example of this, though other examples abound.) Not having studied quantum mechanics, I can't really imagine how projective spaces would be used to formalize what I know intuitively about the way QM works. Can someone provide a very simple example?", "label": 1}
+{"snippet": "Recently, I have had a debate with a friend that \"brings all the boys to the yard\" is an idiom and he refuses to accept it. Since this has been used as a part of a rapper's lyrics, he says this is not an idiom. All in all, is it an idiom and how to find out if some phrases are idioms or not? Is there a specific dictionary or a thesaurus? The lyrics go like this: My milkshake brings all the boys to the yard, And they're like It's better than yours, Damn right, It's better than yours, I can teach you, But I have to charge See full lyrics at AZLyrics.com", "label": 1}
+{"snippet": "Recently I wanted to write an essay about the women in Jane Austin's time. I wrote the women at that time were concerned much about how to be engaged to a decent husband. Not like women nowadays, they want to be treated equally as men and realize their value in society. So I want to say the women back in Jane Austin's time, their viewpoint toward life was too vulgar. I am not sure if I use this word correctly or it will convey a totally different meaning. Could you please help me?", "label": 1}
+{"snippet": "So according to my understanding, the free energy of the system should be a continuous function of temperature. This is because if the free energy is not continuous at temperature T, then at this temperature the free energy can have two values (i.e. two states) and the two states will mix to eliminate the difference in their free energies. Is that a reasonable explanation for the continuity of free energy? The free energy is a continuous function of temperature does not mean it is differentiable everywhere, because at the point where the phase coexistence start to occur the free energy is not differentiable. Is that the case?", "label": 1}
+{"snippet": "I've been reading some Feynman's books. There's a point that intrigues me. It's the fact how we understand a physics equation, not only mathematically, but digging deeply into its roots as a physicist. I'm just a first- year- physics student, but I would like to understand the basic equations I'm studying through its physical meaning, but to be honest I don't really know what Feynman meant. I hope you can help me. For example a equation such as: F=ma Thanks!", "label": 1}
+{"snippet": "Dark energy is introduced as a constant inside Einstein's equations. Its primary purpose, from what I understand, is to make Einstein's equations compatible with the accelerating expansion of the universe. As a consequence, of the \"predictions\" of dark energy is the expansion of the universe according to Hubble's law. I know there are numerous experiments that verify this expansion (and its acceleration), and thus indirectly support the dark energy theory. My question is: Are there other factors that give credit to the existence of dark energy? Are there any experiments that support this theory, but not only through the verification of Hubble expansion?", "label": 1}
+{"snippet": "Consider the category of finite dimensional vector spaces with morphisms being linear transformations. Is it still true that monics and epics are actually injective and surjective linear maps, respectively? The converse is surely true since the category is concrete. I know this monics and epics are precisely the injective and surjective maps in the category of Sets and in the category of groups, but it is not necessarily true in the category of topological spaces, so I'm just curious if it is true or not in the category of f.d. vector spaces, and if so why?", "label": 1}
+{"snippet": "We were learning about Boyle's law (pressure is inversely proportional to volume of a gas) and in the experiment to prove the law, we were told that we cannot change the volume of a gas too rapidly without affecting its temperature. I have two questions about this: Why does temperature of a gas change when its volume changes very rapidly? This process (rapid changes in volume) is used in the liquefaction of gases. How is this done?", "label": 1}
+{"snippet": "In my Astronomy class, I learned that temperature results from the speed of air molecules colliding into your skin. Thus, if the air molecules in the room have a high kinetic energy and thus collide with you at high speeds, your temperature will increase. So how does a breeze of wind, in which I imagine air molecules would be moving very fast (or if they're not moving fast, YOU are moving fast relative to them), result in feeling cooler?", "label": 1}
+{"snippet": "When I say \"I cannot attend to it\" it sounds like I'm saying \"I'm not able to attend to it\", while what I want to express is that I'm capable of doing it, but I just don't need to. In Slavic languages it's resolved by changing the negation particle position: [negation] [can] [do something] vs. [can] [negation] [do something]. In the first case I negate \"can\", while in the second I negate the \"do\" verb. How to achieve the same in English and not be ambiguous?", "label": 1}
+{"snippet": "I'm studying basic topological, metric and normed spaces and I am curious why one of the axioms of both a metric and a norm is the triangle inequality. It makes some sense to me having the triangle inequality satisfied sometimes, but I don't quite understand why you necessarily need it for a general metric/norm, since there are still topologies arising from it. Could someone maybe elaborate a little bit?", "label": 1}
+{"snippet": "I guess the title says it all. However, I have skimmed through several books, and while they all tell you how to use generating functions to find an expression for the n'th term of a recurrence relation, none of them say why it works. I think I have a somewhat intuitive understanding of what is going on, but I think I need a more definitive explanation.", "label": 1}
+{"snippet": "Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form \"gravity wells.\" Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing?", "label": 1}
+{"snippet": "Let us assume that the standard model is correct up to Planck mass. (Yes, I know, this is a big assumption.) If we continue the running of quark masses with energy (due to renormalization), what are the mass values we get for the six quarks at Planck energy? Is the sequence of mass values the same at Planck energy or do some quarks \"catch\" up with others? Is there some literature on this issue?", "label": 1}
+{"snippet": "I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary derivatives with covariant derivatives. But I have read somewhere that this generalization is not unique and it is just the simplest one. Can anyone introduce some resources about this subject and how electromagnetism and Maxwell's equations are generalized to curved spacetime?", "label": 1}
+{"snippet": "Possible Duplicate: How does gravity escape a black hole? If nothing in the universe can travel faster than light, how come light can't escape a black hole? I mean, Einstein's relativity says nothing can travel faster than light, but yet, light can't escape a black hole. Does this mean that light really isn't the fastest thing? That the pull of the black hole is really faster than light? That Einstein was wrong, even though it's been backed up by scientific evidence? I'm very confused. If anyone would be able to answer my question, I would appreciate it: Why can't light escape a black hole if nothing can travel faster than light?", "label": 1}
+{"snippet": "I am having trouble understanding this concept, and have not found any good resources on google that explain it in a straightforward manner: An adjacency matching in an undirected graph G is a collection of disjoint edge pairs in G such that if two edges e and e' are paired, then e and e' share a common endpoint. I am asking clarification of this as it is concept presented in homework, to which I will have to develop an algorithm to solve for - in other words, I am asking about the question itself and not the answer.", "label": 1}
+{"snippet": "I would like to know if there is a technical term to cover both interpolation and extrapolation. The reason why I am asking is that I am writing a computer program to do interpolation and extrapolation using a functional-object language called Scala. In there, I would like to define a class/template that abstracts the notion of interpolation and extrapolation. At the moment it is called interpolation but that's not really reflecting all of what it really does since the same methods can be used to do extrapolation. Is there a general term that mathematicians use that cover both these areas?", "label": 1}
+{"snippet": "Recently I wrote the following words. Age gives you the wisdom of experience while youth gives you the intelligence of mental flexibility. There is a horizon time when you have both of these things to a significant extent. Afterwards I looked up \"horizon\" in online dictionaries and I couldn't find a definition that matched this usage. I see it as similar to calling the point after which light cannot escape a black hole the \"event horizon.\" Is this usage correct?", "label": 1}
+{"snippet": "I was wondering if we could find a set of basis vectors that span the cone of positive semidefinite matrices? I know this question is hard, but I would really appreciate if even someone can share a related paper about this topic in the literature of Linear Algebra. I could not find any paper about this issue. I should mention that any answer to this question should be highly related to the topic of semidefinite programming in the area of mathematical optimization. Thanks", "label": 1}
+{"snippet": "Parallelogram ABCD is bisected by diagonal AD, and produces two triangles ABD and ACD. Prove that triangles ABD and ACD are congruent. My proof (or at least attempt): note I am not a high school student and have yet to learn geometry, I'm attempting to familiar myself with proofs beforehand though. And yes, I know my spelling is atrocious and I should use LaTeX. Thank you!", "label": 1}
+{"snippet": "When calculating the amount of time elapsed for an inertial reference frame over the course of its travel at constant velocity between two points, are the effects of both length contraction and time dilation taken into account (i.e. the distance seems shorter to the traveler and the time for the traveler seems to pass more slowly to a stationary observer), or is only one or the other effect used to calculate the amount of time elapsed in the inertial reference frame in motion? I believe the answer is only one or the other, since the effects are really two sides of the same coin, one applying to an observer within the frame and the other applying to an observer outside the frame.", "label": 1}
+{"snippet": "Ferromagnetism depends on the arrangement of orbitals and spin in the valence electrons of an atom (below its Curie point). But what is so special about the orbitals of iron, nickel and cobalt, to make them the main ferromagnetic materials, and everything else more or less pale in comparison? Please note that I am not asking \"how do magnets work?\". I know about domains, EM and the like, but on a strictly atomic/QM level, I would like to understand what sets these materials so greatly apart from dozens of others with seemingly similar orbital arrangements.", "label": 1}
+{"snippet": "What's the right word to indicate a type of education based on memorizing facts or a superficial understanding of things, without real insight or critical mind development? In my native language (Italian) we have expressions like \"nozionismo\" or \"educazione nozionistica\" or \"didattica nozionistica\". But, after I looked in the dictionary, it seems to me that the word \"notion\" in this case is a \"false friend\". In fact, \"nozione\" seems different from \"notion\", which is rather like an opinion.", "label": 1}
+{"snippet": "Noncommutative algebraic geometry is a developing field. Things have not yet got the final form as in commutative geometry. But one might wonder whether things are any better in the case of skew-fields, ie division rings, ie possibly noncommutative rings in which each nonzero element has a multiplicative inverse. Algebraic geometry is much simpler in the case of fields. So are things better in the case of skew fields? For instance, is there any particularly nice geometry over the quaternions, like there is one over the complex numbers?", "label": 1}
+{"snippet": "The definition of an inner product in Linear Algebra Done Right by Sheldon Axler assumes that the vector space is over either the real or complex field. PlanetMath makes the same assumption. Is there a definition of an inner product over, for example, finite fields? I sometimes find finite fields easier to reason about, so it would be nice to have a definition of an inner product for vector spaces over them.", "label": 1}
+{"snippet": "I am a sophomore in high school. When I approach a math problem or concept, I normally try to determine a formula or systematic method of solving all similar problems. However, since I entered precalculus, I have found that this approach does not work. I really love math and find it interesting and exciting, but I find that I am unable to solve the kinds of conceptual problems that I have been doing more recently. For example, when I try to do a counting problem, it is often unclear how to approach it. How can I improve my problem-solving and critical thinking skills? Also, how can I approach problems logically to solve ones that are not clear at first?", "label": 1}
+{"snippet": "Alright, so David Griffiths in his \"Introduction to Electrodynamics\" states that the Twin Paradox is not a paradox at all since the traveling twin returns to Earth. By returning to Earth, the twin had to reverse direction, thus undergoes acceleration, and therefore cannot claim to be a stationary observer. However, what if the traveling twin simply Skypes the twin that is on Earth. The twin on earth will still appear older, which would make no sense since in that case the rocket can be seen as the stationary frame of reference while the Earth \"travels\" at a speed close to the speed of light. No acceleration is undergone, yet the paradox remains. Is Griffiths just completely glossing over important nuance again?", "label": 1}
+{"snippet": "Is there any case in classical (non relativistic) mechanics where the strong form of Newton's third law does not hold (that is, reaction forces are not collinear)? For example, if we consider a system of two point particles in equilibrium with each other upon which a constraint acts so that the reaction forces are directed in a direction that is not collinear. Is such a situation possible?", "label": 1}
+{"snippet": "My professor in class went a little over chaos theory, and basically said that Newtonian determinism no longer applies, since as time goes to infinity, no matter how close together two initial points are, the distance between them will increase greatly. But why isn't this merely a matter of the imprecision of our measuring instruments? If we can somehow know our initial conditions exactly, wouldn't we still be able to calculate what the system will be like at some time t in the future?", "label": 1}
+{"snippet": "Is there a word (other than asshole) to describe someone who always says things in a way that makes other people look incompetent in order to make themselves look better? A different word to describe their language would also suffice. Edit: for clarification, here are a few sentences they might use: \"I wouldn't have done it that way\" \"Do you even know what you're talking about?\" (Implying that they do and you don't.) \"Well, it wouldn't have happened if you knew about such and such.\" Basically a kind of blame-passing system to cover up the fact that they are the actual problem.", "label": 1}
+{"snippet": "I'm having a bit of trouble understanding the semiconductor band gap diagram on Wikipedia: (from Band gap article). Why is the size of the band gap increasing with the Density of States (DOS) in the semiconductor material? I would expect the opposite given the intuiton that more occupiable energy states would mean a higher probability of an electron moving from a valence band to a conduction band? Should the x-axis here maybe be something like \"# electrons in the conducting band\" to show the increasing amount of energy needed to promote electrons to the conduction band as a function of the electrons already promoted to the conduction band? And why the ovoid geometry, which I've seen elsewhere?", "label": 1}
+{"snippet": "I am interested in finding out about the current status of the planned book: The Triangle Book by John H. Conway and Steve Sigur. I understand that Steve Sigur died some time back. I got no reply from Prof. Conway; is there someone who knows the fate of this project. Is it abandoned or is it still under preparation? Here is some information about the planned book.", "label": 1}
+{"snippet": "It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero. What exactly is the reason behind this? Except for, of course, the mathematics behind it. Is there any logic why the field intensity should be zero within a sphere? For example, it is logical to say that the field intensity would be zero at the center, as all the intensities cancel out. However, this cannot be the case for any point within the sphere.", "label": 1}
+{"snippet": "Let's say we have a multi-slit experiment with N slits.Since the central fringe has the most intensity, is there an equation to calculate the intensity of central fringe in terms of the intensity of the original light wave? I searched Fraunhofer Diffraction and Fraunhofer Diffraction Equation but neither of them helped me since they calculate the intensity of a fringe in terms of the intensity of the central fringe.Thanks.", "label": 1}
+{"snippet": "I understand that one of the great things about LaTeX is that, as long as you're using the same source file, the output is guaranteed to be identical regardless of the platform that you're generating it on. I'm assuming this is the case because LaTeX is controlling everything from the typesetting to the fonts themselves. If I use XeTeX, do I get the same guarantee, even assuming the I use the same TrueType fonts on two different platforms?", "label": 1}
+{"snippet": "Adiabatic approximation or the Born-Oppenheimer approximation is used whenever the electronic motion is too fast that the electrons effectively see static nuclei and the nuclei, in turn, see an averaged electronic cloud. My question is: As the word 'adiabatic' suggests no heat/energy transfer, does this mean that the energies associated with nuclear and electronic motions are non-transferable? If my understanding is right, the limiting criterion of the approximation is when transfer can no longer be neglected. My other question is how to judge when the transfer is significant?", "label": 1}
+{"snippet": "I'm confused about the how the notion of distance is used in Conformal Field Theory. Let's take for example the Operator Product Expansion (OPE). In a conformal field theory, due to the scale invariance only angles - and not distances - matter. But in the very definition of the OPEs one speaks about two operators evaluated at nearby points. How can one make sense of this apparent contradiction?", "label": 1}
+{"snippet": "I am developing a database application where a user should be able to store multiple ways of contacting someone in a database table. This database table can for e.g. contain: phone numbers mobile numbers email addresses twitter IDs facebook IDs whatsapp numbers Now I am looking for a table name. The obvious choice would be contacts. However, the term 'contacts' is used when referring to people and not ways of contacting this person. I am looking for a single word to describe all ways of contacting a person.", "label": 1}
+{"snippet": "Im wrong about something here, but Im not sure what. As far as I know the product of two normal distributed variables is not normal distributed. However, if the joint distribution of Y and X is bivariate normal then Y given X is normal distributed as well as the marginal distribution of X. Furthermore, the joint distribution of Y and X is the product of the condtional distribution of Y given X and the marginal distribution of X which are both normal. If we define a new variable Z to be distributed as the condional distribution of Y given X, then the product of Z and X (which are both normal distributed) is bivariate normal. Am I on the right track or did I miss understand something somewhere?", "label": 1}
+{"snippet": "Suppose you have a tetrahedron. It doesn't have to be regular. Now suppose you have another tetrahedron contained inside the first tetrahedron. Again do not assume it is regular and do not assume that both tetrahedrons are similar. Could it happen that the perimeter of the tetrahedron in the inside is larger then the tetrahedron on the outside? Whether it is or not prove it. Do a proof by contradiction. This one is tricky. I have been thinking about this problem for a long time now and do not see any way to come up with a reasonable solution. The help would be greatly appreciated!", "label": 1}
+{"snippet": "Recently some of my colleagues has started using the phrase \"touch space\" a lot, for example in sentences like \"I just called you to touch space\", or \"I will touch space with him tomorrow\". I can deduce that it means something like \"talk to\" or \"meet with\", but what is the original meaning, what is the advantage of using \"touch space\", and where does it originate from ?", "label": 1}
+{"snippet": "I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was Galois theory. I am interested in doing 'my own' research, if you catch my drift. That is, I would like to apply the Galois theory I will be studying to something, and do some research. My professor mentioned some possible applications within coding-theory and cryptography. Do you have any specifics in mind? I would be happy to hear your insights.", "label": 1}
+{"snippet": "I want to tell someone the following: \"I bring an e-reader with me on the bus every day so that I have something to do during my commute to work.\" Does the phrase \"commute to work\" clearly refer to the trip there and the trip back from work? Or is it more proper to say \"commute to and from work\" in order to ensure that it is clear that I mean both directions?", "label": 1}
+{"snippet": "I want to get the density of a fluid going through a pipe. I can measure the flow and pressure with a flowmeter and the temperature using a thermometer. With this information, I want to calculate (or approximate) the instantaneous density of the fluid passing through my instruments. How would I go about doing this? I'm looking at a liquid (not a gas), mostly incompressible. Think water with varying amounts of solute (salt, sugar) in it.", "label": 1}
+{"snippet": "Just wondering, what would happen in this experiment. In the experiment you would first have two entangled particles. Then you fire one of the particles, lets say \"Particle A\", at a double slit towards a detector. While in transit to the detector, what if the other entangled particle, lets call it \"Particle B\" was observed / had it's wave function collapsed? Would \"Particle A\" still generate a wave-like interference pattern or would the wave function for both be collapsed? In theory you cannot send classical data by entanglement, so this experiment must somehow fail, but I can't quite figure out why. If this experiment were to succeed, then you could read and send data about wave function states over entangled particles.", "label": 1}
+{"snippet": "I am trying to remember the phrase that describes a particular kind of folly - trying to \"beat the house\", or willingness to play a rigged game. As I recall it has the form of \"a fool's errand\" - that is, the game is referred to as belonging to the person who is silly enough to play it. I'd appreciate knowing the origin of the phrase, too.", "label": 1}
+{"snippet": "I believe that pigs can fly I think here \"that\" is being used as a conjunction to combine the independent clause (pigs can fly) with the dependent clause (I believe) That the boys painted the pig green annoyed the pig. This one I'm not so sure about. \"The boys painted the pig green\" is an independent clause, and \"annoyed the pig\" is a dependent clause; but in this case \"that\" doesn't join them. Any insight?", "label": 1}
+{"snippet": "The critics against Copernicus and Galileo argued that, if the earth moved, then, a heavy body that was dropped from a very high tower should fall to the west of the foot of the tower. Galileo argued, however, that this body would fall slightly to the east. My first guess is that the body would fall directly under the point in which it was dropped. Who is right?", "label": 1}
+{"snippet": "I'm attempting to build a regular expression that will accept only strings of the form: Begins with: /# Ends with: #/ Contains the following in between /# and #/: Any combination of {a, b, /, #} but not the combination #/ Bascially, a regular expression that determines whether a string is appropriately comment delimited. I've tried many expressions, but can't find anything that quite works. I'm not sure how to allow all other combinations of a,b,/,# but disallow #/. Any help putting me on the right track would be much appreciated.", "label": 1}
+{"snippet": "I have been trying to approach this by finding the gravitational torque of the person on the merry-go-round, however I can't find a way to relate that to angular velocity in the given circumstances. If this problem requires angular momentum to solve, then I won't need to know the solution because it won't be on my final, however I still want to make sure that I'm not missing something.", "label": 1}
+{"snippet": "I read this article where the title suggests the iPhone was dropped from space, but it looks more like it was dropped from an airplane I would think that if astronauts dropped an iPhone from space that it wouldn't land on Earth, but rather, float on for infinity (our Universe keeps expanding), or would the iPhone be captured in some planet's gravitational force and drop there. Help me understand this physics principle.", "label": 1}
+{"snippet": "Please, take a look at the following: \"Friends\" and \"foes\" are, according to Carl Schmitt, defined in function of their capacity to respectively enhance or diminish the power of one's own state. Does \"in function of\" equal something along the line of \"in relation to\"? I'm aware that the \"in function of\" thing was once covered here, but I'm afraid there was no answer there I'm now looking for. EDIT: THANKS EVERYONE FOR THE ANSWERS.", "label": 1}
+{"snippet": "I have been recently reading quite a little about Kaluza Klein theories. I am still far from mastering this but I am curious if any experiment that may disprove or give hints of the existence of extra spatial dimensions is to be expected to be performed relatively soon. This page of CERN, for example, says that the LHC might give some clues, but it doesn't really dive into much detail. So, in some detail, which experiments might say something about this, and when might they be expected?", "label": 1}
+{"snippet": "I just finished reading Richard Feynman's lectures on Quantum Electrodynamics (QED: The Strange Theory of Light and Matter) and it fascinated me. However, there's an unanswered question I have from reading it. If, as Feynman argues, \"light doesn't really travel only in a straight line; it 'smells' the neighboring paths around it and uses a small core of nearby space\" (though it is overwhelmingly likely to appear to be traveling in a straight line over long distances), how does this not defy the law of conservation of momentum? My understanding is that this law applies to light as well, with a momentum defined by p = E/c. If so, light curving would clearly defy it, would it not?", "label": 1}
+{"snippet": "I was wondering where the term 'button-down' comes from. I tried to do some research but I was not very successful... How was the word button-down formed? Is it a compound ? Does it originate from the noun \"button\", which then became the verb \"to button\" meaning to fasten? Then, how did it become an adjective ? If the adjective \"button-down\" originates from the verb \"to button (stg) down\", shouldn't the adjective be \"buttoned-down\"? If so, how did it change to become only \"button-down\" ? I looked up etymonline and the online merriam-webster but could not find any answer. Can anybody answer this ?", "label": 1}
+{"snippet": "If I grant someone a Boon, I am granting them a temporary positive effect. If I were to grant someone a temporary negative effect, what would an adequate word to describe that be? I was initially drawn to Bane, as it's another four-letter B-word, with a negative connotation, but I'm not sure if the two terms are inherently equitable. Is this an appropriate usage of Bane? Is there a better word entirely?", "label": 1}
+{"snippet": "A friend of me who is not studying mathematics now needs to deal with integrals, double integrals and triple integrals within his study of chemistry. He asked me to give him a suggestion for a basic book that explains basic facts, rules etc., about integrals. I think this means Riemann integral and that it should not be too complicated. I do not know such a book, do you know a book that deal with basic things concerning integrals for a non-mathematician? Thanks for your tips!", "label": 1}
+{"snippet": "What word aptly describes a job or position that requires more than is reasonable from the person occupying it? An example of usage might be: \"Today, John finally resigned his ___________ job.\" To clarify, John is fully qualified to perform his duties and genuinely enjoys his work. Unfortunately, John's job at Evil Corp is unreasonably demanding. John's superiors have been frequently forced to increase his workload while lowering his pay. Long term employees are leaving the company in alarming numbers. John has a very loyal personality that has urged him to stick it through, but alas, John has reached his limit and must resign.", "label": 1}
+{"snippet": "Possible Duplicate: Are collective nouns always plural, or are certain ones singular? Which is correct: The rest of the staff is or are? The rest of my family is or are? I've done a bit of research and I understand that \"family\" should be preceded by singular or plural verb depending on how you want it to be treated. For example, His family is one of the oldest in the county. and His family are all doctors. These are apparently both correct. But in the following instance, could a grammar expert tell me which should be be? When his family are abducted or When his family is abducted ? Thanks.", "label": 1}
+{"snippet": "I know that at the research level, it's common to use different areas of Mathematics to solve a problem. But my question is whether at the undergraduate level it is possible to have a problem or exercise in which to solve it, it is necessary to use subjects that are not normally seen together. For example, a problem involving at the same time Differential Geometry and Differential Equations, or Abstract Algebra and Calculus or Linear Algebra and Combinatorics... In short, is this possible? Could someone give me examples ? PS: I'm not talking about subjects that are pre-requisite to each other like Analytic Geometry and Calculus. And remember, I'm referring to the undergraduate level.", "label": 1}
+{"snippet": "I have a data logger that is recording the temperature readings from thermocouples at a specific interval. This gives me data points that I can graph where the x-coordinate is time and the y-coordinate is temperature. For each set of data points that I graph, I can connect the points and make a line - usually curved. I need to find the derivative of each line and graph those as well. There is no known function that creates these curves, so I can't simply find the derivative of a function. All I have is a huge list of (x,y) coordinates. How do I take a derivative and graph it in this case?", "label": 1}
+{"snippet": "Wasn't there a mathematician who was convinced that \"god\" was out to get him? When he was travelling by sea he would write a friend a letter claiming that he had finally proved a difficult theorem (even though he hadn't). His reasoning was that he would always reach his destination safely since god couldn't stand to let him die on the dangerous voyage while leaving the rest of the world thinking that he had actually come up with the proof... There was also some story about rainy days and sports games, but I can't remember. Who was this? I tried searching with Google, but couldn't find anything and didn't know exactly what to search for...", "label": 1}
+{"snippet": "Can you suggest books/articles on Function approximation Let me quote from the above wiki: Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. Any books/articles dealing with the above mentioned problem.Preferably with examples.", "label": 1}
+{"snippet": "I have checked OALD. I looked up \"disinformation\" which according to dictionary means \"false information that is given deliberately, especially by government organizations\" and \"Misinform\" as a verb means \"to give somebody wrong information about something\". However, there is no explanation of the word \"Misinformation\" as a noun. What exactly is the difference between these two? I would like to know if there is any nuance between these two words or if they can be used interchangeably.", "label": 1}
+{"snippet": "The universe is expanding at an ever increasing rate. Thus the following three-part question. Are there any theories that suggest the expansion is a consequence of a pull from some unknown source rather than a push from the presumed dark energy? Regardless of the cause, and assuming the expansion continues at an ever-increasing wheee, when will the most distant parts reach the speed of light? And then what happens?", "label": 1}
+{"snippet": "Possible Duplicate: Confused about the role of mass I know that two different masses fall at the same rate in the same gravitational field because the greater gravitational force of the heavier one is exactly offset by its greater inertial resistance. What I don't understand is why the larger mass wouldn't fall more slowly at first and then once the inertial resistance is overcome, it would then accelerate faster than the less massive one. It seems that the rate of acceleration (not velocity, which obviously does) would vary according to the distance of the fall", "label": 1}
+{"snippet": "The concept of reversibility always gives me a hard time.In a reversible process the change of entropy is zero. On the other hand for irreversible process it is not.But there comes another topic which is 'internal reversibility'. I couldn't quite grasp the concept. Can any one simply explain the following topic in plain words for me? What is internal reversibility or internal reversible process? Difference between internal and external reversible process?", "label": 1}
+{"snippet": "I added the hyperref package and got some errors. Thus I deleted the auxiliary files and compiled again. This time there were no errors, and the links work except in the cites (bibliography), where I get question marks and links that send me to the first page. Any ideas? In fact I don't need the links in the cites, so if there's a way I can solve the problem by having just the links in the figures and in the index it's welcome.", "label": 1}
+{"snippet": "I am trying to decide on a symbol for a particular mathematical quantity, it has three different types of indices and I'm running out of places to put sub-scripts/super-scripts. I have a few ideas, but would like input on what looks best (or any additional ideas you may have). Since you are all typesetting experts, and anyone who uses TeX likely has some affinity for aesthetics, I figured this was a good place to ask. Here are my ideas so far: For context, the symbol is used in equations similar to this:", "label": 1}
+{"snippet": "I know the difference between the two. Breath is a noun and breathe is a verb. It was taught to me that way and I've never mixed them up in any way because their different pronunciation reflects their difference in spelling. This is reflected in this NGram chart which shows extremely few documented cases of incorrectly using \"to breath\" as a verb. However, I've recently noticed many, many, many people on the internet using \"breath\" as a verb (e.g. \"I need to breath\"), and it is quite confusing and irritating. Is there any history behind this misuse?", "label": 1}
+{"snippet": "I've just had a discussion about using \"to separate\" when relating to events in time. A colleague of mine used the word to describe that an event occurred between two other events while the events aren't necessarily continuous. For example, he'd say \"Monday and Friday is separated by Wednesday\". I think that the separator should be \"thicker\" to fill the gap between the two endpoints fully. So I'd say \"Wednesday is between Monday and Friday\" or \"Monday is separated from Friday by Tuesday, Wednesday and Thursday\". Which explanation sounds better? Would you use other words to describe that something happens after something else has already ended and the next thing hasn't started yet?", "label": 1}
+{"snippet": "So tonight's Quatrantids shower got me thinking. Why does the debris from comets and former comets hang around so long? Each year the earth sweeps through the region of space that the comet went through. However, the comet doesn't come by each year, so the earth must be going through the same cloud numerous times. And each time we get a meteor shower as a result. I suspect an answer, but I'd rather hear from professionals.", "label": 1}
+{"snippet": "After recently going through a short program of self-study in quantum mechanics, I was surprised to find a quote attributed to Feynman essentially saying he was extremely bothered by the computational process of renormalization. It's \"dippy\" that anyone should have to subtract one infinity by another in order to arrive at a finite answer. What's he referring to there, in rough terms? And what's the latest in attempts to replace this computational procedure with something more physically plausible, so that the theory can have more meaning and less dippiness?", "label": 1}
+{"snippet": "I'm writing a Cover Letter and I'm including the following sentence: \"Furthermore, I have a passion for dealing with- and meeting- new people.\" I recall an English professor suggesting something like this because, here, the \"with\" and the \"meeting\" both relate directly to \"new people.\" Is this correct? Or should I just stick with commas and get on with my life (as below)? \"Furthermore, I have a passion for dealing with, and meeting, new people.\" <-- seems weird. Thanks for your help!", "label": 1}
+{"snippet": "Possible Duplicate: In what ways can TeX be used beyond document production? What else can we create in LaTeX besides aesthetically beautiful typeset documents? I know we can create theses, monographs, books, we can draw using PSTricks or TikZ and create slides with Beamer, but what else can we do? I do not know, but how to create mailers? How to create animations? These are just a few suggestions. What else can we create in LaTeX? How to go beyond LaTeX?", "label": 1}
+{"snippet": "I have programmed a counter. It counts at one point per second until it reaches ten points, at which time it resets back to zero and begins to count at two points per second. Again, upon reaching ten points it resets again and begins counting again at three points per second... and so forth, continuing to increase the points per second by one each time it reaches ten points and resets back to zero. My question is, what is the process to construct the formula that will tell me how many resets have occurred after t seconds? Thank you.", "label": 1}
+{"snippet": "I've read the textbook Groups and Their Graphs by Grossman, and I'm interested in learning more about graphs. I know about O. Ore's book in the same series (Graphs and Their Uses), but I'm interested in a book which will tell me more about the relation between graphs and groups. I don't know any advanced mathematics (I only about group theory and graph theory from Grossman's book), so please recommend books which are not too complicated. I would also be glad for recommendations of books which are about group theory but have a focus on graphs.", "label": 1}
+{"snippet": "As far as I interpret it, the law of ever increasing entropy states that \"a system will always move towards the most disordered state, never in the other direction\". Now, I understand why it would be virtually impossible for a system to decrease it's entropy, just as it is virtually impossible for me to solve a Rubik's cube by making random twists. However the (ever so small) probability remains. Why does this law underpin so much of modern physics? Why is a theory that breaks this law useless, and why was Maxwell's demon such a problem? Does this law not just describe what is most likely to happen in complex systems, not what has to happen in all systems?", "label": 1}
+{"snippet": "Here is the situation: Kids in a small yard are about to play soccer. There are no goalposts in that yard (or \"goals\" or whatever you call it, I mean those metal frames on each side of the soccer field that have nets on them. Once the ball is in the net, the score changes). So, one boy picks up some sticks from the ground and tries to mark out the goalposts for each team. While doing that he says: \"This will be your team's goal and that will be our team's goal\" Is the first goal that he mentioned the one that his team will be defending or trying to get the ball into?", "label": 1}
+{"snippet": "The default twoside memoir document style makes the right margin really large on recto (odd) pages and the left margin really large on verso (even) pages. This seems counter-intuitive to me. It seems to me that you want the large margin against the spine of the book, to compensate for the part of the margin lost to the binding process. So is the default style really what one wants for publishing, or do I need to customize the margins to be the opposite of what they are by default?", "label": 1}
+{"snippet": "As I was reading about the experimental arrangement for photoelectric effect, I saw a diagram that puzzled my knowledge of electrodes. I found that in the experimental setup the cathode of the photoelectric plate or emitter was connected to the positive terminal of the cell. Why is it so? How can a negative electrode be connected to positive terminal of a cell? I read Wikipedia article on cathode and it said \" In a device which consumes power, the cathode is negative, and in a device which provides power, the cathode is positive\". What does this mean?", "label": 1}
+{"snippet": "I understand that for a set of vectors to be linearly independent, none of the vectors in the set should be a linear combination of some other vectors in that set. But why on earth should I care about it? How does it help me? For example imagine a simple situation - I have a system of inequalities, which defines a set of points (vectors) which satisfy all these inequalities. Why should I care whether this set of solutions to the system is linearly dependent or independent?", "label": 1}
+{"snippet": "Being a mathematician with mathematician friends, my friends and I occasionally like to joke about the peculiarities of the English language. This one came up recently: Obviously, most English sentences and phrases cannot be read backwards and forwards and maintain the same meaning. For instance, \"watch this\" and \"this watch\" have clearly different meanings. In mathematics, we call this non-commutativity, and it is deeply interesting. So the question is, can anyone think of a phrase or sentence which has the same semantic meaning when the words are read from right to left?", "label": 1}
+{"snippet": "The result of an imbalance of electrons between objects is called static electricity. It is called \"static\" because the displaced electrons tend to remain stationary after being moved from one insulating material to another. Please can any one explain to me what does it mean by the word stationary in the definition? Does it mean that the displaced electrons do not spin around the nucleus in another material's atom?", "label": 1}
+{"snippet": "The vast majority of the time when I see the word \"myriad\" it is in a sentence like \"He had a myriad of things.\" However I don't like the extraneous words so I normally use it like \"He had myriad things.\" My boss corrected the latter usage while editing something I wrote. I averted an argument by simply changing the sentence to \"He had various things.\" but was I incorrect?", "label": 1}
+{"snippet": "I saw someone write the sentence \"Of course they're\". As a native English speaker, this instantly seemed wrong but I couldn't come up with a good reason as to why. I did a bit of research and there seems to be a rule called \"stranding\" where if there's an object before the clitic then it can't end like that but I don't entirely understand it.", "label": 1}
+{"snippet": "I am trying to create a machine that moves on two points (Wheels or legs). Because of the extremely difficult nature of perfectly balancing the parts, I am wondering is there any way to create a mechanical mechanism to balance it. I know that it can be done with many different electric circuits, but I am wondering is it even theoretically possible to create such a system? And if it's possible, does anyone know of any systems that do that? P.S. Could someone retag this appropriately? I'm new to this SE, and I'm not sure how to tag it.", "label": 1}
+{"snippet": "I frequently hear people quoting widely-used idioms or proverbs as if they are fact, simply because they are used frequently by many people. For example, \"An apple a day keeps the doctor away.\" Can these be called a \"truism\" even if not true or must they be actually true to be called a \"truism\"? Are there more precise terms for the two meanings, \"widely believed ideas, which really aren't true\" and \"widely believed ideas, which really are true\"?", "label": 1}
+{"snippet": "Sometimes, I feel that the term \"first generation\" is used sort of vaguely sometimes. So it confuses me (because my situation) is a little bit complicated. My dad, was an immigrant from a foreign country and lived here long enough to get a passport. That way, he has an American citizenship. My mom, wasn't born in the US and doesn't have a US citizenship. I wasn't born in the US, so am I a first generation American? Or do I just have a citizenship (because of my dad's American citizenship)?", "label": 1}
+{"snippet": "I use TexStudio to create a tex file and save it in my DropBox in the Cloud. I then use CloudConvert to make a pdf file, which I then save on my Windows Pc. This works OK, but isn't there a simpler, more direct way? I'd like to execute a Windows program which inputs a tex file and outputs a pdf file. I have MiKTeX installed on my PC.", "label": 1}
+{"snippet": "Let's say we have a normal circuit with a light bulb, with wires and a battery. When one places a capacitor in this circuit, how is the light bulb able to light up, even when the capacitor prevents the flow of charge? Also, why does it dim and then go out eventually? Then when the battery is removed from this circuit, how is the light bulb still able to light up? And what is happening when the light bulb dims and goes out in this situation as well?", "label": 1}
+{"snippet": "My question is about the use of would in the following sentence. He grew up around cars that would later become classics. The use of would in this particular sense always looks confusing to me because it's so different from: I would like to know... I don't think he would agree to that... Would you mind.... Would it be alright if I... etc. The above sentence, as I see it, means \"he grew up around cars which were going to become classics in the future\". Is that correct? If yes, does it also mean that the cars actually became classics later?", "label": 1}
+{"snippet": "I know that for rigid bodies only the work-energy theorem states that the net work done on the body equals the change in kinetic energy of the body since a rigid body has no internal degrees of freedom and hence no other forms of energy such as potential energy. Is there a most generalized form of work energy theorem that is valid for rigid as well as non rigid bodies and for conservative as well as non-conservative force? I would like a work-energy equation that would be valid for point particles, rigid bodies and non-rigid bodies.", "label": 1}
+{"snippet": "Assuming that the earth is spherical, that its temperature is continuous, and that some other more or less realistic conditions hold, we might think that the Earth's core temperature should be about the average of its surface temperatures. This is not the case, as the core is hotter than all but a few spots on the surface. Can someone explain where the assumptions break down? Is it that the temperature is not static?", "label": 1}
+{"snippet": "For introducing a field of science, usually we require a definition which summarizes the goal which is intended to be achieved by this field. Linear Algebra is one of the most important parts of mathematics which has not only interesting pure mathematical ideas but also a lot of applications in physics and engineering. So it seems reasonable to have a Complete, Clear, Brief, and Delicate definition for this important branch of mathematics. I am wondering that what is the best fit for such a definition. For example, the very first sentence that the Linear Algebra Done Right by Sheldon Axler starts with is Linear Algebra is the study of linear maps on finite dimensional vector spaces. What is your definition of Linear Algebra in few sentences?", "label": 1}
+{"snippet": "We all know the \"Inertia\" of a particle is actually related to its \"Mass\". But when we talk about \"Moment of inertia\" of a body, we actually are talking about its \"Mass distribution\" about some point/axis. So depending on how the mass is distributed in the body (what shape a body has), its moment of inertia could be determined. So my question is can we do it vice-versa? I mean if we had the moment of inertia of a body about some axis, can we construct its shape?", "label": 1}
+{"snippet": "I'm quite stuck with this problem. I know that I have an object in orbit. I know the eccentricity of that orbit, as well as the semi-major axis of the orbit. Giving a true anomaly, how do I find the speed and altitude of that object? The true anomaly is the angle between the line made with the focus of the ellipse and the position of the object. Thank you! P.S. I'm more looking for a general help, more than a specific answer. That's why I didn't give any numbers.", "label": 1}
+{"snippet": "Imagine driving in a straight line on a ice lake, when you hit the brakes, if your goal is to stay in straight path with no spinout, which wheels would you choose to have locked: front or rear? Assuming the steering wheel is kept fixed in both cases, I learned that it's better to have front wheels locked in this case. But can someone explain in accurate terms why? Thanks.", "label": 1}
+{"snippet": "Generally speaking, the rainy season is in the summer in tropical climates, and in the winter in mediterranean climates. (I admit that is a gross oversimplification) What is the cause for this difference? Purely speculatively, it seems intuitive that hot weather would lead to higher humidity, which in turn would lead to more spontaneous rain clouds. This would obviously be maximized by summer weather. But why is the rainy season in the winter in colder climates?", "label": 1}
+{"snippet": "As I understand it, trans means \"an individual whose gender identity is different than what they were designated at birth\". However, I also hear the terms transgender and transsexual used for similar meanings. I know that personally I only refer to myself as trans or rarely transgender, and never transsexual, and the latter sounds very odd to me. I'm interested in why there are several words for roughly the same meaning, and if they do have different meanings or simply based on geography and time period.", "label": 1}
+{"snippet": "I was playing a table-top rpg with a friend. It was set... well it was pretty weird, so I won't get into it. Suffice it to say the bad guy had a stick of dynamite and we were on a volcano. I hit the dynamite with my slingshot, knocking it into the lava directly behind the villain. My DM said the dynamite melts away. I said it should have blown him up. Needless to say, as a couple nerds (we were, after all, playing a fantasy game and then arguing about the physics of it) we were pretty upset with each other. What would have happened in this... totally realistic scenario? Would the stick of dynamite exploded? Or simply melt away?", "label": 1}
+{"snippet": "I have a basic question regarding the ramifications of P vs NP. If P=NP, then SAT would be in P. If I understand the definitions correctly, this would imply that there is a Turing machine which decides SAT in polynomial time. However, does this mean that there would actually be a polynomial-time algorithm for producing a solution of SAT? For instance, what if there were some mysterious polynomial-time computation one could do to a given instance of SAT which would tell you whether or not it was satisfiable, without actually producing a solution (I'm thinking of primality-testing, where for arithmetic reasons it can be easier to verify prime-ness than to actually exhibit a factorization)", "label": 1}
+{"snippet": "I'm in need to implement Monotone Cubic Interpolation for interpolate a sequence of points. The information I have about the points are x,y and timestamp. I'm much more an IT guy rather than a mathematical person, so I'm looking for an example of implementation. What I need to do with the resulting functions is store them for future analysis. My favorite syntax are PHP, Python, Java, Delphi, VB or a generic algorithmic language of your choice.", "label": 1}
+{"snippet": "Lines and conics have clear geometric meanings that are coordinate-free, but cubics seem to rely entirely on cubic equations and coordinate systems. Are there ways to define cubic curves without cubic equations? I thought about this question by trying to generalize tangent lines and osculating circles. Since a tangent line is defined by taking the limit of two points on the curve, and an osculating circle is defined by taking the limit of two tangent lines on the curve, I thought about taking the limit of two osculating circles on the curve, but after playing around with evolutes and involutes, I couldn't come up with anything.", "label": 1}
+{"snippet": "I'm an ESL teacher. Normally I teach lower intermediate but I also teach a mixed level grammar review class. I pride myself on being able to explain things clearly but today I found myself in THREE sticky situations all in the same class! I'll explain here the two problems involving conditionals. First Case: Is it better to say... If he knew that I WERE/WAS home now, he would call. OR If he knew that I AM home now, he would call. Does the second verb in the if clause also take the subjunctive form because it is in the if clause or should it take the present simple form because it is not a hypothetical (I am home now is not hypothetical, his knowledge of it is.)", "label": 1}
+{"snippet": "I find it really amusing when other people misuse words but my sense of humor fails when it's me. I have always used \"notwithstanding\" to mean \"assuming that A doesn't impact B\". For example The delivery will be on time, notwithstanding the holiday. To me, this meant, the delivery should be on time, but you never know what impact the holiday will have on it. Turns out, notwithstanding means almost the opposite: in spite of, regardless of. So my question is, what word should I be using instead?", "label": 1}
+{"snippet": "Suppose we look at the twin paradox where the twin traveling at high speed relative to an observer on earth has a clock which counts time by sending photons of light across a distance within the spaceship (perpendicular to the direction of motion) to a detector which counts off 'time' as the interval between photon detections. If the speed of light is constant in both frames, and the distance the photon travels is equal in both frames (no length contraction in the perpendicular direction), won't both observers say the same amount of time has passed in both frames at a later time (suppose the observer on earth uses an identical clock)? Wouldn't a difference in observed time intervals imply differences in the speed of light?", "label": 1}
+{"snippet": "A guy walks into a bar. His buddy laughs and says, \"Don't worry, I didn't see it either. What is the meaning of this joke? What makes it funny? (Is it supposed to be funny?) I saw this joke in the mood message of a British guy. It is a kind of bar joke but there is usually a connection. (For example: a guy with dyslexia walked into a bra). I didn't get this one. Can it be a meta-joke?", "label": 1}
+{"snippet": "I'm trying to analyse the Ballad of Serenity Valley which is the theme song for the tv series Firefly: take my love take my land take me where I cannot stand I don't care I'm still free you can't take the sky from me My interpretation relies on the meaning of 'take' in the second line, being different from the third line, which are a rhyming pair. Is there a name for this scheme or pattern?", "label": 1}
+{"snippet": "There is plenty of information about how to encode arithmetic given the lambda calculus. The wikipedia article on Church Encoding seems complete to my inexpert eye. My question is \"how about the other direction?\" What's a good way to encode the lambda calculus in ordinary real or integer (or even matrix) arithmetic? It would seem that an application of Godel Numbering would do it, but I have been unable to find any writing on Godel Numbering for the lambda calculus specifically. It also seems plausible to encode the lambda calculus in arithmetic in some way more efficient than Godel Numbering; perhaps someone has done that? I might settle for the SKI calculus or some other Turing-complete language that's easier to encode than the lambda calculus.", "label": 1}
+{"snippet": "If you are using a word that normally wouldn't start with a capital letter, should it be lower case after an e.g.? Also should e.g. have a capital E at the start of a sentence? Example phrases: Should I always plug in electrical items? e.g. Electric hairdryer, phone charger... Should I always plug in electrical items? e.g. electric hairdryer, phone charger... Should I always plug in electrical items? E.g. Electric hairdryer, phone charger... Should I always plug in electrical items? E.g. electric hairdryer, phone charger...", "label": 1}
+{"snippet": "I'm interested in the eigenmodes of the membrane for various mediums, such as vacuum, air, water, etc., which impose a damping effect on the membrane. This cannot be done by merely changing the value for the wave propagation speed, c, because this value belongs to the string/membrane itself, and not to the medium around it. Can the influence of medium be incorporated in the wave equation for vibrating string/membrane?", "label": 1}
+{"snippet": "What is the word to describe a person who popularized a sport? The person does not need to be one of the original players nor even currently active. An example is Arnold Schwarzenegger popularizing competitive bodybuilding. There were many superstar bodybuilders before him, like Eugen Sandow, and he has been inactive for a decade. Arnold is, no doubt, the reason why many people started bodybuilding.", "label": 1}
+{"snippet": "My English teacher just asked us to write a random sentence in English. Off the top of my head I wrote \"I like to eat apples and bananas\". She highlighted \"apples\" and said: \"man, this is blatantly wrong\". \"Uh, what's wrong, M'am?\" \"It should be bananas and apples. English people always enumerate things in reverse alphabetical order. Always. Just like when they enumerate parts of the body, they always converge to the heart. Always. We do that automatically, without even thinking about it. Not doing it is wrong\". Granted, I'm not a native speaker, but I've never heard anything like this before. Bullshit or what?", "label": 1}
+{"snippet": "Possible Duplicate: Electrodynamics textbook that emphasizes applications I am a graduate student in applied mathematics and I am looking for a concise introduction to Maxwell's equations / basic principles of electromagnetism. (I have enjoyed the book by Purcell, Electricity and Magnetism, as an undergrad but I have forgotten most of it). I would like something that covers the conceptual details in a quick way and not necessarily a big textbook. You may assume that I have the necessary mathematics background. I am looking for something that will explain the physics, i.e not a huge textbook with intricate calculations but a short book to get a feel for what is going on.", "label": 1}
+{"snippet": "So, I finished my undergrad with a degree in applied mathematics, but when reading some graduate level texts and/or papers, I often find myself struggling. I eventually get there, but I often feel like I lack the intuition necessary to be able to come up with concepts on my own. I feel like I'm just missing some pivotal step in the journey to mathematical maturity. Does anyone have any books/references/advice? PS: If this means anything at all, as I was not a mathematics major, I did not take analysis or abstract algebra.", "label": 1}
+{"snippet": "The first thing that comes to my mind when I hear the term marketing is a word that is related to advertising, business and commerce. A colleague once said to me that she went to do some marketing. I came to realise that she meant shopping for grocery in the supermarket, only after dwelling further onto the subject. But this is something that is rarely used in such context based on my own personal experience. My question is: Is the usage of the term marketing in the literal sense still appropriate in the English speaking community?", "label": 1}
+{"snippet": "Say I had a plastic water bottle that was slightly crushed, I could uncrush it (mostly) by covering the opening with my mouth and blowing air into it hard. Would it be easier to do this if the bottle was full of water? or while empty (full of air)? Why? My thoughts are that it would be easier if it was full of water because water doesn't compress as easily as air and so more force will be applied to the walls of the bottle. Is this correct thinking? Are there other factors involved?", "label": 1}
+{"snippet": "Let's say you have a garden hose connected to an ordinary water tap which is opened fully. If you pinch the end of the hose, water leaves the hose at a higher speed (and this can be useful while watering plants, to reach pots which are further away). However when a tap (with no hose connected) is opened only slightly, water flows out at a low speed, possibly even in drops. The actions of pinching the end of a hose and of almost-closing an open tap seem similar, so why the difference in behaviour?", "label": 1}
+{"snippet": "The cosmic microwave background that we observe uniformly around us is usually explained by assuming that our universe is the surface of a four dimensional sphere. That way the uniformity makes sense since there is no center. My question is if this is true then what is the explanation that describes the fact that the farther we look into space, the further we look back in time. I can't perfectly picture this and see how it would coexist. Help me out.", "label": 1}
+{"snippet": "In my research, I make use of a tool which provides a platform for researchers to investigate phenomenon X in a variety of ways. I want to frame it this way in a paper that I am writing: \"Using the --- platform provided by the tool for investigating X, we develop and illustrate a novel method to assess aspect Y of X\". I am looking for an adjective to fill ---. \"Versatile\" comes to my mind. But I feel like there might be better adjectives to use. I don't mind restructuring the sentence if that makes it sound more professional. Any help is appreciated!", "label": 1}
+{"snippet": "Given the sentence, We discourage people from committing crimes by using law enforcement, religion and education. I see two possible interpretations: [We discourage people by using law enforcement, religion and education] from committing crimes. We discourage people from [committing crimes by using law enforcement, religion and education]. Of course the second interpretation may not make sense in this particular case, but generally speaking both interpretations are equally valid. So my question is, how to rearrange the sentence for it to be well-structured and have only one clear interpretation?", "label": 1}
+{"snippet": "I was reading Frankenstein and I've noticed that the word after the exclamation mark usually isn't capitalised (unless it's a noun). Some of the quotes I've found: Alas! who is safe, if she be convicted of crime? and Alas! to me the idea of an immediate union with my cousin was one of horror and dismay. and Great God! what a scene has just taken place! Why the word after the exclamation mark does not begin with a capital letter? Has the rule for using exclamation marks changed and when did it change?", "label": 1}
+{"snippet": "I was waiting on a red light the other day and was wondering. If I'm in my car, not moving and I see a car that's going to hit me from behind. Would I (my body) be safer if I put on the break or if I put the car in neutral? I assume there's no car in front of me and there's no posibility to be hit by an other car. Also, the car crashing into me is going at a good speed.", "label": 1}
+{"snippet": "What is an English phrase to describe a video that is not running smoothly, but rather has interruptions in it, becoming sort of like a GIF? This typically happens due to technical problems such as low memory or CPU power, which is why I'm afraid I can't think of a way to demonstrate exactly what I mean (e.g., I cannot paste a link to a video like that). I am not necessarily looking for an adjective; any phrase will do. I would also like to include another related question: what's a word/phrase for almost the same situation but with sound rather than video? I.e., when the sound comes and goes (e.g., over the phone).", "label": 1}
+{"snippet": "I need to construct a sentence, in which I'm referring to a feature of each of the animals in a given species. I don't quite know what the possessive of species should be, both in singular and plural. Example: (Talking about a single species with fuzzy ears.) The species' ears are notably fuzzy. Is the above correct? What if I had to mention multiple species all having fuzzy ears?", "label": 1}
+{"snippet": "Here are the examples of compound subjects: Everything on the bed and everything in the closet was organised in under an hour. Everybody who witnessed the shooting and everybody in the room were interviewed. Anyone on the soccer team and anybody on the basketball team was eligible for the scholarship. Should I also use was instead of were in the second example? Or the first and the third examples are incorrect that I should use were instead of was.", "label": 1}
+{"snippet": "Not all equations of motion admit a Hamiltonian. Several questions and answers on this site concern this correspondence, for example Hamiltonian or not?, When can an autonomous system be written using a Hamiltonian?, and What are the necessary/sufficient conditions for a system to be Hamiltonian/non-Hamiltonian?. My question is who was the first to establish that not all equations of motion can be described in a Hamiltonian fashion? Hamilton himself? Someone else? In which paper or book was this lack of total correspondence first exposed? Who has then developed the details of this correspondence? What is the current state of affairs? (From Hamiltonian or not? I gather that it is still a matter of trial and error to obtain a Hamiltonian from the equation of motions?)", "label": 1}
+{"snippet": "Does every convex, nonempty, body have a supporting line at every point on its boundary? This seems intuitively true to me, but I am having a hard time figuring out how to prove it. I was thinking of using a slicing argument. That is, cut a line through the body and then we have a set of curves which are convex. So more generally, do we need to prove that every convex function has a supporting line at every point?", "label": 1}
+{"snippet": "What are some interesting applications of the Mean Value Theorem for derivatives? Both the 'extended' or 'non-extended' versions as seen here are of interest. So far I've seen some trivial applications like finding the number of roots of a polynomial equation. What are some more interesting applications of it? I'm asking this as I'm not exactly sure why MVT is so important - so examples which focus on explaining that would be appreciated.", "label": 1}
+{"snippet": "I am trying to conform to the British practice (specifically Oxford Style Guide) and I am a little confused which to use to mark a nickname: Andrew 'Andy' Johnson Andrew \"Andy\" Johnson I know following the rules I should use single inverted commas, however the first one looks a tad weird to me. I have seen the latter option a lot on newspapers and business cards but not the former. I am going to use that for email signatures and names on business cards.", "label": 1}
+{"snippet": "I am trying to find a verb which can be used to indicate that someone is acting pedantic. I first considered \"pedanticise\", but, having found only one source for this, I thought I'd broach the question here. Edit: To clarify, I am defining pedantic to mean: excessively concerned with minor details or rules; overscrupulous. -- Google Or: overly concerned with minute details or formalisms, especially in teaching. -- Dictionary.com An example of this word used in a sentence would be, \"Because Ellie spent the whole day ____ing over the grammar choices in her emails, she didn't get any work done!\"", "label": 1}
+{"snippet": "There is a phrase in Malay that goes \"prepare an umbrella before the rain\", meaning one must be prudent and proactive of future challenges by making all the preparations necessary. I would like the English equivalent of such a phrase. Thanks in advance, and apologies if this has been asked before! (I checked as much as I could) EDIT: What I'm looking for is the act of preparing a solution to a specified problem before the problem happens. So anticipating rain, one prepares an umbrella.", "label": 1}
+{"snippet": "It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a fundamental particle (with the photon being the most prominent exception). They are instead composed of a number of fermions, which can not occupy the same state. Is it possible for more than one of these composite bosons to be in the same state even though their constituents are not allowed to be in the same state? If the answer is \"yes\", how does this not contradict the more fundamental viewpoint considering fermions?", "label": 1}
+{"snippet": "I keep hearing from native speakers the phrases like these: There is a lot of cars (books, hotels) There is a couple of cars (books, hotels) There is five (ten, etc.) of cars (books, hotels) There is a few of cars (books, hotels) Nevertheless, somebody told me that the phrases like above are incorrect for sure and there should be there are instead of there is. Whom could I believe?", "label": 1}
+{"snippet": "When someone makes an assertion, the distinction between \"how did you know\" and \"how do you know\" seems to be that \"how did you know\" implies that the person in question is correct in their assertion. \"How do you know\" is normally an inquiry into the person's credentials, and often expresses that the assertion is incorrect and/or ungrounded. Does anyone know what the reason for this distinction is? Why does simply changing the tense of the verb change the implication so strongly? I suspect that, linguistically speaking, the \"did\" might be a different tense than the past tense, but I'm not sure what it is, or I could be entirely wrong.", "label": 1}
+{"snippet": "I know, that if a polynomial function fails to have any real root, then, by the fundamental theorem of algebra, it must possess at least a pair of complex roots having non-zero imaginary part. The real roots are points of intersection of the curve, with the horizontal axis, on the real plane. My problem is in visualising location of complex roots. Can I make use of Argand Plane in visualising?", "label": 1}
+{"snippet": "I found that some theories about quantum theory is similar to Fourier transform theory. For instance, it says \"A finite-time light's frequency can't be a certain value\", which is similar to \"A finite signal has infinite frequency spectrum\" in Fourier analysis theory. I think that a continuous frequency spectrum cannot be measured accurately, which is similar to Uncertainty principle by Hermann Weyl. How do you think about this?", "label": 1}
+{"snippet": "I study cognitive neuroscience and I periodically run into physics related questions in the context of neuroimaging technologies. My question specifically refers to electric and magnetic fields that can be measured by electroencephalography (EEG) and Magnetoencephalography (MEG), respectively. One interesting difference between the EEG and MEG signal is that unlike the electric field, the magnetic field is unimpeded by differing conductances across brain, skull, scalp and other tissues. I was wondering if somebody could explain what differences between the two fields account for these phenomena.", "label": 1}
+{"snippet": "I know that many questions on topics similar to this one have been asked before, but I have read many of them and still not able to solve my problem. You could attribute it to my poor command of English. My question relates to two weird sentences, and I want to know which sentence is correct: I am so hungry, it feels like my tummy is eating myself. or I am so hungry, it feels like my tummy is eating me.", "label": 1}
+{"snippet": "Based on my very basic understanding of the Johnson noise, it's not just a DC phenomena, but should change with frequency in a system, where there is a frequency dependent, real component to the impedance. I think both the skin effect and eddy current losses contribute to the effective resistance of an inductor, so Johnson noise should increase at higher frequencies. Am I being dumb?", "label": 1}
+{"snippet": "I had a confusion in the diffraction experiment about which I was taught in school. According to the formula we Derived The width of the central maxima decreases on decreasing width of slit and vice versa. But what i wonder is what happens to the max intensity of central maxima in these cases? I asked two physics teachers and they gave me opposite answers-one said it increases on decreasing slit width which i feel is right but the other said it would be the same as light is of constant wavelength(monochromatic). What do you think? Please explain:)", "label": 1}
+{"snippet": "As a result of the Ehrenfest Paradox, the geometry of a rotating disc is non-Euclidean. However, while reaching this conclusion, we assumed that \"the radius doesn't undergo Lorentz contraction\", because \"the radius is always perpendicular to the velocity vector\", which is equivalent to : \"in a circle, the radius is always perpendicular to the tangent at that point.\" But this is an Euclidean assumption (We have to use the parallel postulate to prove it.) Therefore it doesn't work in Non-Euclidean geometries, and we shouldn't be able to use it.", "label": 1}
+{"snippet": "Good evening everybody, I'm stuck with the following problem from an old exam in Linear Algebra. One is given two Eigenvectors with corresponding two Eigenvalues and told that the trace is negative. I figured out a third orthogonal eigenvector and tried to get to the matrix via diagonalisation, using a parameter alpha for the third eigenvector. Then I set the trace of this matrix equal to the sum of the known eigenvalues plus alpha. But my method does not work out; it does not give me a negative value for alpha. Where am I going wrong? How could I make this work? Thank you so much.", "label": 1}
+{"snippet": "For example in the models for holographic superconductors we can calculate the conductivity. Also there is an energy gap. I can understand that it describes a superconductor. However I have also heard people talk about superfluidity in holographic QCD. I believe they are talking about the condensates such as the pion or the chiral condensate. Where is the superfluid in holographic QCD (quark gluon plasma maybe?) and how do I know that it is a superfluid?", "label": 1}
+{"snippet": "I would like to produce some diagrams (preferably using TikZ/PGF) using the visual notation given in Enterprise Integration Patterns by Hohpe & Woolf. I'm aware of stencils from the above site, based on Visio, but I'd rather be able to compose them directly in my LaTeX documents. Is anyone aware of PGF library packages that I can use, or failing that how I can create reusable symbols for use in a TikZ/PGF figure?", "label": 1}
+{"snippet": "Even though I can find this command hiding somewhere on the internet, I though it might be useful to have it up here for the LaTeX community in general. How does one run TeX from the command line interface (Terminal) in Linux? Are there any required parameters? What if the command is part of a bigger script, how does the script know when the TeX processing is done to continue with any subsequent actions needed? Is there a clear manual for this somewhere? A starting point might be: pdflatex [options] filename.tex latex [options] filename.tex xelatex [options] filename.tex", "label": 1}
+{"snippet": "If I understand correctly, axioms are those statements that we assume to be true, instead of proving to be true. I have seen that in topology theory, various axioms of countability and separation axioms seem to be definitions of some concepts, instead of being assumptions. So I was wondering if \"axioms\" in topology theory are really axioms? If no, is this kind of naming rules common in all other branches of mathematics? Thanks and regards!", "label": 1}
+{"snippet": "Imagine I have a vertical straw, and that it is partially filled with water. If I were to decrease the radius of the straw at the bottom end, eventually surface tension would allow the water to remain in the straw (i.e. the force of gravity would not be enough to overcome the surface tension and for water to flow out of the straw). What I'm curious to understand is for a certain (small) radius at the bottom, how much force/pressure would be required at the top of the straw to overcome surface tension and force the water out of the bottom of the straw at a certain (volume flow) rate. Any help would be greatly appreciated!", "label": 1}
+{"snippet": "If we have two complex numbers, in polar form, as the numerator and denominator of a fraction, and we are asked to write them as a single complex number, is there an easier way to deal with them rather than the usual procedure? (By usual procedure I mean first expanding them by writing the value of each term and then realizing the denominator, etc.) Thank you.", "label": 1}
+{"snippet": "Why is Erbium Doped Fiber Amplifier (EDFA) preferred over Erbium Doped Waveguide Amplifier (EDWA)? The question has been asked from an engineering point of view, but obviously I would also be interested in Physics of it. Is it just because of the difficulty of constructing a waveguide, or is there something more? I understand the individual benefits and limitations of a fiber amplifier and a waveguide but cannot understand the preference in this case. http://en.wikipedia.org/wiki/Optical_amplifier#Doped_fiber_amplifiers", "label": 1}
+{"snippet": "I have been using TikZ to draw game-trees for my game-theory lectures (mostly using the automata package) but I could not figure out how to draw an arc across the edges the leave a given node. When we want to denote that a player has a continuum of actions available at a node, we usually draw an arc across the edge leaving such node. For example see the arc crossing the edges that leave the first node in this picture: Any suggestions on how I could try to implement this in TikZ? Thanks!", "label": 1}
+{"snippet": "We have a car dealer around here with an ad that reads \"No Fake Lures\". Now, as I understand the concept of a lure, if it doesn't attract attention, it's not a lure. And if a lure does attract attention, it's a lure, so no matter what is used to make the fake lure, it's a an actual lure. Therefore, it's not possible to have a fake lure. What do you call a statement like \"No fake lures\"?", "label": 1}
+{"snippet": "I've been looking around about LCD monitors, and how they polarise light. When a pixel needs to be black, the light is \"twisted\" so that it can't go through the polarising sheet in front. What happens to this light? Does it relfect back into the screen? Surely that would mean the screen would get quite hot if you leave it on a black image for a while? (but I've never noticed that happen). What happens to the energy (from the electricity used to create the light) when it's blocked by polarisation.", "label": 1}
+{"snippet": "I'm currently converting my thesis into LaTeX, and i have an issue: being an IT thesis, I have tons of code quotes. The problem is not about the blocks of code: they are not that many and i can wrap them with {verbatim} tags. The problem is about the millions of inline single terms which should be formatted the same way. Is there a way, for example, to define a macro or shortcut or whatever which, is i select one word and click it, automatically wraps it with {verbatim} (or equivalent) tags? Hope I've been clear. This could really spare me hours of tedious work, thank You in advance!", "label": 1}
+{"snippet": "I am writing a novel and am constantly trying to figure out how to describe the action when someone gives a sort of small cough or a quick \"huh\" in agreement. I suppose it would be the non-word equivalent of \"I'll say\" or \"You think?\" To be specific, I'll use it in a dialogue. \"He must really hate Ian, then.\" Clarissa [insert word here]. \"Yes.\" It's usually used when the speaker is trying to convey that the subject is much more serious than their conversation partner is taking it.", "label": 1}
+{"snippet": "There are many kinds of integrals, with the most famous being the Riemann integral which is taught in elementary calculus classes. The motivation behind the Riemann integral is to find the area between curves by using rectangles of infinitely small width. When i first studied calculus, i was fascinated by this formulation and thought it was indeed ingenious. My question is: what are the limitations of the riemann integral? What could be the link or the motivation to be able to \"create\" new ones like lebesgue, or darboux?", "label": 1}
+{"snippet": "Heard an English teacher claim that: \"Dogs is not my cup of tea\" is correct; whereas \"Dogs are not my cup of tea\" is incorrect. The explanation was that the verb form of 'to be' must agree with the singular noun 'cup' and not the plural noun 'dogs'. Checked Google on this and it appears that this is an extreme minority opinion at best. Nonetheless, can the teacher's argument be authoritatively refuted, or must this person be allowed to continue impressing pupils with their dubious insider's knowledge of the English tongue?", "label": 1}
+{"snippet": "I took my son to a science museum where they had a solenoid oriented vertically with a plastic cylinder passing through the solenoid. An employee dropped an aluminum ring over the top of the cylinder when there was no current going through the solenoid. Then they turned on the current going through the solenoid and they aluminum ring went flying up and off the top of the solenoid. What law of electro-magnetics causes the force on the aluminum ring?", "label": 1}
+{"snippet": "While studying Electrostatics, I was wondering about whether a charged sphere gains or loses mass while just adding electrons? If it is possible then the negatively charged sphere will have more mass than positively charged sphere, but according to me I think that since the mass of electron is so negligible then there must be no change in mass just because of electrons. So is it possible or not ?", "label": 1}
+{"snippet": "For a paper I'm writing, I need a bit of second order logic in order to convey a few steps in an inference. I've completed the introductory and intermediate/advanced logic classes at my school (second order logic wasn't included in the curriculum, unfortunately). I use predicate logic in most of my classes, so I'm comfortable with it. I'd like to learn just enough to properly notate the steps of the inference. Is there a concise tutorial on the subject available online?", "label": 1}
+{"snippet": "As far as I know, whenever we talk about a black hole, we refer to a static or stationary solution to Einstein field equations. I know the formation of a black hole can be discussed by the numerical GR, but I have never saw an analytical solution which can describe the formation of a black hole. So do anybody know that there actually exists such solution which has power to describe the formation of a black hole? Even the simplest case, for example, the spherical symmetric collapse of radiation into black hole can satisfy me very well.", "label": 1}
+{"snippet": "In Chemistry, an amount of energy has to be supplied for a reaction to occur. This energy, known as the \"activation energy\", breaks up the bonds between molecues in the substance. It is equivalent to the total bond energy of the reactants. However, in high school I learnt that the energy required to start a nuclear reaction is the difference between the binding energy of the reactants and the binding energy of the products. Why is it that the minimum required energy is not the binding energy of the reactants, similar to a chemical reaction?", "label": 1}
+{"snippet": "Which are the differences between Polar curve and Nyquist plot in System Control Theory? I wasn't able to figure it out myself. Are they the same thing? As googling for these two concept returned similar plots, but from the theory I can't find any similarities between them, or I am not able to understand how they are related to each other? Edit: Even though I edited this after more than two years from posting it, I just realized that the terminology that is used at my university, Nyquist plot and Polar Curve mean the same thing.", "label": 1}
+{"snippet": "I am curious about the vibration of metal objects as a sign of an impending lightening strike. This is apparently a common occurrence; so much so that a quick google search will yield many pages instructing people to head for shelter if their keys (other other small metal objects) start to vibrate in the midst of an electrical storm. One climbing site even mentions that a vibrating rope is a sign of a lightening strike. Can someone explain the mechanism behind this? My guess is that it a piezo electric effect, though this contradicts my (limited) understanding that atmospheric electricity is static. Thanks :)", "label": 1}
+{"snippet": "I collected the following \"top eight\" text books on computability (in alphabetical order): Boolos et al., Computability and Logic Cooper, Computability Theory Davis, Computability and unsolvability Hermes, Enumerability, decidability, computability Hopcroft et al., Introduction to Automata Theory, Languages, and Computation (thanks to Bill Province) Kleene, Introduction to Metamathematics Minsky, Computation Sipser, Introduction to the Theory of Computation(thanks to Prajwal Kansakar) I know it's opinion-based, but which important text books did I miss?", "label": 1}
+{"snippet": "I would like to get the formula on how to calculate the distance between two geographical co-ordinates on earth and heading angle relative to True North. Say from New York to New Dehli , I draw a straight line THROUGH THE EARTH - as they were two points in space. How can I calculate that angle from say New York to New Dehli if I was to draw a straight line through the surface of the earth . What kind of mathematical calculation/formula would be involved in order to do that?", "label": 1}
+{"snippet": "There are three Sakharov conditions of baryogenesis: CP symmetry violation. Baryon number conservation violation. Thermodynamical equilibrium violation. In SM the first one is satisfied by CKM phases, the second one is satisfied by instanton-like transitions for zero temperature and sphaleron-like transitions for non-zero temperatures. As for the third one, I've thought that EW phase transition provides violation of equilibrium, but after reading Gorbunov and Rubakov book \"Introduction to the Theory of the Early Universe: Hot Big Bang Theory\" I've started to doubt. They write that this transition is of second type one; thus it doesn't provide sufficient thermodynamical equilibrium violation. So can EW phase transition provide baryogenesis?", "label": 1}
+{"snippet": "I'm interested in the following question: I want to visit where my grandmother was born. To me it seems like a noun clause because I could replace the clause with a noun. For example: I want to visit Ireland. Is this the correct way to check? The definition I read for an adverbial clause states that Adverbial clauses of place modify the main verb in the sentence and provide information about the place that an action takes place. This definition has confused me about the difference between a noun clause and an adverbial clause. How about the following sentences: We can go wherever you want. You can show me where it is. Thanks for your help. Patrick.", "label": 1}
+{"snippet": "I can calculate the derivative of a function using the product rule, chain rule or quotient rule. When I find the resulting derivative function however, I have no way to check if my answer is correct! How can I check if the calculated derivative equation is correct? (ie I haven't made a mistake factorising, or with one of the rules). I have a graphics calculator. Thanks!", "label": 1}
+{"snippet": "I am teaching English to my cousin, but I am not sure how to explain phrasal verbs correctly. For example \"take off\". I explain it as two words but a single entity. When I ask her to name a verb in the sentence The plane is taking off, I expect to hear \"to take off\", not \"to take\". Do I understand this concept correctly? Update: In the sentence \"She put her hands around her hear and squeaked.\" Is \"put around\" a phrasal verb or there are separate verb and preposition?", "label": 1}
+{"snippet": "Does the demonstratives refer to the next word or previously mentioned statement? The medieval center is Prague Castle and St. Vitus Cathedral. An evening view of these illuminated landmarks is one of the most memorable sights in Europe. In the above sentence, does these refer to \"Prague Castle and St. Vitus Cathedral\" or to the \"illuminated landmarks\"? I'm a little confused about this. A clear explanation would be great. Also, what's the difference between demonstrative determiners and demonstrative pronouns?", "label": 1}
+{"snippet": "Full disclosure: I'm taking my first complex analysis course as a graduate student and the title of my question looks like a dumb question to me. In any case, there's a problem in my book that deals with a sequence of \"holomorphic polynomials\" converging to a \"holomorphic polynomial\". Is this just a redundancy or is there some weird world where certain polynomials aren't (complex) differentiable?", "label": 1}
+{"snippet": "Imagine two entangled quantum particles in the singlet state, one held by Alice and the other by Bob. Alice and Bob are both widely separated. Bob measures his spin in some axis and finds it to be up (say). And that puts his particle now into the prepared state of spin up. Entanglement means Alice, if she were to do a similar measurement would find spin down. But assume Alice does not actually do any measurement. So does Bob doing his measurement mean that Alice's particle has immediately and spontaneously collapsed into a prepared state of spin down? Or is the state of her unmeasured particle unchanged? The literature, and popular press, are both vague and inconsistent on this seemingly important point.", "label": 1}
+{"snippet": "About a month ago I posted this question about eigendecomposition of a special matrix; and I received an answer. This is not my main field of study and I came to this as part of the proof for a method I developed to address a bioinformatics problem. Now I am interested to learn more about this area. Could anyone suggest some references and relevant literature that I can read. Moreover, I may end up publishing my method. How should I acknowledge and cite the stackexchange users/website ?", "label": 1}
+{"snippet": "Suppose you have a set A which has the same cardinality with real numbers R, which means |A| = |R|. Also suppose that you have a finite set B , which of course has finite cardinality. Also suppose A is a proper subset of A union B, I mean there are some objects which are not an element of A but they are an element of B. Now is the cardinality of A union B greater than the cardinality of real numbers, also if so is this cardinality of A union B equal to cardinality of the power set of real numbers ?", "label": 1}
+{"snippet": "I often find myself in the situation of wanting to capitalize the phrase \"Enterprise IT\" due to its frequency of reference as the title of my industry. It feels appropriate when I write: \"In Enterprise IT ...\" \"The Enterprise IT industry...\" I would not be surprised if my capitalization is off here. Could one of you help me with a definitive answer to the argument?", "label": 1}
+{"snippet": "Forgive me if this is a non-question, but I could not find anything regarding this. I only know parts of GR, and I am not familiar with the math. Since energy and matter density curve spacetime, does this mean that when entropy increases, spacetime curvature flattens? Hypothetically, if the universe is destined to reach total entropy and be in equilibrium, would this mean that the spacetime curvature of the universe be mostly flat?", "label": 1}
+{"snippet": "I am interested in the history of functions. Why did Euler introduce them? When and why did they become central to mathematics? I know the second question has something to do with the famous Fourier-Cauchy dispute over the heat equation, but don't have any sense of the details. By the way, I'm asking because I would like to give a short, historically informed explanation to high school students why functions are important.", "label": 1}
+{"snippet": "When a trap is set up to be active, is it \"sprung\" or \"unsprung\"? I'm confused by the ambiguity of the verb \"spring\". That is, a trap that is set up and active could be \"sprung\" in the sense that a spring is compressed and ready to launch, but it could also be \"unsprung\" in the sense that it hasn't yet sprung to action because its spring force has yet to be released. And after a victim walks into the trap and causes it to spring, the same ambiguity (in my mind) seems to apply.", "label": 1}
+{"snippet": "My dad's an author (English books with some Arabic) and until recently has been using WordPerfect for DOS for all his writing. He's been moving to Word and hates the lack of control he has compared to WP. I'm looking for options and LaTeX seems to be a good one. Here are the things I'd like to be able to do: Arabic inline text Support for chapters (as separate files) Support for ebook output (epub/mobi) Cross platform environment (Mac and Windows) Some way to move from WP and Word Is this realistic with LaTeX, and what would be the best way to start for a newbie?", "label": 1}
+{"snippet": "I've read 'Axiomatic Set Theory' by Patrick Suppes, and one thing I've noticed throughout is that he seems to be obsessed with definitions, and he tries to allow for urelements. Is this standard for ZFC? I thought in general when we say 'set' in ZFC we really mean 'pure set', and so avoid having to worry about individuals. In addition I've never seen such a fuss over definitions in any other mathematical book I've read, is this something I should get used to in Set Theory? If this is not standard, can anyone direct me to a book similar to Suppes' which builds (from the axioms) all the usual set theoretical structures needed for other areas of mathematics that is?", "label": 1}
+{"snippet": "I quite frequently use a word that sounds like \"shtook\", to mean, trouble with the law or other authorities, as in, \"You'll be in dead shtook if you do that\" or \"you'll be in real shtook if you don't finish your homework\", but I have never seen it written, and don't know how it is spelt. Can anyone shed some light on the matter. A search like this doesn't get very far; the real dictionaries don't recognise it and the Urban Dictionary here has only a typically obscene interpretation not in the least bit like I remember it.", "label": 1}
+{"snippet": "I am undergraduate in economics. As you may know, most prestigious departments in economics now require their aspirants to have taken Real Analysis (and Linear Algebra, too) before entering their programs. I have time to take these courses but don't know whether any college will give admission in their math program to an econ undergrad. I don't know whether distance learning courses will help me. Can anyone suggest me how to take math courses? Your replies will oblige me.", "label": 1}
+{"snippet": "I am learning Fourier transforms, Z transforms etc. in Digital Signal Processing and I can work easily with integrals. However, I don't understand how a Fourier transform converts time domain signals to frequency domain signals or why it is invertible. I also have a very basic understanding of linear algebra, not suitable for fourier analysis. I looked up books on fourier analysis but they don't explain anything I don't already know. So should the next logical step be to learn spectral analysis? Also, which books would you recommend for linear algebra? I already know matrices, eigenvectors, but not Hilbert spaces.", "label": 1}
+{"snippet": "I was watching a TV show, and this girl said: I just wish that once, I'd bring a guy home that they actually liked. Shouldn't it be like this? : I just wish that once, I'd bring a guy home that they actually like. Didn't she mean 'I wish they'd like my future boyfriends'? I think this is OK: I just wish that once, I brought a guy home that they actually liked. But the way she said it sounds strange to me.", "label": 1}
+{"snippet": "I am writing an article for a magazine about my visit to my village. I want to use a better word or phrase for 'my village' or 'my native place'. The following is the part 'When i heard of stories of hardships and suffering from my grandparents I realized how fortunate I was to live in the city I now call home. When the day came to visit \"my village/my native place\", I felt uncertain and nervous..' And better word or phrase to make the content more appealing?", "label": 1}
+{"snippet": "In Euclidean space, There is a classic Theorem claims that: The length of every rectifiable curve can be approximated by sufficiently small straight line segment with ends on the curve. Now, The question is that: Is there a similar thing happen on plane of constant curvature? I.e., Can the length of every rectifiable curve on the plane of constant curvature be approximated by sufficiently small geodesic line segment?", "label": 1}
+{"snippet": "In any cubic meter of space in our solar system there is predicted to be some amount of dark matter. Also in a cubic meter of space is a known average amount of cosmic ray energy. What is the ratio of cosmic ray energy to dark matter energy in our solar system? I'm curious if they are on the same order of magnitude or far from it.", "label": 1}
+{"snippet": "Imagine two charges A and B separated by some distance. Charge A emits a photon which is absorbed by charge B. Is the recoil momentum received by charge A always equal and opposite to the momentum gained by charge B? Is this true both for static Coulomb fields and radiation fields from accelerating charges? I suppose there is no momentum \"left over\" in the EM field after the interaction so that all the momentum lost by A is absorbed by B. Is this how it works?", "label": 1}
+{"snippet": "I have always thought it acceptable to say and write, \"She looked at me disgusted.\" However, I know some consider it ungrammatical, saying it must instead be either \"She looked at me disgustedly\" or \"She looked at me, disgusted.\" Please give me your opinions and explanations as to whether any of the foregoing sentences must be deemed grammatically wrong. Briefly, my own analysis is as follows. It is correct to say, \"She looked disgusted.\" So why would it be incorrect to say \"She looked at me disgusted\"? (She was disgusted while looking at me--or, she was looking at me while disgusted.)", "label": 1}
+{"snippet": "In \"Pragmmatic Programmer\" by David Hunt and Andy Thomas, there is a sentence: Do you ever watch old black-and-white war movies? To my best english grammar knowledge, present perfect tense should be used here: Have you ever watched black-and-white war movies? Is the version of the authors correct? If so, what's the difference between these two variants and what is the appropriate way to use each? PS. I checked this sentence in the translation of the book in my native language and it was translated exactly as if the orginal sentence was in present perfect form.", "label": 1}
+{"snippet": "I read here that there is a general rule to write an adjective order. But I didn't find any explanation if the rule has a specific order for colours, especially for primary colours. This may sound stupid but I'm just wondering. I mean is it preferable to say: red and white flowers Or: white and red flowers Or is there really no grammatical rule to obey?", "label": 1}
+{"snippet": "I heard an interesting argument from a colleague recently that went something like this. Whenever we are using an axiom scheme, we are essentially choosing one of the instances of this scheme, and hence, whether or not we include the axiom of choice in our axioms, we are implicitly using some kind of choice principle to choose that instance. My gut feeling is that this argument seems fishy, but also interesting, and I lack the expertise to give a good answer. My question is whether this argument holds or not, and whether it makes a difference if the axiom scheme is uncountable. I realise that the question is somewhat vague, but I hope there can be some interesting answers anyway.", "label": 1}
+{"snippet": "An isomorphism indicates that two structures are the same, using different names for the elements. Therefore it's obvious that every (algebraic) property of the first structure must be present in the second. However, homomorphisms only indicate that the two structures are \"similar\", so it's not quite as obvious that every property will be preserved. Yet all the properties I've ever seen are preserved under homomorphism: commutativity, cyclicality, solvability... What are some examples of properties of algebraic structures not preserved under homomorphism? Feel free to use any algebraic structures you like, but I'm particularly interested in your garden variety structures: group and rings, say.", "label": 1}
+{"snippet": "This is potentially a very stupid question but I'm going to ask it anyway. With all these huge buildings such as the Abu Dhabi Mosque, where an unbelievable amount of materials such as marble was moved from one side of the earth to the other, is it possible that if we 'shift enough stuff' that we could change the earths centre of gravity, and potentially alter its orbit?", "label": 1}
+{"snippet": "There is no \"action at a distance\" in nature. Attraction of a piece of iron by a magnet, attraction between distant electric charges of opposite sign, have to be mediated by something. The virtual particles are proposed as an explanation. If they have an observable effect, it seems like they must exist. If so, why do we call them virtual? It can't be that they have short lifetimes, as there are short-lived particles (resonances) that we don't call \"virtual.\" On the other hand, some people say that the so-called virtual particles only exist on paper, or that they are just a technique to help us handle our equations. So what is the meaning of the word \"virtual\" here? Do these particles really exist, or not?", "label": 1}
+{"snippet": "Why it is said that the Microchannel Plates can be operated in vacuum? What is the maximum pressure in which it can be operated? Also, while it is not operating, should it be kept in vacuum? Is this because the semiconducting property of the channels can be affected by the atmospheric pressure? Or while operating the gas molecules can be ionized and burn the detector?", "label": 1}
+{"snippet": "A friend of mine corrected my sentence but I couldn't understand it. Just hoping someone can explain it properly for a non English speaker. My sentence is: \"Finally your passport GOT ready for pickup\" My friend (native English speaker) corrected it to: \"Finally your passport IS ready for pickup\" Or \"Finally your passport got processed and is ready for pickup\" Why can't i use \"got ready\" in the above sentence just like in sentences \"We got ready for bed\", \"Alpha team got ready to play\" Thanks in advance.", "label": 1}
+{"snippet": "I'm looking for a single word to indicate a point in time which is either the beginning or end of an event. Edit, for a better example: A bell rings at the start a round of boxing. A bell rings at the end of a round of boxing. Assuming the bell rings at no other times, we can say the bell always rings at the BLANK of a round. Currently, for BLANK, I'm using the phrase \"start or end.\" It feels clunky. I'd like to replace it with a single word, if possible.", "label": 1}
+{"snippet": "I couldn't clearly understand the phrase \"credential mongering\" as used in an article in the New Republic about the Ivy League. The extract, from \"The Trouble With Harvard\" by Steven Pinker, is as follows: Admission to the Ivies is increasingly seen as the bottleneck to a pipeline that feeds a trickle of young adults into the remaining lucrative sectors of our financialized, winner-take-all economy. And their capricious and opaque criteria have set off an arms race of credential mongering that is immiserating the teenagers and parents (in practice, mostly mothers) of the upper middle class. Is it to do with attaining qualifications by any means? Or is the phrase itself imprecise? Thank you!", "label": 1}
+{"snippet": "This suggests that the current MLDA is not effective. However, the estimates in this paper challenge that claim and show that the effects of the current MLDA is statistically significant in all cases we observe. This suggests that the current MLDA is not effective. However, the estimates in this paper challenge that claim and show that the effects of the current MLDA is statistically significant in all cases that we observe.", "label": 1}
+{"snippet": "I'm using latexdiff to highlight the differences between two versions of a tex document, using the default style which is UNDERLINE. This style formats added text in blue with a wavy underline, and removed text in red with a strikethough. I'm interested in formatting the output such that added text is in blue but without the wavy underline (and removed text is in red as before). Is there a command for achieving this? I wasn't able to figure it out from the man page. Another way would be to modify the CCHANGEBAR style, which formats added text in blue and removed text in red but without the strikethrough, to add the strikethrough to the removed text (my question is how).", "label": 1}
+{"snippet": "I'm looking for an equation that looks like the image below. I am comfortable constructing functions that pass the vertical line test, but as this is a relation, I am not really sure how to start. Would this need to be defined implicitly? An explanation on how you constructed it would be great as well! I should note that the scale does not matter, just the general shape.", "label": 1}
+{"snippet": "Group theory is all about symmetries. Can this be seen from the axioms defining a group? Or equivalently can the group axioms be motivated from this point of view? Of course one can look at several examples and check that the group axioms are fulfilled, nevertheless this doesn't make clear why the axioms have to be precisly like they are. Any ideas would be much appreciated.", "label": 1}
+{"snippet": "A few years ago I read a short little article about how big our eyes would have to be to observe microwaves (or any long-wave radiation for that matter). I don't remember enough about the article, or know enough about observing EM waves to reconstruct the equations, and I can't find the article again. So my question is simply this: is there some equation or rule of thumb that says if you want to observe ('see') a wave of length x, then your observing tool ('eyes') have to be such and such a size?", "label": 1}
+{"snippet": "I am currently doing a one semester course on groups and rings where we have learned about (so far): Definitions of groups, subgroups, cyclic and normal subgroups, the symmetric group, homomorphisms, isomorphisms, The Correspondence Theorem, Product and Quotient Groups. As of yesterday's lecture we learned about the First Isomorphism Theorem and a little bit about rings. By the end of the course we should have done rings, endomorphisms, The Orbit-Stabilizer Theorem and subjects which I am not sure about. I am wondering if this would be sufficient to start Atiyah Macdonald; I have opened the first few pages and it looks hard. For those who have done it, what do you think are the prerequisites before doing this? Perhaps something like Herstein's Topics in Algebra? Thanks.", "label": 1}
+{"snippet": "I've noticed people use (in speech) the word godness for \"feminine god\", e.g.: Oh my godness! However, in classic texts it is goddess, e.g. Shakespeare's \"King Lear\": Hear, nature, hear; dear goddess, hear! Suspend thy purpose, if thou didst intend To make this creature fruitful! Into her womb convey sterility! It is my understanding that godness can be an urban slang for \"divinity\", but not for an impersonated deity. Is godness just a mistake?", "label": 1}
+{"snippet": "I am trying to understand pure and mixed states better. If I have N quantum particles in an isolated system. The many-particle state is a superposition of the product of single-particle states by the appropriate statistics (bosons, fermions, or distinguishable). Would this state be still considered pure since there is no interaction with the environment? Does that mean isolated systems or microcanonical ensembles are always pure?", "label": 1}
+{"snippet": "I have studied that topologically equivalent metrics produce the same open and closed sets. They also produce same compact and connected subsets. Does it mean that topologically equivalent metrics have same open, closed or compact subsets? In what context topologically equivalent metrics differ from each other? Intutively, how can we explain topologically equivalent metrics? Can we say that two topologically equivalent metrics have same topological properties? Thanks and regards", "label": 1}
+{"snippet": "If you were going to teach you kids programming and asked me what book to use as a guide, I would recommend you either Java programming for kids or Python for kids. But what if I want to teach kids math including derivatives, integrals, differential equations, set theory, etc? What book can provide me with a road map I can use (assuming kids are smart enough to learn what I give them)?", "label": 1}
+{"snippet": "I am a beginning graduate student with (almost) no background in algebraic geometry. I would like to learn the proof of the Riemann hypothesis for curves over finite fields, including all prerequisites. I am looking for books to get me there. I am not necessarily looking for the quickest way, but rather for self-contained well-written books that will get me to this result. Nevertheless, I prefer to be focused and study only the needed prerequisites in the adequate generality (in particular, I'm focusing on the case of curves, rather than more general varieties). (my knowledge in group theory, field theory, and algebraic number theory is equivalent to what appears in J.S. Milne's notes, but as mentioned - I have almost no background in algebraic geometry).", "label": 1}
+{"snippet": "This question is related to another question. If we have a Riemann surface with punctures of negative Euler characterstisc, how can one define a complete hyperbolic metric? I know that in this case the universal cover is the hyperbolic plane and it has a complete metric. Do we project this metric to the puntured surface? If so, why is it complete? I will deeply appreciate if somebody gives an example or a good reference.", "label": 1}
+{"snippet": "I'm not sure of the name of this problem so haven't really been able to research it. I have a complete weighted graph with a start and end node and n distinct sets of nodes (lets call them red, blue and green), each with m member nodes. I need to find the shortest path from start to end and must pass through exactly one red, one blue and one green node; is there an algorithm for this? An extension would be that I need to find the shortest path while visiting blue first, then green, then red (again, exactly once each); is there one for this?", "label": 1}
+{"snippet": "Let's say for example: Two people sing the same note (frequency) and volume (amplitude) together. Why is it that the two persons sound louder than they would individually? I would imagine that since the traverse waves generated by the two persons would randomly be louder or softer, based on the phase shift between the two sound waves. But that hypothesis is obviously untrue since in the real world a choir is clearly louder than a soloist.", "label": 1}
+{"snippet": "What is the exact word for someone who always pretends to be nice to someone's face but makes fun of them behind their back? When they are talking to you, they'll treat you very well, like a good-mannered person. They care a lot about their image in front of others and show a positive image of themselves in front of an audience. But they are not actually good in their heart. Any word except hypocrite.", "label": 1}
+{"snippet": "How do you say to someone that you will reuse a sentence (or a joke) you've just heard from them, as-is, because you liked it a lot ? In Italian we say \"Questa me la rivendo\", that translated is \"I'm gonna resell that one\" (ri-vendo / re-sell is the idiomatic part, the other words could be recombined / replaced). I can't find anything in the web, so... what is the English version ?", "label": 1}
+{"snippet": "I'm looking for a noun for a person to convey two things: their particularly keen appreciation of aesthetics, and their ability to create aesthetically appealing objects. For example, Steve Jobs. A man with a famously keen sense of what is beautiful, at every level, be it user interface design, the connectors on cables or the stairs at retail stores. The closest I've got is \"aesthetician\", but that conveys more the study of aesthetics, rather than the appreciation and ability to craft aesthetic perfection. Any ideas?", "label": 1}
+{"snippet": "I work for a client at the rate of X USD (United State Dollars) per hour. Recently, he accidentally paid me at the rate of Y USD per hour. Y is greater than X. I notified him of his mistake and he replied with the following sentence:- Go ahead and keep the difference to be applied to the next round of work you do for us. What does this mean? Should I accept the payment at the rate of Y USD per hour or correct it to X USD per hour?", "label": 1}
+{"snippet": "Recently I've wondered about two idioms which have a strange relationship. Come Hell or high water and Lord willing and the creek don't rise Grammatical accuracy, alternative formulations, and questionable folk etymologies, and literal meanings aside, why do these two phrases (often used interchangably) have such different implications? My thoughts so far have centered around the former being an expression of an internal locus of control (i.e. I will make this happen) and the latter of an external locus of control (i.e. I hope this won't not happen). Why does the more apparently positive formulation reference Hell while the less (certainly) positive one mentions the 'Lord?'", "label": 1}
+{"snippet": "I always have doubts whether to use a singular or a plural noun when I refer to certain peoples. For example, we say Americans, Italians, Brazilians, Russians and Austrians. But we say The British, The English, The Portuguese, The French, The Spanish, The Chinese, and The Irish. When it comes to those nationals I rarely hear of, I'm never sure. These would include people from countries such as Azerbaijan, Armenia or Kenya. Is there any rule as to whether we should use singular or plural ?", "label": 1}
+{"snippet": "I have come across many hand dryers that attempt to dry your hands really fast after you wash them. Here are two of them: XLERATOR http://www.exceldryer.com/ Dyson Airblade http://www.dysonairblade.com/homepage.asp So I guess I have a ridiculously high standard cause I think even these are too slow. Would it be possible to create a large static electric field to attract the water molecules off of your hand? Can someone offer some ideas that would remove the water off of your hand using some type of electric field generated by charged plates or something?", "label": 1}
+{"snippet": "I am a high schooler who really likes math, and I am interested in pursuing it in my undergraduate years. I have a basic facility with proofs, and I am currently exploring several different areas of math (analysis, graph theory, and topology). I am interested in seeing if I can contribute to mathematics even if it has no applications, mathematical or otherwise, however most areas of math don't seem to have any \"low hanging fruit\" so to speak, so I'm looking for a different, more obscure area where I can learn all that is known, and maybe contribute myself.", "label": 1}
+{"snippet": "Prove or Disprove: If V is any vector space and with an orthonormal basis B for a subspace W of V, then V has an orthonormal basis C with B as a subset of C. First Question: Can you have an orthonormal basis for any vector space or can you only have an orthonormal basis for inner product spaces? Second Question: Does it also make a difference whether or not V is finite-dimensional or infinite-dimensional?", "label": 1}
+{"snippet": "I always find it difficult to discuss the meaning of a word because I don't really have a definite meaning of word in my head. Cook refers to the verb (to cook) but it can also refer to the noun (a cook). Would you say cook is one word with multiple meanings or that the verb and the noun are separate words? Is a word simply the arrangement of the letters?", "label": 1}
+{"snippet": "I'm trying to come up with some math problems (word or otherwise) that get to the meaning of adding zero, but I'm getting stuck because it seems just too simple to me. I have come up with questions like \"John is having a birthday party and he invites five friends over but nobody shows up. How many people are at the party?\". While this question gets to the problem at hand, it might be too simple to understand the meaning of adding zero. This problem also suffers from the possibility that first graders will answer like so, \"Well there would be three people at the party because John's mom and dad would be there too.\" Any ideas?", "label": 1}
+{"snippet": "As the title says. For example, if I take a fat metal wire with non-negligible thickness, and then wind it into a spiral, but such that none of the parts touch one another (there are no topological 'holes'), then if I add a charge to the wire, would it equally distribute over the wire? Or would the charges from neighboring 'loops' of the spiral interact with one another somehow, similar to a capacitor almost?", "label": 1}
+{"snippet": "Outside of your field of research / application, how much of your undergrad education have you retained? Thought experiment: How would you fare today if handed old exams from your introductory topology / number theory / differential equations / whatever classes? No studying or preparation. I've always wondered how much of this material one should expect to have internalized, and how much is acceptable to forget over time and need a reference aid.", "label": 1}
+{"snippet": "In Mac OS X, the home/end keys per default throw you at the beginning/end of the document instead of the beginning/end line. I have changed my system key bindings to get the latter, \"usual\" (Windows- and Linux-like) behavior. However, texmaker seems to ignore this setting. It is horribly distracting when I have to search for my editing position in a longer text each time after unconsciously hitting the end key. I did not find these commands in the \"configure texmaker\" dialog. Is there a way to persuade texmaker to respect the system key bindings, or can I modify the setting in texmaker individually?", "label": 1}
+{"snippet": "On the new Astronomy.SE site, I was having a short discussion on one of my answers. The basic discrepancy was; can MACHOs like black holes/brown dwarfs/neutron stars be termed \"dark matter\"? My reasoning is that these objects do not radiate EM radiation on their own but they do gravitate, and thus constitute a small part of the total dark matter in the universe. I agree that there is a lot of dark matter which doesn't In other words, can the term \"dark matter\" be applied to nonradiating (or faintly radiating) bodies which still participate in the electromagnetic interaction (baryonic or otherwise)? Or is it necessary for all dark matter to not interact electromagnetically?", "label": 1}
+{"snippet": "It is quite common to hear in newspapers and television about the increasing temperature, i.e. global warming. But I am interested in something else. How does global warming affect the internal energy of the earth, or else how does this change the gravitational potential energy of a point mass and the earth? This is a open question and everyone should feel free to make any plausible assumptions in estimating the increase or decrease. I thought of global warming as causing the expansion of the atmosphere, possibly changing mass distribution of Earth's atmosphere.", "label": 1}
+{"snippet": "In my school and university I was taught to say \"Not at all\" or \"Don't mention it\" in response to \"Thank you!\". Now I rarely hear these phrases used, but rather something like \"You're welcome\", \"It's OK\", \"My pleasure\", or \"No problem\". My real life conversation experience is very poor. I often listen to some English learning podcasts, and watch some films in English. So I listen to dialogs, which are probably not from the modern real life world. How do native English speakers tend to respond to \"Thank you!\" now? What I should care about, when choosing from the available options?", "label": 1}
+{"snippet": "Are there any big controversies in contemporary mathematical research? Other domains contain big controversial research topics (for example string theory in physics). The specific nature of mathematics however, makes me suspect that there isn't much room for any serious disagreement, or at least less room in comparison..? Is this intuition right, or completely ignorant and absurd? --- This is not a question about mathematics per se, but more a question about the people doing it. I hope the question is still appropriate in this stackexchange. ----", "label": 1}
+{"snippet": "If for some reason I want to create the lightest document (in terms of the weight of the output file, not the font), what would be some good practices? Specifically in terms of: Packages: do they add significant weight to the file? Are there some which are particularly heavy? Graphics: should they be EPS, PDF? Some other format? Is TIKZ code always lighter? Classes: do some add more bulk than others? (Some other important things I'm sure I'm missing...) Of course I could just start trying to \"play\" with the above mentioned elements, but I was hoping to get an informed answer, not just the result of trial-and-error experiments.", "label": 1}
+{"snippet": "From The Assassination of Jesse James by the Coward Robert Ford: Ed Miller: I was with a girl once. Wasn't a squaw, but she was purty. She had yellow hair, like uh... oh, like something. Dick Liddil: Like hair bobbed from a ray of sunlight? What does bobbed mean in this context? I guess it means \"cut\", but I would like a native speaker to verify.", "label": 1}
+{"snippet": "I am aware of the idiom like a fish out of water. What intrigued me is an article using like a fish takes to water. Teo Zhen Ren, the swimming sensation from Singapore, took to swimming like a fish takes to water. Is like a fish takes to water a valid usage? Is it an idiom? I thought the usual phrase was like a duck takes to water.", "label": 1}
+{"snippet": "Is there a systematic treatment of (finite dimensional) manifolds with corners in the literature which carefully introduces all usual differential topological notions (submanifolds, embeddings, etc.) and which includes proofs of the usual statements in geometric topology like the existence of collars or isotopy extension theorems in the generality of manifolds with corners? Most of the common textbooks treat the case without corners nor boundary and mention the case of boundaries. Some of them take care of boundaries more closely, but I am not aware of a detailed reference covering the situation with corners.", "label": 1}
+{"snippet": "I have to translate a Washington Post article on Trump but I cannot understand one part: It's post-policy politics. It's about having the right feelings instead of the right proposals. Now, that doesn't mean that we shouldn't point out when he's contradicting himself or when his plans don't add up. But it does mean that we should probably be a little less credulous about this supposed policy pivot or that change in message. There has to be one for that to happen.", "label": 1}
+{"snippet": "It's logical to think that the time it takes a microwave to heat the food would be proportional to the mass heated. But since a microwave is based on dielectric heating, I think that if you increase the mass of food there will be more water, which will heat the food faster (due to thermalization). Is this reasoning right? Is there an optimal quantity of food to heat and the time it takes?", "label": 1}
+{"snippet": "If I had a rigid body, such as a wardrobe, so that its centre of mass is above the ground and I tilt it slightly. I have read that the normal force of the floor on the wardrobe must be equal and opposite to the weight of the object as we have no translational motion. However if I let the wardrobe topple over, its centre of mass is now lower. How can the centre of mass have changed positions if the normal force and weight are equal and opposite to oppose any translational motion?", "label": 1}
+{"snippet": "Why doesn't a plane wave solution represent a single photon? And what is meant by the quantum-mean field being zero? EDIT: This post is an extension to a previous post I made asking about the photon in QFT. I was asked by the person helping me to start a new question so he can respond in the form of an \"answer\" post and thereby keeping all \"answers\" on topic. The link is here Quantum State of Photon Question", "label": 1}
+{"snippet": "The mechanical advantage is given by MA = Load/Effort which is quite universal (at least in my short experience with them). However when i reviewed over the mechanical advantage of simple machines, especially levers , the formula for mechanical advantage stunned me, instead of MA = Distance of Fulcrum to Load / Distance of Fulcrum to Effort it was instead MA = Distance of Fulcrum to Effort/ Distance of Fulcrum to Load Does this not contradict what the MA formula is? Thank you for your time", "label": 1}
+{"snippet": "There must be a name for this sort of after-the-fact non-argument. Sorry, this is the only way I could find to describe it. Debbie finds a kitten. Kitten has been burned over half its body, but it's alive. Debbie says, 'The kitten wants to live!' and takes it to a vet. Bob says, 'The kitten is suffering and will continue to suffer horribly, the kindest thing would be to euthanize her.' Debbie refuses; the kitten continues to suffer for months but in the end manages to survive. Bob says, 'The kitten suffered unnecessarily.' Debbie then says to Bob, 'The kitten would now be dead had it been up to you. You have no respect for life.'", "label": 1}
+{"snippet": "In a crystalline solid each atomic level 'splits' into n levels (n = number of atoms in the system). When the number of atoms is large each level becomes replaced by a band of closely spaced levels. In a semi-conductor we have an empty \"conduction band\" and a fully occupied \"valance band\". Conductivity arises because electrons get excited to the conduction band. Question: Why can't electron in the valence band freely move around and therefore conduct electricity? My question also applies to metals where the conduction band is already half-filled. What's special about this conduction band that allows electron to move around freely?", "label": 1}
+{"snippet": "According to the popular Solar System formation models, what are the bounds on the Gas Giants' cores (note I am only interested in the bounds for our Solar System). For example according to Wikipedia on Jupiter Assuming [a core] did exist, it may have shrunk as convection currents of hot liquid metallic hydrogen mixed with the molten core and carried its contents to higher levels in the planetary interior. This suggests that a core would shrink over time, which would put an upper bound on the size today. Are there other bounds? I would like numbers together with some reasons for those numbers.", "label": 1}
+{"snippet": "I have two books on algebra where one makes the definition of isomorphism to be a bijective homomorphism, while the other makes it as an injective homomorphism. I am doing the exercises from one book and learning from the other (not optimal I know), and so I am wondering what definition is considered the convention. If both are conventionally okay, is something lost by removing the surjective part of the bijection and if so what? I realise it's a rather uninteresting question, but if someone has the time I would appreciate the answer. Thank you!", "label": 1}
+{"snippet": "I'm trying to draw a chain of arrows going under and above each other, as depicted: The issue isn't labelling the arrows, I can easily do that, but I don't know how to get them to curl, have the arrow head in the middle (ideally, though not necessary), and have one on top of the other. Any help is appreciated. If a solution exists without TikZ, I would prefer it. For those interested, the above is an eigenvector of the Cartan generators of a Lie algebra acting on a state as a raising or lowering operator, used in the roots and weights method to classify all semi-simple compact Lie algebras.", "label": 1}
+{"snippet": "I'm having trouble with a problem in Propositional Logic Using induction I am supposed to show that if a well formed formula (wff) X has no repetitions of sentence letters then X is invalid. The hint in the back of the book says \"Instead of trying to show directly that every wff without repetition of sentence letters has the feature of PL-invalidity, find some feature F that is stronger than PL-invalidity (i.e. some feature from which PL-invalidity follows), and prove that every wff has that feature.\" What does invalidity follow from?", "label": 1}
+{"snippet": "It is well known that the Lagrangian of a classical free particle equal to kinetic energy. This statement can be derived from some basic assumptions about the symmetries of the space-time. Is there any similar reasoning (eg. symmetry based or geometrical) why the Lagrangian of a classical system is equal kinetic energy minus the potential energy? Or it is just because we can compare the Newton's equations with the Euler-Lagrange equation and realize how they can match?", "label": 1}
+{"snippet": "After a hot shower, the mirror in my bathroom steams up. When I try to clear it with a towel, it immediately refogs. Yet once I use my hair-dryer, it will clear the fog and the mirror will stay clear. I'd like an answer to the mechanics behind this difference. I suppose it got something to do with the heat, and maybe the refogging is only delayed due to it. But that is just me speculating, and I'd like a concrete answer on this phenomenon.", "label": 1}
+{"snippet": "I can see this is true for the sum of two roots of unity with some basic trigonometry (the resulting argument is the half the sum of the original arguments, and so must also be a rational multiple of Pi) but trying to extend this method to the sum of more than two doesn't seem to work. Is there some other way of showing this? It seems related to this question: Sums of roots of unity but I'm not sure if that can be extended to this.", "label": 1}
+{"snippet": "I am studying Hyperbolic Geometry. At this part, I have proved that semicircles and straight lines orthogonals to the real axis are geodesics in the hyperbolic plane. But how I proof that this geodesics are uniques? That it does not exist others geometric places between two different points that minimizes the hyperbolic length? I have seen a topic related to this, but I do not know nothing about Riemannian Geometry. If someone could indicate to me some references to this proof(or the idea behind) I will be very grateful!", "label": 1}
+{"snippet": "I need to show through a proof that the set of nonnegative numbers is denumerable I know a set is denumerable if its members or elements can be put into an order and counted. I am supposed to show this through a proof as well. I was considering using Induction possibly but I'm not sure if this is a viable or feasible method to use. Any help is great appreciated", "label": 1}
+{"snippet": "I have a rather large text file that I'm trying to convert into a table. I'm pretty new to Latex, so I was using this other answer from this site as a guide to help me: save table on a separate file and I got some great results, but I realized that my table needs to be split up across many pages, which they say to use longtable to achieve. I don't completely understand where you would add that in or which part you would replace with that, and I was hoping that someone could explain that to me. Thank you!", "label": 1}
+{"snippet": "We know that gravity affects time. More the gravity, slower the time, and vice-versa. Now consider a hypothetical condition where two people are walking next to each other. One person is subjected to a lot of gravity and the second person to a lot lesser. How would first person see motion of second person? Since time would be running slower at first person's place and faster at second person's, would the first person see the second person to be moving faster than we usually see? Like a video is being fast forwarded?", "label": 1}
+{"snippet": "In the phrase 'in the field instead of behind a / the desk', would you use 'a' or 'the'? It seems to me that 'the' is the more sensible option, as English has other expressions of the 'the N' form which denote an activity associated with the object referred by the noun, e.g. the bar as signifying the legal profession, the pen as in 'the pen is mightier than the sword'. However, a search on Google shows that 'in the field instead of behind a desk' exceedingly outnumbers the other version.", "label": 1}
+{"snippet": "According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) are physically equivalent to a gravitational field of the same strength. Refer: Einstein's thought experiment of a Physicist in an Accelerated Box. I find that the 'How' part of this question is somewhat easy to understand Mathematically but hard to visualize physically and on the 'Why' part I am totally blank.", "label": 1}
+{"snippet": "A chain of some mass, forming a circle, is slipped on a smooth cone. If we consider an infinitesimally small section of the chain, a component of gravity will try to accelerate it along the surface of the cone. So there must be some tension in the string that prevents the acceleration. What will be the direction of the tension on this section of the chain? Will it be towards the height of the cone, parallel to the ground?", "label": 1}
+{"snippet": "In mathematics, we talk about tangent vectors and cotangent vectors on a manifold at each point, and vector fields and cotangent vector fields (also known as differential one-forms). When we talk about tensor fields, we mean differentiable sections of some tensor power of the tangent or cotangent bundle (or a combination). There are various natural differentiation operations, such as the exterior derivative of anti-symmetric covariant tensor fields, or the Lie derivative of two vector fields. These have nice coordinate-free definitions. In physics, there is talk of \"covariant derivatives\" of tensor fields, whose resulting objects are different kind of tensor fields. I was wondering, what is the abstract interpretation of the general notion of a covariant derivative in terms of (tensor products of) tangent vectors and vector fields.", "label": 1}
+{"snippet": "Let's say you wanted to calculate, for example, the average (i.e. mean) cost per day for a hotel to accommodate a tourist. If only aggregate cost data is available, is dividing the average cumulative cost for one person's stay by the average person's duration of stay an acceptable method? Would using the median cost and median duration of stay be better? Worse? The same? I know the median is less susceptible to outliers than the mean, so if both the median and the mean work the same I'd rather use the median.", "label": 1}
+{"snippet": "Richard Feynman showed that Quantum simulation on a Turing machine will have an exponential slowdown. If that is so, does this put quantum simulation outside of P (complexity class)? I thought quantum simulation was polynomially possible on quantum computers, but there is still no proof that BQP is strictly bigger than P. So either quantum simulation has not been shown to lie outside of P, or it is not in BQP. I can't seem to find the answer.", "label": 1}
+{"snippet": "So I was wondering about the event horizon on a black hole. And wondering if the point of no return for radio waves vs gamma rays would be different. I guess the logic being, since gamma rays have more energy than radio waves, their point of no return might be different. But I'm not sure if gravity has the same affect on all frequencies of electromagnetic radiation. I'm sure the answer for this would lie in gravitational lensing, ie are different colours of light lensed by the same amount? or do higher frequencies lens less?", "label": 1}
+{"snippet": "I was watching a Physics TV show, When someone called Alex Filippenko said that when there was the Big Bang, the Space extended at a speed faster than speed of light. He said that it wasn't against the Theory of relativity because space isn't a particle and can go faster than speed of light. So I wanted to know if that is a fact? And otherwise how could the light go further if space around wasn't going at least as fast as light?", "label": 1}
+{"snippet": "I've been reading my Stewart Calculus book and I honestly find most of the coverage of sequences and series easy to grasp (excluding power series, Taylor and Maclauren since we haven't covered those just yet). However, when the book guides me to a test to use to solve a problem I don't have an issue, but if I'm given a bunch of problems and told to choose a test to use I honestly have no idea where to begin. How can I intuitively know how to attack a given problem? I realize the thought process is quite similar to integration, but I still feel like integration is much easier than determining convergence and divergence of a sequence/series.", "label": 1}
+{"snippet": "I have been interpolating cubic splines to some data, but it is now clear that I need my curves to be monotonic. Wikipedia and StackExchange sources describe how to impose the monotonicity condition while fitting with cubic Hermite splines. However I need my splines in B-spline form and I'm not sure how to translate from Hermite form to B-spline form. Is there a method to do this monotonic interpolation so that the resulting curve is explicitly in B-spline form (i.e. a list of knots and B-spline coefficients)? If not (and this might warrant its own question) how does one take a spline in Hermite form to B-spline form?", "label": 1}
+{"snippet": "I would like to write a sentence to thank a number of colleagues. I would like to express the idea that it was a pleasure to spend time with them. Which of the two sentences below is better? I also take this opportunity to thank a number of colleagues with whom I had the pleasure of spending time these past two years. I also take this opportunity to thank a number of colleagues I had the pleasure of spending time with these past two years. Can you think of an improvement?", "label": 1}
+{"snippet": "if I make a circuit with a battery and a capacitor (with a dielectric inside), how it is possible to get a current in the circuit? If electrons go from one pole of the battery and they arrive to one plate of the capacitor they cannot flow to the other plate of the capacitor because the plates are separated by a dielectric and this dielectric doesn't have free charges, they are bound charges. How can I explain a net flow of electrons in this circuit? Thanks.", "label": 1}
+{"snippet": "I have been told that industrial mixing machines (say, for cake batter) switch directions periodically, first stirring in one direction, then the other, because this mixes the material more thoroughly. I imagine (but don't know for sure) that stirring in only one direction will tend to create helical structures in the mixed material, where each helix is more or less uniform but two helices might be quite different from one another; and that switching directions tends to break up and mingle these helices. Is this at all correct? Is there a way to quantify the effectiveness of different methods of stirring? If so, how much better is it to stir in alternating directions, and how often should one switch directions?", "label": 1}
+{"snippet": "I am thinking of a (greatly simplified) computer simulation of a universe that followed something like Newtonian rules. Inside the simulation are A.I.s that are made from those same rules, and can only use those rules interact the world around them. Would there be some fundamental limits on what those A.I.s could work out about their universe, like their own version of an uncertainty principle? Sorry for phrasing this question in such a convoluted way. If anyone recognises what I am asking, and can point me in the right direction that would be appreciated.", "label": 1}
+{"snippet": "I quoted the following from a pamphlet: Please read the instructions carefully before filling out the application form. The application will be returned to you and the registration may be delayed, if the information is not filled in completely. Does \"filling out\" equal to \"filling in\"? The words in and out have opposite meanings, how can they produce almost equal meaning in these phrases filling in and filling out?", "label": 1}
+{"snippet": "I have not idea how to call these things, but I just saw a paper with the following figure and I was wondering how one would go about doing it in LaTeX. The closest thing I saw on TeXample.net was the Ford Circles example, but that's for a very specific case. I would like to see a way use this as a plotting device. At this point, I am not even sure how to do it in \"normal\" programming language, so perhaps the question is ill-placed. At any rate, I'd love to hear what people think!", "label": 1}
+{"snippet": "Is there a term for when a person is getting really irritated/frustrated by someone, but they don't want to yell, so they do that thing where they exhale sharply through their nose? Say, for example, in customer support the operator has to explain and re-explain a procedure over and over, but the caller can never seem to get it right. To be clear, I'm talking about the act of blowing air out of the nose when angry/frustrated as opposed to breathing an exasperated sigh out of the mouth. It's just air; there's no vocalization or loud sound like a snort.", "label": 1}
+{"snippet": "Is there any difference between the mass defect and the mass deficit? I have read that the mass defect of a nuclide is never negative and have also been told that the mass defect is the same as the mass deficit, which can be negative. Is it purely a sign convention? As a result of this is the binding energy of a nuclide ever negative?", "label": 1}
+{"snippet": "While studying about band theory of semiconductors, I observed that when the electrons were excited from the valence band to the conduction band, they left behind holes in the valence band. From my existing knowledge, I believe that the valence electrons alone occupy the valence band which tells me the valence band is negative. For the holes to exist, the valence band has to be neutral. So, why is the valence band neutral? If my reason for the valence band to be negative was wrong, I would like to know the reason.", "label": 1}
+{"snippet": "I've been watching this little HBO show by the name of Game of Thones. Perhaps you have heard of it. In the most recent episode the following line is used (and also happens to be the title of the episode): Now their watch is ended This sounds foreign to my ear. I would be inclined to say \"Their watch has ended\". Is there a subtlety in the English language that alters the meaning of the sentence by changing \"is\" to \"has\" and vice versa in the context of a simple sentence such as the above?", "label": 1}
+{"snippet": "I have an upcoming statistics exam and I'm studying it on my own. I was recommended Hogg's Introduction to Mathematical Statistics, but I didn't find it helpful. I just want a book which covers basic mathematical statistics and statistical inference: stochastic convergence, estimation of parameters, testing hypothesis, etc. all at an elementary level (suitable for a math undergraduate), with good introduction to the required background for such concepts. Can you provide me a good source?", "label": 1}
+{"snippet": "I was discussing about particle accelerators with my friends and it came to my mind whether it is anyway possible to make a table-top accelerator(accelerator that can fit on a table). I asked this to my professor and he mentioned something about plasma field accelerator.He said that charged particle passing through a plasma created by laser pulse can get acclerated. How can plasma accelerate charged particles? What will be the maximum energy we can achieve using such accelerator?What is the progress towards the development of such science? Will it be really a table-top accelerator?", "label": 1}
+{"snippet": "I have developped a little tool in matlab to fill directly some .tex files and then compile them in a pdf file (I use the command pdflatex to compile). It is well working on my computer because I have MiKTeX installed. Now I would like to make a installer (using Inno Setup) to share this tool but I need to include the compiler in the setup. Does someone know if there is a way to only install pdfTeX for the furure users of my tool or do I need to require them to install the whole MiKTeX?", "label": 1}
+{"snippet": "This is more of a general question rather than anything specific but I was just wondering if someone could point me toward resources which discuss singularities in a PDE rather than in an ODE (by singularity I mean as in https://en.wikipedia.org/wiki/Singularity_(mathematics)). I did a bit of work with singularities in ODEs, but it seems working with singularities in PDEs is harder, and I can't seem to find any material on it. I have a first order PDE so it shouldn't be too difficult (I think) to work with singularities with it, but seeing as how I'm from a more probability/stats background I can't be too sure about it... Thanks in advance.", "label": 1}
+{"snippet": "I've looked up both and seen the answer to \"why do we say 'soup up.'\" Having always thought myself that the phrase was \"to soup-up,\" I've been lately surprised to see a significant amount of usage of \"suped-up\" with claims that it's from the term \"to supercharge\" or \"super\" and that \"soup\" is the misspelling. Is there a definitive word on whether \"suped-up\" is a real term for \"supercharged\" or if it's a misspelled variant of \"souped-up\"?", "label": 1}
+{"snippet": "I hear people say things like \"inside a black hole the laws of physics are not valid\" or \"there can be parallel universes with different physical laws\" or \"before the big bang there was nothing\". Can physics really make such predictions? Is not there a logical issue here, namely, is it possible to predict a system where all physical theories break, by using only validated/well-established/working theories of physics?", "label": 1}
+{"snippet": "Is there a difference between \"headquarters of\" and \"headquarters for\"? It is the headquarters of many branches. It is the headquarters for many branches. It is the headquarters of the party. It is the headquarters for the party. Intuitively, \"for many branches\" seems correct and \"of the party\" seems correct. I can explain the conceptual difference between branches and party, but I can't connect my intuition to any rules. Any thoughts on this? Thanks.", "label": 1}
+{"snippet": "I am working on a project whose object language is in non-monotonic logic. Since the project involves reasoning about the models, I am thinking of translating a non-monotonic problem into a first-order logic, use model theory in first-order monotone logic to solve the problem, then translate the results back to a non-monotonic logic. However, this seems cumbersome. Could you please provide me with a book or paper reference on model theory in non-monotonic logics. Preferably, classical topics such as Compactness theorem, Incompleteness theorems and Stable theories should be included.", "label": 1}
+{"snippet": "I'm interested in the semantic implications of using the words quote and estimate in a business scenario. Here's the situation: When someone wants to purchase a service that I provide, they can fill out a form on a Website with information about the work to be done. Based on that info, they are instantly given a predicted price. This is intended only to be a ballpark. Once I manually review the work order, I will contact them with a personalized, much more accurate guess at the price. My instinct is to use estimate for the ballpark and quote for the more precise guess, but I'm interested in both your opinions and the more subtle distinctions and implications of the two words.", "label": 1}
+{"snippet": "I want to say something like: The system stores the crazygonuts data separately from the data feed. I think this is wrong (maybe I am wrong in that), but I'm not sure exactly why. One alternative I thought of: The system stores the crazygonuts data separate from the data feed. I checked some dictionaries online, and I did not find separate listed as an adverb, so this also seems incorrect. I want to keep the verb (stores) in there. Is there any way I can keep this same sentence structure without sounding silly? If possible, I would like to use the word separate (or something sufficiently close, like distinctly); or is this formation doomed from the start?", "label": 1}
+{"snippet": "Most modern texts spend some time deriving the LSZ reduction formula that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you are calculating. Yet some earlier texts and even some modern texts (e.g. \"Student Friendly Quantum Field Theory\" by R. Klauber) seem to skip right past this, working everything out in the \"interaction\" picture. It seems there must be something going wrong with this latter procedure, but I am not quite able to put it together.", "label": 1}
+{"snippet": "I'm trying to read about anabelian geometry and obviously the things to start with is the algebraic (etale) fundamental group. Every now and again I encounter authors talking about the arithmetic fundamental group, especially when they're talking about curves. Are these really the same thing, except the term algebraic fundamental group is used when talking about arbitrary schemes and the arithmetic fundamental group when talking about curves?", "label": 1}
+{"snippet": "Possible Duplicate: [Singular] Is/Are [Plural]? I'm currently writing my master thesis on Bitcoin and I'm not sure which version of this sentence is correct: \"The first most important part of the Bitcoin infrastructure are all applications that communicate with the Network.\" \"The first most important part of the Bitcoin infrastructure is all applications that communicate with the Network.\" Or perhaps both of them are wrong? EDIT: Finished sentences.", "label": 1}
+{"snippet": "Possible Duplicate: Unbreakable block I have a block of text (possibly comprising many paragraphs) near the end of a page. The page break is being inserted in the middle of this block--how do I prevent that? (How do I tell LaTeX that this block of text needs to always stay together on the same page?) This question should apply to all formats, but in my case I am using the memoir class, and am willing to include any necessary packages.", "label": 1}
+{"snippet": "Currently i am reading about bandgap engineering in zinc oxide. I read that using external dopents likes magnesium or cadmium we can increase or decrease bandgap of zinc oxide,thus giving unique optical and electrical properties to zinc oxide. But how adding an external dopent causes changes in the bandgap of zinc oxide. I tried to search research article regarding this but was unable to find a mechanism for this phenomenon. Advance thanks for your help", "label": 1}
+{"snippet": "If the coproduct of a family of objects of a Poset (seen as a category) is the least upper bound, who is the coproduct of a family of objects of a Preorder (seen as a category)? My intuition tells me that is the lub again but I'm having trouble writing the proof formally due to it is my first time with category theory and I'm not a mathematician, can you help me?", "label": 1}
+{"snippet": "I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? From what I saw in the books, most topics were just simple linear algebra. I am looking for an area which is mathematically richer, and uses maybe more concepts from theoretical computer science, number theory, discrete maths, algebra, etc. Classical cryptography is an area on the interface of maths and TCS which uses many areas of maths such as number theory, algebra, elliptical curves. Is the quantum cryptography also rich in mathematics? What are the prerequisites? If not, please could you suggest some areas that I are mathematically rich in QIT?", "label": 1}
+{"snippet": "Is the phrase \"item is ignored for deletion\" grammatical and idiomatic? The context is a software program. I have a list of items to be deleted from a database, and if an item from the list is not in the database, I want to display a message saying that the item is ignored. Since this message can appear among other unrelated messages, I want it to be as informative as possible but laconic.", "label": 1}
+{"snippet": "Can the word dear replace expensive, as in \"That new T.V is too dear\"? The dictionary says so, but I was completely unaware that it had that connotation. I want to use it in writing because it's a shorter, simpler sounding word with a regular comparative/superlative, dearer and dearest, but it doesn't sound idiomatic at all. No one round these parts would say that. Does anybody else in the English-speaking world say this? I tried searching a corpus but all results came back with dear used as a term of endearment.", "label": 1}
+{"snippet": "I am beginning to learn quantum mechanics. Since determining the position of an object involves probing by electromagnetic waves and since i have read a simple derivation of Heisenberg's uncertainty principle which says that uncertainty in momentum of a quantum particle is proportional to the momentum of light (or e.m.) used, I am beginning to wonder whether the theory of quantum mechanics is solely based on measurement using electromagnetic waves? In that case it is not a fundamental law. If we measure the position of a particle using its gravitational field change, does then the uncertainty exist? Pardon me if my question sounds silly.", "label": 1}
+{"snippet": "I was wondering if a library of mathematical expressions in Latex was existing on the web (I don't know if the library term is appropriate) which would help us copy and past them. It would save a lot of time when using, for instance the normal law... PS: I'm not sure of the tag below, tell me it's not the right one, I will change it right away.", "label": 1}
+{"snippet": "A question was recently asked on Musical Practice & Performance, asking what physical properties of silver would contribute to the sound of percussion instruments. It is likely to be off-topic there; I wondered if any of you physicists/material scientists would be able to offer a humble musician information on this site. It would also be interesting to know what contribution solid-silver or silver-plated components would make to brass/woodwind instruments, and what properties of silver are responsible for this.", "label": 1}
+{"snippet": "In many forums, I have seen people keep saying to avoid repetition of the same word in a paragraph. But in the sentence like below, how do you avoid the repetition? Suddenly, the dog stands up and stares at something in the hallway. A shadow of something enters the living room from the hallway. The dog continues to stare towards the hallway. I have to repeat the word hallway three times, and see no way to avoid it. Why and how should I avoid?", "label": 1}
+{"snippet": "I am looking for a word or expression, that describes the specific distance in the space that lets the observer appreciate and completely understand the object of observation. For example, when one is in a museum and stands too close to an impressionist painting, one can only see the brush strokes but not the flowers. But if one stands at the right distance, one can easily recognise the flowers and the whole garden. Is there an expression that describes the right distance to appreciate fully a given object? Thank you very much! anak", "label": 1}
+{"snippet": "I am starting to write my master thesis in latex. So far I have only written article-like texts, so this is my first big document. I would like to start with some good general good practices. Specially since I might go into academia and pursue a PhD. What are good principles to keep in mind?. For example, do you have one single huge tex file, or do you have several smaller files for each chapter?", "label": 1}
+{"snippet": "This was something I understood when we first went over it in class, but my text doesn't really cover it and I cannot find a direct answer online: If I use, say, the midpoint rule on a contour map to get the approximate value of an integral how can I determine if it is an over-approx. or under-approx.? Thanks! I should clarify that I am working with contour maps and double integrals- not single integrals.", "label": 1}
+{"snippet": "I am studying for the Berkeley Math Tournament (BMT) and I was wondering if anyone had any ideas on what I should study to prepare. This is my first math competition and would like to have as much practice before hand as possible. Also, taking a look at last years competition there are a lot of problems that I am unsure of where to begin approaching them, if anyone has any references that would help me learn the ideas and mathematics behind the problem it would be greatly appreciated. Thank you!", "label": 1}
+{"snippet": "Mass appears to attract other mass, irrespective of position or orientation. That is, gravity is attractive no matter what. Contrast that with electrostatic forces which could attract or repel depending on the charges involved, or a voltage between two metal plates which has a specifically directional force on electrons travelling through it. How do we know gravity attracts in all directions at once? What experiments have been done to confirm this?", "label": 1}
+{"snippet": "There's a word, I think that starts with a 'p', that describes doing something to solve a situation before it happens. For example, if a hurricane is approaching a store might take __ action to prepare for the flood of people that might come. In a fictional world, an organization might take __ action against crime based on some foreknowledge of a person's future actions. Edit It's not \"preparatory\", \"precautionary\", or \"preventative\".", "label": 1}
+{"snippet": "I'm looking for a word that is used quite often to mean something that feels real like you can reach out and grab it. Like it has substance. It's used most often around me to refer to user interface or game design. Like when a UI has weight and feels like it has substance behind it you say it's ............... I originally thought of... Visceral Corporeal Ephemeral (although I was looking for an antonym of this) But none of them are correct. But it is a word with the same \"al\" ending I think.", "label": 1}
+{"snippet": "As the title indicates, I'm trying to find books where the exposition of the main course of thought is done entirely or mostly in outlines of proofs, or as exercises with or without hints. I'm trying to force my reading to be more \"active\", and I think that such a book would be good training-wheels. No particular topics, but preferably something on the introductory level. I'm particularly interested in basic Differential Geometry and/or Algebraic Topology related topics right now. (I have \"undergraduate level\" background in Real Analysis, Abstract Algebra, Linear Algebra and General Topology, and I'm trying to get started with Algebraic Topology and Differential Geometry for my own personal and educational enrichment.) Texts on other topics would be welcome for later reference. Much thanks.", "label": 1}
+{"snippet": "I just finished reading (and understanding) Steiner's proof of the isoperimetric inequality. His proof (which is sadly incomplete) seems to rely much on the fact Steiner symmetrization preserves area and decreases perimeter. The only resource I've found which provides proof of those two things are Andrejs Treibergs' beamer slides , however ,they are confusing as he is a bit heavy on notation. Can someone please point me in the right direction on where I could find an alternative resource providing detailed proofs. If possible, a proof if you don't know a resource would be highly appreciated.", "label": 1}
+{"snippet": "Person A says to B: \"I thought you were smarter/stronger/better/more trustworthy than that. I should have known better.\" I was thinking it would be termed passive aggressive, but after reading up on it, that doesn't seem right. I'm tripped up on how focused on the Person A the two sentences are. Typically an insult would be \"You're not very smart\" and that would be that. But this is \"I'm disappointed in myself for thinking better of you.\" Is there a good term for this sort of insult?", "label": 1}
+{"snippet": "I have been using Windedt with Texlive since many days. But I stopped using it for a while, and when I now compile a tex file, its giving error \"The system cannot find the file specified\". I don't know wats wrong. I have used this before. I tried re-installing Winedt, no use. I have recently changed the System Path for installing some software. Has it affected in anyway?? Please help me.", "label": 1}
+{"snippet": "Please have a look at these two definitions: Chevalley-Eilenberg complex Koszul complex (German Wikipedia) Both are from Wikipedia pages on Lie algebra cohomology, and they look rather similar. Since I'm not very solid on the notation, I'm unsure about what's the difference between them. Furthermore, since both Wiki pages are about Lie algebra cohomology, and no page defines the \"other\" chain complex, I'm not even sure whether they are different at all. What's the essential difference between them?", "label": 1}
+{"snippet": "Does a definition need to provide a unique or near-unique description or can non-unique descriptions also be categorized as definitions? For example: Is the statement \"An apple is a fruit\" a definition of apple? Is the statement \"A car is something that gets people from place to place\" a definition of car? Are these simply descriptions (or categorizations) of the objects in question or are they also poor definitions?", "label": 1}
+{"snippet": "I've got a sci-fi based Physics question that involved Dark Energy... So I've been watching a lot of Doctor Who recently, and I'm very interested on how his \"Tardis\" is bigger on the inside. Here you can see the Tardis looks small on the outside. But inside, it's much bigger. So here is what I've been thinking. What if you got a box (like a Police Box), and somehow filled it with Dark Energy! Im hoping that the Dark Energy would expand space inside the box, thus making it \"bigger on the inside\". My question is, could this actually work? Thanks for your help. (This is just a fun question btw)", "label": 1}
+{"snippet": "Just as the title says: is there a formal name for a convex polygon on a sphere, of which the vertices are connected not by great circle but by small circle segments? My end goal is to intersect two (or more) of such shapes, and find the area of the shape where the two small-circle polygons overlap. It would therefore be helpful to get to know some basic and/or special properties of such shapes, what equations apply, etc.", "label": 1}
+{"snippet": "I'm trying to get the facts straight here. Suppose I'm throwing a ball with no angular momentum. It collides with the ground and Newton's third law tells us that a force opposite to the gravity will be applied to the ball at collision. During collision, the momentum will be converted to potential energy and then become kinetic energy again. Am I right to say that some of the kinetic energy can be converted to angular momentum, thus making the ball rebounce not straight up? (assuming some friction)", "label": 1}
+{"snippet": "It's just a casual observation, so I wanted to check it: A regular spring, when not completely compressed, looks an awful lot like a sine wave. The idea of a circular shape stretched out in the third dimension also seems to support it. But I can find no mention anywhere that such a spring actually is (or isn't) shapes like a sine wave. I don't want to tell my pupils this unless it is more than just an observed similarity. So is a stretched spring, if seen from the side, shaped like a sine wave?", "label": 1}
+{"snippet": "I want to read particularly about diophantine Analysis and Elementary Number Theory from a novice level. The books which I found on net: A Guide to Elementary Number Theory by Underwood Dudley Diophantine Analysis by Robert Daniel Carmichael Diophantine Analysis by Jorn Steuding Help me with good suggestions as I think M.SE. has people from novice to professional users. Thanks. P.S. I have searched M.SE. for this type of question, I didn't find any. If you know someone, you may give the link.", "label": 1}
+{"snippet": "What are some quantities often used to measure the sparseness of a graph? For example, in a graph, with the number of vertices fixed, the smaller the maximum degree is, the more sparse the graph is. With the maximum degree fixed, the bigger the number of vertices is, the more sparse the graph is. For another example, the more sparse the adjacent matrix is, the more sparse the graph is. Then it leads to another question: what are some quantities to measure the sparseness of a matrix? Thanks!", "label": 1}
+{"snippet": "I would like to know if a discontinuous local martingale with paths of finite variations almost surely is a martingale. I feel that it should be the case but can't find a straightforward argument. As noted by Did in its comments below, the continuous case follows easily from the widely known fact that continuous local martingales have paths of almost surely infinite variations. So I modified the question to make it more specifically about discontinuous local martingales. Best regards.", "label": 1}
+{"snippet": "Prove that a) the medians b) the altitudes and c) the angle bisectors drawn from the base angle of an isosceles triangle are congruent. Looking at this problem, I feel that this statement is just false. If you have an isosceles triangle given in the following link Link. Then clearly these are not congruent. Is there something in the problem that I am missing? Thanks", "label": 1}
+{"snippet": "I was told that a dielectric slab inserted into a capacitor connected to a battery (constant voltage) will be repelled, because the energy stored in the capacitor increases when the dielectric is inserted, due to increased capacitance. What is the physical origin of this force? The attractive force by a constant charge capacitor can be explained by fringe field, but why are the two cases different in terms of forces?", "label": 1}
+{"snippet": "What is the official rule when mentioning a city/ state in a sentence? I always thought there was a requirement for a comma between the city and state, however is there also supposed to be a comma afterwards? Tim also enjoys football games, jumping on his motorcycle and being a guide for the Fredrick, Alabama, restaurant scene. I personally think it looks clunky, however I'm told that it is opinionated and that the above is correct. Should the sentence be written like this? Tim also enjoys football games, jumping on his motorcycle and being a guide for the Fredrick, Alabama restaurant scene.", "label": 1}
+{"snippet": "I am new to studying abstract algebra (and math in general). I've been reading Gilligan and Pinter's books. I am trying to improve my understanding by doing exercises. However none of the books I am reading seem to come with exercise solutions. Is there an abstract algebra book with lots of exercise with solutions? I am confused as to why none of the math books come with complete exercise solutions. How do people verify that their answers are right.", "label": 1}
+{"snippet": "Using packages like minted (thanks to Pygments), LaTeX can generate beautifully highlighted/colored source code. Literate programming tools such as noweb and cweb can generate beautifully typeset and readable documentation. Ideally, I would like that the docs generated by noweb and cweb have high quality syntax coloring, and this seems like a problem that someone on either community may have tackled. So here is the question: Does anyone know how to get noweb and related tools to use minted or a similar LaTeX package for syntax coloring?", "label": 1}
+{"snippet": "I saw in my abstract algebra textbook that defines the gcd of a polynomial over a field (i.e. the coefficients of the polynomial is taken from a field). My question is that what happens if the field is not a real numbers? I mean intuitively, I always think of it as real numbers. Is there anything wrong in taking of it this way. Can someone give me an example of a polynomial taken from other fields such that thinking of it as real numbers will result in a misconception. Thank you.", "label": 1}
+{"snippet": "Is there any text that I can use as a short reference for the standard techniques for solving basic ODEs? I currently have been using Boyce and diPrima as my ODEs text, and it is far too wordy for my taste. I'm also not too interested in expositions of applications of physics or phase plane analysis, as I have other books for that. Basically, I'm looking for something short that can quickly remind me how to use techniques like integrating factors, series solutions, etc. which I keep on forgetting.", "label": 1}
+{"snippet": "I have two matrices(the first one is mxm, while the second one is nxn, m>n). They store data pertaining to human speech. The second matrix contains a data segment that acts like an acoustic \"signature\". I need to find where this data occurs in the first matrix. Which mathematical tool(s) or method(s) can I use to get it done? I know convolution can help me out but is this the best(more importantly fastest) way?", "label": 1}
+{"snippet": "For each relation, determine which of these properties are present: reflexivity, symmetry, antisymmetry, and transitivity: I know the definitions of each of the properties but unclear as to how to apply them to each relation. {(a,a), (a,b), (b,a), (c,c), (d,d)} {(a,a), (a,b), (a,d), (b,a), (b,b), (b,d), (c c), (d,a), (d,b), (d,d)} {(a,a), (a,b), (a,c), (a,d), (b,b), (b,d), (c,c), (c,d), (d,d)} Does anyone know what I would need to do to solve this?", "label": 1}
+{"snippet": "I'm looking for an adjective that describes that tasks should be approached \"one-ly\". To give some context: [Task] must be performed in one way and exclusively one way. or There must exist precisely one method of performing [task]. I am looking for an adjective that describes this \"one-ness\". The adjective does not need to specify what the method is, it should merely prescribe that the task should be approached in precisely one way. The closest word I could think of is \"uniform\".", "label": 1}
+{"snippet": "I just came across the term quantifier-free first-order formula, I first thought that might be similar to a propositional formula, but then after a closer evaluation I realized there are more concepts in first-order logic then just the quantifiers. I believe the difference is the following. A quantifier-free first-order formula can still contain: Function symbols Predicates where as a propositional formula does not have these concepts. Is that correct? Did I miss something?", "label": 1}
+{"snippet": "Please compare He shrugged. and He shrugged his shoulders. Is there anything else that can be shrugged, besides shoulders? To me it sounds like duplication when used in this way. I'm aware of constructs like \"He shrugged it off.\" but that's not what I'm interested in, and it also implies the use of shoulders, doesn't it? So why the need to specify the shoulders as an object? [edit: I also find \"he shrugged his eyebrows\" but that's rather rare.]", "label": 1}
+{"snippet": "Does the expression \"to add another dimension to the situation\" imply that the situation has become more complex? In Arabic we would say something like \"adds another dimension to the situation that has become more complex\". But I know English tends to be very economic and implicit. So if I wanted to express that idea, would \"adds another dimension to the situation\" be enough? Or do I have to say that the situation has become more complex?", "label": 1}
+{"snippet": "The statement of the Cayley-Hamilton Theorem is fairly straight-forward. I now know how to find characteristic polynomials from a given matrix (or at least a matrix with certain properties that I am unaware of!). I know that the eigenvalues of the matrix are roots of the polynomial. But what does having such a polynomial mean? Wikipedia says that the characteristic polynomial \"...encodes several important properties of the matrix...\", but once we have switched to \"matrix form\" of the equation, what can we conclude? In other words, what does the Theorem do for us, besides allowing us to say, \"Hey, I know a matrix solution to this polynomial\"?? Is there an abstraction of this in abstract algebra (rings, fields, etc.)? Thanks for your time.", "label": 1}
+{"snippet": "Is there a name for the practice of composing sentences in such a way that they don't contain proximate consonants which cause difficulty when read aloud? For example: Under this criteria, \"dogs and cats\" is preferable to \"cats and dogs,\" because the consecutive d s in the latter are difficult to pronounce clearly and distinctly and will force the speaker to either interrupt the flow of speech or elide the first d.", "label": 1}
+{"snippet": "During a sunny day the walls of my house warm up (no surprise). My question: how much of this warming up (if any) comes from visible light? I associate infrared with thermal energy. If my house was floating in space (to prevent any thermal exchange with its surroundings) and I installed a giant infrared (and UV) filter between it and the sun, would it still warm up (compared to its rest temperature in full darkness)?", "label": 1}
+{"snippet": "Does a matrix with all non-negative, real entries have all non-negative, real eigenvalues? Where might I find a proof of such? Ideas: Perhaps we can multiply a prospective eigenvector so its biggest entries are positive, and then show that it is a contradiction for it to have a negative eigenvalue? I am currently looking at the Perron-Frobenius theorem on Wikipedia, but it seems not to mention this issue. (I suspect my conjecture is not true.)", "label": 1}
+{"snippet": "I think the title says it all. I am planning on giving a talk in a few weeks about the Banach-Tarski paradox and I have some pdfs found online which describe the paradox a little but I am looking for a solid reference which covers the construction from A to Z and on which I can extract the main ideas for my talk from (I understand the ideas beneath the paradox, I am just looking for a formal proof with no details excluded,i.e. a well-structured document). Anyone has a reference in mind?", "label": 1}
+{"snippet": "For instance, would you rather say \"It became increasingly hard\" or \"It became increasingly harder\"? From my understanding, both are possible, but their meaning is slightly different. The first simply means that it became \"harder\". The second literally refers to an increasing rate of getting harder. Though in practice, I believe the second is still used to express the exact same as the first, while sounding somewhat awkward.", "label": 1}
+{"snippet": "I am looking for a specific word to describe a concept such that its meaning is linear and one-way. Such is the case for the title of this question. X would be of this concept and Y would not, Y would be the opposite of this concept. For example, all automobiles are motor vehicles but not all motor vehicles are automobiles. I cannot seem to find any word to relate to this. Any advice/guidance is very much appreciated.", "label": 1}
+{"snippet": "Traditional English prescriptive grammar teaches that these two verbs, to see and to hear, when describing their sensory nature, should never be used in the progressive aspect of tenses. Thus I am seeing you/I was seeing I am hearing you/I was hearing you would be incorrect. But in spoken English, whether it be in the movies or on television, this usage seems to me to become ever more often used. I am seeing you for I see you now I am hearing you for I hear you now When did this usage become so universally accepted? Is it still considered colloquial English? Or is it already considered standard English?", "label": 1}
+{"snippet": "I would like to create a table (cf. attached figure) and use curly brakes to summarize some of the cells. I did a lot of research and found this solution (Curly brackets around a table), but it doesn't help me much as it is only math content and I would like to enter text only. Does anyone have an idea about how to solve this problem elegantly? Cheers", "label": 1}
+{"snippet": "I realize there are questions on the correct usage of \"but\" and \"however\". In this case, I am concerned with correctness in a formal context. I have heard it said that however should be used in formal mail communications instead of but because the word \"but\" has a negative connotation. Which should I use in, say, an email to a client? Examples: We understand the issue you have pointed out, but we cannot consider it as a defect in the application since the current behavior was requested by your team. We understand the issue you have pointed out. However, we cannot consider it as a defect in the application since the current behavior was requested by your team.", "label": 1}
+{"snippet": "As I read on Wikipedia, the Rutherford atomic model is not correct according to classical electrodynamics, as it states that electron must radiate electromagnetic waves, lose energy and fall onto the nucleus. I don't understand this explanation. It is clear to me that with given acceleration directed to nucleus and proper speed, electron can move around the nucleus. I don't understand explanation about energy, but I understand that there must be some force directed to nucleus. Also this force must not be constant because if it is, a larger speed could keep electron moving around the nucleus. So what is that force? Why does this explanation on Wikipedia and on other resources operate with energy, not with force?", "label": 1}
+{"snippet": "I'm reasonably happy with the dictionary functionality in TeXworks but I am struggling to see how I can 'find' all the spelling mistakes in my (painfully long) tex file. I was hoping for a Wordesque spell checker in which I can scroll through each of my errors and accept or ignore the suggested changes. I could install another editor that has this functionality but would prefer not to do this if possible.", "label": 1}
+{"snippet": "I am wondering if the verb expect is used as a stative verb in the following sentence: I entered the classroom and [to expect] to see some students but instead I found a note which said [...] Would it be possible to say \"I was expecting\"? Or is the verb stative in this context? Because then we can't use it in a continuous form, according to my grammar book.", "label": 1}
+{"snippet": "Can anyone please explain why light reflects at the boundary between two regions with different impedances? This sounds very simple but I got confused when I tried to think of how light and atoms interact with one another at the boundary. This question can actually be generalised to the reflection of all types of waves. I have to admit I have no understanding of the microscopic detail of reflection.", "label": 1}
+{"snippet": "I believe I am stuck with only these two options, but would appreciate an alternative usage. I am somewhat limited on sentence structure as this application is part of a mail merge document. The purpose of the business is to own and operate The Tutoring Center franchise location. OR The purpose of the business is to own and operate a The Tutoring Center franchise location. Since the business will be a franchise (one of many), I feel the article \"a\" is necessary. Help is much appreciated!", "label": 1}
+{"snippet": "What are the desirable pre-requisites to be able to learn model theory well? In particular, it seems that connections to algebra are used heavily especially as examples. I would like to know if a good grasp of algebra is essential for a deeper understanding of model theory and whether a good grasp of analysis and topology would compensate for lack of the former. Thank you.", "label": 1}
+{"snippet": "I have started learning some basics of Category Theory.Currently i am trying to understand the concept of Direct limit and Inverse Limit but i find this concept really hard to digest. Could some one explain me with some details the good idea to think about Direct Limit and Inverse limit in practice? I have knowledge of subjects like Module Theory,Galois Theory,Commutative Algebra(at the level of Atiyah Macdonald),Basics of Lie Algebra and of course elementary topics like Group theory and field theory etc.", "label": 1}
+{"snippet": "I'm interested in using TikZ to draw rooted trees whose leaves should all be on the same level, pretty much like this: Please don't pay attention to the fancy style and colours, I'm only interested in having all leaves at the same level. Anyone knows how to do this? I've looked into the manual and the appropriate section on Texample, but had no luck so far. UPDATE: a while after this question was answered, I found out about the LaTeX newicktree package, which allows you to draw such trees in an extremely simple way, just by specifying them in the format people in phylogenetics already use. This is obviously much simpler than resorting to TikZ, but thanks anyway to everyone who contributed to helping me.", "label": 1}
+{"snippet": "My understanding is that dark matter cannot be (or is at least highly unlikely to be) an exotic form of any known particle. On the other hand, articles about particle accelerators seem to say that the Higgs is the last piece missing in the Standard Model jigsaw puzzle. If dark matter is determined to be some form of new particle, what are the certain implications? Might such a discovery \"stand to the side\" of the Standard Model or would it certainly change the foundations? (Forgive my extremely lay understanding and vocabulary -- please feel free to correct my mistakes.)", "label": 1}
+{"snippet": "If I pick up a rock and set it on a ledge above my head, I do work in the process. The work I do is termed \"potential energy\". We know how to recover the energy (i.e. let it fall back to earth). However, while resting above the surface the energy is said to be \"stored in the gravitational field\", presumably meaning the space between the elevated rock and earth. Suppose we perform this experiment on the moon where we know the space between the elevated rock and surface consists of an empty vacuum of space which contains absolutely nothing. How can empty space store energy? That is, how can \"nothing\" have any properties whatsoever?", "label": 1}
+{"snippet": "I was writing an email and faced the following situation: I am coming to Oxford this summer. If you are still around, I would be glad to hang out with you. Now normally we don't construct the conditional statement like the one above, where a present verb is followed by would. But if I change the second one to will it kind of becomes very direct and that's not what I want. So is the construction above still correct or should I go with something else? If it's correct, could someone explian the technical details behind it?", "label": 1}
+{"snippet": "Im studying old exams and came across this one Question: a. Find a (discrete time or continuous time) random process that is wide-sense stationary (WSS) but not strict-sense stationary. b. Also, is it possible for a strict-sense stationary random process not to be wide-sense stationary? Answer: a. A sequence of uncorrelated random variables with common expected values and common variances constitute a WSS discrete time process, but is not strict-sense stationary if the random variables are not identically distributed. b. A seqeunce of independent identically distributed random variables with infinite variances constitute a strict-sense stationary discrete time process that is not WSS. a. Can anyone give a simple example of such a process? b. Our course litterature says WSS processes are always strict-sense stationary?!?", "label": 1}
+{"snippet": "I remember being presented a mathematical puzzle some years back that I still can't solve. The problem is defined as follows: We have two points on a plane, and using only a compass, how do we find other two points, so that all four of them would be vertices of a square? I'm not sure whether the first two points were supposed to be vertices of the same edge of a square or not, so solutions to both variants are welcome.", "label": 1}
+{"snippet": "I know the word uxorious that is used to describe a husband who dotes on his wife excessively. What is the corresponding word for a wife who loves her husband dearly? I cannot pull anything out of my memory... and I feel it is very harsh on men if such a word weren't there! Example: He was an uxorious man who assiduously took care of all of his wife's needs. She was a __ woman who assiduously took care of all of her husband's needs.", "label": 1}
+{"snippet": "I don't know if the title of this question is accurate or not. My vacabulary of grammar is very limited. May you could understand me by the following example: She told me that the earth is moving around the sun. She told me that the earth was moving around the sun. Which one is correct? Should the tense in that clause always agree with the tense in main clause?", "label": 1}
+{"snippet": "A lot of text books mention that one of the reasons that classical mechanics failed to explain atomic and subatomic processes is that electrons which accelerate should release energy in the form of electromagnetic radiation, which would lower the atoms overall energy level, but this does not happen. One place where I discovered this, for example, is in the description for the Bohr model. What I don't understand is why everyone takes for granted the fact that the electron is accelerating. I thought the electron orbits the nucleus at a, more or less, constant velocity. Are people referring to specific situations when the atom is excited? Furthermore, I was under the impression that electrons already travel at the fastest allowable speed, the speed of light.", "label": 1}
+{"snippet": "Okay, I am in no way a mathematics student but I happened to be writing a program on a map with coordinates of locations displayed on the map. My problem is that the points could be scattered on the map with an indefinite boundary and I need to find a boundary (rectangle) around these points and thus I need to get a formula to form an algorithm so that the program will find the optimum boundary itself. I hope this is understandable and thanks in anticipation of any response.", "label": 1}
+{"snippet": "I'm a high school student. The head is hydrophilic, the tail is fatty acid, in other words hydrophobic. Here is the thing I don't understand, all textbooks state that water is repelled by hydrophobic tail, why? The hydrophilic head is composed of polar molecules, and water is polar, so they will attract each other. But why hydrophobic tail will repel polar molecule? Isn't hydrophobic tail is just composed of non-polar molecules?", "label": 1}
+{"snippet": "Consider this situation: You sent an application for a job, then the company boss sends you an email, and tells you if you are in town, he likes to meet you in person. Is it correct to say? \"It could have been a great pleasure to meet you, but unfortunately I am currently in Russia.\" I'm not sure what tense I should use, and I'm pretty sure the above sentence is incorrect. At the same time, I want it as much as possible in a formal and polite way.", "label": 1}
+{"snippet": "I am trying to use IEEETrans to write a scientific paper in two column format. The issue is that one is not allowed to place figures in the left-hand side column of the first page. Figures should start on the top of the right-hand side column of the first page or alternatively, on the second page (any column). Is there any way to restrict the placement of floats to avoid using the left-hand side column of the first page?", "label": 1}
+{"snippet": "In sports, we have the term \"Commentator's curse\", (humorous) The supposed propensity of a player to blunder after having his/her talents pointed out by the commentator. [Wiktionary] Is there a phrase that emphasizes that the sportsperson performed brilliantly soon after the commentator's talk highly about their achievements? For instance, a Cricket player hitting a six immediately after the commentator says that he has the highest number of sixes for his team. Or a Football (Soccer) player scoring from way outside the D-box just when the commentator says that the player had scored from a similar distance in the previous game. It might be termed as \"pure co-incidence\" but I'm just looking for something humorous/ emphatic as \"commentator's curse\" itself.", "label": 1}
+{"snippet": "I know that massive gravitational bodies will curve the path that light travels. I think that quantum optical mediums also bend light. I am still confused of whether quantum optical mediums actually slow down light or if they just use absorption, re-emission, scattering, and delaying to create the illusion that light slows down in a medium. I do not see a fundamental difference between the two theories, because both describe \"optical\" phenomena of light. I am not sure if gravitational optics is a real field of study or a made up name. My question is there a mathematical equivalence between gravitational optics and quantum optics or are they mathematically incompatible theories?", "label": 1}
+{"snippet": "Most of the references I found online simply note that \"see you later\" is a farewell or parting phrase but nothing discussed when it is appropriate to use the phrase. Is it acceptable to use \"see you later\" in each of the following circumstances? When you will be seeing the person again later that day When you will be seeing the person soon (e.g., in a few days) When you will be seeing the person again at some point in the future (e.g., next year at Christmas) When you are suggesting that you want schedule something specific Whenever you say goodbye, regardless of whether or not you will ever see them again", "label": 1}
+{"snippet": "I am reading up on splines and as a beginner I have a basic question - Does it make sense to say - \"I will fit a cubic b-spline to the data\". As b-spline is just a representation of spline in terms of its bases. I think, a more accurate statement will be - \"I will fit a natural/not-a-knot/clamped/etc. cubic spline to the data and present results in terms of its basis.\" My question arises out of my limited understanding of relevant concepts. Could someone please confirm this. Many thanks!", "label": 1}
+{"snippet": "At the moment I'm a bit baffled. What sentence part is \"visitors\" in \"I'm not allowed visitors\"? I would not call it an object or a subject complement as \"to be allowed\" is no linking verb. The only idea I have is to say the sentence is elliptic and the full form would be \"I'm not allowed to have visitors\". Here \"visitors\" is object of the to-infinitive. So is it possible to say \"visitors\" is object of a to-infinitive (to have) that was deleted?", "label": 1}
+{"snippet": "As far as I understand, the incident photon interacts by photoelectric, Compton scattering or pair production with the electrons of the crystal (NaI(Tl) in our case). The electron that emerges from these interactions generates a number of photons in the UV or visible which are proportional to the gamma ray energy. Then, the light produced can be read out with photodiodes, photomultpliers, avalanche photodiodes, silicon photomultipliers, and other photo sensors, right?. So, how are those electrons converted into UV or visible photons?", "label": 1}
+{"snippet": "I've read here that microwaves are blocked by the holes in a microwave window because the holes on the door are small enough to prevent the microwaves from passing through. However, if wavelength is only the distance between successive crests of a wave, why should that decide what a certain wave can fit through? Why is amplitude not the deciding factor and is there a way to explain this visually?", "label": 1}
+{"snippet": "Projectiles containing delicate elecrtronic equipment may be damaged if they are subjected to high accelerations. For this reason, such projectiles may be fired from guns with long barrels but not from guns with short barrels. -Explain why a projectile fired from a long-barreled gun is subject to less acceleration than a projectile fired from a short-barrelled gun if the range is the same in both cases. This question has been a nightmare for me when i was in highschool and until now i cant have a good answer your help would be appreciated.", "label": 1}
+{"snippet": "I am new to LyX so I'm sorry if this question is really naive. I'm using LyX on a MacBook and I'm hoping to use the AEA document class on it. Since it is not available automatically, seems that I need to somehow install it on my own. All the help pages I can find talks about layouts and stuff that I, as total layman, have no idea what they are. Can somebody please show me how I can do it with simple language?", "label": 1}
+{"snippet": "I'm reading about how a \"straight line\" depends on the geometry of space. While I think I understand this, the example people give is: \"Imagine a straight line on earth connecting two cities. It's actually curved because the earth is curved\". My response to that would be \"Well no, because a truly straight line would cut through the earth. Like a straight string would cut through an apple\". So question: If two people took an infinitely strong and light string, stood on opposite ends of the earth, and pulled almost infinitely tightly, would the string curve around the earth a few feet above, or would it cut through to the core?", "label": 1}
+{"snippet": "I am currently reading the following paper by F.Takens: Multifractal analysis of dimensions and entropies. This paper discusses two different measures. One is generalized entropies and the other is generalized dimensions, however as far as I can see it doesn't discuss any association between the two. Can somebody please in a qualitative or [even better] quantitative give me an explanation about the relation between the two?", "label": 1}
+{"snippet": "Our course slides offer the following definition: \"A parametric probabilistic model is a set of probability distributions indexed by a finite-dimensional parameter vector.\" This description defines \"parametric probabilistic model\" in terms of \"parameter\", which isn't particularly helpful. But it brings to mind some vector of indices which tells you where to find a row (or rows) in a table. It is not clear to me whether \"parameter\" in this sense is related to my CS understanding of a parameter (i.e., a \"knob\") or even if a model's parameters have something to do with its random variables (e.g., are the parameters fixed values of a random variable?). Furthermore, what does it mean to \"parameterize\" a model?", "label": 1}
+{"snippet": "I have this question on a homework assignment. I sat down with two other people for a long time and we derived the alternating harmonic series example, but I don't think that's valid because the question explicitly asks about sequences and not series. Note that it's for an analysis class and so far we've covered open and closed sets and balls, preimages, and cluster points.", "label": 1}
+{"snippet": "I've read through answers to similar questions, and I haven't been able to find a satisfying answer. I've heard it said that in order to make out something, you need to use light with a wavelength at least as large as the object. In what way can you mathematically derive this heuristic? Moreover, does this apply generally? The other day I was thinking in the context of sound waves and how fruit bats use them to resolve insects- is this a reason why they use high frequencies?", "label": 1}
+{"snippet": "Question: What are some interesting or useful applications of the Hahn-Banach theorem(s)? Motivation: Most of the time, I dislike most of Analysis. During a final examination, a question sparked my interest in the Hahn-Banach theorem(s). One of my favorite things to do is to write a math blog (mlog?) post about various topics so that I can better understand them, but I know very little about Hahn-Banach and a quick google search didn't seem to point to anything neat. I was interested in seeing what you all liked (if anything!) about the Hahn-Banach Theorems. Also, I can't seem to make this a community wiki, but I think it ought to be one. If someone could either fix this, I would appreciate it! (If not, please delete this!)", "label": 1}
+{"snippet": "is it possible to use participial prepositions in the following sense, or am I creating a dangling modifier. Moreover, is the punctuation correct? Considering his broken leg, Peter was not able to walk anymore. Peter was not able to walk anymore considering his broken leg. Understanding Einstein's statements is neccessary, since Peter wants to graduate in Physics in order to get a good job. Since Peter wants to graduate in Physics understanding Einstein's statements is neccessary, in order to get a good job. Can participial preposition be used as subordinating conjunctions? Maybe a native could help me out here. Thanks!", "label": 1}
+{"snippet": "Special relativity theory says simultaneity is relative, meaning that different observers will not agree on what happened first and what second. Does it then make sense to say that looking at distant stars, we see them how they looked \"billions of years ago\" and not how they look now? Does it make sense to talk about what these stars look like now? How do we define this \"now\" if simultaneity is relative?", "label": 1}
+{"snippet": "So there is this kind of building located in the centre of a fork in the road (maybe in streets too). I don't know how to put it into words, but it looks like this: Or this: Is there a single English word for that kind of building? If it is a house, is there another name for that? In my native language (Indonesian), it's called Rumah Tusuk Sate. Which if translated bluntly into English, it's Skewer House, which sounds a bit weird to me.", "label": 1}
+{"snippet": "Possible Duplicate: Why the use of 'would' in the following When we tell a joke or narrate a story in simple present can we use 'would' in some cases? For example: He goes up to this man and punches him in the face. The man looks straight into his eyes and tells him that he will take revenge He goes up to this man and punches him in the face. The man looks straight into his eyes and tells him that he would take revenge", "label": 1}
+{"snippet": "According to this extract from Wikipedia, the pronunciation of the term piste meaning \"a ski run of compacted snow.\": varies slightly in English, with British English using a long \"e\", (e.g. rhymes with \"beast\"), and American pronunciation using a short \"i\" (e.g. rhymes with \"list\"). Actually, references such as the Cambridge Dictionary or the ODO suggest that the pronunciation is the same in both dialects, that is, with a long \"e\". Does the AmE pronunciation of \"piste\" really differ from the BrE one, or are both versions correct?", "label": 1}
+{"snippet": "I am finding hard to understand application of inclusion and exclusion in Matching problem? Suppose that n- n male-female couples are at a party and that the males and females are randomly paired for a dance ? what is the probability that none of the couple are paired together? I don't understand why we have to take Union then use inc-ex principle to solve it? Can some one help me to understand ? Thank you", "label": 1}
+{"snippet": "I'm struggling to find a way to express the idea that it's possible that something was done before something else was done. I'm not sure if I'm just tired, but the idea is this: In the present perfect, you would say \"it has been done before\". When you add \"may\" it becomes \"it may have been done already\". In the perfect past, you would say \"it had been done before\". How does that sentence look like when you add \"may\" to it? \"It might have been done before\"? \"It may have been done before\"? Or even \"it may have had been done before\", as clumsy as it sounds? None of these sound particularly correct, so I'm at a loss as to what the solution here is.", "label": 1}
+{"snippet": "If we consider two spins, we can think of the spins as being either parallel (up|up or down|down)or anti-parallel (up|down or down|up). Or we can think of them as being in the triplet or singlet configuration. Is one description more correct than the other? Or is it just a matter of choice between two basis sets? It would seem to me that using T/S is correct because it accurately reflects the symmetry needed in the wavefunction.", "label": 1}
+{"snippet": "Find the distribution of U=min(X,Y) where X and Y are independent random variables and both exponentially distributed with parameters lambda and mu respectively. The only headway I have made is that P(U< u)= P(X< u)P(Y< u) by considering the joint distribution of X and Y and the fact X and Y are independent; is this right? If it is then U isn't a 'named' distribution function so is just stating the cdf enough to answer the question?", "label": 1}
+{"snippet": "I've noticed \"At this stage\" preceding delivery of the negative to the reader. What's the reason for this? \"At this stage, unfortunately (for you), we won't be proceeding further with your application.\" \"At this stage, your application has been declined.\" \"At this stage, travel arrangements will be at your expense.\" This is used when there are no other stages. Why do people use this adverbial phrase? do you think it helps the reader to deal with emotional pain?", "label": 1}
+{"snippet": "In Thomas Harvey's Elementary Grammar and Compsition he says: A complex sentence whose subject or predicate only is a clause, need not be separated into principal and subordinate clauses in analysis. Later in the section he gives the example, \"That he is very sick, is evident,\" parses the sentence, then gives a sentence diagram. I'm curious how one would break this sentence into its principal and subordinate clause.", "label": 1}
+{"snippet": "I am studying probabilites and the notion of poisson random variable was introduced in the class. But it seems to me that the introduction of poisson random variable is to provide a easy approximation of the binomial random variable conditioned that n is large and p is small. Besides, the preconditions in the poisson distribution that events are independent of each other seem to come from the fact that binomial random variable is composed by many independent bernouli variables. So I wonder if originally, poisson distribution was invented to model binomial distribution or was it invented to solve a particular kind of problem", "label": 1}
+{"snippet": "For some pdf ebooks, Adobe Reader displays the cover page alone even though the display mode is \"two page view\". Other than the cover page, the rest of the pdf content is displayed as two pages at once, which is expected in the \"two page view\" mode. My question is: Is it possible to enforce this behavior if I use pdflatex, and if so, how could I achieve that? The document class I'm using is memoir.", "label": 1}
+{"snippet": "In algebraic geometry, we often consider a complex algebraic curve, and in order to get some intuition, we often draw it on the plane as if it were a plane curve. In most cases it turns out that the plane drawing really helps us thinking of the curve for instance when counting the number of intersections. Then I wonder, to what extent the plane drawing is legitimate (or not misleading) to \"represent\" the complex algebraic curve?", "label": 1}
+{"snippet": "I have noticed that when certain tube-lights are switched 'ON' , they make certain noise corresponding to their \"blinking\". In blinking, there are alternate periods of the tube lighting up and then going out. The \"sound\" is heard at the instant the tube lights up. I can not properly describe the \"noise\" or the \"sound\" I'm referring to, but it seems as if the tube-light is struck gently with something. It feels as if the gas molecules inside the tube-light are striking its inner surface. Can anybody explain this ?", "label": 1}
+{"snippet": "In this question... Why does a photon colliding with an atomic nucleus cause pair production? ...I asked why a photon colliding with a atomic nucleus can become an electron and a positron. The answer that I thought was most illuminating explained that a photon spends some of its travel time as a particle-antiparticle pair of an electron and a positron. If it strikes the nucleus at the right time, this pair will be separated. It was explained that this is because 'Quantum Electrodynamics allows it'. Why does Quantum Electrodynamics allow a photon to exist temporarily as an electron and a positron?", "label": 1}
+{"snippet": "In batteries, what exactly do we mean by negative and positive charges? My understanding is that the negative charge of the anode is basically an atom with an extra electron in the last orbital and a minus electron in the last orbit of the positively charged atoms in the cathode? And so the electrons keep flowing and interchanging because the atom is trying to reach a stable state. Is this correct or am I wrong? If my understanding of positively/negatively charged atoms is correct, what do we mean by saying that the electron in itself has a negative charge?", "label": 1}
+{"snippet": "Most books on strongly correlated electrons claim that when the number of itinerant electrons is small and the screening length is large, that the system becomes \"strongly correlated\", (i.e. the independent electron approximation breaks down). If this is the case, why isn't doped silicon (or some other semiconductor/insulator) a strongly correlated electron system at low temperature where there are no thermal carriers? What are the critical ingredients that make a system unwilling to abide by the independent electron approximation?", "label": 1}
+{"snippet": "I am trying to draw an activation stack. I am really bat at TikZ, so I hope you can help me out. As you can see, there are four boxes stacked one on top of the other. Each box has a name, put on the right, and is made of an upper part, where variables and numbers are displayed, and a lower part which is divided in two halves. The left half has to contain an arrow pointing to one of the boxes placed under it, the right half contains only a few characters. The box at the bottom hdoesn't have a pointy arrow, because it doesn't have to reference anything. I really hope you can help me out, I really appreciate it.", "label": 1}
+{"snippet": "A lot of textbooks and exam boards claim that light incident at exactly the critical angle is transmitted along the media boundary (i.e. at right-angles to the normal), but this seems to violate the principle of reversibility in classical physics. How would a photon or ray travelling in the reverse direction \"know\" when to enter the higher refracting medium? It can't know, so I conclude that such light is simply reflected? Is this correct?", "label": 1}
+{"snippet": "My question is regarding effect of Sun's gravity on earth. I want to know that if Sun's gravity can change Earth's landscape in long duration (i.e. billion of years) or not? Means if earth is dead planet and all other planets are not present in the solar system and Earth is as near as Sun as mercury currently orbiting. And also suppose Earth's surface is not smooth (because of hitting with other small bodies at regular interval) then can Earth's surface can be smooth in long duration by gravity of Sun or not?", "label": 1}
+{"snippet": "Let A and E be opposite vertices of an octagon. A frog starts at vertex A. From any vertex except E it jumps to one of the two adjacent vertices. When it reaches E it stops. Let a(n) be the number of distinct paths of exactly n jumps ending at E. Find a(n) Is it right if I conclude that number of steps has to be an even number ? Also I don't know how to go further with that except I think recursion is involved. P.S. I'm having trouble solving questions in probability and combinatorics where recursions are involved like finding expected value ones. Can you provide me suggest me some links/books through which I can understand it better. Thanks", "label": 1}
+{"snippet": "I have a question that I am just curious about. Two principles: Magnetic fields and Magnetic susceptibility Supercavitation is the use of cavitation effects to create a bubble of gas inside a liquid large enough to encompass an object traveling through the liquid, greatly reducing the skin friction drag on the object and enabling achievement of very high speeds. Can a magnetic field hold a state of supercavitation if a magnetic field could be placed inside of the bubble of the supercavitation?", "label": 1}
+{"snippet": "Some people love creating or fostering the creation of events that are noisy, chaotic and fun, such as parties, arguments, reunions, etc. Sometimes there's a negative connotation to this (like in provoking an argument), but sometimes there is not (like in organising a big, noisy party). The word I'm looking for would be the English equivalent to the Spanish armadanzas, just in case this is helpful. Any ideas?", "label": 1}
+{"snippet": "Earlier, I asked here whether one can have spontaneous breaking of the Lorentz symmetry and was shown a Lorentz invariant term that can drive the vacuum to not be Lorentz invariant. How relaxed are the assumptions in the CPT theorem? Can one have the theorem to be valid for a Lorentz invariant theory with a vacuum that breaks it? Can someone point me to the original and alternate proofs of this theorem? Also, is there any connection between CPT invariance and renormalizability?", "label": 1}
+{"snippet": "Why is it said that electric current always flows from higher potential to lower potential? It's said that current flows from a positive terminal to a negative terminal, but I've read that it is actually the [negative] electrons that flow from the negative terminal to the positive one. Rather isn't it that the protons don't even move? My question here is in reference to electric circuits with batteries generally used in textbooks.", "label": 1}
+{"snippet": "\"Half of the time I was working from about eight in the morning until eight at night, and the other half I was incapacitated by excruciating pain.\" This is what I have currently. Is this correct or is there a better way to approach this sentence? To be specific, I am wondering about my comma usage, and whether or not more commas should be added, however, all tips are welcome. Thank you.", "label": 1}
+{"snippet": "I learned a lot from prof Tao's notes and books because unlike many authors, he seems to prefer writing more words, explanations and intuitions rather than just mathematical formulae. His approach is also very pedagogical, and quite often, when talking about one concept, he also talks about similar concept in other fields, like group theory, differential geometry, etc. (due to his very broad areas of expertise). This makes me understand (superfically) how mathematical concepts are related to each other. I would like to know if there are some books or blogs on probability theory, stochastic processes, Monte Carlo and convex optimisation, with similar writing style and approach. Many thanks!!!", "label": 1}
+{"snippet": "I'm new in this study and I don't know much about the foundations of mathematics, so I have a question. If I'm doing category theory, and I need to talk about \"small categories\" , \"locally small\" and etc, I need to have some set theory foundation like NBG where I can talk about this things, right? But, if I want to take the category of all categories, I will have some problem in this context with NBG as foundation?", "label": 1}
+{"snippet": "I'm looking for a foundational book that builds up ideas like transcendental functions. For example, how the trigonometric functions are truly defined when plotted as continuous functions. I believe Shilov briefly touches on this in his \"Elementary Real and Complex Analysis\", but I'd like a more broad and in-depth treatment - book that, in general, deals with mostly functions (and maybe continuity/their limits). Meant for a freshman mathematics major. Books that are entirely dedicated to this topic are preferred over others wherein this topic is only treated in passing.", "label": 1}
+{"snippet": "We all know that it uses less energy to go by wheeled transport than walking if the terrain is smooth and there are not too many hills. We also all know that when going up steep hills we get off whatever wheeled transport we are using and walk. To make things concrete, let us consider a child's scooter. How can one calculate the steepness of the hill at which point you would use more energy to scoot than to walk?", "label": 1}
+{"snippet": "The phrasal verb \"sit on sth\" means \"to be a member of a group of people\". Well, according to Longman, \"to sit in / on sth\" means \"to be a member of a committee, parliament, or other official group\", the same thing. I don't know why my phrasal verbs book \"says\" just \"sit on sth\" and doesn't say the \"in\" too. Perhaps Parliament can only be used with \"in\" with this meaning, I don't know. When I found the meaning of \"sit on sth\" for the first time, I realised that I could say \"To sit on a Parliament\" and not \"To sit in a Parliament\". Is my phrasal vebs book incomplete? Can \"sit on a Parliament\" be correct? I hope you understand my question.", "label": 1}
+{"snippet": "I was wondering how one would actually calculate how much oxygen would dissolve into water given the necessary initial conditions, and what those initial conditions would need to be. I assume they would be pressure, and initial concentration, but I really don't know where I would go from there. Clearly air and water have different concentrations of gases and liquids, despite having been in contact for thousands of years. And once in water, is oxygen still considered gaseous? I assume it is, but why is it called gaseous-what quality of it deems it a gas despite being surrounded by liquid?", "label": 1}
+{"snippet": "I'm designing a space ship for a comic I'm writing. I was just finishing up the first sketch when I thought whether such a design would actually be possible. Hence my question: A spaceship is located in deep space. A propulsion system (let's make it a rocket) is attached to the side, and thus not in one line with the ship's center. Would this spaceship travel in a straight line, or rotate?", "label": 1}
+{"snippet": "Let S be the intersection of diagonals in a cyclic quadrilateral. Let p be a circumcircle of a triangle ABS and it intersects BC in M and q is a circumcircle of a triangle ADS and q intersects CD in N. Prove that M, N and S are collinear. I tried proving that vectors NC and DC are the same, and also that vectors CM and CB are equal but nothing seemed to work. I'm probably not thinking right.", "label": 1}
+{"snippet": "Question: Why is ionic lattice energy inversely proportional to the radius of the atom? Most heterogeneous covalent molecules are polar to some extent. The degree of polarity, or the dipole moment, depends on the difference in electronegativity difference between the two atoms. The larger the dipole moment, the higher the ionic character. What I know: Electronegativity decreases as you go downward in a group, however, the size increases, usually, as you go downwards in a group. Thus, ionic character will increase upon going downward, but the ionic lattice energy will decrease? This seems contradictory. Is this true? And if it is, why is it so?", "label": 1}
+{"snippet": "As far as I know, a magnetic field can only be produced by a moving electric charge, or from a particle's spin (this is how a permanent magnet works, all the spins are in the same direction) What is strength and direction of the magnetic field of a stationary electron at the origin with spin oriented straight up? I suspect a function of cylindrical coordinates is most convenient.", "label": 1}
+{"snippet": "I would like to know the status of the following problem: Given a simple graph, is there a walk traversing each vertex at least once and each edge at most once? (I am asking for a complete trail, a sort of cross-breed between Eulerian and Hamitonian walks, in a way.) In particular, is that problem known to be solvable in polynomial time, or NP-complete? Or is it suspected to belong in NPI? More generally, what is known on it? Variants: One could also ask for a circuit rather than a trail, and/or consider oriented graphs instead. Thanks in advance!", "label": 1}
+{"snippet": "Sometimes I'll look at a word for too long and I become convinced that it's spelled or pronounced incorrectly. This happens most frequently with \"spider\" (I think that should be pronounced \"spih-dur\" [like \"spitter\"], not \"speye-dur\") and happened just now with \"finger\" (\"fin-gur\", not \"feen-gur\"). There's a similar variant to this (discussed here), but that's related to a word losing it's meaning. To me, the word just looks incorrectly spelled, or I convince myself that everyone's pronouncing it incorrectly. Is there a difference between what I'm describing and Semantic Satiation? If there is a difference, does this one have a name?", "label": 1}
+{"snippet": "I'm currently studying Single-Variable Calculus independantly through MIT OCW. I can only focus on one course at a time independantly since it takes up so much time, and I really want to study Linear Algebra next instead of Multi-Variable Calculus. My question is simply this: after understanding Single-Variable Calculus, would I be able to continue into and understand Linear Algebra, or should I do Multi-Variable Calculus first?", "label": 1}
+{"snippet": "I've just been wondering about how atoms and molecules can be quantum mechanically thought about, and I have a question. It is often said that intermolecular bonding is purely \"electrostatic\". I hope what this means is that it is easier to consider molecules as point charges that are attracted, but in reality, there is some sort of orbital superposition, but the small distances between different charges within a molecule don't really matter. Is it correct to say that the essential physics is captured by considering the particles as classical Coulomb charges?", "label": 1}
+{"snippet": "Are binary systems (in case of stars and other celestial bodies) more favorable than independent existence? I've been going through an article regarding pulsars, where it was stated that 'many pulsars are found in binary systems.The companion of pulsars have been found to be normal stars, planets, white dwarf stars, neutron stars and even another pulsar. So what are the criteria to form binary systems ? I know that their sizes should be comparable, and that leads to the equilibrium of the gravitational attraction between the bodies, etc. As it is a known fact that neutron stars and pulsars are quite heavy and dense, how are they able to co-exist as binary systems with other stars, planets, etc.? Search this @ http://outreach.atnf.csiro.au/education/everyone/pulsars/", "label": 1}
+{"snippet": "Source: gradestack.com This is a problem I am trying to solve for a long time. But still not able to proceed. After spending some time, I got a doubt whether this question is correct. Because, in a rhombus, diagonals bisects each other. Here PA=PC. That means, P is the center point of diagonal AC. So PD must be equal to PB which is not the case. Why I am wrong here? Please give pointers in how to solve this problem. thanks.", "label": 1}
+{"snippet": "I am interested in why many small animals such as ants can lift many times their own weight, yet we don't see any large animals capable of such a feat. It has been suggested to me that this is due to physics, but I am not even sure what to search for. Could someone explain why indeed it is easy for smaller objects/lifeforms to support several times their own weight, but this is harder as objects/animals become larger?", "label": 1}
+{"snippet": "A set of r marbles is selected from an infinite supply of red, blue, white and yellow marbles. A selection must satisfy the condition that either the number of red marbles is even and the number of blue marbles is odd, or the number of white marbles is even and the number of yellow marbles is odd. Does it mean a selection is invalid when both red is even and blue is odd as well as white is even and yellow is odd ? Do we discard this case while counting the number of selection ?", "label": 1}
+{"snippet": "I am looking about similar triangles and I always see the word corresponding but I always forget to include it in the definition. I am trying to think of an example I can use to show the importance of the word corresponding. So here is the definition: Ex: \"If the measures of the corresponding sides of two triangles are proportional then the triangles are similar.\" So if the word corresponding is not in the definition: \"If the measures of the sides of two triangles are proportional then the triangles are similar.\" but what is so important about the word corresponding? Any ideas?", "label": 1}
+{"snippet": "Most of the proofs of the Cauchy-Schwarz inequality on a pre-Hilbert space use a fact that if a quadratic polynomial with real coefficients takes positive values everywhere on the real line, then its discriminant is negative(e.g. Conway: A course in functional analysis). I think this is somewhat tricky. Moreover I often forget its proof when the pre-Hilbert space is defined over the field of complex numbers. Is there a more natural proof (hence it's easy to remember) which is based on a completely different idea?", "label": 1}
+{"snippet": "Autorefractors are being used by eye opticians for eye diagnosis. I searched internet for articles and wiki page as well but I wasn't satisfied. I am interested to know how do they actually work. How the machine is able to focus sharp on retina automatically. How do they figure out spherical/cylindrical aberration for human eye. I even asked optician as well but he tricked out of this position saying it does all happen automatically. LOL! A detailed answer would be much appreciated. Please don't hesitate to write any technical details or mathematical derivations. I would love to know how these machines actually work. Thanks in advance!", "label": 1}
+{"snippet": "I received an e-mail including the following sentence: I am not asking for a facetious grade change, just one that would allow me to pass. What the writer means is that the request isn't frivolous or petty. This use sounds wrong to me, but the literal dictionary definition doesn't contradict it (the dictionary definition includes, for instance \"flippant\"). My question is whether this is a use typical in some situation or dialect I'm not familiar with, or if it's actually completely nonstandard.", "label": 1}
+{"snippet": "The product of nonempty sets is nonempty. I am fascinated that such a simple and seemingly intuitive statement can lead to rather astonishing results such as the Banach-Tarski paradox or the solution to this riddle. I am also intrigued by the seemingly innocent results that rely on AC (the existence of algebraic closures, any ideal is contained in a maximal ideal) and I wonder if I am missing some intuition to see how truly remarkable they are. My question: What are other examples of seemingly magical results whose proofs rely explicitly on AC, and what are examples of seemingly innocent results that rely on AC that upon further examination turn out to be fairly remarkable themselves?", "label": 1}
+{"snippet": "Let G be a finite planar graph, then there is a natural walk around the outer (i.e. the unbounded) face of G. It might happen that a vertex v is visited more than once by this walk. Proof that this is a cut-vertex. This is a task which might be obvious at first glance, but I wasn't able to do it rigorously, i.e. by citing any of the used arguments from a book and proving everything else. I would also be satisfied with a book which I could cite. Thx.", "label": 1}
+{"snippet": "I am looking for a good mathematical rigorous introduction to solid state physics. The style and level for this solid state physics book should be comparable to Abraham Marsdens Foundations of mechanics or Arnols mechanics book for classical mechanics or to Thirrings Physics course for quantum mechanics. Any recommendations? Edit: As a reaction to Peter Shor's comment, I try to narrow the scope of the question a bit and give some more specific subareas of solid state physics I am in particular interested in: semiconductors and applications the quantum hall effect superconductivity", "label": 1}
+{"snippet": "Is there any way to tell how many clusters there are with respect to all the roots of a polynomial? Specifically, I'm after the multiplicity of each root but since I would like to work in floating-point arithmetic I'm afraid I have to deal with clusters. I don't mind any method of finding out: be it by numerical-iterative means during the convergence, a priori/a posteriori guess, maybe some matrix method would help..? If I have to set some small disk radius, that's ok, too.", "label": 1}
+{"snippet": "Example: The three picked up their chopsticks and started on the food. The scene seemed strangely normal to Naomi. It was as if everything were OK, and her mom were perfectly healthy. In fact, she looked more lively and energetic than Naomi remembered. The whole illness issue seemed like a distant, bad dream. Something that belonged to another reality. Still, Naomi couldn't take the thought out of her head, so she decided to ask. If I changed still for yet, would the sentence mean the same thing?", "label": 1}
+{"snippet": "As I've been trying to wrap my head around the principles of decoherence and quantum behavior I am left wondering why fundamental particles are 'allowed' to exhibit quantum properties even in ideal conditions ( close to absolute zero and in a 'box'). If a particle/photon behaves in a probabilistic superposition state as seen in the double slit experiment then wouldn't we expect the multiple coincidental states of the particle to interact with each other and thus cause decoherence? This would in turn lead to an innate instability of any system above a zero point energy thereby making quantum properties not identifiable at all..but indeed we do have verifiable and replicable evidence of quantum mechanics.", "label": 1}
+{"snippet": "This will depend on whether he's suitable for the job. This will depend on whether he's suitable for the job or not. This will depend on whether or not he's suitable for the job. It is still not defined whether we're following that approach. It is still not defined whether we're following that approach or not. It is still not defined whether or not we're following that approach. \"Or not\" doesn't really seem to be needed to complement \"whether\". Why do people use it then? Is it redundancy and nothing more? Or is it for emphasis? Or are there cases when \"or not\" is required for the sentence to be grammatical?", "label": 1}
+{"snippet": "Please see the sentences: I scheduled to stay after school with you today, but yesterday I was assigned a detention for today too. I scheduled to stay after school with you today, but yesterday I was assigned a detention for today also. The sentence ending in also sounds better to me, but I am not a native speaker, and I don't know it it's correct to use also at the end of a sentence. Which one is the correct form?", "label": 1}
+{"snippet": "Wikipedia defines the notion of a pure set as follows: a hereditary set (or pure set) is a set whose elements are all hereditary sets. Why does this definition make sense? It seems to be circular. Also, wikipedia says: The inductive definition of hereditary sets presupposes that set membership is well-founded (i.e., the axiom of regularity), otherwise the recurrence may not have a unique solution. Why does the definition sometimes not have a unique solution? Is the problem the existence or the uniqueness? Can you give an example of a situation where the recursive definition from above does not have a unique solution in a setting where we don't assume regularity?", "label": 1}
+{"snippet": "The original sentence is \"The Spaniards brought horses to the Americas.\" I recently have made a final-term test question like this: Q: Where did the Spaniards brought horses? A: ______________________________________(Make sure to use the 'it-cleft') Not a few students answered like this: \"It was the Americas that the Spaniards brought horses to.\" But, I think that only \"to the Americas\" is a right answer. Does the preposition 'to' need to be next to the noun? So, Separating 'to' and 'the Americas' seems to be awkward. What do you think about it? I'd really appreciate it if you could help me...", "label": 1}
+{"snippet": "We have terms like 'high culture' and 'high art'. They are used to describe things deemed of a higher quality, or held in higher esteem, than products of popular culture. We also have terms like 'art music' and 'art film'. What I'm looking for is a similar term to describe literature. Like high literature or art book or art novel, none of which I've heard being used. For example, we can say: John wouldn't like Transformers. He only watches art films. But what about: Harry wouldn't like Tom Clancy. He only reads ..... (what?)", "label": 1}
+{"snippet": "I'm looking for a way to truncate outliers in a time-series graph. Some context: I'm plotting two different metrics on a single graph. It's important to understand what portion of \"Metric A\" takes up respective to \"Metric B\". \"Metric B\" can at times spike to a high value thus increasing the Y-Axis scale which then minimizes the visibility of Metric \"A\". Are there any good formulas that help normalize this data or visual treatments that can make the graphic honest as well as accessible? See screenshot for more context. The blue area is \"Metric B\". Thanks!", "label": 1}
+{"snippet": "Context: I'm programming a system for exams, each exam has people on it, in the industry we would call one of these people a 'Delegate'. Unfortunately in the programming language c# 'Delegate' is a reserved word and I can't really use it without my code looking terrible. I need a word to represent a person who will be on an exam. A colleague suggested ExamSitter but I think that might have been tongue-in-cheek", "label": 1}
+{"snippet": "How does quantum electrodynamics actually explain HOW reflection occurs on a microscopic scale? Note that Feynman's QED lecture series/book is not sufficient, as he only assumes that light DOES reflect ('turn around and go back') in order to expound his path integral theory. My question is why does light have the propensity to turn around in the first place. Is it just the absorption and re-emission of photons, and if so, why does it happen so uniformly (i.e. on a shiny thing, entire scenes are reflected near-perfectly). In essence, why are flat things shiny? Are all the molecules arranged at exactly the same angle?", "label": 1}
+{"snippet": "I'm not very advanced in LaTeX. I don't know what e.g. XeLaTeX or LaTeX->dvipdfmx are. I only use ShareLaTeX and used to use Overleaf. I need to be able to insert thumbnails in a document which when clicked would display their bigger version in a popup or something. This gif is a perfect example of what I want to achieve. Is it possible to achieve something like that in one of the mentioned sites? If so, how? (if there's a way to achieve it online but on a different site, I'm still interested)", "label": 1}
+{"snippet": "According to Wikipedia, the past tense (and past participle) of the verb to output is either output or outputted. Are these two forms entirely interchangeable? Or do they have certain nuance in meaning or context (e.g. in programming one of the forms is preferred)? Instead of correct results, my program output/outputted garbage. Which one should I choose? My logical sense tells me output is better because it derives from put, but intuitively I tend to use outputted when I speak and don't have time to think.", "label": 1}
+{"snippet": "So one of the exercises I am doing is to prove (or disprove) that 'Every compact set on a metric space is bounded'. Verbally, I can 'prove' this by simply stating: \"If the every compact set on a metric space is not bounded, then there exists an infinite number of open covers, and if something is compact, there are only a finite number of open covers. This is a contradiction, and thus every compact set on a metric space is bounded.\" Two questions: is this argument right? And if so, how to I learn how to represent this formally?", "label": 1}
+{"snippet": "I've heard people using this idiom, such as \"each day is better than the next\", or \"you hope that each experience you have is better than the next\" (heard this one on a TV show not long ago), apparently in a positive way. However, if taken literally, I find the meaning very negative - if the current thing is better than the next, then the next thing must be worse, so things would just keep getting worse and worse. How do you explain this phrase/idiom?", "label": 1}
+{"snippet": "Linkin Park sings \"wash the poison from off my skin\" in Castle of Glass. Shawn Mendes sings \"ripping all the skin from off my bones\" in Mercy. As far as I can remember these are the only two occasions where I have heard that expression. To me it sounds like it should be \"off from\" (if at all). Is this normal, or did the artists just do it to get another syllable for their rhyme?", "label": 1}
+{"snippet": "I have been on and off of this problem for three days and need to present the proof tomorrow. I am thinking that because I know for any element in the additive group of integers modulo n the order for that element is the ratio of n and the greatest common factor of that element and n then I can say,[...chirp, chirp, chirp...] and my mind goes blank. What can I say? I have also tried using the division algorithm to say the order of any element in the group can be written as a multiple of n and some other integer but I am coming up blank. There is something I do not fully understand and would like for you to point out my oversight. Thanks.", "label": 1}
+{"snippet": "\"My female cousin working for a finance company was dismissed. Disappeared along with her job were her confidence and smiling face.\" There is a very complicated system in Chinese for naming different relatives. For example, in Chinese, different words are used for a female cousin and a male cousin. Also, the word for an elder female cousin is different from the word for a younger one. I'm having some trouble writing this sentence in English. I used \"female cousin\" in the first part, to translate the word that actually means \"elder female cousin\" in Chinese, but it still sounds awkward. I suspect that the \"female\" may be redundant too, because in the second part I use the pronoun \"her\".", "label": 1}
+{"snippet": "I am trying to implement Microsoft Excel's GROWTH function in JavaScript. This function calculates predicted exponential growth by using existing data. What makes it tricky is that it must work with multiple sets of known_x's values. I could not find any reference equation. Any suggestions? The part that might be relevant is the reference equation. I cross-posted the question here because someone suggested it in response to the same question originally posted on stackoverflow. Thanks in advance for your help.", "label": 1}
+{"snippet": "I'm interested in writing a numerical integrator to solve the motion of systems of pendulums. For example, a simple case would be the double pendulum. The motion can be quite complex in general. Is there a way to determine if a system of pendulums is going to produce stiff DEs before actually trying to integrate them? Usually the masses and lengths of the pendulums are considered to be identical for the classic double pendulum system, which I suspect makes the system quite tame. But I have nothing to back that up.", "label": 1}
+{"snippet": "I am fairly new to this so apologies for informal terminology. After I discovered what space filling curves are, I came to the conclusion that any point in any number of dimensions can be represented as a single number along a space filling curve, given that the curve covers enough space. I also imagine that it is possible to rewrite any operation on these points in terms of movements along the curve. Is this correct to assume?", "label": 1}
+{"snippet": "I've found plenty of blog posts and papers where the authors claim that the Higgs mass divergence (usually presented with a momentum cutoff) doesn't show up under dimensional regularization. Unfortunately I've never seen a book or paper which explains this with any more detail: it's usually just stated as a fact. Is there some specific reference that people can point to for this? I'm well aware that dimensional regularization just hides the hierarchy problem until physical particles are added, but I want to include a reference to motivate the introduction of new particles without going to through dimensional regularization.", "label": 1}
+{"snippet": "I need some assistance with a calculation I'm trying to do. I have access to surgery waiting times data (date arrived, date completed) and I want to figure out the expected waiting time for a new patient - this should take into account the number of patients already waiting and those who have completed (I think). I've tried looking at the average time to wait for the past three hours but this doesn't seem the right way to do it (too simple I think). I've also thought about perhaps looking at the average wait time for the same day of the week for a previous week...would that be sensible? There are so many variables to consider but I need something relatively simple...", "label": 1}
+{"snippet": "People on Reddit often comment \"I lost it\" while quoting the funniest part of a joke to highlight how funny that part is. As I don't speak English much, I am not sure if this is Reddit-specific, but I guess not. Where does this come from? Is it related that laughing from a joke is similar to \"losing your mind\"? That seems far-fetched. \"I lost it\" would intuitively mean \"the joke stops making sense here\" (i.e. \"I lost track of the joke here\"), which is the exact opposite of what it actually means. What is the etymology of this phrase?", "label": 1}
+{"snippet": "I've searched the question in the forum, and found the following conclusion : - \"In electromagnetism, electric flux is the rate of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a virtual surface. But, It doesn't make intuitive sense to me, that electric flux is just something that we can count like no. of lines, I don't think electric field is passing in lines literally, so what exactly is Electric flux? and Rate of flow suggest that it's moving like water flow in river. These ideas are difficult for me to grasp, please clarify.", "label": 1}
+{"snippet": "I've heard mentioned in various classes that neutron stars, like superconductors, are described by BCS theory. I know that in superconductors a key element in forming cooper pairs is a net attractive force between the electrons which would normally repel one another. That attractive force is accounted for via lattice vibrations (phonons) created and \"absorbed\" by electrons. So my question is: what provides the attractive force between neutrons? just gravity? If it is true that neutron stars follow BCS theory, by what means was someone able to verify that?", "label": 1}
+{"snippet": "I have to submit some paperwork for the approval of an activity. However, I have already got approval, the paperwork is only necessary to submit the specifics (the date, people involved, and other details which have already been approved) for sign-off. What is the word (or expression, but preferably a single-word) to describe this kind of action? Examples: I already have approval, so submitting this paperwork is a ____ act. I already have approval, so the paperwork is just ____. It's not \"futile\" as it's still necessary, I'm not \"going through the motions\" as I really mean it and my heart is in it, so how can I describe this paperwork?", "label": 1}
+{"snippet": "I've been studying the representation theory of groups from Tung's \"Group Theory in Physics.\" I understand Young symmetrizers of different Young diagrams are essentially primitive idempotents in the group algebra of the symmetric group and then all inequivalent minimal left ideals as well as all inequivalent irreducible representation can be obtained. However, the construction seems unintelligible to me, while the property of Young symmetrizers is so striking. What is the idea behind the construction?", "label": 1}
+{"snippet": "What is the meaning of the text quoted below? In the physical world, if a system is described by an equation that is first order in time, the system is general dissipative (has energy loss). If the equation is second order in time, the system may be non dissipative. Such a system has time-reversal symmetry. Can somebody explain what it really means to be first order and second order in plain English?", "label": 1}
+{"snippet": "I'm thinking of those old U.S. wartime movie-theater newsreels that celebrated victories, but combined with aspersions and taunts on the enemy. \"We're great and those guys are idiots.\" Not necessarily in film format like a newsreel; maybe a printed publication. Example: The Mouth of Sauron Magazine, the ??? of Mordor, celebrates its victory at Minas Morgul and continues to mock the armies of Minas Tirith.", "label": 1}
+{"snippet": "Several people I know were good in mathematics when they were in high school and they loved it but when they joined a university (specializing in mathematics) they felt mathematics is hard and that they were somewhat deceived because this wasn't the type of mathematics they loved and joined the university to learn. How can we overcome this problem in contemporary curricula? and why there isn't a universal mathematics curriculum? (I mean mathematics is not country-dependent like languages or history)", "label": 1}
+{"snippet": "After reading this answer about the gravitational force I wondered how that applied to the electric force, since both have the same basic form - product of the masses or charges over distance squared. If I was in a charged metal-walled elevator that was \"falling\" in an electric field, would I be just as oblivious as my friend who was in another elevator falling in a gravitational field?", "label": 1}
+{"snippet": "I asked a question on one of the stackexchange sites and one user edited a sentence I made from \"We were relocating so we....\" to \"We were moving house so we....\". As an english speaker, I have never heard of \"moving house\" in context of relocation in a sentence before. Presently I am even doubting if relocating is correct in the context of : \"Moving all your belongings in a house you onced rented into a newly rented house\"", "label": 1}
+{"snippet": "In many mathematics texts I've seen \"ordered n-tuple\" appear, and in such texts, there isn't any mention of just \"n-tuple\". So I'm wondering: are there really cases where one writes \"n-tuple\" and somehow it's not ordered? If not, I'm thinking the \"ordered\" in \"ordered n-tuple\" is really not necessary and can be shortened to just \"n-tuple\". Please let me know if there is significance is writing \"ordered n-tuple\" that I'm not seeing.", "label": 1}
+{"snippet": "I had to edit my question because I think it led to misunderstanding. For me, the definition of \"immunity\" is quite different from \"impunity\", and I know the differences. But what I don't know is that is the law the thing that draw the line? It seems to me they both refer to exemption from punishment. for example, a police officer can kill a criminal, whereas I cannot. Another example is that a diplomat raped and tortured two women but nothing happened. But if a man who has a powerful and wealthy father did that, the word impunity would be said. So, here is the question: Does only the law define the differences?", "label": 1}
+{"snippet": "Which is the better verb to use with data: feeding or entering? Furthermore, which is more common in the literature of the field and which do people who work in the field say more often? Are they used for different kinds of input systems? If the data are automatically continuously input by a machine (e.g., the Mars probe), is feeding data used, but if the data are individually input by someone at a keyboard (e.g., entering data into a user database), is entering data used?", "label": 1}
+{"snippet": "I want to use beamer (Madrid style) for a presentation I'm giving next week, but I am forced to use the institutional title page. That means that the whole background is filled by an image and the title itself cannot be in a coloured box. In the worst case I will have to pdftk the title page onto the presentation, but I'm sure there must be a way to force LaTeX to do it. I've tried using a PlainFrame with a TitleGraphic, but I can't get the image to stretch across the whole page the title itself will still be in a coloured box Any ideas???", "label": 1}
+{"snippet": "My teacher made an example to explain DFA, it was about paths (URL paths), the rules were as follows: S ::= / S ::= /O O ::= [a-z] O ::= [a-z]R O ::= [a-z]S R ::= [a-z] R ::= [a-z]R R ::= [a-z]S Examples of paths could be: /foo, /foo/, foo/bar and so on. However, I don't understand why you would need the R rules since they are equal to the O rules. Can I write it without the R? If not, why?", "label": 1}
+{"snippet": "The problem is, that I fail to unambiguously understand this phrase. There are two ways in which I can understand it (and a number of similar phrases): I may never be able to do this = It's impossible for me to ever do this ('never' negates 'may') I may never be able to do this = It's possible that I will never be able to do this. ('never' negates 'be able') Which is the correct one?", "label": 1}
+{"snippet": "According to Newton's laws, if net force is zero on a particle then the particle is at rest or in uniform motion, and if it is not zero then it is accelerating. So when a car moves on the road, friction helps it to accelerate. If the acceleration is zero, (i.e) it is moving with constant velocity, the net external force must be zero, so friction is zero. Then with friction equal to zero how is the car moving on the road?", "label": 1}
+{"snippet": "I have to do a final project for my PDE subject and last year I did one about Game Theory (specifically, Prisonner's Dilemma and Snowdrift game) for my ODE subject, which the rest of the students enjoyed and which my teacher thought it was a fun approach to the contents of the subject. I want to do a similar thing, but every Game Theory problem I have seen only involves ODEs. Until now we have seen first order PDEs (both linear and non-linear) and second order (hyperbolic, parabolic and elliptic) PDEs. Also wave equation and heat equation. What would be some fun PDE related problems to discuss? (I hope I put the right tags, because it is the first time I ask a soft question).", "label": 1}
+{"snippet": "The title gives away pretty much the entire question except for the fact that the class of functions I am interested in is a subset of twice continuously differentiable functions. I think that if an odd function (defined on the whole real line) is concave on the positive real line, then it is convex on the negative real line. If it is supposed to be convex everywhere, then it is linear on the negative real line. The argument goes also the other way. So it is linear everywhere. So maybe I don't even need the monotonicity property. This is the first question I am posting here that has no equations. So I hope that is allowed. Is my reasoning correct?", "label": 1}
+{"snippet": "Do you know if the concept of chemical potential can be properly defined for nucleons in the nuclei? I mean, if I can picture the nuclei like an interacting gas of nucleons, then may I think of a chemical potential for nucleons, similarly to the case of an electron liquid. Of course the nature of the interactions is different for the two cases. My idea is related to the liquid drop model of nuclei.", "label": 1}
+{"snippet": "So imagine you're at the beach; you go into the water and the moment you enter the water you stop hearing anything from the outside world. The same happens vice-versa: your friend shouts at you from inside the water but you only hear the bubbles rising to the top. So the questions are: Why does that happen? Would it also happen if you used a hydrophone?", "label": 1}
+{"snippet": "I am writing a title and I was wondering whether I can skip the second article just like you would say a pen and pencil. Can I say, \"A cap and tie for Zed,\" or must it still be \"A cap and a tie for Zed?\" Have been searching the net and books for some answers but have been unsuccessful. Would appreciate a quick response from some Grammar Genius! Need clarification here to finish up my work. Thanks ya.", "label": 1}
+{"snippet": "The usual solution to fix lines that overflow is to rewrite it. However, that hardly works with bibliography entries that experience the same problem. So what can I do to fix it? I can't rewrite anything since the information needs to be \"as-is\". I can't provide a minimal example because if I take the entry that overflows in my document, then the problem fixes itself as the font, font size and margins change. EDIT Even though I've accepted an answer, please submit more answers if you have a good approach for addressing this issue. Maybe it can assist someone else who have the same problem and don't want to resort to using \"ragged right\".", "label": 1}
+{"snippet": "I have studied in a course several algorithms to integrate ODE's numerical: Runge-Kutta, Predictor-Corrector methods, Taylor... However the teacher failed to show which is the best for every particular situation. The only thing I know is that implicit methods are appropriate for stiff systems. But how do they compare Runge-Kutta (of any order) with predictor-corrector methods or with Taylor method? Which is best for each situation? Heuristic answers based on experience may be good enough!", "label": 1}
+{"snippet": "I have a paper copy of some old LaTeX notes, but I lost the source file. If I scanned them as a .pdf, does any OCR software exist that could convert the scanned .pdf to LaTeX source (.tex)? I also have a paper copy of some old notes created using Microsoft Word's Equation Editor. While I am considerably less hopeful, I ask the same question -- does an OCR software exist that could convert a scanned .pdf to .tex? Thank you for your help.", "label": 1}
+{"snippet": "I came across a problem where I have to find out the longest path in a given graph. I have list of edges ( eg.{AB, BC} ) which states there is an edge between vertices/nodes (A,B,C). Now i want to figure out the longest path possible (not repeating the vertex) such that it covers maximum nodes starting from any vertex/node. What can be the best way to solve this? I have to implement this as a program. I looked up google for Minimum Spanning Tree, Dijkstra's Alogorithms , hamiltonain path( which i think suits- but not sure ) and many more. but can't figure out what would suit best for this problem. Any help or reading references would be much appreciated.", "label": 1}
+{"snippet": "Here is an example sentence, written by a pupil of mine: Through the British Empire, which resulted out of Britain's urge to build up its economy, Britain was connected to a lot of different countries The sentence clearly has several issues, but I am only interested in one of them here. I would only use \"result from\", as a native British English speaker. My pupil has one American parent and one German parent, and lives in Germany. Would \"result out of\" be acceptable in written, academic American English? Can it be said at all?", "label": 1}
+{"snippet": "What are the possible applications of Countable Infinite Sets and Power Sets in areas that are not strictly mathematical? Also I want to know the significance they carry. What was not possible before the concepts of countability and power sets were introduced and what became possible afterwards? How did the introduction of these concepts change our thinking and outlook and the areas they affect? Please explain in plain language, possibly with examples, as I am from a non-mathematical background. Thank you in advance. PS: The applications need not be in strictly practical fields either (as Asaf Karagila keeps pointing there aren't any). Please help!", "label": 1}
+{"snippet": "What is the best word or way to describe a person who just has to try and do everything themselves because they think, either rightly or wrongly, that only they are good enough to do the task in hand? The type of person I'm thinking of will attempt to take over any situation. So if you're having a BBQ only they are good enough to cook the food or if you're planning a day out then they decide only they are good enough to drive you there.", "label": 1}
+{"snippet": "My understanding of irony comes from the movie \"Reality Bites\": It's when the actual meaning is the complete opposite from the literal meaning Frequently people use the term incorrectly, applying it where the actual meaning and the literal meaning are surprisingly similar in unintended ways. A perfect example of the incorrect usage is the picture below. It's definitely not irony, so what word can we use? (Just in case the link has broken, it's a picture of a building with a plaque saying \"George Orwell Lived Here\". Pointing out in front of the building is a security camera.)", "label": 1}
+{"snippet": "Why is it true that the lower sums of f with respect to some partition is less than the lower integral (which is the supremum of the lower sums) I think what I'm confused about is the difference between a lower sum and the lower integral, how can the lower integral be the supremum of the lower sums when a lower sum is a single number?", "label": 1}
+{"snippet": "Gravitational force is mediated by graviton exchange. If I am standing outside a black hole, I can of course feel the attracting force towards the black hole. This should correspond to gravitons mediated between the matter inside the horizon and myself; but then these gravitons should cross the horizon from the inside to the outside. My question is: how is this paradox precisely solved? I guess a starting point for an answer is that these gravitons are off-shell, much like in QED where photons exchanged between electrons that feel each other are virtual. But still, this confuses me a bit - is there some references explaining this in detail?", "label": 1}
+{"snippet": "I'm writing an essay for a grad school application detailing my unique characteristics as an individual. I am leaning towards words & phrases like \"thirst for knowledge\" and \"earnest curiosity\". I feel these phrases are underselling this attribute though - I feel so genuinely interested and invested in how things work and how people think, and thus how others perceive stimuli in comparison to my response. Is there a word for this constant absorption of external data in order to think critically and formulate theories for why the world works?", "label": 1}
+{"snippet": "I am trying to understand the following question: \"How much experience do you have gathering data for web analysis?\" I understand the concept of \"web data analysis\", and I understand \"gathering data from the web for analysis\", but the above question is not clear. Perhaps I am being too literal or picky, but the question sounds like I would first gather data, then put it on the web, and then analyze it, which is not logical. If you have any ideas, could you please provide a specific example of what kind of work would satisfy the question. For example, maybe the question means I would download Apache Server logs from a website, import into Excel, and perform analysis?", "label": 1}
+{"snippet": "Is there a word to describe the co-opting of a well-known phrase in the course of regular conversation or writing? For example, a sentence regarding death might refer to \"shaking off the mortal coil\" without mentioning that the phrase is taken from Shakespeare (perhaps assuming that the audience will be familiar with the reference). If it's not an exact quote, this could be called a \"paraphrase\" of Shakespeare. But what could it be called if it is an exact quote? Example: What adverb could be employed to complete this sentence: The phrase \"shuffled off the mortal coil\" was made famous by Shakespeare, and is used by this author ______y.", "label": 1}
+{"snippet": "The book < Geometry and the Imagination > (written by David Hilbert) introduces a property of a Quadric Surface without a proof. Property : The cone consisting of all the tangents from a fixed point to a quadric cuts every plane in a conic, and the points of contact of this cone with the surface form a conic. Moreover, the quadrics are the only surfaces having any of these properties. It was easy to prove the property itself, but i found it difficult to prove that it is a sufficient condition for a surface to be a quadric. (the statement starting with \"Moreover, ...\") I would like to know the proof of this statement.", "label": 1}
+{"snippet": "Ok, so I am trying to computationally model a Carbon Nanotube FET and I need to know a lot about the actual equations and PDEs(Partial Differential Equations) involved while modeling such a material. I had taken a course in material science in my sophomore year , but that just covered the basics of CNTs and its applications. I would really like to know if there are some good books out there that give an in depth understanding about CNTs ( structure, properties, behavior in presence of Fields, Equations and PDEs, Fabrication and applications, etc)", "label": 1}
+{"snippet": "I am having a hard time figuring out how to configure TortoiseHg to do colored word diffs for my TeX and LaTeX documents. I found the following two threads How to use Mercurial for version control of text documents? Good strategy for line breaks with paragraphs of LaTeX source but they don't go in detail how to to set this up on TortoiseHg. I was wondering if anybody in the TeX/LaTeX community has figured this out already?", "label": 1}
+{"snippet": "Given an urban area such as a shopping mall, is there a statistical model that estimates how often during a working day the area becomes depopulated and what is the maximum time of depopulation? By depopulation I mean that the number of people per unit area becomes zero. In particular I am interested to know the answer to this question: Can we say that typical urban areas are usually populated (during the working day) and there is an upper-bound for the depopulation time? any article that exposes some research regarding this subject would be useful.", "label": 1}
+{"snippet": "In the following paragraph, is it appropriate to use the term \"transversely\" to describe something that has the opposite effect? Tests have shown that the lower the range, the more likely that a submatrix will be singular. Transversely, the larger the range, the least likely that a submatrix will be singular. If not, is there another word that I can use instead? I know that, in this instance, I cannot use the word \"conversely\" as this means something totally different.", "label": 1}
+{"snippet": "This was an experiment I saw in my son's workbook. It said to mark out the top of your forehead and the bottom of your chin on a mirror using a whiteboard marker. Then slowly move backwards, and investigate what happens to the size of the reflection subjective to the two marks made. It actually got me quite flabbergasted. I always thought the reflection would get smaller as you moved away from the mirror. Why is this?", "label": 1}
+{"snippet": "While explaining the quantum adiabatic theorem recently, I appealed to a thermodynamic analogy: when slowly contracting the walls containing a classical gas, the relaxation timescale can be taken to be fast, so the system remains always in thermal equilibrium. By analogy, the quantum system remains always in a stationary state. The hidden assumption here is that stationary states (eigenstates of the Hamiltonian) are in some sense attractors of the system: that a system in some energy-superposition will, over time, relax to a single energy eigenstate. Is this actually true? It seems like maybe it isn't, since for example coherent states of the harmonic oscillator are stable (?). Maybe it's true in neighbourhoods around the stationary states only?", "label": 1}
+{"snippet": "She will (or already has) leave for Jamaica soon. She will leave (or already has left) for Jamaica soon. I'm uncertain which of these (if either) is more correct. Should I simply not use this language construct, opting for this instead: She will leave for Jamaica soon, if she has not already. I find the previous constructs, despite being awkward, do a better job of conveying the uncertainty of tense. Is there a better way to construct the parenthetical version to avoid tense conflicts?", "label": 1}
+{"snippet": "As I understand: Accelerating electrons generate electromagnetic waves. An emitting antenna have an alternating current (electrons are moving) which generates an electromagnetic waves. The electromagnetic waves reach the receiving antenna and makes the electron inside move. Greate, the communication is done. However, since the electron in the receiving antenna are moving too, the receiving antenna is generating an electromagnetic wave too. How is this not affecting the incoming wave? Does it have a different wavelength?", "label": 1}
+{"snippet": "I'm looking to communicate the idea that performing a task would be less costly (more than just financially; technically, or when risk is considered) if you start from scratch or anew, instead of attempting to alter or change some existing object or entity. The closest phrase I can think of that satisfies this is \"it may be cheaper to build a new house than to renovate an old one\". What other sayings exist?", "label": 1}
+{"snippet": "Is it always true that projective objects are retracts of free objects? I know that retracts of projective objects are always projective, so in particular, retracts of free objects are projective. To prove the converse for modules, write your projecive module as a quotient of a free module, and then take its kernel to get a short exact sequence. This sequence splits because it ends with a projective object and so by the splitting lemma our module is a direct summand of the free module. How to generalize these to an arbitrary algebraic theory? I guess we should somehow look at the kernel pair of the quotient map?", "label": 1}
+{"snippet": "A question regarding drawing checkers pieces and boards using TikZ has been asked here previously and I'm aware of the chessboard package. However I want to draw a Chinese checkers board: I want to draw it as opposed to using an image because I want to be able to edit the locations of pieces. The question is how I would go about drawing the board. Two options I see are: Draw the board as rows of circles and then draw the outline similar to the above. Draw the board as rows of equilateral triangles as seen here. Either way is fine, but drawing either one is a mystery to me. Any tips?", "label": 1}
+{"snippet": "When a sensor registers electromagnetic radiation, such as that used for the transmission of communication like light or radio waves, does this radiation \"abrade\" or \"erode\" the material of the sensor? Are there any traces of the received radiation that can be detected, even if only theoretically? An example from a biological background would be that high energy light (such as that in the UV range) destroys the pigments in the eyes, which is why animals that live longer than a few years cannot see in the UV range. Maybe something similar happens with man made sensors for different wavelengths of electromagnetic radiation.", "label": 1}
+{"snippet": "I was about to use this word in an email to refer to its recipient, as in: I was the guy who nabbed you as you were leaving to ask about ... I'm going for a friendly, familiar tone. Is my usage of 'nab' inappropriate? Looking it up in the Oxford Dictionary: verb (nabs, nabbing, nabbed) [with object] informal catch (someone) doing something wrong: the Feds nabbed a suspected terrorist take, grab, or steal (something): Dan nabbed the seat next to mine", "label": 1}
+{"snippet": "I'm currently studying Action. I've been reading about how a particle has particular probabilities of ending at an infinite number of events. Say I have a free particle that isn't experiencing any external forces (no potential, or friction). I give it a particular kinetic energy, whilst it is at some arbitrary event A. Why doesn't the particle stay at position A, \"lose\" its kinetic energy and reduce the action to a minimum? Why does it travel in a particular straight line? You can't argue from conservation laws since they are dependent on the idea of the stationary action principle. I'm curious to know the answer, cheers!", "label": 1}
+{"snippet": "Today, in the midst of chatting on other SE sites, the term \"bum buddies\" was used. Some other users took this to be offensive, saying that it was just a slightly less egregious version of \"butt buddies\". I was not offended by the term, but others informed me that it has homosexual connotations. I always remember using the term to refer to close friends, almost as a synonym of \"bosom buddies\". Can someone guide as the correct usage (so I can avoid using inappropriate terms in the future)? If there is any history on the term that could be useful as well, please include it.", "label": 1}
+{"snippet": "This was said by one of my mates while retelling a story. The story runs that there was a court being held, and there was a recording-clerk as well. But this was a humor story, and the story continued that everybody was telling the recording-clerk to take out what was previously said, to the point that the clerk lost his temper and \"dropped the pen and threw up the sponge.\" Does this saying mean that he resigned?", "label": 1}
+{"snippet": "Let's say the objects are marble size or even single atoms or quarks. They are placed in an otherwise empty universe(expanding or non-expanding) at opposite ends of the universe with an arbitrarily large distance between them. With a combination of great enough distance and small enough mass will the gravitational pull between the two objects ever equal zero or merely approach it? Given an infinite amount of time would they ever meet?", "label": 1}
+{"snippet": "I've come across many pages, articles and texts which say something like When X does Y, God kills a kitten When X happens, God kills an elephant Like here - God kills a pigeon here - God kills a kitten What does it exactly mean? Does it mean that something great was achieved, so a sacrifice was made? or Does it mean that a particular action/event is bad and should be avoided?", "label": 1}
+{"snippet": "Two non antipodal points on a sphere have a geodetic which is a segment of a great circle on that sphere. I'm trying to calculate the Euler angles that would rotate the \"equator\" great circle of the sphere (in my case, the normal to this plane is the y axis) into the great circle that intersects two points specified by two pairs of angles (theta and phi, latitude and longitude, whatever. Though, yes, latitude and theta aren't the same, I know.) I feel like I've made it way more complicated that it needs to be and I'm stuck.", "label": 1}
+{"snippet": "I came up with this question when I received an email from a committee with a sentence 'We have decided not to publish it', which seems really strange to me because the grammar I learned in English classes is 'decide not to do something' and 'decide to not do' was told incorrect. I searched for answers to this problem online, but did not find a clear as well as persuasive answer. In terms of grammar, is 'decide not to do' correct ? If it is incorrect, is there a reason why people say 'decide not to do' even in official letters ?", "label": 1}
+{"snippet": "I was wondering if anyone knew how to make music notation that looks like the below: I'm not even sure where to start with this kind of thing, I've tried doing it by hand before in Inkscape, but I did not find that easy, algorithmic, or professional looking. I was hoping some kind of package might be available in TeX. This is another, similar example:", "label": 1}
+{"snippet": "For a particle attached to a rope moving along a circle that has the length of rope as radius, the tension provides centripetal force and work done by tension is zero since velocity of particle is perpendicular to tension at any instant. But I am thinking about this case: Here, a particle is tied to a vertical cylinder and is given a velocity perpendicular to rope. My doubt is the work done by tension. The length of rope decreases and the particle moves towards P which is along the direction of tension. So the work done is non zero. Am I correct? (Let the particle move in a frictionless surface)", "label": 1}
+{"snippet": "I am wondering if there is a word to describe a person who likes chaos. By this I mean a few specific things: The person is pleased to hear when chaos is created, or confusion emerges The person will take opportunities to create chaos or confusion The person enjoys taking part in chaotic or disorganized situations. I can't seem to think of a word to describe the type of person who would act in this way. I hope this question is clear. EDIT: Below gbutters sums up nicely: What I wonder is if there is a word for a generally good-natured person who just likes some good old-fashioned chaos. It seems like any person that thrives on chaos would have to have some extra baggage.", "label": 1}
+{"snippet": "I need a good book containing many challenging exercises (or problems) on Convergence Concepts in Probability. The topics I have covered are: Borel-Cantelli Lemmas Modes of Convergence and individual properties Laws of Large Numbers Central Limit Theorem Levy Convergence Theorem and Kolmogorov's Maximal Inequality Expectation and Limit Theorems like MCT, DCT and Fatou's Lemma. I know that there are several books offering enough theory but I am in no need of those. I would want a book containing stimulating problems because just by studying theory, I cannot be sure that I can apply those concepts in relevant areas. Thank you.", "label": 1}
+{"snippet": "What does the noun \"lucker\" mean? It's not in the Webster, but Google does give search results for such key phrases as \"I am a lucker\" or \"He is a lucker\" (and those are not misspellings like \"luckier\" or \"lurker\"). So people DO use that word. I myself heard it a number of times. And if they use it, it should have some meaning. So, here is my question: what does the noun \"lucker\" mean?", "label": 1}
+{"snippet": "I am being told that \"sports\" is a singular noun. This is creating a problem for me (as a teacher) because it sounds 'odd' even if it is correct (i.e. one of the exceptions to the rule). e.g. Sports has (rather than sports have)... I always thought sports referred to more than one team activity (e.g. football, rugby, golf, bowls etc.); hence, it was plural. For example, I like playing sports. Sports have always been of interest to me. QUESTIONS Is sports a collective noun? Which usage is correct?", "label": 1}
+{"snippet": "A busy intersection sees two traffic accident per month on average. Suppose the number of accidents follow a Poisson distribution. Starting from January next year, which month do you expect to be the first one in which there is no accident? I figured it would be the same for every month (as in every month is equally likely to have no traffic accidents), and can't figure out why a particular month would be expected as the first one to have no accidents. Any reason a single month is more likely than others?", "label": 1}
+{"snippet": "I'm looking for the appropriate term to use for what gets \"used up\" as potential energy is converted to heat and work. For example, some of the the energy in solar radiation is converted by photosynthesis to chemical energy; much of the rest is lost as waste heat. The bio-chemical energy is used to power various biological functions until it has all been lost to waste heat. At the various steps along this path what term would you use for what there is less and less of? It can't be \"energy\" since that's conserved. It's potential energy, but is that really a standard term for what's lost when potential energy is converted to waste heat?", "label": 1}
+{"snippet": "What would happen if an object (like a space ship) was to stop its orbit around the sun. would time slow down with that object (the same way time sped up for the characters in that great film Interstellar). Or even more so, if that object was to stop its orbit around the galaxy so to speak. And so on and so on. At what point is an object considered motionless? Could it be that the finite origin of the big bang has no time?", "label": 1}
+{"snippet": "If the mass of A is greater of the two, and if air resistance is the same on both, which ball will reach the ground first/simultaneously? I thought that since the acceleration acting on them is same, both will reach the ground simultaneously. But the answer in the book says that ball A (the one having greater mass) will reach first. I mean, isn't this what people thought before (I guess it's true) Galileo performed his experiment, until they were proven wrong?!", "label": 1}
+{"snippet": "Which would be correct? What is your favorite song, and explain why? (I'm thinking this is right.) What is your favorite song, and explain why. This could be written as, \"What is your favorite song? Explain why.\" But that seems kind of clunky. Looking at similar questions on this site I see that maybe there isn't a great answer to this (or maybe that this question is more straight forward than what I was looking at). I dislike the Chicago Manual of Style format, so ideally one of the two choices above would be correct.", "label": 1}
+{"snippet": "I want to create a separate file for tables so that the main latex file doesn't get cluttered. I know I can define tables in new file and add the same file in the main file using input{Tables.tex}. However, I am not sure how can I ask for/produce (not refer) the tables using the labels of tables in the main document? Any suggestions would be appreciated. Thanks.", "label": 1}
+{"snippet": "I want to make someone a present by subscribing for him to a mathematical journal. (It should appear every month or every two months). The contents should be comprehensible to an undergraduate in mathematics, and be about a broad selection of topics (for example not only analysis). I expect the content to be something like proposing interesting problems and then giving solutions with some references for further study. Are there some famous journals you could suggest me?", "label": 1}
+{"snippet": "I have seen that sometimes, in particular in number theory and combinatorial commutative algebra, our questions are somehow related to finding the number of points with integer components in a region/shape. Since this seems to be related to some open problems and conjectures, does there exist a branch of mathematics that specifically study such questions? If yes, what it's called and what prerequisites one must know to study it.", "label": 1}
+{"snippet": "I think it may not be possible. Given all the pair correlation functions (e.g. calculated from Ornstein Zernike theory), it seems possible to obtain the internal energy (assuming different species interact through pair-potentials (i.e. potentials that do not involve more than two bodies)). To obtain the free energy, the \"naive\" way is to obtain the partition function and take logarithm. Yet it seems not easy (except possibly through cluster expansions? which is not exact.) Any help will be much appreciated.", "label": 1}
+{"snippet": "Assume an airtight bag occupied by air such that the pressure inside the bag is equal to the atmospheric pressure. Assume the surface tension of the bag is negligible. What is the change in air pressure inside the bag relative to a weight placed on it? Is it possible to approximate the weight of the object on top of the bag by the air pressure inside the bag, without knowing the volume of the bag or the area of the object?", "label": 1}
+{"snippet": "Ionization energies/Electron affinities are well mapped. I wonder about opposite processes... I imagine for anion the necessary energy will be equal to the electron affinity (energy released when the anion was created). What about cations? If I had an cation and free electron (both with low kinetic energies) will it automatically recombine? Or if I had let's say grounded metal surface and near it a cation of some gas, will it do the same (and how would react an anion in this case)? Thank you for answers. If you could direct me to the proper literature I would be grateful :) (I know it requires QM for any decent description).", "label": 1}
+{"snippet": "The American convention in quotations is (typically) to place punctuation inside quoted text. But I always run into situations where the punctuation of the quote interferes with the punctuation of the sentence. How would you punctuate this (American, non technical)? When my friends ask, \"What do you want for your birthday?\", I never know how to respond. It seems odd to place the last comma outside the quote simply because of the question mark. Is that the preferred (i.e. most often accepted) standard?", "label": 1}
+{"snippet": "I have heard that in my next semester, our quantum mechanics teacher will be giving a great emphasis on difficult integrals with the most of them having to do with gamma functions. Does anybody know a book(or any other source) that I can learn about and practice gamma functions integration (with applications to physics and more preferably quantum mechanics if possible)? The only thing I have found are books that just list the integrals of gamma functions in tables rather than having a few examples and them some practice problems.", "label": 1}
+{"snippet": "Hullo, Im just starting up with LaTeX. I keep getting error messages even though I feel as though everything has been done correctly. I am just doing the intro exercise which is shown from the help tab from my MikTeX install. I am getting errors like article.cls not found. Can I download a LaTeX editor from somewhere, or is the MikTeX which I installed mising some files. Can someone please help me?", "label": 1}
+{"snippet": "I've heard this phrase used many times. e.g. -Got a completion date back on your new conservatory? -Ha! Chance'd be a fine thing. I think I have a general idea of what it must mean from its context. But I just don't see how it makes sense. What does it actually literally mean, and why? It doesn't seem to make sense to me. What does \"chance\" have to do with anything?", "label": 1}
+{"snippet": "So, in the field of metallurgy, there are a few varieties of phase diagram that are used to predict the post-processing characteristics of alloys. These include Time-Temperature Transformation diagrams and Continuous Cooling diagrams. Currently, I've found myself working with metal oxides, and I'm trying to find what the equivalents are in this field. It looks like so-call Oxidation Curves are a commonly used tool, but this doesn't give me any information on the microstructure or properties I can expect out of bulk materials. Are there such references?", "label": 1}
+{"snippet": "Dual spaces are home to bras in quantum mechanics; cotangent spaces are home to linear maps in the tensor formalism of general relativity. After taking courses in these two subjects, I've still never really understood the physical significance of these \"dual spaces,\" or why they should need to exist. What is a dual / cotangent space? Could someone explain why they are necessary, and what their physical significance is?", "label": 1}
+{"snippet": "I'm working on a collaborative project and I like to organize all the supporting files for my tex documents (rather than just having everything in one flat folder). This involves referencing figures/files/etc. by a (relative) path. The difference in slash convention between linux/windows means that collaboration between users on different systems becomes annoying. Is there any easy way of dealing with path references between systems?", "label": 1}
+{"snippet": "Suppose I take a vacuum tube and accelerate electrons in it by electric fields then collide it on a copper plate. Will the electrons then go inside it and generate an electric current by putting a positively charged panel on the opposite end to create a potential difference? If yes how can I extract the electrons from the positive plate back into the vacuum tube? Thanks! Also you can see a diagram I made for what I am trying to say,", "label": 1}
+{"snippet": "I have three questions: (i)Does rank of a square matrix same as the degree of its characterstic equation. (ii)Do elementary row transformations of a given square matrix result in a characterstic equation different from that of given square matrix (iii)Geometrically speaking what do cofactors of a square matrix mean. What is significance of some of them becoming zeros or all becoming zeros. These are theoretical questions and so if you could refer to me some book or online resource which can explain these concepts it would be a great help. Also it would be nice to know what other members think about these topics. Thanks in advance", "label": 1}
+{"snippet": "I have a few issues to discuss linked to the Future Subjunctive. Can \"If I were you.\" mean the same as \"If I were to be you.\" In other words, can \"If I were you.\" have the reference to the future which \"If I were to be you.\" has? If I were you at tomorrow's competition I would win. ? = ? If I were to be you at tomorrow's competition I would win. Would you understand, if told, that \"If I be you\" means \"If I were to be you\"? Is this construction still used in contemporary English or is it totally obsolete? If I be you at tomorrow's competition I will win. Is this construction possible? If I am happy at tomorrow's competition I will win.", "label": 1}
+{"snippet": "Equation of continuity says us that if we insert some fluid in a tube, the same amount of fluid will come out from the other end. If we make a small hole in a hose pipe, water will come out with a great speed. The bigger the hole, the slower the speed. This is a direct consequence of the equation of continuity. But at the case of water tap, when we start to turn on the tap slightly, the velocity of water is slow. As we turn on the tap more, the speed increases. This is contradictory with equation of continuity.", "label": 1}
+{"snippet": "I'm TeXing a course for a teacher of mine, and he wants me to have the section titles in the headers (I use fancyhdr to achieve this). He also wants me to retain the section titles he gave me in the original (word) file. Since some of these section titles are too long to fit in the header title, is there a way to define a shorter version that is to be used in the header? Enabling multiple header lines would also do. I'm using the book class.", "label": 1}
+{"snippet": "So I've been reading a section about energy levels and came across this statement: \"As the atoms of a material are brought closer together to form the crystal lattice structure, there is an interaction between atoms that will result in the electrons in a particular orbit of one atom having slightly different energy levels from electrons in the same orbit of an adjoining atom.\" What I don't understand is that how could be an interaction of atoms of the same material occur, if they have the same potential, number of e- and structure. And why would they have a difference in energy levels??", "label": 1}
+{"snippet": "Is there really a difference between using \"allows for\" and just simply \"allows\" as in this scenario? To me, both of these sentences mean exactly the same thing. Does having the 'for' make the sentence mean something even slightly different at all? I have searched all over but have not encountered anything that is similar to this scenario. Any help is much appreciated. Music allows me to express myself. Music allows for me to express myself.", "label": 1}
+{"snippet": "Taking into account gravity, air resistance, and wind velocity and direction. (And also temperature if it's actually relevant.) I know the muzzle velocity, the total distance the bullet traveled, its diameter, mass, length, and the angle from which it was fired at. Now, I do not know its drag coefficient, so how do I calculate it? (The muzzle velocity is supersonic.) The question is, what is the velocity of the bullet by the time it traveled the total distance? What are the formulae that I would need to use to calculate that? Much obliged.", "label": 1}
+{"snippet": "The gist of my problem is that Slovene isn't supported in babelbib. I've got a half-done .bst file which translates some of the needed words, but not all of them. I also noted there exists a slovene.mbs file in miktex. However, when I tried creating a new bibliography style with makebst, I still didn't get the words translated. Since my bibliography is pretty simple - the only thing I'm missing is translation for 'edition' - I felt it would be best if I edited the existing .bst. How do I go about that?", "label": 1}
+{"snippet": "I say that \"whoever\" is the correct grammatical choice in the following sentence: Give the raise to the hardest-working employee, whoever/whomever that may be. I say \"whoever\" is correct. The reason is that, when we isolate the \"whoever/whomever\" clause (\"whomever that may be\"), the phrase converts to \"It may be he\". \"It may be he who is the hardest-working employee\", not \"It may be him who is the hardest-working employee\". Thus, I believe \"whoever\" is the correct choice here. Am I right? And is my explanation in determining \"whoever\" on point? This question is different because the \"whoever\" clause is at the end of the sentence.", "label": 1}
+{"snippet": "Yesterday, I told an Indian my English name is 'Melao', he smiled and asked me if there's any special meaning. In fact, I get this name from a song with Latin style -- 'Corazon De Melao', I think it's legibly. So, I wonder if there's any special meaning in English-speaking countries when it is used as a name? Or what's your feeling when you hear a boy with a name 'melao'? Thx in advance.", "label": 1}
+{"snippet": "I am trying to solve the following problem using proof by strong induction. the problem is: Assume that a chocolate bar consists of n squares arranged in a rectangular pattern. The entire bar, or any smaller rectangular piece of the bar, can be broken along a vertical or a horizontal line separating the squares. Assuming that only one piece can be broken at a time, determine how many breaks you must successively make to break the bar into n separate squares The farthest i have gotten is the basis step, but i dont even know if that is correct Potential basis step that i got it is P(n), but besides that i am clueless", "label": 1}
+{"snippet": "I am writing a research paper in which my thesis concerns how a character matures through his merging of characteristic traits in his relationships with other characters. How can I introduce this topic with an analogy \"attention-getter\" that demonstrates this idea of merging things together to form something new? In another words, I'm looking for an analogy that compares how an individual who combines attributes that he acquires from his relationships can actually create a new, and better, identity for himself.", "label": 1}
+{"snippet": "What's the difference between pronunciation and enunciation? I learned this a long time ago in English class but forgot what it was. Clarification For example, Wikipedia says: Good enunciation is the act of speaking clearly and concisely. The opposite of good enunciation is mumbling or slurring. See also pronunciation which is a component of enunciation. Pronunciation is to pronounce sounds of words correctly I can't tell from this what the specific difference is. When is it correct to say someone's pronunciation is off versus when their enunciation is off? Merriam Webster's definition defines enunciate as : articulate, pronounce That would seem to say it's the same as to pronounce. Is there a specific example of incorrect pronunciation verses enunciation?", "label": 1}
+{"snippet": "It''s quite common for academic papers and such to have a short title intended to catch the casual browsers's interest, followed by colon and a longer more explanatory alternative. I know this is a lousy example (I couldn't easily find a better/shorter one), but even so I'm sure this Catchy Title : Longer version conveying more information about the work format is also used in fictional works. Is there a standard name for that secondary title. It's not really an \"alternative title\". The only thing that comes to mind for me is byline, but I know that's not right either.", "label": 1}
+{"snippet": "I have seen several proofs that there exist nonstandard models of arithmetic, but they all seem to rely on the compactness theorem, which is not implied by ZF. So are there any proofs in ZF that there's exists a nonstandard model of PA? Tennenbaum's theorem, which states that every nonstandard model is uncomputable seems to hint at the possibility that there are models of ZF that contain no nonstandard models of PA.", "label": 1}
+{"snippet": "I'm attempting to document a change that will make two things more congruent. I'd like to use a word in this way: This change [makes similar] the two items. The best I've been able to find by searching is \"assimilate\"; however, I feel that this word has unpleasant connotations in some cases and could be misconstrued. Is there a better word? For a little more context on this specific situation: I'm making the interfaces of two different software libraries more similar. They're remaining separate libraries, but they do nearly the same thing and are now more similar in their behavior.", "label": 1}
+{"snippet": "This is a follow-up of my previous question regarding loading image using latex command. @erik kindly informed me that latex only supports images in eps format. I converted my JPG file to an eps file using bmeps.exe in the miktex/bin directory. I can see the image in the dvi file generated by latex. But the original color image in the JPG file becomes a black-white or gray scale image in the eps file. Is it possible to get a color image in eps format using bmeps.exe? Does latex support color image? A minimum woking example can be found here.", "label": 1}
+{"snippet": "English is used all over Europe in (more or less) academic papers and books that are not necessarily related to reviews and publishing houses based in UK or US, and that are not necessarily intended for UK or US markets. English is largely used between non-English speaking areas as lingua franca. What is the main trend in this field concerning the use of British vs American English? Are there certain guidelines (or even EU directives) on the matter?", "label": 1}
+{"snippet": "I read a quote somewhere and it seemed flawed in its language and word usage. Take a look at it: \"Trust a person to that extent, that he feels guilty to cheat you & care for a person to that extent, that he fears to lose you.\" The letters in bold are the clauses that I found flawed in particular. Shouldn't it be: \"Trust a person to the extent, that....\" At the same time I find \"care for a person to that extent, that...\" sounds alright.", "label": 1}
+{"snippet": "I have a problem regarding supply distribution. I distribute widgets on a monthly basis; I have many customers and each of them request a different quantity each month. My monthly supply is limited and I cannot fill every order. How do I distribute fairly, across the board? There must be some sort proportional way to do it. Let me know if I need to provide additional information. Thanks", "label": 1}
+{"snippet": "A friend uses this ____-whore construction all the time. I challenged her to find a better way to say it. I suggested addict, enthusiast, devotee, and several other words. She said none of these convey her meaning the way whore does. She says she'll watch anything. I told her she's not being paid to watch, and whore would imply that she is. Can anyone suggest a better alternative?", "label": 1}
+{"snippet": "I am a freshman in high school who needs a math related project, so I decided on the topic of fractals. Being an avid developer, I thought it would be awesome to write a Ruby program that can calculate a fractal. The only problem is that I am not some programming god, and I have not worked on any huge projects (yet). So I need a basic-ish fractal 'type' to do the project on. I am a very quick learner, and my math skills greatly outdo that of my peers (I was working on derivatives by myself last year). So does anybody have any good ideas? Thanks!!!! :) PS: my school requires a live resource for every project we do, so would anybody be interested in helping? :)", "label": 1}
+{"snippet": "Is there a theory of constrained optimization with complex variables, do you know any textbook on that topic? The typical textbooks on constrained optimization deal with real variables. I actually found some references which loosely explain the procedure of derivating w.r.t. the complex conjugate to obtain optimality conditions but could not find a rigorous mathematical justification. In particular I am interested in using a Lagrangian, and couldn't find any reference on that. Thanks.", "label": 1}
+{"snippet": "At a homecoming dance, no boy dances with every girl, but each girl dances with at least one boy. Prove that there are two couples, gb and g'b', who dance, such that g doesn't dance with b' and g' doesn't dance with b. I'm not sure where to start. Hints only please, NO SOLUTIONS. I will most likely reply back to your hint to ask you more, so please stay online :)", "label": 1}
+{"snippet": "People in London, who live in the suburbs, may tell you they work 'up town', meaning in the City or the West End. In other large cities in Britain, Birmingham, Manchester, Leeds etc., I think people who earn their living in the City Centre (equivalent to Downtown with capital D) will say casually that they work 'in town'. I think I'm right when I say that only Londoners go 'up town'. So where did the idea of 'Downtown' come from?", "label": 1}
+{"snippet": "To complete college (or what the equivalent in Denmark would be) I will have to write a text about a topic that I choose. I have chosen to write about mathematics in business economics, and specifically, I want it to be about investment analysis and risk assessment. I am seeking some inspiration for possible mathematical topics to include. My knowledge in math is at bachelor degree, but I am up for a challenge. I already have a few ideas, e.g. I am pretty sure I will include something about the poisson distribution. Any answer is appreciated. Thank you in advance.", "label": 1}
+{"snippet": "Someone else asked Are camp followers prostitutes? and the answer seems to be that while not every one who follows a military camp is a prostitute, if you aren't referring to a prostitute, you should probably pick another label for the person. A similar effect can be seen with sexually themed words like \"mistress\", \"madam\", \"ejaculate\", and \"escort\". I assume this linguistic process has been studied and I'm curious what its name is.", "label": 1}
+{"snippet": "I'm looking for reading assignment ideas for my students. I'd like them to read up on results in mathematics in layman's terms. For example, the Monty Hall problem, or Borsuk Ulam as the \"Ham Sandwich Theorem\". I feel a good source for the types of things I'd like them to read is this post. I would have each (group) student do a write up on a particular subject. Does anyone know of any books that give a list of results that are understandable for a calculus student?", "label": 1}
+{"snippet": "During review of an article I found an erroneous sentence: The known predators of the plant are sheep, donkeys ... I am an engineer, with not so much knowledge in ecology. Based on my earlier studies I suggested to change predators to consumers. I checked it with a search on the net. Surprisingly I found too few hits in my search. Consumers of a plant is acceptable? Can you recommend alternatives?", "label": 1}
+{"snippet": "I understand that structures with the properties of the real and complex numbers can be defined and derived from the axioms of ZFC set theory. But can a structure with the properties of a (possibly uncountably infinite dimensional) vector space be derived from ZFC or is it axiomatic statement that a vector space is a set (and that therefore the axioms of set theory apply to it) ? I think the question becomes relevant in the proof that every vector space has a basis (from Zorn's lemma = axiom of choice). It's not just a matter of whether one accepts the axiom of choice in set theory, but how one gets to believe that a vector space complies with set theory axioms.", "label": 1}
+{"snippet": "Most physics textbooks and even questions in stack exchange answer the question why there exists a charge buildup in the bends of a current carrying conductor. But what I am unable to understand is: why a surface charge gets developed in the straight region of a current carrying conductor? why there is a gradient of the surface charge density along the length of the wire?", "label": 1}
+{"snippet": "I managed to install some english dictionaries as shown on https://github.com/TeXworks/texworks/wiki/SpellingDictionaries#mac-os-x. Then I was able to select Edit->Spelling->English-UnitedStates(en_US). At that point, all misspelled words were underlined in red. However, I would like to ask, once you finish writing your document, is there a way to search for any red-undefined misspelled word? The reason I am asking is to help my students, who will be writing projects in Texworks during the fall semester. When they are done, how can they check the spelling in their full document?", "label": 1}
+{"snippet": "A condensate of open strings with both ends attached to the same D-brane can be equivalent to a displacement of the D-brane with no open string condensate. A solution to the D-brane Born-Infeld action gives rise to a semi-infinite string extension which is entirely equivalent to an open string with one end attached to the D-brane. Why aren't D-branes and strings independent degrees of freedom?", "label": 1}
+{"snippet": "When I first learned algebraic geometry, I naturally wiki-ed the subject and there was a line there that said the old school Italians used the notion \"generic points without any precise definition.\" Now that I know what a generic point is, I am curious as to how did the Italians think about a generic point and/or what their intuition about it was and what kind of results did they prove using this notion. Any answer would be greatly appreciated!", "label": 1}
+{"snippet": "As I was familiarizing myself with different methods of computing complexities of recurrences, I stumbled upon the Akra-Bazzi method. Seeing such a beautiful result literally made my day. I was able to come up with a proof that makes use of an inductive argument, but induction alone isn't all that satisfactory. Does anyone know of a material that illustrates a constructive proof of this wonderful result?", "label": 1}
+{"snippet": "Let's say you have a spherical charge distribution of radius R. This distribution has some charge density as a function of radius. I know that I can determine the electric field outside of the charge density by forming a spherical gaussian surface around the charge distribution and apply gauss' law. But what if I want to find the field directly on the surface. That requires that my surface intersects some of the charge of the distribution. In that case, when I apply Guass' Law. How do I determine the charge enclosed by the sphere. Do I discount the charge which exists on the surface or is that counted as enclosed by the sphere?", "label": 1}
+{"snippet": "This is quoted from an U.S. TV series. Warden: Brad. Brad (Captain): Any updates? Warden: None. They were last seen at that cemetery in Oswego. Brad: They'll get them. They'll get them. Warden: It's been handed over to the FBI. Brad: Well, that doesn't mean we can't work it. Warden: It does, actually. You and I have been pulled off the pursuit. Brad: Why? Warden: We're going to find out shortly. We have to report to the DOC headquarters. I will meet you there. Brad: Sir, we can get these guys. Just give me a couple more days and I swear I'll get them. Warden: Brad! We've got to go.", "label": 1}
+{"snippet": "I have several items of clothing for which their dark colours could run on washing. Some have a warning label in that says 'wash dark colours together'. Some have a label that says 'wash dark colours separately'. These apparently contradictory labels actually tell me to do the same thing, when context is taken into account. What other examples are there, either out in the wild, or that could be constructed, of opposite messages meaning the same thing?", "label": 1}
+{"snippet": "I am writing up a paper on magic squares, and I would like to include the lo shu magic square, but I'd like to do this using XeLaTeX as opposed to just including a picture. The following picture is what I want to produce: Does someone know how to produce what's above? I thought something like tikz would probably have to be used, but I'm not very advanced with LaTeX just yet.", "label": 1}
+{"snippet": "What is the best word to refer to the person that I (directly) supervise, in the context of a corporate workplace? The closest I can think of is employee, but that doesn't directly convey a direct supervisor relationship. Other options I can think of are apprentice (usually used to refer exclusively to someone who is still learning where I come from), underling (patronizing), and worker (again not specific). For example when describing a project: My employee designed the front-end of the system while I worked on the critical business logic.", "label": 1}
+{"snippet": "(Quantum) integrable systems, that belong to solutions to the Yang-Baxter-equation, are often solved by the (algebraic) Bethe Ansatz. Solutions to the Bethe-equations lead to the eigenvalues of the transfermatrix and in that way also to the spectrum of the hamiltonian. However, suppose you already knew an eigenvalue of the transfermatrix, is there a way to construct the Bethe-roots, that would have lead to it? If any additional explanations are needed to answer the question, just let me know. I think the answer to the question is in general no. If there are however some specific exactly solvable models, where it is possible, that would be also of interest.", "label": 1}
+{"snippet": "What is the meaning of the phrase \" you rolled them sevens with nothing to lose \" ? In the song entitled \" The weary kind \" which is a sound track of the \"Crazy heart\" movie , there is a line that i can't understand. Your heart's on the loose You rolled them sevens with nothing to lose, there's ain't no place for the weary kind Could you please help me to understand that phrase ?", "label": 1}
+{"snippet": "Do predation and predating share a common etymology? Predation seems to imply that one species holds precedence over another species in the food chain, whereas predating seems to imply that one event holds precedence over another in the linear progression of time. Both words obviously share the prefix pre, but my question is more about the dat part of each word. What is the origin of dat in early English or in Latin or the Romance languages Latin gave birth to? And how does that origin explain the meaning of the modern words predation and predating?", "label": 1}
+{"snippet": "I want to prove that a certain metric space is totally disconnected. In a metric space context this is the same as saying that every connected component is a singleton. I think another way of proving that a space is TD is proving that there is a proper, nonempty open and closed set. Is that right? Please let me know any alternative equivalent definitions you might now. Cheers!", "label": 1}
+{"snippet": "I have this problem where I have two lines given and I have to find a transversal. However, it also has to be perpendicular to a given plane (lines are not necessarily in the given plane). My guess was that I would have to find perpendicular lines to the plane and then see if they are also transversals of those lines. But I've been stuck. Is this the right approach? Or should I start working from the lines and then tend to the plane and transversal being perpendicular?", "label": 1}
+{"snippet": "I'm referring to this one: Any man who is his own translator has a fool for an editor. The resemblance that this expression bears to the one about any individual who chooses to represent himself/herself in a legal case is undeniable. Yet, even when the meaning of the latter expression is pretty clear to me, I'm not sure I get the point which whoever made up the translator/editor variant of the proverb was trying to make... I would be really glad if, in addition of getting an answer for the question in the title, you could help me unravel the meaning of the expression under consideration. Let me thank you in advance for your learned replies.", "label": 1}
+{"snippet": "I know this on our hands/in our hands discrepancy has been discussed here in a broad way, but since it's idiomatic, I think it would be helpful to consider a few specific examples, like the one here. Would you use \"on our hands\" or \"in our hands\" here, and why? It refers to something you invented and produced, and you're guessing it will do well on the market. So you're not having anything literally in your hands. You don't know if it's a top-seller yet, you just think it will become one. That's why \"on our hands\" seems right to me. Am I wrong?", "label": 1}
+{"snippet": "Is there a word to describe the competitive advantage gained from sabotaging a competitor, or more generally the advantage gained from dishonesty? An example: Your office receives pamphlets advertising an office cleaning service. Your current office cleaning service steals and hides that pamphlet before an employee at the office can see it. What words can one use to concisely describe the advantage that your current cleaning service has gained?", "label": 1}
+{"snippet": "I recently installed AucTex on a new computer, and am having an issue that I do not recall with regards to accessing environments. Using C-c C-e, auto-complete etc., I am only able to access a handful of environments. Auctex does not detect align, matrix, or any other math environments. It is possible to simply enter the environments by hand, or create custom environments, but this seems tedious for something that I wouldn't expect to be happening. Perhaps there is something I am missing.", "label": 1}
+{"snippet": "It seems Optimal Estimation/Control Theory requires a lot more than undergraduate maths. Any good book that would help me get started? I have so far referred the following books but found them quite difficult. Is it just me? is it the subject? or are there better books? Extra points for someone who gives a detailed road map of how to go about learning Optimal Estimation/Control Theory H.W Sorenson - Parameter Estimation Dan Simon - Optimal Estimation Theory Arthur Gelb - Applied Optimal Estimation", "label": 1}
+{"snippet": "I am working on the lyrics for one of my songs and english is not my first language. Here's the question - which of these sentences is correct? No thorns to prick your heart No thorns to prick your heart with (Meaning that the character of the song has no 'thorns' (figuratively) he/she could use to prick the heart of the one he/she addresses to) Thanks in advance", "label": 1}
+{"snippet": "When someone says, I barely understand that. Does he mean: He almost doesn't understand [which means he understands a bit] He almost understands [which means he doesn't understand] Or if someone says: Your brain is barely used. Does he mean: Your brain is almost not used [which means, it is used, but very rarely] Your brain is almost used [which means it isn't] I used to think that it was the first option. But a friend, out of the blue, said it was the second one. Which one is it? Or have my friend and I got it entirely wrong? Are there other words with similar meanings to barely? Is nearly one of them?", "label": 1}
+{"snippet": "So a stage whisper is defined as (American Heritage Dictionary): The conventional whisper of an actor, intended to be heard by the audience but supposedly inaudible to others on stage. A whisper that can be or is intended to be overheard. Is there any good description of the opposite? For example, if I'm in a crowded place, and I mock-yell under my breath so that only I or a single friend am actually aware of it, how could we describe that?", "label": 1}
+{"snippet": "I noticed that her eyes had been dancing as she looked out at the scenery. It appeared in a state-sponsored high school leaving examination in Slovakia last week and it seems to have been adapted from a short story by a native speaker, so it really ought to be correct, but I don't see how or why. Past continuous seems the obvious choice, this just seems wrong as it's all happening at the same time.", "label": 1}
+{"snippet": "I have read that electromagnetic waves carry momentum because they carry energy, while energy is equivalent to mass. So they carry momentum. But this explanation is in the context of special relativity. I don't know whether mass energy equivalence is necessary for wave momentum. So I hope you can discuss in the contexts of both Newtonian or special relativity. A quantitative definition like the Maxwell stress tensor of electromagnetic wave is better.", "label": 1}
+{"snippet": "I find that when learning more abstract concepts, it helps to have a 'simple' example tied to every theorem in order to fully appreciate the theorem or property. However, the course notes I am currently using for my studies of Measure Theory (this is a first course for me) do not have many examples. It is highly rigorous and detailed, but lacks examples. Are you aware of any introductory books on Measure Theory that has a good number of examples tied to each theorem? In other words I guess, do you know of very 'gentle' books on this topic?", "label": 1}
+{"snippet": "Claim A directed graph has an Eulerian cycle if and only if every vertex has equal in degree and out degree, and all of its vertices with nonzero degree belong to a single strongly connected component. I was looking for this proof in the Internet, but all i have found are the proofs for undirected graphs. I would be glad, if someone can give a link or name of the book, where i can find proof for this claim.", "label": 1}
+{"snippet": "The last few years I've noticed a trend of people posting articles or news stories on facebook that had offended them, and commenting with a sense of outrage they seemed also to relish on some level. Today I heard the term outrage porn for the first time, and felt delight in hearing this phenomenon succinctly and accurately named. I got to wondering if there was a word that described the surprise and satisfaction of hearing a concept captured by name for the first time... I'm not looking for general words describing the satisfaction of insight or clarity -- but a word or phrase that applies specifically to hearing a concept named for the first time.", "label": 1}
+{"snippet": "In high school we learned to say \"than I\" and \"as I\" because you could potentially add an \"am\" to the end of the sentence. Examples: \"She is smarter than I.\" (Think: \"...than I am.\") \"He is as tall as I.\" (Think \"...as I am.\") So analogously, shouldn't it be \"like I\" as well: \"He is sincere, just like I.\" (Think: \"... like I am.\") But universally, it seems that we use \"like me\". Where does this reasoning break down? Is there history here?", "label": 1}
+{"snippet": "When I use the word \"sorry\" for something I did wrong I'm sorry I bumped into you. I would be apologizing. However, when I used the word \"sorry\" to express pity for something that is not actually my fault, I'm sorry you couldn't figure that out. I'm sorry for your loss. is it still called an \"apology\" in English? In Chinese, we wouldn't use the same word in these different sentences. I would love to know what this type of sentence is called.", "label": 1}
+{"snippet": "I've been asking myself this and other questions in the field of philosophy of mathematics. Could we, if we were isolated from any kind of sensory experience, be able to learn mathematics? Also, what does it take to learn math?, is there a 'module' or a 'structure' (like the one theorized by Noam Chomsky in his studies on linguistics) in our brain that lets us apprehend mathematics?, do we need a language (be it natural, be it symbolic) to learn mathematics? PD: I'm a beginner to SE, if this question if off topic please do tell and do recommend me where should I ask it.", "label": 1}
+{"snippet": "I'm looking for command to use in one terminal so as to know the following facts. Is there one LaTeX distribution installed ? What is the path where to put local classes or packages ? In my Mac, I know that it is '/usr/local/texlive/texmf-local/tex/latex'. The command will be used by one Python script so as to automate the installation of my personnal little classes or packages. The solutions given in the following comments work well on Mac, and I think that this works also under Linux, but I don't know how to do under Windows...", "label": 1}
+{"snippet": "I have some TikZ code in my LaTeX document. Whenever I edit other parts in the LaTeX document, I recompile it. But repeating recompiling unmodified TikZ code can be time-consuming. I was wondering if there is some way to avoid re-compilation of unmodified part of LaTeX document? If such methods exist, do they apply not just to unchanged TikZ code but also unchanged non-TikZ code? Thanks and regards!", "label": 1}
+{"snippet": "I am in need of help figuring this out-- If the only straight lines in hyperbolic geometry are those that pass through the center, then isn't there a right angle? (horizontal and vertical) Which fulfills that requirement of the definition of a rectangle. That leaves the other two sides as hyperbolic lines with negative curve and extending infinitely, resulting in three acute angles, right? Aren't the two straight lines passing through the center parallel to their opposite hyperbolic line? Which also fulfills the definition of a rectangle. I'm sure I am overlooking something or have gotten myself very confused. Please help.", "label": 1}
+{"snippet": "Slightly tongue-in-cheek this one but written in good faith... I am a competent user of LaTeX and use it with Eclipse as IDE, MacTexlive as install, and XeTeX as engine to author my PhD. However, there are times when I like to procrastinate and love LaTeX as an end in itself not just as a means to an end. What would you recommend as a good way of procrastinating whilst usefully extending my capabilities and abilities to use LaTeX? In the past SVN, biber and beamer have served to distract me from my thesis. Any more potentially fruitful areas?", "label": 1}
+{"snippet": "Can fusion and fission happen at the same time, in the same place? I was talking with a friend, and he thinks that fission and fusion happen at the same time at the sun, is that true? I guess this would cause perpetual motion, then I speculated that they could happen, but in different proportions and I believed that fusion is happening in a higher proportion than fission. What do you think? I've searched on wikipidia, and I still found no mention to fission happening in the sun.", "label": 1}
+{"snippet": "This Batman equation thing got me thinking: for an arbitrary curve drawn on the Cartesian plane, can you write a corresponding equation which is not piecewise? What about closed shapes, a la the Batman symbol? I assume that there are limitations, such as that the curve would have to be differentiable and/or continuous everywhere, but is this possible for any random squiggle? Or is it not?", "label": 1}
+{"snippet": "The English wikipedia page for Nothing starts with the sentence: Nothing is a pronoun denoting the absence of anything. I was expecting Nothing is a pronoun denoting the absence of everything. since in the context a positive answer is expected. Googles: N-gram viewer shows that anything is more common than everything in this context, so I assume that anything is the natural choice here. But why is that?", "label": 1}
+{"snippet": "I am in a situation where i am expecting some data from my client. I want to write the same in a very polite manner that \"i am expecting the data, even after my repeated intimations.\" Here i wanted to use a sentence as I'm just sending this mail to remind you that, currently i am awaiting for data. I am confused i should use wait or await in this context.", "label": 1}
+{"snippet": "I would like to know if there is a common abbreviation for days of the week in a two letter form. I mean: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; can be abbreviated as Su, Mo, Tu, We, Th, Fr, Sa? Is this the common form? Note that I have also seen Sn for Sunday, and some times St for Saturday (but I think less frequently). It will be used in a tabular data program to show information about free work days of employed and each column can't have enought space to include full week day name. For \"common form\" I mean, what are the abbreviations that is more used in programs.", "label": 1}
+{"snippet": "Are there any (mathematical) puzzles that are still unresolved? I only mean questions that are accessible to and understandable by the complete layman and which have not been solved, despite serious efforts, by mathematicians (or laymen for that matter)? My question does not ask for puzzles that have been shown to have either no solution or multiple solutions (or have been shown to be ambiguously formulated).", "label": 1}
+{"snippet": "If a couple are having a romantic or sexy get away where they're staying in bed and having sex and otherwise hanging out - is there a term use for the periods where they're not actually in the act of having sex? Perhaps pillow talk is the closest term I can think of here - but this seems to refer to the act of just talking, whereas I'd like to encompass anything else they might do - like eating, watching TV etc. eg. During [something period] we had a tickle fight, I organised my to do list, and she knitted some socks. I'm looking for something you might use in a romance or sexy novel.", "label": 1}
+{"snippet": "I'm not a native english speaker (so forgive me for my poor language skills in general :) ) and I'm puzzled by this \"whose / which / of which\" issue. I have a sentence like this: \"BLAA is a project whose purpose is to build and...\". To me it sounds that it should have which instead of whose. I was always tought that whose refers to a person and which to a matter, and based on that I would use which but all the articles I read about it seem to say that whose is the way to go. What to do? And please keep the explanations in KISS form ;) Thanks! -Heidi", "label": 1}
+{"snippet": "I intend to study linear algebra during my summer vacation.I will be thankful if anyone could please point me to a good text.I do not care about the difficulty as long as the book is self contained.I do have some experience with problem solving and proof-writing. Edit:I don't care about applications.I prefer one which is quite theoretical. Secondly,here is a book I came across.I request comments on that book too.I will make a choice after some deliberations.", "label": 1}
+{"snippet": "I was wondering if there was any way to flip a transistor or similar node component around in the circuitikz package? For the bipoles it's fairly simple as you just reverse the start and end, but for more advanced circuits I'm having trouble (things such as current mirrors or what have you). I've seen various solutions on scaling up and down, but none on flipping.", "label": 1}
+{"snippet": "I was aked to solve the following problem: Guiven three lenghts and a triangle ABC, from every vertex whe draw one of the three lenghts, find the conditions such that the three lenghts meet in one point. Then I suposed that at least two lenghts and a side makes a triangle, supose that the side is AB and the two lenghts meets at P, then using the cosine theorem to the triangle ABC and tha traingle ABP and I get a very large expression involving only lenghts, but it was very complex, and I think it can be simplified. Then my question is, if there is a synthetic solution to the problem. Please I don't want a full solution. Thanks.", "label": 1}
+{"snippet": "I've seen constraint and restriction used quite often in scientific literature. For example, This algorithm needs to be further improved due to severe space constraint and restriction. I simply can't figure out the subtle difference between constraint and restriction. They seem to be circularly defined according to each other. I assume that they must be different in some way. Otherwise, they wouldn't have been used together so often. If they were really close enough in meaning, why not just drop one and use the other? Or are they used in combination to place an emphasis?", "label": 1}
+{"snippet": "I am looking for a high school/ pre-college level Algebra book that is self contained for self-study. Nothing special, I don't want a book about number theory, but a book in preparation of high school geometry, trigonometry and calculus. I have noticed that recommendations for Algebra books on this site, start with books that are really advanced (for my level) and overshoot the mark with suggestions for abstract Algebra or number theory. I am someone that is rebuilding my math skills and need to get a strong foundations before I move up in intellectual weight.", "label": 1}
+{"snippet": "In my report, I am defining/describing some terms. What is a proper way to start and format a sentences like: The term crawling denotes the practice of ... Should I put the word/term crawling in quotes, bold, italic, or something else? I think The term \"crawling\" denotes the practice of ... looks a bit ugly but is probably easier to read. On Wikipedia, most terms seem to be formatted in bold font.", "label": 1}
+{"snippet": "This might seems off topic or something, but I am a middle school student and i'm really into Quantum Field Theory and String theory and every video on youtube or article on the internet shows only the concept and Intro to these theories but I want to know about the maths envolved and do the maths myself as well , so i would love it if you guys would be suggest me a site or anything else where i can learn from scratch all the maths involved in Quantum Mechanics and maybe Einstein's Relativity as well.", "label": 1}
+{"snippet": "So the category of affine schemes is dual to the category of commutative rings, Stone spaces are dual to Boolean algebras, localizable measurable spaces are dual to commutative Von Neumann algebras, and I'm sure there are many more examples. In general, a category of algebraic structures is going to be dual to some related category of geometric structures. My question is, then: is there an analogous story for coalgbraic things? If I take a category of coalgebras for some comonad and flip the arrows around, will I get something interesting? Are there any good examples of this over familiar comonads (say, the costate comonad)?", "label": 1}
+{"snippet": "I've been trying to find one single word that covers knowledge concerning both the properties and cultivation of plants, but have come short with some words. Here are some of the words I thought of, but eventually found lacking: Botany: I feel this implies purely scientific research on plants, ignoring the cultivation of plants and things like crop rotations and irrigation techniques. Agriculture: I think this word only covers food crops and plants commonly grown for decoration. I feel it misses out on the more thorough knowledge of all (not just commonly cultivated) plants, including currently unknown ones. Ultimately, I'm looking for a word that encompasses the subjects of both Botany and Agriculture, but have come short for now.", "label": 1}
+{"snippet": "I'm trying to come up with a better word to describe a \"driver\" or \"conditional\"; basically, the name of an object or event which is a trigger for something else. Would it be appropriate to say that a button which turns on a light is an affector? If I believe I understand its usage in this context, it would only be an affector while triggering the event (the button is pressed). I've been unable to find support to convince me that this is the appropriate use of the word.", "label": 1}
+{"snippet": "I just need to know what exactly happens when charging/discharging a capacitor. Is there any heat transfer between the capacitor and the surroundings? Is there a heat transfer between other parts of the surroundings (wires, the battery)? Another thing I don't understand generally... How do we know if a process is reversible or irreversible? Should we take the third law of thermodynamics as a principle and calculate the change in the entropy of the Universe through the formula given for entropy? If so, how about a process like the free expansion of a gas in which there is no heat transfer but the entropy increases? What about an adiabatic process? Where is the start point for calculating the change in entropy of the Universe for charging/discharging a capacitor?", "label": 1}
+{"snippet": "Me and my dad are having a dispute over if this is is a run on sentence or not: From making silly pictures on Photoshop to playing a game that brought me to another world, and even being dubbed as the IT guy in elementary school. He argues that it's a run on, and the ending can't stand on it's own. I think otherwise. May anyone help settle this debate?", "label": 1}
+{"snippet": "I was wondering if there is a method for finding primitive idempotents of a finite dimensional algebra (over a field)? or in other words is there any way to build the complete set of primitive idempotents from one (idempotent)? Or if it is impassible to find a method, I believe a good reference or some tricks (general notes) on idempotents is also going to be very useful to me.", "label": 1}
+{"snippet": "Sometimes, I forget to use the proper form when an adverb is required. Or sometimes it simply doesn't appear to me one is required, unless I actually consider the grammar of my sentence. I suppose that's mostly because in my native language (German), there is no morphological difference between an adverb and an adjective. This led me to wonder: Is this distinction in English merely an idiosyncrasy or can I really semantically convey something other than intended, if I omit the suffix by mistake?", "label": 1}
+{"snippet": "I'm doing an analysis, of client contracts that contain the following factors: The per-unit license price (A) The initial order quantity (B) The recommended retail price (C) What I'd like is a single figure that represents \"How good of a deal\" the client got, with the quality of the deal being a low license price in comparison to both the initial order quantity and recommended retail price. Generally speaking, The per-unit price decreases as the initial order quantity increases. The per-unit price increases as the recommended retail price increases However, as the contracts were often negotiated, there is a lot of deviation between the individual contracts. How can I go about this? My math is embarrassingly super rusty.", "label": 1}
+{"snippet": "This is perhaps a beginner/simple question, but how does includegraphics determine the \"box\" encapsulating a vector graphic embedded on, say, a letter-size paper? When I read my EPS files (generated with Matlab) using GhostView, they appear in some corner of a full-size, otherwise blank page. Do the various page properties (like orientation, type, etc.) matter? And why does there need to be some blank page underneath the saved graphic for that matter? I'm trying to understand how best to prepare figures for publication. Thanks in advance.", "label": 1}
+{"snippet": "What is the principle behind centrifugation? I understand the idea that you spin something around the centripetal force will cause an apparent force on the spinning system. However I don't quite grasp how particles (in the non subatomic sense) with different density should be affected differently. Quite coarsely, I would expect to write down Newton's second law, but then the mass would simplify and the acceleration of every particle would be the same, regardless of mass. Is friction the answer? Or am I missing something silly?", "label": 1}
+{"snippet": "For a long time I have been investigating this question on my own, but it seems impenetrable. The question is this: To find a method whereby it becomes possible to convert proof A into proof B, where the proofs A,B can be of anything, e.g. a lemma, theorem, etc. For example, it is possibly in geometry to solve something by means of coordinates or by means of euclidean geometry. However, these proofs are usually found one after the other, independently, and not derived one from the other. I am asking if it is possible to derive the euclidean geometry proof directly from the coordinate proof, or vice versa. I would really appreciate any insights regarding this from experts, or papers/articles that touch on this topic. Thanks.", "label": 1}
+{"snippet": "I have some confusion over the ER=EPR conjecture. In what way does entanglement in the laboratory lead to black holes? I must not be reading the literature correctly. Perhaps it should read \" It's possible to entangle particles near an Einstein-Rosen Bridge in a way to effectively show ER=EPR by appropriate measurements. Perhaps some confusion on my part on what the target of the conjecture is so I can image what sort of measurement would be used. It's difficult for me to think of physics without a measurement.", "label": 1}
+{"snippet": "Here is an example from Murphy's grammar textbook: You are in a restaurant. You and your friend are looking at the menu. Maybe your friend has decided what to have. You ask her/him. You: What ...? The correct answer is \"What are you going to have?\" My question is: the decision is being made at the moment of speaking, so shouldn't it be \"What WILL you have?\"", "label": 1}
+{"snippet": "So everybody says the gravitational field has no curl, and is not comparable to a liquid swirling around a drain. Observationally, of course, there are many examples of vector fields (which I think are gravitational fields) which look like they have some curl. A pair of stars, for example, one being slowly devoured by the other. The path of the swirling gas seems to trace out a field with a lot of curl in it. Just as if you were to pour dye into water that is swirling around a drain. How do you reconcile the observed vector field with the gravitational field which is not supposed to have curl? Is there some way to work them into a single model?", "label": 1}
+{"snippet": "I am looking for a book (or article, or notes...) explaining details about the link between integral points on varieties defined as complement of certain divisors and integral solutions to the equation(s) defining the divisor itself. Namely, if I have a projective space defined over a number field and a divisor defined on it by a polynomial, I can define integral points on the complement of such divisor (quasi-S-integral points, following Serre). I know I could do (and I have done) the work by myself, but I am pretty sure that an expert review could give me examples, insights and references I am missing. Thanks!", "label": 1}
+{"snippet": "It's common to say that a pregnant woman is expecting, but is it acceptable to say that her husband is expecting? I ask because my male teacher's wife is expecting in a week. In case you didn't know, to be expecting means (for a pregnant woman, at least) that one will be giving birth soon, but it could generalize to males as meaning \"will have a new child soon.\"", "label": 1}
+{"snippet": "I was reading about function and I came across this text, If A and B have same number of elements and particularly if A = B then we only need to prove one of either onto or everywhere defined to prove that it is a bijection. Now I don't get this point. I will be thankful if someone can elaborate this with an example. Thanks in advance.", "label": 1}
+{"snippet": "I have found out that using the verb be in passive constructions such as: I had my house be burned down is incorrect, therefore it should be I had my house burned down. But is it possible instead of be to use get? E.g. The wire is passed through the pliers in a specific way to avoid having it get bent. The rope had its surface wear. The rope had its surface get worn. The rope had its surface worn. The first two sound very odd to me, but just for clarification could you please point out the errors and which ones are correct? Or is using get, be it in -ing or the to infinitive, in any situation along with have incorrect?", "label": 1}
+{"snippet": "Serre's Duality Theorem is well known and well studied and, as far as I know, there is a \"big\" algebraic proof for the general case, which is now kind of standard, and can be found in Hartshorne and other references done pretty much in the same way. On the other hand, there is an analytical proof for the small case of complex algebraic curves (compact Riemann surfaces), which makes use of differential forms, meromorphic functions, residue Theorem and so on. Since the curve case looks special, I was wondering if anyone knows of the existence of a more simple algebraic proof of Serre's Duality Theorem and can give me references. Thank you very much in advance.", "label": 1}
+{"snippet": "In layman's terms, how do you determine the resistivity constant of a non-ohmic material having measured voltage and current? I understand that non-ohmic materials don't follow Ohm's Law, but will this still be able to be used to determine the resistance? Otherwise how can I determine an initial resistivity in order to use R=[rho]l/A to figure out the resistivity? Is there a different formula for this circumstance, or will I need to collect more data? (Yeah, even I know it's a totally dumb question)", "label": 1}
+{"snippet": "Suppose there's a box with one face cold, and the opposite face hot. So when the air molecules hit the cooler face, it will transfer its momentum and energy to the wall, bouncing back with less momentum. And when molecules hit the hotter face, it will bounce back faster. And the hotter side will be hit more frequently by air molecules. So will the box feel any force due to the temperature difference?", "label": 1}
+{"snippet": "If I place two positive charges of different magnitudes on the x-axis (one at the origin, one at the some position x), as the two charges repel each other are the forces that they impart on each other the same? Why? Edit: I'm working on a problem that has that situation, and the problem asks for me to find the position of one of the charges if the other one is at a given position. Why can't I just set the two forces equal to each other and use that to find the position of the other charge?", "label": 1}
+{"snippet": "I have to do an experiment about light. I preferred to measure the speed of light by the experiment of Michelson and Morley. When you do the experiment, it will result in an interference pattern by changing the distance of one of the mirrors. I know they had the intention to measure the speed of light relative to the ether and the earth. But how could they derive the speed of light with the resulted interference pattern?", "label": 1}
+{"snippet": "If I call my mother when I am done shopping in the morning, I might tell her \"I am coming home\" if she is at home, but \"I am going home\" if she is not. That afternoon at home, discussing the day's events with my father, I could say \"I had already planned to come home after shopping,\" or \"I had already planned to go home after shopping.\" Which is preferred, and why?", "label": 1}
+{"snippet": "A pattern that begins a word is generally denoted as \"prefix\", one that ends a word is generally denoted as \"suffix\". Is there a word that indicates a pattern that surrounds a word. For instance (hello), is there a word that indicates the parentheses? So if I have several patterns i.e.: \"hello\" (hello) {hello} [hello] etc. What word do I use for the surrounding pattern?", "label": 1}
+{"snippet": "I am not a native speaker of English and I am now reading a Sci-Fi book called Dune. I am unable to grasp all the sentences but I do get the overall meaning of paragraphs. But this sentence is completely puzzling me. One of the slave-concubines permitted my father under the Bene Gesserit-Guild agreement could not, of course,bear a Royal Successor, but the intrigues were constant and oppressive in their similarity. Here are my doubts: The \"could not\" refers to the agreement or the permission by the slave-concubine? The \"intrigues\" refer the details of the permission or the agreement? Could someone please help. I really enjoy the book and would love to understand it better.", "label": 1}
+{"snippet": "A person repents to God. Then God responds to their prayer and (v) their repentance. What verb goes here? What is the correct collocation? The only examples I can find on the internet are : 'I was earnestly begging of God to give me repentance.' and 'Then hath God also to the Gentiles granted repentance unto life.' However, the meanings of these sentences are unclear. Does 'give/grant repentance mean that they were given the chance to repent? That's not the meaning I'm looking for.", "label": 1}
+{"snippet": "I've just lost a word I use frequently whenever talking about the reasons for punishments. The word should (I think) fill the blank: Punishments, such as jail time, __ people from doing crime. The word is related to stopping, hindrance, incentive, restrict, etc. In this usage, it should also imply that it stops people from committing crime because they don't want to go to jail. Jail also stops people from committing crimes because they can't leave jail. It should fit both of these simultaneously. I hope this isn't too far of a stretch.", "label": 1}
+{"snippet": "I'm using TextMaker. This is my first time using bibtex. I tried a simple example found in forums where I created a .bib file and ofcourse a .tex file. Problem occurred when I tried to run my bib file. It says \"Log File not found!\". My .tex file runs fine. I know this is not supposed to be that complicated. As I just want to create a simple bibliography using bibtex.", "label": 1}
+{"snippet": "I have seen some similar questions but I admit I'm a newbie when it comes to cgi and general server setup and need some direction. I have a personal domain hosted on yahoo.com that I would like to install LaTeX on. I would like it so that it works in the following (or similar) way. Typing <img src=\"www.mysite.com/latex.cgi?{my formula}\"> will create a rendered gif that I may post on other websites, mainly forums without LaTeX support where I like to help others. Only basic packages are required for my uses (at least for now), things such as Tikz are not needed. So is this very difficult to do?", "label": 1}
+{"snippet": "In many religious calendars, the day goes from sunset to sunset. When translating to the civil calendar, you can divide that day into two parts: from sunset to midnight (A), and from midnight to the following sunset (B). For terminology, \"eve\" works well for part A. Is there a term for part B? The closest I've found are \"day\", \"morning\" and \"morrow\". Is there another term that could be used?", "label": 1}
+{"snippet": "Do you think that the following sentence structure is correct? \"Attach any material you need included\". I meant to say \"Attach any material that you need to include\". I agree it may not be formal but I don't think it is wrong or difficult to understand. Do you think that the sentence is wrong? If yes, where do you think the problem is? Could anyone help me with this?", "label": 1}
+{"snippet": "I'm trying to understand the symmetry content of the conductivity matrix: one information is, presence of time-reversal symmetry causes the off-diagonal terms to vanish. When this is broken (e.g. in Hall effect) off-diagonal terms become finite. (A side question is, why is the conductivity matrix always anti-symmetric?!) Apart from that, does it contain any information about the spin of the charge carriers. My guess would be it should not, as one computes conductivity using classical theory. If I take a spin-orbit coupled (SOC) system (where inversion symmetry is broken), will the SOC information be present in the conductivity matrix? If it is, then how? What other symmetries in the system are relevant for the conductivity matrix?", "label": 1}
+{"snippet": "I have heard that in America, and likely elsewhere as well, we are beginning to be more gratuitous with our use of extreme words when not entirely accurate, such as the words \"awesome\", \"always\", \"never\", \"crazy\", etc. Is there a word or phrase to name this phenomenon? What are the implications of this behavior with respect to our use of language and its effect on our lives?", "label": 1}
+{"snippet": "In the photocurrent experiment, if the intensity of light is kept constant, but the frequency is slightly increased, what's the effect on the saturation current? I think saturation current should decrease because the number of photons should decrease. But, all my reference books say that the saturation current depends only on intensity, and since it is constant, hence there will be no change. Can you please tell me which reasoning is correct? And why? EDIT: Another confusing factor is the energy of electrons. If the electrons have more energy due to the increased frequency then I would take less time to get to the anode and that should increase the current. Now, which factor is more dominant? And how do i know that?", "label": 1}
+{"snippet": "I couldn't help but wonder every time I saw such a noun phrase. I've seen both forms used equally often, so I guess both of them can be used interchangeably. But do I guess right? Some examples: Here is a frequently used compound nouns list. Here is a frequently used compound noun list. I usually rephrase them into something like this. Here is a reference list of compound nouns.", "label": 1}
+{"snippet": "I think I understand both the centrepedal effect and Einsteins curved space time. However I am confused about which best describes the motion of a planet ( or other orbiting body ). Simply put, does the earth experience any centrepedal effect or does it just follow the geodesic line and therefore not experience any centrepedal forces. Can someone please explain or let me know that science has yet to answer this question.", "label": 1}
+{"snippet": "So I have to write a report paper for a course and I would like to prove that the q-Gaussian is the distribution which arises once one maximizes the Tsallis entropy. But I face difficulties in proving it. Actually I am quite new to the field of Statistical Mechanics and not really familiar with the methods of going through a proof like that. Could it be possible that someone providess a reference which provides the proof or show me how to actually maximize a distribution, so that I am able to start at least from that? Thank you!", "label": 1}
+{"snippet": "Every word I say is true; this I promise you. I think the pronoun 'this' is the direct object of the verb 'promise' and 'this' should be be placed after 'you', but it is placed at the beginning of the sentence. Because this sentence is on a web page about English grammar at http://grammar.yourdictionary.com , I believe this is not grammatically wrong. Is this an exception? Then, how can it?", "label": 1}
+{"snippet": "Is it theoretically possible for an object or particle to change to the opposite direction without making a complete stop first? Lets say I have a fictional hammer swing setup like this: I fire an electron to the hammer and the hammer smashes it back, is it possible for the electron (or any other particle or body) to change direction without slowing down and making a complete stop? If not, which law defines that? Note: the question isn't about the hammer part but that was just the first thing that came up in my mind.", "label": 1}
+{"snippet": "I have recently been reading about Quantum Electrodynamics which I found very interesting, but even more confusing. I understand photons mediate the electromagnetic force and interactions between charges can be described by virtual photon exchange. And that in Quantum Mechanics particles paths can be evaluated by sum over all paths... An electron travelling from one point to another will take all paths, emitting and reabsorbing virtual photons. Does the electrons take all paths including those that involve faster than light velocities? Is this question null, Does it mean anything to ask about properties of virtual particles? Do I have the wrong idea about what virtual particles are?", "label": 1}
+{"snippet": "Lets consider the following: The book doesn't explain, \"What's the wisdom behind education?\" Changing this to an indirect question becomes the following: The book doesn't explain what the wisdom behind education is. Now, I found many instances on Google where structures like this weren't really converted to indirect questions. For example: The book doesn't explain what's the wisdom behind education. \"[She] doesn't say what's really on her mind.\" Edit: And consider the following: What's the logic behind it. (a) I wonder what's the logic behind it vs. (b)I wonder what the logic behind it is. (a) sounds better but why? And are these constructions acceptable?", "label": 1}
+{"snippet": "I vaguely remember seeing something like a \"picture\" of various groups a while back. It was as if the elements of the group were each associated with a point and many points had segments connecting them, but not all were connected. Does anyone know what I am talking about? If so, would you care to take the time to explain the basics (or point me to a resource, if you think google won't help)? Thanks.", "label": 1}
+{"snippet": "Is it possible for a black hole to be ejected from a galaxy after an encounter with the central supermassive black hole? What would be the impact of the passage of the hyperV-BH through the galaxy? Is it observable? Have we observed any hypervelocity black holes? What experimental techniques do we need to be sure (how should current methods to discover gravitational lensing be modified)? Please note that arXiv papers and articles out there mostly talk about hypervelocity stars.", "label": 1}
+{"snippet": "I'm thinking of writing a paper on a new way of deriving the conservation of energy from symmetry principles and the Galilean transformations, but I'm not sure where to publish. Taking a look at AJP, it tends to be there for teachers at universities writing papers on how best to teach a certain topic, and to clear up misunderstandings. On the other hand, my paper certainly isn't to do with cutting edge physics, but merely another approach to something that is understood in other ways, and therefore not worthy of being published in Physics review, say. So where should I publish? More generally, how are the papers physicists publish mainly categorised, and which main journals publish papers in these areas?", "label": 1}
+{"snippet": "Hmmm... You can definitely drop down the voltage, and ideal capacitors don't dissipate any power. So it seems, at first glance, that you could use a capacitor divider as a lossless voltage step-down device for AC. So you could use a cheaper variable cap divider as a replacement for a Variac? And it would be continuously variable, too, whereas the Variac is only variable in discrete windings. There has to be something wrong with this. What am I not thinking of?", "label": 1}
+{"snippet": "I am stuck in this problem for a while, and the main idea will be important for some exercises, so I really want to know how to find an example like this I need an example of an proper ideal, let's say M, of C[x,y] (the ring of the complex polynomials in x and y) such that the quotient C[x,y]/M do not admit a homomorphism f(x,y) -> f(a, b) (for a, b complex numbers) from C[x,y]/M -> C.", "label": 1}
+{"snippet": "I've been wondering if there is a word to express that something was current at the time of its creation. It (in bold) should plug-in into a sentence similar to: The results are based on an analyses that deal with the then-current methods. As far as I can tell, both \"contemporary\" and \"current\" refer to now, whereas I would like to express something was \"current\" in the past.", "label": 1}
+{"snippet": "I am looking for a textbook in control theory (for a friend) that covers topics such as Pontryagin's maximum principle. My friend is not a mathematician by trade, but holds a degree in applied mathematics (and is thus not math-shy, but prefers to skip detailed discussions on regularity and prefers intuition). Recent aspects of control theory (e.g., viscosity solutions) need not be present. (I apologize for all the parameters)", "label": 1}
+{"snippet": "What would you call someone who does things knowing specifically that his/her actions will cause pain and/or conflict or completes an action just to get someone in trouble or hurt them? For example, in Private Peaceful there are two people that are in love, but the Colonel goes out of his way to tell the father of the girl that the boy is a thief and would be bad for their reputation. What is a word that would describe him?", "label": 1}
+{"snippet": "In the phrase \"My dog wiggles it's butt\" there seems to be a division of opinion as to whether the use of the apostrophe is grammatically correct. I suggest that as the dog in question is the owner of the butt in question and that said dog is an animate object replaced by the use of the word it then the apostrophe is a correct. Just as we use the apostrophe to show possession in the phrase \"Mary's head.\"", "label": 1}
+{"snippet": "To negate a participle phrase we use not at the beginning of it, as in \"Not having heard the news, he had no idea what was going on.\" Can we also use the negative particle in some other porition in the sentence without it making any change in the meaning of the sentence? As in \"Having not heard the news, he had no idea what was going on.\" Is it entirely wrong or is it used in spoken English by native speakers (even as a common mistake among native speakers of English)?", "label": 1}
+{"snippet": "So I've been correcting an architectural piece translated into English, wherein a sentence befuddles me: ...A wooden table... marked the location of a previous bench. What the author tried to say is that a wooden table is now located where once stood a bench. This usage of previous simply doesn't feel right to me. Any advice? PS, what about location in that sentence? For me, if a noun has to be used, locality seems to work better in the sense of \"the fact or condition of having a location or position in space\" of the word. Or am I over-scrutinizing things here?", "label": 1}
+{"snippet": "I would like to express that I fundamentally upgraded something in a concise way. That is, I did not create that something, but it is almost as if I completely redesigned it and made much better. The word would be used in the following way: I fundamentally upgraded the manufacturing process to allow for considerably higher modularity and efficiency. 'Improve' or any of its synonyms are too weak, whereas 'fundamentally upgrade' seems too clumsy to me. I guess 'revamp' is pretty close but it seems to me that this word might be too informal or not be appropriate in the given context. Do you see any alternatives?", "label": 1}
+{"snippet": "Currently using BibDesk with TeXShop (for mac). The apalike bibliography style is pretty much perfect for how I like (and more importantly my advisor likes) to do my references. The only problem is that the citation that comes up in the text [Author, Year] is repeated before each entry in my reference list at the end of the document. Is there a way to remove this so I may just have the Author, Year, Title etc. as normal just without this extra square bracketed part at the beginning? Here's what it looks like: Many thanks for any contribution you may be able to give in advance!", "label": 1}
+{"snippet": "If there is a mechanical device which is controlled by electronics, these electronics can be hidden inside the device itself or hang outside it and connected to it by wires. Is there a word which indicates the second option, without writing a lengthy sentence? Example: instead of: \"... a device with a controller connected to it by wires\" something like: \"... a device with a controller _ wires\". (in wires? on wires? by wires?) \"on wires\" would seem to be the logical choice to me, but I couldn't find a single relevant phrase on Google.", "label": 1}
+{"snippet": "Not too long ago, someone began to discuss the thinking and motivation behind the Lagrangian and its formalism for the Newtonian framework and an intuitive understanding of such formalism. Somehow, it ended in the case that the Lagrangian can be understood in terms of conservation of information (largely) without having to rely on other laws. Is this line of argument correct? And, more importantly, would this mean that unitarity is a stronger statement than conservation of energy?", "label": 1}
+{"snippet": "I would like to hack a new BibTeX style file based on plain.bst, in which I make it possible to display the value of a location field in the inproceedings entry type. I have started as follows: I have added location to the list of defined fields in the ENTRY block. In FUNCTION{inproceedings}, I have simply inserted the line location output right after where it prints the booktitle. This works! However, now I would like simply to enclose the value of location in parentheses. I have tried defining a FUNCTION{format.location}, but I don't understand the BibTeX language well enough to get this right. Any suggestions for the function? And how do I call it in FUNCTION{inproceedings}?", "label": 1}
+{"snippet": "I just don't get the concept behind why a lens or a mirror forms a reproduction of the object at present. Is it to do with the object blocking parts of the light source? I just don't understand why an image of that object is produced. The question is essentially trying to understand what causes the image to be produced from the object, in the first place.", "label": 1}
+{"snippet": "I am rather puzzled and confused, I have been trying to get a clear understanding of how would spectral clustering work for an undirected weighted graph, I have used the normalized Laplacian, but I always get complex not strictly positive eigenvalues, all the resources I am finding build on the results that the Laplacian is real symmetric positive semi-definite matrix, hence real non-negative eigenvalues. Any guidance is greatly appreciated, specially in the answer to the question if I take the norm of the normalized Laplacian would spectral clustering algorithms be still valid with same results.", "label": 1}
+{"snippet": "Is there any \"second-countable\" theorem ? With this i mean if there is any result like Nagata-Smirnov Theorem (that states necessary and sufficient condition for a space be metrizable), but for second-countable spaces. Also, with Urysohn Metrization Theorem it's straightforward to prove that if a space is compact and Hausdorff, then is secound countable iff is metrizable. Is there any result like this but with the hypothesis that the space is only Hausdorff (i mean, something like : Let X be a Hausdorff space. Then X is second-countable iff [something]) ? Thanks a lot !", "label": 1}
+{"snippet": "As an external observer at infinity, I observe a star collapsing. But because the surface of the star will be infinitely redshifted, I will never see the formation of the black hole. For me, there will be always some matter outside, it never crosses the event horizon. So, can I observe the Hawking radiation if I never observe the formation of the black hole ?", "label": 1}
+{"snippet": "A finite presentation is a presentation where the set of generators and the set of relators are finite (Source) I'm studying for an exam where one of the \"exam topics\" is: The example of the infinite presentation. But what is an infinite presentation? From the finite presentation my first thought was a presentation where the set of generators and the set of relators are both infinite. But since I can't find any example on this in my notes, I suspect that the definition only requires that the set of relators is infinite.", "label": 1}
+{"snippet": "So basically, you have three different types of 'things' (for lack of a better term): You have that which is necessary, that which is contingent (you have a choice), and that which is necessary but only because it must be so after a contingent choice has been made. So it's necessary, but not to begin with, and is necessary in a very different way. I guess you could call that which was necessary to begin with, necessarily necessary, and that which is necessary by choice, not necessarily necessary. But of course, am sure there's a better word, or at least term, to describe this phenomenon.", "label": 1}
+{"snippet": "I took matrix computations course, our course book is Numerical Linear Algebra and Optimization. As a computer science student, sometimes I get the impression that I lack some fundamental background knowledge about it. It'd be great if you could introduce some useful but not very long elementary linear algebra sources (not very long, since I should get back to my course book ASAP). Please note that I've Googled the subject and got some cookbooks but I am looking for some sources which are specifically related to the above mentioned book and covers those topics.", "label": 1}
+{"snippet": "I have see a lot of people said it is not possible to draw a circle by Bezier Curve. However, I want to know why? I did see somebody explain, but I am not quite sure what they mean. Like, Bezier curve is parabola, so it is impossible to draw a circle by it. But how can I proof it? proof that Bezier curve is only parabola and never be circle?", "label": 1}
+{"snippet": "I know that demonstrating the Mandelbrot Set is connected requires a non-trivial proof, and that Mandelbrot himself was fooled at first. But can it be demonstrated visually that the set is connected? If the Set were known to be path-connected, I might hope for a computer program that would let me select two points in the set and demonstrate the path between them. Showing connectedness visually seems harder to me. Is there an intuitive way to do it? Perhaps allow the user to draw a region R and then identify at least one point on the boundary of R is in the Mandelbrot Set? Unfortunately that seems less satisfying than demonstrating a path.", "label": 1}
+{"snippet": "I'm currently studying electricity on my own, and as I read in a metal electrons are moving across the metal freely (depending on the attraction of the nucleus). As we close the circuit, an electromagnetic waves spreads into the metal moving the electron from the minus pole to the plus pole. Can someone explain to me why is there an electromagnetic wave created when we close the circuit and why it forces the electrons to move like this? Thanks a lot", "label": 1}
+{"snippet": "Which one should it be? One of the guys' One of the guy's EDIT: Never mind, I think I answered my own question. I realized it would probably be related to the object being possessed. E.g.: \"One of the guys' swords\" means \"There are multiple guys. They own multiple swords. I am referring to one of those swords.\" \"One of the guy's swords\" means \"There are multiple guys. One of them owns multiple swords. I am referring to one of those swords.\"", "label": 1}
+{"snippet": "Can anyone please explain exactly how formulas like Tupper's self referential formula can be constructed? I'll like to see the reasoning behind the derivation of such formulas and the steps required to create a new one. NOTE: I know Tupper's self referential formula is not as 'self referential' as it is claimed but some form of 'universal' formula capable of producing any bitmap of a given size, given the value of N.", "label": 1}
+{"snippet": "Imagine a structure that is held above the water by pylons that are grounded on the ocean floor. In between these pylons is a pontoon that, when tides are rising holds and lifts a heavy weight. When the tide is falling the weight is supported by the structure, which can gradually let the weight down, and in doing so create electricity. Would this be a practical or even viable way to create electricity? Why or why not?", "label": 1}
+{"snippet": "I have a image in a beamer and I want to overlay a table on that image. How can I achieve that ? I have a figure that I created in powerpoint which is as follows: In the above figure, the statistical parameters such as RMSE and NSE are added later. Is it possible to add similar thing in latex beamer ? I want to show the text first on the upper panel and then on the bottom panel. Thanks.", "label": 1}
+{"snippet": "I wonder what could be a good book to start learning in depth all aspects of the Fourier transform up to the FFT algorithm, and beyond. I am going to dedicate quite some time on the subject, so I expect something with a lot of exercises (calculus, demonstrations) and solutions, from the basics up to the most complex topics. Could be nice to also have some exercises (with solutions) with practical applications in Matlab or Python/Numpy. Any pointers? Tutorials, books, chapters, websites? thanks! :)", "label": 1}
+{"snippet": "I was trying to measure the noise of a device with metal probes. I was not sure whether I should trust the results because I was told contact noise might contribute to some degree. I am a little confused about the notion of \"contact noise\". Is it because of the contact resistance (every resistor is a noise source)? Or is it something related to other factors such as probing materials or surface? Could anyone make a brief explanation? I am eager to know the origin of this \"contact noise\", and how I can evaluate such noise.", "label": 1}
+{"snippet": "Usually, I think \"have to\" indicates obligation, which is pretty similar to \"must\". But today I found this sentence and its usage of \"have to\" confused me: (it is from NYTimes.com) Long-term forecasts seem to me rather like time capsules, designed more to provide retrospective amusement for those who eventually have to read them, than to be taken seriously as they are first uttered. It would be uncomfortable to interpret have to as must since we are not \"compelled to read them\". Can anybody explain this for me?", "label": 1}
+{"snippet": "For Hausdorff spaces the following are equivalent: Every point admits a compact local base. Every point admits a compact neighborhood. Every point admits a precompact neighborhood. Every point admits a precompact open neighborhood. (Among these the local compactness is the usually applied one.) For non-Hausdorff spaces: What are examples where neither of them are equivalent? What situations make the latter two become important? (I'm just wondering as these are almost always taken as definition.)", "label": 1}
+{"snippet": "In German, there's a term \"Reizblase\" which describes the bladder of someone who has to hit the bathroom every ten minutes. The dictionaries suggested \"irritable bladder\" as a translation which - seeing how other \"Reiz-\" organs are also called \"irritable\" - makes sense. The thing is, the German word holds up nicely in a highly colloquial sentence. I'll try to emulate that in English. Dude, again? WTF? You really got yourself one irritable bladder right there. I am not a native speaker but I feel like \"irritable bladder\" doesn't fit in with the rest of this sentence because it is a different register. Is there a more colloquial term? If not, would people say a sentence like the one in the example?", "label": 1}
+{"snippet": "Basically a friend of mine and I have had this hot debate for a little too long, I contend that these two tools are not only logically unconnected but they require different assumptions (I believe one requires a continuously differentiable function and another requires it to simply be continuous). We've even gone through the proofs and disagree on how the assumptions are used. I don't see the connection... Maybe I'm wrong, maybe they are equivalent (you have one as a tool if and only if you have the other). Anyway, any fresh perspective would be welcomed and any deeper discussion on either appreciated, thanks.", "label": 1}
+{"snippet": "There are many books, in which Yang-Mills theory is introduced \"just like that\". But I didn't find some book with set of historical arguments, which had led people to using it in quantum field theory. Can you tell me about this? Maybe, my question leads to the next question: how did people guess that they need to expand the group of local gauge invariance for describing, for example, quarks?", "label": 1}
+{"snippet": "When saying a sentence like: Nikola Tesla __ famous because he was a genius. Should the blank be replaced by is or was? Or is it dependent on when the person is/was famous? If so, what exactly are the rules? I searched on Google and English.SE but didn't find an answer, even after using quotes to counter the amount of stop words in the question...", "label": 1}
+{"snippet": "When I look in old mathematical textbooks from the seventies and before, mathematics is always upright. Their use of italic letters in other contexts, however, shows that this is not because of technical limits. On the other hand, all textbooks I have seen with italic math look very TeX-like. So I was wondering if this is a coincidence? could italic math be an invention by Knuth introduced in TeX? Does someone know the history of italic math?", "label": 1}
+{"snippet": "In compton scattering, a photon may deliver only some of its energy to an electron. But when dealing with photon electron interaction in an atom, it's all or nothing. Why the difference? Also, within compton scattering, given the initial wavelength of the photon, we get a relationship between scattering angle, and wavelength of the scattered photon. But we can't know the scattering angle without knowing the wavelength of the scattered photon. So there's a free variable. What determines the wavelength of the scattered photon? Is it some type of random process? Thanks in advance.", "label": 1}
+{"snippet": "Possible Duplicate: Is the word 'whose' referring to an inanimate object correct in this sentence? Is there a more appropriate word? Basically I'm wondering if a sentence like this is grammatically correct: \"Meaning is thwarted by its delivery, whose poetry is relative to taste.\" I cannot avoid it with, \"Meaning is thwarted by its delivery; its poetry is relative to taste\" because 'its' seems to refer to 'meaning.' There needs to be a word like 'whichs' or something. Or is there? Please clarify my question if you know the proper grammatical labels for what I'm talking about; I know them not.", "label": 1}
+{"snippet": "I was going to post a comment on my own theory about Mars and Jupiter colliding, but I just read the rules and it breaks it...badly. I was looking for informal peer review. So my question is, has there been any mainstream published work about the possibility of planets colliding or interacting greatly? (Velikovsky doesn't count obviously, I'm thinking an actual scientist) (besides the Earth-Moon of course) I can't seem to find any.", "label": 1}
+{"snippet": "Question: Find a conformal map from the exterior of the closed unit disk to the unit disk. Also, prove that it is indeed a conformal map (bijective and holomorphic along with its inverse). I missed that the two days we covered conformal mapping due to chaos in my life. I have been trying to find worked out examples and have been reading up to get some insight, but I am lost since I can't find something that details a complete worked out problem. p.s. If anyone knows a great resource that would help me out to further my grasp of conformal maps in complex analysis it'd be much appreciated if you could disclose this.", "label": 1}
+{"snippet": "Consider the following situation. You are standing in a room that is perfectly circular with mirrors for walls. You shine a light, a single ray of light, in a random direction. Will the light ever return to its original position (the single point where the light originated from)? If so, will it return to its position an infinite amount of times or a definite amount of times? Will it ever return to its original position in the original direction? I thought of this little teaser when reading about a problem concerning rays in a circle and wondered about this question. As for my attempts, this is well beyond my skill.", "label": 1}
+{"snippet": "An proverbial anecdote I've heard for a problem solving deadlock is something along the lines of: A farmer needs to fix a bucket, which requires this, that then requires that and so on and so forth until it requires a bucket to fix the bucket. However I haven't been able to find this particular proverbial anecdote for a problem solving deadlock, so I'm wondering: What is the most common (folksy?) proverbial anecdote for describing a problem solving deadlock?", "label": 1}
+{"snippet": "What does this phrase from The adventures of Tom Sawyer sentence mean: \"True, the knife would not cut anything, but it was a \"sure-enough\" Barlow, and there was inconceivable grandeur in that -- though where the Western boys ever got the idea that such a weapon could possibly be counterfeited to its injury is an imposing mystery and will always remain so, perhaps.\" Thank you!", "label": 1}
+{"snippet": "Given a Matroid (E,I), I is a set of independent subsets of E, right? And independent subsets means that no two of these subsets must have an element in common, right? Now according to the hereditary property of Matroids, if A is a subset of B which is a subset of E and if B belongs to I, then A also belongs to I. If A is a subset of B, then all the elements in A are in B, then how are these two independent? All the sets that are supposed to belong to I (i.e. A and B in this case) must be independent (i.e. must not have any common element) right?", "label": 1}
+{"snippet": "I am currently reading about the subject given in the title of this thread. The definition they give for equivalence classes in my textbook is a rather ostentatious in its wording, so I just want to make certain that I am understanding it properly. They say to let R be an equivalence relation on a set A, meaning that this this particular relation is reflexive, symmetric, and transitive, right? Essentially the rest of it seems to say that you can partition off the elements that make the relation reflexive, thereby creating a subset of the relation R. Does that seem right? I could really use some help, thank you!", "label": 1}
+{"snippet": "I am studying various crystals and the two-dimensional materials that could be potentially obtained by cleaving them (isolating a region bounded by two parallel planes). In elucidating the properties of these materials, it would be good to know what symmetries could the cleaved material possess given the symmetry of the original crystal. What is the best way to approach this problem? My question can be alternatively interpreted as follows: how to find all the layer subgroups of all the space groups? (\"Look them up\" is a legitimate answer for my purposes, if you can tell me where to look!)", "label": 1}
+{"snippet": "Are there any resources online for astronomy experiments that I can perform myself? I am looking if anyone knows any measurements to take while looking for various objects during the evening particularly using a telescope/binoculars. A couple of examples would be determining the orbits of the moons of Jupiter through an evenings observations or trying to measure a stars parallax from measurements throughout the year. I can think of a handful of other ones but was wondering if there were any other resources to provide some more ideas.", "label": 1}
+{"snippet": "So, I've noticed over time that I see both \"afterward\" and \"afterwards\" at different times. Having a pet peeve (though I'm not certain it's actually a well-founded prejudice, lexicographically speaking) against hearing \"anyways\", I've started to wonder recently about \"afterwards\". With a quick bit of web searching, I turned up this analysis, which I find to be somewhat helpful, I'm just wondering if there's more that people could say to help me get an intuitive understanding of when to use which, or otherwise why to use one versus the other. I suppose (as mentioned in the linked article) this question could also apply to forward, backward, toward, etc. Which shall I use? When? Why? Does the 's' indicate some sort of plural meaning, or something else?", "label": 1}
+{"snippet": "I am an undergraduate in Mathematics writing his dissertation on General Relativity this year. The next couple of months will be dedicated to learning the math (geometry) and the physics, and to this end I am looking for must-read/must-watch material on the topic. General book recommendations are welcome, but keep in mind I can use Google! I am mainly looking for really good introductory content that I would have a hard time finding myself, whether it be videos, course notes, books or blog posts. My apologies if this is a duplicate!", "label": 1}
+{"snippet": "I am trying to determine if the plane on which two triangles lie intersects for a collision-detection implementation. Unfortunately, I'm stuck at step one, which is finding the plane on which a triangle lies. I tried looking around on Google and what I can find seems to imply that I need to find the normal to the plane instead of the plane, and the direction of the normal. Can anyone explain why I just need to find those two?", "label": 1}
+{"snippet": "You often hear that black holes are so strong in their gravitational pull that matter, even light cannot escape. But this seems to contradict the laws of conservation of energy. Is it possible that perhaps light (photons) are not themselves elementary particles, and within the immense gravity of black holes decompose into some other sub-particle or dark matter that we cannot yet measure/see? I know there is no way, yet, to measure or determine this, but it seems like there is a more simple explanation than matter just \"disappearing\". Thoughts?", "label": 1}
+{"snippet": "If A is a closed set,then what can we say about closure of A^C ? It is a closed set.But my doubt is whether A and closure of A^C is disjoint or not? what i had tried is: if A is closed, A = closure of A. A and A^C is disjoint, so closure of A AND A^C is disjoint.Can anyone help me to understand whether they are disjoint or not..", "label": 1}
+{"snippet": "In terms of dollars per watt, using theoretical efficiency limits, what technology holds the most promise to become the primary solar energy capture technology? My hunch is carbon-based modules, since materials are abundant and relatively easy to manufacture; however their efficiency currently is nowhere near silicon-based semiconductors. In the future, assuming that scientists will push very close to the theoretical limits, what will provide the most power for the lowest cost? If this is relevant at all, I am trying to decide where to focus my graduate studies in physics, and I want to contribute in getting the most promising technology to its limit. If you can at least point me in the right direction to figure out the answer myself, I would greatly appreciate it.", "label": 1}
+{"snippet": "Possible Duplicate: How does gravity escape a black hole? How can gravity get out of a black hole? If a black hole is so powerful that even light does not travel fast enough to get out, and gravity, or rather, gravitational waves, travel at the speed of light, how does gravity get out? And please don't say that the black hole creates a \"well\" in space that other masses \"slide\" down. Such a well would be unstable and, if two black holes pass near each other, neither would be able to \"slide\" down the other since both are infinitely deep. These wells would make gravity selective.", "label": 1}
+{"snippet": "If I have a cup of water filled with air at the bottom of a pool, then when the cup is \"upside down\" the air doesn't leave because the water pressure is pushing it up against the top of the container. But then when I flip the cup, such that it is no longer upside down, the air rushes upwards. But why on earth does this happen? I mean the water's pressure is pushing this air downwards against the bottom of the container. If I were to draw an FBD which force is causing this air bubble to rush upwards? Thanks", "label": 1}
+{"snippet": "Many years ago I heard a radio broadcast featuring a beeping sound that always seemed to come from behind me. The announcer said that the sound would have this quality and it did, even when I turned around. It was a plain beep, and the radio only had one loudspeaker. It was a complete mystery to me then and it still is, so can anyone explain the effect? (Previously posted at https://www.newscientist.com/topic/lastword/its-behind-you/.)", "label": 1}
+{"snippet": "I wrote a technical article in which I used (probably overused) constructions of the form \"The main point is that...\", \"The problem is that...\". As I am a native Italian speaker, these sentences have the natural form that I would use in my language. One of the reviewers suggested that a better way to formulate these sentences in English is \"As the main point,...\", \"As the problem,...\". I feel these sentences carry \"less power\" than my original ones since the main word is not the subject anymore. Any thoughts? Is the construction I used incorrect, inelegant, or good English? Thank you", "label": 1}
+{"snippet": "What do echo and reverbation have in common? They are the reflection of sound waves, they are formed when sound waves meet a hard surface, they cause a repetition of the sound. The waves keep having the same frequency (the source doesn't change); They have the same speed and length as they had before the reflection, because the environment doesn't change. Is there anything else?", "label": 1}
+{"snippet": "I am working (writing and typesetting) on a book for children. I have used the memoir class. The book looks good for an adult audience. But I had ideas of making it more interesting for the children. More specifically, how about adding little thumbnails to the table of contents page? These will be tiny images placed randomly and rotated randomly. Or a different pattern border around each page? Like bright colored zigzag pattern for one page and may be, colored crayon strips on another? With my limited experience and expertise in latex, I could not crack this one. Any ideas/ suggestions/ solutions?", "label": 1}
+{"snippet": "\"Working for the man\". Does \"Working\" act as a noun, verb or something else in this case and why? If I said, \"I am working for the man.\" Then clearly working is a verb. However, I'm confused by the colloquial phrase \"working for the man.\" It seems to have a \"poetic\" tone if you will. Because the subject does not exist I wonder if \"Working\" is a state of being in this case? As \"Peter Shor\" pointed out Maybe the answer is that because this is not a complete sentence then we don't know what role \"working\" plays in the sentence. FWIW, I'm imaginging how I can translate the phrase into Japanese. Which word I use for \"Working\" depends on whether it is a noun or a verb.", "label": 1}
+{"snippet": "Is there an intuitive way to understand the convex duality? If the primal problem is minimization, the dual is maximization over another set of variables - but I would love to have a geometric visualization of this and an intuitive way to understand why this ought to be true. I'd also want to see strong duality present in such an intuition. Textbooks are dense in the math, but I haven't come across a place where this could be imagined in our minds without variables and equations. Could someone here help me out?", "label": 1}
+{"snippet": "If I have two points at different X/Y coordinates, I know that: They are vertically aligned if both are at the same X coordinate; They are horizontally aligned if both are at the same Y coordinate. Based on the X/Y coordinates of one in relation to the other I can also tell the distance between them, etc. Now, how can you tell that the points are diagonally aligned by following the same logic?", "label": 1}
+{"snippet": "We still hang up the phone, even though we really only push a button, not suspend it in a cradle. Sometimes we tape a television series, even though the DVR does the heavy lifting, not the analogue insides of a VCR. Is there a term for these words and phrases? I'm not sure about using words like obsolete or archaic, because the methods they describe may be, but the phrases themselves are not.", "label": 1}
+{"snippet": "Reading the article \"Emergence of scaling in random network, by Barabasi and Albert\" I faced a lot of results obtained by simulations of the A-B random graph model. I always wanted to do such simulations, but honestly I don't know how to start. There is a better programming language? There are packages? There is a special software to handle heavy data? To put everything in one question: how they do that kind of simulation?", "label": 1}
+{"snippet": "As kind of a real-life example, I'm struggling to write a description of the Crusades from the point of view of a Catholic pope. I know that through the Crusades, the Christians basically \"rescued\" the city of Jerusalem from the so-called \"filth\" that inhabited it. (Note: Please do not be offended by my use of the word \"filth\") You might say there's a tip-of-the-tongue phenomenon going on here.", "label": 1}
+{"snippet": "I'd say both of these uses of \"he was shot\" make sense: \"How did he die?\" -- \"He was shot in the street\" [meaning shot dead] \"He was shot in the street, but luckily the bullet only hit his foot.\" [meaning shot at -- there was a bullet coming his way] Would you agree? And what would you think of a headline \"He was shot in the street\". Is the man dead or was he just 'shot at'?", "label": 1}
+{"snippet": "As an American, a large part of my impoverished experience of British accents comes from ancient BBC comedy imports on PBS. I'd very much like to identify the regional accents the following actors are using: the farmer Maurice Moulterd in Are you being Served? Again! (aka Grace and Favour) (the second series where they're running a country inn). Alice Tinker and Owen Newitt in The Vicar of Dibley Onslow from Keeping Up Appearances All four have distinct ways of speaking (not necessarily the same, but then that's the problem, I can't tell). Which accent does each of these four use?", "label": 1}
+{"snippet": "In this question different people understood different things when talking about topological manifolds. Some argued they they have to be Hausdorff, some that they have to be second countable and some, both. When I studied them, my teacher showed us examples of non-Hausdorff (the line with two origins) and non-second countable (the long line) manifolds. For me, a topological manifold is a locally Euclidean topological space. What are the different definitions of a topological manifold you know? What it depends on? What author you read when you studied them? Who was your teacher? EDIT: What properties have the topological manifolds if we define them as second-countable and Hausdorff that they don't have if they are only locally Euclidean?", "label": 1}
+{"snippet": "The problem says \"In a factory, m workers work h hours to do j jobs. If p new workers are hired, how many hours will the work force have to work to do j jobs?\" I worked out the answer logically, but I'd like to know if there's a formula that I can go to to make it simpler and faster when this kind of question arises again. Also I'm really not sure what the type of problem is called, so sorry for any confusion in tagging/titling.", "label": 1}
+{"snippet": "I was surprised to discover my dictionary had this entry for dilemma: a situation in which a difficult choice has to be made between two or more alternatives, esp. equally undesirable ones The notion of dilemma meaning two or more flies against what I was taught about the word. The very idea of a false dilemma is specifically based on the number two. Has my dictionary merely updated its definition to encapsulate the many people who use dilemma for more than two equal choices? Or was someone in my youth being unnecessarily pedantic?", "label": 1}
+{"snippet": "What is the word a deep desire that some external force has kept you from gaining it? For instance in the movie Foxcatcher, the rich guy always wanted to be wrestler but his mother didn't let him because she thaught it was a low sport and it was beneath him and this made a 'deep desire' in him to be a wrestler. Is there a word for that? The word I'm looking has some kind of negative meaning. This 'deep desire' makes you do stupid things and kind of has a bad effect on your personality.", "label": 1}
+{"snippet": "I am learning Mean value property (MVP) of the heat equation. MVP of Laplace equation was relatively easy to understand I think it is because of the spherical symmetry. But I am not able to appreciate the MVP of heat equation. It's not very easy to imagine the \"heat ball\" in the following theorem from a note: Here are questions: How do I define a heat ball? How does it actually look like?", "label": 1}
+{"snippet": "I have read this is true for all hyperbolic triangles, but I am trying to find an extreme example, or a limit behavior, were the sum of the angels of a hyperbolic triangle are minimized. Is there a min/ inf? Also, why do all hyperbolic triangles have angles sum less than pi (if that is true)? To avoid ambiguity, I am referring to hyperbolic triangles in the open upper half complex plane.", "label": 1}
+{"snippet": "Consider the examples from the Free Dictionary: That summer, she up and died. He had lived here for twenty years, and then one day, he up and left for good. Is this a contraction of a longer phrase, making \"up\" a particle (as in \"get up\")? Or is \"up\" meant as a verb, but mysteriously not inflected according to tense/person? (in which case, how did it end up not being inflected?)", "label": 1}
+{"snippet": "If we can think about the universe as a wave function then many particles should be entangled with many other particles in the universe. The obvious question arises why we don't see those entanglements in everyday circumstances. One standard explanation given is those entanglements average out and cancel so we can ignore those. However, hardly any mathematical justification is given for them to cancel. My question is how much trust one should have on that particular assertion? Is there any mathematical arguments already put forward by anyone?", "label": 1}
+{"snippet": "Do matter and antimatter eliminate each other or release their equivalent energies? I'm almost certain it's the latter as mass can't be destroyed, but when speaking of the big bang it's said if there were equal amounts of both matter and antimatter there would be nothing left. I wonder how that can be true if they don't destroy each other. It may have something to do with how energy decays into matter.", "label": 1}
+{"snippet": "Got curious about polynomials and Galois theory the other day and realized I have no idea how current mathematics treats polynomials (or rather polynomial like expressions) that have arbitrary algebras for the exponents. A quick search yields polynomial extensions like Laurent polynomials but I couldn't find anything that uses any other groups for the exponent, like Gaussian integers, complex numbers, cyclotomic rings, hypercomplex numbers and other algebras. What are these structures called and how is their behavior similar and different with ordinary polynomials?", "label": 1}
+{"snippet": "Let's consider a partition of the words in the english language according to respective use frequency. Looking at the frequency graph it should be easy to find classes of words with approximately the same frequency. Now I'm interested in the size of these classes. I know that the size depends on the relative cut-off points, but I'm more interested in a general classification, i.e. are there more common words, or more uncommon words?", "label": 1}
+{"snippet": "I have recently come across two key concepts in quantum optics: shot noise and back-action noise. This is very important for me to know: first, are shot noise and back-action noise the same? Please let me know if there is any other equivalent term for back-action noise among the quantum optics community. I am also wondering whether back-action is the nature of light beam in vacuum, or is it related basically to measurement detector like homodyne? I really like to know exclusively the characteristics of back-action noise to be able to model it.", "label": 1}
+{"snippet": "There are so many famous paradoxes which are examples of how humans are unable to intuitively understand probability -- there's a discrepancy between their supposed actual experience and the mathematical evidence. There's things like the birthday problem where what we would expect the probability to be is much less than the actual, but also the monty hall problem where the confusion comes in why the answer is what it is. My question is, what is the cause of this? Why are we biased into thinking things are more or less likely than they really are? Why do we find it so difficult to accept and understand the correct probability in the case of the monty hall problem, burnt pancake problem, etc.?", "label": 1}
+{"snippet": "Recently I was proof reading an email that a coworker was going to send to a superior and I pointed out that the valediction wasn't capitalized. He said it didn't need to be because it was the start of a phrase or clause and not a sentence, and that people only do it because other people do it. But in the back recesses of my mind I'm thinking that there is a rule that says that it should be capitalized. Is my coworker right and capitalization is unnecessary in this case? If I'm correct, what rule or guide can I point to, to prove my stance? (T/t)hanks, Jeremy", "label": 1}
+{"snippet": "I've been thinking about this, I want to use this as my science project. The two viable solutions I've thought of so far are magnet or rotary based. Pendulum clocks could be powered once a day and run the clock for the whole day. From the rotary motion, could I easily generate electricity? A magnet on the pendulum could generate energy through coils. Does anybody have any suggestions? I'm just a highschool student so the project should be easy and small. Any blueprints or tips will help. Thank you.", "label": 1}
+{"snippet": "so my goal is to detect an odd-cycle in a directed graph. I know for the undirected graph, the graph contains the odd-cycle iff it's non-bipartile. So I can check whether or not the graph is bipartile. If it is then the undirected graph doesn't contain the odd-cycle, otherwise it does. For the directed graph, does the same algorithm apply? Do I need more condition for the directed graph to have odd-length cycle? Thanks", "label": 1}
+{"snippet": "I have always wondered about the similarity of the two words Astronomy and Astrology that describe two very different things but have their beginning in common and are sometimes confused in everyday language. The linguistic difference (if one can say so) between them is only in the endings '-onomy' and '-ology'. Two further examples are Topology and Topography Geology and Geography where now we have the endings '-ology' and '-ography'. What are the meanings of the different endings '-onomy', '-ology' and '-ography' ? I would also be curious about whether it is a coincidence that '-ology' appears in all the examples above? Does it maybe have historical reasons? And furthermore, are there more such pairs to be found? (I can't think of any others)", "label": 1}
+{"snippet": "In the quote in the title, \"of\" refers both to the material that makes up the cup and to the stuff that the cup holds. I remember reading that there is a literary device that describes this, but I can't remember what it's called. The device, if I remember correctly, refers to the parallel structure of a phrase whereby a thing is described in two aspects or, as in this case, an aspect and a function. Shakespeare commonly used it, though I can't think of a quote. Syliva Plath uses it in the line: I am silver and exact to refer to a mirror--what it's made from and how it does its job. Could someone tell me what this structure is called.", "label": 1}
+{"snippet": "I am looking for a phrase that is in the same spirit such as \"single point of failure\", or \"bottleneck\". Example: Being two engineers short is <-term goes here-> in this situation. If we find two engineers, the project will meet the deadline. Another one: Electric cars are improved enough to be on par with internal combustion engine cars. However, the long charging time is <-term goes here-> behind the problem that electric cars are not as widespread as internal combustion engine cars.", "label": 1}
+{"snippet": "What constructions allow a writer to preserve strict logical coherence and reduce redundancy when conjuncting two noun-phrases? Example Many cultures have used gold or silver bullion as a currency. That sentence could imply that many cultures have used gold -in any form- or silver -only when cast as- bullion, but I intended it to mean that many cultures have used gold bullion or silver bullion as a currency. Moreover, a reader could interpret the sentence to mean that many cultures have used gold -in any form, for any purpose- or silver -only when cast as- bullion -and only- as a currency. How can I construct that sentence to ensure it imparts only the meaning I intend it to impart?", "label": 1}
+{"snippet": "When the word that is used in a sentence to introduce some relative clause it is always an essential element which follows. Therefore, no comma is required. Example: I'm sure that you are lying. When I leave out the word that, it is still a correct sentence, right? Do I have to use a comma then? Because, when you read the sentence aloud, it kind of feels like there is a pause. Examples I'm sure you are lying. I have the evidence right here in my pocket (that) you are lying. Especially in the second case, I would prefer a comma at the place of the that. Is there a strict rule?", "label": 1}
+{"snippet": "In the following sentence, what is the function of \"You\"? You, go to the store. I know the sentence is in the imperative mood, and that generally means there is an implicit second-person subject. If we dropped the initial \"You\", the subject would be that implicit subject. While \"you\" matches that second-person subject, that seems just incidental and it seems like it is just an expression of address that happens to match the implicit subject. Is it the subject, or merely a vocative expression? Or in other words, is the subject the \"You\" in the sentence, or is it the implicit subject from the imperative mood?", "label": 1}
+{"snippet": "I have to show that if a metric space is path connected and countable then it is complete. I'm pretty lost where to start this at all. I have the basic definitions of complete, path-connected, compact and sequentially compact spaces. Any help how to do this would be great (this is a past paper question-non assesed, just for practice so I think it should be reasonable simple) Thanks very much for any help", "label": 1}
+{"snippet": "can anyone help me by using geometric transformations to solve this problem: construct the triangle whose sides bisectors and their intersection point is given; my professor told me that if I assumed the problem to be solved I would notice that we have compositions such as symmetries, reflections, rotations . I can't really understand what he meant, if anyone can help me with a hint or the solution I would be very thankful", "label": 1}
+{"snippet": "I'm sitting here in the metro station, drinking a bottle of water, and watching how the flow of water out of my mouth changes as air rushes into the bottle. My questions is: in space, obviously the effect would be different. How is this effect different as compared to with earth, and can the change in behaviour be solely attributed to the effects of gravity?", "label": 1}
+{"snippet": "I want to randomly distribute some(in thousands) objects over a surface. This I can achieve with a function say x,y = rand(). This will evenly distribute objects over the surface, but is it possible to have some control over the randomness like having some groupings (some objects close together). I can try to achieve this with multiple iterations of distribution, but that might run into objects overlapping. So was looking for some kind of parameterized algorithm that might help in this area. I do not have much knowledge in mathematics so would appreciate some help. Thanks!", "label": 1}
+{"snippet": "I'm looking for an adjective, saying or idiom for an analogy which makes the things even harder to grasp, that was supposed to make things easier to understand. Examples: A guy makes an analogy to express that playing violin and driving a car is similar, when he teaches driving cars. But since very limited people know how to play violin, it does not make things easier. A guy teaches culinary on Youtube. But he rather than he explains the basics of culinary (say boiling water), he says 'oh this process is similar to gamma radiation'. It is not important if the analogy is good or bad. Just it makes things harder to understand.", "label": 1}
+{"snippet": "I am seeking a word, should it indeed exist, that describes a dramatic or literary device found when a new character is introduced into a story which disrupts the natural equilibrium, driving the story. For example, in J. B. Priestley's An Inspector Calls, there is a natural equilibrium at the Birlings' home. This exists, however, until the Inspector arrives - disrupting the natural order, it seems, and goes on to defining the narrative.", "label": 1}
+{"snippet": "We know that a small object moving fast enough can pass by a planet and escape its gravity. Would this be (theoretically) true in reverse? Meaning a planet moving fast enough past a stationary smaller object would not assert its gravitational pull on the small object? Would this mean that gravity is mitigated by velocity regardless of whether the more massive object is moving as opposed to the small object?", "label": 1}
+{"snippet": "Humans see only a narrow band of light wavelengths. Many animals see much deeper into infrared. Maybe one clue to explain why we don't see IR naturally, has to do with the light intensity as a function of wavelength? How would such a function look like on Earth in daylight and at night respectively? I suppose that shorter wavelengths are less intense, because they are harmful. But what about IR, is it more or less intense than visible light in daylight outdoors?", "label": 1}
+{"snippet": "I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to have the sample rate considerably faster than the plant dynamics, but the physics of this system are such that this is inherently impossible. I can get some control of the system by hand-tuning a PID, but it seems considerably sub-optimal. Is there a strategy for developing a controller like this? Edit: I should add that the plant is this situation is a relatively complex LTI plant with reverberations caused by pure time delays. The delay cycles are a bit slower than the Nyquist frequency. The plant is stable.", "label": 1}
+{"snippet": "I've been thinking about the following pattern for some time: Linseed oil... soaks into the (visible and microscopic) pores When I was a kid, this wasn't the way I was taught to use parentheses: they go after an idea, and explain it further. Yet it makes perfect sense--\"visible and microscopic\" is an aside, explaining details. Is this the right punctuation? Is it informal, or only acceptable in technical writing? My gut says brackets might be more correct, but I can't justify it: Linseed oil... soaks into the [visible and microscopic] pores", "label": 1}
+{"snippet": "I'm using the document class scrartcl and appendix. This currently results in a letter instead of a number for section enumeration in the TOC and section title (\"A My Code Listing\"). I need to change this to \"Appendix A My Code Listing\", i.e. add the word \"Appendix\" to the section title. I have found a manual workaround on http://web.reed.edu/cis/help/latex/thesis#appendices but would like to know if there is a way to change this automatically.", "label": 1}
+{"snippet": "I'm going to teach very elementary combinatorics (limited to basic enumeration) during two weeks to middle school students. At the beginning, I want to demonstrate the importance of counting in real life or technology using concrete examples which students are familiar with, so that they appreciate what they are learning. In this discussion, almost all examples are advanced and are not appropriate for middle school students. I'm looking forward to your suggestions. Thanks.", "label": 1}
+{"snippet": "Is there a character in any established alphabet (I couldn't find anything in the IPA) to denote a sharp intake of breath, as if by surprise? I want to include it in a character's name. Initially I thought \"!\" would suffice, making the name, for example, \"!Davis\" (pronounced -breath-Davis) based on its usage in demonyms like \"!Kung-San\", but it seems I have mis-remembered what the exclamation point here does. Googling just gives me information on \"a sharp intake of breath\", which I'm sure is wonderful but is of little use to me at the time of writing. Thanks.", "label": 1}
+{"snippet": "I recently encountered this word while reading an article and found that its two basic definitions are \"Bewildered\" and \"Unfazed.\" How can the word mean both these things as they seem to be direct opposites of each other? Should the sentence in which it's used always explicitly reveal the intended meaning? And while many of us might be a little taken aback if Mom showed up at our offices, Secrist is utterly nonplussed, even happy about it. source In the above sentence, it's obvious that Secrist is \"unfazed\" without even knowing the definition of nonplussed. Instead of adding clarity to the meaning being conveyed, \"nonplussed\" seems to just add confusion. Then again, maybe I'm missing something. Thoughts? My first post here so please edit/re-tag as appropriate.", "label": 1}
+{"snippet": "The definition of a topological space is a set with a collection of subsets (the topology) satisfying various conditions. A metric topology is given as the set of open subsets with respect to the metric. But if I take an arbitrary topology for a metric space, will this set coincide with the metric topology? I'm trying to justify why we call the elements of a topology \"open\". If my above question is true, then at least in a metric space, the set of open sets is equivalent to the topology of the metric space. So am I right in thinking that when we remove the metric, we are generalising this equivalence by defining the open sets as those that satisfy the conditions of a topology?", "label": 1}
+{"snippet": "If i put a pen on a table in its horizontal position and then i try to move it horizontally by giving it a small push, so that it would fall off a table, i expect it to move horizontally but my pen ( and all other pens too! ) moves diagonally when it starts moving down the table!When i remove the notebook , the pen moves like,its shown in the picture ( if i keep it horizontally also, it gives the same result)- Why does this happen? Why does it not move horizontally ?", "label": 1}
+{"snippet": "I'm looking for a word that can describe a long-term inhabitant (inhabitant is the best I've come up with so far) of a hospital. Specifically, a soldier living (retained? - again, word might fit here too) in a War Hospital not long after the First World War, however the answer doesn't have to take into account the time period, as I feel there is a word at the back of my mind I simply cannot find right now which means \"inhabitant of hospital.\" I'd like to be able to use it to complete this sentence: The gravel pathway was bordered by short, waist-height shrubberies behind which were the colourful flowerbeds intended to pacify the hospital's ________.", "label": 1}
+{"snippet": "I've got an undirected weighted graph G with c:E(G)->IR. Now I want to find a spanning tree, such that a node v arbitrary, shall be an internal node, and among all spanning trees, in which v is only an internal node, it has got minimal weight. My Idea: Use Kurskal. If v is an internal node than stop. But if v is not an internal node I'm not sure what to do. Do you know how this could be solvable? Thanks in advance.", "label": 1}
+{"snippet": "I often heard that it is possible to show by using the inverse function theorem that if a function is smooth (i.e. arbitrarily often differentiable), a bijection between open sets, and has a non-singular jacobian, then it is a smooth diffeomorphism. but somehow the inverse function theorem that I know and that wikipedia seems to know, only states that if it is a continuously differentiable bijection with nonzero jacobian, then its inverse function is also continuously differentiable. But how do you get from this, to the statement that I proposed above? I don't see the implication.", "label": 1}
+{"snippet": "I was going through a text about ancient civilization. There, I found a sentence which says, \"Some ancient human being recognized even cannibalism.\" After reading that sentence, I started to think that, as the word 'cannibalism' is disgusting, the writer would had written this sentence in another way e.g. \"Eating human flesh too was practiced by some human beings in ancient period.\" What do you think about which one of them sounds better--- 'cannibalism' or 'eating human flesh'?", "label": 1}
+{"snippet": "I'm trying to speak about the nature of music; I want to say that the very nature of the medium of sound, a kind of universal language, makes it impossible not to interpret what is presented to us. (The laws of physics make music from different cultures ultimately very similar.) How might I express this with some interesting parallelism? I tried using the read-understand pair, but I'm not sure if this makes my meaning obvious enough. I feel like there's some word that I can't think of that would make this analogy (or another) work. It is possible to read and not understand, but impossible to listen and not hear.", "label": 1}
+{"snippet": "Terminal Velocity depends on two things: surface area and speed. These are inversely proportionate. If both these variables affect terminal velocity, why do parachutes slow you down? Initially you had a small surface area but a fast speed- with the parachute you have a larger surface area but lower speed. You have increased one variable but decreased the other. Therefore why do parachutes decrease speed?", "label": 1}
+{"snippet": "I am not sure how to approach this problem. A similar question has gone unanswered before. If the conductor was at rest, then the charge would have distributed evenly. Now all the charges will feel pushed out due to the rotation of the sphere. However the amount of \"push\" is proportional to the distance from the axis (centripetal force is proportional to the radius if angular velocity is constant). But the electrons would not like to accumulate together, so they must be resisting the urge to group together (near the equator). Have I missed any other electromagnetic effect (other than the Coulombic repulsion)?", "label": 1}
+{"snippet": "Edit note: This question with some good answers does not explain (or ask) why it is an adjective that's used as opposed to an adverb in this type of construction: Is this an objective complement or adjective phrase? My Question: Consider this sentence: \"Garlic can be eaten raw or cooked\". In the dictionary, \"raw\" is an adjective only and is not an adverb. \"Cooked\" is also an adjective. So, why can an adjective be placed after \"eat\" as in \"Garlic can be eaten raw\"?", "label": 1}
+{"snippet": "I am looking for an idiom or a phrase to denote the situation where someone is unfairly taken advantage of (Ex: Gets a lot of work dumped on his lap on a Friday evening like Harold in Harold and Kumar series) because that someone is nice and does not say no. In my mother tongue there is a usage for this; when translated verbatim it sounds like this \"keep on digging where it is wet\" - is there something similar in English?", "label": 1}
+{"snippet": "I'm in doubt about a situation that I've seen sometimes: imagine we have a resistor in parallel with a resistor and a capacitor in series. Since I don't know how to generate figures of circuits to post here, the situation can be described as: a single resistor on the right, and on the left a resistor and a capacitor in series. If there was no capacitor, I know I could replace the resistors by an equivalent one. My doubt is, do this continues to be true in this case? I mean, can I replace this configuration by one capacitor with one resistor in series such that this resistor is equivalent to the other two? If we can, what's the argument beyond this?", "label": 1}
+{"snippet": "I'm developing a website on which photos and videos will be shared. But I couldn't decide on the main menu name to use under which there will be two subcategories Photo Gallery and Videos. Which one do you think makes more sense to visitors: multimedia or media? Once they see it, they should immediately realize this menu is all about photos, videos and things related to graphics.", "label": 1}
+{"snippet": "The question is Suppose that events A and B are that people have diseases a and b, respectively. Suppose that having either disease leads to hospitalization H = A U B. If A and B are believed to be independent events, show that P{A | BH} < P{A | H} I think I understand why this holds but do not know how to explain it. I know that P{A|H} is equivalent to P{A} since it's independent from H and I also (think I) know that P{A|BH} is equal to P{AB} and since they are independent this equals P{A}P{B} but now how do I go about proving P{AB} < P{A}? Assuming all the assumptions I've made are correct.", "label": 1}
+{"snippet": "I saw the word admixture used in a sentence recently and looked it up in the Paperback Oxford English Dictionary only to find that its definition is \"a mixture\". This is the sentence: The 'Natura' section features a series of sixteen prose poems, redolent in many ways of Hill's Mercian Hymns in their admixtures of natural and urban landscape, dramatised autobiography and historical reference, fomal and colloquial styles. Why is \"admixtures\" used here rather than \"mixture\"?", "label": 1}
+{"snippet": "I'm working on definition essays. As I read a couple of sentences, I came up with a question. I'll appreciate your help: \"Two years ago, I read a story which revolved around the life of a spoiled family \"--> Wouldn't it be more appropiate to use the present tense for \"revolve around\"?, as the story's plot was and still IS the same Another example: \"She said: 'I became a teacher because I want to change the world.' That got me thinking about what being a teacher really meant.\" -->Shouldn't the writer've said \"means\"??", "label": 1}
+{"snippet": "Diproton is an isotope of helium without any neutrons. It commonly forms in the Sun, where protons are fused constantly. However, it is extremely unstable, and will revert back to two protons almost immediately after. Now, nucleons are held together by the strong interaction. So if the electromagnetic interaction is weaker than the strong interaction, why won't the protons stay held together instead of repelling one another?", "label": 1}
+{"snippet": "I have to do a project for my high school calculus class. I am interested in figuring out how to create equations for simple outlined shapes like this bird if I were to plot it on a coordinate plane. I have investigated the Fourier Series, but I am not quite sure how to implement it (where to start, I guess). I assume I should start by taking coordinates from the curve once at certain intervals, but I'm not sure where to go from there.", "label": 1}
+{"snippet": "I want to use a word/phrase/idiom etc. to describe someone action by which they try to stop another person talk or sharing their plans. I want specifically to use it in following situation: During conversation with my uncle, he was telling me their future plans to sell house but my Aunt stopped him by secretly putting her finger on lips as a gesture to shut up.", "label": 1}
+{"snippet": "In his book \"Origins\", Neil deGrasse Tyson says that \"if you seek to split iron nuclei apart, you must them with additional energy. On the other hand, if you combine iron atoms they will also absorb energy[...] For all other elements only one or the other half of this dual description applies.\" According to him, that is the reason why stars can't make iron. Maybe I'm forgetting something important here but to me that reason is not clear. Is it because up until iron all lighter elements when fused released energy, while when it's time to fuse iron the stars actually lose energy? If this is true than the other part of the sentence (fission) is irrelevant. What is the actual explanation?", "label": 1}
+{"snippet": "To my understanding, work is done on object A when object B is applying a force on object A, causing object A to displace. Since energy is the ability to do work, what work does a moving object do, due to its kinetic energy? I mean, if I kick a ball, it has kinetic energy due to its velocity, but what force does it apply? On what object?", "label": 1}
+{"snippet": "The Big Bounce theory says that before the Big Bang there were other Big Bangs over and over. For example, the universe would have a Big Bang within it and then this new mini-universe would expand, then start collapsing, and as it finishes collapsing, it would \"bounce\" back into a Big Bang, while the greater universe stays constant. Since this is a big explosion, nothing resists it, so we can't find any trace of the other universe ours started in, but would we be able to find evidence for this in the small dimensions that exist in string theory? They're so small they would resist the Big Bang. If the LHC found these dimensions, would it confirm the theory?", "label": 1}
+{"snippet": "What is/are the word(s) for a person who writes/speaks with the attitude of always being right, having the final answer(s), never having their position or interpretation questioned, having the final say on a subject? One who positions him- or herself as the ultimate and final authority on a subject, who entertains no possible alternatives to their interpretation of a subject? \"He writes as though he is the ______ on this topic.\" Not the authority, but a word meaning the presumed authority - seeing this as a negative trait.", "label": 1}
+{"snippet": "\"abuse\" is often defined as improper usage. When speaking about an illegal drug, it seems impossible to properly use it (I mean here recreational consumption, not specially licensed medical or research use). So then, is any consumption automatically abuse? EDIT: I see that somehow, several users appear to have misinterpreted my question. I would like to clarify: Even substances which are illegal may be used legally by people such as medical doctors and scientists, by special permit. Obviously this is not abuse. It falls within the special exemptions provided by the law. I am asking about using the word \"abuse\" to describe use of these drugs outside such special permits, when the law considers the use clearly illegal.", "label": 1}
+{"snippet": "Let F be a field, E a finite field extension of F, K the field of separable elements of E over F, C an algebrically closed field containing F. Is it true that every F-homomorphism from K to C extends uniquely to E? If yes, why would it be true? The point should be that the minimum polynomial over K of an inseparable element of E has only a root, but I can't prove this fact. Thank you for help.", "label": 1}
+{"snippet": "What does a subspace say A spanned by another subspace B and a vector x mean ? Does that imply anything about a basis or does it just mean that every vector in subspace A is either present in subspace B or can be expressed as linear combination of vectors from B and x. Or anything else perhaps ? Any help would be much appreciated.", "label": 1}
+{"snippet": "I have exhausted everything I know about solving for the determinant after operations have been done to it following the general principles of matrix determinants. I see that the first row was multiplied by a scalar and the second row was multiplied by a scalar. It was my general assumption that I would take the original determinant and multiply by the first scalar and then add the original times the scalar multiplied by the second row. Obviously got the wrong answer and feel like I am missing something very basic here. Thanks for the assistance.", "label": 1}
+{"snippet": "As is shown in wikipedia: Click [here] (http://en.wikipedia.org/wiki/White_noise#Mathematical_definitions) A random vector (that is, a partially indeterminate process that produces vectors of real numbers) is said to be a white noise vector or white random vector if its components each have a probability distribution with zero mean and finite variance, and are statistically independent. Here comes my question, does the vector is still white noise, if the variances of the components are not the same any more? Thank you very much.", "label": 1}
+{"snippet": "Thin has a meaning of \"not well fleshed,\" but does it also carry a meaning of \"being weak or feeble\"? In the Merriam-Webster, it does carry a meaning of \"lacking substance of strength,\" but it uses \"thin plot/broth\" to make the example. Is it okay to say someone is to thin to do anything which needs a lot of strength? I just find it misleading to say, because thin doesn't always means weak. If you google, there is a title such as \"Michael Jackson is too thin to play live.\" Is it OK to say so? Somebody argued that it's a euphemism to say so.", "label": 1}
+{"snippet": "The definition of explicit that I wish to use: stated clearly and in detail, leaving no room for confusion or doubt. E.g. the speaker's intentions were not made explicit. My motivation: I'm analyzing 'Follower' (by Seamus Heaney) right now and I want to comment on the word \"exactly\" in 'Mapping the furrow exactly'. My comment is something along the lines of \"Mapping the furrow\" already attributes a high level of skill and precision to his father. The use of the word 'exactly' adds an extra layer to the phrase and makes it explicit.", "label": 1}
+{"snippet": "I wonder about this. If you pour water in a closed tank, it makes a noise. I have noticed that as the container becomes more and more full, the pitch of this noise also increases. Why is that? I do not study, nor have any knowledge of beyond basic concepts, of the physics involved in sound and vibrations. However, my hypothesis is that this happens because the \"chamber\" where the sound is produced gets progressively smaller, therefore it behaves like a flute - as you change the shape of the chamber, the sound that air makes as it passes also changes.", "label": 1}
+{"snippet": "If I have two sub-areas confined in a larger area, and I have the intersection of these two sub-areas. If I replace one of the sub-areas with a new sub-area, which is the same size. What is the probability of the new intersection being bigger than the old one? (By that I mean how could I solve this?) If the question is too vague or written badly then just comment aand I'll try to explain it a little better. Thanks Keri", "label": 1}
+{"snippet": "Does the uncertainty principle imply the non-deterministic universe, or just the fact that our model of the universe, the one based on observation, can be at most non-deterministic, since we will not be able to measure with perfect accuracy, even if such would exist (and therefore we will have to provide probability distributions rather than an event which should happen with overwhelming probability (term used by Terence Tao))?", "label": 1}
+{"snippet": "As a web developer, this is a question that has bugged me for some time: when providing a way for users to reset their password, which link wording is more suitable or is the \"proper\" use? \"Forget your password?\" (as in, \"Did you forget your password?\") \"Forgot your password?\" (as in, \"Have you forgot(ten) your password?\") There is a nicely related post here (Is it correct to use 'Forgot password' or 'Forgotten password'), but that addresses \"forgot\" vs. \"forgotten.\" Thank you for your insight!", "label": 1}
+{"snippet": "Could anyone tell me the difference between \"have wanted to do\" and \"have been wanting to do\"? I often say \"I've been wanting to go there!\" when someone invite me to the restaurant that I got to know before and has been thinking I want to go since then. But one of my friends said \"I've wanted to go there.\" in the same situation today. Which is correct/common usage?", "label": 1}
+{"snippet": "Inevitability just sounds so depressing to me. The \"inevitability of death\" is a glaring example. There has to be a word that means \"unavoidable but in a good way\" right? Edit: The sentence I'm trying to make right now is about \"the [inevitability] of technological progress in our society\". Technological progress at least in what I'm arguing for is good so I'm looking for a word that would be a positive replacement for [inevitability].", "label": 1}
+{"snippet": "Environmentally induced decoherence makes wave function collapse unnecessary. But the environment, usually taken to be some heat bath, introduces a preferred frame. (That in which the total (spatial) momentum vanishes.) So, doesn't then the decoherence time depend on the motion of the prepared state relative to the environment? And, doesn't the ultimate environment, all particles in the universe, introduce a preferred frame into quantum mechanics in the sense that the decoherence time is relative to this frame? And would this be measureable, at least in principle? I.e. I could go into a frame with high boost relative to the CMB restframe and notice that the decoherence time changes?", "label": 1}
+{"snippet": "I'm near the end of Velleman's How to Prove It, self-studying and learning a lot about proofs. This book teaches you how to express ideas rigorously in logic notation, prove the theorem logically, and then \"translate\" it back to English for the written proof. I've noticed that because of the way it was taught I have a really hard time even approaching a proof without first expressing everything rigorously in logic statements. Is that a problem? I feel like I should be able to manipulate the concepts correctly enough without having to literally encode everything. Is logic a crutch? Or is it normal to have to do that?", "label": 1}
+{"snippet": "In order to collect all pokemon Tazos, I went to a shop and bought bags of chips. Now I am worried whether I have bought enough bags of chips or not. You need to tell me the probability of getting all the distinct Pokemon Tazos from the N bags of chips. Lets say N is the number of bags i bought and K is the distinct pokemon available. So how do i calculate probability?", "label": 1}
+{"snippet": "I would like to put an address in my document as follows: | | | Name | | Street #| | City | | ZIP | | | where the | mark the left and right page borders. I would like the items of the address (Name, Street etc.) to be left-flushed, but the box right-flushed so that the longest item touches the right page border. Is there a simple way to accomplish this?", "label": 1}
+{"snippet": "I'm writing a short story set in an artificial planet-sized sphere with an ecosystem in its inner surface, whose \"gravity\" is created through spinning. Energy sources aside, what other interesting physical characteristics should I take into consideration, apart from varying force levels as one moves relative to the direction of the spin (may be minute given the size of the structure), as well as increasing \"weightlessness\" as one gets closer to the axis? Also, with sufficient mass in its shell, what is the effect of (real) gravity on objects on the inner surface?", "label": 1}
+{"snippet": "When driving on a wet highway at night, any surface emitting or reflecting light will have a reflection right under it that is blurry and seems to stretch to infinity. This is not exactly what I am picturing in my mind, but I couldn't find better images. Anyway, I think it'll do. Does anybody know why it is such a long reflection? I never figured it out myself.", "label": 1}
+{"snippet": "English.SE, Hi, first time being here. I have had this confusion about the pronunciation of \"a priori\" and \"a posteriori\" for a long time, normally I just read the last vowel as /i/, however today my office mate asked me about this for he saw the pronunciation on Merriam-Webster online dictionary shows that the last vowel reads as /ai/, this reminded me that the philosophy professors whose lectures I took before didn't agree on this pronunciation either. Since I learned that Immanuel Kant borrowed these words from Latin, I wonder what is the correct way to pronounce these words in Latin or at least in a Latin'ish way.", "label": 1}
+{"snippet": "I have a question on electron and non-polar optical phonon scattering in GaAs. Is it allowed to consider intravalley electron non-polar optical phonon scattering in L-valley of GaAs? I found in the literature, people only consider intervalley (L to L) electron non-polar optical phonon scattering in GaAS. I wonder if anyone can help me why this is the case? Why do not people consider intravalley non-polar optical phonon scattering in L-valleys of GaAs?", "label": 1}
+{"snippet": "Black is the absence of light because it absorbs light, but when we create black paint or black objects, light is always reflected, either in all directions in matte or smoothly in shiny black objects, making it never a true black. Would it be possible to use polarization to create an object that does not reflect any light, creating a truly black substance, without any shadows or reflection of light?", "label": 1}
+{"snippet": "I see all the files in titlesec here at ctan: http://www.ctan.org/tex-archive/macros/latex/contrib/titlesec/ I also see a titlesec folder in my texmf-texlive tree. Apparently what happened is that during a fresh installation of texmaker, the installation process cleared out the titlesec.sty and related files. Why it would do such a thing, I do not know. It seems obvious to me that I should just put all the files on the ctan site into the titlesec folder. Do I have to download all those ctan files individually or is there another way?", "label": 1}
+{"snippet": "I have seen the following line in mail replies from customer care executives - Thanks for your patience They write this when they are not yet ready with a desired solution. They write in the mail that it will be ready after some more time. Writing \"Thanks for your patience\" in such a mail seems like we are assuming the other person is patient, whereas he actually may not be, and instead, what is probably desired is to ask the person to be patient. What would be a polite way of asking the same, knowing that the person desires the solution ASAP.", "label": 1}
+{"snippet": "As far as I know, a measurable function is Lebesgue integrable if and only it is absolutely integrable. It is simply because the definition of the integrability requires each of the positive part and the negative part has a finite integral. However, some theorems explicitly state that a function need to be \"absolutetly integrable\". For example, Fubini-Tonelli theorem says that if one of the iterative integrals or the double integral is absolutely integrable they have the same value. What's the point / importance of the absolute value here? Can I just replace the condition of absolute integrability with just integrability?", "label": 1}
+{"snippet": "It's easy enough to show that the theory of algebraically closed fields of characteristic p is decidable (since its complete). But does it follow from this that the theory of algebraically closed fields of any characteristic is? I suspect that the answer is \"yes\", but I'm not quite sure why. The reason for my suspicion is that we can simply that the greatest lower bound of each of these theories and arrive at the right set. But I'm not sure if decidable sets are closed under countable intersections.", "label": 1}
+{"snippet": "I've used this site to my benefit in the past, and now I have my own question. I have looked through some of the answers (although I admit not every one as I am short on time) and cannot find what I am looking for. Could someone help me regarding punctuation of my sentence? I find an airplane's symbolic freedom appealing: whether it is soaring through the sky; industriously filling and disgorging passengers; or exultantly defying gravity on take-off, it remains independent and far-reaching in all of its manoeuvres. Is this correct British English or do I need to change the colon to a comma? Also how is that last tacked on bit?", "label": 1}
+{"snippet": "I was recently studying Pair Production and Annihilation. The author mentions that a nearby nucleus is required when the photon materialises into a particle and an anti-particle. The explanation given is that the momentum and the energy must be conserved. However, there is no calculation given that shows the violation of energy. The reason is just blankly stated. Is there more to this concept. Please explain? As far as I know that from the knowledge of Particle Physics, virtual photons can violate the conservation laws if the time scales are very small due to the Heisenberg Uncertainty Principle. Then why can't we apply the same idea here? PS: I've read the other answers but none of them include the contribution of Nucleus' energy/momentum to conserve momentum or energy.", "label": 1}
+{"snippet": "I have a document with quite a number of figures, some of which have a longer figure caption (in particular some take multiple lines). The image shows such a case: I would like the second and consecutive lines to be aligned with the 'F' from 'Figure', i.e. get rid of the white space below the figure label. The gecko expample from the wikibook (https://en.wikibooks.org/wiki/LaTeX/Floats,_Figures_and_Captions) shows this. But they seem to do nothing special to achieve this. Maybe a different software version? How can this be done? Thanks Soraltan", "label": 1}
+{"snippet": "We know that space cannot spread a sound wave as there is no \"air\" or a medium that would support the spread of a sound wave. However if we put ourselves in the vicinity of an exploding star, would it be possible to hear something? The question arises from the idea that within the explosion of a star (first few seconds or less) you may hear a noise due to the explosion of the star...", "label": 1}
+{"snippet": "For me the relevant number of subgroups of a finite group is the number of non-isomorphic subgroups. Mathematicians seems to have an other opinion. There is a related classification called automorphic subgroups, when there is an automorphism on the main group that maps a subgroup on a subgroup, which seems to be a stronger condition. A weaker condition than automorphic subgroups is conjugate subgroups. What is the relation between conjugate subgroups and isomorphic subgroups? Why isn't isomorphic subgroups more interesting in mathematics?", "label": 1}
+{"snippet": "Given the fact that the force stopping me falling through the ground is the electromagnetic repulsion between the electrons in my feet and the ground, would it be possible to increase this repulsive force? Also is friction generated due to this repulsion of angular faces at a very small scale ? if so could a material be made so smooth it had zero friction because the electromagnetic force simply kept the two apart instead of causing friction? Sorry if its a stupid question but im very interested to find out and why not if i am wrong.", "label": 1}
+{"snippet": "I would like to understand the difference between reflection of light and re emission. Indeed in both case an observer far from the object will se an electromagnetic field coming to him. When we take a perfect conductor an a E.M wave going to it, we know that the wave is \"reflected\" but can we also see it in the way that the material absorbed the light and re emitted it ? Is the difference based on the fact that in re emission the energy is stored for a finite amount of time in the material and the re emitted as a ray whereas in reflection the energy of the incident beam is never stored by the material ? Thank you for your answers.", "label": 1}
+{"snippet": "Experience and hardship come to mind but they seem too general and they don't communicate the end result. They can be used depending on the context of course but there might be a word for a type of experience that conveys this proverb better. (if not a single word, a two-word phrase). Example sentence: I've suffered through a lot of adversity in my life, experiences that didn't kill me, but made me stronger, turned me into a fighter. These ordeals were (my) _______.", "label": 1}
+{"snippet": "This is a newbie question, but I don't quite understand the forces at work when an object is rotating. So I've read that i can use my right hand to determine the direction of the force at the axis which depends on the direction and the magnitude of a spinning wheel. (Fingers pointing in the direction of rotation, thumb is pointing in the direction of the resulting force.) Does that mean that in a car, the wheels on one side constantly want to fall off, while on the other side they want to move to the enter of the axis?", "label": 1}
+{"snippet": "Suppose that in the future a highly resistant spacecraft went to the Sun and collected three samples of the Sun: one from its surface, one from its core, and one midway. The three samples were put into three high-tech jars which could preserve the samples perfectly (so the temperature, pressure, etc, of the three samples are not altered). The three jars were then brought back to Earth, and exposed into a museum. What would we see? Would the three samples look almost identical to each other? Would they look like some kind of fire/flames? Or would they just look like some kind of boring gas? Please provide pictures if you can.", "label": 1}
+{"snippet": "The word visualization is often used to describe an image or interactive piece of media that represents a data set. I am trying to think if there is an equivalent for something that is not only visual, but also tangible. That is, an object that represents data and that people can touch and see. If there is no word for this, can you think of a neologism for it e.g.\"tangiblelization\"? EDIT: By tangible I mean an object that can you can youch with your hands.", "label": 1}
+{"snippet": "Any action of a finite group on a (non-empty) tree has a global fixed point (in the sense that there is a vertex fixed by all group elements or an edge fixed by all group elements). There is a hint which says we can consider the diameter of the corresponding orbit is minimal. However I don't find the definition of diameter in the book. Can someone clarify the diameter? Or give the details of proof? Thank you.", "label": 1}
+{"snippet": "Why does special relativity exist? Via studying the outcome(s) of such relativity, one can end up with all the equations involved in special relativity. Thus one runs into things such as contraction, dilation, transformations, velocity addition, etc. But these are the outcomes. My question is what is the cause of special relativity, and is the knowledge of this cause currently being shared in the world of physics? Or, to put it another way, is it currently accepted despite there being no cause that is known of, thus an acceptance of an effect without a cause? If you give this question a negative vote, please present your reasoning and or evidence to support such a vote.", "label": 1}
+{"snippet": "This question has been asked before under other guises. I am not a scientific profesional however i have some schooling in pyhsics and mathematics and have a keen interest in these subjects. It seems plausible to me and was a thought i had my self many years ago whilst at college, that the universe could possibly be expanding from within itself. Ie matter and space were expanding at the same rate as each other. I observe there is no relative distance increase between the objects i see on a day today basis and as such this type of expansion wouldn't change our perception of this relatively speaking. Everything we observe would remain the same and we would be unaware of the expansion..", "label": 1}
+{"snippet": "I need a word to describe going out and doing something, which is thought through but not necessarily fully planned. Like all of a sudden thinking \"I want to go to a club\" while sitting on your couch, then going out and just doing it. A contextual example will be: You're doing nothing and want to do something. You're presented with a list of possible chooses that may interest you. You pick one, and just do it.", "label": 1}
+{"snippet": "My brother asked me this question: You can be disruptive, but can you be ruptive? For example, one can be disrespectful and it is also possible to be respectful... I thought ruptive would have to mean the opposite of disruptive (because...pattern?). I have looked up the definition of ruptive and it seems that both ruptive and disruptive have the same meaning. Why is this so and why is there a distinction if they both mean the same thing? Upon further investigation eruptive and irruptive are also in the same boat. Again why? Is this a common pattern? Examples?", "label": 1}
+{"snippet": "I have been seeing phrases \"The board of directors resolved on the budget.\" but have never heard, and in dictionaries have not found, a combination of \"resolve\" with preposition \"on\" to refer to the topic that a body must make a decision on. The OED says to resolve in this sense generally takes an object clause, such as \"The Committee resolved that it accepts the chairman's proposal.\" or \"The shareholders resolved to go forward with the takeover bid.\" But when the actual tenor of the decision is not stated, only the topic on which a resolution must be passed, is it correct to use \"resolve on\"?", "label": 1}
+{"snippet": "How can an image pass through a window if the atoms in the glass randomly emit photons in any direction? I've read that glass is transparent because the atoms don't readily adsorb visible light, so it passes right through. But then how can a glass lens refract anything if it's not even interacting? Yet magnifying glasses burn ants! I've also read that refraction has to do with the difference of velocity of the wave in different mediums, but I thought that had to do with adsorption also. Maybe it's because a small number of photons get adsorbed and that holds the whole wave back some how? Or is this just another one of those places where classical intuition breaks and you have to go mathy/qm?", "label": 1}
+{"snippet": "Does Gravity / curved space cause rotation? Meaning, if a spaceship is heading not directly toward Earth, but slightly off to one side, and when finally being close to the Earth it falls into earth orbit, does the spaceship continue to point in the same directions as it was when approaching the earth, or does it now rotate at a frequency that is equal to its orbital frequency? I would expect the spaceship to be pointing in the opposite direction after completing one half of an earth orbit.", "label": 1}
+{"snippet": "Well, I guess the 'odds' in 'overcome the odds' means kind of 'diffculties'. But I cannot find such kind of explaining in dictionary (oxford dict online) nor in \"Practical Everyday English (by Steven Collins)\". The closest explaining, seem to me, is 'The chances, probalility of winning, being successful'. But then it doesn't explain well for the following sentence (from \"BBC Life Story\") Animals have just one goal at the end of this journey, to leave offspring, and everyone begins its life with an irrepressible instinct to survive and overcome the odds. What does 'odds' mean here?", "label": 1}
+{"snippet": "I have following propositions: p:Grizzly bears have been seen in the area. q:Hiking is safe on the trail. r:Berries are ripe along the trail. I need to convert following compound statement to logical expressions by using logical connectives. If berries are ripe along the trail,hiking is safe if and only if grizzly bears have not been seen in the area What I think is true is: ~p <-> (r^q) Note:I have considered comma in above statement as and. But answer given at the end of book is: r -> ( q <-> ~p )", "label": 1}
+{"snippet": "I used to think that things called \"parabolic\" must have something to do with parabolas or their defining quadratic equations. In fact, terms like parabolic coordinate, parabolic partial differential equation and so on, are indeed related to parabolas and their equations. But, why are parabolic groups in algebraic group theory (correspondingly, parabolic subalgebras in Lie algebra theory) named \"parabolic\"? Do they have anything to do with parabolas or parabolic equations? Thank you very much.", "label": 1}
+{"snippet": "My guess is that when you throw a ball, which is held by your hand, using you arm, the radius of the circular path being constant, the outermost part of the ball has a bigger radius than the innermost part, therefore greater linear acceleration for the outermost part of the ball. And so when you release it, the outermost part is always ahead in the direction of rotation than the innermost part.", "label": 1}
+{"snippet": "I am currently studying mathematical course at my college, and I cannot seem to grasp the concept of inequalities. What troubles me is that, like it's said, \"triangle inequality matters because many other theorems are dependent of it\". But I have no idea why triangle inequality matters, why bernoullie's inequality or why sin function inequalities matter? I would be grateful if anyone explained all of this. Practical examples would be much appreciated.", "label": 1}
+{"snippet": "In my current project we are writing a program to convert a newer protocol to an older one. These conversion programs are being referred to as adapters, but the team cannot agree which spelling to use: adapter or adaptor. I personally plump for adapter, as adaptor sounds like its a person (like actor, realtor, etc.) rather than a device. Is there a case for using one rather than the other?", "label": 1}
+{"snippet": "Is there a name for a pair of words or phrase that can have a double meaning? I was thinking homophones, but I thought that homophones are only applied to single words (ie their, there, and they're). The example: The term \"werewolf hunter\" can have two meanings A hunter who is also a Werewolf A hunter who hunts werewolves The term \"English teacher\" can have two meanings A teacher who is English in race A teacher who teaches English Is there a specific term for this kind of phrase?", "label": 1}
+{"snippet": "I am making a video game, and when player tries to walk into wall he should slide along it. However I am confused how to resolve the vectors for it. Here is image illustrating problem: I know the v vector, as well as angles A and B (although angle A is wrongly illustrated here, it should be counter clockwise). How do I find b vector?", "label": 1}
+{"snippet": "It might be a silly question, but one of my friends just got asked this question at an oral exam, and he could not answer it, and didn't receive the answer either (Or at least he forgot). And I've been thinking a while, and I'm not sure what would really happen. If I take, lets say a wedding ring, made from a conducting material, placed it on a table, and turned on an external electric field, what would happen ? The inside of the ring is field free, right ? So does anything even happen, and if so, is it only on the surface of the ring ?", "label": 1}
+{"snippet": "If decoherence time of quantum decoherence is zero, or if off-diagonal elements of density matrix of quantum system (without environment considered) vanished immediately after interaction with environment, then one can say that \"classical\" probability transition occurred, and this is why we get appearance of wavefunction collapse and measurement. However, decoherence time is almost always not zero, and off-diagonal elements of density matrix of system, as far as I know, do not vanish to zero even though they remain very close to zero. If this observation is correct, then I wonder how quantum decoherence explains how/when measurement occurs - with emphasis on \"when\".", "label": 1}
+{"snippet": "Since the Lagrangian of our quantum field theories is covariant under Lorentz transformations I'm asking myself if there is any link to some symmetries (like that we get from gauge transformations which also let the Lagrangian unchanged)? So is it possible to apply Noether's theorem to this invariance or doesn't this makes any sense? So what is the mathematically difference between this two transformations and their behavior?", "label": 1}
+{"snippet": "Possible Duplicate: Biblatex: remove commas between last and first names in bibliography Is there an easy work-around with the last-first biblatex macro so that the comma after the last name in the bibliography entry can be removed? The goal is to print Kruse, JS as Kruse JS To see some more background to this question, you may refer to my post: biblatex conditional for printing an extradate.", "label": 1}
+{"snippet": "I'm working on package that (among other things) writes an external file during compilation. I'd like to provide an option to the package to not write the external file. I know I can set up a boolean and test for it everywhere in the package the writes take place. But it would be nice to just set the openout command at the beginning to write to /dev/null or its equivalent. Is that possible? I need to keep this package supported on Windows, Mac, and Unix.", "label": 1}
+{"snippet": "The last couple of days i have been thinking about temperature and heat and i thought : What happens to temperature if i continually supply a particle with energy? Then i thought at sometime i would run out of energy (the energy of the whole universe) so that would be the limit of temperature. But temperature is proportional to the jiggling of the particle but the particle cannot move as fast as light so i used an equation from thermodynamics from Kinetic theory of gases which suggests that: So i figured the limit of Temperature would be : Can you follow this possibly crazy train of thought? Please explain to me: Does temperature have a limit? If so what is it?", "label": 1}
+{"snippet": "I am trying to find the correct opposite of a delegate in the context of a person being a representative of someone else that have allowed or chosen them to be their delegate. What would you call that \"someone else?\" The only word I could find is a delegator (which isn't a real word in English) or assigner, but they are technical words rather than descriptive. Any other word I could use? Think of it in a sentence like this: Here is a list of all the delegates in the company. But that is the list of their _ _ _ _ _ (what can go here?). I am trying to avoid fillers such as: bosses, agents, managers, etc.", "label": 1}
+{"snippet": "How can I visualize Lorentz transformations? I know it's four dimensional, but without a visual picture in my mind I can't understand any of this. For example how do: Time reflection Space reflection Proper Lorentz transformations Improper Lorentz transformations Homogeneous Lorentz transformations Orthochronous Lorentz transformations Antichronous Lorentz transformations look like? I don't have any idea about how they look like. Maybe this can be explained with Minkowski diagrams or in some other form.", "label": 1}
+{"snippet": "Question: If air was significantly compressed, and then the force compressing it suddenly disappeared (no container), what would happen? Side Question: I'm imagining significantly compressed, but what kind of pressure would be necessary for that? Thoughts: It has been a while since I took chemistry and physics, but what I think is that it would rapidly expand and exert similar pressure to whatever the container was exerting on it in all directions? So similar to what an explosion from heating gas or what not would do?", "label": 1}
+{"snippet": "In my dialect of American English, the word \"tush\" or \"tushy\" is a dimminuitive of \"rear end\" (e.g., something you'd say about a baby, not as harsh as \"butt\" and a word you aren't ashamed to say to your mother). The word derives from Yiddish, and I am from a Jewish family in the New York area, so I'm generally understood when I say it. How broadly is this word understood? What do folks who don't use it say in its stead?", "label": 1}
+{"snippet": "What is the best strategy to survive a free fall naked out of a jetliner at cruising altitude (ignoring temperature)? For instance, my strategy would be to streamline my fall so that my terminal velocity was very high. Then at some critical distance above the ground I would pitch upward and attempt to use my forward velocity to achieve lift. Presumably this would slow my fall to some survivable speed. (This is roughly what the space shuttle does after all.) Would it work? And idea if it would be survivable?", "label": 1}
+{"snippet": "My question is this: suppose we create two different standing waves in a string . So, is the energy of the standing wave dependent on the frequency of the wave ?(assume that the amplitude is unchanged) My guess is this: the energy of the standing wave is equal to the sum of the energy of the individual waves. Since the energy of individual waves remain the same( as the amplitude is constant) , the energy of the standing wave remains constant too. Am I right?", "label": 1}
+{"snippet": "What do you call the practice of using (overly) complex words specific to a subject? I am thinking of scientific or academic fields where the common terminology used in the field is very unapproachable to someone not in the field. The situation I am imagining is when one professor gives a lecture using field specific language and the topic seems very difficult to approach to the lay person. On the other hand, another professor may give a lecture conveying the same information using terminology and phrasing easily understood by outsiders. Is there a word to describe this difference in style practice?", "label": 1}
+{"snippet": "\"I would like to talk today about what I think is one of the greatest adventures.\" In this sentence, is \"what I think\" is used like this \"I would like to talk today about what, I think, is one of the greatest adventures.\" or like this? \"I would like to talk today about what I think is (the thing I think is) one of the greatest adventures.\" Any explanations please? Which is correct?", "label": 1}
+{"snippet": "I was going through the book HANDBOOK OF PRODUCT GRAPHS by Richard Hammack, Wilfried Imrich, and Sandi Klavzar. In the preface section, application of direct product of graphs is mentioned. I am interested in gaining more information about the real life applications of other graph products. Can anyone suggest me a link or good book as a reference? This will be very helpful to me. Thanks a lot for giving time.", "label": 1}
+{"snippet": "I am interested on drawing (I suspect that using pgf/tikz is one of the easiest ways to accomplish this) a picture like the following one It is supposed to be a grid of the plane (I only care about the points with natural coordinates), where there are some \"red bags\" which contain some of these points , and there is a region that is coloured on yellow (one of the red bags corresponds exactly to the points in the yellow region). Any idea about how to use pgf/tikz to draw something like this?", "label": 1}
+{"snippet": "The following sentence is from a mathematical lecture note here: It takes a little bit of getting used to the idea of a function that cannot actually be evaluated at any specific point, but with some practice you will find that it will not cause any significant conceptual difficulty. Is there anything wrong with this sentence? I guess it is supposed to be \"It takes a little bit of time for getting used to the idea...\". Any idea for understanding the sentence?", "label": 1}
+{"snippet": "I would like to know about the larger picture, current state and future prospects of the sequence of papers that were written by Sheldon Katz and Cumrun Vafa on F-theory. (Freddy Cachazo was also a co-author in many of these papers) I guess the same is also known as \"geometric engineering\". (Kindly explain if that is not the same) There have been recent works on F-theory by Cumrum Vafa, Jonathan Heckman and others. I would like to know of how this recent work fits in with the earlier work by Katz and Vafa and where do people see this pursuit to be going and what does the community think of its future prospects. Are these Katz-Vafa works a prospective field for beginning grad students?", "label": 1}
+{"snippet": "Lots of people have wondered why English seems to be one of very few languages with such irregular spelling, far from its pronunciation. The answers include the Norman invasion, and the Great Vowel Shift. Ok, cool. But why did all those other languages not have the same thing happen to them? German, Spanish, Italian, all Slavic languages, etc. They don't have a silent 'e', they don't have the day/date poke/soak treat/tree vowel dualities, etc. They still ascribe vowels the same sounds they ascribed them many centuries ago. Is it because England had more trade contact and colonies? Or because they're on an isolated island? Or why?", "label": 1}
+{"snippet": "I'm trying to figure out the angle between the direction to an objective point relative to a player looking a certain direction. This will be used in making a direction indicator for a game. Here's a diagram made in Geogebra that shows the scenario Updated diagram to avoid confusion I have X,Y coordinates of the player and objective and I have the rotation of the player to work with.", "label": 1}
+{"snippet": "Say, you buy some new office furniture. You get the furniture parts delivered including the service to put the different parts - for example the desk top and the desk legs - together to complete furniture ready for usage. Is the person who carries out this service called \"Assembler\", \"Installer\" or \"Fitter\" and is his service called \"Assembly\", \"Installation\" or \"Fitting\"? Are the words interchangeable? Do they have different connotations? Are there other contexts where they are not interchangeable?", "label": 1}
+{"snippet": "I am searching for math competitions for college students. Of course I am familiar with Putnam, but I am looking for a lower ranking competition. Either US-national or regional (South/Texas). I tried this list but my first three links were stale. So I thought I ask a live audience. If you have organized such competitions for your students I would like to hear your reviews and rankings. Also, if you have used high school-level competitions for university students I would like to hear your views about that as well.", "label": 1}
+{"snippet": "I've been pondering over a questions from a while. Please forgive me if I am being too naive. We all know that because of Pauli's exclusion principle no two electrons can populate one state. This prevents the electrons from being collapsed into nucleus, as explained here from the anti-symmetric nature of their wave functions, also as explained in a comment by ACuriousMind. Is there any simple man perspective (classical analogue/picture) why there should be any such principle in the first place?", "label": 1}
+{"snippet": "One of my relatives had a probability question that they asked me that was a little puzzling... What do you think? Can anyone explain how to do a problem like this? A container has six yellow marbles and nine black marbles. Ruth and Dave each start taking a marble. They choose these marbles at random and Ruth was the first to draw a marble. If they do not replace any of the marbles, until one of them get's a yellow marble. What is the probability that Dave will be the one to draw the yellow marble. If anyone could explain how to do a problem like this, that would be great. Thanks!", "label": 1}
+{"snippet": "Just like the previous question, Even I have been studying Hawking's A Brief History Of Time and even I was thinking of Einstein's General Relativity. But I was unable to accept his view of GRAVITY. I have been working on a theory which needs that Gravity effects Light. And so my question is that, Is there any kind of mass for Light? as it was being effected by Gravity? Excuse me if any mistakes were done. Plzz answer me.", "label": 1}
+{"snippet": "I am in a serious doubt about it. Consider a battery of emf E and we connect it to an inductor. Initially the switch is open, now we close the switch. My question is: What mechanism happens just after closing the switch? When we close the switch, the electric field produced in the conductor by the battery causes the electron to flow in the inductor. As the electrons flow inside the inductor, the flux changes and an emf is induced, my question is that how is this induced emf Ldi/dt is equal to the external emf e, not simply by saying Kirchoff voltage law but by the mechanism happening that it should be E only?", "label": 1}
+{"snippet": "How do molecules absorb and retain heat, and how is that heat able to still affect nearby molecules? On Venus there is a green-house effect where the large, dense Carbon-Dioxide atmosphere absorbs heat from the sun and traps it- but how does that occur? What is the interaction between light and a molecule which causes heat to transfer and be trapped? Thanks for your time! Sincerely, Sigismund", "label": 1}
+{"snippet": "In AmEng vernacular, is the word tab specific to restaurant and bar checks, or can it also be used for hotel bills? E.g. Guest: We'll be checking out early tomorrow morning, so if it isn't too much trouble, I'd like to close out my account right now. May I get the tab, please? Front Desk: Certainly, Mr. Smith. Just one moment, please. I'll print it out for you. tab: A creditor's statement: bill, check M-W chiefly US and Canadian A bill, esp. one for a meal or drinks Collins English Dictionary informal, chiefly North American A restaurant bill: the waiter brought three drinks and a new tab ODO", "label": 1}
+{"snippet": "I would appreciate any suggestions for book or notes on ANT at a level that I would characterize as advanced beginner. I.e., something assuming familiarity with topics in Dummit & Foote, that is a little less than Samuel or Marcus. I would especially like accessible discussions of topics such as fractional ideals, ramification, and ideal classes. Any suggestions would be appreciated. (I have seen several enthusiastic endorsements of Stewart and Tall.) Thanks.", "label": 1}
+{"snippet": "There are words to modify justifications or reasons given. One means \"the real motive\", and the other means \"a plausible explanation, but not the true motivator\". I searched quite a bit, but was unable to find anything. I think one of the words is like \"obstinate\", but not that, and now that it's in my head, it's all I can bring to mind... Does anyone know the words I am trying to think of?", "label": 1}
+{"snippet": "I wrote this sentence: Living a busy life, full of stress, sweat and sacrifice, can make us think that we are actually doing something worthy with our lives. Which is actually saying is that being busy can give us the illusion of doing something worthy with our lives. Is it clear enough or ambiguous (is it possible for the reader to misunderstand this sentence as \"being busy really makes our lives worthy\"?)?", "label": 1}
+{"snippet": "This question is a follow-up of Macro: Replace all occurrences of a word, but I would like the same for different colours, that is to have different pre-defined sets of text strings which will be coloured in a predefined way, where the colour depends on the set they are in. Requirement: Each string should be able to include spaces and/or punctuation marks (e.g. a string could be foo's foo doesn't foo). Edit: I was asked to provide a MWE, and while I was making one, suddenly I achieved an answer which I failed in creating before. Trial-and-error-and-trial-and-success.", "label": 1}
+{"snippet": "This answer of mine has been strongly criticized on the ground that it is no more than a philosophical blabbering. Well, it may well be. But people seem to be of the opinion that HUP alone does not ensure randomness and you need Bell's theorem and other features for the randomness in QM. However, I still believe it is the HUP which is all one needs to appreciate the probabilistic feature of QM. Bell's theorem or other such results reinforces this probabilistic view only. I am very much curious to know the right answer.", "label": 1}
+{"snippet": "They most often come as advice on how to solve problems that seem the reverse of what would be expected: In order to think of a solution you must stop thinking about the problem. In order to be a good leader you must know when not to give orders. I'm sure there must be a name in rhetoric at least, they often have the quality of being immediately pleasing or slightly amusing in the same way a joke or a pun does. Sort of like a stronger form of antithesis that goes beyond putting opposites together and suggests the opposite is actually the solution.", "label": 1}
+{"snippet": "I am wondering if someone could provide me with additional information with regard to the so called Yale sparse matrix format, other that what can be already found here: https://en.wikipedia.org/wiki/Sparse_matrix In particular, which specific programms make use of it? Which (research or practical) goals does it achieve as compared with other options? Can it be considered a standard way to make a sparse matrix out of a dense one? Thnaks in advance.", "label": 1}
+{"snippet": "Consider the situation when a cell of an unknown emf is being measured using a potentiometer. We slide the jockey so as to obtain the null point. Now, is there any current in the potentiometer wire at the null point? Since we know that there is no current in the arm containing the unknown cell, its terminals have acquired equal potentials,how is it possible that there is any current in the potentiometer wire when that is in parallel to that cell. Potential difference across AB= Potential difference across CD?", "label": 1}
+{"snippet": "Oxford defines \"close\" thus: Adj (With reference to a competitive situation) won or likely to be won by only a small amount or distance: \"the race will be a close contest\" \"she finished a close second\" My question: Based on the same sense of the word, can I describe the 'difference' or the 'differential' between two numbers or amounts of something as 'close'. For example: The differential between what you owe and the credit you have is close. The difference between their numbers of followers on Twitter is close. Does this sound nearly native? If not, what would be? I know we usually say \"small difference\" but I wonder if 'close' would be more effective, especially in the second sentence.", "label": 1}
+{"snippet": "I was wondering if Quantum Fluctuations are completely unpredictable, but do our observations tell us if these fluctuations happen evenly through space or are there regions where more quantum fluctuations occur than others? If they are completely unpredictable and are forming at specific places, could this be reasoned why they are being created in these areas MORE than in other areas of our universe? If possible can you present any observations or any evidence, for your answer?", "label": 1}
+{"snippet": "I would like to learn exterior algebra, wedge product and geometric product along with their applications in physics. Is there a good source you can recommend? Should I study differential geometry in order to grasp them? I started studying tensor analysis but even the concept of contravariance and covariance is not explained well enough in most of the textbooks. I would be grateful if you point at a source that guides one well and assumes no prior knowledge of the topics except calculus and linear algebra.", "label": 1}
+{"snippet": "The dot is placed in a position that is relative to the other dots and the timing as to when the item was posted I'm okay with the first half of this sentence (the part before and). I'm wondering if the second half is a legitimate ellipsis here. If so, how does it interact with the first half? In other words, what could be the full form of the entire sentence?", "label": 1}
+{"snippet": "I'm writing a document in which I need to state that my work is unsupervised instead of supervised. I have thought in these two sentences, but don't know whether they are correct, or whether is there a better one to explain this situation. \"from an unsupervised decision making point of view\" \"with an unsupervised decision making approach\" also, what's the correct way, \"decision making\" or \"decision-making\"?", "label": 1}
+{"snippet": "Should I use a comma before the word who? This sentence is confusing me: I made this blog because I want to help all of the other people who have problems that are similar to mine. If I did use a comma in that sentence, then what would be the benefits & disadvantages? In what cases should a comma be put before the word who?", "label": 1}
+{"snippet": "In granulometry, say I have a tube with an heterogeneous mix of particles of different sizes (sand and stones, by instance). The tube is vertical in the usual gravity field and is placed in the air. If I randomly shake the tube, the smallest particles will eventually be at the bottom, and the largest ones at the top. So the particles are now sorted by size. Why? A friend of mine considers a volume of the bottom part of the tube has a greater density (or mass) than of the top's. And denser things go downward. I consider however, by shaking the particles, small ones can fall through the space left between larger ones. What is the correct explanation?", "label": 1}
+{"snippet": "What is the word that means a 'what if' phrase? In a college course, I vaguely remember, the instructor wrote a word on the board that loosely meant or perhaps described any sentence that was a what-if statement. If I remember correctly it was essentially a word for classes of phrases, like say an appositive phrase. It was a more technical word, not something common like hypothetical, and for the life of me I can't recall it. Any help would be much appreciated.", "label": 1}
+{"snippet": "If a set is closed and open, it may be bounded (e.g., the empty set), or it may be unbounded (e.g., the set of real numbers). But what about a closed set that is not open? Such as: a singleton a set of finite points a closed interval the union of a finite collection of closed intervals the nonempty intersection of an arbitrary (possibly infinite) collection of closed intervals These are all examples of closed, non-open sets, and they are all bounded. Prove that if a set is closed and non-open, then it is bounded; or disprove by providing an example of a closed, non-open set that is unbounded.", "label": 1}
+{"snippet": "I plan on asking my professor what he meant by \"average continuous function,\" but as it is possible that this is a concept as vague as the statement, I was hoping to get some interesting answers/interpretations from stack exchange first. How do you think of the average of some infinite group of things? Or does this just mean that the real line is so dense/big that it is somehow likely that a function would bounce around everywhere except on some countable number of points? I'm sorry this is vague, I will be sure to post his response if I get a good one. I would also appreciate any resources or reading; googling around hasn't been fruitful.", "label": 1}
+{"snippet": "In a global company, I often need to address someone in another country without knowing his/her gender in emails with a third person or with a group of people. It's awkward and inefficient to spell his/her name every time in reference of this person, especially if it's a long name. The only solution seems to find out the person's gender after all. If I have to do so, using emails only, Should I ask someone who knows him/her or should I ask the person directly? Personally I feel awful to approach the person with this kind of questions. How should the question be worded to be appropriate? Examples? Please indicate the culture background of the answer if you don't mind.", "label": 1}
+{"snippet": "I\"m attempting to efficiently describe a threshold of when someone has moved from being a consumer to a contributor. My context is a church setting. I'm responsible for drafting a description of the different barriers or thresholds a person encounters or crosses in the process of integrating into a local congregation. Here is what I have developed so far: The first threshold is called resonance. This is the process of tentative agreement with the beliefs of the church, initial trust of the church leadership and sensing that this is a place where one can develop rewarding relationships. The next threshold is participating in a class or small group and volunteering. I had hoped to find a word with some weight or vibe like \"resonance.\" Perhaps induct?", "label": 1}
+{"snippet": "There are three generations of electrons, neutrinos, and quarks. The second and third generations of electrons and quarks are unstable and decay into lighter particles. Why are there exactly three generations? Is it possible that there are more generations of increasingly massive and unstable particles that we aren't able to discover yet (for instance, at higher energy levels that we are capable of), or is there some known reason why it has to be exactly (and can't be more than) three? edit: in addition to the link above, I also found this question helpful: What Do We Get From Having Higher Generations of Particles?", "label": 1}
+{"snippet": "There is a quantity known as scattering cross section which is given as a function of frequency. It means the ratio of the scattered power by the particle to the ratio of the incident power on the particle. Is radar cross section the same thing as scattering cross section? Some electromagnetic solvers (like CST studio) give radar cross section and absorption cross section only, so I guess it should be the same as scattering cross section.", "label": 1}
+{"snippet": "When using quantifiers, it is probably important to pick up certain habits that veterans agree upon as early as possible. Since it was pointed out to me by a highly esteemed member that it's sometimes better style to avoid quantifiers, I was wondering what the convention is with respect to when to use them and when to avoid them. Since they are logically equivalent to the words spelled out in plain English but do it in less space, I was under the impression it would never really hurt to use them, but that is probably a naive view to take, so I'm looking for some advice there.", "label": 1}
+{"snippet": "Several trade products, especially food, have been named after their places of origin throughout the centuries. To mention just a few, champagne, after Champagne, France. calico, after Calicut, India cashmere, after Kashmir, India/Pakistan port, after Oporto, Portugal muslin, after Mosul, Iraq alsatian (a German shephard) after Alsace, France china (tableware), after China canary, Canary Islands spa, after Spa, Belgium Is there, in linguistics, a phrase or term for naming something after its place of origin? Edit - Re Tim's answer, although most of them are trade products, the term I'm looking for also includes animals, behaviors, recipes, etc.", "label": 1}
+{"snippet": "I have a probability book (for actuarial exam preparation) and the author states as an assumption that \"if the probability space is rectangular\" in order to show two random variables are independent: I could not understand why we need this assumption, so I looked at my math stats book, and it appears the author here does not mention the rectangular region assumption: What is to be made of this?", "label": 1}
+{"snippet": "What is the job title or name for people who creates content for a social media website to drive traffic. For example, a new social media site wants viewers so they have a small group of people who are content experts write posts and answer other posts. They may or may not be paid. Options I've got so far: Volunteers, moderators, early adopters, betas... For the record, I don't like these options...", "label": 1}
+{"snippet": "I'm a little confused on what to answer to this: Determine whether the function floor(x) is big omega of x. The above function holds for integers but not for real numbers. According to the definition of big omega x could be either real or integer so I'm unsure what is the right answer although I've seen that the solution is that it does hold according to some online solutions. Could somebody explain the correct answer for this? Could I say on my answer that it holds for integers and not for reals? I'm taking a basic course on discrete math so I'm relatively new to this concept, thanks for your help.", "label": 1}
+{"snippet": "This is a follow up question to the link below: Remote bibliography I have the same problem, I can't use a bib file from Google drive. I'm sure I'm running Biber and biblatex, because if I use a local location it works just fine. Yet Biber wouldn't find the remote bib file... What I'm not so sure of is whether I'm getting the URL correctly. What I did was make the for public and the downloaded it after which I could get a URL. That was the URL I used. Is that the correct way to obtain the correct URL?", "label": 1}
+{"snippet": "The Wikipedia article on deep inelastic scattering suggests that the experiment shows baryons have three point of deflections (corresponding to three quarks) and mesons have two points of deflection. How are the electrons fired in this experiment being detected, and how exactly do the two or three points of deflection appear in the data? Are they fired at a target consisting entirely of baryons, or are collisions with non-baryons somehow filtered from the data?", "label": 1}
+{"snippet": "In Carroll's we read ...The Unruh effect teaches us the most important lesson of Quantum Field Theory (QFT) in curved spacetime, the idea that \"vacuum\" and \"particles\" are observer-dependent notions rather than fundamental concepts. I wonder are we talking about the same observer or two different observers using two different frames? Put it another way, can the same observer who observed nothing using a frame detect a thermal spectrum if switched to another frame that is uniformly accelerating with respect to his previous frame? Does it apply both ways? I mean if an observer detects particles, does this observant-dependent notion of particle content of a given state, implies that he can switch to another frame in the blink of an eye, and detect nothing?", "label": 1}
+{"snippet": "Blue is perceived darker than yellow by the human eye, because of biological principles within the eye. I can understand that therefore, when making a picture black&white in software like Adobe Photoshop, the software takes this perceptual information into account. However, in very old analog photographs, blue also appears darker than yellow. What is the reason for this? Is this just a lucky coincidence of the chemistry of the photographic film? Or is blue in some way really darker than yellow?", "label": 1}
+{"snippet": "Here is a sentence, slightly modified to be generic, for an award. My supervisor insists that the sentence is incorrectly written, although I cannot spot the error. ...the person was located and after XXX, BOB was immediately deployed to the frigid river to render assistance. Bob expertly directed the recovery of the severely hypothermic survivor and provided critical medical care enroute to XXX Hospital, saving her life. Sure, there are other ways to write it, but space is an issue and I feel this is the most effective way of writing the sentence. I was given the advice that it might be a dangling participle, but I am not sure it is. Thoughts?", "label": 1}
+{"snippet": "Is photon interaction , electrostatic interaction outside the nucleus and gravitational interaction is all due to electromagnetic waves ? and CAN be identified as with the de Broglie waves ? I thought of a theory in which is assuming that photon interaction , electrostatic interaction outside the nucleus and gravitational interaction is all due to electromagnetic waves and can be identified as with the de Broglie waves in order to explain how the force of gravitation act between particles . So can this assumption stand a chance of being theoretically and experimentally correct . Please add your comments regarding this in your answer and please explain why or why not .", "label": 1}
+{"snippet": "Adobe Typekit fonts install themselves in application fontlists (Word, InDesign etc.) but do not install in the Mac Fontbook. They are rented so this is their way of enforcing licence terms. Since they are effectively hidden in the directory structure, I cannot find a way of using them in Latex documents with the fontspec package. Has anyone managed to work around this and use them with fontspec??", "label": 1}
+{"snippet": "I'm just going to use the standard article class to create my slides manually. The question is, what pagesize is appropriate, and why? Should I take into account my projector's resolution and/or the laptop's resolution? How should I set a custom pagesize, in case I need a substandard one? Actually: I used a projector at school once and gave a presentation of slides created with Beamer. It worked fine (although I'm not sure I could have improved the resolution to better fit the projector/laptop). How can I bring the default Beamer pagesize over to the article class? That might work too.", "label": 1}
+{"snippet": "Mica is a good conductor of heat but an electrical insulator. According to free electron theory (which applies only to metals) free electrons carry heat and electricity. Therefore, thermal conductivity is directly proportional electrical conductivity. What about dielectric materials? In the case of mica, it conducts heat but not electricity, so what are the carriers responsible for this behavior. If the are electrons as they are in metals then why they don't carry electricity too?", "label": 1}
+{"snippet": "Having a tad bit trying to prove this question, Show that the set of reflections is a complete conjugacy class in the euclidean group E. Also, do the same for the set of half-turns and inversions. For the first set (reflections), I have that the set of reflections is a complete conjugacy class in E because the conjugates of a reflection are reflections with a translated, rotated and reflected mirror plane. Hence, the conjugate closure of a singleton containing a reflection is the whole E group. (This I got from some definitions). I don't know quite how to prove the question. Any help would be great or any suggestions. Thanks in advance.", "label": 1}
+{"snippet": "I'm trying to find the fixed point for the system (see document attached) but it seems so hard and I don't know what Im doing wrong. Can somebody help me with this. I need to find the to look for the value where the bifurcation occur (for that process i need to evaluate the jacobian matrix for the system on the fixed points and the looks for the delta, which is really easy) but this is the only part where I'm stuck. Please see document attached", "label": 1}
+{"snippet": "I am attempting to write a personal statement at the beginning of a resume and am having a quandry as to how to write the following: I am a super hero with seven years' experience in blowing out fires with my exhalation... I assume that since the experience doesn't belong to the seven instances of years, this is incorrect use of the plural possessive. How can I write this statement properly?", "label": 1}
+{"snippet": "I'm working with algorithms that filter their input (that is, remove part of it), and I'm not sure this phrase is unambiguous: This function returns the filtered elements. Is it obvious that filtered here means the elements that have passed the filter? Or could it mean the elements that have been filtered out? If both are present, I believe it's easier to eliminate the ambiguity: This function returns a pair of lists (filtered_out,filtered_in) . This function returns a pair of lists (filtered_out,filtrate). Buf if I see just a variable named filtered, without the _out and _in suffixes, I'm not sure which one should be inferred.", "label": 1}
+{"snippet": "Is the matrix that we get from diagonalization the only possible diagonal matrix that can be transformed from say matrix A? Assuming that A is diagonalizable? I think it is but I don't know how to prove it? The way I look at diagonalization now is that it is an algorithm but I am not sure if the matrix that we get from it is the only diagonal matrix that we can transform from A. Can someone please explain to me. Thanks.", "label": 1}
+{"snippet": "The game of Go is... or The game of go is... Apparently the International Go Federation capitalizes it. Its dictionary entry doesn't appear to be (from what I have seen). It seems to fit the definition of a proper noun as it isn't preceded by an article (such as \"the\" or \"an\"). So which is it? Also, where does that put checkers, chess, basketball, football, etc. They are never (or at least not regularly) capitalized, yet they seem to have the same characteristics. I predict the argument is going to be that Monopoly is capitalized because it is a brand and go should not be capitalized since it is not a brand and it is not referring to a specific instance of anything. Is that correct?", "label": 1}
+{"snippet": "I'm studying the first chapter of Hartshorne's Algebraic Geometry by myself and I found this book really hard for a beginner like me, but my advisor said to me that I had to study Algebraic Geometry by this book during my vacations. Then any part of the Hartshorne's book which I find very dry or superficial I search the same subject in another books or notes available online which are easier to read and have more exemples. Then my question is where I can find more material of this concept of dimension and height explained in this page of Hartshorne's book: Thanks in advance.", "label": 1}
+{"snippet": "Legolas prodded him across the bridge (\"You'll beg for mercy, but you'll get none from me, oho no!\"), up the beech-lined path (\"You'll never work in this country again, I'll bloody well see to that!\") Source. What's the meaning of the expression \"I'll bloody well see to that!\"? It means something like \"I'll make sure of that!\" I am not sure what it really means.", "label": 1}
+{"snippet": "A sometimes online sparring partner of mine recently wrote: Men (as opposed to women) have had a purpose that should serve us well should this new transhuman world ever actually materialize: We provide; we protect; we invent; we drive the engine of economies. Normally, I wouldn't separate the items in a series after a colon with semicolons unless one or more of them included a comma of its own. But here the items are independent clauses, which makes me think that semicolons should be used, regardless. So, what's correct?", "label": 1}
+{"snippet": "Einstein in his derivation of special relativity came upon the equivalence of energy and matter, and given the right circumstances, the relation can go either way - matter can become energy, and energy can become matter - right? So my question relates to the second process - energy becoming matter. While I know energy does not literally condense into matter in the sense that steam condenses into water, by analogy does the (rather loose) saying: \"matter is essentially condensed energy\" have any merit?", "label": 1}
+{"snippet": "Why is it that supergravity is an extension to general relativity? In what ways? What I have read until now says the following: GR got itself concerned with gravity after the revolution of special relativity. Then supersymmetry was a plausible new theory and after the investment of supersymmetry in general relativity, supergravity was born. Thus, this chain tells us that Sugra is an extension of GR. If this is right, I don't think this is the only way to explain it, is it? How can I technically understand how this is true?", "label": 1}
+{"snippet": "I would like to know more about the idiom \"to get going\" especially in the meaning \"to depart\", I mostly use it to mean \"get started\" but I've heard that it has very many other meanings. Is \"get going\" in the following sentence an idiom or not: We should get the car going soon or else we'll be late. Side question, where does this idiom come from?", "label": 1}
+{"snippet": "I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these locations, and also space missions that have sent spacecraft to them have overlapped in time. As part of the same question I wonder how close to each other these spacecraft are at this points. I assume that in real life Lagrange points are not really points (mathematically), but there is a margin to them? I believe that some of the points are not that stable and require spacecraft to make adjustments. Maybe this control capability also helps them be together at these locations?", "label": 1}
+{"snippet": "I've noticed this paper which explains that they have observed the \"Hawking radiation\" emitted by a black hole analog. In which sense the Bose-Einstein condensate described by the paper can be considered a black hole analog? It is essentialy that the \"analog of an event horizon\" for sound waves is created or are there other relevant aspects? And what has been observed which mimics Hawking radiation? Is there something in this experimental observation that can only be explained by quantum effects, such as phonons?", "label": 1}
+{"snippet": "I am studying graphs through an online course and came across the idea of a \"connected component\", a \"subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the subgraph.\" This means that a single graph need not be connected. So my question is: what, if not connectivity, defines a graph and separates it from another graph? And as an aside, if there is no such boundary, is it ever useful to think of all graphs being connected?", "label": 1}
+{"snippet": "I guess I can call them 'politician words' but.... What do you call a word/phrase that has a lot of emotion behind it, but doesn't necessarily have any specific meaning. E.G.: Freedom, Liberty, Terrorism, Patriotism, etc. Speech words doesn't quite get it. Rhetorical dynamite words? Nahh. Sending vague messages to your medulla oblongata to scare you into voting for me is highly accurate, if unwieldy.", "label": 1}
+{"snippet": "I used to make my presentation with PowerPoint and Keynote which both were easy but this LaTeX is driving me crazy since you should add anything you want in a hard way! In fact, I have tried to search about different types of effect I can use for LaTeX presentation but I was not successful to find many. Is there anyone knows a good source, different effect command, etc.?", "label": 1}
+{"snippet": "So recently in the blog post on tetration, it talked about tetration with nice clean powers (calling them these because I don't know the right term). But how does it work when given a complex power? How about a decimal power? Or even just a negative power? And one final yet somewhat unrelated question: can you use some sort of method to reverse tetration by using tetration?", "label": 1}
+{"snippet": "It's often convenient to add line numbers to a page automatically and the lineno package generally does the trick. But I've had two problems with it It doesn't seem to align the line numbers with the actual text lines - linenumbers drift between lines and occasionally skip lines as well as a consequence. Sequences of equations get skipped. Now I've seen this work properly in other PDFs and so was wondering if there's some magic option I'm missing. All I do is include the package and then turn line numbering on.", "label": 1}
+{"snippet": "Negative probabilities are naturally found in the Wigner function (both the original and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the Klein-Gordon equation. Is a general treatment of such quasi-probability distributions, besides naively using 'legit' probabilistic formulas? For example, is there a theory saying which measurements are allowed, so to screen negative probabilities? Additionally, is there an intuition behind negative probabilities?", "label": 1}
+{"snippet": "I'm reading Jerome K. Jerome's 'Three men in a boat' The above is about fishermen's bluff. My question is in the above paragraph a man knocks ashes (from his pipe) against the bars. But what is bars? On the counter? or on the window bars? But it is not likely under the circumstances, so I just wonder if 'bars' mean something different or particular meaning in this context.", "label": 1}
+{"snippet": "I've spent some time on Halmos' Measure Theory and must upvote such a good book. I want to solve most exercises in this book. I'm not sure whether there is a solution manual or instructor manual that can be downloaded or read online coz solutions are very important for self-study. I've tried to google it several times and results corresponding to my search were not satisfactory.", "label": 1}
+{"snippet": "Writing \"enough\" three times in such a short sentence seems too repetitive. So is there a different or more succinct way to write it? Horrible example sentence: I am drunk enough, fast enough and dumb enough that it just might work! Just removing the first and second \"enough\" would change the meaning, no? I am drunk, fast and dumb enough that it just might work! So can I write the sentence as follows and get across the same meaning as the example sentence or did I just come up with nonsense? I am drunk-, fast- and dumb enough that it just might work! Thank you for your replies!", "label": 1}
+{"snippet": "I was doing a question about resonance of sound box connecting to a tuning fork. It asks why the sound lasts for a shorter time with sound box than if the tuning fork is struck identically without the sound box. Is it because the sound box dampens the vibration of tuning fork, or because due to larger contact area of box with air the box transfers vibrational energy at higher rate to air, or these two reasons are actually the same thing? So does it mean that resonator will always dampen the driving oscillator? I'm quite confused between the idea of energy transfer in resonance and damping. Thanks in advance:)", "label": 1}
+{"snippet": "When I am composing a large document in LaTeX, I often compose the chapters in separate documents. When I do this I have to copy and paste a large block of header text to the chapter I am editing so I can make sure the formatting is correct while I am writing it. How can I import a header file of formatting information with a single line?", "label": 1}
+{"snippet": "Considering the fault of any experimental evidence from LHC for supporting the supersymmetry idea until now, can we say that it is dead? Generally the people who are working on this subject say that MSSM probably is dead but we have some new extensions of it such as NMSSM. This argument seems weird a bit. Sometimes I feel that it is a vain try to keep an idea live because they have invested their scientific life on it. On the other side, I have to confess that the supersymmetry is a beautiful idea. But it seems that the nature does not like it and we have to accept it. Other related question is, if the supersymmetry fails, can we say that the superstring fails too?", "label": 1}
+{"snippet": "Please tell me the meaning of stereotype in the following passage Reflexes: This is the behaviour in which movement takes place in a particular organ. This movement is very fast, stereotype, and for a short duration such as knee jerk, blinking of eyes and withdrawal of hand from a hot place\". This is a behavioral science term, not sociological. Edit: Thank you everyone for the reply. Finally I got the answer from Britannica - Stereotyped response", "label": 1}
+{"snippet": "When someone practices something, they do it often/as a habit. When someone says something is practical, they usually mean it is pragmatic/sensible/applicable, yet not necessarily practiced. And my teachers have used practicum to refer to a test, which is an examination, not an instance of practice. What is the common root of these words, what does it mean, and why do these words seem to mean different things?", "label": 1}
+{"snippet": "Suppose you are given a differential equation and a set of initial conditions (or boundary conditions) pointing to a unique solution. Is there any way to know off-hand if the solution will be an even function, an odd function, or neither? This is, I suppose, tricky, because the fundamental set of solutions could include both even and odd functions (say, sine and cosine). The trick is knowing a priori that, for a given set of conditions, the constant coefficient for all of the odd solutions is zero and the constant coefficient for all (or some?) of the even functions are non-zero values. Or vice versa. Can this be done?", "label": 1}
+{"snippet": "Within the multicol environment I want to be able to fix a figure to be displayed at either the top or bottom of a column (as in a scientific journal). The figure environment cannot be used in multicol and I've tried using wrapfig and even creating a minipage to do this, but the figure always seems to be placed where it is inserted in the text and therefore must be moved every time an edit is made. Is there a way to force a figure to be positioned at the top or bottom of a column in multicol?", "label": 1}
+{"snippet": "Is there some relationship between the correlation of two random variables, and Bayes Theorem? A bit of background intuition, if W = random variable denoting number of women in a room, and L = random variable denoting number of long-haired people in the same room, we can infer about one variable given the other either using the correlation value or the conditional expectation value as given by Bayes Theorem (though Bayes deals with events, probability densities are tied to expectations anyway) Thanks", "label": 1}
+{"snippet": "For something to be a blackhole, it must have gravity and the radius must be smaller than the schwarzschild radius for its mass. -Electrons have gravity -Electron are theoretically believed to be infinitely small points Since it has gravity it is capable of being a black hole. Since its radius is infinitely small, it must have a schwarzschild radius and thus be a black hole.", "label": 1}
+{"snippet": "I have read online that light can produce a weak gravitational field (for example antiparallel beams should, in principle, attract weakly). This made me wonder if light can produce minute gravitational waves? Even if the waves were extremely weak (no disregarding of those high order terms in the applicable equation, whatever equation that may be), could the gravitational waves dissipate energy (on the order that is expected for cosmological redshifts) when light travels across cosmological distances? I was thinking about the debunked tired-light hypothesis regarding the cosmological redshift, and I wondered if anyone has considered a mechanism whereby gravitational waves dissipate energy.", "label": 1}
+{"snippet": "I'm deeply interested in understanding delayed choice eraser experiment. Although I understand the experimental results, the retro causality is causing a big headache. From what I understand, the hidden variables theory is a no - no, due to experimental verification of the Bells inequality... A recent PDF that I came across confused me, hence this question... The PDF claims that the superposed eigenstates will continue to evolve, if not interrupted by a detector. My question is: Can it be established that it continues to evolve despite not being measured? Doesn't that violate the Copehagen interpretation -or- is it an understanding that is implicit to the quantum processes itself? Or am I making a noob mistake?", "label": 1}
+{"snippet": "I'd like to quantify over all cardinalities of sets. My end goal is to make a category-theoretic arguement: For all cardinalities of sets, in the category of sets with maps as morphisms: the subclass of objects with that given cardinality is closed under the class of isomorphisms, thereby forming a subcategory, for each set cardinality, where the morphisms are isomorphisms. Can I quantify over a class that isn't a set? Is there a good way to specify this class of cardinalities? Is there a better way to go about this?", "label": 1}
+{"snippet": "Consider two different shaped containers having same area: one is cylinder, the other is like an inverted pyramid (roughly). Both have the same level of water, the weight of the inverted pyramidal container will therefore be greater than that of the cylinder. But I know from Pascal's law that the pressure should be same in both containers. If the base areas are the same then the force (weight as measured by a scale) should also be the same. Why are the weights different?", "label": 1}
+{"snippet": "I am working on size dependent surface energy of metals. I need to know the different energies between the atoms. Different papers use different energies but their meanings seem alike, therefore they confuse me a lot. The concepts I confuse are: bulk free energy, cohesive energy, Gibbs free energy, binding energy Can someone tell me the correct definitions of them and show their differences in detail?", "label": 1}
+{"snippet": "Usually it is said that black holes cannot have electric or magnetic dipole, only electric charge and angular momentum are allowed quantities besides mass So, it would seem that black holes behave as perfect diamagnets that don't allow field lines to enter into the event horizon? If I place a magnetic dipole pointing near an event horizon, what is the boundary condition of the magnetic field on the horizon? does the field lines flow around the event horizon perfectly?", "label": 1}
+{"snippet": "What is the act of making something ownerless? All I've seen is to \"declare something ownerless\". However, in this statement one isn't so much as announcing as he is transferring something property. Moreover, if one wants to discuss his act of transferring, it wouldn't make sense to use the word \"declare\" (i.e \"his declaration of making this item ownerless was ineffective\" sounds like a mouthful).", "label": 1}
+{"snippet": "I'm studying model theory nowadays, and I understand how one-sorted (classical) signatures and structures work. However I am also interested in groupoids, which can not be described as a structure for a one-sorted signature. Looking up online, I came to the notion of many-sorted signature: nLab, Wikipedia. According to nLab, these can be used to describe, for example, directed (multi-)graphs, which seems easy enough: Take sorts for edges and vertices, and source and range maps from edges to vertices. However I can't see how can we describe a signature for categories in this language. We need all the ingredients for graphs (edges=arrow, vertices=objects), and at least one function symbol for composition, but since composition is only partially defined, I don't see how this can be done.", "label": 1}
+{"snippet": "I'm trying to write a program that lets the user put in the center point of a circle and its radius, and the put in two points to form a rectangle. Then I'm wanting it to print out whether the if the circle is touching/inside the rectangle in any way or not. I feel that I need to know all points the circle touches in order to know if its touching the or inside the rectangle at all. Not sure if I made that completely clear, but any ideas?", "label": 1}
+{"snippet": "In cosmology: A comoving observer is the only observer that will perceive the universe, including the cosmic microwave background radiation, to be isotropic. (Wikipedia) According to this definition, is Earth considered as a comoving reference frame, or are we supposed to have a \"peculiar velocity\"? What is the current precision for measuring if a frame is comoving or not, and for measuring its peculiar velocity? Or: From which speed (with respect to Earth) a frame would be considered as peculiar?", "label": 1}
+{"snippet": "I have recently been studying Bayesian as well as Frequentive Statistics (mostly null hypothesis significance testing) and am confused as to the meaning of the distribution of the likelihood and observed data in both. According to my understanding, Bayesian school of though treats the distribution of the sampled data to be same as that of the likelihood of th data conditioned over the hypothesis (For example if data follows a normal distribution then the likelihood function is also normal with same mean and variance) whereas in the frequentive school, the likelihood or null distribution is basically the distribution followed by the test statistic which is different from the distribution followed by the data. Could someone explain whether my understanding is correct?", "label": 1}
+{"snippet": "Very simply put, if one places a block of some material on a level surface and pushes it horizontally, a certain coefficient of friction is measured. If one tightly couples an oscillator of some sort to the block such that it vibrates, a much smaller coefficient of friction is generally observed. Any explanations of this effect, with varying frequencies of oscillation? Worth noting is that the vibrating coefficient of friction is less than the normal dynamic coefficient of friction. While perhaps not more efficient energy-wise, it appears it could be a useful effect.", "label": 1}
+{"snippet": "Suppose a system A which is a vessel of water with two electrodes, connected by a resistor, placed in the water. If you apply voltage to the electrodes, energy is transferred from the battery (not included in system A) to system A. I read in a book that the form of energy transferred is work, and not heat. But basically what happens is that the resistor heats up and transfers heat to the water, am I wrong?", "label": 1}
+{"snippet": "It's strange that he should say so. She tiptoed lest the guard should hear her. It's crucial that she should have her own car. . I've seen those three sentences somewhere on the internet. I found them very unintuitive and quite deceiving, so I've been looking for the explanation, yet did not find one. If you could explain the usage of \"should\" in those sentences, I should be very grateful.", "label": 1}
+{"snippet": "I'm building a site with two main categories. One side is portfolio work, the other is written work. Among the written work, there will be personal blogs, tutorials, more in-depth articles, etc. I'm looking for a short, preferably single-word name for all of my written work. I thought about using 'writings', but it feels a bit like bad choice because it's so close to the verb to write. Does anyone have opinions on this option or suggestion for a single word?", "label": 1}
+{"snippet": "I am required to find a research topic in this domain, so I'm really interested in finding out what kind of problems are covered in this domain, and how others are using these techniques to solve them. Preferably, I'd be more interested in if/how one can use them in Machine Learning or Pattern Recognition. I know this is a very open-ended questions, so I will not get a concrete answer. At this point, I only require a board answer to help me get started to get acquainted more with this area.", "label": 1}
+{"snippet": "I translate some spiritual texts and this word revelation is very tricky to translate to another language that really does not have a similar word. For example: \"God has sent a new revelation to the world.\" What could be good synonyms for it in a general (non-Christian) spiritual context, where I am coming from. The original text is in American English. Possible translations: New message New information Insight What else? Dictionaries mainly refer to Bible and book of Revelations, but that is just confusing, because this text is not about Bible and should not be confused with it.", "label": 1}
+{"snippet": "Possible Duplicate: Would you be weightless at the center of the Earth? The issue of weightlessness at the center of the Earth has obviously already been discussed, however I am curious as to know what will it feel like as a human. Will it be absolute weightlessness as experienced by being in space, or will the mass of the Earth surrounding you pull you apart in all directions in a free floating expansion with your eyeballs popping out, etc.", "label": 1}
+{"snippet": "When the context is science, the word \"theory\" means a logical/mathematical framework which tries to explain the phenomena. Infact in science \"Theories\" carry some \"Claims\" or \"Predictions\" while every sub-discipline of science could be presented in many number of theories. But in \"Mathematics\" the word \"Theory\" seems to merely refer to a sub-discipline of a mathematical field of study. For example I could call \"Number theory\" the discipline of \"Studying Diophantine equations\" or \"Group theory\" the \"Study of certain types of algebraic structures(namely Groups)\" or \"Differential equation theory\" the \"The methods of solving differential equations\". Does the word \"Theory\" in mathematics have some special meaning like bringing some claims or predictions or is it just a reference to the mathematical sub-discipline we are studying?", "label": 1}
+{"snippet": "Work is force applied over distance. Is it also reasonable to say that work is (the same thing as) the transfer of energy? When work is done, the equivalent energy is transferred. But if energy is transferred, such as by heating something, is that (or could that be) called work? Also, if a black body is subjected to a stream of energy, which it absorbs and radiates away, is any work done? The black body, let's assume, remains at a constant temperature, but energy is transferred to it and then radiated away. Is any work done? So what I'm really asking about is how the term \"work\" should be used.", "label": 1}
+{"snippet": "I was just wondering that is it ever possible that some object produces only invisible light when it catches fire? Something like invisible flames. If this is possible, can you please give one example? I have checked a phenomenon called Back-body Radiation and energy emitted by excited electron when fall back to lower orbit, which are responsible for colour of the flame. It looks like it is possible to produce invisible flames. Please correct me if I am wrong on any point.", "label": 1}
+{"snippet": "Stephen King (author of \"The Shining\") in his book \"On Writing\", writes: American grammar doesn`t have the sturdiness of British grammar (a British advertising man with a proper education can make magazine copy for ribbed condoms sound like the Magna goddam Carta), but it has its own scruffy charm I'm interested to know what King means by \"sturdiness\" here. Can anyone give some examples or more insight into what exactly King is talking about?", "label": 1}
+{"snippet": "I could only find this blog that suggests that complacence is \"is a calm satisfaction with oneself\" whereas \"complacency means a self-satisfaction but coupled with a lack of awareness of what is happening around it.\" Is there a difference between the two and if not, is one more proper than the other? What would be the grammatical term for such a difference in the ending of a word? I just remembered that stagnation is probably the preferred word, so perhaps ignore the stagnancy vs stagnance part (stagnancy seems to be entirely incorrect anyway).", "label": 1}
+{"snippet": "I've heard a grammar rule which is, if there is any verb followed by a preposition except the 'to' preposition, the verb must have a 'ing'. As example, I've this sentence: I am going for playing. Where the 'play' verb is in 'ing' form. But in this sentence: I am going to play. the 'play' verb is in normal form. I just want to know that is the rule correct? If correct then is there any other exceptional preposition like 'to'?", "label": 1}
+{"snippet": "If I marry a woman and she has a child, I am a step parent. But what if the sequence is reversed? For example, suppose I am married to a woman, get divorced and she subsequently has a child by someone else. Is there any word in the English language to describe what my relationship (if any) is to this child? This is my situation; I'm close to this child and always at a loss to describe our situation as other than family friend. Can anyone offer another suggestion?", "label": 1}
+{"snippet": "I am new to LateX and I would like to know if there is a class which allows for creating a book cover design to send to the printers ? I already have the book cover design done in Adobe Photoshop with the front cover, spine. In other words, the final image is ready. How would Memoir Class work for this ? Now i only need to get it ready for printers, so I need to know how to set bleeds, spine, crop marks etc. to be able to send the final print ready pdf to printers.", "label": 1}
+{"snippet": "Today our teacher said that dual spaces are \"big\" and told us that this is a consequence by Hahn-Banach's theorem. So I was wondering whether the dual space of a space is always \"bigger\" or equal compared with the space itself? I thought a good way to check the adjective \"big\" by mathematical methods is to ask whether there is an injective map in the dual space. I am very interested in any comment on this.", "label": 1}
+{"snippet": "They say inflation must have occured because the universe is very homogeneous. Otherwise, how could one part of the universe reach the same temperature as another when the distance between the parts is more than light could have traveled in the given time? Why can't this problem be solved without inflation? If each part started with the same temperature to begin with, then they can have the same temperature irrespective of the distance between them. Am I missing something here?", "label": 1}
+{"snippet": "I have a set of numbers (each one corresponding to a payment made from the same person) and I would like to assign a probability value to a new specified number given that historical data. I've looked at the Chebyshev's inequality as a simple means to do that but I don't get the expected results. The formula evidences only obvious differences from the time series and also gives too little probability value to numbers that are lower than at least one of the historical ones.", "label": 1}
+{"snippet": "Assuming I rotate a disk, I want to know how long it takes to completely stop, and the number of revolutions it made since I removed my fingers off the disk. Lets say a DVD I rotate with my fingers. I only know the radians per second (velocity) of the last moment I touched the disc. Can you guys tell me where to start? Im trying to implement this on an iPhone app. So it would be nice if you mention equations. It should not be exact.", "label": 1}
+{"snippet": "What is the term for words that can be used as the opposite of themselves? I know there are a few of them out there, it is possible to 'Dust a cake with Icing' and if the cake were on a shelf for a long time (must be a bad bakery) then it would be acceptable to 'Dust the cake' to remove any dust particles... In this case, 'Dust with Icing' implies the addition of something to the cake where 'Dust the cake' implies the action of removing dust from the cake Other examples: Bolt - To hold in place or to Run away with haste... Trim - To remove a small portion or to add small bits that make it pretty...", "label": 1}
+{"snippet": "In an English-language text I wrote recently, I used this sentence It ain't pretty, but it'll keep! to describe the durability of a newly erected wall that (due to my poor masonry skills) looks hideous, but should withstand the floods it'll be shielding the property against. In my native German dialect, this is a valid use of \"keep.\" But is it actually in English, too?", "label": 1}
+{"snippet": "I saw this expression: \"the aim of the activity is \"to show the fly the way out of the fly-bottle\". \" (It is connected with this other expression: \"I don't know my way about\".) I grasped the general sense of the expression but I don't understand clearly how it is formed, i.e. it's logical analysis (e.g, is \"fly\" a noun in this case?). Which are the logical analysis and the literal meaning of the expression \"to show the fly the way out ot the fly-bottle\"?", "label": 1}
+{"snippet": "So, from a cursory understanding of English history (and I am very happy to say that) I was able to, one might note that the cultural history of those who lived in England might proceed: Britons who spoke Brythonic Romans who spoke Latin Angles, Jutes, Saxons, et. al. (Anglo-saxons) who spoke various Teutonic dialects Normans (ironically, from the same stock as the former, but trained in French) My guess (and correct me if I'm wrong) is that the Latin influence in English was more to do with the Church and the Normans than it was to do with the Romans directly, but I was wondering if there are words which may be shown to be direct descendants of the ancient Britons' tounge?", "label": 1}
+{"snippet": "I am writing a short description of a social experiement. The objective is to get a better idea of the way people think. I have some troubles to understand the difference between those two phrases: To encounter people and better understand their way of thinking To encounter people and better understand the way they think Is there any difference in meaning between those two phrases? If so, could you please tell me what their are? Thanks a lot for your help!", "label": 1}
+{"snippet": "Say a roller coaster car is going up a ramp to a drop. At some point it needs to traverse a curve to get to the drop. In general, since the car is constrained to the rail, how is it able to move around on curves without breaking the car? Does there exist some kind of free motion for the wheels to move a little bit? Otherwise it seems like the car would bend.", "label": 1}
+{"snippet": "I understand that increasing current decreases the time taken for a capacitor to both charge and discharge, and also increasing the potential difference and charge increase the time taken for a capacitor to charge while decreasing the time taken for it to discharge. However, I am having troubles with deducing what effect resistance will have on it? Is it as simple as V = IR, and increasing resistance with a constant potential difference will decrease current (and thus increase the time taken for a capacitor to both charge and discharge?)", "label": 1}
+{"snippet": "Given a plane with an unbounded number of random points, is there an economical algorithm to find the Voronoi zone of any one selected point? I've considered making a \"sweeping\" circle from that point, adding a line to the zone boundary as I meet points of increasing distance; would this solution be correct as soon as I have enough lines to enclose a polygon? (The obvious corollary question is \"If stopping as soon as the point is bounded isn't correct, when do I stop?\")", "label": 1}
+{"snippet": "are you aware of a diagram showing all the connections between tex-related methods/engines. It would use terms such as tex - latex - context - luatex - xetex - xelatex - pdftex - pdflatex - etex and could even be extended to terms like xdvipdfmx and so on? All this is getting confusing, I think and it would be a good way to summarize. Thanks", "label": 1}
+{"snippet": "I have demonstrated that weight only is measured based on the gravitational pull of where you live. For example, the gravity on the surface of Mars is three times smaller than the gravity on the surface of Earth. So my question is simple: If we take into account that weight is only measured based on gravitational pull on that mass, if there was no gravity how would we define mass? That is, would mass weigh anything if no gravitational pull acted on it? Then what would be mass?", "label": 1}
+{"snippet": "I was recently shown a pretty cool video about common cosmological misconceptions. It got me reviewing the different between event horizon (current distance within which we will see/interact), particle horizon (current distance within which we have seen/interacted, and the Hubble Sphere (distance at which things are currently receding at the speed of light). I've found the following figure extremely helpful: But I'm very confused about the event horizon currently lying outside of the Hubble Sphere. If the universe is accelerating in its expansion, then it seems like everything outside of the Hubble Sphere at this moment - will never be in causal contact, never be within our light-cone, and thus be outside of our event horizon. Is this figure correct?", "label": 1}
+{"snippet": "If black holes must be in black holes in all reference frames, does the formation and or evaporation of SEVERAL black holes occur in the same order in all reference frames ie if one observer determines that black hole A formed, then black hole B, then black hole C, would any observers in any reference frame also be able to derive the same sequence for the formation of the black holes (or for the evaporation)?", "label": 1}
+{"snippet": "Possible Duplicate: How to prevent the paragraphs to spread out over the page? When I try to put some tables in my document I get lots of white space between the section (which I am guessing its because latex is trying to adjust positioning of the tables). Sometimes I get tables appearing on a single page by themselves. Is there a way to avoid this? Below is an image of a page showing the ugly spacing. (The boxes represent text areas)", "label": 1}
+{"snippet": "QKD protocol is a technique that allow two parties to share common secret key for cryptographic purpose and defined as being secure, by definition. But I am still wondering how can we measure that QKD is secure? In terms of what? and how can it be clearly proved? Is it possible by code it in any programming language like Java? well I am still looking for a good research topic under this area.", "label": 1}
+{"snippet": "Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule. According to right hand rule, if you hold the axis with your right hand and rotate the fingers in the direction of motion of the rotating body then thumb will point the direction of the angular velocity. The direction of angular velocity is above or below the plane. But what does it mean? I mean in linear velocity the direction of velocity is in the direction of motion of body but what does it mean that body is moving in one direction while the direction of its angular velocity is in another direction?", "label": 1}
+{"snippet": "Give some Lagrangian we use the principle of stationary action to find the desired euqations of motion for something (e.g. a field). A lot of modern physics seems to be based on the principle of stationary action. I read it works for classical mechanics, general relativity, Quantum chromodynamics, quantum electrodynamics, weak interactions and more stuff. However, is there a field where the principle of stationary action does not yield the desired result or where it fails (contradicts some experimental result)?", "label": 1}
+{"snippet": "An object that takes physical, material, or corporeal form can be held and seen by humans. When we describe the opposite, something that cannot be held or seen by the naked eye, words like spiritual or non-material are used. I'm looking for a word that's more specific: something to describe the sequences of numbers packed into data chips and technology whatsits. \"Information, whether of material or ________ form, can be found at the library.\" Assume that the library carries books and CDs/DVDs. In order to avoid wordy descriptions, does anyone have any suggestions for a single word that can fill the blank? I avoided antonyms of \"physical\" because they refer to things that are otherworldly.", "label": 1}
+{"snippet": "I'm trying to decide which sentence is correct, or if they both are. which would you recommend as easier to read/understand for the average reader? Hop the rocks quickly and get the star. Quickly hop the rocks and get the star. I'm using this in a promo for a game I made. Assuming both are valid, would it be better to use the first sentence since it begins with a shorter word?", "label": 1}
+{"snippet": "There is evidence that some galaxy clusters may experience some bulk rotation. If this is true, how valid is it to use the Ideal Gas Law to estimate the mass (actually, it calculates the acceleration needed to create the pressure gradient - from which the mass is derived)? One of the conditions for an idea gas is that collisions with the 'container' are elastic. If the galaxy cluster is rotating, then gas plasma particles will pick up velocity as they travel outwards (due to the centripetal force) and not bounce back as far inward. This is clearly an inelastic collision.", "label": 1}
+{"snippet": "I was reading this introduction to EPR and it seems to imply both that there is a unique g-factor of a given compound, but also that we can calculate multiple g-factors for a compound. For example, here's a picture on that page This clearly shows more than one g-factor for mitoNEET & Fdx. So is there only one g-factor or is it the g-factor at each specific value of the magnetic field that is unique? P.S. Is there a good book/ primer you could recommend to learn more about EPR spectroscopy?", "label": 1}
+{"snippet": "Since one can use singular they to avoid sexism in a way or another, I got stuck trying to figure if there is a polite word meaning something like \"a group of both Ladies and Gentlemen\" that could be put in the following phrase without implying in sexism: Do the Gentlemen need something? I thought about using Gentlemen, however, I have no clue if it implies in a group of men only. Can you help me out?", "label": 1}
+{"snippet": "I want to create a cloud of magnetic particles that will levitate in an electromagnetic field with an electromagnet. Is that possible? Is it easy to do or has it been done? I already have the magnetic nanoparticles and I just want to levitate them to form a 'cloud' so that each particle will stand in the air at specific distance from the others. They have the same size/weight. Would that be a problem? They need to sit in the air with specific distance between each other. Any ideas? Thanks!", "label": 1}
+{"snippet": "When I pronounce the phrase: \"I'm proud of you\" to communicate that I'm proud of the person I'm talking to, do I only need to stress the word \"proud\" a bit? I think that stressing the pronouns \"I\" and \"you\" are only needed when we want to make contrast between people, but it's probably less common. Am I right? The common stress pattern I think is something like: da-DA-da-da.", "label": 1}
+{"snippet": "I am trying to setup the Predictive Mode of Emacs and to use it with the LaTeX-mode. I have one problem: as soon as LaTeX-mode is loaded, it loads \"auto-overlays\" and it takes up to two minutes before I can begin to work, which is very annoying. I believe that this \"auto-overlays\" is used to switch between dictionaries according to where I am in the LaTeX document. Here is the part of my .emacs that concerns the predictive mode: (require 'predictive) (autoload 'predictive-mode \"predictive\" \"predictive\" t) (set-default 'predictive-auto-add-to-dict t) (setq predictive-main-dict 'dict-english predictive-auto-learn t predictive-add-to-dict-ask nil predictive-use-auto-learn-cache nil predictive-which-dict t) (add-hook 'latex-mode-hook 'predictive-mode) (setq completion-use-hotkeys nil) (setq predictive-ignore-initial-caps t) (custom-set-variables '(auto-completion-syntax-alist (quote (accept . word)))) Do you have a solution?", "label": 1}
+{"snippet": "So, I was at the bar last week, Behind the bar they have these signs with jokes on them. One of them said \"If your drinking to forget, please pay me first\"(This isn't the question, I get this joke). Somebody at the bar, noticing it, said to the bartender: \"I don't have a drinking to forget, but if I did, what about it?\". The bartender, looked confused, and then the guy pointed to the sign. The bartender still didn't get it, and he laughed at her. But I didn't get the joke either. This sentence doesn't make any sense to me. Why is it funny?", "label": 1}
+{"snippet": "I'm relatively new to TeX, which means I did nothing more than homework and some math things with it. Now I'd like to write invoices with LaTeX (for reusability etc.) I am not searching for a template. What I'm looking for is actually more a starting point and maybe some resources that already helped other people to get started with writing invoices or similar kinds of documents. Where should I start in order to learn to write more complex documents with LaTeX? What helped you?", "label": 1}
+{"snippet": "If A,B,C are normal subgroups of a group G where B is a subset of A. Then show that A intersection BC equals B(A intersection C). I m a newbie in abstract algebra n i m new to rigourous mathematical proof. I know that to show two sets are equal i must show that each one is a subset of the other. Plz solve this question", "label": 1}
+{"snippet": "In diagrams I often see light waves depicted as little sine waves that travel through space. And often when describing polarizers, the explainer will angle their hand to show the angle of polarization and bob it up and down in a sine wave action, apparently emulating the amplitude of the wave. My questions is, is the amplitude of light really like this? Where it moves up and down or side to side in space? Or, is the sine wave relationship just an analogy?", "label": 1}
+{"snippet": "All the time I see people replying with \"of course I will\" or \"yes it is!\" (to \"it's not that good\" and not placing a comma after \"of course\" and \"yes\". The second case seems even more extreme, as even placing a comma would not help - it would still be a comma splice. However, if I do place the commas, the sentences become very confusing, as many people would probably read that as \"I will, of course\" and \"it is, yes\". Now, to me it seems that grammatically, there is no option but to leave the commas in place - though, again, this may cause confusion. Any ideas?", "label": 1}
+{"snippet": "Higher algebra by hall and knight states that\"A compound ratio can be formed by multiplying together the fractions which denote them or by multiplying the antecedents to form new antecedent and multiplying the consequents to form new consequent\" but what is the meaning of the word compound ratio.If ratio is used for comparison then what is the purpose of compound ratio? Can anyone help me?. I will be grateful.", "label": 1}
+{"snippet": "Which of the last three verb patterns apply to the verb 'recommend'? I recommend that you wait. (present subjunctive, American usage) I recommend that you should wait. (substitute for present subjunctive, British usage) I recommend waiting. (subject of the gerund not mentioned) I recommend you/your waiting (subject of the gerund mentioned) I recommend to wait. (subject of the infinitive not mentioned) I recommend you to wait. (subject of the infinitive mentioned)", "label": 1}
+{"snippet": "Is a good example of 'intestinal fortitude' when someone faces his/her fair share of adversity and bounces back from it? Or when a boxer is repeatedly pummeled and knocked down in a fight, and he keeps returning to his feet to continue notwithstanding the beating endured (he's showing a lot of heart, internal strength and 'guts')? Can you say 'He had the intestinal fortitude ('guts') to call me a buffoon'? Is 'ovariological fortitude' the female equivalent of this term?", "label": 1}
+{"snippet": "In Lagrangian Mechanics we choose the path of least action. Given a uniform gravitational field, and a particle of finite mass; and fixing two points the start & end-point we consider all paths connecting the two points and minimise the action. This turns out to be a Brachistone, as first shown by Bernouilli. When we fix the end-point vertically below; the Brachistone is in fact astraight-line. But is there a principle in Lagrangian Mechanics that allows me to choose the point vertically below? Of course, we know from Newtons Mechanics that this must be the case. But how do we determine that end-point entirely within Lagrangian Mechanics?", "label": 1}
+{"snippet": "In the context of usable security (related to computer science), a major challenge is to provide security means in such a way that all of the people including those with some disabilities (e.g., blindness and deafness) be able to use information systems. So, in some cases we need to refer to these two general group of users. The question is how to do so in a respectful way. For example, referring them as ordinary and disabled users is a bit harsh. Also, I don't like using \"disabled users and users without any type of disabilities\" to refer them. What's the best way to describe these two group of users? Shorter options are preferred!", "label": 1}
+{"snippet": "Classically, if one has an electron orbiting a proton, how can the magnetic field felt by an observer with the same instantaneous velocity as the electron be calculated? It seems that I may find the magnetic field felt by this observer by boosting the proton to the same frame as the electron at some instant, and then calculating the B-field generated by transforming the E-field of the proton in the rest frame. Is this not the correct reasoning? If not, why so?", "label": 1}
+{"snippet": "Can I make a heat pump beat the Carnot efficiency? Why is the Carnot process the most efficient one? If I have a heatpump that is sphere shaped, and cascaded in layers like a onion can I beat Carnot efficiency? Heat would be transferred and concentrated from the outermost layer that is in contact with ambient air, and brought towards the center to heat a fluid.", "label": 1}
+{"snippet": "Please, help me to clarify this question. Assuming that there are many books I owe to a person and some of them are here on my table, is it correct to say: \"The books I owe you are on my table\"? Will it show that those books just belong to ones I owe to the person, and somewhere else are other books I owe him? Or will it strictly mean that these are the only books I owe? The confusion is because \"the\" is often used for an exhaustive list. And if to say: \"The book I owe you is on my table\" - the same question - can it just show that this is one of those books and there are other books I owe somewhere? Thanks.", "label": 1}
+{"snippet": "I am wondering if saying \"tune to this music\" would make sense? Guitars can be tuned to particular note, can people tune to song, or music, or idea? Google doesn't return many results for \"tune to\" so I guess it sounds strange, but I found a song \"Tune to the Music\" by Status Quo. I am asking this question because I am looking for a name for new web site related to music and songs and tune-to also came to my mind.", "label": 1}
+{"snippet": "I was doing so research on neutron stars and I bumped into this stock exchange page. Does a neutron star burn? Quote from an awnser: The Pauli exclusion principle causes the neutrons to resist further compression. That is, the neutrons, being identical fermions, can't all be put in the same state. So to get them closer and closer together you have to go into higher and higher energy states. This confused me, how can a neutron be in an energy state. Does this relate to nuclear strong force in any way?", "label": 1}
+{"snippet": "Person A uses the phrase \"eager beaver\" to mean an enthusiastic person. Person B chuckles. Basically my question boils down to who the weirdo is, so to speak: A, because \"eager beaver\" is outdated and the sexual connotations are too strong to hope that one should understand the \"normal\" meaning B, because \"eager beaver\" is a perfectly benign phrase with no sexual meanings whatsoever. Anyone who sees sexual connotations in this phrase is simply being immature.", "label": 1}
+{"snippet": "Can someone please comment/elaborate on the statement: \"The normal distribution is a common model of randomness.\" I would like to understand it more deeply. Source: Perhaps someone can point me to a theorem or proof supporting this statement. So my question for this thread really comes down to: If a process can be modeled well by a normal distribution, is this a necessary and sufficient condition for the process to be called \"random\"?", "label": 1}
+{"snippet": "I took screenshots of both the question and answers provided, however there are a couple of steps I did not understand and i put red arrows over equal signs i didn't get. (normally there's an asterisk above the equals sign and an explanation, but none for this question). I'm asking if someone can explain both where the formulae come from and also what's going on in the transformations.", "label": 1}
+{"snippet": "Please, I am not a mathematician so highly mathematical textbook language will not make sense, that is why I am forced to post this question here. I am reading about Checksum and CRC data integrity techniques and I have come across the terms \"primtive polynomial\" and \"prime polynomial\". I will really appreciate if someone could give example of these and explain what makes them primitive and prime. e.g about polynomials used in Cyclic Redundancy Check that are implemented using hardware feedback registers it says \"The best ones are not necessarily prime (irreducible) nor primitive\"", "label": 1}
+{"snippet": "The following is a comment made by a poster in response to this article: Absolutely correct. Intentionally obscuring who you are and what your desires are may lead to heartache and in rare occurrences broken lives. I personally, unlike this articles author never ever want to come close to breaking another individuals life. What does it mean when your life is broken, or to break someone's life?", "label": 1}
+{"snippet": "Which of these forms is better: list of tasks or tasks' list? Another question is whether I should use an apostrophe or not (tasks's list vs tasks list). Other phrases which are similar to this, but aren't quite what I'm looking for, are list of projects and task's action (one task this time). Maybe the answer is obvious, but English is not my native language so I need to understand it.", "label": 1}
+{"snippet": "What is the difference between a battery and a charged capacitor? I can see lot of similarities between capacitor and battery. In both these charges are separated and When not connected in a circuit both can have same Potential difference V. The only difference is that battery runs for longer time but a capacitor discharges almost instantaneously. Why this difference? What is the exact cause for the difference in the discharge times?", "label": 1}
+{"snippet": "\"It don't make any difference,\" he said. \"I'm washed up anyway. Some nose puts the bulls on me tomorrow, next week, what the hell? I just didn't like your map, pal. A nose means a person, I guess, but is there a idiom like 'put the bulls on somebody'? Or if has something to do with 'put balls on', it doesn't make much sense in this sentence. I understand this sentence as 'somebody would kill me.... but I don't care.\" (from 'Red Wind' by Raymond Chandler)", "label": 1}
+{"snippet": "I can't find the difference between these two words. I want to describe the property of something that is repeating at a fixed period (don't ask me to use periodicity, that would be for another question). For instance, in the sentence: I can see that there is ... in candy sales. People are buying on average more at the beginning of the month than at the end of the it. Which of the two terms \"cyclicity\" and \"cyclicality\" would best fit, and for what reason?", "label": 1}
+{"snippet": "I would like to know whether there is a grammatical or semantical difference between \"notion of \" and \"-notion\". I do not know what to search for to answer this question so maybe someone can help me here :-) For instance \"development of a notion of IT-Infrastructure\" vs. \"development of an IT-Infrastructure-notion\". The first one is very long and doggerel, but the second one is maybe wrong/not good style. In other words: I need a section title where I develop (extract literature, derive facts, ...) a notion or understanding of the term IT Infrastructure. What would be a correct one?", "label": 1}
+{"snippet": "I usually tend to see the behavior in which someone takes an action, and people criticize, and even suggest what they should have done, yet when they take that same suggestion people still criticize. For instance: I'm slim; when I eat with my family, everyone exclaims at the amount of food I'm eating. When I eat normally, they ask \"Don't you know, you should eat more so you can grow better?\" When I don't eat, the same shouting takes place. So in other words, is there a word I could use to describe them or their behavior in this regard?", "label": 1}
+{"snippet": "I am using a template from, \"The Legrand Orange Book\" (name of tex file is main.tex) and the author has a very nice template that looks like: However, after using \"Make Index\" from WinEdt, my index comes out all plain and no color like that above. He mentioned in his template to run: makeindex main.idx -s StyleInd.ist from the command line. How can I implement this index template in my document. In the folder that he has available, he already has the .idx and ind file. But whenever I run WinEdt's \"Make Index\", it gets over written to look like: How can I make the index in WinEdt to look like the first image above?", "label": 1}
+{"snippet": "I can relate to what it says, I feel, but I don't quite understand it - does that make sense? Probably not. My first language is not English, so the confusion is great! How would you interpret this in plain English: As long as I retain my feeling and my passion for Nature, I can partly soften or subdue my other passions and resist or endure those of others.", "label": 1}
+{"snippet": "What is a Christoffel symbol? I often see that Christoffel symbols describe gravitational field and at other times that they describe gravitational accelerations. Then, on some blogs and forums, people say this is wrong because Christoffel symbol is NOT a tensor and thus has no physical meaning. Which of these statements is the right one? What is the significance of a Christoffel symbol in differential geometry and General Relaivity?", "label": 1}
+{"snippet": "What is the correct term for a person who twists facts and provides misinterpretations in an effort to appear infallible? The kind of person who is given a simple logic puzzle, fails to solve it correctly and tries to persuade others that he was in fact correct e.g. by denying obvious implications that were necessary to be deduced in order to find the correct solution.", "label": 1}
+{"snippet": "As the title says, I'm looking for a word to describe some clip-on module which provides a new ability that improves the base concept/entity. Some context, such a word could describe: A warp drive module on a space ship A standalone plugin which provides a completely new feature set If possible, the word might imply a necessity, that without such an add-on the entity is lacking and incomplete.", "label": 1}
+{"snippet": "I am writing some software documentation. There are data structures that are organized in trees and every element in the structure can be child or parent \"to\"/\"of\" every other element. I am not a native speaker and my instincts are pretty divided on the matter themselves, so I guess I have to turn to higher powers to answer that question. Hence, I turn to you: Is it \"to\" or \"of\" in that case?", "label": 1}
+{"snippet": "I only have a very basic understanding of general relativity, so this might sound stupid. But as I see that gravitational objects orbiting each other, even if one of them is massive, as long as their paths don't lead to collision, they curve back, like a sling shot. So since singularity is supposed to have zero radius, it seems nothing should actually collide with it. And even if it's non-zero, only near zero, there could still be a possibility that a particle falling (depending on its initial orbit) could eventually just get a sling shot around it, never colliding with it or falling into it. Does that make sense? Or do all paths really lead directly at the exact the center of the singularity?", "label": 1}
+{"snippet": "I have started my Differential equation course recently. And My professor was interchangeably using the term boundary condition and initial condition. I'm wondering what are the differences of their meaning in this context when dealing with the partial differential equations. I thought one would not need a boundary condition if a system extends to infinity, but the case of wave on a string would need, since it's a finite system For the initial condition, it always mean the initial state of the system. Can anyone tell me if my understandings are correct. Thank you!", "label": 1}
+{"snippet": "I have done the following experiment: A DC generator is worked by an object falling and connected to the DC generator via string. The DC generator is coupled to a LED in reverse direction. The observation was the following: As long as the object falls, the LED is off. When the objects hits the floor, the LED very shortly lights up. Why is that? It seems to be a Reverse-recovery effect but in the opposite direction.", "label": 1}
+{"snippet": "Wikipedia states \"a vacuous truth is a statement that asserts that all members of the empty set have a certain property\". Clearly the statement: 'all elements of said (empty) set possess said property' is vacuously true. However, one could argue that the negation of the statement: 'no elements in said set posses said property' is also true. Shouldn't that mean that the statement is both true and false. I understand there may be slightly different definitions of what constitutes a vacuous statement, but I suppose this particular issue will show up nevertheless.", "label": 1}
+{"snippet": "Say I have a data point with included errors and I want to build some continuous distribution around it. Normally this might be a Gaussian because one knows the sigma and mean right off the bat. However, if you have asymmetric errors it becomes a lot harder. It seems like you should be able to model a Gaussian about a data point with such errors using a skewed normal distribution, let me know if I am wrong. Essentially, I would like to know if there is a way to generate a standard normal distribution if you know the mean, max, and min? The mean being the data point, max being the data point plus the upper bound, and min being the data point minus the lower bound.", "label": 1}
+{"snippet": "Mostly I read that the x-rays are produced from the matter surrounding the black hole which spirals into the black hole due to its gravity and is consequently heated up. If the black hole has a main sequence star or a giant star as a binary partner, the BH pulls matter from the partner, which then forms an accretion disk around the black hole. But sometimes I read that Hawking radiation is also producing X-rays or even gammarays. So is this possible or very rare and only occuring within very old BH? Or is Hawking radiation only about virtual particles wich often annihilates each other or one going into the BH and the other becoming real?", "label": 1}
+{"snippet": "As we know electrons are charged particles, hence they have a field surrounding them, which has some energy. Now in electron diffraction the electrons have their influence on other electrons and themselves also get affected. So my question is that why this influence of an electromagnetic wave (because of electronic charge) not considered to explain this phenomenon, as that interaction of EM wave may lead to that pattern.", "label": 1}
+{"snippet": "Is it possible to solve an equation with different operations in it correctly without using orders of operation? I was having a discussion with my friend who believes you can solve an equation from left to right no matter what the operations are. I told my friend that the answer you get would not be correct, but they still insist they are right. Who is right and why?", "label": 1}
+{"snippet": "I need to know the typical energy balance of an IC engine and where this energy goes, but I am unsure what exactly they are asking? Engines are not my main strengths, so I could do with as much as help as possible and as simple as it can be please? I tried researching this but everything I read was very complex and I didnt really grasp it. Could anyone please help me?", "label": 1}
+{"snippet": "I've always been confused by the terms washroom, restroom, bathroom, lavatory, toilet and toilet room. My impression is that Canadians would rather say washroom while Americans would probably say bathroom or Saint John's in the same situation. I guess the difference here is not only in different kinds of English, but also in whether one is referring to a room in their house or in some public place. Which do you usually use? Please specify the difference if you use more than two from those six with different meanings, and also where you are from (i.e. what type of English you speak).", "label": 1}
+{"snippet": "I understand that, given some function space, distributions lie in the dual space. In that sense, they can be thought of as functions of a \"function of a real variable\" variable. But the common representation of the delta distribution as an infinitely large \"spike\" of a certain infinite magnitude suggests that perhaps they can also be thought of as functions of a real variable, where the codomain is some expanded set of which the reals are a subset. Is this possible, or is delta a special case?", "label": 1}
+{"snippet": "Let's take a bottle (no cap) with half its volume filled with water. If we rotate the bottle at some slower average velocity, water does not drop out of it. The same principle works on Roller Coasters. Wikipedia says that the phenomenon of Vertical Loop is used here. What is the physics behind this? (I mean, Which opposes or equilibrates gravity during the vertical loop?)", "label": 1}
+{"snippet": "Are there any necessary and sufficient conditions on types of generating functions which guarantee the existence/nonexistence of a closed form for the sequence they enumerate? Generating functions based on linear recurrence relations clearly always do (by annihilators), but are there more general statements to be made about other types of OGFs? What about DGFs and others? Does limiting the generating functions we consider to be ones obtained from different varieties of recurrence relations allow more concrete answers to be produced? Also, if there are books, journals, or specific papers on the topic, please link them! This is fascinating stuff.", "label": 1}
+{"snippet": "I'm studying modern physics and have some questions about these three different scattering. In the book and wiki all tells me Raman and Rayleigh scattering are inelastic and elastic collision separately, but what about Compton scattering? Does Compton scattering include this two type of scattering since the picture in the book give me two angle of scattering with one differ from the original angle while one remains unchanged? Or it can't be categorized in any of above since it interact with an \"electron\"? Hope to know the details, by the way I'm studying modern physics by Serway", "label": 1}
+{"snippet": "Is there a word that describes someone having a false sense of knowing? In other words, one believes he knows X, but X isn't true. Here is an example sentence: However, consent forms give people only a false sense of knowing. The sentence means that people are not given full knowledge or information but they think they are. This is close to being misinformed but not quite.", "label": 1}
+{"snippet": "I'm using tex-live on a Ubuntu machine. I got a customized graphics.cfg file (configuration file for the graphix package) that I'd like to use as default on my system. I've tried to locate the graphics.cfg used on my system: locate graphics.cfg but I got many results: /etc/texmf/tex/latex/config/graphics.cfg /usr/share/doc/texlive-doc/latex/latex-graphics-companion/inputs/graphics.cfg /usr/share/doc/texlive-doc-en/latex/latex-graphics-companion/inputs/graphics.cfg /usr/share/texlive-base/graphics.cfg Which file should I substitute with the desired one? Thanks for the help P.s. I know that I might modify the one in my local tree, but I'm writing a tutorial and would like to write a section explaining how to modify it system-wide and user-wide.", "label": 1}
+{"snippet": "I'm a guy and I change my appearance to look like my female counterpart just so that I can physically see someone that could understand and relate with me even from just the mirror. I would wear feminine clothes if I could, but I wouldn't want to wear them always, neither am I gay. I'd probably wear them, look at the mirror then take 'em off afterwards. What am I called?", "label": 1}
+{"snippet": "It means \"to write literary works, knowing that they will not pass censorship and be published\". I am looking for some English equivalents that can be used to describe not only writing but also doing different things like taking photos for example for oneself and refusing to publish them. Thank you very much in advance Let's just find an equivalent for \"doing things for yourself and not caring whether it will be published or not\". A good example is Kafka most of whose books were published after his death", "label": 1}
+{"snippet": "I know there are other questions i.e. Do quantum computers manufactured by D-Wave Systems, Inc. work? , What can the D-Wave quantum computer do? , etc. But I can't seem to find my answer. What is getting in the way of determining if D-Wave is a quantum computer? Why can't we just analyze the way they built, and see if it's quantum? Is there a problem with patents getting in the way? Why can we still not tell?", "label": 1}
+{"snippet": "I'm wondering if there are more-commonly-than-not held connotations for terms regarding occupation that would differentiate between one's own personal experience in a field versus the description of the field as a whole. E.g. I am an engineer at company A, this is my job, but engineer is my profession. The example is arbitrary. To me I associate job, occupation, and career with a more personalized representation of employment while profession or vocation are less so. NB: I am trying to model certain relationships in code and want to choose the best names for some objects in the hierarchy so that it is at least somewhat evident by their names what the relationships are. I understand that there may not be any one \"right\" answer to this question.", "label": 1}
+{"snippet": "Consider a model of the empty unsorted signature. Equivalently, a model of the signature having a single sort, and no function or relation symbols. Intuitively, such a model should be called a \"set.\" However, the emphasis is all wrong. For example, in ZFC everything is a set, but I don't feel comfortable saying that everything in ZFC is a model of the empty signature. Firstly, because its just false. Secondly, because we should only talk about models up to isomorphism, however your average ZFC set is interesting beyond its cardinality; that is, beyond its structure up to isomorphism. We care about more than just the cardinality of your average ZFC set. Is there a good word to mean \"a model of the empty signature\"?", "label": 1}
+{"snippet": "The depletion region reduces as the forward bias is increased. Does at any point it reach zero or negligible length? Knee voltage of a diode is defined as the minimum amount of forward bias required for the diode to show significant conduction. It denotes the potential barrier created across the depletion region via accumulation of charges, i.e. negative charges on P side, and positive on N side", "label": 1}
+{"snippet": "Needles to say I am a visitor here. I do not belong to the science world;) But I have read both of these things before: Apple falls to the ground because curved spacetime pushes it there (same force as keeps moon in orbit) Apple 'falls' to ground because the ground is rushing up to meet the apple (which is actually suspended in space) because of Earth's acceleration through space. I don't think these can both be true. I'd appreciate any clarification - thank you.", "label": 1}
+{"snippet": "Can you use packages on math.stackexchange? The help associated with the editor does not mention packages, so I am guessing it's not possible. But if it is, how? I am particularly interested in the centernot package at the moment. If there is documentation or a prior question for this, please direct me to it -- I have searched for this answer with no luck. There are responses on package use on tex.stackexchange, but they do not work as-is on stackexchange. Finally, is this a good place to ask questions about TeX usage in stackexchange? When I tried such a question on meta.math.stackexchange, I got scolded and sent here. Well, it was a generic TeX question, and this one is specific to stackexchange. Thanks.", "label": 1}
+{"snippet": "land |land| noun the part of the earth's surface that is not covered by water, as opposed to the sea or the air. Many writers in countless books and various writings use the terms \"dry land\" to describe earth's surface that is not covered by water. \"They walked on dry land.\" Why, when simply, \"land\" will suffice according to its definition? Do we call the earth under our oceans, or any body of water, land? If so then I would agree that using \"dry land\" is not redundant, but by definition it is.", "label": 1}
+{"snippet": "Here are three ways to say the same thing. I wonder if there are particular rules regarding to the position of adverb phrases: Then play those passages over and over again in your memory Or, Then play those passages in your memory over and over again Or, Then play over and over again those passages in your memory I think the last is the worst choice but the first twos seem ok. The first is better because \"over and over again\" is closer to \"play\" so it is emphasized. Agreed?", "label": 1}
+{"snippet": "How can we get the mass of an uncharged proton, i.e. how varies the mass of the charged proton if i remove the electric charge? For the isotopic spin theory neutron and proton have the same mass and it is possible to distinguish that particles only for the different values of the third component of the isotopic spin. This is an approximated symmetry because the masses are different and the charges too. In a ideal world we can remove the electric charge from the proton and we get a \"uncharged\" proton. The question is how the mass changes. You can interpret that question as what it is the contribution to the mass due the charge, not only for proton but for all particles.", "label": 1}
+{"snippet": "In the good ol' days I drew figures with xfig and generated LaTeX source to directly include in my papers. But I now find powerpoint to be a faster drawing tool and sufficient for most of my needs. What's the best way to embed the resulting image in LaTex? I current output to pdf, then include using the graphicx package. But the resulting scaling and positioning trial-and-error session is often extremely frustrating, and the documentation on the package is quite sparse and unhelpful. Is there a better way?", "label": 1}
+{"snippet": "I need to store data. I'd like to store them in Metric units and use a tool to convert them to and from other units that these data points will be displayed in. As the title states, my constraints are Distance, Pressure, and Temperature. Distance I know, but it is added here as an example: I store the data in meters and convert to feet where needed. What are the metrics unit for storing Pressure and Temperature? Further, I am assuming here that metric units would be the most universal. If there is a more universal unit for Distance, Pressure or Temperature, please let me know.", "label": 1}
+{"snippet": "In Texmaker, in the caption environment, why does spell check not work if the figure has a label? This is an example I made to show this 'feature': From the first line, we see that the spell-checker is working as normal. This also follows in the figure environment, but not in the caption environment. I tried playing around with it to see what exactly caused it... turns out it's the presence of a label. We see from the second caption that the spell-check is performed correctly.", "label": 1}
+{"snippet": "Can someone help? \"Dave killed Peter.\" Dave asked Susan, \"why was Peter here?\" Susan said, \"Maybe he would have told you if you hadn't have killed him.\" Would there have been any difference if she had said \"Maybe he would have told you if you hadn't killed him\"? According to my understanding, Susan wants to emphasise the fact that Peter would have told Dave why he was here if Dave hadn't killed him first. Right? Meaning, Susan thinks Dave would still kill him anyway, before or after Peter told Dave why he was here.", "label": 1}
+{"snippet": "If I have a rod of some material and submerge one end in hot water then leave the other side exposed to room temperature air. How would I go about calculating the temperature of the end of the rod that is exposed to the open air? It's alright if it requires two or three equations and some problem solving to figure out I'd just like some mathematical way to solve this if there is one", "label": 1}
+{"snippet": "I'm working on a digraph problem in which bidirectional edges need to be treated separately. As such, we could consider them as undirected edges. Clearly, if I replace bidirectional edges with undirected edges I get a ``mixed graph'' (one with directed and undirected edges). But can a mixed graph have bidirectional edges in addition to undirected edges? Can a mixed graph have a directed edge and an undirected edge between two vertices? The Wikipedia definition is not crystal clear on this. A paper, Enumeration of Mixed Graphs indicates bidirectional and parallel mixed edges are disallowed. The definition in this article claims that the ``complete mixed graph'' has a undirected and bidirectional edge between both vertices. What are ``mixed graphs'' typically defined as?", "label": 1}
+{"snippet": "I wonder if there is some advantage in using individuals when defining set theory and if this has something to do with the use of classes. This is essentially because I have seen that some books start by defining the empty set whereas others consider it to be a primitive symbol. In the first case there are only sets in the domain of discourse, but in the second there are also what they call individuals. What is the purpose of using individuals compared to the other alternative? Also, the way I understand individuals is that they are entities at the begining of the hierarchy, at the same level of the empty set, but maybe I'm misundersanting this. Could you guys please help me claryfy this...", "label": 1}
+{"snippet": "On a recent trip the US, someone explained to me that saying \"sorry\" meant taking responsibility for causing the loss. Thus you should only say sorry if you intended to fix the situation. (And potentially even had implications for insurance and litigation). I'm an Australian - generally when people say \"I'm sorry\" it means \"I can display empathy for your loss and can put myself in your shoes\". [implicitly also that no responsibility is taken - nor any effort being made to restore the situation] My question is: Do English speaking subcultures attach different meanings to the phrase \"I'm sorry\"? (This is different to the other questions relating to the meaning of 'sorry' because it considers the legal and restorative implications as well as the geographic context).", "label": 1}
+{"snippet": "the classic rhombic dodecahedron (RD) can be used to fill space as shown here I know I cannot recreate a bigger RD by stacking RD together because you never have two touching faces on the sames plane. I am wondering if joining the center of stacked RD you would end up with a bigger RD ? I've tried making origami model and it looks like it is not the case.", "label": 1}
+{"snippet": "Besides sports in which an attacker is an offensive player, is there any difference between assailant and attacker? a person who attacks somebody I guess attacker can also be used for animals but not assailant. Is there anything else or are they fully interchangeable when describing a person who physically attacks somebody else? Can both words also be used when talking about psychological attacks, like insulting, bullying, etc?", "label": 1}
+{"snippet": "I've found it in a book and assume it's got to be correct, but I cannot understand why the Past Perfect of I had been offered. Would was offered not have been clearer? I explained that when I was in high school I had been offered a job teaching tennis at a local country club because I had been one of the best junior tennis players in the area", "label": 1}
+{"snippet": "One of the most useful black hole analogies I've seen imagines that space is \"flowing\" like a river into a black hole, and the point at which it flows in faster than c is the horizon. This analogy leads to the idea that a tachyon could escape from the \"c\"-based horizon and perhaps penetrate a bit further. Given that the tachyon has finite speed there would presumably be a horizon closer to the singularity that applies to the tachyon. However, could a tachyon device send us information about what's going on beyond the c-horizon? Let's assume tachyons exist and we have a device that can generate an interpretable message transmitted w tachyons (the Apple iTach, if you will).", "label": 1}
+{"snippet": "What would be another way of saying \"It'll do more harm than good\" but in the context of \"it'll do nothing for you?\" Here's some context. The common mistake, however, is believing that only lifting weights multiple times a day will get us to where we want to be. This is wrong, and unfortunately, it may even do nothing for you. I'd like to rephrase this to match and compare like \"Nothing more than something\" but that sounds really stupid.", "label": 1}
+{"snippet": "In Malayalam/Indian, there's a saying \"Thala Irikkumbol, Valu-attaruthu!\", which literally translates to: When the head is present, tail should not wag. It means that one should not act out of turn in the presence of one's superiors. Consider: Mafia bosses A and B discussing stuff; a low-ranking member M chimes in interrupting them; A puts a bullet between M's eyes saying something-cool-here. I'm not limiting answers to mafia style, though that would be cool. What are other English idioms equivalent to this?", "label": 1}
+{"snippet": "When referring to the time of a particular event, should I refer to the local time or the time zone most relevant to the audience or always include reference to the time zone? It can be further complicated when having to specify Standard or Daylight Saving times. It seems that you would have to reference all times as Greenwich Mean Time (GMT) to avoid having to list multiple times.", "label": 1}
+{"snippet": "I am developing a Trading Card Game and I am in need to extract functionality from two of my classes as they are both doing almost the same. it is about the Deck and Graveyard constructs which are visible on the field. The Deck is where the cards are which you can still draw, the Graveyard is where your used cards are. What word could I use to describe both a Deck and a Graveyard, Stack is already taken unfortunately (by the Java language) and I'd personally describe it as a Pile, but not sure if that is the best wording.", "label": 1}
+{"snippet": "Possible Duplicate: Why does the sound pitch increase on every consecutive tick at the bottom of a filled cup of coffee? A colleague suggested this experiment this morning : Get a cup of coffee Spin the coffee in the cup using a spoon Tap the bottom of the cup with the spoon Observations : As the coffee slows down, the sound produced by the tapping gets higher in frequency. I'm very curious about this, does anyone have an explanation ?", "label": 1}
+{"snippet": "I'm translating a course manual but I'm struggling with something. The manual could be read by a man or a woman. In my own language, he or she or it doesn't exist, so I'm not sure how to make my texts easier to read. The student can meet his/her Inner Guide who opens his/her heart chakra. The teacher guides his/her student so he/she can advance more in his/her life. I'm going to open his/her chakra and so he/she can express his/her emotions easier.", "label": 1}
+{"snippet": "I have learn some basic knowledge of Heat in my class, and I got confused when dealing with the change of state. Basically, what the textbook say is that the molecular kinetic energy keeps constant during the change of state and the molecular potential energy increases. However, my problem is, how do the particles manage to change their molecular potential energy without moving faster? How does the energy supplied to that object actually helps it increasing or decreasing it's molecular potential energy? What I want is some sort of \"model - like\" stuff so I can understand what is going on in micro-view.", "label": 1}
+{"snippet": "I know that in evaporation process highly energetic molecule get latent heat and it changes the phase and rest of water is cooled,but I think water at high temperature is at up and low temperature at the bottom because of high density of water,but how is energy transfered from water at low temperature to high temperature to gain latent heat,how is it possible ?I am so confused?", "label": 1}
+{"snippet": "It sounds like your proposal would make a great feature request for the existing module. I'm unclear why you consider it was not a good idea. Does replacing I'm unclear with it is unclear to me make the sentence more clear? Are there any contexts where I'm unclear would have a different meaning? Is it used in some regions/dialects to mean something different from it is unclear to me?", "label": 1}
+{"snippet": "I just watched the dubbed version of Code Geass anime series, and there's a sentence puzzling me. The actions one takes are answered by consequences waiting at the conclusion. I was wondering whether the usage of the sentence is formal or not. Can action use answer as a verb? I found nothing on the internet about \"the actions are answered by...\" What does \"consequences waiting at the conclusion\" mean? Can wait use at as a prep? I'm a non-native speaker of English.", "label": 1}
+{"snippet": "I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant. Does dimensional regularization see \"all\" kinds of divergences? I mean - what does it exactly mean when one says that power law divergences and IR divergences disappear in the dimensional regularization. So is more regularization needed in general over and above dimensional regularization? Does anything about the divergences get specially constrained if the theory is scale invariant? I have often heard it being said that dimensional regularization \"preserves\" scale invariance.", "label": 1}
+{"snippet": "It is well known that the family of conics is derived by slicing an infinite double-napped right circular cone, with the specific type of conic depending on the angle of slice. Separately it is also know that these conics may be defined by its focus (or focis, as the case may be) and directrix, from which standard equations are derived. What is not obvious is how these two concept definining the family of conics are to each other. Question: Show that the cone-slicing defintion of conic sections is equivalent to the focus-directrix definition. Indicate where the focus and directrix are located in relation to the double-napped cone. Diagrams would be helpful.", "label": 1}
+{"snippet": "I am working on a sonnet. This pretty much mandates the use of iambic pentameter and therefore requires that I have a good grip on emphasis. However, I'm not exactly sure how to properly research words for emphasis. I was attempting to comprehend Merriam-Webster's Pronunciation Guide, but that just further confused me. Merriam-Webster has a system for indicating the stressing of syllables; almost every page has a set of symbols delimited by backslashes, describing the word's emphasis. I was wondering if anyone experienced in the emphasis and or word pronunciation could help me understand this notation with an example or two.", "label": 1}
+{"snippet": "I remember when staying a few months in the US years ago that I saw some people using the abbreviations below. However, I can't exactly remember in which contexts I encountered them, (whether I saw my teachers using them when writing something on the board, in papers or in personal notes etc.) So my question is: Are those abbreviations below commonly used and in which contexts is it okay to use them (e.g. formal texts, personal notes,... or better only used in personal note taking?) w/o without w/ with b/c because PS: Are there similar abbreviations that are commonly used?", "label": 1}
+{"snippet": "This construction and its variants always sound strange to me. If I was asked to write a sentence with the same meaning, my choice would be: I don't want a robot running the empire. Logically, don't want (...) no robot conveys rather the contrary for me: want a robot. Can someone please clarify the choice? I had just read it in Asimov's Forward the Foundation. Thank you.", "label": 1}
+{"snippet": "When one pours water out of a bottle, it first flows smoothly but then a pressure 'blockage' develops and the pouring becomes interrupted and turbulent, so that the water comes out in splashes. This seems to slow down the flow of water from the bottle. What is the optimal way to pour the water so that it completely empties fastest? Possible strategies: Holding the bottle at a certain angle Wildly shaking the bottle Squeezing the bottle Other... It probably depends on the shape of the opening and/or the bottle itself, but we shall assume this beautiful example of a standard water bottle: CLARIFICATION The question is asking how to pour the water the fastest, so no straws, hole insertion and evaporating lasers allowed...", "label": 1}
+{"snippet": "I don't know exactly how to ask this in a comprehensible way. I am trying to find a solution to my problem which is to find how many sphere of radius r are lying on the boundary (which means that in some way this little sphere intersect the boundary of the big sphere) of a sphere of radius R (with r smaller than R). For example, one simple law could be dividing the surface area of the sphere with radius R with the area of a circle of radius r.", "label": 1}
+{"snippet": "I have an example image here from Modern Physics textbook. I also like the chapter styles (I am thinking I could do them with the memoir document class, but that is for later). Right now, I am trying to figure out how to make the section numbers and titles show up in the margin of the chapter title pages. Also, does anyone think this could work in the book documentclass instead of memoir?", "label": 1}
+{"snippet": "So I am trying to find the relationship between fractals and newton's method, and I am trying to use software to generate the fractals pattern. which software can I use to do that and how? Also i am trying to compare two different types of Newton;s method - the normal one and a new type of newton's method called relax newton's method. The new type maintains a quadratics convergence in most situations, but how can I generate fractals for this new Newton;s method?", "label": 1}
+{"snippet": "I am victim of the known biblatex-biber bug described here which leads to mass spurious missing citations, resolved only by deletion of the biber cache (dozens of files). Previously it was occasional but now it is driving me up the wall - I have to delete the cache on every single compile across multiple projects. Anyone know the status of this bug and the purpose of the cache before I resort to abandoning biber completely.", "label": 1}
+{"snippet": "How could I estimate the force I apply when I squeeze a new toothpaste tube? I want to either be able to calculate it without having to perform an experiment, or refer to some scientific journal with a similar calculation or rough estimate. I was thinking that I could use Hooke's law and calculate the force exerted when a similar force to that of gently squeezing the tube is exerted on a spring with a spring constant similar to the resistivity of the toothpaste tube...I could make numbers up (as the value of the force I am looking for can very much be an estimate), but I have no clue what an estimate k value and x value would be to calculate the force using Hooke's law.", "label": 1}
+{"snippet": "I noted the question above had been posted. And I wanted to comment, but nay, it was locked out. However, what of the old 'CRT' tubes, in which magnetic fields are used to steer the electron stream ? Now I know the 'Electron's' do not get attracted, or repulsed directly to the source of the magnetism, but the magnetic field certainly has an effect. So if one were to extend the CRT tube to ... well, rather long, would the electron eventually move to, or away from the 'North' or 'South' pole ?", "label": 1}
+{"snippet": "(a) The rise of price of goods burdens the people. (b) The rising of price of goods burdens the people. (c) The ban of plastic bags is a good way to reduce environmental problems. (d) The banning of plastic bags is a good way to reduce environmental problems. Which form should I use for the words 'rise' and 'ban' before the preposition? Gerund or noun?", "label": 1}
+{"snippet": "I have seen it on the Internet as follows (abbreviated as IMAO): Only the Muggles will find it offensive IMAO. I know it's contrasted with the common phrase \"in my humble opinion,\" but I still don't know what impression it tries to convey, nor what is the appropriate situation for it to be used. Is it a somewhat unfriendly phrase? How do I use it right?", "label": 1}
+{"snippet": "Can anyone suggest a book on rings explaining concepts using visual diagrams, similar to the one visual group theory book by Nathan Carter for groups.The problem with me is that after reading that book I am visualizing everything in terms of Cayley's diagram,cycle graphs etc. and now I'm feeling if I'll use a standard book i'll be missing some great things. I'll be grateful for any help.", "label": 1}
+{"snippet": "It is my understanding that clouds are largely made up of water, which is known to split white light into its frequency components, and that's why we see rainbows sometimes. My question is, with sunlight being practically constant throughout the day, why aren't there rainbows all over, all the time? I mean, we can see monochromatic changes in the color of the \"sky\" throughout the day, but rainbows seem to only happen sometimes, why? In short: Rainbows that we can see come from water droplets, not collections of droplets.", "label": 1}
+{"snippet": "A phobia is an irrational fear of something. An intolerance to something is usually an -ism, not a -phobia, as in sexism racism ageism Yet people who object to homosexual practices or discriminate against homosexuals are labelled \"homophobic\" and their intolerance is labelled \"homophobia\". But homophobia should logically be an irrational fear of things that are the same (and indeed is listed with both meanings in this list of phobias) and an intolerance to a particular sexuality should surely be sexualism, sexualityism, or a similar word. So... how did the \"sexualism\" meaning of \"homophobia\" come about? Is there another word for intolerance of / discrimination against people of a particular sexuality that doesn't imply irrationality or fear?", "label": 1}
+{"snippet": "Where can I find the problem talked about in the following paragraph regrading Maxwell's laws of electromagnetism - Every time Maxwell rearranged his equations to make the speed of light the subject and plugged in the numbers he got a very strange result. The speed of light always came out the same, regardless of the speed of the light source. This result seemed absurd! It's common sense that anything cast from a moving body will have a speed that's calculated from both the moving body and the object. as seen on here in the paragraph titled as 'An impossible Result ?", "label": 1}
+{"snippet": "Say I run an experiment measuring some parameter A on a sample group of a population where A is a non-negative real number. Is there some way of knowing if my percentile results are reasonable? Ideally, I'd have confidence intervals around my percentiles to know their ranges in the population as a whole instead of just in the sample group. TL;DR want confidence intervals for percentiles", "label": 1}
+{"snippet": "I am attempting to show communication between states in a Markov process, basically something like this, although the arrow angles aren't of any importance, simply having that relation between the nodes : I have looked into TikZ (which I've never used) and have tried finding some info on the simplest way to create nodes like this, but most sources I've found seem overcomplicated for how simple a task I'm trying to accomplish. Any ideas?", "label": 1}
+{"snippet": "Real photons do have frequencies, which is directly related to its energy. So, can virtual photons that take part in EM interactions have frequencies too? When my hand is pressed up against a glass window, do the virtual photons taking part in the EM interaction keeping my hand from falling through the window have a frequency compared to the photons that passing through the window (visible spectrum) or those reflecting off it (frequencies the glass is opaque to)? Also, since virtual photons may be massive and definitely have four-momentum, they definitely do have some energy - so is there any notion of frequency?", "label": 1}
+{"snippet": "Turns out there's tritium illumination - a tiny very strong plastic tube will be covered in phosphor and filled with tritium. Tritium will undergo beta decay and a flow of electrons will cause the phosphor to glow. This gives enough light for illuminating hours marks on a wristwatch dial and the hands of the wristwatch for many years and is claimed to not pose health hazard. Now how it is possible to have energetic enough radioactive decay and no health hazard at the same time?", "label": 1}
+{"snippet": "I want to buy some text books at graduate level. I have got enough money in my contingency grant, as there is a chance, i thought i should buy some good books not thinking about the cost. The areas that i am interested in are Commutative algebra, Algebraic geometry, Algebraic number theory, Homological algebra, Representation theory, Algebraic topology Any thing a bit advanced is also welcome. I do not want to buy so many books on same subject for the reason that there may be some repetitions in the content and all. Please suggest some thing regarding this.", "label": 1}
+{"snippet": "I'm not really a programmer but I'm quite interested in learning how to use LaTeX/TeX. I've looked it up on Wikipedia and scanned through it and the documents created through this way of editing is just beautiful. Formulas are also available within it too, so writing math thesis or physics papers would be amazing. Is this system just for programmers, or can normal people use it too? (I'm mainly a designer, so I usually edit it in Word or InDesign.)", "label": 1}
+{"snippet": "According to inflation theory, the inflation itself took place at some short yet finite time after Big Bang, so there should be some gravitational interactions present before inflation, some objects started accelerating towards other objects etc. However after inflation many of those objects were scattered outside of their neighbours' light cones and as gravity propagates with the speed of light the interaction between such objects should be interrupted. Yet what about the initial acceleration that these objects gained before the inflation occurred? Shouldn't these objects still be moving in their original pre-inflationary direction? And how would such forces shape the present Universe?", "label": 1}
+{"snippet": "I have some datasets and I need to find spikes in them. Imagine the data looks like trading data. If the spike is big enough, I need to log it, otherwise, proceed in the analysis. I tried with a moving average approach, but cannot detect all of them. Is there a better way? Also, I would like to know if there is a robust approach to calculating the baseline, so I can filter it out.", "label": 1}
+{"snippet": "For someone maybe stupid question but im quite curious and didnt find an answer for this. If elecricity is just a flow of electrons and we can power things by movement of electrons, Why we cannot get electricity/energy from electrons that are orbiting every atoms nucleus. Is it related to uncertainity of the position of the electron or that the electrons of atom are not orbiting in the same direction? Or it is related to the charge of the whole atom and we actually cant separate the energy of electron and nucleus. Is it possible for the electrons of an atom to stop orbiting its nucleus. Thank you for your thoughts :)", "label": 1}
+{"snippet": "A friend has said that there is a word meaning the outcome is something very different from that originally envisaged. For example: The Australian government introduced a \"First time home owner\" bonus. Where if you were buying your first house you would get a lump sum cash. Of course everyone selling a house in that price backet put the price up by the same amount as the lump sum and first time buyers didn't benefit at all. Does anyone know if there is a word meaning this and what it is?", "label": 1}
+{"snippet": "I came across a question in a book. It says: If any of the following sentences show that something happened in the past, make the italicized verb simple past by adding -d or -ed. If you cannot tell whether the past or present is intended, do not change the verb. I realize that you are right. My Mother appear at the door. What should be the answers? I am a bit confused with those two sentences.", "label": 1}
+{"snippet": "Theoretically we can convert a body into black hole by compressing its mass below some radius (known as Schwarzschild Radius). Suppose such object after becoming black hole has a radius which is comparable to atom and nucleus radius. Now my question is: what happens if we run this object into double slit experiment setup (single black hole at a time)? Shall we get interference pattern on the detector wall because its radius is in quantum domain (say we somehow know when on detector screen this black hole will hit) or simple-particle pattern (i.e. classical way) because of the mass associated with that black hole? If you have a really tiny black hole, will it behave as a classical particle, or will it exhibit quantum behavior?", "label": 1}
+{"snippet": "I am learning english, an I am wondering if I would be \"correct\" in using only the past tense and never using the present perfect tense. I might be over-simplifying the english grammar ... So, are there some situations where it would be incorrect using the past tense instead of present pefect ? (the following link gives some axample where past tense shall be used instead of present perfect, but no example where present perfect shall be used instead of past tense: Present perfect for past action with present effect) Many thanks for your replies, Thierry", "label": 1}
+{"snippet": "I have seen usage of both super and superb. I also searched for meaning of these two words and found they are almost identical. Example sentences - She is a super girl. His performance in the last game was superb. Use of any of those two words doesn't change the meaning of those above sentences either. Need suggestion of proper usage of these two words. When to use and why?", "label": 1}
+{"snippet": "In Dutch we use the translated equivalent of not hindered with any knowledge to indicate somebody without any knowledge on the subject. It is not necessarily negative. It can mean that somebody is complete open and new to the subject, which may lead to new ideas, insights etc. But in a different context it may also carry a sarcastic tone indicating somebody with the biggest mouth and slightest knowledge. Is this equivalent comparable and usable or are there better constructs?", "label": 1}
+{"snippet": "I have to prove the following: The line segment xz is an edge of the convex hull CH(A) iff all other points of A lie in one of the closed half-planes induced by the supporting line l(x, z) of xz, i.e., on (x, z) or to one side of the previous. So far the only idea is to start somehow with the basics that a convex combination is a linear combination of points but no idea of the next step", "label": 1}
+{"snippet": "I am trying to compose a sentence, and I am currently stuck for the right word. I am trying to say: In a job interview, the audience would be the employer and the --------- That is the word I am looking for. I cannot put \"employee\" as he has not been employed yet. Is there a single word for someone looking for a job? \"Job-seeker?\"", "label": 1}
+{"snippet": "What are the differences between net, network, mesh and grid? If I have a look at the OED entries, I have a feeling of rather a circular definition: mesh Material made of a network of wire or thread... net A piece of open-meshed material... grid A network of lines that cross each other... Could you list some most common collocations with each of the words and explain why this particular one is used? Such as why do we use mosquito net and not mosquito mesh?", "label": 1}
+{"snippet": "Astroturfing is a word used to describe a fake or counterfeit grassroots campaign. The clever term is derived from the notion that one kind of fake grass is astroturf. Another more niche example is from mathematics. We call the \"germ\" of a function the part at the bottom of a stalk in some sheaf. We call this a germ because it is like the germ for the stalk of a plant. In both of these examples, one makes an analogy to create a term, and then related terms, carry on this analogy to build terms related to the first. Is there a specific name for this sort of term?", "label": 1}
+{"snippet": "There is always a debate around Earth Hour every year, and the opposite side of Earth Hour usually claims that The (sudden) decrease and increase of the power usage in the start and end of Earth Hour will cause much more power loss (than the save of power), and even do damage to the power supply system. Is this statement true? To what extent? Thank you very much.", "label": 1}
+{"snippet": "I'm currently working on some graph theory, and I'm checking the robustness of graphs, by removing random vertices from a graph and then check how many vertices are outside the giant component. Then I'll do that for a lot of vertices, and plot them using ListPlot. This takes along time to calculate, is there a way I can visualise it, that it plots something everytime a value is calculated. thisFunctionTakesVeryLongAndReturnsAList := .... ListPlot[thisFunctionTakesVeryLongAndReturnsAList [graph]] thisFunctionTakesVeryLongAndReturnsAList calculates a value that can be plotted all the time", "label": 1}
+{"snippet": "If two stick two magnets the mass will be less than sum of the individual magnets. They lose certain mass while they stick together. Probably, they release some energy. My question is: when the magnets are separated, whether their original mass is restored to its original level? If that is right then after performing sticking and separating several times of the two magnets, they should vanish.", "label": 1}
+{"snippet": "Possibly two questions in here: Are these sentence constructions logical, and if they are, why are they different? I swam across the Ocmulgee River. I swam across the Pacific Ocean. I swam across the Red Sea. I swam across Lake Winnipeg. I can't think of a way of phrasing the lake example while using an article with a proper noun. I thought at first it was because Lake Winnipeg is different; it's generic portion (the \"Lake\") comes first and the name of that body comes second, but I swam across Falls Lake is the same. Yet the sentence I swam across the lake sounds right to me. ...Why?", "label": 1}
+{"snippet": "There is a similar question that gives a bit of an explanation, but little mathematical proof here: force applied not on the center of mass I would like mathematical proof that shows that the velocity of a rigid body when a force is applied to the center of mass is equal to the velocity of the same rigid body when the same force is applied to a point on the body other than the center of mass. Thanks in advance!", "label": 1}
+{"snippet": "Via Cantor's back-and-forth method we know that the linearly ordered set of all rational numbers and the linearly ordered set of all real algebraic numbers are isomorphic. But from the point of view of what people usually do with rational numbers or with algebraic numbers, the order isomorphisms yielded by Cantor's proof are icky. Are there any that are well behaved and have nice mathematical properties?", "label": 1}
+{"snippet": "Okay, so recently I ended up saying this: Well, that is unfortunate... sometimes it happens, sometimes it doesn't. Okay. You know, just saying \"Sometimes it happens\" already tells you that something happens sometimes and other times it doesn't. But, sometimes, I need to make very clear that this \"something\" doesn't happen always. That's why I say sometimes it happens, sometimes it doesn't But is there a way to shorten this phrase? To make it simpler, but still making very clear the fact that this \"something\" may not happen? Repeating \"sometimes\" is not very much of my liking...", "label": 1}
+{"snippet": "There are many businesses that hosts other related or unrelated business as part of their service. Example a plaza/shopping mall will have various stores, owned and operated by others, a university may host other organisations such as book stores, restaurants, computer stores etc. The University of Technology, Jamaica has an organisation/business called the Technology Innovation Centre (TIC), that is a business incubator. TIC itself hosts various businesses not relating to the University. All these hosted businesses uses the address and name of their host as part of their own address.What name is given to these type of businesses that play hosts to other businesses?", "label": 1}
+{"snippet": "I have a forum where you can Like a reply. After you press that button it changes from Like to Liked. Now I want to add a Dislike button so I would like to replace the \"Liked\" text for something that would also include \"Disliked\". I think the word should be close to something like \"Done\", \"Voted\", or \"Pressed\" but also related with the original text. Do you have any suggestions?", "label": 1}
+{"snippet": "I am working on displaying source code for which I pass a path to a macro. Now I am wondering if it is possible using xstring or stringstrings to match from after the last delimiter, i.e. / to the end of the string to determine the filename. Example: I might pass ../code/subfolder/project/code.java to the macro for which I want to extract the substring code.java. It seems easy to match the first occurrence of a character, but not the last.", "label": 1}
+{"snippet": "I am aware that the universally accepted style is to put an apostrophe-s at the end of the second possessor's name. Example: Amy and Steve's car My question is not whether that is the common rule; I know it is. My question is whether anyone knows of a style guide, grammar, or other authority that condones writing this in the usual style of a plural possessor; that is, with an apostrophe on the end of the compound/plural owner's name: John and Jacks' house John Merrill, Stephen Arthur, Chuck Williams, and Donald Smiths' law firm Thanks!", "label": 1}
+{"snippet": "In photography the negative means the lightest areas of the photographed subject appear darkest and the darkest areas appear lightest. But I was wondering: is this the way how negative should actually be described at all? What if the negative just meant that you reverse the (visible) spectrum. What kind of image would that produce? Would the whites still be whites? (unlike in the \"traditional\" negative where white -> black)", "label": 1}
+{"snippet": "In order to answer a question I have to take a look at a document that is not with me by the time that question was raised. Which of these sentences is more suitable to express that idea? I am not able to answer your question without taking a look at document X; I cannot answer your question before taking a look at document X; Feel free to suggest any other sentence that you may think appropriate.", "label": 1}
+{"snippet": "The dispersion of white light beam while passing through a triangular prism is well known. Considering the reversibility of optical path, it should be possible to reverse the experiment. How can one implement the reverse experiment of lights' dispersion in experiment? What are the necessary and sufficient conditions of the incident light beam(s) in order to obtain a white light beam after passing through a dispersive prism? For example, can one remove some of light beams with specific wavelengths or adjust their intensity but still obtains white light beam?", "label": 1}
+{"snippet": "In my understanding, Alternating Direction Method for Multipliers (ADMM) is widely viewed as a tool to parallelize large-scale convex-optimization problems arising in statistics and other related fields. The following paper by S. Boyd is a good reference https://web.stanford.edu/~boyd/papers/pdf/admm_distr_stats.pdf But one can also use, like Help needed to define a constraint in an optimization problem?, ADMM to solve non-convex problems I am looking for a paper that I can cite when ADMM is used for solving otherwise non-convex problems?", "label": 1}
+{"snippet": "Initialisms are pronounced as words and acronyms are spelt letters. However, some words sound the same, said and spelt. e.g. Input Output can be abbreviated as IO. It can be spelt I-O or pronounced Io as in the moon/god. There is no way to tell the difference in how it is said or written. Is a word which is pronounced the way it is spelt, an initialism, an acronym or both?", "label": 1}
+{"snippet": "The plural of 'passerby' is 'passersby' with an 's' acting like an infix (W-B says that this is the only plural form of the word). This seems like a very interesting exception, so I thought I would ask a question. Are there any other English words that are made plural by an 's' put inside the noun? One criterion has to be met: the singular noun is composed of one (unhyphenated) word only.", "label": 1}
+{"snippet": "A customer want to place his gold to bank account. He shows up in a bank with his gold bars and says that he wants to put it to his gold account. I was unable to choose the correct word here. Customer delivers his precious metal bullion to the bank. Customer leaves his precious metal bullion in the bank. Customer gives up his precious metal bullion to the bank. Customer leaves out his precious metal bullion to the bank. Customer leaves his precious metal bullion to the bank. Customer submits his precious metal bullion to the bank. Customer puts away precious metal bullion to the bank. Customer ... precious metal bullion to the bank. Which word should I choose?", "label": 1}
+{"snippet": "I am confused about some definitions in logic/ axiomatic set theory: We stated in our logic lecture the ZFC axioms and called the members of a ZFC-model \"sets\". But to define formulas and structures, we needed sets as in \"A structure is a non-empty set with functions and relations\" and also for formulas, we needed, e. g. a variable set. Could you help me solving my problem? For me it currently seems circle-reasoning. Best regards", "label": 1}
+{"snippet": "A toy is randomly put in a given Cereal box as a promotional gift. There can be N different types of toys and each one can be of any type N (IID). (a) Find the expected number of cereal box one has to buy before she can have atleast one toy of each type, (b) If she has already collected m toys, what is the expected number of different toys she has collected. Can someone explain how to model this problem using Indicator Random variables.", "label": 1}
+{"snippet": "\"Gas prices are going up.\" Which of the following is also a general statement about gas prices: The price of gasoline is going up. The gas price is going up. And could you tell me why? I have this question because although I know, for example, both \"Tigers are big\" and \"The tiger is big\" are generic constructions, but I am not sure how to use \"the\" when it is a noun phrase instead of a single noun.", "label": 1}
+{"snippet": "This is going to sound stupid but anyways. I am currently in a physics class and my teacher likes us to use dimensional analysis which I do not understand how to use or what to do with it! So firstly can someone explain that? And secondly, I can do all of the work (my way) and show all the work and my units, he just doesn't know \"how I did it\" but I still get the right answer and have all the work stated and he docks points for this, is that at all fair? Any opinions from other teachers would be greatly valued here.", "label": 1}
+{"snippet": "I'm using in hopes that in the following sentence. However, it does not seems to be formal and appropriate for a scientific paper. Is there any similar phrase that has the same meaning but more formal ? Thanks. To overcome this crucial issue, a popular solution has been used where a task is assigned to many workers and the results for this task are aggregated in hopes that the aggregated result is actually the correct one.", "label": 1}
+{"snippet": "I have a PDF document, evidently produced using LaTeX, which has wide white margins and crop marks. I'd like to remove these margins and corresponding crop marks. Is there a tool to do it automatically? EDIT Werner suggested to use pdfpages package to include PDF's pages in a LaTeX document. I should actually include only the pages of the PDF I'd like to crop and use options to trim it. I'm waiting for an help in recognizing the most appropriate options to do so.", "label": 1}
+{"snippet": "Is there a word that describes the case of using an adjective to describe a noun that already suggests as much? Examples the pretty model won all of the awards the smart genius answered every question the dangerous monster ate the man the fast jet the floating buoy Some of these examples might not be the best, but I hope they give the right idea. I know they are superfluous, but I'm not trying to define the adjectives themselves, but the act of using them.", "label": 1}
+{"snippet": "With How do I change color settings in TeXStudio? and How can I set a dark theme in TeXstudio? I managed to change the colour of the editor (in this case to a darker theme to prevent eye strain). Now I would like to change the colour of The toolbars The Structure and Message / Log File menus The line numbers at the left of the editor The Line, Visual column, Text column counter below the editor I already tried the advanced options from Options -> Configure TeXstudio.", "label": 1}
+{"snippet": "I have observed while driving at night the yellow marks on road seem white. What I understand is the color of an object is the visible light wavelengths it does not absorb. In other words the yellow line does not absorb yellow light. The head light of my car is normal and thus is slight yellow light. So from my understanding the color of the line should not really change and still be yellow. Can somebody confirm the same observation (or is something wrong with my eyes) and tell me the reason.", "label": 1}
+{"snippet": "On points arranged in a parallelogram lattice, like on the image in this Wikipedia article, how to calculate the maximal distance any point on the plane may have to its closest point from the lattice. Or alternately, the maximal radius of a disk that can be placed on the plane such that it does not contain any point of the lattice. As input I have the side length and both diagonals of one possible parallelogram that fits the lattice. Edit: I meant the lattice not grid, i.e. only the sparse set of intersection points of a parallelogram grid.", "label": 1}
+{"snippet": "As you see in the picture, the blonde woman is kicking another woman in the stomach. Can the blonde woman say: Take my kick. (I mean that she wants to give her kick to another woman and she humorously offers the other woman to receive her kick) And what is your opinion about this picture? Can the African woman say: Take my punch. If these sentences are not correct, what would a native speaker suggest? Thank you .", "label": 1}
+{"snippet": "I am in search of a word that has the meaning of 'capacity of a person to habituate to a new environment'. I can use adaptability. Like he is more adaptable than others. But 'adaptable' may not necessarily imply to a place, it may imply adapting emotions also. So is there any word that signifies the capability of a person who habituates to a new environment quickly. f I call it X. I can say as. He is Xer than others.", "label": 1}
+{"snippet": "I've just saw in Maclane and Moerdijik's book (\"Sheaves in Geometry and Logic: A First Introduction to Topos Theory\") about the Cohen forcing viewed in a categorical way using Topos theory. Is there any reference for forcing techniques using categories and Topos? Can the other kinds of forcing (iterated, Prickry, etc.) be viewed in the same (analogous) way? Any reference for the last question? Thanks in advance.", "label": 1}
+{"snippet": "Many intuitive knot invariants including Jones' polynomial are inspired by statistical mechanics. Further profound connections have been explored between knot theory and statistical mechanics. I was looking if similar connection have been found for graph invariants. I am interested to know if any attempts have been made form statistical physics community to solve graph isomorphism problem. Since both knot problem and graph isomorphism are problem about testing structural equivalence there might be connection between them.", "label": 1}
+{"snippet": "I was reading linear vector spaces. When doing some exercise to prove some statements based on the properties defined for linear vector spaces, i suddenly noticed, outside the things defined, i'm using a common notion without proof. This notion also surfaced when i was studying Group theory. After giving a thought i come to the conclusion that i've used it in all systems which are modeled after euclid. I mean first i give some postulates. Then i derive statements from those postulates. Euclid also has it as \"common notion\" : If equals are added to equals, the wholes are equal. So i started wondering that if anybody challenged this or attempted to build a system without this.", "label": 1}
+{"snippet": "If the explanation for the B-field due to a current in a wire that I've heard (length contraction by moving electrons in conductor) is true, would you really need to be moving to feel the \"B-field\" of this wire? What I mean is, if the electrons within the conductor are moving quickly enough, then they will already be (barely) length-contracted along their path. Since there is no \"moving positive-charge\", as electrons are the only charges that are moving, wouldn't this length-contraction of electrons immediately come off as an increase in negative-charge density?", "label": 1}
+{"snippet": "I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators etc, certainly the modern mathematics). If there isn't something similar please give me a reference to the book that is strictly supported by mathematics (given a set of mathematically descripted axioms author develops the theory using mathematics as a main tool).", "label": 1}
+{"snippet": "In this Phys.SE answer Ron Maimon stats: there is no relativistic particle formalism in which the particles have postive energies and casual propagation. You can either deal with fields in which case the particle notion is non local or you can deal with particles. But then they go back in time. Is this true that there can be no particle interpretation where particles only travel forward in time? I'm not asking about path intergrals but the particle interpretation in general, I'm also aware the field interpretation is the more popular.", "label": 1}
+{"snippet": "We easily find probabilities by counting the number of ways we can meet a condition and dividing it by the number of total possible outcomes. This is using combinatorics to solve probabilities. Im looking for a scenario, or a type of complicated combinatorial problem, in which the approach at counting the number of ways of meeting a condition is actually easier by multiplying the probability of meeting the condition (determined in other ways) by the total possible number of outcomes. I realize this may be an absurd question, but its been in the back of my mind for some time. Can anyone imagine up such a problem? This is for the sake of education, so that we may all learn of new problem solving techniques.", "label": 1}
+{"snippet": "What is wind? I think it is kind of a vibration of air particles. If so, is it a longitudinal or a transverse wave? Or is it just a bunch of air particles being pushed? Smells disperse in wind so the latter explanation might be a better. And breath also consists of movement of air particles. But how can wind travel so far without stopping? Can it be the pressure produced by temperature difference pushing it? So could you say it can be attributed to a wave? Any help would be appreciated, thank you.", "label": 1}
+{"snippet": "I've read it can be due to 'intrinsic semiconductor conduction' and surface conduction. The LED I am looking at is InAs, which is apparently prone to surface conduction. I have tried out what these two quantities are on google but have been unsuccessful. In particular because I have no extensive mathematical knowledge of the subject, and so am looking for a qualitative answer. And why does reverse leakage current increase with higher temperatures?", "label": 1}
+{"snippet": "Q: Is the italicised verb form correct in this sentence? Jane's pale face suggested she could be ill: her parents suggested that she have a medical examination. A: The sentence is grammatically correct. The subjunctive remains in force even though it is likely the patient will follow the doctor's advice. To actualize the blood test with \"has\" would be telling an untruth. The subjunctive holds the notion of a suggestion in place. Thus does grammar make its own modest contribution to truthful speaking. I don't see how this sentence can be grammatical. Please could you offer any comments.", "label": 1}
+{"snippet": "I am just about to create my beamer file for my upcoming presentation in which I need to open another program (NetLogo if it helps) to show it to the audience. Is there any possibility to create a shortcut or link so that I only have to press 'next' or click on that shortcut to open the program? Or do I have to close the PDF my self and open the other program? I'd be most thankful for your answers.", "label": 1}
+{"snippet": "I am sure all of us have played with rubbing things and producing static electricity and when I was charging my comb by rubbing it on my hair and watching it attracting a small piece of paper, I heard a very feeble noise just like an electric buzz sound. I could feel the electron \"cloud\" all around the comb and the paper it I could find no reason as to why a sound should be produced. From where is that sound coming from?", "label": 1}
+{"snippet": "This is a historical question partly, and maybe too broad for this site, but would require some familiarity with modern physics research practice so hopefully appropriate here. Einstein's later years, after general relativity, were (as I understand it) taken up predominantly by his effort to find a unified theory that explains both gravitation and electromagnetism and their interrelation. And from what I understand his approach was mainly mathematical, trying variations of functions and so forth, looking for something that fit - and doing his work predominantly on paper. Had he access to modern computers - programming languages, mathematica, etc. - how might that have changed his progress, and willingness to give up perhaps? And in what ways have computers in general changed / revolutionized theoretical & mathematical physics?", "label": 1}
+{"snippet": "Lately, I have been watching sparks while connecting my electronic devices and I can notice that electricity is kind of blue, and theoretically it's blue because it reflects blue wavelengths?? And that makes it a particle (like if I said that light is a particle because photons). So am I correct? If electricity doesn't have that color because of that, then why is it blue?? After asking this now I think the following questions: Does electricity have the exact temperature to produce blue light (in terms of the EM spectrum)?? If the answer is no, why does electricity have color??", "label": 1}
+{"snippet": "If context is needed, I'm happy to supply it.. The sentence I want to rephrase: Some selection of this kind has for some time been imperatively called for, by the wants of the gardener, farmer, and amateur, the multiplicity of sorts in the larger works and catalogues rendering them nearly useless to those who merely wish to know those kind adapted for family or market supply. I'm at a loss of words for interpreting the sentence into concise rephrasing for elementary comprehension. It's from a book by Robert Buist titled \"The Family Kitchen Gardener\" (Full book). The sentence is under PREFACE a few paragraphs down.", "label": 1}
+{"snippet": "According to Wikipedia, A set of states C is a communicating class if every pair of states in C communicates with each other. A communicating class is closed if the probability of leaving the class is zero. Would you call an absorbing state a closed communicating class since it cannot be left and it communicates with itself? However, one problem with calling an absorbing state a closed communicating class is that since it consists of only one state (obviously) - and this might not satisfy the definition of a set of states.", "label": 1}
+{"snippet": "English has a \"intricate\" relationship between graphemes and phonemes,i.e. there is no sure way of knowing how to pronounce something by just looking at its written form. Generally any language has this property, but English is much more complicated in comparison to - say - Italian (which happens to be my native language). This fact is known, and I remember stumbling upon a very nice sentence by an English Author, who leverage on this fact and wrote a sentence whose words did not make any sense together, but if you read them, then the \"sounds\" formed a perfectly meaningful phrase. I seem to remember something concerning \"god\" and a \"fish\"? Not sure though. Anybody remember that?", "label": 1}
+{"snippet": "In a research problem in an unrelated area, me and a student found it necessary to count the number of directed graphs with every vertex having one outward-pointing edge, with no restrictions on the number of edges pointing inward. Not being a graph theorist, I was wondering if this is a well-known class of directed graphs. Is the number of such graphs for fixed n known? If it is unknown or an open problem, we'll work on it together, but it seems likely to be known.", "label": 1}
+{"snippet": "I am writing an ad and would like to write: \"Our team of economists are at your service and available by phone or email. They will be happy to respond...\". I know that grammatically speaking, 'team' is the subject of the sentence and, being singular, would dictate that 'it' is \"at your service\". BUT, it just feels better reading this and it evokes a picture of a bunch of economists doing what they do rather than a single unit\". Is what I'm doing OK? Should I be arrested by the grammar police?", "label": 1}
+{"snippet": "Possible Duplicate: Temporarily increase line spacing I tried to follow these examples here Temporarily increase line spacing but in my case it didn't change anything. I have to use a latex template, which is provided by my university. My title looks currently like this: as you can see, the third line has not enough spacing. Can anyone help me to fix this issue? You find the entire template (already with my title in it) for downloading on my webspace: http://www.easteregg.ch/DDIS-diploma-thesis-template-en-long-title.zip just run the \"ddis-thesis-EN.tex\" in the root folder and you will get probably the exact same issue.", "label": 1}
+{"snippet": "Does a first-person possessive pronoun have to come last if it is in a list with others?\" \"My irresponsible sister loves jewelry, so she took both Sally's and mine. \"The same room was marked on Joe's and my map.\" I know it is much better to simply use a plural pronoun such as our or their, but I can not find the answer to this anywhere.", "label": 1}
+{"snippet": "Situation: Someone says i want to meet the first monday of each month. And i want to tell them that the first wouldn't work. But i want to say it like: Please choose a different xxxxx. IE: if i wanted to change the day i'd say. \"Please choose a different day\" I'm thinking something close to frequency or ordinal..but i'm sure there's a term for it.", "label": 1}
+{"snippet": "Does a magnetic field have concentrations of magnetic force lines as seen when putting iron filings over top a bar magnet or are these imaginary? I.e. are they just an artifact of the iron being a 'conductor' of the magnetic field lines making them look like they are concentrated along these path lines but are really continuum of strength around the bar magnet when there are no filings are present? Also I learned that field lines do not cross, yet there are magnet configurations who's forces are explained as the magnetic force vectors are indeed crossing and are additive such as a Halbach Magnet Array. So what is actually happening here?", "label": 1}
+{"snippet": "In an airplane, the lady attending you is known as the attendant, besides sometimes being called a stewardess or air hostess. What does she do? Just serve you. Then what is that my maid does? Nothing but serve me. Can I therefore call my maid, my attendant? What about my other servant? Can I call him my attendant too, since I cannot call a male person my maid? Is gender the only difference? Then who and what are pages? I am looking for a clear distinction between these four terms.", "label": 1}
+{"snippet": "So I asked a question earlier similar to this, and the solution made sense; however, the graph was very simple with only five vertices. If the graph is more complex like this one then how would you determine if the graph is a bipartite? When I asked earlier, I was shown the method of trying different color combinations for all the vertices, and checking if the edges connected opposite vertices that way, but is there another way to do it for a more complex graph like this one?", "label": 1}
+{"snippet": "I do understand the concept of Naive Bayesian classification, as it tries to calculate the probability of an outcome of a class given multiple evidences. It comes from the Bayes theorem and it is called naive as it tries to each of piece of evidence as independent. This approach is why this is called naive Bayes. However, I wonder why in the derivation of the mathematics behind Naive Bayesian Classificaiton, we take logs and odds. So my question is basically the following: Why odds and log odds transformations are meaningful ?", "label": 1}
+{"snippet": "I would like to understand the first law of thermodynamics, but I have some problems with the basic concept. How to define exactly the internal energy? As I see it, given a system of particles, which the principle of work is in force for. Can it be considered 'per definitionem' the isolated thermodynamical system? If yes, the diatermic system can be defined as a system where the priciple of work isn't met. Therefore, if we define the internal energy as the sum of kinetic and potential energies of the particles, there is a term missing from the equation of the sum-work in diatermic case, called heat, which the first law postulates. How can heat be mathematically characterized?", "label": 1}
+{"snippet": "It seems to me that in and of work equally well in sentences such as these: Habitat selection in birds is frequently studied. Habitat selection of birds is frequently studied. Variation is a key concept in statistics. Variation is a key concept of statistics. The function of behaviour is an important theme in evolution. The function of behaviour is an important theme of evolution. Should either in or of be favoured in the above sentences?", "label": 1}
+{"snippet": "Is there some way to produce these figures using TeX itself preferably using TikZ? If yes, then I would also like to add labels right next to the nodes rather than using a legend. This is a screenshot from a paper I am reading and I would prefer using TeX to create them than using some external tools. EDIT I read the answer here but I would like to add the 'crosses' on the line instead of a gray colored line pointing to where the cross must exist. Moreover, I don't know how to change the crosses to the different symbols given in the diagram drawn above.", "label": 1}
+{"snippet": "I'm writing a book and need help finding a word to describe a boy who immediately jumps to do what he is told. This is the sentence it will be used in -> \"Ulric bring me a glass of water,\" Yohann says, in a raucous tone, as he turns back to the window seeming to forget about the ________ boy who scrambles to follow his grandfathers request. I might need to rephrase the sentence...", "label": 1}
+{"snippet": "I'm uploading a very simple tufte handout based paper to arxiv and I'm getting an error: ! LaTeX Error: Option clash for package hyperref. but I am not loading hyperref anywhere. I'm only loading amsmath, babel, graphicx, polski (the polish latex package), booktabs, untis and multicol packages. I'm not chaning any hyperref options explicitly. Is there a general problem with arxiv supporting the tufte class?", "label": 1}
+{"snippet": "I don't know how to describe exactly my issue, but I'll make a try: I am writing a document on Lyx, and I am using the module \"report\". I have customised the page margins but when I write paragraphs, some sentences do not obey the margin and some words are not in the same line. Graphically: From a PDF that is created with Office there is a tool (a ruler I think) with which you can make the paragraphs in order to be all the words in the same line. For example: How can i fix this issue?", "label": 1}
+{"snippet": "Is there a word that refers to an official interest group held in school where registration is totally optional but members once registered are expected to come? Official means the school keeps records and members who do not reach a certain attendance threshold would be kicked out. I was thinking of school club but that seems to suggest that attendance is totally optional since clubs have the notion of come-and-go-whenever-you-like. On the other hand, the word association or organization sound too business-like. Besides school club, is there a better word that has a closer meaning to official school interest group?", "label": 1}
+{"snippet": "I have the following figure: As of now I create this in Word/Powerpoint and paste the screenshot in a LaTeX file. Is there a way to create this natively? Also, what would be the advantage of doing so? The tables are just place holders and actual table design/content may change. But I prefer if it could be editable and not fixed. I'm not sure I even know where to start or how to go about it. I've never needed to draw anything in LaTeX before.", "label": 1}
+{"snippet": "By my current understanding of the two words, the sentence: The preciseness of this precision is very definite is grammatically correct. Correct me if I'm wrong, and if so; what is the distinction between the two words? OED definition of preciseness: Exactness, accuracy; definiteness; minuteness. OED definition of precision: a. An instance of exactness or preciseness; a particular, nicety, minute detail, esp. of language. b. The fact, condition, or quality of being precise; exactness, accuracy. Also, what is the word for the situation in which this can occur? (I want to say it's the opposite of an oxymoron?)", "label": 1}
+{"snippet": "I did the best I could. The sentence above can be rephrased: I did the best that I could. In these two examples (that) I could is a relative clause. However, I am not sure whether it is modifying best or the best or an ellipted element. What exactly is this clause modifying? Secondly, what type of phrase is the best here and what type of word is best?", "label": 1}
+{"snippet": "Humour me for a minute here and let's imagine that all interesting and plausible supersymmetry models have been \"cornered\" out by the experimental data; what sort of alternatives are there for having quantum field theories with Poincare symmetry that are allowed to have nontrivial internal symmetries? i.e: that the Coleman-Mandula theorem does not apply? What other assumptions of the theorem can be relaxed or dropped, and still leave us with workable QFT? Are we forced to drop full Lorentz-Poincare symmetry or will the theorem still apply with slight violations of that symmetry?", "label": 1}
+{"snippet": "How does one go about creating a TiKz library (is it even possible)? Is this a formidable task for a beginner? As a chemical engineer, I would very much like to have a library to create a process flow diagram, like the one below, in which you place nodes with certain shapes and connect them based on specific ports. Update: I actually found out that there are a couple of libraries for this purpose: chemplants PIDcircutTikZ", "label": 1}
+{"snippet": "We observe in static electricity experiments that a comb rubbed on dry hair lifts tiny pieces of paper.This is due to the attraction force exerted by the charge collecting on the surface of the comb on the opposite charges collecting on the hair.This is a very small amount of force.But our body is always exerting gravitational force on all objects around it.Still it cannot draw such tiny pieces of papers.Why?", "label": 1}
+{"snippet": "Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily decreases its von Neumann entropy and, depending on how you define it, reduces its temperature. Can a stronger connection be made between thermodynamics and CP maps? To what extent do non-unital CP maps reliably cool states that aren't infinite temperature?", "label": 1}
+{"snippet": "Layperson here. In a theoretical big crunch with space contracting faster than the speed of light, would information be travelling faster than speed of light? Because the points A and B themselves would be moving towards each other FTL. Maybe this is obvious or I have made a wrong assumption. Either way, please answer. Also, forgive if this has already been asked. I did search and couldn't find such a question.", "label": 1}
+{"snippet": "Precision is usually understood as the number of significant figures in some experiment. Accuracy is the difference between the best measurement and the real value. How are precision and accuracy determined from a given experiment? Or equivalently, how are systematical errors and statistical errors calculated. Statistical errors are usually treated approaching \"the normal distribution\". But I am not sure how systematics are determined...Perhaps making some \"pattern\" measurements?", "label": 1}
+{"snippet": "The Centroid point (at intersection of medians) divides a planar triangle into three equal-area smaller triangles. In case of spherical triangle, the three geodesics joining the vertex to the midpoint of the opposite side of spherical triangle intersect at a (Centroid-like) common point. But, when geodesic is constructed to join this Centroid-like point to the three vertices, the resultant smaller spherical triangles do not have equal area! A different geometrical method or a formula for implementing the exact division of spherical triangle into three equal-area spherical triangles could not be found in literature.", "label": 1}
+{"snippet": "My question is very simple. I just would like to know what do they mean by: \"I believe you're up\" I've heard this expression in a movie and here is the script: I already met your dad. He loves me. Love is very strong word. Well, he at least likes me, right? We're busy tomorrow night. Okay, and we're back. Amy, I believe you're up. Oh, oh. Okay, I got this.", "label": 1}
+{"snippet": "Our company uses project management software called Jira. In Jira you can mark one issue so that it 'escalades' another, or 'is escaladed' by another. I think that is something like 'cause', but you can set 'cause' or 'is caused', so they are different. And I find the meme 'that escalated quickly', and looks like it has a similar meaning to escalade. Can anyone tell me what escalade means in 'one issue escalades another'? Can I use escalate instead?", "label": 1}
+{"snippet": "Some concepts are just too difficult to be fully understood. Take for example the multivariate causes of the recent recession: who among us can honestly say that he or she grasps the situation completely? With respect to topics like this, although it is not possible to thoroughly grasp the concept, attempts can be made to elucidate--at least partially--the more mysterious parts. Accordingly, is there a phrase that means, \"To make less mysterious, but not explain completely because the concept is too difficult\"?", "label": 1}
+{"snippet": "The hotter something is glowing the more white/blue it appears. A dying medium sized star expands, cools and becomes a red giant for a while, but eventually it is going to gravitationally collapse (once enough Iron (Fe) is accumulated in the core). Then it blows the outer layers away and what is left collapses into a white dwarf. What makes the dwarf shine? and why is it white? Does the luminosity decreases as the object cools down, or is there some other reaction that keeps it glowing for a long time? Can a white dwarf turn brown or black never to be seen again? Do all white dwarfs turn into Neutron stars eventually?", "label": 1}
+{"snippet": "I recently heard about the possibility of the creation of a \"baby\" universe or \"pocket\" universe from our space time,the theory says that concentrating enough mass into a tiny volume of space (like in black holes) a pocket of false vacuum would form e perhaps it'll continue to expand following it's own inflation period and go on forever completly disconnected from our space time without influencing it any way. Now my question is : supposing that we live in a metastable vacuum we know that true vacuum bubble could form via quantum tunnelling and begin to expand into our space time where these false vacuum bubble (or pocket/baby universe) are supposed to go and expand ?", "label": 1}
+{"snippet": "Possible Duplicates: Salutation in an Email How do you greet multiple recipients in an e-mail? How do I use the initial words while writing an e-mail, in particular, to my superiors? Suppose somebody is writing a letter to the HR representative of a company, requesting a letter, approval, information, etc. Should the salutation be written like: Hi or: Dear or her/his name: Dear Jenny Are any of these proper way? Or, should I leave it blank and start with the crux of the matter right away? Does it matter whether I know the person or not, or if the person is not my superior but is a colleague or junior?", "label": 1}
+{"snippet": "According to the work of J. Scott Carter you can draw pictures of knotted surfaces in four-space in several different ways. I know the man is a real artist in this, but did anybody come across some software that does this for you ? See for example: http://www.jscottcarter.com/) I guess you can figure out a parametric equation for a knotted sphere, and pay a trip to Mathematica-land, but I haven't done this. This is probably a more specialized version of Topology software)", "label": 1}
+{"snippet": "I'm looking for a positive word or phrase - though ideally, a single word - that suggests that old dubious beliefs are being re-examined and questioned. \"Self-doubt\", has a negative connotation and I would like this to indicate a sort of personal growth. For example, it could describe someone who used to be paranoid and believe that everyone was conspiring against them learning to become more trusting.", "label": 1}
+{"snippet": "In this problem are only truth tellers and liars. When meeting two people, A and B, you ask A: \"Is any of you a truth teller?\", to which A replies: \"If B is a liars, then i'm a liar\" What are A and B? What I got so far is: If A is telling the truth, then the statement must be true when B is telling the truth, and false when B is lying. If A is lying, then the statement must be true when B is telling the truth, and false when he is lying. I can't seem to find a way to logically formulate this, and I'm thinking this might be because I'm missing something. Have I got it right?", "label": 1}
+{"snippet": "A colleague once disparaged his own research to me by saying that it didn't involve any sort of cohomology. It does, in fact, seem like homological ideas appear across disciplines...and are considered to be mathematically \"sexy\". I wonder what the deep reason for this is? (The answer \"because these ideas prove many things\" seems cheap, or ad-hoc here.) Where can I find a \"bird's eye\" modern view of general homology/cohomology?", "label": 1}
+{"snippet": "I'm writing a thesis and would like to have the pages on which a new chapter start look fancier than they currently do. I like the example on this page: how can I create a chapter heading like this? However, since the abstract is defined in the preamble, it appears the same in each chapter. Obviously, different chapters need different abstracts and I don't know how to correct this? Secondly, for some reason, the contents of this preamble are changing the font style of the rest of my document and I'd like the bulk of what I'm writing (outside of chapter title and abstract) to stay in the standard font that LaTeX uses. Thanks for any help.", "label": 1}
+{"snippet": "I asked a similar question on SciComp, but it is a little out of the domain, so I thought I'd give it a try here as well. Give n points, I would like to place them in a periodic box (periodic such that the distance between two points \"wraps around\" to the other side) so that the minimum distance between any two points is as large as it can possibly be. How do I do this? I imagine analytically this could be quite difficult, but is there at least a numerical procedure?", "label": 1}
+{"snippet": "The sentence is: \"Since they were first invented, we have advanced, and designed stylish glasses for people whose vision need to be corrected.\" I've been told that the verb needs to be \"need\" and also that it needs to be \"needs\". Need: The argument is that the need refers to \"people's need\" and therefore by implication refers to a plural group, i.e. people need ... Here the antecedent is considered \"people\" ... Needs: The argument is that the need refers to \"vision\", i.e. singular ... Here the antecedent is considered \"vision\" ... Which one is grammatically correct?", "label": 1}
+{"snippet": "I'm trying to dive under this incredible world of non-WYSIWYG. So, for my first main challenge I need to write my master's thesis with LaTeX. And I found some difficulties at the very beginning of my work: the cover page. I need to customize the cover page like this model (it's the mandatory model for our thesis in my university): I need the university logo to be within the dotted retangle. I tried to fit it there without success.", "label": 1}
+{"snippet": "In class my prof said that when showing a system is at equilibrium it suffices to show that the moment at one point is zero. Why? Why does showing the moment at a point is zero imply the moment of the whole system is zero? If I misunderstood him and the statement above isn't true, how do you show the system is at moment equilibrium at all points of the system? You obviously can't show the moment is at equilibrium for infinite points individually.", "label": 1}
+{"snippet": "To me, that means: I can start dreaming after buying a lotto ticket. This is weird because without the lotto ticket, I can have my day-dream anyway. Shouldn't this be something like \"your chance to realize your dream has arrived\"? This slogan kind of gives me the opposite feeling about buying a lotto ticket, as if it is always nothing more than a day-dream to win the lottery.", "label": 1}
+{"snippet": "A human ear responds to a wide range of frequencies. My teacher already has said me, when you are speaking about a part of your body that it belongs to it- it is not artificial et cetera- you must say the following: the eye the ear . . et cetera. But, I just have seen the above sentence. Would anybody kindly elaborate it? Many thanks", "label": 1}
+{"snippet": "A variation of \"smother\", obviously, to describe someone with an inclination to smother other people. \"You're just too needy and smothersome.\" Thoughts? Corrections? Suggestions? Edit: Apologies and clarification. I did find a Google search result that states that this word is an adjective which describes something that is easily smothered. But to me, this word sounds akin to \"bothersome\": causing bother, troublesome. To me, \"smothersome\" wouldn't describe something that is easily smothered, instead it would describe something that does the smothering...", "label": 1}
+{"snippet": "I am getting familiar with some basics ins probability theory and I have a question concerning moment-generating functions and characteristic functions. The following is cited from Wikipedia: A key problem with moment-generating functions is that moments and the moment-generating function may not exist, as the integrals need not converge absolutely. By contrast, the characteristic function always exists (because it is the integral of a bounded function on a space of finite measure), and thus may be used instead Is there a connection between the following two facts? the characteristic function is (real) analytic moments of all order exist Furthermore I have one question in mind somehow: If a distribution has a characteristic function that is analytic, is the distribution then moment-determinate?", "label": 1}
+{"snippet": "I came across a shop selling the fruit jam that my sister had been looking for. But the fruit jam came in apple and peach flavours, I was not very sure which one my sister liked better, so I decided to buy both. Now, given that situation, I want to explain why I bought both apple-flavoured and peach-flavoured jams to my sister: I bought two fruit jams in different flavours because the jams would be sold out. I could not [take any chances / take any chance] . Thank you Kitty", "label": 1}
+{"snippet": "I want a word for a person who accepts advice of others. Basically, I am reading a play and in that there is a ruler who accepts the wise advice of others. What word can be used to describe such a person? Example : That man is indeed __________ since he imbibes the noble qualities of the wise by the accepting their advices. Please provide a reference sentence with your answer.", "label": 1}
+{"snippet": "Is there any particular problem or scenario where quantum logic may be applied? If so, what is the benefit of using quantum logic instead of classical logic? I've been reading quite a lot on this topic but it still seems like pure theoretic considerations to me. If there is so much effort put into forming new type of logic based on quantum mechanics, are there any practical uses of this type of logic?", "label": 1}
+{"snippet": "Earlier I asked this question. So, similarly, imagine the same type of list with elements having a guest and probability of attending, but now each guest also has an age. How can we calculate the expected average age of the guests of the wedding? I can heuristically group the guests into age ranges and then compute the expected number of people in each age range, but this doesn't tell me the expected mean.", "label": 1}
+{"snippet": "Hi I am very new to this aspect of physics and I am having trouble with the derivation of the Rayleigh-Jeans from the steps shown at the hyperphysics web site. I have emailed Dr. Rod Nave who is listed as the person-in-charge at the site but it appears there is no one at that email perhaps. It would really be much appreciated if anyone can have a look at the uploaded image file here and follow the queries I make on them.", "label": 1}
+{"snippet": "Following the measurement of gravitational waves, many sources described them and explained they carry energy away. What I don't get is how this energy will get transfered back to anything else. If the fabric of space-time itself is vibrating, it would seem to be in impossible for any physical object to gain this energy. What am I missing? How would one hypothetically get energy out of gravitational waves? If impossible, does the universe end up with nothing but GW?", "label": 1}
+{"snippet": "It is to my understanding that it is grammatically correct to say: If I be [something], then [something]. because 'were' is the subjunctive of 'to be'. However, is it correct to use the subjunctive of other words in a similar way? For example: If he jump, the trampoline will shake. or I request that he file these papers. If it is correct, is it incorrect to use the simple present tense in those contexts?", "label": 1}
+{"snippet": "http://freespace.virgin.net/hugo.elias/models/m_perlin.htm This method involves getting a random dataset, sampling it at various resolutions, and adding together the result. I've heard it claimed that this is actually \"Fractal Noise\" or something diffe http://www.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf This PDF claims that there is mass-misinformation about what Perlin Noise is, and explains a completely different method (I'm not talking about the discussion of Simplex noise at the bottom, but about his summary of Classic Perlin noise). Who is correct?", "label": 1}
+{"snippet": "I use pst-eucl package and I am not so happy with the names defined for its keys (because the names are difficult to remember). I want to rename some of the keys for my own purpose by creating a new package wrapping the package. For example, I want to rename: PtNameMath to PointLabelMath. PointNameSep to PointLabelSep. PosAngle to PointLabelAngle. PointName to PointLabel. Could you show me the new package wrapping pst-eucl with renamed keys above.", "label": 1}
+{"snippet": "What is the proper adjective that best describe the way a person keeps looking at any other person or object so that as if his eye is about to get out. As an example, when a man keeps looking at a beautiful lady for a long time without even twitching. Sometimes it might be considered an envious look or sometimes it might be due to profound admiration", "label": 1}
+{"snippet": "Like other words that start with \"arch-\", archenemy is partly derived from arkhi or arkhos from the Greek (Wikipedia), meaning chief. But why is it said differently, using a \"ch\" sound, from archipelago and archaeology, which use a \"k\" sound? The \"ch\" in archenemy is pronounced similar to that in archbishop and archdiocese, even though they're followed by consonants in the latter, but a vowel the former. What made it break from the rules?", "label": 1}
+{"snippet": "How do we check the geometry of the phase space ? I mean in classical mechanics we use position and conjugate momenta as a space of all possible states of the particle. How do we know that this phase space is flat? In other words, is phase space of classical pendulum flat or curved like a cylinder? Any reference concerning theory of dynamical systems for physicists and chaos would be useful.", "label": 1}
+{"snippet": "I read online a statement to the effect that (I'm paraphrasing): Goedel's incompleteness theorem shows that we cannot even have a complete and consistent theory for the natural numbers. I am under the (qualitative) impression that this statement is true within the axioms of natural numbers themselves, so that if one expanded the of axioms one could prove all of the true statements that can be expressed solely in terms of natural numbers. Note that this larger system itself is not complete and consistent. Does Godel's incompleteness theorem have the feature that it shows that these larger systems are somehow representable with the axioms of the natural numbers?", "label": 1}
+{"snippet": "Mom was saying that dad wanted me to mow the lawn and asked what time I would be coming home. In the sentence above, who is asking what time I would be coming home, mom or dad? If it's mom, why isn't it dad? And if it is the dad, why isn't it mom? Basically which subject is the and for? Mom or Dad? What are the rules?", "label": 1}
+{"snippet": "Why do we have a situation where the past of \"to blow\" is \"blew\", but of \"to glow\" is \"glowed\"? And don't say \"flew\" if you mean \"it flowed\". The poem Lovers, by Phoebe Cary has many examples of these. How did these differences originate? Did \"blow\" and \"glow\" come from etymologically distinct backgrounds that have just come to be spelled and pronounced the same way? Is there a general rule for words like these?", "label": 1}
+{"snippet": "I found myself writing this: .. and this is before we consider mathematics proper. It seemed like a natural kind of thing to write, but I couldn't find an example of it. I get the impression it's OK to use it in this way; to mean the major mathematical schools in this case (rather than people who just do mathematics). Is there any objection to this?", "label": 1}
+{"snippet": "I am designing a wedding card, I need to know how to start it, these are some samples: Mrs. & Mr. Xyz invite you.... Mr. & Mrs. Xyz invite you.... Mrs. Abc & Mr. Xyz invite you.... Mr. Xyz & Mrs. Abc invite you.... Which is the best one to suit a wedding invitation? or suggest me some other lines which looks correct and polite in reading too. Note: Couple inviting here are mom and dad of the bride.", "label": 1}
+{"snippet": "I want to draw two cylinders connected with a common belt around them. Therefore, I need two cycles and two tangents to these two cylinders. I know there is a general solution for my problem How can I draw a tangent ending smoothly in a circle?, but there are two specifics I cannot resolve: I want the belt to have another thickness (i.e. both tangents and outer lines of two cycles) I want to draw a vector of specific length along the belt between two cycles Is there any way to achieve these two goals?", "label": 1}
+{"snippet": "The motivation for my question is understanding how electricity gets through your skin as opposed to running along it, and how the presence of things like water on the skin affect the relative deadliness of electricity, or ability of it to permeate the skin. I don't understand how to view the body as a resistor, as the skin, and all the components of the body have different resistances and thicknesses. How do I know what parts of the body carry significant current? And how much current in total?", "label": 1}
+{"snippet": "My question: In this version of the experiment, doesn't the single photon source's direction define which slit the particle passes through. Also, with reference to the apparatus described here, where there is an additional single slit, does it mean to say that diffraction happens even for single photon's at the (first) single slit. I understood what the experiment says after the particles pass through the slit, but I'm not able to understand how the single particle/photon source set up works. Hope someone can help me understand how that works.", "label": 1}
+{"snippet": "Is there intuition for \"mathematical\" entropy. I know that physical entropy tracks the order in a dynamical system, for thermodynamics. As entropy goes up, general randomness and disorder goes up. However, what is entropy in the mathematical sense? There seem to be many kinds of entropy, but what is there a general defining characteristic or use that is common among them all? I'd appreciate some intuition for this interesting subject. (Edit: Alex R. provided a great link for the above) Pertaining to my interests, what is Entropy over a Fractal? Is this Entropy taken by treating the Fractal as a probability distribution? What purpose does taking the Entropy of a Fractal serve?", "label": 1}
+{"snippet": "The shape is somewhere between a v and a u. I'm almost certain it's a letter character as they have both lower and uppercase (used for specific and total volume respectively). Since the v and V characters are also used for things like voltage and velocity, it's important for me to be able to distinguish these. The top six symbols below are what I want, the first four being lowercase and the next two being uppercase.", "label": 1}
+{"snippet": "So, we were ask to consider the Fresnel Equations for parallel and perpendicular waves (with index of refractions). Then, we are ask to prove some equations in which \"... for nonmagnetic non-conductors\" The Fresnel equations got reduced and the indexes of refraction disappeared. I do not really know where to start, but in our reference book we have: normal incidence and oblique incidence topics. Any help?", "label": 1}
+{"snippet": "Some nouns used in medicine ironically contain the letter that is difficult for the sufferer to say, or difficult to deal with: Lisp ('s') Rhotacism ('r') Blaesitas ('b') Dyslexia (difficult to spell) Hippopotomonstrosesquipedaliophobia (fear of long words is a long word) Aibohphobia (fear of palindromes) Lamdacism ('l') Stammer/stutter (hard consonants easier to stumble over) The closest I found was 'jocular terms', but this seems a bit too cruel. How did they come by these names? Is there a collective term that isn't so cruel? I've looked at this ESE question and this reddit post hoping for an answer to this, but it didn't cover the collective term and more pointed out the cruel irony of it.", "label": 1}
+{"snippet": "So, if your promotor is kind, you would thank him as: \"I thank Prof Smith for his kindness.\" Now, what if your promotor is demanding, as in tough and exigent when it comes to work? How do you express this quality? It seems to me the following is not correct English: I thank Prof Smith for his \"demandingness\". Which is the right word to replace \"demandingness\" above? If it could help the forum choose, I need here to convey also the impression of \"at times excessive but on the whole beneficial\".", "label": 1}
+{"snippet": "Excuse my terrible English knowledge, but I have been wondering this for some time already: What is correct for the next phrase?: And he was there. alone. sad. and crying... or And he was there. Alone. Sad. And crying... or And he was there, alone, sad and crying... On the first and second cases, I use periods for separating the state of the subject. For some reason, I like it to give better suspense. Given the way I am using the periods, should I use Capital letters after them, or not? These periods are pretty much like commas... ... But maybe I am terribly wrong and should never use periods for such purpose? Should I always follow the third case? Just using commas?", "label": 1}
+{"snippet": "I am having trouble using the term \"secular\" to convey a sense of bringing a religiously neutral ground to government, society, and culture. What term is better than \"secular\", that is less localized than the US-connotative sense, but conveys the same general meaning to multiple countries? Secularism is often denoted the same, but from country to country it is practiced on a sliding scale in terms of how truly neutral laws are. Some of us on the Atheism.se are trying to broaden the scope of the site and are interested in methods for doing this. The usage of \"secular\" (that I am looking for) should convey taking secularism and using it as a tool for atheist questions to hone in on issues regarding equal rights, activism, promotion.", "label": 1}
+{"snippet": "As a very bad speller I love to find justification for my lack of ability. I'm wondering about the reasoning/history that 'Flower' and 'Florist' have such different spelling. I'm guessing it has something to do with 'flow' where a flower is a thing which flows and it would be too much to have a person working with such things be a flowerer. Any better explanations?", "label": 1}
+{"snippet": "Why are both the terms 'structure' and 'model' used in mathematical logic / model theory? Are they just holdovers from different subjects or is there a principled reason for having both? For clarification, I'm not confused about any actual definitions or usages, just why both terms came to be used; I could, after all, survive perfectly well using exclusively one or the other with little chance of confusion.", "label": 1}
+{"snippet": "I woke up recently to find the following structures on my lawn; they resemble bubbles, but are formed from ice (we had a moderate frost overnight). There were eight of these 'bubbles' on my lawn and one smashed one on the adjacent path. They were only present in my garden, and nowhere else. What processes could have allowed these 'bubbles' to form in this shape? 'Bubbles' on grass: Damaged 'bubble' This was found on the paving slab and was not touched:", "label": 1}
+{"snippet": "To my knowledge, the contents of a float environment are put into a box when the float is defined. Is it possible to proccess a user defined command/macro when the float is actually typeset, e.g. to put a watermark on that specific page (which isn't necessarily the page the float is defined on)? Is it necessary to add something to the definition of the float enviroment or can I use some command within its body?", "label": 1}
+{"snippet": "When we have a set of data, where X is the cause, and Y is the effect, we can use linear regression to predict values for Y, based on values of X. I have learned that you may only safely apply this for values of X that fall into the domain of X for the input data. Can we also use linear regression to do reliable predictions about values of Y for values X that lie outside of this domain, and if so, what can we say about the reliability of these predictions? I would love some answers and possibly some interesting sources on this subject.", "label": 1}
+{"snippet": "The reply to a question about nucleosynthesis, that heavier than iron elements are produced in supernovae explosions, raised for me the following question which I could not answer by googling. Partially because the search for planets and stars brings out astrology answers! Explosions are dispersive, nevertheless we find minerals in clumps, not only uniformly dispersed in the ground. Is there a coherent presentation that explains how minerals end up in veins and bands?", "label": 1}
+{"snippet": "How is it possible for a grad student to do research in any modern area of string theory like AdS/CFT or ABJM if they need to start grad school by having to learn QFT from scratch? Is there a time-line over which this is even possible? Or one necessarily needs to come to grad school knowing at least Polchinki level string theory to be able to understand AdS/CFT or ABJM? I mean even if one has worked through enough of Polchinki's book one is likely to stare blank at the ABJM paper. Then is it even possible for someone to get to research level with something like this if they start from basic QFT in grad school? I would like to know what if is a practical implementation.", "label": 1}
+{"snippet": "The question Why is a black hole black? states that stuff can't escape the event horizon and must ceaselessly pull inwards towards the singularity. At the singularity the forces become infinite. However, I heard that Hawking radiation (but not information) can escape the event horizon. Can something similar to Hawking radiation escape the inside of the event horizon and the singularity? Would a person inside the event horizon see Hawking radiation emitted from the singularity? It is hard for me to understand this because I think as soon as one photon is emitted one quantum step out away it starts to fall back to the singularity at the center of the black hole again.", "label": 1}
+{"snippet": "I know that It is time (understood: for the speaker or for a group of people including the speaker) to do something. and It is time I or we did something. do not mean the same thing: the first is a simple statement of fact, whereas the second means there is some kind of emergency. How about these same structures when the action is to be performed by a second or third person? Does the nuance stated above cease to exist between It is time for you/him/her/them to do something. and It is time you/he/she/they did something. ?", "label": 1}
+{"snippet": "I've seen a video by Walter Lewin in which the magnetic pull between two wires is unaffected when an aluminum plate is situated between them. Can you explain what materials let magnetism pass through and how this can happen? does that give clues on the nature of magnetism? I originally thought Lewins says that conductiveness is the key factor, but I discovered that superconductors don't let it pass", "label": 1}
+{"snippet": "What is the best word/expression to describe a phenomenon or tool that, despite its disadvantages, is used by people? In fact, there are some alternatives for them, however, there is a weird inclination toward them. As an example, smoking is a good one that most of people know its harms and probably its alternatives, however do not give it up. Update: As another more specific example, take Microsoft Office. There are several (probably more powerful) alternatives for that, however, remarkable numbers of users are still using MS Office. Is it only a habit?", "label": 1}
+{"snippet": "I know that as you heat something it expands, but this is proportional to the change in temperature, so if I compare the density of a liquid right before freezing and right after then the thermal expansion would have a small effect. However, when a material changes state the density can change rapidly. I know water gets less dense as it freezes, and I remember this is not typically the case, but do any substances have approximately the same density in both liquid and solid states?", "label": 1}
+{"snippet": "I have been thinking about these adverbials for a long time to understand this connection of \"early/later\" with \"on\". These adverbials are used for introducing a sentence or they are placed at the end. My first explanation was \"on\" is a kind of intensifier, almost meaningless. Now I tend to see this \"on\" as a clear marker to indicate that \"early/later(adj/adv)\" are used as adverbs. But all the same I don't find a formula from which I can derive these adverbials by using the two words. ... early ... on ... / ... later ... on ... - What words could one use to get a formula that means \"early/later on\"?", "label": 1}
+{"snippet": "A Doppler redshift would also give the illusion that galaxies were rotating more slowly then they are with the degree of illusory slowing in proportion to the degree of redshift. Do more distant galaxies appear to be rotating more slowly than closer in galaxies on average, and would this not constitute additional evidence for expansion, or if not would it not constitute evidence against expansion?", "label": 1}
+{"snippet": "In the usual circle topology (open arcs), it seems that the intersection of a finite number of connected sets is either empty, a connected set, or the disjoint union of two connected sets. Can we construct topological spaces in which the intersection can be the disjoint union of more than two connected sets? If so, how are these topological spaces called due to this property?", "label": 1}
+{"snippet": "In any double slit experiment, which particles are passed through slits, and what do the detectors look like - both the one at the end of the apparatus and the one at the site of the slit? Oftentimes, photons or electrons are used as examples. However, as far as I know, in real experiments much larger particles like silver atoms are actually used. My expectation is that any apparent weirdness will naturally follow from the setup of the experiment.", "label": 1}
+{"snippet": "Physicists studying the foundations of physics and some mathematicians sometimes look at theories which are similar to general-relativity, but do not coincide with it. Often these theories contradict with what we know about our world. What should one do in order to check one of such theories? Which papers/books should one read in order to be able to understand mathematical theories similar to general relativity, and understand when such theory is compatible with what we know about our world?", "label": 1}
+{"snippet": "When a Hadron and its antimatter equivalent annihilate, what happens to the QCD \"soup\" (for lack of an appropriate term) from each? Eg, the valence quarks in a proton - antiproton event, to they pair off and annihilate \"in the moment\"? What about the quark soup at progressively higher energies? How do we account for this? (for that matter, if it's relevant, why only two gamma rays, and not more?)", "label": 1}
+{"snippet": "I have a question regarding matrices and eigen values. If SVD decomposition was performed on matrix, and the inner matrix of singular values has only one non zero value. Should the left and right singlular matrices be only a matrix of one vector? The reason I ask is that I have performed SVD on matrix in matlab using function svd, and it turns out that there is one eigen value but the right and left matrices are not one vector Thanks", "label": 1}
+{"snippet": "I would like to find a sinusoidal wave whose period or frequency change to half (or double) with every step, someting like this But I cant find the precise coefficients for the period to decrease (or increase) twice. Can someone help me? I want to use it to map the different pitch (or notes) of voice, to certain values. In our speech, and singing, the range of the first octave is half of the next octave, so I need a function whose period is twice as big each time to cover all the octaves. it need not be a sinusoidal it can be any periodical function.", "label": 1}
+{"snippet": "I was trying to understand why curl measures a vector field's tendency of rotation. Two examples from physics seem to answer my question: Curl of the velocity field is twice the angular velocity Curl of the force field is the torque. But I can only prove the first one when the velocity field describes a uniform circular motion. How can I show that the two examples are true in general to show that curl is really the measure of rotation.", "label": 1}
+{"snippet": "Consider a body which can freely rotate with respect to the inertial frame, and a rotating disk whose axis is fixed in body frame. When applying the lagrangian method (does that make a difference?), is the kinetic energy of the disk with respect to the body frame (for constant disk rotation rate, the kinetic energy is constant) or with respect to inertial frame (for constant disk rotation rate, the kinetic energy depends on the rate of the parent body)? Parent discussion: Defy gravity torques with gyroscopes?", "label": 1}
+{"snippet": "Lets take a very big rotating star ,after the finish of the nuclear fuel the star is going to contract under its own gravity.Now to conserve its angular momentum the star is going to rotate faster. But how will you explain it in terms of force without involving the concept of torque and angular momentum (Intuitively)?what forces helped to rotate the star faster? If you do not like to think about a star,think about twirling ice skater who pulls her arms? Edit:Let me add here,this is actually a question from the famous book ,The flying circus of physics,and the author is saying the ans is coriolis force. But I did not get it", "label": 1}
+{"snippet": "A lot of my calc II students are asking me what are the real world applications of what we are studying in Calc II (right now we are studying methods of integrations, so of course one of the applications is in finding areas and volumes, are there any other cool applications? I mean something that can be explained in a simple way to a calc II student). Later we will study series and sequences. I'm just looking for ways to pick up the interest of my students, do you have any ideas?", "label": 1}
+{"snippet": "Background to the sentence: a system activates itself after temperature has been deviated for [X] seconds. Now I want to describe what X does and I just cannot figure it out. My best attempts are: The value X specifies the time period for which the temperature has to be deviated. The value X specifies the time period during which the temperature has to be deviated.", "label": 1}
+{"snippet": "In winter, our glass window serves as a separator of coldness outside and warmth inside our room. We know that the window feels cold when we touch it. Since the air temperature is different in different sides of the window, why does the window choose to be cold ? What's the temperature of the window ? Is it closer to the temperature outside or inside ? Why ?", "label": 1}
+{"snippet": "Let us say that we have shape AXQY: And line AX is congruent to AQ. Line QY is congruent to XY. I do not believe that we have enough information to say whether this is a parallelogram or not, because we do not know if side AX is congruent to QY and AQ is congruent to XY. So, if this is a square, it is a parallelogram. Correct?", "label": 1}
+{"snippet": "What would be the most important implications of finding an even number that cannot be expressed as the sum of two primes? Would the existence on one such number in anyway predict the likeliness of any more such numbers? Moreover, will there be any other theorems that can be proved/disproved because of this? P.s. The answer to the latter is most likely yes, I just asked that additionally for future reference (for myself and others)", "label": 1}
+{"snippet": "I am a Tango for D adopter and appreciate it very much but I am very concerned with a threatening trend. I noticed that many prominent early members leave it. I perceive that as a strong vulnerability signal to the community because it's not outweighed by new entries. I am looking for an appropriate idiomatic way to convey the fact that they abandon/leave/quit with emphasis on the threat that it involves (Something akin to the French: \"Ils quittent/abandonnent le navire\").", "label": 1}
+{"snippet": "What phrase, expression, or even well-known literary character signifies a 'bad/poor/incompetent/incapable teacher', that is, someone who is not good at teaching. I would like to describe a teacher in the same way that quack describes a doctor. Unfortunately 'incompetent' and 'incapable' are not very funny or witty, or insightful, or enlightening (nor are those words nouns), and I'd like my word to be rather less prosaic if possible. For example: Mark Carlson is a ______ , he cannot teach a thing.", "label": 1}
+{"snippet": "If I were to personify death is their a better statement then \"delay death\". I have considered saying \"negotiate with death\" but that does not sound formal enough for the tone of my essay. I am trying to express that science continues to negotiate with death in order to delay it. Preferably with a negative connotation. I have considered \"parley\" however I dont know if that is the proper use for it nor if I should use it as \"parley death\" or \"parley with death\"", "label": 1}
+{"snippet": "I have a problem to understand isolated systems..If I have a ball and throw it upwards..then the momentum is not constant because the system is not isolated...and the reason is the external force from the earth (weight)...But if I see earth-ball as a system then I have an isolated system and as the ball moves upward the earth moves downwards..(Thing that we can't understand) because of inertia......THE PROBLEM IS THIS....Ican explain the movement of a boat from the air because of the external force from the air.....but what if I think boat-air as one system that is isolated....then the force from the air is internal...what is happening here with the conservation of momentum???", "label": 1}
+{"snippet": "This question came up today in the office. We sell single direction bus trips through our site (wanderu.com) but have not agreed on which English word(s) should be used in text. Is it one-way or one way? Does one or the other communicate that \"way\" is a noun (e.g. direction) as opposed to a verb (e.g. method to an end)? We consulted the Wikipedia disambiguation page, One-way, which links to pages like One-way traffic. This English for these pages would suggest \"one-way\" is the appropriate word. The images on the traffic page, however, has two words. Thanks in advance!", "label": 1}
+{"snippet": "I am a chinese student and one of my friend, a chinese, wrote sentences like this: Just a little above me, he was fighting with all his might. On the summit of the mountain, he cried with joy. He was pretty certain that these sentences were correct but I am not so sure. I've heard sentences like His eyes bright, he talked vigorously or Her coat barely on her shoulder, she dashed out of her house, but I have never seen sentences like the ones my friend wrote, the ones with no subject in the front. Can anyone tell me the name of the sentences my friend wrote? And if possible, can you also tell me if the name of the sentences I wrote is verbless clause? Thanks.", "label": 1}
+{"snippet": "You can obviously hear wind. From everyday experience, the stronger the wind, the louder its sound. But this sound is always similar, and quite distinctive, noise-like. Can one compute the spectrum of the noise generated by the wind? There is an inkling of an answer provided here: \"Any way, once the wind starts doing non-linear things, it can generate periodic stresses, and from that you get the whistling or humming noise we all know and love.\" Could anyone expand on this, or provide references with more quantitative detail?", "label": 1}
+{"snippet": "I've always been taught that a vowel before a double consonant following another vowel should have a short sound. Conversely, there are many situations where a vowel preceding a single consonant and vowel gets a long sound. Short Sounds: Mississippi - All I's except the last get short sound Communication - First O gets short sound Oppose - First O gets short sound where second O gets long Long Sound: Ape - A gets long sound Popery - O gets long sound Oppose - First O gets short sound where second O gets long Yet, I hear people use a short O in \"operator\" when using the word. Is this the correct pronunciation?", "label": 1}
+{"snippet": "Even further, I would be happy to see a definition of the tikz language in the usual manner programming languages such as Java and Pascal are defined. The reason I ask is that I keep getting mysterious error messages for the tiniest typos. Essentially, incorrect use of the underlying languages leads to a \"crash\" of the compiler. This crash sometimes gives useful error messages, but sometimes they are hard to decipher.", "label": 1}
+{"snippet": "All the words or phrases I know for people who stay up at night merely describe the habit of not sleeping (e.g.: a night owl or insomniac) I am looking for a word or phrase with an emphasis on working hard at night. These people work are different from insomniacs because they have no problem sleeping but they refuse sleep to work. They are different from night owl because they wake up early in the morning. To give more context, suppose a nurse with kids who has a normal day life like most people and takes care of the kids but also works most nights in a hospital.", "label": 1}
+{"snippet": "This might be a very simple question, so sorry. I have encountered the expression \"radiative particle decay\" quite a few times now, and none of the sources ever explain what they mean by radiative: I imagine it is trivial, but I would like to know exactly what it is implied by that. Does it just mean that it is a decay during which other particles are produced? I.e. other particles are radiated?", "label": 1}
+{"snippet": "I was sitting close to a speaker and I could feel the sound coming from it all over my body, especially in my heart, and it pounded with the loud beats of the music. Was my heart pounding because of the excitement at listening to the music or was I really feeling the sound in my heart and all over my body? I have some understanding that it is all about sound waves & acoustics (bass/low & high pitch/low and high notes etc.) but it is not clear to me. I hope I have correctly framed my question.", "label": 1}
+{"snippet": "I know that stop can be a synonym for wait,btw. I know telling someone to wait means for someone to pause until a certain time. But telling someone to stop just means the person has to pause without a defined amount of time to resume (I hope this makes me sound smart haha). Here are some examples: \"Wait! I want to tell you more.\" Would it be the same saying- \"Stop! I want to tell you more. \" I want to note, that I am a native speaker. I'm just a curious person and a thinker. :-)", "label": 1}
+{"snippet": "Possible Duplicate: The effect of the anonymous letter I have a bit of a programming question, and I think it's in line with what LaTeX (XeLaTeX in my case) is suited to do. I would like to randomly use a font (from a list of fonts) for each glyph being typeset. I wanted to do this for a project in the style of a \"ransom letter\" - imagine individual characters being clipped from a different source. I wanted to use a set of fonts that were modelled after typewriters, all opentype fonts. How would I approach this? Ideally I would type the text normally, and have TeX do the heavy-lifting of randomly picking a character-set for each glyph.", "label": 1}
+{"snippet": "Is there any word in English, which describes combination of username and password? Let's say, I want to say Enter your \"this_word\", meaning Enter your username and password. EDIT: I'll exlpain, why I need this (because I see that it's being asked), though I see some answers, which fit my requirements. I'm a software developer (freelancer) and I'm creating a Desktop application, where login/password pair is present. But after releasing the first version of application I got the feedback, that It isn't clear for 'stupid' (no offense, just expression) users what they have to enter. So before it was like: |username (placeholder)| |password (placeholder)| and after the feedback I want to change it to something like Enter your Google 'word' |username (placeholder)| |password (placeholder)| so, that's it.", "label": 1}
+{"snippet": "This question arises from the commentspace in this question on stats.SE. My comment was: Last I checked Terry Tao was the pre-eminent mathematician of this generation? To which another commenter replied: Which generation is that? Note that I said \"this generation\" as opposed to our generation. My question is: does \"this generation\" associated with a date (timestamp) uniquely identify a generation, particularly in the academic context? How else can I identify a generation -- through reference to a specific person?", "label": 1}
+{"snippet": "In Preskill's notes, John Preskill goes as If we scatter a photon off of a periodic array of needles , the photon is likely to be scattered in one of a set of preferred directions , where the Bragg scattering condition is satisfied. and further These preferred directions depend on the spacing between the needles , so by scattering just one photon , we can already collect some useful information about the spacing. How can the analogy with Bragg's diffraction help me understand Simon's problem ?", "label": 1}
+{"snippet": "I'm using Lyx and I have problem with equations. I would like to add label to equation, but somehow I can't add label if formula is in table or float. Ok, I can take them outside and then I can label them. But(!), then I can't move the equations to left. Tried everything. The best would be, if I can keep equations in table, so I can adjust them easily. The result should be same as the last three equations with label. /poor English", "label": 1}
+{"snippet": "When I put my little, cylindrical coffee straw into my coffee, the liquid immediately rises about half a centimeter up the straw without provocation. This is also the amount of coffee that the surface tension of the coffee will allow to stay in the straw when removed from the liquid in the cup. Keep in mind that all the while, the top end of the straw is open. Why does the level of the liquid in the straw insist on being higher than the level of all the liquid in the cup?", "label": 1}
+{"snippet": "I have seen the answers to How can I center text/math inside a list environment. The accepted solution there, however, does not allow me to reference displayed equations. Another solution given there is a \"crude\" solution, requiring me to insert a command in each displayed equation. Is there a way to modify the accepted solution to the above question so that displayed equations can be labelled and then referenced? (My MWE is similar to that presented in answer to linked Q)", "label": 1}
+{"snippet": "For mechanical and structural systems, one can often use the energy as the Lyapunov function. In electrical power systems, some methods have been used to determine Lyapunov functions and one can define feedback loops based on this. For Hamiltonian systems, the Hamiltonian can be taken as the Lyapunov function. However, how does one define the physical meaning of a 'Lyapunov function' in dissipative systems? Say for example, an ecosystem forest growth over centuries with rain and fire as the other variables?", "label": 1}
+{"snippet": "As you know, the option ocgcolorlinks of the hyperref package disables colors of all links presented in a PDF file by printing it from Adobe Reader (and by compiling with e.g. pdflatex); as a result, they are printed in a default color. My questions are: Is it possible to disable not the color, but entire text (of the link), i.e. that it would be completely disappeared on the printed paper? Is it possible to do the same with an arbitrary text (i.e. not with the text of the link) or with an arbitrary figure?", "label": 1}
+{"snippet": "If I have a curvilinear coordinate system and supposing I impose the condition that back transformations to Cartesian coordinate system are not permitted. I perform a rotation of the three axes( say latitude, longitude and a proprietary vertical coordinate) to a rotated system (with new latitude , longitude and vertical coordinate) can we still use Euler angles to define these three rotations ? These three axes are non orthogonal to each other.", "label": 1}
+{"snippet": "The sentiments expressed in the tweets can be as accurate a measure as is found with precedental researches. If I change this sentence into the following ones, which one would be correct? The sentiments expressed in the tweets can be as accurate a measure as the sentiments that is found with precedental researches. The sentiments expressed in the tweets can be as accurate a measure as a measure that is found with precedental researches.", "label": 1}
+{"snippet": "In his text \"On the Application of the Theorem of the Equivalence of Transformations to Interior Work\", Clausius wrote If the cyclical process is not reversible, the equivalence values of the positive and negative transformations are not necessarily equal, but they can only differ in such a way that the positive transformations predominate. Maybe my doubt is related to my inattention on reading the text, but which proposition he made use of in order to assert that the \"net transformation\" is necessarily positive?", "label": 1}
+{"snippet": "I recently read a blog post on literate programming and that tex was written using this paradigm. So I thought it might be a good idea to read the original tex program's source, by Knuth himself (the pascal version) in the literal programming style. However, having downloaded the distribution, I only find the raw file tex.web in the directory, and the tooling available via package managers (ctangle, cweb) only works with C files. So I was wondering whether a PDF file with the literate programming output was available on line, yet an hour of searching online did not yield a result. So: Is there the literate programming output for humans available for the tex processor?", "label": 1}
+{"snippet": "I was solving a practice Physics GRE and there was a question about springs connected in series and parallel. I was too lazy to derive the way the spring constants add in each case. But I knew how capacitances and resistances add when they are connected in series/parallel. So I reasoned that spring constants should behave as capcitances because both springs and capacitors store energy. This line reasoning did give me the correct answer for how spring constants add, but I was just curious if this analogy makes sense, and if it does, how far one can take it. That is, knowing just that two things store energy, what all can you say will be similar for the two things.", "label": 1}
+{"snippet": "Let A be a an infinite set. Let B be a subset of N, where N is the natural number Say there is a one to one correspondent between A and B. However, B is not the whole natural number. B is only a subset of a natural number. Intuitively, this is very clear. N is even \"bigger\" than A. However, how to go from that to actually finding out that there is a one to one correspondence between A and N? Basically I am checking several different definition of countably infinite. One requires a one to one bijection between A and N. The other requires only an injection from A to N. The latter seems to be a weaker requirement.", "label": 1}
+{"snippet": "I took a course in vector analysis this year. It was a two fold course. The first part covered linear algebra and basic euclidean geometry. The second took to more advanced areas such as differential geometry, and the integration theorems. We used vector analysis by Schaum(author: Murray Speigel). I was wondering if there are more books on the subject? Please make sure you state the things covered in the textbooks you mention.", "label": 1}
+{"snippet": "When Studying the phenomenon of precession a classic example installation is this: a wheel spins around the Y axis, gravity applies and the upper part starts spinning around the Z axis. The textbook explained this with angular momentum, looks simple, but it is really weird when I try to think about this in other ways. Usually when i see something start spinning, i think there is an force pushing it, but in this case I can't find such a force. There is a kind of gap in my head, and it really disturbs me. Please help me.", "label": 1}
+{"snippet": "Suppose there is a slanted capillary tube and a fluid rises in it. Why does the fluid rise to the same vertical height as when the tube is perfectly vertical? If I'm right surface tension force balances the weight of the lifted fluid. But in the case of a slanted tube, more fluid will be lifted and thus weight also increases. So why will fluid rise to same height?", "label": 1}
+{"snippet": "Raring definition: very enthusiastic and eager to do something. I want to use rares, as in: He rares himself up, ready to tell her. I'm wanting to use it as in the cited example, meaning he gears himself up, sort of like an instant pep-talk, like readying himself. But it looks as though rares isn't a word for what I need it for. Can I use it like this or not?", "label": 1}
+{"snippet": "I am thinking about possibility to parse LaTeX document. What I really need is to track category codes of symbols. As I understand TeX expands all of macros in his mouth and tracks changes of category codes without executing anything. Is it possible to check if the next token is a macro, collect it unexpanded (together with arguments), execute it and move to next token?", "label": 1}
+{"snippet": "Could anyone clarify to me the following: Lightning gives off high current when it hits a car/vehicle, and since the electrical components of the car is grounded on the chassis, are there possibilities that these high currents can destroy or damage the electrical components,battery, antenna etc through the 'grounding'? what are the 'areas' or 'lightning zones' on my car which have the possibility of getting struck by lightning? My friend says the car is being 'positive' with respect to the ground(Earth) hence the lightning which is mostly negative flash tends to strike the car, How can the car be positive when the entire exterior of the car is mounted on the chassis which is negative?", "label": 1}
+{"snippet": "If we have n gaussians where they have different scale and location parameters -- are they orthogonal to each other? By orthogonal I mean that the inner product is zero -- like it is for two cosine functions that have a different phase. So, by Gaussian I mean the normal function used for it's properties as a function and not as a source of Random variables.", "label": 1}
+{"snippet": "This can also be applied to client-server interactions (which is what I need it for). For example, if you (the client) send data to the server or retrieve data from the server, what is the name of the server in that instance? Or, if the server sends data to the client or the server receives data from the client, what is the name of the client in that instance? Both of these names should be equivalent. Basically, I'm looking for a word (or words) for the other person/entity when the two are connected.", "label": 1}
+{"snippet": "I use Kile on Linux and WinEdt on Windows both with same version of MiKTeX. While using KILE, when I compile \"PDFLaTeX\" , it updates my opend output pdf file and does not close the file. Where as in WinEdt it closes the already opened output pdf file and open it again after compiling. What irriatates me is while it opens the new output and it goes to first page rather than the page (of output pdf file) I edited. :( Any remedy would be appreciated.", "label": 1}
+{"snippet": "There is a company out there that 'prints' magnetic pixels, a.k.a. maxels, into a material. In doing so, they're able to choose the distance of effect of magnetic fields they create, independently of the magnitude of the field, leading to some really interesting properties. Can anyone shed some light upon how theyre able to 'print' a 'maxel' into a material? Here is a good video by Smarter Every Day about this company and their process.", "label": 1}
+{"snippet": "After reading \"Is everyone\" singular or plural?\", I would refrain from asking this question, but the husband of a colleague of mine (English professor, native speaker of British English) stated against it, so I am looking for further enlightenment. He advocates some should be solely used to refer to plural forms. Thus, some non-existent towns is perfectly correct, but some non-existent town should be replaced by a non-existent town Is that true?", "label": 1}
+{"snippet": "Many basic types of physics have ready and obvious everyday applications. For instance, basic electromagnetism vector calculus can give great insights into how something as simple as a bar magnate works. And obviously the more people understand the science the easier it is to apply it. My Question: What are some examples of useful or practical applications of classical electrodynamics and quantum electrodynamics? I'm hoping that by getting some examples it will help me better understand why physicist seek these elaborate tools to describe physical phenomena.", "label": 1}
+{"snippet": "I find it difficult to understand the sentence as shown in the title. Is the card data? Is the card processing? Is the card a method (or style) to process data? I'm Chinese. If I express the sentence with Chinese I'll say The punch card was the main method of data processing back then. NOTE: I'm a programmer and I know what a punch card is. So please don't waste you precious time to explain the punch card.", "label": 1}
+{"snippet": "I understand how to get the vertical (descent speed) of a parachute and its payload, but how could one find the horizontal speed/velocity of this parachute depending on the speed of the wind? (yeah I understand the higher the wind is, the smaller it's influence is as well) I'm having a hard time trying to figure out what the winds influence on a descending balloon is. I know it would push the parachute, but how much would that matter? I know it would push the payload, which trying to figure out a CD for would be rather hard!", "label": 1}
+{"snippet": "I am looking to test some properties of elliptic curves and I would like to have a variety of different families to test. I was wondering if there was, say, a catalogue of the different interesting families of elliptic curves that have been found. Some types of families I am interested in would be: families of high rank, families of a given rank, one-parameter families, or families of even rank. Thank you in advanced.", "label": 1}
+{"snippet": "English is my second language. I heard someone saying \"Now that the right people are telling the vote...\" I wrote down 'telling' but I don't think it was that word. What could that verb be that could sound like 'telling' to mean \"...now that the right people are voting...\"? I'm pretty sure it wasn't \"casting\". Situation is like in the 'survival' show. There are two teams and the loser team was to pick someone to leave. That line is said before they are going into the area to pick each one's 'worst performer' choice.", "label": 1}
+{"snippet": "As the resistance of a circuit goes down, the power increases because the current increases, assuming constant voltage. Why is this? I feel like resistance and current are inversely proportional, so lowering one should just raise the other, and power should stay relatively constant. What is it about power that makes it work like this? Edit: Again, namely I find it confusing that decreasing resistance actually has a net increase in power used. I feel like while the current will increase, it should be countered by the lowered resistance...", "label": 1}
+{"snippet": "This is related to this question:Does the weight of an hourglass change when sands are falling inside? At Brigham Young University, there is a display consisting of a sealed off liter bottle with a sunken sealed off hourglass. When one turns over the bottle, the hourglass floats as the sands flow down. Eventually, the hourglass reaches some transition, and precipitately changes from floating to sinking. It has a sign next to it saying that it's for a fishing lure,and that you should not reveal the answer if you get it. What causes it to change from floating to sinking so quickly?", "label": 1}
+{"snippet": "How do I represent the -ed in witnessed (or any other similar word) phonetically? Is there a reference sheet somewhere for these? I notice that other endings do not get shown in most dictionaries either (for example -es in phrases) I use Word web which has a pronunciation guide for the root of the word, but I can't find anything to write the -ed part phonetically. It does not seem to be on this Wikipedia page. I would prefer the same format as Word web. Many people could probably figure this out for themselves (without a direct reference), but I do not trust myself.", "label": 1}
+{"snippet": "Considering a Science Fiction question, it occured to me that in \"populated\" space, with no atmosphere, you might expect to find more EM interference than on Earth. Basically, if you are outside of an atmosphere, are there issues with using radio as a mass communication method, based on the difficulties with spectrum management when the atmosphere isn't degrading signals? And would there actually be more interference from the radio emissions of celestial bodies once you leave Earth's atmosphere?", "label": 1}
+{"snippet": "I encountered the following two examples: Moreover, the proposed scheme is designed in an ID-based setting and so the necessity for certificates and some related problems are eliminated. Our scheme also achieves setup-freeness and so a user can enjoy the fairness provided by the fair exchange scheme without interacting with the arbitrator for registration. Is this type of construction (and so) correct? Should there be some commas somewhere? Are they not just two independent clauses joined by and so?", "label": 1}
+{"snippet": "What do you call someone who, merely by their presence, gives a morale boost to the people he is responsible for? What about someone who gains power from being supported by their troop? If possible I would like to have word with military connotation, but a more \"civilian\" approach is also interesting. EDIT: Jez gave a lot of interesting examples, but I am also interested in nouns, and all of Jez's example can't be \"translated\" into nouns that easily.", "label": 1}
+{"snippet": "I have some doubts about the usages of that and who. Sometimes I read sentences such as You are someone I love. You are someone who I love. People were asked to describe the qualities they look for in a friend. People were asked to describe the qualities that they look for in a friend. Why are who or that omitted in some of these sentences but not in others?", "label": 1}
+{"snippet": "This question is related to Compiling documents online. I store my LaTeX documents in a git repository on GitHub. Is there a web service which offers a post-commit hook for GitHub which automatically fetches my document and compiles it? For example, ReadTheDocs provides compilation for documentation of Python projects stored in GitHub repositories; the documentation is fetched and compiled after each commit to the repository.", "label": 1}
+{"snippet": "I cannot think of any single word that means a person's life changed for the worse. While there are many phrases, i.e. fallen heroes for good guy turned bad, or take a turn for the worse, turning to the dark side,I cannot think of a single word that describes this phenomenon. An example would be in my subjective opinion, how Lindsey Lohan a child star took drugs as she grew older or Harvey becoming Two-face in Batman. The sentence structure should be: He/She __________. And they would get the idea that their life turned bad or took a change for the worse.", "label": 1}
+{"snippet": "I've started studied eigenvalues and eigenvectors. If there is a transformation T: V->V I can find out a matrix of T with fixed basis and characteristic polynomial of T. With this characteristic polynomial of T, I can find out eigenvalues and eigenvectors Does this mean that this transformation T: V->V has eigenvalues and eigenvectors? And, If there is a transformation T: S->V, S is a subspace of V. then Matrix of T is not square, and therefore I can not find out characteristic polynomial. Does this imply that there exists no eigenvalues and eigenvectors under Transformation from subspace into Space ?", "label": 1}
+{"snippet": "While working on a menial task in front of a clock today I was distracting myself by proving that all three hands only align twice a day. That lead me to wonder how one would deal with more complex problems involving modulo arithmetic. I know several rules for reducing equations involving all sorts of operators from simple addition up through very complex triple integrals and the like. But, I never learned any rules for manipulating the modulo operator. What are valid operations that can be used to reduce equataions involving multiple modulo operators?", "label": 1}
+{"snippet": "Having taken none of the prerequisite rigorous treatments of mathematics during my undergrad years, I feel at a disadvantage to the people in my major what do have that analysis/abstract math background, I always find myself struggling to understand those more rigorous papers that use concepts from real/complex analysis, topology, set theory and the slew of abstract math concepts that you don't typically see in engineering at an undergrad level. What sources are especially good for starting to understand more rigorous math and why are they good? I specifically deal with controls, stability of dynamical systems and probability, so any books that are especially good for those fields are even better.", "label": 1}
+{"snippet": "I remember at more than one university math department there being a set of glass cabinets with a number of physical models of surfaces. They were all algebraic varieties on the reals (of limited degree). I am looking for a reference (online or physical book) for a systematic listing that would show images of these surfaces. I looked at the Mathematica site but it seemed to only have polynomial functions. Is there an online or library reference for these?", "label": 1}
+{"snippet": "I think of mathematical objects as individual things that exist by their own (either abstractly or concretely) and can be represented mathematically. When thinking of subsets, I'm in doubt if they are really mathematical objects because they must be related to something (a set) to exist and be called subsets. If they are not related to anything, they are just sets, mathematical objects for sure. So, are subsets really mathematical objects?", "label": 1}
+{"snippet": "I am learning about the degree of algebraic sets. I know the definition from Wikipedia, but it is not too clear to me what it is. Could someone possibly explain to me exactly what property the degree of an algebraic set does capture, or how I should think about it? PS: This was part of another question of mine, Basic question regarding degrees of algebraic sets, but I thought that maybe it would be better to ask this separately.", "label": 1}
+{"snippet": "You are walking around a circle with an equal number of zeroes and ones on its boundary. Show with induction that there will always be a point you can choose so that if you walk from that point in a clockwise direction, you will always have seen at least as many zeroes as you have ones. So, suppose the P(k) case holds. In the next case, where an extra one and an extra zero is added, I can see that the old path will suffice so long as you will encounter the extra zero before the extra one. But what about in the other situation, if you encounter the extra one before the extra zero?", "label": 1}
+{"snippet": "The four words\"weakness\", \"shortcoming\", \"demerit\" and \"defect\" are four words shared with the similar meanings. In the dictionary, \"weakness\" and \"shortcoming\" have more to do with one's characer, while \"demerit\" and \"defect\" are used in a general sense. However, in this sentence, \"The ___in David's character has hindered him from advancing in his character.\" Why the correct answer was said to be \"defect\" rather than the other three?", "label": 1}
+{"snippet": "Does the word nationalism specifically imply a feeling of kindred superiority in a secular sense? For instance, if country X opposes themselves to country Y based on religious practice or reasons, would we still refer to country X's behavior as nationalism? In this scenario let us assume country X has no issue with a third country where the same religion is practiced as in country Y. What if country X's claim to their homeland is based on a religious belief, would any behaviors which would have been classified as nationalism now be called something else?", "label": 1}
+{"snippet": "My question is about the interact mode in Asymptote. On a OS X terminal, I type asy -v <name-of-file>.asy and go to the interact mode. A window containing the relevant picture shows up. After playing around, I have worked out an appropriate camera position and I would like to use the camera position that the picture is currently set in. Is this possible? In other words, how do I recover some data about the camera position? /p/s/ Although this question is a priori TeX related, the end application I have in mind is inclusion into a document I am writing using LaTeX. :-)", "label": 1}
+{"snippet": "I was searching for information about the original novel \"House of Cards\" and from following site, in the middile of the page, there's sentence which compliment Kevin Spicey as shown below(http://www.michaeldobbs.com/house-of-cards/): He's not only one of the most talented actors of our age but kind, too. I don't think the \"Kind\" here means Spacey's a nice guy, I guess it might imply that he's a good actor of \"man kind\" (our kind)? I couldn't find any sentence with similar structure as an example to support my guess, so please anyone can explan to me the real meaning of the word \"kind\" here, better with some example, thanks.", "label": 1}
+{"snippet": "Commonly seen in physics(and statistics) are the concepts of moments of order zero(mass), one(center of mass), and two(moment of inertia). In statistics a third moment (referred to as skewness) also exists and is used. Actually, mathematically the moment can (of order n) be simplified to an operation in the form of: Once I look at this equation it begs the question: what if n is a ratio. What could be some physical applications of this fractional-order moment?", "label": 1}
+{"snippet": "I will not in any case kick the ball. I will in any case not kick the ball. I in any case will not kick the ball. I will not kick in any case the ball. I think only the fourth one is wrong, and all of the others seem fine to me. Please tell me if there are any wrong ones (and why), because after looking at them for so long, I just lost my sense of English. Also, please tell me if some of them have to be used with commas like below: I, in any case, will not kick the ball.", "label": 1}
+{"snippet": "I have a set A with three elements. I'd like to express another set B in terms of a limited number of elements (two in this example) from set A. In this case I realize that there would be a number of possible B sets, but I'm interested in expressing that B could be any of those sets. Alternatively, set C which is one of the possible B sets. Is this possible, or should I be looking for some other notation than set theory?", "label": 1}
+{"snippet": "I understand the electrons in circuit travel down the path of least resistance, however are electrons attracted by the emission of virtual photons emitted by a source with relatively low electron concentration or positively charged? Thus, relating this to a battery in a circuit, does an anode (in electron-flow notation) emit an electrostatic potential force that attracts electrons, aside from the path of least resistance? I am a bit new to physics, so if my question seems silly or wrong, please explain why.", "label": 1}
+{"snippet": "All these classical ideas are pointless and obsolete today, because in quantum mechanics, the particles are completely different objects, defined by quantum motion of fields, not by the location of classical points (at least not in a causal field picture). The notion of a point particle was replaced by the more subtle notion of a quantum point particle, which has a probability amplitude to be at various places. This quantum point particle can reproduce the quantum field if it is allowed to go backward and forward in time. Ron Maimon That was quoted by Ron Maimon. From this - Can I gather that in reality, particles travel backward and forward in time or, is this just a mathematical expression or model?", "label": 1}
+{"snippet": "While searching for the meaning I got this: Workaround - a method for overcoming a problem or limitation in a program or system. Which means almost the same as \"solution\". So, can we use \"workaround to this\" instead of \"solution to this\" in a sentence? For example, This issue is getting more complicated. I want a workaround to this. Math is not real fun unless you have the workaround to these equations. Is it okay to use this combination in a sentence? Does it hold a different meaning? And what are the other precautions?", "label": 1}
+{"snippet": "Assume that I am advertising that a payment will be asked only if we actually execute a given job right, and I say: \"if we don't do it right, we have been working for free\" \"if we won't do it right, we have been working for free\" \"if we don't do it right, we would have been working for free\" Can you tell me what is the most effective and correct way to express (advertise) the idea (especially the correct choice of verbs), and are the above sentences wrong ?", "label": 1}
+{"snippet": "It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state. Does this claim specifically mean that the entropy of the initial universe was zero? Is zero-entropy state unique for given physical laws? Is it possible that entropy was growing always so that only difference in entropy has physical meaning rather than absolute value? Was there ever negative entropy state?", "label": 1}
+{"snippet": "It is certainly possible to create a mapping between hierarchies and some of the fractals: http://davis.wpi.edu/~matt/courses/fractals/trees.html According to wikipedia it is possible to deviate from the original fractal formula: https://en.wikipedia.org/wiki/Finite_subdivision_rule , so my (not so) educated guess would be that it is possible to write subdivision rules to display any kind of hierarchical data. By some of the non-hierarchical graphs we are lucky, since we can use clustering to make them more or less hierarchical and we can probably use the same rule inside the clusters: https://en.wikipedia.org/wiki/Scale-free_network#Hierarchical_network_model So my question is: Is it possible in theory to use fractals or subdivision rules to display random network data (which I guess cannot be clustered efficiently)?", "label": 1}
+{"snippet": "I saw a lot of usage of machinery, mechanism, to be used with similar meaning as techniques, ways, methods,.... For example, my math teacher said the machinery in the proof of some theorem is not heavy. Mechanism is also used to describe how something works. I have actually been confused if they can mostly be exchangeable. Also are there similar terms that can be used in this kind of scenario? PS: I have asked similar questions before here, but the post got closed. cerberus encouraged me to ask again.", "label": 1}
+{"snippet": "How far apart do scientists estimate was/were the dying star(s) that supplied the elements that comprise our sun, planet, and us? With stars so far apart and expansion of space (as I understand it) carrying things further away still, it would seem to be a low probability occurrence for sufficient quantities of elements blown out from across many light years to accumulate to birth a star system. And another related question, it would seem that when a star went supernova and blew heavier elements in all directions, that would result in mass densities for future star nurseries far away from the dead parent that were much lower than what the parent had, so won't favorable conditions for star births monotonically decrease?", "label": 1}
+{"snippet": "Possible Duplicate: Capitalising a sentence whose first word is explicitly lowercase Should I change the structure of a sentence/add filler words to make sure that the sentence always starts with a capital letter? In programming language documentation, it is common for keywords to appear in titles. Assuming that the keyword is strictly lowercase in the language, how should that keyword be capitalized if it is used as the first word in a title? For example: int int is used to specify an integer type. -- or -- Int int is used to specify an integer type.", "label": 1}
+{"snippet": "I want to describe a recurring situation that happens in the modern day when people craft an email that is \"perfect\" in that person's mind, and they end up re-reading the sent message over and over. Maybe they are re-reading the email because they are satisfied that all the details are covered, or to appreciate the email's conciseness and focus, or even appreciate the tone and word choice. Relish is the closest I've found, but since I'm describing a person who enjoys the written word, I would hope there is a way to phrase it in a way that is more poetic to the situation. E.g. the word or phrase itself should have special meaning, intellectual or otherwise, to writers.", "label": 1}
+{"snippet": "What is \"the thing that, in its simplest form, has a receiver and a button, and we use to open the door when somebody rings the door bell\" called in English? When I'm speaking English I almost always ask somebody to answer the door or I answer the door myself but today I was thinking, what is that \"thing\" exactly called, is it a \"Door Answerer\" or an Intercom? In my native language, it is called 'AiPhone' or 'EF-EF'.", "label": 1}
+{"snippet": "Would it be proper to use a valediction (\"complimentary close\") in a newspaper or magazine message wholly devoted to congratulating the media's readers with the New Year or some other holiday? An example message from the staff of a made-up media: Dear readers! From the bottom of our hearts we... Yours sincerely, Russian Industrial News' editorial staff. Or are valedictions more fit for personal communication? P.S. In Russia, such congratulatory newspaper messages are ended with a no-frills bottom-positioned line like \"Editorial staff of [name of media].\" I became curious whether this would work in an English-language media, or should one add something to embellish the ending.", "label": 1}
+{"snippet": "As you know, graphs can be factorized in their component subgraphs, factors such as eventually semilattices, and so on. I would like to know about the precise nature of the relation that might hold (if any) between such graph decomposition(s) and the (unique) factorization of an integer number in its prime constituents. Is there any known theorem regulating such an alleged relation? Thanks in advance (examples are welcome).", "label": 1}
+{"snippet": "Is there a word that means accessible to all? Possibly starting with \"omni\"? Specifically, to describe information: information that could be accessed by anyone is [omni...] \"Public\" would be a reasonable description, but perhaps there are similar words. The problem is that \"public\" information is not necessarily accessible. Scientific journals are public, but are not necessarily free to access. Books are public, but not everyone can access a library, etc. I suppose it doesn't have to be a specific word. I wanted a convenient term for describing the kind of information that does not currently exist: information that in an ideal world everyone could get to (Edited in response to the many valid comments)", "label": 1}
+{"snippet": "Is there any reference (book/review article etc.) where the physics of heavy ion collisions is overviewed? To be absolutely clear about things, I am looking for a introductory review which covers the physics aspects of the progression through the following stages stable nuclei fireball quark-gluon plasma formation (cooling) hadronization hadron interactions and decay final observable particles (leptons, photons etc.) with special emphasis on parameters like time for these stages, relevant temperatures, particle densities etc. Apparently all the literature I have scanned through talks about bits and parts, a comprehensive big picture is unclear to me largely.", "label": 1}
+{"snippet": "I came across this phrase in school and I became quite confused with whether it should be seen as a personification or not. It may be a collocation but does that mean it can't be a personification? 'Gathering' to me usually entails the getting together of people/ animals (animate) so if it is placed next to something that is inanimate (Storm clouds), do we automatically classify it as a personification?", "label": 1}
+{"snippet": "NASA published a computer generated black hole image. In the image you can clearly see the event horizon and the light of background stars graduating from \"smeared\" to normal. However, between the event horizon and the smeared stars there is an area which looks rather normal. Why is this? If the smear is due to gravitational force, it should start right from the event horizon across the image, and not after some seemingly random distance.", "label": 1}
+{"snippet": "A very basic question of mine: Whenever I read a proof I am able to remember it only for a couple of months. But I really want to remember it for at least one year or so if not more. Is it the natural way or is it that once you read a proof of a theorem you are able to recollect it even after a few years I am feeling quite frustrated in this regard because for an interview in Mathematics the interview committee asks all the basic proofs involved in solving any given problem What should I do? I know that there are many Mathematicians here who are able to share some thoughts on this topic", "label": 1}
+{"snippet": "I'm willing to teach some software for high school students next summer, I have chosen Mathematica. What other scientific software could I teach to high school students? (Matlab and Maple don't offer much if they know Mathematica). Does Microsoft Excel offer anything that will help with the teaching of mathematics? What about middle school students? what should they learn? is Logo suitable for them or for high school students?", "label": 1}
+{"snippet": "Each of the following sets spans a subspace of the complex vector space of all functions from C to C. (Here the scalar field is C, not R.) In each case find a basis for the subspace and prove it is a basis; state the dimension. exp iz; cos z;sin z exp iz; cosh z;sinh z i posted a similar question before, but this is in the Complex field and not real. someone please explain how to prove this?", "label": 1}
+{"snippet": "I was browsing through KHAN Academy videos when I met the one which Explained why SSA is not a Congruency postutate. But I had this Diagram in my Mind(Different from the video) Click Here to see diagram Sorry that I cannot embed the image, as I have insufficient reputation Here AC = PR, BC = QR, ANGLE A = ANGLE P Now I feel that this information is enough to prove the Triangles congruent but my Book has no mention of it. Please Explain", "label": 1}
+{"snippet": "When a person sees the word LaTeX the first time, they are likely to think of a rubber material whose name is simply typed with a weird choice of uppercase letters. This strange name leads to much confusion (even ridiculing) and is thus not the best choice from a branding perspective. Is there a good historical reason why, of all letter combinations you could put in front of TeX, Lamport had to choose La? Because of his own name? In other words, why is it called LaTeX?", "label": 1}
+{"snippet": "Suppose one constructs a dialogue in which a second participant is clearly there just to provide ballast while the first participant (the author) promotes a point of view. You could refer to the second as a stooge, a prop etc. But I'm looking for an adjective, and \"the stoogy guy\" doesn't sound all that learned. (-: A better noun than 'stooge' might lead to a good adjective, but all I really need is the adjective.", "label": 1}
+{"snippet": "I just stumbled over the verb \"to wake\", which according to various sources has two valid forms for the past tense: \"woke\" and \"waked\". Some further research stated, that there seem to be two (Old / Middle) English verbs - one strong, one weak - today's \"wake\" stems from, hence the two forms for past tense: waken, meaning to cease to sleep and wakien, meaning to stay awake, keep watch Now, as there are two origins, I'm wondering: Are there (subtle?) differences in meaning when using \"woke\" or \"waked\" today?", "label": 1}
+{"snippet": "I have a follow up question to this question: Should you use a comma/period after \"Thanks\"/\"Regards\" in email signatures? My question is: when should you add a comma when starting a letter/email with Hello John, It was fun to see ... I am pretty sure that a comma goes after the name, but lately I have seen several people (academics) write Hello, John, It was fun to see ... with a comma after the Hello. I am wondering when a comma there is appropriate. I see this question Where should the comma be placed in the salutation of a letter? but I am wondering about the situation where you have a comma after the name also.", "label": 1}
+{"snippet": "Wiktionary reads: concinnity: The harmonious reinforcement of the various parts of a work of art. Call it corporate social responsibility at work if you wish, but we simply think that under Howard Shultz's inspired and inspiring leadership Starbucks is just a damned well-managed company that has achieved the concinnity that distinguishes companies operating under the nontraditional FoE business model. (Google Book's source) Since I don't have OED access, can anybody say from where this metaphorical usage of the noun 'concinnity' comes? And what is, precisely, its meaning in non-literary contexts? P.S. Considering the relevance of this word in an economics context, I tagged this question by 'economics' tag.", "label": 1}
+{"snippet": "Looking at this page about Bibtex I see that the article entry should be used when the work has been published in a journal or in a magazine. Suppose that I have a small manual/guide, which probably has not been published, but which totally looks like an article (in the classic Latex meaning), then I can't use the article entry in Bibtex because the journal is a mandatory field. What kind of entry should one use in these cases?", "label": 1}
+{"snippet": "Suppose a metal ring is suspended inside a vertical inductor (with an elastic string ) when the circuit is open. When the circuit is closed, does the metal ring tend to jump up or fall down? Why? I tried to check the magnetic polarities. Initially similar polarities seem to be induced on the near sides of the ring and the end of the inductor, like S-S and N-N, so there will be repulsion at both ends. In such a case what should the motion of the metal ring be?", "label": 1}
+{"snippet": "In a text about properties of aerogel I read some interesting facts - clothes with aerogel proved to be impractical, being far too warm to wear. If you isolated a house with aerogel and lit a candle in one of the rooms, after a few days the house would become too hot to live in, just accumulating the candle heat. What properties (thermal mechanics?) of aerogel allow it to be this good a thermal isolator? Would a sealed box made of aerogel work just as well maintaining the temperature of enclosed (solid) items in void - with no air inside the box?", "label": 1}
+{"snippet": "I am writing a text which I will review later again and want to comment out only a part of a line (in between), something like this: Once upon a time, there was %in some galaxy far away% a nice and cute rabbit... When I review it again, I could decide if it is better to include that part or not. Is it possible to do such a thing?", "label": 1}
+{"snippet": "I've just learned a word forbear which means to abstain from something or refrain from something. It was fine until that point, but the moment I learned the meaning of forbearance, I was confused because it had tolerance as its synonym. When forbearance is used to mean tolerance, is it implied that enforcement is what is abstained from? Then, why did it happen? Why did it become to also mean tolerance, not just abstaining from something?", "label": 1}
+{"snippet": "Is it possible to extract any particular ion ( either positive or negative ) from ionized gas ( or plasma ) without spending any kind of energy for doing so. I want to design a system for my weekend project where I can separate out positive and negative ions from an ionized gas container, thus leaving behind only one kind of a charge in the container.", "label": 1}
+{"snippet": "Across the world summer is a season of the year and we all talk about 'the summer' - do you have plans for the summer ? etc. But In America it is often taken to refer to the period of college vacation when students take temporary employment etc. e.g. She did charity work over the summer. This would not imply necessarily the climatic summer season, so much as the college vacation. It is my belief that we do not use summer in this way in Britain, unless we say something like What are you doing over the summer break? Can anyone supply further insight into this different nuance which is placed on what is simply a season of the year?", "label": 1}
+{"snippet": "Let K be the class of all finite groups. Show that it is not a variety (closed under H, S, and P) and therefore not an equational class. It sounds pretty reasonable that K is closed under H and S. I guess you can create some direct product leading to an infinite group then, but why is it so? Shouldn't every direct product of finite groups again be finite? Of course, I have an uncountable amount of finite groups, but still I have to end at some point for my product.. and it should therefore again be finite.", "label": 1}
+{"snippet": "If you have a sealed container partially-filled with water and then flip it upside down, the water will fall to the base under gravity. Would it be possible to increase the internal gas pressure sufficiently to stop this from happening? As in, could you have a gas pressure exert enough force onto the water to keep it from moving? Obviously would need a very strong container etc.", "label": 1}
+{"snippet": "First part: The question is both about the continuity of the water vortex(whirlpool) to vortex in air in time and in space. About continuity in time,does the vortex of the water slowly produce a vortex in the air because the vortex at the surface of the water(circle) causes frictional forces on the air molecules and thus makes them move in a circle(on the boundary of water-air) and because air is a continuous medium it also creates a vortex? Second part: When does a vortex stop?And why(detailed explanation if possible-my knowledge in fluid mechanics go as far as the navier-stokes equations)?", "label": 1}
+{"snippet": "It's just a matter of angle-chasing to show the following: Extend the sides of a convex quadrilateral. Draw the in-circles of the triangles (open or not) defined by an original side and the extended adjacent sides. Their centres are concyclic. Having produced the first cyclic quadrilateral we can iterate the construction. Playing with Geometer's Sketchpad suggests that, if we begin with any even-sided cyclic polygon and perform the same construction, the in-circle centres will always define a cyclic polygon. Am I right? Can anyone prove/disprove the conjecture? By dissecting the polygons into quadrilaterals sharing a vertex we can show that alternate angle sums are equal, a condition sufficient in the case of the quadrilateral itself but I suspect not in the general case.", "label": 1}
+{"snippet": "The usual question and answer seem to be of the form What do you want to be when you grow up? I want to be a singer when I grow up. Should it not be What do you want to be when you have grown up? I want to be a singer when I have grown up. Here we have interpreted grow up as the process at whose end one becomes a singer. Should the first pair be considered correct simply because of its accepted usage, or is there an alternative explanation for this?", "label": 1}
+{"snippet": "I'm looking for a professional-context appropriate synonym for the word \"a lot\", but with the additional expression of \"each contributes only a little\" For example, To fill up that vat you'd need a crapload of tennis balls. Here \"crapload\" implies that each individual tennis ball is actually worthless on it's own. Where the vat is big, \"crapload\" serves to color the sentence. Unfortunately \"crapload\" is unprofessional. \"A lot\" is just colorless. Suggestions?", "label": 1}
+{"snippet": "I'm looking for a phrase like \"transcendental language\", but meaning eloquent rather than other-worldly. In particular, I want to refer to a [literary] sketch as \"_ language\". This sketch is A Gotham Reverie by Fanny Fern, in which a prostitute is referred to [revealed as a prostitute] in very abstract terms, such as \"her name was Magdalen\" (I'm paraphrasing), \"her own unrelenting, unforgiving sex\", etc.", "label": 1}
+{"snippet": "Yet another a part of Circular Staircase, by Mary Rinehart: \"Not out in the hall!\" she gasped; \"Oh, Miss Rachel, not out in the hall!\" trying to hold me back. But I am a large woman and Liddy is small. We got to the door, somehow, and Liddy held a brass andiron, which it was all she could do to lift, let alone brain anybody with. I listened, and, hearing nothing, opened the door a little and peered into the hall. Are any words omitted in the sentence that includes let alone brain anybody with? Something looks missing from this sentence.", "label": 1}
+{"snippet": "It is well known, that a human being can not imagine new colors which are not obtainable by just combining the already known ones (red, green and blue). Actually I can draw parallels to physics and may ask you: Imagine a new physical quantity, which you must not obtain from simply combining any of the already known ones and without using anything you have ever experienced in your live. But how would you find a new physical dimension, which you have never experienced in any way? Wouldn't this be like to imagine a new color? Are we thus somehow bound to never know everything, not because we have too little time or possibilities, but because it literally lies beyond our imagination? insert dramatic music", "label": 1}
+{"snippet": "Please have a look at this sentence: \"Multiple citations of my work during the short time since their publication indicate its quality.\" Here work is referring to many publications. I have a tough time reviewing a statement particularly because of this sentence. Is this sentence grammatically correct? I mean are \"their\" and \"its\" used correctly here? Should it be \"... indicate their quality\"? But that's not right because of work?! How about \"works\"?! The mix of \"their\" and \"its\" is very confusing.", "label": 1}
+{"snippet": "I'm reading a book on description logic and I found white and black squares at the end of some paragraphs. I would think they stand for Q.E.D., but since there are two types used in one book, I believe the black square states for something else. What could it be? Is there some convention for it? (I checked and there is no list with explanation of symbols used in the book).", "label": 1}
+{"snippet": "For rental agencies and companies, the cars owned would be a fleet. Several cars escorting a VIP would be a motorcade. However, what if I want to say: I dislike being the lone driver in an empty stretch of highway, so I may end up speeding to get from the [group of cars] behind me to the [group of cars] in front. Is there a good collective noun that would apply to this situation? Or would it be a matter of choosing a general term, like group, cluster, block etc.", "label": 1}
+{"snippet": "Working with Kirchhoff's rules, I am attempting to device an algorithmic approach to finding the unknowns of the problems, I am of a Computer Science background and I am finding it difficult to identify proper closed loops within the circuit and I am curious if there is a generalized pice of sudo code applicable to these problems, or perhaps a matlab or sympy script available?", "label": 1}
+{"snippet": "Although I feel the answer to the following question is negative, I can't get any precise results neither find anything to read. The question is: Would a complete oracle from some level of arithmetical hierarchy anyhow boost the complexity classes, in terms of complexity? For example, would a P machine with halting problem oracle be able to solve anything from EXPTIME? Or LOGSPACE machine with the same oracle to solve something from PSPACE? Thank you.", "label": 1}
+{"snippet": "This is something that has always bugged me. I am never sure where to place the question mark, or whether to place it at all when the end of the sentence does not finish with a question, or a number of questions from the begining For example: The question nagging me is to what extent can we encapsulate all what we observe in nature into a set of simple computational rules, within which we can leverage our existing knowledge. Should the final full-stop (period) be replaced by a question mark? Or perhaps even the comma?", "label": 1}
+{"snippet": "I'm interested in the size of atoms (extent of the outermost electron cloud), in particular its cross-sectional area and how it scales by increasing Z. (I trust that this won't be affected much by the number of neutrons?) I recognize that for a given atom/ion one can simply look up the data, but I'm interested in a more 'first-principles' kind of view. The distances of electrons in given orbitals is not constant across different atoms, since as the nucleus gains protons the orbitals tend to get crushed somewhat closer I believe. (In fact my final goal will be to determine scattering for charged particles, which is based on much more than the geometry, but I became interested in this particular subproblem apart from that ultimate question.)", "label": 1}
+{"snippet": "Usually when I read about AdS/CFT complementarity as a particular case of the Holographic principle, it suggests that physics evolution on a boundary has a map to physics evolution on the bulk. But what of sort of boundaries does this apply? I've usually seen it applied where the event horizon is the boundary and the outside space is the bulk. But does it hold for imaginary boundaries as well, like the typical Gaussian surfaces one consider to study Maxwell equations as well? If not, what special properties needs to satisfy the boundary so that the holographic principle holds?", "label": 1}
+{"snippet": "Possible Duplicate: Set table position to top My document (book) has text and floats. There is not enough text, so that all floats can be placed before the text finishes. Then pdfLaTeX puts the remaining float right in the middle of an otherwise empty page. This does not look good. Is there a way to position these floats at the top of the page instead in the middle? Placement specifiers are already given [t]. Also combinations of [h,t,!,H] don't help.", "label": 1}
+{"snippet": "Possible Duplicate: What do you call words that look like a negation but are not? I found these poor orphaned words that only exist through the life-giving quality of their affix: feckless, ruthless, unruly, inept, dishevelled, dismayed, disgruntled I'm sure there are more. They have the familiar appearance of antonyms... Antonyms to something that doesn't exist. It's as if they've lost their positive attitude. Do these words have a common name? How did they get this way? They all have standard english affixes with known meaning, so it seems like they should be able to stand on their own. Were the original words lost? Is there a list of these recognized words somewhere?", "label": 1}
+{"snippet": "When my hair gets long I start doing a little flick of my head occasionally to get my hair out of my eyes. This grows into a habit though, and for the first few days after cutting my hair I end up doing to same action. Interestingly enough when I have short hair I feel physical pain. How come the same action hurts when I have short hair, but feels completely natural when my hair is long?", "label": 1}
+{"snippet": "Possible Duplicate: Maxwell's Demon Constant (information-energy equivalence) I was reading: Demonic device converts information to energy : Experiment inspired by a paradox tempts a bead uphill. Its good to see conservation of energy is violated. :) I want to know more about it. What other resources are available (that doesn't involve too much math). Especially, I want to see that beed experiment. Are there any demonstrations available on net? EDIT: I did learn more about maxwell's daemon from this:", "label": 1}
+{"snippet": "Does corona discharge charged insulator? I draw a diagram to make it simpler to understand. Electrons form negative side is accelerated due to electric field and accumulate on insulator surface. Gas on the positive side was ionize giving off electrons and flow to positive terminal. Am I understanding this correctly, When I place plastic sheet between HV terminals and when I remove plastic sheet I got an electric shock, so I think corona discharge might charge plastic sheet.", "label": 1}
+{"snippet": "Possible Duplicate: How to preserve hyperlinks in included pdf? After I merge PDF documents with pdflatex and pdfpages as described here, the URL-s are either broken (PDF files from OpenOffice), or their colorbox is missing (hyperref), or if they span over two lines only the information from the first line is kept (the original PDF was correct). Can this be fixed? Or is it a known issue?", "label": 1}
+{"snippet": "I'm using memoir class to write a novel. As it is widely known, writer comments inside novel characters' dialogues are usually enclosed between long dashes which in turn are written as a triple dash in LaTeX. However I'm experiencing trouble when those long dashes (which always follow or precede a word with no space between) are near a linebreak: breaking word is not hyphenated most of the time and thus the line exceed the break margin. How can this be fixed?", "label": 1}
+{"snippet": "I'm writing a scene in which I wish to describe a typical street beggar - his way of dressing in particular. Check for example such a dude as the one below I could use descriptions such as: snobbish, dirty, bizarre, rugged, barbaric, etc but feel those are not adequate to building a picture of a beggar in the minds of my readers. I want words that would describe a sort of beggar that typically, you'd wish to avoid - one very pitiful, but also repugnant? What words or phrases would you use for such a description?", "label": 1}
+{"snippet": "I just played a game from the start to the end of main story, there are many other challenges in the game left untouched, so I think I can't say 'game completed', can I? I know the following possible candidates 'completed' 'ended' 'walked through' 'cleared'(well, in Japan they use this word) But I'm not satisfied with these ones, what is(are) the right word(s) to describe that I have seen the outro of a game? Thanks in advance.", "label": 1}
+{"snippet": "While it is fairly established that both fast movement and the presence of gravity make time pass slower as compared to a system at rest / free of gravity, does that mean that there is no way for time to pass faster than in vacuum, or does general relativity also have \"faster\" metrics? To be more precise, is there any frame into which one could go for a while, and on returning to vacuum less time would have passed there?", "label": 1}
+{"snippet": "Some of the distant galaxies appear to be receding from us faster than the speed of light due to stretch of the space between us and those galaxies. By an analogy with the ant on a rope paradox, the light emitted from those galaxies can actually reach us. Is it true that, at one point of time, those galaxies suddenly disappear from our view, and then after sufficiently large times (which may be more than the lifetime of the universe), they come into view again? And by the same reasoning, would more previously hidden galaxies will become visible at some time?", "label": 1}
+{"snippet": "Hello I am new to operational research and would like help classify the following transport problem. I have a model which simulates a taxi like service, it a has a range of inputs that can be changed (no. vehicles, starting times, vehicle capacity etc) and then the model spits out a set of outputs (time spent idol, time spent travelling with passengers, time passengers spend waiting) which I apply some kind of associated cost to both the inputs and the outputs. What kind of techniques would you apply to this problem so that I can minimise the total cost? I imagine some algorithm would iteratively run the model and adjust the inputs and measure the outputs to form the data. However this is just my uneducated guess.", "label": 1}
+{"snippet": "I read the \"Catcher in the rye\" and I found it difficult book for not native reader (Compared to for example Steve Jobs biography. There is a lot of guessing what the author means by particular sentence. Context : \"Her mother belonged to the same club we did,\" I said. \"I used to caddy once in a while, just to make some dough. I caddy'd for her mother a couple of times. She went around in about a hundred and seventy, for nine holes.\" I wonder what the main character refer to by : She went around in about a hundred and seventy, for nine holes. Are the numbers refer to numbers in golf? What does : \"Go around\" means here ?", "label": 1}
+{"snippet": "As I understood, we choose to mark the current with arrows going from the plus pole to the minus pole (even though we know that in reality it is the contrary). As I'm looking at electric circuits, I notice that arrows for generators are going from the minus pole to the plus pole, and that for resistors it is the contrary (for the voltage) How do someone determine the direction of voltage arrows in a circuit? Is there a physical reason to choose a direction or the other? If, for example, I choose to use the red notation to mark my circuit, what's the reason behind this? Giving one notation for the generator, how am I supposed to mark my resistor?", "label": 1}
+{"snippet": "When I use the calculator to get the result of this integral I get a decimal number. However, in my calculus book, as shown on the picture, the answer was represented using some trig symbols! Is there is a way to show the same result, but not in decimal only? I want to use symbols like pi or sin to represent my answer. Just like my book. could it be done using the calculator?", "label": 1}
+{"snippet": "There are many different types of fields such as electron field, magnetic field, higgs field, electric field, quarks field etc, my question is do these fields interact directly with each other? Particle can form when the field becomes excited and different particles may interact with each other directly. Electric field and magnetic field are interacting with one another to become photon right? Or photon is the excitation of electromagnetic field which is a standalone field from others?", "label": 1}
+{"snippet": "Certain disciplines, generally called pseudosciences, falsely claim that they make actionable truthful statements about observable objective reality. Examples are astrology, homeopathy, psychiatry. How would you call a sincere practitioner (not a researcher/populariser) of such a discipline? Not \"charlatan\" - the perpetrator is as deluded as the victim. Not \"pseudo-scientist\" - just like a practicing surgeon would not be called a \"scientist\": this term seems to imply \"original contribution\" to the discipline as opposed to simply \"plying the trade\".", "label": 1}
+{"snippet": "Is there strong supporting evidence of discrete electron shells or orbitals surrounding atomic nuclei? I realize the math works out and we have energy frequencies emitted, perhaps even atomic diameter measurements. But these still seem indirect and allow for other possible explanations. Is there direct experimental evidence for these? The orbitals concept is always shown almost as fact, not theory, so wondering what experiments must support such strong conclusions and don't mention any other alternatives?", "label": 1}
+{"snippet": "I'm a pretty bad fellow myself,' the stranger remarked, 'but Macfarlane is the boy - Toddy Macfarlane I call him. Toddy, order your friend another glass.' Or it might be, 'Toddy, you jump up and shut the door.' 'Toddy hates me,' he said again. 'Oh yes, Toddy, you do!' The extract is taken from the Body Snatcher by Robert L. Stevenson. Toddy seems to be just a name, but this word may insinuate another meaning in the above situations. And Macfarlane is the boy, which means he is 'worse' than the speaker?", "label": 1}
+{"snippet": "I was looking for a characterization of the dimension of an nvs using Heine Borel theorem. suppose i have a Compact operator between an Hilbert space and itself, i want to proof that the autospace generated by the eigenvectors associated to one eigenvalues (i'll call it A_L) is finite dimensional. I know from the previous theorems and lemmas that A_L is closed, now my question is: if i show that the orthonormal base of A_L is bounded, precompact therefore compact, is it finite dimension?", "label": 1}
+{"snippet": "I want to compare the time that it takes to slide a particle in a frictionless hypocycloid curve, so time would be given by the arclength divided by the velocity So I need first compute the arclength of the hypocycloid curve, but in general the arclength is given by And by conservation of energy, velocity is given by Substituting in the integral results Solving the indefinite integral results in So now I would just substitute the function y corresponding to the hypocycloid curve Is my reasoning right? Then finally to compare times I would just make a graph of the time functions corresponding to the brachistochrone and the hypocycloid", "label": 1}
+{"snippet": "I know how to prove that the Riemann integral of a function does not change if one point of the function is changed. However, extending that result to a finite set by use of induction is something I have struggled to prove. I just need a hint as to how I should start off the proof. Looking forward to an exchange of ideas. An answer I found for a single point is given below.", "label": 1}
+{"snippet": "Here is a literally-quoted passage from Martyrs in Paradise: Woman of Mass Destruction by Terry Reese Downing: \"How nice of you. And thank you,\" she again was appreciative. \"My pleasure. Go back to rest and sleep. Let me know if you needed something and don't hesitate to wake me up,\" he told her. Is the use of past tense common in these kind of contexts? Does the use of past here get the point across in a less direct way?", "label": 1}
+{"snippet": "I would like to express, in one word, the tendency to concentrate excessively rather than disperse. This is applied in a sentence where I describe a set of data, which has too much focus on one aspect and miss out on other aspects. For this I use the word \"constringences\". The results collected and presented earlier are limited by ambiguities, paradoxes and constringences. However, it seems some dictionaries do not know constringence, while others do. So is it a word or isn't it?", "label": 1}
+{"snippet": "I read the following sentence in a newspaper about a restaurateur's reasons for abolishing tipping: \"Many of the owners other reasons sound like the typical complaints of British tourists, who are perpetually confused by whom to pay and how much.\" \"By\" preceding the use of \"whom\" does not sound right to me. For me the word \"by\" introduces the performer of an action, whereas I always thought \"whom\" refers to an object. This must be good English as it was in reputable newspaper, so can anyone explain how this makes sense?", "label": 1}
+{"snippet": "I'm trying to find a way to describe improving the Signal to Noise ratio of a communication/message succinctly. Using the entire phrase over and over gets clunky. Phrases that are close, but don't have as much of a technical connotation as I would like: \"Tuning\" as in tuning a radio \"Demunge,\" but it implies the message is scrambled, and I think it's programmer jargon anyway", "label": 1}
+{"snippet": "Common phrases are draw drapes or shades, draw a bath (pull water?), draw a conclusion (out of someone) and other uses of pull. Why does draw mean pull? It becomes confusing when something that had a visualizable meaning - pulling drapes across a window - has been extended to something that does not make sense - turning Venetian blinds from the open position to closed position. How did this happen?", "label": 1}
+{"snippet": "Is there an english word fitting the longer description 'the visible part of something as seen right now' or 'the thing as it can be understood as of this time'? The word 'Impression' seems to cover this somewhat, but it has the added baggage of being someones opinion, rather than describing the factual state something has, as well as having a different meaning of being a physical depression of an object on another object. Is there an alternative?", "label": 1}
+{"snippet": "I want to produce two versions of a book, one with footnotes and the other with endnotes. I'm using the endnote package to convert the footnotes to endnotes to produce the second version. But I need to alter the text on the heading and get the headers on each page to look the same for the endnotes as the other chapters in the book. For example, currently the heading says \"Notes\", say I wish to change this to \"Myheading which is underlined\" and then have \"something else\" appear in the headers of the pages on which the endnotes themselves appear. Is there a simple way to do this? Thanks", "label": 1}
+{"snippet": "From a Bibtex file I want to create a References section where each reference has its own abstract. For the abstract, I'm using abstract.bst mentioned in another question. I am using Lyx. When I generate the bookmarks, it only references the start of the References section. This is no good because I want to able to skim the abstracts and also have the document in a printable/shareable form. How do I generate the bookmarks with a bibtex file such that it creates a bookmark for each reference? Also, I don't consider this question Lyx-specific.", "label": 1}
+{"snippet": "Find one possible pair of values for x and y. If x,y and x-y are two-digit numbers. x is a square number, y is a cube number and x-y is a prime number. Is it as easy as I am thinking it is? Or I am trying to complicate things by looking for the equations here. The simplest way I can see is to write down all these two-digit numbers and then choose on possible option. But, is it??", "label": 1}
+{"snippet": "Edited version. If an electrical charge like a lightning bolt seeks ground (think of a lightning's rod's purpose), and if all matter is seeking ground (gravitational pull), and if all energy and all matter are various forms of vibration (electromagnetic spectrum), what is the likelihood that all forms of energy are directly or at least indirectly also seeking ground? I'm just looking for an energy's basic common behaviors with other energy (and matter) Specifically I'm thinking of mechanical (vibrational) energy once it attaches itself to an object. Thanks,", "label": 1}
+{"snippet": "Every algorithm I've found so far begins by computing st numberings, which in turn requires a biconnected graph in order to work with an arbitrary vertex pair (s, t). In the following graph, edges [A, B], [F, G] and [H, I] violate the i < j < k property of an st numbering: https://i.stack.imgur.com/XQmju.png It can obviously be planar, but how is the embedding computed?", "label": 1}
+{"snippet": "Is this double/triple negative grammatically sound? Ordered operations require that space on disk is allocated sequentially, so spatial ordering corresponds to chronology of operations, but actual disk writes need not to be neither atomic nor ordered. Explanation: Words neither and nor emphasize on the fact that both conditions are (independently) allowed to remain unsatisfied, that both are optional. To be more formal, \"need not be atomic and need not be ordered\". But then again, it becomes a concoction of two negations joined by a conjunction.", "label": 1}
+{"snippet": "G is a given sphere in the space. For any line e that has no common point with G, define the line f as the conjugate of e with respect to G if f joins the points of tangency on the two planes tangent to G passing through e. Show that two lines of the space passing G are skew if and only if their conjugates with respect to G are skew.", "label": 1}
+{"snippet": "Let's says there is a fundamental particle: That is so massive that it is a black hole by itself (Compton wavelength < Schwarzschild radius) That carries a conserved quantum number (e.g. charge of an exotic interaction) which no lighter particle carries Would it be able to emit Hawking radiation? If not, does it contradict with the classical arguments (entropy analogy, pair creation at the horizon etc.) regarding the origin of Hawking radiation?", "label": 1}
+{"snippet": "I am a programmer and I am doing a camera simulation, I am stuck in a matter of how to know where arrives every ray of light after traveling through the lens and being refracted. Every point of the object gives an infinite number of rays, but in my simulation I will take five random rays to trace from every point from the object. The rays from one point of the object should also come to one point on the film. How can I know this specific point on the film for each point from the object? Hope to find some help here about this problem.", "label": 1}
+{"snippet": "I'm going to start a degree course in physics next year. So far in high school I covered some physics without calculus. I know that I will start everything from the beginning at university, but I would like to prepare in some ways. Then the question is: what should I do? Should I revise what I studied? Should I go head? Can you suggest (from your experience) what should I do before starting a physics degree course? PS In case you recommend to study some material, can you suggest a book?", "label": 1}
+{"snippet": "There are so many books teaching how to take derivative and integration of a function. I think I'm good enough (enough for me lol) in those parts, my problem is that I can't start solving a question and even don't know where to start (finding or making the correct function or equation, kind of calculus applications in area, volume, etc.) - what should I do? Plus I wanna know if there is a good syntax in calculus; like if I should write constants and variables in a special way (capital, small, etc.), so that my writing is more readable and clean?", "label": 1}
+{"snippet": "This question is quite specific but I am not sure which verb tense I should use when committing/checking in code. If I fix a bug and checking in the code, should I write: Fixes bug on feature A Fixed bug on feature A I always use past tense because the bug was fixed before I check in but it looks a bit strange when I look at file history. Should I use one over the other and why?", "label": 1}
+{"snippet": "I'm writing a short bio of my character who has made a contract with a demon and is now required to do her bidding. He's not necessarily a slave, he still has the freedom to do whatever he likes, I guess it's kind of like a DnD warlock-patron type of relationship where she occasionally has tasks for him to do and he's bound by contract to complete them. The sentence I'm writing is like \"[Character] made a contract with the demon [Demon Name] and is now [word or phrase I can't think of] to her bidding.\" I swear there's just a single word for it (I keep thinking of words like \"vulnerable\" and \"liable\" but they're not really right), not a phrase (though if you can think of one that fits then I might end up using it if I can't figure out the word), and it feels like it's on the tip of my tongue but I can't remember it at all and it's killing me.", "label": 0}
+{"snippet": "Is there a standard, formal or defacto, for what exactly a TeX distribution is and what programs/features need to be supported to be a TeX distribution? I feel like this question has had to have been asked before, and while my searching turned up a number of similar questions none got at the heart of what I was after. For context, I'm trying to understand what TeX and LaTeX are from a software point of view. I've been using TeX/LaTeX for years via the pdflatex command or indirectly via pandoc but I've never really had a good feeling for what, exactly, I'm installing when I install a TeX distribution. For example, right now on my Mac I have a pdflatex command that's located at /Library/TeX/texbin/pdflatex and the /Library/TeX/texbin/ folder has a few hundred binaries in it. So is a TeX distribution just folks deciding which of these programs to make available? Or is there more to it than that? Put another way: If I wanted to create a new nominal TeX distribution (which, trust me, I don't) what exactly would I be doing/have to do? I realize this is a pretty big question with answers that could have varying levels of detail. If the answer is RTFM that's legit -- but I'd appreciate a pointer to which part of which manual I want to be reading.", "label": 0}
+{"snippet": "I'm feeling kind of stumped on this, even though I think I know the answer. If I had written this sentence, I would just rephrase it to avoid the issue, but I came across it and found myself wondering. The sentence: \"All that stuff like cars and planes is releasing carbon dioxide.\" At first glance, it seemed wrong and I immediately thought it should be using \"are\" instead of \"is\". But then I stopped and thought about it and realized that it's likely correct, since the sentence would be \"All that stuff is releasing carbon dioxide\", which is correct, if I took out the examples. It just sounds really awkward and wrong the way it is. Is there any grammatical rule that would justify using \"are\" in this context? Would it make a difference if the list was longer, like if the sentence was \"All that stuff like cars, planes, and factories is/are releasing carbon dioxide\"? Or is just a correct grammatical sentence that sounds bad?", "label": 0}
+{"snippet": "My question: What is Happening During Particle Collisions if Particle Location is Defined by a Wave Function? From my understanding, we can define particle location by a probabilistic wave function from Schrodinger's equation. So the particle doesn't exist in one exact spot naturally. So what actually happens then when two particles \"collide\" (which does seem to imply a single location of contact, at least in classical mechanics)? My guess would be it counts as being \"measured\" and the wave function collapses to a single location for each particle, but I'm unsure what interaction between the particles would cause it to count as a \"measurement\" (measurement might be the wrong word but I don't know a more generic term for this). Maybe I'm not fully grasping wave-particle duality here in this specific case. Any help would be appreciated.", "label": 0}
+{"snippet": "I would like to buy a book to study multivariable calculus. Currently, the texts I have in mind are: Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach by Hubbard & Hubbard Multivariable Calculus with Applications by Lax & Terrell Functions of Several Real Variables by Moskowitz & Paliogiannis I want a book that has a clear expositions of the subjects of multivariable calculus. Also, I would like a book that avoids leaving proofs as excercises to the reader, or at least that does not do it most of the time. If possible, a book that also contains multiple examples/exercises with (fully) detailed explanations/solutions to at least some of the examples/exercises. I do not mind a rigorous approach to the subject as long as the content is explained with detail. Which of the books mentioned above fits best the description? Also, if you have other books in mind, feel free to recommend them as well. Thanks in advance! Note: I have taken two proof-based calculus classes and one proof-based linear algebra class.", "label": 0}
+{"snippet": "I always assumed that the word censorious meant someone or something that is given to censorship. Like if you say that a community, an organization, or a person is overly-censorious, that means they frequently or unnecessarily censor content. But I just looked up the word in my favorite dictionary and found that censorious has a different meaning than what I thought: censorious Addicted to censure and scolding; apt to blame or condemn; severe in making remarks on others, or on their writings or manners. Implying or expressing censure. So, a censorious person is not a person who is quick to censor. Too bad, because I thought that was a useful word! Is there an actual word that means \"being given to excessive censorship\"? Example: I might criticize a film distributor as being _____ because they often censor controversial content whenever they release a new edition of a classic film.", "label": 0}
+{"snippet": "Everything I can find says that time dilation approaches infinity at the event horizon of a black hole. Black holes evaporate over a finite amount of time. Wouldn't this imply that somebody falling into a black hole would eventually just see the event horizon shrink away from them as fast as they fall into it. This seems to imply that its impossible for anything to fall past the event horizon, everything just gets very close to the event horizon and then the black hole evaporates from underneath them. Ive read through as many posts as I could find addressing this. The most direct one being this one: https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html In all the posts that claim to have a definite answer I don't understand it. And all the posts I feel like I understand don't claim a definite answer.", "label": 0}
+{"snippet": "In the Wikipedia page for the Ising Model it is written without citations: One of Democritus' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in materials[citation needed], as when ice melts to water or water turns to steam. My question is: Is this statement historically accurate? If so, did Democritus have an argument or explained his intuition on how exactly atoms explain sharp phase transitions? A related question, would be how this relates to a a modern statistical mechanics viewpoint and If one really needs an atomistic description: From a continuous model of matter like a classical field theory, could one arrive at a first order phase transition from first principles? I know you could just 'artificially' impose a phase transition, but I'm thinking of a procedure like taking the large-scale limit of a classical field theory and arriving at a new theory with phase transitions.", "label": 0}
+{"snippet": "I am working on TeXmaker and all of the sudden this message popped up (this problem occured after closing and re-opening the program and the code is correct, there i no error inside of it). I tried to run the same code on TeXstudio but it gave me the same problem. I tried to search everywhere in the internet to see if there was a similar cases, but all of theme were useless or not exactly like mine. I get the same message also for older files and new ones. This makes me guess that this is a problem of MiKTeX since it doesn't compile neither on TexMaker and TeXstudio. I tried to use the command prompt as suggested on reddit (I wrote \"pdflatex filename\"), but I really don't know how to exploit this feature. Do you have any idea of what could cause this problem?", "label": 0}
+{"snippet": "I am learning about EM waves and am getting confused. Here is a picture from an intro. textbook I am using. Looking at this, it is clear that both E and B are perpendicular to the direction of motion, and all is fine. However, let's say the wave was propagating at an angle theta to the z axis. In this case, you can still draw the E and B field perpendicular to the direction of motion (with E in the same plane as the direction of motion and B perpendicular to the plane of motion as in the picture), but now there would be a component of the E field that is in the direction of z, even though the E field is still perpendicular. In this case, why wouldn't the EM wave propagate with this longitude component? What am I missing here? Here's a crappy picture of what I mean: In the picture you see that the wave is propagating in a direction with a non-zero x and z component and clearly the E field also has nonzero components in the x and z direction, so wouldn't these components be \"longitudinal waves\" as they are propagating in the direction of motion?", "label": 0}
+{"snippet": "Most explanations of the integer quantum Hall effect start out in the grand canonical ensemble, where the plateaus arise when the chemical potential (or equivalently the Fermi energy) is in the gaps between the Landau levels. However, they then usually continue with a statement that working at fixed chemical potential is actually imprecise as the system is in a canonical ensemble (i.e. fixed particle number,) and so we need to include disorder to get the plateaus. While I understand why disorder is needed if we work at fixed particle number, I don't understand why the experimental systems are assumed to be in the canonical ensemble to begin with. Don't electrons flow in/out of the material when you measure resistivity? If this is the case, why is working in the canonical ensemble justified?", "label": 0}
+{"snippet": "In set theory, the notions of set and membership are considered primitive. We only specify some of the properties that we think our primitive notions have using the axioms. Usually, the very first axiom of set theory is the axiom of extensionality which specifies that two sets are equal if and only if they have the same members. My discomfort with specifying this axiom as the first is that we haven't said anything about how the notion of membership relates to the notion of set in any previous axiom. That is we haven't specified that it makes sense to say something is a member of a set. Yet we use this notion in the axiom of extensionality. Why we don't have an axiom that exclusively talks about the membership of things in a set?", "label": 0}
+{"snippet": "I have been searching for an automatic method (a computer program) to evaluate any first-order logic (FOL) formula given some knowledge base. The most common approach to do this is to use PROLOG. The issue with PROLOG is that it employs a subset of FOL which, for example, restricts the use of quantifiers. When searching about this, I have learned that PROLOG uses the resolution algorithm, which requires formulae to be in Conjunctive Normal Form (CNF). I have also learned that there is a process called Skolemnization that can be used to remove the quantifiers from a formula and help convert it into CNF. Therefore, my question is the following: Can the resolution algorithm be applied to any FOL formula? By this, I mean if there exists some algorithm that takes as input any FOL formula and normalizes it (using skolemnization and other methods) into CNF so that resolution can be applied to it?", "label": 0}
+{"snippet": "To \"empathize\" with someone means to \"understand and share the feelings of another\" (Oxford dictionary). In science fiction, an \"empath\" is \"a person with the paranormal ability to perceive the mental or emotional state of another individual.\" (Oxford dictionary) Is there a word to describe the \"opposite\" (behaviour in nature, not antonym) of an \"empath\" - someone who can communicate in such a manner that it is very easy to empathize with them because you can easily understand or recognize the feelings behind what they are saying? More details: As pointed out above, an \"empath\" has the ability to perceive the mental or emotional state of another individual. I am seeking a word (if it exists) that describes the ability to communicate in such a manner as to \"create a mental or emotional state\" - an emotional connect - to make others more easily relate and empathise with them. (Something that most story tellers do effectively). (Some commenter thinks my question is about Sci Fi. No, I am just looking for a word to describe something in plain English. But it doesn't matter if it is an uncommon and rare word from old English or even a modern slang).", "label": 0}
+{"snippet": "The second law of thermodynamics states that the entropy of the universe increases over time and this has lead to theories like the heat death of the universe and the big rip. What this means in effect is that all matter and energy has an expiration date, beyond which it gets divided accross infinite space and this is irreversable since entropy does not move backwards. The first law of thermodynamics states that energy cannot be created or destroyed. The only explanation this leaves for the universe's existence is that energy has existed since always and never had to be created. And herein lies the contradiction: If energy has been around for an infinite amount of time, why hasn't the heat death or the big rip already taken place? How come we are able to observe the universe in its current fairly organized transitional state unless A. energy was created a finite amount of time ago or B. Energy has existed since always but it can freeze or move backwards entropy-wise allowing us to observe it in its current form. Either way one of the two laws is violated. How do physicists reconcile this paradox?", "label": 0}
+{"snippet": "The other day I wasn't feeling so well so I visited a doctor. He recommended that I take a break and get intravenous therapy so I did. I laid on a bed and the nurse inserted a needle into my left arm which was connected to the pack of liquid containing vitamins. I soon fell asleep. More than half an hour later I woke up. The pack was practically empty. However blood was slowly flowing out of my vein. I frantically called the nurse, who apologized for not catching it earlier. I thought the sole factor that delivers the fluid to my body was gravity, since the pack is hung in the air much higher than my arm. But given that the direction of flow reversed once the pack was emptied, my assumption is probably false. My new theory is that the vitamins are delivered because the pack's pressure is higher than my vein's when there is enough liquid in the pack. However this still doesn't explain why I started losing blood as when the two sides' pressure reaches parity all movement should stop. Since the pack's initial pressure was higher, There should be no change of direction until reaching equilibrium. Why did I lose blood and are there any precautions I can take to prevent this incident in the future?", "label": 0}
+{"snippet": "Many elementary explanations of the Einstein-Lorentz transformation derive it using Einstein's special relativity postulates, combined with some thought experiments considering light sources and observers. However, I have read that these thought experiments often do not hold when subject to rigorous mathematical scrutiny, and that Einstein himself did not use them when making his arguments. Further, it is obvious that Lorentz did not use Einstein's postulates when deriving his transformation because at that time he did not trust in Einstein's postulates. Rather, from what I have read, the actually rigorous way that the transformations were derived is using more complicated math such as hyperbolic geometry. I cannot seem to find a good resource that walks through the derivation in a rigorous way; especially one that does not assume prior knowledge and explains the math being used. Can someone please either provide a rigorous derivation here, or point me to a good resource for me to find it? I am especially interested in learning the approaches of both Einstein and Lorentz.", "label": 0}
+{"snippet": "I have two rectangles of different sizes side by side. I want to scale them both (each maintaining their original aspect ratio) so they each end up with the same height and together equal a specified, fixed width. I would like to find a formula that will work no matter what the sizes of the rectangles are (some may be bigger than the target width, some may be smaller - thus some will have to be scaled up and some down). I found what appears to be a very similar question here, however the only solution provided seemed to imply a universal scaling factor. That doesn't work for my situation because the rectangles need independent scaling. I am also only scaling two rectangles instead of three, and the resulting widths of my rectangles must together add up to a specific width (the other question just didn't want to exceed one). Any help would be incredibly appreciated.", "label": 0}
+{"snippet": "I'm reading Carroll's GR book. I'm able to follow it for the most part, but a couple of paragraphs are a bit hard to decipher: According to the WEP, the gravitational mass of the hydrogen atom is therefore less than the sum of the masses of its constituents; the gravitational field couples to electromagnetism (which holds the atom together) in exactly the right way to make the gravitational mass come out right. What exactly does \"couples to\" mean? Right now that's just a vague phrase to me that implies gravitational field has something to do with EM - but what's the precise notion behind it? Sometimes a distinction is drawn between \"gravitational laws of physics\" and \"nongravitational laws of physics,\" and the EEP is defined to apply only to the latter. Then the Strong Equivalence Principle (SEP) is defined to include all of the laws of physics, gravitational and otherwise. A theory that violated the SEP but not the EEP would be one in which the gravitational binding energy did not contribute equally to the inertial and gravitational mass of a body; thus, for example, test particles with appreciable self-gravity (to the extent that such a concept makes sense) could fall along different trajectories than lighter particles. I have no idea what the statement in bold means at all. Could anyone please explain this so that a layman like me could understand?", "label": 0}
+{"snippet": "As we know, the recent Nobel prize was awarded for the creation of attosecond light pulses. I read this excellent answer, describing both how the pulses are created and what applications they have. I understand how the pulses are created by the addition of waves with harmonic frequencies in a classical sense. However, from a quantum mechanical point of the view, light comes as photons with quantised energy, with the energy of each photon related to its frequency. As the attosecond pulses consist of many frequencies, I wonder how they relate to photons. My guess would be that the attosecond wave describes the probability of detecting a photon at a particular location/time, but that the photon detected can have the energy corresponding to any of the constituent frequencies. Is that a correct guess, or is that too simplistic? When we detect individual photons of the attosecond pulse, what frequencies can they have?", "label": 0}
+{"snippet": "First, let me acknowledge there are numerous posts on this question already. The most pertinent to my specific question is probably this one. To restate the problem: \"A family has two children. Find the probability that both children are girls, given that at least one of the two is a girl who was born in winter.\" The solution offered in the text includes this step: \"use the fact that {both girls, at least one winter girl} is the same event as {both girls, at least one winter child}\". This subtle shift is necessary to reach the correct answer. But it seems to come out of nowhere, right? I wonder if the change was motivated by a desire to be able to invoke independence. Since {both girls} and {at least one is a winter girl} are clearly not independent, while {both girls} and {at least one winter child} are. Hard to get inside the author's head, but that's my best guess. What do you all think?", "label": 0}
+{"snippet": "There are various threads on this site explaining the mathematical details of how, in QFT, position operators are non-relativistic. I can follow some of the math, while some of it goes over my head. But even with the parts of the math I can follow, I have a hard time relating it to anything conceptual -- that is, all the mathematical explanations I've seen have a feel similar to proofs by contradiction in that they show that it's true there are no relativistic position operators, but not why it's true. So, to be clear, what I'm looking for isn't a nonmathematical explanation necessarily, but just an explanation that feels like more than just a bunch of algebraic manipulations -- something that connects all those calculations to the actual objects we're trying to model and their properties. To clarify what specifically I'm confused about, I don't get why bringing in special relativity should mess up the notion of position at all. I understand that position is a relative property, so that if we change reference frames any position operator would be affected. But momentum and energy are also relative, and yet there doesn't seem to be any issue with defining relativistic versions of their operators. What makes position so different that we can't just define it in some given reference frame and apply the Lorentz transform as needed? Does it have something to do with the geometry of spacetime being hyperbolic?", "label": 0}
+{"snippet": "I've read several threads over the past several days talking about how photons don't have wavefunctions in the same way as massive particles do because they don't have non-relativistic limits. If I understood correctly, that's because the usual position operator introduced in introductory QM courses really only applies to non-relativistic theories. The Newton-Wigner operators kept being mentioned as the closest QFT analog to the position operator from non-relativistic QM, so I've been trying to find information on them, but the relevant Wikipedia page is very sparse and vague and everything else I found was very long and technical. All I really want to know is: What's the actual definition of the Newton-Wigner operators? How does it differ from the definition of the position operator from non-relativistic QM? From what little the Wikipedia article did say, I know the Newton-Wigner operators aren't Lorentz covariant, which, if I understand correctly, means they're reference-framed dependent w.r.t. the Lorentz transform. But is that the only difference between them and analogous operator from non-relativistic QM? If so, then why does position in particular often get singled out as being different in relativistic and non-relativistic QM and QFT, when other properties, such as energy and momentum, are also reference frame dependent?", "label": 0}
+{"snippet": "As a caveat, i am not a mathematician but rather a programmer with an amateur interest in patterns, fractals, sequences, data science. That said, i have been following recent developments in aperiodic tiling with interest. I've had an idea for an application for it, but I don't know enough in the field of mathematics to know if: It's obvious, been done, move on It's an interesting idea worth exploring, or It'll never work or be useful, just stop now. The thought is as follows: By definition, aperiodic monotiles don't repeat on the plane, therefore They are effectively a visual representation of an infinite, non repeating sequence. They can be computed relatively easily (e.g. see here), and the next tile can be calculated based on the position of the previous one. Therefore, you effectively have a pseudorandom number sequence, given a seed of the coordinates to start at. Is this worth exploring, or just a rabbit hole leading to a dead end?", "label": 0}
+{"snippet": "Consider a sample of an ideal gas kept in a pouch of some volume. This pouch is then kept in a bigger container of volume V. As soon as we open the pouch then the gas will expand irreversibly in the container. Also consider that this expansion is adiabatic in nature and no energy flows in or out of the container. If we let the system be kept isolated for a sufficient amount of time in which it approximately achieves steady state, then can we say that in this steady state condition every molecule in the gas sample will approximately have the same speed? I thought that the entropy of the system would be maximum in this configuration as the energy is tending to be spread out equally among all molecules. Is this notion of entropy being a measure of the distribution of energy logically correct? Also if it is not correct then is there any mathematical way to find the distribution of the molecular speed of the gas sample?", "label": 0}
+{"snippet": "I would like to know if there are any books on combinatorics and number theory that follow an axiomatic approach akin to that of Sierpinski's General Topology. I have found some books for both subjects that might follow this axiomatic approach but they aren't explicit about it. The books I am referring to are: Aigner's Combinatorial Theory, which one user on Amazon said follows an algebraic approach but I don't know if that is equivalent to an axiomatic approach. Landau's Elementary Number Theory, with the author having written an axiomatic book on Analysis called Foundations of Analysis, which I have a suspicion might be axiomatic. And Sierpinski's Elementary Theory of Numbers by the author I mentioned above with my suspicion being that it also follows an axiomatic approach. I have scoured the internet for such books but to no avail. I haven't found posts on stack exchange that address this question, specifically for number theory and combinatorics, either so I decided to write one myself. I really hope someone here might have found such books. More specifically Brualdi's book on combinatorics states that the multiplication principle is a consequence of the addition principle while Vinogradov's number theory book states that division with remainder is a generalization of the quotient of two integers. I would like the books to follow such an approach, stating what is essential and deriving everything else logically. I don't think I can be any more specific but I hope you get the gist of what I am saying.", "label": 0}
+{"snippet": "This is probably a really common word and I'm having a moment, but it occurred to me the other day that I can't think of the verb that describes the action of sweeping a knife across a pat of butter, which has the effect of scraping butter from the pat onto the knife. It's kind of the opposite of \"spreading\"; i.e., the action to deposit butter from the knife to the bread/toast/whatever. \"Scraping\", I suppose, is close...but it doesn't feel right. Intuitively, I feel like scraping involves a fair amount of effort to remove the surface layer, which is usually hard, contrary to the properties of butter at room temperature. \"Peeling\" or \"paring\", perhaps, but again I'm not convinced: butter doesn't have a peel and paring is more of a cutting action. The artefact of the process is a \"curl of butter\", so maybe \"curling\", but I've never heard that used in this way.", "label": 0}
+{"snippet": "Suppose two particles A and B collide. Consider the position vs time plot of the trajectories of A and B, shown in green and red in the following diagram. The two trajectories \"meet\" at coordinates (x', t') indicating collision, although according to the Pauli exclusion principle, two particles cannot be at the same position at the same time. Now, it is clear that the trajectories A and B are continuous and differentiable, indicating that both A and B have well-defined velocities throughout their trajectories. But now consider trajectory C formed by the part of the trajectory A before collision, and the part of the trajectory B after collision (at the point of collision, assume trajectory C has the value of trajectory A). Trajectory C is shown in blue: My question is this: is trajectory C continuous and differentiable at the point of collision (x', t')? That is, does it have a well-defined velocity at point (x', t')? My own thoughts on this problem so far is that trajectory C is not continuous at (x', t'), because the left-hand limit of trajectory C is the point on A's green trajectory near (x', t'), while the right-hand limit of trajectory C is the point on B's red trajectory near (x', t'). But I want to understand/formalize/prove this more rigorously.", "label": 0}
+{"snippet": "I do understand that we can't experimentally verify anything we imagine about the interior of a black hole. If we were to apply what we know about the physics of the observable universe and assume that those laws remain valid on the other side of an event horizon, then are the following assumptions at least plausible? Anything that falls into a black hole might experience perpetual free-fall, because everything closer to the singularity will experience a much stronger pull than things farther away. The observer, similarly, will experience a constant acceleration away from the event horizon, so objects that cross it after the observer does will always be moving away from them, from their point of view. Objects within the event horizon of a black hole can't interact with our observable universe, but there doesn't (to me) seem to be any reason why they can't interact with each other. So they could clump together in volumes that are small enough where the tidal forces don't rip them apart. In this way, wouldn't the inside of a black hole look like a universe where everything is constantly accelerating away from each other, but in smaller scales can still bind together through all the normal interactions that we observe on \"this side\"? I hope this question doesn't break the rules of stackexchange, and I'm totally ready to have all of the above bullet points torn to shreds.", "label": 0}
+{"snippet": "I've encountered a few possible definitions of a \"connected ring\" and am having some confusion relating them. The first one is defined for any commutative ring: A commutative connected ring has a spectrum which is connected in the Zariski topology. But there is also the concept of a topological ring, where the ring itself (not the spectrum) is endowed with a topology. In this case, it also seems natural to consider a topological ring to be \"connected\" if the the ring itself is a connected topological space (irrespective of the spectrum). My concrete questions are thus: For a commutative topological ring, is there a relationship between \"connectedness\" in the spectrum-sense vs in the ring topology-sense? More broadly, is there any relationship between the topologies on the two spaces? They seem unrelated to me. When I read results on ring theory, I'm often confused whether topological statements refer to the ring itself or the spectrum. Take for example the following: Every compact Hausdorff ring is totally disconnected. I'm assuming here that the ring in question is a topological ring, and \"compact Hausdorff\"-ness is refering to the topological properties of the ring itself. But here, is \"total disconnected\"-ness referring to the ring topology, or to the spectrum topology that results in the definition of a \"connected ring\" above? Am I getting tripped up on overloaded terminology here, or is there some deeper connection that I'm missing? Thanks for the help!", "label": 0}
+{"snippet": "I understand that the state space representation is mathematically equivalent to the transfer function representation for linear systems, and that it allows us to solve the corresponding DE by finding the eigenvalues of a matrix. However, for nonlinear systems, the transfer function can only represent a linear approximation, while the state space form can represent the full system. But what's the advantage of using state space form for nonlinear systems, if we can't generally solve them by matrix methods? How does state space representation help us analyze or design nonlinear control systems any better than we could by sticking with the original DE representation? Some background: My impression was that the state space form of linear systems is essentially just syntactic sugar for the final result of transforming a nth order DE into a system of n first order DE's, and writing that system as a single matrix equation. It \"hides\" the derivatives under the extra parameterization variables. But for nonlinear systems, we can't just get a system of linear equations and write it as a single matrix equation that doesn't explicitly involve derivatives. So I don't see how the state space form simplifies anything for nonlinear systems.", "label": 0}
+{"snippet": "In my school, I learned that when two blocks are placed on the ground with one block above the other, if a force is applied to the lower block, two opposing forces of friction act on it: one from the ground and the other from the upper block's surface. Consequently, according to Newton's third law, the upper block experiences a friction force in the forward direction. However, I have a question regarding this scenario. If the external force applied to the lower block is significantly less than the limiting friction of the ground, the lower block won't be set into motion due to the opposition from the static friction of the ground. In addition, I believe that the static friction of the upper block also plays a role in opposing the motion(as it does when the block do move). Consequently, the upper block should experience an equal and opposite reaction that sets it into motion as well. However, this doesn't seem to happen in reality. What misconception do I have in this situation?", "label": 0}
+{"snippet": "In analyzing Compton scattering we consider the conservation of both energy and momentum. However, in analyzing the photoelectric effect only the conservation of energy is taken into account. In fact, if the momentum of the photon is taken into account there seems to be a violation of the law of conservation of momentum. The momentum of the photon is into the metal but the momentum of the ejected electron is out of the metal i.e. the momentum of the ejected electron has a component opposite to the momentum of the incident photon. A way out would be to argue that the process of ejection is complicated and that it is actually the atom which ejects the electron. There is, however, a problem here. Experiments with linearly polarized x-rays or ultraviolet light show that the electron is always ejected in a direction parallel to the electric vector i.e. perpendicular to the direction of the incident beam of photons. This suggests that it is indeed the photon which ejects the electron, not the atom. Is there an explanation in either quantum mechanics or classical electromagnetism or both?", "label": 0}
+{"snippet": "I'm not sure if this is an appropriate question for here, so fair enough if it gets closed/down-voted. I'm self-studying mathematics, did basic real analysis (Riemann, not Lebesgue integraton) and complex analysis, and I'd like to move on to functional analysis shortly. I have two books: Muscat's Functional Analysis (Universitext), and Axler's Measure, Integration and Real Analysis (GTM). It seems to me that Muscat is rigorous but still lighter (not meant in a bad way) on the maths, but covers more topics than Axler. But Axler spends a lot of time on measure theory (of course) and does also cover the basics of Hilbert spaces and Banach spaces and linear operators on Hilbert spaces. At this moment I'm more inclined to start with Axler, since I suspect after covering Axler I'll have a stronger foundation and more easily pick up on the topics covered in Muscat but not in Axler. Would this be wise? Other recommended books welcome.", "label": 0}
+{"snippet": "I was playing with numbers in my middle school math club and found a beautiful pattern. I presented my idea in front of my club mates. The teacher was impressed with my result and suggested I write a short manuscript and have it published somewhere. I thought it was a great idea so I agreed. It took over six months to get used to latex but I think it was worth it. I had some previous experience with the Lua language so I chose LuaLaTeX for my document. It was a short one page article but I was still satisfied with it. I searched for journals that had writings similar to my skill level. I sent them my LuaLaTeX file and the pdf file resulting from it via email. They reacted positively to the content but asked me to write in plain latex because they do not use LuaLaTeX. It took a few more weeks to convert to LaTeX. I have never maintained a journal so I didn't know that it wasn't as simple as just ordering the articles in the right order then gluing them together. Will I face similar barriers in high school, university and beyond if I keep using LuaLaTeX and not LaTeX? Are engines that extend beyond LaTeX such as LuaLaTeX and XeLaTeX to be avoided in environments where I do not produce all the content of the publication?", "label": 0}
+{"snippet": "I encountered several times a certain type of sentences (in colloquial contexts) which were clearly grammatically incorrect but seems to be widely spread and, as a non-native English speaker, I would have liked to have more information about that. It is about the conjugation of the modal verb to be. I have heard many times the following type of sentences: \"We was playing basketball\" \"They was eating dinner\" \"I were there\" \"He were with me\" where the last two were used without any conditional of any sort. These sentences are obviously wrong in standard English (as far as I know) but still seem widely used in everyday life conversations. Therefore, my question was the following: How wrong are these grammatical structures ? How strange will I sound if I use them ? Also, is it some kind of dialect/slang and in what kind of context do we use them? Unfortunately I do not have any neat example to provide for I've heard it in an everyday life conversation with my office mates who are from Scotland. (I did not dare to ask them directly as I barely understand when they speak) If someone could provide me more information about them I would be grateful.", "label": 0}
+{"snippet": "Imagine an air hockey table where there is a puck P and a rectangular slab S. Both are free to move as there is zero friction. The slab is at rest in the middle of the table. The puck is moving towards the slab and collides with it in an elastic collision. The puck is not spinning before the collision. As this is a closed system, the total momentum, angular momentum and energy of the system should be preserved. But after the collision the slab will be spinning about its centre of mass, but does that mean the puck will also be spinning in order to conserve the angular momentum of the system? I feel like the elastic (frictionless) collision won't be able to impart any spin on the puck. I understand that the puck and the slab will also change their linear momentum and energy but overall in the system these will be conserved. How would you calculate the velocity vectors and angular velocity for the slab and the puck post-collision? Assume the puck and slab are made of the same uniform-density material and the puck has radius r and the slab side lengths a and b.", "label": 0}
+{"snippet": "I do not feel comfortable with such constructs that contain \"one's work ...ing\" as the following: \"University of British Columbia marine biologist Amanda Vincent has won the prestigious Indianapolis Prize for her work protecting seahorses.\" \"Learn more about her work protecting the rights of women and girls.\" No matter how I feel about it, there is no denying that it is done and it is fairly commonplace, so I am not going to say it is wrong. However, it does not sit well with me. How would you explain this phrase grammatically? Is \"protecting\" a present participle? If so, construct wise, \"her work\" will have to be the subject of \"protecting,\" but meaning wise, it is clearly wrong; the assumed subject is she. The only explanation I can come up with is that this is an idiomatic expression. Maybe \"protecting ...\" is a gerund and it is an appositive to the immediately preceding \"her work\"? Your input will be much appreciated!", "label": 0}
+{"snippet": "I know that we can consider an object as point object, if its size is negligible as compared to distance traveled by it in reasonable amount of time. But in my book Ncert there is questions which asks to determine which of the following are point objects: (a) a railway carriage moving without jerks between two stations. (b) a monkey sitting on top of a man cycling smoothly on a circular track. (c) a spinning cricket ball that turns sharply on hitting the ground. (d) a tumbling beaker that has slipped off the edge of a table It states that (a) and (b) can be considered as point objects but (c) and (d) cannot. Why cannot we consider them as point object if we do not the distance they have travelled and their size?", "label": 0}
+{"snippet": "If we place a conductor between the plates of a capacitor, the conductor reaches an electrostatic equilibrium with the surrounding electric field. At this equilibrium state, the charges within the conductor have redistributed such that the electric field inside the conductor is nullified. Now, what happens if we separate this conductor into two halves, each containing the redistributed charges corresponding to one side of the conductor (meaning we have one half that is positively charged and one half that is negatively charged). We did not take the conductors out of the field. Would there be an electric field between the separated halves of the conductor if we look at the complete system (Capacitor and its field and conductors and their interaction)? My book says there is no field because it would cancel out the external field of the capacitor but I always thought that electric field lines always end on charges, which would not make a superposition possible.", "label": 0}
+{"snippet": "I am working on an English-language online resource. It seems an obvious good idea to allow users to choose a version in British English or American English spelling. However, I've noticed that spell-checkers also provide options such as Canadian English, Australian English, South-African English, Jamaican English, Hong Kong English, and so on. I have always assumed that these variants are all basically British or American, with maybe a few minor details that are different. So my question is: Are any of the other variants of English spelling significantly different from British or American spelling? With significantly different, I mean that they don't just add a number of new words, like \"wee\" or \"bairn\" in Scotland, or French loan-words in Canada, but that basic English words are spelled differently, in the way that e.g. \"colour/color\", \"analyse/analyze\" and \"theatre/theater\" are spelled differently in the UK/USA. (To be clear: I'm only interested in how great the difference is to an outside observer, not how important it is to e.g. a Canadian person to be able to select \"Canadian English\" instead of having to select \"British English\". I'm also not interested in differences in grammar.)", "label": 0}
+{"snippet": "Physicist Grigory Volovik has put forward some ideas about the universe undergoing a topological phase transition (especially in the early stages of the universe). He published a book called \"The Universe in a Helium Droplet\" where he explained his ideas. You can find a brief discussion about it here. In one discussion I had with Mr. Volovik, he mentioned that depending on the type of topological phase transition that could have occurred in the universe, all the fundamental symmetries of the universe (spacetime symmetries, translation symmetries, CPT invariance, internal invariances...) could be all emergent from a more fundamental state without symmetries (like in Holger Nielsen's random dynamics proposal where all symmetries in the universe would be emergent) I asked him if this was all speculation or if there was some truth behind and he replied that although we don't know if the universe actually took this \"path\", we know that this topological phase transition would be possible. But is this true? Would that be possible according to what we currently know about physics (although we don't know if this actually occurred at some point of the universe's history)? Or, on the contrary, we don't even know if these transitions are even possible to begin with?", "label": 0}
+{"snippet": "There are examples in physics in which a simple law results from an immeasurably more complicated set of underlying interactions. Consider Hooke's law, for instance: there is a very simple equation that relates the extension of a spring to the force required to extend it further, yet the underlying physics when considered at the level of the trillions of individual electrons and ions that form the spring is of an entirely different order of complexity. Is it possible that we need to find some new theory to replace quantum mechanics which is as different to quantum mechanics as quantum mechanics is to Hooke's law, or are there any considerations that limit the additional complexity we might encounter in a more fundamental theory. For instance, our current model of reality assumes a set of fundamental particles, and there have been attempts to model the particles as vibration modes of strings. Might it be that strings are themselves composite entities composed of countless smaller parts- in the way that springs are composed of atoms- or do we have firm physical grounds to suppose that there is a fundamental limit to the divisibility of matter which prevents strings, for example, from being composit entities at a much more granular level.", "label": 0}
+{"snippet": "Gravitational waves carry energy. The sticky bead argument shows that this energy can be extracted: https://en.wikipedia.org/wiki/Sticky_bead_argument But Lee Smolin points out that \"In principle, nothing can screen out the force of gravity or stop the propagation of gravitational waves, so nothing can be perfectly isolated. I discovered this important point during my PhD studies. I wanted to model a box that contained gravitational waves bouncing back and forth inside, but my models kept failing, because the gravitational waves passed right through the walls\". Gravitational shielding is considered to be a violation of the equivalence principle and therefore inconsistent with both Newtonian theory and general relativity, and there is no experimental evidence for it. If energy from gravitational waves can be extracted, does this mean that partial gravitational shielding exists?", "label": 0}
+{"snippet": "I read this from Div, Grad, Curl and All That: The second reason for introducing the electrostatic field is more basic. It turns out that all classical electromagnetic theory can be codified in terms of four equations, called Maxwell's equations, which relate fields (electric and magnetic) to each other and to the charges and currents which produce them. Thus, electromagnetism is a field theory and the electric field ultimately plays a role and assumes an importance which far transcends its simple elementary definition as \"force per unit charge\". The first reason was basically about how finding the field first, then finding the net force on a charge due to the net field simplifies calculations, but I don't understand the second reason. What is this fundamental importance of an electric field that the author is referring to? (PS, I am unfamiliar with Maxwell's equations and classical field theory)", "label": 0}
+{"snippet": "I am currently writing the conclusions of my bachelor's thesis on convergence spaces and there are a couple of points I would like to make, but lack the proper references to cite in order to do so. The first point I would like to make is that one of the starting points of General Topology was trying to axiomatize the notion of convergent sequences and hence the notion of a convergence space is much closer to the origins of topology. I recall reading somewhere that the first attempts of defining topological spaces were like that, but I can't find where. The second point is that the category of convergence spaces is much more adequate than Top, because it has exponential objects. I know there is a whole discussion of the importance of having cartesian closed categories of spaces, but I by myself cannot argument that, because my background on category theory is really small. Therefore, I need to cite someone who knows that for a fact and can give reasons why that is. Hopefully I am not breaking any rules by asking two different sources in the same post. I thank gratefully for any answer.", "label": 0}
+{"snippet": "Crossposted on MathOverflow I am an undergraduate mathematics student with a keen interest in pursuing research in the formalization of natural languages (from a more mathematical-logical approach), yet there aren't many resources that provide an overview of this very technical field. I wish to be able to provide myself a general map to navigate this subject more clearly, so I will attempt explain my basic understanding of an overview of the fields that tackle with this subject, and I'd greatly appreciate any correction or addition to my limited insight. From my understanding, (loosely speaking) there are two prominent mathematical-logical approaches in formalizing natural languages: Categorial Grammar and Montague Semantics. While Categorial Grammar uses methods borrowed from category theory to (mainly) study the syntax of natural languages, Montague Semantics, as the name might suggest, (mainly) focuses on the semantics of natural languages by implementing methods from Lambda Calculus. In terms of subareas of each of these two fields, I have not seen much discussed in terms of the subareas of Montague Semantics; however, Categorial Grammar seems ripe with subareas (although I have heard some of the fields mentioned below are only closely related to Categorial Grammar rather than being a strict subfield of it): Combinatory Categorial Grammar Lambek Calculus Type-Logical Grammar Pre-Group Grammar Proof-Theoretic Semantics In addition to any corrections or additions, I would greatly appreciate any suggestions for resources, references or books that deal with these subjects or their prerequisites", "label": 0}
+{"snippet": "It seems that there are many terms in linear algebra that have multiple names. For example, unitary and orthogonal both refer to the same general idea, a Hermitian is essentially a self-adjoint matrix, invertible and nonsingular, and there are definitely more that I can't think of off the top of my head. I've noticed that I've seen terms like orthogonal and self-adjoint in more classes/texts that feel like they consider linear algebra from a more abstract algebraic perspective, while I've seen terms like unitary and Hermitian in physics and more applied settings. I was wondering if there was some kind of history behind these terms? Why do we have multiple terms for the same thing? Is it just a coincidence that I've seen Hermitian and unitary in these kinds of settings, or was the subject simply considered with different motivations by different people studying different things? If this is the case, I would love it if anyone could suggest references for where these terms originated, and also if there are multiple motivations/perspectives for linear algebra, are there any references for the origins of these different motivations/perspectives? I recall one of my physics professors mentioning briefly that mathematicians and physicists had independently developed the same theory only to realize later that they had been working on the same thing all along. Is there anywhere I could learn more about that history? And are there fields other than linear algebra where this has happened?", "label": 0}
+{"snippet": "I'm a current MA student doing research in formal semantics, which is an application of, among other things, logic and model theory to the study of the semantics of natural languages. I'd like to build up a stronger foundation in formal logic before tackling other topics / projects. I love the interplay between logic, algebra, and topology. Model theory is very interesting to me, and I'm keen to learn more on that. I'm keen on extensions of first-order logic, as well (higher order logic, modal logic, etc). I also have Formal Semantics and Logic, by van Fraassen, and I'd like that text to be more accessible to me. There's so many introductory texts to logic, and a lot of them seem to spend time on things like deductive systems and such, which I'm not very interested in. Given the somewhat eclectic list I gave above, are there any logic texts that would be a good match?", "label": 0}
+{"snippet": "I have a conceptual question about graphs which I couldn't find the answer to. I am calculating some node centralities and using them as features for a machine learning problem. I am using Networkx python library. I noticed that for the degree centrality the library does the weighting of the values by the highest possible number of connections. In other words, the degree centrality of a node is defined by the number of connections the node has divided by the number of nodes in the graph minus one. Although, from graph theory literature, the degree centrality of a node is simply counting the number of edges a node has. As far as I understand. I wonder what is the implications of this weighting of the values by the library? Doesn't it completely changes the concept of the degree centrality?", "label": 0}
+{"snippet": "I'm currently writing my master thesis on \"Differentiable Stacks\". I'm really fascinated by the idea of generalizing manifolds to include also orbifolds/leaf spaces of foliations/moduli spaces... I formally understand the construction of differentiable stacks as stacks on the category of smooth manifolds possessing a representable epimorphism. And I formally understand why they generalize smooth manifolds. What I'm having some trouble to get is: how does one come up with such a definition? I really read many sources on the topic and none of them justifies the choice of such a definition for differentiable stacks (I mean the existence of a representable epimorphism aka an atlas). This \"intuition problem\" is getting better as I familiarize more with this object but I feel like I'm just \"getting used to it\". I'd like to know how this object was born and what's the idea behind it.", "label": 0}
+{"snippet": "According the classical physics, the electron should radiate energy and fall to the nucleus in a short period of time. However, this was not the case. Hence, Bohr proposed his theory, suggesting that electrons existed in specific orbits, where they did not radiate energy. These orbits had quantised or discrete energies. Moving between these orbitals meant the emission of specific amounts of energy, emission of photons. However what was so revolutionary behind this idea? It seems to me, he solved this radiation problem, by simply stating that it didn't happen, \"electrons exist in specific obrits, where they don't radiate energy\". Did Bohr know why this actually happened or did he just state it? Currently, I am struggling to understand what was so revolutionary about Bohr's contribution to the previous nuclear model of the atom.", "label": 0}
+{"snippet": "There was an open dump yard a few miles away from where I used to live for an internship. It was not noticeable during the daytime, but once the sun sets, the dump yard reminded us of its presence through its stinking odor. The smell came every evening and left the following day as if on a schedule, and my colleagues shared the same experience. One of my friends said it might be because of the temperature, but that didn't make sense. Smells, or the gases that cause those smells, travel faster at higher temperatures, which is why food has a more intense smell when served hot, as opposed to when taken out of a fridge. That would mean that we would get the smell during the day, and not during the night, which is the exact opposite of what is happening in reality. What might be the reason then, why we can smell the dump yard at night, and not during the day? P.S: There is no activity going on in the dump yard, apart from people throwing garbage during random intervals throughout the day. It used to be a barren land, and at some point in history became the nucleation site of the garbage of an entire city.", "label": 0}
+{"snippet": "We know that Carleman's condition is a sufficient condition for the determinacy of Hamburger moment problem and the Stieltje's moment problem. The first one look at measures on the real line, and the second one look at measures on the positive side of the real line. There is a third problem called Hausdorff moment problem that looks at measures on the bounded interval. The interesting thing about this problem is that if the measure that fits moments exists, it is also unique. My question: Is Carleman's condition also sufficient for the determinacy of the Hausdorff moment problem? I figure that it should be since Hausdorff moment problem looks at smaller set of distribution than the Hamburger moment problem. I looked around but I couldn't really find this anywhere. I just want to makesure that I am not missing something subtle.", "label": 0}
+{"snippet": "I am simulating a simple Lennard-Jones fluid confined between two fixed walls and I am analyzing the autocorrelation function of the velocity along the direction of the confinement (normal to the walls). I observe an exponential like decay which is in line with the rough expectation, but in addition I observe periodic peaks. These peaks turn out to be the sound modes reflected back and forth between the two walls, as the time between the peaks increases when I increase the walls distance. And when I calculate the sound velocity for my system, it turns out to be equal to the walls distance divided by the time between the peaks. Now I know about the sound mode, I am not satisfied with just having the velocity autocorrelation for looking at the sound modes. I would like to visualize the mode with more geometric features such as the velocity field, as I expect rich structures. Of course the problem is that in such equilibrium simulations a snapshot of the particle velocities is just a random pattern, so some kind of averaging over the particle trajectories and velocities should involved to make the sound mode visible. Any suggestion ?", "label": 0}
+{"snippet": "\"Weed\" (the annoying plant you don't want in your garden) and \"weed\" (the psychoactive drug) are treated differently grammatically. Just some example sentences \"There are weeds in my garden\" vs \"There is weed in my garden\" \"There is a weed growing in this pot\" vs \"There is weed growing in this pot\" \"How many weeds are growing there\" vs \"How much weed is growing there\" \"I'm going to get rid of twice the weeds\" vs \"I'm going to get rid of twice the weed\" \"Here are two types of weeds\" vs \"Here are two types of weed\" Basically, the two words are treated completely different grammatically. I was wondering how in particular the two words are categorized that links to their different treatment. (e.g. maybe one is a proper noun, and the other is not [I know that's not the case, but it's just an example of the kind of answer I'm looking for]). Or is this just some weird slang thing that only applies to the drug \"weed\"? P.S.: I swear I'm not high while asking this question >.<. The impetus was actually because an anime brought up \"happa\", which could either mean \"leaf\" or \"weed\" in Japanese, and I wasn't sure which they were referring to. And then I got down this line of thinking >.<.", "label": 0}
+{"snippet": "I just thought of this question, and a quick wiki search did not turn up anything. So, here is the question: Rel is the category whose objects are sets, and whose morphisms are binary relations. Is there a way to differentiate between morphisms that are functions and morphisms that aren't using purely category theoretical means (that is, not using the set structure whatsoever). Followup question: If the answer turns out to be yes, let's call a generic morphism that follows the definition an f-morphism (for function). What are the f-morphisms in other, more commonly used categories, like Set, Top, Grp, Ring, etc.? What are the co-f-morphisms (i.e. morphisms defined dually to f-morphisms)? Note that I have not yet given the question serious thought, so it may be extremely difficult or extremely easy to answer.", "label": 0}
+{"snippet": "I'm currently working on a variant of a non-convex low-rank matrix completion algorithm, whereby we take a uniform sample of entries in a (symmetric) matrix and look to complete said matrix. For various reasons, we're interested in trying to reduce the bandwidth of our matrix initialization for our algorithm, and our first idea was using the reverse Cuthill-McKee algorithm to do this (mostly just because it's pre-built in matlab). However, the output structure of the Cuthill-McKee algorithm provides a poor initialization for our algorithm. I'm mostly just curious if there are other bandwidth reducing algorithms that people use regularly. I did a brief literature search and found some papers using neural networks to try and learn permutations to decrease the bandwidth, which looks interesting but is more work than I think is worth for this particular problem.", "label": 0}
+{"snippet": "In some linguistics papers that I have been reading, it has been argued that a false sentence has the same semantic status as a noun phrase that fails to refer. A classic example of an English noun phrase that fails to refer would be the present King of France, if uttered today. This is because, of course, France has no monarchy any more. However, one of the examples discussed by several papers is the highest prime number. Now, intuitively it seems to me, even as a lay non-mathematician, that there are obviously an infinitely large number of prime numbers. But that's just my intuition. My intuition as a schookid would have been that it would be easy to predict which numbers were going to be prime and which weren't. So much for intuition then. Do we know that there are an infinitely large number of prime numbers? Is it possible to explain how we know (or don't) to a non-mathematician like me?", "label": 0}
+{"snippet": "It's commonly stated in the literature that the free distance of a convolutional code is the minimum Hamming distance between the all-zero path and any other (non-all-zero) path in the trellis originating in the zero state and ending in the zero state. (The free distance of a code is defined as the minimum Hamming distance between any two distinct codewords.) My question: Is this true in general? Or is it true only conditionally (e.g. when we assume that the code is terminated in the zero state)? If it's the latter, what's the condition for it to be true? It appears to me that a sufficient condition is that the convolutional code is a linear block code. This includes the finite length \"zero-tail\" codes and \"direct truncation\" codes. The former refers to codes which include all paths that end in the zero state; the latter means the codes allow the paths to terminate in all possible states. Am I mistaken?", "label": 0}
+{"snippet": "I have a setup consisting of two lidar sensors with a known extrinsic calibration. Both lidars have messages with the same timestamps (no timedelay between them). My goal is to estimate odometry using the data from these lidars. To achieve this, I have performed a scan-matching algorithm (ICP) and obtained transformation matrices between the consecutive pointclouds. However, I'm facing difficulties in transferring the translation and rotation frames from one lidar to another to put into some filter. The lidars are mounted on a level arm and do not have the same translation due to the Euler rigid body equation. I would greatly appreciate your assistance in understanding how to appropriately transfer the translation and rotation frames between the lidars. Any insights, suggestions, or code examples would be highly valuable. Thank you in advance for your help!", "label": 0}
+{"snippet": "I'd like track my LaTeX projects using git, especially when collaborating with other authors. I'd also like to track my texmf directory in a separate git repository. My desire is to add my texmf repository as a git submodule to each LaTeX project. However, I can't figure out how to tell latexmk (really, pdflatex) to see my project-local texmf. Ultimately, I want my LaTeX projects to be standalone, i.e. they depend on nothing other a TeX Live install and the files in the project directory so they can seamlessly be compiled on different machines or in a CI pipeline. How can this be done? Note: I have tried the solutions presented in similar questions, e.g. here (the TEXMFHOME environment variable seems to be ignored) and here (requires updating system texmf.cnf), to no success so far.", "label": 0}
+{"snippet": "I have a relatively strong background in the theory of numerical analysis of partial differential equations (PDEs) and functional analysis, particularly applied to the numerical analysis of PDEs using the finite element method. I'm also very interested in graph theory. I was wondering if there are any theories or research areas that unify these fields and that I could explore given my background. Are there any connections between graph theory, functional analysis, and numerical analysis of PDEs that I should be aware of? I am aware that there is another question about this, but I am interested in it being in the context of PDEs and numerical methods. Also I am looking for open questions to initiate a research project, so I am seeking topics where the intersection is significant and there are open problems. Thank you in advance for your assistance.", "label": 0}
+{"snippet": "In Borevich & Shafarevich's Number Theory, the authors define integral equivalence of quadratic forms as follows: Two forms of the same degree with rational coefficients are called integrally equivalent if each can be obtained from the other by a linear change of variables with rational integer coefficients. They further state a second definition In the case of forms which depend on the same number of variables, this is equivalent to saying that one of the forms can be transformed into the other by a linear change of variables with unimodular matrix. But I cannot see how to prove the equivalence of the two definitions. Specifically, it seems to me that to show the first definition implies the second, one has to prove that the two linear changes in the first definition are inverse of each other, or that both changes are nonsingular. Can anyone help? edit: Mr. Stucky's example in the comments has shown that the two changes occurred in the first definition need not be invertible. But still, I think to prove that the first definition implies the second, one has to show the existence of two nonsingular changes, as is pointed out by Stucky.", "label": 0}
+{"snippet": "Here is the sentence in dispute: In humans, the femoral angle shows no correlation with femoral length. The question: why would 'femoral angle' receive a definite article, but not 'femoral length'? I feel like it does, but my co-author says no. I can't really justify it, but I feel like 'angle' somehow needs the article whereas 'length' does not. Thoughts? Thanks for all the answers. Yes, I am aware the anatomy may be esoteric, and apologies for that. In this case, the angle is measured in degrees, or fractions (in decimal) of degrees. The length is similarly measured in centimeters or fractions (in decimals) of centimeters. (And there really is only one of each on a person's leg.) So while I felt like angle requires a definite article because of the way I have always seen it used, in this case I can't logically defend the difference between angle and length.", "label": 0}
+{"snippet": "In Reed-Solomon codes, the symbols of a code word contains multiple bits. Since the error correction and detection happens at the symbol level, it doesn't matter how many errors there are within the same symbol, it only counts as a single symbol error. Because of this, Reed Solomon codes are considered to be a great candidate for transmissions that are subject to burst errors. On the other hand, BCH codes are always considered to be a good candidate for random errors. But is that also true in an apples to apples comparison where you compare total number of message and parity bits (not symbols!) are the same for a Reed-Solomon code and a BCH code? Would there be any way in which the BCH would lose against the RS code in terms of error correcting capability?", "label": 0}
+{"snippet": "I'm a graduate aerospace engineering who's really interested in the topic of numerical methods and in particular for structure preserving schemes. Hopefully at September I will start a phd in this subject, as a consequence of my work of thesis. However, I do feel my mathematical background is kinda poor, coming from an aerospace engineering master degree. Indeed, I'm already excited to follow some of the courses I will in my phd courses about advanced linear algebra and functional analysis. During the summer I have some spare time, and I would love to study some of the books I encountered during my work of thesis. In particular \"Geometric Numerical Integration\" by Hairer et al. As soon as I started reading this book I encountered some mathematical topics that I never encountered during my degree courses: Lie algebra, Lie groups (groups in general) and manifold. I would like to know what are the books you suggest to get into these topics. I saw that \"Lie Groups, Lie Algebras, and Representations\" by Brian C. Hall is a really good book as a starting point for this topic, but I know there's a more general introduction to lie groups which is related to manifolds. So which books do you suggest to introduce me to these topics ? Also, I would like to refresh some knowledge about the algebra courses I did in the past, but I don't really know which book I should refer to. Thank you so much for your help.", "label": 0}
+{"snippet": "I was going through the derivation of a mathematical equation for the upthrust exerted on a body which is given in my book. It says that the downward pressure exerted on the upper surface is less than the upward pressure on the lower surface. Thus, there is a net pressure acting in the upward direction and therefore, a net upward force. The lateral pressure gets counterbalanced. I am able to understand that the pressure in the downward direction is due to gravity and the lateral pressure is due to the fluid's tendency to flow. However, I am not able to understand how the fluid exerts pressure in upward direction. I have worked on the problem and arrived at two different explanation:- The pressure inside a fluid is due to the collision of the particles. Since, collision is random, pressure can be considered to be equal in all directions at the same horizontal level. The fluid exerts a pressure and thus, a force on the bottom of the container and the reaction of this force exerts upward pressure. Question:- How does a static fluid exert pressure in the upward direction? Which explanation of mine is correct?", "label": 0}
+{"snippet": "While I was reading the book \"In Search of Schrodinger's Cat\" I found an interesting excerpt on how Max Planck used Boltzmann's statistical equations to solve the Blackbody radiation problem. The book mentions that there will be very few electric oscillators at very high energy end and at the lower end, electric oscillators would not have that much energy to add up to any significance. So most will be on the middle range. But my question is why and how this distribution of electric oscillators comes into picture. I mean why can't be the this distribution skewed, so that we may have electric oscillators concentrated at high ends. More specifically how this probability distribution was derived by Boltzmann? ( I am a layman interested in Physics so please be simple in your explanation)", "label": 0}
+{"snippet": "I was reading a Mathematics books and it gave the axiomatic definition of a function as being a mapping from a set called \"The domaine of the function\" to another set called \"The codomaine of the function\", and at first I thought the codomaine is the image of the domaine by the function (i.e. the set that contains and only contains the images of every element of the domaine). Turns out that's the range or image of the domaine which is only a subset of the codomaine and is equal to the codomaine only if the function is surjective. My question is : Why not define a function as a mapping from a domaine (the set A) to the set B (defined as the set containing and only containing the image of every element of the domaine)? Why the need for the Codomaine set with extra elements? Isn't the complement of the range in the Codomaine irrelevant to the function? In other words, aren't all functions surjective in the end? Sometimes they say that the codomaine is the set of possible outcomes of a function, but I don't understand what they mean by \"possible\" in this context.", "label": 0}
+{"snippet": "I have a hard time understanding GR. I understand a lot (from a math point) about (pseudo)Riemannian manifolds, and I also learned about Einstein's elevator thought experiment. So let me elaborate: From a physics point of view, you can take the elevator and derive that light has to bend, also that there has to be gravitational time delay. So far so good. Then almost all the literature I saw, turns to the next chapters, and assumes from the previous discussion that it is clear the (pseudo)Riemannian metric is all what matters now. For me, there is a bit gap, a 'how'/'why'/'what' in between. I do not see how the metric tensor relates to accelerated reference frames. I feel like I am missing something very obvious, but what is it? Can somebody elaborate?", "label": 0}
+{"snippet": "I'm trying to create a transition effect in a situation when a character suddenly finds himself falling, and his last word, which ends in '-y', is transitioning into an unintelligible scream. However, English is not my native language, and when I've tried to write it as 'Maryeeee!!' it was criticized as awkward and weird. At the same time, the counter-suggestion of simply extending the '-y' at the end and writing 'Maryyyyy!' doesn't feel right to me. It may be grammatically correct, but my goal was to create an impression of a word seamlessly transitioning into a scream, preferably making it clear that it is an unintelligible scream and not just the character's speech trailing off, and if the resulting word would be a horrible mess, it was fine for as long as I achieved the desired effect. So the question is, how should I go about it?", "label": 0}
+{"snippet": "I'm working on a problem where I need to convert an undirected and unweighted graph with cycles into a tree while preserving the edge information (all the edges from the graph are preserved in the resulting tree). For the resulting tree, the height and nodes duplication should be minimized. Nodes duplication can happen because in order to preserve the edge information from the graph, we will need to break the cycles by removing the edge(s) and then make a copy of the node(s) then connect it in the tree, or in other scenarios that I haven't thought of. I don't think minimum spanning tree algorithms will work because the algorithms will lose the edge information. So far my heuristic is: For choosing the root node of the tree, pick the vertex with the highest betweenness centrality in the graph. Because that vertex likely serves as a bridge which many shortest paths flow. When breaking the cycles, remove the edge whose nodes have the least total sum of degrees. This works for some examples I crafted.example My question is, how can I verify the heuristic is indeed optimal and provide a formal proof? Or is there a better strategy? Any insights, references, or alternative approaches would be greatly appreciated!", "label": 0}
+{"snippet": "I am beginning to learn chemistry/physics, and I have recently read about JJ Thompson's experiment which led to the discovery of the electron. In every source that I've read, the writers note that Thompson used an anode and a cathode to conduct electricity. In addition, the magnet supposedly had N/S ends. I did not know what a charge was, so I looked it up. But, frustratingly, I always get answers that refer to electrons and protons. That is, things that are negative have more electrons than protons, and vice versa. This gives me no idea as to how Thompson inferred that electrons are negatively charged from his experiment. My question is, can you define charge without talking about electrons and protons? Thompson didn't know electrons existed, so it seems to me that he must've had some other working definition of charge in order to determine that electrons were negatively charged. What makes an object a cathode or an anode, without referring to protons and electrons? If that question doesn't make sense, is it possible to adapt it just for the sake of understanding the experiment?", "label": 0}
+{"snippet": "My understanding of a simple k-vector is that it is the wedge product of k vectors. Also, two simple k-vectors are the same, when their magnitude, attitude and orientation match. Now my question is, could I just define a simple k-vector in this way? Meaning \"a simple k-vector is an equivalence class of ordered k-tuple of vectors. Two tuples are equivalent if their attitudes and orientation match, and if the parallelograms they span attain the same magnitude.\" Especially a reference where this is stated would be greatly appreciated! I feel like I have read something like this somewhere, but I cannot find it anymore. I am only using k-vectors for something I am writing for university and having to explain the wedge product would deviate from my topic a little. That's why I am trying to avoid this definition.", "label": 0}
+{"snippet": "So I am writing a program that works with regular polygons, and in part of that I need to represent circles that are inscribed and/or circumscribed upon the polygon. As this is programming, I need to refer to the relationship between the polygon and these circles. I have searched all around, but all of the places I have found that educate on calculating these circles never refer to this relational quality. As I said, I need a way to refer to this relationship and I cannot seem to find a word that represents whether a circle has the quality of being circumscribed or inscribed upon a polygon. Does any such word even exist? This pseudocode example might help clarify what I am trying to find: var myPolygon = new Hexagon(); var myCircle = CreateCircleOnPolygon(myPolygon, CircleType.Inscribed); ^^^^^^^^^^ ............ if (myCircle.CircleType == CircleType.Inscribed) { ... } ^^^^^^^^^^ ^^^^^^^^^^ The name emphasized in the above example is what I am currently using; however, considering that there are lots of different possible parts of my code that could need a different \"type\" of circle, the usage of the name CircleType is a little too broad in this context. I suppose the word \"quality\" is what I am going for, but I thought I would reach out to the language experts to see if there is a term I am unaware of that is more appropriate.", "label": 0}
+{"snippet": "I can imagine a relatively simple experimental setup whose resulting data could easily be compared with theoretical predictions: Send two identical atomic clocks into orbit and settle them at rest relative to each other. Then synchronize them. Then use thrusters attached to one clock to oscillate it, causing it to experience a series of counterbalanced accelerations (not changing it's average distance from the non-accelerated clock). Then collect data from both clocks to measure their desynchronization over time. My preliminary calculations suggest that the energies involved to reach relative velocities between the clocks that should produce measurable desynchronization in a matter of days or weeks are feasible, since atomic clocks are so accurate. I know the twin paradox isn't really a 'paradox' and that the predictions in general relativity are completely coherent. I've read a bunch of responses to related questions, explaining exactly what is predicted. But I can't find any experiments that confirm those predictions directly.", "label": 0}
+{"snippet": "As I understand, for elevation mapping using InSAR, one typically requires an out-of-plane baseline to create the required phase difference between images to detect objects at height. This usually requires either multiple satellites flying in formation or waiting for a repeat pass of a single satellite. This paper, A New Single-Pass SAR Interferometry Technique with a Single-Antenna for Terrain Height Measurements, suggests that one could achieve this in a single pass (along-track interferometry), if we are able to image at a high squint angle. The idea is that a grazing-angle difference is still present in the along-track case when squint angle is high. This is not the case for broadside imaging. However apart from this paper, I was not able to find any other sources to cross-reference the viability of this approach, nor does it seem that anyone else has reproduced the results. The mathematical principle behind seem sound to me. If it works, why is this concept not being used more often, and if it doesn't actually work, where is the error in the logic?", "label": 0}
+{"snippet": "I would like to ask your opinion on the point that looks simple. Consider the group of orthogonal matrices of order n over the field R of reals, equipped with the topology induced by the Euclidean norm of matrices. Let g be one of such matrix and denote by X the topological closure of the cyclic group generated by g. My question: May I find a matrix g with the property that: if the identity matrix I is the accumulation point in X of some sequence of powers of g, then the sequence is definitely trivial, that is, all the elements (except finitely many) equal I? In other words, can I exclude that, for a suitable g, the identity I is obtained as the accumulation point of a non trivial sequence in X? I don't think such g exists but I'm not be able to exclude it with a direct argument. Thank you very much for help.", "label": 0}
+{"snippet": "Perhaps another way to put it is, what exactly does it mean to quantize the EM field and why is it necessary? What mathematical properties does the quantized version of the field have that the classical version doesn't and vice versa? For context, I was reading a thread about where specifically classical E&M fails and we hence need QED to get accurate predictions, and stuff like the ultraviolet catastrophe and the photoelectric effect were mentioned. I get why those things necessitated the introduction of quantum mechanics and especially modeling photons as wavefunctions. What I don't get is why we can't just use \"regular\" relativistic QM with Maxwell's equations and the same mathematical E and B fields (which together form the EM field) from classical E&M. What goes wrong if we try to do this and how exactly does QED fix it? Or, to put it another way, what properties does a field modeling photons as wavefunctions need to have that the classical EM field doesn't have?", "label": 0}
+{"snippet": "I am new in Linear Algebra and I have encountered the concept of Solutions of linear equations. According to the textbook I use, a solution of a linear equation is a vector whose components satisfy the equation. However, I am puzzled by the choice of \"vectors\" specifically. Why is it not defined as a point whose coordinates are the same as the values that satisfy the linear equation? After all, a vector is more than just its components; it is also a set of points and its \"components\" define its magnitude and direction. A point, on the other hand, is a single entity with no additional properties. No magic. I think It's just a bit more intuitive to think of it this way instead. I can also anticipate that Vectors have a deeper meaning that relates them to linear equation systems but I can't tell what exactly. I'm going through the chapters and I'm still waiting for the \"Bingo! I figured it out.\"", "label": 0}
+{"snippet": "I have been reading the Loop Antenna section of Antenna Theory by Constantine Balanis and trying to understand how exactly a ferrite core improves the performance of a small loop antenna. Balanis writes, The radiation resistance, and in turn the antenna efficiency, can be raised by increasing the circumference of the loop. Another way to increase the radiation resistance, without increasing the electrical dimensions of the antenna, would be to insert within its circumference a ferrite core that has a tendency to increase the magnetic flux, the magnetic field, the open-circuit voltage, and in turn the radiation resistance of the loop. How exactly does increasing the magnetic flux (adding the ferrite core) increase the antenna's radiation resistance? Balanis claims the voltage increases, and presumably deduces that the radiation resistance increases likewise from the equation V=IR. However, this would only follow if we knew that the current I did not increase as the flux increased, which is not obvious to me. It also is not obvious to me why the voltage increases in the first place!", "label": 0}
+{"snippet": "I've been really stumped on this particular concept. In Case A, when a bar magnet is brought towards a copper coil around a soft iron core, in accordance with Faraday's Law of Electromagnetic Induction, the the pole facing the magnet acquires a North Polarity while the opposing pole acquires a South Polarity. Now by Lenz's Law, the direction of the induced EMF must oppose the cause that produces it, but the current is in the same direction as the moving magnet. The galvanometer deflects in the same direction too. Why doesn't this obey Lenz's Law? And additionally, in Case B, by merely reversing the winding of the copper coil, the current flows in accordance with Lenz's Law and the Principle of Conservation of Energy. My question is, why does changing the winding of a coil defy Lenz's Law in Case A and then follow Lenz's law in Case B? Something such as the Principle of Conservation of Energy and Lenz's Law should apply in any case. The method of winding shouldn't matter that much right?", "label": 0}
+{"snippet": "Is it correct to say that, in English, when you use the Present Simple tense in the Interrogative Negative form you are either implying the negative or just confirming the affirmative (depending on the order of \"Do\", \"subject\" and \"not\"), but no other possibility? Like in the scene of The Lord Of the Ring - The Return of the King, when Eowyn is talking to Aragorn just before he leaves to see the dead army in the mountain. Eowyn: \"You cannot abandon the men. We need you here.\" Aragorn: \"Why have you come?\" Eowyn: \"Do you not know?\" In this last line, given the context, she is clearly implying that she thinks he knows she loves him, and thus, she is asking it just to confirm it (as I understood it). But then, if she had used the other form \"Don't you know?\", it would change the meaning, as she would appear to be asking it to really have a first idea on his feelings, not presuming anything. Then my question is: can the Interrogative Negative have only these two possibilities?", "label": 0}
+{"snippet": "Have studied traditional point-set topology, but find there's a fairly large gap between the preparation typical point-set courses give you, and the level assumed in algebraic topology texts. Looking for a good introductory book on topology that uses more categorical / modern language - something that would segue smoothly into, for example, Tammo tom Dieck's text Algebraic Topology - at least covering most of the topics mentioned in the first chapter of his book (subspaces, quotients, products, sums, compactness, proper maps, paracompactness, topological groups, transformation groups). Have perused the MIT textbook 'Topology - A Categorical Approach', which looks decent, but isn't so comprehensive. Have found one text that looks good (Grundkurs Topologie by Laures and Szymik) - but unfortunately it's in German! (Anyone know of an existing English translation?) Open to recommendations. Thanks.", "label": 0}
+{"snippet": "I'm studying nonlinear control systems, especially the Pontryagin's minimum principle and its applications. Throughout my studies, the authors have always defined the control systems with state variables and output variables. However, in this article Optimal Control of an SIR Model with Delay in State and Control Variables and so many others, it doesn't seem like control systems in epidemiology has output variables equations (or at least clear ones). Why is so? And is it possible for a nonlinear control system not to have output variables? I have found this answer: It is possible for a nonlinear control system not to have an explicit output variable, depending on how the system is defined and what its purpose is. In a control system, the input variable is typically the signal or information that is used to control the behavior of the system, and the output variable is the variable that is being controlled or affected by the system. However, in some control systems, the purpose may not be to directly control an output variable, but rather to achieve some other goal. Is it correct?", "label": 0}
+{"snippet": "This might be a stupid question, but, why is it that gamma rays are able to penetrate almost any barrier without question? We know that gamma rays are simply high frequency waves with massive amounts of energy. However, what processes can enable it to go through layers of bonded atoms of metals and just about anything else? On another note, we know that beta particles can pass through paper but can not penetrate a thin layer of metal. What is different about the bonds of metal so that an electron can't squeeze through? I assume it is because of the tightly bonded metallic bonds and the high volume of electrons that flow throughout the metal that causes this. However, if this is the case, what would a beta particle do if it is \"rejected\"? Would it join the flow of electrons in the metal, would it just stay on the same side of the sheet or would it rebound in the opposite direction due to the equal, opposite force exerted on it by the sheet?", "label": 0}
+{"snippet": "I am studying interacting QFT in the context of quantum fields in curved backgrounds, and I am getting some confussion about the concept of particles. To study some gravitational phenomena involving particles (e.g. Unruh effect, Hawking radiation, etc.), it is typically sufficient to deal with free fields, which are expanded in mode functions and particle/antiparticle operators (i.e. its energy eigenstates form a Fock space). This can be done, in general, because the Hamiltonian of free fields is quadratic in the field operators, and therefore one can calculate a single-particle Hamiltonian which can be diagonalized, giving rise to a band structure by means of which we describe this Fock space (eg. for the case of Dirac fermions, the vacuum state, prior to a particle-hole transformation, amounts to a filled lower band/Dirac sea). However, when one considers an interaction term, the Hamiltonian is no longer quadratic in the fields, and this band-structure cannot be obtained by direct diagonalization of the single-particle Hamiltonian (I am not even sure whether the notion of band structure remains). As a consequence, I do not understand if particles/anti-particles can only be defined when the Hamiltonian of the theory is quadratic, i.e., when the evolution of the theory preserves tha Gaussianity of the states. If this is the case, I imagine that a mean field approximation, which turns the Hamiltonian back to a quadratic one, would recover the notion of particles, is this the case?", "label": 0}
+{"snippet": "I'm working on a set of beamer class slides in TeXstudio. Usually upon compile, the preview slide visible on the right will be at the position of the cursor - instead, for me, it consistently jumps two slides behind. This is reflected in the behaviour of the preview when I enable the \"scrolling follows cursor\" option - there, too, the preview is always two slides behind where the cursor actually is. If the cursor is on one of the first three slides, the preview stays on the first one. I get this behaviour on two different machines, so I assume it's not some super specific local bug but something more broad. It also persists independently of whether or not the document is compiled in handout mode. Any help on resolving this would be very much appreciated, as this behaviour is quite annoying.", "label": 0}
+{"snippet": "I noticed that in several 'throwing' sports like the javelin throw and the shot put there have been a few cases where competitors tried to introduce a technique where they throw the projectile further by rotating their entire body (these techniques were then banned for safety reasons). As an example, there is the cartwheel shot put, where the person performs a cartwheel and rotates their body before throwing. I am not sure what advantage this has apart from that the ball is pushed over a slightly longer distance so that there is more kinetic energy. In the spinning javelin throw, instead of throwing the javelin with a regular technique, the athlete spins around and slings it out of their hand at high speed so that it flies forward. Again, I am not sure why this gives a distance benefit but I assume that it's different to the rationale behind the cartwheel shot put?", "label": 0}
+{"snippet": "I am wondering if the esteemed members of this forum can help me with these questions, which have bothered me for a long time and are what have brought me to this forum. One thing I struggle to understand and work with is the use of the \"editorial we.\" I am a copyeditor and proofreader, and I have a client who consistently likes to use the first-person plural voice for his works. I have asked my colleagues, and I got mixed, unclear answers. Here are a few examples: We will be able to feel magnificent light in our souls... Does \"souls\" have to agree with \"our\"? Should it not be \"soul\"? The chair or pillow may not be so comfortable, our kids may get rowdy, our spouse may need our help with this and that... Here, I have no issue with \"our kids,\" because a person can certainly have more than one child. But should \"spouse\" be plural like \"our\" and \"kids\"? It is a constant issue that we must face our entire lives. \"Entire\" here does not seem to fit with \"lives.\" But then \"our entire life\" does not seem to be correct as the singular \"life\" does not agree with the plural pronoun \"our.\" I would be grateful to learn more about the proper use of the \"editorial we\" in this regard and to hear suggestions on how to deal with this issue. Thank you all in advance.", "label": 0}
+{"snippet": "In a textbook for thermodynamics, it considers a situation where work is done to a system by an irreversible work source through a thermally insulating piston, and it states \"any irreversible work source can be simulated by a reversible work source\". It briefly explains the reason; what the work source does is simply to apply force to the piston, and therefore it does not matter how the force is applied, whether or not it is applied by an irreversible work source. I have a difficulty to fully convince myself with the statement, and can anyone kindly help me with this? The textbook is a non-English one, and it is not available online as an electric file. The way how it defines the work source is simply that it is any system, which is connected with the system of our interest only through a thermally insulating piston. That is, there is no heat exchange between the two system. Let me rephrase my question: Suppose that system A is interacted with system B (irreversible work source) only with a thermally insulating piston. They exchange energy only through work, but not heat. My question is if it is possible to replace system B with a reversible work source in an indistinguishable manner, i.e., any mechanical reaction that system A receives from system B remains exactly the same. Thank you so much for your time.", "label": 0}
+{"snippet": "As per my understanding: Multiple fermions cannot have the same quantum state (as per Pauli exclusion principle) Multiple fermions can occupy the same physical space as long as they have different quantum states (or numbers or properties such as spin) If both these statements are true then, part of the second statement \"as long as they have different quantum states (or numbers or properties such as spin)\" doesn't become necessary. Because first statement implies that \"multiple fermions always have different quantum states\". Hence, the second statement simply becomes \"Multiple fermions can always occupy the same physical space\" (For a moment let's consider only fermions, their quantum state and physical space they occupy. And not other factors like electromagnetic repulsion etc) However, at multiple places on the Internet it has been stated (and seems like widely accepted) that: Multiple fermions cannot occupy the same physical space as per Pauli exclusion principle, and that is why matter structures exists in the universe. Can someone please help me trying to figure out where am I making mistake?", "label": 0}
+{"snippet": "According to wikipedia, the aurora borealis is primarily caused by charged particles from the solar wind being redirected to the poles by earth's magnetic field and slamming into the nitrogen and oxygen atoms in the upper atmosphere. This slamming gives the electrons in those oxygen and nitrogen atoms enough energy to escape their electron clouds. The light comes from when electrons emit photons in order to rejoin an atom. Hence the colors, green corresponding to oxygen atom readmittance and purple to nitrogen What I am wondering is what role dissipative absorption plays in the aurora borealis. I mean we have a bunch of accelerating charged particles right? Even if speed is constant their direction is changing due to the magnetic force and since they're charged they must be emitting some kind of em radiation right? Not to mention when the actual collisons take place between electrons. Not all of this em radiation will correspond to the energy levels of nitrogen and oxygen right? So shouldn't we see more colors as all sorts of em radiation ought to be emitted? If nothing else you would expect the electron clouds of oxygen and nitrogen to oscillate in response to the emitted em radiation of the incoming solar wind right? Why do we tend to see only green and purple?", "label": 0}
+{"snippet": "Suppose I have a hose pipe connected to a tap. I turn on the tap and water flows out of the other end of the pipe. Now imagine I install two valves at different points along the pipe. Water will flow normally if both valves are open, but not if either one of them is shut. No doubt you can now see where this is going. If the spacing of the valves along the pipe is sufficiently long, and the duration for which the valves are open is sufficiently short, we can always imagine a second reference frame in which at any given time at least one of the valves remains shut, so how can we account for the fact that water flows in that frame even when the valves are not both open? I imagine the resolution is somehow to do with the fact that the flow requires a pressure wave to propagate along the pipe when a valve is opened, but I haven't been able to find a convincing resolution. Has anyone come across an analogous problem before?", "label": 0}
+{"snippet": "I'm implementing physics for a computer game, and came accross something that looks unintuitive to me. Consider two bodies at rest: Let's say we momentarily apply the same amount of force to them, but in different locations: at the center of mass for one body, and off-center for the other. The second body will gain angular velocity, while the first one won't. Both will gain rightward velocity, in the same direction. But will the second body gain less velocity than the first? Or the same velocity? Naively I would expect less velocity, since some of the force was \"expended\" on giving it angular velocity, but I googled around and experimented in Algodoo, and it seems the velocity ends up the same. Is that correct? Is there an intuitive explanation for that?", "label": 0}
+{"snippet": "I've got a few months to go before I enter in graduate school, but I have to say that my math background is not as good as I would like. Thus, I would like to take the opportunity to strengthen it and work on undergraduate analysis. I had in mind to work on the Rudin book I've heard so much about, the book is very concise and covers a wide spectrum of mathematical analysis (and a bit of topology) seen in undergraduate so I thought it was suitable for what I want to do with it. But I'd like to hear your opinions and recommendations if you've ever been in this situation and/or know of any other cool books (I'am also interested in functional analysis and especially Hilbert spaces so...) for the self-taught to get through the summer. Thank you a lot !", "label": 0}
+{"snippet": "Let's assume we have a standard double-slit experiment, just for illustration's sake. When an electron collides with the detector, is its momentum parallel to the emitter's output, or is it something else? I know that the uncertainty principle forbids us from knowing too much about the momentum when we know the position, so let's assume we have a magic detector that will only give us the momenta and not the positions. This magic detector can detect the momentum of a single electron. If we shot one electron through this apparatus at a time, what would we see (on average)? I say on average, because there's a non-zero chance that the electron lines up with the emitter by chance. We should still be able to see the standard deviation of the momenta; if it's tight, then the momenta line up with the emitter, otherwise, it's relative to something else. I'll admit this question may be nonsense, but to my knowledge, the only limitations to this are engineering ones (due to the magic detector), not physical limitations. If this experiment is nonsense due to a physical limitation that I've misunderstood, I'd like to know why.", "label": 0}
+{"snippet": "I've been reading some category theory texts for my undergraduate monography, and I've found that one can talk about small and large categories using small/large sets, or do the same using sets/classes. Most introductory texts just shrug formalisms off, mention one of these formalizations and goes on. I've noticed that most category-focused authors and texts (such as Categories for the working mathematician and Sheaves in Geometry and Logic by Mac Lane) tend to prefer the small/large set approach, while texts that don't focus that much on categories (Topology and Groupoids by R. Brown) tend to prefer the class/set one. My question: Is there a categorical/set-theoretical reason to prefer the small sets approach? I'd assume that there's a benefit in having a set of objects even in large categories, but fail to see an actual difference. I found the paper Set Theory for Category Theory by Michael Shulman, but it was way out of the scope of what I can understand.", "label": 0}
+{"snippet": "I'm looking for a real analysis book that covers measure theory and I've been recommended Folland's or Royden's books, but their price is quite high and I was wondering if any of the books below would serve as a cheaper substitute. Theory of Functions of Real Variables by Lawrence M. Graves; Real Variables with Basic Metric Space Topology by Robert B Ash; Theory of Functions of a Real Variable by I.P. Natanson; Real Analysis by Gabriel Klambauer; Nonstandard Analysis by Alain M. Robert; Foundations of Analysis by David F. Belding and Kevin J. Mitchell; Foundations of Mathematical Analysis by Richard Johnsonbaugh and W. E. Pfaffenberger; Mathematical Analysis by Tom M. Apostol; Elementary Real and Complex Analysis by Georgi E. Shilov; Foundations of Modern Analysis by Avner Friedman; Real Analysis by Norman B. Haaser; Introductory Real Analysis by A. N. Kolmogorov; Introduction to Analysis by Maxwell Rosenlicht.", "label": 0}
+{"snippet": "I'm having a little bit of a hard time understanding some concepts to do with self-inductance in class. I understand mutual inductance. That's when a loop has some time-dependent current going through it, and because the current is time-dependent, the magnetic field the loop produces is also time-dependent, and the magnetic flux in a nearby loop is time-dependent. With self-inductance, though, is the idea that a single loop carrying a time-dependent current gives rise to a time-dependent magnetic field, and that very same time-dependent magnetic field gives rise to a change in flux in the single loop itself, which then generates an emf? If I'm correct in this reasoning, then that should mean that the new emf gives way to a current, which opposes the previously existing current. Why doesn't this just result in an infinite loop creating an opposing current, and then one that opposes that, and then one that opposes THAT...etc.?", "label": 0}
+{"snippet": "Given a mapping f: R->R, what properties must f have in order for its range to be countably infinite? I'm personally not sure, especially in terms of formalization, but ideas of non-monotonicity or some construction of countably infinite equivalence classes come to mind. For context, in quantum mechanics it's said that a system's energy can only take discrete values, but this confuses me since energy is defined as the sum of a function of position and a function of momentum, which can both take any real value. The indexing of the sets doesn't make much sense to me, especially since the kinetic energy, the function of momentum, is very clearly uncountable since it's strictly monotonic. So even if the potential energy has a countable range, it doesn't make sense that the total energy would be since the union of a countable set and an uncountable set is uncountable. Like I said, I'm more concerned with the question I asked above rather than this confusion that created it, as I'm sure an answer will either lead me in the right direction, or at least give me the means to reasonably formulate a new question- so don't worry about addressing this. Any answers or information are greatly appreciated. Thank you!", "label": 0}
+{"snippet": "I was solving this question in my coursebook and was not able to understand it conceptually. Though I did understand the mathematical approach to it. Now I understand that when the rod is given an initial velocity towards right, due to its motion an EMF is induced across it. Current starts flowing until it reaches a steady state. However, once the current becomes constant, no potential difference exists and the current slowly starts dying out at which point the rod starts moving back to its mean position. Then the velocity is in the opposite direction and the 'polarity' of the induced EMF reverses and current starts flowing in the opposite direction. My questions are- Doesn't it take an infinite time for the inductor to reach its steady state (where it behaves as a connecting wire). So, wouldn't the rod move in the direction of its initial velocity forever? What will happen once a steady current is achieved in the circuit? Will it be correct to say that since the potential difference across the ends of the rod is zero, the current wants to decrease to zero immediately, but the inductor only supports a slow decay of current? Can we also say that the reason the circuit doesn't heat up due to short circuiting is because there is no actual battery in the circuit? I tried asking my teacher but I couldn't get a satisfactory answer.", "label": 0}
+{"snippet": "Consider a circular horizontal plane (like a round tabletop) rotating around its center. Consider a body A resting on this tabletop. Since the tabletop is rotating around its center, the body is moving along with it in a circular motion around the center of the circle. I understand that in circular motion, there's always a centripetal force, pushing the object towards the center of the circle. And in this case, this force is the static friction force, operating on the radial axis towards the center. I have two questions regarding this: I was under the impression that a static friction force, or any friction force, always operates in the opposite direction of some other force which operates on the same body. Is this correct? If so, what is the additional force (opposite to the friction force) that I'm missing in the above scenario? Is the static friction force operating only on the radial axis towards the center? Or is there also static friction along another axis?", "label": 0}
+{"snippet": "I'm wearing glasses with a sunglass clip-on. This means I have my regular glasses and, on top of them, I have a second pair of lenses that work as sunglasses and attach to my regular glasses using tiny magnets. I'm also in a car, and I'm looking through a window layered with Insulfilm. Curiously, when I look through the Insulfilm with the sunglasses on, I see a rainbow pattern. If I keep my glasses on, but remove the sunglass clip-on, the rainbow is gone. If I look through a window without Insulfilm, the rainbow also seems to be gone. If I look through the Insulfilm with the sunglasses clip-on, but without my regular glasses, the rainbow is there. I believe my sunglasses are polarized, and the rainbow fades away when I tilt my head a little. Why exactly is this phenomenon happening? I guess it has something to do with polarization due to the rainbow fading when I tilt my head, but I can't figure out why it is a rainbow and why I can't see it without the sunglasses.", "label": 0}
+{"snippet": "This popular question got me wondering if there is a simpler way to reduce radon in homes. Our house has a fairly standard radon mitigation system. It has a lot of parts. There is a hole cut in the basement floor. There is a thick pipe which goes up through all the floors with lots of bends and turns, like the old Microsoft \"pipes\" screensaver. There is a powerful, always-running fan in the attic pulling the air up and out through a roof vent. There are also other components, such as a manometer and other sensors. It all has to be serviced by technicians. Like any system with a lot of components and a lot of puncture points through surfaces, there are many points of potential failure. Why not have a standalone unit in the basement with a fan that blows the air through an electrostatically-charged baffle of gills or fins or whatever, collecting the radon until it decays? At least then it won't end up in the lungs, where it causes the damage. We could put lead shielding around the unit, if necessary.", "label": 0}
+{"snippet": "I found a few questions that are similar to mine, but I do not think that either of them answers exactly what I want: Is there a Birkhoff-like theorem for stationary axisymmetric metrics? or Gravitational Collapse: Kerr solution is a vacuum solution but not for any rotating body? My question is this: When we look at simple models of gravitational collapse for spherically symmetric matter distribution (such as Oppenheimer-Snyder) we always exploit the fact that the solution to the Einstein field equations just outside any spherically symmetric collapsing matter is Schwarzschild and that this is the only possible solution. This is thanks to Birkhoff's theorem. An analogous theorem exists also for charged matter. Unfortunately, no such theorem exists for rotating matter, as the spherical symmetry is broken. This means that we can't approach the gravitational collapse of rotating matter the same way we would for spherically symmetric charged or uncharged matter collapse. So how do theorists actually study rotating black holes? Do we need some sort of computational or numerical methods?", "label": 0}
+{"snippet": "My friend was sitting in a wheelchair, with a cup of coffee in one hand. That made me wonder, how would the wheelchair move if he turned only one rear wheel? He tried it, using his right hand to turn the right rear wheel. The wheelchair starting moving in a circle. No surprise. But I was interested in the radius of the circle. The circular track of the right rear wheel on the ground, had a radius that was slightly larger than the distance between the rear wheels (i.e. the distance between the two points of contact between the rear wheels and the ground). What determines the radius of the circular track of the left rear wheel (the unturned rear wheel)? Possibilities that come to my mind are: Location of all four wheels The size and shape of the contact patch between the wheels and the ground The coefficient of friction between the wheels and the ground, and the weight of the system The diameter of the wheels Angular speed of the right rear wheel How the person is sitting within the chair (centred, or leaning to the left, leaning to the right) (Assume the wheels are in parallel planes.)", "label": 0}
+{"snippet": "I apologize if this question has been asked before, but I haven't been able to find a post which covers this exact question. Let's say that we have a driving car which is moving forward. At some point, one of the rotating tires hit a stone on the road. Which way does the stone move, in relationship with the angle in which the tire hits the stone? Can the stone ever be thrown backward onto another car? Does the general direction (forward, backward, sideways) depend furthermore on the shape of the stone? Whether it is for example perfectly spherical or asymmetric? I am kind of struggling how I would answer such a basic question, since there seems to be many factors at play here. Can you even answer this question without fully knowing all the nuances and details?", "label": 0}
+{"snippet": "Suppose we have an isolated n-type semiconductor having varying concentrations of carriers over x. After some finite time, the concentration becomes uniform for a given constant temperature. We always say that this is because of diffusion which allows the movement of charge carriers to move from higher to lower concentrations. But shouldn't this diffusion occur because of the repulsive forces between electrons? why do we say it's because of the random motion? (the random motion allowing for the carriers to rearrange should be because of the electric field produced by them due to the gradient of charges). If we see some excess charges added to an isolated conductor, then the electric field produced by these excess charges allows the charges in the conductor to redistribute to settle on the outer surface where the net force experienced by the excess charges is zero. Shouldn't the same principle apply to semiconductors? What exactly is happening inside? I hope to get a clarified answer. Diagrams will be highly appreciated.", "label": 0}
+{"snippet": "I'm trying to deepen my understanding of Von Neumann entropy (out of interest in the quantum Bekenstein bound) by learning more about the reduced density matrix (aka local density matrix), which is given by the modular Hamiltonians (aka entanglement Hamiltonian). As I understand it, modular Hamiltonians are only known to be local (i.e. an integral of a local operator) under three specific situations. When the state is the vacuum state in a half-plane (the only case where the modular Hamiltonian is given by the traditional Hamiltonian) When the state is the vacuum state and is limited to a ball and the field theory is a CFT When the state is the vacuum state and is limited to an arbitrary piece of a null plane I could not, however, find any explanation for how or why these are the three known cases where it is local (and additionally why only the first one is given by the traditional Hamiltonian). I'd appreciate any insight you could provide on this matter.", "label": 0}
+{"snippet": "Adjectives and adverbs can be formed by adding \"y\" or \"ly\" to e.g. a noun, such as: heart -> hearty, heartily However, sometimes these words are not in use, or make no logical sense, such as: chair -> chairy, chairly Although you could come up with a situation where you'd use \"chairy\", e.g. \"this block of wood looks quite chairy\", you'd probably be more likely to use \"chairish\" or \"chair-like\". And if you read all the books in the world, you'd probably never come across the word \"chairly\" or \"chairily\". What is the status of words like these? Do they exist because they are technically correct and their meaning is obvious? Do they not exist until someone (notable) uses them in a (notable) text? Or, to make the question more specific: if I were to create a spell checker, should I allow or disallow these words?", "label": 0}
+{"snippet": "I am teaching students at a high school about bending of a beam (the beam is clamped at one end and then an applied force acts downwards close to the end of the beam to bend it). I thought that it did not require further explanation that the deflection of the beam due to the force at the end is inversely proportional to the stiffness of the beam, proportional to the size of the applied force, and that it is dependent on the distance from the fixed point where the beam is clamped. However, I have been asked to provide justification for these statements and not to appeal to physical intuition which is not obvious to students who are not seasoned physicists. What type of justification would be enough to use these statements at an elementary level? How could I explain that these statements are true?", "label": 0}
+{"snippet": "Compressive strength is how much inward force a given area of material can withstand before failure. The force tries to compress the atoms closer together. Mohs hardness is the difficulty of a material to be scratched. Abrasion resistance. However, when an object scratches another, there first is a point of contact where the harder material is forced into the surface of the other, and then lateral forces shear off a grove from the softer material. But at this point of contact, the forces are compressive, trying to force the atoms together, until one of the materials give way. As such, I would expect materials with a high Mohs hardness to have a high compressive strength and vice versa. This holds for ceramics such as silicon carbide, aluminum oxide, and others which have both a high compressive strength and a high Mohs hardness. Does this trend hold for most/all materials and to be expected for the above reasons? Are there any counterexamples? If so, what could explain a high Mohs hardness and low compressive strength or vice versa?", "label": 0}
+{"snippet": "I really don't like the phrase \"excited for\" which seems to have become very common in recent years, as in \"I'm excited for the weekend...\". My sarcastic reply would be \"I don't think the weekend cares or appreciates you being excited on its behalf\". Anyway, I'm aware I have to accept that language changes, even though here I think it's just bad grammar. The question is ... are there any studies looking at how (the wrong use of) this phrase came about? I have a theory based on absolutely nothing, that perhaps it came from Spanish where 'por' can be used in this sense, e.g. Google translates \"excited about this weekend\" to \"emocionad(o/a) por este fin de semana\". Is it possible that this usage came via speakers of Spanish, perhaps in the US?", "label": 0}
+{"snippet": "\"Longingly\" is the adverb form of \"longing\". Depending on where you look, \"longing\" is described as an adjective, a verb, or a noun: Oxford defines it as either a noun or an adjective. Cambridge, Collins, and Merriam-Webster seem to define it exclusively as a noun. Wiktionary says it's either a noun or the present participle verb form of \"long\". Despite the disparate definitions, I can see justification for all three forms. This raises a question: which distinct form of \"longing\" is \"longingly\" derived from? Or is the adverb formed indistinctly? I know that adverbs ending -ly are typically formed from adjectives, but English is full of exceptions. I checked a few etymology sources but they either only had information on \"longing\" itself, or only described longingly as being formed from longing as a general word.", "label": 0}
+{"snippet": "My question is closely related to the answer of this question: Why is general relativity background independent and electromagnetism is background dependent? General Relativity is often stated to be \"background independent\", because it calculates how spacetime is curved. That's in contrast to other theories like classical electrodynamics which act on the manifold without interacting with it. I understand that GR interacts with spacetime (and that that's a great advancement in comparison to the theories before) - however, I do not understand, why it's called \"background independent\". Matter curves spacetime. That means to me that there has to be a spacetime first which can be curved by matter. If the universe is empty (in GR), Minkowski spacetime is still there. If spacetime were produced by matter like the electromagnetic field is produced by its sources I would understand the term \"background independence\". But to me it's only interacting with the background, not background independent. (Like an artist who is forming any possible object out of clay is not independent of clay... Just acting on it in every possible way) How shall I understand the term \"background independence\"? Is the term not precise? Did I get something wrong?", "label": 0}
+{"snippet": "Quite naturally, the observable Universe is the only bit of the Universe we can extract information from, as light from farther away has not reached us yet, and there are zones from which we'll never even be able to extract information, as they are causally disconnected from us due to their high speed. Therefore, how do we know the cosmological principle holds at larger scales if we can't observe them? It just seems to me a quite bold assumption to make that the entire Universe is homogeneous and isotropic. Perhaps it presents irregularities which we'll never know of, and which would be necessary for us to not mess up with our cosmological models. Frankly, I don't quite see the point of building cosmological models if we only know what seems to be a small portion of the Universe, just like it makes no sense to try to see the picture of a jigsaw puzzle just by examining one random piece of it.", "label": 0}
+{"snippet": "Recently I came across Normal matrices and their properties, one of which states that their eigenvectors are the same as their adjoint and are orthogonal. I've gone across some proofs and I understand it but when I tried to prove the same using the inner product, It somehow states that the above is true for any arbitrary matrix. Can someone possibly help me point out where I'm going wrong? Let's say A is a matrix and B is its adjoint. If x is an eigenvector of A with eigenvalue k, then, < x | A | x > = < x | kx > = k< x | x > also < x | A | x > = < Bx | x > hence < Bx | x > = k< x | x > = < kx | x > So, x is also an eigenvector of adjoint of A.", "label": 0}
+{"snippet": "In the English language there are many words where the letter \"a\" is pronounced as a short (continental European) \"e\". Or at least very close to it. However dictionaries point out that in these cases the correct pronunciation is more an \"ae\" sound. Several websites on English pronunciation take the same view. So I decided to test this assumption. Over a period of weeks, whenever I watched an English or American television program, I payed attention how these \"a\"-words where actually pronounced by native English speakers, and made notes of my observations. I found out that in fact there are many words that have the pure \"e\" sound. A few examples: back, cash, cat, fact, relax, track, crash. So what is going on here? Are this words pronounced incorrectly, or are the dictionaries and websites promoting viewpoints about pronunciation that are outdated? Or has it to do with regional variations (dialects)?", "label": 0}
+{"snippet": "In Photoshop (and many other computer graphics applications) there are are various ways that images/layers can be composited with their underlying background. These are sometimes called blending modes. One blending mode in particular is multiply, which has the convenient feature that it eliminates white backgrounds from black line illustrations while properly dealing with anti-aliased edges (see the example below). Is there a way to do this in LaTeX? I have a large number of images with a white background that need including in two documents with different coloured backgrounds. I'm looking for a quick way to remove the white background from the images without having to manually add an alpha mask to every image in Photoshop. Normal blending mode: Multiply blending mode: Close up of anti-aliased edge, properly feathered:", "label": 0}
+{"snippet": "I found this MC question that asks about a soft iron bar entering a solenoid: At first, my answer was (B) because the iron bar should increase the magnetic field induced by coil M and, according to Lenz's law, this magnetic field should oppose the original current, making the lamp dimmer. Also, the magnetic field created by M should then induce a current in N in the opposite direction to the current in M (also Lenz's law), so since the current in M is right to left, then it should be left to right in N. I wasn't too confident in my answer though. Then, I noticed that they had drawn a DC power source in M. This would indicate no changing magnetic field, thus no current induced into either M or N. This would mean that the lamp doesn't change brightness and there is no direction of current in N. Right? Is this just a mistake in the question, or am I missing something? Thanks to anyone who can help.", "label": 0}
+{"snippet": "Given a path, how do the magnitude of the velocity and acceleration vector along the path correlate? I am confused due to the fact that the acceleration is the change of velocity over time and in general if you plot the velocity and acceleration over time, you can see a correlation (e.g. constant velocity means zero acceleration). So I expected the same relationship for the magnitude of the velocity and acceleration vector. Moreover, I got confused because the magnitude of a vector is always positive and in the general plots of the velocity and acceleration over time it is not the case (e.g. linear decrease in velocity means constant negative acceleration). Therefore, can someone clarify if there is a clear relationship between the magnitudes of the velocity and acceleration vector and how this is defined? And if not, is there a relationship between the velocity and acceleration vector, so you can verify if your velocity and acceleration vector are correctly calculated?", "label": 0}
+{"snippet": "Relativistically, the electric field of a moving charge is not purely radially directed, but is instead concentrated perpendicular to the line of motion. So, a current loop consisting of electrons as charge carriers should generate a \"charge separation\" effect, where the negative electric field is concentrated perpendicular to the loop, and is not perfectly cancelled by the stationary positive ions in the (electrically neutral) conductor. Conversely, in the plane of the loop, the positive electric field should dominate. This \"charge separation\" effect is separate from the magnetic field produced by the current loop, as it should have the effect of accelerating stationary charges in the surrounding space, which are unaffected by a magnetic field, because their velocity is zero. I have never heard of such an effect, which should be small but measurable, hence I am asking the question.", "label": 0}
+{"snippet": "A term in a Lagrangian is gauge invariant if one makes sure to use quantities which transform in proper representations of the group of gauge transformations. This means that one cannot write terms in the Lagrangian using a 'bare' gauge field, but one can use the associated field strength or act on a gauge field with a covariant derivative. On the other hand, if one writes a term using a 'bare' gauge field (for example, a combination of the gauge field and the associated field strength tensor), although it will not be gauge invariant, will this term still be invariant under diffeomorphisms of the spacetime on which the field theory is defined? Since diffeomorphism invariance is sometimes taken informally to be ''background independence of the field theory'', I guess that this term should be invariant under diffeomorphisms? Or does diffeomorphism invariance fail because it is a specific example of a gauge symmetry?", "label": 0}
+{"snippet": "This may be an amateur question, however here goes. I understand the double slit experiment creates a situation where detecting which slit the particle/wave goes through causes a collapse of the wave function and for the particle to act like a particle and not cause an interference pattern. What I want to know is this: If say for example, the detector emits a signal to a speaker if it detects the particle and the speaker emits an audible sound, my understanding is that the wave function would collapse - we measured the outcome. However, what if we left the detector doing its thing, but turned off the speaker so that we didn't know? Would this still be considered \"measurement\" or does measurement require recording/knowledge (future included) of the outcome?", "label": 0}
+{"snippet": "I'm considering to choose between \"Convex Optimization\" by Stephen Boyd and Lieven Vandenberghe, and Yurii Nesterov's \"Lectures on Convex Optimization\" to supplement for my university course. I have had Calculus and Linear Algebra, my course covers constrained and unconstrained convex optimization, linear programming and constrain programming so i want to know which one of these two books will be good for me. The lecture i'm having mostly just focus on the implementation of the method but not the mathematical proof behind it so i want to learn more about the math behind optimization algorithms. I've read a few section from each book and personally i think Yurii Nesterov's book is more rigorous and easy to understand, but i still want to ask because i don't have enough time to study both and i want a strong foundation on this subject for my AI major. P/S: I'm also really enjoy rigorous books like Apostol's Calculus I,II so i want to know which of the two books above have similar style.", "label": 0}
+{"snippet": "I often see \"functional\" used as an adjective in situations where I think that \"function\" would actually be the better choice. Specifically, I am referring to translations of German compound nouns. Here is an example: Funktionsarchitektur. This is the architecture of the function/functions. To be specific, we are talking about a technical function in a machine or vehicle. This is the architecture of the devices, control units, etc. which perform the specific function. ABS would be one example. In this case I would use \"function architecture\", translating it as a compound noun in English as well. For me, \"functional architecture\" is an architecture which functions and not an architecture of/for functions. I see a lot of cases in which the adjective \"functional\" is used instead of expanding the compound noun. Any thoughts on this?", "label": 0}
+{"snippet": "while working on problems related to fluid mechanics i came across a problem in which we were asked to find the kinetic energy of a sphere which is under pure rolling and has non viscous fluid filled inside it. here you can see the figure : so my initial thoughts were to write the moment of inertia of the whole body about center of mass and then proceed as normal. But to my surprise this was not correct so i thought more about this and made a conclusion that if the fluid is non viscous then maybe we don't have to consider its rolling motion. This assumption made me do this question but i am not sure whether it's correct or not. I want to know what you guys think about this assumption.", "label": 0}
+{"snippet": "I tried finding a decent book to study nonstandard analysis from and found Goldblatt's Lectures on the Hyperreals. However, I was very disappointed to find out that the text is not rigorous at all --- Goldblatt doesn't even prove the transfer principle. Are there any completely rigorous treatments of the hyperreals? Ideally, I would like them to cover the same content that Goldblatt's book does: construction, nonstandard analysis and miscellaneous applications. However, I'd be more than satisfied with just construction and nonstandard analysis. I would also like the book to be more-or-less self-contained in this regard. That is, if the book simply states the transfer principle is a consequence of some stronger model-theoretic theorem, I don't gain anything from that. Of course, some knowledge of analysis, algebra and logic must be assumed, and I'm fine with all of those on a basic level. To clarify, I am also not interested in axiomatic approaches to these structures. So, for example, a construction of the hyperreals would be much preferred over an axiomatic introduction.", "label": 0}
+{"snippet": "A popular misconception in the layman public is that the Big Bang was some sort \"explosion\" at a single point of space, where originally all matter was concentrated and then it \"exploded\" outwards. This is of course different from the modern general-relativity understanding of reality, which is that it is space itself which expands - not the content of the space moving, and the Big Bang did not start at a single point, but everywhere. My question is - what experimental evidence do we have that can convince people that the explosion model can't be right. Note that I'm not asking why GR guarantees that the space-expanding is the correct model, not the \"explosion\". I know that. I also know that GR has a lot of experimental evidence for its correctness at least in smaller scales. Rather I'm asking which evidence we have from astronomy, CMB measurements, or whatever, showing directly that the \"explosion\" model simply cannot be a valid explanation of the universe's history.", "label": 0}
+{"snippet": "You know how when you talk to someone about a bad time you're going through, and they feel the urge to one-up you to achieve some sort of imaginary victory point? E.g. School is challenging because I have to catch a bus early in the morning. Pfft, that's nothing, I used to have to WALK to school. I did the dishes and the laundry this morning so I'm a little tired. You're tired from that? That's nothing, I swept and mopped my entire house AND my parents' house, I'M tired. Are there words/phrases that describe this behaviour? Either as verbs to describe the act itself, or as nouns to describe the competition. I've seen \"struggle Olympics\" used before and that's pretty accurate but I'm pretty sure that's just internet slang.", "label": 0}
+{"snippet": "A sufficiently strong electromagnetic pulse can/will destroy smartphones and computers. I know somebody who went into MRI machine and forgot a Visa credit card in his pocket. The card was toast and he had to get a new one. A mobile phone in an MRI probably wouldn't fare better. But a big part of the human body itself is based on electric signals. The brain and nervous system, including the heart, works on electric signals. And those signals have to go to very precise places. There is an area of brain processing vision, another is responsible for speech, etc. Also the heart function depends on precisely timed signals traveling very specific routes. So it would seem that a trip to an MRI scan should totally fry anyone's possessing brain and heart. Except it doesn't. An MRI scan is harmless (if you are not allergic to those injections they give). Why? And then there are those electromagnetic pulse devices they show in Hollywood movies. While totally trashing electronics of bad guys, fellow humans are always shown unharmed. Again, why should the brain be different?", "label": 0}
+{"snippet": "Suppose there are two arbitrary side lengths of a right angled triangle that are known to us. There are two possible cases here that I can see: Either one of the side lengths given is the length of the hypotenuse. Both the sides lengths given are the lengths of the legs of the right angled triangle Now, additionally one arbitrary acute angle measure is also known. There are again two possible cases that I can see: The angle lies between the two sides that are known to us (in which case it will then be confirmed that one of the sides given is the hypotenuse). The angle does not lie between the two sides that are known to us (in which case it will then be confirmed that the sides lengths given are the lengths of the legs of the right angled triangle). Now, I want to know if there is any possibility of determining the third side of the right angled triangle using the conditions given above (two arbitrary sides and one arbitrary acute angle) and without any additional conditions for eliminating the cases given above. If possible, please tell me the formulae/procedure to follow. Thanks in advance.", "label": 0}
+{"snippet": "While the gravitational path integral is not a well-understood concept mathematically, a number of works (particularly in recent research connected to AdS/CFT) emphasize the importance of integrating over metrics on surfaces with nontrivial topologies as well as surfaces diffeomorphic to a flat spacetime. These metrics are obviously not continuously deformable to a flat spacetime metric. A superficially similar concept occurs in Yang-Mills with the notion of a large gauge transformation, which relates gauge configurations that are equivalent but not homotopically equivalent. In Yang-Mills one can also introduce a \"topological term\" which has no effect on the equations of motion, but computes the homotopy class of the gauge configuration. There is a somewhat analogous object in gravity, the Gauss-Bonnet term, which has no effect on the EOMs and which computes the Euler characteristic of a spacetime. My question is: is there a sense in which integrating over nontrivial topologies in a \"gravitational path integral\" approach to quantum gravity can be understood as including large gauge transformations in the gauge group of the theory?", "label": 0}
+{"snippet": "I am new to algebraic geometry. I can't understand why an etale space is considered locally homeomorphic to its base space. The analogy I have heard is that etale space can be visualized as \"stacked over\" the base space, or that it is like a \"puff pastry\". I understand that we can (locally) map this stacked/pastry space to the base space, but I don't understand how an inverse map could exist. It seems to me like the inverse map would be multi-valued as it takes a point in the base space to several points in the etale space. As an example, consider the base space to be a circle and an etale space to be a circle winding around itself twice. The map from the etale space takes two points to one point of the circle. Doesn't this mean that the inverse map is multi-valued? Michael", "label": 0}
+{"snippet": "I know that white light, upon entering another medium from air/ vacuum, disperses into its constituent colours. Essentially when travelling in the air, all of the constituent colours have the same speed but when entering another medium, they travel with different speeds and hence they are refracted by different amounts - red the least and violet the most among the seven colours. So we are able to see the constituent colours (especially in the case of a prism since they are diverging.) But I came across the following situation where green light (mono-chromatic) changes into red, as perceived by the human eye as well as the camera. Attaching an image of what happens: Why does this happen? I am a high school student and I haven't read anything so far that could explain my observation. Also as far as I know the properties of light are dependent on its frequency and frequency does not change from medium to medium. I saw the other posts but it would be nice if someone explained it in a much simpler language.", "label": 0}
+{"snippet": "We commonly anthropomorphise or personify non-living things by giving them human characteristics: \"the angry storm\". We zoomorphise things by giving them animal characteristics: \"the storm roared\". But what word would describe giving general (not necessarily animal) attributes of living things to non-living things: \"the storm died\"? A more specific example would be treating geomorphological landforms as if they have a life-cycle, but in the context of drawing parallels with the life-cycles of trees and forests. The additional human or animal connotations of \"anthropomorphise\" and \"zoomorphise\" do not apply, so it would be good if there were a more general word for this practice. This is very similar to the question \"Equivalent for \"personify\" that's not human-specific\". However the accepted answer in that case was \"zoomorphise\" since the OP was talking about a self-driving car being \"hunted\" [like an animal], whereas I am looking for the right word for a more general case.", "label": 0}
+{"snippet": "Semantic consistency of a theory T is defined by there being a model M in which all theorems of T are true. Syntactic consistency of a theory T is defined by there being no formulas A such that both A and it's negation ~A are provable. So let's assume semantic consistency and then assume syntactic inconsistency. Since T is inconsistent, both A and its negation ~A are provable. But since it's also semantically consistent, there must be a model where all of its theorems are true. So there must be a model M where both A and ~A is true, which is not possible. So semantic consistency implies syntactic consistency. Is this conclusion right or am I severely misunderstanding something? I thought that semantic consistency only implied syntactic consistency under the additional assumption of soundness, but soundness was not assumed here. Is this conclusion a consequence of defining semantic consistency too broadly? Should it be limited to there being a model where the axioms are true?", "label": 0}
+{"snippet": "In classical mechanics , the Laplace-Runge-Lenz (LRL) vector is a characteristic feature of the Kepler problem. This enables a very simple discussion of the properties of the orbit for the problem. It is an extra conserved quantity besides the total energy and angular momentum for a particle moving under the influence of an inverse-square force field. More importantly, this is associated with some symmetry of the problem. However, if we consider motion in the gravitational field of a black hole, the analysis of the orbits of test particles become more complicated and we require to use general relativity. So, is there any analog of the LRL vector in general relativity? The description of black hole geometry by pseudo-Newtonian potential (e.g., the Paczynski-Wiita potential for non-rotating black holes) is a well-known concept. Is the LRL vector applicable in such systems for motion around non-rotating black holes having spherical symmetry?", "label": 0}
+{"snippet": "So I've recently started taking maths seriously in hopes of doing physics at university and have gotten pretty good at algebra and learned some very basic calculus but I'm having trouble finding a good introductory geometry textbook. I know this question has already been asked at least twice before and I looked at the at some of the recommendations, but I feel they're geared toward more undergraduate study as I'm assuming the guys who asked the questions already did high school geometry which isn't what I'm looking for. I'm looking for comprehensive high school equivalent introductory geometry textbook that's fairly challenging and would set me up for learning more in depth topics that crop up in physics later. (I say fairly challenging because, like I said, I feel like I'm pretty good at algebra). Consider me somebody who has never done geometry before because that's basically what I am. Thanks. (PS. I've never asked for book recommendations before so forgive me if I'm being too vague, I'll gladly amend my request if anyone needs clarification)", "label": 0}
+{"snippet": "I am struggling to see the motivation behind Radon measures. In many places I see that they are described as measures that \"interact nicely with the underlying topology\", but without further elaboration. On Wikipedia it states A common problem is to find a good notion of a measure on a topological space that is compatible with the topology in some sense. One way to do this is to define a measure on the Borel sets of the topological space. In general there are several problems with this: for example, such a measure may not have a well defined support. Yet they go on do define a Radon measure as being defined on Borel sets so how does that solve the problem they mentioned? What is the usefulness of Radon measures and why are they defined as they are?", "label": 0}
+{"snippet": "Background: My understanding is that model-theoretic semantics (MTS) and proof-theoretic semantics (PTS) differ in the following ways. In MTS, you first define the notion of truth in models and then having this notion you develop a \"good\" (sound, complete, decidable) proof system. In PTS, you just define a proof system and take this system itself to be the the definition of \"truth\", without even talking about models. So both MTS and PTS have proof systems, but these proof systems have different roles. I understand why proof systems are needed in PTS: because that's the only thing you have in PTS -- there are no models. But what is the motivation behind studying proof systems in MTS, given that in MTS there is already a notion of truth (with respect to a model) defined? Why do we need an extra apparatus of proof system specifically in MTS?", "label": 0}
+{"snippet": "I'm confused by how thermometer works based on The Zeroth Law of Thermodynamics. The Zeroth Law of Thermodynamics said that \"If a body, A, be in thermal equilibrium with two other bodies, B and C, then B and C are in thermal equilibrium with one another.\" Then, about thermal equilibrium, it said that \"If when two bodies are placed in thermal communication, one of the two bodies loses heat, and the other gains heat, that body which gives out heat is said to have a higher temperature than that which receives heat from it.\" Then if we use a thermometer to measure our body temperature, if the temperature of our body is higher than the temperature of the liquid inside the thermometer, will the heat flow from our body to the liquid inside the thermometer to reach the thermal equilibrium? If yes, then will our body lose heat and temperature of our body decrease? How does the Zeroth Law of Thermodynamics on Thermometer actually works?", "label": 0}
+{"snippet": "Greetings fellow physicists. I have some questions about the ability of different electromagnetic waves to pass through materials that I hope you can clarify. It seems that microwaves can go through concrete, wood, etc. since we can listen to the radio inside houses. However, it doesn't make sense to put a TV antenna indoors because the pictures might flake; so it is apparent that radio frequency doesn't have trouble passing through walls and so on, but the TV frequencies have. I'm guessing as the frequency increases, it gets harder for waves to get through non-conductive stuff. That would explain why we can't see inside boxes - visible light reflects instead of going through. Things get more confusing with X-rays and gamma rays. They seem to move through matter easily, like how X-rays image our skeletons and are used for security screening. Also, radiotherapy uses gamma rays to reach tumours inside patients. So I'm not sure if microwaves really penetrate concrete and other materials or not. But visible light, x-rays and gamma rays acting so differently is puzzling. Can anyone explain the physics behind why different waves can or can't pass through various materials? Some insight would be greatly appreciated!", "label": 0}
+{"snippet": "In Australia, we use the expression Tall poppy syndrome for a \"social phenomenon that occurs when someone's success causes them to be envied, resented, criticized or discredited.\" https://en.wikipedia.org/wiki/Tall_poppy_syndrome Conversely, is there a term or expression that's used for a social phenomenon where successful and popular figures are respected and blindly defended only because they are, well, popular and successful. I notice this behaviour in the YouTube world where smaller channels (or lesser known Youtubers) get extreme flak for criticizing popular channels, no matter how right they can be. Example: Critic: I cannot stand this person. His opinions have no basis. I can't believe he's so popular. Fan: Oh my god, you're such a pathetic jealous hater. Get a life! Critic: Wow, you sure suffer from [insert expression or word]. People like you are hilarious. I am fine with an idiom, a single word or an expression. Just whatever fits.", "label": 0}
+{"snippet": "I would like to know of any techniques that can be used to measure the electric field strength precisely and accurately in both time and space. I know that there will be physical/ practical limitations to this and that it is not possible to measure at an infinitesimal position, but I would still be interested to know what techniques are out there. Assume the electric field I am interested in varies significantly in all spatial directions, and in time (I believe this means the use of a typical antenna is not possible as it sort of depends on a plane wave i.e. non-varying field in the z and x directions at a point in time, if the wave propagation is in the y direction). Assume that any electric fields are oscillating at frequencies at or below microwave frequencies. Thank you in advance for any insight.", "label": 0}
+{"snippet": "I've asked this question in Quora and the answers I got were: First answer: Using \"more\" and \"less\" helps maintain clarity and consistency in comparative forms. It provides a straightforward and predictable way to form comparatives and superlatives without relying on irregular or unpredictable suffixes. Second answer: Longer adjectives often have complex or multisyllabic structures, making it more challenging to add suffixes like \"-er\" and \"-est\" without affecting the pronunciation or flow of the word. Using \"more\" and \"most\" allows for a smoother and more natural-sounding comparative form. Third answer: Using \"more\" and \"most\" for more-than-one-syllable adjectives maintains consistency with two-syllable adjectives that also use \"more\" and \"most\" for comparison. This avoids creating separate rules or patterns for different types of adjectives Is there an identifiable reason for tending to restrict the forms -er, -est to single-syllable adjectives? It may be one of these I suppose; or something else.", "label": 0}
+{"snippet": "I am actually having an introductory course in Special Relativity in which I was looking at the Michelson Morley experiment. And I have this silly confusion. The setup for the Michelson Morley experiment looks something like this in every textbook (assuming the observer is in the comoving frame) When this same setup is being observed by the observer in the hypothetical frame of \"ether\" (which this experiment was designed to detect) , then the vertical beam of the light is no more vertical but along the hypotenuse(the dashed red line) and this should be true so that the two observers agree on the results of the experiment. But I really don't understand why the light should not go vertically as the shown path of the light beam seems to violate the laws of reflection as the angle of incidence is no more equal to the angle of reflection. So how can then the two inertial frames be equivalent ? PS :- Nobody in the class bothered about this, not even the instructor of the course.", "label": 0}
+{"snippet": "I know that the tangents from a point to a conic section subtend equal angles on the focus. However, I have mostly studied conic sections from the perspective of coordinate geometry, so even when there are properties common to all conic, I have to prove them separately for parabola, ellipse, hyperbola, and circle. The only common denominator between these figures I know of is that they are the locus of points which have a constant ratio of distance from a fixed line and a fixed point. However, I haven't been able to use that much to my aid, having hardly any experience in dealing with these figures in such a way. Observing the apparent simplicity of the result, is there a simple proof for the theorem? P.S.: I would be thankful if someone could suggest resources that deal with such results about conic sections, especially if they use synthetic geometry.", "label": 0}
+{"snippet": "The Leibniz formula for determinants starts with multi-linearity and the alternating property and builds from there. I asked a question about why we should start with multi-linearity: What's so special about multi-linearity?. And the response (which had an excellent alternate motivation for the determinant which I wasn't aware of) seemed to be that there is indeed no good reason. The thing that keeps bothering me is that we are talking about linear maps here. And the determinant is really a property of the linear map. And given the definitions of linearity in the context of linear maps and the multi-linearity of determinants look exactly the same, I would assume a statement like this exists - \"because the determinant is a property of linear maps, it clearly must satisfy the property of multi-linearity because _____\". Is there no way to fill in the blank?", "label": 0}
+{"snippet": "I just stumbled across this older video of a girl trying to \"talk\" to Alexa (the voice assistant). She says \"I am trying to talk to you, hen\". Now, I am not a native English speaker, but I am familiar with the endearing term \"honey\", also sometimes written \"hunny\" or even \"hun\" or \"hon\" depending on the pronunciation. However, the pronunciation \"hen\" made me think of the word for a female chicken. I've heard the word \"chicks\" to refer to females (but I think this is generally not an appreciated term? - again, not a native speaker), so there is a connection to use terms for poultry to refer to people. So my question is, in Scottish, what is the root/etymology of \"hen\"? Is it related to \"honey\" or to \"hen\" (chicken), or maybe something completely unrelated?", "label": 0}
+{"snippet": "Consider a metric space with a path between any two points, so a real line segment of some length between them, and the length of this line is the same as the distance between the two points in the metric. This is called a geodesic metric space. Any two points are connected with a shortest path. There could also be multiple such paths as with the antipodes of a sphere. What I mean by homogenous is that any point can be mapped to another while preserving the structure of the space. Another way of looking at it is that the space is the same no matter what point is taken as the origin. Geometries like Euclidean and non-Euclidean geometry would be examples. However, I am curious about examples which are not locally Euclidean. So, they would behave kind of like Euclidean space in that there is a measurable shortest path between two points and everywhere in space is the same. So you could \"move around\" in a given \"direction\" in this space, but it does not locally resemble Euclidean space. Is this even possible? If so what characteristics would these spaces have and could they be classified? What about the underlying topologies of these spaces?", "label": 0}
+{"snippet": "Say that I have two long cylinders of material as shown that are in a region of oscillating magnetic field where the field direction is aligned with the long axis of the cylinders. I want to calculate the inductive heating of each cylinder (let's pretend for a moment that none of the parameters like resistivity are temperature independent). I know how to calculate the skin depth and therefore the heating when only one is present, but don't know how to deal with two cylinders. Does the inner cylinder \"steal\" some of the magnetic flux by reducing the flux from its own induced current? If so, how much? I would think there would be time lag between the flux and the induced current. Any thoughts or references explaining how this can be attacked? Thank you", "label": 0}
+{"snippet": "I hope that this is the correct site to ask this question, but since I was unable to find one specifically for modeling, I decided to ask here (and please feel free to correct me, if any of my statements is bogus): There are tools which allow one to do parametric modeling like Rhino's Grasshopper or Blender's Geometry Nodes. The modeling happens in a bottom-up manner, e.g., twisting and bending some input shape according to some parametric functions. And then there are implicit modeling tools like nTop (formerly \"nTopology\") which allow modeling with implicit functions, and therefore enable a top-down workflow, e.g., you have some shape and describe with combinations of implicit functions that is shall have rounded corners and be filled with a fancy pattern. But the implicit modeling tools are, I think, relatively new on the market and generally only smaller and light-weight tools. I specifically wonder about the reasons for that. And my question would be: Is there something that can easily be done with parametric modeling which is hard to be done with implicit modeling? And if so, what and why?", "label": 0}
+{"snippet": "I have been interested in hyperbolic (negatively curved) space and I have been reading enough about it to feel that I understand it relatively well intuitively (e.g. the Poincare disc). But the problem is when I flip the curvature sign in my head to positive curvature and elliptic space nothing seems to make sense. For instance: In elliptic space, locally \"parallel\" lines will converge and intersect given a great enough distance, but if there is really a positive curvature, then it seems like the lines will eventually converge after the intersection to intersect again. This leads to the result that the lines will intersect an infinite number of times. Is this correct? I cannot find the right search terms to find this answer. Is elliptic space really a sphere? Does the positive curvature mean that if you travel far enough, you will end up back at the starting point? If so, then it seems to imply that elliptic space is finite, where Euclidean and hyperbolic space are infinite, which seems wrong. I likely have some misunderstanding of elliptic space, so If you can correct me where I may have gone wrong, please do. Thanks", "label": 0}
+{"snippet": "I'm looking for the best BE substitute for the AmE word \"ornery\" in the phrase \"an ornery bunch\". Complicating the task for this second-language speaker of English is that according to the Oxford Dictionary of English, \"ornery\" means \"bad-tempered and combative\" in AmE whereas it means \"bad-tempered or difficult to deal with\" in BE. Does this mean that BE speakers tend to understand the word \"ornery\" slightly differently than Americans generally do (that BE speakers may perceive ornery characters as not necessarily being bad-tempered?)? Also, are there any synonyms that BE speakers usually prefer as substitutes for \"ornery\", or do BE speakers rather use several words to cover the AmE meaning of \"ornery\" (in the latter case, for my task: instead of \"an ornery bunch, perhaps \"a coarse and combative bunch\"?)?", "label": 0}
+{"snippet": "When I compile my document with pdflatex with natbib and either the plainnat or the dinat style on my computer, the author list is translated to German. E.g., I get \"und\" between authors instead of \"and\" and instead of \"et al\" I get \"u. a.\". I am very puzzled, because I don't know why. In my bibliography file all references are in English and I also write \"and\" between each author. So the original is in English and there obviously happens an unwanted translation somewhere. When I upload the very same document (i.e. all .tex files and also the .cls file, exactly as they are on my computer) to Overleaf, everything is fine and the compiled document has all references in English. I use TexStudio to write and I also compile from TexStudio. Could it be because of TexStudio? What could I change to make sure that nothing is translated?", "label": 0}
+{"snippet": "Consider two samples of visit lengths to two different Emergency Departments. We want to test whether or not the means of the samples are different. A basic requirement is independence between and within samples. However, while we know that there are no patients that had visits in both samples, there are patients who had multiple visits within a given sample. Therefore, we cannot consider the visit lengths within a given sample to be independent. How do we deal with this? The visit lengths are labeled with patient identifiers. If, for every set of visits associated with a patient (most of which will contain a single visit) we randomly sample one visit, can we use the resulting sub-sample for hypothesis testing, or will this process inject bias? If so, how could we control for the bias? I've done a fair amount of searching on this topic, but there's a lot of obfuscation. Maybe I just need someone on here to tell me what terms I should be searching for.", "label": 0}
+{"snippet": "I started running a tabletop RPG campaign set in the distant future where mankind has degraded to a primitive hunter-gatherer society, and I'm looking for flavorful terms for NPCs to describe directions. As research, I started watching the show \"See\" which has a similar premise, and they use the term \"sun grave\" to refer to west, because that's where the sun sets. And I love it! But what about the other directions? (I'm only midway through the first season of \"See\" and I haven't noticed them refer to another direction.) East could be \"away from the sun grave,\" but what about north and south? \"Right of the sun grave?\" That feels awkward to me. Is there another more primitive way of describing a perpendicularity like that, or perhaps another point of reference besides the sun?", "label": 0}
+{"snippet": "I saw this post which says: The way you do it is just a simple logic. Imagine a tennis ball and imagine you can't really see it, just like you can't see an electron. So the only way you can see where the tennis ball is is to hit it with another tennis ball or with an enormous amount of light that it will actually displace the tennis ball position, move it that is. At that moment the light brings you the information into your eyes and you see the tennis ball. Does the author mean the reflected light? Because if the light isn't reflected (i.e. a new photon emitted), how would we see the electron or tennis ball? It seems like, unless light is reflected/a new photon is emitted, we won't be able to see the electron. If my reasoning is correct, then we can't detect electrons in the photoelectric effect this way, because no photons are emitted in that case, but we can in the Compton effect. Is my reasoning correct or did I make a mistake?", "label": 0}
+{"snippet": "I am doing some research into social interactions and the data is represented in a series of square matrices for analysis. I am interested if the grouping of matrix elements above/below off-diagonal, as highlighted by blue and green in the following diagram, are known by a specific name? These groupings of matrix elements differs from the upper/lower triangular matrix as they don't include the main diagonal and all the elements can be greater than zero. I have searched for a name but have not found anything yet. Also does the sum of these groupings have a specific name? (Akin to the sum of the main diagonal being called the trace). If there are no conventional names, I am okay to defining a name for each grouping and their respective sums as part of the research.", "label": 0}
+{"snippet": "I am trying to understand the basics of quantum mechanics and I am having some issues in understanding the main mathematical properties of quantum operators. In particular, it's clear to me that: Quantum operators must be Hermitian to guarantee: real eigenvalues, that can be measured an orthogonal basis, so that after each measure the state of the system collapses onto a precise base-state Unitary operators are needed because they preserve norms: if we apply a non unitary operator to a system, its total probability would not be preserved. It's clear to me that the Hamiltonian is both a hermitian and unitary operator. In any book I have read, I have only found statements such as \"operators in quantum mechanics must be hermitian\" or \"time evolution is unitary\", but I've never found a statement such as \"operators must be both hermitian and unitary\": why is that? Shouldn't all operators be both, to guarantee measurability and conservation of norm?", "label": 0}
+{"snippet": "Although neutron stars are mostly made of neutronium, the pressure at the surface is not very high which allows regular atomic matters to exist. Emission spectrum can reveal the chemical composition of distant stars. However, neutron stars are surrounded with extremely strong magnetic field which is enough to distort the atomic structures. Atomic nuclei should be more resistant against the magnetic field because they are much more compact and tightly bound, but I am not sure if atomic nuclei emit characteristic spectrum like the electron clouds. If we can determine the composition of the neutron star crust, will there be any variations? Neutron stars formed due to iron core collapse should have an iron crust. Some neutron stars are formed due to the electron capture of the O-Ne-Mg core. Would these neutron stars have a different chemical composition in the crust? Many neutron stars are accreting hydrogen and helium gas from companion stars. Will the accreted matters show up on the surface?", "label": 0}
+{"snippet": "this is my first post, please excuse my non-technical language. I would like to simulate the return of a stock, that is correlated with other stocks, that meets the mean and variance of a given empirical time series. The usual way to do this is to set up a geometric brownian motion and to use a cholesky factorization on the correlation matrix of the returns of a set of stocks. As far as i know the moments of this GBM are functions of time but the log of the GBM doesn't contain any skewness. My question is: In what way can i extend the GBM to introduce a target level of skewness while keeping the other moments as in the standard GBM? Would you mind providing the explicit form of the SDE? Thank you very much in advance! Thomas", "label": 0}
+{"snippet": "Ok, this is my first question on this site. But it's one I've been thinking about for a while. Say through whatever means, we place a device capable of generating thrust/ kinetic energy on the surface of the Earth. The goal being to remove Earth from its orbit and exit the solar system. By \"perfect conditions\" I mean that hypothetically when this does happen, no other planets or space debris will be in its path. I'm thinking that first it would be easier to stop the rotation of the Earth, and then use our device, but I don't quite know how the Sun's gravitational field will affect all this. Also, there can be two versions of this: one where the device generates continuous thrust and the other where it's more of an impulse. How much energy would the device need and, if any, what other conditions are needed in order to exit the solar system?", "label": 0}
+{"snippet": "I'm a native English speaker, and I noticed that I sometimes use accusative pronouns (him, her, me) to replace actors in certain clauses. I have a feeling this is prescriptively considered incorrect usage, but I want to be able to describe it. \"What does that have to do with me not coming to class?\" \"I want to hear about them starting a new game.\" \"Him winning that contest has nothing to do with his family.\" Maybe the prescriptively correct form is the possessive, and this is confusion based on \"her\" which is the same in both? Or maybe it is because when the clause comes second, the pronoun makes sense as an object of the larger sentence? But that doesn't apply for the third sentence as much unless you flip it around: \"His family has nothing to do with him winning that contest.\" How do you describe what is happening here? Why does it happen? Is it considered \"incorrect\", and if so, how widely? (I have the intuitive sense not to write it in an essay, but it comes so easily out of my mouth...)", "label": 0}
+{"snippet": "\"Such\" has many meanings, one of them being to refer to something of a particular kind/type (see \"of this or that kind\"). However, in many legal documents and laws in Malta, \"such\" is used instead of \"this\" or \"that\", or instead of \"the said thing\". For example, a legal document might read as follows: The following are the terms and conditions regulating the relationship between A and B. Such terms and conditions are.... Here, \"such\" is not used to mean \"of this or that kind\", but is used instead of \"these\" (the terms and conditions previously mentioned). Is this use of \"such\" limited to the legal English used in Malta or is this a common feature of the legal English used in the UK, USA and countries where English is an official language?", "label": 0}
+{"snippet": "Not really sure if physics question or engineering question. If we can apply energy to make an object in space move faster, the reverse should be possible - we should be able to extract energy while causing the object to slow down. So in theory, if we use rail gun to launch a projectile in space, we should be able to extract energy out of it if we \"catch\" it with another rail gun. Considering that, since we can use gravity slingshot to accelerate objects, we should be able to extract MORE energy out of the projectile when we \"catch\" it. The extra energy would come from the gravity of the celestial body used for the slingshot, which is practically huge. We could use part of this extra energy to redirect the object to the original course, thus creating a stable loop that would allow us to extract vast amount of energy from the gravity of other planets. Why wouldn't this work?", "label": 0}
+{"snippet": "I ordered a book online, unseen, and the invoice told me the book, or at least its pages, were 'foxed'. I had never come across the expression, did not know the word could be a verb and discovered : Foxing is the age related browning, or brown-yellowish spots, that can occur to book paper over time. When this aging process happens to the paper in a book it is referred to as \"foxed\". The term may come from the rust brown color of the paper aging process or from a chemical used to coat paper called ferric oxide. Foxing may also be caused by fungal growth on the paper, chemical reactions, or high humidity. Biblio.co.uk Is there any more information anywhere to clarify the idea of ferric oxide being involved, which sounds a little far-fetched to me, or to demonstrate the history of the word in that particular context?", "label": 0}
+{"snippet": "In condensed matter and materials physics it is often assumed that the response of a condensed phase to some perturbation is determined by the fluctuations of the system at equilibrium (without perturbations). For example, the electric resistance of a liquid (the response of the current to an applied field) is determined by the mean squared displacement of the charge carriers (the fluctuations) at equilibrium. Pictorially, this makes sense because if the charge carriers move slowly at equilibrium it will be probably not be easy to make them move, so for small fluctuations the current response would probably be small. Another way to say this, the difference between motion at equilibrium (without field) and motion out of equilibrium (with applied field) is that there is a small bias in the direction of the field, but the motion is otherwise essentially the same. Formally, this relation is proven by the fluctuation-dissipation theorem for a statistical mechanical (micro-canonical or canonical) system subject to small perturbation (small term added to Hamiltonian). My concern is that I think that the validity of this FDT relation can be formulated for systems more general than statistical mechanical (micro-canonical and canonical) systems. Pictorially, I think whenever the system can be described as a stochastic variable fluctuating in some potential landscape between some potential minima, then the response should always be related to the barrier heights of those minima, which also determine the magnitude of the fluctuations at equilibrium (without bias). So is it possible to derive FDT also for this setting ?", "label": 0}
+{"snippet": "In order to obtain phonon spectrum, we usually do Born-Oppenheimer approximation and assume that the electrons are always at the ground state when the atoms move, and by calculating the force on each atom (usually using DFT) we are able to assemble the dynamic matrix of the atoms and obtain the phonon modes. After this we can calculate the electron-phonon vertex and then do Feynman diagrammatic calculations to get things like polaron. So the whole formalism is based on the BO approximation. The question then is how we can write down a set of Feynman rules about both electrons and atoms without the BO approximation. Can we still define phonons (hence phonon propagator, etc.) in this case? If we already have a theory under the BO approximation, is it possible to, say, add more interaction vertices and/or adjust the coupling strength to go beyond BO?", "label": 0}
+{"snippet": "In An Argument Against Abolishing Christianity it is written: Another advantage proposed by the abolishing of Christianity is the clear gain of one day in seven, which is now entirely lost, and consequently the kingdom one seventh less considerable in trade, business, and pleasure; besides the loss to the public of so many stately structures now in the hands of the clergy, which might be converted into play-houses, exchanges, market-houses, common dormitories, and other public edifices. I hope I shall be forgiven a hard word if I call this a perfect cavil. I readily own there hath been an old custom, time out of mind, for people to assemble in the churches every Sunday, and that shops are still frequently shut, in order, as it is conceived, to preserve the memory of that ancient practice; but how this can prove a hindrance to business or pleasure is hard to imagine. What if the men of pleasure are forced, one day in the week, to game at home instead of the chocolate-house? Are not the taverns and coffee-houses open? I looked up chocolate in Wiktionary and chocolate house in Wikipedia. Of what chocolate house does Swift write here?", "label": 0}
+{"snippet": "In a power grid, the grid itself has a certain amount of inertia from all the spinning loads and generators. If at a given moment in time the production and consumption of active power does not match, the power mismatch will be provided/absorbed by the spinning energy stored in the grid, and the frequency of the whole grid will raise or lower in lockstep to compensate. Eventually the generators' governors and the load/frequency relationship will arrest the frequency drop, and it will arrive at a new steady-state value, but it's not something that happens immediately. Does it work similarly for reactive power? If a capacitor bank supplying reactive power suddenly trips, does the voltage immediately drop to its new steady-state value? Or is there a period of voltage decline as the missing reactive power is siphoned from somewhere?", "label": 0}
+{"snippet": "Suppose there is a plank on a smooth surface and a man is standing on one end of it. The surface of plank is rough. Now the person starts to move towards the other end with some acceleration and the plank also starts to shift to keep the COM stationary as the only forces acting here are all internal. Now my question is,as the direction of the friction force on the man is in the direction of the displacement of man and same is the case with plank. Then in this case isn't work done by friction on the whole system coming out to be positive which should not be happening as if it is the case of static friction then the net work done should be zero and if it is the case of kinetic friction then the net work done should have been negative? Also please tell me whether the friction present here is kinetic or static.", "label": 0}
+{"snippet": "Note: this question is not a duplicate of the following questions: How to remove vertices from a graph that are not coverable by cliques? How to remove vertices from a graph while preserving clique coverage of specific vertices? This question is with respect to removing vertices that are not reachable from a set of vertices, regardless of clique membership. How can I remove vertices from a graph that are not reachable from a given set of vertices? Here is a toy example and solution: In the graph below, I want to remove the vertices that are not reachable from any vertex with an \"x\". The orange vertices are the vertices to be removed. toy example graph image The current approach is doing depth-first search from each of the vertices marked with an \"x\", and keeping track of which vertices are visited. All vertices from the graph that are not in that set of visited vertices are removed from the graph. However, this could take a while if the graph is large, so I was wondering if there is a faster way of doing this.", "label": 0}
+{"snippet": "Let's say we entangle four electrons based on their spin. Now, let's say we measure the spin of electron A along the z-axis (up/down), and we observe a spin of 'up'. My understanding is that this means that the remaining three electrons would need to have some combination of spin which adds up to 'down'. Next, we measure the spin of a second electron, but along the x-axis (left/right), and say we observe 'right'. My question is, what does this mean for the up/down spin of the entangled system? I'm thinking since it can't be that the remaining two electrons add up to a 'down' spin, it must be that the second electron we measured also still has a state for up/down spin that has not been observed yet. But that would also imply that it's still entangled with the other electrons; this is where I'm confused, cause it was my understanding that a measurement would break entanglement. Is that correct, or no? What actually breaks the entanglement in this case? Hope the question makes sense, and thanks in advance!", "label": 0}
+{"snippet": "I need a word that describes someone who advocates for harmful laws or policies; it would describe someone who writes policy without listening to the people it affects or someone who doesn't pay attention to actual effects of that policy, kind of like politically or socially tone-deaf. They might continue to stand behind that policy even after it was proven to be ineffective or harmful. It would be like ignorant or deluded, but specifically regarding knowledge of people's situations or societal problems and solutions. A word to describe the actions of that person would be helpful as well. As an example: It was very __ of the senator to vote for the harmful bill that would require every homeless person to own a car. The word wouldn't refer to someone doing this knowingly and maliciously, but I would like it to have a negative connotation. Thank you!", "label": 0}
+{"snippet": "I want to start learning model theory for my master's thesis, but I can't find the right book for me. For some context, last year as an undergrad I had a class on logic where we learned the following: So I already had contact with formal languages, structures, models, and both the semantic and syntactic aspects of first-order logic and now I want to follow from this and start learning some real Model theory. I started using David Marker's \"Model Theory. An Introduction\" but I'm personally not a big fan of that book: It's full of typos and I don't like how informal some of his proofs and expositions are, for example, this definition: Do you have some recommendations for a rigorous book/resources to learn Model theory, ideal for someone with a little background on the subject?", "label": 0}
+{"snippet": "Whenever I get into a disagreement with an individual I notice that this phenomenon always occurs. (I either notice it during the argument or afterward.) Allow me to provide you with an instance to help describe exactly what I am talking about: I am having a disagreement with an individual regarding bottled water VS tap water. I am supporting the consumption of tap water and simultaneously attacking bottled water. At one point, it seems like I have won the argument as my points outweigh his. However, he then starts bringing up additional points and he now feels that he has won that argument. I tell him, \"Any argument could be supported with the English language, due to its vast vocabulary, but my points are logical and outweigh yours\". Therefore, here is a summary of what I am asking for help with: What is this phenomenon called when someone uses the vast vocabulary of the English language and all associated knowledge to formulate points to support their argument? What is a good word for this phrase/How could this phrase be reworded to a simpler form without out sounding cruel? - \"any argument could be supported with the English language, due to its vast vocabulary, but that my points are logical and outweigh yours\"", "label": 0}
+{"snippet": "I'm trying to understand how Newton's third law works with springs. If we hang a block on an ideal spring mounted to the ceiling, in equilibrium, the block is affected by gravity downwards and the spring force upwards. So according to Newton's third law the spring itself is affected by the spring force downwards. This makes sense in my brain, but what would be the force upwards, since the spring is also in equilibrium, right? Is this the reaction force to the gravitational force on the block? That wouldn't work if the block was accelerating e.g. downwards, since then the spring would be accelerating upwards which is not what's happening? There also has to be some force from the spring on the ceiling, does the reaction force to that just always cancel out the reaction force to the spring force so the spring stays in rest? But shouldn't that force depend on the weight of the block somehow?", "label": 0}
+{"snippet": "My question may be simple but I'm curious, let's say I start bouncing a ball like a footballer with my foot on an elevator, and it starts moving upwards (with acceleration) and then it stabilises itself moving upwards with no acceleration at a constant velocity. My question is if the ball will or not start bouncing less due to the upward motion of the elevator. My thoughts are that it depends, if the elevator is accelerating upwards then the ball will get a force pointing downwards so that it will start reaching less height than if we would be bouncing it on a stationary case. And if the elevator is not accelerating but moving upwards with constant velocity, it doesn't feel any difference with the stationary case since there is no acceleration, but I don't know", "label": 0}
+{"snippet": "I am wondering how this sentence is to be paraphrased: At weekends they prefer to stay home and visit some friends. I am not sure which ones are close to the original: They like to remain in their house at weekends and they also like to go and see their friends. They like to remain in their house at weekends and to go and see their friends. They like to remain in their house for a while at weekends and then go and see their friends. They go and see their friends on weekdays but would rather remain in their house at weekends. They generally go and see their friends but would rather remain in their house at weekends. They like to remain in their house at weekends or else to go and see their friends.", "label": 0}
+{"snippet": "The task is: The farmer has several sheep, each responding to one or more names, and several sheep may respond to the same name. Each sheep answers to at least one of the names, the farmer knows which sheep respond to which names. The farmer has two paddocks for food and a haircut. A farmer can say a name, and then all the sheep who answer that name go to another paddock. Prove that farmer can say names several times, so that at least half of all the sheep will be in the haircut paddock. I really want to solve this problem using probabilistic method - I need to show that probability of this event is more than zero, then the task will be solved. But I can't come up with a strict solution how to do it. (I am new to probabilistic method) Please, help me out!", "label": 0}
+{"snippet": "I was talking to a colleague professor the other day and he said something that got me curious. The way I remember it, he said basically that in experiments a Bose-Einstein condensation is usually trapped by some external potential, which I imagine to be an electric or magnetic field. Then, the temperature is considerably lowered, the trap is turned off and one studies the evolution of this state. Can someone further elaborate this kind of experiment? For instance, it was not clear to me what exactly one tries to measure with it; as far as I understood, the temperature is cooled down so to form a condensate in the first place and the release of the external field is intended to study its evolution. What one wants to understand with the evolution of such a condensate? Moreover, what material is used in such experiments? (I am thinking about liquid Hellium?)", "label": 0}
+{"snippet": "If all matrices can represent a linear transformation, can I refer to some general notion of the transformation associated with the matrix to make conclusions about the matrix? For example, I want to prove a simple true/false statement, \"If A and B are square matrices such that AB is invertible, then both A and B must be invertible.\" I believe that the statement is true for the following reason: Assuming AB is well-defined and A and B are square, A and B have the same dimension. The product, AB is square as well then. AB is invertible and square, so the transformation AB represents is an isomorphism, thus the transformation associated with AB is a bijection. The transformation associated with AB is a bijection, so the transformation B represents is surjective and the transformation A represents is injective. Since both A and B have square matrices representing their linear transformations, injective and surjective respectively, the transformations must also be isomorphisms. Hence the transformation associated with A and B has an inverse, and thus A and B (the matrices) are invertible. This feels convoluted and likely isn't the simplest solution. I am just wondering if it is OK to bring in the notion of the transformations the matrices could represent like this? Am I missing some subtlety?", "label": 0}
+{"snippet": "I do not understand at all why, if an object is sitting on a spinning platform, the friction force is towards the center. I understand the need for a centripetal force during circular motion, but friction is only in opposition to a force being applied to an object / system, why does it act as centripetal? I understand for a car, for example, the wheels providing the forces needed, but, for example, a penny sitting on a rotating disc, why would the friction be towards the center, would it not be in opposition to the impending motion of the tangential velocity? I have seen a lot of explanations on why there would obviously be a centripetal force, the need for one because there is a change in velocity, etc, but none of these explain why friction acts as this force, or how.", "label": 0}
+{"snippet": "A flat spiral in immersed in a homogeneous magnetic field. An electric current is flowing in the spiral. The directions of the B field, the spiral and the current can be seen in the picture. As the result of the electric current and the B field, Lorentz Force appears acting on the electrons, aka the Hall Effect. The electrons are flowing from the edge to the center of the spiral, the Lorentz Force F also points to the center. Seemingly the Lorentz Force is helping the electrons to move to the center of the spiral. If that reasoning is correct, can we say that e.m.f. (electromotive force) is created because of the Lorentz Force? The bigger is the current, the bigger the emf gets, as opposed to the Ohm Law. Voltage is created out of nothing. How would you justify the energy conservation? If you think I am wrong, please point out my mistake concretely.", "label": 0}
+{"snippet": "It is stated that an object in motion acquires \"kinetic energy\" while an object under the influence of gravity when raised to a height acquires \"potential energy\" but I have a doubt that what leads to the object acquiring the energy in actual sense? What special is happening that an object in motion or an object at a height acquires the ability to do some work(i.e. energy)? If I start thinking about it more energy is just an \"abstract thing\" so is it just that we assign this value to an object under a specific condition and we say that it \"gains\" this energy? Also, isn't this energy just a \"numerical value\" with no real meaning so what is it even representing under a specific condition of motion or change in height? P.S. I tried searching for similar questions on the internet and Physics S.E but couldn't find a satisfactory answer yet.", "label": 0}
+{"snippet": "I am doing an experiment with the overall research question of: To what extent does the amount of fluid within a hollow cylindrical can affect its dynamics while rolling down an inclined plane I was able to derive an equation for acceleration for the case of a fully solid cylindrical shell and then used law of conservation of energy to determine equations for the velocity of a solid and hollow cylinder and I understand that the moment of inertia's of the aforementioned cans can also be found easily using the radius. However, I am finding difficulty in finding a method to determine the moment of inertia for cans that are partially filled other than the parallel axis theorem which I am not sure can be applied to this scenario. Furthermore, I am also unsure about the actual experiment that I am doing to answer the initial research question (I have access to a motion sensor and photogate sensor) and was wondering if I should simply measure the final velocities and relate it to varying moment of inertias if it is possible to calculate but would appreciate any alternatives to this experiment. Finally, I am not sure if I should treat the water as an inviscid fluid as that would mean there would be no effects on the moment of inertias but the mass would still change so that would affect it in that regard, right? For now I have been treating it as an inviscid fluid for the purpose of the derivations that I have made.", "label": 0}
+{"snippet": "Also, how do different sets of principles affect the results we can get in our meta-theory? The more concrete questions that lead me to ask the above two questions are stated below. If we are studying intuitionistic logic, should we also drop the excluded middle rule in our meta-theory? Besides, in classic logic, I seem to notice that a proof of the compactness theorem must utilise the axiom of choice, be it directly or indirectly. The proofs I ever saw so far all implicitly assumed the axiom of choice in its meta-theory. (Actually, so are the proofs of the completeness theorem.) Does that mean, if we are to drop the AC, we can't even have the compactness theorem? What if we are studying a set theory without the AC? Should we assume the AC in our meta-theory when studying a set theory with the axiom of determinacy instead of AC? Or maybe we should adopt the AD instead of AC? Are we supposed to use the same rules in meta-theory as those in our formal theory?", "label": 0}
+{"snippet": "I've been exploring the concept of gravitational wave (G-wave) emission from symmetrically accelerating systems and have encountered a puzzling question. Standard sources typically state that symmetrical systems, such as a perfectly rotating sphere, do not emit G waves. As they require a changing quadrupole moment, which such systems do not exhibit. However, this leads me to draw parallels with concepts like standing waves and the Fourier transform of a static field, where individual waves can cancel each other out, resulting in what appears to be a static field. My question, therefore: Is it that each part of a symmetrically accelerating system never actually emits any gravitational waves, or is it more accurate to say that any potential gravitational waves are effectively cancelled out due to the system's symmetry? To illustrate this, consider a hypothetical scenario: If a rotating spherical mass were to suddenly appear in an ideal space-time, would an observer detect non-zero gravitational waves during the initial moments when the gravitational effects from different parts of the sphere begin to propagate at the speed of light (c)?", "label": 0}
+{"snippet": "Is the essential argument that these systems are microscopically chaotic enough that we can approximate their evolution as random (vastly simplifying calculations) and still make accurate experimental predictions? Or are there deeper physical/mathematical foundations? A related question: how does one interpret the distributions we end up using (e.g. over particle velocities)? E.g. when we calculate expectation values are we (A) implicitly averaging over an ensemble of universes with different microscopic system configurations? If so, why is it \"okay\" to make predictions about measurements in one universe from an average over universes? Does one have to invoke some kind of further self-averaging argument? Or (B) are we taking a more Bayesian perspective, where there is only one universe, with the distribution representing our uncertainty over the system state? If this is the case what other assumptions are made? Should we think of the distributions we manipulate as posteriors, given some prior? If so, what is that prior? Or are (A) and (B) equivalent in some sense? Or am I thinking about this the wrong way entirely?", "label": 0}
+{"snippet": "So, I have been studying thermodynamics, in it I read that state functions are those functions which depend only on one state of the system and are independent of the path taken, which is pretty easy to understand. And this clears why properties like enthalpy, pressure, volume etc are state functions. Then there was the statement, Change in a state function is not a state function. which took me some time to understand, but I got it once I referred to the original definition of a state function. But now when I read about Hess law, which basically states that change in a state function is independent of the path taken, I'm confused as doesn't this imply that change in state function is infact a state function. Can someone please clarify this.", "label": 0}
+{"snippet": "I often come across materials discussing convergence spaces and their relevance in various contexts. It's commonly mentioned that the existence of a natural convergence on the space of continuous functions (turning them into exponential objects) makes the category of these spaces a suitable environment for studying homotopy. However, I've found only a limited number of resources that actually delve into this idea (mainly this and this). As someone who doesn't engage with algebraic topology on a daily basis, this leaves me with a few questions. Are there any works that effectively highlight the significance of these spaces for the typical algebraic topologist? If not, could the issue possibly be attributed to an \"excessive\" use of filter-related terminology? I would greatly appreciate any insights or references that could shed light on this matter.", "label": 0}
+{"snippet": "Say we're drawing marbles from a box. The marbles can be labeled X, Y, or Z and can be either black, brown, or white. The probability of drawing a marble with each letter label is unknown but fixed and marbles are replaced after each draw. A marble labeled X is half as likely to be brown as the other colors. A marble labeled Y is half as likely to be black as the other colors. A marble labeled Z is half as likely to be white as the other colors. Say on our twentieth draw from the box you see a black Y for the first time. Question I came up with: What is the best estimate for the probability of drawing a marble labeled Y from the box?", "label": 0}
+{"snippet": "In the \"talk\" tab for Wikipedia Heat Engine article, someone is questioning whether an internal combustion engine can be modeled as a heat engine - and therefore is limited or is not limited by Carnot efficiency. The arguments are that the input is chemical energy, not heat. And also that IC engines dont operate on a closed cycle. Fresh air enters and is expelled each cycle. There are some answers there as well, but I'd like to get input from you guys to settle this matter once and for all! Is it ok to model IC engines as heat engines? And in a wider sence; can you model a solar cell as a heat engine and calculate carnot efficiency with T_c being the air temperature, and T_h being temperature of the sun. (I saw this in a textbook once, I believe.) https://en.wikipedia.org/wiki/Talk:Heat_engine (section headline: \"Internal combustion engines can't be considered heat engines\")", "label": 0}
+{"snippet": "If I were sorting, for example, audio recordings based upon the performer, then \"Vince Guaraldi\" and \"Bob Seger\" would be sorted as \"Guaraldi, Vince\" and \"Seger, Bob\" On the other hand it's not immediately clear to me how I should sort a recording by \"Vince Guaraldi Trio\" or \"Bob Seger & The Silver Bullet Band.\" My instinct is that this is now an entire proper name for a group and shouldn't be split up (just like I wouldn't sort things under \"Zeppelin, Led\"), but in both cases the group name is created to highlight the most famous member. Both of my print style-guides are silent on this; the MusicBrainz style guide, is clear that e.g. \"Guaraldi, Vince, Trio\" is correct, but I'm not sure if that's just a quirk of a single site, or if it is something more universally done.", "label": 0}
+{"snippet": "I am thinking about the following question: when I look at the atomic emission spectrum of a specific element and I am only interested in the visible section of this spectrum and the method of retrieving it is via putting the element inside a flame, does the type of the flame in any significant way impact the observed spectrum? For example, does it matter wheter I excite lithium with a standard propane flame or instead a hydrogen or acetylene flame? I am trying to find ressources on this online but so far I haven't found any spectrum of any element that was measured using anything else than \"the flame method\" which I suspect refers to using propane gas (or other falmes with less known composition) as the exciting medium. I was tasked to find such spectra measured using different types of flames but since I couldn't find anything on this I am wondering if this question makes sense in the first place.", "label": 0}
+{"snippet": "Suppose we have a loop of copper wire moving perpendicularly through a constant finite rectangular magnetic field directed into the screen . When the loop enters the field, the induced current would be counter-clockwise and when it leaves the field the induced current would be clockwise according to Lenz's law if we view the loop moving through the field from above. But the question here is that when the loop is moving through the middle of the field where it is neither entering nor leaving the field, can we say that the magnetic flux is changing and thus producing an induced current in the loop? The field is constant throughout, so will the change in flux be zero? But if not, how can we tell in which direction the current will be flowing? How could Lenz's law be applied to such a case?", "label": 0}
+{"snippet": "I'm studying about electric field and referring to an article about electric field in wikipedia And in here, there are some doubtful sentences: The electric field is defined as a vector field that associates to each point in space the electrostatic (Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point First, in this sentence, i'm doubtful about 'electrostatic force'. As i know, moving charges also make electric field. This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields. And i think, in here, there is electric field which is not belonging to 'electrostatic field and field time-varying magnetic fields'. For example, steady current, not in wire, makes electric field but don't make time varying magnetic field.. Is there something I'm thinking wrong? I think above sentences are uncomplete", "label": 0}
+{"snippet": "In the vacuum state, particles and antiparticles can spontaneously emerge as virtual pairs due to the uncertainty principle. These virtual particles have a brief existence before they annihilate each other. This process is a manifestation of vacuum fluctuations. Similarly, in particle interactions, intermediate states involve virtual particles that can exist for a short time before contributing to the overall interaction process. These virtual particles mediate the exchange of momentum and energy between the initial and final states of the particles involved. If the intermediate state is represented by virtual particles, should we distinguish the actual physical process of the in-between, intermediate state from the vacuum state? Are intermediate states just mathematical constructs only useful for calculating; or they have a physical significance within the framework of quantum field theory? We cannot think of the intermediate state as the vacuum state despite having the same description involving virtual particles that cannot be observed due to their brief existence?", "label": 0}
+{"snippet": "I am what most of the world considers a \"non-native\" speaker of English. I, however, consider myself a \"native\" speaker of English because: I grew up speaking English since birth, English is the language that I am most fluent at, I have never formally studied English, I just picked it up as a child as the first language that I acquired. Recently, a \"non-native\" friend of mine asked me whether it is \"a helicopter\" or , \"an helicopter\", and I realised that I would personally say \"a helicopter\" when the stress in the sentence was on the noun helicopter, but when the stress was elsewhere, I would say \"an helicopter\". Is this correct in the main standard dialects of English or is this some bad habit I have picked up?", "label": 0}
+{"snippet": "In all of the treatments of elementary Euclidean geometry which I've seen so far, the section about triangle congruences introduces S.A.S. criterion as the basic postulate from which A.S.A. and S.S.S. criteria are deduced. I remember reading somewhere that one could choose any one of these three as \"the congruence postulate\" and deduce others from it. I am able to produce proofs for S.A.S. by taking A.S.A. as an axiom and vice versa, but S.S.S. seems to be the \"odd\" one since I cannot reach either S.A.S. or A.S.A. by taking it as the axiom. I was unable to find anything online that shows such a proof so my question is whether the premise that any one of these three criteria can be picked as the axiom is true or not. If it is, how can we prove, for example, S.A.S. through S.S.S.?", "label": 0}
+{"snippet": "How would little, native English speaking kids say \"Tell me a story about the bear!\"? In my language, they might say something like \"Tell me the bear!\". Does \"Tell me the bear!\" sounds like a valid \"little English\" question from a little kid who is catching up the language? Context: Each language has different logic, and the kids build up the logic differently. I am very much curious about how young kids in native English environment build up the logic of the English language. For example, in my language, they might say something like \"Tell me the bear!\" instead of \"Tell me the story about the bear!\" Do English-speaking kids make similar mistakes, like saying \"Tell me the bear\"? What are the common mistakes they make in this context?", "label": 0}
+{"snippet": "I hope this question hasn't already been asked, but I looked and couldn't find a question with a similar title. It is my understanding that Maxwell's equations and the Lorentz force law form the foundation of classical electromagnetism. These are fundamental because (in the classical limit) they are always obeyed, in contrast to Ohm's law, which is still a valid empirical law, but is restricted to a specific scope. As I understand them (correct me if I have made a mistake), these describe basic assumptions used to create a model of electromagnetism: the net outflow of electric field lines through a closed surface is proportional to the amount of and polarity of the charge inside the net outflow of magnetic field lines through a closed surface is zero a magnetic field that changes with time will create a circulating electric field an electric field that changes with time will create a circulating magnetic field, taking into account the polarization current the electromagnetic force on a charged particle depends both on the electric field and the magnetic field I've encountered some equations pertaining to phenomena described by QED, but I was wondering if there is a set of fundamental equations like Maxwell's equations and the Lorentz force law that describe all of the core requirements for accurate predictions in its model. In other words, can I summarize QED the same way as I have done above for classical electromagnetism?", "label": 0}
+{"snippet": "I am currently reading \"No-Nonsense Quantum Field Theory\" by Jakob Schwichtenberg and in several derivations in the book it'll pull a partial derivative operator out of an integral, or change the order of full and partial derivatives on a function, etc. without explanation. So my question is: Are the differential and integral operators commutative? Is this always true? And if not, what are the conditions for it? Furthermore, in the more general sense of abstract algebra, if/when are unary operators commutative? A proof to accompany a given answer would be much appreciated, or at least the citation of one which is free and public. It's certainly intuitive that this is true, at least in the special case of the calculus and physics in this book, but I'm not sure why it is in a more fundamental, mathematical sense and I'm also curious about the general case of all unary operators. This is the kind of thing I would love to try to solve and research on my own but I simply don't have the time right now and I'm having trouble finding a straightforward answer online, so any help would be greatly appreciated. Thank you!", "label": 0}
+{"snippet": "I would like to learn Mathematics for understanding GR, Differential Geometry, Riemannian Geometry and related research papers rigorously. I would like to carve out a clear path to understand these topics by listing out all the necessary prerequisites. I have undergrad Math under my belt such as: Real Analysis, Algebra, Topology and ODEs. I am missing intro to PDEs at this point. I have also created a diagram of the prerequisites in which each bubble represents a subject along with textbooks written in blue. Please take a look at the attached image/file. UG means \"Undergrad\" in the diagram. Specifically, I need help with the following questions: Is my goal (the center bubble) well defined? I know it may not be specific enough yet, but I have tried to list down some topics I am interested in RED color. Have I listed all the subjects? Am I missing any subject? Is Lie Groups worthy of mention here? Or, would it just fit under Algebra? Is Hyperbolic Geometry worthy of mention here? Is it relevant? How do I learn it? Any textbooks for it? Would anyone please help me break down the following subjects into specific topics that are necessary for my goal: Manifolds, Riemannian Geometry, Real Analysis (grad version), PDEs (grad version), Algebra (grad version).", "label": 0}
+{"snippet": "I was explaining the tidal locking phenomenon to a friend. First I started with the formation of solar system and how at the beginning the planets were actually like balls of magma-esque rocks. And then how the force of gravity would eventually affect their shape and mass distribution and consequently, moment of inertia. But I myself wasn't satisfied with this abstract argument and tried to come up with a more intuitive one. So I said: imagine a fresh egg. Its yolk is at its center (almost) and the mass is evenly distributed. Then after a few days, the earth's gravity pulls the yolk down and moves it closer to the shell. This changes its moment of inertia. But I didn't know how to continue and pull a tidal locking explanation out of this. So I said never mind!! There are large-scale forces and objects involved in tidal locking that I cannot scale them down to something more accessible and easier to demonstrate. Now this has gotten on my nerves. I thought a lot about it and also searched [fruitlessly] quite a lot to find an intuitive, accessible way to understand this phenomenon. We may not be able to demonstrate the effect of gravity on a small scale, but can we use another force that behaves like gravity (e.g. static electricity) to design an experiment for tidal locking?", "label": 0}
+{"snippet": "I've recently started using Texmaker to edit on my LaTeX documents (up to now, I mostly used Overleaf or TeXworks), so I am still new to this program's shortcuts. I have been looking for a shortcut in specific that I can't seem to find, and I would like to know whether this is something this specific LaTeX editor has. I am working on a lengthy file that has several chapters saved as separate .tex documents, which are all called by a single main.tex document. As such, any time I want to edit a specific part of the compiled .pdf file, I need to know in which line of which of my subfiles that specific part of the document was encoded - which is always a bit annoying to find. In Overleaf, this is made simple, since double-clicking on the corresponding line of the .pdf I wanted to edit would link me to the corresponding code line in the document. Does Texmaker also support a similar shortcut? And if so, what is it?", "label": 0}
+{"snippet": "This is a question that a high school student asked me and I couldn't give him a satisfactory answer. He started by saying that An object appears red because the energy corresponding to a \"red\" (don't take it literally) photon isn't equal to that of the energy gap of the elctronic energy levels of the object. And now if I take the same object in complete dark and shine a red laser from above why don't I see a red beam coming out from the bottom surface the object ? My first reponse was that 'since the object is opaque it reflects most of the red light falling on it' but he wasn't convinced and I think that he is basically trying to ask what causes an object to be more reflective than refractive from the atomic point of view . Can someone help me with this ?", "label": 0}
+{"snippet": "I would like to find the distance function for a curve comprised of all points within a lune that are of equal perpendicular distance to both circular arcs. In other words, what's the minimum distance by which a given point inside of the lune would need to move in order to become equidistant to both arcs? My use case would require both arcs to be of equal radius, if this helps. Constructing a signed distance function for the lune itself is fairly straightforward, but this particular problem seems considerably harder. I've been mulling over it for a few days without any real idea of how to approach it. Can anyone point me in the right direction? Edit For clarity, the curve marked in red is what I would like to find the distance function of:", "label": 0}
+{"snippet": "I am searching for a book on group theory that follows in the style of textbooks written for math students (since I was one), but that covers all (or at least most) topics that would be needed in physics, such as in QFT for example (Think of the topics in Zee's Group theory in a nutshell). My problem with Zee is that it is too verbose and not as mathematically rigorous as I'd prefer (I can understand the concepts better when they are presented in a formal mathematical way). And my problem with other standard group theory books for math is that they usually do not cover all the topics needed for physics (Lie Algebras, Poincare groups...) A single or many-book-combination recommendation that would fill in these criteria is welcome.", "label": 0}
+{"snippet": "Please correct me if I am wrong. Electron is fundamental and is zero dimensional (probably made up of strings). Electron is bound to the nucleus. Electron in an atom has velocity and position which are statistically distributed. Electron mainly interacts electromagnetically. Temperature is the measure of statistical kinetic energy of particles. In the nucleus of an atom, proton and neutron have temperature because they are a bag bound by color forces , valence quarks and a sea of quarks and anti-quarks. Quarks interact electromagnetically. Saying that protons and neutrons have temperature means that there is a randomness in the kinetic energy of the constituents of proton and neutrons. Electrons are bound to the constituents of protons and neutrons through electromagnetic force. Therefore if there is randomness in the kinetic energy of the constituents of protons and neutrons then the electrons must be experiencing wobblyness in its orbit, that is , it must be experiencing some kind of little randomness in its motion around nucleus. And therefore the electron must have a little temperature in the atom. My question is : Does the electron have a temperature in the atom?", "label": 0}
+{"snippet": "I am a veteran of the wars in Iraq and Afghanistan. When talking about the people opposing us, I have always referred to them as the \"enemy.\" Now, as I get a little older, and a little more aware (specifically, as I became a determinist), I have lost any hostility I feel towards them, and I feel that calling them the \"enemy\" demonizes them in a way I no longer wish to do. So, I was hoping there was some neutral term applied to enemy combatants, even if it's historical or in another language. I think opponent comes close, but it's not quite there. I was hoping there was a word like \"interlocutor\" meant for combatants of war. I have checked the OED (paywall, I think, I get it through my library), and the words I think that come closest are two obsolete words \"contrary\" and \"adverse.\" (obviously those words are still in use today, just not in the noun sense of a contrary or adverse being someone who opposes you). Does anyone else have any better matches? One note, some may suggest I call them by the name they go by, such as the Taliban. The problem is that the Taliban is one of dozens of different groups of fighters and we rarely knew who belonged to which. So, I was hoping for a neutral term I could apply to all of them.", "label": 0}
+{"snippet": "I recently received a newsletter from an entity I previously thought to be credible which is embarking on a brand/campaign around the concept of ambition which makes me wonder if my understanding of the word is \"off\". Can the following be examples of Ambition? Starting a new hobby. Getting out for a walk on the beach. I would have thought that while the above are goals/things a person may strive for - they are not ambitions because they are not substantive enough to qualify as an ambition. Similarly I see an ambition is a goal you strive to reach, while the \"Ambition\" campaign in question is about the journey (and indeed with no expectation of completing the journey) In other words I think \"Planting a new garden\" would qualify, but \"Planting some plants in my garden\" would not, or \"Completing a marathon\" would qualify, but \"getting out for a walk on the beach wouldn't\". Do I misunderstand the meaning of the word?", "label": 0}
+{"snippet": "I got a bit confused about independent clauses,so I decided to ask ChatGpt, which has given me three different answers for the same sentence I think he is getting too old, suffering from Alzheimer's disease. The sentence is: I bring a natural positivity and a can-do attitude, allowing me to effectively solve challenging problems even under pressure. Here are my questions about that : First of all \"allowing me to effectively solve challenging problems even under\" is that a gerund clause functions as an adjective for the main clause describe it Now regarding the clause I have two possible analyses The first one is that: \"allowing me to effectively\" is a gerund phrase that acts as a subject. \"solve\" is the main verb. \"challenging problems\" is the direct object. \"even under pressure\" is a prepositional phrase that acts as an adverb The second one would be: . \"allowing me\" is a gerund phrase to start the caluse \"to effectively solve\" is an infinitive phrase \"challenging problems\" is the direct object to solve \"even under pressure\" is a prepositional phrase that acts as an adverb Does anyone have a clue which analysis is right and why?", "label": 0}
+{"snippet": "I was reading a paper on black-hole information loss and it mentioned backreaction. I had never heard the word before so I googled it and was surprised to find no cohesive definition that I could understand. The best I found was this wikipedia article which gives a definition akin to \"a backreaction is a field that is often used to calculate forces in quantum systems.\" However, it gave no strict definition or real physical justification. I was wondering if someone who understood the topic could explain them to me better, because right now they seem to me to be more like quantum epicycles than anything. P.S. I also found this article talking about back-action in quantum measurement which used the term back-reaction once. I could't quite figure out precisely how they were related though.", "label": 0}
+{"snippet": "I am currently studying Linear Algebra Done Right (LADR) by Sheldon Axler and also How to prove it by Daniel Velleman. Currently I am in the chapter of Bases in LADR and I already read the chapter on equivalence relations in How to prove it. I tend to be somebody who looks for analogous things and something that I wanted to verify was whether there is a resemblance of Vector Subspaces and Equivalence Relations: Can one think of subspaces being equivalence classes? What I would suggest would be to say that vectors in a subspace form an equivalence class if they can be written as a linear combination of the basis vectors of that subspace. Moreover, there is a theorem which says: Every subspace of V is part of a direct sum equal to V. Wouldn't then the vector subspaces be analogous to a partition? Am I thinking along the right lines? Doesn't that mean that there is a sort of universal structure of mathematical topics?", "label": 0}
+{"snippet": "A common construct for comparison (making parallels) is \"the X of A is similar to that of B\". Quoting an example here ... the animals' situation is similar to that of the plants. which is equivalent to the situation of the animals is similar to that (i.e. the situation) of the plants. I often wondered whether this construct can be extended to make parallels in more complex scenarios, where one needs to compare or contrast two relationships (between two pairs of objects). A contrived example is as follows: \"The difference between werewolfs and vampires is similar to that (i.e. the difference) between wolfs and bats.\" Here, what I am trying to compare are two relations: the one between werewolfs and vampires and the one between wolfs and bats. As the two relations are each between a pair of objects, should one say \"... is similar to that between X and Y\"? If not, what is the proper way to express such comparisons/parallels? (I thought about using such patterns from time to time, but haven't seen it used. Hence the question here.)", "label": 0}
+{"snippet": "I have the following diffraction pattern produced by a fabry-perot etalon The red represents the center of that pattern. Taking the mean intensity of the pattern as a function of the radius from the red dot and applying a cut-off radius results in This clearly shows a superposition of at least two diffraction patterns. Is there any way to automatically decompose the patterns? I originally tried Fourier analysis but that resulted in a complete mess as the peaks appear to be Gaussian, not sine functions. I can fit Gaussian to all the individual peaks. But then my question is if there is an algorithm or method that would allow me to determine which gaussian belongs to which diffraction pattern. I have quite a few more diffraction patterns some of which are more complicated and I wanted to see if there is a way to automate this?", "label": 0}
+{"snippet": "Two up quarks in a proton lead to an imbalance, which results in the proton having the ability to attract electrons. Two down quarks in a neutron lead to balance in the electromagnetic force, leading to no interactions happening with electrons. The strong force and electromagnetic force appear to be directly related. Unless I am misunderstanding something, it appears that a particular arrangement of quarks leads to a specific kind of baryon that has a specific kind of electromagnetic behavior - meaning the strong force is indirectly leading to the behavior of the electromagnetic force. I don't understand why the electromagnetic force is considered to be a separate force than the strong force for the following reasons: Quarks clump together to form baryons due to the strong force, not the electromagnetic force. I understand that quarks have electromagnetic charges, but I don't understand whether the cause for this is due to it \"fitting into the math\" or it actually being a fundamental property of the quarks. I understand that the strong force overpowers the electromagnetic force, but how do we know for certain that quarks even have charges? Any insights or references would be greatly appreciated! Thanks for reading. So, my question is: why is the electromagnetic force considered separate than the strong force?", "label": 0}
+{"snippet": "I am trying to simulate the reflection of a sound ray, that goes from a sound source, bounces off a wall, and is received by a microphone. The wall has a an absorption coefficient, and a specular reflection coefficient, both of which vary by frequency. Thus, the sound reflected by the wall specularly can be characterized by a certain frequency response curve. LTI filters are characterized by a frequency response and a phase response. Thus, we can treat the contribution of the wall's specular reflection as a LTI filter (applied to the source signal) if we know the correct phase response. The reflection path (shown in red above) corresponds to a time delay proportional to the length of the path. If we assume a constant time delay across the frequency spectrum we get a linear-phase filter, that is symmetric about the time-delay corresponding to the reflection path length. However, this filter clearly has \"anti-causal\" components: the filter is nonzero before the red line. Thus, the filter begins to have an effect on the signal before the length of the reflection path would suggest that it should. It seems that either the assumption of constant time delay across the frequency spectrum must be wrong then? If so, I wonder what the correct phase response of the filter is.", "label": 0}
+{"snippet": "I have a couple questions on the mechanism for how solar projection through a telescope works: I recently took a small telescope focused at infinity, aimed it at the sun, and held a sheet of paper behind the eyepiece. It projected a focused image of the sun onto the paper. When I changed the focus away from infinity in either direction, the picture became less focused. I'm confused as to why this works since I always thought a focused telescope produces a virtual image that can never be projected onto a screen (and your eye turns it back into a real image for your retina). How can one focus setting for the telescope make an image that your eye can see and that can also be projected onto a paper? If the image coming out of a telescope can be projected onto a paper, I assume it is a real image. However, I find that no matter how far or close I move the paper, the image remains in focus. I always thought that a real image is projected onto a single focal plane at a fixed distance from the lens, so how does this work? Any help would be greatly appreciated.", "label": 0}
+{"snippet": "Suppose we have two bodies at different temperatures, and we let them interact thermally in such a way that the process is not quasistatic (e.g. two different metal spheres touching). Do we arrive at the same final temperature as if the same spheres had equilibrated via a quasistatic process? If so then, rigorously, why? Of course I expect the answer to be yes but I can't convince myself of why in the context of thermodynamic theory. Edit: I think I see that since I can establish that in a final equilibrium, they have equal temperatures, then I can imagine a quasistatic process taking them to this final state? It seems thus that in the case of non-quasistatic heat transfer, ceteris paribus, we have the same entropy change as for the corresponding quasistatic heat transfer?", "label": 0}
+{"snippet": "Clarification: the word \"important\" is ambiguous. Here, I use \"important\" to mean that we want to know the value of a quantity accurately. For many optimisation problems, it looks as if we are more interested in finding the minimum value, rather than finding the argmin. For instance, in machine learning models, we care about how well the model can predict, and we do not care about the internal argmin inside the black box that makes this possible. For a linear programming problem, say, for an airport, we do not really care about the exact way to schedule flights to get the maximum efficiency. We just want to come up with a plan which can be completely different from the optimal one, but have similar efficiency in terms of saving time. This is due to the existence of many equally good solutions. Note: one might argue that we do need to know a solution. Of course we do. But we don't care which solution we get, as long as it is a good solution. So it is unimportant to know the solution itself accurately; only the objective value is important. Nevertheless, argmin is discussed a lot in literature (like parameter estimation in statistics). However, I have not seen anywhere why this is useful. Could anyone give an example application where the argmin is more important than the min?", "label": 0}
+{"snippet": "Some English nouns are identical to their verbs (and their adjectives) both in spelling and pronunciation, for example: \"This is fake\"; \"to fake\"; \"this is a fake\" \"To tear\"; \"a tear\" \"To parody\"; \"a parody\" \"A misfire\"; \"to misfire\" There are some examples where the (disyllabic) noun is spelt exactly like its verb but the noun is pronounced with the opposite stress (at least, in the standard accents which I hear day-to-day in the UK), for example: \"An escort\"; \"to escort\" \"My recall of the event is faulty\"; \"I cannot recall what happened\" \"To repeat\"; \"a repeat\" (this last one is a bit weak since people use either stress pattern in different contexts) This phenomenon is observed with some verb-adjective pairs too: \"To perfect\"; \"this is perfect\" In all three cases, I would be interested in: The corresponding formal linguistic term (if there is one) Examples! Although I know there are plenty more than I've shown here, they elude me. What's worse is that there's a fair few I've thought of but can no longer recall. Bonus: are there any examples of noun-adjective pairs that are pronounced with opposite stress?", "label": 0}
+{"snippet": "Imagine a situation where I'm moving at the same velocity as the electrons in a conducting wire. In this scenario, from my frame of reference, the electrons appear to be stationary and thus there is no current from my POV. Now, for a brief moment, these \"stationary\" electrons come into contact with (or pass right next to) a light bulb in the vacuum of space and closes the circuit for a brief moment, causing it to illuminate, and then we all continue moving together. (water this down as much as possible to reach \"spherical cows in a vaccuum\" state for the purposes of this problem) Question: From my perspective, the light bulb lights up even though the electrons (which I observe as stationary) aren't \"flowing\" in the traditional sense. How is this phenomenon explained? Would I effectively be seeing a light bulb illuminating without any observable current thus creating something out of thin air (obviously no). Or rather, what do i have to \"give up\" for the laws of physics to be consistent.", "label": 0}
+{"snippet": "I am trying to check if my understanding is correct. This is not really a question but a request for validation. I hope this is allowed. When painting with a heat reflective paint there are two options A- The room does not contain a significant heat source. This will always lead to a reduction in ambient temperature as heat from the outside is not allowed in. Heat by convection and conduction will still penetrate but overall the energy transfer will decrease. B- The room contains a heat source emitting IR rays. The rays will keep bouncing over the painted walls until it is absorbed by the air or the body of the heat source itself. Depending on the ratio between the external and internal IR sources, a IR reflective paint can lead to either increase or decrease of ambient temperature", "label": 0}
+{"snippet": "In algebraic number theory, we would like to study rings of algebraic integers but sometimes they are not PIDs and thus they don't possess good properties. Because of this, we have introduced the notion of Dedekind domains, in which rings of algebraic integer are included and one can study the nice properties of Dedekind domains to understand algebraic integers. While doing algebraic geometry and commutative algebra, I have encountered polynomial rings in several variables, whose properties are quite different from polynomial rings in one variable, as the former ones are just UFDs while the latter one is a PID. So this \"degeneracy\" of polynomial rings from PID to UFDs reminds me of the similar case of rings of algebraic integers but I don't think they are related since the dimension of polynomial rings depends on the number of variables , which does not fit the definition of Dedekind domains.But I wonder if there is a way to classify polynomial rings of several variables(especially those over an algebraically closed field) into a specific type of rings, such that this type of rings has nice properties just like Dedekind domains and from which one can classify the prime ideals as well as determine the irreducibility of polynomials easily?", "label": 0}
+{"snippet": "I came across a question a while back. It stated that a oil droplet was suspended vertically within an electric field. The man who suspended it had left to eat a very LONG lunch, and came back to see that it was splattered on the top plate (nothing with the setup had changed), and the question asked us to state a physical reason for such an event. I thought it was because of a transfer of momentum from electrons moving from the negative plate on the bottom to the positive plate on top, which just so happened to collide with the oil droplet. Someone else answered saying that the droplet evaporated slightly, which caused it's mass to decrease and so the force acting upon it managed to accelerate it more than that of gravity, causing it to move upwards slowly. That was the correct solution, but I'm just a bit confused, since wouldn't it lose some charge when it evaporates as well? So overall the q/m ratio would still be the same? They said it was unlikely that it evaporated some of its charge, so I'm just wondering how the charge within an object is distributed. Is it distributed evenly throughout, or is it more concentrated in some areas?", "label": 0}
+{"snippet": "I have learned some basic measure theory as covered in the first chapter of Durrett's Probability: Theory and Examples, which includes the construction of Lebesgue integral (from simple functions to bounded to positive to integrable ones), as well as some basic properties such as Fatou's Lemma, monotone convergence theorem, dominated convergence theorem, the Fubini theorem, etc. I will be officially taking Real Analysis (measure theory), next year. However, as sometimes functional analysis turns out to be sometimes illuminating for my undergraduate research in mathematical optimization, I want to have a basic pass through the most fundamental concepts of functional analysis. I have read some posts here stating that it's possible to learn functional analysis before measure theory, but the other order is preferred due to the need for integration. Since I don't have much time nor want to stumble upon something that requires measure theory, does anyone has some recommendation on a list of topics or theorems that might be needed for a basic read on functional analysis? Thanks in advance! Edit: I have some basic background in general topology.", "label": 0}
+{"snippet": "Google dictionary (based on Oxford dictionary) has an entry for the verb \"reveal\" as follows: make (something) known to humans by divine or supernatural means. And it includes one example: \"the truth revealed at the Incarnation\" Based on the definition, I find it hard to understand the role of \"the truth\" in this example whether it's an object (as denoted by \"something\" in the definition) or a subject (that is supposed to \"make(something) in the def.)? My best guess is that it's an object because after checking other dictionaries such as Collins, Merriam Webster, Cambridge, etc., I found that they all define \"reveal\" to be a transitive verb. So I guess that the \"to be\" may be omitted in this case and the full sentence should be: \"the truth IS revealed at the Incarnation\". However, no resources I found have mentioned such type of ellipsis like this one. So my question is, is my guess correct. If it's indeed correct could you give me some resource covering such type of ellipsis?", "label": 0}
+{"snippet": "If I have a stick that has a spinning disc on the end of it, and I try to rotate the stick, I will feel more inertia the faster the disc is spinning because I have to transform its rotational energy into a different axis. It seems intuitive to me that this would apply to electromagnetic fields as well, since you have to move all the energy in the field to another axis. So if you had an MRI machine on an airplane and the plane tried to rotate, would it rotate more slowly when the machine was powered vs unpowered? If so, does this depend on whether the axis of the field is aligned with the axis of rotation? If they were aligned so that the dipoles are parallel to the body of the plane, could it roll without extra inertia? I may be describing the Einstein-de Haas effect or gyromagnetism, but I am confused whether they are describing the same thing as me in different words or just a related concept.", "label": 0}
+{"snippet": "Often we define a quantum phase of matter as a set of ground states of a gapped family of Hamiltonians, where the gap does not close anywhere in the family. Equivalently, we can define it as a set of states which are related by constant depth quantum circuits with local gates (equivalence of these two definitions is shown by the adiabatic theorem). Now consider a family of states which are ground states of a gapless family of Hamiltonians, and assume they have similar correlations and can be considered a \"phase of matter\" in the sense that all their observables vary analytically with the parameters of the Hamiltonian. Can we use the circuit definition of a phase of matter in the same way as the gapped case? That is, is it reasonable to define a \"gapless phase of matter\" in terms of states which are related to each other by a constant depth-quantum circuit? Maybe there are counter-examples to this which demonstrate this is not true. In particular, it seems reasonable to define gapless phases of matter in this way as (a) local unitaries do not change long-ranged entanglement properties, which intuitively define phase (b) unlike the Hamiltonian case, we do not need to worry about excitations to higher energy levels. Is there any literature on this at all?", "label": 0}
+{"snippet": "This question might be very silly, but I am really confused about it from several days. Look transverse waves on a string propagate along the string due to the electromagnetic (EM) forces between adjacent particles of the string. So when one of the particles is displaced, it will drag nearby particles and thus the disturbance travels. In case of electromagnetic waves, the electric field values oscillate with time. But is there anything physical that connects the electric field at a point to that at its nearby points (just like we had for strings)? If not, then why does this information travel? And if yes, then what is that \"thing\"? Also, I would like to add that for strings the direction of displacement at nearby points was completely determined by the source point, but for EM waves the direction of electric field at one point does not necessarily imply that the electric field at nearby points will be in the same direction (take the case of unpolarised light). Why is that?", "label": 0}
+{"snippet": "I am working on automated templates, and I want to use latexmake with luaLaTeX, as suggested in a comment on this question, where I attempted a similar setup with XeLaTeX. However, I am facing challenges with the configuration. My goal is to automate the process of typesetting my documents with luaLaTeX using latexmake, and I believe this will save me a significant amount of time. I have tried variations of latexmake main.tex -lualatex -outdir=output -auxdir=auxil in the terminal but it tells me that lualatex is not recognized as an argument For the code examples, I have a template that works and needs lualatex but needs several compilations. Hence the need for a latex maker. I also have tried to read the documentation for latexmake but I didn't find any solution and there isn't much content about this library online. If someone could provide guidance on how to configure latexmake to work with luaLaTeX, it would be greatly appreciated. Thank you!", "label": 0}
+{"snippet": "For context, I watched PBS Spacetime's video on virtual particles (link goes to relevant timestamp) where they say that virtual particles aren't mathematically necessary, because the lattice version of nonperturbative QFT doesn't use them, and yet still makes all the same predictions as perturbative QFT. I was satisfied with that, until I had a brief exchange with someone in the comments of this answer where he says that, in most cases, it's impossible to actually do computations in nonperturbative QFT, and, when I asked if this was just due to not having sufficiently efficient algorithms, he said Note that in particular that even establishing the existence of a non-perturbative Yang-Mills QFT (which is what the standard model / QCD / QFD are) is a millennium problem. which implies that we don't currently even have a nonperturbative version of the standard model and that it's unclear whether one exists. However, PBS Spacetime is, in my experience, typically a reliable source for high-level explanations, so I wouldn't have expected them to mention nonperturbative QFT as the reason not to think virtual particles are physical if that theory wasn't actually useful for nontrivial calculation. Is it that most physicists think there probably is a nonperturbative version of the standard model and it just hasn't been discovered/created yet?", "label": 0}
+{"snippet": "Let S be a compact orientable surface and U an open connected subset of S with finitely many ideal boundary points (or ends). U has a prime ends compactification which is a surface with boundary (following Mather). Let b be one of these ideal boundary points and Z(b) its impression in S. If Z(b) has more than one point, then there is a circle C(b) of prime ends associated to b. Each prime end e of C(b) has its impression Y(e) (another impression, the intersection of the closures of the sets of a chain that define e). This seem to be known by experts, but I could not find it written anywhere. Does anybody knows how to prove it? Knows a reference? I think I can prove it using scaffolds, a powerful tool created by Mather to prove various properties of prime ends. But it is a lot of work. Any good hint? Thanks.", "label": 0}
+{"snippet": "In the situation above, we have a power line which uses an alternating current. This alternating current causes a change in magnetic flux through the loop below the power line, which induces a current according to Lenz's law/Faraday's law, which eventually goes to the farmer's equipment. This is classed as power theft. However, I was wondering, does this power tapping by the farmer in some way reduce the power delivered by the power line or cause an energy loss from the power line? If so how? If it doesn't, then how is this situation exactly consistent with conservation of energy? Does the induced magnetic field in the farmer's loop somehow cause energy to get lost in the power line? (Where does the energy from changing magnetic flux come from in the first place?)", "label": 0}
+{"snippet": "I have a hard time understanding time dilation and special relativity; each explanation seems to contradict the other, and don't explain the apparent paradoxes they cause. Say clock A orbits clock B at a very high speed. According to the explanations I've heard, B would perceive A as ticking slower than B, because of time dilation. But since A has equal right to claim to be stationary, it should observe B as orbiting A, thus ticking slower than A. If at any moment the clocks' time would be measured, would their respective elapsed time be different? In other words, is one clock actually slower than the other? This seems unreasonable, since the respective situations of the clocks are identical. If the answer is no, what exactly happens if the clocks suddenly stopped orbiting each other and become stationary relative to each other? If each clock has perceived the other as ticking slower for a while, would the clocks instantly jump to the same time? This also seems unreasonable, since orbiting each other for a longer time then would imply a different outcome when stopping, even if the events of stopping are identical. How can this be resolved?", "label": 0}
+{"snippet": "Usually when we introduce postulates it is so they are of some use to us. I do not see the reason for these two. The Line Separation Postulate: Each point on a given line divides the line into three disjoint sets: the set containing the point, and the two half lines on either side of the point. The Plane Separation Postulate: Each line within any plane divides the plane into three disjoint sets: The line and the two half-planes on either side of the line. I understand the postulates and what they are saying, but I do not see how they can be used. And I have not yet found a proof that uses them in the book. I guess I am not convinced of their fruitfulness so if anyone can help convince me these are useful/necessary postulates that would be of great help.", "label": 0}
+{"snippet": "Suppose that, as a manager, I am creating a campign to evaluate employees based on the NPS (Net Promoter Score) of their sales - the objective is to reward high perfoming employees. However, due to the different nature of each role, some employees have a lot more sales than others. What is the best way to create a ranking system? The data available is: NPS for each sale for each employee (the value can be null, if the survey has not been answered by the customer). I thought about using a bayesian ranking system, but I think that it would be unfair to low seeling employees which sell little beacuse of their specific role. In a more abstract sense, how can I compare samples of varying sizes without skewing the comparison towards bigger or smaller samples?", "label": 0}
+{"snippet": "I've noticed while playing Minesweeper that when I have too few bombs, I get very easy to play games. In other words, I get games that can be solved with very simple algorithms. When I play games with too many bombs, I get unsolvable games or games that can't be solved without guessing. There seems to be a region in the middle(not too few, not too many), where some games are solvable but require increasingly complex algorithms. I've also read that Minesweeper is NP-complete, which I take to mean that there is no upper bound to how complex these algorithms can be as n, in an n-by-n game of Minesweeper, is allowed to grow. This seems relevant to information processing(halting problem?) but not exactly sure how. First, is my phrasing correct? And second, where can I search for clarification in my thinking?", "label": 0}
+{"snippet": "In an office, there are typically various different kinds of environments in which each employee carries out their work. Some have their own rooms, some have cubicles, some only have a desk in an open landscape etc. I'm looking for a word for the place where an individual employee carries out their work, regardless of if it's in a room, at a desk etc. Things I considered: Workstation - probably the best I've got so far, but it sounds kind of techy to me (associating with a workstation computer perhaps) - does this work also for someone not using a computer such as writing by hand (!), manning a reception etc? Workplace - to me this sounds like a common word for the entire office/building? Am I wrong? Furniture - kind of encompasses all kinds of surfaces you can work at, but it sounds too broad (and plain silly!) Equipment - to me this sounds more like advanced/specialized lab gear (labs, fume hoods, ...)? Does anyone have a good suggestion? Imagine e.g. this sentence: \"All employees in the office are guaranteed their own [ ... ] where they can carry out their work\". And I don't want to go too broad with abstract terms such as \"location\", \"spot\", etc.", "label": 0}
+{"snippet": "There are Two different defintions for the event horizon of a black hole. The Absolute horizon and the Apparent horizon. An apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards and those directed outward but moving inward. While and Absolute Horiozn is a boundary defined with respect to the external universe, inside which events cannot affect an external observer at infinity. Normally these horizons coincide but they can differ during event such ad black hole mergers. Technically, knowing exactly where the Absolute horizon is requires knowing the entire future history of spacetime. So it seems to me therefore that in a universe destined to even in a big crunch, black holes wouldn't technically have Absolute horizons, only Apparent horizons.", "label": 0}
+{"snippet": "I interpret the expression 'If P then Q' as asserting that if P is true Q is automatically true. So, we would say 'If P then Q' is true only when it indeed is the case that P being true implies Q is true. However, in logic, the truth of 'If P then Q' is determined solely on the basis of the truth values of P and Q individually and not by verifying whether Q follows from P, or is implied by P. So I just don't get how we can decide the truth of if-then statements by just looking at the truth values of P and Q. For it to be true don't we need to prove somehow that the truth of Q follows from the truth of P? In one of the logic books that I read, they explained conditional statements in this manner: 'If P then Q' asserts that it is not the case that P is true and Q is false. I liked this. It makes me understand the truth table of conditional statements well. However, by this explanation, I'm not able to see why would one use the words 'If then' then. How the idea that it is not the case that P is true and Q is false follows from the meaning of words 'if then' (or 'implies' for that matter). Should I completely forget about the meaning of if-then sentences as used in ordinary language and assign them a new meaning?", "label": 0}
+{"snippet": "One possible formulation of the second law of thermodynamics is that the work extracted during the change of a thermodynamic system between two thermodynamic states is at most equal to the free energy difference between those two states. One possible derivation of this empirical result from statistical mechanics is the derivation of Jarzinski relation in the canonical ensemble. Also, the Jarzinski relation was also derived in a stochastic setting by Crooks. For the sake of further simplifying the statement of the Jarzinski relation, I consider a Brownian particle fluctuating within a double-well potential in one dimension, i.e subject a Langevin equation on the real axis with known potential and noise. What I can say for this system is that the particle will be undergoing transitions between the two wells with a rate that is exponential in the barrier height of those two wells. Also, the equilibrium distribution of the particle will be a bi-modal having a peak at each potential minimum, and the height of each peak is given by the barrier height. Now which additional useful information does the Jarzinsky relation tell me about this simple system ?", "label": 0}
+{"snippet": "I'd like to prove: Given two points A and B and a straight line connecting them AB, any smooth curve passing through A and B will, at some point, have a derivative that exceeds the slope of AB. My proof uses the Mean Value Theorem. So, any curve passing through A and B has, at some point, a derivative equal to slope of AB, call this point C. Consider lines AC and BC. Together with AB, they form a triangle. Noting the angles a and b, we know that the slope of either AC or BC exceeds the slope of AB, and, by the Mean Value Theorem, there exists a derivative on any curve passing through either A and C or through B and C that equals the slopes of the lines AC and BC. Therefore, any smooth curve passing through A and B will, at some point, have a derivative that exceeds the slope of AB. Perhaps this is trivial, but for me it is important.", "label": 0}
+{"snippet": "I'm trying to understand where heat energy goes in a substance. I've seen that mainly it's translation at lower temperatures, rotation at mid range, and vibration at high range, but I'm not sure of that. Someone made the claim that an atom can expand as it is heated, which I don't think is right, but in a way, this is a good description of black body radiation? Does anyone know some approximation of percentages for how much heat energy goes towards motion (translation, rotation, vibration) and how much is radiated as blackbody? And, does this change between the different phases: solid, liquid, gas, plasma? I'm just looking for a general concept here, so no constraints. If there's some special constraints to note, then please list them and the energy distribution within that particular system for comparison.", "label": 0}
+{"snippet": "Recently I saw a video talking about the Yoneda lemma from category theory being used in neuroscience. It was my first introduction to category theory. In category theory we have objects and maps between the same objects called morphisms. For example we have one type of object called set and its morphism would be the function. A function is a map from one set to another. Another example would be the object vector field with its morphisms being linear transformations. This just looks like we are renaming the same stuff. Is a vector space not just a type of set we construct to obey our desired axioms? If so then introducing linear transforms would be truly just renaming stuff. And if they are not sets, why not allow non linear transforms?", "label": 0}
+{"snippet": "My first name is \"Jean-Baptiste\". \"Baptiste\" is not a second or middle name, however I noticed that it's not unusual for native English speakers to address me just as \"Jean\". I don't mind it at all, I'm not offended and find it actually charming, but it would be quite unusual for a speaker of my native language (France's French) to call me like that (either native speakers address me with my full first name, or they use various nicknames - and the nickname is never \"Jean\"). So I'm curious as to why many native English speakers seem to spontaneously call me \"Jean\". The two hypotheses I have is that either my full first name might be a bit difficult to pronounce (so just saying \"Jean\" is easier), or because they mistakenly think that \"Baptiste\" is my middle name - as compound first names are unusual in English (correct me if I'm wrong). I'd tend to think it's the second option, as I noticed that it also happens in writing, but I'd be interested in having the insight of people who know English language and English-speaking cultures better than I do. Maybe I'm completely on the wrong track! When it happens, I usually don't have the opportunity to ask people why they are calling me like that (e.g. in a professional context we usually don't have the time for that, plus in this kind of situation I don't want to make people feel like they offended me), that's why I ask this question here. Thank you,", "label": 0}
+{"snippet": "An event horizon appears in the Schwarzschild metric when considering a positive point mass in General Relativity. But for a negative point mass in the negative mass Schwarzschild metric, which repulses test particles, no matter how big the negative mass is, no repulsive event horizon forms. Intuitively, a big negative point mass should also create a repulsive event horizon, i.e., a region of spacetime that cannot be traversed from outside, due to respulsive gravity. If I make the negative mass big enough, I should create a region in which masses are so much gravitationally repelled, that they cannot enter (a repulsive event horizon). Why can't a repulsive event horizon form in General Relavity with negative mass? Is there any other metric which contains a repulsive event horizon with negative mass?", "label": 0}
+{"snippet": "I am interested in calculating the power received by an object near a black body radiator. Say, for example, I had a piece of paper perpendicular to the earth's surface normal. If I make assumptions about the earth's temperature, I can calculate its black body radiation. If I had a range of wavelengths I was interested in, I could calculate the power in that spectral range. Now if I assume my paper is itself a blackbody in the spectral range of interest, then I believe I could say that if it were placed very, very close to the earth, then the power it absorbed would be the power emitted per unit area by the earth multiplied by the area of my paper. This is based on the image below. My question is, what if I start to move my paper up? Is there anything I can say about the power it receives at different ranges from the surface of the earth? (Assume we are not so far from the earth that it can be treated as a point source). What I would like to be able to say is that the paper receives that maximum possible power when it is very, very close to the earth's surface. I am unsure how to prove this or if it is even true. Any kind of bounding limit on the received power I could derive would be helpful", "label": 0}
+{"snippet": "I would like to ask correspondence between Euclidean and non-Euclidean geometries. In the science and hypothesis, Poincare says that non-Euclidean geometry can be translated into Euclidean geometry with the following correspondence. ref)https://mathshistory.st-andrews.ac.uk/Extras/Poincare_non-Euclidean/ Space -> The portion of space situated above the fundamental plane. Plane -> Sphere cutting orthogonally the fundamental plane. Line -> Circle cutting orthogonally the fundamental plane. Sphere -> Sphere. Circle -> Circle. Angle -> Angle. Distance between two points -> Logarithm of the anharmonic ratio of these two points and of the intersection of the fundamental plane with the circle passing through these two points and cutting it orthogonally. Etc. Etc. Does he talk about Poincare's disk here? I cannot understand the meaning \"Sphere cutting orthogonally the fundamental plane\". If possible, can you please illustrate this? In addition, he says an theorem of Lobatschewsky's geometry: \"The sum of the angles of a triangle is less than two right angles,\" can be translated thus: \"If a curvilinear triangle has for its sides arcs of circles which if produced would cut orthogonally the fundamental plane, the sum of the angles of this curvilinear triangle will be less than two right angles.\" I would appreciate if you explain the above meaning more easily. Thank you for your help.", "label": 0}
+{"snippet": "When it comes to topologies, my understanding is that we designate elements of that topology as 'open.' In the context of a metric space, a topology is formed by selecting open sets, as defined with respect to a given metric. Moreover, a normed vector space is equipped with an induced metric derived from its norm. This metric allows us to associate it with a metric space and, consequently, with a topology. In the realm of topology, a closed set is one for which the complement is open. In the context of metric spaces, it refers to the set containing all points to which sequences converge. Now, in regard to normed vector spaces, when discussing Banach spaces, it's often mentioned, as seen in Riesz's lemma, that a certain subspace is 'closed.' I wasn't familiar with a concrete definition of what a 'closed' vector space entails. To the best of my knowledge, this term has been used to describe the property of addition and scalar multiplication remaining closed operations. Furthermore, are the concepts of 'open' and 'closed' equivalent in these structures? Does dimension play a role? In the case of finite dimensions, all norms are equivalent, and open sets are the same regardless of the induced metrics.", "label": 0}
+{"snippet": "My wife, a native Spanish speaker, today asked me about why a youtuber would call themselves 'craftypants'. I explained that -pants was added to something as synecdoche, so for example an intelligent person might be called a 'smarty-pants', a poor-humored person a 'grumpy-pants', etc. However, I then realized that while this is common in the US, in the UK 'pants' by itself usually means what this Yank would call 'underwear', while what I call 'pants' would appear over there as 'trousers'. How do such expressions as 'fancy-pants' sound to speakers in the UK? Are they understandable in meaning but recognizable as being North American? Does putting a -pants ending on a word remove the association with intimate clothing? Does it just sound bizarre? Do parallel expressions like grumpy-trousers exist? Are some combinations acceptable in polite speech, but others (e.g., pissy pants) not? Edit: There is much discussion in comments, and some in answers, about whether -pants is synecdoche. That's fair, and I am happy to have the point challenged. However, that's not my question. Even if I am wrong, my question is how \"-pants\" sounds to UK speakers, and whether it is clear or not that it is different from \"pants\" (underwear).", "label": 0}
+{"snippet": "I've studied in my physics class, absorption and emission spectra for gases or more \"spread out\" molecules like what is done in atomic absorption spectroscopy (learnt that one in chemistry). As in what discrete wavelengths of light a singular atom absorbs and why it only absorbs those specific wavelengths because of what energy levels its electrons are available to jump to. I was wondering if this worked generally the same for solids and liquids? Like, when you have something painted black, is the black paint designed to be composed of molecules that absorb enough wavelengths of light to make it look black (it wont be entirely black of course), or is it more that when light hits the surface of the paint, it travels as far as it can through it before using up all its energy to cause electron (and to an extent proton) vibrations? Is it both? Sorry if this comes off as confusing, I've tried to convey my question(s) as best I can.", "label": 0}
+{"snippet": "I have been reading into X-ray and gamma spectroscopy. I have found that they can both be done with scintillation detectors and work off similar principles. That is to say that when a sample is bombarded with high amounts of radiation, electrons will be excited, and electrons from other shells will fill the spot of the excited electrons. The ejected photons from this event then hit a scintillator, turning it into light (usually a NaI crystal), which is then turned into an electrical signal via a photomultiplier tube. It is then possible to ascertain the identity of the element using modern analysis tools. My question is: Is it possible for a scintillation probe meant for gamma spectrometry to be used to perform X-ray spectroscopy and identify the chemical composition of samples What would be different and have to be modified for such a setup to work with X-rays instead of radioactive isotopes?", "label": 0}
+{"snippet": "Now this might be a very dumb question but this has been bothering me from some days. Imagine I want to create the real number line and for that I start with the rational numbers. So I start to put the numbers on the line (like toppings on a pizza). Now I know that between any two rational numbers I can add another rational number. So I keep on adding infinitely many rationals between any two rational numbers by adding more and more digits in the decimal expansion. I can keep on doing this forever but I don't think I will ever reach a point where I can't put a rational and only an irrational number can go there i.e. I don't think there will be any gap between two rationals which can be only fit in by an irrational (or is it ?) So where do irrationals actually fit in on the line ? I know this entire argument can be done the other way starting with irrationals too.", "label": 0}
+{"snippet": "In accordance with special relativity, if we take into account length contraction then ideally the Planck length which is the smallest possible length possible should be frame dependent. Well we know that the number of particles are invariant in different frames. So, a frame travelling with some relative velocity will see the same number of particles but their length contracted by a factor. According to this logic, the Planck length should change with different frames. Yet it is defined by using the fundamental constants G,c and h which obviously do not change with frame. This could only imply two things :- One of the fundamental constants G,c,h are frame dependent (which I do not believe could be since they are fundamental constants) The shortest possible length cannot be written only in terms of fundamental constants The second conclusion seems more apt but is it right or is there something more to this?", "label": 0}
+{"snippet": "I am a Canadian, but I study in Edinburgh, Scotland. I have discovered a peculiar feature of my speach that seems to surprise most people from here. When ill befalls others, I use the phrase \"that's too bad\" to express my honest heartfelt sympathy with the victim. I have been surprised to find that most people here interpret the phrase \"that's too bad\" more negatively, closer to \"well- sucks to sucks\" and such. I have posed this question to a few folks from both Canada and the UK, and the Canadians seem to \"agree\" with my usage, and the British folks seem to take it negatively. Maybe I just have a small sample size. My question is: is this a feature that others know about/have evidence for? Or is my sample size just small, and it's pure chance.", "label": 0}
+{"snippet": "What is the simple relationship expressed verbally between flux, circulation, div, and curl, as captured by Green's, Stokes', and Gauss' Theorems? Below is what I've been able to assemble: Can you confirm or improve it? Given a vector field, we can measure its instantaneous rate of change in multiple ways, the two most important being div (a scalar) and curl (a vector). Each of these can be accumulated in a region. These theorems shows that this accumulation equals a property of the region's boundary: Flux (through a boundary) equals the accumulation of divergence (in the bounded region). Circulation (around a boundary) equals the accumulation of curl (in the bounded region). More fundamentally, neither flux nor circulation is limited to boundaries: they, or their equivalents, can be measured in non-closed curves as well. Only in that case, there is no relationship to any accumulation. That is: Flux can be measured across a simple curve or surface that is not closed. But this has no relationship to divergence. Likewise, a quantity equivalent to circulation can be measured through a simple curve or surface that is not closed, but if the curve isn't closed, it's called a line integral or work integral (or, for a surface, a surface integral). Neither has any relationship to curl.", "label": 0}
+{"snippet": "I have been frequently stuck on this question since first realizing it in the shower. While watching the hot water drop from the above shower head, and then watching cold water drop, I realize they both appear to be moving at the same speed. This puzzles me, because I know that when an object is hot, its atoms are moving fast, or otherwise have energy that is propelling them to \"move fast\". Correspondingly, when an object is cold, its atoms are moving slowly, since they do not have as much energy to propel them to \"move fast\". I was wondering, if cold water appears to be moving at the exact same speed as hot water, then where does my misunderstanding come in? What law of physics and thermodynamics am I misunderstanding, or otherwise unaware of? Thanks for any answers!", "label": 0}
+{"snippet": "The title might be a bit misleading, but basically I've been self studying differential equations so I could apply them in electronic circuit design. I was wondering what books could be recommended on differential equations, the Fourier, Laplace, and Z transforms, PDEs up to solving the wave equation, convolutions, filtering, and both discrete and continuous approaches to signal processing. One book that's caught my eye was Differential Equations: A Modern Approach with Wavelets by Steven Krantz, but I'm not sure how relevant wavelets are in modern signal processing. But regardless, if there are any books you've enjoyed a lot, please let me know! Also, if possible, I was wondering what a good book on information and coding theory would be, specifically with a focus on communications? I just want some physical reference books on these topics I'm learning by other means, since holding physical books is different from using an ebook. Thank you for your time!", "label": 0}
+{"snippet": "I'm looking for an existing word that roughly means \"the process or idea of replacing bad/negative elements/deeds with good/positive elements/deeds, such as when a negative thing is eliminated at the same time that a positive thing is added\". In terms of words that would not fit this goal are words that could (to some people) mean only the elimination of bad or the addition of good without the other half. Here is an example sentence showing the usage: I live my life with _____ so that I'm not just removing bad habits, but I'm filling the hole created by removing the bad habits with the addition of good habits, which both maintains my ability to fight returning to the bad habit while also creating a positive element at the same time.", "label": 0}
+{"snippet": "I am trying to do ray tracing for an endoscope, but I don't see how it could form a sharp image that could be viewed at the eyepiece. In the diagram the box in the middle is the \"fiber\", but the light from the object (the dot on the left) comes out of the fiber as if they originate from two locations (top and bottom), and if viewed through the eyepiece at the end, wouldn't two images form (the two dots on the right)? Also, if just looking at the image end of the fiber by eye directly without eyepiece, one should still see the image of the object, right? I don't see how it would work with ray tracing in this case either. And should the image in this case be inverted or upright, or left/right flipped, or does it depend?", "label": 0}
+{"snippet": "I've been struggling with this one... I'm trying to figure out whether it's okay to use the expression \"call of the blood\" to describe the phenomenon of doing something naturally (or coming to like it naturally) because it's in your blood, because your ancestors did it/were skillful at it, etc. For example, my ancestors were always good at horse riding, and I should also be good at that, at least like that because it's in my blood- in English, could I call this the \"call of the blood\"? We do have this expression in Russian. The words themselves seem pretty self-explanatory, but since there are so many expressions involving the word \"blood\", I thought to ask the native speakers and English language specialists here. (What I found during my research online were the similar-sounding expressions \"call out for blood\", or \"blood for blood\", but theseare not what I need in terms of the meaning.) So, can I say \"call of the blood\"/\"the blood call\"?", "label": 0}
+{"snippet": "It is said that most of what we call \"mass\" of nucleons are in fact from the kinetic and binding energies of quarks, and that the rest mass of quarks, from the higgs mechanism is much smaller compared to the nucleon. There are other examples, like the binding energy of a nucleus, that show how energy contributes to the mass of things in the subatomic world. My problem arises from the fact that it is also said that the gravitational effects are not really affected by how fast the object goes. Thus, a object won't get infinitely attracted to a planet even it goes at the speed near light. This seemed different from the previous examples, since in those cases the energy did affect the mass(in the classical way), which is basically what builds us up. What would be a appropriate way of understanding this discrepancy? Thank you for your time in advance.", "label": 0}
+{"snippet": "I've been playing around with the concept of entropy and how it can be manipulated when I came onto the complex workings of quantum waves. To my understanding, everything we know as a particle is a wave on a quantum field. Those waves are the result of energy being introduced to, and then propagated through, the field---ei. The waves carry energy. Further, the wave's entire existence is defined by the energy it carries, no energy, no wave. This caused me to ask the question, is there anything in our reality that is fundamentally real? Is there anything that exists that is not just the extrapolation of the process of moving energy from a to b? To be clear, I think that, to a certain extent, the fabric of space-time counts, but it's not what I'm really looking for. Space-time is what our reality is built upon, but it does not constitute it. It is the physical stuff that is built upon and held within space-time that makes reality, and it is from that that I ask if there is anything that is fundamentally real.", "label": 0}
+{"snippet": "I just watched a rather unreliable (or so I think) Physics YouTuber who asserted that absolute acceleration is impossible to measure, because it is impossible to ever calibrate an accelerometer accordingly, and I'm rather stumped by this argument. My understanding for all these years has been that acceleration can be absolute, and it can be measured easily with an accelerometer, but the YouTuber asserts that all accelerometers that are calibrated are done so in a frame that may or may not be accelerating, and to \"correct\" for this acceleration means having knowledge of an \"absolute\" inertial frame, which is defined using the accelerometer in the first place, thereby making the logic circular and invalid. Is he correct? Or is there a hole in his explanation? Or is this just an engineering problem, with a fairly easy fix in pure physics? What am I missing?", "label": 0}
+{"snippet": "In a recent conversation with my professor, he explained to me a misconception I had, in that given how physicists says that the Higgs \"gives\" the mass of all other particles, I was under the impression that a particle's interaction with the Higgs field is what gives it the property of mass. However, my professor explained that the Higgs boson was simply the first term in a perturbative series where each term can be recursively defined as the one before it. So knowing the first term allows us to calculate all the other terms. The other terms were the masses of all other particles and the first term was the mass of the Higgs boson, so discovering the Higgs's mass allowed us to calculate (\"gave us\") the masses of all other particles. This topic came up because I am doing research in QFT with him and in the book we're using I recently got to the part where it describes self-interactions and Yukawa interactions of fields (not yet quantized) using perturbative analysis. So, my professor used the Higgs as an example of this which I may have heard of and I had to explain my misconception to him. My question is: Where exactly does this perturbative series come from, what was it attempting to describe, and what does it and its derivation look like mathematically? it's difficult to read the literature on this and, to be frank, I don't quite have the time. Any help is greatly appreciated. Thank you!", "label": 0}
+{"snippet": "We know that a static charge only produces an electric field and a charge in motion (be it constant velocity or accelerated) creates both magnetic and electric field. But recently I came across that \"changing electric field changing magnetic field, and a charge moving with uniform velocity doesn't create a changing magnetic field, and hence electromagnetic waves aren't emitted\". Now I am confused since I can't find a clear explanation of accelerated vs uniform velocity in case of charge anywhere. Let's assume a source charge in space and the corresponding electric field associated with all points. Now if the charge starts moving (irrespective of uniform velocity or accelerated), since the position of the source charge is changing, the electric field associated with all the points in space are experiencing a change in both direction and magnitude and hence electric field is changing. So according to \"changing electric field creates changing magnetic field theory\" shouldn't electromagnetic waves be generated in this case? I really am finding it hard to understand the concepts. It seems that the electromagnetic waves are generated, only if the field lines are disturbed according to the following picture, but I am finding it hard to reconcile between the two concepts.", "label": 0}
+{"snippet": "The diffusion coefficient is known in the traditional physical literature as an empirical parameter of Fick's law. Here the observation is that spatial gradients of densities are suppressed by a rate proportional to the gradient of the density, and the diffusion constant is identified as the constant of proportionality. An other empirical definition is the identification of the constant of proportionality between the mean squared displacement and the square root of time of colloids. One insight of the paper on Brownian motion by Einstein was that these two definitions are consistent with each other. However in the last decades we additionally learned from the computational physical literature that if we take N classical particles interacting via Lennard-Jones pair forces, we consistently observe the linear MSD vs square root of time dependence. However I never came across an attempt to derive this result analytically, that is, for a set of known LJ parameters (sigma, epsilon, T, V, N,..), is it possible to analytically show or derive this linear correlation ?", "label": 0}
+{"snippet": "According to my environmental science textbook and various sources on the web, the thermosphere has the second highest density of any part of the atmosphere. It falls only behind the troposphere which can be explained as the most dense because the force of gravity holds gas particles there. But here is where I get lost, The thermosphere is located at a higher altitude than the stratosphere or mesosphere and has a higher temperature. It collects most of the thermal energy released in radiation from the sun. The thermosphere is more dense than the two layers directly below it (stratosphere and mesosphere.) But why is that? Pressure and temperature would be higher, but those shouldn't effect density. If density is mass/volume, then shouldn't the density be lower in the hottest part of the atmosphere due to Charles' Law? I can't really find any reason why it would be more dense other than this theory from Einstein that adding thermal energy to a gas particle would increase its mass. (can someone explain why this would be, I get increasing its kinetic energy but thats cause of speed increase, not mass.) Attached is a graph detailing temperature, density, and pressure in the different altitudes, I've been turning about this for a few hours and any input is greatly appreciated!! :)", "label": 0}
+{"snippet": "Consider a simple chemical reaction, such as the association of two hydrogen atoms within the gas phase to form one hydrogen molecule. It is known that this reaction is related with energy release in the form of heat because the hydrogen molecule is more stable than the two hydrogen atoms. Within a gas containing hydrogen atoms and hydrogen molecules, kinetic energy can be stored in several modes, including translation, vibration and rotation. If the energy of the reaction is to be released as heat, then directly after the reaction the temperature should slightly increase locally near the reaction. This local increase of temperature results in a transfer of energy to the \"bath\", and this transfer of energy is the heat. Which one of the above mentioned modes of kinetic energy do you think is first activated directly after the reaction ? If I imagine two hydrogen atoms that decide to make a covalent bond at some \"t\", then directly after time \"t\" they feel a strong bonded radial force, and directly before they feel a weak \"dipole force\". So they should be pulled toward one another, possibly overshooting the equilibrium distance of the molecule, then relaxing back. So I guess the energy is dissipated in the vibration mode. For my understanding, I would first like to focus on the case without radiation.", "label": 0}
+{"snippet": "I have been reading this article about the quantum vacuum state, and in the section that I linked to, there is a video showing an experiment that shows visibly that quantum fluctuations are actually happening (see the video in the link). The quantum fluctuations are visible because they amplified them using Spontaneous parametric down-conversion Now from what I learned here, quantum fluctuations (or virtual particles) do not exist (and links therein). They are just tools of perturbation theory in QFT when taking into account interactions to make the mathematics work. Another reason I learned is that the fluctuation-dissipation theorem states that when a system is in fluctuation, the energy dissipates as heat or other forms of energy. So then, the vacuum cannot be fluctuating. I seem to be confused now. Is the video fake or is what the video/wiki claiming not true and is something else entirely? This question is sort of a follow-up to my previous question.", "label": 0}
+{"snippet": "I'm trying to figure out if a hexagonal grid can embed rectangular coordinates in whole numbers of \"Y-steps\". In the image below, one \"Y-step\" is the spacing between red hexagon centers in the Y dimension. For some arbitrary hexagonal grid size, how many hexagons do I need to produce some whole-valued number of \"Y-steps\" in the X dimension? Another way to ask this might be: Select four hexagons whose centers create the corners of a square. In the hexagon grid orientation shown below, how many horizontal hexagons are needed to create such a square, and then how many vertical \"steps\" are needed in the Y dimension? Both X and Y values need to be whole integers. In case it helps, this site provides great info in hexagonal coordinates, but I've not figured out how to pin down a way to solve this. We are using the \"pointy top\" orientation.", "label": 0}
+{"snippet": "I would like to perform something that resembles a curve fitting optimization but for which i could not find much info. Lets say i have a function that yields a time series. What i would like to do is tune the parameters of this function so that the time series it yields has a specific shape. For instance i want it to output a step, or two steps back to back. What i don't know (or care about for that matter) is the height of the steps. For a single step, a naive solution would be to simply take the average of the output and compute the RMSE of the output to it's average and minimizing it. However this gets more and more complicated for more complex shapes (the two steps example is already a pain with this method) Would there be a mathematical tool that would facilitate this?", "label": 0}
+{"snippet": "Classical mechanical systems observable on a dynamical scale are subject to Newton's laws. In this case, knowledge of the Hamiltonian allows us to minimize energy taking into account inertia. This allows us to calculate trajectories, find equilibria and derive many properties. Classical mechanical systems consisting of large sets of particles are subject to Boltzmann's law. In this case, knowledge of the Hamiltonian allows us to minimize energy and maximize entropy. This allows us to calculate phase space weights and derive many properties. Is it possible to proof that the two approaches are equivalent in some cases ? That is, proofing all assumptions made in micro-canonical and canonical formalisms based on Newtonian mechanics ? Or that the average properties generated by Newtonian trajectories are equivalent to Boltzmann average properties ? Or is it maybe possible to observe some kind of transition between the two cases if they are not equivalent ?", "label": 0}
+{"snippet": "I have observed that when an insect is electrocuted in a bug zapper, there are typically a few sparks or flashes of light. Sometimes the insect will catch on flame in a tiny fire, and the body will burn for a few seconds before stopping burning. The lights and flames stop after a few seconds, but the insect body often, instead of falling, remains in position still connecting two wires. Given that the body is still in position connecting two wires, why is it that after a few seconds, sparks or flashes of light stop appearing, and any fire is extinguished? Does that mean that electricity is no longer flowing through the insect's body, and if so, why does the electricity stop flowing if the body is still connecting the two wires?", "label": 0}
+{"snippet": "Is it okay (in terms of usage) to use present participle clause for an action that follows another action as a result? For instance, the following sentence seems correct to me: The bomb will explode, sending shrapnel everywhere. Yet the following sentence does not correct at all to me: I will run one mile to reach my target, grabbing him. I don't know how I feel about this sentence, I think it feels fine: The cat leaped into the air, landing in the river. This sentence feels pretty wrong: I noticed my target, shooting until I hit him. But this sentence feels fine: The man took off from one end of the street, reaching the other side just in time. And then obviously this sentence feels not great: I will live a good life, dying. But then this sentence feels fine: I will live a good life, dying when it reaches its conclusion. What's the differentiator here? Are my feelings correct?", "label": 0}
+{"snippet": "The following problem has bugged me for a while, ever since I noticed it. On the Visible Spectrum Wikipedia, the following is the visible spectrum: Now, in Photoshop, or really any colour picker, the hue slider looks something like this: Or sometimes this: I noticed that in both of these, the colour loops back to red. Why is this? I believe that this doesn't happen on the visible spectrum. The visible spectrum goes from a violet-ish colour to a maroon-ish colour, with a whole range in between. But where does the magenta colour from the hue slider fit in? I take it that it is possible to have a purely yellow object, or a purely teal one, as it is on the colour spectrum, yet are magenta things and pink flowers inherently reflecting multiple wavelengths of light, from opposite ends of our particular viewing spectrum? All of this seems awfully odd to me, so I was hoping someone might be able to clear it up.", "label": 0}
+{"snippet": "I understand why the temperature of the hot reservoir has to be minimally higher than the temperature of the hot working fluid during the isothermal expansion phase of the Carnot cycle (to limit new entropy being produced in the working fluid that we have to get rid of). But during the isothermal compression phase why do we need the cold reservoir to be only minimally cooler than the cold working fluid? The working fluid looses the same entropy independent of the temperature of the cold reservoir, so why do we need to minimize the new entropy created in the cold reservoir? What is wrong with just letting the cold reservoir get more and more entropy as long as the working fluid returns to the same state as before the cycle?", "label": 0}
+{"snippet": "So, as I was browsing a bunch of the tachyon questions throughout the years in this forum, and an oddity of these hypothetical faster-than-light particles came to mind. Ordinary particles with mass always have an inertial frame of reference where they are at rest, thus their rest mass can be measured. Lightspeed particles, while never at rest, have an invariant velocity, so different frames of reference can agree on their energy. Not so for tachyons. Tachyons not only are never at rest (like lightspeed particles), but their measured velocity is frame-dependent (like ordinary particles with mass). So, my question: Question: Is there anything analogous to a rest mass that can be used as a common point of reference when working out the mass of tachyons, or is it completely frame-dependent? And, no, we cannot say the tachyon's frame of reference, because they cannot be treated as observers (same as with lightspeed particles, we cannot treat a photon as an observer).", "label": 0}
+{"snippet": "Electricity is used for many things. One of the biggest uses is transporting energy, almost instantly, from a power plant to the machines in my home and many others'. I was wondering if a similar energy transport grid could be created using a fluid under pressure. The power plant would use its energy to pump a fluid into the main pipe, which extends all over the country, with many sub pipes coming out to each house. The high pressure liquid would act like high voltage electricity, ready to be tapped into by a user. At home, one would open a valve in the pipe, causing high pressure fluid to come out. This jet could be used to spin a rotor mechanically, in other words, energy was transmitted almost instantly from the power plant to my home. We would probably need to have the used fluid go back into another pipe which goes back to the power plant to be pumped again. In other words, something similar to an electric circuit but using fluid instead of electrons. Knowing about the analogy between electric current and hydrodynamics, I was wondering if my strange idea could be practical or at least physically valid.", "label": 0}
+{"snippet": "I hope this isn't the completely wrong community for my question, please let me know. I did search for 'varifocal' and got some hits, it seems (still getting used to these glasses, so it is a bit hard to use my PC) So, it seems that when you get these glasses - we call them varifocal in UK, not sure if that is the international name? - they have these three zones with different strength, but for some reason, there are two blurry areas in the lower right and left corners. The top has the distance vision all across, but the computer- and reading strengths are only in the middle. I haven't been able to find an explanation online so far; does anybody here know of a good, technical reason for not simply providing three zones in the full width?", "label": 0}
+{"snippet": "Even though a black hole has a Scwarzschild radius that indicates a finite small distance to the center of the hole, the distance traveled by an infalling particle seems a lot bigger than the Schwarzschild radius due to the extreme curvature of spacetime. An infinite curvature even seems to imply an infinite distance. Two particles falling into the hole, one after another, end up spatially separated. This holds true for all particles that fall into it. This seems to imply that the distance traveled is actually infinite. I mean, if particles end up spatially separated because of spaghettification, and they all fall the same distance to the singularity, only an infinite distance will do, so it seems. What (if) is the flaw in my reasoning? EDIT I'm not sure if the linked question is a duplicate as it asks about the time it takes to freely fall to the singularity. I'm asking about the distance traveled, and I read in a comment by @MichaelSeifert that there is a good explanation for why the concept of distance isn't well-defined in this case. I can't see why that is so. What if you, the freely falling indestructible observer, have an infinite rope, one end of which you attach somehow just above the horizon? Can't you see how much rope has rolled off from your device when you hit the singularity?", "label": 0}
+{"snippet": "Short introduction to my understanding: As far as i understand, virtual particles are usually defined to be the internal lines in Feynman Diagrams. But we know that those are just useful tools to calculate amplitudes in interacting quantum field theories. In a free theory I have no interactions, hence no internal lines and no virtual particles. Virtual particles show up when, in interacting QFTs, we have the so called contact interactions showing up in the perturbative Dyson-Schwinger equations as deltas. My question: Can we regard virtual particles solely as mathematical tools needed to make predictions in perturbative interacting theories because we don't fully understand how interacting theories work? (I mean how they work in a non-perturbative setting) If the latter is true, and from my actual understanding I think it is true, what is our \"hole\" in the understanding of full interacting QFTs?", "label": 0}
+{"snippet": "I was reading about effective field theories and wondering how much an EFT can tell you about the ''underlying'' theory which is then reflected in the EFT. Can one extrapolate back from what one sees in the EFT to derive features of the theory for the high energy degrees of freedom? As an example, general relativity is considered to be an effective field theory for quantum gravity, but that does not tell us much about what the correct quantum gravity theory would look like, with many people arguing that this underlying theory would be a string theory and not even a field theory. However, are there cases where one can say more or come to definite conclusions about the underlying theory? What is the systematic way for doing this? For example, in lecture notes of Pich on EFTs with Nambu-Goldstone modes, he mentions that one can ''uncover fingerprints of new physics scales'' from couplings in the EFT.", "label": 0}
+{"snippet": "So, just to expand on the question in the title, I know group representation theory, and especially character theory, are quintessential tools for anyone hoping to study finite groups. That said, from what I've seen and read, some people study characters in and of themselves (say, density of zeroes, Brauer characters, etc), while another set of people uses them as tools for studying questions concerning the groups themselves (i.e., it's not clear from the get-go that characters will even get used; they are a part of a toolkit). My question is: what's the intersection between these two sets of people? Can a person spend some time working on Brauer characters and blocks and then move on to study, say, the subgroup structure of finite simple groups? Or are the areas far enough apart that character theorists simply don't have enough baggage to work in general problems on finite groups and vice-versa? Sorry for being a bit \"vague\", perhaps... I'm just very curious about the distinction (if it even exists at all!), since I really love both topics! Thanks so much in advance!", "label": 0}
+{"snippet": "(Honestly I fear this is borderline off-topic... be gentle with the downvotes ;-)) Most of the packages I've written are for personal use but a couple of them are used by some other people. These packages change relatively often as I'm constantly implementing requested features. Right now I tend to ship out the most recent stable version by e-mail but then I get either answers of people that are not interested any more, or requests from other people who aren't in the mailing list yet. I do not want to upload the packages on CTAN for two reasons: There's maybe a dozen users. It's highly unlikely the packages will be useful to someone else. I find there is enough bad code on CTAN without me contributing to it. For now I've got an institutional home page but that may change any minute, so posting the code there for download (which I've done) might not be a long-term solution. Any advice? (My personal texmf tree is on Dropbox, if that may spurt a solution.)", "label": 0}
+{"snippet": "It seems correct to write \"A host of tools exists...\" or \"A range of tools exists...\", i.e. the verb reflects the fact that you are referring to one collective noun. But, if I want to continue to talk about that collection of things, it often seems natural to say \". They aim to solve...\" or \", which attempt to model...\", i.e. now I am referring to the capabilities/intentions of the things within the collection. Which is strictly correct? And putting strict grammatical rules aside, which is an English speaker most likely to say? a) \"A host of tools exist, which aim to solve...\" b) \"A host of tools exists, which aims to solve...\" c) \"A host of tools exists, which aim to solve...\" My instinct is to avoid the construction and write \"Several tools exist, with the aim of solving...\"", "label": 0}
+{"snippet": "It is currently understood that gravity is not actually a force, and a fact that is often used to show this is that an object in free fall doesn't \"feel\" that it is accelerating and is thus an inertial frame. However, it seems to me that Newtonian mechanics can already predict that this will be the case. Since all the parts of the object are being accelerated by the same amount simultaneously (at least approximately, like near the surface of the Earth) there won't be a tendency for this object to contract, and thus \"feel\" that it is accelerating. This isn't the case, for example, when I push the same object. In my understanding, the force needs to be communicated from the point I apply it to all the rest of the object, and this delay is the cause of a contraction/increase in internal forces or tension, allowing it to effectively \"feel\" that is accelerating. Now, suppose that there is a uniform field that accelerates any particles with constant acceleration. Like gravity, a free object in this field will not be able to detect that it is accelerating, since all of its particles are accelerating equally at the same time. My question is: Is this object inertial, or is it only inertial if this field is a gravitational one?", "label": 0}
+{"snippet": "What is the current consensus about the age variation of the existing galaxies in our observable universe? Not to be confused with the age of very distant galaxies as observed today by our telescopes which is actually observing these distant galaxies as they were many billions of years ago in the early formation but instead I am asking about their absolute age today assuming they still exist? I mean, a hypothetical observer located in these very distant galaxies and looking at our home galaxy would also see our galaxy not at its current state but how it looked like billions of years ago. I am not asking this but if all the galaxies were formed more or less at the same time according to the Big Bang theory? In general how you estimate the age of a galaxy?", "label": 0}
+{"snippet": "Let's assume that a cylindrical magnet is clamped by an horizontal arm extending out of the wall. The top of the magnet is its north pole and the smooth face facing down is its south pole. If I bring another cylindrical magnet and position it perfectly in line below the fixed magnet, with its top being its north pole and the bottom being the south pole, would it be possible that the weight of the magnet going down and the magnetic force attempting to pull the magnet upwards balance out so that the magnet can levitate in mid air? Conceptually, it seems to make sense as in this case, the magnet is not prone to flipping since it poles facing each other are not repelling. However, I'm not sure if this violates Earnshaw's theorem. It it's not possible, then why isn't it possible? Did I miss something in my assumptions? And if it is possible, Is it also possible for the levitating magnet to rotate about its central vertical axis and still remain suspended in space?", "label": 0}
+{"snippet": "I'm looking for an accurate method to measure the tension in a guitar string, without using a sonometer setup nor by measuring the frequency. the current method that I have in mind is to measure the force perpendicular to the string and the string's displacement, and then try to resolve the vectors (the method is explained in more detail here), but I don't think that is an accurate method for a couple of reasons: we have to consider the uncertainty of the newton meter and the ruler the propagation of uncertainty when resolving vectors makes the final uncertainty much larger even after resolving the vectors, we are calculating the tension in the bent string, not the equilibrium position. are there any other methods I can use to measure the tension more accurately?", "label": 0}
+{"snippet": "Clicking through the OEIS I found this sequence that seems curious - the number of \"labeled\" groups. It cross references the usual sequence of the number of groups up to isomorphism (the very first sequence in the OEIS) as well as saying it is \"a sequence related to groups\". So I've tried to look up this concept, but Google with \"labeled group\", \"labeled group maths\", \"labeled group theory\", and so on, to no avail at finding anything. Groupprops (essentially a wiki for group theory) doesn't seem to have anything either. I've clicked through the links on that OEIS entry and cannot find anything of help. So as a last resort I'm asking here (I know this isn't necessarily the kind of place for definition questions though, sorry). So, what is a labeled group?", "label": 0}
+{"snippet": "Neither my wife nor I have English as our mother tongue, but we use English to communicate to each other, which sometimes causes confusion. My wife often uses the expression \"until now\" to mean \"so far\" or \"yet\", meaning that the action is not yet finished. I didn't receive any answer from the landlord until now. To me \"until now\" means that for some time she didn't get answer but now (recently), she did. So I'll usually reply something like: Nice, so what did he say? And she looks at me weirdly, as if I would have asked something silly and we both laugh. My question is. Does \"until now\" always imply that the action you are talking is now finished, or can sometimes be used with the same meaning as yet?", "label": 0}
+{"snippet": "If i place some charge on a conductor then it will distribute itself in such a way that electric field everywhere inside is zero. My text book says that only one kind of such charge distribution is possible. Or if i place charges outside the conductor then charges will be induced on the surface of a conductor to make field inside zero and again such charge distribution is unique. Intuitively it all seems correct but i am trying to figure out right arguments for this. One such argument is that suppose i place some charge on conductor then i can solve poisson's equation to find potential at the surface(at boundary). Charge distribution outside the conductor is known. Then uniqueness theorem says that only one such potential function is possible which satisfies the given/known boundary conditions and poisson's equation outside. Since a particular potential function corresponds to a particular charge distribution the charge distribution must also be unique. This argument seems correct to me but at the same time something seems missing. Am i correct?", "label": 0}
+{"snippet": "I'm looking for a word similar to \"free\" or \"without cost\", but that makes it explicit only that no money is exchanged, while still allowing (or implying, or explicitly specifying) that some other exchange of some value has taken place. For example, if I rent a room to a friend in exchange for language tuition, I have a form of non-monetized exchange. I would like to say that the room is rented for free, except that it isn't for free here, because tuition is given in return. I still have to pay taxes and bills in money, and to describe this I want to say that the room is rented for zero-money (that way pointing out that I can't use the exchanged tuition service to pay the bills, and that therefore the exchange is somehow of less value than its cash-value equivalent). Saying it's \"free\" is not correct, because something of value is given in exchange. \"Costless\" I think has similar issues. \"Barter\" is a related meaning, but here I'm dealing in an on-going exchange-of-services relationship, for which \"barter\" doesn't seem right. \"Non-monetized exchange\" or \"on a non-monetized basis\" is the best I have so far. I can't think of term that is succinct and gets this meaning clearly. Any ideas? A technical accounting term would do, but ideally I'd have something that is clearly understood by a lay person.", "label": 0}
+{"snippet": "Imagine a train moving relativistically according to an observer at rest wrt to the tracks it's moving on. The train seems contracted in the direction of motion. At the points where the wheels make contact with the tracks, the wheels have zero velocity, so the distance between these points is not Lorentz contracted (like the caterpillars of a tank are at rest). Now what will happen when the train suddenly decelerates, simultaneously at all parts, as seen from the observer at rest? Obviously, the wagon will expand, but what will happen to the wheels? Will they follow the expanding motion, which leads to friction between the wheels and the track? On the other hand, when the train starts to accelerate from zero velocity, the distance between the wheels will not Lorentz contract, so the wheels seem to have to slide with friction, dragging behind the contracting wagon, so to speak. Will the reverse happen when decelerating?", "label": 0}
+{"snippet": "I had a recent conversation with a professional mathematician about the status of relations, functions and predicates. I was arguing that it seems intuitive (to me at least) to classify them in this hierarchy (as to which is more primitive): All predicates are functions. All functions are relations. The obvious problem here is that it seems intuitive that unary or even nullary <predicates/relations/functions> are more primitive than their n-ary variants. Is there a way to compose functions as at least unary relations or vice versa (relations as unary functions)? If not, is it possible to order them in such a hierarchy given the binary restriction. Finally, if there is something more primitive that has a formal definition, then that would do as well. A resource or explanation pointing to how at least functions, relations and predicates are composed using this notion would be helpful.", "label": 0}
+{"snippet": "It's well known the effect of Rayleigh scattering on the color of the sun, and it's explained several times on this website. Here's one of them. The summary of these explanations is, that when light travels through a colored medium, that color is being \"used up\" to make the medium the color it is, and only the other colors will go through. Make very much sense. But the problem is that our experience in everyday life is just the opposite. When we shine a light through a colored medium, the light becomes the same color as the medium. Although it's hard for me to understand why (this was asked here without an impressive answer). And that's also happening with sunlight that goes through colored glass. So why does the atmosphere behave different than anything else? And is there anything I can experiment with that would have the same behavior as the atmosphere?", "label": 0}
+{"snippet": "I did some online search and found the explanation using the following two diagrams. It's not perfectly convincing to me. Or at least it is not clear to me in the following details of the process: For the secondary rainbow to have the inverted order of bands, do the light rays have to exactly reflect twice and cross each other twice inside the water drop? If so, what are the necessary and sufficient condition for that to happen? It seems to rely on the relative direction of the incident light and the surface of the water drop and the position of incidence? The diagram only shows one particular position and angle of incidence, so it seems kind of accidental to me that it inflects twice and cross each other twice and got to the inverted order.", "label": 0}
+{"snippet": "I was reading a physics problem related to astronomy, and upon re-reading it, I realized that it could be really indicated to extrapolate some really interesting physics-related information. One of these is: How could we measure the ratio of a planet's radius to a star, for example using transits? The only idea I have is to compare them when the planet passes exactly in front of the star (i.e. they are aligned with our view), but this only makes sense if the distance between the two is much smaller than the distance between us and that star system (which I think is true enough for every system except the Solar system) and if it is possible to obtain such high resolutions (and I already had my doubts about the distance between the two, which should be much greater than their radii anyway).", "label": 0}
+{"snippet": "Suppose I have a nonlinear ordinary differential equation, in several variables, with a stated initial condition. How would I go about finding a nonlocal linear approximation? What is known about such approximations? By nonlocal approximation I just mean that the would-be approximation minimizes the maximum distance between the solution of the approximation and the solution of the original, nonlinear initial value problem, or meets some other criterion such as minimizing the integral of the square of the distance. At least in the case of minimizing the integral of squared distance, this problem amounts to a nonlinear least squares problem, and the criterion is a differentiable function of the parameters of the linear approximation, so maybe a Gauss-Newton type algorithm or even simple gradient descent (at this point I'm not worried about efficiency) could be applicable. For the problem I have at hand, I constructed a linear approximation at the initial point, via the Jacobian of the original system of equations, but the solution of the local approximation is very different from the solution of the original nonlinear IVP at later times, which inspires me to look for a nonlocal approximation.", "label": 0}
+{"snippet": "While reading the Wikipedia article on Drag Crisis, I found: The drag crisis is associated with a transition from laminar to turbulent boundary layer flow adjacent to the object. While, the Wikipedia article on Turbulence states: In general terms, in turbulent flow, unsteady vortices of many sizes appear which interact with each other; consequently, drag due to friction effects increases. If drag (due to friction effects) increases due to turbulence, then why does drag crisis occur when flow shifts from laminar to turbulent? Shouldn't drag be less for laminar as compared to turbulent flow? Why else would surfaces smoothen due to drag over time? The Wikipedia article on Drag Crisis also goes on to say: For cylindrical structures, this transition is associated with a transition from well-organized vortex shedding to randomized shedding behavior for super-critical Reynolds numbers, eventually returning to well-organized shedding at a higher Reynolds number with a return to elevated drag force coefficients. I am having trouble understanding this. A related question, Drag Crisis and Terminal Velocity?, examines the relationship between drag coefficient and terminal velocity.", "label": 0}
+{"snippet": "I'll put pictures from the book (Introduction to the Structure of Matter: A Course in Modern Physics by John J. Brehm and William J. Mullins) as I think they are relevant to understand my problem: I have trouble understanding the case where the observer watches the source in a direction perpendicular to the magnetic field. The electron will rotate around B axis, so the observer will only see a linear oscillation of the electron hence linearly polarized light. But how can the Lorentz force explain the splitting of spectral lines (i.e. the change of the frequency of the electron)? The book suggests to view the linear oscillation as a combination of two counter-rotating motions like this: But if this is the case, the Lorentz force would act in a plane perpendicular to the image so it won't explain the change of the frequency of the circular motion of the electron (and so the Zeeman splitting, classically). Instead the situation is clear when we observe along the direction of B, as in that case Lorentz force would act radially.", "label": 0}
+{"snippet": "The standard explanation in textbooks goes that in the presence of electric field (e.g. external electric field) the free electrons inside the conductor will keep moving until electrostatic equilibrium is reached and that they will create a field which will cancel out external field (e.g. electrons move to one side leaving positive charge on another side, this creating electric field that cancels out the external field). But what if the external field is so strong that there is just not enough free electrons to cancel out external field? What if there is nothing left to be moved? E.g. I have electric field lines going from left to right, all free electrons move to the left surface, there is nothing left to move, but it's still not enough to cancel out external field. Will there still remain an electric field inside the conductor then? If not, what will happen?", "label": 0}
+{"snippet": "I'm looking for a phrase that describes a problem whose complexity starts to increase exponentially, either because the problem is recursive, the definitions/conditions of the problem interlink with themselves, or it turns out that it's connected to a great many other issues, and changing one changes all the others in turn. This phrase would be useful when, say, discussing how to solve a simple, harmless, trivial little bug in some software...that now has eight people standing around debating business logic and corollaries to corollaries and exceptions to exceptions. Phrases that are close, but not what I'm looking for: \"Tip of the iceberg\" could be used later on when describing the original difficulty, since it would become much worse later, but the rest of the situation wasn't originally an issue or complicated, and only by investigating the original, simple issue did the full complication arise. \"Can of worms\": the rest of the difficulty isn't inherently a problem; the original, minor issue is the only part that's an actual problem, and the rest of the complication is created by trying to solve it. \"Cure is worse than the disease\": it's not that the solution is bad or undesirable, but that the original problem was far more complicated than it first appeared. \"Gordian knot\" describes a problem that is already complicated known to be difficult; what I'm looking for is a situation that seems simple or even easy until you try to solve it.", "label": 0}
+{"snippet": "A congruence is a useful notion in general relativity, relating mathematcal definition and physical interpretation: \"A congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold [...]\" Following up some intuition (mostly concerning timelike congruences) I find the following description further down on the Wikipedia page especially relevant: \"The integral curves of the vector field are a family of non-intersecting parameterized curves which fill up the spacetime. The congruence consists of the curves themselves, without reference to a particular parameterization.\" The emphasis on non-intersecting is placed in the Wikipedia article already; however without any further supporting explanation or link. To me, this raises an ambiguity: The phrase \"non-intersecting curves\" might be understood as referring to each of the (unparametrized) curves as a set (consisting of events), meaning that the intersection of any two of these sets is empty. In other words: (pairwise) disjoint sets. Or: The phrase \"non-intersecting curves\" might be understood (in a geometric sense) as allowing the possibility of at least some instances of being tangent to each other; corresponding to the general geometric description of such mutually tangent curves as \"touching but not intersecting\"; thus allowing at least some pairs of curves to have at least one point (event) in common, \"in which they are tangent to each other\". Accordingly (and without hinting at my intuition) my question: Which is it?", "label": 0}
+{"snippet": "In my physics textbook, the foundation for work is derived using newton's third law, where F_surr = - F_gas, where surrounding represents a piston-cylinder device and gas is pushing against the inner surface of the piston towards the right. My questions are: Given this information, it is obvious that W_surr = - W_gas. So, shouldn't the terms cancel each other and result in zero acceleration of the piston, i.e., the piston remains stationary? I understand that newton's third law is applicable for forces acting on different objects in contrast to second law which is used for analysing forces acting on a single object. So using second law, if i were to dissect the system and piston into two bodies and assuming no friction, we will have F_surr acting towards the left on the gas and F_gas acting on the piston towards the right. So, I am confused here, shouldn't F_surr being the only force on the gas cause it to compress and F_gas on the piston cause the piston to move towards the right? Finally, during a quasi-equilibrium process, will there be any accelerations of the piston at all at each equilibrium states or is the equilibrium state like a point at which the system and surrounding are in complete mechanical equilibrium and are stationary? Essentially, I am having a hard time applying newton's second and third law to derive work equations.", "label": 0}
+{"snippet": "Given two probabilistic distributions (red and blue) it is well known that a linear interpolation between them is well defined (see this). For example, by the Wasserstein metric we have the following interpolation: When I first saw this approach, it crossed my mind that the Bayes 's posterior could be explained by a similar geometric argument. Perhaps, the mean between these distributions by the Wassertein metric. However, when I plot the Bayes's posterior (in green) we see that it does not belong to this linear interpolation. My question is: is there a geometrical reasoning that we can use to interpret the Bayes 's posterior? If there isn't a geometrical reason , can there be a variational one (the Bayes's posterior is the minimum of some energy in this space)?", "label": 0}
+{"snippet": "I am curious about magnets and their interaction with the electromagnetic field. So I tried to find this answer and stumbled upon (Magnetism and Photons), this is an interesting description that I quite like, but it doesn't really explain how a magnet can keep a piece of metal on a string hovering in mid-air indefinitely, the magnet is not moving, yet there is an interaction there, as I understand it via photon exchange. I did read in a magazine (New Scientist particle physics special from memory) that electron spins create a non homogeneity that interacts with the electromagnetic field that then \"tends\" to allow virtual elements to appear through particle/antiparticle annihilation, with a resulting photon being generated. I don't love this explanation, perhaps because I find it hard to get my head around it. Any advice or references you can point to explain the electromagnetic field (this is confusing in itself, I thought long ago we gave up on the idea of an \"ether\", it seems it's back) and then the interaction of electron spins (magnetism) on this field. Thanks in advance, Tibor", "label": 0}
+{"snippet": "I am looking at a tutorial create for the FENICs finite element method package. The tutorial shows a system of advection-diffusion-reaction equations occurring in a solution that is moving according to the incompressible navier-stokes equations. In the tutorial, the authors simply present the weak form, without explaining the derivation. I was hoping someone might be able to explain how to derive the weak form, or even identify some good references to look at to find these derivations. The system of equations is below. [NOTE: I included the equations as images because I could not get the latex formatting to work for an aligned environment. I can put in the latex, but might need some direction on how to format the equations.] The provided weak form is as below. I understand the steps in computing a weak form, especially the integration by parts piece. However, I am not clear on all of the steps in the derivation below, such as why a vector PDE is represented as a single equation. I imagine that the different species are tracked in a vector, and hence the sum makes sense. BUT, in the equation below, it is a bit difficult to see those nuanced elements. Hence I was hoping someone could explain this derivation or provide some links to resources that provide a more detailed derivation of this weak form.", "label": 0}
+{"snippet": "I am really confused about the part where the photon shares a part of its energy with the electron. It is said that the photon loses some of its energy to the electron causing the change in its wavelength. In my understanding photon isn't something that contains energy, it's the energy itself. A single photon has a fixed amount of energy (E = hv) ;the smallest possible value of energy of the photon at that particular frequency. How can it break into something smaller, doesn't that voilate the postulates of Plank and Einstein about the quantum nature of light? Or does a photon break into many, in that case, is the quantized nature of light even meaningful anymore? Moreover if the x-ray photon has surplus energy after knocking the electron out of the atom, why doesn't it contribute to the electron's kinetic energy? Like it does in the case of photoelectric effect. And it leads to another confusion I have now. If photons can share part of their energy then can't we simply increase the number of photons hitting the photoelectrode such that the free electrons can slowly store enough energy to break the required energy thershold.", "label": 0}
+{"snippet": "A person might say on one day: It is hot outside - let's go out for a picnic! It is healthy. Another person might say on the same day in the same place: It is hot outside - stay inside where it is safe from extreme weather! It is unhealthy. The weather and health together is our internal model of what is happening at a physical and biochemical level. It is not actually what happens - simply an analogy we can use to communicate an idea. Let me give another example: One teacher might say This group of students are so quiet. It's unhealthy. We need to break up the group. Another teacher might say for the same students on the same day: This group of students are so quiet. It's so healthy. We need to encourage more students to be like this. In this example health is a metaphor for something that is assumed - but not defined. It is used both ways. The analogy of 'healthy group behaviour' is ambiguous in this conversational context. One possible answer to this might be metaphysical conceit - but that seems like a poetic term, and possibly limited to spiritual poetry. My question is: What is a word for when an analogy could be used for both sides of an argument?", "label": 0}
+{"snippet": "I have two lists, and six elements: V V V M M M I would like to compute every possible combination of those elements into two lists (left and right): So, five possible solutions could be: ([V, V, V], [M, M, M]) ([], [V, V, V, M, M, M]) ([V, V, V, M, M, M], []) ([V, M, V], [V, M, M]) ([V], [V, M, V, M, M]) My first approach was reducing the problem to that which had less elements (two). So, all possible solutions in that case are: ([], [V, M]) ([], [M, V]) ([V, M], []) ([M, V], []) ([V], [M]) ([M], [V]) I can't seem to fit this problem into a basic standard combinatorics one, but perhaps there is something I am missing. How can I approach this problem ?", "label": 0}
+{"snippet": "I need clarity on some definitions and mathematical \"skepticism\". In a recent video by Matt Parker, he says \"(...) although the existence of the sign function, which says if a value is positive or negative, upsets some people (...)\". What does he mean by this, and can this \"upsetting\" be extended to functions like the absolute value or the indicator function of a set? Any suggestions for further reading would be highly appreciated! Edit: Before this question is closed, I would like to clarify that by no means is this question intended to incentivize discord or negative emotions regarding certain groups of people. I do not wish to offend, nor suggest I am taking part in any ideology regarding the nature of mathematics and its definitions. I am merely curious about what Matt meant, and what is the deeper motivation behind his brief comment, hopefully generating a healthy discussion. Thank you.", "label": 0}
+{"snippet": "Consider the following sentence: \"This paper introduces a new alternative for generating synthetic data based on images.\" What I want to say is that \"the new alternative\" is \"based on images\". Thus, the noveltiy of the new alternative is in the fact that it is based on images. What I would like to avoid is that one think that I mean \"image-based synthetic data generation already exists and I propose a new alternative to it.\" So, to avoid the ambiguity I add \", which\" to the above sentence, so it becomes: \"This paper introduces a new alternative for generating synthetic data, which is based on images.\" However, after looking for the usage of \", which\", I am still not sure that the sentence means what I mean. More precsisely does \"which is based on images\" refer to \"generating synthetic data\" or to \"new alternative\"?", "label": 0}
+{"snippet": "I'm a native English speaker, but I'm drawing a blank on how to describe this complicated exchange of situational emotions in words. Maybe someone can help. I'll just illustrate the situation with a narrative scene. Two doctors examine a patient. \"Have you been eating any protein-rich foods lately?\" one of them asks. \"No,\" answers the patient. \"No protein at all.\" Their suspicion confirmed, the doctors looked at each other, nodding _____ly / nodding with _______. What emotion am I looking to describe? I can picture the facial expression in my head, where the doctors aren't personally involved in the consequences of what's going on, feel somewhat sad about what the other person is going through, and yet understand that the consequences are justified based on the person's actions, all of which is shared between the two people who both come to this conclusion. In this case, they both know the patient should've been eating more protein so they wouldn't have this affliction, are somewhat apologetic that the patient didn't know this, but have some sympathy in explaining afterward that in order to stay healthy, one must consume protein. Anyone know what words I'm trying to express?", "label": 0}
+{"snippet": "In the nuclear physics book by Krane, I was reading about how mathematically and numerically Q value of the reaction are measured. So he decided to prove it by solving it in Lab frame, And he goes saying this, \"Let's apply them (the formulas he wrote to measure Q value) first to the laboratory reference frame, in which the target nuclei are considered to be at rest (room-temperature thermal energies are negligible on the MeV scale of nuclear reactions). If we define a reaction plane by the direction of the incident beam and one of the outgoing particles, then conserving the component of momentum perpendicular to that plane shows immediately that the motion of the second outgoing particle must lie in the plane as well.\" So my first doubt is, what is a reaction plane, and why the nuclear reaction always occur in a plane only. I read some more stuffs online but was unable to understand this reason as why nuclear reaction occur in a plane. Why is so that the momentum perpendicular to plane is to be conserved and is of interest?", "label": 0}
+{"snippet": "This is a follow up to a previous question. I use pandoc to create PDFs from markdown files, which uses pdflatex behind the scenes. After a bunch of system upgrades, the type in my printed PDFs started to look off.The weight was heavier, and the the kerning was bunched up. At first I thought this might be a problem with LaTeX or my MacTex install, but now I believe it's a problem with MacOS. When I print on MacOS via Preview or Acrobat, I get the font that looks janky.If I switch to a windows machine and print there (just via the Edge web browser) the type matches more closely to what I see on the screen and used to see when printing from my Mac. I now think the \"bad\" font I see is just good old Times New Roman, being substituted as a default. Does anyone here know why PDF viewiers/printers on my mac might not see fonts embded in PDFs generated by pdflatex?", "label": 0}
+{"snippet": "I work in quantum field theory in curved spacetime. Within QFTCS, we have a bunch of phenomena showing that the notion of \"particle\" is quite subtle. For example, the Unruh effect let's us know that the notion of particle is actually observer-dependent. As a consequence, I tend to be quite skeptic about fundamental theories that rely too much on the notion of particle. While I am far from being an expert in string theory, the things I've heard about it make me feel as if that is precisely what string theory does: to take the notion of particle seriously and change it into a quantum string, which would then be able to solve numerous problem within quantum field theory and quantum gravity. I have also heard one or two words about \"string field theory\", which appears to be a quantum field theory with infinitely many fields. The name, of course, also suggests it is somehow related to string theory. With this in mind, my question is: QFT is a theory about fields, in which particles sometimes appear as cute interpretations. Does the same thing happen in string theory? How exactly (to the best possible presentation for someone who knows nearly nothing about string theory)? Has string theory (or string field theory, or any other similar idea) successfully derived the Unruh effect or is it only \"likely to be there\" based on being a generalization of QFT?", "label": 0}
+{"snippet": "I have a GRIN lens with the refractive index varying linearly with y, and supposedly this lens tilts the wavefront. Since the rays are travelling normally in both refractive index materials, they stay normal to the plane of the lens at all times. However the wavefront travelling with them tilts because of different speed of light for different indices, and gives a wavefront like this. Is this correct? Or do the rays themselves tilt? I don't think this is a possibility since the rays are always perpendicular to the plane. If my reasoning is correct, does this satisfy Huygens' Law? It states that the wavefront must be perpendicular to the path of the waves at all times, but this doesn't seem to be the case here, which leads me to thinking its the waves themselves that are tilting. Diagrams like this can be found on the internet, but I do not understand how are the waves tilting when they enter normally, What am I missing? I found this situation while solving a problem in a book (Pathfinder for Olympiad Physics) but upon thinking a bit more was fell into this confusing situation.", "label": 0}
+{"snippet": "When one studies representations of (bosonic) Lie groups in physics, whether dealing with spacetime symmetries or gauge symmetries, it is often left implicit whether the representations are over real or complex vector spaces, without acknowledging of course that the representations of an algebra or group can be different over different base fields. A simple example is that the adjoint representation of the Lorentz group is irreducible as a representation over the reals, but reducible when take as a representation over complex vector spaces. When it comes to spinors, often people wish to treat components of spinors as Grassmann variables - this being the 'classical limit' of the fermion anti-commutation relations. My question is whether or not there has been a rigorous treatment of the representations of semi-simple (bosonic) Lie groups over Grassmann-valued vector spaces. EDIT: I suppose the direct analogy I anticipated isn't there. When we allow complex fields, we also allow complex changes of basis. This changes the reducibility of representations, because real Lie algebra elements now can have imaginary components even though the boost/rotation parameter remains real. For Grassmann numbers, it appears that we dont extend the reals as in the complex case, but supercede them. So we dont gain access to a new change of basis like before, where the algebra elements would have Grassmann-valued components while keeping the boost parameters real. Unless I am mistaken and people do work with spinors with \"real parts\" and \"Grassmann parts\".", "label": 0}
+{"snippet": "What's the term for a line of dialog that is repeated later in a different context? Christopher Nolan seems to be fond of these lines. In Batman Begins, Ra's first says: Always mind your surroundings And then in the climax Batman says You never learned to mind your surroundings. In The Dark Knight Rises, Bane first says: Then, you have my permission to die as he's breaking Batman, and later Batman claps back with Then, you have my permission to die. Same line, different contexts, often as witty comebacks. I've thought of a couple of possibilities I've heard of, none of which works quite well: Callbacks seem to be a reference to a previous gag, rather than an exact quote. Comebacks and clapbacks can be any kinds of clever retorts, not necessarily the use of your opponent's words against themselves", "label": 0}
+{"snippet": "The general bin-packing problem is NP complete. I have read several papers and other source but I am still not clear about whether a bin-packing problem with a fixed number of bins is NP-hard. Wikipedia says: \"Computationally, the problem is NP-hard, and the corresponding decision problem, deciding if items can fit into a specified number of bins, is NP-complete.\" and later: \"On the other hand, bin packing is solvable in pseudo-polynomial time for any fixed number of bins K, and solvable in polynomial time for any fixed bin capacity B.\" In another paper \"Bin packing with fixed number of bins revisited\" I have read that for a fixed number of if the sizes of the items are polynomially bounded integers, then the problem can be solved in time n^(O(k)). My specific problem is the following. I have a fixed number of bins m with fixed capacity. The items arrive online. I one case the set of items is known in the other case it is not. Given on what I have read I assume this problem is not NP hard as it could be solved by exhaustive search.", "label": 0}
+{"snippet": "I'm learning about functional programming, In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can. This allows programs to be written in a declarative and composable style, where small functions are combined in a modular manner. -Wiki And.. I started to wonder, how it would be if we tried to adopt this method as foundations to mathematics. Would it be meaningful to consider mathematics with functions being taken as the fundamental object rather than, say, that of the set or non function types? If it is, what would be the difference between the produced mathematics of that procedure, and that we have when we consider sets as the fundamental objects? What would be the advantages/ disadvantages to this approach?", "label": 0}
+{"snippet": "I am seeing many people claiming that cumulus clouds that sometimes form periodic wavy patterns (see images for \"altocumulus undulatus\" or \"Radiatus\" for instance) have no explanation aside from being chemtrails, and I'd like to be able to respond with a sound scientific explanation. I'd like to understand the phenomenon and my guess is that it's about the cloud blanket being forced by winds with the result of a periodic pattern appearing, much like sand waves form in shallow water at the beach. But is it really the case? Searching for a more detailed explanation I ran into Tollmien-Schlichting waves that are a path to turbulence, but I admit I did not understand much, so here is my question(s): What is the physics behind such cloud formations? And Given an estimate of the spatial period of these cloud waves and the cloud height, can one infer the windspeed at that height?", "label": 0}
+{"snippet": "If we are moving a block on a rough surface extremely slowly (quasi-statically) with the help of an external horizontal force, then is it the case that no heat will be produced, but the work done by friction force will still be equal to the work done by the external force for any given displacement? The reason this question comes to my mind is, in thermodynamics, if we say that a process is reversible when it is slow, then there should not be any heat production despite having frictional/viscous forces in the system when the process is slow. So, this implies that the existence of a reversible process rests on the idea that friction should not produce any heat. So, it is correct to assume that friction can do work without producing heat when the process is extremely slow? Because if in all the examples we see around, we see that work by friction is always accompanied by heat production. Kindly help.", "label": 0}
+{"snippet": "Suppose we have a system of electrons a very tightly confined space (like a tiny magnetic trap). Let's say we continually increase the degree of confinement such that the electrons are confined into a smaller and smaller space, to the point where the degeneracy pressure reaches a scale comparable to the masses of the other charged leptons. Does there come a point where it's favourable for an electron to \"decay\" into a heavier lepton due to degeneracy pressure (producing neutrinos and antineutrinos in the process)? My thought is that this process would be somewhat analogous to the formation of a neutron star (or hypothetical quark star). What would happen if we kept confining the particles into a smaller and smaller space to increase the potential further? Would even heavier particles be produced?", "label": 0}
+{"snippet": "Consider a simple experiment, such as boiling water in a pot in your kitchen, is it possible to estimate the time needed for the water to boil based on elementary properties of water ? In the physics and chemistry literatures we find many computational and theoretical works attempting to predict the boiling temperature of water, from elementary properties, such as the molecular bonding strength or angles. But what about the boiling time ? The basic parameters for the boiling time should the heating power, the heat conductivity of the pot, the heat capacity of water, and possibly other properties that characterize the transfer of energy from the environment to the water. My question is about the time needed from the moment where the water temperature is close to boiling point, to the moment where water has left its initial liquid state. It is mentioned in many lectures and textbooks that nucleation is a limiting step in the formation of a new phase, in particular for the boiling of water. But I was never able to find a critical comparison of such statements. So I would appreciate any references or indications. Which kind of computations do you expect to be necessary ? What kind of empirical parameters enter in the calculation ? Was this done in a reference?", "label": 0}
+{"snippet": "Suppose we place a current carrying loop of wire in a magnetic field. Of, course its easy to see that for a uniform field the wire will experience uniform force in all directions and so it'll get stretched out into the shape of a circle. But I wanted to ask if we could make any comments about the shape of the wire, in any random magnetic field without knowing the exact function describing the field. At places where the field is stronger, the wire will tend to get stretched out more so I suppose the local radius of curvature there would be less as compared to a point where the magnetic field strength is lower. But thats just a qualitative rough way of looking at things. Is there some exact way to find out the answer to this", "label": 0}
+{"snippet": "I just started reading about the conduction mechanism in polymer. From what i read, polarons are used as method of charge transportation in non-degenerate polymer. While for degenerate polymer, both charged soliton and polaron will do the job. As i go a bit deeper, polaron can be defined as: A polaron can be thought of as a bound state of a charged soliton and a neutral soliton of which the midgap energy states hybridize to form bonding and antibonding levels. A Quasiparticle that is created through the interaction of charged particles ( electron or holes ) with Phonon. If i understand it correctly, the definition of the polaron contradicts with its existance in non-degenerate polymer as non-degenerate polymer doesnt have soliton due to its topological reason. Also, as i am quite new to all these terms (polaron, bipolaron, soliton, charged soliton and phonon), i tend to get confuse and couldnt differentiate each of them precisely in layman terms as most of the literature are mostly explained in what could say too \"academic\" for a starter like me. Would someone be able to help me clear my confusion? Any help, advice and guidance are really appreciated. Thanks in advance", "label": 0}
+{"snippet": "Basically, as the title says. Maybe this is trivially true or false, but I have not enough intuitions about topological surfaces or aperiodic tilings. To make it a bit more precise - I mean the kind of aperiodic tilings such as Penrose tilings or the tiling generated by the recently found hat tile. By \"gluing\" the patch into a torus (or some other surface) I mean essentially just like you fold a net into some geometric shape by connecting edges. And the edges should be glued in such a way that all matching rules of the tiling are satisfied. If this is possible - would the resulting \"tiling of the surface\" also be aperiodic, or could it be made to be? Here I would consider \"aperiodic\" to mean that there are no non-trivial symmetries between any two tiles on the surface.", "label": 0}
+{"snippet": "I saw a question asking \"If the Moon was moved to the surface of the Earth, from how far away on the Earth's surface would it be visible?\". (The question says to ignore any other factors like gravity making it smash into the Earth's surface and effectively destroying both bodies). Basically, it's this, I think: We know AB, which is the radius of the Earth, and we know CD, which is the radius of the Moon. AC is the sum of these two. Even though it doesn't really look like it in my sketch, I think that the lines CD and AB are parallel, and that ABE and CDE are both right-angle triangles. We need to work out the angle at A, which we can use as a ratio of the circumference of the Earth (which obviously is another known quantity), to work out the distance around the circle to B. Are my assumptions correct? Is it possible, from those givens, to calculate the angle at A?", "label": 0}
+{"snippet": "EDIT: Completely rewritten because of the 'needs clarity' tag and some useful related questions appearing in the side-bar. I hope this is clear now This answer gives a long list of properties of particles whose value differs by a minus sign when comparing a particle to its antiparticle. We know that anti-particles exist, so apparently for every particle there is a particle where the value of all the properties in this list are 'flipped': i.e. the same magnitude but of opposite sign. My question is: given a particle, say an electron, does there exist a different particle where some of the properties in the list in the linked answer are flipped and some are not? If the answer is no, why is this not possible? If the answer is yes, what is an example of such a pair of particles?", "label": 0}
+{"snippet": "I am beginning to learn some very basic electronics. I was learning how and why lightbulbs light up. It turns out it happens because they have a very thin filament which makes the passage very narrow for electrons so they lose a lot of energy colliding with the molecules making up the filament instead of using it to drive the passage of the current. This causes three things. Voltage drop Decrease in intensity Transfer of the electrons' energy to the atoms making up the filament so they vibrate causing it to heat up, and the energy is also used to excite electrons to a higher energy level momentarily where they release the energy in the form of photons where the lower the wavelength, the brighter the light color and the greater the energy. So the filament also glows and lights up. I am interested in the latter and I have a couple of questions. Why don't the electrons remain in the higher energy levels? Why do they choose to release the energy as photons?", "label": 0}
+{"snippet": "I've been struggling with proposed answers to the twin paradox. I know that an object traveling at relativistic speed ages slower than a stationary object. This must be caused by some interaction with spacetime that leads to a slowing of time. But how does this work when we are looking at relative time dilation between two or more individuals. Imagine a huge crowd of relativistic rockets moving inertially and crossing each other in all directions at different velocities. How can one pilot claim to be younger than another, while the other is younger than a third who is younger than the first? Then it came to me that this all might just be the same as relativistic length contraction where it is only occurs while they are in motion, and all effects stop once they stop moving. Once they stop the only age effects are measured against an earth clock. We know that for kinetic length contraction, the man on the train station platform will see the relativistic train length contracted while the main on the train will see the train station platform length contracted. But the instant the train stops moving, all measurements return to normal. Is it the same with the twin paradox? That any age difference as seen by one pilot over another disappears once the motion stops? And the only real aging is when measured against an earth clock?", "label": 0}
+{"snippet": "Exactly what the title asks. \"Diode\" comes with it the ideas of depletion layers and forward/reverse biasing and electron-hole recombination, but SPAD physics doesn't seem to be dependent on any of that. You just put a giant electric field on, and as soon as a photon comes and promotes a charge to the conduction band, it gets so much energy that it can knock other electrons out of their atoms, creating the avalanche. In other words the fact that it's \"reverse-biased\" relative to the doping of the semiconductors seems irrelevant, as does the fact that the reverse-bias is above the breakdown voltage. Could I take a piece of undoped silicon and use it as a SPAD if I put a sufficiently large voltage on it? Or else why is it important that it's a diode?", "label": 0}
+{"snippet": "I have figures which I use in several places, some of them in dark context and some of them light (for example, a my obsidian vault is dark but a PDF of my thesis is light). As such, some of the figures are colored to work in a dark environment, and some in light. But sometimes I want to take a figure from a dark context and use it in a light context, or vice versa. So far I have created a copy of the figure for the light/dark mode by simply inverting the colors. I use color schemes in which this looks mostly fine. But manually inverting the colors and saving a copy is exhausting, and inefficient. I want to do this automatically, and possibly without saving a copy of the original figure. Is there a way to invert the colors of a figure while compiling the output of a latex document? Thanks a lot! Edit: I saw this question, but the answers were basically \"you can't\". Since the answers are unsatisfactory and the question is VERY old, I thought it would be best to open a new one. But if this is not the custom here, please let me know and I'll ask there instead.", "label": 0}
+{"snippet": "Noether's theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law. Energy, however, is not conserved in an expanding spacetime because there is no symmetry on the time axis. This enables dark energy to exist and is the reason that general relativity does not conserve energy (except in symmetric situations). My question is about how this translates to theories of quantum gravity that predict the existence of spacetime that becomes spatiotemporally isolated near the center of a black hole. Examples are white holes, fecund universes, and collapsing wormholes. I know that black holes conserve energy, at least for an outside observer. So can energy be created in a disconnected region of spacetime at the other side of a black hole center for certain theories of quantum gravity? Or does Noether's theorem prevent this? (Bing insists that the theorem applies here, but I don't trust the answer.)", "label": 0}
+{"snippet": "I was taught that there are four types of nouns: singular countable: journey, sheep, child plural countable: journeys, sheep, children singular uncountable: travel, water, fruit plural uncountable: groceries, customs, thanks Some words are only used with: countable nouns: one, two, three, many, number, few uncountable nouns: much, little, good/great deal, quantity, amount Am I right? What about the word 'cattle'? You can say neither 'three cattle' nor 'much cattle'. (According to Practical English Usage) What type of noun is it? If it is an uncountable noun why I can say 'many cattle' but not 'much cattle'? Isn't 'many' used only with countable nouns and 'much' only with uncountable nouns? Also, you might consider 'staff' or 'jeans'. You can say for example 'four staff' but not 'a staff'. (According to Practical English Usage)", "label": 0}
+{"snippet": "While trying to understand General Relativity, I'm struggeling with disentangling coordinates and curvature. The metric tensor contains information on both: coordinates as well as curvature. Curvature is a physical characteristic of spacetime, while the coordinates can be chosen completely arbitrary. Is there a method to disentagle coordinates and curvature? (Stephan Hawking must have had one as he managed to show that the singularity at the event horizon of a black hole is only a coordinate singularity, not a physical one...) I fistly thought that one could simply use cartesian coordinates - and then would be left with only the curvature (in this question: Determinant of metric tensor in Cartesian Coordinates constant in vacuum) However, I was taught there, that cartesian coordinates can only be used in flat spacetime. Now, I'm totally clueless again how to disentangle coordinates and curvature. I'm looking for a tensor/measure/metric/field, where only the physical curvature is in - and no coordinate curvature. Where the coordinates are flat like in a cartesian grid. Where the metric tensor is simply that of a flat spacetime in cartesian coordinates, if the spacetime is flat (Minkowski spacetime).", "label": 0}
+{"snippet": "We know that a complex manifold with a hermitian metric h is Kahler if and only if the corresponding Kahler form (which can be obtained from Hermitian metric) is closed.The complex manifold has an underlying real smooth manifold whose Riemannian metric can be found from the Hermitian metric of the corresponding complex manifold (Re(h)). We also know that a Riemanian manifold is Kahler if and only if there exists a smooth almost complex structure on it which is metric compatible and whose covariant derivative is zero. Now, the question is: if a complex manifold is Kahler then does this imply that the underlying real smooth Riemannian manifold will be also Kahler? I think that it should be Kahler as if the manifold is already Kahler in complex case so there should be no obstruction to the existence of compatible almost complex structure with vanishing covariant derivative.", "label": 0}
+{"snippet": "I have been using lists inside multicols for a \"condensed\" typesetting of lists of short items. However, I do not like what happens if a page break occurs inside, and I couldn't find a way to automatically force a page break before multicols if it cannot fit onto the current page. So I have been thinking about using some kind of a table environment to typeset a single-row table with lists in cells. However, I would like to make the lists in cells spread vertically so that their tops and bottoms be aligned (except when this wouldn't make sense), like columns in multicols. So far I do not see how to make a table whose height is determined by the maximal natural height of its cells, and where I could make the contents of any cell spread vertically to align top and bottom baselines. Is it possible? How? This might look like not a very natural thing to do, but I am used to the behaviour of lists in multicols, and I would like to avoid situations where, despite having the same number of items, the bottoms are not aligned because of accumulation of minor height differences.", "label": 0}
+{"snippet": "In quantum field theory (e.g. lattice QED), perturbation theory can \"break down\" when interactions become too strong. Can something like that happen in classical non-linear optics? Can there be any combination of material (absurdly non-linear) and light (attosecond pulses, petawatt lasers, etc.) which can (somehow) be described by classical electrodynamics but the usual \"expansion of polarization density inside the material in powers of electric field\" (maybe later adding magnetic field as well...) breaks down and doesn't work? I.e., where no finite expansion order gives a reasonable description? Alternatively, if the \"describable clasically\" assumption is weird in this context, is there a regime where some very strong coupling leads to the perturbative non-linear optics approach breaking down for a stable bulk material that can be produced on earth? I mostly care about \"shooting light at something and describing the light that comes out\". I've read claims about high harmonic generation (HHG) being such a phenomenon but it's not really clear to me how/why the perturbation theory (at any finite order!) does not apply. You can do it in bulk crystals but I guess the \"classical system\" restriction would not apply there, as it is usually described using some semi-classical models? For example, Wikipedia on \"nonlinear optics\" writes about some series \"not converging\" but it's not quite clear what is meant there. Some articles on HHG (e.g. this) use the phrase \"non-perturbative\" but what exactly do they mean by that?", "label": 0}
+{"snippet": "Plasma and fusion physics experts, help me with this one: Suppose we have a D-T plasma with net positive electrical charge inside a positively charged metal sphere. As the containment sphere's net positive charge increases, my ignorant intuition would expect the plasma to be compressed and its internal pressure to increase. Sputtering would likely occur as electrons from the plasma escape and are drawn towards the containment sphere, releasing atoms from the containment metal into the plasma and cooling it - but ignore that for a sec. Suppose we could both arbitrarily increase the temperature of the internal plasma and the charge of the containment sphere. Would this be a viable means for nuclear fusion containment? Help me shoot down this idea. What are some practical limitations that would prevent this from working? For starters, at arbitrarily high positive charge, the containment medium itself would disintegrate due to the electrostatic repulsion of atoms in the containment vessel, correct? Is there any existing means of calculating charge distribution in a plasma or solid at very high positive charge? Or is there a means of calculating the theoretical spatial gap between the plasma and containment vessel in such an arrangement?", "label": 0}
+{"snippet": "Consider a horizontal long rod that is undergoing free fall. Consider the torque about an axis through the rod (perpendicular to the rod and to the direction of gravitational force), that is a little to the left of the rod's centre of mass. Clearly, there is a net torque about this axis, but we know that the horizontal long rod will only translate downwards. I suspect it arises from somehow this reasoning being inapplicable for some cases of translating axes about which torque is taken, but in the case of a cylinder rolling down a rough inclined plane, the same paradox is not seen by taking torque about the axis passing through the centre of mass of the cylinder, even though this axis is translating downslope. What's going on?", "label": 0}
+{"snippet": "Is there a distinction that we make between what we call \"elements\" and what we call \"sets\" in Von Neumann type set theories? Two textbooks I have used for an introductory study of NBG both made distinctions between sets and proper classes (the prinipal primitive undefined notion being that of \"class\"). The distinction was ofcourse made to avoid various logical paradoxes, in particular, Russell's Paradox. However, what wasn't clearly stated in either textbook is whether the concepts of \"set\" and \"element\" are identical. Both did state that a \"class\" is considered an element if and only if it belongs to another class. Would it be safe for me to identify the notions of \"set\" and \"element\" completely interchangeably? I don't see an elementary distinction between the two. Then the only two distinctions we should make are of \"sets\" (elements) and of \"proper classes\" with the general notion of \"classes\" referring to either one of the two distinctions. Thank you in advance.", "label": 0}
+{"snippet": "When studying supersymmetric QFT's, it is very common to compute the moduli space of the theory by solving all F-term equation (derivatives of the superpotential). More precisely, one should also quotient by the complexified gauge group. Here are three fact that I believe to be true about moduli space and IR flow: Let us consider a supersymmetric QFT, dumbed theory A. Let us now take flow towards the IR and obtain an affective theory, called theory B. The moduli spaces of theory A and theory B are not necessarily the same. More generally, the moduli space of a theory changes with the flow. Now, on the contrary, a moduli space can be seen as the space of theories, i.e. the set of all possible vev's configurations for all the scalars. Choosing a point in the moduli space therefore introduces a scale, and implies that we are at a certain point in the flow of the theory. Certain regions of the moduli space can then correspond to strongly coupled or weakly coupled regimes. The moduli space of a theory, i.e. its space of vacua is the most low-energy thing you can do, no fields can be excited so they all take their minimum values, i.e. their moduli. So the moduli space could be seen as the bottom of the IR flow. Those three pictures are clearly in contradiction. What is the problem with this way of thinking ? I would be very interested by references about the link between RG flow, low energy-limits, and the moduli space.", "label": 0}
+{"snippet": "I had a guess from three years ago that I couldn't prove It is impossible to find a polyhedron whose perimeter (represented by the sum of the lengths of its edges) is equal to its area (represented by the sum of the areas of its faces) and numerically equal to its volume It is easy to find a similar shape with any shape such that two of these are equal to each other, but the question is whether all three are equal to each other. All I have been able to prove is that this shape cannot be a Rectangular cuboid, I also proved that it is impossible for it to be a Platonic solid but I do not know if this would hold in the general case. Here is a proof of the condition of the Rectangular cuboid by arabic language", "label": 0}
+{"snippet": "The infinite square well (and variations) are some of the best-studied systems in quantum mechanics and are often used as the starting point for any quantum mechanical education, as the Schrodinger equation is easy to solve for such a system. I'm looking for specific research papers that describe experimental results that affirm the particle-in-a-box theory because, while the theory is beautiful, it is nearly always presented to students without any discussion of experimental confirmations. Obviously, any real system is going to be more like the non-infinite square well. I'm well acquainted with the other experimental results that affirm other introductory aspects of quantum mechanics, such as the double-slit for affirming particle-wave duality, the stern-gerlach experiment for spin, and various interferometers for superposition, but have yet to come across any for particle-in-a-box theory. The best that I am aware of is Bose-Einstein condensate experiments, but those are typically focused on affirming that bosons can indeed occupy the same state and are not so much what I am looking for. The simplest practical system that comes to mind to demonstrate what I'm looking for would be something along the lines of a Jaynes-Cummings model single-atom cavity experiment where the atom is repeatedly found in the most likely predicted locations. Is this question misguided? Are there actually no such experiments and we only know the theory to be true because more sophisticated developments of the theory align with experiments and extrapolate that the basics of the theory must therefore also be true?", "label": 0}
+{"snippet": "I am aware that this series is incomplete, but it has a large body of existing content, and I am also aware that it is written to be \"accessible to non-specialists\", but that is obviously quite vague. All that really tells me is that I don't have to be a CFSG scholar, and on the other end that I can assume it's probably not, yknow, an undergraduate text. But what is the actual background needed to follow it? Group theory is a pretty vast field, and it is unclear to me whether GLS is written for people on the level of \"grad students who took abstract algebra courses\", \"PhD candidates in group theory\", or what. Specifically the kind of answer I want is describing what the curriculum might look like for a hypothetical course whose purpose is GLS reading prep.", "label": 0}
+{"snippet": "When a tiny spherical charged particle (having a conductive surface) moves at a relativistic speed, the Lorentz transformation for EM-fields predicts that its electric field increases at the top and bottom of the charge whether or not it has been made of something conductive, whereas the field decreases at the left- and right-hand sides along the motion direction. On the other hand, we know that as the tiny spherical charge moves at a considerable portion of the speed of light, its geometrical shape shifts to a spheroid. Taking account of the fact that the charge density is no longer uniform and it increases at the top and bottom of the spheroid, I want to know whether it is the new arrangement of the charged particles that implies the electric field to be like that shown in the figure for the relativistically moving charge, or the Lorentz transformation predicts the EM-field independent of the charge distribution. Remember that the electric field of a charged conductive spheroid is very similar to that predicted by the Lorentz transformation, however, I do not know how far they match.", "label": 0}
+{"snippet": "My only familiarity with topology is the basic theory of mereotopology, so apologies is this sounds strange. An open region is a region without a definite boundary--that is, there is no way to draw a boundary including only points in the region such that every point in the region is inside that boundary. I think of it as the interior of, for example, a polygon without the edges that define the polygon. A closed region includes a definite boundary. The complement of a region is all of the points that are not in the region, so in a normal topological space the complement of a closed region is an open region and vice versa. This strikes me as related to continuity in the real numbers. If you imagine the real number line as a topological space where a range of numbers is viewed as a region, then an open range is an open region and a closed range is a closed region. In this case, the statement that the complement of an open region is a closed region seems equivalent to the statement that every range has a least upper bound and a greatest lower bound--which is equivalent to continuity of the real numbers. Does this make sense, and am I right about it?", "label": 0}
+{"snippet": "I have combed through various sources on the internet and I don't have a definitive answer for the above question: The best that I can come think is the following: Because when I remove synthetic clothes, the body gets charged one way, the clothes the other way. Then as I continue the process of removing the piece of clothing off my body, the charge build up is significant, owing to which the potential difference between the cloth and my body is greater than the breakdown potential of the air. Thus, electrons flow between my body and the piece of clothing I am removing. The air heats up, gets ionized, energy is dissipated in the form of heat, light and sound; in other words, as sparks. Also one more follow up question: Do the sparks flow \"inwards\" between my body and the piece of clothing? Or just dissipate \"outwards\" into the air, towards nothing in particular? Is the above reasoning sound? Also, does the same reason hold when I comb my hair? However, if this were true, why do I NOT SEE any sparks when I comb my hair but only hear a crackling sound?", "label": 0}
+{"snippet": "Consider two free-falling observers in the Earth's gravitational field, A and B, who meet at point C, where A orbits the Earth at a constant radius from the Earth's center, and B falls towards the Earth's center along a constant radial line: Can either detect the other accelerating locally at C? As an attempt to answer this myself: it's worth noting that I can detect the acceleration of an object dropped onto the surface of the Earth where I am, and that the Earth is free falling along a geodesic within the solar system. However, I don't think the Earth's surface is a geodesic because I can drill a small hole from the surface towards the Earth's center so that a small mass will accelerate towards the center where, at the center, it will experience a zero acceleration. Hence an observer at the Earth's center can't measure the acceleration of another moving mass there, and on another geodesic. So I'm inclined to believe that neither A and B can detect one another accelerating at C locally when they meet, and that more generally: observers on different geodesics can't detect one another accelerating wrt one another locally when they meet.", "label": 0}
+{"snippet": "I am using the word 'avatar' in my work in the sense that an avatar is the physical representation of some higher entity. We could say that a particular person, animal or object is the avatar of a deity, or that a symbol or picture is the avatar of a person, or that a player-character in a computer game is the avatar of the player. For example, my Stack Exchange avatar is a red 'W' on a blue and green field. I am looking for a single word, or failing that, a short descriptor that is a generic term for the person or entity that has one or more avatars. To use an example from mythology with the correct semantic context for my question, we have the sentence: Rama says, 'I am an avatar of Vishnu'. I'm looking for a word (or short phrase) to fit in the paraphrased sentence from the example above: Rama says 'Vishnu is my _____'. Where _____ is the relational antonym of avatar. Edit: 'opposite' changed to 'relational antonym'.", "label": 0}
+{"snippet": "Nondeterministic refers to a system or process that does not have a single predictable outcome. In other words, when a system is nondeterministic, it means that multiple outcomes are possible for a given set of inputs or conditions. Given that it can be associated with randomness. For physics nondeterministic is the lack of predictability (am I right?). The unpredictability in classical regime (say the motion of classical atoms in a box) is given because of existence of many variables that is hard to keep track of and also the ignorance of the human with regard to the system. The quantum mechanics has nondeterministic behavior only in the measurement process. My question is that other than the measurement which is nondeterministic (in the sense that the outcome would be randomly distributed over a probability distribution), is there any other process that has such property (in any other regimes such as relativistic)? If yes what and if no, why quantum measurement seems to be special in this case?", "label": 0}
+{"snippet": "I've seen the notion of the models in the title a lot in the context of automorphic forms and representations, but I wonder if there's any nice reference for the definition of them for general reductive groups, with some motivations for their namings. I'm pretty sure that the name Whittaker model comes from the Whittaker functions that give Fourier-like expansion of Maass wave forms, and somehow generalize the notion of Fourier coefficients for the general automorphic forms. But I have no idea with the rest of them, although I've seen the definition of them for some classical groups in many papers, especially related to Gan-Gross-Prasad conjectures. My naive guess is that Bessel model should be motivated from the classical Bessel functions but don't know how. Also the name Jacobi in Fourier-Jacobi may come from theta functions, since all the Fourier-Jacobin periods I've seen are defined in terms of Weil representations and theta functions.", "label": 0}
+{"snippet": "I want a term for someone who generally doesn't care about their individual popularity or how other's view them and as such is willing to break social expectations about behaviors and do their own thing, even hen doing so may affect how other's view them. So something close to the phrase \"Marches to their own drum\", but I'd prefer something more concise and possible less colloquial. I don't want a term that implies one is incapable of understanding societal expectations, I prefer the implication be a choice or lack of desire to try to fit expectations rather then an inability to do so. I also do not want to imply a willingness to harm other's as a result of ignoring social expectations, via causing someone embarrassment, hurting feelings, or general rudeness for example. The term should focus on situations where ignoring of expectations would mostly only affect the person ignoring them, not when doing so is likely to harm others. I'm okay with, and may even prefer, if the term comes with a implication that the person is less popular, less understood, or even mildly ostracized as a result of their ignoring social expectations.", "label": 0}
+{"snippet": "I have some idea of what the main concepts of calculus are about but I have never actually taken a calculus class or studied myself. My general understanding is that before the concept of limits were formally defined by later mathematicians, the first people that actually invented calculus explained the idea of derivatives and integrals using the hyperreal numbers, something for which they were actually criticised by some for the concept being more intuitive rather than mathematically provable/valid. I also believe that modern, standard calculus does not deal with hyperreals at all but rely solely on real numbers in explaining all of its concepts. So I was thinking whether it would be a good idea to get the gist of what hyperreals are and how they relate to limits as a foundation before actually taking on calculus, or would it be not worth it. I'd appreciate any comment/suggestion you guys would make.", "label": 0}
+{"snippet": "Could you simulate a Turing machine by a sequence of Turing machines each with strictly fewer states than the simulated machine? By a sequence of Turing machines I mean this: the first machine is given the input tape, then executes until it accepts, then the contents of the tape are given to the next machine in the sequence as input, and so on until the final machine accepts. If any machine in the sequence rejects, the simulated machine would reject, and if any in the sequence would fail to halt then the simulated machine would fail to halt. If this is possible, the more interesting question would be whether there is a bound on the number of machines needed to simulate a machine with more states. The motivation behind this question is that Busy beaver numbers are known for very small machines, so I was curious about whether machines with many states could be (reasonably) reduced to machines with fewer states. It seems to me that there must be some error in reasoning or understanding if the number of machines needed to simulate another could be bounded, because that would imply any machine could have a bound on steps needed before halting, but I am unsure where that disconnect is.", "label": 0}
+{"snippet": "I recently came across some discussion on the fact that \"no bueno\" is not gramatically correct Spanish, and generally not a phrase Spanish-speakers use, unless they find it funny. Of course, \"no bueno\" is just a literal translation of the common English phrase \"no good\". Sometimes, the phrase appears with the implied subject/verb attached: \"it is no good\" or \"this is no good\" (accompanied by a sad shake of the head, or a downcast expression). One can of course say \"It/This is not good\" or for short \"not good\", which is unimpeachably fine grammar, but I'm not so sure on the \"official grammatical status\" of just \"no good\". Note: there is the hyphenation \"no-good\", which can be used as an adjective, but that is not the usage I'm talking about in this post.", "label": 0}
+{"snippet": "sorry if the title seems vague. English is not my first language and I dont know what to search to find the answer to my problem. I will preface this by explaining the purpose of this question. I have a robot that I know the position of (x,y) through odomotery. and I also have an IMU that returns the robot's yaw angle with respect to the positive x axis of the map. In this map are objects, that I need to rotate the robot to face them. I will attach an image of how It would look like. Some sample cases My problem is I cannot find a generalized way to cover all cases of robot's position and yaw with respect to the object and map. If someone can point me in the right direction or tell me how I could solve this I would be very thankful", "label": 0}
+{"snippet": "I have a data set of values each with a different associated error. If I take the mean, I can use standard error propagation to calculate a much smaller error. This will therefore incorporate the individual uncertainties of each data point. However, is there a method to propagate the individual uncertainties when taking the median? If I take the standard deviation this only provides a measure of the data spread and not the individual instrumental errors. I have tried adding the standard deviation and the uncertainty on the actual median value in quadrature. However, as this only takes in to account one data points' uncertainty this is high and so my total error does not get reduced. Is there a way to propagate these errors when taking the median?", "label": 0}
+{"snippet": "What would happen to metals or ceramics (non-porous) when subjected to extremely high pressures (dozens of GPa) ? I feel like the sample will deform elastically only. So a ceramic object (think carbides) wouldn't crack. Typically, we assign a maximal compressive strength to metals and ceramics. After which, they undergo plastic deformation or fracture but these compressive strength values derive from experiments involving the pressing of a sample with an hydraulic press. So in these experiments, there is \"space\" without stress on the sides where the material could expand. But that isn't the case in an hydrostatic context where stress/pressure is applied evenly on all surfaces. Also, in the case of ceramics, I feel like fracturing would create more volume which seems contradictory to me as the sample is being compressed.(in the sense that work should be done against the pressure if the sample gets more voluminous and that wouldn't minimise the energy) If I am correct, you could have solid matter even at gigantic pressures. Any idea?", "label": 0}
+{"snippet": "I'm interested in writing a document following not only the Chicago Manual of Style in principle but also very literally the style used by the University of Chicago Press in their publishing. In other words, I'm not just trying to follow the style guidelines outlined in the manual, but also directly emulating the full style used in their publications. Here is a sample page: Obviously their style has a large number of rules (many more than used on that particular page) and I may not need to use all of them, but even a small subset would be painful to implement manually. So what I'm wondering is, is there an existing (la)tex template that has already implemented most or all of their style? When I search, I only find results for templates for their bibliography style, and that's more about following their guidelines rather than directly reproducing their formatting.", "label": 0}
+{"snippet": "Suppose we have an arbitrarily well-isolated empty region which we initialize with a cold, diffuse, homogenous photon gas, such that the only energy density gradients are random thermodynamic fluctuations and the only massive particles are those that are created after initialization. Thor pokes a tiny hole in the arbitrarily isolating boundary, puts his magic omni-detector on the hole, and measures an interaction event every time a particle - typically a photon, but sometimes perhaps a massive particle or antiparticle - reaches the omni-detector. Magic omni-detectors always interact with every kind of particle. However, Loki has secretly tampered with Thor's omni-detector so that it records everything as if time was proceeding many times faster - not just the time stamp on each measurement, but also the values measured, as if the SI Second had been re-defined to be some multiple of its current value with all the downstream consequences on other units and constants. Is there any way Thor can tell, by looking at a subset of his data (i.e. not just comparing the total run time of his experiment to a clock that hasn't been tampered with), that he was looking at a large, diffuse, cold region, and not a small, dense, hot region?", "label": 0}
+{"snippet": "I have been revising some maths and in particular I have been focusing on vector calculus. Today I have just finished looking at surface integrals. I do understand how we parametrize a surface integral starting from a region R, but I am having troubles actually understanding how these integrals are put in context when having a scalar function or a vector function. For instance, a popular example is that you have a surface (for instance a metal sheet) and then you have a function which gives the density of each point of this metal sheet (if I were to plot this function, would it have the same shape of the surface?) Further, I dont understand why calculating the surface integral of the density function gives me the mass (isn't the definition of density mass/volume and hence I would need some kind of volume?) Thank you for whoever can explain this in simple terms", "label": 0}
+{"snippet": "Something got messed up in my lyx settings and now the editor window previews the text in a very ugly and informal looking font. The pdf output is still the regular latex font. How can I reset the editor window font? This would probably be fixed by a complete uninstall and reinstall of lyx, but I can't figure out how to do that either. Here are some screenshots of what the editor window and pdf output look like For context, this happened after I tried to add a lyx -> markdown converter (https://wiki.lyx.org/Tips/ConvertMarkdown). I couldn't get it to work, and quickly gave up. But not my lyx font is hideous! Things I've tried: Uninstalling and reinstalling, but all my previous settings are maintained, including this font issue. I tried looking for any saved files in the indicated directory here, but don't see any files. How can I completely uninstall lyx? Tweaking the screen fonts options, but not exhaustively Running \"tools/reconfigure\", which produces an error", "label": 0}
+{"snippet": "My question is both naive and subtle. Naive because I don't know much more than the layman about physics and in particular quantum physics. Subtle because physics is an attempt to model the world, and as a computer scientist, with a strong interest in machine learning but also formal logic and models, a model is just that, a model. Not necessarily reality. It is not because a model fits reality that the model is the truth about reality. From my understanding, we know that: the quantum physics model has not been contradicted on the notion of superposition that it introduces there are experiments that can be explained using the quantum model where the classical model fails Am I correct to say that this only proves that the classical model, is just that, a model, and therefore incomplete? And that for those cases quantum mechanics has a better predictability power. Now the question: Has it been somehow proven that a physical entity can a some point in time and space have a dual state (independently of the model)? Or is it only that quantum mechanics is the only known model that allows us to explain things we otherwise couldn't? I would like to know if objects of our world can be in two states at the same time or that it is just more practical for predictability purposes to model things this way.", "label": 0}
+{"snippet": "I live in an arabic speaking country, and while I was sitting in a food court today, I noticed that the sound of the crowd was the same as the one I see in the stereotypical sound of the crowd. I have seen many threads discussing this on different forms, eg: Quora , reddit, Metafilter, and on this site, there is this tangentially related question. The problem with all of these is that, none of them is concrete, in sense of not having any calculative evidence. Going down the reddit rabbithole and reading the metafilter thread gives me some idea on how a calculation should look like, but I don't feel so confident in my abilities to do it, could someone provide a fermi type calculation of this? Else, link to a source which does?", "label": 0}
+{"snippet": "Recently I was on an airplane on a sunny day. The sun was shining on the other side of the plane and noticed a bright patch on the ground following beside us. Eventually I noticed a dark centre to this bright patch, the plane's shadow, which became more distant as the plane descended. When the plane flew over a city road signs in this bright patch lit up brightly because of their retro-reflective paint. My question is, what was acting as a retro-reflector to produce this bright patch when it wasn't passing over a road sign? When flying over water the bright patch disappeared, or was very faint. I could see it over forests, more clearly over cut grain fields and, at least faintly over a wide range of terrain.", "label": 0}
+{"snippet": "For a general linear map, there are infinitely many matrix representations. You choose a basis of the vector space, and this gives you a certain matrix for the linear map. You choose a different basis, and this gives you another matrix different from the first. For a linear map that does nothing however, we only get the identity matrix no matter what basis we choose. It isn't hard to see that the identity matrix will always do what we want from this linear map mechanically. But I feel there is some deeper intuition for why the matrix for this linear map shouldn't change with the basis, without thinking mechanically about the matrix. On a side note, is there any other linear map where the choice of basis doesn't change the matrix representation or is this the only one?", "label": 0}
+{"snippet": "In quantum mechanics, unbound states will tend to spread out in space over time according to the Shrodinger equation. So it seems to me there is a degree of freedom for \"wild\" particles (i.e. those have not been prepared in the lab) as to how much they are spread in space and momentum. So my question is: do we have any knowledge of how disperse \"wild\" particles (i.e. those which have travelled a long way such as photons from the Sun or cosmic rays) are? Is there any way to tell, or are we completely unable to extract this knowledge? Fundamentally we can't for an individual particle, but I mean statistically. I know that the spread must satisfy the Heisenberg uncertainty---my question is what do we know beyond that?", "label": 0}
+{"snippet": "Why can't we see light from beyond the observable universe? I've done a lot of research on this and all I've found is unsatisfactory answers and straight up nonsense. Some claim that the universe \"expands faster than the speed of light\" beyond the observable universe. Such a claim doesn't even make sense because the units of speed are m/s and for expansion are Hz. That's like saying \"the area of this square is larger than the volume of this cube\". All that the expansion can do to light (as far as I know) is redshift it. And light doesn't have a minimum possible frequency or energy value. So even if the expansion of the universe is very rapid, why does the light of distant objects \"never reach us\". Surely it still would, just extremely redshifted. In this case it does still reach us, and yet the claim is that it cannot. We often detect redshifted light, and that light has not been slowed down. When we detect it, it still goes at c, even though (in fact a better word than \"even though\" here is \"because\") it is redshifted. Light is always propagating at c no matter the reference frame. More precisely: does the light really never reach us, or can we just not detect it? If it never reaches us - why? If we cannot detect it although it does reach us - why?", "label": 0}
+{"snippet": "Let's suppose the earth is perfect sphere and let's ignore its rotation and movement. What would happen if i would be in the center of the earth? Would the gravity be zero in any direction so i wouldn't feel any gravity force? Or would there be 'pulling' forces (of half of the gravity force on the surface) that would attract me in every direction. Or in other words - If i would be in the center of the sun, would i be in a weightlessness state or would i be torn to a pieces (except of having a serios sunburn of course)? I know there are similar questions here: Effect of gravity at center of Earth Would you be weightless at the center of the Earth? but they are ot answering whether there would be no force or there would be forces to all direction. Some answers implies that the forces would be the same but in every direction so they would 'cancel' each other. But i'm not sure what does it mean. If I'm dragging a paper to different directions the forces are not zeroed, the paper is torn apart.", "label": 0}
+{"snippet": "If I'm trying to advertise that you can scroll through this webpage to find additions that go in/on your home, would it be... \"Find new additions for your home.\" \"Find new additions to your home.\" Does \"find for your home\" technically mean that your home itself is literally looking for new additions and you're looking on its behalf? And therefore \"to\" is correct? The problem is, what if it were something like advertising gift-giving, and said... \"Find shoes for your friend.\" In that case, it could be read as finding shoes on behalf of your friend, but also finding shoes that suit your friend. Certainly, \"find shoes to your friend\" is absurd. So, why does it work in the home example (assuming \"to\" is correct in the home one)? Thank you :)", "label": 0}
+{"snippet": "I was once asked the question: What French word is commonly used in English for which an English word is commonly used in French? The answer was respectively rendezvous and date, which I found very unsatisfying. So, does such a situation exist, in which a French loanword is used in English to mean something for which an English loanword is used in French? Criteria: Both loanwords should be fairly common in the language that borrow them. By that, I mean that it is expected of the general population to know this word. A more precise definition of this criterion would be the absence of the \"specialised\" tag in the Cambridge dictionary. Both words should ideally be actual loanwords, meaning that their spelling hasn't changed, except for any punctuation. (\"Gastronomy\" or \"beef\" wouldn't count.) Research done: I've looked at various lists of French words used in English and did not find a match, as well as this related question. ChatGPT was no help.", "label": 0}
+{"snippet": "I am working with optically active nanomaterials (quantum dots, perovskites), that have pretty large exciton binding energies and can form multiexcitonic complexes, e.g. biexcitons, relatively easily. It has been well established that they also exhibit biexcitonic lasing/ASE under above threshold excitation, so here I have a question. To have lasing behavior/ASE, stimulated emission process should occur which requires population inversion between upper (biexciton) and lower (exciton) states. However, in the current literature when this effect is reported for any new material, population inversion requirement is barely ever mentioned and I wonder why. Is it for some reason biexcitonic recombination is a \"special\" transition, and therefore this requirement is lifted, or population inversion indeed takes place? If any of these options is correct, could you, please, elaborate why that happens? What is the mechanism lasing or inversion build-up? Thank you!", "label": 0}
+{"snippet": "Massive compact halo objects (\"MACHOs\") include a wide variety of hardly detectable bodies such as brown / white / black dwarfs and black holes, to name a few. If we take into account the inevitable end of all stars into either a white dwarf, a neutron star or a black hole and we compare the average lifespan of a star with the time star formation has been active since the Universe started, then we can tell galaxies already contain many dead stars which still have mass and can therefore interact gravitationally with the rest of the bodies in said galaxy. Furthermore, stars tend to accumulate in the galaxy's bulk (primarily) and in the galactic disc as well, so if dark matter happened to be MACHOs, which are distributed in said proportions, then this would account for the fact that models such as the dark matter halo need to have a density such that it decreases the further away we get from the centre of the galaxy. Finally, MACHOs are bodies we know to exist for a fact, whilst particle dark matter (e.g. WIMPs) has not been found. Is there a reason for which MACHOs are not the most likely candidate for dark matter?", "label": 0}
+{"snippet": "I have recently watched a couple of lectures in order to revise some of the notions that I will have to tackle in the coming months, and as I did so I have stumbled over something which baffled me a tad. Now, within these lectures the lecturer described a relation as being a function solely if it maps one element from the domain to one sole, unique element from the codomain (or range assuming it is a surjective function we are dealing with); I found this a tad confusing since, ever since I can remember we considered functions to map a value from the domain to one sole value from the codomain/range, and if no value from the domain is mapped multiple times to the same value within the codomain/range then it is injective, hence abiding to the lecture's definition of a function. Have I been missing something, do people automatically discard non-bijective, or at least non-injective functions for whatever reason?", "label": 0}
+{"snippet": "According to Archimedes' principle, the buoyancy force on a submerged object is given by the product of the mass of the displace fluid and the gravitational acceleration. Effectively, it is determined by the net pressure difference of the fluid between the bottom and the top of the object, or in other words the weight difference of the corresponding columns of fluid. However, if we have a weight placed on a scale for instance, this weight will change if we accelerate the scale upwards or downwards. As scale in freefall for instance will register zero weight. Now as the buoyancy force will accelerate an object initially at rest, should it not be reduced as a result of this (the buoyant object can be considered the scale here and the fluid column the weight being measured)?", "label": 0}
+{"snippet": "I want to start learning some optimization theory (mainly to get into ML in the future but I'm also just very interested in mathematics that intersects heavily with engineering) and I would like to get some recommendations to start tackling the subject. I found two books: Bierlaire's Optimization book and Convex Optimization by Boyd and Vandenberghe but the former seems to lack convex optimization which I've heard is quite foundational and the latter seems to target more practitioners of optimization algorithm where I want to get into theory to understand exactly why the algorithms work and both mention that they target engineers in their preface and I'm not sure if that's a good or a bad thing. So are there any other introductory references to the subject that target mathematicians which I'm missing?", "label": 0}
+{"snippet": "Very roughly, dark energy tends to cause space to expand and mass tends to cause space to contract. If nothing gets in the way, the math on that contraction breaks down when it forms a black hole singularity. So the question is, can enough energy halt the contraction before it forms a singularity, but after it forms a black hole (i.e. an event horizon)? Are there any theories that have tried to use this to avoid the the math breaking down? Edit: after some digging, I have found that the Penrose-Hawking singularity theorems gives conditions where a singularity must form, but I've yet to find a description of what happens (or could happen) if those conditions are not met. Namely, it seems like \"interesting\" thing might happen if negative energy became part of the conditions inside a black hole.", "label": 0}
+{"snippet": "For each segment of a piecewise Lyapunov function that exhibits asymptotic stability, we can utilize the LaSalle-Yoshizawa theorem and solve it using a differential inclusion. This allows us to merge all the piecewise Lyapunov functions and demonstrate that the entire system is asymptotically stable. Now, if each segment of my piecewise Lyapunov function achieves finite-time convergence, specifically in the form of square root, how can I utilize the differential inclusion? Can you explain whether the overall system is finite-time stable? Upon searching through some resources, I found that these studies generally assume each segment to be asymptotically stable and then prove that when the function obtained through the differential inclusion exhibits square root convergence, the overall system is finite-time stable. However, if my current equations do not exhibit asymptotic stability for each segment but instead demonstrate finite-time stability, how can I prove it?", "label": 0}
+{"snippet": "I'm not a physicist in any way, but I'm curious enough to watch and attend some pop-science lectures. Let's imagine the following situation - there is a free-standing unbound electron. It has its wave-function describes probabilities to find it in particular position. Also there is incoming photon with a proper wave-length to be absorbed. How the electron \"decides\" to absorb it, from what distance? If it's probabilistic too then electrons can absorb photons from centimeters away? And we shoud be able to verify it statistically by observations of many photons and electrons. Since the photons are stretched out by cosmological expansion, then I assume that they have the length in physical space. Is the absorption instant or does it take time to absorb the \"whole\" photon? If the absorption is not instant then it's possible to make a trick: make the electron annihilate with positron - after it started to absorb photon, but right before it finished. What will happen to \"unabsorbed part\" of photon? What is a correct theoretical answer to my questions?", "label": 0}
+{"snippet": "Was all the energy that is the universe today, present at that femtosecond theory has pushed back to or was there an influx of energy for a period of time? My question was: is the big bang like a pin prick in an infinite balloon of water? Initially, you have very high pressure, then as the hole expands the pressure drops but the flow doesn't stop. In the case of the universe is the big bang still pouring gluons and muons in everywhere at about the same rate as it always has, it's just that over this much larger volume it is less dramatic than the first few centuries. Does our universe create a back pressure at its various stages that would explain the changes in rate of expansion over time? It is equally likely I am fundamentally misunderstanding what it means to be in an expanding universe. I suspect it's fairly obvious to those that might answer that I've watched more science documentaries than is healthy but fail to comprehend most of the wikipedia pages describing the physics and maths that support them. I expect you see lots of these stupid questions and I suspect this has been asked before, but I couldn't find it.", "label": 0}
+{"snippet": "I was interested in electromagnetic induction in loops, since ground loops and such tend to be a problem in electronic system engineering. To me, it seems like induction in loops may tend to cancel out. For example, if the plane of a simple wire loop (that is just a ring of wire and nothing else) is perpendicular to an electromagnetic wave, using the normal rules for induction in wires, the E-field of the electromagnetic wave would be parallel to the top and bottom of the loop, and induce a current in the same direction in both the top and bottom. The sides, would be perpendicular to the E-field, and have no electromotive force on them. I asked about this on Quora, and was told that a \"counterclockwise circulation\" would be induced per Lenz's law. I know inserting a north pole into a wire loop does that, but, that was not what I asked. I found this question here on Physics Stack Exchange, EM waves from AC current in a loop?, and it seems to suggest cancellation of forces for a radiating wire loop. A receiving wire loop seems like it might have similar behaviour. So my question is, what current is induced in a wire loop whose plane is perpendicular to an electromagnetic wave, when the electromagnetic wave passes over it.", "label": 0}
+{"snippet": "We, as humans, given our height and size, view the world from the same general perspective. An ant, on the other hand, will understand the same world in a completely different way, given how limited their knowledge and experiences can be. When we spend a couple seconds taking a step out onto our front yard, it might have taken a microbe years to travel that same distance (assuming it can survive and all that). To the ants living in your front yard, your back yard might just be the \"edge of the Universe\" for them, let alone the other side of the city or continent. For an organism smaller than even Planck's length, assuming such thing exists, then Planck's length might just be the limit of their world, and who knows what's going on down there. Let's reverse that thinking and apply it to something that's bigger than us. Now, we are playing as the \"ants\" or the \"organisms smaller than Planck's length\". A bear, for example, can travel farther than a human given the same amount of time, and what we view as \"further apart\" might seem \"closer\" to the bear. To something as big as a planet, the Earth might be its \"front yard\" and the moon its \"back yard\". For something much much bigger, the size of a galaxy, lets say, what would be its \"other side of the city\"? By \"taking a step\", that thing would travel a distance worth of many light years in just a few seconds, right?", "label": 0}
+{"snippet": "I am very poor at English, so I used ChatGPT to translate my question. My question is here (Is my idea right?): Is it possible to conceive concepts like a coordinate system in a completely empty space? I believe that without some reference, even establishing an origin becomes impossible. In a space where there is just one object (please consider the object is very small), it is possible to consider an origin. You can regard the location of that object as the origin. However, I think it's not possible to conceive axes in this context. In a space with exactly two objects (please consider the objects are very small), it is possible to establish an origin and one axis. You can choose a location of one object as the origin and define an axis with a positive direction towards the other object's location. Nevertheless, I believe it's not possible to conceive the other two axes. It is only when there are three objects (please consider the objects are very small) in a space that one can begin to consider a coordinate system.", "label": 0}
+{"snippet": "I have been looking up at available database that had dielectric constants for metals since I need them for my research and wanted to get an idea of what the values were before I focus on actually calculating them numerically if ever it is needed for my research. Thankfully I was able to find this website https://refractiveindex.info/?shelf=main&book=Ti&page=Johnson However I noticed that there are two values for the relative permittivity when it came to metals and I was wondering why this is the case. From what I know so far, metals should have a negative permittivity, so I was confused as to why it shows that Titanium also has a positive permittivity. Can someone enlighten me as to why this is the case for the permittivities that I found on the website. Apologies as well for the question since I dont know a lot yet about the properties of materials when it comes to permittivity and permeability.", "label": 0}
+{"snippet": "If a quantum particle is described by a certain wave function and we express it as superposition of for example its possibles energy states, after we measure it the wave function collapses and we observe the quantum particle as having a certain energy. I have a couple questions. No matter what happens to that particle or what I do with it everytime that I observe it again it's going to be in that same energy state? If after measuring energy I now try to measure something else like position could the energy state change when I measure it again? In general I'm trying to understand what it means that the wave function collapses because by what I've studied it sounds like it's undoable but that doesn't make much sense to me. So far I thought that when we observe a particle's energy for example we measure a certain energy but then if we measure it again right after we could measure any of the other possible energy states but I'm told this is wrong. How does it actually work then?", "label": 0}
+{"snippet": "Reading Harris' Modern Physics, specifically the classic example of Anna holding two lightbulbs on a moving train. I find myself confused about this passage: Before moving on, we emphasize a vital point: The preceding arguments had nothing at all to do with Bob's specific location in his frame or the time it takes light to reach his eyes. The issue here is not which beam reaches Bob first, which does depend on where he stands, but rather which begins first, which has nothing to do with where he stands. Attempting to blame the effect on optical illusions is the comfortable yet incorrect way out of accepting a counterintuitive notion. The truth is more challenging. Bob could be standing right next to one flashbulb when it flashes and have an assistant, Bob Jr., standing next to the other flashbulb when it flashes. Each records the time of his flash and neither has to wait for the light to reach his eyes. They record different times. Anna, in her frame, causes the bulbs to flash simultaneously, but Bob and Bob Jr., from their frame, determine that she causes the bulbs to flash at different times. I guess my understanding of the relativity of simultaneity was dependent on thinking about the path that light took to travel to Bob. If Bob/Bob Jr can be right next to the lightbulb, I am failing to see how that's any different then them being on the train with Anna.", "label": 0}
+{"snippet": "Context: I would like to talk about how a book questions the reader's traditional, conservative values about family structures. I want to say we are introduced to a shared household wherein there isn't a typical nuclear family structure, the children are not trained in table manners and everything is loud, lively and disorganised. This contrasts the presumed reader (at the time)'s traditional beliefs that a house should have a nuclear family, children should be taught table manners, etc. The sentence I want to say is, \"The reader is positioned to feel [insert word], as their beliefs are subverted and challenged.\" Words I've tried so far: Unsettled Uneasy Disturbed These are the closest words I could find but I feel like they have a more negative association, and creates a malaise in the reader. I feel that the effect of the book is more subtle and just lightly 'shocks' the reader, positioning them to just take notice of their preconceived beliefs, rather than evoke a negative reaction. Destabilise Bewildered These words suggest that the representation of these households are completely weird and confusing, however, that is not the case. It's not so weird that a reader wouldn't comprehend it, these households are just different to the mainstream households. Source for definitions: Google dictionary", "label": 0}
+{"snippet": "Background: I tile lidar and photogrammetry products as part of my job. Project areas are typically single polygons outlining an area, and can be quite irregular in shape. Overall there is a lot of data and I am required to achieve a maximum file size per tile by creating square tiles that cover the project area. I know from experience what this tile size is but it differs by product. Although tiles are square, they are allowed to hang over the edge of the polygon. I'd like an algorithm to take a polygon and a square tile and return the tiling which has the fewest number of tiles that completely cover the polygon. The square tiles must not be off-grid or rotated, they must be orthogonal. If possible I'd like actual code, preferably in python and utilizing arcpy, however I'm willing to accept any answer that provides the algorithm I'm after. Bonus - multiple polygons representing disjoint areas need to be tiled using one tiling scheme. Tiles that don't cover any project area aren't needed, but all tiles must be on the same grid.", "label": 0}
+{"snippet": "Levitated pits were introduced after after solid pits. In this design the tamper is separated from the fissile with an airgap. From the Nuclear Weapon Archive: The original Fat Man pit design used a Christy solid plutonium core, surrounded by a close fitting natural uranium tamper. The Sandstone devices all replaced the contiguous tamper-core approach with a \"levitated core\" in which the core was suspended within a larger hollow space within the tamper so that a gap existed between them. The collision between the tamper and core would create more efficient compression of the core than the explosive-driven shock in the wartime design. Other vague descriptions I found: The first improvement on the Fat Man design was to put an air space between the tamper and the pit to create a hammer-on-nail impact. Efficiency of the implosion can be increased by leaving an empty space between the tamper and the pit, causing a rapid acceleration of the shock wave before it impacts the pit. I recently started studying shockwaves and I don't understand this. How does leaving an empty space increase schokwave acceleration? If I remove the airgap, the mass of the core won't change but now I can use the extra volume for more explosive. Inside the pit, compression of the fissile is the result of work performed by the explosive charge, so how is it possible that I can increase compression by reducing explosive volume ??", "label": 0}
+{"snippet": "In table tennis it is often desirable to produce as much spin on the ball as possible using a glancing contact. (The rubber covering of a table tennis bat is typically highly elastic and has a high coefficient of friction.) Anecdotally, the view is sometimes expressed that acceleration at the point of contact is more important than speed. I take this to mean that when the ball is hit with the bat at the same angle and travelling in the same direction, it is possible for a bat at a lower velocity but with some acceleration to impart more spin on the ball than a bat travelling at a constant higher velocity (higher than the maximum speed of the accelerating bat) without acceleration. Is this true? If so, why, and how can the optimal contact (in terms of speed and acceleration) to produce maximum spin be determined?", "label": 0}
+{"snippet": "One English rule is to hyphenate two or more words when they come before a noun they modify and act as a single idea, called a compound adjective. This is the most common use of the hyphen I've seen. For example: A non-cloud platform Some cloud-based platforms What happens when there are three adjectives before a noun? Should I hyphenate all three? This example looks awful, but maybe that's because it's joining two compound adjectives that we usually see by themselves: Non-cloud-based platform That compound adjective would look better without the two hyphens. For most groups of three or more hyphenated words, they tend to form expressions that behave like compound adjectives, e.g. up-to-date, hit-or-miss, trial-and-error, etc. but they would also look alright as phrases by themselves. The three-word compound adjective in my example doesn't fall into that category.", "label": 0}
+{"snippet": "I heard that Lagrange mechanics can be derived from Newtonian mechanics, and Newtonian mechanics can be derived from Lagrange mechanics. I've heard many times that they have equal explanatory power. But I encountered that there is a tricky point in deriving the law of conservation of angular momentum in Newtonian mechanics. On the other hand, theories that use the principle of least (or stationary) action derive each conservation law from the Noether's theorem by assuming each symmetry. So, is my understanding appropriate? That is, while Newtonian mechanics itself derives conservation of linear momentum without any additional assumptions, and requires some manipulation to derive conservation of angular momentum, but Lagrangian mechanics cannot derive both without the assumption of symmetry, or derive both if the assumption is made. Then, it seems that it can be explained by Lagrangian mechanics, but there is something that is not correct in Newtonian mechanics, or it seems that more assumptions are made in Newtonian mechanics than in Lagrange mechanics. Which of the two makes sense? I'd also like to ask if Newton's third law conflicts with Lagrange mechanics, and if it's possible to find a set of Newtonian laws that have the same explanatory power as Lagrange mechanics. However, I want to know (even short) to just the above two questions.", "label": 0}
+{"snippet": "I have problems in understanding the terminology used in Sylvester's Criterion about the \"sign\" of a matrix. I got the \"positive-definite\", the \"negative-definite\", the \"indefinite\" and \"non-definite\" (the last one is when the determinant is zero, whilst the penultimate refers to two eigenvalues with different signs). What it's really unclear are those two: positive semi-definite: \"all its eigenvalues are non negative\" positive semi-definite but non positive definite: \"there is one zero eigenvalue and the rest are non negative\". I would really understand why one has to complicate the terminology in such a horrible way. Why shall we use \"non negative\"? Just say \"Positive\". Also, what's the difference between \"all its eigenvalues are non negative\" and \"there is one zero eigenvalue and the rest are non negative\"? I don't get this. If zero is counted as \"neither negative nor positive\" then wouldn't positive semi-definite mean positive definite? It's all so messy.", "label": 0}
+{"snippet": "My current level of maths does not allow me to understand any of the proofs I was able to find online for the Fundamental Theorem of Algebra. I find it very unsettling having to continue learning about polynomials without being able to grasp such a fundamental property of them that is there exists a complex root for any polynomial with complex coefficients. My question is, is there a way I can reach the same conclusion of the Fundamental Theorem of Algebra for polynomials with real coefficients instead of complex coefficients. In other words, to prove that at least one complex root exists for a polynomial with real coefficients. Does restricting the coefficients to be real instead of complex make things any easier? If the answer to my question above is no, then I would appreciate it if you could provide any sources that I could've missed, that explain the Theorem by using the least amount of mathematical notation and advanced concepts as possible. If I cannot figure this out, I am going to have to accept the existence of a root as an axiom going further, which is something I really don't want to do.", "label": 0}
+{"snippet": "I've been thinking about the critical point of water, which has three distinct and specific properties: critical temperature, critical pressure, and specific critical volume. However, when I draw a PV and TV graph I can't seem to think of any way in which to bring the water to its critical point because in order to get one property to its final state you have to change one of the others. For instance, if you already have the water at its critical temperature and pressure, you would have to decrease or increase one of those values to get it to its critical volume. To this end, I'm wondering whether it's even possible to bring water to its critical point - because once you achieve two of the three intended properties, it seems impossible to me to get the third property to the correct state without changing one of the other two.", "label": 0}
+{"snippet": "I am reading up on Christol's theoreom and an important part is that k-uniform transducers (where k is somehow related to prime numbers) preserve the algebricity of a formal power series (taking the coefficients as a sequence). So basically, we start with a formal power series that has roots (my friend told me that algebraic means there are roots or zero crossings), run the coefficients through a k-uniform transducer and, when we use the values that come out as coefficients for a power series, that power series is again algebraic. There is a lot I still need to understand here clearly (like, what is a \"formal\" power series vs a \"business casual\" power series...), but I'd like to start by understanding what is so special about a power series having roots. Just for context, I have nearly no formal background in mathematics but came across Christol's theorem and thought it was very cool and maybe related to my area of work (computer science, temporal logics, and automata). Any help is appreciated!", "label": 0}
+{"snippet": "Is there a conceptual problem in formulating of Liouville's theorem and the BBGKY Hierarchy for classical field theories? I always see treatments of Lioville's theorem only in the context of classical mechanics. I also know that most references treat linear response theory only for classical mechanics and do not touch upon linear response theory aspects of classical field theories such as Kubo formula. One can definitely take the continuum limit of a classical mechanical system and obtain some sort of Lioville's theorem or BBGKY hierarchy for the continuum field theory. I would like see if this is discussed in some rigorous way in any reference. In particular, I'm looking for references which discuss aspects such as the phase space for classical field theories, BBGKY and Green-Kubo Formula. I'm not a mathematician so a good systematic treatment I'm comfortable with for classical mechanics is David Tong's lecture notes and the text by Evans and Moriss. I'm looking for similar treatments for classical field theories.", "label": 0}
+{"snippet": "When we calculate the excess pressure on the concave side of the meniscus of the liquid surface formed in a capillary tube, we balance the force by the atmospheric pressure, force by the pressure on the the side of the fluid , and the force due to surface tension, to derive the expression for the excess pressure on the concave side of the meniscus, but, my question is, when we balance the forces acting on a body, we balance the net external forces on a body for it to be in equilibrium, but here the surface tension force is an internal force on the surface, applied by the surface molecules themselves, then why do we include it in the equation for balancing the net external force on the meniscus?", "label": 0}
+{"snippet": "I'd like to get some clarity about how nice the problem of decomposing semigroups using the wreath product is compared to the problem of decomposing groups, and where this apparent difference in niceness comes from. Looking at the Krohn-Rhodes theorem for finite semigroups, one can decompose a finite semigroup as a wreath product of finite simple groups and really basic \"reset automata\" semigroups. If I understand the Krohn-Rhodes theorem correctly, if one applies it to a finite group, you don't get any \"reset automata\" semigroups, so it gives us a decomposition of our group as the wreath product of simple groups. Is this correct? On the other hand, Meaning of factorization of groups and looking into the extension problem for finite groups leads me to doubt that the case for finite groups is that simple. So is it not as simple as \"there's some kind of wreath product-like construction that allows us to reconstruct a group from its factors\"? I'd greatly appreciate some clarity about this.", "label": 0}
+{"snippet": "I have been trying to define the notion of a product of second-order classes using (finitary) second-order and if needed third-order logic. It seems to be possible to define the product of finitely many classes, because I can just express this using a finite second-order sentence. The problem is that, when I try to define an infinite product, I seem to need to be able to refer to an indexed family of classes. More specifically, so that I can use an infinite index class. But something tells me this should not be possible to do in higher-order logic, because intuitively, it seems to involve some circularity. Do you know if it is possible? Also, someone suggested me that type theory should help me with this problem, and if so, do you know why?", "label": 0}
+{"snippet": "Im reading make: electronics, and I have investigated a little bit about displacement current and how a change in electric flux can create a magnetic field in a vacuum. A can understand that, however there is one effect which I don't comprehend the physics behind it. The effect that I'm talking about can be resumed in the next quote from the book: \"A sudden change in voltage on one plate in a capacitor induces an equal change in voltage on the other plate, as if is reacting in sympathy\". An image from the book showing the voltages in both plates of the capacitor in respect to time. My theory: So my theory is that since there is a current displacement there is also a change in magnetic flux, and this change in magnetic flux can generate a similar voltage on the other plate, since the plate has thickness and thus inside the plate there is an area that is perpendicular to the direction of the magnetic field, which will lead to a magnetic flux, and if you change the magnetic flux a voltage is created (according to Lens and Faraday). However, I don't know if this is right, and at the same time trying to find information on the internet about it is impossible. If anybody has an answer I will be delighted.", "label": 0}
+{"snippet": "I am seeking answers from experts in mathematical logic about the amount (if any) of university mathematics I need to know in order to understand mathematical logic and later hopefully do meaningful (independent) research on the subject in general and Godel's Theorems in particular. I am proficient in high school math and have a bachelor's degree in Physics. I have also recently taught myself some calculus, linear algebra, and parts of real analysis as I assumed you must need at least undergrad math to eventually get proficient in a certain math discipline. Earlier I had decided to learn up to grad level math but after I glanced through some logic books it appears they make close to zero use of even undergrad math. Also, I have come to know that philosophers too do research in mathematical logic, and as far as I know, they don't study any university math. So, my question is should I first teach myself undergrad (and grad math) or just dive into mathematical logic as I don't want to later find myself in a position where I have to study all that university math before I can make further progress in logic? If that is the case I would consider enrolling myself in a math program first and doing the research later in the conventional way.", "label": 0}
+{"snippet": "My understanding is that the word means a rephrasing of something the person has said in expressing the same sentiment or idea. But I think people use the word to mean essentially, say something in a similar way to mean something else. A simple example: Marge is talking to a bullied Bart: \"If they beat you up, I do not think they are your friends.\" Someone who wants to borrow this sort of phrasing to apply to the situation where someone has more extremely pushed an acquaintance off a roof and this is reported in the news as \"Woman's friend pushed her from roof\" and says, \"To paraphrase Marge Simpson, 'If someone pushes you from the roof, I don't think she is your friend.'\" In the above, is \"paraphrase\" being misused and if so, what is a better word for such borrowing/reuse with modification of a phrase?", "label": 0}
+{"snippet": "I'm currently working as a (undergrad) TA for a mutlivariable calculus class and while covering the topic of multivariable differentiability, one of our students suggested that it'd be nice to have some actual functions we could use as examples to navigate how the theorems can be used to both establish differentiability and to flip them back around to deduce things about the partial derivatives if they're not differentiable. In particular, we were discussing a sufficient condition for differentiability which, roughly, states that if all of the partial derivatives of a scalar field are continuous at a given point, then the field is also differentiable at that point. But more specifically I was warning them about how the contraposition of this statement does not forbid a function from being differentiable while having discontinous partial derivatives, as this beautiful example shows. The previous example has all of its partial derivatives be discontinuous, but then a student asked if I knew any scalar fields which only had one or two discontinuous, while the rest remained continuous at the given point. Here's where I ask for your help :) I have looked around in some of the literature but haven't been able to find good enough example of this, although in principle this should be possible (from what I understand). Also, if you have other interesting examples that show how differentiability can be wrinkly or deceiving I'd really appreciate it (and our students would too)!", "label": 0}
+{"snippet": "I have read this question (no answer, just comments): Light, including pulses of light, consists of many photons. A very short pulse has a wide range of frequencies. See The more general uncertainty principle, regarding Fourier transformsA single photon can also have a long or short duration, and a narrow or wide range of frequencies. I have never heard of single photons with a wide rage of frequencies. Each photon is always supposed to have a single quantified energy/frequency, otherwise the quantum effects would not occur. Can you refer to studies that show single photons with a range of frequencies? Relation between attosecond light pulses and photons? And this: This is very fast for a pulse of light, and it is actually so fast that the pulse of light is no longer a periodic electric-field oscillation, and instead it lasts only for a few cycles. But it is still not fast enough. What is an \"attosecond pulse\", and what can you use it for? Now we have had single photon emitters for a while and the photon is the smallest amount (quantum) of EM energy. But then the question remains, why are attosecond pulses better (for example to track electron orbitals) then single photon emissions? Very naively thinking, if you shoot single photons at the electron (atom), you are using the smallest quantum of energy to do so. Then why is attosecond pulse generation superior to single-photon emitters? Question: How can an attosecond pulse be shorter than a single photon (quantum) emission?", "label": 0}
+{"snippet": "In practical engineering we are limited in the upper temperature of thermodynamic cycle due to the material properties. So, after the max temperature is fixed, we want to make our cycle as close as possible to a Carnot cycle with the same max temperature. It is clear that the compression and expansion should be adiabatic and we are technically close to the realization of this. Also, we have to cut lower right angle of the Carnot cycle, because each next turbine stage should be larger in diameter, and building them becomes economically or technically impractical at a certain point. But the process of heat addition is a bit more tricky to understand. Consider the case of Humphrey and Brayton cycles in the same range of temperatures: The heat addition process is more vertical in case of faster heat addition, but according to Carnot process it should be more horizontal to be more efficient (i.e. close to isothermal). However, we do know that faster heat addition is more efficient (detonation engines are more efficient), so Humphrey cycle should be more efficient. Can't solve this puzzle...", "label": 0}
+{"snippet": "I have viewed the definitions of the Hubble Sphere and related cosmological concepts, as well as various explanations, yet Im still struggling to comprehend a full visualisation of this, which I would prefer instead of taking its word for it. To phrase the question that would most help me, the following follows: so from the moment that a celestial object crosses the hubble sphere boundary, as in going out of our hubble sphere scope, the images of that object will never reach us, the observer, from that point on, and we are left with a developing and cascading history of prior images only just reaching us now. If what I said is accurate, and requires no correction, my question now is how will the developing and changing history of past images for this celestial object play out in our view for the next millions of years until that moment in the old present where it crossed the Hubble Sphere boundary? How would it appear to us, the observer, over such a long term period? My intuition is telling me that such a celestial object will continue to age in our view of its past images, but also becoming increasingly redshifted until phoof, it is no longer visible due to being outside of the Hubble sphere.", "label": 0}
+{"snippet": "I understand that infalling objects reach the speed of light at the event horizon. Any associated clock would be observed to stop, according to SR. But isn't the key here 'observed'? An infalling observer at the event horizon would observe a remote clock to stop. Who is to say which clock stops. No clocks actually stop in SR, because it is symmetrical. But there is gravitational time dilation. In this case clocks really slow down. But you would expect the force of gravity to be infinite at the singularity. It is here you would expect gravitational time dilation to be infinite and clocks would really stop, not just be observed to stop. The force of gravity is nowhere near infinite at the event horizon, so why would clocks stop here rather than just slow down? Do properties at the singularity transfer themselves to the event horizon? Perhaps because there is no physical singularity?", "label": 0}
+{"snippet": "This paper has the following abstract: We theoretically consider a graphene ripple as a Brownian particle coupled to an energy storage circuit. When circuit and particle are at the same temperature, the second law forbids harvesting energy from the thermal motion of the Brownian particle, even if the circuit contains a rectifying diode. However, when the circuit contains a junction followed by two diodes wired in opposition, the approach to equilibrium may become ultraslow. Detailed balance is temporarily broken as current flows between the two diodes and charges storage capacitors. The energy harvested by each capacitor comes from the thermal bath of the diodes while the system obeys the first and second laws of thermodynamics. Can someone explain the importance/meaning of the claimed result for a layperson? In particular, how does this not violate the second law, if it's \"thermodynamic fluctuations\" being harvested?", "label": 0}
+{"snippet": "I am working on this problem. A hexagon is inscribed in a circle. The length of five of its sides is a, while the length of the six side is b. My question is : a. How to find the area of this hexagon? b. how to find the each of the diagonals's length? What I have in mind is that, since only one side is different from all other sides, the figure is still symmetric. Then I can calculate the area of the two trapezoids. I think I should use the condition that it is inscribed in a circle. However, I am stuck with how to find the angles or what other fomula should be used here. Then for the length of the diagonals, I am thinking that once I got the two trapezoids, I got them. Anyway, I think I lack of the knowledge of some intermediate theorems. Thank you for the help in advance!", "label": 0}
+{"snippet": "This question closely ties into a question I had about verbless clauses. However, I am writing a new one at the suggestion of a user. Polarity-sensitive aspectual-related words are those such as 'still' and 'already.' I have established that modifiers like 'obviously,' which I believe to be evaluative in nature, can function as modifiers in an adjective phrase, as determined by the answer to my question linked above, where I confused them to be part of verbless clauses. But can 'still' and 'already' also be modifiers in an adjective phrase? Below is an example similar to the one from my previous question, using 'still' instead of 'obviously.' I have highlighted in bold what I believe to be the complete adjective phrase. He was crying, still sad because of the passing of his father.", "label": 0}
+{"snippet": "According to my current understanding of special relativity, photons do not experience the passage of time. It is as though the universe is completely 'paused' for them. I know that objects with mass cannot accelerate to the speed of light. But isn't the whole point of relativity to predict the motion of an object from a different frame of reference? The universe also tends to increase its size with time. In that case, consider the following thought experiment: Let's go back in time to when the universe was relatively young. There was once a photon which, when created, observed the universe to be completely stationary as it didn't experience the ticking of time. As the time does not tick, the universe doesn't expand (relative to the photon) and instantaneously, it exits the universe. So my question is, what part(s) of the above statements is false?", "label": 0}
+{"snippet": "I made the claim on a manuscript that all manifolds possess an acceleration field. The referee rejected the idea saying \"The nature of this acceleration field has not been seriously discussed and the theory lacks justification in physics\". This confused me as I understand that a field, in physics, is a region of space for which each point is associated with a specific physical quantity. Velocity is a physical quantity. If we impose an evolution parameter, then don't all points on this manifold have a velocity (vector) quantity? Is that not sufficient to claim the manifold has a velocity field? Can we not also take the second derivative of the position with respect to our evolution parameter and say that every point on a manifold has an acceleration (vector) quantity? Does that not also qualify as a field? Is there an argument to be made that all smooth, differentiable manifolds do not possess an acceleration field?", "label": 0}
+{"snippet": "I am looking for a word that describes something whose meaning is instantly recognizable, that is so simple as to be offensively lazy, and yet completely apropos. Such a word might describe Kazimir Malevich's painting Black Square: Chef's kiss conveys artfulness and minimalism, but not to the point of laziness or offense. I like sophomoric for its literal translation \"wise fool\", but the word is not used to suggest brilliance. Cunning has the right connotation of artfulness, but its connotations of subtlety, and further, deception, make it inappropriate. Stupidly/offensively obvious almost works, but is boring. Unsubtle is ok; blunt better. Both don't convey the artfulness that I'm looking for. I love the divine feel of manifest; I'm wondering if this is the best I can do. I'm tempted to coin kazimirean, but of course that's too indulgent.", "label": 0}
+{"snippet": "Let's bring a positively charged rod near a conductor. Now since some electrons in outer shells are not strongly bound to atoms,they will get to the side near the rod. But why does it mean that dipole is formed in that conductor? We take the vertical cross sections of the conductor. Now,in each vertical layer,there will be atoms. So electrons from each vertical layer will get to the side of the rod. If that happens,except from the region closest to the rod,there will be positive charge in every cross section. Hence,apart from the very region towards the rod,the entirety of the conductor will be positively charged since electrons have left from each of the cross sections. As we can see dipole(positive at one side and negative on another side) hasn't been created,rather negative at a very small region and positive charges throughout the rest of the conductor. The logic that the rod will push the positive charges at the extreme end also doesn't work since atoms are firmly immovable. So why is it still said that dipole is created as a result of electrostatic induction whereas we have proved that it isn't the case?", "label": 0}
+{"snippet": "In basic physics lectures, the teacher or professor in my class never explains the behavior of rotating two or many body particles. In my experience and intuition doing physics, two-particle or many-body systems tend to rotate about their center of mass. For example, the earth-sun rotates around its center of mass, or two black holes rotate around its center of mass; also in ideal conditions, without air friction, a stick when a force is applied to it at the end edge, stick will rotate around its center of mass. Can anyone explain the physics of a system of mass that tends to rotate around its center of mass? I tried to solve this problem and read some reference books, but I don't have any conclusion. most of the books I read just explain what rotation or torque is. Or, is my intuition wrong?", "label": 0}
+{"snippet": "I'm hoping maybe this is the right spot for this question, if not, I would love for someone to suggest a better spot I am attempting to use SOLIDWORKS flow simulation to simulate the airflow through a ram air duct. Think like a venturi tube on an airplane, but the convergent divergent duct is embedded in the structure rather than being a protrusion. The issue I'm having, is that for the area ratio of the entrance to the throat, I don't get the velocities I expect at the throat when doing an external flow sim. When I build just the duct itself and put lids on it and do an internal sim I get the numbers I expect. Is there any deficiency in the Flow Simulation when using the external simulation and the flow must through a completely bounded flow area? Or is the simulation giving me true results and the flow through the duct is that degraded by being embedded in the larger structure moving through the air?", "label": 0}
+{"snippet": "Intuitionistic logic can't prove as many sentences as classical logic, for example: Peirce's Law; Reductio Ad Absurdum; Double Negation Elimination; and Tertium Non Datur, which are all equivalent in classical propositional calculus and they can't be proved in intuitionistic systems. I can prove their equivalences in some famous system, but I can't prove that we can't prove all of them in intuitionistic proof system especially without using semantics. I would like to prove this fact only using syntactic properties, i.e. proving these formulas are not in the set of provable sentences or proving that there aren't any proof of them in the set of proofs of intuitionistc proof system, without interpretation into some semantics: Kripke models or Heyting algebra. Where can I read this topic? is there any great book for this proof?", "label": 0}
+{"snippet": "I'm using pandoc in my website to allow my content creators to use Word, which would simplify developmnent immensely. The only issue I have is that Pandoc seems to output very little information about document styling. It's possible for me to manually re-add these with CSS later, but that somewhat defeats the pupose of using Word. Hence my question. Can I get pandoc to spit out more information about how my document is structured, such that I can apply more generic styles and have the document looking comparable to how it was written. Example, I've got a table with user-defined centre-aligned text (the person centred the text in Word). When I export my document to HTML using the following command: pandoc --from docx --to html --embed-resources --reference-doc ./reference.docx --section-divs. (I'm streaming in the contents of the file via stdin, as it isn't guaranteed to be in a consistent location)`. When the HTML comes back, the contents of the table elements are simply paragraphs. I'd like them to be wrapped in <center> tags or the equivalent - just something to identify that they need to be centred. There's a number of examples like these that I'd like to introduce, but momentarily, centring text is a priority. Thanks for any pointers", "label": 0}
+{"snippet": "When there is wind at a surface, and a rotating cylinder is placed there, mounted in a way that it is free to reorient itself, can it be predicted if the cylinder will align itself in a certain way? Perhaps it is easier to first consider the same scenario but without a surface. So, simply, a rotating cylinder in wind. Can it be predicted if it will prefer to orient itself in a certain way? A cylinder with its axis perpendicular to the wind direction, will for example experience lift. Is there anything to suggest a rotating cylinder, free to orient itself in any direction, will prefer to orient itself perpendicular to the wind (its axis perpendicular), such that it also develops lift? And, what if a surface is then added? May be possible to make an analogy to how cylinders rotating in the same direction repel while those rotating in opposite direction attract. In this case, the surface with wind over it may \"appear\" similar to the surface of a rotating cylinder.", "label": 0}
+{"snippet": "It is very common in physics, when we refer to the most diverse theories, on the most diverse length scales, we also refer to their energy scale. It is through the energy scale that we classify a theory as being classical, quantum, or relativistic, for example. Likewise, on such a scale, we know whether we are dealing with sub-atomic or sub-nuclear particles. Thus, when constructing a theory, it seems to be of vital importance for the physicist to understand where such a theory lies on the underlying energy scale. However, for a young physicist student, it is not always easy to make such a correlation and find available material that deals with the subject in a didactic way. So, the question of how to determine the energy scale of a physical theory and classify it in the energy scale of physical phenomena remains somewhat nebulous, without many students realizing the importance of knowing how to classify the energy regime of a given theory. From this, as the question in the title of this topic already delivers, I would like to know how, given any physical theory, one can determine its energy and classify it according to the cosmic energy scale (I don't know if I can call it so: \"cosmic energy\" scale.). I would like, if possible, indications of references that deal with the subject.", "label": 0}
+{"snippet": "I was walking by the sidewalk during the night when I noticed a swarm of flies circling a street lamp. It was difficult to see at first, so I tried looking in different angles. The security gate came in by pure chance between me and the streetlight. Now the insects became crystal clear. I tried to capture this in camera, and the same effect can be observed. Now the object between me and the streetlight doesn't matter. My umbrella, or even my hand also works. I would like to know why exactly the blocking of the dominant light source allows the less dominant ones to be seen. The light from the less dominant ones were still present before blocking the light. What roles does blocking play here? Many a times me and my friends have to abandon astrophotography camps in the night due to an overly bright moon or street lamp nearby. Can this same method be utilized to capture a clear image of stars in the night sky?", "label": 0}
+{"snippet": "My teacher gave us the assignment to find the moment of inertia of any shape you want. So I decided to find the moment of inertia of our milky way galaxy. I found out that our galaxy is shaped like a warped disk, not a flat. After I found out that, I looked for the equation of the shape and density distribution of the Milky Way to find its I. But, to me, Nasa's and some high university papers had so many big wards that I could bearly understand what they were talking about(I'm Korean.. ^^). I'm sure that I can understand the equation if I had it, but I just can't find any information about them. I would really appreciate it if someone could tell me what you know about this equation(shape & density distribution) Thank you! (Img)Dorota M. Skowron, A three-dimensional map of the Milky Way using classical Cepheid variable stars", "label": 0}
+{"snippet": "I was watching this video on Hall effect, and to demonstrate that it is not electric fields that are bending the electron beam, the presenter puts a metal plate between the magnet and the beam. So, my question is, say there was a charge instead of the magnet. How will the metal plate shield the electric field produced by a charge? My reasoning till now was, say, you put a positive charge in front of the metal. Since the electric field inside the metal is zero, negative charges will develop on the face near the charge, and to maintain charge conservation, a positive charge will develop on the other face of the metal. So, in effect, the plate has done nothing. There are still positive charges pointing toward the beam, and the beam will still perceive a force from the charge. So, how is the metal plate acting as a shield? ( If I assume that the plate is grounded, then I can say that the plate will serve as a shield. But in the video, it is not grounded.)", "label": 0}
+{"snippet": "Some visuals are so obvious that you would think proofs are not needed. But then trying to proof them rigouresly is a whole other kettle of fish. I was stumped by the following puzzle I made for myself: (really it is no homework question) How do you proof that the axis of an ellipse are perpendicular? Yes you can see it, it is obvious but seeing in itself is no proof. Yes you cannot construct a countermodel, but again that is no proof. I am really stumped with this one, it is so obvious, and easy to see, but a proof? As definition of an ellipse I want to use: (reused from Wikipedia) An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the points is a constant. As definition of the axis i want to use: (all made up by myself, so maybe incorrect, the second one, defining the minor axis, was a real struggle ;) The first axis of the ellipse is the line containing the longest segment possible between two points on the ellipse. The second axis of the ellipse is the line containing the midpoint of the two focal points and the shortest segment possible between two points on the ellipse,", "label": 0}
+{"snippet": "Good afternoon everyone, I am currently resetting my mac and reinstalling everything in a clean way. I would love to have guidance here if possible. I currently installed TexLive and TextDist but now i am guiding myself with this : https://github.com/James-Yu/LaTeX-Workshop/wiki/Install If anyone could explain to me this section : Setting PATH environment variable After installing TeX Live, you must add the directory of TeX Live binaries to your PATH environment variable except on Windows. See the official document. LaTeX Workshop never touches the variable. If VS Code cannot find executables of TeX, it means that the setting of your system is broken. For the ways of setting environment variables on Windows, see link or link. On macOS and Linux, see the documentation by the rbenv dev team. Very detailed information is also available on stackoverflow for macOS. Notice that you have to restart VS Code and the operating system after changing the variable. If you can not fix the setting of your system, you can also override PATH with the env property of LaTeX tools in LaTeX recipes. Notice that, to set the PATH environment variable for VS Code Remote Development, you usually have to edit .bash_profile or .profile instead of .bashrc. See the document for WSL and an issue for Remote SSH. If you want to know about environment variable itself, please read Wikipedia and stackexchange. I do not really understand how it is important and what to do if anyone could help here !", "label": 0}
+{"snippet": "I often have to translate sentences such as: The Department of Environment has offices everywhere in the country, and we would love for you to join us [us as in \"the whole department, and not a specific team]. Or: The Police Department is assigning as many resources possible to the case, but we [the Police Department] cannot counter these threats alone I've been told quite a few times that a switch from the third person singular to the first person plural like that is to be avoided in French (supposedly because \"we\" could refer to anything and cause confusion, even in simple cases like these), and was wondering if the same kind of rule applies in English. I couldn't find any grammar or style guide to help me with this. All help is appreciated, thanks.", "label": 0}
+{"snippet": "I have a great interest in synthetic geometry since I was in senior high school. Although I have graduated from university I still like them now. When I was in high school, I read many textbooks and exercise books about synthetic geometry of mathematical competition and learned many interesting things like harmonic range and inversion transformation. But I think people must have invented something new. I am really curious about what new techniques synthetic geometry has developed other than I learned in old textbooks and I want to know if there are any reference on modern synthetic geometry. Also I want to learn how synthetic geometry studies other curves such as conic curves, especially ellipses. I have read the book Geometry of Conics, and the Conics Books by Apollonius, but I hope I could read more such books with deeper results, like those ordinary mathematical competition books with various theorems and interesting and difficult exercices. On a Chinese forum I find out that there are many people discussing modern synthetic geometry and writing short essays on various topics, but I hope I can read some systematic reference books. Thank you in advance.", "label": 0}
+{"snippet": "I have a problem I fail to research properly, so I hope you may at least push me in the right direction (or maybe even provide me an answer right away?). I know how linear regression works, that it attempts to find a linear curve such that the sum of all residual errors to the square of the given data points is minimal (least squares). Now, how does one go about, when data points have deviations attached? I have a set of data points, where every point has a unique deviation. The linear regression should still work as usual, but how do I get the resulting error bar of the linear regression curve? Also, since deviations fluctuate, I'd assume some sort of weighted method would make more sense in order to prioritize those data points with less deviation relative to those with larger deviation. What weighted method would make most sense in my case? Thanks a lot for your reply!", "label": 0}
+{"snippet": "I've read other answers about how vinyl records reproduce sound, but they don't quite address a main thing I'm curious about. Play Middle C on a piano or a Clarinet, its the same note that can be played at the same volume because the main note is the same. You can tell the instruments apart because there is a different timbre in the instruments due to the components of the other harmonics present in the sound that differ between the instruments. You can break this down using Fourier Analysis. Part of the reason for these differences is the natural frequency of the materials involved. Strike metal with a small hammer, you typically get a higher pitched sound than if you strike a similar volume of wood. A vinyl record has its own natural frequency, yet it can sound just like instruments neither of which sound like each other. Somehow the natural frequency of the vinyl doesn't matter. What's going on there?", "label": 0}
+{"snippet": "If an isolated conductor has a net zero charge and is not in an external field, would the free charges still move to the surface of the conductor eg. a conducting sphere? Wouldn't this create an electric field inside the conductor pointing radially outwards as there would be positive ions within the conductor and negative charges on the surface? And then wouldn't the electrons move back to join the positive ions? [I understand how free charges will move in a conductor to cancel any external field, cancelling the external field inside the conductor, but then wouldn't there still be a field pointing radially outwards?] I also don't understand this in terms of energy - why is it a lower electric potential energy position for the charges to go to the surface - wouldn't it be lower energy for the electrons to go back to the positive ions? Gauss's law talks about there being no charges inside a conductor, but wouldn't there still be all the positive ions left there if the conduction electrons have gone to the surface? My guess is that people are usually talking about any NET charge going to the surface of a conductor. But wouldn't an isolated conductor at equilibrium (as in the general textbook questions on this) be net neutral and so then not have charge on the surface?", "label": 0}
+{"snippet": "I understand my question sounds stupid but hear me out. I wondered if protons or any charged particle could generate photons and I found this wonderful answer that says yes: Does shaking an atom produce photons? The issue now is that the more I thought about it the more I became confused and here is why. If any shaking charged thing can make a photon, well, which way does the photon choose to go into? I don't have a clear understanding of photons so maybe that's the problem, so to better answer me I'll give my understanding. Photons are packets of energy that represent an oscillating electric and magnetic fields. Please correct me on that if i'm wrong, I'm mostly using the visual model of a photon when i describe it. How does a photon decide in which direction it moves in? Is it just completely random?", "label": 0}
+{"snippet": "I've gotten some contradictory answers on where the definition of the element within a set comes from. From a quick Google search, I got this strange idea that the definition of the element comes from the definition of a set. I reached this conclusion because some websites state simply that the element is A member of a set But I feel this results in some type of circular logic (At least I think that's what this logical fallacy is called). Since the definition of a set is A set is a collection of objects whose contents can be clearly determined. The objects in a set are called the elements of the set. (Robert blitzer college algebra) I am almost certain that the issue here lies in the definition of an element I found, But I can't seem to find a definition of the element that is independent of the set so to speak. I hope you guys can help clear this up for me thanks", "label": 0}
+{"snippet": "Suppose the situation where an object undergoes linear motion at a constant velocity on a frictionless surface. This motion is often introduced as inertial motion, which is the motion described with Newton's first law. On the other hand, suppose the situation where a person applies a force to an object on a surface with friction, adjusting the force to balance the kinetic frictional force and causing the object to undergo linear motion at a constant velocity (here assuming no torque). In terms of the fact that net force exerted to the object is zero, I know there has been recognition that the motion of the latter case can be interpreted as inertial motion according to Newton's first law. However, is such motion really an example of inertial motion? Such motion seems to be rather different from the motion of the former case (close to Galileo's original thought experiment in which the essence of inertial motion is highlighted in idealized situation with no friction). Or is it just a problem of how we define inertial motion?", "label": 0}
+{"snippet": "I have an understanding of electrical circuits, however I am very interested to know more about electromagnetic waves radiation. In particular I want to know how an oscillating voltage causes the electrons move inside a conductive antenna. Voltage is only a difference in electrical potential in our local circuit, it is only difference between electrical potential of two nets (ex ANT and GND) so how the ANT net can itself cause movements of electrons inside an antenna? (because in some circuits the antenna is only connected to ANT.) I want to know which physics model explains this phenomenon? as far as I know circuit theory doesn't explain this behavior. so It should be something else. I know there are some formulas to model electromagnetic radiation, however I want to build an intuition around this, I don't need formulas to solve problems. Also I know that speed of the light has relation to design of the antenna, so I think the theory should include speed of the light as well. I prefer to not get very deep in physic subjects, so I am looking for the most higher level theory/model which is able to fully explain this :)", "label": 0}
+{"snippet": "This is a discussion I was having with a friend: Its very likely that the temperature of the water you place a tea bag in while change the flavor of the tea (although I don't know why exactly from a physics perspective) But suppose I have water at a certain temperature: If I let the teabag naturally sit and soak in the hot water.... compared to taking a spoon and pressing/squeezing the teabag as soon as it lands in the hot water: will the flavor of the tea be different? From a diffusion perspective, I know that squeezing the tea bag in the hot water changes the color of the water much faster compared to letting the tea bag rest. But based from a physics perspective, looking at the interaction of the water and the tea molecules - will accelerating the diffusion process of the tea by pressing/squeezing change anything about the tea? (e.g. intensity, flavor). Are there any physics related equations (e.g. statistical mechanics, thermodynamics) that can explain this (if this hypothesis is true)? Thanks!", "label": 0}
+{"snippet": "I downloaded a latex template for Wiley journal articles, and can open the template file but cannot seem to get Texstudio/Miktex to find the .cls file. The template comes with a latex file which uses the class as an example, and if I open that right in the extracted ZIP folder, all is well; however, if I save-as anywhere else, I get a \"cannot locate name.cls file\". I have made sure that I saved the extracted ZIP folder within a directory listed in the MikTex path (have tried two different locations) and I have refreshed the filename database (multiple times) but still the same error occurs. This also happens if I open a blank file and attempt to use the class. I have closed and opened TexStudio a number of times, but I am unsure of what else I can try.", "label": 0}
+{"snippet": "During the last few days I have been interested in the gravitational hierarchy problem and the different explanations for it/solutions to it. Among the most \"concrete\" (insofar as anything this complex can be concrete) explanations are several realisations of the so-called \"brane cosmology\". In these, whether they be the original ADD model or some string theory model, the standard model particles/modes are confined to a brane (either due to them being open strings or some other effect) while gravity/gravitons can freely propagate into the so-called \"bulk\", therefore allowing gravity to \"leak\" away from \"our\" spacetime thereby explaining why it's so weak. Common to these theories is that while these dimensions can be taken to be either compact or non-compact (but often are assumed to be compact) they are \"large\" extra dimensions. Now in your \"garden-variety/lift pitch\"-string theory the necessary extra dimensions are assumed to be very, very small and compact. My questions now revolve around the parallels of these Kaluza-Klein compactified theories and the brane cosmology ones in regard to the hierarchy problem: Can standard model particles/modes access the extra dimensions? I seem to recall that this should only be possible at \"high enough\" energies but I am unsure. Can gravity/the graviton access the extra dimensions even at low energies? If so, why? What is the mechanism/explanation for this? If neither of the above yields a similar solution to the hierarchy problem as in the brane cosmology scenario, how is the hierarchy problem solved in these \"classical \", small-extra-dimensions Kaluza-Klein types of theories?", "label": 0}
+{"snippet": "So imagine the classic science experiment where you take an empty aluminium can and a rubber bar that you charge with fur. At first, that can is electrically neutral. Two different cases now that I want to discuss: If I put the can on a desk made out of wood, the can will be attracted by my charged rubber bar due to influence. So the electrons in my rubber bar push away the electrons being in the can as far away as possible (the other side) and so the rubber bar only \"sees\" the protons. If I put the can on a desk made out of a metal which is grounded, what happens then? Still influence? Or is the electrically neutral can now positive due to electrons escaping to ground? Would love to hear some thoughts. Best regards", "label": 0}
+{"snippet": "Can we determine the truth value of the statement \"if A then B\" knowing only that B is definitely false whenever A is true, for example, \"If you live in Paris, then you live in London.\" From what I understand about truth tables, this on the face of it is indetermined because it could be true or false based on whether you live in Paris and not in London, or you don't live in Paris. But at the same time, the fact that we know that whenever A is true B has to be false, seems to go against the purpose of implication, that whenever A is True B has to be True, and from that alone, the conditional statement can't be anything other than false? The book I'm reading says that the statement in the above example is false.", "label": 0}
+{"snippet": "The existing English language term needs to refer to a robot that can navigate environments and it incorporates a human who is present virtually inside the robot from a remote location. The human navigates the robot and communicates with the environment in real-time. The closest example are the so-called telepresence robots being tested for use in classrooms or offices, but they are not exactly what I am describing. I feel like there is a term for such a machine vessel that 'embodies' a human, or that there should be such a term. The terms robot or cyborg do not describe this vessel. I can imagine in the near future a humanoid robot that is not driven by AI but by a human from a remote location using VR with ability to sense the environment (e.g. sense of touch). For example, this would benefit persons with significant mobility disabilities by allowing them to be present and interact with environments, the idea behind the current telepresence robots but in a much more integrated way between the remote human and the machine, and more interactive with the environment. So, to recap, is there a word for such a machine vessel virtually occupied by a human?", "label": 0}
+{"snippet": "In the picture below, mountains farther away blends into the color of sky, this is \"atmospheric perspective\", caused by atmospheric scattering. This effect is also called \"fog\". But dark blue appears in the middle of the [green -> light blue] gradient somehow. Why? Is there a physically-based model to explain that? In many video games, they used linear gradient to simulate the fog. The color what we see is a linear interpolation between the color of the object and the color of sky. It looks like the gradient in the right side of the picture. But that isn't realistic because of the missing \"dark blue\" color, so mountains in video games usually looks too grey. My guess: The dark blue color is caused by Rayleigh scattering. The white color at the farthest mountain is caused by Mie scattering. Somehow combine them makes the fog both blue and white. But I have no idea how.", "label": 0}
+{"snippet": "In a room at normal room temperature, certain materials, such as metal, glass, ceramic, or rock, will feel cold to the touch, but others, such as wood or plastic, do not so much. Which physical properties do the former materials have in common that cause them to be cold to the touch but the others lack? The fact that wood is porous? Solid plastic pieces still do not get/feel as cold even though they are not porous. Most sources point to thermal conductivity, but how can that alone be the answer? Rock and rock-like materials (such as glass and ceramic) have a very poor thermal conductivity whereas metal has a very high thermal conductivity. I know that because rocks take a long time to heat up and cool down in a fire, but metal takes not very much time. Which physical properties (might be more than one) determine whether a material at ambient temperature will be perceived as cold or not?", "label": 0}
+{"snippet": "As a forward, I'm no a physicist or a student of it. In fact I'm pretty ordinary. So if I mischarecterize some concepts, bear with me. So I was reading up on some of the new technologies and then I had a moment. I am wondering if you could use quantum entanglement to transmit data across a vast distance, theoretically even light years, in an instant. I was debating this in a youtube clip where there was a whistle blower from the antarctic and they were speaking on this. My \"opponent\"(I guess?) Stated that measuring any entangled particle removes the connection, but quantum computers can use gates that flip an electron spin without disrupting the connection. Another objection was multi light year transmission, but I thought that should be fine since according to the theory, it's instant, no matter the setting. So basically I'm wondering with the current tech that we have, technically couldn't we set up an experiment to send a byte of data via quantum entanglement by changing the state of an electron, using a gate to measure it on the other end, and translating that to a binary digit? In other words, do we have Faster-Than-Light communication on the horizon?", "label": 0}
+{"snippet": "My understanding: electrocaloric effect relies on polarized molecules lining up to an external electric field, which lowers the local entropy and thus heat is given off to the surroundings. When the field is removed, the molecular dipoles again arrange randomly, which increases the local entropy, thus heat is taken in from the surroundings. I ask about a macro level system. Here I have micron sized particles, each particle made of two hemispheres using different materials from the triboelectric series. These serve as my \"molecules\". Upon initial shaking, the surfaces rub and so each particle has a dipole. Before shaking: After shaking: Now I turn on an electric field and vibrate the container a little so the particles loosen and align themselves to the field. This vibrating is kind of like of how they used to hammer the living hell out of heated iron in a strong magnetic field, so the magnetic domains align as the object solidified. Now I can't think of any reason why this won't display the electrocaloric effect. And since here we don't rely on the molecule shapes, crystallization, polarization and the intermolecular forces that prevent the dipoles from completely aligning themselves, I think this could display interesting levels of cooling and heating. Of course, I'm a nobody, so to you experts I hand over my question. Will this work, and if yes, can we quantify the effect using any equations?", "label": 0}
+{"snippet": "I'm looking for a word that effectively conveys an attitude showing a preference for having a child related to oneself ... ie, a lineally/genetically-related child. In particular, a word that would fit the following example: Michael had a _____ attitude, he wanted children of his own and / or possibly a noun form: Michael was a _____ unlike Sam who was a non-_____ which would be helpful in distinguishing between people that prefer to have their own children and those that are happy to adopt, foster, etc. I had considered \"autogenic\" ... \"auto\" meaning self, and \"genic\" meaning \"produced by\" ... and even \"progenic\" (or \"progenetic\" possibly) which might work here, \"pro-\", I take to mean \"following\" or \"in favour of\" which in combination with \"genic\" / \"genetic\" relates to genetic lineage or heritage. However, I'm not sure I've constructed them appropriately, or whether they're right or not.", "label": 0}
+{"snippet": "Scientocracy (to my understanding and as my intended meaning) is government by results, i.e., eschew policy debates to instead argue and then agree on metrics, run an experiment and then transition to whichever solution produces the best outcome as determined by the agreed upon metrics (of course, if cultural, climatic or other considerations make a new policy ineffective in a certain place, the policy should be revoked or adapted there). My question is what is the 'ism' associated with this? Scientocracism isn't a word, and ends with racism, so that doesn't really work. Technocracy (a related, if more loaded term) has the same problem. An example sentence would be: I believe in representative democracy, but I also believe in [] because while I think that we should be able to elect people to represent our interests - and fire them when they fail - I also believe in results.", "label": 0}
+{"snippet": "In the preface to Landau and Lifshitz's Statistical Physics, they comment the following In the discussion of the foundations of classical statistical physics, we consider from the start the statistical distribution for small parts (subsystems) of systems, not for entire closed systems. This is in accordance with the fundamental problems and aims of physical statistics, and allows a complete avoidance of the problem of the ergodic and similar hypotheses, which in fact is not important as regards these aims. After explaining that they will consider (macroscopical) subsystems of the whole closed system, they claim A fundamental feature of this approach is the fact that, because of the extreme complexity of the external interactions with the other parts of the system, during a sufficiently long time the subsystem considered will be many times in every possible state. But this is very similar to the ergodic hypothesis, is it not? From my Stat Physics lecture notes, Given a sufficiently large time, any closed system will approach arbitrarily closely any point in phase space I don't understand how considering subsystems overcomes the need for this hypothesis, neither what advantage it has. It seems to me that the authors are using the complexity of the interactions between the subsystem and the rest of the system to grant credibility to the claim that the subsystem will eventually have populated the entire phase space. But why isn't this equally credible to stating the ergodic hypothesis?", "label": 0}
+{"snippet": "Im not necessarily talking about emf (and also not considering rotation) , but rather the potential difference created due the induced electric field to balance the lorentz force on the electron. For example if the disk is moving toward the right and the magnetic field is into the screen then the lorentz force is acting on an electron downwards pushing it down. now due to the excess of electrons downwards an electric field is created top to bottom which increases until the lorentz force is equal to the force due to the electric field on the electron, resulting in an electrostatic condition. So my question is does this actually happen? if not why dosent it happen? Im a bit bothered by this because according to faradays law there should be no emf induced in the disk but according my reasoning there should be a potential difference. Is there a difference between emf and potential difference?", "label": 0}
+{"snippet": "As I understand it, the (real) index of refraction is given by the ratio of speed of a monochromatic light wave in vacuo versus speed in medium. When it comes to the question of propagation of a light pulse in a (dispersive) medium I know that I need to calculate the group refractive index to obtain the propagation speed of the pulse. My question specifically now is, if it is possible to use radiative transfer theory to calculate light pulse propagation in a scattering environment embedded within a medium (not vacuum)? If the former is possible, can that speed be said to be the effective group velocity of the mixture of the scatterers and medium? Further can this effective group velocity be used to calculate an effective group refraction index? Background: Although I have no working experience with radiative transfer theory I can imagine that it would be possible to use it for calculation of attenuation related values such as the imaginary part of the index of refraction, but I cannot see how it would be possible to get at the real part of the index of refraction.", "label": 0}
+{"snippet": "I've recently watched this video about an electromagnetic ring accelerator. I get how it works: it uses controlled electro-magnetic coils to accelerate metal balls' Passing trough one of the coils has two stages: when the coil passes enters the coil, the coil is powered on, generating an electro-magnetic field, accelerating the ball towards the center as the particle passes trough the origin of the coil, the coil is quickly powered off and the ball continues forward What I am curious about is exactly what forces act on it. Searching online there appear to be some inconsistent answers, but it always either is the magnetic force or the Lorenz force law. From what I understood the magnetic force is purely for describing magnetic attraction, either between two magnets or a magnetic (ferromagnetic?) object and a magnet, while the Lorenz force law is the combination of the magnetic and electric laws. Could somebody explain which of these two is and what exactly their formulas are in the context of the balls passing trough the coils?", "label": 0}
+{"snippet": "For example, ZFC and ZF. I have come across the notion of pure and applied mathematics, and how the development of the former can (and is usually intended to) lead to the furtherance of the latter. In this case, how do we know that the axioms we do pure maths with are \"sound\"? For me, there is no point in doing something as rigorous as maths unless we are certain it could at least possibly provide a practical use to us, however subtle that use may be: otherwise, it is just an elaborate (and hugely unproductive) mind game. I suppose my question boils down to why we do maths and what it is. If its a way of abstractly describing physical natures and phenomena (like Plato thought), I'd have thought you could test axioms with the scientific method, in which case there would be no confusion surrounding, for example, the millennium problems. There is so much nuance about axioms and proofs, truth, falsity and their natures that really interests me, and I would like to know more about, but I don't know where to start. I have heard of \"metamathematics\" as related a field of study, which is why it's included in the title, but I honestly don't know much about it. I also appreciate that ZFC and ZF may be bad examples, in which case please point out why. Thank you!", "label": 0}
+{"snippet": "In Slavery in Massachusetts, Thoreau writes: But it chanced the other day that I scented a white water-lily, and a season I had waited for had arrived. It is the emblem of purity. It bursts up so pure and fair to the eye, and so sweet to the scent, as if to show us what purity and sweetness reside in, and can be extracted from, the slime and muck of earth. I think I have plucked the first one that has opened for a mile. What does for a mile mean in this sentence? I looked up for in a dictionary, and methinks the author might mean the first lily that he came across, and that was opened, after walking a mile. Or does Thoreau mean something else here?", "label": 0}
+{"snippet": "Shouldn't acoustic oscillations created by primordial matter anisotropies create multiple peaks and troughs when those oscillations are frozen by decoupling ? It's not unthinkable to imagine that the exact calculations of the expected amplitudes of each will lead to a result where the first peak is much more significant than the rest, but do those other peaks and troughs theoretically exist, just at very small currently non measurable amplitudes ? In other words, the BAO peak corresponds to the first peak in the CMB power spectrum, but am I wrong in assuming the other peaks and troughs are theoretically also present in present matter distribution, just at negligible amplitude ? As a bonus, if the answer is indeed yes, why are the other peaks so negligible ? I understand that the first one has the greatest amplitude, but why are the remaining ones so vanishingly small as to remain undetected in current matter distribution, despite being nowhere near insignificant in the CMB power spectrum ?", "label": 0}
+{"snippet": "A current-carrying loop of wire is placed in a uniform external magnetic field as shown. If the current in the wire is traveling counterclockwise in the picture, what do you predict the loop will do when released? The answer provided for this question: From the RHR for loops, place the heel of the right hand in the plane of the loop so that the fingers are curled in the direction of the current. The extended thumb points in the direction of the B-field. Since it is anti-parallel to the external B-field, the loop will flip over and then remain at rest. I don't understand what causes that. When you apply the Right-Hand Rule or Flaming Left-hand Rule I prefer, the force induced is inward around the loop. How come it makes it flip over? I must be missing something deep here. What is the underlying concept that causes the wire to flip over?", "label": 0}
+{"snippet": "If I take a pair of classical particles with some energy interacting via Lennard-Jones potential, then the motion of the two particles will be in such a way that the distance oscillates around the equilibrium point (if the energy is not too high compared to barrier depth). If I consider a large number of Lennard Jones particles packed into a crystalline lattice, then intuitively I expect that each pair of particles should have a distance close to the equilibrium distance of the pair potential. In other words the \"lattice constant\" should be close to the equilibrium of the pair potential. But is it actually the case ? Can we consider a pair of neighbors in a Lennard-Jones lattice to be roughly an equilibrium of the pair potential with small corrections of further particles ?", "label": 0}
+{"snippet": "The situation: I'm trying to generate my resume with Latex, and get a pdf with all the text - no problems here. When I copy all of this text into a plain .txt file though, the formatting transforms all whitespaces (newlines etc.) into a single space, it seems. For example, lists are not vertically placed anymore, but placed sequentially. Does this maybe have something to do with how Latex files are built up (compiled) differently than ordinary text documents, causing it not to have any classical newlines characters, for example? In that case, would there be some way to insert those, allowing for a proper copy-and-paste functionality? I tried to make use of the pachage cmap, which assists with Unicode mapping, but could not get it to work. Anyone who knows a fix to this, possibly with cmap, or possibly another package?", "label": 0}
+{"snippet": "I'm working on performing a linear stability analysis on a system with fluid undergoing applied vibrations. Now, usually these systems are analyzed with no fluid velocity. Under these conditions, it can be shown that the system reduces to the form of a Mathieu equation (or a modified Mathieu equation in the case of viscous fluid). For Mathieu equations, it's known that there are discrete regions where the system response is either Harmonic or Subharmonic resonance, which is in line with the Faraday instability that's observed on the fluid interface. However, what happens when the system equations cannot be reduced to the form of Mathieu equations (for example, for complex fluids or fluids with flow)? Can the system allow resonance at frequencies outside of Harmonic and Subharmonic, or is there something more fundamental that says that these are the only allowable options? Should I also consider the possibility that the response might not even be periodic? Analysis procedure for inviscid Newtonian fluids Analysis procedure for viscous Newtonian fluids", "label": 0}
+{"snippet": "All explanations of jet propulsion that I've seen are formulated as \"due to conservation of momentum, air with momentum coming out of one end means the rocket must gain momentum in the opposing direction\". However it can't be the case that particles simply exiting some area with a momentum means all of a sudden something else must gain opposing momentum. If we had a straight pipe open on both ends, particles suddenly exiting one side (maybe a chemical exploding inside or the like) does not mean the pipe will all of a sudden start moving in the opposing direction. You need one side of the pipe to be closed in order for the pipe to move opposingly. Similarly it can't be the case that particles suddenly exiting an inflated balloon or rocket means the object must propel in the opposing direction due to some 'rule'. I'm assuming what is actually happening is a case of 'particle collision averages'. In the case of a balloon the air inside is constantly bouncing off the walls in all direction. So when I let go of an inflated balloon I have disturbed this average. There are now particles hitting a side of the balloon with no opposing force, as the particles opposing that wall are now simply exiting the balloon. Assuming my above formulation is correct, does this mean all statements regarding conservation of momentum are simply a rule of thumb for this above 'particle collisions average' explanation?", "label": 0}
+{"snippet": "I was trying to find some references for modelling the equations of motion of a simple dynamical system (say a pendulum on a moving mass) when I realized that the very vast majority of the material you find online or even in textbooks suffer from the following problems: Reference frame poorly defined, wildly assigned or even implicit. No idea which point is considered to be origin, which direction positive, etc. Free body diagram completely unprincipled and/or confusing. Confusion between magnitude of a vector (e.g., Force) and the vector itself (not mentioning switching back and forth) No general form for basic laws of motion. Sometimes when the authors apply Newton's second law, for instance, they are applying it implicitly along some dimension. Constants are stated and used without derivation or motivation, e.g., moment of inertia are mysterious constants that you would look up from a table And many more problems. Does there exist any textbook on modeling classical dynamical systems (pendulum, masses, multi-link robot) from scratch?", "label": 0}
+{"snippet": "While reading the Wikipedia article on infinite sets I found the following quote: A set is infinite if and only if for every natural number, the set has a subset whose cardinality is that natural number. If the axiom of choice holds, then a set is infinite if and only if it includes a countable infinite subset. This raised an interesting question; without AC, is it possible to have a set where, given any natural number, you can find a subset with cardinality great than that number, but not necessary one equal to it? For example a set where all definable subsets have even cardinality? Edit to clarify the question: are there sets that satisfy the intuitive meaning of infinat but not the definition as quoted above? FWIW, id be interested in both the case where \"subsets larger than n exist\" requires those subsets be finite and where they don't. (Though I suspect the second case is uninteresting as most of the interesting properties would be trivially true.)", "label": 0}
+{"snippet": "Let's say the origin is an equilibrium position for a particle. If we have a case such that a slight displacement of the particle in x direction makes it return to the mean position (stable equilibrium) and a slight displacement of the particle in y/z directions makes it go further away from the mean position (unstable equilibrium). The directions of displacement for which particle is in unstable equilibrium are more than directions of displacement for which particle is in stable equilibrium. I have seen this question but the answer didn't clearly state whether there will be an equilibrium type defined for that position or will that position have no type of equilibrium (and the comments on that answer about Unstable equilibrium \"winning\" over Stable equilibrium confused me even more). So what will we actually call the equilibrium type at the origin? Or will we just define its equilibrium associated with direction (like stable in x direction and such)?", "label": 0}
+{"snippet": "My understanding from popular science articles is that the boundary is a field theory that has no gravity and has one less spatial dimension than the bulk. However, I am not sure I understood this picture correctly. I just read a recent article at quanta magazine that states: \"A solar system in the central anti-de Sitter region, for instance, can be described as a collection of particles scattered around the boundary that obey only quantum theory and have no sense of gravity or space-time at all\". So my question is, did the quote mean no curved spacetime, or there is not even a minkowski spacetime associated with the physics in the boundary? I dont even understand how it is possible to have a quantum theory of particles without either space or time.", "label": 0}
+{"snippet": "I am trying to understand Turing's halting problem proof by applying the same paradox to a similar problem where, instead of determining if a given code will halt, you instead determine if it will return True or False (assuming it will always return eventually). Obviously such a machine can exist, as it is simply a standard compiler. However, when run through the paradox: We assume h is a function that determines if the return is True or False We construct a machine P around h in the following way: def P(i): return not h(i, i) P(P) As we can see, if P returns True then P returns False, and vice versa. Thus compilers cannot exist, as a compiler is an example of h. Can someone please help me find the error in reasoning?", "label": 0}
+{"snippet": "According to this and this answer, and as far as I understand these answers, dark matter halos cannot collapse to a black hole because, due to uncoupling from the EM field, they are unable to radiate their kinetic energy, and hence, getting closer to some gravitational center point also means that they get faster and so they resist further \"collapse\". But what about the motion perpendicular to the galactic plane? I would naively expect the dark matter to gravitationally fall down on the galactic plane on both its sides, until it concentrates there. Depending on whatever the type of dark matter may be, this may cause other forces (e.g. weak interaction) to take over (possibly at nuclear distances) or it may oscillate until it becomes spherical again. One way I imagine that this might happen is a small-scale alternating velocity variation in the dark matter field, so that dark matter is alternately falling to/moving away from the mid plane from location to location, and these regions simply pass by one another infinitely. If this alternating pattern in the velocity field exactly balances, the dark matter halo is able to maintain a spherical shape. But even the slightest imbalance might result in a global oscillatory motion between spherical and disc-like. Have the available observations been investigated with respect to these possible oscillations of the dark matter halos? And isn't it likely that such oscillatory motion (if it existed) would eventually stop due to second order dissipation (dark-matter to ordinary matter to radiation).", "label": 0}
+{"snippet": "I am working in an algorithm to order a bed of close-packed spheres. In the case where I have got four spheres, I understand that the fifth sphere position and radius is determined by the positions and radii of the four other spheres. It seems that there would be different solutions: one that produces a sphere that is similar in size to the other four, and a second solution in which the four spheres are encompassed in a bigger sphere. What interests me is the first solution. Any ideas what equation system solves this? The input data for the systems would be the positions of the original four sphere centres and their respective radii, and the output would be the position and radius of the fifth sphere. It is also important to notice that the four original spheres can but do not need to be tangent between them. Thanks a lot in advance!", "label": 0}
+{"snippet": "From what I understand, each particle has an energy called kinetic energy. When we consider a system of particles, in addition to their individual kinetic energy, there is an energy associated with the systems which depends on their relative configuration which we call the potential energy. Mathematically a system of particles can be analysed at the individual particle level by assuming that system of particles induces a field and associate potential energy for each particle and then sum up over particles to get the potential energy for the system of particles. So I thought that potential energy is some sort of energy associated with the field (which is a mathematical construct). But later I studied that fields are real and they have their own energy. So is the potential energy the same as field energy, if not how are they related? Additionally, just as the energy of a particle is decomposed as potential and kinetic energy, can we do the same for the field, i.e., potential field energy and kinetic field energy? If so, then how is the potential energy of the particle related to the potential energy of the field? Also, potential energy in my mind is related to the shape a system of particles takes. Changing shape releases or absorbs energy. Entropy is a concept which is also related to the structure/order of the system. So how does the entropy relate to the potential energy?", "label": 0}
+{"snippet": "Can we answer the question: \"What are all the types?\" i.e. can we recursively generate all the types in a given type theory according to a certain set of rules? Pardon for asking such a weird question. Question/personal background: I'm leaving this question intentionally vague with regards to what I mean by \"type theory\" because I guess I'm just interested in the status of this question for type theories in general. My background is pure math and I am comfortable with proofs in ZFC and FOL but I can't write a single line of code in any programming language. I hope to understandthe basics of using type theory for proof like Lean does, and started reading about type theory yesterday in preparation, although I've heard snippets about type theory in passing elsewhere.", "label": 0}
+{"snippet": "Let's say you're looking at your keyboard on your phone.. let's take the letter g. Light from g is going in every direction.. we know this because we can see g from all angles above the phone. So light from g is also hitting your eye where you would see all the other keys,screen and background objects however we don't see g in those areas.. just wherever g is located. What happened to the images of g everywhere else but where we see it? We should be seeing g in all places but something happened and we don't.. if you're getting what I'm saying I you should be as perplexed as I am.. also knowing this now think about how a camera can take a picture with light from all objects being scattered in all directions.. it shouldn't be able to take a picture like it does.. how on earth was it even made???? It shouldn't be able to work but it does!!! Does this prove something else about life?", "label": 0}
+{"snippet": "In the same vein/spirit as the UIPAC books for standardising systematic names and formulae of chemicals, the SI units for units of physical measurements, or the INN for generic drug names, have there been efforts to write every statement in mathematics (eg. axiom, postulate, result, theorem) in a standardised language? This standardised language might be a formal logic like those touched upon in mathematical logic textbooks or monographs, or it might simply be a set of standardised terms or statements in a natural language like English. (I'd like to emphasise that a standardisation effort need not necessarily be one in a formal language.) I'd like to know if there existed, or there exists currently, a consortium, an organisation, an initiative etc. like this.. I tried searching for this on google but couldn't find one so far... Ermm, do put aside the debate on whether such an effort is desirable or not.. I just like to know if there is/was such an effort, not whether it is a good/bad thing.. I've come across TPTP.org, but not sure if this is the largest/most well-known/most followed/most active effort so far in mathematics.. Do let me know if there's any better..", "label": 0}
+{"snippet": "In google translate, the word \"bizarre\" means \"very strange or unusual, especially so as to cause interest or amusement.\". But I believe that this description is more suited for \"eccentric\". For example, the character of Jack Sparrow from Pirates of the Caribbean is eccentric. On the other hand, AI chat GPT says that \"bizarre\" usually means something odd and unsettling. And I have seen people make use of the word \"bizarre\" for criticizing something, rather than an expression of fascination. In Meriam-Webster site, \"bizarre\" means odd or eccentric in stye. This means \"bizarre\" and \"eccentric\" share the same meaning? But \"Jack Sparrow is such a bizarre person\" and \"Jack Sparrow is such an eccentric person\" don't seem to resonate. I got different vibes from them. Or is it just my feeling? Both means \"unconventional\"? What are their subtle differences, and can I have one example for each that would enlighten me about their differences?", "label": 0}
+{"snippet": "Almost every text on Category theory uses categories such as Ab, Grp, and so on as examples to work with but can category theoretic methods actually help us understand the structures better? In particular, does Category Theory aid us in proving some significant abstract algebraic results that are otherwise tedious to prove? Furthermore, is there any structural insight about abstract algebraic objects that is not readily apparent from algebra itself but becomes crystal clear with a category theoretic approach? I do not have a specific format for the answer in mind. As category theory is quite general, the answer may also include ways to say use results from other branches such as analysis or topology, so as to prove an abstract algebraic result which was tedious to prove using an algebraic approach. In this light, any insight about the relationship between category theory and abstract algebra is welcome.", "label": 0}
+{"snippet": "I find it amusing why the infimum norm or supremum norm defined on function spaces work actually? It's difficult for me to reach to an intuition where I would see the infimum or supremum as a natural way to represent distance between two functions. Is there any intuition which can motivate the norms defined on function spaces ? How do we make sure that two functions having the same infimum or supremum don't deviate too much from each other and that the function which is a limit under such a norm satisfies the properties the functions in the sequence have ? What is the norm measuring in function spaces I went thorugh the above question but could not find an intuitive way to address the last question in the first paragraph of my post . Disclaimer : I am not a pure maths student , please pardon my immaturities . I was just trying to find an intuition here.", "label": 0}
+{"snippet": "Im working on a nonlinear control based on Lyapunov theory and its working really well. I am able to implement it on a dynamical model of the system in simulink. However I think it has a really big limitation and that is: I cant guarantee that the real system will have the exact parameters that I am modelling. I want to make my lyapunov controller into a more robust controller by adding parameter estimation too it. I see some texts based around system identification, but I do not need to go that deep, I know what the system looks like. I just need some kind of method to zero in on the drift between my modelled and real components. Is this possible? I am controlling an DC to AC power converter. Physical System model: Model: Controller:", "label": 0}
+{"snippet": "Often metaphors are likenesses where there's a direct connection. For example on the news somebody describes a crash/ earthquake/ explosion as It was like a bomb going off. What about where the two things are not similar. Her painted toe-nails were an explosion of colour. (Exploding feet anyone!) This poem Cherry Ripe by Thomas Campion is full of insinuations rather than direct likenesses. There is a garden in her face Where roses and white lilies blow; A heavenly paradise is that place, Wherein all pleasant fruits do flow: There cherries grow which none may buy Till 'Cherry-ripe' themselves do cry. Those cherries fairly do enclose Of orient pearl a double row, Which when her lovely laughter shows, They look like rose-buds fill'd with snow; Yet them nor peer nor prince can buy Till 'Cherry-ripe' themselves do cry. Her eyes like angels watch them still; Her brows like bended bows do stand, Threat'ning with piercing frowns to kill All that attempt with eye or hand Those sacred cherries to come nigh, Till 'Cherry-ripe' themselves do cry. My question is: Are there technical terms that distinguish between: (a) Direct likeness. eg sky-blue eyes (b) Not really like at all. eg eyes like angels (c) Over-arching 'big metaphor'. eg garden in her face", "label": 0}
+{"snippet": "I am using TeXstudio with LaTex on Windows I also know about Git. In fact, I use Git to collaborate on RStudio but on TeXstudio I cannot. While typing on TeXstudio on my own without collaboration, I had my first problem saving different versions of .txt files on the same project, which sometimes confuses me. When I was writing my PhD thesis, I would send the PDF to my professor, which he could not edit. How do I solve these two problems? WHAT I WANT I have read different posts on reproducibility on TeXstudio, but I cannot figure out my foot on any. I want a step-by-step guide on achieving reproducibility and collaboration on TeXstudio using Git. I want to be able to revert to my previous changes without saving multiple documents.", "label": 0}
+{"snippet": "Goldblatt gives a brief overview of adjunctions in his \"Topoi\", and one of the exercises asks to characterise the partial arrow classifier in terms of some universal arrow. Well, I gave it some thought, and I'm not even sure where to go from there. The main problem I have is that in the \"there exists\" part I have only one arrow (the PAC itself), and in the \"such that for every\" part I'm given two arrows (the \"top-left\" components of the PAC pullback), and I'm just not sure how to construct a category and a functor into/from it that'd allow for both. I tried something along the lines of the diagonalization functor used for (co)products derivation via adjoints, but it didn't get me far (or anywhere, frankly). So, how would I do that? Again, my exposition to adjoints is limited to several pages of \"Topoi\", so I likely miss some otherwise well-known results.", "label": 0}
+{"snippet": "In statistical thermodynamics we can prove that the evolution of a system minimises some potential with units of energy (e.g. energy). This can be done purely statistically, by using the first two laws of thermodynamics, and showing that the state where the appropriate potential is minimised is the most likely one. Therefore, minimisation of energy is just an argument about entropy. Is there a similar (or any other) proof of the principle of least or stationary action? I have seen it referred to as an axiom, but is there at least a possibility that there exists an underlying theory from which it can be derived? Can it be shown that systems where action is stationary are the most likely ones? Also, it is interesting that the Lagrangian has units of energy as well. Edit: To clarify on the first paragraph. I was referring to quasistatic systems that satisfy a sepcific set of conditions. Energy is minimised in the stable state of an isolated system (where entropy, volume, and the number of particles is conserved). For a system where the temperature, pressure, and the number of particles are constant, the Gibbs free energy is minimised etc.", "label": 0}
+{"snippet": "I am at a loss to understand the justification behind the following statement being false and would appreciate someone explaining what this particular argument is saying: The set of all finite subsets of a countably infinite set is uncountable. Answer: False. Any countable set has a bijection with the naturals, and one can list the subsets in order of the sum of their values. Every finite subset has a finite sum and therefore will appear in the listing. I am not sure how this argument proves the falsehood of this statement, or what the process of its logic is. Do we not have to say something about how different subsets will have the same sums? I would appreciate a more formal version of the above argument so I could understand what point it is making.", "label": 0}
+{"snippet": "In common parlance, we say \"s/he pretends s/he doesn't understand\", for people who ignore the context of the conversation and require hyper-specific definitions to keep the conversation going. (hyper-simplified) example of the above, in the form of a dialogue: Q: Hey, how's your day? A: In what sense? Q: Uh, let's say for the sake of argument, how's work? A: What do you mean by that? In terms of what? Q: What are you up to? A: I do lot's of stuff, you have to be more specific - is there something in particular you're interested in? Q: Nope just in general, are you enjoying it? A: Sorry I don't understand, define \"enjoying it\" in the context of work and so on... Is there a term for what the person (A) is doing?", "label": 0}
+{"snippet": "Based on the double slit experiment we know that in the case of a single particle system the wave function or state vector of position is in a superposition of possibilities before measurement. But does this rule apply in the case of the vacuum state? Is it in a superposition of (non degenerate energy) possibilities before measurement? A physicist has replied to this question, in a personal correspondence, by noting that: It is thought that in quantum field theory, different vacuum states are essentially classical, and don't get superposed quantum mechanically. The reason is their effectively infinite spatial extent, so the distinct vacuum configurations are mathematically very distant. Yet I am not well convinced by his answer. Isn't a quantum state, either a single particle or a vacumm, a nonlocal object in the Hilbert space and independent of physical space? So why the vacuum state is an exception from the general rule of quantum theory that applies to position or momentum quantum state? Why being \"mathematically distant\" rules out being \"superposed\" in the case of vacuum. This is not trivial to me. Is there a theorem about this? Should we suppose that there are multiple Hilbert spaces and therefore in a single Hilbert space there is only one quantum state for vacuum? and \"by mathematically very distant\" we need to consider another Hilbert space with its own vacuum state?", "label": 0}
+{"snippet": "I have the following books about QFT: Peskin-Schroeder Lancaster-Blundell Iliopoulos-Tomaras I would like to know if there is a QFT that is as concise as Dirac's book about general Relativity. What I found useful about Dirac's book was that it developed most mathematical machinery \"from scratch\" with very little comments. I would like a \"quick reference\" QFT book that allows one to study the matter from a more mathematical perspective, rather than using a lot of physical analogies as in the books I have read. As an example, I would like to see \"This is the QED Lagrangian. Those are the consequences\", but a more classical, experiment driven approach is appreciated if it is strictly functional to the development of the theory and if it is kept as concise as possible. Ideally the book should be: More or less \"self-contained\", allowing a student with all prerequisites to learn introductory QFT from scratch (at least to renormalization) As concise as possible (ideally also in the number of pages) I would also like lecture notes or papers, it does not have to be a book.", "label": 0}
+{"snippet": "I would like to use this template from Overleaf for a PhD dissertation at the University of Aberdeen, offline on TeXnicCenter. (This appears to be a legitimate thing, according to my supervisor.) I have looked at this; it didn't help. My main issue is that I'm not sure how to use the cls file. There might be other problems once that is sorted, so if you could explain to me how to do it, please, I would be most appreciative. I'm not sure what I can offer in terms of context. But here: I did both my MMath and my MPhil dissertations using TeXnicCenter, along with much smaller projects, so I have a fair amount of experience with it. Like I said, I think the issue is with the cls file. I believe it is something like a package, but one that I have to install myself - I don't know . . . I am likely to award a bounty to the first answer that works when I try it!", "label": 0}
+{"snippet": "Three non-collinear points are placed randomly inside a unit circle. Question: What is the probability that if you were to connect these points, forming a triangle, the triangle will have the center of the circle contained inside (including the periferi)? Here are two examples, A and B, illustrating what I mean: where you can see that A works and B doesn't work. What Iv'e tried so far is illustarated in the following image: Two randomly points are obviously always collinear. So we can connect the two. Now let's draw a staright line, starting from each point, through the center and finish on the circumference of the circle. The grey shaded area represents the region where the third point needs to be in order to create a triangle that works. Now, as you can see there can be all kinds of regions depending on where the first two points are located. So I'm simply looking for a method/approach that can answer this question. If you have a another approach than my example feel free to use it. I'm not sure if this is very complicated or if there is a nice solution.", "label": 0}
+{"snippet": "If we are given that propositions P and Q can never be true, is it still accurate to say that P and Q are necessary and sufficient for each other, and why? I am conflicted here, as the statement P iff Q is true here and I have learned that this also means P and Q are necessary and sufficient for each other (for context, I have learnt that P is necessary for Q if P must be true to conclude Q is true, and that P is sufficient for Q if Q must be true to conclude that P is true); however, it seems counterintuitive to stipulate conditions for propositions being true (by deeming other propositions as necessary or sufficient for them) if these are never relevant to the situation, as these propositions are always false anyway. I would appreciate an answer grounded in an explanation of necessity and sufficiency.", "label": 0}
+{"snippet": "I am not well versed in TikZ and PGF Plots, and I am hoping someone would be able to help me with developing the structural code for a Parabola with its Focus and Directrix. I found an image of what I am assuming was created via LaTex and was hoping to recreate this somehow. This was a perfect image of what I am looking for, because the conic sections seem to be so lost to time that I can not find good representations of this particular topic without hand drawing it. I found a sample code for drawing a parabola, and when I attempted to recreate it, it does not let me use a fractional coefficient. If anyone has starter code to this image, that would be greatly appreciated", "label": 0}
+{"snippet": "My understanding is this: the Solar surface becomes speckled with more sunspots near Solar maximum, and these spots tend to form groupings known as active regions; each spot is associated with a given magnetic polarity, and often regions will tend to have spots of both polarities that are typically linked in certain ways, but sometimes the formed regions are much more complex, especially as the polar fields are about to flip and Solar activity tends to increase. Now, my question is this, as the title says: which way does current flow in the plasma streams that form the coronal loops and filaments that are generally \"rooted\" in the active regions? Is there a way to determine the direction of current solely from the magnetic polarities of the spots involved, or can current flow in either direction?", "label": 0}
+{"snippet": "In a corona discharge, the air around a conductor locally breaks down but remains an insulator further away from the conductor. Therefore, in the case of a positively charged conductor, the free electrons in the locally ionized patch of air can enter the conductor, positively charging the air too. However, corona currents don't exceed a few micro-amps. What is the reason for this? I know that electrically charging the increases the effective size of the conductor lowering the peak electric field. However, can this current be increased to arbitrarily high values is the charged air sheathing the conductor is removed quickly through some other mechanism? In essence, what I am asking is if the current limitation of corona discharge is due to the sheathing effect of the charged air or something intrinsic to the conductor-air system such as the probability of a free electron jumping into the valance band of the conductor being low. Where can I read about the microscopic nature of corona discharge? Any good books would be appreciated. I would like to learn more about the statistical mechanics behind the free electron and valance band interaction of metals.", "label": 0}
+{"snippet": "Perhaps you might want to take this question as some sort of challenge. I'm really just looking for the \"most efficient way\" of making a table similar to that in the image directly below (in LaTeX, of course): I've attempted several different things, and ended up with a huge mess and a thousand packages in my preamble. (Here \"thousand\" is a hyperbole for \"too much for my brain to keep track of\".) Because I provided an image of what I want, I don't feel like any MWEs are necessary here. Whatever looks most like the image I above, and gives the least headache, I'll mark that as the solution. Notice the days of the week are aligned to the horizontal centre of the cells, unlike the rest of the content. Note. The table I provided as a reference was made using LibreOffice writer, and the immortal CMU Serif font. If you have a good eye, you'll have noticed that the content of the list elements are not aligned perfectly, as the second and following lines of all the list text blocks are pushed ever so slightly forward. This is neither intentional nor wanted.", "label": 0}
+{"snippet": "If I want to calculate the length of a string that is wrapped around a cylinder what mathematical equations can I use? The thread is tightly wrapped around the cylinder, creating a spiral that has no gaps between each consecutive loop. Moreover each complete spiral creates one layer. and as a single layer finishes at the end another start to form up to the top creating a second layer, and so on. The catch is, is that each consecutive layer would require a larger length of string than the one before it because the circumference enlarges. Since the yarn ball is manufactured by machine, it leaves no room for error because the machine is in the same constant motion, the gaps between each string, as well as the gaps between each layer, are all the same, as is the tightness of each loop around the centre cylinder that holds the yarn together. So, how would you suggest I calculate the length using only external measurements and observations?", "label": 0}
+{"snippet": "When a thermodynamic system, like an ideal gas within a piston immersed in a heat bath, is subject to changes, such as compression or extension of the piston, then the work that can be extracted from this process is maximal if the process is carried out quasi-statically, that is, at each step of the expansion the gas is allowed to relax to equilibrium. Why is the relaxation to equilibrium at each step related to more efficient energy extraction (or reversibility) ? Here is another way to ask. If I make a large change for the piston, I imagine there will be an abrupt relaxation to equilibrium and this will be related to large dissipation. But If I make many quasi-static changes, then at each change the dissipation should be small, such that at the end more energy is extracted. But the problem is that I do not see any physical picture or equation why the sum of the very small amounts of dissipated energies during the sequence of quasi-static changes should be smaller than the amount of dissipated energy during the one abrupt change. The difference between my question and similar available questions such this one, Is there a quasistatic process that is not reversible? , is that I insist on pictorial or physical answers of the questions.", "label": 0}
+{"snippet": "Its kinda confusing but I will explain. I saw a term a while ago that explained how people can disagree with another. Instead of disagreeing because they do not like their opinion, the person will disagree because they dont like someone or something that also likes the opinion. Example: Person A thinks that driving on the road should require a license. Person B disagrees because a politician Person B doesn't like agrees with Person A, so Person B decides to disagree. You see that the argument Person A gave is reasonable, and Person B would completely agree, but the problem is that because someone Person B doesn't like agrees with Person A, they decide to disagree. This example is something very popular in politics (ex; only voting for a single political party, instead of voting depending on the politician's opinion). Another thing its similar to is contrarianism. You are disagreeing based not on the logic, but for another reason.", "label": 0}
+{"snippet": "How is the background noise of gravitational waves modeled? Is it a thermal model, giving a stochastic distribution of the curvature tensor (field-strength tensor) in ambient space? That is, every binary star, every orbiting planet, every orbiting black hole or neutron star -- anything that accelerates -- is emitting gravitational radiation. The grand-total of all of these sums up to what looks like noise. Is there a \"well-known\" distribution for this noise? Some power law? Can an argument be made that this noise has a thermal profile? Are there specific equations describing this noise, and what are they? How do they scale? Should one suppose that this varies from galaxy to galaxy, and depends on the local environment? Or can one argue for some generic form that is \"typical\"? Say, for binary clusters? Somewhat related: what is the order of magnitude strength of this noise, compared to the instrument noise in current gravitational wave detectors? Yes, of course, its frequency dependent, so its a graph, but is this \"natural noise\" strong enough to be detectable? (Ignoring Earth-bound sources.)", "label": 0}
+{"snippet": "A non-spontaneous change occurs when an external effort is being done to it. Since the external effort is also a natural source , does this mean that there is no truly any non-spontaneous process in nature (universe) ? Example to illustrate my point : An electrochemical process (like in a galvanic cell) can be reversed by providing an external voltage in opposite direction whose magnitude is higher than the cell potential. This external voltage is given by humans. Humans are basically converting some form of energy like mechanical energy of rivers in a dam into electrical energy. Also, humans are doing so because they eat food and they get their energy to do through spontaneous metabolic processes in their body. Also, the conversion of energy in above process is spontaneous because humans are making use of a spontaneous process ( a river flowing down from a height) . So, is there a truly non-spontaneous process ?", "label": 0}
+{"snippet": "I asked my coworker to fix something in a program. When he fixed it, he replied with, \"I already fixed it.\" -- this wasn't intentionally misleading, but was an incorrect translation of \"ya\". But for a moment I was thinking... \"no, you fixed it after I asked\". It was a bit jarring. Having learned a decent bit of Spanish when I was younger, I paused and realized there was some confusion when translating between \"ya\" and \"already\". BUT...I really struggled to find a clear/cogent explanation to help my coworker--from my English perspective. I finally found an article in Spanish, but honestly it was crazy how many meanings of \"ya\" there were, many of which I hadn't realized, and it was slow-going to read through it and make sense of it. My Spanish skills are rusty. So nobody else whose primary language was English was likely to realize what happened, had they seen this mistake So, here's my question: How can I help both the ESL coworker, other coworkers, and others in general to be aware of this pitfall, and what is a kind, cogent, and English-centric way to explain it? Thanks. Secondary question: And are there blogs/references or sites where I can learn more patterns of this sort of mis-translation across many languages? As a privileged white guy from a homogenous suburbia in the USA, I probably have a number of ways I might misunderstand cultural differences, and likely need to improve my awareness bit by bit.", "label": 0}
+{"snippet": "I want to use Matex for the figures in my plots which I eventually would like to use in overleaf. I create a plot and use Matex in it and right click on it to save as pdf. I then use this pdf in overleaf. So, when I compile the latex file and download the pdf, the Matex font looks rather shabby compared to other text on the plot (such as numbers on axes for which I didn't use mathematica) when I do not zoom in. . The font on latex can be seen on the description of the figure. The Matex font looks spotty with kinda white gaps in it. The problem with this is that when I print the file onto paper, the font doesn't look good. I don't think the problem is resolution since when I zoom into the pdf file, I get a very sharp Matex font. Does anyone know what's going on?", "label": 0}
+{"snippet": "Consider the sentence: So how can a computer think if it knows nothing of what it means to be a human being. Initially I thought that because \"of\" in this sentence basically means \"about\" the latter part of the sentence is not a relative clause as it is not adding any additional information, therefore is the subject of the sentence and cannot use which. Furthermore, as the contents of \"to be a human being\" is not known, \"what\" is used opposed to something like \"that\". However, upon further thinking I'm not sure if this is a relative clause or not as technically it is adding information to the sentence by specifying what the \"nothing\" the computer knows is. However, none of the resources I looked at concerning relative clauses used \"what\" in any example sentences. In other words, I'd like to know why this sentence uses \"what\" and what type of clause/grammar this sentence is.", "label": 0}
+{"snippet": "This is a broad question but it's well documented that GR and QM are very well tested in their own domains but they conflict around black holes. Picture a neutron star slowly accreting matter until it's mass is sufficient to bring about an event horizon. It resists gravity owing to the Pauli exclusion principle and it must surely be comprised of the same 'stuff' as the event horizon forms. Why do we then rely on GR and assume everything collapses to a singularity which seems illogical in nature when the most sensible ('we don't know yet') answer surely should be that there exists a 'black star' under the event horizon? It seems that QM is overshadowed by GR in this instance when GR seems to give more illogical answers. As a thought experiment, if we had a very heavy neutron star and fired one photon at a time at it; I would imagine the surface begins to redshift more and more as time goes on. There would surely reach a point where the miniscule deviations mean that a 'ravine' can no longer emit anything to an observer but a 'mountain' could. It would seem to be on a tipping point of being both a black hole and a neutron star but the mountain is still supported from below from seemingly below the horizon that is forming.", "label": 0}
+{"snippet": "Is there an easy way to draw complex images in LaTeX? By this I mean: Have a look at the following question. Some answers provide incredible pictures, very elaborated. In the (rudimentary) way I can create figures with tikz or pstricks, it would be impossible for me to come up with the correspondings codes. This made me think: Perhaps there are some tools that help write down the code. I am aware of things like tikzcd-editor or LaTeXDraw. I also know about InKscape, although I have never used it myself. Howerver, none of them seem to be appropriate to draw tori or spheres. Yes, with LaTeXDraw one can draw ellipses and create things that resemble those surfaces, but the quality of these draws is as good as the quality of Paint. I am thinking more of some type of image recognition software that identifies the geometric object (as well as some text the figure might have) the user has drawn and produce the corresponding code. Does anything like that exist?", "label": 0}
+{"snippet": "I am seeking a term for what can collectively be referred to as \"the leader and/or the most important and powerful roles\" in the hierarchy of a society. I have an example from the YA series Warrior Cats by Erin Hunter. Warriors are the generic members of society. Meanwhile Leader, Deputy, and Medicine Cat together are the important and powerful positions. A term, for them together, as a collective, is what I seek so I can quickly an efficiently refer to them instead of some nickname like \"the Big Three\" every single time. I would like for a term generally applicable to most of societies, as it can be used in many contexts. I've been unable to think of any possibilities, hence I ask. Example Sentence: \"The X are foundational to how our clan runs.\"", "label": 0}
+{"snippet": "Poi are tethered weights used for dancing, which often have battery powered lights in them. Clearly work is being done on the poi, first to accelerate them, then to keep them going at constant velocity despite air resistance. I'm curious whether it would be possible to power the lights via the work done by the dancer rather than needing to replace/recharge the batteries externally. Obviously the amount of energy the dancer needs to exert would go up as well, regardless of the method. One idea that clearly wouldn't be sufficient would be to use current induced by the Earth's magnetic field. Are there any methods that might produce more power? It'd be cleanest if these methods would work while the poi were spun at constant velocity, but methods relying on variations in velocity or tension in the tether would also be interesting.", "label": 0}
+{"snippet": "When you ask search engines or dictionaries, they don't seem to recognise the word 'orthodontry' and all point to 'orthodontics' and 'orthodontia'. I suspect 'orthodontry' is a mash-up of either of those and 'dentistry'. However, there are many businesses that use the phrase in their advertising and online communications. It seems to specifically refer to the practice of orthodontics. Is this an example where the dictionaries are just behind the times and is 'orthodontry' just an example of a neologism on the rise - a new 'aluminum'? Or is there some good reason the word should really be avoided? Examples of sites using the phrase: https://orthodonticsinlondon.co.uk/blogs/benefits-of-orthodontry.html https://www.columbiaasia.com/indonesia/specialties/orthodontry There's more like it - none of them any kind of language authority on the subject, but I started looking at it because two colleagues (I live in Australia) mentioned it independently in chat, and upon asking, one shared a mail from their orthodontist that had the word in there.", "label": 0}
+{"snippet": "you are a player in a game where each contestant has to choose between three boxes to win a prize. The prize is distributed uniformly between the three boxes. Each player makes a choice independent of one another. many or none of the players could choose the right box which is revealed at the end of each round. However, you have info that the other players don't- you know that the prize will be behind a different box from the previous round. Find the probability that you will have chosen the right box more than the other players by the end of the game. The problem doesn't give me how many rounds per game or how many players there are which made me first think that there was an issue with the problem, but i'm not sure. Would appreciate if someone could please confirm or help me out if its possible. Thanks", "label": 0}
+{"snippet": "I wonder what are the advantages of using the MPS-MFS (method of particular solution combined with method of fundamental solutions) for nonhomogeneous PDEs? In order to implement MPS with radial basis functions (multiquadrics or compact supprt, doesn't matter) you still need to mesh the entire domain (like in FD) but, unlike FD, you eventually end up with either a fully-populated matrix (when using MQ) or something anyway denser than in FD (when using functions with compact support). So, if anything, the MPS-MFS must be more expensive than FD, not less. The only advantage compared to FD or FEM seems to be that MPS-MFS is a meshless method in a sense that you don't need to build the connectivity matrix (which takes anyway just a fraction of the total time in a typical simulation job). Am I missing something?", "label": 0}
+{"snippet": "I want to self study Real Analysis, and I want to choose between these books. This is my background I am a teacher of mathematics for highschool, which means (at least) in my country, that I had seen abstract algebra untill ring theory and calculus untill integral in several variables, but not things like Stokes theorem (because standards for teachers in my country solicites some very basic ODE and, so I had seen ODE instead Stokes). This calculus class was a mix level between engineering and pure mathematics Could you tell me about the pros and cons of each of the following Real Analysis books? (Suitable or not for self-study, content quality, difficulty of the exercises, etc.) Real Mathematical Analysis, by Charles Pugh Mathematical Analysis, by Tom Apostol Principles of Mathematical Analysis, by Walter Rudin", "label": 0}
+{"snippet": "If we look at the majority of useful or industrial materials surrounding us, like metallic alloys, glasses, ceramics, or plastics, it is often the case that these materials went through really hard times or difficult stages of their life during synthesis and processing. For example this could be the heating of a metal to an extreme temperature and abruptly putting it in a cold environment to quench it, thus typically resulting in good mechanical resistance. Perhaps the question may be not so precise, but is there some abstract reason why good material properties (mechanical, thermal, electrical, and so on...) are typically obtained through procedures that really drive the materials out of their native solid stable states? Can this somehow be related to the difference in phase flow topology between very stable states (liquid, solid, gas) and the \"non-equilibrium\" states obtained through extreme conditions (like heat-treatment and so on)?", "label": 0}
+{"snippet": "I use Beamer presentations in workshops where I set questions, have students work on the answers, and then display some sample answers. I give the students a version of the presentation without the answers, so they can read back through the presentation as needed. It seems the usual way of doing such conditional processing in LaTeX would be to define a command to mark up an answer and then provide two definitions of the command, one that includes the answers and another that omits the answers. The usual way of switching between these definitions is to use distinct top-level source files. I would prefer to avoid creating an extra top-level source file for each presentation and instead control the formatting behaviour using command line arguments, an environment variable, or such like. Then I could write a script to format the presentation twice, once with the answers and once without answers. Looking through the arguments of pdflatex, I don't see a way of passing a flag that could be used in the LaTeX source to choose between the definitions. Related questions and solutions: Passing parameters to a document has answers that solve my problem, but the question does not express the context and requirements as clearly as the question here. Conditional text lines latex document - expresses a similar requirement. The exam package - seems to require multiple top-level source files.", "label": 0}
+{"snippet": "I know the heading may be a bit misleading one. But I can't find a better one. Anyone can suggest a good one. By writing Weird function I mean those functions that are integrable but not easy to do so. I have come to know that uniform convergence of a series of integrable functions on some set confirms the fact that we can interchange the order of sum and integral. In other words, this leads to perform term by term integration for infinite series of functions. I am very curious about: Can we write any weird function as the limiting function of uniformly convergent series of simple integrable functions? If the answer is yes, then I think we can integrate those functions easily. But then after integrating we again have a series, that must be again uniformly convergent I think. In that case it may not be possible to write it as closed form. Is my observation is correct?", "label": 0}
+{"snippet": "I'm trying to replicate a specific script 'X' that I'm seeing in a textbook: This lines up pretty well with the computer modern script X: But I'm using the unicode-math package, and the script characters in the default font (latin modern) look nothing like the script characters in computer modern (even though it's supposed to just be a modernized version). The unicode-math documentation includes a symbol list of a few included fonts, of which the concrete math font gets the closest: But I really don't like the uniform stroke thickness - it really doesn't match with the rest of the characters on the page (since I'm otherwise using computer modern / latin modern). Does anyone know of an OpenType math font that has a similar script X that I'm looking for?", "label": 0}
+{"snippet": "Maybe the questions is too stupid to be asked or I do not know the technical words, but I could not find any answer to this question. Here is how I started to think the title: First I thought of if we look far enough if we could see Big Bang theoretically. The answer was \"No\", due to reasons such as opaqueness of the early Big Bang and expansion. This is okay. However, then there was a second question arised: Even if we could, which direction to look at? Then I thought if it is the furthest and the oldest, it should not matter. Because any direction we looked at furthest and oldest we should see the Big Bang if we could. Then, I know I made too many assumption, but does this conclude that we are surrounded by Big Bang and the universe is expanding not outwards but inwards? As I said maybe question was way too stupid, but still I want to hear some ideas/facts. Thank you. By the way this is the first time I post a question, I have no experience, so sorry about any mistakes I made.", "label": 0}
+{"snippet": "So I'm writing a book, and I've used straight quotes (\") in my latex files throughout the entire project. Now whenever I compile my document in Overleaf, these, to no ones surprise, come out as no starting quote, and a straight quote at the end of what's quoted. What I wish is for all straight quotes in my tex files is to actually appear as straight quotes in the generated pdf, regardless of whether they are situated at the front or end of a word. Here's an example: % In my .tex file This is a \"nice quote\". I want this to appear exactly like this in my document: This is a \"nice quote\". Is there anything I can do to override the default behaviour? I really do not want to go through my entire project consisting of many .tex files finding and replacing characters, all I want is simply the straight quote symbol to appear as an actual straight quote in my text regardless of whether it's a start-quote or an end-quote.", "label": 0}
+{"snippet": "Consider a person pedaling a bicycle, if we consider the system consisting of the rider and cycle as a total and apply work energy conservation we can see that whatever force the rider applies on the pedal will also have an equal and opposite reaction and as both the pedal and the foot of the rider will have equal velocity the net power cancel outs? I don't know where the mechanical energy is generated in this process. I have attached a picture of a question from my engineering textbook (Engineering Mechanics by P.C Dumir) from which I got this question. I have attached a portion of the solution as well, I am not sure why It has considered the reaction force to be acting at point B and not the foot of the rider, due to which it has calculated the power by taking the difference of velocities of the subsequent parts.", "label": 0}
+{"snippet": "My understanding is that without acceleration the \"movement\" of a body is a relative concept, i.e. we can choose an inertial frame of reference where the body is at rest and there is no property or experiment that can tell us that the body is in movement, because it's a meaningless question. In the same way, can I say that the movement of earth is arbitrary, just choosing a non-inertial frame of reference? The fact that I need to include fictitious forces to explain for example the movement of a Foucault pendulum, means that the earth rotation is \"absolute\"? The law of physics should stay the same if I choose the earth as frame of reference, but does that mean that there is nothing absolute about the movement of the earth?", "label": 0}
+{"snippet": "Traditionally, mathematical work is presented in a linear fashion. Books, papers and articles are single streams of text meant to be read sequentially, from beginning to end. However, mathematical content often has a not-so-linear underlying structure. Sometimes it can be imagined to be tree-like, with nodes being results and directed edges being dependencies. Question Is there a format for presenting maths that is faithful to some underlying logical structure of the work? The 'logical structure' could be defined by the author. Using digital devices, we are obviously not restricted to linear text anymore. Have you seen such an 'untraditional' format being used? Prototype Imagine a PDF-viewer that can collapse and expand certain blocks of texts, as defined by the author and with the possibility of nesting. In proofs there are often steps which are very unclear to some readers and trivial to others. These steps could get elaborated on in an expandable block -- providing the necessary details for the people who want it while maintaining reading flow and brevity for the others. Using layers in LaTeX something similar can be achieved as described in this question", "label": 0}
+{"snippet": "I'm writing documentation for a piece of software I worked on and I came across an odd sentence format that puzzled me. I was wondering if there might be a conclusive answer on the matter: In the event that a complex compound sentence contains two independent clauses and one dependent adjective clause, but each independent clause would require different articles to tie with the dependent adjective clause, would the best article to use be the lattermost article? Example: \"create a\" vs. \"update your\" Everyone needs an updated google account to access the document. Please create, or update, your account before the meeting. I do not have a background in English, please excuse any incorrectly used terminology! I did some googling beforehand in order to better articulate my question so it's possible I misunderstood something in my haste.", "label": 0}
+{"snippet": "In order to define my question, I will demonstrate what I consider an appropriate answer. My question is as follows: How do I develop fast \"shortcuts\" in math? What I consider a shortcut is a means to solving a problem in a fast and creative way. My own answer would be to look for patterns and model a formula to solve the statement in an appropriate and timely manner. Maybe one could also introduce something brand new to the problem, like the perfect square technique. As one can see, I am not asking how to approach the problem, but what to do to find new and fast ways to solve it. This is obviously getting back to my question. How do I develop fast \"shortcuts\" in math? I value the community's intelligent feedback on this question. Thank you for your time and patience with me.", "label": 0}
+{"snippet": "It is my understanding that there are two types of random number generation used in computer science. True random number generators that use principles of a physical property to determine their generation and pseudo random generators that use algorithms based upon mathematics such as chaos theory. True random number generators use a proposed indeterminate properties of the physical world because of the principle of uncertainty and pseudo random number generators employ chaos theory which are non linear deterministic equations whose outcomes are sensitive to initial conditions however they are deterministic and with the same initial conditions the outcome will be the same. My question is the principle in true random numbers generators and the principle of using chaos theory in pseudo random number generators the sane, as both principles use a deterministic factor the schrodinger equation in true random number generators and deterministic equations of chaos in pseudo random number generator,so what's the difference? Is randomness actually certainty? or vice versa?", "label": 0}
+{"snippet": "I work in tech but I at some point I almost took a career path into theoretical physics. I changed my studies very late to data science and machine learning (my last masters year) and before that I was in physics and solid state physics. I am looking for research papers that could be interesting to read for a non-expert like me. I am used to read physics research papers (mainly solid state physics and spintronics). I am looking for papers that do not have super heavy mathematical development. An example would be the famous \"More is different\" from Anderson. It describes very well what I'm looking for although I'd prefer some mathematical perspective if applicable (but again not too much of it). The idea is to read about topics like General relativity not from Wikipedia but from research papers that are either foundational or educative/pedagogic. No books however I don't have time for them, I am not looking to study these subjects but rather acquire some insight and basic knowledge. I am looking for now in papers in : general relativity", "label": 0}
+{"snippet": "In papers studying or searching for topological order (intrinsic or symmetry-protected) in various condensed matter systems (e.g. Field-tuned and zero-field fractional Chern insulators in magic angle graphene), a common refrain of motivation goes as follows: Topological physics began with the experimental discovery of the integer and fractional quantum Hall effect, for very clean two-dimensional electron gases in a large magnetic field. The large magnetic field is unfortunate, and it would be nice to get rid of it. In fact the large field is not necessary, and equally interesting physics can arise in our system due to strong interactions, time-reversal breaking, etc. But I realized I never really understood the second point: why is a large B such a problem? What applications or lines of scientific inquiry does it challenge? To what degree are these challenges insurmountable?", "label": 0}
+{"snippet": "My problem is as follows: I would like to use the upright fourier package symbols together with dsfont. This produces: I therefore want to scale the dsfont symbols down to the same size as the fourier letters (or vice versa scale fourier up). I tried using scalerel, however for some reason pdflatex and Anki (a flashcard software) doesn't seem to like this. It declares no error message, however it doesn't scale the symbol (or any others I've tried for that matter). Overleaf does scale with the same code, so it's not the code. Are there any alternatives to scalerel to scale dsfont (or scale the fourier package - although this isn't preferred). I've also tried using the mathalfa package to load dsfont (although this doesn't load), as it has a scale feature. Some notes: I'm using mathastext with nosmalldelims enabled, if this makes a difference. Any help is appreciated:)", "label": 0}
+{"snippet": "I recently encountered a quirky situation. A student wrote a sentence, and it was much more technical than this example (actually for a literature review on microbiology), but this examples illustrates the basic issue: John said, \"The cat is on the table\" with great anger. A parallel example: John said, \"The cat is on the table\" when the cat climbed up. I was always taught to offset complete quotations with commas, but I tend to only see examples with the signal phrase beginning or ending the quotation (e.g. \"The cat is on the table,\" said John...). While I understand the sentences could easily be rearranged to terminate with the quotations and to improve style (e.g. With great anger, John said...), how should these be punctuated as they stand? Should there be a comma where the quotation terminates? Obviously, if the quotation were a regular clause, no comma would be used (the first due to a prep phrase, the second a dependent clause following an independent). But how does the quotation impact this rule? Thank you!", "label": 0}
+{"snippet": "Localized ferromagnetism refers to materials where the magnetic moments are primarily associated with localized atomic orbitals. Ferromagnets, such as those made of iron or nickel, are called itinerant because the electrons whose spins aligned to create the magnetic state are extended and are the same as the ones responsible for conduction. I don't understand how can localized ferromagnetism exist at all. From my understanding, a large gap insulator will always be non-ferromagnetic because the full valence band always have electrons paired up and leave no net electronic magnetic moment (while nuclear magnetic moment is negligible for ferromagnetism). The energy favorability of spin alignment is much smaller than overcoming the large band gap, so the spins are always paired. This means ferromagnetism can only occur in metal or small gap insulator where the energy favorability of having aligned spins is larger than the energy favorability of strictly filling the spin-unpolarized states below the fermi-level (before considering the interaction of electron spins). Is my understanding of the necessary condition for ferromagnetism correct? (ie, energy favorability of aligned electron being larger than band gap)? If this is correct, how can localized ferromagnetism exist at all?", "label": 0}
+{"snippet": "I have been studying Condensed matter physics, and there are some basics that are confusing me. Basically, when we find the dispersion relations of electrons in a lattice using the nearly free electron model, I do not get what the dispersion relation signifies physically. If we have one electron per orbital, I know that the band will be half-filled, which means that we have electron waves with those particular k values, but then how is the concept of Bloch wave packets incorporated? In Yang and Grivin, when the Bloch envelope is introduced, they integrate Blochs function over all k values, from which I thought all these electron waves superpose to make a wave packet of some average momentum. But then going forward, when considering the dispersion relation I got confused that will we still be looking at electrons in particular states individually? When we consider Bragg reflection at the boundaries of the Brillouin zone, does it mean that electrons with that crystal momentum form standing waves, all the while the other electrons with the other k values continue to propagate, and they all superpose to form a resultant wave or is it like when the wave packets k value becomes the k value at the boundary, it forms a standing wave?", "label": 0}
+{"snippet": "The potential at the surface of a conducting sphere is KQ/R where 'R' is the radius of the conducting sphere and even the electric field on the surface of the conducting sphere is maximum. And while taking a test charge from the surface to the inside the potential neither increases nor decreases because electric field inside the conducting sphere is zero, so whatever potential is on the surface, it is the same inside. But my question is why don't we need to do work on the test charge kept on the surface against the electric field on the surface to move the test charge to the inside of the sphere where electric field is zero? And if we would need to do work against electric field on the surface to move charge inside then potential inside will also be different from the surface. Thank You! NOTE- i am assuming that the conducting sphere is positively charged.", "label": 0}
+{"snippet": "Recently I have been learning about optimisation-techniques and built a simple \"gradient-descent brachistochrone solver thingy\" to try out some methods. One thing currently still hurting the results is the distancing of the points. Obviously, if they are first generated an equal distance on the x-axis apart from each-other, when the resulting graph becomes non-linear the distances between them start to vary quite significantly. Especially between the first two points there is obviously a massive \"hole\". What I would like to as is, if there is any well-established method of spacing these points by their distance from each-other instead of evenly along one axis. This at first doesn't seem to be too hard a problem; just move them a bit to be at the right place for their heights. This doesn't really work however, because when changing the \"x-position\" of the points their height must be re-adapted as well, leading to another distance-discrepancy and so on and so forth. As all algorithms I came up with required an ungodly number of iterations to complete, and I was unable to find the correct keywords to google this problem, this is now asked in form of a post on this forum. Thanks, Robbe.", "label": 0}
+{"snippet": "Now here is a potentially stupid question about something that has really been annoying me recently. In the pdf viewer panel in Texstudio, there are two buttons in the toolbar that change your type of cursor: a magnifying glass and a blue scroll 'cross-arrow'. If you never click on any of the two buttons, your cursor is the standard (Windows) white arrow cursor. I made the mistake of clicking on the magnifying glass, and there seems to be no way of getting my nice white arrow cursor back - instead I am stuck with either of the two Texstudio cursor types and I find them very ugly. There is no button to choose the standard cursor, nor does it revert if you open and close the panel, or Texstudio itself. Any help?", "label": 0}
+{"snippet": "In order for the jars to be sterilized for pickling tomatoes, they need to be boiled. But when one of the inverted jars was standing on the rack in the pot, it started sucking in the water that was boiling there (and sucked out almost all the water). The jars were turned over so that their open side was completely submerged in the water (so that approximately the entire surface of the neck of the jar was in contact with the grid). An approximate drawing of what is happening from the side: I took the jar out, emptied the water out of it, and put it back, but after a while it filled up again. The plastic grate on which the jars stood was uneven, and had holes in it. Why does this happen? Thank you!", "label": 0}
+{"snippet": "According to Kepler's First Law, the orbit of a planet is an ellipse round the sun with the sun at one focus. There's an inherent asymmetry in this. Instead of the sun being in the dead center, its shifted over a little bit. In the hydrogen atom, all the orbitals of the electron are symmetric about the proton at the dead center. Why is there no similar asymmetry? You can convert the function for the position of a classical simple harmonic oscillator with respect to time to a space dependent probability distribution where the probability is higher at the classic turning points where the velocity is at its lowest. The ground state of the quantum harmonic oscillator has a higher probability exactly between the classical turning points. The quantum solutions more closely match the classical probability at higher quantum numbers. I was thinking the classic \"lopsidedness\" of gravity could be recovered at higher quantum numbers for a Coulomb like potential Schrodinger Equation. But higher principle quantum numbers just enlarge the orbitals, they all remain symmetric about the proton. So that can't give you higher probabilities on an ellipse. The technique to recover classical behavior that works for the harmonic oscillator fails for Coulomb like potentials. Are there circumstances where any asymmetry appears in the probability of the electron, in particular, concentrations of probability along an ellipse?", "label": 0}
+{"snippet": "The Question: Boolean algebra is to classical logic like what is to relevant logic? Context: I guess this is a terminology question, so there's not much I can add, except that I've been interested in paraconsistent logic for a long time. Is the answer de Morgan algebra or is that something else? Meta Question: Is the question well-formed? Perhaps the question ought to be something like, Boolean algebra is to classical logic like what is to paraconsistent logic? I don't know. But: If the answer to the Meta Question (MQ) is yes, then please answer the main question. If the answer to the MQ is no, then please feel free to tell me why and answer what I hope will be a clear intended question. If the answer to the MQ is nonclassical, please explain.", "label": 0}
+{"snippet": "If I launch a ball into the sky it would reach a distance after which it would return into the ground transforming the potential energy into kinetic energy as it hits the ground This is similar to what happens at galactic scales, where material (like gases) from an outflow get expelled from the galaxy, they reach a distance where they turn back, and fall again into the galaxy, increasing their kinetic energy as they are attracted by gravity towards it However, the presence of dark energy at galactic scales, causes outflows to be less bound to their galaxy (and could even reach a distance where the influence of gravity and dark energy are balanced, beyond which, it would be expelled from the galaxy to never return: Is there a distance from a gravitational source where the influence of gravity and dark energy are balanced out?). This then can make these outflows reach a greater distance before turning back into the galaxy. Then, as the material would travel more distance towards the galaxy, and there would be a point in this trip where the influence of dark energy would be negligible (only leaving gravitational attraction), would the infalling material have more kinetic energy in this scenario (than in one without dark energy)?", "label": 0}
+{"snippet": "I finished calculus books like Thomas and currently reading a book on advanced calculus and another one on real analysis. I noticed recently that I don't solve enough \"hard problems\". I usually just solve the exercises on my books. so I figured that I need problem book(s) on calculus. I want a book(s) that has many exercise on calculus topics like Limits(without l'hopital) ,derivatives, integrals , series and sequence , multiple integrals etc... I also want them to be challenging and interesting problems and not \"too hard\" I consider myself on an intermediate level as the advanced exercises on Thomas book seems very easy to me, I also don't want \"forward substitute questions\" which is plugging numbers in formulas or straight forward use of a theorem or equation as I want to increase my problem solving skills. I will appreciate any suggestions ,thank you in advance .", "label": 0}
+{"snippet": "There is much talk of using lasers to bring down drones. That talk is followed by talk of protecting the drones by surfacing them with mirrors. Would that work or does light falling on a mirror impart all its energy to the mirror first before it can get re-emitted? I am aware that lasers themselves use internal mirrors to reflect the light so it would seem that if lasers don't destroy themselves then the energy is not absorbed: or lasers are cooled, I don't know which is the case. There are two questions here really: the Prime question is about the possible efficacy of protecting a drone by mirror surfacing. The more general 'underneath' question regards reflection of light. Is it so that all light falling on a surface must be absorbed by that surface before it can be 'reflected' ? It is my belief that it must. That 'reflection' is in fact re-emission.", "label": 0}
+{"snippet": "The textbook I'm using to study integral calculus usually assumes for it's proofs that the function takes on only positive values. The author says that if we divide the x-axis into intervals, and pick the point in each interval for which the value of the function at that point is a minimum at the interval, then we can approximate the area under the curve using inscribed rectangles. Specifically, the author says, this would be the lower sum. The upper sum is achieved by picking the point at each interval for which the value at that point is the maximum of the interval. I was thinking: wouldn't this be the opposite for negative functions. Because the upper sum would be achieved by taking the minimum at each interval, at the lower by taking the maximum at each interval. If I were to prove the same theorem for negative functions as well, is this the only difference that it makes? Or is this not the case? Because if the upper sum is always the greater numerically, and the lower sum is always the less numerically. And if \"negative area\" is a thing, then the lower sum would still be the one that is formed by taking the minimum at each point, and the upper by taking the maximum. So I am confused with the exact definitions right now and would enjoy guidance. Thank you in advance.", "label": 0}
+{"snippet": "If we spectroscopically observe a cloud of hot gas, which is on the whole not very absorbent, and which is not illuminated by a source behind it, we observe emission lines. How does this type of spectrum form? I had thought that those lines are those in which there are transitions of atoms is true, but I don't think that's enough. Why should all the material as a whole emit like that. Why are there these electronic transitions? And then: if there is a light source behind the material, one observes a spectrum that is in a way the negative of the one I put, i.e. the lines become absorption lines. I had thought that something different must be happening in the two cases, although I don't know what. And then again: if we knew nothing about electronic transitions and only wanted to consider the macroscopic properties of the gas (which could be composed of complicated molecules, in which there are not only electronic transitions but also other phenomena), could we still justify the fact that the emission and absorption spectra are the negative of each other? Thank you for any input; complex, articulate and in-depth answers are also welcome.", "label": 0}
+{"snippet": "Saw this on reddit: A: I'm a gun owner and I think any sort of gun sticker on a vehicle is cringe. -> B: Ditto any sort of camo, esp. grey/urban camo prints, sure go ahead and tell the world you're itching for an excuse to defend yourself with a gun while you wait for your latte -> -> C: But the hunting community uses camo! Do you think hunters are looking to kill people? Etc, where C continued to belabor the edge case. Now, to me, C misunderstood what B was saying and just continued to argue when it was clear that B didn't think that hunters were included in the group that they were talking about. It feels like C went out of their way to think that B was saying something about ALL people who wear camo -- but to me unless someone says \"ALL ___\" they just mean \"in general the people who ____\". Is there a term for \"deliberately misunderstanding what someone said so that you can argue about it\"? I see it all the time in forums/reddit/insta. Strawmanning doesn't seem adequate -- that's more about mischaracterizing someone's point so you can dismiss it. My best attempt at this is \"reaching for outrage\" but I've never heard any say that.", "label": 0}
+{"snippet": "In a recent Introductory course on logic, we were introduced to first order and propositional logic. The purpose of these concepts is portrayed as being a way for us to formalise the reasoning we use when we compose proofs in other branches of mathematics, but something about this bothers me, namely that in defining these theories, we extensively used set theory, and the axioms that it grants us, however one needs first order logic to actually describe the axioms of set theory, and so neither of these theories can truly \"precede\" the other. I read around a bit, and to some other question on this site, someone commented that this is fine, since for example we use the English language to describe the grammar rules of the English language, and we are satisfied with that, so w should be satisfied with this. But there's a reason language and mathematics are different fields of study, and I find this answer unsatisfactory. Is there some way to avoid this circular dependency in a meaningful way? Edit: from my understanding of the answers given to the purposed duplicates, the consensus is \"no we cannot\". Can we do one better and in fact prove that a sufficient formalisation without this property is not possible?", "label": 0}
+{"snippet": "I am studying the solubility of gases in liquids (flowing then into the study of oscillations of gas bubbles out of the liquid phase). The task at the moment is to familiarize myself with the laws of solubility of gases in liquids, gather material, etc. However, the only law I've discovered is Henry's Law. So far I'm only studying the simple case like water as a solvent and air as a gas. (no electrolytes in the liquid, no chemical reactions or anything). But for such a simple case, apart from Henry's Law, I have found nothing. Also I could not find any literature that could help in studying this question. I am wondering if there are other laws or equations of gas-liquid solubility for the simple air-water case, or is there nothing else besides Henry's law?", "label": 0}
+{"snippet": "I have been reading recently about tension. I don't exactly understand how it works. Here are my major doubts: Here, Tension is said to be acting in the opposite direction of mg. I will assume tension is not the net force across the rope because net force is zero due to newton's third law. Thus, tension must simply be the force exerted on an object by another one through a rope/chain/rod, etc.In this case, since in all cases of an object exerting force on another object, since the other object exerts an equal and opposite force, the tension here is really the reaction force to the force of gravity. However, if pulling a box along the ground with a force F, tension along the rope is said to be in the same direction as F, but can't it be said that it exists in both directions as both the pulling body and the mass exert equal forces on each other? What decides which direction is assigned to tension?", "label": 0}
+{"snippet": "Hi I was working on a problem concerning euclidean topology. I was doing the following exercise : The first statement seemed not to be true because for (i) to be the basis some topology the intersection of any most belong to the basis. As the intersection of any two open squares parallel to the axes is not necessarily a square, possible a rectangle. I assumed it wasn't the basis for any topology. This however didn't make sense when I looked at (ii) as far as I know the collection of all open discs is a basis for the euclidean topology. But the intersection of two disc is not always a disc. Which would mean it isn't the basis for any topology which left me confused. Does anyone know where I could be wrong? Thanks in advance.", "label": 0}
+{"snippet": "Original question: If continuity is the only requirement, here is the solution: Dimension of space of continuous functions But the proofs use trigonometric functions and polynomial functions, which are not monotonic. A further question is, what if I would like to impose additional features on the functions, say, concavity? It seems that one has to search for new bases if using constructive proof because the bases in the original proof may not satisfy the additional feature. I was wondering whether there is a generic way of proof to circumvent this problem (My guess is that no matter what the feature is [as long as the set is a linear space], the set of functions with this feature on an interval is infinite-dimensional). Edit: Thanks for pointing out it is not a vector space. So I changed my question (I thought this new question is equivalent to the original question but it turned out they are not). Edit again [revoked]: I think maybe I should add another constraint that the functions are bounded, or even more stringent: the codomain is an interval...Otherwise, the answer seems to be obviously \"No\".", "label": 0}
+{"snippet": "I'm currently starting to self study probability and statistic, a friend recommend me to use a book he has but his book does not go deep in the theorem and formula, instead it just state the equation and when to use it along with some properties but not the proof for the equation (for example: the chapter about the Poisson random variable just tells you how to use it and when, but lacks the proof of how mathematicians arrive at that complex equation ). I would like a book that is rigorous and proof-based for every problem in it ( like Tom M. Apostol's calculus books for example), im a colleague student and has good calculus and linear algebra background so an more advance than regular books is ok with me. Do you have any recommendation ?", "label": 0}
+{"snippet": "I'm new to Kalman filters. I have a use case similar to the one-dimensional train example. But I have railroad track with switches and mergers. So it's a non-trivial topology. I would like to model the system as a graph with N nodes and E directed edges. Each edge has length (weight) L. So the system state (e, x, v) consists of the current edge e, the distance x along the edge and velocity v. The edge e is a discrete (categorical) variable, which does not fit the standard Kalman Gaussian methods. Can the Kalman filter be extended to this? Measurements: I do have measurements of (e, x) and related position error err_x. There is no error related to the measured edge e. Prediction model: We can assume a constant speed model with zero-mean acceleration as in the Wikipedia example. In case of a prediction through a node with multiple outgoing edges (rail switch) I'm not sure if I should return a multi-modal distribution. I don't have a requirement that this should run in real-time, so it is possible to look ahead in the data and see which edge is taken. Or to use some kind of backwards smoothing is also ok. The graph is in priciple cyclic, but in practice length of the edges are way larger than the measurement errors.", "label": 0}
+{"snippet": "According to general relativity, if an object keeps moving and warping space and then gets lost by entering a black hole, do all of the distortions in the space caused by that object get lost? Or do the distortions get back to where they began? There is an answer by \"Navid\" that says it is possible for the distortions that happened in space by the object to disappear. Well, first of all, my imagination says that space will keep warping if an object keeps moving. Meaning that the peak of the distortion keeps increasing; now if there is a case where the distortions will disappear, then wouldn't this come to mind that a new black hole would happen because there is a loss of space? By new black hole, I mean the disappeared or lost space between the destination black hole and the beginning position of the object. My other imagination is that when objects move in space, they carry the space with themselves and don't keep stretching or warping the space.", "label": 0}
+{"snippet": "This question could be really out of the blue and might receive lots of downvotes, but bugging me quite a time and would appreciate your thoughts easily explained. We know that when we do work against nature force, we increase the potential energy of an object. Lifting a ball and putting it on the table increases potential energy of it as my putting work into it is transferred to the ball's potential energy. So as a sum up, for something to gain potential energy, some work must be done externally in opposite of nature. The same happens with charges. Taking away negative charge from positive increases potential energy of negative charge. It's all clear till this point, but if we imagine that worm by default appeared on a mountain, how would it have potential energy? As I understand, some external work must be done so the work is transfered/converted into its potential energy. What energy is transfered into worm's potential energy? I don't believe that gravitation itself gives potential energy to the worm.", "label": 0}
+{"snippet": "Industrial printing is based on autotypical colour mixing, the simultaneous effect of subtractive and additive colour mixing. This makes it possible to render a large set of colours using only four standardized colours (CMYK): I do understand additive and subtractive colour mixing but I struggle to understand how two dots next to each other, i.e. with no overlapping, additively mix to another colour. This is illustrated in the lower part of the following diagram, e.g. a red dot and a green dot are perceived as a blue dot (provided they are small/far enough): I guess the answer revolves around the size of the dots, the amplitude of the resulting light wave and some properties of the human eye but I could not find any detailed physical/mathematical relation between them so far.", "label": 0}
+{"snippet": "Assertion:Energy changes the kinetic only, and changes in potential require an intermediate change in kinetic. Reasoning: eg:when I throw a ball upward I do work/transfer energy,At the topmost point, there's a changed potential which is an effect of changing its position through its ke. eg:when I lift a weight at constant ke,Im transferring energy to increase the kinetic as I'm doing work against gravity , I can't change the potential without changing the kinetic. I did some research but the only answer I could find is an input of energy can increase both kinetic and potential but I don't see how it changes the potential without changing the kinetic. this seems to make sense for a lot of situations and i need to realize where im going wrong with this My question is: Is this valid and if it is does it hold for all fields in physics? Can energy only change the kinetic and require an intermediate change in kinetic to alter the potential?", "label": 0}
+{"snippet": "This is my current understanding of convolution after having read through this blog post The convolution operator can be thought of as an operation of linear superposition. If we have the response of a linear system to a unit impulse, the overall response to an arbitrary input signal may be constructed by taking a linear superposition of the unit impulse responses accordingly translated and scaled. This can be done through the convolution integral. On the other hand, the convolution theorem allows us to perform the equivalent convolution operation by first taking the pointwise product of their Fourier transforms, then taking the inverse transform. In other words, the convolution operation is diagonalized in Fourier space, and acts on each Fourier component of the input signal by multiplying it by its eigenvalue, the corresponding Fourier coefficient from the unit impulse response. While I follow the logic leading up to either approach, my difficulty is in finding the connection between the two - how does it intuitivly make sense that superimposing unit impuse functions accordingly to the input signal has the equivalent effect to multiplying the Fourier spectra of the two functions?", "label": 0}
+{"snippet": "There are two different senses in which we use the word \"attribute\"; for example, I can describe someone as \"blond\", which is a hair color. We say \"blond\" is a characteristic or attribute, but it is clearly the characteristic or attribute with regards to the characteristic or attribute \"hair color\" - \"blond\" is not how they smell or how tall they are, it's one of a set of attributes that fall under the attribute \"hair color\". I have called both \"blond\" and \"hair color\" with the same word, \"attribute\", here, and, as far as I know, all the popular synonyms of \"attribute\" really are synonyms - \"characteristic\", \"trait\", \"property\", etc. Is there any way or term or expression to verbalize the difference between an attribute in the sense of what it is - in this case, a person really being blond - and an attribute in the sense of what \"category\" that attribute belongs to - in this case, blond being a hair color? To put it another way, for the sentence \"For the attribute \"hair color\", he has the attribute \"blond\".\", I would like to find a different word for one or both of the uses of \"attribute\" here, so that the words used unambiguously convey that one is the actual attribute (blond), and the other is the \"category of attributes\" (hair color).", "label": 0}
+{"snippet": "When conic sections are taught in high school, the concept of a focus is introduced from the geometric prespective. Well, at least if your teacher is any good. Later, once the algebraic equation of the conic is established, we find that this special geometric point can be in some way derived from the coefficients of the expressions in the algebraic equation for the conic. This is typically derived in school by moving back and forth between arguments involving that of geometric observation and that of algebraic manipulation. From an algebraic prespective, it seems quite unintuitive to me that there is a special point outside the curve which is so critical to understanding the curves' geometric properties. In a way, I see it as more of a meaningful quantity than a root. Now, my question is: Using advanced mathematics, what is the algebraic intuition behind the focus? Can we generalize this intuition to talk about foci of higher degree curves? And, are there analogoues to points like focus for higher degree algebraic curves?", "label": 0}
+{"snippet": "The classical analogy for understanding gravity in Einsteinian physics is picturing a sort of fabric that sinks when an object rests on it. Thus, due to this curvature, objects will move towards each other because of the inherent structure of the fabric-object relationship. However, in this analogy, the objects move towards each other because gravity acts on them. In other words, the curvature itself is not enough to explain this phenomenon. Thus, howcome gravity be defined as the curvature of space-time if curvature itself is not enough to have an effect on two masses? I feel like this analogy tries to explain one concept (gravity) as the unison of two concepts (curvature and a force akin to gravity (redundant)). I mean, try doing this experiment in space. Set a fabric, add two masses and curvature but for some reason the masses don't move towards each other; because gravity doesn't act on them! (I know technically it does but for the sakes of the mental experiment it doesn't).", "label": 0}
+{"snippet": "I have a doubt in this question, Diagram given below In the Question it is asked that \"calculate the final velocity of the block in the figure\" and in the solutions it is given that the work done by normal force exerted by the surface is not considered when applying the work-energy theorem but according to the proof of the work-energy theorem, the \"'net' external force X displacement upto which the force was applied is equal to the change in kinetic energy of the object.\" (could use integration by taking the variable force to be constant for infinitely small time intervals) but by this definition normal force should also be added to calculate the net external force on the object as it also always acts in opposite directions to gravity (with different magnitudes obviously) So why is the normal force not considered here? Is the question/solution wrong? If it is correct, why? And what is the mathematical proof of not considering the normal force when applying the work-energy theorem?", "label": 0}
+{"snippet": "Most introductory logic textbooks that I have skimmed through in a while, keep the terms 'sentence' and 'expression' undefined. I would intuitively see Earth is round. Why didn't Harry come to the party? Come here, Harry! x lives in Norway. all as sentences. However, 'x lives in Norway' is usually not taken to be a sentence in logic because it contains a variable. It rather gives sentences after variables have been replaced by constants. It seems to me that the term 'expression' has a broader meaning and sentences are special cases of expressions. But still what exactly is an expression? Would arh ahfb hghd udh be an expression? Would 'arh', 'udh', etc. be expressions? If 'arh ahfb hghd udh' is an expression , would it be a sentence? Is it necessary for an expression to have a meaning? All these troubles imo are stemming from a lack of definition of terms 'sentence' and 'expression'. How exactly can we define these terms?", "label": 0}
+{"snippet": "So, as I have read and even been taught by my teachers, sign convention in trigonometric functions is based on the location of the respective x and y points denoting the coordinates of a particle going around a circle. Although I am kind of sure that I am right but I still want to confirm this one thing: When determining the slope of a graph, we encounter both obtuse and acute angles (the angle made by the tangent of the graph at a particular point on it with the x axis). So, is it just a coincidence that tan(a)(the angle made by the tangent) is positive in case of acute angles and negative in case of obtuse angles in both this graphical sense as well as tan(a) for a point on a circle? Because if a is obtuse(graph), that would mean that the quantity in the y axis is decreasing and if it is increasing, the angle is positive. So, I just want to ask that here tan(a) just happens to be equal to the slope of the graph right? I checked for other trigonometric functions and well sin(a) seems to be negative if the angle is obtuse in the graphical sense but positive in the circular sense. Edit: I have added a picture for clarity about my definition of graphical and circular sense.", "label": 0}
+{"snippet": "I want to learn calculus by myself, I searched a lot on internet as well as math stack exchange for suggestions for best calculus books, I know a lot of famous books like Stewart Thomas but I do not like the way it is presented. I want to learn rigorous mathematics from books like Apostol Spivak Courhant Serge-Lang, but I am not sure if I can take them, the level of proofs and logic they need, I am afraid if I buy them and not able to solve because high advanced level they are, some motivations is needed and also guide me if I need some more books as prerequisite to understand Apostol Spivak Courhant I am reading books like how to solve it by George Polya, if you can suggest some books which refine logic and thinking please suggest me. I am also someone who enjoys mathematics but not want to learn just basics. its more like dream if I one day able to read and understand books like real analysis by Walter Rudin THANK YOU", "label": 0}
+{"snippet": "I am trying to write down a complete/detailed definition for the parity symmetry. Symmetry as a concept is different in mathematics and in physics. There are also many other concepts which differ in their use in physics and mathematics i.e : symmetry group, discrete/continuous group, continuous and discrete symmetry etc. I am trying to consider the following concepts and phrases for the definition: Parity symmetry. Parity transformation. Invariant property (invariance and symmetry while similar they also differ in use) parity symmetry group. discrete symmetry group. Then: In physics: \"Parity symmetry it describes the invariance of a system, it's properties, under the parirty transformation, a spatial transformation, represented via the symmetry group of parity, a discrete symmetry group.\" Is my definition, while including the above listed phrases accurate? Also, can someone show me the fact that there is a group for parity? I.e elements, neutral element, inverse etc? In other words, which are the elements and the operation in the symmetry group of parity?", "label": 0}
+{"snippet": "As we know, two bodies undergo radiative heat exchange due to each emitting a spectrum of light according to its temperature (blackbody radiation). When one body is hotter than the other, it emits a higher magnitude of light at each frequency. Thus the heat flow is from the hotter body to the colder body, even though light is exchanged in both directions. My question: as the photoelectric effect showed even a large magnitude of light of the 'wrong' frequency can't eject an electron, has the experiment been done where a large magnitude (high amount of W, i.e. not according to blackbody radiation) of low-frequency light was directed to an object to observe if the large amount of low-frequency light heats the object? Or is it not possible for other reasons?", "label": 0}
+{"snippet": "Suppose you trying to sell the idea of the Yoneda embedding to perhaps a rather mixed bunch of students (so you can't presuppose too much mathematical background). Still you can say Think of a group-as-a-category (one object, all the arrows isomorphisms). Then applying the Yoneda embedding theorem we get ... [a bit of chat] ... hey, Cayley's Theorem. Think of a poset-as-a-category. Then applying the Yoneda embedding we get ... [a bit more chat] ... hey, the familiar result that a poset is isomorphic to a certain bunch of subsets of its objects (upper sets) ordered by inclusion. Those are in fact the usual textbook offerings. But what third or fourth examples of such embeddings (not requiring the fully caffeinated Lemma) might work as equally accessible? Or maybe not quite as accessible but more interesting??", "label": 0}
+{"snippet": "(Look at the picture) Let's assume there is an horizontal plane impacted by diagonal airflow with components from coming downwards and ahead. If we say that the airflow is fully deviated by the horizontal window (which isn't allowed to move through space), the outcoming airflow has only an horizontal component greater than the one it had before. So, if the wing generated a force in order to change airflow direction, the airflow generated an opposite force on the wing. According to this theory as long as the horizontal component of the airflow isn't reduced, the wing is pushed both upwards and forewards, even though the airflow comes from ahead (which is counterintuitive). Is that correct or am I missing something, since I would normally think the wing must be pushed backwards?", "label": 0}
+{"snippet": "I'm finally closing some gaps in sound waves, so forgive me for lots of questions. In metal, it's said sound travels fastest. The reason is molecules are tightly packed(more dense) in metals than in air lets say, and collisions with each other will be fast as each molecule doesn't have to travel long before it collides with another one, hence it travels faster. Though, I wonder even though it will be faster, we should have disadvantage here which is the signal created by source won't be much weak than it would be in air. My logical thinking is since molecules are tightly packed, it will be harder to transfer energy from particle to next particle(more tightly packed, harder to vibrate the same frequency as created by source). So even though sound travels fast in metal, it should give us weaker signal in the end than in air. Would this logical thinking be correct somehow?", "label": 0}
+{"snippet": "I'd like to know how the parallel transportation behaves in non-Levi-Civita connections and how does one realize it formally. I know that parallel transportation along some piece-smooth curve is defined through moving by geodesics: say, in case of conformal connection, one transports a vector along a short geodesic close to a piece of the given curve preserving the angle at each moment of moving, so, for example moving by a horizontal line in the flat realization of the Lobachevsky plane (where geodesics are semicircles and vertical lines) one gets that a vector rotates uniformly. But how does one understand the parallel transport in general (of a general connection given on a principal bundle)? So, are there any axioms of the parallel transport except being an isomorphism between model spaces in close points on a smooth manifold and \"additivity: moving along one piece of a curve and then the second\" and \"inverse: going in both sides\" axioms?", "label": 0}
+{"snippet": "I heard that if a dish of mercury is heated by a moving flame placed under it, the mercury will spin around - Sanderson [Ivan T. Sanderson, biologist and paranormal researcher] then goes on to make the basic observation that a circular dish of mercury revolves in a contrary manner to a naked flame circulated below it, and that it gathers speed until it exceeds the speed of revolution of said flame. Now, as in this question Why is mercury magnetic? , if an electric current is passed through the mercury in the presence of a magnetic field, the mercury will spin around, but I can't find any reference to a version with a flame. Is this true/would this theoretically be true? If so, why? Or was the person who said this just misremembering the electric current version?", "label": 0}
+{"snippet": "While calculating the electric potential at a point near charged bodies such as a uniform ring, hollow shell and solid sphere, iv'e seen that the potential at a point is equal to: V = KQ/D(avg) Here D average denotes the average distance between point of potential measurement and the elements of the object. It is somewhat like the distance between the \"Centre of charge of the body\" and the point of measurement. This seems to work out for my few cases which ive tried. It also sometimes works for electric field at a point by replacing D with D squared, but fails in some cases such as with a uniform ring. My doubt: Is this approach of calculating \"Centre of charge\" always applicable for potential at a point? Why so? And if yes, why does it fail for electric field strength at a point?", "label": 0}
+{"snippet": "I read several times about global warming leading to more exteme weather events, i.e. flooding, droughts and even winter storms occuring at higher rates and with more intensity. So, higher temperature supposedly leads to an increase in the variance of the probability distribution of the weather. This is not obvious at all. Naively, one might think that climate change would just shift the temperatures by several degrees. So, is there any physical mechanism, explaining the increase in the variance of the weather? I thought about the equilibrium vapor pressure of water at higher temperatures but I did not come useful conclusions. Btw, a standard physical model is the damped harmonic oscillator. Is there any similar model to demonstrate the effects of globabl warming or meteorolgy and climate change? I'm thinking of something like a closed box with stone islands and water under some radiation.", "label": 0}
+{"snippet": "Suppose a player wishes to move on a square lattice graph without diagonals. Vertices on this graph have a chance (fixed or time-dependent, e.g. cumulative density of X~Po(t) with range n to infinity) to become a \"point of interest\". Upon visiting such vertex, it will revert to a \"normal\" vertex, which can become a \"point of interest\" again. The player wishes to visit all \"points of interest\", but travelling through the least number of edges. The Elevator Algorithm seems to solve a simplified version of this problem, where the \"player\" can only travel in two directions. My guess is that, if the player starts from the center of the lattice graph, the optimal choice would be either try to walk over all the vertices exactly once for multiple rounds (Hamiltonian path maybe?) or to stand still. However, this guess only works for the fixed-chance scenario. Thus, I wish to know how an optimal strategy would be derived, given a certain number of lattices are already \"points of interests\", especially when vertices convert to \"points of interests\" with a time-dependent chance.", "label": 0}
+{"snippet": "I was recently reading about the Hafele-Keating experiment and asking, how does time in the plane which has flow westwards could have passed faster than on the surface of the earth if the frame of reference was here. It was then I realised that the frame of reference in the experiment was chosen to be the center of the earth. But now I'm asking what would have happened, if one really chose the frame of reference to be on the surface of earth. Then, the plane should have had a velocity greater than that of the inertial observer on the surface of the earth in both direction (in one even greater due to earth's rotation) and time should have passed in both situations slower with reference to the observer on the surface of the earth. I'm not sure if these assumptions are correct, as I've just started to learn SRT on my own.", "label": 0}
+{"snippet": "Isobars are atoms (nuclides) of different chemical elements that have the same number of nucleons. According to the https://en.wikipedia.org/wiki/Mattauch_isobar_rule if you have two adjacent elements on the periodic table have isotopes of the same mass number, one of these isotopes must be radioactive. The decay can happen by positron emission, Electron capture of Beta decay. When electron capture occurs, there will be a hole in the first electron shell that will quickly be filled by an electron from a higher shell, giving of what's called a https://en.wikipedia.org/wiki/Characteristic_X-ray Something I've realised though is that if the Isobar with more protons is the heavier Nuclide, but the mass difference is less then the Characteristic X-ray of the lighter Nuclide, then it would be impossible to decat via capture of an electron from the innermost shell. Are there any Nuclides where this is the case?", "label": 0}
+{"snippet": "This may be a very basic question, please excuse my lack of knowledge but I don't seem to understand the concept of anti-matter gravity. Upon research, many sources align with the conclusion that anti-matter reacts to gravity similarly to matter. ie. that it space-time warps around its mass. If we consider a particle/anti-particle pair we would expect and conclude that there is no gravity (warp in space-time) by this. ie. Just the vaccum of space. However, if we consider them as separate particles, then their corresponding gravities -pulling spacetime in the same direction, would add together (since gravity is not reversed for anti-matter). We would expect to increase the total gravity as they approach each other (greater density of mass in space-time). However, as we know, a pair would have no gravitational effects. It's hypothetical but to clarify; consider a plane vacuum with one particle and one antiparticle beginning to collide. Disregarding their electrical attraction, they each warp space-time in the same direction due to their masses. However, after the collision (as a pair) there is no gravity. So, how would their gravitational potentials dissipate and react as they approach each other and collide.", "label": 0}
+{"snippet": "I'm trying to create a cheap concave lens effect for a class I'm doing. It seems like a convex lens starts to create a similar effect anywhere passed twice it's focal length. It also makes everything upside down, but that's okay. Are the effects of a convex lens a demonstrational equivalent to a concave lens once you pass double the focal length? Ignoring the upside down aspect. This is for a hand made kaleidoscopes library program to give you some idea of the stakes. EDIT: I set up a magnifying glass and walked some distance away from it. What I see through it is: upside down, in focus, and inclusive of a wider view than what it blocks. I can see an entire shed within the lens, while it does not block me from seeing the shed around it.", "label": 0}
+{"snippet": "Applied Force is our label for a contact force that a person exerts. When an applied force acts at an angle, it is actually a combination of two forces: normal and friction. The component of the applied force that is perpendicular to the surface is a normal force, and the component parallel to the surface is a friction force. I have two questions; When the applied force is at an angle then forces of friction and normal are between the surface of the object and the hand, not between the object and the ground so can we say that the parallel component of applied force is responsible for the acceleration of the object? (Is it okay to say that it is the friction force between our hand and the object that accelerates the object)? What will happen if an applied force acts on a thread also can we say that the applied force is the combination of normal and friction force between my hands and thread if so then tension force will be also called a combination of normal force and friction force or if I am wrong then please correct me.", "label": 0}
+{"snippet": "I believe this question would have been asked before, but not like this. The popular answer to this question is that the slide-release action of a bow sets up vibrations in the strings, of which ultimately only the resonant frequencies would survive. Plucking a guitar string sets up a transverse oscillation on the strings at its resonant frequencies. But when you play a violin, you slide a bow over the strings. We know that the strings first attach to the bow, then release once the static friction is overcome, and this process repeats again and again. But how does this process ensure periodicity? We don't hear a discontinuous noise from a violin; rather we hear smooth continuous notes. How do the strings know when to catch the bow, and when to release them ?", "label": 0}
+{"snippet": "Bell's therorem seems to disprove localism because measuring, let's say spin of an entangled electron, seem to communicate the measurement to it's another pair instantaneously. But isn't another thing possible? Maybe the electrons are not communicating anything and instead the two instruments which are measuring the electrons \"know\" at what angle the other instrument is measuring the other electron and that is a part of the measuring process of instrument and thus the Bell's equality is violated but local realism is still valid. Here the two instruments and the people who are performing the experiments are in some kind of weird sync where they cannot measure arbitrarily in any direction but instead the measurement angles are predetermined before hand and the instruments already know the angles with of each other which are used to measure, hence the spin directions can be correlated. This would mean that Universe is deterministic but also locally real. Is this at least theoretically possible? If it is possible wouldn't it be more saner theory to adopt rather than throwing local realism away? Why? Why not?", "label": 0}
+{"snippet": "In \"Gravitation\" by Misner, Thorne and Wheeler the authors pose the following puzzle: The metric perturbation of the wave changes the scale of the distances slightly, but also correspondingly changes the scale of time. Therefore does not any possibility of any really meaningful and measurable effect cancel out? And they also give an answer: The widened separation between the geodesics is not a local effect but a cumulative one. [...] When one investigates the separation of geodesics [...] over a large number of periods he finds a cumulative, systematic, net slow bending of the rapidly wiggling geodesics toward each other. This small, attractive acceleration is evidence in gravitation physics [...]. Is LIGO measuring only a net acceleration (or maybe a net displacement as a cause of the net acceleration) of the mirrors instead of a wiggling? The LIGO collaboration states the opposite. On the FAQ page (https://www.ligo.caltech.edu/page/faq) you can find Back and forth the waves pass through (interfere with) each other as the arms themselves change length, causing light interference that ranges fully between totally destructive to totally constructive. In other words, instead of nothing coming out of the interferometer, a flicker of light appears. And how could we obtain the frequency of the gravitational wave when averaging over a large number of periods? But if I misunderstood the statements in the book \"Gravitation\", what is the correct solution of the puzzle stated in the beginning?", "label": 0}
+{"snippet": "Consider a simple gas (or fluid) within a box at thermal equilibrium. I manage to give a kick to one particle within the gas, such that it acquires some momentum. After some time, it should be expected that this localized energy (or momentum) input would be just distributed such that Boltzmann distribution is recovered. But how does this recovery take place ? The simplest mode of transport of this momentum disturbance could be for example a sound mode, that is, a sequence of kicks in the same direction of the initial kick is generated starting from the kicked particle. But I can also imagine that after the first kick, momentum is transferred in random walk slow manner. Here the momentum disturbance would be tracing a some kind of random trajectory instead of a linear trajectory as it would be for a sound mode. How to know which kinds of modes are taking place (roughly depending on kick strength, density, temperature and so on..) ?", "label": 0}
+{"snippet": "In this post Reconstructing isomorphisms via the bijection between the corresponding posets of subobjects I asked for the possibility of constructing an isomorphism via the order-preserving bijection between the corresponding posets of subobjects. In the case of the category of sets just work with the singletons to define the bijection - I'm working with classical NGB set theory - Now, an interesting counterexample has been exhibited in the aforementioned post. However, I've another question. Well, which are the categories sharing the same property as set (i.e. to give rise to an isomorphism between the corresponding posets of subobjects). I was thinking to toposes. Might it be a good way or are there also counterexamples coming from toposes? Actualy, there exists a paper by Barr and Diaconescu entitled \"Atomic Toposes\" (https://www.math.mcgill.ca/barr/papers/atom.top.pdf). Well, I think that what I'm searching for is related to the fact that the subobject lattice is atomistic, i.e. every element may be expressed as the join of its atoms. It is property related to my problem?", "label": 0}
+{"snippet": "If something is said and people understand it, sounds like a word to me. If people didn't understand it, I would think they would rather say, \"what do you mean?\", than making it a word after a definition is explained. Or are there exceptions I'm not thinking of? Dictionary or not, if people understand something, even if just locally, it's a word. Of course, there is some irony in people seemingly claiming to have a mastery of language who do not know what the word 'word' means. One example may be this David Cross bit I've heard, where he said 'irregardless' isn't a word, even though it's been used for a long time and is understood. However, it is considered nonstandard in at least some dictionaries. There may be cases where something incorrectly thinks that a valid word isn't part of standard English even though it actually is. I would still include this in the scope of the question, because they they think it's wrong, whether they are right or not. If someone is making a mistake, if it's still understood, it'd still be a word, for that moment, at least. A more common example may be the use of \"ain't\". (Kids exclaiming 'that's not a word' out of disbelief would be an exception, but I think it's a rather different usage.)", "label": 0}
+{"snippet": "I read this fascinating paper (RG). The total collision is a well-known singularity in Newton mechanics: the distances become zero and, therefore, the potential becomes infinite. In a paper before that one above, Paula Reichert describes a try to calculate through the singularity using shape dynamics. In shape dynamics, the absolute background space is abandoned and only relative positions and especially angles are considered. Unfortunately, shape dynamics alone turns out not to be sufficient to calculate through the singularity. Then, in the paper above, they make a reference to this paper where they calculate through the big bang singularity by adding a scalar \"stiff matter\" field in the Bianchi IX universe. How can one understand this scalar field? Since shape dynamics doesn't rely on an absolute space as a background, it comes to my mind that this scalar field may be interpreted as space itself, space that surrounds every single mass point as a field. Is that interpretation right or wrong? If wrong, how can one get an understanding for this scalar field?", "label": 0}
+{"snippet": "I'm attempting to develop an understanding of how equations are developed and wondered whether or not all equations started their development in the quest to document observable phenomenon or are there any 'purely synthetic' equations, which are developed from the basis of a thought in order to produce numeric results which are useful in some way. Put another way: Do observations of phenomenon drive the development of equations or does a conceptual need for a tool drive their development instead? The reason I ask, is because as someone who is a novice in mathematics (arithmetic skill, elementary algebra and descriptive stats), the choice of the construction of equations / their form always leads me to wonder why this form was chosen. In particular as I delve further into stats I have seen descriptions where certain equations may be adjusted based 'on ones need' which further deepens the difficulty of just using a tool blindly and wondering at what point or in what way I can develop the skill to discern how to choose how to alter an equation to better fit a desired outcome... I attempted to articulate this originally HERE, then asked about whether it made sense to start a new question HERE, but for lack of feedback in either, I decided to open this query and post any positive results as link backs to those two questions for the community's later use. If there is a better way to approach asking this please let me know and I'll be happy to adjust accordingly.", "label": 0}
+{"snippet": "In a laboratory a vessel was built which can sustain high pressure, thermostats and pressure gauge were connected, assuming closed system, dry ice was introduced in closed vessel, the temperature of vessel was increased the sublimation of dry ice resulted in formation of gaseous carbon dioxide increasing pressure in vessel, the increased pressure and temperature resulted in liquid carbon dioxide formation, after more heating critical temperature was reached and superfluid carbon dioxide was obtained, at these state gas and liquid phases became indistinguishable, ice was put upon vessel surface which resulted in decrease of temperature and the liquid carbon dioxide appeared again. My question is if we see typical pressure vs volume diagram it is observed that above critical conditions it is not possible to condense fluid by reducing temperature since the point will lie above the dome, then how come we see condensation of superfluid carbon dioxide in our experiment ? Note: the boundary liquid gas interface was seen disappearing in as it's typically seen in superfluids hence it's confirm that we had superfluid carbon dioxide.", "label": 0}
+{"snippet": "I encountered a proof that the empty set is a subset of every set via this comment(Is \"The empty set is a subset of any set\" a convention?) which shows that it cannot be false that the empty set is a subset of every set. Without necessarily going into a proof of how the empty set is a subset of every set, I was wondering why the fact that it cannot be false that the empty set is a subset of every set shows that this is true- could it not be the case that the concept of subsets is meaningless with regards to the empty set, and it is not enough to show that it could not be false; that this statement could neither true or false as it has no meaning in this context? Also, I would appreciate some explanation as to how this condition holds \"vacuously\" as far as terminology, as I have learned that for an implication to be vacuously true, it is true when it's hypothesis is false. Thanks", "label": 0}
+{"snippet": "I have a very abstract at the same time awkward question. In many formulas across physics we need to take several approximations and often we derive formula from previous formula which had certain approximations in them. By error analysis we know that errors keep getting carried forward. Hypothetically can there be situation in future when almost every advanced formula we use, which is a result of derivation of several heavily derived formulas(I am referring several heavily derived formulas as those which are derived from highly approximated formula), be filled error quite significantly high and our calculations are thrown off by huge percentage of error and inaccuracy. Can the error propagation in formula and theorems be a major problem we face in the future of physics? (Please note that I am not talking approximations involved in process of integration.) I am just curious to know to what level the approximations we take, effect the calculations we perform.I know this is a very awkwardly framed question. If you have any suggestions on improving the language of the question or any other changes, please let me know.", "label": 0}
+{"snippet": "Per wikipedia: natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force. Let's take a wine glass as an example. The wine glass sits on a table, it is not visibly moving. But since natural frequency exists, therefore it is oscillate on some minute scale. Where does the oscillation come from? Is it from the electrons and protons that are whizzing inside of the glass and getting excited due to stochastic heat? Is it because protons are hitting the surface of the glass? Or is it oscillating due to the minor tremor in the earth? Or perhaps the minute attractive force exerted upon it by all other objects? In each case, it is clear that there is a driving force: heat, proton's impact force, tremor. So clearly natural frequency must be associated with a type of oscillation that's not any one of the above. So where does the oscillation come from instead? It seems that given any source of this oscillation, you can identify a driving force. Hence such driving force is never absent, hence there is no natural frequency. Are all objects naturally oscillatory and that natural frequency is like a fundamental aspect of an object, such as its 'mass'? If so, can we identify this natural frequency in some way? E.g., I want to know my body's natural frequency at this moment.", "label": 0}
+{"snippet": "My admittedly limited understanding of QM is that it is a matter of probabilities whether or not a photon is (re)transmitted through a polarising filter and that these are a function of the relative orientation of the polarization of the photon and that of the filter. Unfortunately, a single detection event cannot distinguish a very likely from a very unlikely one. Since the same applies to a case in which the photon is absorbed, it seems that not much information, if any, can be gained, when what would be nice is that we could learn something about the polarisation of the photon for example. Even if statistics are collected on streams of successive photons, they're likely each to be oriented differently in relation to the filter, so not much information can be gained by examining the statistics either.", "label": 0}
+{"snippet": "Currently i include png/jpg files with graphicx package compiling with lualatex, no problem, in particular no error message because of bounding box not found. This question is about historic ways to compile because I don't want to break old code. First question: Is it true that when compiling into pdf with any of the modern compilers like lualatex with graphicx package command includegraphics, there is no special treatment necessary to get a bounding box? Second, I seem to have no problem with bounding box either when compiling into dvi. What makes me a bit nervous is, that I remember that message. I am sure i used package bmpsize and also command ebb to get the bounding box and this was necessary to avoid the error message cannot determine the size of the graphic But I cannot remember the details. My question is whether the issue with the bounding box is resolved by new compilers, even if compiling into dvi or xdv. I made a remark by hand, that bmpsize does not work with xelatex. Is it obsolete? May it be the case that behavior depends on the source of the jpg/png? Are there aspects related with the dvi to pdf converters? Are there other formats needing bmpsize or ebb? Please feel free to mention other aspects also. I am afraid about dropping ebb or bmpsize when there is still a use case. In the meantime I found out that my problem is specific for texlive distribution. Seemingly miktex neither provides bmpsize nor ebb.", "label": 0}
+{"snippet": "The following pop science video discusses the experimental difficulty of measuring \"quanta\" of gravity. It seems to me that a significant argument involves how it would be difficult to investigate fluctuations of gravity on the plank scale, requiring detection methods that have densities that would collapse as a black hole. In optics, one way of \"seeing\" a photon is by interfering it with using homodyne detection to interfere it with a strong signal. The strong signal essentially magnifies the signal, allowing it to be seen by detectors that are much less sensitive than single photon level. Could such a scheme be used to measure gravitons? For example, if strong gravitational waves can be detected by LIGO, shouldn't a sufficiently strong wave already be measuring the \"amplitude\" statistics of the graviton? Similar to how a local oscillator (in a balanced homodyne detector) measures the shot noise (amplitude statistics) of the vacuum. I suppose the issue is that this needs to be a particuarly strong wave signal so be above experimental noise?", "label": 0}
+{"snippet": "In the diagram, OA is perpendicular to PQ. O is the centre of the circle. AC and EP meet at B on the circle and QC and AE meet at D on the circle. The goal is to prove that AP=AQ. I had tried to prove this by drawing a line through E parallel to PQ and I had proved some of the triangles were similar. However, this is the part where I got stuck. I drew a line parallel to PQ through E. I named the meeting point between PE and QC \"G\", between the line produced at E and CQ \"F\" and between CA and the line produced at E \"H\". I then proved that triangle CBG is similar to DEG, CAD is similar to BAE, HBE is similar to ABP, FDE is similar to ADQ and FGE is similar to PGQ. It is at this point when I got stuck.", "label": 0}
+{"snippet": "Recently, I tried to understand the effect of Quantum levitation. I read that there is some well-known fact: Relative distance between superconductor and magnet must be preserved, because of flux pinning mostly occurred in type II superconductor. My rough understanding about this is, quantisation of (penetrated) magnetic flux inside the superconductor, and continuity of magnetic flux depending on the distance from the magnet, induces the fixation of relative distance (It couldn't move continuously after fixation because there is no no-jump-but-continuous motion). I could understand the second part of the video. I guess it's because of the circular symmetry of magnetic field. There is nothing hard to understand the story. However, what about the first part? If we rotate the magnet, then what makes the superconductor follow it? Obviously, it's due to the preservation of relative distance in layman's terms. However, could we more elaborate on it? For instance, in the context of classical electrodynamics, someone could try to explain this by the induced electric fields and currents from time-varying magnetic fields. However, it may not be an answer because of the quantum nature of a superconductor. The quantised flux varies by the time dependent magnetic field, but could we describe such a variation in terms of the motion of the magnet?, and so, could we derive and describe the equation of motion of a superconductor?", "label": 0}
+{"snippet": "I've noticed this quite often from Disney sound tracks. Lyrics are in a certain rhyming scheme - one line happens and the next line approaches the end of the line, but the last word subverts the rhyme. I have looked at this question and feel it's related, but not the same effect. Example: \"In Summer\" from Olaf in Frozen Da da, da doo, a bubba bubba boo The hot and the cold are both so intense Put them together ? it just makes sense! Rata ta ta dada dada da doo Winter's a good time to stay in and cuddle But put me in summer and I'll be a happy snowman! Obviously, the expectation is that the word is \"puddle\" It feels like a lyrical version of deceptive cadence, but I cannot find a succinct term for such an effect. The linked question accepts the answer \"Broken Lyric\" or \"Enjambment\", which may still be the answer here, but I am certain that these are two different effects.", "label": 0}
+{"snippet": "I am a first year student of applied mathematics. I currently find myself always trying to explain any phenomenon with mathematical models- the few ones (models) that I encountered till now. I always try to fit phenomenas to models like a data scientist does when he fits data to models. Recently I found this book: Robert B. Banks Growth and Diffusion Phenomena: Mathematical Frameworks and Applications This book is different from other applied mathematics books in the sense that it focuses on a particular model unlike others that try to model the whole world in a single book. It particularly focuses on growth and diffusion phenomena. Which is , to me , great because this book studies these two models in great detail rather than just stating many models on the surface level. I also found some book that is specific to some single phenomenon like this book on Hysteresis Mathematical Models of Hysteresis and their Applications Can someone please recommend to me some books like these that describes a certain phenomena or discusses a certain mathematical framework to study in detail and apply some phenomena? Any book that discusses and models in detail some phenomena: could be growth,could be decline, could be (what happens in the limiting case)- type of thing, could be something else, could be anything...", "label": 0}
+{"snippet": "The boundary of a simple closed curve has each point on it, touching two adjacent points one on each side. Can the entire boundary be represented as a series of circles of the same diameter \"d\" where each circle is touching the adjacent circle at exactly one point only without overlap in areas between the two circles. This will allow us to approximate the simple closed curve with a polygon where each side of the polygon is represented by a line joining the centers of adjacent circles and at a distance equal to the diameter \"d\" of the circle. Such approximation would imply that a inscribed square exists on the polygon (Toeplitz conjecture special cases) and therefore an \"almost square\" whose vertices are within the error range of the diameter of the circle must exist. Shrinking the size of the circles used will reduce the error of the \"almost squares\" to smaller and smaller values.", "label": 0}
+{"snippet": "I'm working on an algorithm to allow a vehicle to reverse and then line up and stop on a given spot facing a specific direction. The best approach I've been able to come up with involves two internally tangent circles with the larger extending from the point of tangency of the vehicle. Vehicle starts at point A and is parallel with tangent line T. Vehicle reverses to B, then moves forward to C, then to A so that it is parallel with the vector displayed instead. r represents the minimum turning radius of the vehicle Given that line AC is always arranged vertically and knowing point A, but that the tangent line T can vary, is it possible to be able to determine points B and C? If not what other info is needed? Medium tangent Steep tangent Shallow tangent For simplicity I've made it so that the radius of the larger circle is twice the radius of the smaller. If this restriction is not required to solve the problem how could this larger radius be determined as well?", "label": 0}
+{"snippet": "A few days ago, I came to an amazing intuition while using GeoGebra, and I could not prove whether it was previously discovered or is it new, please mention a source if it already exists... The sum of the lengths of the tangents of two circles touching a conic section, each of which touches it at two points, and starting from a point on the circumference of the conic section is equal to the distance between the centers of the two circles multiplied by the reciprocal of the coefficient of central difference, where the lengths of the two tangents are two vectors and the shortest of them will take a negative value if the point taken from the segment is not located between the two circles. These are illustrations that include different relative states: direct result: The length of a tangent to a circle tangent to a conic at two points that radiates from the point of tangency to another circle tangent to it at two points is equal to the distance between the centers of the two circles.", "label": 0}
+{"snippet": "I've read some description of certain house design as below: Living and dining rooms are towards the front with kitchens to the rear, with bedrooms either off the hallway or upstairs if it's a two-storey terrace. and here's the corresponding house plan: the definition of \"off\" in google: as I understand, and which can be seen from the floor design, \"bedrooms are off the hallway\" sort of indicates that bedrooms are separated by and adjacent to the hallway, and here \"off\" is preposition, but I'm not sure which one of the two preposition definitions fits it. The definition \"situated or leading in a direction away from (a main route or intersection).\" seems close but I think it's used to describe something not adjacent to the main route such as in \"my house is off the main road\", which is obviously not the case in above house plan example. Thanks in advance for your help!", "label": 0}
+{"snippet": "Suppose we have a closed circuit composed of a time constant voltage battery, a resistor and superconducting wires connecting them in series. In the equilibrium state, both the free charge the electric field in the interior of the superconducting wire should vanish, lest the free charge accelerates and there be no equilibrium/steady current. The electric field generated by the charges in the battery should be counteracted by nonzero surface charges on the superconducting wire in order to generate the zero electric field inside the wire. At the locations of the wire that are far from the battery and with small curvature which should approximate a straight wire, the surface charge density should be close to uniform. However, I have often read people claiming a superconducting wire with a constant equilibrium (direct) current should be free of surface charge. I would like to know what the bases is for their argument. Are there some references on this topic?", "label": 0}
+{"snippet": "why potential at any point in a uniform electric field is not same i.e. why potential difference between any two points in the uniform electric field is not zero? According to me if i bring a test charge from infinity to a point A in uniform electric field [assume the field is due to a positive charge] then i will have to apply external force on the test charge against the electrostatic force by the uniform field such that external force is equal to electrostatic force so that kinetic energy of test charge would remain constant thus some potential energy will be stored in the test charge at point A.....NOW if i will bring the test charge from infinity to some another point in the uniform electric field...let the point be B then according to me i will do the same amount of work done on the test charge to bring it to point B because i will apply the external force that will also be equal to electrostatic force by the uniform electric field.....and because the electric field is uniform the test charge will experience the same amount of electrostatic force at each point on the uniform electric field i.e. electrostatic force at both the points A and B due the field will be same. Hence according to me the potential energy at each point on the uniform electric field will be the same thus the potential also. Kindly explain.... why not? thanks!", "label": 0}
+{"snippet": "In the Hertz experiment, when light falls on the anode, electrons are emitted and they move towards the cathode and thus flow through the circuit. However, when reverse voltage is applied and the polarity of the electrodes is reversed, electrons being emitted from the anode (formerly, a cathode) only come out in the air/vacuum of the glass tube and do not flow in the circuit even though voltage is applied. How is it so? The emitted electrons should be repelled by the cathode and should enter the circuit through the wire attached to the anode as the increase in free electrons results in increase of current. The applied voltage should also direct the electrons to pass through the anode. In this way, a sort of capacitor might be created. Instead, the current is said to reach zero as stopping potential is reached. How can this be justified?", "label": 0}
+{"snippet": "In fluids, in the state of equilibrium, there can only appear internal normal forces and these forces always have a tendency to compress the bounded volume in the fluid. Cited - Physics Galaxy ( Ashish Arora ) Would it be apt to say that in context with fluids, if I drop a block, the pressure exerted by the fluid on the block will be the effect of a compressive internal normal force over an area ? In addition, why is pressure independent of the amount of fluid above it, since it is the weight of the fluid that is causing the compressive force to act? What i think: Maybe somehow Pascal's principal acts on this, equalizing the forces and leading to pressure equalizing at all heights irrespective of the shape of the tube, if I'm right, could you elaborate on how it actually happens?", "label": 0}
+{"snippet": "I want to recreate a plot where the area that is not visible from a certain point on earth (latitude and longitude) trough a full year. An example of this plots for example can be: Where in white is marked the zone a telescope is not seeing over all year. I searched in internet but i can not find anything related on how to do it, also Astropy don't seem to have any tool to do this calculus. My first idea for the approach can be first of all maybe represent in equatorial coordinates where this areas should be straight lines (but i don't know how to calculate the coordinates that this straight lines will have). And maybe after we can transform to galactic coordinates somehow. If someone have an idea on how to do this will be helpful.", "label": 0}
+{"snippet": "Some examples needing an explanation, thank you for the help. \"I came up with (an) idea, we can do...\" We should use \"an\", shouldn't we? But why, if we have a specific idea explained further? What about \"He gave me a/the idea to admit to the university\" then? \"The conclusion is ...\" Why should we use \"the\", when it's the first mention of the conclusion. Maybe because that conclusion is specific, only for that situation. Then should i use \"the\" in the next sentence \"I came up with the conclusion. The conclusion is...\"? \"I have a/the feeling i don't love him\". \"The\" because i tell what specific feeling i have further? \"I am gonna watch a/the video\". What if only i know that video, and i want to watch a specific video, but another person in a dialogue doesn't know that video.", "label": 0}
+{"snippet": "Consider for example the open sentence, x lives in India where 'x' is a variable, which can be substituted by various constants to make declarative sentences. For instance, Harshit lives in India Carol lives in India Zaid lives in India where 'x' has been replaced by constants 'Harshit', 'Carol' and 'Zaid', respectively. I don't understand how do we exactly come to know which constants can substitute the variables in an open sentence. I mean, if someone says, significant substitutes are names of people, in this example, I would say why not of pets? Why not just of people of a particular City or ethnicity? Since, this question is from logic, which is a prerequisite (AFAIK) of set theory, I would humbly expect no notions from set theory to be used.", "label": 0}
+{"snippet": "In the most known incarnations of string theory, we have to compactify the needed, additional dimensions that are then taken to be a.) periodic and b.) \"small\" in some sense (most of the time their size/radius is taken to be on the order of the Planck length). Some models do propose so-called large extra dimensions but even in these the extra dimensions are compact. Now my question is, are there any string theory models in which some or all of the extra dimensions are non-compact and if there are, can you recommend me any literature? I am thinking of brane world scenarios such as this, but with six or at least some non-compact dimensions (but I would be glad about any example, even if it is not a brane world scenario).", "label": 0}
+{"snippet": "Find the perspective sequence that maps collinear points A,B,C,D to D,C,B,A. Attempt: If we need to find a sequence of three perspectives that (A,B,C)->(A,C,B), where A, B, C are collinear, then first we mark p is a line through A, B, C, let S be some point that does not lie on p, let q be a line through A and S, let p' be a line through A different from p and q, let B' be an element of the line BS and C' an element of the line CS, and let S' be the intersection of the lines BC' and B'C. Then the first pespectivity maps us from the line p to the line p' and has its center in S: A->A, B->B', C->C', and the second one from p' to p and has its center in S': A ->A, B'->C, C'->B.", "label": 0}
+{"snippet": "I would (like many before me) like to take my lecture notes using LaTeX. As writing pure LaTeX-code is very time consuming and not nearly as fast as handwriting, I can only really consider switching to LaTeX if I can use snippets and anything else that makes notetaking faster. I have discovered this post on how to get faster using vim, but at this point I don't really want to learn vim anymore. I know it is very hyped, and probably worth learning, but I have so much else do learn already that I don't know if I will ever find the time. At the moment I am very happy with VS Code (or really VSCodium) for all developing, scripting and stuff that I do, and as I can perfectly do just about everything within this one editor, I would very much like to keep it. Saying this, has anyone an idea or a hint for me on how to set up something like the blog post describes using VS Code? That would be very appreciated.", "label": 0}
+{"snippet": "I am confused whether I should use \"a\" or \"the\" when I refer to an object given/identified by some other object. For example: The package is now in [a / the] deposit box with the number you received by SMS. For me this is the deposit box I previously stored the package in, but it seems to me, that for others (including the listener), it is still just some deposit box in the given vault: if I make a typo in the SMS message, my listener may hear from the front desk of the vault: A box with this number does not exist in our vault. Regardless of any such mistake, my assumption at the moment of speaking is that the listener will be able to find or identify the box unambiguously based on the number. Which is the correct article in such situations?", "label": 0}
+{"snippet": "Take a primordial black hole and measure the Hawking radiation over a large amount of time by gamma-ray detectors, as well as a Large neutrino detector. Using theoretical calculations about the composition of Hawking radiation combined with the detected neutrino flux you can determine the neutrino luminosity. Combine that with the luminosity in the form of gamma rays and whatever particles the Black hole is hot enough to produce, and then compare that with the loss in mass over time. If you detect a discrepancy, it's likely the missing flux is in the form of gravitons. Would this experiment work? I did also consider using a primordial black hole cold enough to not emit neutrinos but the Hawking radiation calculator I used gave a black hole lifetime greater than most estimates of the lifetime of a proton.", "label": 0}
+{"snippet": "Many problems in classical mechanics, classical and quantum field theory among others require the study of systems of partial differential equations where questions like existence and uniqueness cannot be answered with the typical counting-equations/variables arguments - questions which have physical relevance and that need to be addressed before going to numerics. For instance, problems in surface mechanics always involve the Gauss-Codazzi equations which is a non-linear overdetermined system of PDE. The most powerful technology to properly study general systems of PDEs are Exterior Differential Systems, and there are some canonical references in the mathematics literature like Bryant et. al. I found this challenging for a standard theoretical physics graduate because it requires a solid background in non-conventional math topics for physics like commutative algebra and number theory, so I wonder if there is any reference treating EDS for physicist.", "label": 0}
+{"snippet": "I'm looking at a few English sentences, and I've realized that many verbs can be used as nouns in their infinitive form. For example. I am going on a run and in the present tense I am running. There are many more verbs that this can be done to. Are you going to take the jump? Why did you do three pitches? You know he would have hit one of them. (baseball) Can you please do your exercise elsewhere? It is too loud right here. So 'pitches' in the example is not in the true infinitive, but is in the plural infinitive, so this may not be a true example. 'jump' and 'exercise' are however. Normally, I would say that these are gerunds, however, after looking online for a while,. it seems that gerunds always use the present tense, and never the infinitive. What is the name for these verbs that can be nouns when in the infinitive form?", "label": 0}
+{"snippet": "I'm writing longer mathematical texts (lecture notes) regularly, and I don't know where else to ask this question. I regularly find myself enunciating (in the typographical sense) every statement I make. This means that I will put any even vaguely mathematical statement, not only theorems, corollaries, definitions, etc., into an enumerated environment in Latex. As of now, I always use Remark for them, and I feel like I'm overusing it. Question: When do you write mathematical comments in some numbered environment, like Discussion, Observation, Remark, Idea, etc., and when do you write mathematical comments standalone in the running text? What other environments do you use to mark up mathematical comments? Edit: The reason why I enunciate this often is simple: Later on in the text or in the lecture, I might want to refer to this comment. E.g. in a mathematical comment, we combine all results in an informal discussion on how to compute fibres of maps between prime spectra. This result is somewhat important as it will come up every now and then, but its statement in the lecture was more or less like an argument, making it difficult to encase this as a corollary.", "label": 0}
+{"snippet": "I have written a long book in latex memoir. I now want to feed its content to a machine translator into another language (say, German). I will use the automated translation for a first pass for a better human translation. Translators do not understand latex. There are a couple of methods to go about feeding them. I could use some online latex parsers, write a quick parser myself, etc. It occurs to me that I could also ask latex to create a pdf that is better suited to pdftotext (poppler). It should make big spaces between paragraphs, not break paragraphs across pages, etc., probably take out tables and figures, page headings, footings, and sidemargins, footnotes. (Eventually, I will also need to write a parse-match to integrate the translation back into a latex document that uses the original structure, but just replaces the text. Thus, I am thinking of adding a number for each paragraph, so that I can take the translation input and output and reconstruct a latex file.) Has someone written a style file to improve the results of pdf text extraction? or found a better solution?", "label": 0}
+{"snippet": "I am trying to learn about neural networks. I was reading the paper An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem which uses graph neural networks such that given a graph we get a hamiltonian cycle which hopefully is nearly optimal. However, they use as ground truth the concorde algorithm, which when I ask google and chat-GPT seems seem to be an exact algorithm but in section E (solution visualization), there are some cases where the author say : The model predicts a shorter tour than Concorde for this instance by choosing a different contour around the nodes at the top-left of the graph But how can it be better? Doesn't concord compute the optimal solution already? Did I get something wrong about the traveling salesman problem?", "label": 0}
+{"snippet": "i have taken two course in complex analysis, one variable and the other in several variable and the begining of complex manifolds, my understanding in one variable go well but in several variable our prof use two books, one of krantz and the other of Hoermander, i think due to my lack in the theory of integration(multiple and differential forms integration) i don't understand some proofs,in particular some construction for Hartog's extension theorem and the other about separate Holomorphicity And this brings me to my questions: do you think a good understanding of Lebesgue integral and Mesure theory can replace Riemann integration theory. what to study in complex analysis to develop geometric intuition,in particular for abstract algebraic geometry and sheaf theory, and if possible is there an approach that don't depend on functional analysis and PDE. and thanks", "label": 0}
+{"snippet": "I use LaTeX for a lot of my classwork (worksheets, graphics, etc). One thing I have not transitioned is my exam writing. An example page of an exam might look like this. This is just a portion, doesn't have the header and such, I'm comfortable working with those. I've not moved to LaTeX because of my need to be placing the answer boxes and blanks in specific spots on the page, and it's frankly pretty easy to drag little rounded text boxes around MS Word to achieve my layout. But there could be a fair bit of programmatic benefit in being able to make some of those blanks more consistently, layout chemical equations more simply, etc. I also have a page of multiple choice for each exam that I'd love to shuttle off a lot of that layout work to LaTeX. Is achieving looks like this reasonable with enough flexibility to be able to shift around those blanks and such on a question-by-question basis? I've found this page about using a zero-sized box. Seems like it be applicable, but just want to check before I start down this path. Any resources or general code ideas for doing what I'd like would be appreciated. I'm sure in the future I'll come back with some MWE, but for now just gathering info on even executing this. Also if the answer is \"Probably more work than it's worth and keep using MS Word\", I can accept that too :)", "label": 0}
+{"snippet": "I am posting the specific problem I am dealing with for reference and then explain the part I am confused with. My Understanding and approach to the problem I identified that in the ground frame the disc will have some inertia and thus simply remain stationary as the plank below slides away.When viewing from the plank's reference frame it's acceleration will be added to the COM of the disc in the opposite direction.So initially the instantaneous center of rotation is at the exact center. The Confusion I am unable to visualise how the instantaneous center of rotation will change as the COM gains velocity due to the acceleration. The solution that I found said that the points that have tangential velocity along the acceleration will have some added velocity while those against will have some net velocity in the direction of the acceleration.According to me if that happened then the rotation would completely stop which does not make any intuitive sense. Here's the solution for reference Conceptual Confusion The main concept I am struggling with is the instantaneous centere of rotation of the disc.I tried reading up about it on wikipedia but that doesn't clarify it for me.", "label": 0}
+{"snippet": "This question is born out of the riddle where there are two characters, one that always lies and one that always tells the truth, and you want them to tell you which of two doors is the \"good\" or \"bad\" door. You can ask either character, \"what would the other character say is the good door?\" And the lier will answer with the bad door, and the truther will also answer with the bad door. My question is a variation, given two characters where each character might always tell the truth, or might always lie, but both characters think the other always tells the truth, are there any questions you can ask that allow you to determine more information about the composition? For example it could be that character A and B both always tell the truth (and each thinks the other always tells the truth) or it could be that character A and B both always lie (but again each thinks the other always tells the truth), or it could be that one character always tells the truth and the other always lies (but again they both think the other always tells the truth). Are there any questions that can be asked to determine the composition?", "label": 0}
+{"snippet": "Is there a possible slight difference between protons and electrons behaviour while they are accelerated at speeds that cause relativistic changes to their mass. Why am I asking that? Because for a proton we know that it is made of several components which of them are the three quarks. If they have some speed inside the proton it is logical that this is not the same as they have no any intrinsic speed and that this speed does not matter as a portion that is added to the overall speed of the proton that is accelerated to a relativistic speed. Should that small part of the overall speed make a difference between the theoretical calculation of the particle speed to relativistic mass ratio and the empyrical results as the theoretical calculation threats the proton as an elementary particle because the intrinsic speeds of proton components are neglected in the formula?", "label": 0}
+{"snippet": "An electromagnetic wave is usually illustrated with two sine wave shaped fields, one for the electric field and one for the magnetic field. As in the picture below: But as how I understand magnetism, it consists of two poles, north and south (alternatively described with field lines, with a direction, where north and south connects). So to focus only on the magnetic field (the red, B) in an electromagnetic wave; where are the poles located in such a sine wave (the red part)? Is only one of the poles illustrated, such that another sine wave could be added for the other pole? Update: In this video, Maxwell's second equation is described as the field lines in the magnetic field is always connected (north and south pole) - how these field lines are organized in a wave is what I don't understand. Later in the same video, the fields emitted from an antenna, are illustrated as \"bubbles of fields\" - quite different from how the \"arrows/vectors\" are illustrated in my picture above. Field lines from the video:", "label": 0}
+{"snippet": "Lill's method is a visual way to find the real roots of a polynomial equation. It involves drawing a straight line with lengths equal to the coefficients of the polynomial. The solution can be found by using a slope of a right triangle. Lill's method - Wikipedia The values of a polynomial function can be \"defined\" as a distance between the vertice of the last polynomial coefficient and the path that we draw using right angles. Polynomial function's value Cubic function with defined function's value What I want to do is to find the local maximum and minimum in Lill's path. So, I'm curious if I can \"define\" a line that represents the first derivative of a cubic function and let it equal to zero, or if it can't be done. What I have done is by using the derivative's definition, and I got that a point (P in the picture) is the derivative of a function which its value is zero. But I think that's not the correct way to do it. My way to do the derivative in cubic function I drew the function and its derivative with the same \"first coefficient\" Please correct me if I'm wrong, Thanks.", "label": 0}
+{"snippet": "I need to retrieve Roll and Pitch (but not Yaw) rotation values from rotation matrix (or euler angles, or quaternion, input can be different, fortunately, it can be converted from one form to another). [Info table] X points Left. Y points Up. Z points Forward. Rotation around local X axis is Pitch. Rotation around local Y axis is Yaw. Rotation around local Z axis is Roll. If I just use Euler Angles then, in some situations, I get wrong values. As I think, this due to rotation can be represented with multiple variations of Euler Angles, so it breaks when rotation around X axis (Pitch) and Z axis (Roll) is represented also using Y axis (Yaw). gif (How it works | How it should be, but I need rotation without Yaw axis) Also algorithm is running in time, so, solutions, computing some delta rotation, are also accepted.", "label": 0}
+{"snippet": "When fluids are subject to external perturbations or put in certain geometries, they always show arguably the most fascinating structures : Starting from the eddies and vortices in pipe flows at large Reynold numbers, vortices of flows past an obstacle, or the vortices in fluids confined between two rotation cylenders. Yet, a fluid at rest is often thought of just as a completely structureless phase : Apart from very small-scale features such as the arrangement of nearest neighbors or solvation structures in liquids, it is just a random phase and the trajectory of a tagged particle from the fluid simply obeys the Brownian law, without any other features. But what I somehow intuitively expect is that most of the above mentioned \"non-equilibrium\" structures appearing under well defined conditions are present in the resting \"equilibrium\" fluid. This means if were to look at the trajectory of some fluid particle I expect to see imprints of the coherent non-equilibrium structures in the equilibrium trajectory, and not just see a Brownian trajectory. Can you somehow relate to this ?", "label": 0}
+{"snippet": "Lets imagine you have a universe where the average matter density is extremely close the the boundary between one that will expand forever and one that will eventually re-collapse. Now lets imagine that there are very large scale fluctuations in density at the Gpc/Tpc scale and above. Could this result in differences in the rate of expansion between some parts and others, causing parts of the universe to collapse and parts to expand forver? If yes what would this look like near the boundary? What if the region was non simply connected. (E.G. a torus, or hollow ball.) How about a universe with bee marginally above the critics density with some very large under dense regions, perhaps ones large enough for the centre to become causally disconnected form the edges.", "label": 0}
+{"snippet": "There is a good discussion here (Referring to past times with \"hence\") that concludes that hence can't be used like \"ago\" to refer to a past event, not even to describe how much time has passed \"since\" that event. However, what if using the past perfect and then referring to time forward from that point, Could \"hence\" be used there? The specific construction I'm wondering about goes like this: They had left me there to die. Even now, one-and-a-half moons hence, it would be a simple matter to follow their trail. In that case, \"hence\" is a time forward from a point in the past as made clear by use of the past perfect (\"had left me\"). Is that appropriate usage, or can \"hence\" only refer to the actual future, not a future relative to a point in the past?", "label": 0}
+{"snippet": "There is a closed continuous loop, and you have a stick of a random fixed positive length,so that You can slide the stick on the loop. Take the stick's midpoint. It's track will form another closed continuous loop. Take another stick of another random fixed positive length. Slide it on the new loop again. It's midpoint will form another loop. Do this again and again. Will the shape of the loops tend towards a circle(well, the area of the loop may decrease, but you can magnify the area to not let it become a point)? Or could it become another shape? The thing I found was that circles and ellipses will tend towards a circle, and I think the question is intuitive, because this operation of sliding sticks round's spikes and makes concave shapes convex.", "label": 0}
+{"snippet": "Imagine a ball with diameter \"a\" at rest and another observer at rest at a distance of 'l' w.r.t to the ball in this rest frame.Say the ball suddenly starts moving at velocity v towards the observer .(Assume it accelerates instantaneously).What does the observer measure the distance between them?What does the observer measure the diameter of the ball to be?If the diameter is contracted by gamma factor then why is not 'l' contracted by the same?Because acc to me by time dilation,as the time interval is zero wrt to the observer between the events (ball moving and ball at rest),so the distance moved is zero acc to observer and hence observed distance remains 'l'.I asked my professor,he also said that diameter would contract but distance of ball wrt observer wont , but I didnt understand why this partial treatment of two lengths ?.They are identical in properties with regard to lorentz transformations so if one contracts wrt observer the other should also.", "label": 0}
+{"snippet": "Maybe this belongs on \"Linguistics\" but since it's about an English word, I suppose they'd only send me here. Over time, some words gather more and more meanings to themselves. Ironically, these words are often small like, \"by\". Other words seem to shed meanings, or rather, they devolve meanings to new words. In the New Testament, Jesus tells people to \"arise\" from their bed, elsewhere \"the resurrection\" appears. But this is actually just the noun form, i.e. \"the arising.\" Now, no one except by poetic license would refer to their \"resurrection\" from bed; it has become a specialized form of \"standing up\" (from death.) Is there a pair of words to describe on the one hand the accreation and on the other the fragmentation of words and their meanings?", "label": 0}
+{"snippet": "In my current understanding, I have been told that the spin of quantum particles is simply intrinsic to them. That, particles are simply right-handed or left-handed... just because they are. To me, that seems then that we should then treat handedness like it is just as distinguishing of a property as mass, or charge, or color charge. Almost like the standard model should be doubled, or mirrored. Like, right-handed, blue, up quarks should be considered as a wholly different particle from a left-handed blue up quark. But wouldn't something HAVE to catalyze the spin? Like a ball rolling down a hill hits a rock, and how it first strikes that rock determines whether it continues its rolling spinning to the right or to the left. Could spin be acquired, for instance, during the big bang, by the first interaction of a particle as it \"hits\" the higgs field? And some characteristic of the particle to that point determines which way it \"glances\" off of the higgs field?", "label": 0}
+{"snippet": "At the end my document, I get a new page that contains, Temporary page! LATEX was unable to guess the total number of pages correctly. As there was some unprocessed data that should have been added to the final page this extra page has been added to receive it. If you rerun the document (without altering it) this surplus page will go away, because LATEX now knows how many pages to expect for this document. I know that by just recompiling the document, I can get rid of this error, but I was wondering why does this occur and what unprocessed data that LaTeX couldn't process. For citations, table of contents, table and figure references, LaTeX needs to be run twice, but I have never ever seen this \"Temporary page!\" page before.", "label": 0}
+{"snippet": "As we know, in EM wave, with the oscilation charge (for simplicity, charge was moving at constant speed, then accelerated and then continued moving with constant speed again), kinks are produced. The funny thing is as the kink moves outward, its length actually increase(the joint vector between the new field line and old field line) due to the fact that new field lines move at a higher speed then old ones. I wonder what we exactly call a wavelength of wave then. Is it the kink's size ? but if it's kink's size, then it means with just one acceleration, kinks size increase and wavelength increases as well which seems to me wrong. one acceleration only should produce one wavelength. So what's the connection between kink and wavelength? If there's no correlation between kink and wavelength, then wondering what's the wavelength truly is in terms of EM wave?", "label": 0}
+{"snippet": "I want to simulate typewriter style typesetted math articles. There are a few major requirements: All characters in all environments be tt style and of the same size and width (including super and sub scripts in math mode). In math mode, sub and super scripts should be one character higher than the base. All emphasizing should be replaced by underline. Spacing between all kinds of lines, including spacing between lists or figures and texts, should be always integral multiples of character height. The multiple can vary according to the height of inline equations (e.g., when too many levels of superscripts, should leave space for superscripts to avoid overlapping). All spaces being the same width as characters, no adjustments to fit line breaking. If a word cannot fit in one line, leave it to the next line. To conclude, all elements should be arranged as if the page is separated into \"grids\", each grid of the size of a tt character. All elements should be placed exactly fitting one or multiple grids in both vertical and horizontal directions, there is no \"half\" space or something like that. Is it possible to fulfill these requirements in LaTeX?", "label": 0}
+{"snippet": "We know that when the wave model of light was being used in physics there was Thomson Scattering Model to explain the interaction between a free electron and a light. The Thomson Scattering was explaining the force that acts on an electron when a light hits it, with the force that the electrical field component of that light possesses. (Rather than billard ball explanation) However, I do not understand Thomson Scatter in relation to Doppler Effect and Low-Intensity waves. For the wave model of the Photoelectric effect, it was clear for me to understand where was the wave model wrong when explaining the necessity of the quanta of energies. But, How was Thomson wrong when talking about Doppler shift and low-intensity waves not being able to explain the movement of electrons? I know for a fact that low-intensity waves were insufficient to supply energy for an electron to have the speed and kinetic energy it is supposed to have. I am not sure how built-up energy by low-intensity waves have been thought to be a supply of energy for the acceleration of electron in the first place and how is this related to the Doppler shift by Thomson.", "label": 0}
+{"snippet": "I am trying to have better understanding of localized wave functions. Apparently free particle de Broglie waves are NOT normalizable and act as delocalized functions which was the original rationale behind their use for explanation of electrons in double slit experiment. so far so good ! But then we use Fourier transform to make them localized that they can represent a particle and behave normalizable . Here is what I can not understand: if wave function gets localized ( say to the size of an electron - which actually is supposed to be point-like ) , then such wave can not cover the distance between both slits to be able to make interference patterns in the double slit experiment, .... and if wave function remains delocalized , then it will not be able to get normalized and consequently its wave function will not present accurate probability amplitude . The only way I can think of this is to have a localized wave function that is substantially larger than the slits distance but vanishes at the infinity, but it will be much much larger than a particle - let alone a theoretically point-like particle. My question is: when making a localized wave function, how big the particle size or wave area should be to make interference patterns and be normalizable at the same time? are there known limits for that Fourier section?", "label": 0}
+{"snippet": "I want a tool to easily make geometry diagrams. For example, say I wish to overlay two circles, and then fill their overlap with the color red, whilst coloring other areas with other colors? Let's say I want to make a triangle with curved sides and a flat bottom side; that could be done in no time with the right tool. I could insert a square and then delete circles from its upper two quadrants. To be more clear, here are the list of features I'd like: A gallery of shapes that can be sized and colored as one wishes. The ability to fill any area enclosed by lines with a color. The ability to draw lines between highlighted points on shapes, like the centers of their sides, their corners, points between the quadrants of the circumference of a circle (allowing the drawing of diameters), etc. The ability to insert text into the diagrams. Is free to use. To give examples of close contenders: Draw.io has all features except number two. Microsoft paint and sketchpad has all features except number three. Does an app that has all features exist?", "label": 0}
+{"snippet": "Much of physics education focuses on equations of known possible reactions, how to balance them, how to predict the result if certain elements happen to react with each other. What I don't see a lot of is an explanation of what chemical reactions are likely to happen in a complex system. Assume I was building a physical simulation where I know the position/velocity of any number of elements or compounds. What would the process be to determine which chemical reactions are most likely to occur? Given my assumption: Treat the collision of each atom as a sphere of varying size depending on the size of the type of atom's valence field (sphere collision is to reduce computational complexity). Calculate magnetic attraction/repulsion between local atoms and manipulate the velocities accordingly. If the valence fields of two atoms overlap (or are near each other?) due to attraction, electrons are exchanged, and other atoms that are the least magnetically attracted are either re-positioned or rejected from the compound depending on the magnetic forces and electron availability. I assume \"heat\" based reactions can be derived from velocity of a collision? Would this be a sufficient model to predict an arbitrary chemical reaction or non-reaction?", "label": 0}
+{"snippet": "I am studying the Newton's Law's of Motion, and really confused about one thing. I know that bodies of very small mass get attracted to our earth due to a force it exerts, due to its huge mass. So that, according to the Newton gravitational equation, a given small mass on earth will be attract by a certain force and depends on the distance of separation from earth's core. Right now I am dropping a pen on a table and observing the sound. Higher the height from which I drop it more the sound it makes, showing that (I believe) more force is being exerted. Although from Gravitational equation of Newton, we can observe that the same force is being exerted on the pen because I am dropping the same pen from heights not so far away from each previous drop. My question is that from second law of Newton, change in momentum causes force. But from gravitation law of Newton, the same force pulls the pen down. But the change in momentum is happening due to gravity, but the gravitational force is constant so that, the pulling force is constant, thus, why every different drop do I hear a different sound. What is the right thing here? I am really confused...", "label": 0}
+{"snippet": "This question is perhaps more on the use of certain parameters in BibTEX than on the use of TEX/LaTEX itself: nevertheless I think it could be of some help to other persons who, like myself, need to redact large bibliographies. In order to list information on the existence of a review in the ZBmath database on a bibliographic item, I am aware of the existence of the following three parameters: ... zbl = {}, zbmath = {}, zblnumber = {}, ... Until a few years ago, only the last one seems to have been used (possibly my opinion is biased by the heavy use of Jabref I do), therefore I'd like to ask why the other ones have been introduced, if there's one of them which is preferable to use. P. S. Finally, let me point out that the American Mathematical Society always codes the analogous information in the univocal parameter mrnumber = {}, which works perfectly in many bibliography styles.", "label": 0}
+{"snippet": "We know from molecular spectroscopy that incoming light on a molecule can change a molecule's rotational, vibrational and electronic energy levels. If the incoming light is, on the far-infrared and microwave region the molecule gets rotational energy.(microwave spectra) on the near-infrared region the molecule gets both rotational and vibrational energy.(infrared spectra) on the ultraviolet & visible light region, the molecule gets all energy levels rotational, vibrational, and electronic energy (electronic band spectra) We also know that, Rayleigh Scatter does not excite electrons of atoms to another electronic level but only causes them to oscillate. Thomson Scatter happens when an electron is free or quasi-free and it also makes the electron oscillate and more, accelerate. Taking into account that both Rayleigh and Thomson most probably happen at low energies and vibrational and rotational energy changes of molecules happen at microwave and infrared spectra: QUESTION: It is clear that, Thomson Scattering can not cause rotational spectra or energy build-up, which requires the whole molecule to rotate since Thomson Scattering is about free and quasi-free electrons. But what about vibrational energy spectra, or energy build-up on such a free electron? Rayleigh Scattering happens on the atomic level so it begs the question, \"can it cause both rotational and vibrational energy level changes in atoms or molecules?\"", "label": 0}
+{"snippet": "For a given n dimensional chaotic system such as a chaotic attractor or really a time dependent chaotic dynamic system does there exist a higher dimensional representation where the behavior is in fact deterministic? This question comes from a data science problem in multivariate time series forecasting. Most real world behavior is chaotic in nature, such as the stock market or Earth climate cycles (milankovitch cycles etc.). Lets say I could build a really big model that takes into account everything that might impact the system of interest, would there be some set where all the chaos would just go away? Take the TV show foundation based on the books by Isaac Asimov. In there they postulate the Abraxis conjecture which is solved by folding space and is critical to the success of psyco-history (which is really just data science). One of the steepest challenges with time series forecasting is the ease at which it is possible to leave conditions where your inital state no longer applies. If chaos could be eliminated then this problem could be pushed out. Effectively with infinite information we could forecast for infinite time (in the theoretical limit only).", "label": 0}
+{"snippet": "While playing with GeoGebra a few days ago I came up with an initial property of my Cardioid curve, I heard this curve is well studied so I'm not sure on my guess if it's already discovered or new, adding references would be appreciated You have a Cardioid and its circle of perpendicular tangents The red point is an arbitrary point of the circle of perpendicular tangents The violet line is a right angle bisector The blue line is the hypotenuse of a right triangle The green line is the reflection of violet with respect to blue The brown line is the reflection of blue with respect to green The brown line is tangent For giving me Cardioid. I don't have progress on it yet, but I do have other cardioid guesses that I can include in a follow-up question on the site.", "label": 0}
+{"snippet": "I tried lots of research, but still couldn't wrap my head around the difference between free and mobile electrons. Free electrons, from wikipediaLink(I mean free particle bullet point, because other bullet points are not really free electron - as an example valence electron is not free, but mobile) are electrons that don't experience any external force, hence it experiences zero \"electric field\" from others. as for the mobile electrons, they are loosely bound to the atom (valence electrons). Though, even if these electrons are ejected from the atom, they still experience some electric field from other atoms and could jump into their orbitals. If the above is correct, how can both of these cases exist? how can free electrons not experience any electric field, while mobile electrons do? I know that in sun's core, there're free electrons moving through material. Why don't they then experience the electric field of other atoms?", "label": 0}
+{"snippet": "For some extended context, this is how Heads Up Displays (HUDs) and Reflector Sights work: However, as far as a I know, a lens will take collimated light and focus it to a very small point called the focal point. And since the reverse is also true, only the focal point can be collimated and \"focused to infinity\" to create the virtual image in a HUD. The reflector sight diagrams clearly show a source reticle that is larger than a focal point, and HUDs in general usually use an LCD display to create the initial image. Although modern HUDs use several optical elements to correct for aberrations and other distortions, most early HUDs and all reflector sights used a single large convex lens to collimate the image. Is this merely an issue of lens diameter? Would using a larger lens allow for the focal point to be larger in diameter too which would allow for a small display to be completely collimated?", "label": 0}
+{"snippet": "If we bring a separable dipole (say a single ammonium chloride molecule) from infinity to the center of a capacitor, once the dipole stabilizes and the rotational energy is lost to electromagnetic radiation, the net work done is negative. If the capacitor plates be perforated and the field be strong enough to separate the dipole and the ions pass through without collisions, they then may be accelerated in the same direction by two other capacitors with perforations, in the same direction and then may recombine after exiting because of their electromagnetic attraction. Once they combine, they still have the velocity gained by the two additional capacitors but none of the three capacitors lose their charge. The dipole gains some kinetic energy so where does the energy come from? The capacitors are not connected to batteries and are pre-charged, the entire setup is in vacuum and gravity is non existent", "label": 0}
+{"snippet": "Recently, I play a game of Turing completeness where I utilize various gate circuits such as NAND, AND, and NOT to construct a circuit that satisfies the given truth table. I didn't learn digital circuits or relevant content. When I play this game, I want to know whether there are any theory to deal it. For example, given a truth table, is there any theory to get the circuit with least basic gate (or only Nand gate). It seems to be a bit like graph theory (but the vertices are special). On the other hand, I know a little about retina from From Neuron to Brain. The retina responds to certain shapes of light, such as a ring of light. I've always wondered how build a neural network with neurons that respond to ring of light but not solid circle light. Of course, I'm not really asking for the details of these questions. I just feel they may are the thing not liking analysis and algebra. If I want to deal these questions, what book I should begin from ?", "label": 0}
+{"snippet": "A parabola is supposed to be a conic section, obtained by slicing through a cone with a plane, like this from Wikipedia: But if you do this, what you get is just part of an elipse, since if the cone and the plane were bigger, eventually you'd end up with an elipse. And a section of an elipse is not a parabola - there is no possible focal point that satisfies the condition that all points on the curve are equidistant from the focal point and the directrix - at least not when I try to construct this in my CAD software Answered by JonathanZ, the key thing was the parabola needs the slicing plane parallel to the slope of the cone (not illustrated or explained clearly in either Wikipedia or Wolfram IMHO). Here's what it looks like in my construction:", "label": 0}
+{"snippet": "I've attached an image that describes the light-rays refracted through a thin lens. P' represents the first real image that is created when light is refracted through the first convex mirror. But how does this translate to the second image point P'' through refraction? I understand the convex mirror formula and how if you plug in the numbers it just works out that Q'' is where it is, but intuitively, this does not make sense. If the image P' is what P'' \"sees\", as it is the image, how can the refracted image (P'') be on the same side as the object image (in this case P')? As far as I understand, P' acts as a real object for the second surface (the right side of the lens), and the rays that diverge from P' are what get refracted onto P''. But how is this possible, if they are both on the same side? As far as I understand, the model above depicts virtual object through refraction. How is this shown in our case?", "label": 0}
+{"snippet": "The reason we can see the color of objects is light rays undergo scattering in the subsurface of a material, and in their walk in the material lose some wavelengths, and finally exit at a random direction (link) However, aside from this, you see white highlights on an object from the light source. These can be diffuse or specular depending on surface roughness (I'm assuming they're both from surface interactions) Look at the highlights on the shoulder here for what I mean. Not where the arrow is pointing. However, I just found that that aside from metal, most common surfaces, even when highly polished, specularly reflect only a few percent of the incident radiation. How are these highlights then so pronounced, especially for the diffuse highlight case where the light is distributed in all directions.", "label": 0}
+{"snippet": "(Edit: This was closed because it was marked as \"opinion based\" and I was asked to edit the question so that it could be answered by facts and citations. @Fumblefingers gave citations, thank you. On re-reading several times, I think yours is the correct interpretation, rather than assuming the existence of some actual physical flag. It's like as if we referred to captains & sailors dying in the line of duty as a \"badge of honour\", there's no physical badge. In my opinion, expecting facts about poetic allusion is a bit unrealistic. Thank you @KillingTime, I hadn't known about the literature forum. I can ask such questions there, and keep this forum to linguistic questions. ) ORIGINAL QUESTION: Does any English literature expert know what kind of pennant Walt Whitman was referring to by \"a pennant universal\" in the poem \"Today a rude brief recitative of ships\" in \"Leaves of Grass\" ? Flaunt out O sea your separate flags of nations! Flaunt out visible as ever the various ship-signals! But do you reserve especially for yourself and for the soul of man one flag above all the rest, A spiritual woven signal for all nations, emblem of man elate above death, Token of all brave captains and all intrepid sailors and mates, And all that went down doing their duty, Reminiscent of them, twined from all intrepid captains young or old, A pennant universal, subtly waving all time, o'er all brave sailors, All seas, all ships.", "label": 0}
+{"snippet": "I am aware that in the theory of classical infinite sums , one can not generally interchange the order of a double sum or do other infinite sum manipulations. However, these infinite sum manipulations can be valid if absolute convergence is available. I am working on a problem , where I would like to manipulate a double infinite sum but absolute convergence need be satisfied in my context. I am under the impression that these classically illegal infinite sum manipulations can hold under less strict conditions in the context of non classical summation methods. I would be glad if someone can write an answer that discusses when interchanging the order of a double sum is allowed in the non classical setting and direct me to a place where I should read about this. Thank you a lot.", "label": 0}
+{"snippet": "After verifying that it was a real word, I just posted a chapter named \"Processioning\". I have begun to wonder what kind of thing that is. As far as I know there has never been a verb, \"to procession\", and \"to process\" is something else entirely. Yet, \"they were processioning through town\" makes perfect sense. I am thinking that there may be a class of such words, apparent verb forms made from nouns. Am I misguided, or simply ignorant of what the heck that is? It is also weird that processioning would not be used as a gerund, because the noun form is procession. I guess it could be an adjective though, \"the processioning group\". edit: talented musicians an unconvincing argument an enterprising foreign policy a fun-loving guy are sound examples with no corresponding verbs [EA].", "label": 0}
+{"snippet": "Suppose there is a ridiculously large bridge, fixed at either end (light seconds long at least). The bridge is constantly under the influence of gravity. If the ends are severed simultaneously, the whole bridge will fall. I assume simultaneity isn't a problem as the bridge is all in one reference frame? Will an observer in the middle register the change of inertia, but be unable to see or detect any damage to the ends of the bridge until the light from each end or the signal from electronic sensors has caught up at light speed? If so, does this mean that they can infer from the fall that the ends must be severed I.e. have they recieved information about the state of the ends faster than lightspeed? Or will they not begin to fall until the information about the severed ends has caught up?", "label": 0}
+{"snippet": "Usually in a Cartesian form of derivation in math and physics, I have seen that a particular formula is derived for simplicity by taking concerned points say in the first quadrant. Few examples are the derivation of mirror formula, lens formula, lens maker formula, distance between two points. Later, they extend the formula to all cases and say : \"The formula is valid for all cases independent of quadrant and position because we have taken proper care of signs\". For example, see the case of mirror formula derivation in the book (especially the pointed last paragraph): Similarly here for distance formula in SL loney. I do not understand deeply that why do this happen ? I know that it can be proved in the above cases by actually deriving for all cases and observing that it is confirming, but how can we say it generally? So the question is : Why do the sign convention in coordinate geometry work the way it does ?", "label": 0}
+{"snippet": "I am an undergraduated student from a non-native English speaking country. In my country, when doing math, which in many contexts that we will be proving something like a theorem, a proposition. What matter is I feel like we don't have a variety of words while doing math. Everything we used in our assignment are just around \"we have, we get, hence, thus, therefore, we have this, we have that, we have and we have ...\", which is kind of boring to me. I love math and I love solving math problems, but I would love to bring my product with an abundant style of words, just like it's not simply a proof of math, but more like a nice essay of math, to make my products more lively, agile, elegant, refined. So I really appreciate if you guys could enlight me with your knowledge. My very thank you.", "label": 0}
+{"snippet": "We are extracting transformation matrices for different joints from ARKit. These are relative to the parent joint. Since the positions are not very accurate, we have developed a machine learning model that corrects the positions based on ground truth (Vicon data). We only use position data in the model, so now the rotation part of the transformation matrix is no longer valid. My question is: Given that we have the initial transformation matrix (I can have the rotation, scaling, translation separately) is it possible to get an updated transformation matrix that uses the positions of the model? My end goal is if possible to calculate the Euler angles of the updated position for the initial coordinate system. I have checked the Rodrigues' rotation formula but I am not sure if I can use it somehow.", "label": 0}
+{"snippet": "Have an excel financial model, that pretty much is a time series of assets and liabilities. I would like to know what the optimal liability structure / mix is, subject to multiple balance sheet constraints. My objective function is to minimise funding cost. I tried to optimise using Excel Data Solver, but encountered the following issues: Excel may not arrive at a solution (can't converge at times even though there is a solution) Solution is not consistent, eg same starting point (ie initial guess) but different end points (not all are optimum) Solution may not be global minimum Am open to using other softwares like Matlab or Mathematica, with my own \"constraints\" I won't be able to simplify this down to an analytical equation so will need to be in the format of a financial time series model Ideally arriving at global minimum Scalable Are there any guide you can point me to? Open to software suggestions, algorithms, approach, etc... Thanks", "label": 0}
+{"snippet": "In Meissner effect we say that below critical temperature there is an expulsion of external field lines or field lines do not penetrate inside the specimen. But here is what I am not able to understand, if the sample creates a mystical force which do not allow field line to pass then it can be imagined as if there is an field due to specimen which cancels its effect. I know experimentally field lines are expelled, but why they are expelled I want to know the reason like who are the one that causes no fields to penetrate inside it. Somewhere I have read that a persistent current rises in such a way that it creates a field which cancels the external field. Now how is that possible that a superconductor inside in it already has a field?", "label": 0}
+{"snippet": "I've been told numerous times in high school that \"first and second person pronouns in academic writing\" should be avoided. This supposed wisdom is echoed in various style manuals as well. However, if you look at any authoritative text, like The Stanford Encyclopedia of Philosophy A simple search of \"we\" will yield countless articles using the first pronoun all throughout. Given this situation, is it realistic to teach anything stylistically related to using first pronouns? Also, based on experience, trying to stick to this kind of rule damages the entire paper in many ways It takes time to conjure up passive tense sentences which usually is all but required to avoid you/we completely Some concepts more effectively expressed through these words may fall between the cracks and never see it to fruition, which is truly a shame Grades may even suffer trying to stick to the rule -- an irony given that adherence to rules are always motivated by desiring praise and getting good grades, etc. ad nauseum...", "label": 0}
+{"snippet": "Background: ZFC in classical first-order logic. To make a definition, we first need to proof something does exist. So, this question is actually about proving something exists based on a recursion. I know that when you want to prove the existence of a certain function with the domain of ordinal numbers, you can use the transfinite recursion theorem. But our things are not always a function of this sort. For example, when we define the truth value function on the set of formulas in predicate logic, we usually define it recursively based on the number of the logical symbols in a formula(or complexity). But for a certain complexity of the formulae, there're many cases to deal with. I can't figure out how to prove such a definition does make sense, aka the function does exist.", "label": 0}
+{"snippet": "Good day, everybody. I program a simple computer game and there is a \"dumbbel\" inside of it, which should using some kind of rocket engine. The engine is fixed on one side of the dumbbel and creates a constant force F, which is ALWAYS orthogonal to the dumbbel. Since the dumbbel is ideal, the both sides have only mass m and zero size. The junction is absolut hard, has the length l and doesn't have mass. S. also this figure: There are no other forces than F (especially no gravity) and there are no other bodies than the dumbbel. Therefore no collisions or bumping. The motion happens flat. How can I calculate the trajectory of the \"dumbbel\"? Is there an analytical or numerical approach I can use in my game program? Thank you very much!", "label": 0}
+{"snippet": "For all the words I know, I can't seem to find the right word for this strange emotion. Some words I have tried come up short in one way or another. Confusion lacks the underlying hatred, annoyance ignores the triggering bafflement, skepticism is to forward to properly describe the abhorrent serenity caused by this mixture of emotions. I tried looking on Google and several other sites for some synonyms for each of them, but my results kept coming up short. Even my 'Better-words-for-authors' guides proved insufficient. I'm starting to think there might not even be a single word in the English lexicon for this emotional mixture that is hatred and anger caused by disbelief. Example of how it could be used: He couldn't help but feel [blank], had the youtuber really sunken below rock bottom. - or - [blank] began to well up inside of her. The others had resorted to Orwellian new speak to justify their problematic behavior.", "label": 0}
+{"snippet": "The normal proof goes as follows: if H(f) is a program that takes the source code of any program f and return whether it halts, we define G to be if(H(G)){ loop forever } else { halt } Which is a contradiction if you run H on G. My problem is the unjustified assertion that a program like G even exists, as presumably it is able to print its own source code and run H on it (or something analogous to that) and halt or not halt based on that. My intuition tells me this violates some information theoretic result I am not smart enough to know about. Furthermore, since we have no idea what H even looks like, this proof only works if you can prove that for every program P, there exists a program G which can print its own source code, run P on it, and then do some stuff based on that. Since the mere existence of Quines, which still conserve information, is already a deep and complicated result (from what I can tell), the truth of Gs existance is sketchy to say the least.", "label": 0}
+{"snippet": "Suppose I have some process that I believe to be the result of a differential equation. It would be reasonable to regard this as the path of a point particle in some notional space. Suppose further that I know the exact shape thaat the path follows, and it is one with a simple description, such as a conic section or a polynomial in two dimensions of low order. Is there a determinate series of steps that will give me a differential equation which has my specified shape as a solution for some initial value, or produce increasingly good approximations of that shape on iteration? If there is an exact solution tell me how to find it. If there is a way to find increasingly good approximations to a numerical solution, describe that way. If the answer or answers to the questions above are reasonably clear and straightforward, but hard to describe compactly, I will accept a citation to a work that contains such answers. However if it is a citation to a book-length work, I want a page range or small number of chapters that contains the answer.", "label": 0}
+{"snippet": "In ceveral textbooks it is said that an ideal LC circuit does not lose its energy, it just bounces from the capacitor to the inductor coil back and forth. On the other hand, any system where charges are going to be accelerated radiate energy (that's should always happen when involved charges are going to be proper accelerated, which is a consequence of Maxwell equations). But then due to this, even an ideal LC circuit should lose after any cycle a certain amount of its energy as radiation, since the charges there are accelerated at all? Therefore I'm confused at that point: Does Bremsstrahlung not occur in an ideal LC circuit (why? That does not make any sense, the charges there are going to be accelerated, so this should give by Maxwell theory radiation losses)? But if this accelerations of charges takes place there, then the energy loss cannot be ignored even in this ideal case, or can it? Does anybody see how to resolve my confusion?", "label": 0}
+{"snippet": "Everywhere it is written that electrons flow through through wire of an eletric circuit, and the reason given is that the battery maintains high potential at one end, and low at another. But, if you think about it from first principle electricity& magnetism, then one would realize by intuition that the provided reason only would imply that the electron would move from the high potential region to the low potential region, not that it takes the specific route of the wire. To find a specific route, it would involve solving of the differential equations. In regards to solution, many places I've seen have written that the eletric field caused by the battery only exists inside the wire, but how do we know that/justify this approximation? I have found this related question, but I felt the answers quite unsatisfactory in regards to the above problem. Also, I Understand that to study circuits, we need more than Maxwell's equations, that is a theory of the matter (charges involved and such) as discussed in this question, but my question is, what is the basis for the justifying that the eletric field is confined to the wire?", "label": 0}
+{"snippet": "Central idea of Michelson and Morley experiment was that if single speed of light predicted is speed of light relative to ether, then as the earth moves through the ether, light travelling along the direction of motion must travel at a different speed relative to the earth and light moving at right angles to the motion. If I get the argument then something like saying say velocity of ball is fixed in air. Then someone watching the ball from a moving train will see the velocity of ball different in the direction of motion. But in the experiment, the measuring apparatus ( equivalent of person measuring speed of ball in train) and the what is being measured i.e. light are in the same frame (frame of earth). Why should the velocity come different in that experiment as they thought? The argument could have worked if someone to look at this experiment outside earth frame? I know I am missing something just not able to pin point.", "label": 0}
+{"snippet": "I don't know if this site is a suitable place to look for examples, but I have a lot of ideas that I would like to find a good example of, and I try to organize these things in a later book. I hope I get to a place where I can discuss my thoughts so that I find people taking these questions seriously, and I think they are thoughts of many people. I am searching for an interesting example/example of a theorem, issue or case in mathematics, in which there is a specific variable that affects the result, while the intuition tells that the result is independent of this variable. In other words, I would like a case where intuition fails to estimate the effect of a factor on a particular problem and one thinks it is ineffective, while reality is otherwise. Are you welcome to find examples of searching for examples on this site?", "label": 0}
+{"snippet": "Urban Dictionary includes one explanation of \"play\" : Anything to do with sexual relations: fooling around, making out, oral sex or having intercourse. However, most of the formal-language dictionaries don't include this explanation, only interpreting the word as \"to tease\" which can describe something childlike such as flirtation, except the phrase \"play ground\" meaning: Having sexual relations with other people who is not your partner. Merriam-Webster Dictionary also suggests \"play (n.)\" as \"flirtation\", which can be converted into \"flirt\" with \"play (v.)\" Is this a difference between the formal language and slang? This question also leads to an answer which regards \"play\" as a synonym of \"flirt\". word for a person that flirts with everyone? Does the slang term have a much broader meanings than the flirty activities implied in the formal language? Does the term imply being unfaithful?", "label": 0}
+{"snippet": "Any introduction of relative simultaneity usually is like this : Alice on a train car shines two beams of light towards both ends where two clock are. She sees both clocks see the light at the same time. Bob on the station looks at the same event and says the trailing clock was hit before the leading clock. I have no doubt about what Bob is measuring, but if speed of the light stays independent of the source, then it should not matter if the frame of reference is moving with the targets -i.e clocks- or not , both Alice and Bob should see clocks are being hit non-simultaneously . Is there any actual experiment that proves Alice is seeing simultaneous clock hit ? I mean has anyone placed clocks on very fast moving objects to prove light hits both leading and trailing sides at the same time ? Or do radio signals arrive at different times to equidistant Eastern and Western stations due to rotation of the Earth?", "label": 0}
+{"snippet": "This question has come up with me in two different Final Fantasy games, where you want or need to collect every memory or skill through random selection where not all memories/skills are available until late in the (main) game (not in the random selection \"game\"). Collecting a memory/skill does not remove it from the set (you can randomly land on it again) My question is: In terms of getting every entity in the set, does it help (in terms of the expected number of plays to pick every entity) to play this sub-game before all entities have been added to the set (assuming even probability distribution over all entities)? If what I am asking doesn't make sense to you, please ask let me know in a comment and I will try to clarify the question.", "label": 0}
+{"snippet": "I'm trying create a new single-item selection system that has either identical or close to the identical probability of an existing multi-item selection system. The current system has multiple \"tables\", each containing multiple items. Both a table and each item inside of that table have a selection probability. That is to say we determine if a table is used based off of its probability, and then we go through each item in that table and determine if that item is selected based on the specific items probability. Using the new system, I want there to be only one table containing one item. The one table should have the combined probability of ALL the old systems table probabilities and the one item should have the combined probability of ALL the old systems item probabilities. Would this mean that I would simply find the average of all the tables and the average of all the items and that is the new probability for the table and item? I'm also curious if there is way to shift the old systems table probability on to the item? That is to say, the table would ALWAYS be selected, and the probability of the item in that table would adjust based on the tables previous probability. Is this possible?", "label": 0}
+{"snippet": "In the book To Have or to Be Erich Fromm claims using \"have\" in English increased due to the rise of the market economy and Protestantism. Where one is alone in the market, with their personal relationship to God, rather than being part of a feudal economy and church where they are taken care of. How well is another conversation, but the point is they didn't talk in terms of how much they personally have so much, unlike in the market economy, where what they have is all they can depend on, with the rise of private property. He wrote that this is the cause of \"have\" being used in more cases such as \"I want to have a party\", instead of \"I want to make a party\", as one may see in other languages. England was ahead of others in the assimilation of a market economy (besides the Dutch). I'm not sure how English compared to others concerning amendability to change though. I did not see similar explanations in the etymology of \"have\". So the question is, how accurate is his explanation? This question can be answered with examples of people changed lifestyles of people along with changes in language. Things happen for reasons, the answer would give the reason, whether agreeing with the question or not.", "label": 0}
+{"snippet": "When I try to solve a hard problem, I have no idea on what to do before I write anything on the paper: apparently, only after I spent hours on a particular problem I find the key idea by just a coincidence. This makes me feel that training myself by solving tons of hard problems on integration or geometry etc... is a waste of time since for the most of it I randomly run into the solution by coincidence and that is what I mean by randomness when solving a math problem. So my question is: how to overcome that? Should I try to solve each problem on my head without writing down any thing? Or what do you advise me to do? And is this a thing that I can solve or I am just not smart enough?", "label": 0}
+{"snippet": "The main statement is: the EM coupling constant is energy dependent, and the fine structure constant (FSS) is the low energy limit. This means that the flow of the coupling constant vanishes when the energy does not suffice any more to create the lightest charged particles, electrons and positrons (there only remain the classical tree diagrams). Below the electron rest mass energy virtual electrons and positrons are frozen out. Consequently, the FTS is a function of the electron mass, and if the electron mass comes from the Higgs coupling, of the Higgs coupling. All QFT literature is about the scaling limit and high energy (where the electron is effectively massless), and and no clear statements about low energy can be found anywhere. But in statistical mechanics terms the above statement appears to be the only reasonable.", "label": 0}
+{"snippet": "The problem arose of choosing a direction for studying and working within the framework of this topic: neural networks as universal approximators for solutions of partial differential equations. At the moment, as a rule, neural networks are used to obtain more accurate numerical approximations, stable, compared to classical difference schemes. Today, there are many different libraries for training models and predicting solutions. My problem is mainly that I want to try, based on already selected numerical approximations, using neural networks, to obtain a number of analytical solutions. The question is: is it possible in principle to obtain a similar result, and are there any practical problems described in scientific articles in precisely this context (not refining numerical solutions using neural networks, but approximating already obtained solutions and obtaining analytical expression). That is, maybe there is some small problem that has important practical significance, the solution of which can be presented in this form? In fact, my question is quite targeted, since I am not asking for an overview of the available methods for solving partial differential equations using neural networks, but rather solving the inverse problem. In this case, I am more interested in the mathematical formulation of the problem and the mathematical aspect of its solution. If possible, please provide an answer, links to similar topics, and possibly literature. Thank you very much in advance!", "label": 0}
+{"snippet": "I have proven this question but somehow I feel like maybe I have done something wrong or I have been reckless somewhere would you please help me to verify my answer If S is a set with least upper bound and greatest lower bound property assume X and Y are nonempty subset of S such that every element of X <= every element of Y so prove Sup X <= Inf Y I have proven this in the following way from the hypotheses we can conclude everything in Y is an upper bound of X and vice versa. so Sup X and Inf Y exists in s and lets denote them by a and b now lets prove this by contradiction lets suppose a>b since b is infimum of Y everything greater than b is not lower bound and this is in contradiction of a not being a lower bound of Y because a is supremum of X and since everything in Y is an upper bound of X . is my proof true or I am missing something in somewhere?", "label": 0}
+{"snippet": "It is said that if one would attach a load physically to the rotating disc from center to rim no current would flow because both in the load wires and the disc itself currents would be generated in the same directions, everything would cancel out, right? But I don't understand why this is a problem? there is a simple workaround: The wires can lead out of the field or extend far away from the magnetic field range, like so: The blue arrows symbolize induced force vectors when disc with shaft and wires rotates, current should flow from the rim to the center of the disc just like in Faraday brushed version, the upper part of the shaft and the wire does not cut the field lines. However I have build this and no EMF was detected, I don't understand why, the voltage induced in the shaft should not block the current coming from the rim to the center of the disc?", "label": 0}
+{"snippet": "Like 'pretty ugly'. The most used meaning of 'pretty' is contradictory to 'ugly', and it could feasibly be used to mean something like (if it were an oxymoron), 'someone who may be considered ugly, but is actually kinda pretty'. But of course it actually means, considerably ugly. Is there a term to describe such pairings? Edit: I'll add more examples as I think of them: Don't trust casinos, they're fairly rigged. I'm an f'ing celibate. The doctor gave me a sick healthy report. I'm a bad good kid. -- Like they are morally good, but are bad (not morally bad) at actually making much out of it, as some role-models may do. Like they are comparing themselves to others. As opposed to a kid who is generally a good kid, but does still get into trouble some, so they may be teetering on the edge of not being considered a good kid. Which would actually be an oxymoron.", "label": 0}
+{"snippet": "This is a question from an interested amateur. Math welcome (as I or another may investigate it some day) but don't expect me to understand it in your answer. Consider a star emitting light. In order to talk about it simply, think of a point light source, and ignore spatial perturbations (for the sake of phrasing the question). At at time t, the light emitted at a single instant at now-t forms a sphere at a distance from the source. What is the density of photons in the surface of that sphere? Perhaps the reply is that the energy is traveling as a wave, but I understand light energy is quantized - that is, the energy has no representation described by infinitesimals, but will be in minimum quantities. How much must the sphere expand so that there are gaps in the image when sampled at different locations on the 'instant-sphere' image? Or, is there an explanation as to why the energy is quantized, yet can manifest at any separation (due to distance) despite the energy density falling below the quantization when the sphere is of sufficient size? What if the source is a candle? Is the original source always sufficient to 'map' adequate photons to any sphere that may be created in the dimensions of our universe? Are there objects we cannot see because they are so far away (or dim) that we are 'in-between' the photons that form their expanding image? Of course, I may simply not understand, but the explanation would be welcome.", "label": 0}
+{"snippet": "I play football. However, I dislike going and sometimes I just dont want to play it. But whenever someone tells me that i do not have to do it or that I can stop when I want, I put all the work into it. One reason I can assume is that my father played ball and I am the last son, he and my mother want me to play but I have \"mixed\" feelings to say the least. Whenever I constantly tell my parents that I dislike football, they obviously get very saddened and I dont care about that in particular. The strange thing is that when I get the choice alone and with nobody around, I always play ball because it makes me happy. But whenever I'm told that I have to, it feels like a chore. I can't explain this to my parents and I feel the need to get this off my chest as I am heading out soon.", "label": 0}
+{"snippet": "As we know, In a circuit, simple or complex, electric fields created by surface charges move electrons which creates current which creates magnetic field which can be coupled to other lines and induce voltage if it is changing by time, which also creates current and this current also creates magnetic field and voltage drop along where it is coupled so on and so forth. Voltage and electric field are related just like currents and magnetic fields are. Changing electric fields create magnetic fields and the opposite is also true. I mean what is the independent variable here? Everything is like being affected by one another continuously. Is it power or energy or fields? What variable or thing I must I hang on to or take as starting point for better analysis of circuits?", "label": 0}
+{"snippet": "Currently the proven theory is the quantum field theory. This theory defines fields in \"all spacetime\" and particles are disturbances in these fields. These particles are punctual and interact through virtual particles. But string theory is not clear to me. This defines the strings (bosonic or fermionic) as the smallest entities and these \"strings are in a spacetime\" but they are not defined unlike the fields in all spacetime. How is it possible? How is the zero point energy then described? So we must understand that at every point in space there is at least one section of string? Here the difference is analogous to the first quantization with the second quantization. Is a string field already confirmed in all string theories? Is there talk of virtual strings? If I take a field, for example the Dirac field or the EM field, these are defined in all time space. It may be that there are disturbances that we interpret as particles, but if there are not, the field exists the same and has a zero field energy value not equal to zero, with virtual particles being created and destroyed. Or for example, the higgs field directly has a non-zero energy in all space. Do we have a defined string in all space?", "label": 0}
+{"snippet": "I am wondering how heat loss happens in sound waves through air. First of all, for wave energy to be transformed into heat, absorption should happen by a medium. But why wont absorption implicitly translate to faster vibrations which would state that even though wave energy was translated into heat vis absorption, that again must have transfered back into wave energy. My logic is that some particles that absorb wave energy will in turn increase their their own kinetic energy, and those that dont absorb wont. So some particles will vibrate more, some wont. Then due to this difference between particles, redistribution energy will occur and since particles that absorbed energy, they might not actually vibrate in a pattern but randomly start moving who knows where. I believe this random motion and not in direct vibration pattern is why we say energy of wave was lost due to heat conversion. Correct ? But I wonder why absorption(even though it increases KE of particle) does not implicitly give it more vibration in the same pattern as it had before the absorption ?", "label": 0}
+{"snippet": "We call G the formula that in the formal axiomatic system employed by Godel to formalise arithmetic has the meaning of: \"I am not provable in this system\". We know that this formula G is true in that axiomatic system since we can exclude that it is false. But why can we say that it is also true in arithmetic itself? After all, within arithmetic such a formula is only a set of symbols, and even if well formed it can still be a false formula. How can we say that such a formula is also true within arithmetic and not only in the aforementioned formal system that formalises arithmetic? We come to this conclusion because the formula G also within mathematics retains the meaning of: \"I am not provable in this system\" or are there other reasons for considering it true within arithmetic?", "label": 0}
+{"snippet": "In security, we speak about different strategies of protection. Mainly, there are three to consider. First kind, usually called shell protection corresponds to the act of preventing the intrusion before the access. For instance, a door, fence, password on a website or silver galvanization of the utensils. That's usually very powerful and easy to maintain. Occasionally, there's a breach and then, we have problems, unless there's also the other kind of security implemented. Here, we're talking about smoke dispensers, mazes, ambulating patrols, honey pots, fake repos etc. What would be a good term for that? (Extra great if it's formal'ish.) The one I've been using is impregnation protection but I'm not sure if it makes sense, let alone is correct linguistically, let aloner comprehensible to regular people. (The third is deterrent protection and not relevant to this question.)", "label": 0}
+{"snippet": "I have seen videos that interview accent experts, like on why Americans do bad English accents (a reason given is a lack of exposure). But are there something like references that one could point to to rate accents? I would think at least one should survey native speakers to get a rating (I met a Kiwi who said he would get mistaken for British by Americans even). Maybe AI could do ratings nowadays if trained on enough. I figure one would need to do individual ratings for each case, even if a reference existed, like having to break down examples, showing where they messed up. If ratings were compiled somewhere that'd be easier though. Like something one could use to show how bad Americans doing accents in lotr were, except like wormtongue, which one may figure influenced having less in the hobbit.", "label": 0}
+{"snippet": "As oppose to a cylinder in two pieces rotating against each other, as in O'Neill's cylinder, what if the cylinder were all one piece and an external thrust, like rockets, set the cylinder in motion, rotating it, would it rotate indefinitely? Would inhabitants of the cylinder experience artificial gravity indefinitely, or would their movement against the rotation of the cylinder slow it, or would movement with the rotation of the cylinder even it out? Or would neither effect the closed system because they'd be pressing against the cylinder from inside the cylinder? Would friction from the air inside slow the cylinder over time, or would the air turn with the cylinder and artificial gravity? If any of the above would slow the cylinder, how frequently would the rockets around it have to add more momentum to keep the craft spinning? Would it at least be a number of years?", "label": 0}
+{"snippet": "What does it mean, \"gravity is so strong that not even light can escape from a BH...\"? This can physically interpreted IMHO that beyond the event horizon of the BH, light is phase transitioned (accelerated) to a FTL superluminal energy that breaks known physics. The inner of the BH therefore appears in our spacetime as \"Nothing\"! Exactly as the rest of vacuum space appears to us, basically as nothing. Someone could therefore infer that vacuum space we generally describe us nothing is actually something and considering the physics of BHs it points to the possibility that vacuum space could be a superluminal FTL (i.e. faster than light speed c) unknown type of energy. There is light, matter and vacuum in our universe. Seems to me that vacuum could be a different energy than matter and light, defying our known physics which we mastered over millennia and concern more about matter and light and their interactions. The vacuum is still a mystery today. Much to learn in the future. Maybe sci-fi Star Wars creators imagination was right after all when saying \"...prepare for a jump to hyperspace!\".", "label": 0}
+{"snippet": "classical electromagnetism , from my understanding can be derived completely from coloumb's law , charge invariance, superposition principle and postulates of special relativity. Biot savart law and lorentz force law are all consequences of it . For derieving faraday's we need not do any experiments, flux rule : e=-d(phi)/dt (e is induced emf and phi is magnetic flux) can be proved from motional emf . From flux rule , it can be understood that emf is induced when area of conducting loop changes in constant magnetic field or magnetic feild is a function of time with constant area. As the flux rule rule is derived from no experimental information other than lorentz force law biot savart law ,we should be able to prove that changing magnetic feild induces emf and hence current is induced . It seems that magnetic feild cannot induce current because it acts on moving charges (which in our case is not moving).experiments shows that it is non conservative electric feild that induces current , but why do we need to do experiment because we already proved it in flux rule. My question is that this information of inducing emf was in flux rule , but it seems that we can not prove induced non conservative electric feild from basic priciples (coloumb's law , special relativity,charge invariance....)", "label": 0}
+{"snippet": "The photoelectric effect is most probably seen when the incoming light has lower energy than the energy needed for both Compton scattering and pair production to happen. The probability of the photoelectric effect to occur also increases when the matter that light interacts with has a big atomic number and high atomic/electronic density such as Lead, Tungsten, and even better Uranium. Given the energy difference between Gamma and X-Rays, and the for high probability, photoelectric effect requiring low energetic photons to occur, how is it possible that X and Gamma rays are both prevented by the photoelectric effect that is observed in those materials? Is it that energy levels of photons that photoelectric effect has to occur on materials like Tungsten are on the high energy boundary of X-Rays and Low Energy boundary of Gamma Rays, and thus rest of the matter-photon interaction effects such as COMPTON and PAIR PRODUCTION are almost always on the GAMMA Spectrum then?", "label": 0}
+{"snippet": "I was watching Susskind lectures in string theory. There he explains that open strings can both, split at any point, and also join at the ends when the ends touch at a single point. I have one question about each of these two processes. Is not the likelihood that the two ends of a string end up at the same spatial position of measure zero? Or the two ends do not need to really meet at the same point, but only be close and then they will be attracted to each other to make it closed? If and open string breaks at an arbitrary point, would not this create particles of arbitrary mass? as the rest mass is proportional to the length? but we know particle masses do not form a continuum. What am I thinking wrong?", "label": 0}
+{"snippet": "If we shine a light that has less energy than the work function energy of the electron of an atom on a metal, the electron is not released but excited and electron gives off this excess energy as heat or collisions or light. We know that the intensity of incoming light does not affect whether the electron will be released from the metal or not, only the energy of the incoming photon determines it. So, Assume that we hit an electron with an energy lower than the work function energy so that the electron gets excited and builds up with energy. WHAT IF Before that excited electron releases its build -up energy as heat or light or collisions we hit it again with a light that again has an energy lower than work function energy, why isn't it released from the metal?", "label": 0}
+{"snippet": "Current in a wire is defined as the amount of charge that passes through a cross-section of that wire in a single second. By this definition alone, it is clear that a current relies on the motion of some charged particle. I believe it is possible that electrons could transfer energy to each other in every direction and when the current starts flowing those energy transfers are more directional. This could lead to electrons always having the same velocity independently of the current. Is this the case? I came up with this wile trying to understand magnetic force around wire, if electrons are traveling in the same direction their spins would also be in the same direction, which could cause magnetic field similarly that would spinning ball in viscose liquid cause flow of that liquid.", "label": 0}
+{"snippet": "In cubical homology you have to consider the group of degenerate cubics and use the group of cubes module degenerate cubes (Massey). If you not do that you get the wrong homology for one point space. In singular homology (simplices) every textbook explain you do not need to do that because you are going to get the same groups. It is easy to check that you get the correct homology groups for a point space without exclude degenerate simplices. But I would like to know a GENERAL PROOF of that. That is the equality of both groups in general order and spaces (excluding or not degenerate simplices). Because it seems that textbook writers consider that evident for I have seen the statement many times but no proof at all and I am not willing to take it by faith. I have read an old paper by Tucker available in internet by googling: Degenerate cycles bound. But I dont know how to apply that to singular homology Thank you very much", "label": 0}
+{"snippet": "I have a set with unknown cardinality. The cardinality can be from a number a to a number b. How can I indicate the number a (or b)? The question in texts is: \"What is the least value of n(A)\" (A is a set with a few possible cardinalities) How can I properly express this in mathematical notation? I used the notation(If you call it a \"notation\") least of n(A) I have seen this question: Mathematical notation for the maximum of a set of function values The things that differ is that I need the notation to express the minimum (or max) number a function can give for a constant x, not the min (max) for a range of x Also, the set of all possible sets isn't given and is there to be found out by the question solver. (as it implies, each solver may generate a different one) n(A) is the cardinality of the set A I do not have a strong mathematical background. so please avoid very confusing notations. thanks in advance", "label": 0}
+{"snippet": "Clearly particles individually pass through slits, be it a single or a double slit experiment. The fact that wave interference is evident in their trajectory may be due to their interaction upon entering the slits. If water particles, or sand particles can together form waves, one can assume they will act in such way that their individual trajectories will reflect the wave they form, and once that wave, if it were to pass through a couple of slits will alter their individual trajectories to satisfy the interference pattern we see on the plate in the double split experiment. In other words, the interference pattern in the double slit experiment (based perhaps on the my sorely naive point of view), are the result of particles, that together form a wave, and upon the entrance to their respective slits, their altered trajectories through the slits reflect their wave relationship. I need to know if any of this is absurd.", "label": 0}
+{"snippet": "[Note I am asking up to, but not including, consciousness as this bleeds into philosophy and is a much messier question] Assuming that the laws of physics have remained constant across space & time since the big bang, has the way the universe evolved been entirely predetermined? While impossible to know the physical parameters & interactions across all space and time, these unknown states would have been acted upon by consistent forces since their onset. Thus, while not knowable, the universe grew along only a single possible path forward, meaning from the instant of the big bang to (cosmic) now, everything has been entirely determined? Phrased another way, was there any physical process that introduced true randomness that caused the universe to have multiple different potential paths? Note that I don't mean things that seem random - such as paths of specific gas molecules when dispersing - since these are ultimately entirely predictable given sufficient knowledge of states & environment. Or is my premise somehow wrong?", "label": 0}
+{"snippet": "If the Hamiltonian manifold for the moving surface of the standing wave is smooth then it must be minimum surface of revolution. The frequency of the string is the capacity of the manifold that is a periodic solution to the Hamiltonian. The frequency cannot be a rational number frequency = velocity/wavelength because the solution to the Hamiltonian is a real given by the Dirac measure. There is only one Hamiltonian so I think string tension and length are determinative. All I want is the mean curvature of the manifold. You are being asked here to prove the manifold is not symplectic. Obviously, you cannot. I say you must conclude curvature is constant. You have no way out of this except to say I have not explained this to you well enough that the string makes coherent theory. Do you have a calculus for the string as a moving surface?", "label": 0}
+{"snippet": "I. I thought he was swimming - I thought he swam for a while but found out it was a lie I thought he is swimming - I thought he was swimming now, but he's not. I thought he swam - I thought he once swam (don't know when). I thought he has swam - I thought he has already swum recently (a couple of minutes ago). I thought he had swam - I thought he had already swum recently (a couple of hours ago). I thought he ... but i changed my mind, and now i dont think in this way If I can't frame my thoughts in this way, how should I do it? Specify proposals, add new ones? But is it possible to designate meaning with the help of time?", "label": 0}
+{"snippet": "If electric fields are created by an accelerated charged particle, such as an electron, and magnetic fields are generated by electric fields in motion, what are the individual fields that make up Electromagnetic Radiation oscillating between? What is the Y axis in their sinusoid function measuring, and how does that continue to oscilate in the absense of moving charge once the photo is emited? Is the electronic field aspect oscilating between a negative and positive charge relevant to overall energy levels, or is it confined to one side of that? I am asking as I have an incomplete understanding of how a photon, without a charge, continues to oscilate at the speec of light. I fully expect that I have an oversimplified understanding of both repsective fields, and I hope to learn what unknown forces are at play.", "label": 0}
+{"snippet": "Hi there Wise people of the internet, I am trying to do analysis some data gathered from a gamma scintillator setup, its stored in root. So i have to do some coincidence measurements, and i found that in Krane, you normally use a TAC (Time to Amplitude Converter) to check for it. However, this gaussian peak expected there has count per channel in y axis. Should i just divide the counts that i recieve for each channel by channel number? I dont see how that will be useful.(this will disproportionately eat away any meaningful data stored in higher channels, which corresponds to higher energy,after calibration, breaking expected stable background of chance coincidence) I am kinda new to detectors. Any help is much appreciated and also any resources/references will also be. Regards", "label": 0}
+{"snippet": "There is a group in which is embedded the set of rational functions considering the formal composition binary operation? More generally how (and when) can we extend a non-commutative monoid (or semi-group) into a group ? I was looking at the interesting case that the natural numbers can be extended to de integers by the matters of considering it as a monoid over the sum and constructing a group of the fractions and then extended again into the rational by applying the almost same method considering the multiplication operation this time. Thinking in this context i try to apply the same ideia to the set of rational function (with rational coefficients - quotients of two rational polynomials) but considering the composition binary operation as it is associative, has a neutral element, etc... But obviously isn't that simple and after searching for a answer i discover the concept of group completion of but not much more and specially not much for the non-commutative case. I'm thinking in a abstract way, thinking in a rational function as a pair of finite sequence of rational numbers, as was already noted in comments that not all rational polynomial are invertible, but. Considering that the case is analogous to the fact that not all integers are multiplicatively invertible", "label": 0}
+{"snippet": "I am stuck writing this sentence: Relics such as Fortran, B, D and other programming languages continue to stay alive, stories of programming languages in the graveyard, and those that spurred magic have antecedent the continues quest of improving programming. EDIT: Clarity. Think of this as a battle cry among programming language developers. In this battle cry, stories of both success, and failures emerge overtime and historically, nevertheless, the journey is not even complete or done. Essentially, events, programming languages in the graveyard, and programming languages that made magic and allowed some companies to achieve technology never seen before, the combination of all of this has thus, \"......\" the continuous quest of improving programming. I am trying to make the reader, from also previous text and stories discussed in the text, to understand that, technologies that left a MARK in an industry or across industries as a result of a different programming language have caused: a curiosity and quest to build even better programming languages that can move industries forward. I HOPE THIS IS CLEAR ENOUGH.", "label": 0}
+{"snippet": "I've read quite a few things about rarefaction waves in terms of giving weak and entropy solutions to certain PDE problems with fixed initial time data. I understand that the consideration of these solutions provide some sense of density that decreases with the passing of time, but I've not heard much else. My concerns are: Why are these kind of solutions specially noticed as one of the very first examples given in several books?. Maybe it's some sort of \"unwritten\" but written tradition to expose these solutions. Are they directly applicable in some specific physics topic or something? I'm pretty sure they are since every attempt I've done to try to research about the topic results in some content including the word \"density\". Any thought, suggestion or reference could be very helpful to me ;)", "label": 0}
+{"snippet": "Papers often use one example throughout as their ongoing example. Similarly, it is possible to focus on one particular case and show a broader claim by using that case. I remember there was a really nice verb for using x at a test case, or perhaps x serves as a use case. I tried a thesaurus searching for exemplify (which is close, but not exactly right) and some other searches ... but none of these helped much. An example sentence might be: Testing food in general, we verbify eggs. or Eggs verbify food in our context. More elaborate examples: Using the RR dataset as a test case, we investigate how different aspects of metric design affect the computation cost. We perform an analysis study on efficiency, using the popular RR dataset as a test case. As a test case for investigating dataset efficiency, we analyze the results of RR.", "label": 0}
+{"snippet": "Could somebody untangle following statement I found here: the integer cohomology groups correspond to the quantization of the electric charge. I know from pure mathematical side the meaning of cohomology groups, but not understand the translative part between physics and pure math at this point: Could somebody borrow some time to sketch how this identification/ correspondence is in detail established? ie how can the (presumably geometric) quantization procedure be \"interpreted\" / encoded purely in terms of certain cohomology group? And furthermore, what is here the precise meaning of the notion of \"a charge\" from viewpoint of pure mathematical terminology? Up to now I thought that a charge in mathematical physics can be recognized as a quantity comming from the existence of global symmetry of the given system, so in simple terms certain intergral/ number witnessing the existence of such global symmetry. Do they endow in the quoted sentence above certain \"bulked\" meaning to the term \" charge\" in order to making it to becomes the object subjected to quantization procedure?", "label": 0}
+{"snippet": "I am trying to find some sort of motivation as to why we integrate manifold over differential form and why especially does it in some form corresponds to integrating the surface of the area. I have already passed my university courses that have covered these topics, including Stokes's theorem with proof (My uni has this approach of definition - theorem - proof structure in all courses with very little motivation). The issue is that sadly I've never intuitively seen that it could have anything to do with the real area if the manifold would be an earth-like object or any other intuitive geometric structure. Is there any free material/youtube class that illustrates that it truly corresponds well? I don't need to see proof as I quite understand the technical side of things. My issue also is that I cannot see differential form in any other way than only technical mathematical extremely abstract definition. Please keep in mind that my knowledge is limited to European standards of a bachelor's degree...", "label": 0}
+{"snippet": "Let say we have some water in the sink and open the closure.. The water starts to move towards it in a whirpool like manner.. If we have a table tennis ball and leave it near the hole of the sink it will rotate like a planet instead move right towards the hole... If we suddenly open up more the hole the water will start to move faster towards the hole but even the water moves towards the hole the orbiting ball will still be able to detect the change of the water speed due to the hole of the sink being openned more... Can this be compared with gravitational waves where even the spacetime tissue moves towards the BH binary star the orbiting planet is still in position to detect this sudden perturbance moving in opposite direction regarding spacetime tissue simmilarely as the table tennis ball get the perturbance moving in oposite direction than the water moving in direcion of the sink hole?", "label": 0}
+{"snippet": "Hi everyone, lets say we have a circle shaped space station and there was an accident where we got a hole (hole A on the picture) on a station and now most of the station is vacuum except for one enclosed part that is still filled with air. Now if we make holes B and C at the same time in the enclosed part, what will then happen with the air? Will it: because air moves in random directions, half of the air will go through hole B and then through hole A and other half will go through hole C, go through entire station and then through hole A because of difference in pressure all air will go through hole B and then through hole A (I am not sure if this is true or I am misremembering, but I read somewhere that air takes the shortest path to equalize pressure so that is the reason that all air will go through hole B? If this is not the true is there some way to influence all of the air to go through hole B, change the size of the holes, make a longer distance between holes C and A?) this and next scenarios are highly unlikely but I have left them just to cover all possibilities , all of air will go through hole C and then through hole A air will stay where it is and it will not leave the room", "label": 0}
+{"snippet": "First, there are only three type of leaves: enter image description here If we assume lamination is compact ,all leaves is only can be a simple closed geodesic. I want to ask about how could union of uncountably many leaves be a minimal compact lamination,actually all leaves is complete simple geodesic,but all leaf in a compact minimal lamination in a punctured torus can only be a simple closed geodesic cause leaf of compact lamination can not goes up to cusp ,so it can only be closed simple geodesic ,so we take closure of any leaf ,it can only be itself, that contrict to minimal. cause i dont know that question above, i can not understand why we cut a punctured torus along a compact minimal lamination which is not a simple closed geodesic ,we can gent a ideal bigons which is patch two side of two ideal triangels.", "label": 0}
+{"snippet": "If I were to measure some quantitavie metric of a sample population and record its mean, and then I were to split by random selection all members of the population into two groups of equal size and record the means of each group on the same metric. Is their a statistical term/measure of the difference of those means from each other and/or the mean for the whole population. This comes as I'm trying to analyze an experiment in which both the control and sample group where told information regarding the experiment during a pretest where I fell like the information could have been left out due to the large size of the population. My rational behind that is the difference in the split means would decrease as the overall population increases and one could assume that both sample groups are evenly distributed.", "label": 0}
+{"snippet": "The court's ruling is claimed to be (...) because it has only counted specific actions to set up some (...) simple structure of justice that only encompasses the last hour neglecting the history of events. (...) = ? = \"has only lasted for a short amount of time prior to being mentioned\" Referring to current attitudes that have arisen in the general span of an hour or day or other fairly newly developed engagement. \"Of the moment\" \"According to recent neoteric dispositions\" The structure is simple because it is founded on only one or two just-happened pieces of evidence. Adjacent to \"transient\" \"transitory\" \"ephemeral\" but in reference to a newly grown/spoken structure of logic. \"recent\" and \"latest\" seem too general and encompassing an indeterminate amount of time, whereas the word I'm looking for refers only to the nature of the just-referenced events, which is (...) Transient = lasting for a short amount of time (...) = has only lasted for a short amount of time", "label": 0}
+{"snippet": "Simulate a magnet sticking to a metal door. The side that is against the door, means that side is the pulling side, and must be the inwards movement of a toroidal magnetic field, pulling the object inwards resulting in getting stuck to the object! Does this mean, the side that is against the object is the side where the field goes in through the magnet and will always be the actual South pole of any magnet? When the magnet is flipped onto the object, the field is in the opposite direction pushing against the object, which will be the North pole of that magnet. Does this mean that when holding a magnet and you can diffirentiate between the actual physical pushing and pulling side of a magnet, them to know that the pushing side must be North and the pulling side must be South? This has Nothing to do with: Stringing the magnet and it will find magnetic North or South and zero to do with earths magnetic field direction, but everything to do with the toroidal magnetic field of the magnet itself and which direction the magnets toroidal field flows?", "label": 0}
+{"snippet": "In school, I learned the mechanism of high and low pressure areas, which roughly goes like this: In the tropics, the sun warms up the air during the day. Water evaporates, so that the air gets warm and moist. Warm air is lighter than cold air, so it rises up, leading to a low-pressure area because the warm air is now \"missing\", so we need air to horizontally flow in. The rising moist air cools down, so it starts to rain, that's why there are rainforests in the tropics. Some thousand kilometers to the north or south, the air is sinking to compensate for the rising air in the tropics. Sinking air warms up and gets dried, so it is very dry (Azores High), leading to the big deserts in the subtropics, e.g. the Sahara. I hope this is more or less correct. There is one thing I do not understand: Why is the air pressure lower in the tropics, and higher in the subtropics (Azores High)? My intuitive physical reasoning tells me the opposite, for various reasons: The reason warm air rises up is not that because \"it is light\", but that it is lighter than cold air, so the cold air can replace it by flowing under it and lifting it up. So the phrase \"warm air rises up, leading to a low-pressure area because the warm air is now missing\" is very misleading: it is the inflowing cold air that lifts the warm air up. So there is never a \"moment\" when we have a lower pressure - the warm air rises because it gets replaced by cold air, and there isn't a reason why the pressure should drop. The air pressure is more or less the combined weight of the air above us. The heavier the atmosphere above us, the higher the ambient pressure. Now, when the air warms up and gets lighter, it gets replaced by the cooler air flowing in. So after the warm air has risen up, we should have more air above us: the warm air that has risen up, plus the cold air that has flowed in horizontally. So the atmosphere above us is heavier in total, which again means we should have a high-pressure area. Another view could be that since the air in the tropics is warming up, it expands. This large-scale expansion should lead to a high-pressure area. After all, if you expand a large amount of gas, its pressure increases until it has had time to expand properly. I am very much aware that all these reasons must be wrong in some way. I don't doubt the existence of the Azores High or the rainforest. I just miss an intuitive understanding. How can the tropics Low and the subtropics High be explained in intuitive physical terms?", "label": 0}
+{"snippet": "My understanding is that in commercial nuclear reactor operations, fuel rods are not used up to the point where they're fully depleted and unable to support fission, but are replaced while they still contain an appreciable amount of fissionable isotopes, to ensure that the reactor stays in a stable operating regime at all times. However, would it be possible, for any reason, to run a nuclear reactor without replenishing the fuel as long as any useful energy at all could be produced, that is, actually \"running the fuel rods dry\" (or, more formally, until criticality is irrecoverably lost and decay heat is the only remaining output left, at which point the reactor is essentially just a fancy spent fuel pool)? Could such an end state be safely achieved, with power just gradually fading away while the control rods extend out more and more to compensate for the declining reactivity? Or would unstable and potentially dangerous operation ensue, as in Chernobyl where operator response to a poisoned core started a catastrophic chain of events? The question is motivated by the realization that one of the safety-enhancing measures proposed for the RBMK reactor design after the Chernobyl disaster was to raise the enrichment grade of the fuel, apparently to reduce the type's susceptibility for core poisoning and the resulting power fluctuations (at least that's how I understood it). I'm interested if the converse is also generally true, that is, whether it would be hazardous to let the fuel deplete too much in modern PWR/BWR reactors that don't share the design flaws of the RBMK.", "label": 0}
+{"snippet": "In biology, the scientific name of a species (known as the \"binomial name\" or just the \"binomial\" or sometimes even just the \"binomen\") is written as a pair of words in italics (or underlined, which is the equivalent of italics in handwriting). For example, modern humans belong to the genus Homo and, within this genus, to the species Homo sapiens. The first word specifies the genus (meaning a group of related species) and has an initial capital, while the second word specifies the species, which doesn't have an initial capital, even if it is derived from the name of a person, e.g. the scientist who discovered the species. https://en.wikipedia.org/wiki/Binomial_nomenclature For example, that Wikipedia article says, \"[...] the binomial name of the annual phlox (named after botanist Thomas Drummond) is now written as Phlox drummondii.\" Note that in the phrase \"annual phlox\", which is not in italics, \"phlox\" has a lower case initial. So in this case it seems that Wikipedia thinks it is acceptable to write \"phlox\" in all lower case. And yet I've often read that a genus name must always start with a capital letter. For example https://en.wiktionary.org/wiki/genus_name says, \"genus name (plural genus names) (taxonomy) The scientific name of a genus, which is always capitalized; the generic name or generic epithet. Usage notes The scientific name (binomen) of a species is a two-part name and is typeset in italics, the genus name (the first name) has an initial uppercase (capital) letter and the species epithet (or specific epithet) is written with a lowercase (small) letter; for example, the scientific name of the wild Rock Dove is Columba livia.\". First, notice how the dictionary quoted above wrongly has \"wild Rock dove\". It should be \"wild rock dove\" of course. Ha ha. Now, if you will, imagine people somewhere had started to refer to one or more locally found species of the genus Columba as \"Columbas\"/\"columbas\". This could happen because calling them \"rocks\" would be confusing. After all, rocks do sometimes fly, land, and so on. In writing they write them without italics or underlining and sometimes without an initial capital. So my question is: Would the latter be acceptable in formal writing among nonscientists? To me it seems a bit anomalous for something that is a type of animal to get a capital letter. It's as if biological jargon has spilled into ordinary English, and where it conflicts with the rules of the latter, it just brushes them aside. The italics/underlining rule is rarely followed by nonbiologists, so do we really have to always follow the capitalize all genus names rule? Can't we follow the English rule that says types of animal are not capitalized?", "label": 0}
+{"snippet": "The following question was discussed in my Discrete Math class, but we couldn't reach a consensus. Think of a set as a collection of bins. Each bin contains exactly one object distinct from all others. While we are allowed to move the objects around between bins, we cannot remove any object, nor can we place two objects into the same bin. Someone hands us a new object. Can we place that object into a bin, after moving around some of the objects already sitting in bins? A. Yes, for some sets this works just fine. B. Sets are not composed of bins and this question makes no sense whatsoever. C. No, there is no room for another object, all bins are already filled. D. It depends on the new object. I'll try to summarize the general arguments for why each answer is correct or incorrect: A: A few of us think this is right, because we can insert the new object into the set iff it's not already in it. However, this is similar to answer choice D, which was given to be wrong (see below). B: Many of us shy away from the answer because it \"sounds\" incorrect, but I personally believe this is the right answer. This is because I disagree with the representation of a set as a collection of bins (each of which contains exactly one object), for the simple reason that the model does not seem to account for adding new bins (and hence does not account for adding new elements). C: Some thought this was correct, if we assume that the number of bins cannot increase (i.e. if we cannot add elements to the set). Some thought this was incorrect for the same reason; because it would mean we can't add any elements to the set at all. This answer was given to be wrong. D: Most thought this was correct - if the new object is different from all the objects already in the set, then we can add it, and otherwise we can't. However, this answer was given to be wrong. And the fact that this is wrong seems to also imply A is wrong (i.e. the intended answer isn't talking about whether or not the element is already in the set). Could someone give a justified answer to this question using concepts from Discrete Math and Set Theory?", "label": 0}
+{"snippet": "I have seen different explanations to understand why there are no local gauge invariant observables in gravity. Some of them explain that diffeomorphisms are a gauge symmetry of the theory and thus any observable evaluated at a spacetime point will be gauge dependent and therefore not an observable. This line of reasoning then argues for Wilson loops, or asymptotic charges as good (non-local) observables in gravity. This explanation, in my opinion, is purely classical, it doesn't rely on the uncertainty principle, or commutation relations, etc. However, other explanations give the argument that any device trying to measure a local observable will have a finite size, and therefore a finite accuracy. If the device wants to probe local physics, it should be smaller. However, the uncertainty principle forces the device to collapse into a black hole before allowing the experiment to give us local information. Alternatively, it is also explained that the commutator of two (quantum) operators has to vanish for spacelike separations but that a metric that is dynamical and fluctuates will mess with the causality of the theory, therefore making the operators not observable. These arguments seem absolutely quantum mechanical. I have a couple of very similar questions: Is the statement \"no local gauge invariant observables in gravity\" true in classical GR, in quantum gravity or both? If it is true in both, why do people treat the statement \"no local gauge invariant observables in quantum gravity\" as something special? Do statements about observables in classical and quantum gravity mean different things?The arguments given to explain each one are pretty different and seem to involve different physics. The first one relies heavily on diffeomorhism invariance while the second one relies on holographic-flavoured arguments about how much information you can concentrate in a given volume before you form a black hole.", "label": 0}
+{"snippet": "I'm building the Proximal Policy Optimization algorithm from scratch (well, using PyTorch). I've been studying it by my own, but I'm a little bit confused in the optimization phase, here is the thing. From what I know... First, we initialize a Policy Network with random parameters. Second, we start with policy rollouts. At each time step (t) of the episode, we compute the Value Functions (functions approximators) in order to get the Advantage Function A(s,a), also, we compute the clipped surrogate objective (J) of each time step (t). At the end of the episode, we sum all the clipped surrogate objective values, this will give us the expectation of the entire episode of the expected cumulative rewards. In the paper of PPO the equation contains the expected value of all time steps (t). Once we have the value of the expected clipped surrogate objective (sum of all clipped surrogate objective values) at the end of the episode, we compute the Stochastic Gradient Descent (SGD). In order to compute SGD we need a loss function, we have our expected clipped surrogate objective function, so we just do -(expected clipped surrogate objective function) and that will represented the loss, that is the same as computing the Stochastic Gradient Ascent in order to maximize the expected cumulative reward or the objective function. Now my confusion comes in here... I thought that the clipped surrogate objective function was computed at each individual time steps (t) and then at the end of the episode, we sum all of them in order to optimize it (compute SGD). The thing is that some authors say that the optimization process (SGD) is done at each time step (t) of the episode instead of at the end of the episode, but why? doesn't the clipped objective function equation in the paper contains an expectation symbol? if the computation is done at each time step (t) then the expected value symbol in the equation is redundant, isn't it? Also, they say that in order to compute SGD we need a loss, I thought that by setting the clipped surrogate objective function to negative (-) we can get the gradient of it and then minimize it using SGD that it would be the same as maximizing it, but the paper shows another equation as being the loss function that the optimization phase uses, how is this? So my questions are... When and how is the clipped surrogated objective function computed (at each time step (t) or at the end of the episode), is my implementation of the computation correct?. When and how is the optimization phase computed (at each time step (t) or at the end of the episode)? My thoughts about the loss function correct? or what does the paper means with this loss function they show? Thank you in advance:)", "label": 0}
+{"snippet": "I am currently very confused about the \"topological\" prerequisites of Lee's Riemannian Geometry (RG) book, An Introduction to Riemannian Manifolds. I have heard that this is a \"truly introductory\" text for beginners in RG. But as for prerequisites, in his preface Lee states that his other two books on Topological and Smooth Manifolds are a sufficient preparation for his RG text. But from several online forums I've come to the realizations that this would be an \"overkill\" just for studying RG (e.g., one need not study all of his Topological Manifolds text to study most of his Smooth Manifolds text!). So, in general, his preface is confusing to me when discussing prerequisites. I'm confident with my analysis background (inverse/implicit function theorem, etc.) As for the differential geometry stuff, I'm thinking about going over doCarmo's Curves & Surfaces text. I'm a beginner in DG and I prefer E. Kreyszig's Differential Geometry as it introduces tensors early on (something I'm highly interested in learning about). I'm also aware of another \"standard\" text on RG by doCarmo as well. So, here's what I need guidance on: Which of the books among Lee and doCarmo on RG is preferable if one wants to get a decent exposure to RG so that they can pursue research in related areas? How much topology does one need to know in order to tackle the texts by Lee and/or doCarmo on RG? For differential geometry, is Kreyszig's DG book sufficient to prepare for Lee and/or doCarmo's RG text(s)? Or is it preferable to study do Carmo's DG before tackling RG? My ultimate goal is (broadly) mathematical physics, in particular, Relativity and Quantum Gravity. Moreover, I consider myself more of a \"math\"-person and so would not prefer texts that ruin mathematical rigor.", "label": 0}
+{"snippet": "I recently asked this question about whether there was a \"distance\" between two galaxies where both the gravitational force and the influence of dark energy would be balanced. The answers and comments seem to indicate that there is indeed such a \"radius\" around a galaxy. I was very interested in this, so I contacted the authors of this paper about this phenomenon. I asked them if it could be possible to have a satellite galaxy orbiting a bigger one just in the point where there would be a balance between the gravitational attraction of the bigger galaxy and dark energy, so that the satellite galaxy orbit would not decay (through gravitational waves, tidal forces...) and avoiding its fall eventually towards the bigger galaxy. They replied that the answer was basically yes, and that they could keep that orbit as long as there was no external perturbation modifying these orbits. But I had one more question about this scenario. My question is: If that balanced state would be possible, would there still be tidal effects between the two galaxies (So that some of the orbits of planets and stars inside the galaxies could be somewhat modified) but without making the orbits of the galaxies decay over time...? I mean, imagine a satellite galaxy orbits a bigger galaxy just in the radius distance where the influence of gravity and dark energy are balanced out. Is it physically possible (at least theoretically) that the tidal forces between the galaxies may affect some of the planetary systems' orbits in these galaxies (for example changing the orbits of planets around their stars like for example making them orbit their stars further apart)? And would these tidal forces disrupt the satellite galaxy from the distance where gravity and dark energy are balanced out? Or without any external perturbation, it should keep orbiting at that distance (even with these tidal forces between the galaxies or the gravitational waves emitted from the orbits around the bigger galaxy)?", "label": 0}
+{"snippet": "I'm an amateur and this is my first question here, I'm trying to formulate question about a general representation I have in mind after trying to grasp the idea of relativity and the concept of space-time. We always talk about the \"speed of light\", but it's a bit of a misuse of terminology, since we should really talk about \"speed of electromagnetic radiations (EMRs)\". Moreover, we recently confirmed that gravitational waves, despite not being of the same nature as EMRs, travel at the same \"speed of light\". Considering that, according to relativity, an object travelling at the speed of light would not experience time passing, and that it doesn't seem to make sense to envision travelling faster than the speed of light, Would it not be natural to consider the \"speed of light\" as being the \"speed of time\", or, let's say the speed at which the present propagates through space ? This way the speed of light and gravitational waves would be actually instantaneous, or at least as much instantaneous as the universe can be, and each point of the universe would \"communicate\" with the other points at the \"speed of light\". Usually when trying to [in]validate this idea by reading other questions or other sources, I find complex explanations that do not really help me evaluate the correctness of the broad model I have in mind. I do not know if this is something that seems quite obvious to everyone already, but I couldn't find it expressed this way, and this mental picture really makes sense to me. If it does not correspond to our current state of understanding, could you give me some clue of where my formulation does not fit reality ?", "label": 0}
+{"snippet": "I understand that \"laws of physics\" is a bit of a misleading term since all they really are is just us applying a logical statement about observed physical phenomena in a way that allows us to predict or understand said physical phenomena. That said, what my question is getting at is whether there are any laws of physics that \"hold at all levels?\" The idea of the \"invariance of physical laws\" is, and has been, a key notion for developing new theories and furthering understanding of phenomena. But for a lot of given laws, there seems to be some system or situation, in which the laws must be modified or corrected in order to hold, or is simply not applicable. I'm not concerned with the numerical accuracy of physical laws, which seems to be the focus of similar questions on this forum. An example of this would be Newton's laws of motion, which break down at the quantum scale (despite having analogous principles) or at relativistic speeds. Maxwell's equations have been described as the \"solutions\" to electromagnetic theory, but they are only correct up to the point of treating magnetism as an unexplained phenomenon and not the result of relativity. Are there any laws that, with current and modern understanding, are always true (I'm not saying that they couldn't be found to not completely the case in the future, but we believe they are currently)? The only one that I could believe fits this description, is the second law of thermodynamics, in that \"entropy never decreases.\" We have entropies for vastly different systems at vastly different scales, from quantum systems to human scales, to galaxies and black holes. However, this may be a little handwavy, as entropy has different definitions for different levels (Von Neumann entropy and the entropy of a black hole for example) and my understanding is that they do not translate from one another.", "label": 0}
+{"snippet": "I am looking for a term to use as the name of a software project that I am working on. The project is a software tool, and this tool aims to be useful in virtually all software, so I am looking for a term that alludes to it being an indispensable, or perhaps even the most indispensable, tool in a profession, as in: the test screwdriver being the most indispensable item for an electrician the monkey wrench being the most indispensable item for a plumber scissors being the most indispensable item for a tailor etc. A different but equally useful direction of meaning would be a term for an item which is guaranteed to be present in a certain line of business or endeavor. For example: In a tire shop they are bound to have lots of tires, so tires are their ___ (fill-in the blank.) If there is one thing that mountain-climbers are guaranteed to use, that is rope, so rope is their ___ (fill-in the blank.) Every priest is bound to have a bible, so the bible is their ___ (You get the idea.) Besides the word \"indispensable\", other terms near the meaning that I am looking for (but unsuitable) are \"essential\", \"sine qua non\", \"tool of the trade\" and \"staple item\". I was seriously considering the term \"bread and butter\", but after reading about it I have formed the impression that it necessarily has a fiscal connotation, while there is none in my case. Please correct me if I am wrong. (Other than that, \"BreadAndButter\" would be an awesome software project name, despite being unconventional: the modern trend in software project names is strongly towards unconventionality.)", "label": 0}
+{"snippet": "In textbooks on many-body quantum physics (e.g. Fetter and Walecka), Feynman diagrams are typically introduced after formulating the Dyson perturbative expansion of the Green's function using Wicks theorem. Then the Feynman diagrams follow as a way to conveniently represent the resulting integral equations. In most literature however, I have noticed that the language is somewhat different. Typically, after introducing the Hamiltonian a certain quantity of interest will be introduced, typically the single-particle Green's function of self-energy. Then there is often a sentence like: To evaluate this quantity of interest we sum the set of Feynman diagrams shown in Fig. X Then Fig. X will contain the perturbative series already written in terms of Feynman diagrams. It seems that the step where this series is formulated, as I find in the textbooks, is typically skipped. I can think of two possible reasons for this: The actual formulation of the Feynman rules from Dyson's equation and Wicks theorem is seen as trivial, and hence not repeated in typical papers. Even if the system is not a standard system treated in other literature. There is actually a faster or more intuitive way to write down the relevant Feynman diagrams from the Hamiltonian, without having to resort to the perturbative expansion explicitly. If this is the case then I would love to see a textbook where such a procedure is explained. Currently whenever I want to understand a paper I go through the whole perturbative expansion for the respective Hamiltonian, which is a very tedious and time consuming process. I would be very appreciative if someone more familiar with this field could tell me which of these is true. Thanks!", "label": 0}
+{"snippet": "I think this is easier to understand the mapping of injective, surjective and bijective in terms of marraige proposal where men are from set A and women from set B but Is this analogy correct? Injective (One-to-One) Functions: If the marriage process between men from set A and women in set B is injective, this means: Every man proposes to a distinct one and only one woman Some women might not receive any proposals (i.e., remain unmarried), but no woman receives proposals from multiple men. So, in terms of our marriage analogy for injectivity: each man proposes to one woman, and no woman has more than one suitor. Surjective (Onto) Functions: If the marriage process is surjective, it implies: Every woman receives at least one proposal. All men have a marraige proposal and it's possible for a woman to have multiple suitors. For surjectivity: every woman gets at least one proposal Bijective Functions: For a marriage process to be bijective, every man must propose to a distinct woman such that every woman gets exactly one proposal, and every proposal is accepted. No man or woman is left without a partner, and there's no situation where a woman has more than one suitor or vice versa. To sum it up using the marriage analogy: Injective: Every man has a partner (definitely unique since they are not allowed to propose multiple women), but some women might be left without a partner. Surjective: Every woman has a partner and they are allowed to propose multiple men so that no man remains without a proposal Bijective: Every man and every woman have unique partners. Nobody is left out, and no overlaps in pairings.", "label": 0}
+{"snippet": "Trying to solve a problem with a colleague of mine, we prove a theorem that I'm sure someone else must have had to come across but couldn't find anything about it. We needed a way to tell how far away from equilateral was any triangle. A measure for any triangle of its non-equilateral-ness. One idea (that later turned out not to be the best) was this: Let ABC be any triangle (the one we want to know how far away from equilateralness is). Let's take any of its sides, say AB. Let's take the point C' in which ABC' is equilateral, and which lies to the same side of AB as C. Let's measure the distance CC'. Let's take points B' and A' the same way we took C'. What we found is that the distances CC', BB', and AA', are equal. No matter which side of the triangle we start with, the result is the same. Is it known to be found earlier? Edit For the record, the proof goes this way: We have the original triangle ABC and three new points A', B', C' such that ABC' is equilateral and so on. Let's see triangles ABC' and AB'C. Both are equilateral and share the same point A. Let's see the geometric transformation that brings C' into C, B into B' and A into itself. Given that the distances C'A and BA are the same, the distance traveled by C' to go into C must be the same as the distance traveled by B to go into B'. Ergo, distances C'C and BB' are the same. By the same way we prove that the distance A'A is also the same.", "label": 0}
+{"snippet": "I came across this sequence called Digital River, where the next number in the sequence is defined as the sum of the digits of the previous number, plus, the previous number itself. It caught my attention for some reason, and I wanted to analyse it. And I found some curious fractal-like patters. But let me begin by saying I am no mathematician, and I was just doing this recreationally, as I don't have the requisite tools and faculty to unwrap why these fractal-like patterns should appear. So I am posting my analysis notebook here in hopes of finding some answers. Now, I have also come across the summatory Liouville function, and it too has similar fractal-like patterns. So, could it have something to do with, or is related in any way to, digital rivers? Some of the comments say that Liouville has something to do with the Riemann-Zeta function. Could the Riemann-Zeta function also explain why fractals appear in subtraction of digital rivers? If so, could you explain how, in a way that somebody without an undergrad degree in Math can understand the source of these fractal patterns? And in doing so, could we formulate a theory or pattern of what other, similar kinds of sequences can show similar fractal-like patterns? Here are some of the fractal-like patterns I've found, to pique your curiosity to download my notebook: P.S. If this turns out to be an interesting problem that cannot be explained away trivially, and you want to work on analysing it together, then I'm happy to collaborate.", "label": 0}
+{"snippet": "I'm sorry for mistakes if any; English is not my native language, but I'll try to explain myself as thorougly as possible. There is a geomerty topic about construction of different geometric shapes using just a straightedge and a compass (a pair of compasses, more accurately). E.g. a regular pentagon can be constructed under these restrictions, but a regular heptagon cannot. hyperlink My question is: why straightedge and compass but not pencil? I mean, the compass as a drawing tool does contain pencil lead. That's a fact. But using the compass in order to construct straight lines, in my opinion, is not rational. I think nearly all people use a pencil to draw a straight line with the aid of a ruler. And the ruler itself, of course, cannot draw anything on its own. I tried to ask it on a different site. I received two answers. The first answer was very ironical and I considered it rude and impolite. The answerer told me: \"If you wish to add a pencil, than you must also add a boy and a girl (who will make your construction).\" I'm sorry, but I didn't speak about boys or girls. Just a pencil, that's the plot. A very sad and unsatisfying response! And another answer was quite polite but obscure. I think it needs some clarification. The second person told me that maths never changes anything. The ancient Greeks just used the ruler (straightedge) and compasses, and that's all. So we don't have the right to change it. I think I could agree with the second answer, but I am curious and inquisitive. So why is it so conservative, why have the rules remained unaltered and why didn't anybody try to change anything? That will be my secondary question.", "label": 0}
+{"snippet": "We have hydrogen inside a tube, and we induce a voltage on it; a current passes through it and light is emitted. The frequencies of light correspond to the differences of the eigenvalues of the energy operator, which is the observable in question, so it is customary to give a heuristic explanation that the electric energy produced an energy transition and the residual energy was emitted as light. At what precise moment did the wave function collapse in this experiment, if we try to describe according to the Copenhagen interpretation? How does that description work in this case? Can you maybe direct me to a paper that describes this in detail? Some more words to clarify these questions: I would like to understand if the wave function is supposed to collapse the moment the voltage is applied, or the moment the electronic transition happens, or the moment the light arrives at the spectrometer, or the moment it hits the photographic film. It would be interesting to know what event, in that interpretation, triggers the collapse. A worked-out model of the whole situation, explaining how one describes each component of the system, would be most welcome. Thanks a lot in advance! Edit: This post has been marked as needing more focus, I think by people that did not understand the point of the question, to whom I'm nonetheless very grateful for their feedback (but please if you're one of them, kindly explain better what's going on because I also don't understand your position). The question was phrased as a bunch of different questions in an effort to clarify it, but it boils down to this: what exactly is the role of quantum collapse in the standard quantum theory's description of hydrogen atom gas radiating in a tube? Thanks again.", "label": 0}
+{"snippet": "I have a bit of confusion because when doing QFT and QFT in curved spaces this particular issue seems to be avoided. I have this feeling that when we quantize a theory, we somehow choose a chart and we stick to it. This feeling comes from, for example, the way we deal with Lorentz transformations in QFT, namely via unitary representations. In my head, change of coordinates is something more geometrical rather than algebraic as is done in QFT. I also asked a professor of mine and he told me that the usual way of quantizing things is chart-dependent and then suggested I read TQFT and AQFT papers for which I'm not ready yet. Can someone help me understand? I am searching for a mathematically rigorous construction of the quantization process (in canonical quantization) and if it can be done in a coordinate free way. Hope my question does make sense. EDIT: I think my question was misunderstood: I do believe that, of course, the physics in QFT is Lorentz invariant. But in my understanding of the process of quantization what we are doing mathematically is the following: pick a chart, construct Fock space/Quantize and then model in that Fock space Lorentz transformations via Unitary transformations. In this process, if I take another chart I construct a different (but canonically isomorphic) Fock space. So you see: in QFT (I believe) you don't treat change of chart in a more geometric way, but you model it algebraically. I think that what I'm saying can be seen in Wightman axioms: there is no reference on the spacetime manifold (of course the choice of the Lorentz Group comes from the isometries of the Minkowski metric but one can avoid talking about the metric completely) , it's purely algebraic. So are Lorentz transformations.", "label": 0}
+{"snippet": "What's the word(s) for a feeling of disappointment when you've lost something of financial value? For example, let's say I'd just got an expensive LCD monitor from a raffle, but I accidentally dropped it and it broke, and I now lament its loss. I guess \"lament\" works okay, but it's not really a colloquial word, and it seems to refer to disappointment in a more general sense (like the loss of a good friend) rather than strictly about valuable possessions. The \"value\" in question should be strictly financial rather than emotional, meaning that you feel sorry for it being expensive rather than it having been used for a long time. I broke my brand-new LCD monitor. I haven't even gotten a single use out of it. I ... that monitor so much! Edit: Just to drive home the point, there's this word in my language that is very specific, because it's used in contexts where you miss out on something of monetary value, lose something of monetary value. For example, when you almost won a monitor but didn't because of one stupid mistake on a game show; or when you'd just won a monitor, but accidentally damaged it and made it unusable; when you actually owned a monitor, but lost it while moving because the delivery guys dropped it. In all these cases, the disappointment is purely monetary, because the monitor was just too expensive and it'd be hard to ever get another one as good. Even in the case of you having owned the monitor, you still missed it because it was expensive, not because it was with you through thick and thin. As an actual example, I have this tablet that's quite cheap, but if I ever \"miss\" it, it's because of my emotional attachment to it, not because it's expensive, because it's actually very easily replaceable.", "label": 0}
+{"snippet": "There are a few river crossing problems that I have seen that share some common aspects. The cannibal and missionary problem is typical. All these problems involve moving everyone from one side of the river to the other side by using a boat to cross the river. Denote by complement, an arrangement that is equivalent to what you get at any stage of the problem by swapping the shore that each person is at. For example, the final position of the puzzle is the complement of the initial position. One thing that these puzzles have in common is that it is legal to start at the final position and do the moves in reverse order and in the reverse direction, going from the final position to the initial position. I noticed a relatively simple property of some of these problems that I am having trouble describing formally, let alone proving. In the solution to many of these problems there comes a point where a new position is the complement of the previous one. If you start at this position and perform the previous moves (except for the last) in reverse order, the last position will be the complement of the first, making the sequence of moves a solution. I hope that what I said makes sense. How could I state this in a more formal manner? It should be pointed out that you can't actually do a complementation, but you can achieve the equivalent. For example, in the cannibal and misssonary problem, you go from having two cannibals and two missionaries on the far shore to having two cannibals and two missionaries on the near shore. This is done by having one cannibal and one missionary move from the far shore to the near shore, but could have also been achieved using complementation. I thought that the idea of complementation would simplify proofs. Here is a more compact description. Let the positions be represented as (A,B), where A is the set of people on the near shore and B is the set of people on the far shore. The complement of (A,B) is (B,A). The starting position has the form (S,-) and the final position is (-,S). If we have a sequence of moves (S,-)->...->(W,X)->(Y,Z) then we could perform the moves in reverse order, giving (Y,Z)->(W,X)...->(S,-). Suppose that you can go from (Y,Z) to its complement, (Y,Z)->(Z,Y). I would like to be able to show that we could go backwards (Z,Y)->(X,W)...->(-,S), giving a solution to the problem. Here is an idea of what I would like to be able to say. In going from (W,X) to (Y,Z), the boat ends up on either the near shore or the far shore. In going from (Y,Z) to (Z,Y), the boat ends up on the opposite shore. This means that, in going backwards, it will be able to go from (Z,Y) to (X,W) and generate all the complements of the first set of reversed moves.", "label": 0}
+{"snippet": "I saw other posts such as this one but I don't think it's quite the same question, or even if it is, the answer employs the operator formalism and I'm not sure I follow it. I'm wondering, if you have two multiparticle states - a multiparticle state being, in my mind, a complex probability amplitude for each possible configuration of particles, as a function of time - then, is a normalized linear combination of these two states still a valid multiparticle state? Keep in mind they are both functions of time that obey the equations of QFT, so the linear combination is also a function of time, and I'm asking if it still obeys the equations of QFT. I'm trying to think about it in terms of Feynman diagrams. In particular, I'm pretty sure you can linearly combine two multiparticle states at one time with no problem - you just get a superposition rather than a pure state. And since the amplitude for a final configuration is essentially the sum of all propagators from the initial state, well, this sounds linear enough to me. I think you would just sum up the independent contributions from all the pure states of which the initial state was composed. What else could it be? What throws me for a loop is that I've seen several posts here and elsewhere talking about the inherent non-linearity of QFT. But I think they might be talking about linearity with respect to combination of single particle states. I'm not worried about that, however, since I can see that multiple identical particles really form a single mathematical entity (a product rather than a sum, e.g. the Slater determinant for fermions), so linearity wouldn't have much meaning in this context anyway. Still, the whole thing appears rather murky so I'd really like to clear up this point. To put it another way, I know that there is interaction within the evolution of a pure multiparticle state, and this leads to entanglement, which, mathematically, is just the inability of the final state to be factored into a single tensor product of one-particle states. But, is it fair to say there is no interaction between the pure multiparticle components of a mixed multiparticle state? (at least, as long as we don't classify summation of complex amplitudes as \"interaction\")", "label": 0}
+{"snippet": "Context: I ask this as a school teacher reaching past the boundaries of my expertise. A colleague was talking about the standard model with an advanced student, explaining how particles interact by exchanging gauge bosons, asking the student to imagine gauge bosons as little spheres. Of course they got to the issue that this mental model doesn't add up, since in classical mechanics such a process always leads to repelling forces, while the forces in electron-positron-scattering are attractive. He asked me on my opinion on how to rectify his explanation in such a way that a student could still create a mental image of the process. This is what I came up with, and while I'm sure that it can't do the actual physics full justice, I would like you to point out precisely in what ways this is inaccurate, so that I can improve it in such a way that an advanced student can still have a mental image of the process. The mental model: In classical physics, waves typically obey the superposition principle, that is, two waves don't interact, but can pass through each other without influencing each other. This is true for electromagnetic waves, but also all other waves the students might have encountered in class. It is not always true for water waves, however. For instance, two tall waves crashing into each other won't pass through each other unchanged since they lose energy due to turbulences. The correct description of their interaction requires an additional term besides just the sum of the two wave functions. We can imagine something similar to be true for wave functions in QFT: As a particle like an electron is described as a wave function, the interaction of, say, two electrons is similar to that of two water waves in the sense that they do actually interact, yielding more complicated wave effects. A main difference is that unlike classical fields, which don't interact with other fields, the electron field interacts with the electromagnetic field as well, and the nonlinear effects come from one electron wave packet interacting with the em. field, which then interacts with the other electron wave packet. And since photons are electromagnetic wave packets, we can think of the em. part of the interaction as being comprised of photons. So what do you think? How (in)accurate is this mental model of interactions mediated by gauge fields.", "label": 0}
+{"snippet": "I am currently thinking through evaporation over lakes, specifically the Laurentian Great Lakes (a complex subject, I know). Particularly, I am trying to wrap my head around why evaporation peaks in the fall and winter. Based on what I have read, this fact is due to the vapor pressure gradient that exists between relatively warm water and dry air (dry in an absolute sense because the air is cold) and the high winds which continually replace that dry air over the water. I have also read that this evaporation from the Lakes has a cooling effect on the Lakes themselves, causing a temperature decrease in the Lakes. I have seen it insinuated that over-lake evaporation is synonymous with a latent heat-flux. Based on what I have read, latent heat is an exchange of energy to a substance without a change of temperature of the substance. For water transitioning from a liquid to a gas, the required amount of energy to cause this phase change is called the enthalpy of vaporization or the latent heat of vaporization. When the air is colder than the water, where is the energy coming from to supply the latent heat of vaporization that causes evaporation (assuming its a cloudy day)? If the vapor pressure gradient is the main driver of the rate of the evaporation, how can the evaporation still be said to be a latent heat flux, i.e., how is the transfer of particles based on a pressure differential called a transfer of heat, albeit a latent transfer of heat? Does a latent transfer of heat mean that the water particles which evaporate do not change temperature, though the liquid water which they leave behind decreases in temperature? Sorry, that's more like three questions! Hopefully they are not stupid ones :) it seems this is a complex topic, and my initial intuition that evaporation is always higher when the air is warmer than the water (thus transferring heat energy to the water, increasing the energy of the molecules, leading to increased evaporation rate since the water molecules are now higher energy) is simplistic and even wrong, as it depends on so many more factors than that. Our world is not a simple one, physically at least!", "label": 0}
+{"snippet": "As is well-known, classical conserved systems have conserved quantities by virtue of continuous symmetries, which can be derived from Lagrangian mechanics. For example, two masses on a spring can swap momentum between the two, but translational invariance ensures that the total momentum is conserved. But what if we introduce damping, specifically viscous damping, into the equations? If we consider a fluid medium, our two-mass system surely loses momentum to the fluid. But suppose that the spring itself is viscoelastic, so that it generates equal and opposite forces on the two masses proportional to their relative velocity. Then, the system is translationally invariant in some sense and conserves momentum, but is not Lagrangian (at least not in a simple way). Is there a theory of how to calculate conserved quantities based on symmetries in damped systems, analogous to how it is done in undamped systems? I can do this for specific cases, but I'm not sure how to do it in general. A few attempts: Constructing a complicated Lagrangian consistent with damping Declaring that damping is a purely phenomenological effect coming from many microscopic degrees of freedom behaving conservatively, and so concluding that the system should have the same conserved quantities as if there were no damping (problem here is that some of the conserved quantities, like energy, must leak into the unobservable microscopic degrees of freedom). Considering the corresponding conservative system and showing that it has conserved quantities. Then arguing that this is true for each frequency even if the \"spring constants\" are complex and frequency-dependent, and so concluding that damping doesn't really change anything. Again, though, this seems to prove too much, since energy shouldn't really be conserved. By way of motivation, I'm working with a system that has an unusually large and complicated number of symmetries, and I'm trying to determine how worried I should be about damping killing the conservation in a real experimental system.", "label": 0}
+{"snippet": "Imagine we have a hollow metallic toroid, with copper wire winded around it, which carries electric current. That implies we have magnetic field inside the hollow toroid. The toroid has vacuum inside. We have a set up of a high voltage supply and an electron gun that takes the free electrons from the metallic toroid and shoots them inside it. The velocity of electrons shot inside the toroid is low enough so the magnetic field will bend its trajectory in a complete circular path within the boundaries of the toroid. Now the electrons are flying in circular trajectory inside the toroid. But this situation can't be hold forever, as the electrons are centripetally accelerated the irradiate photons and thus loose kinetic energy. As they loose kinetic energy and velocity, at some point they will stop orbiting and will stay still. But unless they still exactly in the geometrical center of the section of the toroid (which is highly unlikely), they will be attracted to the boundary of the toroid due to Coulomb forces. And as they move towards the boundary, they will regain velocity and start orbiting again. Resuming, the electrons will loose energy due to their accelerated motion, then regain energy, and then loose it again. Apparently this cycle will repeat endlessly, meanwhile they will radiate photons as they loose kinetic energy. If my analysis is correct, how the energy conservation principle will be applied here? Radiating photons endlessly means giving endless energy. The second part of my question is as follows. Suppose the electrons doesn't radiate photons, due to some arbitrarily stated postulate (like the Bohr's explanation on why electrons doesn't fall on the nucleus of an atom). Apparently there is no obstacle to hold an infinite amount of electrons inside the toroid. The only limiting factor will be the amount of the voltage applied to fire new electrons inside the torus, as previously fired electrons will create repelling Coulomb force for the new incoming electrons. But there will not be such thing as \"dielectric rupture\" as in the case of an ordinary capacitor, so hypothetically an infinite amount potential difference can be set between the hollow toroid and its inside. Is this assumption correct?", "label": 0}
+{"snippet": "I'm having trouble finding a good phrasing to describe a component of a system that is too important -- in a sense that it distracts a person from all the other components, that should have been, or were formerly, important aspects of the experience. The case where I'm trying use it is something like this: We tried adding a new super-queen to our variant chess game that could move anywhere -- but we found that it was ______, and that none of the other pieces were important to the gameplay as a result. Another example, possibly from academia: We recommend that teachers not offer students extra-credit work during a semester. We have found this to be _____, in that the option routinely distracts students from the main body of work and preparation for exams. The key thing I'm trying to highlight is that participants in the system become hyper-focused in their attention on this one component, to the detriment of the other parts. (E.g., while the chess example indicates an overpowered piece, that's not what I want to emphasize here; it could also be the result of a super-weakness that becomes the only thing you'd want to attack, say.) I could also imagine this being used in a work of art: Say, an element of a painting that is too bright or oddly placed. Or a breakout character in a TV show who takes over what was meant to be an ensemble story (i.e., they \"may... overtake the other characters in popularity, including the protagonist\"). Is there a good word or phrase to indicate this state of being too important, and attracting too much attention?", "label": 0}
+{"snippet": "Scenario Consider an empty universe with just the Earth, Moon and the Sun. The Earth and the Sun will rotate about their center of mass, which is inside the Sun. The Earth and the Moon will orbit their center of mass, which is inside the Earth. The Moon and the Sun will orbit about their center of mass, which is inside the Sun. Assumptions Since the Sun has a center of mass with respect to both the Earth and the Moon, which are moving separately, the Moon pulls on the Sun too, just like the Earth does. This results in the Sun not having a closed loop orbit around their common center of mass. I assume the third body affects the two other bodies in this manner: The center of mass of the Earth-Sun system rotates in the same manner the Earth-Moon system rotates about their center of mass The center of mass of the Moon-Sun system rotates in the same manner the Earth-Moon system rotates about their center of mass These two effects describe the same motion when viewed from different frames (Earth-Sun and Moon-Sun systems) The above scenario is more pronounced if you consider Jupiter instead of the Moon, but I'm looking at the minute details. Question The question is whether all three bodies always revolve around their common center of mass, which also accounts for the motion of all bodies with respect to one another? If I'm wrong, how exactly does motion happen in this three body system? (Explain using simple words) Can this be generalized for an n-body problem? (Although probably not useful for computation but seems good for a mental image) I think this can be consolidated into a two-body problem by considering the Earth-Moon system as a single body at their center of mass, resulting in a single stationary point as the center of mass of the whole system. That is, I'm taking the center of masses of the Earth-Sun system and the Moon-Sun system, and taking their center of mass, and I expect it to be the center of mass of the Earth-Moon-Sun system. Or is it just that bodies only revolve around their common center of mass, and the center of mass of the three-body system has no say in describing the motion, aside from being a static point? References The motion of the Earth and the Moon around the Sun for a month (from a WIRED article) The Solar System's barycenter with respect to the Sun (from the Wikipedia article on Barycenter)", "label": 0}
+{"snippet": "Initially, I was looking for how centripetal force is produced on the surface of the rotating earth for a mass kept at any latitude. I went through the following threads - Which force provides the centripetal acceleration that makes objects on earth's surface rotate about Earth's axis of rotation? Is the normal force equal to weight if we take the rotation of Earth into account? Question about the Normal Force exerted by Planet Earth in relation to centripetal force If the ground's normal force cancels gravity, how does a person keep rotating with the Earth? From there, I understood that the resultant of normal force (N) and gravity (mg) is the required centripetal force. But what is bothering me now is HOW? According to the answers, the normal force is slanted such that it is not exactly opposite to gravity. Thus, they don't cancel out, resulting in a horizontal centripetal force. I'm still confused and have the following questions : Why is normal force slanted in the first place ? (Is it because of the earth's bulge, friction or centrifugal force?) I think there's also a vertically-upwards component of the resultant, why is that? (the resultant of normal force and gravity) This is what I see, what is the reason behind this? Source of the image - https://en.wikipedia.org/wiki/Equatorial_bulge Edit - I've gone through this question Is the normal force equal to weight if we take the rotation of Earth into account? but this doesn't clear my doubt regarding the upward component of the resultant of gravity and the normal force. I posted this question because I wanted some more insight into that poleward force and its relation to the bulge of the earth, which isn't emphasised in that question. kindly reopen my question.", "label": 0}
+{"snippet": "This Q&A did not answer my question. The voltage of a circuit is the difference in each Coulombs potential energy at the negative pole, compared to the positive pole. At the negative pole, there's a whole wire for the electrons to pass through under the influence of the Coulombic forces; a whole wire with atoms between which they can accelerate, before transmitting their kinetic energy into the atoms. The longer the wire, the more durations of acceleration (thus, the more kinetic energy is produced). But, the longer the wire, the more resistance there is, thus, the lower the amperage. A lower amperage means less acceleration between each collision (assuming constant wire diameter). So, as the wire gets longer, there's more durations of acceleration, but the acceleration is lower. The accepted answer to this Q claims that this is the explanation. But I doubt these two factors cancel each other out such as to leave the voltage unchanged with change in wire length. That is, despite this, I still think a longer wire would mean more kinetic energy is produced. More kinetic energy means there must have been more potential energy that was transmitted into it; thus, the voltage must have been higher. But it isn't, so what gives? There's the distance factor; the longer the wire, the further away from the charged poles of the battery the electrons get. However, this would then make the voltage dependent on how close you lay the wire to the poles, which is again contrary to the assertion that the voltage only depends on the battery.", "label": 0}
+{"snippet": "I'm now in the process of writing a report on a lab work i did with an Abbe refractometer. In all sources i found the working principle of this refractometer is described as such: \"Light shines into a illuminating prism who's side that contacts the sample is roughed so light scatters uniformly in all direction into the sample. The sample is held between the illuminating prism and the refraction prism (RP). Rays that hit the sample/RP interface at an angle large than the critical angle of the interface suffer total internal reflection (TIR) and thus do not penetrate into the refracting prism. This creates a zone in the refracting prism where there is a shadow. The angle of that shadow depends on the refractive index (RI) of the sample, and it can be measured by adjusting the light/shadow line\". Additionally, some sources explicitly say that the RI of both prisms must be larger than the RI of the sample. Critically, i did not find any source that said otherwise. If this is the case, how is it possible for there to be TIR in the sample/RP interface if the RP's RI is larger than the sample's? Furthermore, i used https://phydemo.app/ray-optics/simulator/ to simulate the apparatus. I found that a shadow zone only formed when the condition: \"prism's RI > sample's RI\" was met. Of course in this situation there was no TIR. In fact, forcing the situation where there is TIR, absolutely no shadow zone was created. Can someone explain to me how this actually works then? Is there something i am getting wrong? I'm almost sure there is because even manufacturer pages say it works with TIR... But still, it is very confusing!", "label": 0}
+{"snippet": "Whenever I Google to try to find an actual formal statement of the first incompleteness theorem (as opposed to all the oversimplified explanations that talk about \"true but unprovable theorems\" rather than theorems independent of the axioms), the definitions that don't just mention something like a system with \"strong enough to do arithmetic on the natural numbers\" mention a system with an \"a sufficiently expressive procedure\" for enumerating theorems, which is reminiscent of terminology used in explanations I've seen of Turing machines, and so I thought perhaps it meant that the incompleteness theorems apply specifically to Turing complete systems. However, when I posted about this on Quora I got responses saying that Turing completeness has nothing to do with it, whereas, on the askcomputerscience subreddit, I got responses saying that yes, the type of systems the incompleteness theorems apply to are mathematically equivalent to Turing complete models of computation. So which is correct? Is a system with a \"a sufficiently expressive procedure for enumerating theorems\" just a Turing complete complete formal language/model of computation? If not, what exactly does that terminology mean? To be clear, I understand that the first incompleteness theorem states only that a formal language with \"a sufficiently expressive procedure for enumerating theorems\" must be either inconsistent or incomplete (i.e. must either imply contradictions or contain theorems that are probably true in some models of the language and provably false in such models), so I don't need an explanation of what the theorem says, so much as clarification on what types of formal languages it actually applies to. I did see this answer to a related question, which seems to imply that the types of languages/systems the incompleteness theorem applies to are systems that are \"recursively axiomatized\" systems, but it's not entirely clear what that means. Based on other simplified explanations I've seen of the the theorem, I guessing it refers to something like \"a system sufficiently powerful to talk about itself\" which would intuitively seems to match up with the concept of using Godel numbering to construct a statement like, \"This theorem is unprovable\", but that still seems rather vague and nonrigorous. Surely, there has to be a specific and rigorous definition/description of the sorts of systems the theorem applies to though, otherwise how would it be useful?", "label": 0}
+{"snippet": "I have been using '[...]' to indicate skips in the middle of sentences, '[...].' to indicate that a single sentence has been skipped (or that a middle of sentence skip '[...]' is at the end of a sentence and so is punctuated), and '[....].' to indicate that two or more sentences have been skipped (or to indicate that an end of sentence skip '[...]' bleeds into a '[...].' or '[....].'): [...]. Because of this qualitative simplicity of negation that has returned to the abstract opposition of nothing and ceasing-to-be to being, finitude is the most obstinate of the categories of the understanding; [...] finitude is negation fixed in itself and, as such, stands in stark contrast to its affirmative. [....]. The determination of finite things does not go past their end. [....]. But since it looks clunky, I was wondering if this is correct instead: [...] Because of this qualitative simplicity of negation that has returned to the abstract opposition of nothing and ceasing-to-be to being, finitude is the most obstinate of the categories of the understanding; [...] finitude is negation fixed in itself and, as such, stands in stark contrast to its affirmative. [....] The determination of finite things does not go past their end. [....] I have not been able to find anything on the topic of skipping entire sentences within block quotes that incorporate entire paragraphs. I know it would be preferable to avoid this situation in the first place by paraphrasing or excluding parts (some style guides even say that ellipses should never be used at the start or end of quotes), but I can't do that here for multiple reasons.", "label": 0}
+{"snippet": "In the past two months, I had found a wonderful pdf that went through a derivation of the determinant with calculating the area of a parallelepiped as its starting point. The document did not get into the weeds of calculating the determinant given a matrix or even focus explicitly on matrices at all; it was probably the single best description of why the determinant tells us about area I had found and I just really found the document's approach to determinants extremely useful. I'm trying to relocate this pdf to no avail and was really helping someone could help me find it. What I remember is this: it begins with calculating the area of a parallelogram as its starting point. It describes how we want the area to change when a side is scaled and when the image is sheared (I very distinctly remembering these two things being bulleted in the first page of the paper) and goes onto describe how these properties would manifest in a general \"area function,\" that is a function that takes in the vectors as inputs and returns some type of unsigned area. It proves several facts about these functions that begin to show how the determinant \"appears\" from answering this question naturally. After this point, they expand their scope to signed area functions and, building upon the results in the first part, show that any function which returns the signed area of a parallelogram is simply a multiple of the determinant. The paper rounds out with a discussion about expanding these ideas to higher dimensions; it describes the problem of measuring the area of a higher dimensional parallelepiped with regards to measuring the area of its shadow. One of the more distinct parts of this description is that it begins with a hypothetical scenario where you find a floating parallelepiped outside of your window one day and cannot interact with it but wish to find its area. My attempts at googling with these bits of information I remember have not been fruitful, so any help finding this pdf would be appreciated.", "label": 0}
+{"snippet": "Motivated by question Can IC engines be modeled as Carnot engines?. I am wondering whether/how Carnot theorem could be generalized to other kinds of devices performing \"useful work\", such as, e.g.: Motor (or generator) fed by a battery Nuclear power generators Solar cells Water wheels I think that the theorem must be generalized in at least three ways: Operating media is neither a gas nor a liquid - that is the reasoning based on isothermic adiabatic expansions might not apply. Generalizing the concept of temperature (introducing \"effective temperature\"?) - e.g., in case of a batter or a water wheel, we do not have two reservoirs with different temperatures to properly speak of, but rather two reservoirs with different (chemical) potential. Generalizing the concept of useful work - solar cell and water wheel are not really transferring the energy between two reservoirs - the energy already flows, and the device simply diverts a part of this energy into work. But, since the energy flows anyway, it is not clear whether/how the part of it that is diverted is useful: e.g., how is the current generated by a solar cell is more useful than the heat generated in the surface illuminated (which may be also \"useful\" in everyday sense.) Perhaps, there is not much left of Carnot theorem with all these generalizations, and we simply need to consider it as limited to a particular class of phenomena? If so, are there other upper boundaries on converting energy to work (that would be applicable to the devices cited in the beginning?)", "label": 0}
+{"snippet": "The Earth, effectively a non-inertial frame of reference, is where Newton concluded his laws of motion. However, Newton's first law only holds in an inertial frame of reference. In the process of inventing the Newton's laws of motion, since almost all (I suppose) the experiments were done in a non-inertial frame of reference i.e. the Earth, why were people confident enough to believe that Newton's first law is true (to some extent, I am not talking about relativity etc.) in an inertial frame of reference? I am not trying to say that Newton's laws of motion are lies. I just had a logical question: since the research was done in a non-inertial frame of reference, how can we invent the laws regarding motion in an inertial frame of reference? I suppose that's because the Earth can be approximated to an inertial frame of reference as the effect of the self-rotation (which causes the Earth to be a non-inertial frame of reference, in my opinion) of the Earth on the objects on the Earth is quite small. And, therefore when people did the experiments, the uncertainty caused by the self-rotation of the Earth is too small to be significant (or, maybe they didn't even find/realise such an uncertainty!). And therefore, by inference (or guessing?), we can invent the laws of motion regarding objects in an inertial frame of reference. In theory, if we do the same experiment in a true inertial frame of reference, we will effectively get the same/similar results. (This is just my explanation, which can be very debatable!) I want to hear how other people think about this question. Thank you!", "label": 0}
+{"snippet": "Let me try to illustrate what I mean. Consider e.g. a Solar radiation storm (Solar particle event) where high-energy protons are hurled at Earth from Solar flares. I've tried to illustrate my conception of this (I know the protons will typically not follow straight paths out from the flare due to the Parker spiral, but it's a simplification): So the protons get captured by the field (given sufficiently low velocities perpendicular to the field, as far as I understand it) and are then led to the poles due to their drift velocity, as they will almost always have some velocity component that's not perpendicular to the field. Now, to me it seems (and the same applies to the plasma in coronal loops as far as I can tell) that there's a current along the field lines themselves due to the drift of the protons, in the direction they're traveling. This should itself induce a magnetic field surrounding the imaginary magnetic field lines at the centers of the helical proton motion as if the magnetic field lines themselves are current-carrying wires, should it not? Something like this: Am I correct in thinking about it roughly in this manner? If so, does that mean that these new magnetic fields could potentially themselves partially trap particles (although I assume the stronger original field would overwhelm it) and induce new magnetic fields around them in turn? Is there a limit to this \"fractal\" process of magnetic field lines acting as currents inducing magnetic field lines acting as currents, and so on?", "label": 0}
+{"snippet": "My question, right up front, is: what is the term for a modifier that behaves this way? But \"this way\" takes some explanation, and that is the rest of the question. I am a mathematician, and my question makes the most sense in a context where words are formally defined anyway, but you can freely substitute \"foo\" and \"bar\" for any technical jargon. A ring is defined to be a set with two operations that satisfy certain properties. Among these properties, there is not universal agreement: should, or should not, the ring be required to admit a multiplicative identity ('unit')? For a mathematician who does not require this, it is easy to indicate when they wish temporarily to impose the hypothesis: they can just refer to a \"unital ring\". A mathematician who will almost always consider only unital rings might decide to make that part of the definition of a ring, so that they can say \"ring\" where a more permissive mathematician would say \"unital ring\". (This lightweight controversy is discussed in the Wikipedia article.) However, this latter kind of mathematician, on making the rare encounter of a ring that does not have a unit, must either make up an entirely new term for it, or call it a \"non-unital ring\". This usage is almost universally understood, but somewhat puzzling: while it makes sense to understand, e.g., a \"commutative ring\" as being a structure that it is a ring, and also satisfies the requirement that its multiplication be commutative, there is no way that one can so interpret \"non-unital ring\" if a ring, by definition, has a unit. So, what's happening here is that \"non-unital\" is not refining \"ring\" by adding conditions, but changing the meaning of \"ring\" by dropping existing conditions. That is, you know something about a commutative ring even without cracking open the definition of \"ring\" (namely, that it has a commutative operation); but, to know something about a non-unital ring, you must not only crack open the definition of \"ring\", but recognize which among the properties one is expected to remove. I'm looking for a word describing the behavior or function of modifiers that behave like \"non-unital\", in the sense outlined above.", "label": 0}
+{"snippet": "So, I was reading some books by Stephen King, S.D. Perry, and a couple authors I really love. I notice they'll use pronouns or certains words twice in the same sentence. When I read it, it's pleasant and doesn't sound weird in my head at all. I assumed that if something is published under an author like Stephen King or Neil Gaiman, it must be grammatically correct to use something like \"he\" or \"her\" twice in the same sentence. I'm not sure if this is why it doesn't sound strange in my head when I read it, but I've provided an example below. Here it is (bolded words are the repeated pronouns): My example: Martin stared at the ceiling above and grimaced, counting the number of bumps and flecks embedded in its expensive paint. He gave up after some number he couldn't remember, tossed to his side, and yawned. The smell of curing lacquer and stain drifted off a nearby nightstand, burning his nose. And here is another example from It, by Stephen King: When he grinned, there was a ghost of the handsome man he would become in the lines of his face. There examples in multiple Stephen King novels of names repeated in the same sentence as well. I'm using Stephen King as an example, but note that almost every published author I've read does this in wildly different genres and styles. Anyway, is using a pronoun more than once in the same sentence grammatically correct? I know sometimes things are grammatically correct, but discouraged or frowned upon, but that's not my question, here. tl:dr; Is it grammatically correct to repeat a pronoun in the same sentence in any circumstance, and if not, why is there published material that violates this rule?", "label": 0}
+{"snippet": "In my limited knowledge of statistics, I am confused between the meaning of Latent Variables and Nuisance Parameters. Here is my current understanding: Sometimes the variance parameters in a regression model (or the overdispersion parameters) are considered as Nuisance Parameters because we are not directly interested in estimating them In a Gaussian Mixture Model, the weights of each Gaussian Mixture are called Latent Variables because we do not observe them directly (although this point somewhat confuses me because we dont observe any parameter directly, latent or non-latent ... all we observe is data) From an estimation perspective: We remove the nuisance parameters (via marginalization, factorization) because they can bias the estimates. I don't fully understand this, but I think it has to do with degrees of freedom, MLE produces biased variance estimates (in complex regression models, we can not a priori know the correction factor needed to remove the bias). Later, if required, we estimate the variance parameters using a more complicated form of MLE called RMLE We remove the latent variables (again via marginalization) ... because they make the optimization problem easier? (i.e. reduce the dimensionality of the function being optimized) Is this the only reason we remove latent variables? Or is there some other reason ? (ex: the estimation of latent variables is biased?) From here, it looks like these concepts are almost interchangeable: A nuisance parameter is latent and a latent variable is a nuisance. They both complicate the estimation process for similar reasons and we try to remove them through clever math tricks (e.g. marginalization). I feel I am missing something here - any one have hints?", "label": 0}
+{"snippet": "My partner frequently asks me questions that, when read literally, are questions about the past, but in intent and intended response are actually conditional questions: Did you have any thoughts about dinner? Did you want to have coffee? ...where the intent is not merely to inquire about the preferences I have established prior to the time of questioning, but also about what my preference might be at the time of questioning. \"Would you have any thoughts...\" or \"Did, or would, you have any thoughts...\" might also capture intent, but awkwardly. I'm quite literal so I've had to train myself out of interpreting \"did\" as a past tense question of fact, but it occurred to me that it might be a regionalism or other speech pattern where there's a kind of merger going on between \"did\" and \"would\", or other shift where \"did\" is used conditionally in casual settings, maybe in cases where there's the possibility that the answer might have been determined in the past, but also might not have. Even in my examples above, \"would\" does feel a bit stuffy and formal by comparison, but I've never used \"did\" this way myself. Does this interpretation make sense idiomatically outside of the individual context of my partner? Does anyone know if there is any regionalism in play? My partner comes from a family that has lived in Connecticut for generations. My family is mostly from the midwest and south. Please feel free to correct me if I am misapplying \"conditional\" or can otherwise better describe the usage here, I will update as I can! Also, unfortunately I don't have the gift of search terms on this one, so I haven't been able to find any discussion of it elsewhere, but let me know if I can add any research or context.", "label": 0}
+{"snippet": "Double-slit experiment image source: Wikipedia The double-slit experiment can be regarded as a demonstration that light and matter can display characteristics of both classically defined waves and particles. It also displays the fundamentally probabilistic nature of quantum mechanical phenomena. In a double-slit experiment using an electron beam an interference pattern is formed after experimenters record a large amount of electron detections. I have seen this answer by \"anna v\" which states an electron never travels through both slits only one slit per electron and the pattern formed is only a statistical probability distribution for the entire accumulation. But assuming in an experiment in which electrons travel one after the other and each electron travels only through one slit then how could the pattern on the screen be different from the one when we close one slit interchangeably and send electrons only through one slit at a time. (Actual experiments have shown patterns are different indeed) I think an electron through double-slit as a superposition of probabilities of spatial distribution. Like this picture below: But according to anna v picture that come to my mind is below (several electrons illustrated): So I have two related questions: Is the so-called wave nature of particles only a mathematical model or is there some physical nature (properties) to the probabilistic wave that passes through the double slit? Is stating whether the electron passes through both slits or it only passes through one slit just a personal opinion/interpretation that cannot be proven or disproven by observations? Edit: Evidence supporting simultaneous two (path) position: Using a Mach-Zehnder Interferometer to Illustrate Feynman's Sum Over Histories Approach to Quantum Mechanics One particle on two paths: Quantum physics is right by Vienna University of Technology Double-slits with single atoms: Selective laser excitation of beams of individual rubidium atoms by Andrew Murray, professor of atomic physics, University of Manchester, UK", "label": 0}
+{"snippet": "I am working on a problem where I need to extract a connected tree of nodes based on certain attributes while optimizing for the minimum number of nodes. Some attributes of the nodes are known in advance, such as resource capacity. However, I do not know in advance how many nodes will be selected in the final tree, especially the intermediate nodes that ensure connectivity and may act as task-forwarding nodes. The goal is to formulate a mathematical optimization model with a set of constraints to select an ordered tree with the minimum number of nodes, where each node hosts specific tasks. Selecting individual nodes is straightforward, but I am struggling to write the constraints to ensure that: All selected nodes are connected. The hosted tasks follow a desired ordered sequence. For example, if nodes host tasks A, B, C, and D, task A should be in a node that comes before a node hosting task B, and so on. Multiple tasks can be placed in the same node if they do not exceed the resource capacity of the node and do not violate the ordered sequence of tasks. A node with task D may act as a root node in the tree. Most of the existing literature I found online assumes either the total number of nodes in the final tree or the total number of edges in the tree is known beforehand. In my case, it is possible that only a single node may satisfy the required attributes and host all the required tasks, or a set of constraints may be needed to satisfy the required attributes. Any hints or suggestions regarding how to formulate these constraints are highly appreciated.", "label": 0}
+{"snippet": "Sorry if this equation is not phrase in precise mathematical form. I am open to suggestions to improve the explanation, and I have tried to formulate the problem as precisely as I could. I was talking to a friend--postdoc in PDEs--today and he was asking me about obtaining some Yahoo data on stock prices for his students. He explained that he had some students working on stock price data and he was looking for software packages/libraries for time series analysis--like ARIMA, GARCH, ARMA, ETS, etc. I told him that as far as I remember, most many models to stock prices or asset prices use stochastic differential equation like the Black-Scholes models. So I was asking if he actually needed like a stochastic differential equation solver, rather than a time series package. He said something that surprised me. He said that many people used to use Black-Scholes models, but implied that they are not used as much any more. He basically said that many people lost money using these models. I myself don't work in mathematical finance or in banking at all. However, I was unaware of any major critiques of stochastic differential equations and their applications. From a formal perspective, I imagine that these SDE models have a set of parameters (means, variances, etc.) that users can tune against some data using an optimization method. I am not sure what optimization would make sense, I can imagine approximate bayes or something, could work, but there are probably a million choices. So is the claim of a bad fit, mean that the error between the model predictions and the ground truth data too high, or perhaps changing over time, etc. Also, are there a different set of finance models being used as replacements for Black-Scholes?", "label": 0}
+{"snippet": "I have seen that it is possible to approximate the metric in the presence of a gravitational field by the Rindler metric: Does a uniform gravitational field exist? Is there any acceleration in a uniform gravity field? Applying the principle of equivalence to an accelerated frame Rindler Coordinates and homogeneous Gravity Field Gravitational field strength and Horizon in Rindler coordinates Now as some answers in the links have pointed out, this doesn't quite describe a uniform gravitational, because the acceleration described by the coordinates depends on one of the spatial coordinates. My question is, how can we refer to this as a gravitational field at all? The Rindler metric is derived from a coordinate transformation on inertial coordinates on Minkowski spacetime, so we know a priori the Riemann curvature tensor will be exactly zero in the Rindler metric. In doing this \"Rindler approximation\" to the gravitational field, say, near the surface of the Earth, we started out with a nonzero Riemann curvature tensor (indicating spacetime curvature exists), and then we obtained a situation in which the curvature tensor vanishes everywhere in the region we're approximating. Doesn't this render the approximation invalid? Even if you argue that the region of approximation is small (which makes sense), there is no sense in which we can make the curvature tensor outright vanish (because the Ricci scalar, which is a contraction of the curvature tensor, is supposed to be invariant). Accompanying this strange change in the curvature, objects that \"fall into the Earth\" followed geodesic paths prior to the approximation, and under the new approximation, the same objects are now undergoing proper accelerations, meaning they are no longer following geodesic paths. Is there a physical interpretation or the mathematical reasoning behind this change? It seems like we are replacing spacetimes outright as opposed to approximating them. Is this understanding correct?", "label": 0}
+{"snippet": "This question was inspired by the interesting discussion here: Why isn't the T in \"relative\" flapped? It seems like the adverb already and the two-word phrase all ready should be pronounced differently, but as far as I can tell, both sound exactly the same. For comparison, consider the other phrase/adverb pair all ready and already, where there is a difference: \"The suitcases are all ready\" doesn't sound the same as \"The suitcases are already...\" because the stress pattern is different ([all ready] as opposed to [al ready]). Additionally, the \"l\" sound at the end of \"all\" in the phrase goes on for longer than the \"l\" sound in the adverb, corresponding to the separation between the two words. If someone said the second sentence (fragment) out loud, it would leave the listener asking \"already what?\" In contrast, I wouldn't be able to hear the difference if someone incorrectly substituted the adverb altogether for the phrase all together. They both have the same sequence of stressed and unstressed syllables ([all to ge ther] vs. [al to ge ther]). More surprisingly, the adverb also keeps the aspirated \"t\" sound found in \"together,\" even though that t is between a stressed and an unstressed syllable. This seems very exceptional, since that context usually requires the substitution of the \"flapped t\" for the \"aspirated t.\" But, if this were the case, then \"altogether\" could be spelled \"aldogether\" without changing its pronunciation, which it can't. (\"Aldogether\" just sounds like I have a stuffy nose.) This also contrasts with \"relative\"/\"reladive\" like in this question, where the two pronunciations are interchangeable (the flapped t one being more common when it's said faster). \"Relative\" is also not an exception to the rule cited in the accepted answer, since there the t comes between two unstressed (or at least only tertiary stressed) syllables. The cited paper states that flapping the t is optional in that case. I'm interested in what the context (either historical/usage-related or some less well known phonological rules, or something else?) could be behind the pair not being differentiable by sound, and only by spelling, but none of the answers to the other question mention the word \"altogether.\" No one seems to have asked this specific question yet, as this one is about meaning and not pronunciation. Here is a reference for the pronunciation of \"altogether,\" confirming it always has a distinct \"t\" and not a flapped t/d sound: https://en.wiktionary.org/wiki/altogether. This proves that I haven't just been mishearing and mispronouncing the word the entire time!", "label": 0}
+{"snippet": "Euclid based much of his geometry on a theory of magnitudes that looks roughly like this: A general theory of whole and part and how they are related in size (eg: the whole is greater than the part). A general theory of the properties of magnitudes (eg: equals added to equals are equal). A basic rule that allows one to determine in specific cases that one magnitude is equal to another (eg: all radii of a circle are equal; all right angles are equal). Euclid applied this theory to lines, angles, and figures (meaning the area). From these simple foundations, he is able to prove the equivalence of all sorts of things that are not related by the basic rule alone. I've been looking for a modern development of this theory, and though there is some interest in it (Robering), modern work on mereology and mereotopology that I've been able to find online all does things that seem to violate the spirit of Euclid's work; in particular: They treat points as parts of lines and lines as parts of the plane (Robering comments on this). Euclid did not do that. In Euclid the parts of a line are lines and the parts of a plane figure are plane figures. They assume a single universal whole of which everything is a part. This is related to the first issue. Obviously there isn't a single universal line of which all lines are a part. Similarly for angles. Also related to the first issue: the works on mereotopology make use of the concept of an interior part, which basically means, for example, the part of a line segment not including the endpoints or the plane figure excluding the boundary. This doesn't makes sense when points aren't parts of lines and lines aren't parts of plane figures. The works on mereology assume that any two objects form a whole. Euclid only considered connected wholes. They assume completed infinities. Euclid avoided those. Robering treats an angle as the infinite plane section enclosed by the rays of the sides of the angle. I assume this is to turn angles into parts of the plane so they can be part of the universal whole. They assume that there is no maximum-sized whole, but this doesn't work for angles if you treat them as Euclid does as their own kind of magnitude. Can anyone suggest a body of work that I can find online that deals with some of these issues?", "label": 0}
+{"snippet": "The direction of polarization of a transverse wave is defined to be the direction perpendicular to the direction of propagation of wave or the direction of oscillation of wave, right? But in the case of Electromagnetic waves, a class of transverse waves, there are two directions of oscillations that are perpendicular to the direction of propagation of the wave, the direction in which the electric field oscillates and the direction in which the magnetic field oscillates. But while referring to the direction of polarization of an Electromagnetic wave, only the direction of oscillation of Electric field is called the direction of polarization. But why isn't defined to be the direction of Magnetic field? For this I thought like this: \"For transverse waves like waves on a string, to determine the direction of polarization, just put a plane with slit in different directions and the direction perpendicular to the direction of slit in which the wave completely gets absorbed is its polarization direction.\" Now, if I apply the same logic to the Electromagnetic waves by replacing the plane-with-slit with a material that can interact with the electric or magnetic components of the electromagnetic field, i.e., a polarizer, then I can define exactly what the polarization direction of EM wave is. First let us introduce a polarizer that can interact with electric field. Generally these polarizers contain some long chain linear molecules placed in the same direction. If an EM wave is allowed to fall on this polarizer, with the normal of plane of polarizer being in the direction of propagation of EM wave, in different directions each time, then the electric component of EM wave gets blocked if the direction of electric component and the axis of the long chain linear molecules are parallel. Hence the polarization of EM wave is along the direction perpendicular to the axis of such long linear molecules or simply the direction of Electric field. Now if I conduct the exact experiment with such a polarizer that can interact with magnetic field then the polarization of the EM wave comes out to be the direction of oscillation of magnetic field. But when direction of polarization of EM wave is referred, only the direction of oscillation of Electric component of EM wave is considered. Why is that so? Don't the polarizers that can interact with magnetic fields exist? Or between the both directions of polarizations only the direction of Electric component of EM wave is considered conventionally because of simplicity? Or am I missing something?", "label": 0}
+{"snippet": "Firstly: having a lot of difficulty figuring out how to articulate this question due to lack of general math knowledge. There are multiple questions posed below, but I feel like if I knew more they could be condensed into a single question and am hoping someone can suggest and edit to the effect of the below. Thank you in advance for your consideration and assistance on this point! Background I'm taking a course which includes descriptive statistics. In that course they describe the method of calculating covariance and provide that equation. I find myself wondering - why did they choose to define it as they did (using multiplication instead of addition between the terms in the numerator - not even sure if that description is accurate). My question? Are equations for things like covariance derived from looking at phenomenon and 'cracking the code' of how those phenomenon could be described mathematically via a proof? Or does one, at some level of mathematical skill, say: I want to model this phenomenon and I want that model to have these features and qualities to its output, therefore, I choose this particular structure to achieve that goal and then I prove that functionality through a proof? If the latter case - what progression of mathematical learning develops that skillset? Is the same skillset used in both cases? Why I ask If I understand the motivation of the creator of the covariance equation, I could compare it to my own motivation and perhaps come up with a different approach to the same problem that better fits my own goals because maybe our goals are similar but not the same... Thank you again for any advice on how to simplify this..", "label": 0}
+{"snippet": "I'm trying to understand how electromagnetic radiation is created and can propagate through the void. I do understand the concept of an electromagnetic field. But I don't understand how we get from a \"field\" to a \"wave\". I'm not really interested in detailed mathematics of how this happens, rather I'm looking for a complete high-level answer that to the extent possible: Explains every step of how we get from having nothing to having an electromagnetic wave that propagates through space (e.g wifi signal) and Provides clear and intuitive justification for any point/law/fact it uses. Preferably all of this should be included within the answer but I do appreciate inclusion of helpful links and references for additional context. Below is my current understanding along with some more specific questions. To create electromagnetic radiation: You make some charge move (e.g through an antenna by creating an oscillating dipole). This moving charge creates fluctuating electric fields and magnetic fields around it All good so far as this is what you expect a charge to do, however these fields will become weaker proportional to inverse square of the distance and you would expect them to basically disappear at a distance. Electric and magnetic fields somewhat magically interact and now you have a self-perpetuating wave that doesn't fade out like the field. I don't understand this part, e.g how we get from a \"field\" to a \"wave\" and unfortunately most of the resources I tend to skip over why. I believe there should be a better explanation. For example, according to Wikipedia, Faraday/Len/Lorentz laws have to do with this. However all these laws/theories require a conductive \"circuit\" that we don't have in the air in the vacuum of space (I do understand how these laws explain how your antenna would receive an electromagnetic signal). Considering magnetic and electric fields/forces will act on charged particles, this raises a few questions: Does the magnetic field produced by the antenna somehow create charge in the air surrounding it? If the whole wave propagation is based on interactions between the fields and charged particles, then how can a wave propagate through the void of space when there is no charge? Thanks!", "label": 0}
+{"snippet": "I'm an undergrad with an electronics repair background trying to find an explanation for one of the fundamental aspects of a transformer. Every explanation I've found of a transformer's basic operation insists that there is essentially no power loss; that is that VxI in the primary = VxI in the secondary. This suggests to me that if there was effectively no current in the secondary (i.e. it was an open circuit or there WAS no secondary) that current would more or less stop in the primary as well. My instructor adamantly insists that this is not the case, and that current in the primary is constant no matter what might be happening in the secondary which boggles my dang mind as it seems to fly in the face of every explanation I see, and I have not been able to get a clear explanation out of him. If this were the case, then a device with a transformer would consume equal power regardless of whether it was operating or not! Right? It seems to me from an intuitive and practical perspective that the EMF on the secondary should be relatively constant with respect to the voltage across the primary, and that the currents through each should be proportional at any given time, so that a changing load across the secondary should somehow influence the current in the primary, but I can't work out or find an explanation of that... mechanism. I feel like it must have to do with the secondary influencing the magnetic field in the core... Please help! I've been wondering about this for years!", "label": 0}
+{"snippet": "In QFT, many mathematical issues arise. Setting aside renormalization, these deal with rigorous constructions of objects underlying QFT: i) In the canonical quantization approach, the main issue comes from trying to multiply (operator-valued) distributions. My understanding is that mathematicians have formalized some settings in which this makes sense, but you have to be very careful ii) In the path integral approach, the main issue comes from defining the path integral (both in terms of defining a sensible measure on paths, as well as making the integral well-defined despite the presence of oscillatory integrals). My main question is: Are the two issues (one for the canonical approach and the other for the path integral approach) related? If so, intuitively (from a purely mathematical perspective) how is the problem of defining products of distributions related to the problem of defining path integrals? I'm particularly curious as to whether there's some intuition to be gained from the usual proof of the equivalence (between the two approaches) in non-relativistic QM (which begin's with Schrodinger's equation, inserts of bunch of intermediate states, and removes operators one by one). In the case of non-relativistic QM, my understanding is that the canonical approach can be made fully rigorous, while the path integral approach isn't quite so (one can use Wick rotation to compute the integral using the Weiner measure, then rotate back using some analytic continuation argument, but I have read that this is only justified in some cases). Given this, do we expect that the issues of rigor aren't quite the same in the QFT land as well? Disclaimer: Apologies for any inaccuracies in my characterization of anything, as I'm still a beginner grasping with many aspects of QFT I am aware that decades of work have gone into formalizing QFT rigorously, and have addressed many of of i) and ii) for different variations of QFTs. What I'd like to understand here in particular is, if these approaches have given insight into how the different issues I outlined above are related. EDIT: I edited the original question to focus on just one question. Originally, I also asked about renormalization (which is what one of the comments addresses)", "label": 0}
+{"snippet": "Would the positive and negative charges line up on either end of the wire? Or would it induce a current? Or would the wire be unaffected by the magnet? This was deleted for being a homework question. I'm not aware of any homework questions like this. I thought this up in my own head. (I drew the diagram in a program called Biorender, which I use regularly.) This IS a question about the underlying nature of physics. The question I have is this, \"If simply moving a straight wire through a field causes motional emf, why then does a loop of wire require an area and a certain angle to create a current?\" Why wouldn't moving a loop create a current if moving a straight wire creates a potential difference? All of the explanations I can find out there separate the two concepts from each other. \"Because Lenz's law states...\" How are they tied together? It's still a wire through a field. Physically, what happens to the charges when a loop moves through a field as opposed to when a straight wire moves through a field? But before I can even get to how the two situations are the same or different, I had to clarify some things about how a current can be induced in a straight wire. The following image was meant as the answer to my question, but Stack Exchange seemed to feel it went in the question. Now it may not make sense why I needed an answer when the answer is below. But that's why the answer is in the question itself in case anyone is confused about that.", "label": 0}
+{"snippet": "I have been trying to learn about lattice path integrals. Unfortunately, majority of the literature on this topic is in regard to Lattice Quantum Field Theory and Lattice Quantum Chromodynamics. That is fine, however what I desire is literature on evaluating plain, standard quantum-mechanical path integrals on a discrete spatial-lattice, ideally in continuous-time. This could be a simple chain of atoms or a crystal lattice, but it would be a system where the lattice actually exists and is not just used as a regularisation tool for a continuum quantum field theory. For example, what is the \"path integral\" (I imagine this would instead be a summation now instead of an \"integral\") for a free particle on a lattice? Can it be evaluated in that it has a closed-form solution? Even if an ideal closed-form expression cannot be obtained, how far can one go? (E.g. reduce to discrete Gauss-sum or a Jacobi-theta function) In the continuum case, this is just a Gaussian functional integral, which results in a Gaussian. What would it be if space is discretised? Then what is the path integral for a harmonic oscillator on a lattice? What if you add a force term? What about a general quadratic Lagrangian? I have struggled to find mention of these problems in the literature. The standard approach is to introduce the typical time-sliced path integral derivation, and then jump to the Klein-Gordon equation. Are there any resources that do not jump to field theory and instead just investigate these lattice problems for simple quantum mechanical toy models? As a slight aside, I was wondering also if you could start from a typical continuum space path integral, for say a free particle, and add a delta-functional constraint to restrict the continuous path to lattice sites? This would enter the action then as a Lagrangian multiplier and may be evaluable. Thanks!", "label": 0}
+{"snippet": "I've started to study in details quantum optics and I find difficulties in linking the concepts of coherence and correlation among fields, especially because I'm building right now a background on classical optics aven if I already have a strong background in QFT. As far as I have understood, roughly speaking, coherence is meant to be some kind of measure on how similar the properties of one or more waves are at two different spacetime points. To describe with a quantity this feature, we make use of correlation functions to build the coherence factor (I'm thinking about the second degree of coherence): the closest the factor to one, the greater coherence my wave(s) shows between the two points. Furthermore, correlation functions usually arise in photodetection experiment, stemming for the importance of coherence itself in any process regarding the measurement of EM field (I know there are alternative ways to takle detection, but I'm sticking the question to the very basics of quantum optics). Now, this means that correlation functions give me the \"degree\" of dependence between the photodetection probabilities at two different points. This means that they have more or less the same role that in any other QFT. But now, this seems to me conflicting with the nature of coherence itself: more specifically, in (free) QFT we have the so called \"miracolous cancellations\" where spacelike correlation functions vanish due to commutation relations, but in the optical theory spacelike correlation functions are at the grounds of spatial coherence measurements, and thus are usually non-zero. I don't get what am I missing, probably I'm misunderstanding some basic stuff regarding coherence itself, and I'm hoping to get enlightned about it. Thanks for the help.", "label": 0}
+{"snippet": "After reading the first two answers to this question, I've become interested in understanding the concept of (co)tangent complex as a way to get some intuition about homotopical algebra, being somewhat more used to the algebro-geometric framework than to the algebro-topological one. More specifically, I'd like to understand this concept in order 'to do basic geometry - this time calculus - on a singular variety', as stated in the first answer (whatever this means), but not 'mechanically', instead trying always to keep an organizing point of view like the one described in the second answer. Also, I'd like to do so following the shortest possible path from basic algebraic geometry and basic category theory directly to the subject matter, with the smallest possible amount of detours, but comprehensively including all the needed basics. (I've studied some scheme theory and homological algebra before, including derived categories, and also ventured a little bit more deeply in the categorical world, but never dealt professionally with these topics and will have to recall a lot before being sufficiently at ease with them.) In this context, what I'm looking for is a double list of topics, one from algebraic geometry and the other from category theory, both ordered by degrees of complexity, designed to be studied in a parallel manner, showing the highest possible level of correspondence since the very beginning, and if possible accompanied with the most up-to-date literature available for this purpose. I'd be very grateful if someone would spend some time thinking about this and writing a nice answer.", "label": 0}
+{"snippet": "There is a particular Twitch streamer from a video game I played, MermaidonTap. If you subscribed and follow her, not all but most of her public streams, she uses \"fuck\" and a lot of the word \"cunt.\" I am a fellow American citizen, but was not born in US but in an Eastern Asian country, and am trying to learn English. I'm just wondering, is it normal for women to use the word \"cunt\" normally? I took university English and finally passed it on the fifth time growing up in America. So I'm trying my best to understand how the words in English come about and how certain words passed down to certain generations. As I have researched, the word, \"cunt\" is a derogatory term towards women and as well as another meaning as vagina. It just seems like, it's derogatory when men call women cunts. But what about women calling other people \"cunts.\" I still find it derogatory, vulgar and I find it hard on my ears to hear words like \"cunts\" or \"fucks\" from women like her. Also, some of my teachers and some friends and my own mother, they both say that people who curse a lot and can NOT control their word usage, means they don't know any other language but vulgar words. They didn't go through college and university. They're not educated was what I heard and been told. Do you think this is also true or not? Overall, I'm just trying to understand the American English literacy. I don't mean to offend anyone but rather understand the meaning of the word being used at a person or in a public audience, like her on her public Twitch stream, MermaidonTap.", "label": 0}
+{"snippet": "As far as I know, the first statement of the correspondence is between two formal theories named simply typed lambda calculus and intuitionistic propositional logic, which maps types to formulas and terms to proofs. We also have other statements for higher order logics and type theories. But it is also famous to replace the word \"term\" with \"program\" when people try to express the correspondence informally (like Wikipedia). I think that if we assume that programs and terms are same things here, then we can conclude that writing a program, which means expressing a program in a possibly Turing-complete language, is actually proving a mathematical theorem intuitionistically (without the use of law of excluded middle and other proof techniques that are banned for an intuitionist!) Is this true? I think that replacing the word \"term\" with \"program\" is misleading here! Because in any statements of the correspondence that I am aware of, we don't have a Turing-complete type theory, and I don't think that type theories are computational models like Turing machines and untyped lambda calculus. Also I think the fact that untyped lambda calculus is equivalent to Turing machine is also misleading to think that a term in a type theory is equivalent to some Turing machine, while as far as I know the equivalence between untyped lambda calculus and Turing machines is not necessarily a bijection, and even if it is, what does it have to do with simply typed lambda calculus?! All in all, don't you think that using the word \"program\" in the statement is wrong and misleading?", "label": 0}
+{"snippet": "A textbook I'm using to refresh some basic grammar states that indirect objects can be identified by it's answering of questions such as 'to whom', 'to what' etc. (fair enough) and they always come before direct objects in a sentence (this raises questions for me). So the text would identify the pattern in: The teacher gave the students homework. as: S - TV - IO - DO but the pattern in: Tim kicked the ball to Ken. as: S - ITV - Prep. It's been a while, but I was taught the direct object received the action of the verb and the indirect object received the direct object, and also that a verb's classification of transitive or intransitive arises from how it is used in the sentence (i.e. it's not intrinsic to the word itself). So that I would have identified the second example's pattern as: S - TV - DO - IO because the preposition is receiving the DO and therefore is the indirect object. Since 'kicked' can be used with or without an object (i.e. The baby kicked.) I let it pass thinking the text and I could both be correct. But a third example from the text has me questioning how transitivity is assigned: Problems led to desperation. the text again gives the pattern as: S - ITV - Prep. But, 'Led' is almost never intransitive - not unless it's the answer to a question or given some additional context. And so this classification seems more forced to me. The text seems to be implying that the role the verb plays in the sentence depends on how you classify the thing it is acting on and that prepositions can not be indirect objects (despite receiving the direct object as well as answering the question 'to what'). Could someone please clarify, illuminate, or otherwise help me make sense of this?", "label": 0}
+{"snippet": "About a year ago, I came across a really cool property of the envelope curve of a parabola that I couldn't prove. I'm posting it now for help: If we have a straight line and a circle that belong to one plane, then the enveloping curve of the parabola whose focus is a moving point on the circumference of the circle and whose guide is that straight line forms two parabolas that can be drawn with the four information: the perpendicular from the center of the circle on the line is the axis of symmetry of the two parabolas, the distance between the guides of the two parabolas is equal to the length of The diameter of the circle, the center of the circle is a common focus of the two parabolas, the straight line is midway between the two guides. If you start from a circle that does not share the line at any point, the segment will leave traces of two parabolas inside each other, as shown in the picture But if you start with a circle cutting the straight line, leave the traces of two intersecting parabolas at two points on this straight line. But if a circle starts touching the straight line, then the traces of one parabola touching the straight line will be left I was hoping to prove it myself, but unfortunately my level of proof does not allow me. Please do a complete proof that discusses the three cases, please, and thank you. Also, is this feature previously discovered or is it new, please attach a reference if it was previously discovered", "label": 0}
+{"snippet": "My question probably sits more on the applied mathematics side. There is a spring mass system, for the case where the mass moves into the spring (vertically downwards) the spring experiences compression and the second order equation for a spring mass system will provide a solution. However, when the mass moves vertically upwards the lets say that the spring cannot experience tension and thus the mass moves freely without the effect of the spring. It is pretty easy to develop the differential equations for each of the two scenarios individually. However would the following procedure presented a decent manner of modelling the system as a whole: Lets say we apply a displacement as an initial condition which causes compression in the spring. Thus initially the differential equation of the spring governs the system. At each iteration the results are reviewed to check if the spring experiences tension. if the spring has tension then the initial conditions for the last iteration of the spring mass system is used as initial conditions for the differential equation which presents free motion. The above mentioned points will work in both directions, thus if the free motion differential equation is in use and the system begins to move vertically downwards the initial conditions from the last iteration will be used as initial conditions for the spring mass system. I am not looking for a coded solution for this since it can be done easily on Python and Matlab using the ode solvers. Would the presented method provide relatively accurate results for the system?", "label": 0}
+{"snippet": "As a rule of thumb, vapor condensation usually happens at the interface between the system and the heat reservoir. Now, according to my analysis below, it is the only way for vapor to condense, which implies the near impossibility of condensation in the bulk of vapor. : As the temperature drops, within the vapor system, whose thermodynamic behavior can be described by a canonical ensemble, energy is favored over entropy. That is, the energy should escape from the system to the heat reservoir to create a large entropy overall. This means that the system has the tendency to evolve into the low energy configuration when the temperature drops. Thus, for such a phase transition to take place, the passage of energy from the system to the reservoir is crucial. The case for vapor is unique in that its only access to the heat reservoir is on the surface, while for other systems, such as the Ising model, it has access to heat reservoir (the phonons, for instance) within the bulk so that we can see \"bubbles\" of broken symmetry, domain walls, forming inside the bulk. At the interface between vapor system and the heat reservoir, the mechanism for such a transfer of energy is the conversion of kinetic energy of vapor into the phonons of the reservoir. In the bulk of vapor, however, there is no direct way for the energy to be transferred. Classically, the energy released by forming a droplet can only be carried to reservoir by vapor. This process is extremely inefficient, and its explicit mechanism is obscure. Quantum mechanically, it should be possible that the release of energy is in the form of radiation, where the \"radiation background\" plays the role of a heat reservoir. Clearly, these two passages of transferring energy to the reservoir should be negligible compared to the mechanism taking place at the interface. So, in any realistic cases, condensation of droplets never happens in the bulk without impurity. It remains to be checked whether such an analysis is physically well-founded and consistent with the experiment.", "label": 0}
+{"snippet": "I am using ZFC as a tool to demonstrate my problematic logic. In zfc we construct a proof system for zfc in zfc (a simulation of a proof is what I mean); we will call it inner proof system. We establish that if there is a proof in this inner proof system that concludes A then A holds. Turing machines can be formalized in zfc with the notions of halting and not halting. The whole question relies upon the argument that the zfc can prove that for every halting turing machine on a certain input there exists a proof of this in the inner system (which I am not entirely sure it is provable in zfc without further assumptions). A turing machine that takes an input (and treats it like an incoding of a turing machine and also as an input) and goes through all possible proofs (in the inner proof system) that conclude that the input halts on itself or does not halt. If such a valid proof was found our machine does the opposite of the proof's conclusion (meaning that if the proof demonstrated halting the machine would enter an infinite loop and if the proof demonstrated not haulting the machine would halt). Under the assumption that zfc is consistent it holds that this turing machine does not halt on itself. This is a construction used to demonstrate the first and second incompleteness theorems in zfc for computer scientists. Assuming the consistency of zfc, the statement that the aforementioned turing machine does not halt on itself cannot be proven by zfc and thus cannot be proven by the inner proof system. Assuming the consistency of zfc, according to the completeness theorem there exists a model of zfc where the statement: \"the aforementioned turing machine does not halt on itself\" is true and another with this statement false. My problem is with the model in which it holds that this statement is false. This means that the relevant turing machine halts. It follows that there is a proof of that in the inner proof system. It follows that the inner proof system is inconsistent. I know there is something wrong with this logic but I cannot pinpoint it (obiously because I did not formalize this argument sufficiently). Where in this sketch of a proof does the argument fail (for example because a statement is not directly provable from zfc without certain assumptions)? Note: my backgroung is in computer science", "label": 0}
+{"snippet": "\"For classical (non-quantum) systems, the action is an extremum that can never be a maximum; that leaves us with a minimum or a saddle point, and both are possible.\" The above statement is an excerpt from the \"Introduction\" (preface) of the book \"THE PRINCIPLE OF LEAST ACTION - History and Physics\" by ALBERTO ROJO & ANTHONY BLOCH. I want to know whether the \"For classical (non-quantum) systems, the action is an extremum that can never be a maximum\" aspect of that statement is true because it looks pretty definitive. (definitive in the sense certain or assertive) Note: Now I know there are a lot of related questions that look like this, but not any of them looks for a direct and definitive answer for this direct and definitive question, most are descriptive questions for descriptive scenarios and most answer's given are describing particular scenarios, incomplete ones or ones that asserting irrelevance of such question's for actual path determination as we only seek stationary action not whether that is minimum, maximum or inflexion point. (This is intended as to why this should not be labelled as a duplicate, not as a judgement on other questions or their answers as they serve their intended purpose. It is however important to differentiate between the scope of this question and other similar questions. I hope the Phys.SE community will respect the original poster's judgement on the relevance and uniqueness of their own questions unless there is overwhelming evidence to say otherwise.). I have already browsed similar questions as indicated by the system and have not found any definitive question or definitive answer. This definitive question clearly expects a definitive answer, so I hope it will remain a question, not a duplicate.", "label": 0}
+{"snippet": "I am an A-level physics student, and I've been taught that temperature is the average kinetic energy of a particle. So when gas particles are heated, they move faster. This makes sense as an airplane traveling faster does make the nearby air warmer when measured from the plane. Say I release a box of room temperature atmospheric pressured gas in the vacuum of space. Assuming there is no gravity, all the gas particles will be traveling in a straight line as they won't be bumping into other particles. And since space is only a few degrees above absolute zero, the gas particles will cool down after they transferred a lot of their \"thermal\" energy via radiation, and thus should slow down (lower temperature = lower speed). Looking at a single gas particle this breaks the conservation of momentum, as it is quite literally slowing down to nothing. So what's going on. Now imagine there is indeed gravity in space, the gas particles will eventually start traveling and be accelerated toward a source of gravity. So its kinetic energy increases and so does its temperature (higher speed = higher temperature). First of all it is heated up by nothing without any sort of heat transfer taking place, and would there be any distinction between temperature and speed? Why does this only seem to apply to gas and not solids - a fast moving car wouldn't look hotter would it (ignore friction with air). So can anyone point out where the chain of logic breaks down because it is not making any sense.", "label": 0}
+{"snippet": "Many electromagnetic interactions are modeled as exchanges of a real photons: e.g. an excited electron can relax and emit a photon. Somewhere else, a photon and an electron can interact, \"consuming\" the photon and leaving the electron in a more excited state. Electromagnetic radiation is modeled as a flow of real photons. The flux of energy radiated through a surface over a time is the sum of all photons' energy that pass through that surface. Other electromagnetic interactions are modeled as exchanges of virtual photons: e.g. the electrostatic force between two electrons is mediated by virtual photons exchanged between them. I understand that these virtual particles are not \"real\" in the sense that they can't be measured directly, and are just a representation of whatever actual physics our models approximate. They \"exist\" transiently, in infinitude. In a vacuum field, virtual photons pop in an out of existence, with their total energy and momentum summing to zero. Can electro/magnetostatic fields be modeled as flows of virtual photons to/from on their sources? In the absence of a field, the \"positive\" and \"negative\" virtual photons cancel out in energy and momentum. In the presence of a charge, are positive virtual photons flowing one way, and negative virtual photons in the other, relative to the charge? What would the net energy and momentum flux through some surface around e.g. an electron be? Part of why I ask: radiation pressure is quantized in the sense that each individual photon imparts momentum on an object, instantaneously, yet it's difficult for me to imagine the situation for static charges where they accelerate continuously.", "label": 0}
+{"snippet": "When calculating area of a hole in an irregular surface for water flow calculations, what defines that area? I need to calculate the amount of water passing through holes in surfaces in a fixed time, knowing the pressure on either side. This is mostly a straight-forward process (discounting the discharge coefficient, but that is a different matter), but the formulas depend on the area of the hole. What I know about the hole is its boundary. If the surface is planar, this is obvious enough and can be calculated via Green's theorem. But when the hole is in a non-planar surface, it becomes much more problematic. What does the area of the hole even mean? The area of the surface? The hole is exactly where the surface does not exist. Outside the hole there is some surface, which I could presumably find information about (though at a serious increase in complexity), but where the hole is, there is nothing. I cannot even be sure how the surface where the hole was cut was shaped. That information was lost with the hole. \"Yeah, there was a kilometer long capped tube there! Good thing that was where the cut-out needed to be.\" Besides, the water doesn't know how this mythical surface was shaped either, so its behavior will not be influenced by that. Whatever definition of area is appropriate here, it cannot be dependent on the exact shape of some surface. The areas of all possible surfaces filling the hole is clearly bounded below, so there is some minimal area. Presumably this would be the best choice. That is a mathematical rather than physical question, but I want to be sure I am properly handling the physics instead just jumping on an idea.", "label": 0}
+{"snippet": "What is electric current? An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. How do we generate electric currents? We know charge is the property of a particle due to which it can interact with electric fields and experience electric forces. We use this property of charge to have electric currents; we connect a conductor with a potential difference (battery) so there an electric field sets up in the conductor causing the free-charged particles (electrons) to drift opposite to the direction of the electric field. Hence we get an electric current. But electrons have another property too i.e mass, which is the property of a particle by which it can experience Gravitational forces. I need help in designing a setup to produce electric current using the property of gravitational mass of electrons. So if we have a long conductor wire and a Gravitational field is switched on such that it's direction is along the length of the wire then electrons (which are free) will experience a Gravitational force and we should have a flow of charges, the electric current. But there can be some problems in this: The gravitational forces are way more weaker than the electric forces. As free electrons move away from one end of the wire, they leave this end positive, so a mean electric attractive force acts on the free electrons tending to prevent their further movement. Possible solutions and crux Electrons in a conductor are loosely bound to the nucleus and at any temperature they will have enough thermal energy so that they can be free and do continuous random motion like gas molecules in a container which is also called brownian motion. And our sir has told us that brownian motion ceases at absolute zero temperature. If we connect the wire from top to the earth then the charge vacancy can be fulfilled by charge flow from the earth. So above thought experiment suggests generating current using gravity instead of electric potential difference. Some study materials I don't thought that I will need to do it but now I felt the need to do this after an answer asking for \"how one would switch on a gravitational field\" and there can be more like that comments in future maybe. So here is a Wikipedia page about thought experiment", "label": 0}
+{"snippet": "The way I work on homework questions, especially for analysis and topology, might be a little different (or maybe not). I would remember the questions and think of them when I run, take a shower, and during other periods when I don't need to use my brain; later I will write out the solution without much thinking. This typically works well even on harder questions that my professor expects more than two hours to solve. However, sometimes I forgot about what I thought before, and my notes for insights, which are random diagrams or phrases on a scratch paper hidden in a stack of papers, are normally either not found or incomprehensible, so I have to rethink the questions. When I actually write out the proof, it is very readable, but as an undergraduate, I have many other time commitments, so I don't have enough time to completely elaborate or type out what I'm thinking. In that case, how can I record my thoughts quickly so I will be able to reproduce them? Also, sometimes I would try different approaches, and typically most of them do not work, so how can I record these attempts and not go into loops? What is frustrating is sometimes I go back again and again on a \"branch\" that is seemingly close to the answer but is very unrelated and other times I spent a too short amount of time on something that is close to the solution. Is there a way to prevent this? For mathematical research, I would imagine the complexity dramatically increases. For my research project (as an undergraduate working in mathematical optimization), my professor typically introduces to me some very nice lemmas, which help me to prove the optimal goal. However, if I'm working on complicated questions by myself, how can I keep track of all the methods I tried and not worry about forgetting about them the next day? Of course, typing everything out is a solution, but how exactly can we type something that is just vague intuition in our brain instead of proofs for lemmas and theorems?", "label": 0}
+{"snippet": "In machine learning sometimes we build models using hundreds of variables/features that we don't know (at least at first) if they might have a relation with the target. Usually we find that some of them do and others don't. Some of them even have a true relation that we couldn't think of at the begining. Once we build a first model, sometimes we have an idea to include a new variable that we know it has a natural relation with the target and that we didn't think of at first. Sometimes this new variable is sparse, though, what means that it's constant or null for the major part of the data. The problem then is that to use the information that the new variable has, we need to find in some node a cut point of that variable that reduces the loss_function more than all the other cut points of the other variables. However, a sparse variable usually doesn't reduce the loss_function a lot because the major part of the data ends on the same side and only a very few part of the data goes to the other side. Also, when we have that amount of variables, statistically we find cut points in other variables which are not related to the target that reduce more the loss_function for those data points in that node. Not because there is a true relation, but just because of statistics. This ends in overfit and also not being able to use the prediction capacity of our new variable. In this circumstances, what can we do to extract the value of our new variable?", "label": 0}
+{"snippet": "In Einstein's original thought experiment involving \"a (very long) train running along a [straight] railway embankment\", of essential importance appears the prescription that \"[E]very event which takes place along the [railway track] line also takes place at a particular point of the train.\" The constituents of the train are surely distinct from the constituents of the railway embankment and track (especially since they are supposed to have moved wrt. each other; each constituent of the train and each constituent of the track segment under consideration have separately met each other in passing). Is it consequently correct to say that each separate event involving train and embankment/track has one particular constituent of the train and one particular constituent of the track as participants in this event, such that this particular pair uniquely identifies the event ?, and that each such event has two distinct parts, namely one distinctive part attributable to the participating train constituent (which is characterized by the train constituent indicating being met, in passing, by the track constituent; perhaps with additional characterizations), and another distinctive part attributable to the participating embankment/track constituent (being vice versa foremost characterized by the track constituent indicating being met, in passing, by the train cconstituent) ? Note that the event-parts in question are not presumed to be separate from each other, or resolvable, in a geometric (spatial) sense. My question is not whether and how certain sets of (finely-resolved) distinct events may be considered and addressed as one (coarsely-resolved) event; nor whether any one actual particle (or even several) may be considered fully contained in any spacetime region of finite spatial extent. My question is rather conceptually: Whether (at all) and (if so) How to reconcile speaking of an event as \"having distinguishable parts\", as described above, while also speaking of an event as \"a point in spacetime\", or \"a point of spacetime\" with the understanding that: \"A point has no part(s).\" ?", "label": 0}
+{"snippet": "I'm currently taking this college calculus course, and this exercise has stumped me. It is in German, but hopefully what it's asking is fairly clear. To summarize, the problem first asks me to prove that the preimage of an intersection of a family of sets is equal to the intersection of a preimage of a family of sets, where f: A -> B and Ui is a family of subsets of B. To do this, I just gave the general example of x being an arbitrary element of A, which means that x is an element of the preimage of the intersection, which means for all values of i f(x) is an element of Ui, which means x is an element of the intersection of the preimage of Ui. Image of my answer cause I can't figure out MathJax: Then the problem asks to show that for a family Vi, a subset of A, an image of the intersection of a family of sets is not in general equal to the intersection of an image of a family of sets. Yet, for every example formula and sets I can conjure up, I always seem to prove that the two sides are in fact equal. No amount of coaxing and complaining on Bing or ChatGPT causes them to bring an example up either - they just keep giving examples where the two sides are equal. So, is this a typo from my professor and this expression actually is generally correct, or am I missing something? What family of sets and functions would make these not equal? Thank you!", "label": 0}
+{"snippet": "How is quantum entanglement different from a controlled experiment where a pineapple is smashed at a high speed to a perfectly symmetric object and measuring one of its piece in air for spin, speed, direction etc. and finding correlations with other pieces of pinapple in mid air? In quantum mechanics information cannot travel from piece A to piece B at faster than light to explain the correlation so the result is seen as unexpected (at least to people outside the science community like me) and at any time a piece can have any property but once the properties of a piece is measured the wave function will collapse and the properties of other piece or pieces becomes clear. But isn't the correlation simply due to how the piece or particle was generated? No information needs to travel because the particle is simply continuing to react to the same common generation event? If we can call it information isn't it already with all the particles or pieces of pineapples in air already? I (am a beginner, used to be interested in physics but nobody gave me answers so lost interest eventually and took a career in finance. this one was one of my questions) also view quantum mechanics as deterministic rather than probablistic but think the probablistic approach is necessary because we cannot measure all the variables with our very limited measuring and processing capabilities. For example, a roll of die by a machine is deterministic if we measure and process everything from the light fluctuation in power, air movement in real time, mass of the die, initial position, curvature, area of contact, etc. but because that is too complicated we use it as random with a probability. I feel in quantum physics we are doing the same thing as it is simply more practical, but everybody I talk to truly believe I am wrong. Mentioning this as it is related to the question, that is, the properties can be calculated without measuring in quantum mechanics if we have virtually unfathomable knowledge, measurement capability and processing power. We don't have that so in my view too probablistic quantum mechanicsm is the way science can progress, so no question about that, but is it established that quantum mechanics cannot be deterministric in reality? Just want to know where and why I'm wrong. Thank you in advance.", "label": 0}
+{"snippet": "It occurred to me that the limits of possibility to the nature of the universe is it is either deterministic ie we are all at the will of natural laws that determine the outcome of events from the moment of inception and we are philosophically dust in the wind. Or is the world random and our future is uncertain and indeterminate we have freewill and there is nothing governing our future but our free choice or is it both of these scenarios happening concurrently. I am no expert, but from what I gather from quantum mechanics is that the cause of events at the quantum level is indefinite and the outcome of these uncertain and probalistic. There is the principle of uncertainty in which determining the property of a particle results in an uncertainty in determining the nature of another property of this particle is it this principle that makes it difficult to get precise measurement that is a factor in us being able to predict the outcome of events in a linear deterministic equation that gives us the unpredictable nature of quantum mechanics ie there is an equation governing the outcome of events at the quantum mechanical scale and classical scale but we are unable to feed that equation with precise data to enable us to accurately predict their outcome ,kind of like how dynamically chaotic systems are mathematically determined by there initial condition but a small perturbation or difference in initial conditions results in a different outcome. I know its that old chestnut I am not a mathematician or physicist but there can only be three possible scenarios any response will be welcome even if its disparaging.", "label": 0}
+{"snippet": "The proofs presented in lectures, textbooks ect. are usually cleaned up versions that show just the necessary steps for logically proving the theorem, not the thought process that went into the proof. To give a concrete example, I'm working through an (overall quite good) MIT Open Course Ware class on real analysis. I just paused a lecture where the professor said: Now, when you write a proof, as you'll see, it's going to be magic that somehow this h does something magical. That's not exactly how you come up with proofs. How it comes up is you take an inequality that you want to mess with, you fiddle around with it, and you see that if h is given by something, then it breaks the inequality or it satisfies the inequality, which whichever one you're trying to do. And proceeded to just write the finalized proof. Because that's not the part I care about. The main thing I want to learn is the part were you do the fiddling around to come up with the proof to begin with. Verifying proofs other people made is (relatively) straightforward, and the property being proven (Q doesn't have the least upper bound property) is important but I'd be willing to take it as an assertion if I was just trying to learn about Q rather than how to do analytical proofs. I would really like to see examples of someone who is good at proofs showing their work in creating a new one including the dead ends, fiddling around ect. I have tried to teach myself this step by just going out and proving things, and have made a little bit of progress but thing I would greatly benefit from more examples of deriving proofs.", "label": 0}
+{"snippet": "In gel electrophoresis, there needs to be an electric field created in the gel. I realized that I have some gaps related to my understanding of electromagnetism because I cannot fully understand in what conditions a field gets created. Are the electrode plates on either side in contact with the gel or insulated, and if so, how does this affect the field? My understanding is two insulated plates with different voltages would still create a field between them. Is the issue that the surface charges in the gel would align themselves to cancel out this field on the gel inside? Thus, do you need to actually pass a current through the gel in order to create an electric field inside? I think this is related to the nature of the electric field in a current carrying wire (where I treat the gel as a really thick rectangular wire), which I also realize I don't understand. Namely, do the electrodes need to span the full width of the gel rectangle to create a uniform field across the width? More generally, what are the possible ways to create an electric field on the interior of a conductive object such as a gel? Do you have to pass a current through it from one side to the other? My other thought is that a changing magnetic flux would also create an electric field, although it would be of a odd shape. But would this induced electric field exist on the interior or also be subject to some cancelling effect as is the electrostatic case?", "label": 0}
+{"snippet": "Recently I saw a conversation between Sean Carroll and Slavoj Zizek concerning the MWI. One of the questions that drove Slavoj concerned with this question of Ontology vs. Epistemology, as the way Sean had described the current understanding of MWI is that we merely 'don't know' where we are on the wavefunction which seems to keep the openness of reality at the level of epistemology rather than ontology. The question I have concerns entanglement with new information that an object encounters as it is coming in from outside the object's light cone. In my understanding when entanglement-measurement occurs, some pair (or more) objects in the wavefunction take on a correlated value, but then the price of this is that other values become randomized (so electrons take on opposite spins, but then the spin of each electron is not determined). What I am wondering is as we pass from before the moment of entanglement with new information coming in from outside the lightcone to after that moment, some of the information will be consistent (or not consistent) with our current history - that information gets zipped with (or excluded from) the entanglement event, but all the sort of 'random' information that is really new... is it the case that the wavefunction of our object has a different space (or location on the wavefunction) for each of these random timelines before the encounter with new information - or is that space created at the moment of entanglement with the new information? That is... is it the case that our original object is actually already always split into all of its future possible timelines in a way such that various points on its original wavefunction can be assigned to various final 'futures' - or is that split not possible in principle or in the mathematics from the beginning of the calculation (so that in reality many futures pass through the same original point on the wave function)?", "label": 0}
+{"snippet": "I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting. Given hierarchinal demand time series. where the region level time series is the sum of district level time series at each point in time and district level time is the sum of city level time series at each point. sum of all the city level time series at each point in time should equal region level time series. There are also covariate time series (both numerical and categorical) associated with each city's demand time series. e.g. rainfall level, temperature, traffic level, taxi supply amount, date information like weekday or weekend, holiday information and Time invariant features like type of city. (e.g. industrial, CBD, residential etc. ) Note: The city level time series are quite sparse ( have many zeros). How do I go about using a bayesian framework/statistics to model and predict the mutivariate (city-wide) demand time series? The reason for choosing the bayesian framework is to estimate uncertainty in the prediction. Build a strong prior sequentially over time which can capture the fundamental data distribution/patterns without being affected by noise in instantaneous data. incorporate the various pieces of covariate information together to enhance prediction accuracy. Here are my thoughts: Use summary statistics of covariate time series and response time series like ACF to compare similiarities between and try to explain causation. Try to improve dataset quality by (probably using bayesian a hierarchical model using partial pooling) to combine sparse and low quality (lowly correlated time series to response time series) covariates to model a better covariate. Use bayesian sequential learning to sequentially accumulate learned patterns over time into the prior distribution. Could someone give me your thoughts and suggestions on how to go about doing this? Thanks.", "label": 0}
+{"snippet": "When a mathematician says that two categories are the same thing, they may mean there is an equivalence or an isomorphism between them. I am wondering if there is a precise way we can say that two categories that are isomorphic are different categories. I have no idea what I mean, but perhaps it has something to do with models of categories in Set. I just feel there may be justification sometimes when two mathematics feel that two isomorphic categories should be considered independently. Is this possible? Does it ever come up in discussion? For example, consider this language on modules \"The concept of a Z-module agrees with the notion of an abelian groups.\" This language \"agrees\" really means there is an isomorphism of categories. It seems like the theory of categories simply deletes any way of seeing them differently, but is there another way of seeing them where one might say\"No, we consider them differently!\" I think this might have something to do with the way computer scientists talk about monads in a different way than mathematicians. If you've ever looked at these two literatures, they are nearly incompatible at times. This may have something to do with the notion of \"up to isomorphism\" in category theory. When, in category theory, do we say, \"no, I won't forget details that are deleted when we work 'up to isomorphism'\"? Is there category theory that doesn't work \"up to isomorphism\"? Which category theory concepts and constructions only work up to isomorphism and which, if any, go beyond this?", "label": 0}
+{"snippet": "Where from Hawking radiation actually arise? I would like to connect the answer with the technical derivation along the lines of the original calculation by Hawking (a modern account of which is given in Harvy Reall's notes). I have seen this where the three answers apparently don't agree with each other entirely. i. The first answer points out to tunneling process (whose math I would like to see) or particle-antiparticle production near event horizon none of which isn't directly connected to the original derivation. Well, the particle-antiparticle picture is claimed to be somewhat connected because we can find their mention in many \"formal\" places (also) including Hawking's original paper. (Somewhere else it is claimed to be wrong/heuristic). In the technical derivation in which step exactly do we utilize this \"vacuum turning to particle-antiparticle pair\" thing implicitly? I am actually partially convinced with Ben Crowell's answer that the radiation comes not exactly from the horizon but from a region away from it. But then a) How do we justify the use of geometrical approximation far from the horizon in Hawking's derivation? b) In an alternate derivation (for Schwarzschild black hole---not a collapsing spacetime like in Hawking's derivation) detailed in Carroll's book, the author uses Unruh temperature for a static observer and redshift it to infinity to find Hawking temperature; there also the static observer is necessarily near the horizon---otherwise we can't apply the Unruh temperature formula correctly because only the near-horizon geometry of Schwarzschild spacetime is Rindler. These two observation seems to point out the fact that the radiation is necessarily coming from near the Horizon---although the second point seems invalid because accelerated observers do Unruh-radiate in Schwarzschild geometry too. And how do we know that the particles are not coming from a time when the black hole didn't form? If we look at this diagram (adapted from Harvey's notes) used for backtracing things become more confusing (to me) Reading this would be like (according to an observer at infinity)---A wavepacket started from past null infinity away from the horizon at a retarded time after which if it had started it would go inside the hole. It went near the horizon before it's formation at very late times and stayed near the horizon for the rest of it's life while coming to us---the observer. It was joined by another wavepacket coming from infinity which started at a later retarded time, hence heading for the event horizon but got scattered towards future null infinity instead. Much of the results of the derivation follows from the change in frequency of the Schwarzschild modes due to extreme blueshifting near the collapsed matter . So apparently the collapsing spacetime(partially Maimon's POV in the linked answer)/some stuff at past null infinity created the Hawking radiation. So how do we prove that these two are not responsible and the event horizon is the culprit of creating Hawking radiation, from this backtracing framework? As mentioned above, there are reasons to believe in event horizon creating the Hawking quanta but I can't understand how that fits within Hawking's original derivation. This might seem like a duplicate of the linked question but since most of the answerers there are not active members of this community anymore and that many years have passed since the Q/A and (possibly) we have a better picture, I took the risk of reposting essentially the same question but nonetheless with new issues raised.", "label": 0}
+{"snippet": "Consider a loop gap resonator for electron paramagnetic resonance which has static (but sweepable) magnetic field in one direction, \"x\", and a GHz RF magnetic field in a direction \"z\" that is perpendicular to the static field.\" I had assumed that I had built the loop-gap such that the H_z field was constant over the sample volume. We get a reasonable EPR signature from it, can identify some hyperfine components, etc. I finally got around to doing a finite element for the field and to my surprise, the calculation appears to show that I am generating positive and largely constant Hz on much of the \"left\" side of the resonator and exactly the opposite Hz on the \"right\" hand side of the resonator (i.e. negative Hz, with zero field in the middle). I am now completely confused. I would not have thought such an RF field could give any EPR signature because the spin contribution on the left should cancel that from right. If so then my FEM model is wrong and I need to look there. But maybe not... in which case I need to look into fixing whatever is driving the wrong eigenmode because obviously I will get more signal if all the Hz is uniform. So that's my question can you get an EPR signal from an Hz which is flat over two areas of the resonator but such that the average Hz is zero? Or maybe in math terms: Given a computation of the RF field in a resonator and a theoretical spectrum of a species, how can I determine the corresponding EPR spectrum of the sample? E.g. does it depend on |H_z| or H_z ?", "label": 0}
+{"snippet": "In everyday talk we say things like: we must use the fundamental theorem of calculus to calculate this integral; we must use the results of analysis to proof the fundamental theorem of algebra; we must have a function that maps well formed formulas to numbers and that is bijective (Godel beta function); we must have a ring with the fundamental theorem of algebra to be able to proof this result; etc... Sometimes it seems that, when we say this, we are saying that the theorem in question must be made an axiom, then we will try to investigate what results hold with it, or without it, like in the case of the fundamental theorem of algebra. Sometimes it seems that we are saying that to proof some theorem we need to use a central theorem that mobilizes a particular set of axioms, this seems to be the case with the fundamental theorem of calculus, or the case of a theorem that say that some function or property exist and we must use it. In this last case, which is the case I am interested, it seems that the construction we are trying to make needs another construction, that in turn needs a set of axioms. But it's not the case that, if we simply fix it as an axiom, we could see what thing depends or not on it, for fixing it as axiom would turn the axiom system redundant (meaning: one or more axioms could be eliminated). So, my question is: what means to say that a theorem depends on another theorem? Is there some logical analysis of what means to say this?", "label": 0}
+{"snippet": "Constant motion can not be detected by neither particles (because of inertia) nor mechanical waves ( because they need a medium ). However when you consider light for example and assume it does not need a medium to travel through you could detect constant motion. For example, when someone is traveling at the speed of light in the x direction, and fire some photons in the x direction the person would see light as standing still while someone who is not moving will see the light passing at c. So why would we consider constant velocity to always be relative and so on undetectable. Clarify: Its obvious that the discovery was made, however for Einstein to actually get anywhere he needed to assume c to be constant. Which is exactly what I am wondering about, how did he come up with this. So that is why I am asking about constant relative motion and trying to come up with a thought experiment which proves the distinction between being stationary and constant velocity reference frames. However every single object with or without inertia which includes particles and mechanical waves are shown to give no proof of one or the other the one being in constant velocity. Which brings me to a light wave traveling through no medium and then would suddenly give us a way to detect constant motion, because now the so called ether wind is not causing the wave of light to go slower because the \"wind\" is moving in the opposite direction, no, it is now possible to say that light moves at a different speed for one of the two experiments on board the two and then proof that the one where c is slower, is the one actually moving and the one other one stationary. So from knowing this to be forbidden there is only one logical conclusion c must be constant for all observers, its the part where knowing this to be forbidden to c is constant for all observers is where I am stuck. Ps: please don't just give me a mathematical proof, this doesn't really help me, Much appreciated!", "label": 0}
+{"snippet": "A 'blunt' statement is when someone says things to the point and factual. But wouldn't 'sharp' (or some other word that implies frankness or sharpness) be a better word than 'blunt'? As blunt has the meaning that it is not sharp. When someone says something that is not direct or something soft (and if I am to make phrases or rules in English) then I am more likely to use 'blunt' for such a thing. All I am saying is the real meaning of the word is not appropriate(actually opposing) for the phrase. Being direct is never 'soft' and can hurt and blunt real meaning is more close to 'soft' and cannot hurt you (compared to a sharp object). Blunt: (of a cutting implement) not having a sharp edge or point. \"a blunt knife\" (of a person or remark) uncompromisingly forthright. \"a blunt statement of fact\" Etymology here points to some interesting meanings and usages but none quite explain the usage in phrases . Edit: what I am trying to say explained better in comments by other users \"why blunt means what it does, when it doesn't sound like a piercing effect\" The most common, physical meaning of 'blunt' is 'dull', 'rounded', or lacking edges - the antonym of this context is, as you say, 'sharp'. But when 'blunt' is used more metaphorically to mean 'direct' or 'unnuanced', the antonyms are very different. Also \"Blunt knife hurts more\" is creepy thinking and language usages do not take shape on those lines. It is usually simple popular opinions that turn to usages/phrases.", "label": 0}
+{"snippet": "According, to definition, provided, as I understand by Newton, there are frame of reference, where all constantly moving bodies keep their velocity constant, untill the force is not applied to such bodies. Some sources, in particular Russian Wikipedia inertial frame of reference article, state, that there is no inertial frame of reference in the world (translated from Russian): Absolute interial frames of reference are mathematical model, and do not exist in real world Or, for example this answer from this forum: When you ask for a \"perfect\" or \"true\" inertial reference frame you are asking for something that cannot be answered in physics. But each time sources either do not explain why, probably considering it obvious, or the explanation is not satisfying for me. I do not know, do I understand the reason correctly. Is the condition of frame of reference to be inertial applied for any time? Do constantly moving bodies in such frame should always move constantly if the force is not applied, so if the force even only once is applied to the body, which is linked with inertial frame of reference, that frame will never be intertial? Or frame can variate: for some period it can considered absolutely inertial, even in real world, for some period not? Is there no inertial frame of reference because there is no constantly moving bodies, i.e. every body have at least tiny, yet acceleration? If yes, why all bodies have acceleration? Due to mass, and the fact, that gravity force goes to infinity? Okay, I understand, that massless particle will move at speed of light, but what if there is a particle, that doesn't not affected by gravity or eletric field, i.e. will be \"fixed\" at space? Will it have intertial frame? Also what about particle with speed of light? Since their speed is constant, don't they have interial frame of reference? (Extra) Also, since the motion, even non-constant (i.e. with acceleration), as I understand is relative, then for some frame of reference, attached to the accelerated body, there are \"constantly\" moving bodies, that \"actually\" move with acceleration, but relatively to such frame - constantly. I do not understand why this frame is not inertial? Because, by definition, bodies should move constantly and without a force being applied to them? But how do we know is the force applied? No, if someone punches a ball, okay, but what about fields of something like this?", "label": 0}
+{"snippet": "I am in advanced UG (in Elec Engg). I was consolidating a mental model to help in (most of) engineering applications. I read Griffith recently. I learned that there exists no magnetic charge, (although, as Griffith said - how cute the scenario would have been, if they did.) Intuitively so; as Magnetic fields are engendered by time-variance of electric phenomenon (in field or charge (as current)), I never expected their existence. But, why the world needs a concept that is \"charge\"? The Gauss law, firmly relates the charge concept to the field. Intuitively, the field fluxes out of charge. It may seem that charge is engendering the field. But, let's believe in absence of such concept; the field is inexplicably (concentrated) sourced at \"some\" places - say S. Here is an argument - It is ambiguous whether the charge carries the energy or field. In the absence of charge concept; the field carries the energy; then the source to this energy are S. Energy is a transient phenomenon; Charge concept could represent the source to these new perturbations in the field. Coming to the title of the question. There is no magnetic monopole. Why is there an electric mono-charge? Clearly, charge represents transfer of energy from other domain of energy into electrical domain. Transfer of energy is relative. Can't we say the other half of the charge exists in the other domain of energy? (imaginary pole). I have an argument to address the polar nature of charge as well. But, I have already revulsed enough physicists here. (Excuse me, I was just thinking.)", "label": 0}
+{"snippet": "In Einstein's equations the curvature of spacetime and energy-momentum-pressure density are correlated. Is it clear when changes in matter energy density affect causally to curvature and when changes in curvature affect to energy density? Or can these kind of changes be non-local just as gravity correlated with matter in general? Is orbiting-like repetition needed for causality considered? I'm studying the principle of locality in physics. But the curvature of spacetime means that the fly-by has momentum of spreaded curvature of meeting bodies and those keep colliding into each other early. Where is the source of the cause? The fly-by anomalies has been mentioned. Are there any fly-by research projects that take the principle of locality into account? I appreciate answers that focus on localizing the physics so that time travel or any exotic negative energy etc. is left out. My problem is identifying on what basis something is cause or effect with gravity or when it is a non-local correlation of the curvature of spacetime. For example, gravitational waves act locally, but gravity acts non-locally in general. In which situations do changes in the gravitational field transmit causal information? Especially in fly-by passing: where is the origin of the causal information? Another case. Point-like fermion particles obey the Pauli exclusion principle. Although they appear to be free, they are subject to field forces and together other particles can \"feel\" tidal forces - if I interpreted correctly what is meant by \"feeling gravity\". Thus, the local limiting flat tangent space must be considered relative to the surrounding other tangent spaces (even if it is also point-like) and real (e.g. em) forces occur. The farther the particles are from each other, the more significant are the changing field effects compared to Decoherent interaction. How much has been loaded into the finished space-time curvature into the future without the exchange of causal local information and energy? Does it depend on the internal structure of the particles or the size, the mass? On the relationship to the dominant curvature?...", "label": 0}
+{"snippet": "The conservation of energy says that it can neither be created nor be destroyed, it can only be transferred from one form to another. i had this doubt in my mind for a long time that why do we need to save energy if the total energy is conserved. Energy can never be destroyed so why do we need to save energy?", "label": 0}
+{"snippet": "Is there something we can tell about the function, if we know that its Hessian matrix is the zero matrix? Is it concave, convex? What about quasi-concave and quasi-convex? As I am a beginner on this topic, I would be interested, if there's maybe an intuitive answer to this. Thanks!", "label": 0}
+{"snippet": "Why, when calculating contour integrals, we need to avoid the singularities inside the region delimited by the closed path we're integrating over? Wouldn't we need to care only about singularities laying on the actual closed path?", "label": 0}
+{"snippet": "I am looking for exercises/examples of \"simple enough\" morphisms between varieties being flat/non-flat, with solutions. I have only ever found a handful of examples, however very rarely with solutions to check my work. Any help is appreciated.", "label": 0}
+{"snippet": "The English word \"pepper\" comes from Latin word \"piper\". But why is there a double 'p' in the English word, when there is no double 'p' in the Latin word? Where does the English spelling of the word \"pepper\" come from?", "label": 0}
+{"snippet": "I came across this sentence: The dogs bounded past their leader. What does \"bounded past\" mean? I know the past tense of bind is bound. But here the verb \"bounded\" is used. Is the root of \"bounded\" different from the verb \"bind\"?", "label": 0}
+{"snippet": "Is there a point of balance where the gravitational pull of a sphere of electrons is equal to their electromagnetic repulsion? That is to say, could it be possible to create stars that are made purely with electrons and that are stable and don't fly apart?", "label": 0}
+{"snippet": "I initially tried to convert the whole thing into a Conditional via Material Implication but just ended up in a loop of assuming the antecedent and then using DeMorgan's. If anyone has any insight I would appreciate it.", "label": 0}
+{"snippet": "Does the word \"alumni\"/\"alumnus\" always pertain to a particular university or school, or can you say e.g. \"history alumni\" meaning all the people who graduated in history at any university (e.g. in some particular geographical region)? Would \"history graduates in France\" be more correct? Thank you", "label": 0}
+{"snippet": "In an integrable quantum system (say XXZ model), where there is an extensive number of conserved charges, does the set of local conserved charges obtained from expanding the log of the transfer matrix form a complete commuting set? In other words, does specifying all conserved charges obtained from the transfer matrix specify a unique state of the system?", "label": 0}
+{"snippet": "I have recently started to study quantum information theory on Nielsen and Chuang book, but in order to understand the theory better I need to solve more problems, there are in this book. Can you recommend a book or a book of exercises, where there will be problems on the topics from this book?", "label": 0}
+{"snippet": "By reading the first sentence in this article I interpret that, for every projective space, every isomorphism of its underlying vector space gives rise to an isomorphism of projective spaces. Is this also true for affine spaces (and their underlying vector space)? Or, at the very least, is every isomorphism of affine spaces induced by an isomorphism of the underlying vector space?", "label": 0}
+{"snippet": "I've been browsing through a bunch of questions here about how diagonalisation fails for Q. What I am finding hard to wrap my head around is how every bijection from N to Q, if used with the diagonalisation argument, will surely yield a rational. I can't really see how we can go about this. I'd appreciate any help.", "label": 0}
+{"snippet": "I can't think of any reason as to why one would have a directional derivative using a vector that's not of unit length. It would always \"mess up\" the derivative by scaling it by the magnitude of the vector, would it not? I tried searching online but can't seem to find any particular purpose.", "label": 0}
+{"snippet": "In TexStudio, one can open two or more tex files (or .bib, .aux, etc.) in the same window. But with my little experience with TeXShop so far, if I open a tex file and then a bib file, they open in separate widows. Is it possible to make all files to appear in the same window in TexShop as well?", "label": 0}
+{"snippet": "Is the following sentence grammatically correct? The word \"if\" is not used in this sentence, which I'm not sure is a mistake or not. And if anyone has a link to a reference on conditional clauses within relative clauses, that would be great!", "label": 0}
+{"snippet": "Specularity is a value that defines how glossy or matt a surface is. For example, a mirror is highly specular, but a brick wall is not. Is the specularity of a material a fraction of its total reflectance?", "label": 0}
+{"snippet": "I am relatively proficient in most material found in high school math courses but one of my weaknesses is in parametric equations and expressions; I really struggle to understand and apply them. Does anyone know of a good book or online resource written by an expert that really introduces and explains them step-by-step from the very basics? Thanks in advance.", "label": 0}
+{"snippet": "To estimate the parameters of a truncated distribution (lognormal for example), we can use the Maximum Likelihood Estimation or Method of Moments. For the Method of Moments Estimation, one needs to write down the mathematical expression of the expected value of the truncated lognormal distribution. Is it possible to do so? Or can we use a numerical method?", "label": 0}
+{"snippet": "In the textbook I am reading for class it is talking about the interactions of photons with atoms and how when an atom emits a photon it must have the same and opposite momentum of the emitted photon. I am confused on what the book means by \"the atom must also have a 'recoil' kinetic energy\".", "label": 0}
+{"snippet": "Orchestra seats are mentioned in this answer but why are seats closest to the orchestra (or stage) called \"orchestra seats\"? They are certainly not in the orchestra. What is the history/origin of such an expression?", "label": 0}
+{"snippet": "As a speaker of English as a second language, I've long been curious to know why English speakers would choose to say \"Easier said than done\" over \"Easier to say than do\". Why should it be said in the passive voice, not in the active one? Or is it simply a matter of being idiomatic?", "label": 0}
+{"snippet": "Forgive my naive usage of the term 'classical physicists' but what I mean is physicists who were either unaware of probabilistic quantum mechanics or refused it entirely. I am interested in whether they thought there was an infinite amount of matter in the universe, and whether space was infinite.", "label": 0}
+{"snippet": "The parameters is getting updated when you change the project rate. The parameters is being updated when you change the project rate. Is there a difference between these two statements? Which statement is more correct from a grammatical point of view?", "label": 0}
+{"snippet": "When the IV drip for a patient is completed, the patient's blood will flow back. This is apparently due to the pressure difference. However, IV needles are inserted into veins in the direction of blood flow. Hence, the blood is flowing against the direction of blood flow. Is the pressure difference so high? Can someone explain this? A non mathematical approach is fine", "label": 0}
+{"snippet": "I read on this page that an endomorphism of degree one of a smooth projective algebraic variety must be an automorphism. The proof uses Zariski's main theorem. My question is this: are there examples of nonsmooth projective algebraic varieties having endomorphisms of degree one that are not automorphisms? Note that for a morphism, having degree one is equivalent to being birational.", "label": 0}
+{"snippet": "What would you call a place or thing that's well-known or renowned but only among a locality, family, or small group? I've looked into it and have failed to find anything that fits.", "label": 0}
+{"snippet": "Could you please provide suggestions on how to include a list of my publications in my PhD thesis? I would like it to appear at the end of the thesis, following the \"References\" section. Additionally, I would like the title \"List of Publications\" to be listed in the table of contents, with dotted lines connecting it to the corresponding page number.", "label": 0}
+{"snippet": "I'm currently wondering how packages like tikz can possibly work. I've read the TeX Book and found no evidence of TeX primitives capable of drawing things. LaTeX is just a collection of macros so the use of LaTeX cannot provide this capability. Is the pdfTeX engine providing the primitives necessary for producing drawings? If yes, which are those primitives?", "label": 0}
+{"snippet": "Let's assume there are two observers 'A' and 'B'. B is at ground and A is moving with an uniform acceleration ('a') with respect to B. Will A be an non inertial observer with respect to B? (As we know that non inertial observers are those which are moving with an acceleration with respect to an observer).", "label": 0}
+{"snippet": "The ring of representations of the symmetric group is isomorphic to the ring of symmetric functions. The Schur-Weyl duality relates the irreducible representations of the symmetric group and that of the general linear group. Using the Schur-Weyl duality, is there way to find the ring of representations of the general linear group in terms of the symmetric functions ?", "label": 0}
+{"snippet": "I would like to know if there exist concepts of ergodicity and mixing properties for projective representations. If they do, do these properties exhibit similar characteristics to those observed in the context of unitary representations? Thank you in advance.", "label": 0}
+{"snippet": "HAMTREFOIL = {(G,s,t,u,v) | there exist paths s->t, s->u, s->v such that every vertex(except s) belongs to one of the paths} I want to prove that HAMTREFIOL is NP-complete by reducing Hamiltonian path to it but I am stuck in the construction part. Any tips or solutions would be great. Thank you.", "label": 0}
+{"snippet": "I want to make LaTeX Workshop's PDF preview fit my Visual Studio Code's theme, and I managed to change the background color of the previewed file following this guide, however if I make the background a darker color, the black text becomes very hard to read, and I'd like to modify it to a lighter color, but I'm not sure how.", "label": 0}
+{"snippet": "I am studying formalism of QM from the book by Griffiths. He illustrates via two examples that momentum and position operators have no eigenfunctions in Hilbert space. In that case, how can we expand a general state vector (in Hilbert space) in position/momentum eigenbasis, as the eigenvectors constituting the basis do not lie inside the space?", "label": 0}
+{"snippet": "I am an art student and I think my work could benefit from broadening my horizons on mathematics. I am mostly interested in Topology, but starting from high school mathematics I don't know where to begin learning. Could you give me an order of subjects to learn before starting topology? Thanks in advance.", "label": 0}
+{"snippet": "In UK English, the idiom \"more fool me\" means something like \"and I'm a fool for doing so\". But how might you try to understand the underlying syntax? Is \"fool\" an imperative here? A noun? Is the idiom an ellipsis of a longer phrase?", "label": 0}
+{"snippet": "Given a convex quadrilateral, and a point inside it, I want to find all ellipses that are inscribed in the quadrilateral and passing through the given point. My attempt: is outlined in my solution below Your comments, hints, and answers are highly appreciated.", "label": 0}
+{"snippet": "Which is considered (more) correct: wracked by [X] or wracked with [X]? Example sentences: He is wracked with grief. He is wracked by grief. The Cambridge definition of wrack contains examples of historical use of both forms. Thanks! (Apologies if this has already been asked; I searched first, but only saw the more common question of rack versus wrack.)", "label": 0}
+{"snippet": "The sign of the Jacobian determinant of a two-dimensional transformation tells us if the transformation is locally orientation-preserving (if it's positive) or locally orientation-reversing (if it's negative). Is there a similar interpretation of the Jacobian determinant for a three-dimensional transformation?", "label": 0}
+{"snippet": "Could anyone help me understand the use of 'that' in the below sentence? (I took this example from an old book) The morality of Buddhism is essentially that of the Upanishads except in the matter of forbidding sacrifice. What is the role of that in the above sentence?", "label": 0}
+{"snippet": "Distinguishing between distinct unitary irreducible representations is important from the point of view of distinguishing between different sorts of particles; the eigenvalues of the Casimir operators provide a way of doing this. I have never properly understood why this is the case. Is there a good way of seeing why any two distinct irreps must, necessarily, have different eigenvalues for at least one Casimir?", "label": 0}
+{"snippet": "Consider a location-scale family of random variables. Is the variance of a random variable within the family always monotone in its scale parameter? What if the random variable is also symmetric around zero? I would be interested in a proof or a counter example.", "label": 0}
+{"snippet": "Is there a theorem that states that Integer Linear Problems with a Totally Unimodular constraint matrix are solvable in polynomial time? If the answer is positive, is it also valid for Mixed-Integer Linear Problems? And in which books can I find such theorem?", "label": 0}
+{"snippet": "I understand that special relativity is what help creates a magnetic field in currents. But what I don't understand is how this plays into how changing magnetic fields lead to electric fields and how changing electric fields lead to magnetic fields or if special relativity even plays into this. If anyone can clear up my misunderstandings, that would be greatly appreciated.", "label": 0}
+{"snippet": "Recently I started learning about matrices and what you can do with them. I learned how to add them, subtract them and multiply them, but I found out that apparently you can't divide them. Why is this?", "label": 0}
+{"snippet": "Examples: \"Two miles is too far to walk\" vs \"There are two miles\" In the first situation, the noun is seen as singular, while the noun is seen as plural in the second situation. What is the reason that allows this noun to be both plural and singular.", "label": 0}
+{"snippet": "I'm reading this paper \"Billiards In Polygons\" by Boldrighini et al. They say that polygonal billiards have zero measure-theoretic entropy, because a given element of the configuration space is almost surely determined by its forward hit-sequence(the sequence of sides it collides with). Why does being so determined imply zero entropy?", "label": 0}
+{"snippet": "I know that when a cavitation bubble collapses, heat is given off and a shockwave is formed. What else happens? Is there increased water pressure in that region? Can the intensity of this implosion be measured using a hydrophone?", "label": 0}
+{"snippet": "I'm looking for a word to describe a person that is: always trying to treat others nicely, kindly, afraid of saying or doing something that makes others upset, never say or think about what he/she really wants, only try to make everyone happy. This word is usually talking about a child or woman that has suffered from something terrible that made them become this.", "label": 0}
+{"snippet": "There is a famous song called Baby I'm-a Want You. The name sounds wrong. Why is it not \"Baby I want you\"? Auxiliary verb \"am\" and article \"a\" look excessive in this phrase.", "label": 0}
+{"snippet": "What is the intuition behind Koszul graded-commutative algebras and Lie algebras? Why is it an interesting property to study in commutative algebra? I know why it's interesting in homotopy theory but what about in algebraic geometry or commutative algebra?", "label": 0}
+{"snippet": "Why does a changing magnetic flux induce an electric field? When a coil moves through a magnetic field, the induced emf is due to the Lorentz force. But why does a changing magnetic flux produce an induced electric field and emf even though the coil is stationary or there is no coil?", "label": 0}
+{"snippet": "I'm a first year graduate student in math and I'm currently studying fiber bundles. The definition is clear and I understand how it generalize concepts as (co)tangent bundles or vector bundles. What for me is unclear is why we are interested in spaces which are locally product of spaces. What is in general its usefulness? Thanks.", "label": 0}
+{"snippet": "I assume that the Milky Way has a dark matter halo just like any other. If that is the case, if we look at a huge part of our own galaxy, do we actually see the gravitational lensing effect? How intense is it?", "label": 0}
+{"snippet": "When I tried to solve some motion questions, I got complex numbers for time, displacement, etc. And my teacher said my answer was correct. Is it possible to have a complex number solution in the equation of motion? What does the complex number mean in the equation of motion", "label": 0}
+{"snippet": "In a, let's say rectangular container, the water surface always aligns itself perpendicular to the direction of net force acting on it. Why exactly does it happen? (For example when this container is accelerating towards left, the surface of water aligns it self in such a way that the right end of the liquid is at a higher level than left end.)", "label": 0}
+{"snippet": "While researching rotation curves, I've noticed a variety of velocity behaviors in different galaxies. In some, the velocity decreases, in others, it remains relatively constant, and in some cases, it increases, particularly in the outer regions. Is there a mathematical equation or method to objectively determine these patterns rather than relying on visual inspection?", "label": 0}
+{"snippet": "From the movie \"No Time to Die\": Nomi: The world's moved on since you retired, Commander Bond. Perhaps you didn't notice? Bond: No, can't say I had.\" Why did Bond use \"had\" and not \"did\"?", "label": 0}
+{"snippet": "A goat is tethered to a rope of length L. Each end of the rope is attached to a post, the two posts being distance D apart. The rope passes through a ring attached to the goat's collar and can move freely. What is area that the goat can graze?", "label": 0}
+{"snippet": "Is is correct to say that, elementary particles have different masses, because they have different coupling strengths to Higgs field? And if yes. Does it make sense to question, why they have different coupling strengths?", "label": 0}
+{"snippet": "Newton merely stated the law of inertia as: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. How does it prove the existence of inertial frames? I see no mention of it in the original law.", "label": 0}
+{"snippet": "In mathematical logic, there is a notion of \"predicative definitions\". I understand what a predicative definition is, intuitively, but I am interested in a formalization of that notion. Has any mathematician ever formalized and made rigorous a definition of predicative? I would love to see such a definition.", "label": 0}
+{"snippet": "As per the conservation of mass, matter cannot be created or destroyed. Doesn't this contradict the big bang theory? Like, it states that it all started from a single point. But seeing the massive size of the universe, isn't it weird that a single point held this much debris for the formation of planets, stars etc.?", "label": 0}
+{"snippet": "I'm new to Tikz and I've already made a few diagrams. However, I'm having trouble making this one. Would it be possible to help me? It doesn't matter if the colours aren't right, I'm just trying to draw the central block and the two arrows marked \"seuils...\". Thank you for your help.", "label": 0}
+{"snippet": "I am looking for texts that discuss the logic of the game of chess. I am sure there are a few such texts out there. Such a text might formalize chess in first-order logic. I would be very grateful if someone gave me a list of texts on the logic of chess.", "label": 0}
+{"snippet": "As the title says I want to know if the result is true, ie, if a linear projection in a normed space is bounded iff its kernel and image are closed. I know the result is true if the space is complete but I cannot prove nor find a counterexample in the non-complete case. Any ideas?", "label": 0}
+{"snippet": "I'm a final-year physics degree student and I want to know about QFT, but my knowledge about tensor mathematics and groups of symmetries is really low, as my university doesn't offer us advanced mathematical subjects. So, would you please suggest me some books or any other resource that make it clear and easy to understand these mathematical basics and that digs into QFT?", "label": 0}
+{"snippet": "Consider the topological group(s) in https://en.wikipedia.org/wiki/Solenoid_(mathematics)#Pathological_properties This seems like an interesting and bizarre group. It is obviously not a Lie group and obviously not a manifold. However, I was wondering if it satisfies geometric properties like local contractibility? What about its homology groups? Is there a nice reference for the topological properties of this group? Could anyone tell me more about this group? Thanks!", "label": 0}
+{"snippet": "I'm currently trying to figure out a function for a real coordinate space, which satisfies all the rules for an inner product, but with which the standard basis is not orthogonal anymore. Does such a function even exist? Or does someone here know an example of such a function?", "label": 0}
+{"snippet": "Recently, I'm learning FFT and I want to read this original paper(\"Theoria interpolationis methodo nova tractata\", by Carl Friedrich Gauss. ). But I can't get a valid url from Internet. Would someone give me a valid download url about this paper(or just send me that file via any viable method)?", "label": 0}
+{"snippet": "There are many quantum Monte-Carlo methods. Many of them can be used to calculate or estimate the ground state energy. The problem is, is the estimated energy an upper bound of the true ground state energy? We know an estimate based on a variational wave function has this nice property, but is it the case for the QMC methods?", "label": 0}
+{"snippet": "When we speak about Discrete random variables we have PMF. When speaking about Continuous random variable we have PDF. So my question is if we already have PDF or PMF with us then why do we use or calculate CDF, what's the intuition behind CDF", "label": 0}
+{"snippet": "This is a question about the proper use of the word \"thrust.\" Suppose a freewheeling prop is turning in the wind. Is the air coming out the back (downwind) side properly called thrust? I understand the basic physics. I just don't know if thrust is the proper term to use for the air coming out the back.", "label": 0}
+{"snippet": "I was wondering, if I theoretically shake a magnet like a sine wave with a very high frequency (Let's say a frequency in visible spectrum), will I see a visible light coming out of it?", "label": 0}
+{"snippet": "I am looking for a verb with the meaning of ceasing to like something/someone. To dislike is not fitting here, as it means the opposite of like, not going back from liking something to having a neutral opinion about it.", "label": 0}
+{"snippet": "For a differentiable function f, we know that the gradient is orthogonal to the level sets of f. What if f is Lipschitz continuous? we know that its gradient exists almost everywhere. Is the gradient (when it exists) orthogonal to the level sets?", "label": 0}
+{"snippet": "I am wondering when the Legendre transformation is irreversible. I know if Y is a linear function of x, then the Legendre transformation of Y is irreversible. However ,what if Y is a multivariable function? Could anyone give necessary and sufficient conditions when Legendre transformation is invertible? Thanks!!", "label": 0}
+{"snippet": "I have to work with the radial velocity dispersion. Could someone help me to understand what this actually is and how I work with velocity dispersion? What happens if you multiply the radial velocity dispersion with the radius? Is this something that is often done? In which systems does the radial velocity dispersion change with the radius? How is it related to the velocity?", "label": 0}
+{"snippet": "I know that the purpose of differentiation is to find the rate of change of a function. But i don't really understand how this is concept can be used to find the tangent of a specific point. It would be greatly appreciated if you can explain this to me.", "label": 0}
+{"snippet": "You can use the Euler Lagrange equation to show how the shape of a suspended cable with no load is simply a catenary. However, if you suspend a much heavier load (i.e. a bridge) with the cable, the cable forms a parabolic shape. Does anyone know how to show this fact using the Euler-Lagrange equation?", "label": 0}
+{"snippet": "Where did the slang term juice/sauce for steroids come from? I suppose that it may be a metaphor because of being liquid or maybe the similarity in colour. I cannot find any information on its origin, can you help me out?", "label": 0}
+{"snippet": "I'm typesetting a multi-page text with a fancy frame on each page. As you can see on the attached picture, the inner corners of the frame are taking extra space and I would like to increase the margin for the first/last two lines (or for a certain distance from the top/bottom) on every page. Is there a simple way to do that?", "label": 0}
+{"snippet": "I'm trying to find a Scottish colloquial idiom that means that people talk too much (especially in a gossipping, hot air, or inconsequential way). Perhaps this might be along lines of the English 'more babbling than a brook in flood'. I'm ideally after an idiom, not a single word.", "label": 0}
+{"snippet": "I'm currently working on proving an iff statement and was wondering is it allowed for me to prove the two statements required to prove an iff statement using two contrapositive statements. (for example, I'd prove if A then B using if ~B then ~A) and similarly for the second statement Thank you!", "label": 0}
+{"snippet": "I was wondering if there is any connection between number theory and operator theory. Especially the applications of Hardy spaces, de branges-Rovnyak spaces, Dirichlet spaces in number theory. For example to study modular forms, and etc.Something except Riemann Hypothesis. Does anyone know any books or papers about that?", "label": 0}
+{"snippet": "Is it possible to separate fluids or at least alter their relative concentrations in the presence of a magnetic field if one fluid is diamagnetic and the other paramagnetic? If so by how much? Are there any studies or data on this? How could this effect be calculated?", "label": 0}
+{"snippet": "If someone uses the name of a book/object with punctuation in it, does one need to capitalize the word after? Do I write: In the book Who's Afraid of Virginia Woolf? the main character... Or In the book Who's Afraid of Virginia Woolf? The main character...", "label": 0}
+{"snippet": "I'm writing a speech about someone and I would like to describe them as intelligent using a similar phrase to the way that \"she has fire in her belly\" would describe her as being passionate and driven. Something along the lines of She has fire in her belly and {something} in her head.", "label": 0}
+{"snippet": "I am writing a scientific article and I need to describe the two hatched areas in the Figure below. How do you call these? Upward hatching and downward hatching? Or what? E.g. The upward hatching corresponds to newly captured individuals, the downward hatching to the recaptured ones.", "label": 0}
+{"snippet": "I am searching for introductory books that explains in pedagogical way how scattering experiments are done . I want to understand how the experimental apparatus works and how experiments are done. For example in electron electron scattering I want to know what are the initial condition of the electrons like impact parameter, momentum etc,and how the detectors are placed.", "label": 0}
+{"snippet": "I would like to know which of the following sentences is correct: Ideally, we should leave tomorrow early OR Ideally, we should leave early tomorrow? I know an adverb of time comes after the verb or object and usually at the end of the sentence by I'm not quite sure in this sentence. I would really appreciate if someone would help me with this.", "label": 0}
+{"snippet": "I took an English test where I had to complete sentences. After I finished the test I was told that my answer \"If I didn't have...\" was wrong and I should have written \"Hadn't I had...\". That sentence: \"Hadn't I had the chance to make that acquaintance, I would never have been able to enjoy such a huge success.\"", "label": 0}
+{"snippet": "Find all positive integers, if any, such that all of its divisors can be arranged in a rectangular grid where the sum of all rows and the sum of all columns are equal.", "label": 0}
+{"snippet": "I am reading the Wikipedia article on mathematical structure, and it says \"a structure is a set endowed with some additional features\". Features can encompass a metric, a topology, etc... I'd like to know if there exists a rigorous definition of this meaning of structure, especially of this term \"features\". Could \"features\" mean just a signature along with an interpretation ? Thanks in advance.", "label": 0}
+{"snippet": "Recently, I needed some generalized version of Gronwall's Lemma, which I couldn't find in a quick search. However, I discovered that MSE is full of questions differing only in details on this very topic. Hence, I was wondering if there is a general version of Gronwall's inequality which covers most (if not all) of the different cases.", "label": 0}
+{"snippet": "I had a friend over recently and he expressed happiness for our family and home life. He was envious but with no negative connotations. It is something he wants for himself but is happy we have it. What would you call that?", "label": 0}
+{"snippet": "And in general, what else can we say about the set of normal numbers? We know that a normal number must be irrational, and hence it is possible that the set of normal numbers is countable or uncountable, since the irrational numbers are uncountable. I have been unable to find much literature or research about this topic.", "label": 0}
+{"snippet": "I was curious about solving the reflection and transmission amplitudes for the dirac delta potential barrier using fourier transform. I'm able to take the fourier transform but I'm unable to interpret the pole prescription that comes up. I didn't completely understand the following answer: Poles for a particle scattered in a delta potential", "label": 0}
+{"snippet": "I want to create my own latex package with a .sty file in it, and install it via tlmgr command. I've looked it up in Google, and found only this page https://tug.org/texlive/pkgcontrib.html, where I found no detailed procedure to create a new package. Is there any document about this kind of things?", "label": 0}
+{"snippet": "Are there any simple obstructions for the existence of a simplicial map between two given simplicial complexes? A natural candidate would be some simple to compute function that is non-increasing under simplicial maps. In general I'm interested in finding introductory references that explicitly discuss simplicial maps and their properties.", "label": 0}
+{"snippet": "If a website is blocked, and I wish for it to be unblocked, which of the following is the best way to put it? \"The blockade will be lifted tomorrow\" \"The block will be removed tomorrow\" \"Lockdown will be lifted tomorrow\" Or something else?", "label": 0}
+{"snippet": "Is there a reasonably simple (pen and paper) yet good approximation for the refractive index of an ideal gas as a function of temperature, pressure, and density. How would one derive this? Thanks for any help.", "label": 0}
+{"snippet": "I know the average potential over a spherical surface equals the potential at the center of sphere. But is it also true for average over spherical volume ? In both cases the sphere is empty of charge.", "label": 0}
+{"snippet": "I am searching for literature explaining the Spin/Helicity-Density Matrix formalism in order to compute \"spin-dependent\" matrix elements and cross-sections in particle physics. I would prefer if the source would contain minimal examples for elementary processes within QED or even the Standard Model.", "label": 0}
+{"snippet": "In the general treatment of geodesics in the Schwarzschild metric symmetry is used to constrain the geodesics to a plane which is usually chosen to be equatorial. Is there a way to generalize this, without restricting ourselves to the equatorial plane?", "label": 0}
+{"snippet": "I understand that a proton is composed of three valence quarks and a very large number of sea quarks that briefly come into existence and then annihilate as quark-antiquark pairs. Is it possible for the antiquark to instead interact with and annihilate one of the valence quarks and for the remaining quark to replace the valence quark?", "label": 0}
+{"snippet": "Consider a nonlinear dynamical system that evolves with a continuously differentiable vector field that is there exists a compact set within which the solution trajectories exist and are unique. Is it possible that all the stationary points of the dynamical system are stable? (Apart from the trivial scenario of having only one steady state.) Thanks in advance.", "label": 0}
+{"snippet": "I have txt file with table format, I did it in python but now I have to export this table to Latex but I don't know how. I'm not good at all in latex so I'll appreciate if you help me. Thank you!", "label": 0}
+{"snippet": "Which preposition would be grammatically correct? I am confident that I have the character and integrity to be an asset to your organization. I am confident that I have the character and integrity to be an asset of your organization. I am confident that I have the character and integrity to be an asset for your organization.", "label": 0}
+{"snippet": "It is a well known fact that there is a linear algorithm to determine if two given trees are isomorphic. But my question is: is there a (simple) way to expand that result to forests (a disjoint collection of trees)? Thanks in advance!", "label": 0}
+{"snippet": "The following line occurs in Keats's poem 'Ode to a Nightingale': And haply the Queen-Moon is on her throne It seems to me that 'haply' means either, as Merriam-Webster says, 'by chance', or, possibly, the same as 'happily'. So, which is it?", "label": 0}
+{"snippet": "I tried to use Torricelli's law to find the velocity of the fluid but I have to know the pressure inside the bottle, I can not calculate the pressure difference because the surface pressure is unknown", "label": 0}
+{"snippet": "I have seen articles online discussing the roundness of electrons. This goes a bit against my understanding of electrons as elementary point like particles. How can a point have a shape? What does roundness mean in this context?", "label": 0}
+{"snippet": "I saved a .tex file as a pdf with TexStudio. It has made a weird conversion and I was hoping to recover my original .tex file by saving it back as a pdf. However I now have this when I open it in TexStudio. Is there a way to recover my original file ? Thanks", "label": 0}
+{"snippet": "I am looking for an introductory linear algebra textbook for undergrads. The basics: matrices, eigenvalues, change of basis, exponents, pseudo-inversion, SVD and QR factorization. But what I really need is a good set of problems, preferably with solutions. And it would be great if it is online or an open book. Do you know such a book?", "label": 0}
+{"snippet": "How are vector spaces fundamental to higher mathematics (functional analysis, number theory).I'm familiar with vector spaces, basis vectors, inner products, eigenvalues,groups, rings , fields, modular arithmetic etc. I've read Axler's Linear Algebra Done Right and a bit of group theory.", "label": 0}
+{"snippet": "I think I know what the displacement current is. But I don't know why they use the word \"displacement\" exactly. What is the literal meaning of \"displacement\" of the displacement current? Why don't they call it \"electric flux variation current\"?", "label": 0}
+{"snippet": "If hawking radiation is the result of a pair of virtual particles popping into existence just outside the event horizon, and then one falling into the black hole through the event horizon, and the other escaping, how can this process reduce the mass of the Black Hole?", "label": 0}
+{"snippet": "Scientists are always saying that they cannot fully explain how lightning works, especially when it comes to the fact that there doesn't seem to be anywhere near enough potential difference between the cloud(s) and the ground to generate it. How large is the difference between the voltage theoretically required for lightning to strike and that which is actually observed?", "label": 0}
+{"snippet": "I find it hard to choose the most appropriate one among these three sentences: she has been busy recently, she has prepared for an exam. she has been busy recently, she has been preparing for an exam. she has been busy recently, she is preparing for an exam.", "label": 0}
+{"snippet": "What is the path followed by free electrons in a conductor under applied electric field? Is it a zig-zag path (due to collisions with atoms of the metal) or a curved path? Why (in each case)?", "label": 0}
+{"snippet": "I am trying to study, through the Riesz representation theorem applied to a space of compactly supported continuous functions, what hypotheses must be met to establish that the measure given by the theorem (which is unique, regular and Borel) is a probability measure. I have tried to find literature on this but I cannot find it. Any help? Thanks.", "label": 0}
+{"snippet": "I have almost completed my mock test syllabus, but complex numbers are pretty complicated for me. Can anyone give me some tips to approach this kind of problem? There are tons of questions like this in the previous year's papers. Please don't downvote me, I just want a tip to improve in these kind of problems", "label": 0}
+{"snippet": "I was reading about the proof of the Mordell-Weil Theorem in \"Rational points on elliptic curves\" from Silverman and Tate and in Chapter III is the hight function described as an indicator on how \"complicated\" a rational number is. Does this mean that if the hight function of a rational number has greater value that it requires more numbers to write it?", "label": 0}
+{"snippet": "I have been trying to find if a real experiment has ever been done to prove and calculate the magnetic field of a rotating charged disk, whether it's a conducting or a non-conducting charged disk. All I found on Google and YouTube are just thought experiments, so please if anyone had come across an actual experiment let me know.", "label": 0}
+{"snippet": "I thought a lot about it but couldn't come to an answer. It's obvious that there must be an equation telling the answer. If one of the electrons were fixed, by Integral calculus, I would have found an answer, but when both the electrons are free to move, I am struggling to find a solution.", "label": 0}
+{"snippet": "A cyclist and a car, which is twice as fast as the cyclist, are approaching an intersection of two different streets perpendicular to each other. At noon they were at an equal distance from the intersection. Twenty minutes after noon the car was at the intersection. How many seconds from then on do they need to be equidistant from the intersection again?", "label": 0}
+{"snippet": "When I select text in Texstudio it remains highlighted even if deselected. The last selected section of text always has a light-blue highlighting. This is visually very irritating and I have no idea how to get rid of it. I might have turned it on by accident, hitting some shortcut that I am unaware of. Does anybody know how to turn this behaviour off?", "label": 0}
+{"snippet": "I have learned from a knot theorist that quandles were developed in order to more sensitively distinguish between distinct knots. However, they seem to be an interesting algebraic object in themselves. Are there any applications of quandles to quantum theory?", "label": 0}
+{"snippet": "what is the definition of maximal connected subgraph? Is every maximal connected graph of the form K_n (that is n nodes and between any pair of nodes there is an undirected edge)? Thanks in advance", "label": 0}
+{"snippet": "From what I read meteors compress the air in front of them, increasing the air's temperature massively; this in turn is what heats the meteor. My question, which I can't seem to find a clear answer to is: does the resulting extremely hot air primarily heat the meteor through radiation or convection, or some combination of the two?", "label": 0}
+{"snippet": "I was wondering if this sentence is grammatically correct: I am not glad. Such is the sentiment of fools. Am I using such correctly here? I spent a good hour researching its use and couldn't find what I was looking for. I thought that perhaps someone on here could provide me with the answer I seek.", "label": 0}
+{"snippet": "I was studying Quantum Hall Effect and there I came out with a question that why the plateaus in the plot of Hall Resistivity are robust ? I know by solving Schrodinger equation and using Landau Gauge Condition we can arrive at the conclusion of landau levels, but I am not satisfied that why the plateaus are robust ?", "label": 0}
+{"snippet": "Injective objects in the category of abelian groups are precisely the divisible groups. However, despite using injective resolutions of sheaves everywhere, I realized that I did not know a single example of an injective sheaf. I have searched for such examples but unfortunately found none on the internet. What are some easy examples of injective abelian sheaves (if there exist any)?", "label": 0}
+{"snippet": "I'm trying to use Georgian language with vimtex. I found out that I have to compile with XelaTex or LuaTex but i don't know how to make vimtex to compile with them. I would like to keep default compiler and add Xelatex as optional, is it possible? I have tried to read official documentation but I can't understand much.", "label": 0}
+{"snippet": "I'm writing a research paper and for that I'm using TeX Live and TeXmaker. Sometimes I need help (correction, improvement) from my professor. So we want a software or something, in which, if somebody edits, we can see it in real time and all edits will be updated and stored. I don't want Overleaf as it requires a permanent internet connection to edit.", "label": 0}
+{"snippet": "I am studying Game Theory and I have some confusions. Is actually Carrot and Stick strategy is the same as Grim Trigger? Is the Carrot and Stick only for Multistage game? Can you please give me example of case using carrot and stick strategy? I know that it's very basic questions but I am struggling to understand this topic. Thank you!", "label": 0}
+{"snippet": "I am trying to prove the snake lemma. I want to show that the sequence of kernels form an exact sequence. Must I show that the functions that map one kernel to the other are R-module homomorphisms? Thanks in advance.", "label": 0}
+{"snippet": "In Wikipedia's article \"Complete Boolean algebra, the following example is given: The Boolean algebra of all Baire sets modulo meager sets in a topological space with a countable base is complete... This suggests that the Boolean algebra of all Baire sets modulo meager sets in a topological space without a countable base may not be complete. Is this true?", "label": 0}
+{"snippet": "I want to model a pendulum consisting of two magnetic balls with the same 'sign' of the charge. How should I write the Lagrangian of the system? Will the Lorentz force appear in it? Also, what should I change in the Lagrangian in case of hitting one of balls with another?", "label": 0}
+{"snippet": "I want to combine multiple departments of the same university in the institute section. Please refer to the image provided. This will save a lot of space and be much more clear as well. Please let me know what's the best way to go about doing this, as I currently have no idea. I'm using the LNCS template.", "label": 0}
+{"snippet": "I'm not finding the answer to this on the internet after searching. When writing dialogue, do you use capital letters to spell out words? Jamie said, \"I said P-L-E-A-S-E please, and don't you forget it!\" Or should it be lower-case? Jamie said, \"I said p-l-e-a-s-e please, and don't you forget it!\"", "label": 0}
+{"snippet": "I am a beginner with set theory. What is meant by \" analytic set \" ? I see this term in the context of set theory, calculus and real analysis but I have no idea what it means. See here : https://en.wikipedia.org/wiki/Borel_set where it occurs in the non-Borel set part.", "label": 0}
+{"snippet": "I know that the particles that constitute air move freely about. There must be a significant amount of empty space between the bouncing particles. So why is it so hard to compress air without any machines/devices?", "label": 0}
+{"snippet": "Why do vortices in a superconductor (i.e. magnetic flux-tubes) form triangular lattices? In one of the articles I found, I read that a square lattice would cause repulsion but a triangular lattice will cause attraction. Can anyone explain it?", "label": 0}
+{"snippet": "Is there some way to argue that the Higgs VEV is unnatural, without even bringing up the Higgs boson mass? For example, can one show that the Higgs vev receives large corrections from new physics? The literature on renormalizing the Higgs vev doesn't seem to talk about this (or maybe I missed that part).", "label": 0}
+{"snippet": "Some years ago, a weather satellite manufacturer in the SFO bay area was buying small quantities of piezoelectric acoustic guitar pickups from one of the big music supply houses, which greatly puzzled their sales rep. What were they doing with pickups intended to be glued to the underside of an acoustic guitar bridge?", "label": 0}
+{"snippet": "I was trying to use the answer from here to ensure my tables fit to the width of my page. I'd like to redefine the tabular environment so that this change is applied automatically if the table's width exceeds the page width. Is there any way to do this?", "label": 0}
+{"snippet": "I'm writing a report with the sentence: The vaccine has been shown to reduce diarrhea in an in vivo model. Colleagues use a sentence starting with The vaccine has shown to reduce... In my opinion, the vaccine obviously didn't show anything itself, so it makes sense to use passive voice. What is your expert opinion?", "label": 0}
+{"snippet": "Is it true that the cardinality of a hypothesis class with finite VC dimension is less than the cardinality of real numbers? My intuition is that the number of functions in a hypothesis class with finite VC dimension cannot grow arbitrarily and there is a limit on that.", "label": 0}
+{"snippet": "Is there a more accurate way to determine speed? I am asking because this has to do with an accident reconstruction where my son was killed. The investigators are trying to conclude his speed prior to impact and I want to know if this is the only way to determine speed.", "label": 0}
+{"snippet": "I want to create a table of content like box on the left side of every slide with the name of every chapter/section and with the current chapter/section name highlighted while the other are slightly faded. Like in the following picture.", "label": 0}
+{"snippet": "I am reading about the Douglas-Rachford Splitting algorithm and in that algorithm, the two operators resolvent and reflected resolvent are used extensively. I wanted to know if these operators have any graphical interpretations. e.g. What is the reflected resolvent of an operator? What does it reflect and etc.?", "label": 0}
+{"snippet": "I want to know, are there any texts out there that take conditional probability as more primitive and define probability in terms of conditional probability? Perhaps they give some axioms for conditional probability. Anyway, I would be very interested in such texts.", "label": 0}
+{"snippet": "Everyone floats in Dead Sea because it is so salty. Is it true in Great Salt Lake? How about Red Sea and Mediterranean Sea? Is it impossible for anyone to sink in these seas without added weight?", "label": 0}
+{"snippet": "I'm wondering about lithium batteries in electric cars. Could time and technology improvements continue to improve charging speed, to the point where you could \"refill\" an electric car as fast as you can refill a gas tank? Or is there something potentially impossible to surmount there, like a law of thermodynamics?", "label": 0}
+{"snippet": "I can't carry a heavy bag and a heavy heart, either. Is this sentence grammatically correct? Can I say this instead? I can't carry a heavy bag and a heavy heart at the same time.", "label": 0}
+{"snippet": "I'm new to using chemfig. I'm trying to create chemistry handouts and I want to draw the tropylium cation: However I am unable to get the charge to come out of the ring. Any help would be appreciated.", "label": 0}
+{"snippet": "I'm working on a project for which I originally put the title as: Methods for controlling the quality of PET bottle manufacturing process. However, now that I re-read it, I feel like its way more natural to say \"of the PET bottle manufacturing process\". I would normally go with the second variant, but is the original version grammatically correct too?", "label": 0}
+{"snippet": "I'm a mathematician currently working on a problem involving splitting a square into two triangles, either by a line connecting top-left and bottom-right, or top-right and bottom left. I'm trying to think of natural names for these, but the only thing I could think of was acute and grave (after the directions of accents, originally Greek I believe). Are there other options?", "label": 0}
+{"snippet": "I am currently studying X-ray-emitting plasma pervading clusters of galaxies, and I see many studies employ an ideal equation of state to infer the pressure of the plasma. Is this the correct thing to do? Apart from this, it seems like an ideal equation of state is thrown around in astrophysics many times without proper justification. What do you think?", "label": 0}
+{"snippet": "A \"stable\" is the compartment where an individual horse is housed. A \"stables\" is the building which contains multiple stables/horses. So the stables is a singular building, but the word \"stables\" is clearly plural, not singular... Example sentence: \"Where else would you buy a horse other than a stables?\" she said. Is this sentence grammatically correct? If not, how would you correct it?", "label": 0}
+{"snippet": "I'm looking for different criteria of identity for the notion of 'set'. I know that the standard criterion of identity is extensionality but I was wondering if there are others. I looked around but couldn't find any literature on other criteria. I thought you could help me find some material on that topic? Thanks for taking the time. All the best, David", "label": 0}
+{"snippet": "In one study, for instance, bar codes were placed on bees, tracking their activities. Is this correct? Or do we say... In one study, for instance, bar codes were placed on bees to track their activities.", "label": 0}
+{"snippet": "If i have an electron and an antimuon is it possible that they could annihilate into a electron neutrino and antimuon neutrino? Am i correct in saying both spin and charge are conserved in this reaction.", "label": 0}
+{"snippet": "We've been learning in class that when approaching a perturbed Hamiltonian with degeneracies you should try to choose a basis made of eigenstates of both the unperturbed Hamiltonian and the perturbation. But at that point, why do you need perturbation theory? Don't you now have the exact solutions to the Schrodinger equation?", "label": 0}
+{"snippet": "I understand that superconductors have zero resistivity, however, I wonder if there is a relation between resistivity and the work function of a specific material so that a superconductor has zero (or a low value) work function. If so, photons with very long wavelengths can release electrons from the surface of a superconductor. Am I right?", "label": 0}
+{"snippet": "Phonetic spelling is when one spells a word according to how it is pronounced (e.g.; knight => nite). What word would be used to describe the pronunciation of a word based on how it is spelled, ignoring silent letters (e.g.; knife => cuh-nife)?", "label": 0}
+{"snippet": "I understand that a graph is connected if there is a path between any two vertices. However, I am unsure about the number of components of a graph. Is a single vertex considered a component? If yes, is it connected? In particular, what is the number of components in the below graph? Is it one or three?", "label": 0}
+{"snippet": "I wonder how to best phrase this. The idea was to ask someone about their time zone. \"Where do you live that it's morning for you?\" The 'that' feels off / like a literal translation from Czech. \"Where do you live where it's morning for you?\" The double 'where' feels weird too. Are these sentences correct / do they feel natural for native speakers?", "label": 0}
+{"snippet": "This is probably a very naive question, but is there something about Godel encoding that is essentially arithmetical, or is it possible to construct analogous mappings between the objects studied in a theory and statements in the theory itself for non-arithmetical theories (i.e, theories whose objects of study are not numbers). Are there any notable examples of this being done?", "label": 0}
+{"snippet": "I was wondering if the word normal is redundant in the definition of a simple group. I strongly feel that there must be a simple group with at least three subgroups. However, I'm unable to find any. Any help?", "label": 0}
+{"snippet": "I used to use Microsoft Word to draw this type of graphs, but it is not so convenient and it is difficult to be precise and accurate in details. Is there any better tool?", "label": 0}
+{"snippet": "I heard my teacher stating that the base form of a verb is not an infinitive itself, but it is used to construct one of the two forms of infinitives. Edit note This question has been linked to a previous one of mine. However, in that question I was asking about the difference between infinitives and bare infinitives. This is a different question altogether.", "label": 0}
+{"snippet": "I've been looking to understand linear algebra(vector spaces and subspaces) from different sources, then I came across the statement \" the union of x-axis and y-axis\" to the question \"Give a set that is closed under scalar multiplication but not addition\". I don't really understand how", "label": 0}
+{"snippet": "I was wondering what's the order between mode, median, arithmetic mean, geometric mean and harmonic mean in a distribution with positive skewness and in another with negative skewness. Which are the theorems used to prove their relationship?", "label": 0}
+{"snippet": "I am looking for books and papers that treat the physics theory of classical mechanics in a rigorous, mathematical manner. I would love to read such a text. Are there even such texts out there? I have already read physics books on classical mechanics, I am now looking for a rigorous mathematical text on it.", "label": 0}
+{"snippet": "In Baldwin's \"Model Theory and the Philosophy of Mathematical Practice\" I read this phrase. The interaction between the syntactically definable properties of theories and the Boolean algebra of definable sets in their models is crucial. I was wondering what is meant by this \"interaction\", to me it is not evident that there should be such relation.", "label": 0}
+{"snippet": "I just started going through this http://www.damtp.cam.ac.uk/user/tong/qft.html of QFT and I got stuck at the very beginning. The Lagrangian for the field is derived by: I think that the second step in this derivation is integration by parts, however after trying multiple times I still don't get what I need to get. Could someone explain what I'm doing wrong and provide step-by-step derivation?", "label": 0}
+{"snippet": "I was watching a Lecture by Douglas Hofstadter on \"Albert Einstein on Light; Light on Albert Einstein\". And there was a slide which said that Einstein had idea that All periodic phenomena should have quantized energy levels. Can some one explain such idea? Thanks.", "label": 0}
+{"snippet": "Recently I saw a video saying that due to the Pauli's exclusion principle there can only be a fixed number of electrons in a place but for photons it doesn't hold true as it's spin is different. So then is the number of electrons in an unit volume is fixed ?", "label": 0}
+{"snippet": "I want to select a finite number of points on compact Lie groups that maximally cover the manifold in some sense. I have heard that some related aspects are Voronoi diagrams on manifolds and lattice structures on Lie groups. Any relevant literature on these topics would be appreciated.", "label": 0}
+{"snippet": "How does a blackbody actually heat up and change temperature if it emits all the radiation that it absorbs by definition? And by extension, if the absorptivity and emissivity of a body are equal, then how is the temperature actually changing?", "label": 0}
+{"snippet": "Does anyone know any good resources on the the Poisson kernel? I'm really looking for a measure theoretic approach to harmonic boundary problems. If anyone knows any such books, that would be much appreciated.", "label": 0}
+{"snippet": "I have an assignment that requires us to make a continuous rollercoaster. we have to find the derivative of the functions we us and show that the gradients match. I have part of my rollercoaster done but I was wondering whether or not you can somehow connect an exponential function to the rollercoaster. Heres what my graph looks like atm.", "label": 0}
+{"snippet": "For some strange reason, all the figures in a LaTeX document that I'm preparing are being put right at the end. This is despite me specifying precisely the figure placement in the figure arguments (with a ! too). How do I stop this from happening?", "label": 0}
+{"snippet": "I was told the framing of a knot is the linking number of the push-off. But I don't understand why the framing does not depend on the knot but only on the parallel copy. How about a Legendrian knot? (I heard this is more rigid than a topological knot)", "label": 0}
+{"snippet": "I have once heard that the definition of energy is \"the ability to do work\". However, that is a counterfactual definition, because a physical system can have that ability without actually doing work. So, has someone proposed a non-counterfactual, non-modal definition of energy? I want a rigorous definition.", "label": 0}
+{"snippet": "Russians often use the formulation \"take an integral\". Now I noticed it in an article, written by a Russian and I can't recall I have ever encountered it in English. Is it a possible alternative to the basic \"calculate an integral\"? What other options are there? \"Evaluate\", \"find\", ...?", "label": 0}
+{"snippet": "Hello Physics StackExchange Team, I want to know whether it is possible to experimentally determine the velocity at which the free liquid surface is moving/rotating in a cylinder with a rotating disk. The velocity at the free surface will be lower (in comparison to the disc speed) but is there any way to experimentally capture/calculate it? Please help. Thanks.", "label": 0}
+{"snippet": "I've read many definitions for a transcendental number and some of them say that a transcendental number is a number that is not the root of any integer polynomial, while other say is a number that is not the root of any rational polynomial. My question is why such restrictions? Can't we just give algebraic polynomial instead?", "label": 0}
+{"snippet": "I've read that if a state is a product state, the reduced density matrices are pure and if the state is entangled, the reduced density matrices are both mixed. What would it mean if you had a system of two particles, and when you calculated the reduced density matrices, one was pure and one was mixed?", "label": 0}
+{"snippet": "What might cause the pdflatex output from a memoir class book to have two columns per page rather than one? Multiple columns can be used in some articles but not in a book.", "label": 0}
+{"snippet": "In school, I was taught that a line segment must be finite. But a fractal has an infinite perimeter. If you just took two points along that perimeter, and \"stretched it out\" wouldn't you have an infinite line segment?", "label": 0}
+{"snippet": "It is my understanding that the way cosmologists formulate theories like big bang theory, steady state universe theory, heliocentrism, etc, is by observing the sky using telescopes and imagining explanations for what they see. Are there any good books that I can read to learn more about these theories and the scientific processes that lead to them, that go into details?", "label": 0}
+{"snippet": "How do I use LaTeX on an Android device? Can I make animations using it? If yes, how? I am new to stuff like this. What are some good sources and app for using LaTeX on Android?", "label": 0}
+{"snippet": "I have two circular coils facing each other in parallel. Through one coil current flows. I move the second coil in a parallel fashion. What is the direction of current induced on the moving coil? Acc. to me, there should be no induced current as in parallel movement, the flux doesn't change.", "label": 0}
+{"snippet": "Could you please help me to know why transfinite induction only works on well-ordered set and not arbitrary set ? Why the fact that every susbset has a least element is necessary for transfinite induction principle ? Thank you very much!", "label": 0}
+{"snippet": "In software engineering, I sometimes see \"first cut\" in a context where it could mean \"first version\". Is it some idiom? Where does it come from? Does it mean literally \"first version\", or is there any emotional subtext, or did I misunderstand its meaning completely?", "label": 0}
+{"snippet": "In an article of wikipedia, it is stated that : Charge is the fundamental property of matter that exhibits electrostatic attraction or repulsion in the presence of other matter with charge. I can't understand why there is \"electrostatic\" mentioned in this statement. Isn't there attraction or repulsion between two moving charge too?", "label": 0}
+{"snippet": "There is a well known algorithm (Bhaskara-Brouncker) to compute the continued fraction expansion of the square root of an integer, using integer arithmetic only, no floating point. Is such an algorithm known also for square roots of fractions of integers?", "label": 0}
+{"snippet": "A word for when an artist builds up their ability to paint, but over time their art starts regressing. Or perhaps a child, once magnificent at playing the guitar, begins to pluck the wrong string and slur the notes, eventually becoming mediocre.", "label": 0}
+{"snippet": "Why is the construction 'I would love to' so commonly used, and is it grammatically correct? If the word 'would' cannot be used with state verbs like love, think, etc, then isn't this technically wrong? And why is it used so often?", "label": 0}
+{"snippet": "In logic, why do we talk of universal closure of a formula, and don't consider its \"existential closure\" (as far as I know)? I guess that one of the reasons may be that interesting systems like PA are written down much more succinctly and naturally without the universal quantifiers. I think there might be more to it than that, though.", "label": 0}
+{"snippet": "I don't know if this is true or not, I tried to prove and I didn't succeed and the I tried to give a counter example and I also failed. so can someone please help", "label": 0}
+{"snippet": "I have a latex file and a website. On the website I have an input field, in which you can write text. Then when you click a download-button on the website I want that it automatically creates a pdf (with latex) with the value of the input field.", "label": 0}
+{"snippet": "I've been reviewing the double slit experiment lately and I believe it is missing a few crucial things. Thickness of the wall is my primary focus. How could I add thickness into the equation? I'm interested in seeing the effect on a model.", "label": 0}
+{"snippet": "Suppose that I were to jump on the surface of the Earth. The moment I hit the surface, shouldn't the force Earth is applying on me be greater than the force I am applying to it so that I stop completely? If the forces were equal, wouldn't I still be moving?", "label": 0}
+{"snippet": "I hear about \"The Graph Isomorphism Problem\", and am a bit confused as to where the issue is. Isn't the adjacency matrix ( up to permutation ) unique for a graph up to isomorphism? Can't the problem be solved as easily as checking if two graphs have the same matrix up to permutations?", "label": 0}
+{"snippet": "Is there a concept of induced subgraphs for directed graphs? I would intuitively think it is nearly the same as for undirected graphs. I was just thinking that it would be a subset of the vertices such that all arcs from the original graph from one vertex in the subset to another in the subset exists in the induced subgraph edge set.", "label": 0}
+{"snippet": "From my understanding, within the context of the Standard Model, charged lepton flavor conservation is an accidental symmetry due to some renormalization condition. How does this work in the case of pair production? Would the result be different if instead the photon pair produced to an electeon neutrino and a muon anti-neutrino?", "label": 0}
+{"snippet": "Suppose you have a closed differentiable plane curve. Are the tangent lines to the curve at the most distant points on the curve always parallel? What if we assume that the curve is convex? I don't see why this should be the case, but it also seems like it might be the kind of weird geometric property that unexpectedly turns out to be true.", "label": 0}
+{"snippet": "In any path-connected metric space, can we connect any two points with an injective path? This seems possible, for instance by \"removing\" the points where the loop is not injective, but I cannot prove it. Is it true? If yes, how to prove it? If not, do you have a counterexample? Thank you very much, AF", "label": 0}
+{"snippet": "If a quadratic form is represented as a matrix, it may not be symmetric, but there must exist a representation that is symmetric (or Hermitian if complex). But is the reverse true? That is, do all symmetric and Hermitian matrices represent a quadratic form (except maybe in the case where matrices are all zeros)?", "label": 0}
+{"snippet": "As the question states, how would you calculate the t-statistics in GLS? Is it just the same as in OLS? And are these results still reliable? I have heteroskedastic data and so am using GLS, but I'm not sure if the calculations for t-statistics change or the values are less reliable?", "label": 0}
+{"snippet": "What is the difference between \"a memoir\" and \"a biography\"? According to my study, \"a biography of a person A\" is normally written by someone else not A and \"a memoir of a person A\" is normally written by A himself. Also, \"a biography\" is quite detailed from birth to death while \"a memoir\" is not too detailed.", "label": 0}
+{"snippet": "I'm curious as to the purpose of relativity and why the universe would function this way as opposed to a universe with an aether. So what would be different if we had an aether?", "label": 0}
+{"snippet": "The product of two matrices A and B with dimensions (n,k) and (k,m) results in a matrix C (n,m). I remember that my professor used to call this rule after a specific person (I guess the inventor of that rule). Do you know how the name of the person is? Or how do you call that rule in general?", "label": 0}
+{"snippet": "I know that Galois groups let us determine when polynomials are solvable by radicals, and that Lie groups can be used to solve some differential equations. Does there exist an analogous group theory method that tells something about the solutions of recurrence relations? I am interested in both existence/Galois type results and symmetry methods of solution.", "label": 0}
+{"snippet": "I just learnt about Feynman Diagrams, and I've been going through many examples to practice the reading of Feynman Diagrams myself. I have already found diagrams for Positron Emission, Electron Capture, and Beta Emission decays but yet have not seen one on Alpha emission or Gamma decays. Can these decay mechanisms be expressed through Feynman diagrams, or am I just missing something here?", "label": 0}
+{"snippet": "Assuming a charged particle moves at speeds near the speed of the light. Will the electric field generated by that particle get affected by length contraction and time dilation? In other words, will this cause a more dense field closer to the particle which declines faster with distance compared to a stationary charged particle?", "label": 0}
+{"snippet": "I'm trying to optimize plasma cleaning process to be signal driven instead of fixed time. I have a vacuum chamber with hydrocarbon contaminants, I use air plasma for cleaning. Is there an option to terminate plasma, based on the amount of contaminants left in the chamber?", "label": 0}
+{"snippet": "I would like to know if the thermal motion of molecules stays constant if the pressure is increased at constant temperature or not. The viscosity increases with pressure, thus the friction between the molecules also. If the thermal energy is constant, will the motion of the molecules decrease due to higher friction?", "label": 0}
+{"snippet": "I have a question about whether or not to use the plural for a noun in the following sentence: Men, woman, and horses grew smaller as they moved on. Since there was only one woman in the group, I think it is neither necessary nor correct to match the plural nouns with \"women\". Am I right? I appreciate any assistance you can provide.", "label": 0}
+{"snippet": "I've heard that very massive stars can sometimes collapse into black holes without creating supernovae. How does this happen? (I suspect it's something to do with the relative lack of Urca process neutrinos which are active in the cooling of neutron stars).", "label": 0}
+{"snippet": "I am trying to develop a more intuitive understanding of the field produced by magnetization and polarization. I have the following image, and I can derive it from Maxwell's equations what the fields inside and outside are given uniform polarization, but is there a way to understand them more intuitively?", "label": 0}
+{"snippet": "I would like to use the QT Deuce font in overleaf. It is in the LaTeX font catalogue, but the instructions for usage on that site use the fontspec package which requires XeTeX or LuaTeX rather than the pdflatex that Overleaf uses. Is it possible to use QT fonts in overleaf?", "label": 0}
+{"snippet": "In the book entitled \"Algorithmic and Combinatorial Algebra\" written by Bukot and Kukin and they showed that there exists a finitely presented Lie algebra with unsolvable word problem. Can we conclude same result for the case of Lie superalgebras?", "label": 0}
+{"snippet": "According to Birkhoff's Theorem, any spherically symmetric body will not emit gravitational waves. I can understand this for an object that is contracting and expanding because from far away the gravitational force is the same. But now imagine, we have a spherically symmetric body that is linearly accelerating through free space. In this case, would gravitational waves be emitted ?", "label": 0}
+{"snippet": "Cayley graphs are necessarily vertex transitive, but the converse is not true in general. Is there any general/asymptotic result that discusses the percentage of Cayley graphs in vertex-transitive graphs? Or would this be a hard problem?", "label": 0}
+{"snippet": "Fix a finite-dimensional real inner product space. Does a self-adjoint operator have a symmetric matrix with respect to all bases, or just with respect to orthonormal bases? Also, does this change at all when one admits a pseudo-Euclidean inner product, rather than the (standard) Euclidean inner product?", "label": 0}
+{"snippet": "How the slang word \"jacked\" (having well-developed muscles) is formed? The word jack itself may be related to drugs, however I don't think that the meaning comes from there. There is a theory that it has formed from the word jagged (having low body fat), but I cannot find a proof to that.", "label": 0}
+{"snippet": "When reverse bias is applied, why can't electrons from p region that are currently occupying the holes jump into the conduction band of the n region, which according to the image (taken from hyperphysics) would not require extra energy, thus completing the circuit? But this doesn't seem to happen since the current is negligible during reverse bias,why?", "label": 0}
+{"snippet": "Prove that for any finite collection of points in the plane, not all collinear, there is a triangle having three of the points as its vertices, which contains none of the other points in its interior.", "label": 0}
+{"snippet": "my professor asked me to read about Tate's Thesis, but I have looked everywhere and I couldn't find the thesis itself. I found lecture notes and introductions on the the thesis. I am confused. Is Tate's Thesis a thesis? If so, where would I be able to find it? I really appreciate your help!", "label": 0}
+{"snippet": "They thought that the general would lead them to victory. vs. They thought that the general would have led them to victory. Is there a difference between the two sentences above? Is one grammatically incorrect? There is no particular context. I am more interested in learning the difference between the two (if any) and how the subtlety in wording affects the overall meaning.", "label": 0}
+{"snippet": "I'm trying to understand the nature of polar molecules. Have there been experiments where we can say to have actually measured the dipole electric field generated by a polar molecule such as hydrogen fluoride HF? The idealized experiment I have in mind for example is tracking the deflection angle of a free test particle (electron) as it passes near a single HF molecule...", "label": 0}
+{"snippet": "I would appreciate if someone could help me with this problem. I have tried to find a general expression for the multiplication of three matrices but wasn't successful in my pursuit. enter image description here", "label": 0}
+{"snippet": "John Taylor's Classical Mechanics says this... I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the second condition is not? And if so, how are the forces in that situation non-conservative even if they satisfy the second condition?", "label": 0}
+{"snippet": "In an infinite-dimension space, the relative interior of a non-empty convex set may be empty. I was wondering whether there is a concept (as a generalization of relative interior) with the following properties: for any non-empty convex set, Its \"concept\" is non-empty. Whenever the relative interior of this set is non-empty, its \"concept\" is the same as the relative interior.", "label": 0}
+{"snippet": "What is the motivation for studying D-modules? All I know is that they are some algebraic way of discussing differential equations. They are showing up in seminars, and I haven't yet been able to convince myself that D-modules are useful. So what kind of questions were D-modules made to answer, and how is it useful to view differential equations in this way?", "label": 0}
+{"snippet": "I coded a small example of RSA in Python. When filling p and q, I mistakenly put in two numbers that were not prime numbers. And it worked fine anyway. My question is, why is it so important for RSA to take prime number as inputs?", "label": 0}
+{"snippet": "I'm not sure if the use of \"easy to move\" in this sentence is correct. They say that our uniform looks cool and easy to move. It sounds strange to me. I can use the word \"comfortable\", but are there other words or ways to say it? I'd really appreciate your help. Thank you.", "label": 0}
+{"snippet": "Quick question - if the formal name for the solid counterpart of a sphere is a ball, and the formal name for a \"half-sphere\" is a hemisphere, what is the formal name for the solid counterpart of a hemisphere? Half ball? Hemi-ball? Just \"solid hemisphere\"? Is there even an agreed-upon formal name for this solid?", "label": 0}
+{"snippet": "Does anyone know how such a matrix is referred to in the literature? Ultimately my goal is to look for an analytic expression for its determinant. But because I don't know what it's called, it's been very difficult to go through the literature... Thank you so much for your help.", "label": 0}
+{"snippet": "At least for German-language documents (and especially when using microtype) LaTeX, to my taste, puts too much emphasis on preventing hyphenation. Is there any parameter that can be changed so that, in favor of more consistent white spaces, more hyphenation is done?", "label": 0}
+{"snippet": "There is an unhappy colleague in our company and I want to talk about this issue in my next meeting. I want to mean \"A bad apple ruins good apples\" but this sounds so negative. I want to model it positively. How do I do it?", "label": 0}
+{"snippet": "I was learning basic statistics and I read a proof that the standard deviation is always less than or equal to the range. I don't understand how range can ever be equal to the standard deviation. I could only think of one case: when all data points have the same value. Is there any other case possible in which the equality holds?", "label": 0}
+{"snippet": "When doing palatography, one needs something to paint the tongue with. It is usually a mixture of olive/sunflower oil and powdered charcoal. The question is, what can this substance be called? Is it a colouring, paint or/and dye? What is the most suitable word?", "label": 0}
+{"snippet": "I'm seeing some results on Google but it seems quite an unusual word combination. Is it okay to use it or would it be considered \"weird\"? Context: Free for non-companies We believe Open Source should be free for individuals and non-profits. Only companies pay. The word \"non-profit\" isn't usable as it wouldn't convey the same message.", "label": 0}
+{"snippet": "Pretty much the question. Is there a line (figurative) that separates when you'd use one term and when you'd use the other? Is there a distinctive characteristic of one that is not found in the other? Please help me understand. Thanks!", "label": 0}
+{"snippet": "just a quick question about how to determine if a matrix has a JCF - I know that if the characteristic polynomial factorises as a product of linear factors it has one but what if you only know the minimal polynomial factorises as a product of linear factors? Is this enough to say the matrix has a JCF? Thanks", "label": 0}
+{"snippet": "NO SHADOW of the fork! A distinct black shadow can be observed at the bottom of a glass before and after the fork enters the water, but the shadow disappears at the instant of entry, is this a phenomenon of refraction of light? (as shown in the figure) How does it work?", "label": 0}
+{"snippet": "Could someone please tell me how we define CM modular form and non-CM modular forms in the most basic way?Also, could you provide the references to your definition? I have tried searching for the definition. But still the definition is not clear to me.", "label": 0}
+{"snippet": "In the image below, the expression is depicted as a result of multiplying a polynomial by an infinite series, which is represented as an exponential function. Could someone kindly elucidate how the final equality is derived? Thanks in advance.", "label": 0}
+{"snippet": "I'm reading an article where risk measures are defined on the space of random variable (not necessarily bounded), so I want to understand why risk measures are defined at first (for example in Follmer and Schied) for bounded r.v.", "label": 0}
+{"snippet": "If the Earth were perfectly isolated from the rest of the universe - with no exchange of matter, energy, radiation etc - would we be able to recycle all stuff on Earth perfectly? For example, simple processes like electrolysis and burning of hydrogen. If no energy or matter is lost during these events, what's preventing us from reversing and recycling them indefinitely?", "label": 0}
+{"snippet": "I know Pieri's formula for elementary symmetric polynomials and for complete homogeneous symmetric polynomials, but is there an analogue for power sum symmetric polynomial? It seems that it should be similar, but the summation should be carried out by other partitions. Maybe someone knows where to read about it?", "label": 0}
+{"snippet": "How do we judge if a certain ruler-and-compass construction is the shortest? For example \"the shortest construction of a regular pentagon.\" Is there a software that can come up with a construction of a geometrical item given a collection of input data?", "label": 0}
+{"snippet": "Rotating a fluid filled cylinder and calculating the equation of it's free surface is an elementry problem in fluid mechanics. However I was wondering, if we rotate the same cylinder by an axis parallel to the main axis and passing through a point on it's circumference, what would be the equation of the free surface in this case, and what will it look like?", "label": 0}
+{"snippet": "In a cloud chamber, atoms of air are ionized by passing radiation, providing nucleation sites that enable droplets to form. When those atoms are de-excited, one would expect them to release light; does this happen, and if so is this radiation detectable?", "label": 0}
+{"snippet": "Which is correct? Is it, \"Do you want your house painting\" or \"Do you want your house painted\"? Examples of both can be found on the internet. Is there a difference between them? Can you use either?", "label": 0}
+{"snippet": "I would like to know how to write half integrals and generally integrals of nth order in LaTeX, for example in Cauchy's formula for repeated integration, because I didn't find how to do that on the whole internet.", "label": 0}
+{"snippet": "What does the MHD theory predict when two regions with magnetic field of opposed polarization interact? When we take in account the resistivity then we can observe a rearrangement of the topology due to magnetic reconnection but I am wondering what does the ideal MHD equations predict in that scenario.", "label": 0}
+{"snippet": "I was wondering, where I made a mistake in this attempt to disprove the four color map theorem. I hope that you smart folks can help me out. I already apologize, if the tags are wrong. I am not really a math specialist.", "label": 0}
+{"snippet": "I was wonder about following statement. \"Harmonic function is radially symmetric.\" What is correct meaning about above statement? I think it means 'Harmonic function is invariant under rotation' i.e: Let u(x) is harmonic function and x is n-dimensional vector. If A is nxn orthogonal matrix, then u(Ax) is also harmonic function Is it correct?", "label": 0}
+{"snippet": "I have a confusion. At one hand, magnetic moment is forced to align with an external static magnetic field; on the other hand, a magnetic moment can precess around an an external static magnetic field with a fixed angle. Clearly these two phenomenon cannot happen simultaneously. So which is correct?", "label": 0}
+{"snippet": "I am reading again about Lie Algebra, and one main concept is that of the tangent space of a lie group. We consider it to be all the possible tangent vectors as a path crosses the identity element in the lie group... but why exactly the identity element? Why not consider tangent spaces at a generic point?", "label": 0}
+{"snippet": "If an object is projected towards east or west from the equator, we get the coriolis force to be vertical. If this projectile, say, miss its target from below, can this be attributed to the coriolis force?", "label": 0}
+{"snippet": "Can the definite article have two different meanings in front of identical words in one sentence? As in The bicycle is a vehicle but the bicycle in this room is just a decoration. Or perhaps this sentence should be better written as A bicycle is a vehicle but the bicycle in this room is just a decoration. ?", "label": 0}
+{"snippet": "Does anyone know of a relatively simple and easy-to-use graphics app (like GeoGebra) that can graph hyperbolic geodesics on a hyperbolic paraboloid? I'm trying to graph the geodesics on the top image to the surface on the bottom image, specifically to best visualize the hyperbolic case of the parallel postulate. I haven't found a way to do it on GeoGebra.", "label": 0}
+{"snippet": "I encountered this correction in IntelliJ, a tool for editing computer programs: Is this right? I feel like there is an implicit \"that\" in the sentence: I need to borrow some money so [that] I can buy some medicine for Tom. And therefore the second clause is really a dependent clause in disguise. What do the experts say?", "label": 0}
+{"snippet": "I have to do an exploration in maths. I was thinking to do it on how the angle of incidence and reflection vary with the eccentricity of the ellipse. Do you think could be interesting? Do you have any suggestions for the method? I was thinking to extend it on ellipsoid billiards.", "label": 0}
+{"snippet": "If electricity is the flow of electrons, how come it can flow at the speed of light? Shouldn't how fast it moves be limited to a speed lower than the speed of light because it has mass?", "label": 0}
+{"snippet": "I have several times seen stated the fact that the complex projective space with the Fubini-Study metric is isotropic, but i can't seem to find the proof anywhere, can anyone suggest a book or answer with a proof?", "label": 0}
+{"snippet": "I have been learning electrostatics, and I didn't quite understand why charges reside only on the surface. The charges are moved until they reach the surface after which they cannot move further and hence the field that had developed cancels the external electric field. How does this cancel the external electric field?", "label": 0}
+{"snippet": "Lorentz scalars are invariant under Lorentz transformations, which are a subset of linear transformations. I wanted to know if it is possible, for a Lorentz scalar, to NOT be invariant with respect to another kind of linear transformation (e.g. scaling or whatever linear map other than Lorentz). Can you mathematically prove your answer?", "label": 0}
+{"snippet": "x = f(a,b,c), y = g(a,b,c), and z = h(a,b,c) if a,b,c are sides of a triangle, then x,y,z are also sides of a triangle. How can you write sets of functions f,g and h?", "label": 0}
+{"snippet": "I'm wondering if its ever possible to find two non-isotopic knots which have identical jones polynomials but different seifert genus? Attempting to google for this I found this example of non-isotopic knots with identical jones polynomials. But in the first page of the paper its clearly stated that all the knots have identical genus.", "label": 0}
+{"snippet": "So, the thing is i was using this code on overleaf (it worked fine there) and i wanted to switch to texstudio because of the compiling limits on overleaf. So i copied the whole command from overleaf tex file and pasted in the texstudio. But it says \"Error: File 'sn-jnl.cls' not found.\" when i run it. how do i fix it?", "label": 0}
+{"snippet": "Is there a name for the particular part of a circle shown in red? I know the white sections are segments. If the vertex was at the center of the circle it would be a sector. I don't suppose that any mathematician would have been brazen enough to call it the \"ice-cream cone.\"", "label": 0}
+{"snippet": "Is it correct to say that if two parabolas touch, then tangents at the point of intersection have the same slope? If it is true, is there a neat geometric interpretation of the fact?", "label": 0}
+{"snippet": "If I had a pair of entangled particles that were both in superposition, and I put one of them through a interference experiment, such as the double slit experiment, would I see an absence of interference the moment I measure the other particle? And how would this change if both were in an interference experiment and I measure one of them?", "label": 0}
+{"snippet": "Why were multiple layers of absorbers and scintillators used in the CMS HCAL? Couldn't they have used just one absorber and one scintillator layer? Why was the choice made to have multiple layers?", "label": 0}
+{"snippet": "I read book \"A primer of infinitesimal analysis\" John Bell. I was confused when I saw example with area under curve. In that example author mentioned about nondegenerate triangle of zero area. But triangle of zero area is degenerate triangle. How is it possible? How to imagine what author meant in that example? Thanks.", "label": 0}
+{"snippet": "I have read that a net charge in a closed, finite universe would result in the electric field from the charge \"winding\" forever which would lead to infinite energy. However, wouldn't the electric field lines cancel out if they were winding around the surface of a sphere like in the diagram?", "label": 0}
+{"snippet": "I was scrolling through a wiki article on terminal velocity when I spotted an upside down delta. What does this symbol mean? How is it applied in other contexts? EDIT: If possible could someone expand upon \"a covariant vector made of space derivatives?\" I sort of understand how a vector can be made up of partial derivatives, but what does covariant mean?", "label": 0}
+{"snippet": "I am currently setting up a portable LaTeX environment (TeX Live) with VisualStudio Code and the LaTeX Workshop extension as the editor. How do I specify in the LaTeX Workshop settings the path to the LaTeX environment? This is for Windows. Changing the environment variable on every computer used is not desirable. I also couldn't find something in the settings of the LaTeX Workshop.", "label": 0}
+{"snippet": "I am currently reading Falconer's book on Hausdorff dimension. My question is whether Hausdorff dimension is invariant under local isometry between smooth Riemannian manifolds? I think it should be yes, but I am not sure how to choose the covering( needed for calculation of dimension) using the local charts explicitly to get the invariance. Any help would be very much beneficial for my understanding.", "label": 0}
+{"snippet": "I have an html table like <table>...</table> with some css formatting and I'd like to put that table into latex document. I don't want to put it as a figure because I will not ba able to copy its content. How can I do that (preservig formatting and styling)?", "label": 0}
+{"snippet": "I am learning general relativity by myself. I wonder if the equivalence principle is simply equivalent to, in geometrical terms, the statement that a Lorentzian manifold is locally flat, which is a somewhat trivial result from the point of view from math.", "label": 0}
+{"snippet": "Many textbooks derive the single-particle excitation energy gap from the BCS mean-field hamiltonian, and then stop there, implying that this gap is sufficient for superconductivity. To be frank, I cannot see why a gap implies superconductivity. Superconductivity is a transport phenomenon. But the BCS mean-field hamiltonian is just a static hamiltonian; it is not directly connected to transport, right?", "label": 0}
+{"snippet": "Everytime I approach any projectile motion/kinematics problem, I get confused. I don't know how to translate the problem into an operational method, and every time I complete a problem, the next one is a new mystery to me. How should I tackle this issue and master this problem type?", "label": 0}
+{"snippet": "My super basic question is, the (magnetic) force between two steady current loops obeys Newton's third but the (magnetic) force between two charges doesn't. This is surprising given that the former is built out of the latter, so is there any significance to this fact?", "label": 0}
+{"snippet": "I'm currently learning about Radiation in my Physics course, and so far i was interested in betavoltaic batteries that convert eletrons to photons and then eletricity. I'm confused about how to calculate the energy per second (W) produced by eletrons converted to photons. Can someone help me on that?", "label": 0}
+{"snippet": "I am very confused and probably understanding the concepts of renormalization wrongly: If the running coupling constant is a real experimentally observable quantity and the change with scale has a physical interpretation as \"vacuum polarization\", how can it get independent of the scale if we could sum up all orders of perturbation theory?", "label": 0}
+{"snippet": "Can you explain to me the reason why Thomson Scattering can not explain what happens when light meets an electron at low intensity, and what does that have to do with light being a wave or particle or relativistic/QM effects?", "label": 0}
+{"snippet": "I cannot seem to find or come up with an answer to the following question: In mathematics, is it possible to prove that there is only one (shortest) proof of a given theorem (say, in ZFC)? Are there any (preferably natural) examples?", "label": 0}
+{"snippet": "When you write a spline curve as a linear combination of b-spline basis functions, it's called a \"b-spline\". The basis functions are generated recursively by the deBoor-Cox algorithm, starting with degree zero and working upwards to higher degrees. These b-spline basis functions are thus written in terms of (i.e., as a linear combination of) other b-spline basis functions, so they are also b-splines?", "label": 0}
+{"snippet": "I need to run an experiment on the effect of temperature on refractive index of a liquid, and in order to make the change most visible and have the lowest percent uncertainty I need the change in refractive index to be as high as possible. What are some liquid with high changes in refractive index with change in temp, higher change then water ideally.", "label": 0}
+{"snippet": "I have seen some mathematical texts that use words like Lemma, Theorem, Corollary, etc. What would be the appropriate description of such terms? Do they fall under some linguistic category? Is there any general term associated with these kinds of premises?", "label": 0}
+{"snippet": "I'm writing a bullet point in a presentation. I want to say: Our partner and customer commitment remains unchanged. However, it feels like it reads better if I change it to: Our partner and customer commitment remain unchanged. I know if I read them separately, remains is correct. I've searched Google, and \"remains\" is more common. Should I use remain or remains?", "label": 0}
+{"snippet": "My textbook states that when the diffraction gap is smaller, there is more spreading of the waves. However, it seems unintuitive to me, since why would waves spread less if there is more space for it to spread? Is there an intuitive way of understanding it?", "label": 0}
+{"snippet": "I came across a thesis which has a feature in its references. Each reference includes the page number(s) of which the reference is cited. Is this possible to do using Latex? I found it really interesting to use. Apologies for the image being in French.", "label": 0}
+{"snippet": "Say, you have a complex number in standard form and another in trigonometric form, can you do operations with them, for example adding/subtracting, multiplying/diving the two numbers, just like that, or do you have to convert one of them to the other form to be able to do operations?", "label": 0}
+{"snippet": "Is there a name for white noise that has non-constant variance? I have some examples from experimental data where the variance of the white noise increases with time. However, I am not sure how to model this.", "label": 0}
+{"snippet": "For propositional logic, for every formula, there is an equivalent formula in the CNF and DNF. These normal forms have the advantage of being representable in a \"tabular\" form rather than a \"tree\" form, which may be more computationally friendly. Is there something similar for linear logic? I am mainly interested in the additive-multiplicative fragment.", "label": 0}
+{"snippet": "I understand that an algebraic group may not be a topological group because the continuity of multiplication with respect to the Zariski topology is weaker than that with respect to product topology. But is there a nice example that helps to explain this. Many thanks!", "label": 0}
+{"snippet": "I'm looking for a selection of problem books on probability theory, at the level of student olympiads in mathematics. I've already looked at Albert N. Shiryaev Problems in Probability, but maybe you can suggest some more interesting options. Many thanks!", "label": 0}
+{"snippet": "Was just curious, is it possible to obtain the eigenvectors if you only know the eigenvalues and the dimensions of a square matrix? Or what further information from the matrix can you gain from only knowing the eigenvalues?", "label": 0}
+{"snippet": "I know that mechanical computers have been used for a number of different calculations, the most famous (at least on the internet) seems to be the firing control computer used by the US Navy. But were there any entirely mechanical devices (other than a slide rule) that could calculate logarithms?", "label": 0}
+{"snippet": "I am trying to understand Schmidt decomposition. I am stuck in one sentence here. See the example picture. Here, I can understand everything except the line \"For both HA and HB the Schmidt basis is diagonal (Hadamard) basis.\" Can anyone help to understand what the author tried to tell here by using this line?", "label": 0}
+{"snippet": "For example, during refraction, when photons pass through a glass slab, they change direction. Why does this happen? Is the reason for this not applicable when photons strike perpendicular to the glass slab?", "label": 0}
+{"snippet": "Is there a TeXShop directive (something like % !TEX TS-program = lualatex) that I can place at the top of my document and can tell TeXShop to compile using LuaLaTeX with latexmk? That is, a TeXShop directive that does the equivalent of latexmk -lualatex file.tex.", "label": 0}
+{"snippet": "We derive the formula of escape velocity by using conservation of mechanical energy, where we consider that work done by external force is neglected. But to provide the velocity to send an object to infinite distance from gravitational pull of Earth, don't we have to apply an external force?", "label": 0}
+{"snippet": "Is it possible, with LuaTeX, to retrieve the textual content of a PDF (using lua code I imagine)? For my purposes, it doesn't have to be \"clean\" (for example, the order doesn't really have to be respected), it's for \"statistics\" on the words used.", "label": 0}
+{"snippet": "So the context is this: I taught my friend how to play a video game and he's gotten to a point where he's passed all of my stats and records. I'm looking for a word to use like ronin (samurai without a lord or master) and I'm curious as to if that exists. Thank you ahead of time", "label": 0}
+{"snippet": "As the title says: Is there a distance at which the Kerr metric looks like Schwarzschild metric? Edit: if there isn't any such distance (smaller than infinity), can we measure from the outside, with which speed a black hole rotates?", "label": 0}
+{"snippet": "In complex analysis the term branch is used to designate a holomorphic function defined on a region. The most prominent example is the principal logarithm, which is a branch of the logarithm. Does anybody know the history of why the word branch used? I'm guessing branch, tree, decisions, choice.", "label": 0}
+{"snippet": "In the context of optical tweezers, if used in a vacuum and a particle starts off slightly to the right from the center of a beam, would the particle eventually become perfectly centered or would it continuously slingshot from right to left? Does this depend on the strength of the laser?", "label": 0}
+{"snippet": "Is this just an extension of the idea that with a small enough perturbation, the Principle of Least Action will still hold, and the system will continue to take the most optimal path?", "label": 0}
+{"snippet": "Since light travels at the speed of light towards a target, the spatial distance to the target seems to be zero, owing to Lorentz transformation. It seems that there is a logical flaw here. Can someone explain that? Question is similar to this: Wouldn't a photon disappear because of length contraction?", "label": 0}
+{"snippet": "I am using a convex lens in a wavefront-measuring interferometer for testing microscope objectives, where the lens images the exit-pupil of the objective onto my camera. It is my understanding that the effects of diffraction from the convex lens will have some influence on my interferogram, especially around its edges. How can I actually take these effects into consideration?", "label": 0}
+{"snippet": "I came across the concept of topology of time and causality in Reichenbach book, \"Philosophy of Space and Time\". It would be nice to have list of references of recent developments of the same. It could be textbooks, research papers or published articles.", "label": 0}
+{"snippet": "I am searching for optimal control examples in fluid mechanics in which only ordinary differential equations are considered (i.e., in system dynamics or model of optimal control problem) with exact or approximate state and control variable plots. So far, I am getting examples containing PDEs. Does anyone know of any sources (books, journal articles) containing such examples?", "label": 0}
+{"snippet": "On Wikipedia (article:https://en.wikipedia.org/wiki/List_of_trigonometric_identities) I came across this trigonometric identity in the infinite sums section In the article no proof was provided and so I would like to know if anyone here knows a proof of the identity.", "label": 0}
+{"snippet": "Given a pair of inversely similar triangles ABC and AB'C', as shown in the graph, CB and C'B' intersect at F. X, Y, Z are the midpoints of BB', CC', and AF respectively. Prove that X, Y, Z are co-linear. This is a very elegant result, and somewhat alike Newton's line. All proofs welcome, and a geometrical solution would be very nice!", "label": 0}
+{"snippet": "Why doesn't the first line have an auxiliary to make it interrogative? These lines are from Sorry Seems To Be The Hardest Word, featuring Elton John: What I got to do to make you care? What do I do when lightning strikes me?", "label": 0}
+{"snippet": "I'm an undergraduate student and currently I'm approaching tensorial calculus. I was wondering: is there some geometric meaning to the operation of rising/lowering indices (and then if there was any geometric difference between vectors and covectors), or are they only mere formal operations? In case, why don't we simply use only vectors in the definition of tensors?", "label": 0}
+{"snippet": "What are the ways to center headers only without using the titlesec and sectsty packages? If we take the titlesec package, then the question is how to prevent this package from automatically changing header styles?", "label": 0}
+{"snippet": "What is the concept of hypersurface in general relativity? I know it could be characterized into three categories but how do we define hypersurface (in general) in physics? I didn't get what thing it is.", "label": 0}
+{"snippet": "I have always believed --- from somewhere --- that in archaic English, cats were always referred to using feminine pronouns, regardless of what sex they actually were. But I thought to go and find a reference for it and I can't find anything. Was this ever a real thing, or was I just hallucinating?", "label": 0}
+{"snippet": "If I lift a weight to a certain height, where does the gravitational potential energy at that height originate from? is kinetic energy converted into gravitational potential energy as the weight is decelarating as it approaches the maximum height? or is the chemical energy from my body (doing the work) shared between kinetic energy and gravitational potential energy? Hope this makes sense. thanks.", "label": 0}
+{"snippet": "Why do electrons have discrete energy states when they are bound to a nucleas and not when they are free for example in an electron beam. Why doesn't an electron beam have certain specified energies like bound electrons do.", "label": 0}
+{"snippet": "I have seen that a number of packages exist that define symbols. How can I find a list of just the core symbols provided by the Latex Team, but without the use of packages like amssymb, MnSymbol and so on.", "label": 0}
+{"snippet": "I am new, not have expert level knowledge. But I have studied about black hole information paradox. The black hole doesn't kept any information which passes event horizon. Which can break physics. Is there any theory about Information Paradox, to resolve it.", "label": 0}
+{"snippet": "What is a good term for plants whose parts, either as tubers, roots, or fruit/seeds are harvested and consumed? I exclude plants such as hemp and flax whose fibres are used, or, for example, poppies for opium.", "label": 0}
+{"snippet": "i.e. is the comma to signify the boundary between the instruction and the recipient of it (that is to say, \"Hey, stupid! Keep it simple\"), or is it serving the function of an \"and\" (as is sometimes used in US English but rare in British).", "label": 0}
+{"snippet": "I have tried to search a lot about the laws that predicted this behaviour of black body. But haven't really found out. And the ones I found like equipartition theorem, i find them contradicting with classical physics itself. How exactly it was predicted that with increase in temperature, there would be increase in intensity of radiation at each frequency.", "label": 0}
+{"snippet": "I've realized that there are many results in set theory rely on the theorem that states \"the union of countably many countable sets is countable\". However, all of the proofs of this theorem I've found so far, including ones on SE, rely on the axiom of choice. So, I'm wonder without AC is it still true or false or neither provable nor refutable?", "label": 0}
+{"snippet": "What's the difference between these? I will go to the bathroom and brush my teeth I will go to the bathroom and will brush my teeth Perhaps one of these sentences is grammatically incorrect. Which one is desirable to use in technical writing?", "label": 0}
+{"snippet": "I've noticed that both are used though \"point in\" is seemingly far more prevalent. Is there any difference or it's down to one's preferences? E.g. There's no point in talking to you. vs. There's no point talking to you.", "label": 0}
+{"snippet": "Is there a phrase with a similar meaning to the phrase Don't put all your eggs in one basket which doesn't make reference to eggs? I'm writing a story in which one character is a bird and I feel it doesn't make sense for them to use this specific phrase about eggs, given that eggs are essentially bird pregnancies", "label": 0}
+{"snippet": "If the activity involved only me and one other friend, e.g. playing tennis, I know \"I played tennis with Jake\" is correct. However, is it possible to also say something like \"We played tennis with Jake\"? If not, is there a slight adaptation in the structure which allows for the use of \"We\"?", "label": 0}
+{"snippet": "I've heard of the term escortee, but Googling it doesn't turn up any definition. If not that, then what could I use in this sentence: I escorted the girl through the school; she is a ________.", "label": 0}
+{"snippet": "I do not know exactly what shape is a spoon. I feel like it is an elliptical paraboloid but really I don't know. I really need to do this for my math project. Any help would be very appreciated! Image of a sample shape", "label": 0}
+{"snippet": "Is it possible to give an example of countable set, with uncountable derived set, such that intersection with this set and its derived set is empty? I know that if given set is uncountable, then it is impossible. But what if set is countable?", "label": 0}
+{"snippet": "Do internal forces of an atom lead it to move, or can an atom only move when an external force is applied to it? For example, if we had a perfect vacuum with the exception of one arbitrary atom, would it move due to internal forces?", "label": 0}
+{"snippet": "I am proofreading an article and have come across: \"to a focus on a fulfilled (upper)middle-class life\". At first I was simply going to put a space between the closing parenthesis and the \"middle\" but am now second-guessing myself. My question is, in keeping the parentheses, would it be: \"(upper) middle-class\" or \"(upper-)middle-class\" or some other form?", "label": 0}
+{"snippet": "When a railway is laid in a cold environment, should tensile or compressive force be applied? How does this work? I think the answer should be tensile. The railways expand while heated so applying tensile force would mean there is less extension and therefore less stress. Is this a correct explanation?", "label": 0}
+{"snippet": "I have a problem where I have to study \"the geometric properties of the Brachistochrone curve in non-Euclidean spaces\". But I am confused about the definition of the Brachistochrone Problem/curve in any non-Euclidean space. Please offer me some help.", "label": 0}
+{"snippet": "I considered the word \"circumstantial\" or phrase \"circumstantially true\" but I feel like there's another word that better describes this. In an example; if you step in a puddle and your feet get wet then that is the truth in your case, but it is not the case that anyone who steps in a puddle will get their feet wet.", "label": 0}
+{"snippet": "How would I go about drawing something that looks like this (please excuse the extremely lousy Paint image) I am sorry I cannot provide any exact code, but I am basically clueless as to how I'd do this. I hope you have understanding. Thanks in advance.", "label": 0}
+{"snippet": "I've been learning about the density wave theory of spiral arms, and also how the gravitational potential of galaxies is non-axisymmetric, resulting in a sinusoidal spiral potential. I've then learnt that the spiral arms/density waves occur at this spiral potential minima. Why is this?", "label": 0}
+{"snippet": "Is there any word for someone who doesn't accept others' favors? They have no reason for it, they just say no. Perhaps it's because they would feel insecure. Example: -Why does she always say no when I offer her snacks or drinks? -You know she is a [word]", "label": 0}
+{"snippet": "I've been learning spectral methods mainly through reading the book \"spectral mehtods in matlab\" by Trefethen. I have a simple question: Could spectral methods solve first-order differential equations? It seems using spectral methods requires two initial conditions.", "label": 0}
+{"snippet": "Recently, I was reading about a article which tells about something known as \"Susskind Complexity\". The article states that the interior volume of a black hole grows forever. How/why does the internal volume of a black hole grow forever? What is the mechanism/reason behind this?", "label": 0}
+{"snippet": "How to prove that a Hilbert space is the directed colimit of its finite-dimensional subspaces? Does this imply that the category of Hilbert spaces (and bounded linear maps) is the Ind-completion (see here) of that of finite-dimensional Hilbert spaces?", "label": 0}
+{"snippet": "I am looking for a distribution whose mean and median are different, preferably a distribution that share some properties with Gaussian distribution. I kinda know that there is something called skewed distribution or alike that probably would work but I have no idea how it is defined and/or how the expectation/median is estimated. Thanks a lot.", "label": 0}
+{"snippet": "I know \"No, it can't be\" can mean \"It's impossible that it is\", but I don't think \"No, it may not be\" can also mean \"It's impossible that it is\". I know that \"No, it may not be\" can mean \"It's possible that it is not\", but can't the sentence mean \"It's impossible that it is\" like the case of 'can'?", "label": 0}
+{"snippet": "So, I'm preparing for a PTE test and came across this problem in the Fill in the Blanks section. Gators can move through the water oh so silently, barely ___ (making/creating/adding/showing) a ripple. Why is the answer creating the ripple (not making the ripple) here? I just wanted to know the reasoning behind selecting the word \"creating\" instead of \"making\".", "label": 0}
+{"snippet": "Can I use parse as a verb in this example? The clouds began to parse and the day opened up. Meaning the clouds began to separate from one another and dissolve. Parse is commonly used to describe analyzing text or sentences but can also be defined as to resolve into its elements.", "label": 0}
+{"snippet": "If we have a beam of photons (high energy X-ray) and a beam of protons both with the same energy, which one will get further inside the human body and why? Can this be explaind due to LET (Linear energy transfer)?", "label": 0}
+{"snippet": "In a problem, I have the expression of acceleration and velocity in Cartesian coordinates , and it ask me to calculate the tangential and normal acceleration, so we don't know how I can do that, can any one help me?", "label": 0}
+{"snippet": "I have a problem, where I am asked to give a precise definition of the Sierpinski-triangle. The problem describes the usual algorithm to construct the triangle. However, I am clueless on how I should give a different definition. Is there some definition using the union of the points of the Sierpinski-triangle?", "label": 0}
+{"snippet": "From what I 'understand', Noether's second theorem applies to infinite-dimensional symmetry groups. A classic, even historical, example is the invariance group of Riemannian spacetimes, i.e. the set of spacetime diffeomorphisms of GR. Does Noether's second theorem also apply to quantum field theory (= the 'gauge groups')? Or is it confined to general relativity?", "label": 0}
+{"snippet": "I'm wondering what native English speakers call a person (man or woman) who is attracted to a no-make-up look and dislikes it when people wear a high amount of makeup. I can think of no-makeup lover or not into makeup. But is there a specific word being used?", "label": 0}
+{"snippet": "It is well known that the quaternions, octonions, and sedenions are well studied, but I don't find any articles or books in which other hypercomplex numbers are studied. Does anyone know a book or an article in which other hypercomplex numbers are studied? And if so, what is the usage of numbers like pathions, voudons, etc...?", "label": 0}
+{"snippet": "Looking for a reference for a textbook that discusses classical conditions for contraction mapping, such as diagonal dominance. It should contain theorems similar to the one in the picture (which I found on this post without a source).", "label": 0}
+{"snippet": "Basically it means that the vowels must come in the order - E, U, A, I, O and can be place anywhere in the word. I tried to do it by assuming that each of the vowels can come in five different spots. But I didn't get anywhere...", "label": 0}
+{"snippet": "We don't pronounce \"th\" in \"pothead\" as a single logical sound, or \"ph\" (as \"f\") in haphazard. They are consecutive letters pronounced individually. Is there a term to describe such a language phenomenon? I'm guessing no but it can lead to some humorous situations (I think on the Simpsons, policeman Lou said \"poth-ead\" which I found entertaining).", "label": 0}
+{"snippet": "What is the adverb that is commonly used when describing something rapidly/drastically increasing? It's on the tip of my tongue and I can't get it out. It's not tenfold, rapidly, drastically, dramatically, stratospherically, etc. but similar. I think it has a connotation of quickly multiplying. (It's a single word.) It's driving me insane--any idea what it is?", "label": 0}
+{"snippet": "My understanding is for a rigid body the angular velocity between two points fixed on the body is the same for all points. In other words the angular velocity vector would be the same. I can't find a proof of this. To be clear I'm talking translating the origin on the body, not relocating the secondary point you're computing the angular velocity of.", "label": 0}
+{"snippet": "I know that a charge moving parallel to a straight current carrying conductor experiences a force towards that wire due to magnetic lorentz force. I am more curious about the idea where the charge is stationary and the wire is moved parallel to it in the opposite direction at the same speed. Will there be a force on the charge this time?", "label": 0}
+{"snippet": "In Spanish there is a suffix, -udo, that's used for \"in adjectives derived from nouns, it indicates abundance, big size, or intensity of the meaning of the root.\" Is there something like this in English?", "label": 0}
+{"snippet": "I'm thinking of doing a project with some undergraduates soon involving edge ideals, particularly binomial edge ideals. Do you have a gentle introductory reference to this topic suitable for undergraduates? We can assume that the students are comfortable with basic algebraic objects such as rings and ideals, as well as what graphs are and some of their basic theory.", "label": 0}
+{"snippet": "I'm not sure if there's a better way to say this: It would have been better if my brother had died rather than struck a bargain in the red desert. Am I using that right? Ugh! Help me please. This is the first line of my story and my critique group is arguing about which sentence is correct.", "label": 0}
+{"snippet": "I learnt that an optic fibre uses the concept of total internal reflection (TIR) to transmit data at high speed, but why do they not use just simple mirrors instead of using refractive medium and making a light incident at an angle more than the critical angle, so that total internal reflection can occur?", "label": 0}
+{"snippet": "I am currently studying intro to analytical number theory by Tom Apostol. It is a very def-thm-proof kind of textbook, and even after taking notes of definitions and theorems, i still struggle with exercises. Can someone please suggest a method for me to get more out of the book? Also, does anyone have lecture notes that can be paired with the book?", "label": 0}
+{"snippet": "I would like to learn what prerequisites are needed in order to be able to work on a postgraduate thesis on the topic: Invariant Einstein metrics on compact simple Lie groups and Stiefel manifolds. I have noted Lie groups, differentiable manifolds, general theory of relativity, and tensor analysis.", "label": 0}
+{"snippet": "Assuming that a sinusoidal wave with an amplitude a million times bigger than the diameter of a black hole enters a black hole, what happens to those parts of the amplitude that are not inside the black hole? The other question I have is, \"Does the black hole change the amplitude of a frequency that enters it?\"", "label": 0}
+{"snippet": "Sorry everyone. I do not really know if this belongs here, but I can't find a solution by myself, since I have no idea of what could be happening here! I have the fonts installed, but TexStudio says they are missing! How could I start solving this problem?", "label": 0}
+{"snippet": "According to wikipedia: https://en.wikipedia.org/wiki/Affinity_laws, when shaft speed is constant, the pressure is proportional to square of impeller diameter. I am wondering why this is true. Surely, for larger diameter, more air is pumped, so we need a stronger force. But why pressure also need to increase?", "label": 0}
+{"snippet": "Do we know absolutely nothing about what might be the state of matter-energy inside the black hole? Are there existing theories or research that explore the possibility of a metastable vacuum inside black holes?", "label": 0}
+{"snippet": "Say I have a bunch of colors in math mode. How do I remove all of these colors (reset to default or black) efficiently? (If the colors are in text i.e. not math mode, I can just do this: Select text > Text Style > Color > Default > Apply. But when the colors are in math mode, this doesn't work.) Related", "label": 0}
+{"snippet": "In programming it is rather the norm than the exception to have functions whose input are different data types. For example a function who produces a substring of a given string would have the following signature in Java: public static String substring(String s, int n) {..} Are there examples of such functions in Mathematics and what is their application?", "label": 0}
+{"snippet": "According to my understanding we get a lot of energy during nuclear reaction because mass transforms to energy. According to picture below total mass remains the same after reaction. Is the picture wrong?", "label": 0}
+{"snippet": "Minimal sufficient statistics are supposed to have the lowest dimension among all sufficient statistics. Then, is any sufficient statistic having the same dimension (as the mss) a minimal sufficient statistic? If the answer is no, is there any simple counterexample?", "label": 0}
+{"snippet": "Consider these four situations: a tennis ball falling on a wooden floor a tomato falling on a wooden floor a book falling on a wooden floor a tennis ball falling on a soft mattress Why only in the first situation the object bounces?", "label": 0}
+{"snippet": "It seems that paths of the Brownian motion are always continuous (please correct me if i am wrong). Levy process is the generalization of Brownian motion by allowing for jumps at random times. So why always people talk (e.g. using Donsker's theorem) about the relation between random walk and Brownian motion (and not between Levy process and random walk)?", "label": 0}
+{"snippet": "Is there a word (or maybe a metaphor) to cover the idea of religion, mysticism, occult, and philosophy all together? In other words, how would you name a bookshelf with books and other texts by or about the following authors? Thomas Aquinas George Gurdjieff Aleister Crowley Aristotle", "label": 0}
+{"snippet": "Let's say a box is moving to the right and friction is slowing it down. The friction force vector pointing to the left and the object moving to the right, should the vector be drawn on the left side of the object like this: : Or on the right side of the object like this:", "label": 0}
+{"snippet": "Is there a specific name for the following graph? \"Acyclic tree\" is not unique and \"one-dimensional lattice\" doesn't sound quite right. Saying \"line graph\" is, in my opinion, ambiguous. The reason I ask this is because I need to reference this graph without the use of this picture, or any pictures for that matter.", "label": 0}
+{"snippet": "In quantum field theory, consider acting on the vacuum with a local unitary operator that belongs to the local operator algebra associated with a region. In such a way, can we obtain a state that is orthogonal to the vacuum? i.e., Can the one-point function of a local unitary be zero? If so, any examples?", "label": 0}
+{"snippet": "The Hauptvermutung (ie. the question in the title) is known to be false for PL manifolds and topological manifolds, but I can't find a result for smooth manifolds (with boundary), though I recall reading it is true. If not, is something close to this true?", "label": 0}
+{"snippet": "I am trying to self-study probabilistic measure theory after completing my undergrad degree, and I am curious if there are more interesting applications of measure theory aside from Lebesgue integration ? It seems like (correct me if I am wrong here) measure on its own is a rich field before delving in integration of measurable functions.", "label": 0}
+{"snippet": "If someone says something such as, \"I don't know what else to do,\" it kind of implies a request for some suggestions. In the case the person doesn't actually want ideas for what to do, would this be considered a rhetorical statment?", "label": 0}
+{"snippet": "As far as I know, the magnetic properties of a bar magnet is due to the alignment of electronic spins of all the atoms. According to the uncertainty principle the electronic spin is randomly up or down. So, why a bar magnet has certain poles while it may be expected its poles interchange? I appreciate any help about my misunderstanding.", "label": 0}
+{"snippet": "In Latin, it simply means \"an amount\", which can be of anything and of any size. In modern English, especially in physics, it means the smallest amount physically possible, i.e. a physically indivisible amount of something, especially pertaining to energy.", "label": 0}
+{"snippet": "I would like to justify text in lstlisting. If the line gets too long, there doesn't seem to be any way to automatically add a new line. Is there a way to justify text?", "label": 0}
+{"snippet": "In the sentence below, 'do' refers to 'sense the environment' ,which is evident. But can 'do' refer to only a verb 'sense'? Share what you think about this, and please explain why it is or isn't okay. It is lazy and dangerous for the ecologist to assume that all other organisms sense the environment in the way we do.", "label": 0}
+{"snippet": "I have a question about the use of \"as well as\" and \"as did\". Which would fit better in the following sentence? When the earthquake began, at least fifteen men and women fell to the ground, as did many children playing in the park that day. I appreciate any assistance you can provide.", "label": 0}
+{"snippet": "How can Dirac neutrinos exist if neutrinos have no charge? As far as I'm aware, the antiparticle of a particle is its charge conjugate while all of its other characteristics remain same. How then can a neutrino be distinct from an antineutrino?", "label": 0}
+{"snippet": "I've stumpled upon a peculiar usage of the Past Perfect Tense. At the end of the WWII, the Cold War had begun. The world would lay divided between two superpowers. This context seems suitable rather for the Past Simple Tense. I would be thankful for any hints as to why this tense was used. Have a good day, Damian", "label": 0}
+{"snippet": "What are some famous open problems and conjectures in Lie symmetry theory? Is there some kind of list of these problems available or possibly a historical survey of the development of theory of symmetry groups?", "label": 0}
+{"snippet": "What's the phase difference between A and B on the following diagram. Where it is a standing wave. This question doesn't even make sense to me as from watching animations of standing waves, points A and B cannot even appear at the same time. We cannot have two minimums next to each other. So what is it asking?", "label": 0}
+{"snippet": "If i were to make an observation of the orbital motion of the planet Mercury from an inertial frame of reference, would I observe the precession of Mercury's perihelion? or would I observe it moving in the way predicted by Newton's mechanics? And if I will observe the precession of Mercury's perihelion, would my frame of reference still qualifies as being inertial?", "label": 0}
+{"snippet": "I learnt that a point source produces spherical wavefronts and i know the reasoning behind that too and while studying the concept again a question popped in my mind, that \"Are those spherical wavefronts equidistant ?\", most online sources don't have an answer. A clear explanation for the question would be greatly appreciated.", "label": 0}
+{"snippet": "Is there a list giving an estimate of the abundance of every element of the periodic table in the Earth's Core - possibly differentiating by inner core and outer core? I am specifically interested in estimates for extremely rare trace elements.", "label": 0}
+{"snippet": "A steady state is Nash if it is strict and pure. And there can be multiple steady states, but not all of them satisfy the conditions of a Nash Equilibrium. Is this right?", "label": 0}
+{"snippet": "in textbooks I find only results about the weak convergence of univariate stochastic processes. I am looking for a reference text which treats also the convergence of multivariate (vector) stochastic processes. Any hints? Thanks. Ciao Karl", "label": 0}
+{"snippet": "I like to use the cochineal font for my document, however for this font I understand there are no corresponding mathematical fonts. So I am asking if anyone knows of any font similar to cochineal that also supports math fonts or a math font similar to cochineal fonts. I am using the KOMAscript class for the document. Thanks for all.", "label": 0}
+{"snippet": "How do I get LyX to show the reference in full (without the \"...\" ellipsis)? Example: Below, I want LyX to show me \"Ref: VeryLongLabelNameABC\" instead of \"Ref: VeryLongLabelNameA...\" (which in this case is actually even longer and takes up more space)?", "label": 0}
+{"snippet": "Electric potential is the amount of Work required to move a unit positive charge from infinity to a region of an electric field. Why do we need a positive charge for that? Can't we use negative charge?", "label": 0}
+{"snippet": "I couldn't find this sort of question anywhere, but this is similar to possession, like when you say \"Amanda's book\" instead of \"the book of Amanda,\" but those two have slightly different meanings. What's it called when you make the noun go after the word \"of\" and it describes the first noun?", "label": 0}
+{"snippet": "I've come across a question that asks what the subatomic particles are. The answer being the proton, neutron and electron. However, from my understanding subatomic particles also include quarks etc. So what do main subatomic particles even mean? Could someone please provide a cited definition for subatomic particles?", "label": 0}
+{"snippet": "It is possible to create fire by friction. For example - by striking a stone with another stone or by striking a matchstick on a rough surface. My question is: Can we say that, where there is fire there must be some kind friction in the fuel , at atomic or molecular level?", "label": 0}
+{"snippet": "In the above question , one way of approach is definitely multiplying the matrices and comparing the respective elements then solving the equations. But I am not able to figure out a more efficient solution?", "label": 0}
+{"snippet": "We can't use computers for factorising the number, as it's from a math contest where no computers are allowed. So I need to find a way with some manipulations. I can't find a way to approach it.", "label": 0}
+{"snippet": "My question is the following. It is known that any Von Neumann algebra can be uniquely decomposed as integral over algebra factors. It is also know that any mixed state can be uniquely expressed as sum of irreducible states. There is any connection between these two decompositions? Maybe by using the GNS theorem?", "label": 0}
+{"snippet": "I don't know much about logic, but similar to how certain theorems \"require\" their proofs to use the axiom of choice, are there theorems which \"require\" induction? Is there a way to detect them? Thanks!", "label": 0}
+{"snippet": "By using the kernel of both transformations, we can easily check that they're not injective functions (due to the fact that kernel does not only contain the zero vector by seeing both operators as linear transformations) So, what am I interpreting wrong? I'm a bit confused on this. Thanks in advance for the help!", "label": 0}
+{"snippet": "The Rindler coordinates are calculated in an inertial rest frame, from which the worldlines of accelerating observers are determined. How does this coordinate space look like in the frame of an accelerating observer? I was able to find a YT video where the lecturer shows the image below, but I was not able to find more information regarding it.", "label": 0}
+{"snippet": "I want to make a cv. I Found this this (Simple CV) template I want to use but i can't change the language to Greek. I tried using the command usepackage[ ]{babel} but didn't work can someone help ?", "label": 0}
+{"snippet": "If I am standing still, and a car is driving away from me at a constant speed. What would the relativistic effects be? Would it appear to move slower as it got farther away? With each second would I be seeing farther back in time when compared to the cars current location?", "label": 0}
+{"snippet": "I'm reading some Shakespeare and noticing past tense verbs are written as deceiv'd and search'd etc rather than the modern deceived and searched. When did the shift take place in English to the modern way of writing it? Do we know how it happened?", "label": 0}
+{"snippet": "This is a screenshot of a page of a textbook I am writing. The image is a jpg file that was inserted using the environment wrapfigure of the package wrapfig. How can I force the paragraph starting with \"Una rappresentazione grafica ...\" to be typeset at the normal page width?", "label": 0}
+{"snippet": "I.e. compute the Euclidean path integrals of QED/the statistical field theory of electrodynamics? I have never seen anyone discuss this anywhere and I am wondering why? What if there is just an electromagnetic field at some temperature where we don't need quantum effects? That can happen right?", "label": 0}
+{"snippet": "We know that a real sequence which is increasing and bounded above converges to its supremum. Is this possible for a non - increasing sequence as well? State that sequence. I am not able to think of a suitable example for this. Please help me.", "label": 0}
+{"snippet": "I would like to know; if it is possible to force magnet wedges (as seen in picture) together to form a \"Uni-Pole Radial Ring Magnet?\" Also, if it is possible to force smaller \"Uni-Pole Radial Ring Magnets\" (like the one shown below) together to form a larger one? The magnets are neodymium.", "label": 0}
+{"snippet": "When I read Mathematical Typography, I noticed that the prototype font presented (the predecessor of the Computer Modern font family) had different numbers (bottom). My question is, are there any versions of the font available anywhere that still has this number style?", "label": 0}
+{"snippet": "Many results about single-sorted FOL generalize to the multi-sorted setting (see here). Are there aspects that do not generalize or are importantly different when working in a multi-sorted setting? I am starting to work in the multi-sorted setting and am wondering if there is anything to look out for if one is used to working in the single-sorted setting.", "label": 0}
+{"snippet": "If it can be shown that a given NP-complete problem such as Clique cannot be reduced to a given P-complete problem, such as Horn-SAT, then we can conclude that P does not equal NP?", "label": 0}
+{"snippet": "How do you visualize an electro-magnetic wave? If there is a very narrow beam (like the one produced by may be a maser?) confined within a few centimeters (in its wave-front) with amplitude say x, what does that mean in terms of its spatial presence?", "label": 0}
+{"snippet": "Just out of pure curiosity, are there any examples of the consequences of accepting (or accepting its negation) the continuum hypothesis outside set theory? I know for Zorn's lemma, which is equivalent to AC, there are many applications in algebra, analysis, and topology, but I did not really find many for the continuum hypothesis beyond pure set theory.", "label": 0}
+{"snippet": "I'm wondering if there are number systems with bases other than integers? For example, with a fractional, imaginary, irrational, transcendental basis, or with the basis \"infinity\"? If there are, then how is the translation made in and between them?", "label": 0}
+{"snippet": "The potential difference across the terminals of a battery with resistance is equal to the emf when there is no current.But when there is a current there the potential difference decreases or increases depending on the direction of the current.How does this change in voltage occur.Does the charge density at the plates of the battery change? Or, something else happens?", "label": 0}
+{"snippet": "I am working on a thesis and I am using Euler's criterion. I am interested in it's origin, so the first publication of it by Euler. I found some references, though I did not find the original work of Euler. It's not linked in mathscinet, either. Does anybody know where I can see the first usage?", "label": 0}
+{"snippet": "I've written a .sty file, named creator.sty. When I was using TexLive, there is a folder where all .sty files are stored. I'm now changing to Tectonic, and I cannot find such a folder, and I don't want to put creator.sty into every project I develop. Is their any way to install a custom package by Tectonic?", "label": 0}
+{"snippet": "Recently I came across this question, where the top voted answer claimed that all homogeneous equation represent a set of straiight lines passing through origin. I was wondering if this was true generally, and if so, how can we prove this?", "label": 0}
+{"snippet": "Judging by the wiki page I get the feeling that this type of heat pump would not function if it's radiator were hotter than the heat source, but I can't quite put into words why and I feel like there might be something that I'm misunderstanding. Edit: Here is the link to the wikipedia page on it: https://en.wikipedia.org/wiki/Absorption_refrigerator", "label": 0}
+{"snippet": "I was studying vectors and came up with this question Show that the line joining the midpoints of two non parallel sides of a trapezium is parallel to the parallel sides and is equal to half of their sum. Is this anyhow mid point theorem for trapezium or is it applicable here?", "label": 0}
+{"snippet": "Are \"the roof of the building\" and \"a house of stone\" grammatically different prepositional phrase constructions? Or are they both understood to be possessives with the latter not in the usual sense of ownership/possession but something that \"belongs\" to a particular class or category?", "label": 0}
+{"snippet": "Whenever I slightly touch the touchpad on my Mac Texmaker chooses to \"unfocus\" the cursor so I cannot write. Then I need to click the text window again to keep writing. I have tried to find out how to stop this from happening, but I can not find the place to fix this in the options. Any help is greatly appreciated.", "label": 0}
+{"snippet": "Does the fractional quantum Hall effect always occur when the integer quantum Hall effect occurs? In other words, is there an example of a material where the IQHE can be measured without the \"noise\" of the FQHE, allowing us to see the idealized IQHE as shown here?", "label": 0}
+{"snippet": "Given N nodes I randomly pick a permutation of the nodes and use this permutation to define an assignment: I associate one and only one node to each node. This procedure naturally defines a graph made of loops (auto loops are allowed). I was wondering what's the average number of loops in such a graph", "label": 0}
+{"snippet": "I am able to add the figure in a lyx document, by using float and insert graphics. But when I view in the pdf, I don't see the figure in the inserted location. Instead I see the location of the file inside a blank box. See below. I want to know why this is the case and any suggestions on how to fix it", "label": 0}
+{"snippet": "I'm surprised that I can't find any research on this topic. Maybe it's too obvious? Kinoshita proved that contractible continuum do not have FPP, but his example is not locally connected. Maybe if we add this to the conditions it will have FPP? UPD: Continuum as a nonempty compact connected metric space", "label": 0}
+{"snippet": "I am studying the Koopman operator and its spectrum. Koopman spectrum is a new topic for me and It is hard to understand what kind of dynamical system shows the point spectrum and what does not. what are the dynamical systems with point Koopman spectrum? does a dissipative system or more specifically the damped pendulum show the point Koopman spectrum?", "label": 0}
+{"snippet": "How is there so much pressure at the bottom of the ocean and therefore a greater force transmitted by collision, even though the temperature remains constant ? Shouldn't greater pressure and therefore greater molecular acceleration create a higher temperature ?", "label": 0}
+{"snippet": "For the hydrogen atom, a simple separation of variables give the energy eigenvalue of the Schrodinger operator for one electron in a spherical potential. It is well known that there are no such explicit solutions for the helium atom. However, is there a rigorous mathematical proof that the helium atom's Hamiltonian operator indeed has discretized eigenvalues?", "label": 0}
+{"snippet": "I've been trying to learn how to graph some miscellaneous functions and I came across this. I put it in Desmos and this is what I ended up with. Can you let me know how did the graph get its shape? And how can one graph such type of functions on their own?", "label": 0}
+{"snippet": "Consider a damped sinusoid. It has a obvious absolute maxima, but it also has an infinite number of critical points. Is there a general solution to finding an absolute extrema given a function that has an infinite number of critical points?", "label": 0}
+{"snippet": "I was reading multivariable calculus , where there were a few topological definitions on things like open ball, limit points, boundaries etc.i came across the statement \"a limit point of a set need not belong to the set\". Why is this true? can someone give a visual and mathematical proof of this.", "label": 0}
+{"snippet": "I was doing my car license's questions, and it came up this question, why would the stoppage distance (the distance which the car stops after breaking) increase if you add more weight on top of the motorcycle? I thought it would decrease, since the friction force depends on the normal force which increases after adding weight to it, isn't it?", "label": 0}
+{"snippet": "Can photons form black holes the same way as other matter? If there happens to be enough of them concentrated in an area of space so that enough energy exists within a radius to form an event horizon, will an actual inescapable black hole then come into existence?", "label": 0}
+{"snippet": "While working with the Huygens-Fresnel integral, I learned about the Rayleigh integral again, and I can't tell where they apply and whether they can be replaced equivalently. Also, in terms of structured light in a focusing system, which is better to use. Of course, I'd love to get some references!", "label": 0}
+{"snippet": "I have made predictions for the amount of conversions of a particular website. After predicting the amount for every day. I looked for ways to get a prediction interval for every day. The residuals are plotted as follows: Residuals From my knowledge this is not normally distributed. I am curious if there is a way to get prediction intervals.", "label": 0}
+{"snippet": "Which of the two books do you recommend? I have been studying mathematics for three semesters and would like to improve my skills in demonstrating and understanding proofs more easily. I am open to other book suggestions.", "label": 0}
+{"snippet": "As is known, non-zero infinitesimals exist. It can be proved. In the book \"A Primer of Infinitesimal Analysis\" John Bell introduced infinitesimals that indistinguishable from zero. He did it implicitly. How did he know that such infinitesimals exist? He didn't prove it. How to prove it? Thanks.", "label": 0}
+{"snippet": "Has every infinite simple group a faithful irreducible representation? This question solves the finite case. However, the proof requires a non-trivial linear representation of a finite group. I want to know if the conclusion is true for an infinite simple group. If it is not, can you give me a counterexample?", "label": 0}
+{"snippet": "Is there a popular English expression equivalent to this Russian proverb? It translates to: Water wears away a stone. And has the meaning that, step by step, eventually we (it) will get there (reach the goal, etc.). It can also be used to mean that harm or something undesirable can be inflicted over time.", "label": 0}
+{"snippet": "When deriving the expression of momentum expectation value one gets to what's shown in the picture. However, every text I've seen so far simply neglect the first term inside the integral. I would comprehend if there were linear factors of the wave function itself, since it goes to zero. However this is not the case and I don't get why this term's cancelled.", "label": 0}
+{"snippet": "I use a random number generator to generate normally distributed numbers. The problem is negative numbers are unphysical in that particular simulation. So I use \"if/else\" to discard them. My question is: What is the resulting distribution? It's obviously not Gaussian any more since it is cut on the left.", "label": 0}
+{"snippet": "I have just started studying about affine schemes and I am searching for books about Spec as a functor from the category CRings to the category AffineSchemes can you suggest me some? Also I am searching about the geometric results of this equivalence of categories, any ideas?", "label": 0}
+{"snippet": "a newbie here. For my thesis I needed to replicate this graph: I think it needs to be done in TikZ. It would be extremely helpful if I get an ipnut from the experts here. Thanks a bunch in advance.", "label": 0}
+{"snippet": "I'm studying probability theory, and I have a question. From the definition of a random experiment, we don't know the outcome of an experiment, but we can calculate and get outcomes. How? If an event is random, how do we know its random variables and its outcomes? Which definition or axioms allow us to know outcomes?", "label": 0}
+{"snippet": "In dynamical systems, what is the distinction between a homoclinic orbit and a limit cycle? It seems to me like a homoclinic orbit is effectively just a limit cycle with a particular fixed point along the way, but in both cases can't we describe the object as an attractor (or source, depending on stability) curve in phase space, periodically traversed?", "label": 0}
+{"snippet": "It is well known that If in a triangle a median has the measure half the length of the side it is drawn, then the triangle is a right triangle. Is there any trigonometric proof of the above statement?", "label": 0}
+{"snippet": "I know that perhaps some will answer with \"the double slit experiment\" but what is it that makes the double slit experiment something probabilistic? I cannot understand this and please I ask you to explain this as if I were a child", "label": 0}
+{"snippet": "I would like the first line of footnotes to be indented, like below. It seems the easier approach is to override the template using YAML at the top of my input document, but I don't know what to insert in the YAML.", "label": 0}
+{"snippet": "Today, l learned a new word 'supine'. It has multiple meanings, but I am asking about the opposite of the following meaning: Lying on the back facing upwards. In other words, what is the suitable word to describe the following: Lying on the stomach facing downwards", "label": 0}
+{"snippet": "Is proving mathematical theorems one kind of computing? I read somewhere in a book that proofs are one kind of computation. I am not talking about formal proofs, I am talking about the informal natural language arguments that mathematicians use in their daily work.", "label": 0}
+{"snippet": "I have a GitHub link and I want to use it as a reference. How can I put it in a .bib file and then cite it? I am using bibtex. An example GitHub link I want to reference: https://github.com/LLNL/zfp", "label": 0}
+{"snippet": "I am a first year student. I am trying to find a precise definition of cardinal numbers. I am unable to find it anywhere. I am fine with finite cardinalities. I also know that different sets have different sizes. But how to have a precise definition of a cardinal number ?", "label": 0}
+{"snippet": "This might be a random question, but I've always wondered, can the principle of induction be used not only for proving sum formulas, but something else? Is there anything else we can use it for?", "label": 0}
+{"snippet": "The script fancy-preview is obsolete and no longer works in the recent TeXLive versions (see, for example, this question). According to the author of fancy-preview, there are some better options, but he never mentions what the option is. Since his words are not very convincing, do we have any alternative for fancy-preview?", "label": 0}
+{"snippet": "I am interested in writing a chess book in LaTeX. Are there any existing LaTeX templates for writing Chess books in overleaf? Also, is there any streamlined way to use Chessbase directly for writing a chess book, whether it is in LaTeX or not.", "label": 0}
+{"snippet": "Can anyone recommend a nuclear physics textbook which is focused on theory rather than engineering and comes with full solutions to all the problems provided in a separate solutions manual. I MUST have a full solution manual. It may be an introductory text or advanced. Either way I can use it. My query is very specific and there is no duplicate question.", "label": 0}
+{"snippet": "To my knowledge the \"white-sky albedo\" is the surface albedo corresponding to diffuse illumination while \"black-sky albedo\" corresponds to the direct illumination. I am confused with the term \"Lambertian albedo\" used in some radiative transfer models (e.g libRadtran). Is it the same with the \"white-sky albedo\"? If not, what is their difference?", "label": 0}
+{"snippet": "I think the body should not move since maximum static friction is greater than the applied force but my book says that it will roll. Also I have read that static friction is independent of the area of contact. Please tell me where am I going wrong?", "label": 0}
+{"snippet": "As I know Newton physics is used for most engineering, aerospace, mechanical, naval etc. Where we must use Theory of Special Relativity and Theory of General Relativity to get correct results, only for astronomy, big distances/objects etc?", "label": 0}
+{"snippet": "I can understand the logic behind spin-stabilizing bullets, which travel only a few hundred meters on fairly flat trajectories. But I cannot understand the logic for artillery. Won't spinning shells remain the same orientation throughout the trajectory, causing them to belly flop on the target?", "label": 0}
+{"snippet": "Can I use when as a replacement for how often? Is it common to use when to ask about the frequency of an action? ex: Question: When do you do the dishes? Answer: Sometimes I do the dishes.", "label": 0}
+{"snippet": "In the case of a free particle, if you have perfect knowledge of its momentum, the uncertainty in its position becomes infinitely large. Does this imply that there is a finite probability of finding the free particle anywhere in the entire universe?", "label": 0}
+{"snippet": "As I do exercises in my physics book, there are a lot of questions that ask me to list the brightness of rays (reflected and refracted) in ascending order. A very difficult one is shown below. Can anyone explain why the answer is D? And also how I can do similar questions? Thanks!", "label": 0}
+{"snippet": "Heisenberg's uncertainty principle states that we can't mutually determine both the trajectory and momentum of a subatomic particle. According to Einstein, If we take two particles with different masses,join them and let them spring apart. Their velocities and positions will be related , so can we calculate both velocity and position? IS the Heisenberg's Uncertainty principle disproved?", "label": 0}
+{"snippet": "I have the structure for transitive phrasals and for prepositional verbs, but I am having some trouble when I have to draw the tree for a phrasal prepositional verb. I know for sure it must contain a V-core and a V-shell, but I don't know where the \"DO\" should be placed. Is the object part of the PP?", "label": 0}
+{"snippet": "Here is the question I am trying to solve: Characterize paving matroids in terms of their collections of independent sets and in terms of their collection of bases. What exactly does it mean to characterize paving matroids in terms of their bases? could someone explain this to me please? what exactly should I do to solve this problem?", "label": 0}
+{"snippet": "So I've heard that the definition of a singularity is a place where a geodesic cannot be extended smoothly. Which brings up the questions, have there been attempts to do this non-smoothly? Is the result trivial? If you give up smoothness but replace it by some weaker notion of differentiabilty can you do it?", "label": 0}
+{"snippet": "There's a recurring preference for pionless effective field theory in recent papers modeling nuclei for fermion scattering processes (e.g., here). Why is pionless effective field theory commonly chosen? How does the exclusion of pions impact the theoretical framework?", "label": 0}
+{"snippet": "When referring to the \"politically organized body of people usually occupying a definite territory\" in lieu of the proper name, should state be capitalized? Example: He will liaise with State and local governmental regulatory departments.", "label": 0}
+{"snippet": "We can say, \"I had a delicious breakfast\" because of the adjective, as opposed to \"I had breakfast\", where we don't use an indefinite article. As in this former case we have ONE specific breakfast. Why can't we treat the word \"weather\" the same way? \"It was such a great weather\". Isn't it also ONE instance out of many?", "label": 0}
+{"snippet": "According to my current understanding of special relativity, light would not 'see' the universe's time tick. In other words, the universe would remain a snapshot in time according to a photon from the instant the photon was created. Is that true? Also, would a photon 'see' ordinary (moving slowly) objects move at the speed of light? If not, then at what speed?", "label": 0}
+{"snippet": "I'm installing a program called nauty using cygwin. It starts asking to run using \"configure\", so far everything has been fine. However, it asks to perform a \"make\" to compile the installation. I don't know what to write to perform the compilation. I hope you can help me on what I should write to perform the compilation and finalize the installation. I'm using windows.", "label": 0}
+{"snippet": "Is there a word that refers to the organs/appendages used for processing food that do not imply that the organ/appendage in question is around a mouth or other orifice for food? Example sentence: The hammerhead worm's _______ are placed upon its head", "label": 0}
+{"snippet": "There are mixed answers online. Some say 't' is silent. Others say 'e' is silent. Dictionaries don't seem to give a consistent pronunciation for this word, so it's hard know what is correct.", "label": 0}
+{"snippet": "Concerning the Banach-Steinhaus theorem, what counterexamples arise if certain conditions are not met? In the context of the Banach-Steinhaus theorem, what counterexamples arise in the absence of completeness conditions (or when X lacks any Baire second category set)? Alternatively, when considering a non-linear family of operators, what specific instances of counterexamples manifest?", "label": 0}
+{"snippet": "Is there a name for or relevant work on graphs constructed by taking a tree graph as input and changing the edge targets from the parent to the next-oldest sibling (if it exists)? It has come up in some work I'm doing and I'm not even sure what to search for in a literature search.", "label": 0}
+{"snippet": "I'm struggling to find an answer to my question, which is about the difference between Magic Tree and Magical Tree For native English speakers, is there a preferable option that \"sounds right\"? If that's not the case, and there is a rule, when should I use each of them?", "label": 0}
+{"snippet": "In finite-dimensions, the complexification of a real vector space is easily shown to be isomorphic to the original real space by using a proof which involves explicit use of a finite basis. Does the result also hold for infinite-dimensional spaces?", "label": 0}
+{"snippet": "Someone has just messaged me saying as a professional business owner I should know the difference and that my sentence is wrong! I am not sure! Especially as I am from Yorkshire and we all know we speak differently up here! So why wasn't you good enough? Or So why weren't you good enough?", "label": 0}
+{"snippet": "I have an ionic liquid solution phase and an organic phase. They are immiscible. When I place a small piece of nylon fibre in the liquid it always goes to the liquid/liquid interface instead of staying in the aqueous/organic bulk phase. What is the phenomena behind this, and to understand this, what are the concepts I have to search for?", "label": 0}
+{"snippet": "I found in this site that if we use a set of colored lights we'll have colored shadows. But why is that? As far as I know a shadow is where there is no light. So why isn't the shadow that is produced by colored lights just black like a normal shadow that is produced by white light?", "label": 0}
+{"snippet": "If an electrically conductive material has lots of protons, then how will it conduct electrons even though they should be getting attracted? Do the electrons somehow get pulled in the direction of the conductor?", "label": 0}
+{"snippet": "Is it possible to have two table of contents in beamer which contain the contents of two different sections, e.g. the main part and the appendix part. One table of content only includes sections from the main part, and the latter one which is shown after the main part only shows the appendix sections?", "label": 0}
+{"snippet": "given a parallelogram, show that the area of the parallelogram follows the relationship of two adjacent sides times sin of the angle between them. I tried dividing the Parallelogram into two congruent triangles, then finding out if I could get a relationship using the law of sines since I am stuck on how to integrate sin of the diagonal into the relationship.", "label": 0}
+{"snippet": "I am studying mathematics at the undergraduate level and I am interested in the world of mathematical logic. I would like to know the opinion about which books or texts are recommended for an introduction to the subject and then a deepening? I am grateful to all those people who give me their opinion or recommendation of texts or notes, on mathematical logic.", "label": 0}
+{"snippet": "I know how to find the quadratic residues and I know how to determine the quadratic nonresidues by simply taking the complement of the positive integers lower than p against the known residues; is that the only way to find nonresidues? It feels like there should be a method that's more direct.", "label": 0}
+{"snippet": "Given an arbitrary set of Christoffel symbols for a spacetime. How does one identify the Euler, Coriolis force, centrifugal force and linear fictitious force? I suspect it should be possible to do it both from the metric and Christoffel symbols?", "label": 0}
+{"snippet": "Does anyone know of any free and relatively easy-to-use math apps like Geogebra that can be programmed (or were explicitly designed) to draw the geodesic between any two selected points on a saddle surface like the one below? Thanks in advance.", "label": 0}
+{"snippet": "I am interested in reference material for Physical Applications of Stochastic Processes. The playlist does have an associated book, but it is a litte dense, and the derivations are mostly left to the exercises. Is there any book/site that covers the same material (a different perspective), or even one on general stochastic processes.", "label": 0}
+{"snippet": "I want to typeset a truth table where the truth values of a complex formula are aligned with the corresponding connectives as shown in the attachment. Would someone know a solution? Thanks in advance!", "label": 0}
+{"snippet": "A TLDR summary is used to shorten a long detailed article. However, what if you have written a brief and concise summary, but would like to add further non-essential background details at the end?", "label": 0}
+{"snippet": "In @UmbertoP's response to the question, \"Partition of real numbers into dense subsets of positive measure,\" the answer is understandable to a advanced undergraduate; however, I have inadequate knowledge of measure and set theory. I tried to create a more explicit example here but it's too complicated. Question: Is there a more explicit version of Umberto P's answer that's understandable to an average undergraduate?", "label": 0}
+{"snippet": "On the web, I have not found much concerning the argument which is convincing to me. I have then worked out a proof of Fatou's Lemma assuming convergence in measure. I ask you if it sounds fine. Thank you so much.", "label": 0}
+{"snippet": "I know what real projective line is. But what is a formal definition of a projective line? Unfortunately there is nothing on Wikipedia about it. They are always talking about projective line as a part of projective plane. How would one describe projective line without any underlying space? Thanks.", "label": 0}
+{"snippet": "I know latex, but new in xslt (learning now), I need to convert the tex to xml file through XSLT (one of my friend suggest, but i failed to convert). Please suggest or give example to convert the files.", "label": 0}
+{"snippet": "Looking at the P-H diagram, the working fluid pressure drops when it goes through the expansion valve. Temperature drops at constant enthalpy due to Joule-Thompson effect. Therefore the system must be pushing the working fluid to lower pressures when there is not enough refrigerant, but why would it do that? Is the suction pump working harder?", "label": 0}
+{"snippet": "what is the nature of force on electron in atom .Is it coulombic or electromagnetic force? As electron is in random motion so we cannot take it as electrostatic force. Please clear my confusion.", "label": 0}
+{"snippet": "I am writing this document for HR at work and wish to outline what our staff should do to get reimbursed. The sentence should be something along the lines of... All incurred expenses/expenses incurred should be claimed within three months of their taking place. Is there a rule?", "label": 0}
+{"snippet": "When light is refracted through little drops of water the rainbow is formed behind the water molecules. When light is refracted through a glass prism the rainbow is formed inside the prism. Then why when the light is refracted through a bubble the rainbow is formed on the surface of the bubble?", "label": 0}
+{"snippet": "I can find some properties and characterizations of path algebras and its elements in representation theory books but I want some references that study and treat path algebras as invertible elements, idempotents, ideals, etc... without focusing on representation theory. Best regards.", "label": 0}
+{"snippet": "I wonder about the possible influences of the continuum hypothesis or its negation on quantum theory. Could we think about a physical system for which Hilbert space would have dimension cardinality (cardinality of orthonormal basis set) between integers and reals (thus in favour of continuum hypothesis negation)? J.", "label": 0}
+{"snippet": "I know the effect would be incredibly small if there is one. If I were to point a laser pointer at the moon and a gravitational wave were to pass by perpendicularly to the laser would it shift the point on the moon momentarily as the wave passed?", "label": 0}
+{"snippet": "It is well-known that the Laplace-Beltrami operator for a Riemannian manifold takes a relatively simple form with the harmonic coordinates. This operator should be obtained as a product of Dirac operators. So, my question is: What should the form be for this Dirac operator? Does some literature exist about?", "label": 0}
+{"snippet": "This has always bugged me. The energy levels are discrete, so an electron is said to only absorb photons with EXACTLY the energy of the jump between levels. Otherwise, the photon passes straight through right? But isn't photon energy on a continuous spectrum such that the energy match would have to be infinitely precise? How is that possible?", "label": 0}
+{"snippet": "To what extent is the Ising model for the ferromagnetic transition experimentally relevant for real ferromagnets ? For example if one quantitatively compares the magnetization versus temprature data rescaled by the critical points, do the data match with Ising scaling ? Any hints to compilations of data or comparisons would be appreciated.", "label": 0}
+{"snippet": "For example, the paper I am reading states that the current was \"periodically interrupted without changing polarity\" to \"demonstrate that the peaking behavior is not due to a capacitive effect.\" They observe a standard voltage trace. What does \"capacitive effect\" mean in this context?", "label": 0}
+{"snippet": "Is Anti de Sitter spacetime repulsive because of its negative scalar curvature? Will a fluid flowing radially inward experience an opposition that has a radially outward component? And how can one quantify this \"opposition\"?", "label": 0}
+{"snippet": "It is known that it is impossible to have a non-singular vector potential for the monopole magnetic field. How about the monopole harmonics? Could the wave functions be made single-valued and finite on the sphere?", "label": 0}
+{"snippet": "I have seen several suggestions on ways to indicate a person's middle name was preferred over their first name: Firstname \"Middlename\" Surname Firstname Middlename \"Middlename\" Surname Firstname Middlename Surname, aka Middlename Is there any consensus on the best approach in an obituary?", "label": 0}
+{"snippet": "In wikipedia page of tensor product, there is a tensor product of mixed type tensors: I wonder exactly how the map works (it takes in ... and spits out ...). Can someone help me to find an explicit form of this map? I met this problem when looking at second covariant derivative of tensor fields. Thanks.", "label": 0}
+{"snippet": "Consider an electron that is launched towards an atomic nucleus. As the electron gets closer to the nucleus, the electric potential energy between these particles changes, it decreases. According to energy conservation what follows is an increase of energy outside of this electron-nucleus system. Is it now correct to say that the emitted bremsstrahlung x-rays provide this increase in energy?", "label": 0}
+{"snippet": "I am a maths hobbyist, and now I study books on differentiable manifolds and their geometry (tensors, connections). My question is : what is the use (or examples) of the linear connections ? Or later, the Levi-Civita connection, in Riemannian Geometry ? What calculus we can do with them ? Thank you very much !", "label": 0}
+{"snippet": "I'm new to latex and this is my first time using it to write my report. I want to style my Table of contents and list of figure like the following images- table of contents- list of figures- I have no idea where to start and how to format toc and tof like this. I would greatly appreciate your guidance and expertise.", "label": 0}
+{"snippet": "In atomic collisions,does the neutron fuse with the proton of hydrogen and release a photon which is absorbed by the electron which then gets excited to higher energy state? Or do the neutron and proton stay in contact like a deuterium nucleus without any release of photon. In the latter case how is the lost kinetic energy of the neutron absorbed by the electron?", "label": 0}
+{"snippet": "Is it even possible to calculate a particle number of some field in lattice field theory? After all, it's implemented in the formalism of imaginary time path integrals, here's no such concepts as particle number operator, creation and annihilation operators. After searching the internet i didn't find anything useful. I'm interested in bosonic fields.", "label": 0}
+{"snippet": "I am looking for an appropriate word for parking a car at the Workshop, for repair in the coming days. The word deposit gives an impression of a financial transaction. I put/deposited/parked my car in the workshop for repair. What can be the most appropriate word in this context?", "label": 0}
+{"snippet": "It is commonly explained that semiconductors like silicon, germanium, GaAs... are opaque because all of the visible wavelengths are above the band gap so they get absorbed. However silicon and germanium have indirect bandgaps and require a phonon interaction which should be rare. Why are they not transparent to the human eye?", "label": 0}
+{"snippet": "This appears in an Olympiad handout by Kevin Zhou. However I don't get where this result came at all. How would you prove it? I also don't see in what situations the right side of the expression can be more useful than the left side.", "label": 0}
+{"snippet": "The image of things falling into a Black Hole stays frozen on the event horizon forever. So how is it that we don't see the image of a dying star where a Black Hole formed? We see the black, with an accretion disk.", "label": 0}
+{"snippet": "It is well known that there are algorithms developed for asymmetric encryption that take advantage of the fact that the product of two prime numbers cannot be factored in polynomial time. Usually, prime numbers are not used in symmetric encryption. Do you know of any algorithm where prime numbers are used at any stage of symmetric encryption?", "label": 0}
+{"snippet": "Is Shockley-Read-Hall recombination synonymous with all phonon-assisted nonradiative processes? In organic molecules, \"internal conversion\" is used to describe non-radiative decay from excited states. It seems like nonradiative recombination can take many forms (including Auger Recombination, recombination at defects and recombination at surfaces). Looking for clarification.", "label": 0}
+{"snippet": "What ratio of final to initial mass of a rocket to achieves the highest energy efficiency - the highest ratio of final mass kinetic energy to chemical energy expended? And more generally the relation of efficiency to mass ratio. This is a bit hypothetical because we are not usually interested in efficiency in this sense, but the answer is curious none the less.", "label": 0}
+{"snippet": "Bands and solo singers have discographies, (film) actors have filmographies, and so forth. Is there a similar term for television? I've come across \"televisiography\", but the article's author compared its usage to cinematography and not filmography.", "label": 0}
+{"snippet": "As we all know that in a pn junction depletion layer is formed and due to immobile charges electric field is directed from n side to p side but why does this electric field acts as a barrier for diffusion rather than an enhancer for diffusion of charge carriers?", "label": 0}
+{"snippet": "I keep coming across \"quotes\" on the internet that say things like \"psychology says, if a person blah blah\" I'm wondering what the term would be when someone 'mislabels' a field of study (psychology in this case) as a person, as if a field of knowledge is someone talking, I don't know how else to put this. Thanks for any help!", "label": 0}
+{"snippet": "Are there actual equations for the Parton Distribution Functions for quarks and gluons? I've been looking high and low for theory-based papers about this and it seems like a wild goose chase at this point. If the answer to that question is no, are there any theoretical results that can be used to compare to experimental results? Hope to hear an answer soon.", "label": 0}
+{"snippet": "I'm working on a class file in Overleaf, and would like to be able to have the editing tab for the class file and the main file open at the same time, rather than needing to repeatedly switch between them. Is there a way to do this?", "label": 0}
+{"snippet": "I'm not sure how can the following formula be derived. Please explain step by step with reasons: Present value of constant cashflow at fixed rate: Future value of constant cashflow at fixed rate:", "label": 0}
+{"snippet": "Are the most fundamental particles, e.g., bosons, fermions, etc., capable of further subdivision? Are they at their most fundamental? Or do we consider them so because we're just not capable of going any further? theoretically, couldn't any fundamental particle always have some smaller component on which it depends?", "label": 0}
+{"snippet": "Recently, I got an internship as a Content Writer, and they issue a report for the work done using Grammarly for further corrections before finalizing. I have noticed that a lot of the suggested changes by Grammarly were of usage of passive voice. How do I avoid this to begin with and why is considered wrong?", "label": 0}
+{"snippet": "\"This is because of abrupt discontinuity of fields\" I have read this or similar sentences in many papers. I am bit puzzled. How and under what conditions electric field can be discontinous? In my opinion this is unphysical, field lines start at one charge and end at opposite charge. Then how can fields be discontinous midway?", "label": 0}
+{"snippet": "I found a tutorial on converting a PDF to SVG, but this method seems to only work on local devices. I wonder if it is possible to output images from LaTeX using online compilers like Overleaf.", "label": 0}
+{"snippet": "According to the Wikipedia page here, a real, unsymmetric tridiagonal matrix can be brought to symmetric form by a similarity transform. Does anyone know if a generalization of the formula given there exists for unsymmetric tridiagonal matrices which are complex and Hermitian, and; contain nonzero elements in their upper-right and lower left corners (i.e. which are subject to periodic boundary conditions) Thank you!", "label": 0}
+{"snippet": "If a spaceship approaches a rapidly spinning planet, would the planet's inhabitants , the inhabitants of the planet where the spaceship came from , and the spaceship's occupants observe time dilation between all each other due to their relative motion?", "label": 0}
+{"snippet": "I plotted some simulated stellar emission spectrums from PHOENIX which also each came with their respective effective temperatures. With the effective temperatures, I used Wien's law to estimate the peaking wavelength of the spectrums. Why does Wien's law seem to underestimate the peak wavelength? Also, why is the error increasing with lower effective temperatures of the star that emits the spectrum?", "label": 0}
+{"snippet": "I used Google Scholar to export the citations in Latex but they are not written in a correct and homogeneous form for all the references. How can I use Mendeley to reorganize my references already made by Google Scholar? I don't want to do this work manually because I have a lot of references.", "label": 0}
+{"snippet": "I am working on a heavily mathematically project about plasma. In particular, I want to find references that treat the problem from microscopic models that include relativistic and magnetic effects (Coulomb forces, QFT, etc) and obtain kinetic models (BBGKY, Landau equation, Maxwells equation, etc). What are some state of the art papers/references?", "label": 0}
+{"snippet": "Why doesn't the Hafele-Keating experiment settle the twin paradox? It is my understanding that clocks were used, and that the shifts matched the calculations. Doesn't this settle the twin paradox if we replace humans with clocks, implying that the travelling twin is the one who age less?", "label": 0}
+{"snippet": "Given an undirected graph, denote N as the number of vertices and E as the number of edges in the Graph. The Graph consists of k connected components where k <= N. Assuming each connected component is complete, What is the minimum number of edges in G (as a function of N and k)?", "label": 0}
+{"snippet": "\"The phone is ringing\" refers to an incoming call, so saying that is misleading when you've gotten a text/notification. Is there a different word to use in that sentence (\"The phone is _______\") to mean \"the phone is making the sound of receiving text/notification\"?", "label": 0}
+{"snippet": "About a hundred people had already gathered, a guard rail the only thing separating them from the crater's edge. Is it not more proper to say \"About a hundred people had already gathered, a guard rail was the only thing separating them from the crater's edge.\"? It naturally sounds more clear in my opinion when was is used.", "label": 0}
+{"snippet": "Just realized the Japanese word Kawaii is pronounced Ka-wa-ii (three syllables). With that in mind those two last \"i\" in Hawaii look suspicious now. Shouldn't they be pronounced separate, making up a third syllable? Otherwise, what's the purpose of the double \"i\"?", "label": 0}
+{"snippet": "Thinking of compound words or phrases where the order of the words can be swapped around and still make sense: Examples: Lighthouse - House Light Birdhouse - House BirdRacetrack - Track Race So far that's all I've been able to discover. Is there a word for this reversibility phenomenon?", "label": 0}
+{"snippet": "In the formula of the law, we have to find the cross product of the distance(r) and the infinitely small part of the conductor dl. My doubt is why are these both considered as vectors ? Aren't they measurements of lengths ? I'm unable to relate vectors with this concept, kindly help me out :)", "label": 0}
+{"snippet": "I need to plot this algebraic curve in tikz but I don't understand how to deal with these curves in tikz since it's not a function. Desmos tells that it should look something like this I only need a curve without axis or whatever and only in tikz.", "label": 0}
+{"snippet": "I used the program R to calculate the values of the maximums and the points where the new function starts, however, I don't know how to use these points to graph the function I'm looking for. Image of the results I got from R", "label": 0}
+{"snippet": "I came across (a pretty sad) poem by Meggie Royer. She writes: I stood by as strangers stroked her muzzle and she wilted beneath their touch like she did once for mine. For context: she writes about her dog here. I interpret 'wilting' as something positive in this case. Can someone shed some light on this for me?", "label": 0}
+{"snippet": "I have recently been looking at random variables and did come upon the below matrix (in image form because it is too large to copy): I have been attempting to find the inverse of this matrix, and have only been able to find decimal approximations. Does anyone know of any software or site that could compute the exact inverse?", "label": 0}
+{"snippet": "Can the word provenance be used in reference to a person, or should it only be used for objects? For example, would it be improper to ask someone for their provenance? Longman, and AHD, for instance, only mention it being used for 'things' / 'objects'.", "label": 0}
+{"snippet": "I'm trying to trace back the etymology of 'palatable', but what I'm really looking for is the process of semantic expression over time. When did the word begin to be used to speak of things unrelated to food? I will be grateful for any leads, resources, or information.", "label": 0}
+{"snippet": "I am wondering where can I find examples of explicit calculation of Bala-Carter correspondence for algebraic groups of classical types of small ranks. Would you please give me some clues? Thank you very much!", "label": 0}
+{"snippet": "Consider the following (mock) sentence: We use a class of methods in which fruit (here: bananas) are combined with vegetables (here: pumpkins). An editor has proposed instead: We use a class of methods in which fruit (i.e., bananas) are combined with vegetables (i.e., pumpkins). The meaning strikes me as different however. Question: Are both sentences correct? Do they differ in their meaning?", "label": 0}
+{"snippet": "When using the changes package, it highlights the changed text and adds a superscript denoting the author id. Is it possible to suppress this superscript? I use different colors for different authors. PS: This is a follow-up question to this question, but is also a stand-alone question.", "label": 0}
+{"snippet": "Suppose a plane mirror is half-submerged in another medium (say water) and light rays are incident obliquely on mirror at the interface separating two media. My questions - (a)- Will reflected rays suffer refraction ? (b)- What angle will the reflected rays make with normal after reflection? Will angle of reflection be same as angle of incidence (as given by law of reflection) ?", "label": 0}
+{"snippet": "So imagine you have a bottle of water or any type of liquid (like a bottle of milk that has just been opened)that is completely full or even three quarter of it is full,why does the water or milk come out of the bottle in waves when you pour it in a glass?", "label": 0}
+{"snippet": "Can someone please show me the formalisms of the energy and the momentum conservation in the curved space-time for electromagnetic? I know it's going to be two equations. but I couldn't find them anywhere and I couldn't calculate them.", "label": 0}
+{"snippet": "When resolving vectors into their horizontal and vertical components, why must the individual vectors form a closed triangle? I don't understand why vectors must form a closed triangle when one vector is the sum of the other two. Why is this true, and how do prove this?", "label": 0}
+{"snippet": "I've seen in many places, including Weibel's excellent book, that the category of short exact sequences (in an abelian category) has kernels and cokernels, although it is not abelian. However, I cannot find any analogous information about the category of long exact sequences, so: Are there kernels and cokernels in this category? In other words, is it pre-abelian? Thank you!", "label": 0}
+{"snippet": "I was reading this thread Exterior power of a tensor product and I found that the result cited in first answer is very useful to me, but I couldn't prove it myself and what's said there is not enough for me. Can you give me a good reference?", "label": 0}
+{"snippet": "I was playing around with Desmos today and came up with this formula for finding global minima: It works by descending until it finds a negative value. The same method could work with multiple variables using nested products. Would that be a computationally feasible method to use in machine learning?", "label": 0}
+{"snippet": "In our class today we spoke about the Einstein and Debye models. We associated the Einstein model with the optical phonons and the Debye one with the acoustic phonons. But I have a question: what is the argument made for associating acoustic phonons with the Debye model and the optical phonons with the Einstein model?", "label": 0}
+{"snippet": "I understand that wavelength is inversely proportional to index of refraction, which causes dispersion of light (red visible light is deflected less than purple), and total internal reflection. Is there a way to explain, based on these concepts why red objects (as seen in white light) absorb most light other than red light, which gets reflected?", "label": 0}
+{"snippet": "I'm trying refer to a node and its ancestors, but not its descendants. There's a decent discussion about this here but most of the suggestions would include descendants (kin, lineage, blood-line, etc.) Typically I'd just say \"a node and its ancestors\" but I'm trying name this variable in a computer program and I can't come up with anything good.", "label": 0}
+{"snippet": "I would like an alternative way to write the following statement I accept that my brother is a terrorist and condemn his actions with the condition that you accept that your father is a war criminal and you condemn his war crimes. The obvious implication being, my condemnation is conditional. Or is the phrase \"with the condition that\" correct and sufficient in this statement?", "label": 0}
+{"snippet": "My oven has the heating element in the bottom. So the bottom shelf is more directly exposed to it, and should be the hottest shelf. But hot air rises, so the top shelf should have the hottest air, and should be the hottest shelf. I don't know which logic to follow! What part of my oven should be the hottest?", "label": 0}
+{"snippet": "Are these the same thing? I understand the marginal likelihood is the predictive likelihood over the prior, but since the GP the prior is defined on the training set, are these the same thing? Can we show it mathematically?", "label": 0}
+{"snippet": "I don't want to reinvent new names when writing a paper. I want to ask if there is already a name for a \"zero measure\", or \"null measure\", which makes every measurable set measure zero.", "label": 0}
+{"snippet": "Before the big bang, there was a point surrounded by nothing (no space or anything). Then the big bang happened and the universe expanded. so beyond the universe's limits, there is nothing? I don't understand this, can someone help me? I'm not a physicist I just wonder. and also the expanding rate of the universe affects the speed of time or not?", "label": 0}
+{"snippet": "I am a physics undergraduate student currently taking a classical mechanics course, and I am not able to understand what conjugate/canonical momentum is (physically). It is sometimes equal to the linear momentum we know but not all the time. What exactly is potential momentum? It would be great if someone could explain it in simple words.", "label": 0}
+{"snippet": "I find the word \"meta\" to have a unique meaning. People have begun using it as a standalone word, as in, \"That movie was so meta.\" However, I think this is colloquial, and it often means \"philosophical, mind-bending\", not strictly \"a self-referential system\", in the precise sense. What could be a good adjectival form of \"meta\"? \"Metalogical\"? \"Metaistic\"?", "label": 0}
+{"snippet": "I found a post that mentioned this problem where students get confused when interpreting mixed numbers: Avoiding confusion between mixed fractions and multiplication If a student ask \"then when can I assume there is a multiplication sign between two numbers\", what is the correct answer?", "label": 0}
+{"snippet": "If energy exerted is a function of distance and force, the object would not move in this case. But would energy not still be exerted? Simplified the example for sake of clarity; but specifically asking with regards to a person doing something like a bicep curl and learning to only squeeze their bicep, rather than tensing their whole arm and fighting against themselves.", "label": 0}
+{"snippet": "Anti-bumping granules are usually small stones. I presume that the principle of these granules ensuring smooth boiling, is that it blocks the upward motion of solution molecules. Usually the stones have an irregular shape. I am wondering, if the anti-bumping granules are in regular shapes, like a sphere, a cube, will there be some influences to the anti-bumping action of the granules?", "label": 0}
+{"snippet": "I remember there is a term/saying for accidentally speaking something out loud about what you secretly wish for. For example: you like someone, but you aren't awared of it, but then accidentally say it out loud in a conversation.", "label": 0}
+{"snippet": "If I am not mistaken, this video says that X-rays travel faster in glass than in a vacuum. Special Relativity says that information can not travel faster than the speed of light in a vacuum, so what is keeping us from making Tachyon Phones with glass and x-rays?", "label": 0}
+{"snippet": "Since the time it takes for the earth to complete one rotation about itself (i.e., the time we call \"day\") is not constant, then the angular speed is also not constant, that is, there is a non-zero angular acceleration. What is the corresponding torque(s) causing this angular accelaration?", "label": 0}
+{"snippet": "For example, if John has a bike. It's John's bike. It's John, a colleague of mine, 's bike. How do you really write that? I know I can just say \"It's the bike of John, a colleague of mine,\" but that doesn't sound as clean as using 's.", "label": 0}
+{"snippet": "I searched for some answers, but most answers discussed the meaning of torsion, instead of its definition. Not knowing how the torsion is defined (in cohomology) I couldn't understand those answers at all.", "label": 0}
+{"snippet": "I am a non-native speaker and for this very special example I can't find any explicit rules in the literature: The paths, whose lengths are equal, have been created. Is \"whose\" the right word here? I can only find singular examples and wonder if the word must change for plurals.", "label": 0}
+{"snippet": "After spending some time looking for different means and mediums to model blackholes, I came across sonic holes which are modeled through Bose-Einstein-Condensates. However I have not been able to find any other possible methods of modeling blackholes (other than computer simulations). This question addresses the issue only partially. Are there any other proposed or experimentally tested methods of modeling blackholes?", "label": 0}
+{"snippet": "I was wondering if it was possible to have an infinite ray in a finite tree? This is impossible merely from the fact that an infinite ray goes through infinite vertices, contradicting the finiteness of the tree right? Is it fine if I just stated this as an obvious lemma? Thanks.", "label": 0}
+{"snippet": "I understand that anywhere is an adverb in this sentence: We couldn't go anywhere nice to eat. However, I am a little confused about how nice to eat is explained. nice and to eat both modify the adverbial anywhere , but I'm not understanding how that works. I've always learned that adjectives don't modify adverbs. Could someone explain this sentence structure to me?", "label": 0}
+{"snippet": "In quantum mechanics we know that every operator can be represented by a matrix.Being a beginner of quantum optics, my question is does there exist a matrix for squeezing operator also? If does, can the elements of the matrix be parameterized?", "label": 0}
+{"snippet": "It is well known that a covering space of a graph is also a graph. It is also true that the image of a graph under a covering map is a graph? I'm not sure that this is true, but I cannot find a counterexample.", "label": 0}
+{"snippet": "I would like to know the correct preposition for research when used with \"any topic.\" Should it be: It enables us to research any topic with ease. Or: It enables us to research into any topic with ease.", "label": 0}
+{"snippet": "I am struggling with analysing the sentence 'Y happens, benefitting patients with X'. I can see that 'Y benefits patients with X' uses the present tense simple form of the verb. But in the first example, is 'benefitting' functioning as a gerund or an adjective?", "label": 0}
+{"snippet": "I know that in general, nearby paths in a chaotic system tend to diverge exponentially, but are there continuous systems where paths diverge at other rates? For example, is there a system where nearby paths diverge say double exponentially or at some rate determined by tetration? Or are there ones with slower divergence, for example only quadratic or cubic divergence instead of exponential?", "label": 0}
+{"snippet": "I'm looking for a catch-all term. Do we say \"intellectual property work\" or \"intellectual property content\" or something else? For example, At the moment, the best solution is to file their work with intellectual property office in specific jurisdictions where the creators wish to protect their IPs. Could I say \"their work?\"", "label": 0}
+{"snippet": "Is there \"a categorical way\" of speaking of objects in a monoidal category which can't be written as a tensor product? (We have to be careful with multiplication by the unit.) The same can asked for a cartesian category and there might be a smoother way of answering the question. Both questions seem interesting to me.", "label": 0}
+{"snippet": "What's the difference between \"wave\" used with \"to\" and \"wave\" used with \"at\"? Two sentences as examples: She's waving at the person behind me. and The lookout man had waved to me as I approached. Could either choice be used in each sentence?", "label": 0}
+{"snippet": "I'm finding everywhere this fact about this being the simplest knot which is not equivallent to its reverse (same knot, other orientation), but I can't find any proofs out there and I also don't know any invariants that can distinguish these two, so if anyone knows which invariant can do this or where to find the proof, I would be very grateful.", "label": 0}
+{"snippet": "One teacher told me that the bare infinitive cannot be used as the direct object of a modal verb because it is not a noun. But, isn't infinitives with or without \"to\" infinitives?", "label": 0}
+{"snippet": "Equilibrium position of a pendulum is defined as the position where no external force acts on the body and if no force is applied, it remains at rest. In the image, isn't gravity acting everywhere, then how will you define the middle point in the pendulum's motion as equilibrium position? Even if you remove gravity, initial push is required for it's motion.", "label": 0}
+{"snippet": "Urbanization is at the stage when most people are aware of the central importance of infrastructure. Urbanization is at the stage where most people are aware of the central importance of infrastructure. Which is better to use 'when' or 'where' in both sentences and why? In my opinion, 'stage' indicates a period, i'm uncertain which word is more suitable.", "label": 0}
+{"snippet": "This is puzzling to me because I have learnt that a charged sphere has the same electric field and electric potential at a point beyond its surface. So does it mean that a point charge is also inherently a sphere?", "label": 0}
+{"snippet": "What is the current known record for the maximum number of ions that have been successfully trapped in a Paul trap? Could you also share a reference to the scientific article or any form of published research where this achievement has been documented?", "label": 0}
+{"snippet": "I mean thermodynamic equilibrium implies mechanical equilibrium, but mechanical equilibrium doesn't mean to that the system to be in static equilibrium. For some reason, all the systems I have seen in thermodynamic equilibrium are at rest. Am I wrong with this thought?", "label": 0}
+{"snippet": "I have read that moving ions generate a magnetic field as it moves. Similarly, is this also true regarding the nuclear magnetic moments of the atom? In other words, would a moving atom with a nuclear magnetic moment generate an electric field as it moves?", "label": 0}
+{"snippet": "I read 'The Standard Model Effective Field Theory at Work' by Isidor, Wilsch, and Wyler. In a footnote, they say that, in principle, right-handed neutrinos could be included in the Standard Model by extending the fermion content. But these would be completely neutral under the Group of Standard Model. Why is that a problem? Why is the chiral fermion such a necessity?", "label": 0}
+{"snippet": "When I pour dry lentils into a water bowl, I notice many of them form little clusters, with an air bubble in the center. Why does this happen? I'm guessing something about static electricity. But not sure bubbles or lentils have charge...", "label": 0}
+{"snippet": "This perhaps may be very naive question, but could one consider an analogy to the parallel transport (as defined in this Wikipedia article) being a ball rolling on a flat table surface? If so, is then such an example also an example of holonomy or not?", "label": 0}
+{"snippet": "I wasn't able to get a proper reason behind this and the only thing I could find were classical analogies for spin which (when I asked my prof) were not to be relied upon.", "label": 0}
+{"snippet": "While seeing the derivations of the Rayleigh Jeans law and the Planck's Law for a Blackbody Radiation, I came across a fact that they assumed that Electromagnetic Radiation inside a cavity would form standing waves only. Why is it that the blackbody radiations inside the metal box should be a standing wave only in the derivation of Rayleigh Jeans law and Planck's law?", "label": 0}
+{"snippet": "Could you give an intuition about why does MHD requires the following condition in time and spatial scales, please? Thanks. At scales much larger than the mean free path and gyroradius, and time scales much larger than the collision time and gyroperiod, the magnetohydrodynamics (MHD) model is good.", "label": 0}
+{"snippet": "I have tried exploring different periodic functions combined with exponential growth rates, however, all my models fail to overshoot the carrying capacity. I have also examined piece-wise functions that could work, however something that is more elegant would be much more pleasing.", "label": 0}
+{"snippet": "Do you know any trick for including rectangles around references, such as Figures, Tables, and url links, etc. in Texpad editor when the TexpadTeX typesetter is used? While I can manually change or hide these rectangles (or even alter their colors) using pdfLaTeX, etc. (i.e. manual typesetter) these commands seem to fail when using the TexpadTex typesetter. My goal:", "label": 0}
+{"snippet": "I've noticed that \"Diagnostic\" can be used as a plural! Such as in some windows warning messages. What's the subtle difference between Diagnostic and Diagnosis? How do we use each of them in a correct way?", "label": 0}
+{"snippet": "It is easy to see how primitive warfare might sometimes have beneficial environmental effects; it is not clear how they could amount to a cause of primitive warfare. Could you tell me, please, what grammatical tense is meant here, present or past tense?", "label": 0}
+{"snippet": "How far apart do two vertical glass surfaces have to stand for a water droplet that is sticking to both of them to break into two? I apologize in advance for the question possibly being too imprecise .", "label": 0}
+{"snippet": "That test particles travel along the geodesic is assumed in the context of GR. But does it apply to strongly gravitating object, such as black hole in an expanding universe, binary neutron star, etc.? How to justify if so?", "label": 0}
+{"snippet": "I read about the classification theorem of finite simple groups, and I was wondering if there is a topological meaning to spaces that have a simple fundamental group? In addition, is there something that we can learn about spaces with finite simple fundamental groups, by using the classification theorem? Thank you in advance!", "label": 0}
+{"snippet": "I'm in an argument with somebody, about this line. The number of customers increase vs The number of customers increases. We are focusing on the number, but the subject is plural. He's arguing that the subject is \"number\" I'm arguing that it's \"customers\" What would be grammatically correct? If there is a correct way, is there any references on it?", "label": 0}
+{"snippet": "I'm new to LaTeX; is there a way to tell the TeX engine to generate the hyphenation of a given list of words as a text output file? For example: abdomen abduction aberrance ... What I want is something like: ab-domen ab-duc-tion aber-rance ... possibly as text.", "label": 0}
+{"snippet": "I understand that the direction of the magnetic field lines at the equatorial plane is opposite to the direction of the magnetic moment by definition. Is there a reason of physical significance as to why that is the case?", "label": 0}
+{"snippet": "The first post below provides examples of commutative non-cancellative Archimedean semigroups with no idempotents. Can anyone provide a reference to a characterization theorem for commutative non-cancellative Archimedean semigroups with no idempotents? (For example it is known that a commutative Archimedean semigroup with an idempotent is an ideal extension of a group by a nilsemigroup.)", "label": 0}
+{"snippet": "I was just wondering what happens when you see a visible light, for example violet, and that light slowly increases/decreases until it's not visible to the human eye. Will it fade or just become instantly invisible? Could it even injure and cause blindness?", "label": 0}
+{"snippet": "Do you have an example of a path-connected non-hausdorff space on which two points can't be injectively path-connected? (that is, any path between them is not injective). I tried to figure out what such a space should look like, and what its topological properties should be, but I failed. Thank you very much, AF", "label": 0}
+{"snippet": "In Stephen King's The Jaunt, I found this sentence: Five Jaunt attendants circulate, speaking in low, cherry voices and offering glasses of milk. It's either a typo (was supposed to be 'cheery') or something I don't understand. Can anyone think of an idea?", "label": 0}
+{"snippet": "What is the maximum possible rate of change of length-of-day (in units of minutes per day), on Earth? It is well known (and easy to observe) that it's larger near the equinoxes, and at higher latitudes, but how large can it be? (Perhaps we can use Seasonal changes in hours of daylight)", "label": 0}
+{"snippet": "In an interview today, I was asked the definition of transformation group which I was unable to answer. I tried googling the same but I could not find a precise definition. Can someone please give precise definition or reference for the same? P.S: I am aware with groups of mobius transformations or orthogonal transformations etc.", "label": 0}
+{"snippet": "For example, willingness to provide for someone is generosity and willingness to protect someone is bravery, but if we wanted to put both of these (an possibly other values) under an umbrella term, what would that word be?", "label": 0}
+{"snippet": "Could you use me's as in something like this? The person behind me's phone keeps ringing. The person behind me's breathing sounds laboured. I've tried looking at other questions but I couldn't find anything about it in this context.", "label": 0}
+{"snippet": "The correct way to cite an unpublished manuscript in apa is: Author. (Year). Title. [Unpublished manuscript] Department of blabla, University of blabla. However I can't get LaTeX to show me the \"Department of blabla, University of blabla\" part. Notes give parentheses such that: (Department of blabla, University of blabla)", "label": 0}
+{"snippet": "When Hubble determined the distance to Andromeda he based his estimation on Cepheids. However, the result was less than half the current value. What was the cause of this error and could another adjustment happen in the future?", "label": 0}
+{"snippet": "Some examples where we don't speak about abilities, but what is legally allowed: May I drive a car if I hold an international driver license? You may drive a car if you hold a driver license. I have never seen \"may\" in these contexts but I don't understand why I should use \"can\".", "label": 0}
+{"snippet": "In the X-ray experiment, energy lost by the electron is released as a photon. When does this happen? If there is a single nucleus deflecting a single electron how many photons would be emitted? Does the photon emit when the electron is closest to the nucleus? Any links to reading material would be appreciated.", "label": 0}
+{"snippet": "I would like to know what the rest of the sentences is. I would like to know what the rest of the sentences are. Can they both be correct depending on the context? The meaning I am aiming for is that some sentences are cut off mid-sentence, and so I cannot understand what is being said.", "label": 0}
+{"snippet": "What are the best practices for having correct hyphenation in the bibliography section of documents when using Biblatex? Most times my bibliography seems wrongly formatted, especially in two-column documents. URLs and names with a hyphen are also difficult to deal with.", "label": 0}
+{"snippet": "The word I'm looking for is similar to \"claustrophobia\"; it's to describe the feeling of being trapped in a place that feels too narrow, almost like you can't breathe properly in it. (A noun, preferably not a -phobia one.)", "label": 0}
+{"snippet": "I just came across the words from the site \"https://www.androidpolice.com/gmail-mark-all-messages-read/\", which indicate, as for me the same thing but by using different words in the article \"volume bar\", \"volume slider\" and \"volume rocker\". So, my question is do these three indicate the same thing as the volume adjustment function on mobile phones? I've included a screenshot for your reference. Thanks", "label": 0}
+{"snippet": "Do Canadians follow the American English pronunciation with the \"eye\" phoneme or do they tend to stick with the Commonwealth pronunciation, i.e. with the short \"i\" vowel? (Sorry, don't seem to be able to paste IPA.)", "label": 0}
+{"snippet": "I understand magnets require cooling to achieve supermagnetivity. How much of liquid nitrogen do Maglevs carry with them? How much is required to keep them cool? What is liquid nitrogen consumption per distance traveled?", "label": 0}
+{"snippet": "\"Geometric median\" seems like the obvious choice for \"median (but for even number of values, take the geometric mean of the central two values instead of the arithmetic mean)\", but this seems to have a different meaning. Is there a term for this type of median?", "label": 0}
+{"snippet": "Usually a calculus or real analysis book has the following topics Convergence of sequences and functions Continuity Differentiability Integrability I am searching a book with those topics but such that each topic is developed in the most abstract way, i.e. convergence and continuity maybe from the perspective of topology or metric spaces and integrability from Lebesgue perspective. Thank you so much for your help.", "label": 0}
+{"snippet": "Behold the joke in its original glory The judge looked down upon the counsel and said, Judge: Listen, counsel. I have been listening to you for three hours, and I am none the wiser. Barrister: I expected that, my lord, but I thought you might be better informed. How is \"I thought you might be better informed\" a jab at the judge?", "label": 0}
+{"snippet": "I am writing a research paper and I have to write it in LaTeX but I am struggling to recreate the follow image into tikz code. Thank you in advance for your help", "label": 0}
+{"snippet": "The pigeonhole principle seems self-evident, most people would accept it without evidence, but I wonder if we wanted to prove it, would we have to use the excluded middle principle? I would be grateful to provide a proof with or without the excluded middle principle, but I am curious as to which proof does not use the excluded middle principle.", "label": 0}
+{"snippet": "Given a minimization optimization problem of a linear target function over the set of positive semidefinite matrices of some fixed maximal rank, subject to affine constraints, what are (analytical) methods to find lower bounds on the optimal value of that problem? If we had no rank constraints, the answer would be \"convex optimization duality\", but the rank constraint makes the problem non-convex.", "label": 0}
+{"snippet": "I am using the latex workshop plugin in visual studio to write a tex file, everytime I save the document the background task will auto build the document, I have already find the auto compile in latex workshop but failed, is there any way to disable the auto compile process?", "label": 0}
+{"snippet": "By measuring the energies of the emitted alpha particles, how can we say that they have energies less than the height of the nuclear potential well when they are inside the well? How can we be sure that alpha particles are not momentarily acquiring energies greater than the height of the nuclear potential well and coming out without requiring the mechanism of quantum tunneling?", "label": 0}
+{"snippet": "What do you call the long straight pieces of metal, set into the ground, that you find at bus stops (at least in Canada)? People stand next to the post when waiting for the bus. They look like this: Do you call it a bus stop post?", "label": 0}
+{"snippet": "We say that induced potential in a magnetic field is directly proportional to the rate of change of flux but when a wire moving perpendicularly in a uniform magnetic field at constant velocity it is said that a potential is induced.But there isn't any rate of change of flux . So how does it induce a potential?", "label": 0}
+{"snippet": "If I released a giant cloud of Oxygen into space, would you be able to hear sound inside of it before it dissipated? From my understanding, the reason there is no sound in space is because there are no atoms for the sounds waves to interact with. So if you theoretically put atoms in space would they carry the sound?", "label": 0}
+{"snippet": "I have read the neutrino mass problem. The unnatural smallness of neutrino mass implies the existence of new physics so the seesaw mechanism is introduced to solve this theoretical problem. I understand that Dirac neutrino has only the problem of its origin, however, is the possibility that neutrinos are Dirac particle ruled out by the current experimental observation?", "label": 0}
+{"snippet": "I saw that true strain is a sum of strains over many increments. Why would this be more accurate than using engineering strain? Engineering Strain assumes the initial length to be constant which makes sense to me because strain is just a measure of deformation. What is wrong with the idea of assuming initial length to be constant?", "label": 0}
+{"snippet": "Consider the following scenario: There is a wind blowing right above lake surface. This wind will induce a surface current in the lake. I am quite new to this topic, so I would be interested to know if there is a well-known model or perhaps some references that gives the relationship between the wind speed and the speed of the surface current. Thank you.", "label": 0}
+{"snippet": "If a person or thing is the exemplar of a particular virtue, you might say that they or it is exemplary or ideal; but the word \"paragon\" has a particular, even mythical connotation that none of the adjectives I've seen has. Could you say that something is \"paragonic?\" Perhaps \"paragonal?\"", "label": 0}
+{"snippet": "This question is from permutations and combinations i have no approaches it would be fine if someone could just give an approach to this problem. I am a high school student with basic knowledge of combinatorics", "label": 0}
+{"snippet": "I have an antenna that is placed at a certain height over conducting ground plane. If it's measured, I could imagine ripples in a farfield pattern owing to reflection from the ground. Is it correct to use two-ray ground reflection models to predict the complexity of interference patterns (maxima/minima) in the far field?", "label": 0}
+{"snippet": "After discussing this problem with multiple others, I've heard tons of different answers. I understand the explanations for both A and D. I've found differing sources on the web for this question as well, some supporting A and others D, even a few C. Can someone help explain what the answer is and why?", "label": 0}
+{"snippet": "Theorem with Diagram I am taking a topology class, and my lecturer keeps using diagrams like these. I am capable of understanding the theorem, but I must admit that diagrams like these often go above my head. Is anyone able to explain this diagram to me, what the arrows represent in in context with the theorem?", "label": 0}
+{"snippet": "The force exerted by the nucleus on the alpha particles is electrostatic in nature. So, why does mass has an effect? How do we conclude that the electrons don't effect the alpha particles from the fact that the mass of the electrons is negligible although they have the same charge as of the protons in the nucleus.", "label": 0}
+{"snippet": "Q. The smoke ____ out from the chimney. a. left b. rose c. went This question was asked recently in an exam. So which one of the options is the most appropriate option to be filled in the blank ?", "label": 0}
+{"snippet": "I want to write a legal memo using Latex. What class should I use in order to do this? Is there any other advice one could offer when formatting a legal memo to my company in Latex?", "label": 0}
+{"snippet": "I believe I can prove that such a solid doesn't exist, because if it did it leads to perpetual, motion as the solid could not remain still in any position on a horizontal surface once it is set in motion, and that is against the first and second law of thermodinamics. My question is if there is a mathematical proof without resorting to physics", "label": 0}
+{"snippet": "It is well known that steel grains tend to grow larger under heat treatment. Is it possible to enlarge grain size through any other means? I cannot seem to find anything via web search. If steel is too narrow a scope, the question can be generalized to all metals.", "label": 0}
+{"snippet": "Let a vertically polarised beam of laser light pass, at right angles, through a horizontally polarised beam of laser light of much greater wavelength. Does the oscillating magnetic field of the one cause Faraday rotation in the other?", "label": 0}
+{"snippet": "I've had my eye on properly understanding climate, climate change and the wide array of phenomena related. But, as a physics grad student, I'd fancy more exact, math-based bibliography, that treats all these interesting topics in a more formal manner, rather than with vague, high-school level explanations. Recommendations are very much appreciated.", "label": 0}
+{"snippet": "The sentence in question is: Donuts are not a part of healthy eating. I'm debating between the following: Nothing wrong Donuts are not part of healthy eating (because \"donuts\" is plural, is it grammatical for \"a part\" to follow? Or does this not matter?)", "label": 0}
+{"snippet": "When calculating \"antenna element length\" should we use the speed of light in the \"medium between transmitter and receiver (antenna)\" or the speed of light in the \"element material\"? (for example speed of light in air vs speed of light in Aluminum)", "label": 0}
+{"snippet": "I'm looking for resources/references(books, websites, lectures) that cover everything Fourier: right from series(real, complex) to transforms, discrete transforms, and possibly modern topics like FFT. Particularly, I'm interested in the various applications in image and signal processing, so something that covers this contextually is also much appreciated.", "label": 0}
+{"snippet": "The Wu experiment shows how parity symmetry does not hold for the weak force. However, how does this proof that parity conservation also doesn't hold? If my understanding is correct, the absence of parity conservation would mean that particles with odd parity can change to even parity and the other way around. But what changes parity in this beta decay via the weak interaction?", "label": 0}
+{"snippet": "What is the rhetorical purpose of the phrase: \"to be honest?\" I think it has become a way to indicate that what came before was a lie but the speaker does not want to be direct. On LinkedIn, I see it used by Climate Crisis disinformers to smear posts about global warming.", "label": 0}
+{"snippet": "I never use more than nine chapters, sections, subsections, or subsubsections. Therefore, I would like to remove the middle periods (but not the final period) in my section heading, as follows, both in the main text and the Table of Contents. Is this possible?", "label": 0}
+{"snippet": "I am trying to submit to arxiv and facing this error. I have the .bbl file in my folder structure. I cannot seem to find the reason of this error. Also, what are .rels files, these are not created by me. I also saw this solution, and tried. It shows output.bbl in the logs. Do I add this in the main folder structure?", "label": 0}
+{"snippet": "Imagine that a rocket is going up at a high speed and after some time its engine shuts off and it separates from the rocket. In such a situation, drag and gravity are both downwards. Does the same direction of drag and gravity cause weightlessness? If yes, why? If not why? And in general, what does this same orientation cause?", "label": 0}
+{"snippet": "Suppose a particle is in time independent potential and NOT in any superposition of eigenstates. Then expectation value of position is time independent and expectation value of momentum should always be zero according to Ehrenfest theorem.Is this true?", "label": 0}
+{"snippet": "What is a system described by a set of random variables for which there are distributions over subsets of these variables which are not marginal of a distribution over all random variables at once. That is, what is an example of contextual statistics in the real world. I would like an example that is not quantum mechanics please", "label": 0}
+{"snippet": "In motion planning for quadrators the optimization goal is sometimes to minimize the (norm squared of the) jerk and more often the (norm squared of the) snap. Can someone provide an intuitive and theoretically explanation? What optimization goal is used for cars in general (i.e. velocity, acceleration, jerk)?", "label": 0}
+{"snippet": "I recently learnt that more than two photons can be entangled. Are all the three photons are expected to have the same polarized angle due to entanglement? Does measuring one of the three photons collapse the entire entanglement or the other two photons continue to be entangled?", "label": 0}
+{"snippet": "This question has been asked before (see this: Amoeba splitting probability), but I've recently come across this article which uses a biased random walk approach. Screenshots from article attached: What are the \"usual arguments\" being referenced here? Confused as to how he did this.", "label": 0}
+{"snippet": "my friend and i have been debating the answer to this question could someone help me with this by explaining their answer please :) Is it possible to measure the energy of the particle if the wave function psi is not an eigenfunction of the hamiltonian?", "label": 0}
+{"snippet": "Experiments that feature the creation of entangled photons through SPDC often make use of coincidence counters. How can one photon be accurately correlated with its entangled partner by a coincidence counter? Are there any methods or technologies that help decrease the error of coincidence counting methods that help validate the trust in their accuracy that so many experiments depend on?", "label": 0}
+{"snippet": "The ejection of photoelectrons is independent of the intensity of radiation. But the quantity of electrons ejected depends on the intensity. So is there a limit to how much the intensity has to be, below which zero photoelectrons are ejected even if the frequency is sufficient for an emission?", "label": 0}
+{"snippet": "In school we did this experiment. We impacted a laser beam through a solution of sodium bicarbonate and the path of laser was visible in it. Does it have anything to do with coloids? But is this solution a coloid?", "label": 0}
+{"snippet": "This is a picture I found online: I have two questions about this. How do we know that over the power source and over the resistor, the electrical field is parallell to the power source or resistor. I highlighted this with the blue circles. Is the field symmetric around the power source and resistor if we rotate around it?", "label": 0}
+{"snippet": "What metric determines the \"geometry\" of the gravitational field generated by the mass of the sun? Is there a general metric that incorporates arbitrary mass and devolves into the Schwarzchild metric for black holes that conforms with the Einstein Field Equations?", "label": 0}
+{"snippet": "I was wondering if there was a one-word term for this. I suppose a classic example might be the \"Door Close\" button on an elevator. Essentially, a working feature that apparently does something, and the user can activate it but it will not actually play any meaningful role in the operation of the device.", "label": 0}
+{"snippet": "Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? I imagine it should be absolutely massive so that tidal forces are minimal. And if all this is possible, are there any special effects on the Star apart from usual time dilation?", "label": 0}
+{"snippet": "I have a small confusion, do conservative forces obey Newton's Second Law always? Because it depends on the end points and the path taken, the acceleration may vary path to path, but the force doesnt depend on it, so IDEALLY it should defy it.", "label": 0}
+{"snippet": "Does it have connection to the physical act of squatting or is it coincidental? After all, people that occupy a property, may just lie or stand in there, instead of squatting. So this does not seem to be very logical. I can't find any etymology or origin story of the legal term...", "label": 0}
+{"snippet": "I've recently been reviewing the Feynman Lectures. Caltech has posted Feynman's actual handouts from his lectures on the website below. https://www.feynmanlectures.caltech.edu/flphandouts.html Though they are helpful supplemental material, most handouts do not come with solutions. Does anybody happen to know how I can find solutions to them?", "label": 0}
+{"snippet": "What is the formula to find the average value of this waveform? What is the relation between the peak to peak value and average value of this waveform? Note that it's not an alternating wave. It's positive but changing wave.", "label": 0}
+{"snippet": "Can Fukui method be employed for the Chern number calculation in a low-energy continuum model? Let's consider the low-energy continuum version of the Kane-Mele model. If not what are some other ways one can try? Thanks.", "label": 0}
+{"snippet": "Example: Once I click on the main text and press \"Enter\", the Outline Pane automatically switches back to \"Table of Contents\" (instead of sticking with \"Labels and References\", which is what I'd like). How do I stop this?", "label": 0}
+{"snippet": "since its an open problem if NP = EXP, so i want to know the problems in exp for whom no polynomial certificates for output verification have been found so far . Any link or name would be nice", "label": 0}
+{"snippet": "I have a problem getting the right template for IEEE Open Journal of Vehicular Technologies from IEEE Template Selector. I make the right choices but then i get the template for Open Journal of Instruments and Measurements. Where can I find the right template?", "label": 0}
+{"snippet": "I read about time dilation and how to prove time dilation existence with light clock. But how to prove that time slow down on all other type of clocks (biological, mechanical, digital, electric, atomic, etc.)? Is it possible to test it on real experiments? Thanks.", "label": 0}
+{"snippet": "I know that all vectors are contravariant because if we transform into another basis vector we find its components change inversely to its original components. But I don't know why gradient is a covariant. How the components changes same as basis vector changes?", "label": 0}
+{"snippet": "Does \"hash browns\" refer to a countable thing? Or a substance? Have I had too many or too much \"hash browns\"? The word \"browns\" seems to imply a quantity. But, is there such a thing as a single hash brown? Or, are the strands just \"pieces of hash browns\"? (Or of \"hash brown\"!?) Why does this all sound wrong??", "label": 0}
+{"snippet": "Gravity is non-linear, so if it is mediated by gravitons, gravitons must interact with each other. On the other hand, the effects of gravity moves with the speed of light, so if it is mediated by gravitons, gravitons must be massless. How can gravitons interact with gravitons if they are not charged under gravity?", "label": 0}
+{"snippet": "I'm a physics teacher and I'm wondering if there's any game for physics elevator problems (weight in accelerating elevator) that the student can play with to better understand in what situations the weight is less or more", "label": 0}
+{"snippet": "In logic, the completeness theorem in propositional logic consists in showing that a formula is provable if and only if it is a sentential tautology. Suppose now that I have a set of non-logical axioms on top of tautologies. Does it make sense to look for a weakest form of the completeness theorem in that case?", "label": 0}
+{"snippet": "Supersymmetry is a model based on symmetry between bosons and fermions. Bosons carry force and they are described by potentials. Fermions are matter particle and they are described by wavefunctions. Does fermions carry force similary to bosons in supersymmetry? Can fermions be described by potentials instead wavefuctions?", "label": 0}
+{"snippet": "Trying to discern correct use of prepositions. Here's the sentence as I have it: This was proof that he could stay steadfast under conditions in which other men could not! Should it be: \"...under conditions which other men...\" ? Or is there another way that's more correct?", "label": 0}
+{"snippet": "See, it's a simple question.What exactly is stress? Is it the restoring force applied by the body in reaction to deformation force or is it the deformation force itself? I had this doubt because in some videos, they said that stress is the force applied whereas some others said that it's the distribution of internal forces. Please help me clarifying this doubt!!", "label": 0}
+{"snippet": "The Wikipedia article on propagators mentions that the harmonic oscillator propagator can be derived from the free particle propagator using van Kortryk's identity. This is followed by the identity itself which appears formidable. It is not clear to me how to even begin with this. How is van Kortryk's identity used? https://en.wikipedia.org/wiki/Propagator", "label": 0}
+{"snippet": "I believe the title contains all useful information for the problem. I tried to show that this map would have to be an isometry, but I can't seem to ensure that orthogonal vectors in the domain remain orthogonal in the image.", "label": 0}
+{"snippet": "I'm looking for a word to describe the sensation of emptiness, an emptiness endured for so long that it has evolved into physical pain.: Like you cannot breathe but at the same time feel unable to move or speak or do something you once loved.", "label": 0}
+{"snippet": "I am self studying general relativity and there is some especially hard problem (it is called bonus problem in book) I am currently working on it, but I am trully stuck, so I would appreaciate all the help I could get. Thanks!", "label": 0}
+{"snippet": "This is a follow up question asked and answered (Radio-dating and the age of the earth) The answer was given that the mineral Zircon is formed under high pressures and temperatures. How do we know, for example, most of the Zircon on Earth wasn't formed in some extraterrestrial event before the Earth formed?", "label": 0}
+{"snippet": "The verb for lying is \"told\",\"I told a lie.\" Occasionally I will hear, \"I said a lie.\" The latter usage really is cringey to me although perhaps \"said\" is a common usage in some areas. Is \"said\" actually wrong? What do you call verbs that seem to go with specific nouns?", "label": 0}
+{"snippet": "I'd like to create a weighted grid paper template. I'd like it to basically look like a sheet of lined paper, but with faint, equally spaced, vertical lines through it. I looked into the gridpapers template which has a set of templates but I could not figure out how to change the properties of the vertical/horizontal lines.", "label": 0}
+{"snippet": "White holes are described by the time reversed Schwarzschild metric. A test particle which is gravitationally attracted to the black hole's event horizon in the Schwarzschild metric is also gravitationally attracted to the white hole's event horizon in time reversed Schwarzchild metric. Still, white holes are described as a region of \"outward-flowing space time\". How are both compatible?", "label": 0}
+{"snippet": "Non-native English speaker here. Maybe this is easy for native speakers. Wiktionary clearly explaines, that surfaced roads (covered in gravel, stones or tar) are refered to as metalled roads. Why is metalled used as the overarching word? This seems counter-intuitive since all of the stated materials used for the surface-cover are thoroughly non-metallic.", "label": 0}
+{"snippet": "As far as I understand, local OMP (optical model potential) depends only on the relative position, and non-local OMP depends on relative position and momentum. I am searching for more information so as to understand the difference more intuitively.", "label": 0}
+{"snippet": "SPM and Raman scattering both cause spectral (frequency domain) broadening of ultrashort laser pulses. So I was wondering if what we know as SPM spectral broadening is dependent on Raman scattering at microscopic level. SPM is a nonlinear process. What about Raman scattering? If Raman is not nonlinear, then can a nonlinear process be dependent on a linear process?", "label": 0}
+{"snippet": "Is this the correct term for words which are nouns when the first syllable is stressed, and verbs when the second syllable is stressed? Examples include PERmit and perMIT, and CONtract, and conTRACT. There are frequently-occurring suffixes such as '-ject' and '-tract', but are there any other relevant rules and patterns?", "label": 0}
+{"snippet": "I wanted to extend the length of the last line in a minipage, so it touches the minipage margin (creates a perfect box of text). I doubt it has any practical use, but im trying to recreate a poem in LaTeX. Sorry if there is a simple answer, I learned LaTeX basics just today. I hope it's even possible.", "label": 0}
+{"snippet": "I am wondering if a nonlinear map can be considered like a set of linear maps, with a different linear map for each element in the domain. And a linear map would then be the case where the offsets and scales are the same over the whole domain. Or does nonlinear map have more connotations to it?", "label": 0}
+{"snippet": "This is a question about conservation of momentum. Will the inertia of the rotating pencil make the pencil bounce higher? Both cases the pencil is dropped from the same height but the spinning pencil is made to spin by a force couple besides being dropped.", "label": 0}
+{"snippet": "At least, why not try with protons, they are much heavier and at the end, any deflection from Lorentz force will not overshadow the Stern- Gerlach phenomenon. But the question is still, was such experiment carried out or not?", "label": 0}
+{"snippet": "Today the prof. a new sign and I don't know how to draw it. It is like overline, but on both ends of the line go down, so there is half of a rectangle above the letter. Does anyone know, how to make it in Latex?", "label": 0}
+{"snippet": "My friends and family call me Tumbleweed because I'm tall and clumsy, but sometimes I wander if there's more to it when my \"friends\" call me Tumbleweed. I was wandering if Tumbleweed can be used as a nickname for such a person (clumsy and gangly)?", "label": 0}
+{"snippet": "I was wondering...if entropy is a \"state function\" then why does going through an irreversible cycle give a negative value for entropy (Clausius inequality), I know it might be due to the fact that entropy is an unnatural transformation but I want to understand why? cause it is still a cycle... why it isn't a zero value?", "label": 0}
+{"snippet": "I'm looking for a template (or a class) to write a systematic literature review in Public Health Sciences. I can use the article class, or a specific class as oup-contemporary; but I'm wondering if such a template exists? I didn't find any specific template for a systematic literature review. If I can't find it, I can create one with the article class.", "label": 0}
+{"snippet": "In Linux when I want to install packages that are not provided by my distribution's repository, I can manually add entries to sources.list and download them. Are there any such alternative repositories for TeX that provide well-maintained packages unavailable in CTAN? Or is CTAN the one and only go-to for TeX packages?", "label": 0}
+{"snippet": "If a point charge with q charge is brought near a conducting body(especially sphere) how much charge will be induced in the body? Also when will induced charge be equal to inducing charge? Edit:- I want to know when the conductor is earthed and as well as when it isn't, assuming a metallic body in vacuum or medium.", "label": 0}
+{"snippet": "Which sentence is grammatically correct or sounds more native-like? Politicians tend to discuss their sources of income nontransparently, leaving the discussions surrounding them out. Politicians tend to discuss their sources of income nontransparently, leaving out the discussions surrounding them.", "label": 0}
+{"snippet": "I have a picture that is a rectangle and has an open center. I want this image to be my page border. How would I go about doing this? If I try to make the picture fit the entire page then I can't have the text on the same page that the image is on.", "label": 0}
+{"snippet": "This is a graph represents the number of times a week the students in a class walk to school A question asked is \"In total, how many times do all the boys in the class walk to school per week?\" I don't even understand the question to be honest. What is being asked and what is the answer?", "label": 0}
+{"snippet": "Why is it impossible to determine a real inertial frame? We can determine the applied torque on a gyroscope by observing its precession. And thus we can evaluate the acceleration of our non-inertial frame. Is this acceleration relative to a real inertial frame? If so then it should be easy to determine a real inertial frame. Help me on this, IM really confused", "label": 0}
+{"snippet": "How does the above circuit work? My textbook only has potential divider circuits such that there is only one output voltage. Such as this one. Could we replace the arrowed line in the uppermost diagram with two lines? This is the only way the above diagram would make sense to me.", "label": 0}
+{"snippet": "Could someone provide references for a modern treatment of statistical manifolds? I have so far only found treatments that seem quite old, where the notation is somewhat dense to follow, to some extent probably because the font seem adapted to \"old-school\" typewriters.", "label": 0}
+{"snippet": "When a potential explicitly depends on time, energy is not conserved. However, if we take into account what is causing this potential (for example, a machine moving some object(s)), would the total energy of the combined system be conserved? I'd like to know if there's any proof one way or the other in the most general case.", "label": 0}
+{"snippet": "I saw in one place the phrase \"A which means B\" being used as \"A is equivalent to B\", and in another instance the same phrase being used to mean \"A if only B\". Which is the correct usage? My feeling is that it means \"A is equivalent to B\".", "label": 0}
+{"snippet": "Here's the example: \"They are first taught the basic procedures for scuba diving, including safety and communication with fellow divers, then familiarize themselves with the equipment before dipping their toes into the water.\" I could come up with simpler examples but this is the one that I'm struggling with. Is it odd either syntactically or semantically?", "label": 0}
+{"snippet": "Simple question. How did the English word \"possess\" come to have a voiced \"Z\" sound for the first double-S? Are there any other words that have this? Doesn't double-S consistently mean an unvoiced S sound, across a number of Germanic languages, English included?", "label": 0}
+{"snippet": "According to wikipedia page: https://en.wikipedia.org/wiki/Commuting_matrices, there is a characteristic for commuting matrices such that: If A has distinct eigenvalues, and A and B commute, then A's eigenvectors are B's eigenvectors. How to prove this statement?", "label": 0}
+{"snippet": "It is possible to estimate the position and rotation of camara on xyz axis (both location and rotation) from vanishing points ? If so how ? I tried to search the web for an answer but i didn't found anything i could understand relatively easily (i am not at academic level in mathematics and English is not my mother tongue)", "label": 0}
+{"snippet": "I recently learned that position vectors and spin vectors lie in different spaces, and the complete wave is the tensor product of both. I wanted to know that whether we can talk about commutation of spin and position operators. Can we talk about commutation of operators that act on different spaces? If so, how?", "label": 0}
+{"snippet": "What I mean is that are there any elements which we can actually observe decaying into other elements, like a magical transmutation? Just like how a paper burns into ash.(or some other interesting chemical reaction) If yes, then please tell me about them.", "label": 0}
+{"snippet": "The boy who will come to see you tomorrow will bring you that book. Can this sentence be changed to either of the following? a. The boy coming to see you tomorrow will bring you that book. or b. The boy to come to see you tomorrow will bring you that book. Which one would be the better choice?", "label": 0}
+{"snippet": "I make my ice in those little round to-go containers that usually hold sauces/dressings. When using the clear containers, the ice sticks to it and requires heat or violence to get it out. When I use the black containers, the ice slides right out with no fuss. Any thoughts on why?", "label": 0}
+{"snippet": "In the above text it is mentioned that the incident light ray travels along the principal section.But any ray which travels along the principal axis should not go through the double refraction. Then why the text says that the incident light ray split into two rays?", "label": 0}
+{"snippet": "If two random variables does not have linear relationship then they are uncorrelated even if they might be dependent. I am unable to come up with an example where two random variables have linear relationship but are uncorrelated.", "label": 0}
+{"snippet": "The following question probably philosophical and as a result maybe not fit here, but I consider it as a Mathematical logic question: \"If there are no roads, then all roads lead to Rome.\" Is this sentence true or false?", "label": 0}
+{"snippet": "I have studied science till school, but not in grad... so I might very much be wrong ... isn't the wavelength of sound waves larger than the dimensions of atoms? Won't sound waves skip over atoms?", "label": 0}
+{"snippet": "Writing a differential equation for such a figure is an uncomplicated task. It can be accomplished by using snell's law. But the resulting equation probably isn't solvable. I put it in wolfram alpha and it didnt even show it's graph. May be not it's solution, but I'd like to see its graph at least.", "label": 0}
+{"snippet": "I came across this in Khan Academy Integral Calculus. I am asked to find this integral... I did the substitution, and it made sense so far... Then, I was unable to figure how to solve the definite integral. This was their solution... Where did that sin expression come from? I am so confused!", "label": 0}
+{"snippet": "In my thesis I have to cite the references in the style shown in the picture. I think it is more near to apa style, but not exactly same. Could anyone please guide how can I generate references in this format. I am using .bib file and working on overleaf.", "label": 0}
+{"snippet": "If neutrinos are so easy to produce, but it rarely get absorbed or detected, doesn't that mean the universe will be full of neutrinos? Will its density ever reach a balance where its absorption events occur as frequently as emission events? Is the universe already reaching the balance or far from it?", "label": 0}
+{"snippet": "I read some papers that study the global existence of a solution to a PDE. Sometimes, I found the notion of the \"continuation principle\". What do we mean by the continuation principle? any recommended references and thank you in advance.", "label": 0}
+{"snippet": "Maybe this a dumb question, but, is the gravitational dilatation of time caused because a particle travelling through a geodesic in a curved space-time must cover a larger distance than the one travelling through empty space?", "label": 0}
+{"snippet": "I'm interested in knowing if there is a name for a graph G where; Its vertices: Are a subset of the vertices of graph H. Are the terminal vertices of paths in H. Its edges: Are only incident to the terminal vertices of paths in H.", "label": 0}
+{"snippet": "How would we use the phrase \"under one's belt\" if the subject is 'us'? Would it be \"under our belts\" or \"under our belt\" because it is an idiom? For example With a year of successfully running this company under our belt/belts...", "label": 0}
+{"snippet": "I'm reading on Lie group and Lie algebras, but I am confused with the correspondence between them. Does any element in the Lie group correspond to an element in the Lie algebra (tangent space at identity)? If so (such as two-dimensional rotation), why is it only valid near the tangent point? Or is it just a convenience for the first-order approximation?", "label": 0}
+{"snippet": "I am in a heated debate over whether to use \"is\" or \"are\" in the following sentence: \"When I look into her eyes all I see is/are bright lights beaming energy through our path on eternity together.\" Please advise.", "label": 0}
+{"snippet": "For progressive waves we define phase difference as difference in phase angle between two points. However for standing waves, the phase difference becomes something else. We say two points are in phase when they travel in the same direction and with the same amplitude. So why have the definitions changed here?", "label": 0}
+{"snippet": "Diamond dust is a natural phenomenon that occurs when ice crystals form closer to Earth and interact with sunlight. Now diamond dust shimmers because of the reflection and refraction of sunlight. I know that the shimmering of light on water is formed due to specular reflection therefore I wanted to know if the same applies to ice crystals.", "label": 0}
+{"snippet": "I was wondering if a graph existed because I used euler's inequality and it said that theres supposed to be a graph but im having a hard time figuring out what it is. Thank you!", "label": 0}
+{"snippet": "The term is used throughout the literature but I was not able to find a definition or even a paper properly introducing the term. What does a Hamiltonian have to satisfy to be a parent Hamiltonian? An explanation or examples would be much appreciated!", "label": 0}
+{"snippet": "I'm editing a flyer someone else wrote and I have the following sentence: Our storytelling series launches with featured speaker, Aloysius Firefly, professor of arts. I think ought to be \"... speaker Aloysius Firefly, professor of arts.\" What do you think?", "label": 0}
+{"snippet": "Does measuring the energy of the particle cause its wave function (psi) to change if psi isn't an eigenfunction of the Hamiltonian? quite confused about this one on when the wave function changes when taking a measurement and when it doesn't. please help :)", "label": 0}
+{"snippet": "Why does it say \"possibly empty\" in the definition of bipartite graph? Wouldn't that mean that every graph is bipartite, moreover I don't think partitionins can have empty sets. Is this a mistake?", "label": 0}
+{"snippet": "I want some good books recommendation on number theory. I self-studied a good chunk of calculus and I am self-studying analysis right now, and would like to start number theory. I also have a good understanding of mathematical proofs. So, any recommendations for good advanced books on the topic?", "label": 0}
+{"snippet": "I would like to reference this fact (probability measures are closed under convex combination). I found this (for example, probability distributions are closed under convex combination) but I would rather want to cite a paper/textbook. I would be happy if someone could provide such a reference (ideally to a paper or a book for which a PDF is freely available).", "label": 0}
+{"snippet": "I am writing a paper which I want to start with a literary quotation. How do I do this? It should probably appear above my name and the title. It is not \"To be or not to be\" but for the purposes of my question it might as well be.", "label": 0}
+{"snippet": "I have been wondering about this little problem for a while now. Everyone understands that, in the binary, the opposite of 'man' is 'woman', and the opposite of 'gentleman' is, namely, 'gentlewoman'. However, from what I can tell, there seems to be no word that refers to the opposite gender of the word 'lady'. Any ideas?", "label": 0}
+{"snippet": "i have already read carlo rovelli's 'reality is not what it seems' and lee smolin's three roads to quantum gravity, how should i proceed from here and what books do i read that balance theoretical approach with the mathematical approach, i was looking forward to a first course LQG and string theory should i go ahead with them?", "label": 0}
+{"snippet": "Water at absolute zero is, I suppose, ice. At room temperature it's water. At a certain point steam. What happens to it as we approach infinite temperature? (what we might call \"absolute\" hot)", "label": 0}
+{"snippet": "Does a charge moving freely in an electric field's direction, produce a magnetic field? If so, then why is energy conserved in cases of distance of closest approach? If there is a magnetic field it is non conservative, so how is this possible? I tried to find out but could not find the reason for it.", "label": 0}
+{"snippet": "I have two different circles with their formulas, which intersect from different parts of themselves, how can I calculate the area of the intersection and the rest of the circles? Is there some way to do it without using calculus? And how to calculate that area, why? Here is the question, if you find a way, it doesn't matter the exact numbers:", "label": 0}
+{"snippet": "How was the singular value decomposition (SVD) method originally derived? How might one discover decomposition this from first principles? Related Q&As that lend intuition to SVD but not derive or show how one might come up with such a decomposition: Understanding the singular value decomposition (SVD) What is the intuition behind SVD? (cross validated stack exchange)", "label": 0}
+{"snippet": "Consider: \"What are you up to right now?\" \"I hope to secure an appointment with her.\" As opposed to: \"What were you up to just then?\" \"I was hoping to secure an appointment with her.\" Yes, I know it sounds \"more natural.\" But: why does it?", "label": 0}
+{"snippet": "What's a good way to make an interleaved layout having text blocks aligned to one side and images/graphics aligned to the opposite? Or in other words: Imagine a raster of a three column layout where the text spans over the left and center layout column and the images span over the center and right column.", "label": 0}
+{"snippet": "There is the famous isomorphism theorem for measure spaces: All separable nonatomic normalized measure algebras are mutually isomorphic. what about an atomic normalized measure algebras? Is it possible to establish an isomorphism or a measure-preserving transformation from an atomic normalized measure algebra into the measure algebra of the unit interval? These theorems would be helpful in understanding my qeustion. Any help would be appreciated.", "label": 0}
+{"snippet": "Simple question: what is the verb for the phase change from gas (or any other \"regular\" state of matter) to plasma? The best thing I can think of is \"ionization into a plasma\" but is there a nice, one-word equivalent counterpart to other phase change verbs like melting, boiling, subliming, etc?", "label": 0}
+{"snippet": "The sun emits white light, which is a mixture of light from all frequencies. Instead, it should have emitted a beam of light of the same frequency, as the source is the same? So, can you please explain why the sun emits light in all frequencies?", "label": 0}
+{"snippet": "Yes, I know this package can generate structure from .mol and SMILES files. I'd like to know: is it possible to follow the reverse path, i.e. once the structure has been drawn with chemfig, generate the .mol file and/or the SMILES?", "label": 0}
+{"snippet": "Is it possible to draw a Braid like this? (with dots and vertical strands) I tried to use TikZ braids Package but on the documentation I don't see anything similar to this things. Thanks in advance", "label": 0}
+{"snippet": "I recently wrote, on Stack Exchange, in regard to the books of the bible : ... Paul, Mark and Luke's contributions ... I did so instinctively and afterwards realised what I had done. Am I wrong to 'bracket' together without fully stating : ... Paul's, Mark's and Luke's contributions ...", "label": 0}
+{"snippet": "Why doesn't water inside a glass enter a straw when you close the top of the straw before putting it inside the glass. Shouldn't the atmospheric and pressure of water push the water into the straw since I would assume that the pressure inside of the straw is the same as atmospheric pressure which is lesser.", "label": 0}
+{"snippet": "I was reading my book and came across that sample median is unbiased estimate for symmetry distribution with finite expectation. I was able to proof this but is this true for Cauchy distribution? Since mean does not exist for Cauchy distribution. And how can I show that it's an unbiased or biased estimator depending on the result?", "label": 0}
+{"snippet": "In this question here, it was asked whether a black hole could emit protons with energies exceeding the GZK limit via Hawking radiation, the answer given was yes. So I ask, what proportion if observed GZK exceeding cosmic rays could realistically have been produced by said process?", "label": 0}
+{"snippet": "I am currently a physics and mathematics double major graduate student. Looking for a text book and problem sets on the topic of vector field analysis, would be best if the book is advanced and problems is difficult. Also with application to classical electrodynamics/", "label": 0}
+{"snippet": "I'm studying Fourier series and i'm using Desmos to graph the results and it does look like its approximating towards a square wave but is there a way that i can just graph a square wave in desmos? and periodic functions in general?", "label": 0}
+{"snippet": "I've been investigating book layouts for a project I'm working on and I found the title page and book layout from the art and practice of printing I have attempted to create this layout using memoir but to no success. How would I go about recreating this layout in Memoir?", "label": 0}
+{"snippet": "It has been proved by the Red Shift that universe is expanding. But if the universe is actually expanding, it needs energy to do so. I also do not know that with expansion in universe if mass increases. My question is from where do the universe get the energy to expand? How does it not violate the law of conservation of energy?", "label": 0}
+{"snippet": "I was trying to understand problem regarding finding the adiabatic modulus given the isothermal young's modulus. I'm still an amateur in thermodynamics. I just didn't understand the final step where the two adiabats are combined.", "label": 0}
+{"snippet": "I'm in search of an online tool that can: Write both LaTeX equations, as well as normal text. Convert the document into an image and let the user download it Also the tool must be free, because why not!", "label": 0}
+{"snippet": "I have been reading a lot of resources but it seems a little too difficult for me to grasp, I have no background in mathematical competitions and the activities in my college related to competitive math are really limited. Can anyone give me a list of books or pages to start from the very basics to build my way up to the real problems?", "label": 0}
+{"snippet": "Relatively straight forward question I had after finishing a review of the ethereum yellow paper. How might one go about or is it even possible to formulate the general math behind a blockchain as a category with a set of objects (transactions, nonces, accounts), and a set of morphisms ( state change function, block validation function, etc).", "label": 0}
+{"snippet": "Human Assets Development or Human Asset Development The second one has no \"s\" at the end of asset. Which is more natural, and is there a rule for this (for example, use a singular noun (human asset) when the noun is used in a phrase (human asset development)?", "label": 0}
+{"snippet": "Today I learned several vocabs including \"adhere to\". Also the teacher said that \"New rules are adhere to\" is also grammatically correct and used normally. However, I think that it feels weird to me because it ends with preposition \"to\". Can anyone help?", "label": 0}
+{"snippet": "The meme-y term \"dummy thicc\" uses \"dummy\" as an intensifier modifying \"thicc\" (meaning curvy). How common is this usage of \"dummy\"? How long has it been around? Is the etymology here related to the use of \"stupid\" or \"crazy\" as ironic intensifiers? (Wiktionary lists \"Extremely\" as an adverb definition of \"dummy\", but without quotes or other background.)", "label": 0}
+{"snippet": "Is it correct to apply the word fellow to a thing, not a person? For example \"fellow companies\"? Definitions in M-W, Collins and Cambridge all point to fellow being applicable only to people.", "label": 0}
+{"snippet": "I'm looking for ways to visually signify the links between turns in a transcript and found this which I think is a brilliant way to do it in a book by Erving Goffman. Is there any way to replicate this on LaTeX in a consistent way over a large corpus?", "label": 0}
+{"snippet": "Here is a piece of text: But the historical pattern of warfare remains inconclusive, frustrating, endlessly cyclical. States persist in warfare because the mechanics of the balance of power rarely permit escape from it. [link] The first sentence confuses me (especially the words \"inconclusive\" and \"frustrating\"). Please tell me how you understand it? How can it be rephrased?", "label": 0}
+{"snippet": "Can someone give a reference textbook, etc which explains / has examples for polar integration to calculate center of mass. (This is at the level of advanced pre-college physics, say for example the JEE entrance exam, so references that explain in detail are preferred. JEE does not have multivariable calculus. Will prefer refernces that use single integration. Simple shapes will do", "label": 0}
+{"snippet": "Does the region surrounding a bar magnet have a greater abundance of virtual photons, or more energetic (but the same number) virtual photons when compared to a region further away from the bar magnet?", "label": 0}
+{"snippet": "To show dilation in spatial relativity, is it accurate to do a \"god's eye view\" showing a top down view of both trains, or is dilation from one perspective alone (view from Train A or Train B)?", "label": 0}
+{"snippet": "I am working on a heavily mathematically project about plasma. In particular, I want to find references that treat the problem from microscopic models that include relativistic and magnetic effects (Coulomb forces, QFT, etc) and obtain kinetic models (BBGKY, Landau equation, Maxwells equation, etc). What are some state of the art papers/references?", "label": 0}
+{"snippet": "In the Blandford-Znajek Process (which is considered a potential mechanism to explain jets from AGN), the lorentz force is assumed to be vanishing (the force-free condition). But we see that the lorentz factor for the outflow is quite high. If there is no exchange of energy from the electromagnetic fields to the charged particles, how are these two facts reconciled?", "label": 0}
+{"snippet": "Is the dual/opposite of a Heyting Algebra still a Heyting Algebra? What about locales? I don't see any obvious way to prove it but don't know enough examples either to test for counterexamples.", "label": 0}
+{"snippet": "Is there a database or tool that gives all the STY and CLS files that are part of TeX Live or CTAN? I can do some basic web scrapping to retrieve this information, but I would like to avoid having to reprint the roll.", "label": 0}
+{"snippet": "I am writing a stellar atlas and I am using the astronomy and astrophysics template in latex but when making a document the template makes an abstract without me asking. How do i delete the abstract ? (Template can be found on the website https://www.aanda.org/for-authors)", "label": 0}
+{"snippet": "\"The ample supplies have the government urging vaccinations not just for people at highest risk of dying from influenza, but for anyone who wants to avoid a week of aching misery.\" Original Posts Is \"have the government urging\" a causative structures like \"I had John fix the car\"? If so, why we use 'urging' here instead of 'urge' in bare infinitive form?", "label": 0}
+{"snippet": "Is there an alternative description/characterization of the stable module category of Abelian groups? I guess that the category of torsion groups is a subcategory of it, but is it all of it? What is the structure of the image of torsionfree Abelian groups?", "label": 0}
+{"snippet": "The context is to describe groups such as \"Stop Oil\" that claim to be environmentalists, but behave in such a way to garner disdain of environmentalists (like blocking traffic which forces cars to idle and pollute MORE while also pissing off the very people they should be trying to win over), and in turn, their cause.", "label": 0}
+{"snippet": "I am trying to understand how to write the gravity-matter and gravity-gravity hamiltonians in terms of daggered/undaggered operators. Is there any pedagogic review paper on writing such hamiltonians in terms of combined annhilation/creation operators with corresponding coefficients.", "label": 0}
+{"snippet": "I saw this many times but I don't understand why it is an improper subset. The power set has all the elements S has and more so they are not equal making them proper subsets and not improper ones no? Or it doesn't matter that much if I put proper subset or not here?", "label": 0}
+{"snippet": "I was looking for a way to derive a fourth-order error formulation of a second-order derivative at the contact surface of two different materials. Say, solving a thermal diffusion equation with varying thermal conductivity and diffusivity. Thanks in advance!", "label": 0}
+{"snippet": "In Russian, we say \"to have one's bumps\" when we mean that someone makes their own mistakes, thus getting experience and learning from their errors. Is there anything similar to that in English?", "label": 0}
+{"snippet": "Here is an example: I have developed my ability to identify the factors that impact my physical, mental, and emotional health[,] and am beginning to apply this understanding to make informed decisions. Do you agree with the comma I would use (shown in brackets)? Why or why not?", "label": 0}
+{"snippet": "It feels like the transition from a sea of probability of a droplet of precision (or wave, depending what you're looking for) would be a loss of entropy, if so wouldn't this violate the Second Law? Or does Heisenberg's insistence that we cannot ask questions about what happens before observation exempt it from such considerations?", "label": 0}
+{"snippet": "I guess it's a straight line, which is the axis of a hyperboloid of one sheet, and the three straight lines on different surfaces given are a family of generatrix of this hyperboloid of one sheet", "label": 0}
+{"snippet": "Obviously there is a limitation as to how well experimental configurations that depend on coincidence counting can efficiently remove the noise present at any given experiment. This leads me to wondering, how efficient are modern day coincidence counting techniques? A percentage of noise removed, signal to noise ratio, an evidenced estimation, or something of the like would suffice.", "label": 0}
+{"snippet": "For the zeta function itself, I have been using the Riemann-Siegel Z formula implementation as written here: https://web.viu.ca/pughg/thesis.d/masters.thesis.pdf However, my searching skills have completely failed me on the derivative. Is there an algorithm that calculates the derivative that is relatively easy to understand, and/or doesn't involve too much computation?", "label": 0}
+{"snippet": "I am completely new to ConTeXt and have just started to experiment with writing metapost directly within ConTeXt. In Latex , we use the tcolorbox macro package to achieve the effect of code on the left and output on the right, my question is, how can I achieve a similar effect in ConTeXt?", "label": 0}
+{"snippet": "I'm starting to learn the memoir class to use it with a book I'm writing in LyX.I've read most of the memman docuement. When I create a new LyX document I can enter the title, but not a subtitle, half-title page, or the other front matter pages. Do I need to put all this in the LyX preamble? TIA, Rich", "label": 0}
+{"snippet": "I am looking for books and papers that take a mathematical perspective on the physics topic of dimensional analysis. I am sure there are such texts out there. I would be very glad to know of any such texts.", "label": 0}
+{"snippet": "It is not possible to have a process in which the entropy of an isolated system is decreased Does that mean, if we increase the volume of a gas, entropy of gas increases, now when we decrease the volume of gas to its original volume, the entropy of gas comes back to its original state, but the excess entropy is transferred to the surroundings?", "label": 0}
+{"snippet": "Here's a Desargues Configuration with all points on a square lattice: Is there a more compact version, either on a square lattice or triangular lattice? Also, if there a less obvious Desargues configuration that's larger, but still with relatively simple coordinates?", "label": 0}
+{"snippet": "I have proved that pseudocompact implies completeness in a metric space, which is, as I understand it, a step to proving pseudocompactness implies compactness. How do I show complete and pseudocompact implies (sequentially) compact?", "label": 0}
+{"snippet": "Do I need to repeat the subject after a semicolon splitting two sentences that have the same subject in formal written English? For example: He talked to the owners, which was understandable; paid the bills, which was not expected; and, did not even ask for the money back, which was unbelievable. Should I add the subject \"he\" after each semicolon on the example above?", "label": 0}
+{"snippet": "Gaia provides low resolution spectra from BP/RP filters and the values of equivalents width for hydrogen spectral lines are also provided in it's stellar database. How can there be negative equivalent widths of Halpha spectral lines values as shown in the picture below? Shouldn't they all be negative or positive?", "label": 0}
+{"snippet": "I have read this title Pakistan top court orders immediate release of ex-PM Imran Khan. Why they have written \"orders\" in present simple? I mean why not in present perfect or simple past?", "label": 0}
+{"snippet": "I've read in some sources that Entropy is a measure of how much energy is not available to do work but I'm not quite sure what this is getting at. The only thing that I could think of is perhaps that heat cannot be fully converted work in a cycle with a portion dumped out as entropy. Is my interpretation correct?", "label": 0}
+{"snippet": "Is it not a misnomer to call in a non-perturbative setting an irrelevant direction irrelevant? I know that it comes from perturbation theory where an irrelevant direction is irrelevant for the IR dynamics but in a non-perturbative regime an irrelevant direction should have effects in the IR.", "label": 0}
+{"snippet": "There is an idiom that says basically, \"Better to go out in a blaze, than burn out like candle.\" I'm probably totally off, but it's something like that. The point of the cliche is not to let your objection or opposition die with you, but to make it the cause of your departure.", "label": 0}
+{"snippet": "Do I need to make sure the gerunds match in the following sentence: There is not much attention paid to really examining what constitutes this notion, much less scrutinizing the received criteria for it.", "label": 0}
+{"snippet": "Polarization in GWB should carry as much important information as in CMB. However, I've done some superfluous literature research and found little discussion. Is there any planned project for measuring the polarization? Or is there a method to extract the information from existing experiments?", "label": 0}
+{"snippet": "Is there a specifically appropriate term to say \"reading between the lines\" or \"to read between the lines\"? Or to devise inferred meanings and unspoken things, and not necessarily something that's consciously implied but that the other person may be giving away without realising?", "label": 0}
+{"snippet": "I just start learning Physics. The picture shows the ISS orbiting Earth. Suppose now we (or rather, God) put a baseball behind the ISS. The ball is not moving with the ISS, we just put it on the track of the ISS and let go of it. Will this ball fall directly to Earth while things in the ISS are floating?", "label": 0}
+{"snippet": "I was using Latex to write my report and whene I open the pdf generated I had (equations, Notations, list of figures, list of tables...) marked in red or green as shown in the image. How can I get rid of these markers. Any help will be appreciated.", "label": 0}
+{"snippet": "What's an adjective that describes cutting mats that also have grids drawn on them, and specifically distinguishes them from cutting mats that don't have grids on them? I guess if there's no cutting-mat-specific word, the word that means \"this device has gradations marked on it\" (that could also describe rulers, measuring cylinders) would also work. That is a ____ cutting mat", "label": 0}
+{"snippet": "I want to say that I solved a programming bug and has been around for years in my resume. I currently have something like \"Debugged long standing bug\" but I don't think it conveys that point that this issue has persisted for many years. I could obviously say \"Debugged bug that has been around for many years\" but that doesn't sound like resume-language", "label": 0}
+{"snippet": "For this particular diagram below, is there any reason why all the radii of the circles are in a geometric progression? I've tried using similar triangle to try and prove it, but was unsuccessful Any help would be much appreciated", "label": 0}
+{"snippet": "There is a certain premise which I am unable to represent correctly as propositional logic: \"When I play basketball, I wear my sneakers; otherwise, I never wear it.\" (PlayBasketBall -> WearSneakers) <-> (-PlayBasketBall -> -WearSneakers) What changes do I need to make in order to represent it correctly?", "label": 0}
+{"snippet": "I would typically use the term \"electric field\" like so: \"[...] therefore, it has a high electric field\". If I wanted to hyphenate this term with a compound word, how would I do so? Someone mentioned that \"Electric-field-induced voltage\" is appropriate, but I believe \"Electric field-induced voltage\" is (no hyphen in between electric and field added). Which is it?", "label": 0}
+{"snippet": "Every explanation and example uses a t-bar. But what if the \"bar\" was a propeller? I can understand there being no difference if it's a vacuum, but I would think the aerodynamics would change in a gaseous environment.", "label": 0}
+{"snippet": "When we equate (with opposite sign) coulombic force to the centrifugal force for a electron revolving in the orbit. Basically we are equating a conservative force with the non-conservative force. Can we equate the two different categories of force. What is the reason for this?", "label": 0}
+{"snippet": "I have rotation curve data (radius vs rotational velocity) for some specific galaxies. How can I estimate the dark matter density for those specific galaxies by using the rotation curves? Or is there such a method to do it?", "label": 0}
+{"snippet": "If a semiconductor laser is operated in a DC condition, the injected current is higher than the threshold, that is to say, the gain will be larger than the overall cavity loss. So, the stimulated emission will be built up to dominate the photon density of cavity. Is it correct that photon will be generated unlimitedly to get high output power?", "label": 0}
+{"snippet": "I am trying to model a pv system and I want to simulate different angles, and to calculate values of different angles. I am asking if there is any software that allows me to design the figure below and calculate angles.", "label": 0}
+{"snippet": "The difference between \"I can fix the computer\" and \"I could fix the computer\" (present tense) is that the latter expresses more reluctance or doubt. What is this type of sentence called? I can relate it to conditional mood, with an implied condition: \"I could fix the computer [when I feel like it / if I know how]\"", "label": 0}
+{"snippet": "I found in John Bell's book \"A Primer of Infinitesimal Analysis\" such interpretation of time representation: But I can't fully understand this interpretation. Can someone explain easily what John Bell means here? Thanks.", "label": 0}
+{"snippet": "If a water molecule is made up of at least one tritium atom, when the tritium atom(s) decay radioactively, what happens to that water molecule? Does it bond to one or two Helium atoms? Is there any chemical or nuclear equation that defines this process?", "label": 0}
+{"snippet": "I was assigned a presentation on Hypercorrection yet I have absolutely no idea what it is (the definitions I found were really vague). Please help me grasp the basis of it and kindly provide some examples/cases. Thank you so so much!", "label": 0}
+{"snippet": "I am dealing with matrix lie groups, Like GL(n) or subgroups of GL(n). Does geodesics of these matrix lie groups with left invariant metrics are related to one parameter subgroups? Can someone offer some references or examples for me for further study?", "label": 0}
+{"snippet": "According to The book Statistical mechanics by Pathria, The Bragg-William approximation states that \"the energy of an individual atom in the given system is determined by the (average) degree of order prevailing in the entire system rather than by the ( fluctuating) configurations of the neighboring atoms\" What is the reasoning behind the above statement?", "label": 0}
+{"snippet": "I want to create my own Journal template, and I would like to use other people's templates in https://www.overleaf.com/latex/templates/tagged/academic-journal Can I import a class and modify it to my liking? Is this legally ok?", "label": 0}
+{"snippet": "Let's say someone says: Take me to the store right this second. I want to quote the person directly but incorporate it into my sentence my changing \"me\" to \"him\" as follows: He said to \"take [him] to the store right this second\". Is this the correct use of the brackets to change the quote?", "label": 0}
+{"snippet": "Imagine a vertical line representing the lamppost, a point moving away from the base of this line representing the skateboarder, and a line from the top of the lamppost to the skateboarder representing the light ray. The shadow of the skateboarder is the line from the skateboarder perpendicular to the lamppost, intersecting the light ray.", "label": 0}
+{"snippet": "Can we apply the same formula of the \"vector triple product\" and \"vector scalar product\" for complex vectors (that is, vectors with complex entries)? Clearly, I assume we calculate the cross product with the complex vector formula, and that we also calculate the inner product with the complex vector formula (either antilinear to first argument, or antilinear to second argument).", "label": 0}
+{"snippet": "Can we safely say that: Even without assuming Einstein's postulates, experiments have shown that measuring the average speed of light in the vacuum on a closed path always produces the same result: the constant c? Do we need to specify that the measure must be performed in an inertial frame or possibly something else, or can we state this principle in general?", "label": 0}
+{"snippet": "I'm Looking for a book of rings of formal power series, I would like to study the construction of polynomial rings but i did not find a good book yet. Many books give the wrong definition and despite I didn't learn yet ,I know that is wrong.", "label": 0}
+{"snippet": "below screenshot of the same image showing (left) the image as desired in a generic image viewer and (right) after inclusion with XeLaTex and includegraphics. i remember having to deal with something similar years ago but googling did not bring anything relevant to light. anybody know how to get XeLaTex/includegraphics to not change the image background?", "label": 0}
+{"snippet": "I'm trying to do a diagram of forces. I tilted my rectangle with the right angle as well as the vector pointing upwards. How do I make my Weight vector? I want it to point down and to start at the center point of the tilted rectangle, but i'm not getting how. Here's the code.", "label": 0}
+{"snippet": "Could someone help please! I have to find in analytical way (self-calculate) the eigenvalues and eigenvectors of this system. I also have to write the code in matlab by using tfestimate function. Then compare the results.", "label": 0}
+{"snippet": "Wearing swimsuit should be mandatory. Can this be used as an instruction? I suggest Wearing swimsuit is mandatory. But I want to prove why \"should be\" is not correct in this sentence. Can someone help??", "label": 0}
+{"snippet": "What is the equation-of-state for the photon gas ? Remarks: Here Photon gas = Black body radiation. For more background see How does radiation become black-body radiation?, Does thermal energy include the energy of thermal radiation as part of its definition?.", "label": 0}
+{"snippet": "Do low energy cosmological/relic neutrino-antineutrino pairs annihilate to produce photons at all? Their energy is presently too low to produce electron-positron pairs but there should be an indirect, suppressed path to produce photons. Is there an estimate of the rate or time to annihilate?", "label": 0}
+{"snippet": "Since the problem of quartisection of a disc into four parts of the same area by chords coming from the same point can be solved via Dottie number as shown on this picture: I wonder, whether the problems of trisection and quintisection of disc also can be solved using Dottie number.", "label": 0}
+{"snippet": "Do you know how can one extend this trick to find partial fractions coefficients when the roots of the denominator are repeated? From now, I'm just interested in the cases when the roots are algebraic.", "label": 0}
+{"snippet": "I was reading through Josef Albers' interaction of color (a classical art color theory book), where he makes this point: If I see a substance, or pigment of a particular color, doesn't that mean I'm seeing reflections of primarily that wavelength that corresponds to that color? I don't get this point that it consists of all other colors like white.", "label": 0}
+{"snippet": "I know that a space with an inner product are subset of normed spaces, which are subset of metric spaces, which are subset of topological spaces. My question is: What is the relationship of a probability space with all these other spaces?", "label": 0}
+{"snippet": "We generally know that plasma turbulence creates magnetic field (here, I have assumed that it happens through the dynamo effect). it is also affected by magnetic fields. Is it possible that plasma turbulence could be fluctuated by the earth's magnetic field, if so, does it have any applications (like help generate more plasma turbulence through the magnetic field).", "label": 0}
+{"snippet": "I understand that Toponium is only theoretical because the T quark decays too quickly. My question is this, would a right handed T quark live long enough to form a meson? If not, how long would it take to change from a R to L handed quark and then decay versus form a \"stable\" meson?", "label": 0}
+{"snippet": "Hi to everyone. I don't understand why the diagram in which final antimuon and muon are exchanged is not possible (so having in the upper part positron and muon, downwards electron and antimuon). It seems in all diagrams I seen that in the upper part I must have only antiparticles, and in the lower part only particles (or vice-versa). Is there a specific rule?", "label": 0}
+{"snippet": "Many times in question papers we can see that there's a question on \"how death is romanticized in xxxx poem/ story?\" My question is how do we determine that the writer has romanticized death or suicide, what are the indications?", "label": 0}
+{"snippet": "If I have an unbiased ellipsoid with a known covariance, is there a way I can use that covariance matrix to transform all known points on the given ellipsoid to trace a sphere instead?", "label": 0}
+{"snippet": "I use the integration of zotero and overleaf to store the references I use. However, now that the bibliography file is very big, it takes a long time to add every single reference to the .bib file. Is there a way to speed this up? Perhaps a way in which only some files are uploaded?", "label": 0}
+{"snippet": "I am trying to draw a diagram below using Tikz or mathcha. As for Tikz I do not know how to position a node relative to other two or more ndoes. As for mathcha, I do not know how to connect a line with a text or math box.", "label": 0}
+{"snippet": "\"Modeless\" is widely used which is not in the dictionary such as \"Modal and Modeless Dialog Boxes\". Why they do not use \"modaless\"? If \"Modal\" is the adjective of \"mode\", so \"Modeless\" is the opposite adjective of it. What is the difference between \"model\" and \"mode\"", "label": 0}
+{"snippet": "A passing ship creates a large wave. As it moves shoreward, the wave encounters an anchored yacht which rises up. If the yacht is prevented from falling back to its pre-wave floating position, has the wave transferred an amount of energy (equal to mgh) when it reaches shore?", "label": 0}
+{"snippet": "Does air in the atmosphere suffer friction in some way due solely to the planet's rotation? I mean, if you took a rotating planet with an atmosphere (not being influenced or heated by its star, its nucleus or any other element), would the air get some friction only due to the planet's rotation? Does this slow down the planet's rotation?", "label": 0}
+{"snippet": "I use IguanaTex to insert formulae in PowerPoint. However, the generated formulae look like this . That is, the box is very long. I do not know why and how to fix this. I attach my code here .", "label": 0}
+{"snippet": "Is this a cleft sentence or a \"preparatory it\"? It was my tablet which I didn't realize had fallen off the bed and on the floor. Is it correct? I think it should leave out the structure \"I didn't realize.\"", "label": 0}
+{"snippet": "Does glass undergo internal damage in a similar way to wood when struck hard, even if it doesn't visibly break, and is this damage accumulated gradually over time, or does it occur as a binary response, unlike wood.", "label": 0}
+{"snippet": "This is some sort of attractor I have obtained in the digital oscilloscope. The oscilloscope is connected to a chua circuit of my own design. My real question is whether that the phase plot I have obtained on the oscilloscope is a strange attractor or not? Or is it some other attractor?", "label": 0}
+{"snippet": "I noticed in the first exercise itself that one requires knowledge of the Fundamental Theorem of Arithmetic. What introductory books gives the proof of the Fundamental Theorem of Arithmetic? It'd be nice of the book also explained how to extract roots and find the highest common factors of big numbers alongside proofs of the basic geometric formulas-Pythagoras, surface area of a sphere, etc.", "label": 0}
+{"snippet": "Are there any ways to prove if irrational numbers are really irrational and the digits of decimal does not repeat? Or if maybe irrational numbers are actually rational which the repetition of digits are so far apart we see them as 'irrational'.", "label": 0}
+{"snippet": "In the standard model of particle physics, there are four fundamental forces/interactions, each governed or conveyed by its respective fundamental particle: Strong force: quark/gluons Weak force: neutron Electromagnetism: Photon Is gravitation hence subject to the existence of an analogous fundamental particle, the hypothetical graviton? If so, what, if any, empirical evidence suggests it exists?", "label": 0}
+{"snippet": "The sentence was this: In his process of dying; the children, if they are still not independent of his guidance, shall perish. The expression 'are still not' does not seem grammatically correct. What could be an alternative way of framing this sentence using 'still'?", "label": 0}
+{"snippet": "There are some candidates for tetraquarks, pentaquarks or even now sexaquarks/hexaquarks. But, I wonder, what are the highest molecular quark states taking into account QCD? Are there heptaquarks, octaquarks, nonaquarks, decaquarks...stable enough to be found in colliders or Nature?", "label": 0}
+{"snippet": "Suppose U is a subspace of V such that V/U is finite dimensional. V/U is the quotient sapce, namely the set of all affine subsets of V parallel to U. I think we cannot show that V is finite dimensional, but I am confused without any idea.", "label": 0}
+{"snippet": "I want to visualise how various orbitals are arranged in a multi electron atom. And main confusion Im having is how large or small are certain Orbitals. So is the picture attached giving a good estimate of relative sizes? (I got this form Wikipedia.)", "label": 0}
+{"snippet": "I have a problem similar to the one described in this question. However, additionally to having the size given in the file, I would want to give it specifically in axis units (assuming equal axis). How could I achieve that?", "label": 0}
+{"snippet": "If the strong interaction force between the quarks that make up protons & neutrons get stronger with distance, and if the gluons enabling that force split up if enough energy is applied to them, giving rise to new quark-antiquark pairs, how can atomic fission work? How can atomic nuclei be split up if new quark pairs are created when gluons snap?", "label": 0}
+{"snippet": "Not sure if this counts as a ``high quality post\" but I'd appreciate any advice on the LaTeX template/ package source that I can create a callout with: Here's an image of the desired output:", "label": 0}
+{"snippet": "Pasted below is a screenshot from this super interesting website: https://ciechanow.ski/bicycle/ Are the blue and green forces in the diagram below an action/reaction pair? If so, how does the process of equilibration described in the text make sense? If not, how would the drawing be changed to show the relevant reaction forces?", "label": 0}
+{"snippet": "I wish to determine Plucker coordinates of Infinite dimension Sato Grassmannian. I've been reading the original paper by Sato and other related works, but couldn't understand few things Do Plucker coordinates of infinite dim Sato Grassmanian also fulfill Plucker relations ? If yes, how do we go about determining those Plucker relations ?", "label": 0}
+{"snippet": "So any gravitational field will have a gradient, no? But an accelerating object does not experience any gradient of force. So you should be able to tell if you are in gravity or accelerating by measurement. Right? Is it even possible to experience constant gravity?", "label": 0}
+{"snippet": "moment is equal to force x distance but why is is it so. why is it so that greater the distance less the effort needed? i tried understanding it mathematically but it just went over my head. if any body can explain it in any other way ,i would appreciate it.", "label": 0}
+{"snippet": "I am looking for a good book or review on the treatment of a charged particle interaction (an electron typically) with magnetic, electric and electromagnetic fields. Ideally with both classical and fully quantum treatments.", "label": 0}
+{"snippet": "I am studying Automata theory and in its introduction , there is a statement about conditionals, if A then B is logically equivalent to A only if B. But if B is true and A is false , then if A then B holds true. Then, what about A only if B ? Will it also be true?", "label": 0}
+{"snippet": "I know that when a material is magnetized, the electrons of the atoms get aligned in the same way, they point to the same direction. But then progressively they demagnetize. So, how can permanent magnets mantain their magnetism? What property do they have to do this?", "label": 0}
+{"snippet": "Is there a word for the other party when you do not meet your agreements? I would say something like \"duped\", but I don't want to give the impression it was unfair, let alone planned. I suppose something along the lines of \"let down\", but snappier and less sympathetic. I would say something like 'jilt', but it's not marriage specific.", "label": 0}
+{"snippet": "Consider a one dimensional chain of N classical point masses interacting with neighbor harmonic forces. Is it possible to find initial conditions (positions and velocities) such that non-periodic (irregular) oscillations can be observed ? If yes, what is the relative size phase space that leads to this ? i.e how likely is to observe this ?", "label": 0}
+{"snippet": "How can I stop vim-latex from opening my preamble files open loading the main-file.tex? (It opens all preamble files that the mainfile calls at the beginning in a separate buffer which for me is unnecessary).", "label": 0}
+{"snippet": "The negative mass Schwarzschild metric has no event horizon. Why isnt there a particular radius in which spactime flows outwards at the speed of light? This would imply a region of the solution for which exterior particles could not cross.", "label": 0}
+{"snippet": "When beginning a sentence with an apocopated word, does one capitalise the first letter printed--ie, the second or later letter of the word? Or does one just let the apostrophe stand for the absent capitalised letter? Thank you.", "label": 0}
+{"snippet": "I am looking for a reference (preferably a textbook so that additional preparation material is handy) that calculates the exit time of a Wiener process from a region bounded by sloped lines. Thank you, Gary", "label": 0}
+{"snippet": "At low photon energies, the probability of the photoelectric effect to occur increases, but the probability of the photoelectric effect to happen also increases when going towards most inner shells like K shell but inner shells require much more photon energies to be broken, so isn't there a contrast here? How is this EVEN possible?", "label": 0}
+{"snippet": "We know that the vertical anemometer, just like the cup/vane anemometer, works by measuring how fast the cup/fan rotates because of the wind. But how could we possibly know that the fan rotation is due to vertical winds, and not due to the horizontal winds? Wouldn't the horizontal winds affect the readings of this anemometer? Why, or why not?. image credits: link", "label": 0}
+{"snippet": "In this sentence: Some of the sensitive topics that have dominated xxx talks in the past now seem further down the agenda. What is the meaning of \"down the agenda\" in this sentence?, What is the usage of \"down\"? Is it used as a verb?", "label": 0}
+{"snippet": "Looking at the Wikipedia entry on the topic: Superior Highly Composite Numbers It is true of all numbers listed there. Does this commonality continue forever? Put another way: Are all SHCNs factors of all larger SHCNs?", "label": 0}
+{"snippet": "I have to present in class \"The classical version of the Frobenius theorem\". Here is the classic version of the book \"Foundations of Differentiable Manifolds and Lie Groups\" (Frank W. Warner). I want more references on this theorem with example and applications of the PDE. Could you suggest me some, please?", "label": 0}
+{"snippet": "I am self-studying the book Lebesgue Integration on Euclidean Space by Frank Jones. There is no doubt that this is a great textbook on real variable functions, but the large number of unanswered examples interspersed in the main text makes me look very struggling. So where should I find the errata or exercise answers about this book?", "label": 0}
+{"snippet": "My understanding is that the dimensions of objects change relative to an observer so that a moving cube would no longer be cube shaped and its volume might differ. However, what if that object was absorbing radiation based on its surface area: would a stationary observer see a different amount of heating than a person within the cube? And would this be a paradox?", "label": 0}
+{"snippet": "People have extracted so much underground water that it affects the Earth's balance. Most relative clauses start with a relative pronoun, such as \"that.\" What is the subject in the relative clause above? Is it \"that\" or \"it?\"", "label": 0}
+{"snippet": "When I'm reading about color spaces on wikipedia, I noticed that it only concerns about the power spectral only distribution of a illumination without caring about the phases. I wonder if some frequency components of the light would cancel out, why only using power distribution is enough? If two illuminations are not coherent, then how exactly would their power distributions merge?", "label": 0}
+{"snippet": "Is there any literature related to Slip boundary conditions of friction type for magnetohydrodynamic equations? As there is some results for Navier-Stokes equations with slip boundary conditions of friction type but no result I can find for MHD. Can we use the slip boundary conditions of friction type for MHD specially for its weak solutions. Especially, for weak solutions of MHD equations.", "label": 0}
+{"snippet": "In a chemical reaction, I have studied that a reverse and forward reaction occurs every time and neither reactant nor product can be zero. My question is: if the forward reaction and the backward reaction take place at a particular temperature then how can both the backward and forward reaction take place every time simultaneously?", "label": 0}
+{"snippet": "We know that when an electron jumps from shell to shell it produces light waves which produce the sensation of vision to our eyes. But can anything be said about the colour of an atom in particular. Can anything also be concluded about the colour of any subatomic particle.", "label": 0}
+{"snippet": "Title says it all, but some more examples could be: like vs love pleasure vs euphoria carelessness vs apathy etc. ...essentially words that carry more weight than their counterpart despite having similar definitions. I hesitate to call them synonyms- though that may not be incorrect to say, it isn't the term I'm looking for here.", "label": 0}
+{"snippet": "On my way of satudying Heisenberg matrix mechanics, I get blocked by formulas engaging derivations with respect to a matrix arguments. My question is the following : Is there any mathematically rigorous definition of deriving a matrix-valued function with respect to one of its matrix argument ? thanks in advance.", "label": 0}
+{"snippet": "Pretty straightforward question. Does there exist a theoretical upper bound for the acceleration of a point mass? If not, what is the greatest acceleration of a point mass ever recorded, or that will be reached by new technology in the next few years?", "label": 0}
+{"snippet": "From linguistics, I saw typology. By dictionary, typology is the study of or analysis or classification based on types or categories. So I was wondering if there are some relationships and differences between typology and type and category theories? Is typology the application of type and category theories in specific areas?", "label": 0}
+{"snippet": "I would like to have a line with both equations and text, but the math environment takes over. What can I do so that I can include text in the equation display ?", "label": 0}
+{"snippet": "We have a metal sphere completely immersed in a liquid of density A by means of a string. Since the sphere is exerted by the buoyant force due to the liquid the sphere must also exert an equal and opposite force on the liquid. So wouldn't that contribute to the pressure at the bottom ? (Assuming no atmospheric pressure)", "label": 0}
+{"snippet": "Are photons created in Spontaneous Parametric Down-Conversion (SPDC) intrinsically entangled? If, yes, why to construct all complicated interferometers (Mach-Zender, Sagnac) around it? Is it critical that the photons not be entangled in any degrees of freedom other than the one encoding the quantum information? thank you Vlad", "label": 0}
+{"snippet": "Professor Brian Greene covers a unique angle into the twin paradox by having the stationary observer and the rocket release light beams towards each other in fixed intervals according to their proper time. Here is a screen grab from a demonstration from his course at World Science U: Have any experiments been carried out to replicate what has been shown here?", "label": 0}
+{"snippet": "Where can I read about Valleytronics? Are there any good books or review papers on this topic? And which are the most influential papers? The question was also posted at the Matter Modeling site.", "label": 0}
+{"snippet": "I know that the Ihara zeta function being the same for two graphs does not necessitate an isomorphism between the graphs, but say instead the zeta functions were the same and the zeta functions of their Galois covers were the same. What could we say then? What if the same follows for the intermediate covers?", "label": 0}
+{"snippet": "While I was reading dot and cross products I stumbled upon the well known fact that the dot product yields a scalar and the cross product yields a vector. All I want to know is why. Why does the dot and cross products always yields Scalars and vectors respectively. And also, what led us to define the products the way they are defined?", "label": 0}
+{"snippet": "What does the existence of CTC imply for the Causal Structure of the spacetime? Can a strongly causal spacetime have any CTC[without fluctuating the metric]? Is there any such example? Can someone share please? I'd really appreciate if so.", "label": 0}
+{"snippet": "Good morning everyone! I'm pretty new to reledmac package and, although i read the manual several times i still can't figure out how to put the /pstart number on the outer margin of the page (like i can set line number in the inner margin). Here's an example of what i mean:", "label": 0}
+{"snippet": "I just learned the definition of point-free topologies (also known as pointless topologies). Is every point-free topology expressible as a pointwise topology (so the notion of point-free topologies is nothing but an alternative way to look at existing pointwise topologies), or are there point-free topologies that are not pointwise topologies (so that point-free topologies is indeed a \"proper\" generalization)?", "label": 0}
+{"snippet": "enter image description here hi everyone I have this data of wind direction in radians from -pi to pi (picture is added). any idea which stochastic differential equation (SDE) can represent it? i need an SDE that will produce approximatly this behavior.", "label": 0}
+{"snippet": "Texlive/pdflatex used to produce documents I really liked the look of, which was like this: I have since reverted to the defaults: Is there any way to look in the .out/.log/etc files that produced the first pdf to try to reproduce that look?", "label": 0}
+{"snippet": "Is there some classic example of an universally injective ring morphism which is not a faithfully flat morphism? I was not able to find it in any commutative algebra book and neither around here.", "label": 0}
+{"snippet": "How will the absorption spectrum of a doped semiconductor look if we consider both the dopant as well as the exciton energy levels? And qualitatively, what is the difference between the formation of an e-h pair corresponding to an exciton energy state, and similarly, another e-h pair corresponding to any of the dopant energy states?", "label": 0}
+{"snippet": "The white x-ray spectra (bremsstrahlung radiation) when plotted for different incident electron energies in the same graph, looks very similar to the Black-body radiation curve except for starting from a minimum wavelength. Firstly, what is the governing equation for x-ray spectra which explains such curve, and secondly how is it related to the BB curve.", "label": 0}
+{"snippet": "The question is in the title. I've done some reading and seen that assuming AC, existence of such a function is guaranteed since the cardinals are well-ordered. Can we explicitly construct such a function?", "label": 0}
+{"snippet": "Form what I understand a necessary condition for Riemann integrable function is it must be bounded, and a sufficient condition can be that the function is if a bounded function has finitely many discontinuities. Can someone provide an example where it showed that Riemann integrable function MUST be bounded?", "label": 0}
+{"snippet": "To get some insight on the zero locus of the cubic curve, I've tried a couple of online visualisers on Google and mostly failed to generate the plot (run time errors...) except Wolfram Alpha which gave me the following; Is this visualisation correct??", "label": 0}
+{"snippet": "What is the precise definition of a dust solution in general relativity? If the Einstein tensor of a metric has only the first diagonal term non-zero, it that sufficient for that solution to be called a dust solution?", "label": 0}
+{"snippet": "In a state of quantum coherence, if only a part of a macroscopic object interacts with the environment, does the non-interacting part also have an effect? Does the part that interacts with the environment affect the rest of the part that does not interact with it, so that behavior becomes classically unconditional?", "label": 0}
+{"snippet": "I would like to study string-theory on my own and would like to know the knowledge pre-requisite on mathematics and physics I should master before embarking on my journey to study string theory. Thanks", "label": 0}
+{"snippet": "I have a system of nonlinear equations and what define if it is concave or convex. probably it is solved by using Hessian matrix, but I don't know how to do this. Someone can help me?", "label": 0}
+{"snippet": "Consider this locus Now a property of this is that the angle between the tangent at any point B and the line joining origin to B is constant . My question is why does this happening? I was able to prove this but don't understand why this happens.", "label": 0}
+{"snippet": "What is the mechanism and the reasons of this heat release? I know that the molecules of oxygen are solvated and the hydrogen bonds are rearranged. But for what reasons are heat released and what does that concretely mean? Does it mean that the mean kinetic energy of the molecules is a bit increased?", "label": 0}
+{"snippet": "This is the sentence: The auto-negotiating device will link at the speed of the non-negotiating device, and set its port to half-duplex mode. Can someone explain on what is being referred here when \"its\" is mentioned? Its = Auto-negotiating device? Its = Non-negotiating device? Which does it indicate and why?", "label": 0}
+{"snippet": "A perfectly inelastic central collision of two equal relativistic particles whose kinetic energies are equal to their resting energies results a single relativistic particle (and nothing but it). The mass of the resulting particle is greater than the sum of the masses of the particles that collided, but why and how?", "label": 0}
+{"snippet": "We were asked to determine how many square roots can you construct with the root spiral before overlapping. I attached an image of the root spiral in question and an other image wich contains my work on the problem. Any help is greatly appreciated!", "label": 0}
+{"snippet": "I mean we know proton and electron posses charged that are opposite to each other and they emit electromagnetic radiation perpendicular to each other. My question here is where does this charge comes from at the first place . What process is there that provide charge to these subatomic particles ?", "label": 0}
+{"snippet": "I want to add specific pages from a PDF as backgrounds to different pages in my LaTeX document, creating a new command for each desired image. How can I do this? I'm somewhat new and can't find how to do it.", "label": 0}
+{"snippet": "I have read that despite strong connections between prime factorization and DLP an algorithm for the former does not imply the latter directly. But I was reading about the number field sieve and it seemed like the bottleneck was identifying smooth norms. Wouldn't an ultrafast prime factorization algorithm achieve that?", "label": 0}
+{"snippet": "i know that they arn't in the normal sence connected but how is it that when one particle is observed spinning up the other one \"starts\" spinning down. It can't have always been spinning down.", "label": 0}
+{"snippet": "Toby calls Jetta ugly and gets embarrassed when Sarah calls him out and tells him that he should be nice to her because Jetta's done nothing to him. Days later, Toby calls Sabah a bully for responding to the hate she received from another classmate.", "label": 0}
+{"snippet": "I am a scientist not specialized in plasma physics who has little knowledge in transport phenomena. Please, what are the mechanisms responsible for dissipation in collisionless and collisional fully ionised plasmas? Many thanks.", "label": 0}
+{"snippet": "I read in a physics book that Without clocks of extreme accuracy, the Global Positioning System (GPS) that is now vital to worldwide navigation would be useless. What would be effects on navigation of less accurate clocks in the context of GPS?", "label": 0}
+{"snippet": "There are a few \"question words\" that mirror their answer words- When/Then Where/There What/That Who/Thou (might be stretching it here..) Do these words have origins where this makes sense, or is this a coincidence?", "label": 0}
+{"snippet": "How can make style of theorem like this?.Honestly, I took this picture from the internet because I couldn't do it in latex, and I modified it to show what I want to do in the environment of the theorem.", "label": 0}
+{"snippet": "What we learn about physics can usually be divided into two parts: study of Particle or Wave. We later learn wave-particle duality, etc. Particle is somewhat intuitive, but what's so special about a wave that makes it fundamental? Why not other things?", "label": 0}
+{"snippet": "I am using the textbook 'Introduction to Solid State Physics' to learn about 'PARAMAGNETIC SUSCEPTIBILITY OF CONDUCTION ELECTRON' (Book by Charles Kittel) Consider the diagram when a field is applied I dont understand how we can have total energy which is negative. In the case of the 'parallel to field spin', there is section that shows negative total energy", "label": 0}
+{"snippet": "I know that we can have complex inner products defined such as Conjugate linear to first argument: SUM(conj(lhsElement), rhsElement) Conjugate linear to second argument: SUM(lhsElement, conj(rhsElement)) Can we have a complex inner product defined to be conjugate linear to both arguments, such as SUM(conj(lhsElement), conj(rhsElement))?", "label": 0}
+{"snippet": "I am writing a manuscript. There is a sentence my advisor and I keep editing. The sentence: We did not detect significant effects of lineage, initial length, nor status on individual growth rate. Would it be more appropriate to write the above sentence with \"or\" instead of \"nor\"? If so, why? And why do I have to use \"or?", "label": 0}
+{"snippet": "Suppose I have hexagons that like the ones below but I know the area and the points of each hexagon that represent a cuboid of dimensions g,h,d. How can I find the values for g, h, and d? Any pointers on finding a solution?", "label": 0}
+{"snippet": "In the electromagnetic field, there are NxN points on the incident plane. By changing the phase of the electric field at these points, the desired electric field distribution is generated in the target field, that is, the amplitude and phase of the electric field are simultaneously satisfied. If we can use the LM algorithm, how do we represent the Jacobian matrix?", "label": 0}
+{"snippet": "I am currently very interested in texts, books, and papers that combine topology and logic. I recall reading many years ago a journal article that talked about both topology and the axiom of choice. I would be very glad to see some references.", "label": 0}
+{"snippet": "I'm looking for references which provide good surveys and histories of results related to Gateaux and Frechet derivatives and their relationship to Asplundness and RNP. Specifically, any papers or books which explain the underlying ideas and geometry, rather than simply proving results or leaning heavily on other unexplained existence results as a black box.", "label": 0}
+{"snippet": "Although I say \"Listen to reason,\" if I insert \"voice of,\" do I use \"Listen to the voice of reason\" or \"Hear the voice of reason,\" or can I use either? The topic came up in a class I was giving distinguishing between TO HEAR as a sense verb (not deliberate, involuntary) and TO LISTEN as a deliberate, voluntary verb.", "label": 0}
+{"snippet": "Can we say that an object at rest on the surface of the Earth accelerates in the direction of the ct-basevector, as viewed by an observer standing on Earth? Obviously, there is no acceleration in the space direction.", "label": 0}
+{"snippet": "Below is the simplex tableau in optimal format. I supposed to have identity matrix, but instead I got negative values. This means my solutions are negative. How to proceed further in order to find optimal solution to a problem? Simplex Tableau in optimal format", "label": 0}
+{"snippet": "Is \"stump\" for 'leg' a good choice when the goal is to pick a slang word that is commonly understood by Brits? Or, would, for instance, \"pin\", or any other synonymous slang word, be a better choice for that reason?", "label": 0}
+{"snippet": "I tried reading the English translation of Bourbaki's theory of sets. and I am confused, there is little that makes sense to me. I have experience with Naive set theory, so I was looking forward to learning ZFC and surrounding schemes with some rigour but this is too complex and inconsistent.I am looking forward to some dialogue where I get to know something.", "label": 0}
+{"snippet": "Symploce is two or more sentences / phrases sharing the same beginning and end, but a different middle, while I'm looking for two or more sentences / phrases sharing a middle but different beginnings and ends. Such as in the question: A is to B, as C is to what? And Roses are red, violets are blue", "label": 0}
+{"snippet": "I know that the probability of the electron tunnelling out of the orbital is non-zero, but my question is strictly wrt the energy-time uncertainty at zero Kelvin. Is that probability non-zero as well?", "label": 0}
+{"snippet": "There are certain functions that can be non-differntiable but are still solution to a \"differential equations\". This is fine, as a non-differentiable function can still have an integral. The main question is the following: What does it mean by taking the Laplace transform of Non-differntiable functions.? Isnt it a violation of some rules here and there?", "label": 0}
+{"snippet": "I had my purse stolen during my stay in London. In this sentence, \"stolen\" is used insted of \"steal\". In my childhood, I had a fire break out. In this sentence, \"break out\" is used instead of \"broken out\". Why??", "label": 0}
+{"snippet": "Ou high-school professor told us that a time varying magnetic field in a cylindrical region produces a sort of circular electric field which is Non conservative in nature, because Electric field varies radially, however, I fail to understand why that is the case.", "label": 0}
+{"snippet": "Knowledge hoarder and information hoarder refers to a person who keeps knowledge/information only for themselves,I am looking for a term that can be used to a person who gathers knowledge/information,like a common hoarder but they hoard knowledge or information", "label": 0}
+{"snippet": "Why do we get a null point in potentiometer or meter bridge. I mean the battery is connected so current should keep flowing through the circuit. So why do we get a point where no current is flowing as the battery is connected", "label": 0}
+{"snippet": "Is usage of \"thereof\" in a title: Confirming feasibility of attack and investigating improvements to range and reliability thereof correct? My intuition says it is not, but it would be a pity if this is the case as I don't want to make the title overly verbose.", "label": 0}
+{"snippet": "Can I have another phrase for the sentence/phrase; He is a very easy person to scare. Please I need this because I am writing a story which I'm going to produce when I'm finished...", "label": 0}
+{"snippet": "Is objectual a word? I could not find it in Merriam Webster. I am trying to use it in a sentence like this: A phrase signifies the objectual nature of thing in question. Would I be stretching the grammaticallity of the word object?", "label": 0}
+{"snippet": "What is the word for doing something where said thing is a protest against what you are doing? Example, posting a facebook status that pokes fun at people copying and pasting statuses and sharing them however by posting this status you're doing the very thing you're speaking against.", "label": 0}
+{"snippet": "I have seen a video on YouTube on channel Vsauce about the flat earth belief. There he claims that walking to the edges of this flat earth would be difficult. Something like going up an acclivity. Is this claim true and if yes why? Any answer containing maths would be useful.", "label": 0}
+{"snippet": "I was reading mobility in current electricity and there it was written that the direction of conventional current due to positive and negative current carriers is in the same direction but I cannot understand how and why?", "label": 0}
+{"snippet": "I am currently starting to work on LED but I am confused how can I calculate the external quantum efficiency for my LED? like I know the basic idea, I want to know what experimental setup should I used for my LED and how? In my Lab we have Raman spectrometer with CCD detector.", "label": 0}
+{"snippet": "I understand that matrix is a linear transformation of a vector space and matrix multiplication is applying one transformation over another. I couldn't get a geometric intuition as to why multiplying matrix by its transpose give covariance matrix.", "label": 0}
+{"snippet": "Is there a way to run the --shell-escape command for the LuaLaTex engine in Texshop? I know there are editable TEX and Latex commands in the Texshop settings under Engine->pdfTeX settings, but I do not see anything for the LuaLaTeX engine.", "label": 0}
+{"snippet": "In the Born-Oppenheimer approximation, the effective potential energy, is the potential energy that an electron gains when considering all the inter-particle interactions in a molecule? Said in another way, which particles do experience this effective potential? Is it correct to say that the effective potential is the intrinsic molecular potential energy?", "label": 0}
+{"snippet": "Has the double slit experiment been executed with a proton beam? Electrons and photons seem to get all the attention. What about a particle with positive charge, and one said to be composed of multiple charged entities?", "label": 0}
+{"snippet": "Can someone please explain how the boundary points on a circle are also extreme points? If i take a point inside the circle and one point on the boundary, I can take a convex combination of those two to get a third point on the boundary?", "label": 0}
+{"snippet": "I did part a and b but for part c does the fact that when those three vectors are added gives the zero vector does it mean that they are all perpendicular to eachother? So therefore they would all have the same cross product?", "label": 0}
+{"snippet": "If we have a sealed piston-cylinder with gas inside and we heat it from the outside, the temperature changes. At the same time, if we look at it as a control mass system,the volume increases as the gas expands. Mass remains same. Hence specific volume changes too. So how can temperature and specific volume always be independent?", "label": 0}
+{"snippet": "Can someone give me a strict defenition of a constant sheaf. And I need a nice reference for supermanifolds. Second, concerning the commutation of the pullbacks with the restrictions, how cna I check that in the special case where each of the sheaves is a subsheaf of the sheaf of continuous functions, then the commutation is indeed satisfied.", "label": 0}
+{"snippet": "As generally known, FWD cars are more stable than RWD, but I don't know why and I couldn't find the reason. Can anyone explain me with physics concept? Additionally, I also want to know why driving experience of RWD is generally much better(comforter) than those of FWD.", "label": 0}
+{"snippet": "The compression of a gas produces an increase in temperature and therefore greater kinetic energy of the particles due to the exchange of momentum between the piston wall. Is this transferred energy also capable of producing a sound wave?", "label": 0}
+{"snippet": "Where does the interior Schwarzschild metric come from? How is it derived and why does it have NOT a singularity? Would it mean that the singularity is only apparent and for those out of the black hole (who are ruled by the usual, exterior metric)?", "label": 0}
+{"snippet": "What is the word that means the area of work where someone has experience and knowledge? It should be similar to major, but major doesn't include the work/training expertise that you may have acquired beyond college.", "label": 0}
+{"snippet": "I am planning on doing some personal studies and some poster research for some future conferences in Homological Algebra, does there exist a current list of outstanding problems in the field of Homological Algebra?", "label": 0}
+{"snippet": "If the eigenvalues of a matrix all have positive real part, must the matrices diagonal entries all be positive? This is true of symmetric matrices, however I'd like to know if this result holds more generally.", "label": 0}
+{"snippet": "I have asked to find the condition such that the lines joining focii of an ellipse don't subtend right angle at any point on ellipse.. pllz tell me the condition which i have to apply btw the two lines.. whether in slope format or another.. I am a high school student and suffering problem in this question plzz help..", "label": 0}
+{"snippet": "Consider this sentence. X studied fault structure using method A. Y studied fault structure using method B. However, the geometrical complexity of a fault remained poorly understood. Do I have to use 'remains poorly understood' or 'remained poorly understood'?", "label": 0}
+{"snippet": "When calculating the presence of soliton or anti-soliton in the extreme dimerization polyacetylene SSH model, we say that in the case of open-boundary condition and odd number of atoms, we must have an edge soliton. But why is that the case? I understand that we must have a soliton, but why is the edge mode preferred over the bulk case?", "label": 0}
+{"snippet": "How do I merge cells irregularly in tables? I need to do this stuff for homework and don't feel like printing it out, writing it by hand, and scanning it back in to upload. I could just hide the borders on the cells above the Answer column but then text wouldn't flow into that area. I want a real non-rectangular cell.", "label": 0}
+{"snippet": "What is the origin of stretch as it is used in the following sentence? We should eat before the final stretch. In this context, final stretch is used to mean 'last segment', or 'the effort needed before the work will be done'. Is this use present in dictionaries?", "label": 0}
+{"snippet": "What's the difference between the term \"parameter\" and the term \"argument\" in TeX jargon? Are outermost enclosing pairs of matching curly braces of undelimited arguments to be considered components of these arguments? Are delimiters of delimited arguments to be considered components of these arguments?", "label": 0}
+{"snippet": "A colleague has written: If you are encountering any more problems please don't hesitate to reach out. Reading this, I believe it should phrased: \"If you encounter any more problems...\" but I cannot describe why - the language tools I have tested say the original is \"clunky\" or have no complaints. A) Is the original technically incorrect? B) If so, why?", "label": 0}
+{"snippet": "I know that free ultrafilters are defined in contrast to principal/fixed ultrafilters. Nonetheless, is there some categorical way to view the use of the word \"free\" here (e.g. some pair of adjoint functors), or some universal property that free ultrafilters satisfy?", "label": 0}
+{"snippet": "If object is at rest relative to the Earth's surface on a frictionless surface. What is the effect of Earth rotation and orbiting on an object? Does object rotate and orbit with Earth and stays at same position due to gravitational force. Or object stays same location and earth rotate underneath it?", "label": 0}
+{"snippet": "Shwezigon Pagoda's appearance always makes me feel powerful. And it also made me consider how mighty Bagan and our nations were back in those days. Or should I be using \"and also it\" here? Does it make a difference?", "label": 0}
+{"snippet": "I read the octet and decuplet baryons symmetric and anti-symmetric wavefunction from 'Riazzudin and Fiazzudin's book. But I am little confused about the wavefunction of neutral sigma and Lambda baryon. What is the exact form of the wavefunction of baryons?", "label": 0}
+{"snippet": "There exist sites such as https://shouldiblamecaching.com/, https://isitdns.com/, and https://isitchristmas.com/ that use the domain name to ask a question and show a simple yes or no answer. Is there a term that can be used to refer to this category of websites?", "label": 0}
+{"snippet": "Is there a term for a \"union\" or \"meeting\" between Kings? An example would be: four different kings go to a meeting in one's realm to discuss politics. (Though I really don't know if it was a common practice or has a name.)", "label": 0}
+{"snippet": "My friend said that it is 'boae constrictor' since 'boa' is in Latin. But I told him that first of all, it would be more correct as 'boae constrictor(s)', but the actual correct form is 'boa constrictors'. Which one is it?", "label": 0}
+{"snippet": "In a question on a different SE site the title is as follows Writing the introduction section of an academic journal while the question is about writing the introduction section of a paper that will be published in an academic journal. What is this rhetorical device (i.e. saying \"the journal\" while instead referring to an article inside the journal) called in English?", "label": 0}
+{"snippet": "In general relativity, there is a definition of the surface gravity that is associated with the Killing vectors, is there a similar definition for the interior of stars/compact objects? I would expect that if I measure the surface gravity inside and near the surface of the star and outside it should be the same.", "label": 0}
+{"snippet": "Want to know if this sounds OK. Here I am asking a friend if it's OK for me to come over to her place to return her book. Hi, Was thinking to come return your book today, would you be home? Thanks", "label": 0}
+{"snippet": "If I have a spool of thread with a force pulling to the right on a rolling cylinder, how can I mathematically determine the direction of the friction? . .-----------> F . . . . . . . . . . . . . . . . ^^^^^^^^^^^^^^^^^^^^^^^^", "label": 0}
+{"snippet": "What is so different between the molecules that have already evaporated but below the critical temperature than those that exist after reaching the critical point? If there are gases above critical temperatures that cannot be converted back to liquid, are there any critical liquids in the sense that they cannot be frozen back to solids?", "label": 0}
+{"snippet": "could someone recommend some references where the problem of constructing an accurate map of the Earth is tackled from the point of view of general maps between manifolds (so something like this and not like this) ? Thanks!", "label": 0}
+{"snippet": "Considering the hyper-fine-structure configuration of the H-atom, why is its stable, low energy state (or the \"flipped-back\" state) the state when the spins of the electron and the proton point in the same direction, ie are parallel (and not antiparallel, as is sometimes stated in the literature)?", "label": 0}
+{"snippet": "For Vacuum fluctuations based QRNG source, how will the linewidth of the laser source affects the shot noise. If we decrease the linewidth of the laser source, will we get a better output.", "label": 0}
+{"snippet": "I am doing a quantum mechanics question involving the positivity of the norm. So I'm using the fact that the norm will be greater than zero but i want to apply an operator onto the ket on one side of the equation, is it a legal operation to apply the operator to the zero on the other side and say its still zero?", "label": 0}
+{"snippet": "I'm working in ZFC and wondering which axioms can be considered constructive. I find Axioms of Pair, Union, Empty Set, Infinite, Power Set and Replacement to be clearly constuctive. Choice and Regularity/Foundation are non-constructive. I've read here that constructive Zermelo-Fraenkel considers Extensionality. How is Extensionality constructive?", "label": 0}
+{"snippet": "For example, someone spoils a show or says something is poorly written. Originally you may not have thought or noticed that but suddenly your view starts changing to become similar or the same as their view.", "label": 0}
+{"snippet": "It's said that Neutirnos can only make up a tiny fraciton of dark matter. So why can't Dark matter be mostly made up of Neutrinos? Why can't there just be a huge number of them? I suspect myself that neutrinos are so light that they end up being \"too fast\". But I'm not sure myself.", "label": 0}
+{"snippet": "Three forces P, Q and R act along the sides BC, CA, and AB respectively of a triangle ABC in order to keep the system in equilibrium. When will the resultant force touches the inscribed circle.", "label": 0}
+{"snippet": "I was looking at my neice's second grade note book in which was the question \" Where did the four cows live? \" but her mam corrected it to \"Where did the four cows lived?\" I think it should be live as we use first form of verb with did. Am i wrong?", "label": 0}
+{"snippet": "Are there any colours that our human eye cannot comprehend but other animals can see? The ability to see colours is the property of our eyes. For example an average dog would see less colours than us. So does this imply that there could be colours which the human mind cannot comprehend while some animals can see them?", "label": 0}
+{"snippet": "If we put some blocks on a piston and the piston moves downwards giving pressure to the gas, will the pressure by external mass(blocks) on piston and pressure by piston on gas be the same?", "label": 0}
+{"snippet": "Spanish speakers use 'basket,' for basketball, 'smoking' for black tie and 'freaki' for geek. They also use 'camping' for camp site and 'parking' for car park, but the participles retain the same meaning. The latter are loan words, but I wonder whether it's accurate to use the term 'loan word' if that word undergoes a significant shift in meaning.", "label": 0}
+{"snippet": "I have been reading about Hackenbush recently and have learned that the surreal numbers can be represented using RGB Hackenbush. I am having a hard time understanding On, Off, and Oof. What Hackenbush games represent these numbers?", "label": 0}
+{"snippet": "Fascinated by the font of this journal, and found out it's ITC New Baskerville Semi Bold. How to add this font to the overleaf tex, the closest package I could find is baskervillef and librebaskerville.", "label": 0}
+{"snippet": "There should be opposing viewpoints so that discussion can take multiple turns AND people can finally reach a solution that neutralizes both viewpoints. Should there be a comma before \"and\" in this sentence because both are independent clauses?", "label": 0}
+{"snippet": "My question is not why this is different than in the near field where it was measured by Hertz. I am asking for a source with a description of who measured it in the far field and how.", "label": 0}
+{"snippet": "I just recalled the previous winter that I had stood in front of our heater to get warm. I then observed that the heat that was going up had a shadow on the wall behind the heater. I suspect those were the shadow of the air molecules. But I can't prove.", "label": 0}
+{"snippet": "Fermions with no electric charge may carry magnetic moments e.g., the neutron. Since particles with magnetic magnetic moments interact, they're expected to scatter off each other electromagnetically. How does QED describe such a scattering?", "label": 0}
+{"snippet": "As capacitance is the ability to store charge therefore we say conductors can show self-capacitance but why can't insulators? we can store charge on insulators as well so why can't they show capacitance?", "label": 0}
+{"snippet": "I am teaching an introduction to pure maths module. Are there any really good resources on relations? I want something that will have an impact and motivate the learner. I am not really looking for artificial engineering examples but some bona fide real applications.", "label": 0}
+{"snippet": "The energy is not Lorentz invariant quantity since energy depends on the state of motion. Then how come the physics is the same in every inertial reference frame when every inertial frame measures different energy?", "label": 0}
+{"snippet": "I'm new to capillary forces and I found this statement: I found Jurin's law or the Young-Laplace equation, but it's always about capillary tube and I would know how to find this expression. Regards", "label": 0}
+{"snippet": "I was curious as to why the \"Law of Reflection\" is only a law and not a principle. Are there any specific conditions or circumstances where it is not followed by chance? If so, how so? Note: I am not discussing about or referring to anything in special theory of relativity, however the reader may offer information on it as well.", "label": 0}
+{"snippet": "I am trying to input the non numbered section bibliography in my summary in a document using lyx, but it has been appearing only if I number the section. Is there an alternative ?", "label": 0}
+{"snippet": "Why is it that the water which constantly passes through the core of a nuclear reactor doesn't become radioactive? Despite passing so closely to the active nuclear fission reaction, as gamma particles are capable enough to penetrate thick surfaces. It ends up being converted to steam. What actually is going on in it?", "label": 0}
+{"snippet": "From our point of view in our Galaxy, his center, Sagittarius A, is a super massive black hole. At event horizon of this singularity, gravity stop time. Is there any reason why time would not run in reverse, on the other side?", "label": 0}
+{"snippet": "What is the maximum number of operations that can be defined on Cbits (like mechanical switches) and Qbits (like quantum states)? If they are different how will the ratio change if we limit ourselves to Reversible circuits? Edit: By operation I mean that a n-bit state remains an n-bit state", "label": 0}
+{"snippet": "If objects gain mass as they approach the speed of light, is it possible that as a photon \"attempts\" to exceed the speed of light it gains enough mass to interact with the higgs field immediately slowing it back down until it no longer has enough mass to cause an interaction?", "label": 0}
+{"snippet": "Propositional logic and first-order logic are theories in ZFC. The principle of structural induction is a theorem of ZFC. Is that what justifies the usage of structural induction in propositional logic and first-order logic? By justifying I really mean proving, that is, tracing back to axioms. Meaning of structural induction: Sturctural induction.", "label": 0}
+{"snippet": "When Austin Powers says this phrase? Is it considered to be somewhat of an exception to normal use, like with, Myself is often used where I or me might be expected, Or was it more abnormal than that, and was just a joke? I'm not sure of other instances where it's used commonly in a similar manner.", "label": 0}
+{"snippet": "According to Special theory of relativity, magnetic field is equal to electric field if we see it in a frame of electron (in the frame of electron) but why we have to see it in accelerating frame? Why can't we just see in stationary frame?", "label": 0}
+{"snippet": "A lot of sources stop expanding the taylor approximation at the second order Hessian matrix for a multivariable function. I'd like to include the third order taylor expansion. Does anyone have the matrix equation for this and have any sources talking about it? Is there a name for the third order derivative matrix?", "label": 0}
+{"snippet": "From what I understand, the voltage and current waves propagate down the input transmission line, hit the nonlinear oscillator, and then bounce back toward the generator. How are gates such as the X or the Hadamard encoded into these waves?", "label": 0}
+{"snippet": "HOM is a two-photon interference effect where temporally overlapped identical photons coming perpendicular to a beam splitter must leave it in the same direction. How is momentum conserved in this process? Initially, the total momentum of the photons is only on the x-axis, but after the beam splitter, it has a y-axis component. Does some momentum pass to the beam splitter itself?", "label": 0}
+{"snippet": "Electric charges are of two types - positive and negative charges.electrons are negatively charged and protons are positively charged. If the term electric means electrons and electric charge means negative charge why do we include protons? How can a charge be positive? Please correct me if I'm wrong . Thank you", "label": 0}
+{"snippet": "Which are common protocols to measure the light transmittance of glass (example: a window)? I have searched for references and officials standards without success. Which tools can be used to achieve this measurement ?", "label": 0}
+{"snippet": "Which sentence is more grammatically correct? Welcome to a new way to travel Welcome to a new way of travel (We are promoting our airport service which allows one to avoid stepping foot inside the airport to get to their commercial flight. )", "label": 0}
+{"snippet": "So I want to write my notes where there are lists connected with vertical lines. I want the exact format displayed as in the below photo where in the nested lists the \"main\" line is stretched. Also I want this design to be added in the preamble. Thanks!", "label": 0}
+{"snippet": "I have long been curious about a particular English (in parts of GB) phrasing habit. For example: Oh she's lovely, she is. That's a nice one, that is. You should keep doing that, you should. I am curious what that repeat is called, how it came about, and anything else I can find out.", "label": 0}
+{"snippet": "I recently discovered that if is considered a preposition in contemporary grammar. Is \"when\" considered a preposition as well? And in the following sentence, is the chunk introduced by when considered an adjunct, or as integral in that it provides the referent for \"it\"? I like it when you say \"indubitably\".", "label": 0}
+{"snippet": "I am interested in learning about differential graph theory or differential operators on graphs, something related to what E. Bautista introduced in his answer here. Can one suggest a textbook in which such topics are discussed? (The quoted answer refers to some papers, but I prefer a book covering a comprehensive treatment of the topic.)", "label": 0}
+{"snippet": "I am working on a paper on how pivot rule selection influences the time needed for LPSolve to solve a problem. I have decided to write some teory about different algorithms, but i can't find anything about the \"First index\" algorithm. Anybody know what it is, maybe know anything I could use as literature about it?", "label": 0}
+{"snippet": "In this image, power is used to apply voltage to the charged grids. But if no voltage is applied, would ions still be accelerated by Coulomb forces to create thrust? If not, why?", "label": 0}
+{"snippet": "I found these two common English words (snarky and smarmy) that seem like forms of a literary device. However, unlike onamatopoeia, the comparison is not made with sound, but rather it is more from the \"visual\" images/memory that they evoke. What is this called in terms of \"literary technique\" (if not onamatopoeia)? \"Synesthesia\" perhaps?", "label": 0}
+{"snippet": "I am finishing a book with a bunch of complex TikZ embedded pictures, some with complex path decorations and so. I wonder what is better, to include the whole list of usetikzlibrary{} at the top of the LaTeX doc or specify the needed ones inside each tikzpicture, yet repeating", "label": 0}
+{"snippet": "This is more a vocab question than anything else but what \"type\" of thing are injective, surjective, bijective. I fully understand what these words mean but I'm looking for a word to describe the type of properties these might be. Basically \"odd and even\" is to \"parity\" as \"injective, surjective, bijective\" is to what? Thank you all!", "label": 0}
+{"snippet": "Anyone have anything? I'm writing a \"proof\" for something and it came up. I'm stupid (as username suggests) and it would take way too long for me to solve it, and I wouldn't want to delete it since I want to just write QED in place of the proof for the solution", "label": 0}
+{"snippet": "I'm looking for a good noun to describe a character who can use Comakinesis, which is hair manipulation, but \"Comakinesis-user\" isn't good enough. Also, I can't find a word to describe hair manipulation in a magic user word ending in 'mancer' so I'm wondering if kinetic ability names have any kind of word form like that?", "label": 0}
+{"snippet": "Past Perfect can't be used on its own, can it? I mean, if there is a sentence without context, just a sentence on its own, and there is no clause with predicate in Past Simple in it. Is it grammatically correct to use it in American English? Like in this example : John had already given his present.", "label": 0}
+{"snippet": "I've seen loads of cars that skid during a curve due to taking it with a high velocity. I can guess that it has to do with the grid with the road and maybe something to do with centifugal forces?", "label": 0}
+{"snippet": "I have heard a couple of people use intriguement casually but there is nothing online except for a listing in the Urban Dictionary: intriguement the feeling of being intrigued He was nearly as old as her father, much to Martha's intriguement. So, is it an actual word?", "label": 0}
+{"snippet": "When using the proof environment provided by the amsthm package, you get an empty square box at the end of your proof as the default QED symbol. Question: Is there a way to make it automatically put \"QED\" for some proofs but not others? Essentially, can one create a second proof environment which puts a different symbol at the end?", "label": 0}
+{"snippet": "I try to write this equation on overleaf and numbering in second line (the same as in the picture) but I couldn't. Another problem is when I use align or equation, the prime in max' function goes to the center but not the right of max. Help me!!", "label": 0}
+{"snippet": "I am looking for a \"thick\" book on complex analysis, which also has historical details such as the motivation behind it. Which problem lead to the creation/discovery of a certain topic. E.g. what is the reason behind fundamental groups how is it in connection with topology. Thanks in advance.", "label": 0}
+{"snippet": "When calculating the displacement of a rolling body do we just calculate the displacement due to Vcom in a particular time t or additionally need to consider also the displacement that may be produced because of the rolling motion.", "label": 0}
+{"snippet": "I saw the excellent answer here: Did the Big Bang happen at a point? but I have a hard time imagining the initial state. If the distances between all points in the universe were zero at the Big Bang, how is it not a single point in space?", "label": 0}
+{"snippet": "Relation between elements of essential spectrum and the eigenvalue of a self adjoint operator. In particular, is there any way we can say that the element of essential spectrum is an eigenvalue of infinite multiplicities of a self adjoint operator. Any idea or if there any article related to this concepts or any book will be helpful.", "label": 0}
+{"snippet": "Is there any way to reasonably restrict control points of cubic bezier curve so it's oscilating circle will never have radius smaller than r? Bezier curve with it's oscilating circle I need to find the conditions that control points have to meet, so curvature of the bezier is never too large", "label": 0}
+{"snippet": "I used a reference manager for my bibliography and added personal notes to all my refernces to organise them. Now using bibtex (bibliography style unsrt) these notes appear in my bibliography. How can I exclude the notes from my bibliography without having to alter every entry in my reference library?", "label": 0}
+{"snippet": "Is there some interpretation for the eigenvectors of the Laplacian of a (directed) weighted graph? Normally, the spectrum of a Laplacian informs us about connectives, is this also the case for a weighted graph?", "label": 0}
+{"snippet": "I have found lots of numbers that can be done two ways but can't seem to find any that are done three or four ways. I believe there would be a way to use complex numbers to help with this.", "label": 0}
+{"snippet": "from wikipedia (if you say it's false I believe you): A series of independent states (for example, a series of coin flips) satisfies the formal definition of a Markov chain. However, the theory is usually applied only when the probability distribution of the next state depends on the current one by definition, the next coin flip should depend on the current one, no?", "label": 0}
+{"snippet": "I don't feel so confident in the sign convention on this example, wouldn't a clockwise angular velocity mean negative sign not positive? Why is my answer and the books answer positive, and it seems like it should be negative to insinuate clockwise direction?", "label": 0}
+{"snippet": "Just like the title, I really can not understand how brownian-motion can be nonmonotonous. I thinck the probability of a brownian-motion moving in same direction in a really short interval can be a positive number.", "label": 0}
+{"snippet": "I've got this message from a quite respectful software library: A value is trying to be set on a copy of a slice from a DataFrame. Shouldn't it be something in passive voice, like \"The value is being tried to be set..\"?", "label": 0}
+{"snippet": "It is well known that for every monad T, we can consider the Eilenberg-Moore-Category and get an adjunction which induces T, similar for the Kleisli-Category. But since every adjunction induces a Comonad as well, my question is what are the Comonads in the Eilenberg-Moore-Category resp. the Kleisli-Category that are induced by T in this way?", "label": 0}
+{"snippet": "I can't, for the life of me, understand chain rule on conditional distributions of random variables. I can't see the pattern. Like, how do I find out what things like these are: P(A,B|C) P(X,Y,Z|W) P(U|V,W) P(M|N,O,P) P(H,I|J,K)", "label": 0}
+{"snippet": "Recently I have been studying conic -sections in my school . The problems given in the course are good but I am looking for any resources where I can find new theorems and strategies to solve the problems of comics. I want a resource which can provide Olympiad-like geometric problems on conic sections. So please can anyone suggest any good resource for such problems?", "label": 0}
+{"snippet": "My doubt lies in the fact that gravitational waves are produced even before the merger so I kindly ask an expert to make me a clear picture of the source of energy of grav. waves before the merger and the energy after the merger that we are told is gained by the vanished masses of the merging objects.", "label": 0}
+{"snippet": "In other words, would this construction be proper? And if so, is there a name for it? The court then turned to negligence, which issue it easily resolved. (As opposed to \". . ., which it easily resolved.\") Aha. I missed this when I first looked at MW. I think it's the third definition under the first section: https://www.merriam-webster.com/dictionary/which", "label": 0}
+{"snippet": "if we covered all the deserts with solar plates , would that be the solution to the energy crisis ? i mean put a solar plates in ALL the deserts of the earth to harvest all solar power", "label": 0}
+{"snippet": "Much like McGyver meaning \"resourceful,\" Einstein meaning \"intelligent,\" Savant meaning \"gifted...\" I remember hearing and using a name to refer to someone as a charismatic go-getter. Another word that comes to mind is \"maverick.\"", "label": 0}
+{"snippet": "As long as the time dilation is about what the observers think or see, there would be no great difficulty. But the assertions that the clocks run faster or slower cannot be justified.", "label": 0}
+{"snippet": "Power at the receiving antenna is given by the Friis transmission formula, which says that the received power is proportional to the wavelength squared. But energy carried by an electromagnetic wave E=hc/lambda which is inversely proportional to the wavelength. Shouldn't they both have the same relationship with wavelength?", "label": 0}
+{"snippet": "What are the long metal things in stores like Walgreens that hold things like gummy bears or nuts or hair clips? The metal things are straight and then at the end they curve up, and they are connected to the wall to carry things without using shelves.", "label": 0}
+{"snippet": "Why when a person is standing still on a floor we say that the force that this person acts on the floor equal to it's weight? , Isn't the weight the force that the earth pulls the person and acts only on the person, how then this force goes to the ground ?", "label": 0}
+{"snippet": "My teacher told me that in anode ray experiment the electron were emitted from the gas present inside the vacuum tube and the ionized electron form cathode ray and ionized gas form anode ray. So I wanna know thus atoms present inside the vacuum tube were fully ionized and only their nucleus remain? So for my bad English.", "label": 0}
+{"snippet": "From a point just north of the equator, A straight line to the Magnetic North would be through the earth. If a compass was turned on it's side, would the north pointing arrow point toward the ground along that straight line?", "label": 0}
+{"snippet": "I know that currently dark matter and dark energy are separate things, not related and one not deriving from the other. But if both are included in a generalized gravitation theory, the picture can change. Then there may be a correlation between the dark matter and dark energy, and they may then have a common origin.", "label": 0}
+{"snippet": "thank you all. I can translate from language to another manually. Are there any way to translate a lyx document, for example, from English to Arabic in the same way as in a Word document such that the mathematical expressions remain as they were? I want do this automatically by a lyx function if possible.", "label": 0}
+{"snippet": "I have a hexagon with interior with the opposite sides being identified. In order find the identification space I did the following cutting and pasting. My question is : Is it correct way to do the identification? I have heard cutting is not a continuous operation. That's why I am confused. Could anyone give me some suggestions in this regard? Thanks for your time.", "label": 0}
+{"snippet": "Modulational instabilities occur in waves which occur in nonlinear system. A linear stability analysis is done to examine the dynamics in the short-time regime to observe the structures which spontaneously form. What methods are there for examining the structures in the nonlinear regime?", "label": 0}
+{"snippet": "The focus on the exterior of a building alone will lead to the increase in construction cost, making such an endeavour unjustified. I want to know about the grammatical structure of this part: making such an endeavour unjustified.", "label": 0}
+{"snippet": "All chapters begin a new page by default. I want to remove this break between two short chapters. By the nopagebreak doesn't work. What can be the cause? Is there another way to do that? I don't give all my code there, but I can write some details if needed.", "label": 0}
+{"snippet": "I already posed this question Negative energy solutions in Klein-Gordon and Dirac equations but I am not satisfied with the answers. Trying to be very sharp: does Klein-Gordon equation have negative energy solutions like Dirac one or are they (the solutions) somehow different? if they are the same, why the problem of negative energy is always referred to Dirac equation and not to KG?", "label": 0}
+{"snippet": "In my complex analysis course I'm supposed to compute all entire functions with the given requirement for the Real part. How do I work on this? I hav no clue how to work this out. Can someone please give me a hint?", "label": 0}
+{"snippet": "MPM combines elements of both the finite element method (FEM) and the particle-based methods. It is particularly suitable for problems involving large deformations or fluid-solid interaction. Would you apply it (after proper editing) to wave propagation problems, where there is no mass transportation, but only energy transportation?", "label": 0}
+{"snippet": "How does protons collide and produce heavier particles if light particles can not decay into heavier particles ? considering particles can not decay into heavier particles irrespective of their energy. How can we see heavier particles at CERN if only the protons are colliding ?", "label": 0}
+{"snippet": "I am doing a course on rotational movement of solid rigid objects and a professor of the MIT symbolizes the axis around which the object rotates with a symbol that is a letter with a vertical line on top of it and another one below it. Is there a simple way to do that in a line of LaTeX?", "label": 0}
+{"snippet": "\"In physics, gravity is a fundamental interaction which causes mutual attraction between all things that have mass\" \"Light or visible light is electromagnetic radiation that has no mass\" My question is how can gravity swallow light ?", "label": 0}
+{"snippet": "What do you think is a suitable word to use instead of the informal \"stuff\" here, and is \"appropriate\" used correctly in this context? I will give you the number of the appropriate team that will be able to help you with questions with regard to administrative or financial [stuff].", "label": 0}
+{"snippet": "In English, when speaking about going to the center of the town, it's a matter of going to the \"downtown\" so, my question is about the origins of the connotation of some \"descent\" (going down) - moreover, I noticed that the same phenomenon is present in many other languages...", "label": 0}
+{"snippet": "\"As we look on on the conflict\" I want to use the phrase \"look on\" but am not sure how to incorporate it into the sentence. Would be \"as we look on at the conflict\"?", "label": 0}
+{"snippet": "Is there an adjective of intensity (or similar term related to force) that ends in \"-al\"? like: space > spatial, time > temporal, etc. Intensity is meant as the physical attribute/dimension of some physical phenomenon. Sample sentence: \"... the high (...adjetive of intensity needed here...), temporal [adjective of time], and spatial [adjective of space] resolving powers of macroscopic observations require that ... \"", "label": 0}
+{"snippet": "I am new to topic \" Algebraic Grid Generation\". I want to find a simple example where we solve the host equation, let us say the heat equation, numerically in the computational domain then transform it back to the physical domain. All the references I found discuss the general steps without providing a single practical example", "label": 0}
+{"snippet": "What does \"which\" refer to in the following sentence? The final jurisdiction over what an intellectual is resides in culture, which becomes almost coterminous with a singular public opinion.(https://dictionary.cambridge.org/ja/dictionary/english/coterminous) I think it refers to an intellectual, but I'm not sure.", "label": 0}
+{"snippet": "Like in adiabatic process there is closed system but in reality we know there is no such thing as closed system there will be still exchange of heat so it will not work adiabatically means it is only applicable for ideal gas not real gas?", "label": 0}
+{"snippet": "I would like to know if it is possible to use the Concrete font together with the standard LaTeX mathematical font. If it is possible, could someone please tell me how to do this? My thanks in advance!", "label": 0}
+{"snippet": "You encounter them periodically in movies, and, in certain places, in real life. I asked people who live in a region positively studded with castles, and all they could come up with was \"the peeping slidy thingy in the entrance door.\" Which is amusing but doesn't answer the question. What's it called? And the slide - does it have a separate term?", "label": 0}
+{"snippet": "A friend said something to their dog and it was meant for me. I told her that I am pretty sure that is passive aggressive, but don't think I am correct. What is this called? I attempted wording it several different ways, but continually received links that were not applicable.", "label": 0}
+{"snippet": "Such as the natural linewidth is defined to be angular frequency, while the absolute frequency of laser is frequency. By far I haven't found a good way not to learn it by roting. Would anyone be willing to share with me your thoughts if you have a better way?", "label": 0}
+{"snippet": "i am confused about a result in paper related to reflectivity from etched hole in silicon. The reflectance oscillation varies with surface roughness but i am not getting similar oscillation while simulating in fdtd lumerical. the model paper is based on fresnel equation.", "label": 0}
+{"snippet": "It is possible to get quadrature squeezed light where on one quadrature the uncertainty is less than the of a coherent state while in the other one, orthogonal to it, it is larger. Is it possible, by doing an appropriate angle transformation, to go from a quadrature squeezed state to a photon-number squeezed state (sub-Poissonian distribution)?", "label": 0}
+{"snippet": "I have a feeling that the word \"ingredient\" implies that it was intended to be there by human, while catechin is not an additive, but was naturally in the tea leaves. Giving another example, is polyphenol a healthy ingredient of wine, a composition, or a compound of wine?", "label": 0}
+{"snippet": "I believe that electric current is a kind of force (even when we consider it to be opposite to the flow of electrons). If it is so then what is the nature of this force ? And also tell me if there are energy carriers in that constitute this force.", "label": 0}
+{"snippet": "I've learned that the Hamiltonian Operator corresponds to the total energy of the system when applied to a general wave function. After applying and obtaining the measurement (energy), the wave function turns into the eigenfunction. Does the wave function before the operator is applied have to be an eigenfunction of the operator, or can the operator be applied to any wave function?", "label": 0}
+{"snippet": "An interior point of an equilateral triangle ABC is M. The projections of M on the sides of the triangle respectively: points E, D, F. Let G be the centroid of the triangle EDF. Prove that G is the midpoint of OM if O is the circumcenter of triangle ABC.", "label": 0}
+{"snippet": "I remember author of some textbook alluding to Zassenhaus and Knuth's bound of the zeros of a complex polynomial.Unfortunately after even after days of search I could not find some reference or source for it.I would be highly obliged if somebody could provide some source", "label": 0}
+{"snippet": "Assuming that there is no form of resistance in the primary circuit, and that the secondary circuit contains resistance, will current in the primary circuit be infinite? Will resistance in the secondary circuit provide resistance in the primary circuit? Thanks in advance.", "label": 0}
+{"snippet": "I came across a problem where a piston and gas arrangement was present and it was heated, so if the piston is free to move we call it isobaric. But is it only true if it is quasi static (reversible process) or also for a normal irreversible process, and if not will that process be some polytropic process.", "label": 0}
+{"snippet": "This is from a test: What on earth have you done to your hair? Oh. I've had it cut, do you like it? I am wondering if the comma after \"cut\" is justified. Would a period, dash, or semicolon be better in its place?", "label": 0}
+{"snippet": "Regarding linearly polarized electric fields that are produced by a dipole antenna and electric fields from a current carrying wire, are the equipotential surface the same as the magnetic fields? Because both are perpendicular to the electric fields.", "label": 0}
+{"snippet": "I am writing a document using overleaf and spellcheker underlines all words with red, it looks like this: How can I fix it? By some reason it did't underline all words in other documents that I wrote.", "label": 0}
+{"snippet": "I know that random forcing does not add unbounded reals. Is a Cohen real always unbounded? I can proof that the product of two random forcings adds a Cohen real. How can I show that the two step iteration of random forcings does not add cohen real?", "label": 0}
+{"snippet": "Is the equation T=M/F where T is residence time, M is quantity and F is flow rate equivalent to W=L/lambda where W is waiting time, L is queue length and lambda is flow rate? It seems to me that the derivation of either equation would be equivalent to the derivation of the other.", "label": 0}
+{"snippet": "I read a previous question \"superconductor levitating in earth's magnetic field?\" it seemed like the impact of gravity would make this unikely unless the superconductor was super light. Is it conceivable to combine the properties of aerogels and superconductors to create light material that repels the earth's field? basically is the synthesis even possible? and if so what might it require?", "label": 0}
+{"snippet": "Programmer here. I sometimes catch myself saying that something is a Tautology False because it always evaluates to FALSE or OFF. I know Tautology means always True in discrete math but I use it to describe something that doesn't change. It's always constant in being False or Null, etc. Am I being illogical.", "label": 0}
+{"snippet": "By default the hyperlink in the list of acronyms is in the page number. Is there a way to change this such that by clicking on both the acronym and page number it takes you to its first occurrence? Kind of like using linktoc=all in for the table of contents.", "label": 0}
+{"snippet": "when I look up into the night sky I see planets, not twinkling like the other stars, but still illuminated. However, when the Hubble or James Webb telescopes approach planets we see the local features instead of an illuminated sphere in space. why is that?", "label": 0}
+{"snippet": "I am looking for the very first published experiment in a relevant journal with all the following features: Michelson or Mach-Zender light interferometry is demonstrated The arms of the interferometer are optical fibers The light used is a slow sequence of single quanta (aka single-photons) generated with on-demand methods (e.g. Quantum dots). Does anyone know the reference of this article?", "label": 0}
+{"snippet": "A red light and blue light enter a rectangular glass block normal to its surface at the same time. Strictly speaking, after passing through the block, which pulse exits first? Should I consider their paths inside glass slab to be same as the lights are entering normal to the surface?", "label": 0}
+{"snippet": "I am building an online LaTeX editor and now face issues with slow compilation for documents of increased size. Everytime the user changes the document, the compiler has to recompile the whole document. Is it possible to only compile the changed part and speed up compile performance that way?", "label": 0}
+{"snippet": "I know a and l, and that the dotted lines are parallel, how can i determine the angle alpha in terms of a and l? I've been working on it non-stop for the past two days and I can't find a solution, although my system seems fully constrained. Figure", "label": 0}
+{"snippet": "The magnetic field is pointing upwards and uniform. Part C: Since the magnetic field does not do any work, the initial velocity of the bar should remain constant through time. But in the solution of the problem, the velocity is a function of time. Can anyone please explain this inconsistency?", "label": 0}
+{"snippet": "I would like to use something that looks like the following table in my document, but I have no idea of how to make this using TikZ or other packages. Using a matrix leaves too much empty space above in my tries. The cells should be editable, so I can show the parsing steps.", "label": 0}
+{"snippet": "Please could someone help explain to me the choice of delta here. I am unsure how the definition of uniform continuity is being applied. I guess it is something to do with when x and u fall in different intervals J or I? Thanks for your help!", "label": 0}
+{"snippet": "While i'm doing the math homework, I find something very strange. I am confused by a textbook's answer. The Question The textbook's answer So, Does differentiation change the units of measurement in mathematical equations?", "label": 0}
+{"snippet": "Is there a word for \"a diverse amount of knowledge\"? I would be used in a sentence like this: Trying to give a diverse amount of knowledge covering many fields and genres of text.", "label": 0}
+{"snippet": "Electrons have a magnetic dipole moment. If a permanent magnet was held against one end of a copper rod, the delocalised electrons close to the magnet would be attracted and concentrate around the magnetic pole. This should result in the creation of a weak electret because of the uneven electron distribution.", "label": 0}
+{"snippet": "As in, is there a manual for how to get good typography using the LaTeX typesetting system that is similar to Matthew Butterick's web-based book? MB's Practical Typography only shows examples for web, MS Word and Pages which is why I'm asking. That website is linked here: https://practicaltypography.com/", "label": 0}
+{"snippet": "Which statement is correct? The change adds more info to the changelog about the previous commits on May xx, xxxx. Or: The change adds more info about the previous commits on May xx, xxxx to the changelog.", "label": 0}
+{"snippet": "The problem I have is that the line around which the circle must be rotated cuts the circle in two parts. Any hint or help with what to do with it will be useful. Thanks.", "label": 0}
+{"snippet": "I just don't understand how the voltage is adjusted to suspend the droplet. What do we use to adjust the voltage? Because, normally, even when electric and gravitational forces are balanced, the charge will moves with uniform velocity towards the oppositely charged direction.", "label": 0}
+{"snippet": "I see a lot of books of Nonequilibrium QFT and they study the thermodynamics on quatum realms, but what is the difference about that and Quantum Thermodynamics? They study the same thing only with different approach?", "label": 0}
+{"snippet": "Needs to prove that integral can be reduced to another form with specific substitution. Not sure how it can be proved. I think that t=sin(phi) on second stage but I can't understand how to start.", "label": 0}
+{"snippet": "I want to see and compare all the beamer outer themes. Something like this. Is this available somewhere? I know I can generate examples myself, but I prefer to use something already available.", "label": 0}
+{"snippet": "In the below sentence, The mission of the entity may include goals other than maximizing profit. is it implied that \"maximizing profit\" is a goal of the entity OR is it referring to only non-profit-maximizing goals?", "label": 0}
+{"snippet": "I am student of mathematics and I have started to learn algebraic topology . I want to learn visual things . Can you please suggest books that can help me to increase visualization ?", "label": 0}
+{"snippet": "Can Sagnac effect be observed in coiled, rotating electrical cables conducting electric signals, in a similar way to that observed in coiled, rotating optical fibers? And if so then who demonstrated it first in electric cables?", "label": 0}
+{"snippet": "Consider a gas. Now, we already know the particle's duration of a collision is very small and it immediately bounces away from there. Can these be thought of as topological holes in one's phase space (since the particle barely spends anytime there)? What is the volume of these holes and do they obey extensivity?", "label": 0}
+{"snippet": "Some people say that when the electrons are excited beyond the Mott gap, the electrons will just hop to the neighbor ions and stop there so will not contribute to electrical conductivity. Is this true?", "label": 0}
+{"snippet": "One to the power of infinity seems to be undefined. Is the infinite power tower of one also undefined? EDIT What about one to the power of the cardinality of an infinite set? Does that do away with the issue of the (alleged) undefinedness?", "label": 0}
+{"snippet": "Can we say the ability of computers to make decisions is based on a quantum property? I refer to the PN junction in semiconductors, is the phenomena related to PN junction a quantum property? Why I asked that, I wanted to know if the finest element able to make a decision is necessarily at quantum level. In example can we make a choice mechanically?", "label": 0}
+{"snippet": "I know in an isosceles triangle, the height, median and angular bisector to the base are coincidental by SSS or other congruent theorems, but I searched all over the world and can't find whether there's a name for this property.", "label": 0}
+{"snippet": "If object A's momentum is decreased, will it produce less force on object B upon collision, in comparison to a situation where A object had greater momentum? If this is true, does it follow that the velocity of an object is proportional to the amount of force it can produce on another object?", "label": 0}
+{"snippet": "In this Penrose diagram for a charged/Rotating black hole, once your in the new universe you can continue onward to an infinite sequence of black holes/white holes. So I'm asking, where do those black holes and white holes come from?", "label": 0}
+{"snippet": "When water is absorbed by soil for example, it gets dark. But when water is absorbed by tissue paper, and kept closer to another object, that object can be seen pretty clearly through the tissue paper. Isn't it possible that soil becomes translucent and the tissue paper becomes darker in colour?", "label": 0}
+{"snippet": "I have seen that the electric field of a dipole antenna detaches and propagates. For a section of the detached electric field, will the antenna experience recoil if the detached field moves a charged object?", "label": 0}
+{"snippet": "Ball is free to move in hollow tube, if you rotate tube ball will move outward. What force push ball outward in inertial frame and how ball trajectory looks? (I know that centrifugal force don't exist in inertial frame, but without this force I can't explain what force move ball outward...)", "label": 0}
+{"snippet": "Ligo works by destructively interfering light from a laser using an interferometer. Its said that no light enters the photo detector when all mirrors are the same distance. However,based on my research,the light would just create an interference pattern and never completely destructively interfere. How exactly does ligo do this? Can I get it done on a smaller scale?", "label": 0}
+{"snippet": "I am new in the community. I am reading the book \"Linear models in statistics\" of Rencher & Schaalje. Can someone argue if that's correct? How can you express \"some simple sum of squares as quadratic forms in y\"? picture from book \"Linear models in statistics\"", "label": 0}
+{"snippet": "if a matrix A is m by n , and m>n , in this case we have one solution? i don't understand how more rows of a matrix can still have one solution", "label": 0}
+{"snippet": "Hoping for some assistance with my possessive conundrum. If you were going on a trip for leaders (not run by leaders/organised by leaders), would it be: a Leaders Trip or Leaders' Trip? Thank you!", "label": 0}
+{"snippet": "I am writing lyrics to a song, and the first two lines I have written read as follows: The spiral begins as these thoughts are imbued, \"I'm hideous sin and I have no value.\" The idea I want to convey is the negative thoughts that saturate or permeate a person causes a downward spiral that can lead to despair.", "label": 0}
+{"snippet": "The existence of Magnetic monopoles has not been proven or disproven. There are equartions for Charge black holes, There are equations for Rotating black holes, but are there equations for Magnetically charged black holes?", "label": 0}
+{"snippet": "We say \"I had to leave,\" but not \"I'd to leave.\" Why? This is also unlike other auxiliary usage of the verb \"had\" (e.g. in past perfect tense), so the difference is more nuanced than the had being an auxiliary verb or not; why is this not contracted like other auxiliary usage of the verb?", "label": 0}
+{"snippet": "Examples: I can throw a good throw. I want to run a long run today. Scoop me a scoop, please. She gave me drinks to drink. I really like these simple sorts of sentences, but I've never seen any specific term for them.", "label": 0}
+{"snippet": "If I am taking takeout home in a plastic bag, is it better to remove all air from the bag when sealing it so no heat is lost to the surrounding air or keep air in the bag acting effectively like insulation? Let's assume the air is room temp/colder when I seal the bag.", "label": 0}
+{"snippet": "The Theorem on the Textbook Is there anyone who can explain the theorem to me. I find it hard to understand. Thanks! By the way, what's the formal name of this theorem, I found nothing online.", "label": 0}
+{"snippet": "Do you have interesting books presenting abelian variety (over an arbitrary field k) using the scheme point of view? Most of the lectures I know use the point of view presented in the first chapter of Hartshorne (so without scheme). I'm looking for something which presents the modern aspects/questions of those objects.", "label": 0}
+{"snippet": "How to find the lateral surface of elliptical cone? Equation of lateral surface is Lateral surface equation but how to find the value of E in this equation? Here is an example. Example", "label": 0}
+{"snippet": "Why does a rotating body, like a rod or a spring, exhibit elongation instead of compression even though every part of it experiences \"centri-seeking\" force? Is it plausible to understand this in an inertial frame of reference, rather than the conventional pseudo refrence frame?", "label": 0}
+{"snippet": "While it's not too difficult to derive Snell's Law for acoustics e.g. from Huygen's principle like for light, I find surprisingly little resources on an equivalent to Fresnel formulas linking the reflected and refracted amplitudes, mostly limited to perpendicular incidence and sound intensity in dependence of acoustical impedance, but what are the formulas for e.g. pressure or density continuity at arbitrary angles of incidence?", "label": 0}
+{"snippet": "If A and B are two normal matrices with the same eigenvectors, but different eigenvalues, where, A = UVU' and B = UWU', which operations with A and B (sum, multiplication, inverse, etc,.) will change the eigenvectors of the resultant matrix and which will not?", "label": 0}
+{"snippet": "I typed a work using wx Maxima. I am really short on time. Is there a way I can convert wxmx/wxm file to LaTeX or PDF? Pls answers should be very basic (i.e a toddler can understand). Also this work includes long equations and matrices but no diagrams or tables, just plain text.Thanks.", "label": 0}
+{"snippet": "We know that an eigenvalue decomposition of a matrix is to find those eigenvectors that are just scale for some coefficients. But what about Jordan matrix decomposition? I just learn how it is calculated, but I am not sure whether it has geometric intuition.", "label": 0}
+{"snippet": "I am creating a list of special characters used for delimitation in my work. \"-\",\"_\",\" \" are delimiters But the latex code is wrapping on \" \" \"-\",\"_\",\" \" are delimiters How do I treat \" \" as a word that shouldn't be wrapped?", "label": 0}
+{"snippet": "Fractal based measures help quantify the self-similar geometrical properties of set (in this case a time-series signal). It mostly represents the global characteristics of geometry of the signal. But with time series as data, we tend to look for local characteristics where Multi-Fractal Analysis is adopted. If my understanding is right about Multi-Fractal Analysis, what are Multi-Fractal Analysis methods available and can be adopted?", "label": 0}
+{"snippet": "According to Bohr's hypothesis electrons can exist only at certain special distance from the nucleus only on certain particular orbits which is determined by Planck's constant, how does reach to this conclusion and what's the experiment behind it?", "label": 0}
+{"snippet": "I know that composition of dl isn't correct generally, But I read in my text book that we can do that with logarithms and exponential with some conditions So what is these conditions? I don't find them in my text book", "label": 0}
+{"snippet": "Do evaporating black holes emit gravitons? I know that hawking radiation consists of photons, and that for very small black holes it can also consists of sun atomic particles, but what about gravitons? Those are supposedly massless particles, can an astrophysical black hole emit those?", "label": 0}
+{"snippet": "Is there a specific term for a question, such as Are you asleep? and Can you hear me?, where the binary is Response/No Response rather than Yes/No? I feel like there are other aspects of this concept that orbit this specific question, so any related discussion at all is appreciated.", "label": 0}
+{"snippet": "So the way to measure electron spin is to split the beam with a magnet to obtain two beams. Essentially what gets measured is magnetic moment, that is later interpreted as the direction of spin multiplied by Bohr magneton. Is there any \"direct\" measurement of electron spin that ignores magnetic moment?", "label": 0}
+{"snippet": "I know the radius of the Earth and the radius of the orbit (r). I need to find the length of arc (d) along the surface of the Earth given the graphical information presented. Thanks for any help you can provide!", "label": 0}
+{"snippet": "In an RL series circuit where the current rate of change is positive, there is a voltage drop across the inductor, if voltage drop means an energy loss, then in what form the energy is lost in the inductor?", "label": 0}
+{"snippet": "Assume that N points are distributed uniformly randomly within the unit square, and call these points anchor points. What is the mean, mean minimum, and mean maximum distance of a point randomly chosen within the square that is not an anchor point to its closest anchor point?", "label": 0}
+{"snippet": "I want the 'Article Title' to not appear in the header of every page in my springer-nature latex document. May I know what to comment out / replace in the sn-jnl.cls file? Thanks.", "label": 0}
+{"snippet": "I have a task where two equal dipoles are separated by a non-grounded, perfectly conducting thin plate. The dipoles are oriented along the plane direction and can be parallel or antiparallel oriented. I wonder what the force is between the plate and the dipoles and between the two dipoles and whether one can reach perfect force cancellation. Thank you very much! Alexey", "label": 0}
+{"snippet": "Why are the so-called radio-transparent dielectric caps covering parabolic antennas based on a metal frame, which, in theory, will work like a Faraday grid, and if it does not absorb the entire signal, at least significantly attenuate it and create interference due to secondary radiation? Look inside Look outside", "label": 0}
+{"snippet": "I have question about matrix derivation, there are two matrix derivation in png, the first is simple one that i wrote, the second matrix is my main question. I want to know is this true calculation? https://i.stack.imgur.com/yLRNY.png", "label": 0}
+{"snippet": "As eg from Wikipedia: https://en.wikipedia.org/wiki/Notions_(sewing) The term is chiefly in American English... was also formerly used in the phrase \"Yankee notions\", meaning American products I'm wondering if anyone can provide a more detailed explanation of how this word came to have its sewing-related meaning.", "label": 0}
+{"snippet": "He claimed to find the atmosphere vital and creatively invigorating. Perhaps there was something to this: he had taken his languishing novel out of the trunk for the first time in nearly a year. It by Stephen King Could you guys tell what he meant by saying that the novel got taken out of the trunk? Is this some kind of idiom?", "label": 0}
+{"snippet": "Is it possible to create the following effect in latex? The core is that it have a distinct color for each word instead of using a shading, which can mess the text up. It's fine if this is done using javascript and svg. Credits for Celeste for this image...... I'm trying to port wavedash.ppt to latex using dvisvgm, but I'm kinda stuck.", "label": 0}
+{"snippet": "What would be the correct form of this phrase? Atom forge or Atomic forge I know 'atomic' is an objective and 'atom' being a noun is correct when used with forge because you are forging something. But 'atomic' sounds right and I've seen that used before. Just want some clarification.", "label": 0}
+{"snippet": "I have been learning more about sets lately and have stumbled upon notation (or I guess a language) such as this: I would like to know the name of this notation and perhaps some resources to learn it.", "label": 0}
+{"snippet": "Is there a reference out there that only focus on (different)rank of matrices(with all kind of entries: real, complex, integers) and connects then further to ranks of tensors and further with the ranks multi-linear operators. Thank you in advance.", "label": 0}
+{"snippet": "In the rational sequence topology, rationals are discrete and irrationals have a local base defined by choosing a Euclidean-converging sequence of rationals and declaring any cofinite subset of this sequence along with the irrational to be open. Do these choices of sequences matter? Or does there exist a homeomorphism for any pair of sequence assignments?", "label": 0}
+{"snippet": "What is the linkage between Loop Quantum Gravity and the approach of the Polymer Quantization? I know you get a lattice using the correct polymer representation, so that's a good toy model for the full theory of LQG, but what are the assumptions to justify this as toy model? What is that we are neglecting/suppressing of the full LQG?", "label": 0}
+{"snippet": "I am working with some textbook trigonometry. Its proofs always take the LHS and show that it is equal to the RHS, but I find cross multiplication easier and faster. Can we indeed do it my way? For example:", "label": 0}
+{"snippet": "A Euclidean space is an affine space over the reals such that the associated vector space is a finite-dimensional inner product over the real numbers. https://en.m.wikipedia.org/wiki/Euclidean_space#Technical_definition Is the theory of Euclidean space Euclidean geometry?", "label": 0}
+{"snippet": "I want to use different calligraphic versions, mathcal and pazocal, of some letters in the same project. However, when I add the pazocal package, even mathcal letters show up in the pazocal format. Is there a way to use both styles for different letters in the same document? -RD", "label": 0}
+{"snippet": "Was playing around on desmos and discovered that the graph of x! = y does not interact with zero at any point. Was wondering if any maybe complex number or number that desmos didn't properly compute who's factorial equals zero. Keep in mind I am just a highschool student so I might not understand some terminology", "label": 0}
+{"snippet": "I understand it requires Newton's third law but how to prove it. Is it like an axiom in physics like in mathematics. in mathematics you cannot prove it, in physics you cannot explain it elementarly (if that's a word).", "label": 0}
+{"snippet": "I have a question about hyphenating compound nouns when they function as object complements. For instance, should entertainment oriented be hyphenated in below sentence? Much of the radio programming was entertainment oriented. Likewise, well-acknowledged This issue is well acknowledged.", "label": 0}
+{"snippet": "What can I call a thing that is one-of-a-kind? This restaurant's Loganberry Duck is one-of-a-kind, and the Crystal Brush Pulpo is another _______. I want to use it to compliment a dish, to express the \"you can only get this here\" kind of meaning.", "label": 0}
+{"snippet": "I am basically confused as why can't larger nuclei undergo fushion and release energy. One reason I know is because of too much protons than neutrons which generates stronger electrostatic repulsive forces.But another reason is something related to binding energy per nucleon which is making it difficult for me to understand.", "label": 0}
+{"snippet": "So a type of measurement, in units, is length, position, mass, etc, and a unit is meters, kilograms, etc. Is it accurate to say that \"an hour\" is a time measurement, but also a form of length, especially if we're talking about time \"passing\"?", "label": 0}
+{"snippet": "Is it possible to increase the dielectric strength of any or some materials by adding a certain layer on its surface? And do you know any? The purpose is lastly to improve the electrical breakdown.", "label": 0}
+{"snippet": "Frictional electricity makes the charges get separated so when the airplanes are running in air at very high speeds, resistance will be created by the air so due to this frictional electricity will be developed on the surface of the plane, so by this method can we generate electricity?", "label": 0}
+{"snippet": "Is 'clinch' used not for embrace but the romantic relationship itself? I think I've heard it used, though I may be imagining it/misunderstanding. Is it idiomatic enough to be something other than a metonym?", "label": 0}
+{"snippet": "How can I typeset a proof in this style? That is, how can I write proofs with three columns, the first numbering the premise or assertion, the second containing the premise or assertion itself, and the third containing the justification of the assertion (if the second column of that row contains an assertion)?", "label": 0}
+{"snippet": "So lets assume for this question that negative mass exists then will a theoretical planet made of negative mass create an outward bulge in spacetime to create antigravity (repulsive). Also for this question use this image to represent spacetime curvature created by positive mass (Basically regular attractive gravity). I thought that negative mass would make spacetime bulge in the opposite outward direction.", "label": 0}
+{"snippet": "Covariant derivatives take into account for both component and basis changes, thereby applicable for curved spaces - where partial derivatives only take component changes into account - is this statement correct? In a polar coordinate system basis changes, even though the space is flat. Will that be considered in partial derivatives? Or we need covariant derivative for that?", "label": 0}
+{"snippet": "If spacetime is a single enitity, and the Big Bounce is the idea that space itself will collapse back in on itself, does that mean that time will collapse back in on itself? And... what does that look like?", "label": 0}
+{"snippet": "Metric space d(z,w)=|z-w| is complete metric space .i have idea that any sequence in C is Cauchy iff its it's real and imaginary part are Cauchy sequence in thus by using completeness of R can I prove this statement please verify it.", "label": 0}
+{"snippet": "Many physicists use thermodynamics to understand what is happening at a cosmic scale. It feels a bit off. Will most concepts directly apply, or do we need to be cautious while using some formulae?", "label": 0}
+{"snippet": "There is a point (x,y) in the elliptical orbit inclined at theta angle. I know the x, y coordinates and the center coordinates and Major Minor. In this case, is there an equation to find the tangent line?", "label": 0}
+{"snippet": "I can't find the definition of this terminology. Actually, there is a similar question 'what is the split k-algebra?'. But the notes in the answer is unavailable and I can't add comments somehow. So I ask a new question.", "label": 0}
+{"snippet": "Problem Hello, I am studying modeling and control course and I'm struggling with drawing neat figure describing the reactor system and to write the differential equations in detail describing the evolution of the variables of the system. My scratch This is the way I approached. Is there any mistakes or wrong approach/assumptions that I made? Fill free to give me any advice.", "label": 0}
+{"snippet": "This comes straight up from a certain text that I was going through, which of course is in the form of a question which asks 'A solid cylinder is rolling without slipping and how many generalized co-ordinates are required. Are there any quasi-generalised co-ordinates?' Any help is appreciated.", "label": 0}
+{"snippet": "The harmonic series symbol is often denoted by H in LaTeX, that looks like this: On Knuth's Concrete Mathematics book, the symbol looks like this: The book used AMS Euler as the typesetting font, where the normal \"H\" and the harmonic \"H\" were different. Is there any dedicated symbol for the harmonic series in LaTeX?", "label": 0}
+{"snippet": "I know that for a linear vertical spring, the governing equation of motion written in the presence of gravity is the same as the one written in the absence of gravity. We can either undergo a transformation or cancel the terms while balancing the laws using the free-body diagram. What about nonlinear springs? Please let me know the possible explanations.", "label": 0}
+{"snippet": "Why doesn't light simply go more slowly without bending? Is there a macro phenomenon, say a stream of bullets, that will also bend as it changes from one medium to another or is light somehow unique?", "label": 0}
+{"snippet": "As per my knowledge, the node which having the least cost is branched in branch and bound approach to solve n puzzle problem. What happens if there are multiple nodes with minimal cost ?? Any of the node is taken or every node must be branched ?", "label": 0}
+{"snippet": "Since ALL operating systems have a 'Desktop' - The area of the screen that contains your regularly used shortcuts, taskbar, menu and notification areas. It would be more accurate to be 'Workstation' that shows a 'Desktop' for user interaction. Equally, a 'Laptop' or 'Portable' that shows a 'Desktop' for user interaction. ... All PC's have a 'Desktop'", "label": 0}
+{"snippet": "I would like to tie my new connector to my cable tightly using the provided string. This is what the untied knot and the the tied knot look like; unfortunately, the adaptor can still slip and slide around the cable since the knot is loose. What type of topological problem is this? And how would it be asked mathematically?", "label": 0}
+{"snippet": "reflectivity of a mirror is very high but on a microscopic level no mirror is perfectly smooth so all the reflections must be diffused and we should not see any perfect reflection so how do we see such perfect reflections", "label": 0}
+{"snippet": "The question hung in the room we were in, trembling in the cold. Is the antecedent (in the broader sense) of the dependent clause 'we' or 'the question' here? How would you improve the sentence, given that it needs to start with 'The question...\"?", "label": 0}
+{"snippet": "A basis for the density matrix operators is the Pauli Matrices set, but if i'm understanding correctly all Pauli matrices are square and even dimensional, since they are kronecker products of the basic pauli matrices, then maybe they're a base for just even dimensional density operators? if yes there's a way to write odd density operator only as Pauli matrices?", "label": 0}
+{"snippet": "I want to produce a beamer presentation exactly as the one attached, it is like the Antibes theme but not exactly. I need to know which theme it is or if is it a customized theme. Antibes theme does not include the Author or the title at the footer, which is exactly what I need to add.", "label": 0}
+{"snippet": "Dears, I have a sum of two polynomials, and I want the roots of this sum in the left half plane, meaning negative roots. I am looking for some useful theories, but I have not found good things yet. I want to find some condition on each of these polynomials so that their sum has negative roots.", "label": 0}
+{"snippet": "I want to see the page corresponding to edited Tex page when I compile the file on Overleaf, but it always return to the first page in PDF file. How can I fix this?", "label": 0}
+{"snippet": "Sean wasn't as keen about maintaining his gun as a proper soldier should be, and that led to his rifle jam/jamming during the battle. Is there only one right option here, or are both variants valid but have different meaning?", "label": 0}
+{"snippet": "There is a voltage drop between the start and end point of a resistor. How does it achieve this difference in potential? For there to be a difference in potential there must be difference in charges. So do electrons build up at the entrance which in turn creates a difference in potential?", "label": 0}
+{"snippet": "So a dipole antenna is supposed to work with AC supplies. But would it still produce propagating EM waves if pulses of DC are supplied instead of AC current? show in the image:", "label": 0}
+{"snippet": "How can you succinctly say that something is likely to draw the jealousy of others? That would be ____ Especially if it's slightly negative too, attracting not only jealousy but also hate or dislike because of how jealous they are", "label": 0}
+{"snippet": "I understand what reflexive relation on a set is, but I struggle to come up with a practical use of it - why would you even bother defining it? I would really appreciate a couple examples, where reflexions are used, so it would be a little easier to understand - why they are needed?", "label": 0}
+{"snippet": "It seems like most phones, tablets and computers have features when charging to prevent battery degradation. When this feature is activated, it seems the battery does not charge constantly, the best way I can describe it is the battery charge percentage has a similar feature to the enzyme, kinetics reaction. Would a logistical or exponential equation best approximate the charge time.", "label": 0}
+{"snippet": "My professor told me torque can be calculated about any point in space, but would such a torque ever make sense even if the particle is rotating about some other axis, on which the point does not lie?", "label": 0}
+{"snippet": "such as IEEE Transactions on Affective Computing format is shown below, The PDF generated by the template obtained through IEEE Template Selector is not in this format. How do I get the right template? Thanks in advance.", "label": 0}
+{"snippet": "I realize that this editing won't make the question open (since this is against the guidelines to share results and ask to check them). Meanwhile, I'd like to replace a lot of text with a link so those who can see it won't have problems with rendering.", "label": 0}
+{"snippet": "assume a perfectly vertical plane, smooth surface with no deflection and an elastic ball. the moment the ball reaches the lower surface, kinetic energy is at maximum when the ball strikes the lower surface, it then compresses, and some (or all) kinetic energy becomes elastic energy. when the ball has reached maximum elastic compression, does it momentarily stop?", "label": 0}
+{"snippet": "I was wondering if there is some theoretical result (different from the connectedness definition) that characterises the connected subspaces of a connected space. I have looked over my General topology but I do not find anything and I do not see any way to prove something like that. Moreover, if the space is a topological manifold, is there such a result?", "label": 0}
+{"snippet": "I've found this diagram about the conduction band (https://energyeducation.ca/encyclopedia/Conduction_band): But are there other energy bands over the conduction band? Or is the electron simply kicked out of the solid (and so its energy becomes continuous, not in discountinous band).", "label": 0}
+{"snippet": "I would like to draw the following graphs in tkz-graph package. These are the unit-distance colored Golomb graph and Moser spindle respectively. when i try using the regular polygon operation it misaligns the edges and the second graph isnt regular so idk how to draw it", "label": 0}
+{"snippet": "A Smooth Disc with a grove is rotated with constant angular velocity, about its center A block is placed in the grove. What force is acting on the block here to \"throw\" the block outside the grove, if we look at it from the ground frame?", "label": 0}
+{"snippet": "Please can you explain me this notation (B)^I ,where B is basis of topology and I us interval and U belong to topology generated by B and Ui belong to (B)^I and U = union of Ui Thank you", "label": 0}
+{"snippet": "Used be, one gave a gift. It was called gifting, the gift was given. When, why and how did \"gift\" replace \"give\" as in \"I gifted her a bouquet\"? \"Gifted\" used mean talented eg \"a gifted musician\".", "label": 0}
+{"snippet": "In other words, I want to prove that angle is at its maximum when it lands at A. Each of these angles goes through a third of the diameter. That is, if we set O as the center of the circle, Angle A reaches its maximum when AO is perpendicular to the diameter in the figure.", "label": 0}
+{"snippet": "Is there any chance, that you can help me with my problem? I've already used answers from topic: Circle and arrow on a single term of a math equation It works very well. But is it possible to have an arrow going down, when expression is in a denominator? I would like to have something like this:", "label": 0}
+{"snippet": "I have added the image of the part of page (the specific statement is highlighted), why does the text says that the capacitors are not connected in series ? And why the text says that they are not in parallel connection ?", "label": 0}
+{"snippet": "Can proton convert into neutron and another neutron simultaneously into proton in nucleus of a stable element? Which conditions are needed for this? Is this question make sense at current stage of science and technology?", "label": 0}
+{"snippet": "I want to increase the length of the legend symbol (like solid lines, dashed lines, dot dashed lines, dotted lines etc) in the legend box since for dot-dashed lines the length of the symbol is too small to be differentiated by other symbols in the legend box that I use.", "label": 0}
+{"snippet": "I understand some parts of the theory, I've read from here https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Carlip/Hawking_Radiation What exactly is negative energy and how is it different from the \"negative\" or \"positive\" we use when talking about an electron or a proton? Why can negative energy only exist inside the blackhole?", "label": 0}
+{"snippet": "I understand that there are different definitions of finite. They are all equivalent over ZFC, and some of them are even equivalent over ZF, but not over weaker theories than ZF(C). I would like some texts that define various notions of finite, and develop the theory quite a bit.", "label": 0}
+{"snippet": "If everything in the universe happens according to rules, thermodynamic or otherwise, then how would anything (or any choice) ever be stochastic? Multiple choices might be probable, but in any instant the ones that get chosen are based off of those rules. Doesn't that rule out stochasticity?", "label": 0}
+{"snippet": "This problem came in my mocks. I tried writing the sum down and sandwiching it but I could not find appropriate \"sandwiches\" to this. Please help me with this. I nearly spent an hour on it and could not find a solution.", "label": 0}
+{"snippet": "I'm struggling with the correct way to use barrier to entry in the following sentence: Technical interviews are an ever present barrier to entry in the software industry or Technical interviews are an ever present barrier to entry into the software industry Does using 'in' versus 'into' dramatically change the meaning of the sentence and is one more correct in this context?", "label": 0}
+{"snippet": "Usually optimisation problems consist in maximizing a function given some linear constraints. What if one simply has a system of linear equations with some constraints on the variables that come in the form of linear inequalities. Can this be cast as a linear programming problem? If so, how is it classified/where can I read more about it?", "label": 0}
+{"snippet": "Can all verbs with to infinitives in the place of the object complement use both the past participle and to be p.p. form when the relationship between the object and the object complement is passive? I expected my car (to be) repaired soon. Is it okay to use either form?", "label": 0}
+{"snippet": "Is the intersection of two connected set is connected?? I think it is connected, I can't find any counter example to prove it disconnected. My approach is-> A,B connected. Let A meet B disconnected,A meet B =PUQ where P,Q are separated set What next??", "label": 0}
+{"snippet": "Force is defined by acceleration , and acceleration requires the determination of\" inertial frames\". But an inertial frames also requires the knowledge of forces which requires measuring acceleration, but with respect to what ?", "label": 0}
+{"snippet": "Hi could you please let me know if the \"that modifer\" modifies the closest noun (i.e exercises) or further away head noun (i.e. vocabulary), in the following passage. Let's review some vocabulary from the last few reading exercises that I've published here on the blog.", "label": 0}
+{"snippet": "If we place different materials in the microwave owen, they will get hot at different speeds. For instance meals get hot really fast. What material property decides on the strength of the coupling? Resistance? Permeability?", "label": 0}
+{"snippet": "Can't we make a face with just two edges(sides) and two vertices? We just connect those two vertices twice each with different edges and we can make a face between the two edges with only two vertices and edges like the image.", "label": 0}
+{"snippet": "If all matter began from one infinitesimally small point, and flew outward from there. How can we have galaxies colliding? Did they make left hand turns or something? Or it is possible multiple galaxies were created by secondary coalescing and re-exploding of galactic material, flinging them in new directions? Wouldn't that increase the time-frame of the Universe's age?", "label": 0}
+{"snippet": "Is it practically possible to detect big and solid amounts of steel on the ground at long distances? (e.g. vehicles on line of sight) Metal detectors do it but at short distances and suffer of parasitic detections from minerals in the soil and etc. Radars detect it well but can't distinguish from other non metal but big objects.", "label": 0}
+{"snippet": "I know that such correspondence exists when the group is finite. I'm trying to take the basic linear representation theory of finite groups to compact groups. Specifically I'm trying to see if the concept of F[G]-module is well defined.", "label": 0}
+{"snippet": "I have been looking for examples of essential discontinuity but have been confused, as different sources cite different things. I know that it might be non-removable discontinuity and infinite and oscillatory are its types. Am I correct? Can somebody explain with examples?", "label": 0}
+{"snippet": "For example, if you have a battery and you connect both ends with a short circuit with zero or low resistance, why does it short circuit? What causes this internally? What are really happening with the charges that cause this \"explosion\"? edit: I specifically want to know why connecting two ends of the battery with a wire with (hypothetically) no resistance would short it.", "label": 0}
+{"snippet": "Light always moves in a straight line unless gravity acts on it strongly, but since it is made of electric and magnetic waves, shouldn't it be pulled towards different charges and magnetic, or is light neutral?", "label": 0}
+{"snippet": "Can you link action verbs with verbs of being in a sentence? As in say These are people who think critically, solve problems collaboratively, and are prepared to thrive in a global society.", "label": 0}
+{"snippet": "Are there words that describe the directionality of languages? I only see compound words, such as left- to- right or top-to-bottom. I would have thought a human practice so ancient as language would have established words to this effect!!", "label": 0}
+{"snippet": "Im a mathematician which also learn physics, Ive read several papers on sigma models, and it was quite interesting . So my question is where can I read about open problems of sigma models?", "label": 0}
+{"snippet": "When I say 'Been around for a while' I mean like someone who has been somewhere, or been a member for a while. I'm trying to make a role for the people in my discord server for some of the oldest members, you see.", "label": 0}
+{"snippet": "I found that it is a normal concept appearing in condensed matter physics and especially topological order field. I have been aware of the topological defect. But what is a symmetry defect? Could someone explain or give a simple concrete example?", "label": 0}
+{"snippet": "A person who is especially proud to be from a particular city, and puts down others from opposing cities. They rep their city as if it's a sports team. This is especially true in the US. Could you please suggest a single word one could use to describe such a person well (not a gross hypernym like 'supporter')?", "label": 0}
+{"snippet": "If causality is an axiom or a fundamental law in physics, would the existence of causality be a reason which forbids time travel? Because time travel could break causality so we see first the effect and then the cause.", "label": 0}
+{"snippet": "In a opening of the news about several drugs for Alzheimer's disease, the news broadcaster said, He(the reporter) has \"our\" look at the breakthroughs and what they could mean. Why is not just simply \"has a look\" instead of \"has our look\"? What implies \"our\" in that sentence? Thanks.", "label": 0}
+{"snippet": "I come from symplectic/poisson geometry and I am curious about shifted symplectic/poisson structure on stacks. From what I've saw, the general context there is derived schemes/stacks, so, Algebraic Geometry. What would be the shortest (and most useful) reference for learning AG for that? Hartshorne?", "label": 0}
+{"snippet": "Please help me with my query regarding rainbow formation. Many Books gave formation of only red and violet colour whereas middlemost colours are rising doubt.please check the following picture .My Questions are also marked there..", "label": 0}
+{"snippet": "I just came across a snipet of codes where a long vertical bracket is used to mark a loop. I really like that. I wonder what is the best way to implement this in latex? Thanks", "label": 0}
+{"snippet": "If a stone was tied To a string and then we made it undergo uniform circular motion. Is the centripetal force provided by both the weight and tension or the tension only? What force balances the weight if this is not the case?", "label": 0}
+{"snippet": "I'm having a hard time to understand the unification algorithm properly. Why are these two problems: P(x , h(b), h(x)) and P(f(g(y)), y, h(f(g(h(a))))) P(f(g(x)), g(b), h(x)) and P(f(y), y, h(c)) don't have a MGU, although I cannot see any circular dependency or function mismatch here.", "label": 0}
+{"snippet": "Beyond a formal preference for background independence, what is stopping us from setting cosmological time as a de facto universal timeline, analogous to newtonian absolute time? General relativity doesn't entail it on its own, but neither does it forbid us if certain conditions hold (for a given model.)", "label": 0}
+{"snippet": "In nuclear physics literature, both appear very often. HF is easy. It refers to a variational method with a Slater determinant variational wave function. What is HFB? Does it refer to a similar variational wave function which is annihilated by some quasi-particle annihilation operator? The quasi-particle annihilation operator is a mix of some common annihilation and creation operators.", "label": 0}
+{"snippet": "The context that I intended to use the phrase was along the lines of: The registration page no longer works because the workshop is [insert the phrase or word here]. The workshop was free so I was not sure if \"sold out\" was correct. Is there something else I can use?", "label": 0}
+{"snippet": "Im trying to find the Integral over the real Numbers of a constant Number (j-i) with respect to a probability measure P. Im new to lebesgue Integration and would appreciate any help :).", "label": 0}
+{"snippet": "Can anyone can help me why when we rotate a object on oxy ,that is a linear transformation but not nonlinear transform . I can't imagine the relation between when we rotate a point in oxy and matrix ?", "label": 0}
+{"snippet": "Could anyone please point me out in the direction of a book or a paper on Skorokhod topology on caglad functions? Or any other topology on that same space if this one fails. I expect that there is no magic hidden there, but maybe I am wrong.", "label": 0}
+{"snippet": "I cannot comprehend how can we break a seemingly non-ideal choke coil into just a pure resistor and inductor in series according to the following solution of a question. Considering the data in the question (all given values are R.M.S values),krichoff's voltage law is seemingly violated,is the question or solution incorrect or am i missing something.", "label": 0}
+{"snippet": "The pancake theorem guarantees that there is a line that can bisect a rectangle and a triangle simultaneously. The Borsuk Ulam Theorem can be used to prove that theorem. Show that any line through the center of a rectangle bisects the area of triangle simultaneously (the position of the center triangle can be the same as position the center of a rectangle or not)?", "label": 0}
+{"snippet": "When proving the statement above, I completely understand the textbook proof with convergent subsequences and contradiction, but I wonder: when function is continuous by classic epsilon-delta continuity,for all possible points in the closed interval, there is a delta that satisfy epsilon-delta definition, so if we take the smallest delta, will that exact delta satisfy uniform continuity?", "label": 0}
+{"snippet": "I was wondering why is it that I can replace heat going into a carnot engine with the temperature of the \"hot place\" and vice versa, i.e , why can the temperatures of the places replace the heat going in and out of the engine", "label": 0}
+{"snippet": "I see that electrons are quite small in size, moreover it is moving fast but I have a question why do free electrons not leave a conductor (like a wire) ? but they can only move at the edge of the conductor?", "label": 0}
+{"snippet": "What is the equation for the reverse bias current in terms of voltage applied? And this even be analytically derived? If so, how to derive it. I can't seem to find good resources on this topic.", "label": 0}
+{"snippet": "I am trying to change the color of the title block in template GeoURV Poster template. I know that i may change color in the beamerthemeGeoURV.sty. But I would like it to change in the gradient style, let's say from black to orange.", "label": 0}
+{"snippet": "This is the integral I want to calculate. I want to integrate over this range: So I set up this integral: However this gives me the wrong answer. Correct answer is: Why is that?", "label": 0}
+{"snippet": "If salt water is a good conductor of electricity so does it mean if we put a very large voltage somewhere in the sea then person all across the world will experience some current and are there any physical parameters to quantify this.", "label": 0}
+{"snippet": "Please see diagram below showing a rigid rod mass 'm' connected at one end to a fixed frictionless pivot. The rod swings from position A to B changing its orientation around its centre of mass. Can anyone advise how an external torque can be formed that causes the rod to spin about its centre of mass?", "label": 0}
+{"snippet": "I understand that the Coriolis effect is not responsible for the spin effect in the bathroom, but I have never seen a rigorous math prof of this. Where could I find a proof of this? What references could I read to try to proof it? is it very long?", "label": 0}
+{"snippet": "how does an electromagnetic wave detach itself from something rather than fluxing? electromagnetic radiaton. I need the info for a project and simply couldn't find any useable information on YouTube. other than that all the info I saw on other websites where different/didn't answer the question I had.", "label": 0}
+{"snippet": "I was told and convinced that gravity is not a force, and in free fall you're an inertial frame and experience no force, and when on the surface of Earth you would be accelerating upwards. What I admit I can't understand is Earth accelerating, why so? what property of mass explains this? Is there a relationship between an object's mass and its acceleration?", "label": 0}
+{"snippet": "In Special Relativity, the diagram we most commonly see is the Minkowski coordinization of Rindler Spacetime (the accelerating observer's coordinates as seen in the inertial frame). Are there any visualizations of the inverse/ how motion in an inertial frame would appear to an accelerating observer?", "label": 0}
+{"snippet": "I downloaded Mathpix snip but when I was convet to .tex file it just put an includgraphics. I'd like the commands in Latex in order I can edit the formulas. Is this because I'm trying a free version? Could you give more options?", "label": 0}
+{"snippet": "I'm sure this implication is correct. However, are there rules on how one can manipulate with quantifiers? It might somehow be related to whether no free variables are becoming bounded after the operation.", "label": 0}
+{"snippet": "Can't find this after googling thirty minutes. In the following sentence, should I use quotation marks or not? James used the words stupid, dumb, and fidiotic in his briefing. James used the words 'stupid,' 'dumb,' and 'fidiotic' his briefing.", "label": 0}
+{"snippet": "For example, people that are ostensibly unaware but in reality behaving in a methodical way. Playing dumb but also ingratiating yourself in a savvy way. A word to describe politicians, influencers, and the like.", "label": 0}
+{"snippet": "Does \"for all the\" mean a contrast or a cause and effect? \"For all the work he put in, the project was sure a disaster. \" Does this mean because of all the work he put in, the project was bad? May you infer if he the project was good, then he didn't work hard?", "label": 0}
+{"snippet": "I have searched and I know that it is used in mathematics, but can it be used in the context of a sentence? Like the way we do simplification of a sentence, so for this usage, can we say that we perform complexification of a sentence?", "label": 0}
+{"snippet": "My task is to summarize a book and in that summarized version I need to keep both references to page number in the summary and also add manually the page number from the book something like this: I've tried with redefining some of the tocloft commands but it is not working... Thanks!", "label": 0}
+{"snippet": "Some people who try to deny the Cavendish Experiment say that the masses attract each other because of the atoms, not gravity. Doesn't an atom have a null electric field by nature? Is there any other way they could attract each other?", "label": 0}
+{"snippet": "Suppose I blow dry a region with some water on it. Would it dry it faster than otherwise? If yes, why? I can give one qualitative reason against it, since the blow dryer is blowing room temperature air, no real heating is done on the hair. But perhaps there are some effects I'm not considering, so some more authortative answers would be appreciated. Related", "label": 0}
+{"snippet": "After a linear transformation, some vectors may not change direction, they only scale by a number. The scaling factor of those vectors is called eigenvalue. Can we think of singular values in this manner? Since eigenvalues are related to only square matrices, Are singular values the generalized \"scaling factors\" of a linear transformation (matrix)? Thank you.", "label": 0}
+{"snippet": "There's the word luthier for a string instrument maker, but with winds, the only option seem to be more like naming something in modern English, like \"reedmaker\" which would more apply to double reed instrument players who make their own reeds or something like \"wind luthier\" even though that's the best option as far as I can tell.", "label": 0}
+{"snippet": "A colleague who is a ELL used the word \"cork\" to signify a mistake/error/typo on a schedule. I thought that the four-day schedule was a cork. She says she thinks her English teacher was a Kiwi. I can't find any such usage.", "label": 0}
+{"snippet": "To describe transformations from certain programming constructs into e.g. assembler I need a horizontal line with a downward pointing arrow in the center of the line. Is there also a way to achieve this without tikz?", "label": 0}
+{"snippet": "I am looking for a way to determine the rotation of an electric motor externally as i can not see the shaft the outside of the motor is smooth all the way around. is there sufficient magnetic field to have a pull on a magnetic ball?", "label": 0}
+{"snippet": "I wonder if all interrogative pronouns can be used in structures like Where better to learn about the resilience of life? For example, Who better to repair my car? How better to cook potatoes than by baking?", "label": 0}
+{"snippet": "I have seen the doppler effect derived quite a few times when the observer is moving. What is the source is also moving at some random velocity in some angle? How would one go about thinking about this?", "label": 0}
+{"snippet": "I am trying to draw a bold diameter symbol. I imported the diameter symbol by the package wasysymas shown in this answer and looked at several ways how to use bold math symbols as shown here and here, yet none of them seemed to work for me. How can I achieve this?", "label": 0}
+{"snippet": "In a solenoid, when current changes with time an EMF is induced, but it should not be like this, because the wire which is bend to make solenoid is isolated (usually painted to give it an insulation) so each turn of solenoid is not completely a closed loop because the ends of the wire forming the turn are not joined, the coating is joined.", "label": 0}
+{"snippet": "i was trying to show it with polar coordinates but it showed that the limit exist however wolfram alpha stated that the limit does not exist so im confused does not polar coordinates proof is enough", "label": 0}
+{"snippet": "I am a total newbie so I appreciate all your answers as simple as possible. I want to have in my entire document all examples to be \"non-floating\", it means when I write: The following example shows this: IMAGE ...so I want it to be fixed there, below, centred. Is there any way to make that setting permanent in the header of the document?", "label": 0}
+{"snippet": "Quantum fidelity estimation is to estimate the similarity between two quantum states or process. Could quantum fidelity be viewd as a parameter? And what are the similarity and difference between quantum fidelity estimation and parameter estimation problem? Cross-posted on qc.SE", "label": 0}
+{"snippet": "It is clear that the Zorn lemma guarantees the existence. I prove that the minimal element is unique, and obviously the set is totally ordered. So because the uniqueness of the successor of all elements of the set, in same sense it seems reasonable to me that we will find the uniqueness of the maximal element, but i don't know how to prove it", "label": 0}
+{"snippet": "If denser medium tend to decrease the speed of light (that is why the light rays get refracted to travel a shorter distance to maintain the highest speed possible) Then why total internal reflection happen? if light escapes the denser medium then it will be at more speed - right? then why do the opposite of what is intended?", "label": 0}
+{"snippet": "With reference to this article, I'm curious about how the modular inverse of a polynomial is computed. Moudluar inverse of a number with respect to a modulus exists when the two numbers are relatively prime. I was initially expecting this to hold for coefficients of a polynomial function.", "label": 0}
+{"snippet": "My question is what is the name for words that intensifiers cannot be used with. Words like unique or impossible. Something cannot be more unique or more impossible than another thing. I forgot the name for these and am very curious.", "label": 0}
+{"snippet": "In theory, since the stone acquires the velocity of the balloon, it should go upwards slightly before coming down since it's velocity is equal to that of the balloon (in upward direction). But realistically, does it so the same? Asking from the perspective of an observer on the ground.", "label": 0}
+{"snippet": "For a sentence I got this book from Tom, if we simply rewrite it with passive voice, it would seem to be like This book was gotten from Tom. But I haven't quite met such expressions as Something is gotten from somebody. Is it idiomatic to say so?", "label": 0}
+{"snippet": "I am going to help you. What is the grammatical function of to help you here? Reopen note Please note that I did not ask about going to (and that the to belongs with the following verb as shown above, not with going). The question is about the grammatical relations of to help you, not about going.", "label": 0}
+{"snippet": "In the context of a section in a technical document that describes several topics, one of which is essential and others can be skipped, which of the following is better? You can skip the others on first reading. vs You can skip the others at first reading.", "label": 0}
+{"snippet": "A chapter title appears on bottom of page in toc with section titles beginning on the next page of toc. Is there some way to force the chapter title onto the next page?", "label": 0}
+{"snippet": "My actual question is that i want to know the molecular interaction can all takes place between non polar solvents and non polar solutes and also i want to know that why does some non polar substance dissolve in water like sugar??", "label": 0}
+{"snippet": "Forced fun would be the dreaded company outing with icebreakers and other group activities meant for enjoyment but often achieve the opposite. But, what is a single word that defines this? The major drawback in working for ElboniaCo was the unavoidable requirement to participate in the company's ill-conceived ______ activities.", "label": 0}
+{"snippet": "Could someone please help me in downloading the paper 'On the distribution of almost primes in an interval' by Jingrun Chen (journal: scientia sinica)? I was not able to find it on internet? Any hel would be appreciated. Thanks in advance", "label": 0}
+{"snippet": "The title sums it up; are there any practical examples of not uniformly charged line charges and ring of charge? Line chargers: I know they are used in wire chambers for high-energy physics experiments, but usually, they are uniformly charged from what I've read. Connected wire to the battery are chargeless, so I'm kind of clueless now. Thank you:)", "label": 0}
+{"snippet": "Let's say that an AI was created to toast bread. That is its only function, and only use. How would I describe such a thing in one word? For instance: Like a _____, it executed its task.", "label": 0}
+{"snippet": "He made no comment and there was a long and unhappy pause during which the cab leapt forward a foot or so, only to pause and pant again, frustrated. I thought 'frustrated' explained the atmosphere of the whole part of the sentence before it. Then, can I assume it is a kind of appositive?", "label": 0}
+{"snippet": "draw a circuit graph; check the fulfillment of the ergodicity criterion; calculate the marginal probabilities; write down the limit transition matrix; carry out simulation modeling of the system corresponding to the one under consideration", "label": 0}
+{"snippet": "I was using Ipe to draw \"Venn regions\" (not really the classical ones) as this one, However, I have the impression TikZ has better renderings in latex work. How can I produce such diagram in TikZ?", "label": 0}
+{"snippet": "I am using integration by part concept in my proofs in which I will use it recursively infinite times. In this regard, I am wondering, what will be the last term of the resulting series which will have infinite order derivative of the first function. Can anybody give me abstract mathematical form or the resulting infinite sum?", "label": 0}
+{"snippet": "A rod with a fixed pivot is rotated by torque T so that its free end pushes on different masses (see images A, B and C). Let's assume there is no force of gravity involved. Will the combined MOI of the rod/mass affect the contact force value?", "label": 0}
+{"snippet": "I struggle with commas. Not sure if it's because I never learnt any grammar, I have unusual breathing habits, am oddly polemical in speech, or what exactly. Anyway Should you include (the) commas in sentences such as I am, if not stupid, then dim. And why (be as technical as you want)? In general: any help with commas?", "label": 0}
+{"snippet": "I have measured the rotational speed of a bicycle wheel in free rotation up to stop and i would like to have the physical equation (it is not linear). I would like to compute the frictional losses in the bearing.", "label": 0}
+{"snippet": "This is similar to another question on my page but this one is more conceptual: If you have a saddle point, is this always classified as unstable if you're doing a stability analysis? What do they mean?", "label": 0}
+{"snippet": "Does the following sentence sound grammatical to you? There danced a man in the hall With the meaning: A man danced in the hall. And compare it with There died a man in the hall Which one sounds more grammatical? Focus on the verb distinction between dance and die please.", "label": 0}
+{"snippet": "Maybe something like, \"loser loser drunken boozer\"? I couldn't find examples online, other things come up in a search. A scenario to be used in would be when someone loses a competition and they are mocking the loser. Answers should be something that has been used before, in contrast to the original phrase.", "label": 0}
+{"snippet": "When talking about the growth of a production plant, which of the following is correct, and why? We are growing in area and number of employees. Or: We are growing in area size and number of employees.", "label": 0}
+{"snippet": "Simply what is our best estimation of what came first in the the first fraction of time of the BB? Was it the vacuum and then matter popped out from violent quantum vacuum fluctuations or matter then after matter diluted making vacuum?", "label": 0}
+{"snippet": "I am wondering if vertices of a planar graph can lie on top of each other in an embedding of the graph. Also, when drawing a picture/representation of the graph, is drawing vertices on top of vertices precluded? thanks", "label": 0}
+{"snippet": "So I want to start self-studying topology. What do I have to necessarily have some base knowledge in? So which specific mathematical areas should i be decent/good in? Also I'd happily take any suggestions on where to start. Thanks in advance.", "label": 0}
+{"snippet": "I'm searching for a synonym of word like savvy or veteran but I need another expression , which would have the exact meaning of someone reaches very high level of mastery of skill or technique and appears with much respect from other people,and I would thank you all for answering!", "label": 0}
+{"snippet": "why does the sum disapear in this derivation: derivation of loss Mean Squared Error. It comes from the following wikipedia page: https://en.wikipedia.org/wiki/Gradient_boosting. It is the last equation of the informal introduction section. Thank you very much !", "label": 0}
+{"snippet": "Found this formula being used in a polytropic process where pressure was not even constant. So how are we finding specific heat for constant pressure? k in this example was the power in the polytropic equation. What is the derivation and actual use of this formula?", "label": 0}
+{"snippet": "An aperiodic tiling shape, \"the hat\" was discovered recently. If you split a tiled planed into hexagons, containing the borders of the hat, would there be a finite number of unique hexagons. If so, would there be a simple rule to use said hexagons to recreate the tiled hats?", "label": 0}
+{"snippet": "If comets are thought to brought water on Earth could there be water in form of ice on the neighbouring Moon's poles? As water can easly evaporate if there is no atmosphere as in the case of Moon's equator can it 'survive' on cold places like the poles of the Moon?", "label": 0}
+{"snippet": "I am studying about tomographic interferometric sar polarimetry and i don't have enough knowledge about complex hermitian matrix , special unitary groups, their quadratic forms and numerical optimization based on these kind of matrices and forms in linear algebra. Is there some book or books to start learning these topics for my lecture??? Thanks", "label": 0}
+{"snippet": "I want to put multiple figures (with partial regular name) into Latex with section ranking number and picture name, could you teach me how to do that? The picture's format is .jpg, please find the detailed name in the picture below, thanks.", "label": 0}
+{"snippet": "I have no clue on how to solve this problem. Please help me as I do not understand the solution on my book. Edit: Sorry for not sending the solution: The issue is in the fourth line I understand how the process should work but I wonder if there are other ways to solve the problem", "label": 0}
+{"snippet": "Matter is something which has mass and occupy space . So it's indivisible particle must also occupy space . If it occupy space then it must have some boundary surface which encloses its volume . If realy those particles have volume , then what is the charisteristics of the boundary surface? And how do one particles interact with the boundary surface of other wall?", "label": 0}
+{"snippet": "Is it possible to have light refract in one direction, then reflect off a mirror but come back as a straight line like the picture below? The context of this problem is in lens optics when a microdisplay is on the frame of the glasses and light is shining into the lens to project into the eye", "label": 0}
+{"snippet": "I am reading up on finite approximation recentlyenter link description here, can someone help me explain why the author expressed the interval h as a sinusoidal function in this paper? And how did that come about? Or I just don't understand this way of writing, for example, why the symbols s and k are associated with the interval h.", "label": 0}
+{"snippet": "When creating LaTeX language packages for use in by French mathematicians, German , chinese mathematicians and other mathematicians, it is helpful to know what English words various LaTeX commands were derived from. For example, a Chinese mathematician might have difficulty translating dfrac from English into Chinese (or Putonghua). What is dfrac when spelled out in full English words?", "label": 0}
+{"snippet": "Suppose we have a bulk theory that has some holographic CFT dual at the boundary. Suppose we construct an operator that 'looks like' (whatever that needs to mean) a Fourier mode in the bulk perspective. If we consider this as operator purely from the perspective of the boundary theory, what sort of data is this picking up about our CFT?", "label": 0}
+{"snippet": "Dyes and different colorings are often mixed into materials. These are usually a small fraction of the total material volume/mass and aren't painted on so don't have a uniform surface coat but some manage to block all light or all light from a certain wavelength. How does this work? Why can widely/randomly spaces molecules block light?", "label": 0}
+{"snippet": "what we have to see if we replace the electron from proton and proton in nucleus is replaced by electron ? Will it change the atomic structure of every substance or it changes only in calculating reydberg constant?", "label": 0}
+{"snippet": "This is an image representing a part of a page of a book and this are two screenshots showing the fonts used in the PDF of the book Someone know if and how is it possible to use these or similar fonts in latex? Thank you", "label": 0}
+{"snippet": "calculate the angles I am strugling with this one, wouldnt i need to know what triangle it is or can it be done with just these informations? greatfull for any help. If it has a right angle i can just use trigonometry and do it but if im not sure it has a right angle what can i do?", "label": 0}
+{"snippet": "I typically end sentences with the phrase: ...annexed hereto is Exhibit \"A\". In such a case is grammatically acceptable that the period is outside the ending quotation mark? Inside the ending quotation mark just doesn't look right.", "label": 0}
+{"snippet": "Coming from Don't number first frame with allowframebreaks, I wondered, whether it is also possible to not display a number for frame breaks only when there are no frame breaks required. That way, the frame behaves like a normal frame when no frame break is needed and numbering will be used only when frame breaks occur.", "label": 0}
+{"snippet": "In a book I am writing, a girl wants to have PTSD or abuse so her life is exciting. Like, she wants to live in a book or TV show trope. What is the word for wanting a little kink in a boring life to throw you off-course?", "label": 0}
+{"snippet": "In a comment I found online you can see, I assume this answer is sarcasm, because you are not feeding the trolls, are you However, I don't understand this comment. Clearly trolls are bad and online, but why would feeding them be a bad thing? Is the intent for them to starve? And what is troll food historically?", "label": 0}
+{"snippet": "If a body is kept on the surface then it applies its weight on the surface and the surface applies the normal force on the body. Both are being applied to different bodies, then how do they cancel each other out? And what about other forces like reaction to weight and reaction to normal, how do they affect the body?", "label": 0}
+{"snippet": "I marked the red region why the person pushes the boat at that point? What I think is they push the boat at that point to avoid friction between his leg and boat surface. If I am wrong then please correct me.", "label": 0}
+{"snippet": "Look at the picture that this question shows The direction of induced electric field around a changing current wire Will the induced magnetic field (red circle) induce another electric field (blue circles) that circulating around the magnetic field like the picture below?", "label": 0}
+{"snippet": "In my class, we write dot products like <v, w>, but the < and > on LaTeX are too stretched out and become too close to the adjacent elements. The symbol is used in the cover of this youtube video", "label": 0}
+{"snippet": "Consider a damped system with only acceleration - time data is available, how to determine the structure stiffness (k)? Mass of the structure is also known. It moves in a horizontal direction, like a horizontal mass-spring-damper model. The y-axis should be acceleration instead of displacement for the image.", "label": 0}
+{"snippet": "What is the passive form of \"Who knows you?\", is it \"to whom are you known?\" or \"by whom are you known?\"? Some people are saying 'to', some are saying 'by'. I'm confused. If it is one, then why not other?", "label": 0}
+{"snippet": "A normal way to refer to the next president is to call him/her future/next president or president-elect (in case of selecting through an election). However, I'm looking for a pattern to refer to that situation similar to ex- style, e.g. ex-president.", "label": 0}
+{"snippet": "In quantum optics, there are squeezed states that are very precise in one quadrature. You can analoguously have state squeezed in position instead of one quadrature. Can I perhaps make a slightly more bold bet, where the electron is going to be after the third short time interval measurement, than just the quantum mechanical \"It could be anywhere. Momentum is maximally undefined\"?", "label": 0}
+{"snippet": "Can every proper subset of uncountable set be countable? If yes, is there any example of it? If every proper subset of uncountable set is countable, could then there be no injection from the uncountable set to any of its proper subset? Then would that uncountable set be not infinite and not finite?", "label": 0}
+{"snippet": "Im having hard time understading one of the derivation steps in histogram equalization, Wikipedia (added picture). derivation In the last sentence it seems to me like they are suggesting that the CDF of the original CDF is linear, is that true? If so, why?", "label": 0}
+{"snippet": "The context is a path being eroded with use, except it's more like the path is being crafted with love by use. Are there any better words or phrases to fit this use?", "label": 0}
+{"snippet": "I think in very thin air, high average kinetic energy of air molecules might still be perceived as cold because the number of impacts per unit time would be fewer. Is this a measure that combines density and kinetic energy? This measurement might be \"perceived temperature\" or something.", "label": 0}
+{"snippet": "Recently, I've been trying to read up a lot on active matter, and I realize most of what I read are papers that are relatively new. But to dive into the topic as well, I am unable to find much backing with the theory taught to us in classes. Can anybody give me some solid references to start properly in this field?", "label": 0}
+{"snippet": "Is there an converse phrase to \"in writing\", in the sense of completing a task or a calculation in-writing? This should have the sense of \"in explicit thought, but not in physical writing\". PS - Not sure whether this is a phrase-request or an idiom-request, please retag as appropriate.", "label": 0}
+{"snippet": "In Proving the Inverse function theorem in Mathematical Analysis Book of Rudin, when he want to show that V is open, Why he simply does not use that under continuous function (Mapping), the open set U mapped to the open set V. He used this:", "label": 0}
+{"snippet": "I'm establishing standards for my code projects. Among those, is that I want contributors attribute their notes to their GitHub username, in forms similar to: \"@username\". I'll need to document this, but I'm not sure what it's called, maybe \"at-handle\" or something?", "label": 0}
+{"snippet": "The question is this: I believe the answer is A as the gravitational field strength becomes lower for larger distances of the object from the earth, but the model answer as as below: Are they completely disregarding that the weight changes?", "label": 0}
+{"snippet": "From noises/acoustic emissions monitored and data collected by US Coast Guard (or other agencies) was it possible to determine at what depth the fatal implosion occurred? If time differences from three deep stations (in a vertical plane of the Atlantic) are known, Hyperbolic Navigation helps to determine the depth of implosion from sea level.", "label": 0}
+{"snippet": "When it comes to proofs there is no way to tell whether I have done correct or not. In the solution they did in another way which makes me wonder if this correct? For future question, how can I verify whether it is correct or not? I have heard of websites that can check but can't find any that works.", "label": 0}
+{"snippet": "When air molecules are given energy they compress the layer of air molecules next to them and so on which causes a high pressure wave to move forward so does this make any change in the average kinetic energy per molecule/atom of air and change its state like increasing temperature or internal energy and enthalpy", "label": 0}
+{"snippet": "I have doubt regarding how can COP of a refrigerator can be one! It can happen only when heat is more extracted when work inputed or rate of heat absorbed is more than power? Can any one of the reason is correct? Explain!", "label": 0}
+{"snippet": "I am watching Tensor for beginners by Eigenchris, and I was confused when he said that, not all vectors are Euclidean. So, can someone explain me the meaning behind this by an example or visualisation", "label": 0}
+{"snippet": "Instead of giving the past tense form bended, the verb bend fuses together bend and -ed and removes voice, producing bent. Lent and sent are produced in similar fashion. What's the word for the fusion here?", "label": 0}
+{"snippet": "One can certainly create a digital circuit the achieves this - is it possible to do it in a purely \"optical\" manner? If not with light waves, would it be possible with any other type of wave? Low amplitude wave remains unaffected High amplitude wave gets its amplitude lowered", "label": 0}
+{"snippet": "enter image description hereI am stuck on this graph. Not sure how to map this I have research everywhere but can't find satisfying answer. I am asking this question on someone's behalf I do not know how to ask this question properly or what i formation is missing but I do my best to give all information i have. Below is the picture", "label": 0}
+{"snippet": "Is there a way to compare two LaTeX outputs such as DVI compare or PS compare from the LaTeX utilities? P.S: Please do not mention the PDF compared with Adobe Acrobat or other PDF tools or with LaTeXDiff TeX file comparison.", "label": 0}
+{"snippet": "If we have a physical wave, say a waves in ocean, then we can observe still ocean and also disturbed waves on it with sight. But, why can't we do observe still eletromagnetic field with sight?", "label": 0}
+{"snippet": "Mr. smith and Mr. Jones can be expressed as Messrs. Smith and Jones. How can Ms. Smith and Ms. Jones, or Miss Smith and Miss Jones, or Mrs. Smith and Mrs. Jones respectively be so consolidated?", "label": 0}
+{"snippet": "In the following diagram, The human will see the real image, P', standing where they are. But, what if the human is closer to the mirror? Then P' is behind them so they clearly can't see P'. Do they see a blurred image?", "label": 0}
+{"snippet": "ANS GIVEN IS \"B\" I did understand that as the particle on the left oscillates, the tension in the string also oscillates and hence the particle on the left string too starts oscillating up and down as there is no torque on it, but I don't seem to understand why a net upward motion is there. What is the correct reason?", "label": 0}
+{"snippet": "We understand electrons move in the opposite direction of the electric field because of its negative charge. It was said magnetic fields are generated by current flows. What exactly are current flows? Is it the electrons or the electric fields?", "label": 0}
+{"snippet": "The simple definition of optical center for a convex or concave lens was given as point through which a ray passing suffers no deviation from its path, but is there any geometrical location of this point? (i.e. the point of intersection of principal axis and radical plane of two spheres containing centers of curvature or something along the lines of this?)", "label": 0}
+{"snippet": "When we type good in most online dictionaries including Oxford, Collins, Webster etc, various meanings come out. However, when it comes to standard, quality or performance both senses are given: satisfactory or acceptable excellent; high quality How can good mean both of these levels or does the context vary? The example sentences they provide do not really make it any clearer.", "label": 0}
+{"snippet": "It is of course overkill to use string theory for this, but I am still interested in how, for example, the trajectory of a horizontal throw of a mass point could be derived from string theory, after all, everything should be available in this theoretical framework to derive something like this.", "label": 0}
+{"snippet": "If one encodes the real numbers as the surreal numbers with countable birthdays, it seems that the tree representation can be mapped to the naturals by a simple breadth first traversal. What am I missing?", "label": 0}
+{"snippet": "Bakoma Tex software has stopped its services. I purchased the latest version, but now I am unable to install a new system. How to transfer the existing BaKoMa files to a new system?", "label": 0}
+{"snippet": "English doesn't really allow word contractions the way German and Dutch allow or even require. What rules, if any, are there when two nouns should contract to one or not? e.g. Why toolchain and keychain, but then supply chain and not supplychain?", "label": 0}
+{"snippet": "With the Gravitational perturbations among Neptune, Uranus & pluto, Is there anyway to know conclusively that there is no rogue Blackhole roaming the solar system? The Event Horizon may be very small, so no Mass falling in right now or for millions of years to increase the Surface Area, thereby, the Event Horizon...Thanks!", "label": 0}
+{"snippet": "Because if drift velocity of electrons is so slow than the actual speed of electricity which is near the speed of light. Then it might be possible that only electrons at the surface of metallic wire move at the speed of light .", "label": 0}
+{"snippet": "Despite quantum mechanics being in deterministic, is an event such as when the next eclipse will happen on earth be exactly determined since the beginning of the universe? Or the rough shape of and direction of a particular rock formation ? If one knew everything there is to know about the initial conditions of the universe, could one know this with certainty?", "label": 0}
+{"snippet": "While I was reading a book on basic vectors I struck a question that when we define resultant vector of sum of vectors is the vector joining the tail of one vector to head of other vector. But why do we join it? because how do we prove that it is the resultant vector? And sorry for that silly doubt", "label": 0}
+{"snippet": "My English grammar teacher said that English has following rules: A variety/number of something are... The variety/number of something is... We had the examples: A number of my colleagues are from Spain. The variety of monuments in Central Rome is shocking. Is it the only right answer?", "label": 0}
+{"snippet": "A TV presenter of \"Who Wants to Be a Millionaire\" lamented it would be a \"jolly weezer\" if the man made less than his wife on a game show. What did he mean?", "label": 0}
+{"snippet": "Is there any slight difference between these two? She bought two dozens of eggs. She bought two dozen eggs. In an online course a tutor told that second one is more appropriate if both options come in exam. They both appear same to me.", "label": 0}
+{"snippet": "How can I have an option to require some packages in a style file I am writing ? For instance, I can have a Science and Technology Option that makes available certain symbols. And another option to allow use of different fonts.", "label": 0}
+{"snippet": "Can a scenario be considered free fall in physics if the work done by forces other than gravity is zero, but those forces are still present? Or is it necessary for gravity to be the only force present for an object to be considered in free fall?", "label": 0}
+{"snippet": "I know this is out of convention and norm but I am typesetting an exam and using points for each question part and subparts seem to consume a lot of space. How do customize it to pts instead of points? Thanks for your help.", "label": 0}
+{"snippet": "Is Fock state a squeezed state? I assume that 'yes', that is how it beats shot-noise limit the next question is that what is its complementary variable? Basically is delta N -> delta p what is its delta x?", "label": 0}
+{"snippet": "I have a background in fiction writing and creative event planning as well as in business operations in international shipping. I want a word that could help me describe my background. With my ____ background, I possess a unique skillset that lies at the intersection of business development and creativity. Something like cross-industrial? but hoping for another word", "label": 0}
+{"snippet": "In reference frame moving with rocket exhaust speed is constant, so what is with power as speed increase? If power is const. in this frame, how is possible that at frame at rest power rise? Shouldn't any frame you choose must produce same results in physics?", "label": 0}
+{"snippet": "I would assume that complex polytopes (according to Shephard and Coxeter) too could be alternated (snubbed), rectified, truncated, etc. - possibly given some further restrictions. However I have currently no plan on how that might work in details. Could someone explain such operation actions, when being applied to those?", "label": 0}
+{"snippet": "Most sites that had a copy are now blank. I am looking for the version that was based on JRE. There used to be a DField and a PPlane. I am aware of new versions that are tied to MatLab but I am looking for the one that ran without having MatLab.", "label": 0}
+{"snippet": "So, simple question, are the bouyant force applied to an object by a fluid and normal force (Is it even there?) related? If no where is the normal force and why does bouyancy even happen?", "label": 0}
+{"snippet": "Given the spatial overlap of nucleon wave functions within the nucleus, why is the bonding of nucleons only the result of pion exchange and not of gluon interactions between quarks in different nucleons?", "label": 0}
+{"snippet": "In this diagram, as well as our universe, you have a parallel universe. Where does this come from? Is this just a artifact of the diagram, or is it predicted by the maths in some sort.", "label": 0}
+{"snippet": "I'm struggling to understand the statistic relation referring the observations of an HMM. That's clear for me: Output Independence My problem is how this equation can be derived: probability of an observation given the state sequence Thanks", "label": 0}
+{"snippet": "Figure captions stagger out of margin in the Chapter List of Figure created using the package titletoc. How to fix and make sure captions stay within the margin? Using package tocloft changes the heading title from the other chapters.", "label": 0}
+{"snippet": "The kinetic energy of rotation of a rigid body is given by: Write T in generalized coordinates in the form: Determine the explicit form of I opened the cross product with the civita levi symbol and the dot product with the product of the levi symbols, but I can't get the requested answer", "label": 0}
+{"snippet": "The title says it all. This is the polar opposite of this question. Whereas lexxie there was dissatisfied with the default behavior of longtable, I need to achieve this very behavior with tabularray.", "label": 0}
+{"snippet": "Simplified the question. Now if anybody can kindly explain the FBD for direction of normal force. PS: do not need the solution to problem of roller curb at a step but how the Normal force at A is pointed toward the point of application of force and not toward the center of roller", "label": 0}
+{"snippet": "Why the tangent line has two equivalent definitions, one is according to the Angle, the other is according to the limit position of the cut line, how the two definitions are equivalent, please give proof, looking for a long time can not find", "label": 0}
+{"snippet": "The range of electromagnetic waves and gravitational force is infinity and the particles exchanged during these interactions are photons and gravitons respectively. Both are massless following the relation: the range is inversely proportional to why. Then why are the intermediating particle (gluons) massless in strong interactions (as their range is in fermi)?", "label": 0}
+{"snippet": "This is similar to the totient function, but obviously somewhat different. I would be interested to know if formulae exist for counting the positive odd integers and the positive even integers up to a given integer N that are relatively prime to N.", "label": 0}
+{"snippet": "Especially for digital (modern) radar? Also is it possible (in the same configuration to integrate multiple pulses with the same carrier frequency with intrapulse modulation (each pulse has a different modulation pattern between each other ( frequency modulation for example or phase modulation))?", "label": 0}
+{"snippet": "Using pstricks and psaxes I'd like to create the axes just like in the attached figure. I tryed to change Oy, dy and Dy as well as the origin of the axis but I'm not getting the same as the figure. I suppose that it is very simple, but how? Thanks!", "label": 0}
+{"snippet": "So uhhh lets say there is some air, you've just put it onto the surface of the moon. Question being, if you are present within the mass of the air, can you listen to others and talk to them within the space that the air occupies?", "label": 0}
+{"snippet": "What is the difference between linear map, linear transformation and operator? Is linear map a definition requiring the domain and the range have same dimension and the latter two for domain and codomian with the same dimension?", "label": 0}
+{"snippet": "The answer to this question is gonna to be very short: what is the proper command to format the names of big mathematical theories like ZFC/PA/RCA etc. I.e. set theory and Peano arithmetic. I believe that they might be something like sanserif, but I'm not sure. Can someone help to me ?", "label": 0}
+{"snippet": "Anyone knows how to elegantly improve the following wikipedia (wikimedia) image quality from a Lipschitz continuity function to make it vectorial in Tikz or Pgfplots? Wikimedia Lipschitz continuit Visible here below: Thanks for your contribution!", "label": 0}
+{"snippet": "What is another way to say \"the problems that led to it\"? As in, Provides overview of the case, participants, background, and problems that led to it. Arguments for the plaintiff and defendant are thoroughly covered.", "label": 0}
+{"snippet": "I once saw a word for a hole carved out in a wall on purpose to accept a wooden crossbeam that fits into the hole. I think it had a \"p\" in it, something like \"pit hole\" ?...", "label": 0}
+{"snippet": "Why does increasing the magnetic field strength increase the force on a current carrying wire?- as outlined in the equation F= BIL where B is equal to the magnetic flux density around the wire Thanks", "label": 0}
+{"snippet": "People commonly see the insides of their eyelids and see a little amount of light and no amount of light of the insides of their eyelids depending on what environment they're in, What's the difference of seeing the amount of light of the insides of their eyelids?", "label": 0}
+{"snippet": "I am trying to type Python code by using LaTeX. The code is not being formatted properly Example: #PDF var = function(data, parameter= 'compile') #Copy it on my terminal var = function(data, parameter= ' compile ') Does someone has some suggestion how to fix it?", "label": 0}
+{"snippet": "For instance, there are the sentences \"Reading books is good\" and \"To be a hero is your duty.\" Could I say that books and \"hero\" are objects of the verbs reading and To be, and that together( verb and object) act as a noun, more specifically, as the subject of both sentences?", "label": 0}
+{"snippet": "What is the physical significance of electric potential? I know that over dx length of an electric field it varies but let us assume the field to be uniform, how exactly does the potential still change?", "label": 0}
+{"snippet": "I have a prism spectrometer which has two entry slits, two collimating mirrors and a rotating prism. I need to to find the the spectral resolution in respect to the changing width of entry end exit slits. What formula describes this dependency?", "label": 0}
+{"snippet": "My question is very simple I want to use the the LaTeX Math Black Board Font for a commercial design in Inkscape (does no matter file format), but don't know font name, nor download link.", "label": 0}
+{"snippet": "the plot is potential vs deformation, I want to know why there is difference between two potential vs deformation curves for the same and different compound nucleus and why the shape is like that.", "label": 0}
+{"snippet": "I am trying to create a compact database schema similar to the one presented Here and here is a screenshot for that : I am on two column setting too and I looked at this post but it is not as compact as the one in the picture.", "label": 0}
+{"snippet": "If that was the diagonal of a square grid Then, is there a common mathematical termonology of this diagonal ? And what about this Zig-Zag digonal-like shape, is there a common mathematical termonology for it ? By terminology, I mean a common name used in books and references to refer to these aspects.", "label": 0}
+{"snippet": "I know when mass becomes massive we need general relativity. My question is why do we need to incorporate special relativity since the mass is not in high speed .Cant we have Newtons law of gravitation for massive objects(curvature of spacetime without special relativity) Or we can say Curvature of spacetime without special relativity Or lets say curvature of Space, not time", "label": 0}
+{"snippet": "I have a default page header for all pages of my document. And the longtable headers which continue to the new pages overlap the default page header. Is there a way to make the continued longtable to leave enough vertical space to avoid overlap with the default page header? Thanks! Reshmi", "label": 0}
+{"snippet": "i have problem in my preamble, i observed that as the page number for the \"List of Tables\" is taking the page number of the last page of your document for example Tile page (i), Declaration (ii), Certification (iii), Dedication (iv), Acknowledgements (v), List of Tables (xiv) instead of (vi) . what can i do", "label": 0}
+{"snippet": "Two BML models M, w and N, w' are given: in M, w has with infinitely many R-transitions of finite length, and in N, w' has infinitely many R-transitions and also includes an infinite-length R-transition. How can one use bisimulation games to prove that M, w and N, w' are equivalent but not bisimilar?", "label": 0}
+{"snippet": "In a standard jet engine on a standard aeroplane, is the majority of forward force received by the aeroplane (which causes it to be propelled forwards) applied on the compressor blades, the rotor blades, the internal body of the blade surrounds, a combination of these, or somewhere else?", "label": 0}
+{"snippet": "Imagine I bought something, but instead of giving me worse product for what I'm paying, the seller gives me a far better product for my price, without my knowledge. Is there any term for this?", "label": 0}
+{"snippet": "Commands can autocomplete, but ideally, I would have an extension that can also autocomplete main body text. I have this in VS Code, but I like the overleaf editor more. Does anyone know if such a tool or (chrome) extension exists?", "label": 0}
+{"snippet": "As a naive person I thought annihilate meant destroy. Matter and antimatter destroy each other, cancel each other, nothing left over. This pure energy idea is a big surprise also it fits no category of energy as we know it, kinetic etc Can someone bring me to understanding with simplest possible maths, please?", "label": 0}
+{"snippet": "For a symmetric matrix we have: That is comparable to what we do, to what you learn in the first analysis course with one variable. And that was already clear to me, also in linear algebra. But the reason behind it is the following: Can anyone explain the intution behind the second equation? It's a definition in the book I currently read.", "label": 0}
+{"snippet": "Is it true that electron wavefunction can be conceptualized as different periods the electron spends in all possible states, so when we interact with it it's more probable to find it in states in which it spends more time compared to states in which it spends less time just like unfair coin when it lands.", "label": 0}
+{"snippet": "I have a table in .png format and want to place it in half a column, the other half of the column will have text as in this example figure. How do I do that?", "label": 0}
+{"snippet": "Mass(-energy-momentum) curves space(-time). However - what is space-time? Is it (the background) necessarily flat(without something in it) ? If there were an empty universe - is there still spacetime in it - or not?", "label": 0}
+{"snippet": "I am working on a presentation on beamer and i used the theme Madrid but i am obliged to use the title page ppt template given by my institution, how do i have the first page as the template and the rest of the presentation following the theme ?", "label": 0}
+{"snippet": "In the introduction of the book lambda calculus with types by Barendregt, there are examples of typed functions like And I wonder what operation the underlined type expression is for. Although we can surely make an operation of the type, I want to find the real example in functional analysis that the author was thinking about. The cited book is Lax, Functional Analysis.", "label": 0}
+{"snippet": "When one has lost both parents due to death the word orphan is used. This word is generally but not always used for children. It can in spoken English also be used for adults. My question is what about the loss of one parent? Is there a word for this?", "label": 0}
+{"snippet": "Given the following question - I'm required to find all the Perfect Bayesian Equilibrium and specifically state whether they are pooling / separating. Struggling to understand what would be the types (beliefs) in that game, is it <D, D'> are the pooling, and <C' D> , <C' D'> are the separating?", "label": 0}
+{"snippet": "If as water evaporates it carries energy with it and therefore there is a reduction in temperature, why does the temperature remain constant in the phase transition between liquid water and gas water?", "label": 0}
+{"snippet": "Can we define an average time for the entire universe relative to the Big Bang and call this the universal time since the beginning of the universe? (time, averaged relative to all possible reference frames)", "label": 0}
+{"snippet": "I'm using pst-barcode to generate rectangular datamatrix. Although I have problem with the fact \"that the barcode is printed in a TEX box of zero dimension\". The manual suggest using fbox and pspicture environment, but it require to know the both sizes of the code apriori. Specyfying only width results in deformed code.", "label": 0}
+{"snippet": "Consider the attached Toroidal wind Tunnel. The Wind tunnel is in Vacuum and the moving air and the attached wing are only inside the toroidal tunnel. Will the mounted wing on the walls of the tunnel experience force and move the Toroidal tunnel as shown in the picture. Thank you.", "label": 0}
+{"snippet": "I could come up with examples for rings;say for example defining the homomorphism to be a left shift of elements which are taken to be of the form of a countably infinite tuple.Can someone help me out by giving an example for Integral Domains", "label": 0}
+{"snippet": "Do you know any reference where this result is proved? We have already proved it but since we know that this is a known result, we want to omit the proof and cite a proper reference. Here you have a caption of the result, which involves the roots of a monic polynomial and the gamma function Result", "label": 0}
+{"snippet": "I have got a lecture and there were the following frames used in the presentation. Can anyone please tell me which style this is, because I really would like to use this as well.", "label": 0}
+{"snippet": "Does the event when two BH without polar jets merge, cause a short living polar jet on the newly formed BH? As BH need infalling material to activate their polar bursts does the BH falling into another one as it brings the needed material provoke the polar jet?? (Thanks for answering...)", "label": 0}
+{"snippet": "English is a foreign language for me, so I have to use a Google Translate or similar services. They give same translation to my first language, and I feel some nuances are being lost. Examples: Confession with the venerated minister. vs A highly revered missionary from Africa.", "label": 0}
+{"snippet": "Hi I am doing a presentations, and to all of them I use the same tex file with document settings. I'd like to have one folder on desktop with file with settings, and in each presentation a path to this tex file. Is it possible? If so, how can I do this?", "label": 0}
+{"snippet": "I think it is impossible for a group to contain just a left or a right zero, because it would violate the identity property, but I am unable to put it into words. Could someone help out?", "label": 0}
+{"snippet": "What I'm looking for... Do it exist tools \"tracking\" or reporting macros and environments used when compiling one TEX file? Why? To build my unit tests, I need to verify if my package is fully tested.", "label": 0}
+{"snippet": "Talking of memory, which is correct? To my heart Or In my heart If talking of belonging, which one is correct? She always belong to my heart Or She's always in my heart Can I use \"always to my heart\" without indicating \"belong\"?", "label": 0}
+{"snippet": "I need to know if what I said here is true or false. \"can a Bayesian model give a probability distribution over potential diagnoses\"? (HS student) if this statement is not factually correct is using Bayesian analysis for the same use factually correct", "label": 0}
+{"snippet": "click here for image Could I please have confirmation this is the correct way to solve this question using the given information? Note: I could not directly upload the image since it was apparently too large.", "label": 0}
+{"snippet": "Hello there is a problem and a solution to it ,which shows how to find the resonance. There is a solution to the problem which basicly looks at a periodisity of an exponent. but how they got to this conclusion that periodisity of exponent is linked to resonanse? Thanks.", "label": 0}
+{"snippet": "Do only gas planets have discs or even rocky planets may have them orbiting around? If rocky planets are great in volume is then a higher chance for an orbiting disc to exist in the planetary orbit?", "label": 0}
+{"snippet": "The two Spanish prevailing explanations that get repeated are the Spanish vamos and the British dialectical mose about. These explanations are at least two decades old and predate the internet digitization of substantial material. And, from an American perspective, not very convincing.", "label": 0}
+{"snippet": "enter image description here By introspection I think i will have to somehow use a difference of two numbers in the numerator to cancel our excess terms. The main problem I am facing however, is with a clean approach to the min function, namely finding the coefficient of the x-squared term.", "label": 0}
+{"snippet": "These two possible combinations confuse me: The energy required to heat the water is... The required energy to heat the water is... I have always used the first combination, but the AI grammar check generally prefer the second option. Which combination is in your opinion the correct/better one? Why?", "label": 0}
+{"snippet": "Do the running with energy of the electron charge and of the W boson electric charge differ or are they the same? Is there any theoretical or experimental evidence that allows the comparison?", "label": 0}
+{"snippet": "Suppose you specify that the sea must be a royal blue, and no land territory is allowed to be. Does the map then need five colors? Or can the island necessarily be colored with three (non-royal blue) colors?", "label": 0}
+{"snippet": "This is the equation: It's from mynt.T.U book for Advanced engineering mathematics. I just want some hints. Edit: how can I reach to right side of the equation, using the left side and fourie transform. I don't know what to do with (ax-b)", "label": 0}
+{"snippet": "When you charge a lithium battery for instance the electron momentum that coming out of the source is stored in the battery. The problem is that the direction of the electron might change when connecting the battery to consumer", "label": 0}
+{"snippet": "I want to create a solution environment that works somehow like this: If at the beginning of the document, solutions are TRUE I want to show the text in the environment and be highlithed. If it is FALSE, the environment should pretend as if there is no text at all. Is there any possibility to create such an environment?", "label": 0}
+{"snippet": "When a particle leaves vertical circular motion after slacking. Is it possible the body at the end of string will move to the centre and can we calculate that intial velocity in a parabolic motion as well as intial velocity in which the ball is thrown at the starting? Given centre coordinates (a, b)", "label": 0}
+{"snippet": "Consider a circle inscribed into a regular pentagon. (a) How to prove amount of straight lines which can dividing into two parts with equal area the disk and the regular pentagon as much as amount of vertex pentagon. Also (b) amount of straight lines will be same if regular polygon inscribed into a circle.", "label": 0}
+{"snippet": "In the logic context, both the terms operator and connective is used. I wish to know what their differences are. Do we use an operator when we have something that effect only one formula and connective when it some sort of connect two formulae and effect both?", "label": 0}
+{"snippet": "I was doing a test in which it involved the change of variables theorem, but the answer he had was negative. I found out that my professor used the determinant of the u and v, but ignored the absolute value? Is there a reason why that may be the case?", "label": 0}
+{"snippet": "I am currently studying categories without products. I have found that the category of fields has no products Examples of a categories without products, in the proof an endomorphism appears and while I was trying to understand it, I came up with the question Are all endomorphisms identities in a category? I have no idea how to answer that question. Can someone help me?", "label": 0}
+{"snippet": "I want to have a book name Solution manual: Steps in commutative algebra R.Y Sharp I don't have so much experimence about commutative algebra. So someone here have a file or link about this Solution manual book Please help me", "label": 0}
+{"snippet": "since the rotating coil which produces the induced emf that varies sinusoidally the emf produced for one complete revolution of the coil is zero. then for any number of rotation the induced emf should be zero only no then why they are calculating the emf induced", "label": 0}
+{"snippet": "I am unable to find a representation online about the Dirac three polarizers experiment with a time development operator and Griffith's Consistent Histories treatment of the set up. Would anyone like to present it here?", "label": 0}
+{"snippet": "I heard the royals used 'we' instead of 'I'. The royals makes impressed food. So we are gonna roll out the red carpet and spare no expense. Word 'We' means 'I' in this sentence?", "label": 0}
+{"snippet": ". . . and is one preferred over the other? I believe he sent these contacts an email earlier this week. I believe he sent an email to these contacts earlier this week. I feel the second is preferred because \"an email\" is the true object of \"sent\". But I'd like to know why.", "label": 0}
+{"snippet": "Sometimes it is described as a state of disorder and sometimes it is called the inavalability of the thermal of energy of the system to do mechanical work. So How exactly is entropy defined? Also, how does it explain why time flows in one direction.", "label": 0}
+{"snippet": "My university is asking for a specification of an algorithm and provided this block scheme as an example. I an not very good at latex so I googled how to do this with tikz, but did not found something useful.", "label": 0}
+{"snippet": "Two points are moving on Euclidean plane (absolute space) smoothly and in every instance velocity vector of each of them is in the direction of the position of the other one. Is it true that they are both on a fixed line?", "label": 0}
+{"snippet": "What is the analogue of the Malus law for polarized electromagnetic waves to the cause of plus and cross polarized gravitational waves? Bonus: What if gravitational waves have further degrees of polarization like those in modified gravitational theories?", "label": 0}
+{"snippet": "Let say that there is no air drag. A ball is thrown towards me and I hit it with a bat. Here of course I apply some force in hitting it. Then can someone help me out by explaining how does the ball obey first law over the course of its motion.", "label": 0}
+{"snippet": "I do found lots of introductions about the definition some other characters of Half-Plane model. But now I need to study characters of the curves above it, like curvature, evolute. While I fail to find relevant theses or textbooks. I hope someone could give me some suggestions.", "label": 0}
+{"snippet": "I am looking for self study inner functions and Blaschke product from the scratch, yet I could not find any beginner friendly resource out there. It would be much appreciated if you could recommend me a source.", "label": 0}
+{"snippet": "I a book the \"Upper closure operator\" definition is given by: I do understand the concept of the Upper closure operator. But I cannot figure out how to read the last line. Could someone explain it? Thank you.", "label": 0}
+{"snippet": "According to the readme of the ebgaramond package it adds font styles: What do I have to do to set a certain part of the text to semibold? What do I have to do with the sb?", "label": 0}
+{"snippet": "I understand what a taylor series mean and how does it work but I don't understand what it means for it to be about a point or does that point have any outcome on the result of the series.", "label": 0}
+{"snippet": "In figure (A), book shows electric field lines just coming out of each face of the infinite sheet having charge perpendicular to area vector but I thought that the electric field lines which are anti parallel to area vector of both surfaces must also be there, which I tried to show in figure (B).", "label": 0}
+{"snippet": "I want to write some research paper in number theory and graph theory , but dont know where to start , which topics to learn . PLS suggest some topics and new fields under these subject which are under development and research.", "label": 0}
+{"snippet": "I want to determine a suitable range for the efficiency energy conversion of magnetic energy to thermal energy in usual magnetic reconnection because usually it is said that this process is highly efficient but I want to put some numbers there and of course try to compare with other processes to explain why it is an efficient process.", "label": 0}
+{"snippet": "The number dimensions defined by new theories keep going up. Is there a limit as to how many dimensions the universe can have? Weird question. The curse of dimensionality in computer science illustrates how two data points get further apart as more dimensions are added to its analysis. Could a similar analogy be applied to the dimensions of the physical world?", "label": 0}
+{"snippet": "I use Charpit Method to solve the problem but calculation is so big. Is there any another method to solve the problem.I think I need some variable transformation which gives me a standard form then I easily solve the problem.", "label": 0}
+{"snippet": "when I using the kpsewhich to find the system font like this: /app # kpsewhich --format=\"ttf\" Kaiti.ttf warning: kpsewhich: Ignoring unknown file type `ttf'. is it possible to use kpsewhich to search the ttf/otf fonts?", "label": 0}
+{"snippet": "enter image description here It is claimed that an intersection touching the base details of a square prism of this shape must be rectangular, what is the reason for this, can you help?", "label": 0}
+{"snippet": "I am new to LaTeX and I have received instructions from the journal to change my LaTeX references to conform to (journal is Cell iScience). whatever I do I cannot fix this issue, please help me.", "label": 0}
+{"snippet": "Except for the well known one , using the auxiliary quadratic equation, is there another formula, either using only elementary math or not? This is a nice elementary alternative which is nearly a formula.", "label": 0}
+{"snippet": "If a craft is positioned at the strongest point of the earth's electromagnetic field being either positive or negative and the craft activates the same field it would repel each other would it create trust and what speed would the repel be", "label": 0}
+{"snippet": "This is not technically a question but more of a help , I need some books to help me go into the theory of two scales and their applications in Partial differential equations.", "label": 0}
+{"snippet": "like charge is fundamental property of matter which exist in both negative and positive aspect and help us to understand the electro-magnetism ,in the same ways would mass be negative ? in that scenario gravity could be repulsive too?", "label": 0}
+{"snippet": "Is one of you near my office? Are one of you near my office? ChatGPT says that they are both grammatically correct which means people use both (i.e., there exits mass confusion). The subject is \"one\" which would imply the first but that option still sounds weird. I thought it was time to move from AI to RI - that's where you come in!", "label": 0}
+{"snippet": "It was supported by stating that a reliable fabric supplier has been found and that a major competitor is no longer making alpaca overcoats, because of which demand will be high. Why is there a comma in this sentence?", "label": 0}
+{"snippet": "If the JWST has just discovered the furthest away galaxies in one place we can now triangulate to where the centre of what we can see This is observable and appears not symmetric with everything expanding symetrically.", "label": 0}
+{"snippet": "Here we get two energy levels uB and -uB which are discrete, but particles follow MB stats, it means there energy is continuous. I am getting confused, what is the role of the MB stats in such a case?", "label": 0}
+{"snippet": "Current flow from positive to negative terminal in a circuit. But the charges which are moving in the circuit are the electron that is moving from the negative terminal to the positive terminal. Why we chose the opposite direction as electric current, not the real one?", "label": 0}
+{"snippet": "I wanted to align a table of equations all left, no numbering needed. A similar question was asked before, but not answered in a way useful to me: Align equation left The page urged me to ask my own question since I do not have enough reputation. But I have figured it out, so the answer is below.", "label": 0}
+{"snippet": "The lthooks documentation says: But how should one know in advance if the hook with this given label exists or not? In my package I wish to clear the code with a given label in a hook before adding new code with that label to ensure that the code added is not duplicate. How should I do this without triggering the warning?", "label": 0}
+{"snippet": "Those hydrogen or mercury tubes should not be coherent, but when looking at them through a grating without using a small aperture in front of the tube, you still see the discrete lines. Or just any random ceiling light really, without using any aperture you still see rainbow through a grating. How could that be?", "label": 0}
+{"snippet": "With regard to the answer of this question, Full proof of Black Scholes may I know how does the dz was changed to dy in the first few steps and later on switch back to dz?", "label": 0}
+{"snippet": "In a comment of Fractal of the topologist's sine curve is connected and totally path-disconnected? M W asserts that the existence of a dispersion point, a point for which the removal of results in a totally disconnected space, implies that the space is totally path disconnected (even before the removal). Why must this be the case?", "label": 0}
+{"snippet": "is the viscosity of a fluid maximum at the layers adjacent to the surface? I think this because the molecules of liquid now experience a greater friction force because the adhesive forces also resist their ability to flow.", "label": 0}
+{"snippet": "Each of the spectacle lenses in this image cause two separate refraction patterns: The patterns are different between the lenses because each eye is different, obviously, but why are there two different patterns within each lens?", "label": 0}
+{"snippet": "Which exactly is the difference in meaning and usage between choosing whose versus choosing which in this first sentence? He chose to live in the room [ which / whose ] door was broken. How do these compare with this second sentence? He chose to live in the room, the door of which was broken.", "label": 0}
+{"snippet": "As we can see below. The theory says that A,B coeffietionts are depending on excitation. I have simulated a circular waveguide, How do i need to excite my waveguide so i will see the A and B coeffiencts of the field change?", "label": 0}
+{"snippet": "Here are two boy's cars. But. Here are two solutions key points. Why in first example is \"'s\" used and in second one it's not? I checked with LanguageTool and GoogleTranslate. I want to explain to key point for the solution of a problem, then used a tools and get confused. https://www.britannica.com/dictionary/eb/qa/How-to-Make-Possessives-in-English Or is this correct? Here are two solution's key points.", "label": 0}
+{"snippet": "How I do create an index of a text with all words of the text. Words in the index must have the reference of the section, the page and the line where is the word. thanks", "label": 0}
+{"snippet": "I am making a academic presentation. I want to put the reference in the block. But I want to put the reference number directly after word \"Theorem\". so I tried The reference showed up right in the block which is really terrible. It seems that the block affects the footcite. How do I solve it?", "label": 0}
+{"snippet": "I want to find a formula for the nth dose derivative of the function I have tried to use the first line as my start point but am getting confused. I want a set of coordinates that can depict the local maximum of the nth value. the equations above are surge functions.", "label": 0}
+{"snippet": "While obviously not optimal, I've usually found that such an \"algorithm\" is pretty close to the true shortest possible path, and is obviously runnable in polynomial time, with an O equal to your sorting algorithm", "label": 0}
+{"snippet": "I am using a document class report and I need the first page after the title page to have some text on it (it is my layperson summary) and after that the abstract and the main part of the file. Is there a way to do it? I am inputting both that piece of text and the abstract from separate .tex files.", "label": 0}
+{"snippet": "My professor explained me in the best manner possible about the electric potential energy and why it is NOT defined for a single charge, BUT my question is as Electric potential is just electric potential energy with one charge being a unit positive charge, therefore is electric potential also defined for a system of charges?", "label": 0}
+{"snippet": "when I worked with idea of something being homogeneous. I always felt I reverse engineering what we are doing in linear algebra to find the eigenvectors and eigenvalues. could someone explain it simply", "label": 0}
+{"snippet": "I am reading the synctex source code, now I found he comment mentioned two type of coordinates, page coordinates and TeX coordinates. anyone know about the two type of coordinate system? The docs only mention that page coordinate The origin is at the top left corner of the page.", "label": 0}
+{"snippet": "Inside negatively charged ball there is constant electric potential. If electron will be placed inside ball with constants potential will it give mass from electric potential as same as higgs field give mass?", "label": 0}
+{"snippet": "I'm trying to determine electric motor power sizing with requirements given for covering a particular distance within a certain time. The knowns are the vehicle mass, the allotted time, the target distance to cover, and the vehicles initial velocity. The result would be used as the absolute minimum possible motor output power rating that would satisfy the requirement.", "label": 0}
+{"snippet": "Do Solar Eruption occupy more than one rotational layers? Is it possible to confirm this just for most outer layers? Does the number of layers occupied by those eruptions when they happen tell us anything about the relationship between Gravity and Entropy? #Update This is how i imagine Sun's Differential Rotation Each speed on the image has a different value", "label": 0}
+{"snippet": "So it just hit me, \"When is just before\"? Cos just before could be a second ago or half a second ago or a tenth of a second ago and so on. So when? And do the final velocity formulas put this into consideration?", "label": 0}
+{"snippet": "if we are able to create plasma in isolated environment possessing temperature much more than temperature of sun then why are we not able to create something that can go to the sun?", "label": 0}
+{"snippet": "It is always confusing to me what to call the network with which we make phone calls. If mobile network regards to accessing internet with cellular data, then what network it is called to make phone calls?", "label": 0}
+{"snippet": "Just curious how these two magnets are spatially related to? And in case there is no any special preferred particular orientation, what is anyway their spatial orientation relation (relative angles)? Possible varying with seasons or year cycles. There must be a record of these measurements? I cannot find anything about this on the internet?", "label": 0}
+{"snippet": "In mathematics different integer also that mean different rule to for divisibility of integer, But this is not flexible way to learn divisibility of Integer then Is there another way, maybe some kind of formula to learn it? And also if there is, please provide the source, I would really appreciate it", "label": 0}
+{"snippet": "I understand the kernel is the map of everything to zero, but does that mean that the only way for a kernel who is just made up of the zero from the previous area is for the range to equal the codomain.", "label": 0}
+{"snippet": "When I was under the shower I experienced when I look quickly at a single line of water falling from one pore (from top to the bottom) it looks \"drop drop\" instead of continuous. Why is it like that?", "label": 0}
+{"snippet": "Pretty coincidental that time happens to be like the three spatial dimensions.. or is it? Time is one dimensional with past and future, similar to left and right, up and down, back and forward of the other dimensions.", "label": 0}
+{"snippet": "We are currently using the term circularizing (I made it up) as the technique of using artificial intelligence to check something, have devs check what artificial intelligence suggestions, which allow artificial intelligence to spit out new data, that devs have to check, and on and on. Is there a word to describe this process or can I just use what I made up?", "label": 0}
+{"snippet": "If we change slits' width in ydse, what changes will be seen in the fringe pattern and it's density I found a source from a book saying but how could the pattern gets less sharp on increasing the width, if we increase the width less waves will be diffracted thus more sharp please someone help me with question", "label": 0}
+{"snippet": "What maths notation to give to the set of elements composing leaves of a tree structure? Suppose the tree T is n-ary, I want to notate the set {n / n in Leaves(T) } How to do that?", "label": 0}
+{"snippet": "If gamma ray burst contain energy equivalent to the mass of the sun, then it would be bent by its own gravity and refocus periodically, right? It could possibly go on forever without dispersion, enabling it to travel across the universe?", "label": 0}
+{"snippet": "In LMFDB, equation of some curves are given however there are also those are not. My question is \"Is it possible to find explicit equation of curves by using its generating vector?\" I add link for you to see example. The curve that we have its generating vector", "label": 0}
+{"snippet": "We know in pure translation force distributed evenly in each particle on rigid body, so in effect every particle of body moves with same velocity or acceleration in pure translation. What happened in pure rotation, how force is distributed in pure rotation particle by particle to moves a body in pure rotation?", "label": 0}
+{"snippet": "The question is as simple as that. This is the kind of thing I want to achieve: The idea is to make a symbol used for divided differences. It needs to be a true delta letter rather than a triangle, but actually it is not that easy.", "label": 0}
+{"snippet": "the graph of the function[The graph of the functionthe graph of the first derivative of the functionThe attached graph shows the existence of turning point but the first derivative of the graphed function is never zero anywhere within the domain of the function. What does this mean?", "label": 0}
+{"snippet": "In general spectral analysis, we have examples of unbounded from below hamiltonians with discrete spectrum. Is it okay to say that they have no sense in physical context, because for me it looks like particle can emmit infinite energy in some weird sense.", "label": 0}
+{"snippet": "I want to mark a fraction, which I shorten, with an arc. Haver anybody an idea how to start? I wish that it looks like the text in the picture. Is there a way to do it?", "label": 0}
+{"snippet": "i Know elementary and their applications and there is a theorem: \"The inverse operation (function) of an elementary row operation exists and is a elementary row operation of the same type.\" i want to know the proof of this theorem! thanks :)", "label": 0}
+{"snippet": "I am looking to study more about electron impact ionization. I noticed that this topic or anything collision-related, is not present in Chen in detail. Is there another resource that I can use to understand this better?", "label": 0}
+{"snippet": "suppose we have a circle to which we make a target and rotate it without breaking the basic definition of a tangent how many tangents are drawn as rectangles strips i have tried with integrals but I really want to know the answer to this question", "label": 0}
+{"snippet": "I searched on the Internet for the answer and found none. How can one find it? Also, I write \"SLITEX\" because methinks every letter of the name is, even if small, raised or lowered, the capital one but feel free to groundedly correct.", "label": 0}
+{"snippet": "If still charges in a wire loop do not respond to a(or have their own) magnetic field, then how is current is generated by changing a magnetic field? And why only a changing magnetic field? What actually happens at the atomic level?", "label": 0}
+{"snippet": "Though both of these terms come from other languages, they are both said in English, depending on where one is. One (ay wey as a more English form) can mean holy crap!, and the other can mean something similar. Maybe it can be due to a related background?", "label": 0}
+{"snippet": "I have not got any solution after a few try. In latex, how we can comment out a single word from a line. I mean for example Hello %this is so on it comments out this and the rest of the line as well. Is there any way to comment out only this part, not the rest of the line ?", "label": 0}
+{"snippet": "When an ideal gas is compressed isobarically the given energy by the external source is let out as heat alongwith some more heat that comes from the decreement of internal energy. My question is why doesnt the energy given by the external source increases the internal energy and some lets out some heat?? Maybe I am missing something conceptually about so please help.", "label": 0}
+{"snippet": "While proving associative property of vector addition graphically, everything else appears symmetric except the fact that vector a do not have a derived line as part of the final graph. Is it due to a being considered base?", "label": 0}
+{"snippet": "Let the Zhegalkin polynomial for function consist of those and only those monomials that are not included in the polynomial for function . How different can the functions and be? (Write the maximum and minimum number of sets on which they different for each ).", "label": 0}
+{"snippet": "i used to substitute a value into the actual book prescribed answer and the into the answer i got to see if the equations yield the same answer. i now want to confirm if the method i am using is legitimate. this is my solution to the question this is the book solution", "label": 0}
+{"snippet": "This question looks like me value theorem by canceling of a way to apply it in the problem quite yet. An image I messed around with the given equation and tried to set it equal to the second derivative but it I came up with nothing. I'm suspecting that my method to solve this problem is incorrect.", "label": 0}
+{"snippet": "I asked a question a while a go what is a bound state and the question was closed because there is a similar question. Now since best description we have to describe nature in quantum field theory How we define bound states in quantum field theory?", "label": 0}
+{"snippet": "have you ever encountered works on set partition in which the principle of inclusion exclusion is used in the case of a single parameter and reused in the generalized case (with several parameters) ?", "label": 0}
+{"snippet": "Does there exist such a notation? It looks similar to old factorial notation, but its in upper right corner rather than lower left. I need it as math environment or with some simple code so as to achieve: These are made in ms word.", "label": 0}
+{"snippet": "If particles are excitations of fields: how does the field record the spin of a particular particle? There is no space to record the spin states of two particles, of opposite spin, in the field.", "label": 0}
+{"snippet": "I what taught that my last name which starts the Mc that the c should be above the symbol =, does anyone know what this means? I can not really type it out on a key board but if you write it out with a pencil you can see the M \"lower case c with = under it\".", "label": 0}
+{"snippet": "I have the following in my notes: I dont understand the statement 'simple model fails' Is the graph shown supposed to be theoretical model or is that the experimental data. This are equation derived before the graph:", "label": 0}
+{"snippet": "I feel that the reason to define thing like current density is that we want to use the directional nature of the current like a vector quantity and since electric current is not a vector so we define something which has same direction as current but a vector? is is true?", "label": 0}
+{"snippet": "my sir told me that he will get a shock, but why not bird then he replied bird has legs acting as insulators i am in confusion what is the right explanation to this", "label": 0}
+{"snippet": "I make reference at this question: Package pgfkeys: I do not know the key '/tcb/O' and I am going to ignore it and to accepted answer. If the text of question and or of the answer span on the next page, like here: the left arrow dont span on the next page (with both tcoloboxes breckables). Can we solve this problem?", "label": 0}
+{"snippet": "I was at a complexity optimization class and they said all constant sheaves are a twist of a perverse sheaf; is it specifically in complexity optimization or is it true for all constant sheaves?!", "label": 0}
+{"snippet": "I'm using the Overleaf documentation to produce a bibliography with in-text citations, using bibLaTeX (compiler is XeLaTeX, document class is article). I've tried all of the citation styles on the overleaf webpage, and none produce superscript in-text citations (i.e. numbers as superscripts). The closest I can get is numbers in square parentheses. Is there no citation style that has superscript numbers? Or does this indicate that something else is going wrong?", "label": 0}
+{"snippet": "I have seen that the notion of affine scheme is a generalization of the notion of affine varieties where the coordinate ring is replaced by any commutative unit ring, and the variety with the Zariski topology is replaced by any topological space. Does this mean that every affine variety is an affine scheme? I think that if we have an affine variety X and we construct its structure sheaf then the affine variety is a locally ringed space but how we conclude that it is isomorphic to a spectrum of a ring? Or there is another proof of this statement?", "label": 0}
+{"snippet": "Is there any expression in English that refers to the situation when someone who is just an acquaintance (not a close friend) happens to be present around you at a social gathering (be it at a house party, a club ...), and you are debating whether to show them that you have seen them out of being shy or to avoid an awkward greeting? I'm seeking anything that fits the bill, whether it's a single word, or a phrase.", "label": 0}
+{"snippet": "A directed graph G=(V,E) is given and I am asked to prove if there is a tree of shortest path of this graph that cannot be returned using BFS. Meaning to say if it is true or not that for every tree of shortest path a BFS can return it. I thought that the answer is true, for every tree of shortest path there is a way of arranging the adjacency lists of G such that a BFS can return this tree, but I cannot find a mathematical way of proving it. Or maybe it is false, meaning there is a counter example of a tree of shortest path that cannot be returned by BFS but I can't find this example either. I would appreciate some help, thanks!", "label": 0}
+{"snippet": "Airplanes traveling at supersonic speeds produce sonic booms because the pressure waves they create converge to produce an extra high intensity wave. But what about planes traveling at slower speeds? These create pressure waves too (although they do not converge). Are these pressure waves the sound you hear from an ordinary plane in the sky? I always thought the sound of an aircraft came from its engine noise.", "label": 0}
+{"snippet": "Chess is an incredibly intricate game, offering an immense number of moves and combinations. Due to this complexity, determining the precise count of legal chess games poses a significant challenge. As of my knowledge, the total number of possible legal chess games remains unknown due to the vast array of potential moves and positions that can emerge during gameplay. However, I've been pondering an intriguing question: Can we establish whether the total number of legal chess games is odd or even? It's a captivating puzzle that has captured my attention. I've given it considerable thought, but I must admit that I'm still uncertain about the parity of the total number of games. Can anyone direct me how to approach this?", "label": 0}
+{"snippet": "The Hills mechanism postulates that when a stellar binary system is perturbed by a supermassive black hole (SMBH), the tidal forces at play result in the capture of one star while simultaneously ejecting the other. My question is as follows: Why does one star become captured while the other is ejected? Is it not possible for the SMBH to capture both stars and maintain the binary system within its orbit, or alternatively, eject the entire binary system?", "label": 0}
+{"snippet": "A graph is homogeneous when every isomorphism between two finite induced subgraphs can be extended to an automorphism of the whole graph. I was reading Diestel's graph theory where he describes the following graph and says its clearly homogeneous. It's not immediately apparent to me why. If I have an isomorphism between two finite induced subgraphs, and map every other vertex outside the subgraphs to itself, does it become an automorphism of the entire graph? But wouldn't that make almost anything homogeneous? What is special about this one?", "label": 0}
+{"snippet": "Most eye floaters are caused by age-related changes that occur as the jelly-like substance (vitreous) inside your eyes liquifies and contracts. Scattered clumps of collagen fibers form within the vitreous and can cast tiny shadows on your retina. The shadows you see are called floaters. If you look in a mirror while getting floaters would you see an image of the floaters in the mirror? Since they are basically shadows on the retina, I think we should theoretically be able to see an image but practically not because the shadow image would be very small.", "label": 0}
+{"snippet": "I have been trying to find the proof of the derangement theorem, and have checked out some materials on them (since its proof has not been taught to us). But I have not been able to understand much of it. So, I was thinking, is the inclusion-exclusion principle used? Since the expression seems somewhat familiar. If not, then could someone please explain the proof in a slightly simplified manner?", "label": 0}
+{"snippet": "I am trying to understand what fugacity really is. I asked a related question on chemistry stack exchange but am not satisfied with the answer. In many books, such as Physical Chemistry by Engel and Reid, Physical chemistry bh Castellan, etc. fugacity is called as effective pressure. My questions are a)What does the word 'effective' is trying to say? and b) If we already have various equation of states that have already accounted for intermolecular forces, then why is there a need for fugacity? I'm sorry if this is a stupid question but english is not my first language and maybe I am not interpreting fugacity correctly. So any help is appreciated!", "label": 0}
+{"snippet": "Objects appear in different colours because they absorb some colours (wavelengths) and reflect or transmit other colours. The colours we see are the wavelengths that are reflected or transmitted. As far as I understand, when an atom absorbs a photon, one of its electrons gets excited (and unstable). So it drops back to ground state, emitting that energy in the form of photons of a specific colour. This means that we should find objects to be in certain colours, but, for example, hydrogen gas is colourless. How is this possible? Shouldn't Hydrogen gas have a specific colour related to its emission spectra? I was reading an article on this topic today (https://www.khanacademy.org/science/chemistry/electronic-structure-of-atoms/bohr-model-hydrogen/a/spectroscopy-interaction-of-light-and-matter), and this came into my mind. Can anyone please help in clearing my understanding?", "label": 0}
+{"snippet": "What I mean is how the shape of an object affects it's physical properties. I've been studying Marine Biology and there's constant talk of how a fish's shape determines how well it can swim but no explanation of why, say, \"Stream lining\" reduces water resistance outside of it \"just making sense\" and I'd like something more in-depth. Similar phenomena would be: How a blade's shape determines how it cuts, Why certain shapes are more structurally sound, What determines a shape's aerodynamics. Is there a field of research dealing with this? It's been driving me mad.", "label": 0}
+{"snippet": "An excerpt from my grammar lesson: In a formal context, 'due' should always be treated as an adjective, and 'due to' must therefore follow or refer back to a noun, as in: his success was due to hard work. In this case, how is 'hard work' considered a noun? In a prior lesson, a noun was defined as a word that names a person, place or thing. by this definition, isn't 'hard work' more appropriate to be a verb? Am I missing something?", "label": 0}
+{"snippet": "I recently engaged in a lively debate with a friend about whether the term \"hot dog\" qualifies as a misnomer. My argument stemmed from the fact that a hot dog doesn't actually contain dog meat. Instead, it's typically made from beef, pork, or a combination of meats. My friend argues that the term \"hot dog\" supposedly originates from a playful association with the dachshund sausage, given its resemblance to the dog breed and therefore, it shouldn't qualify as a misnomer. While this may be true due to the term's roots in historical references, it still inaccurately portrays the contents of this food today with the lack of any canine involvement.", "label": 0}
+{"snippet": "The connection between Markov processes and Potential Theory is well known, as is conformal invariance of Brownian motion which allows probabilistic proofs of statements in Complex Analysis, like Picard's theorem. What are some results in these areas (Potential Theory, Complex Analysis, maybe Complex or Differential Geometry) that admit probabilistic proofs, and possibly for which no other proof is known? To what extent are probabilistic methods in these areas actually crucial in proving new theory and to what extent are they more of an interpretation of facts that are already known? It would be great if there were some survey about this. Thanks in advance for your answers.", "label": 0}
+{"snippet": "My friend is working on a snow gun, which involves using compressed air to blow apart water coming out of a pressure washer. I read that you can cool air by compressing it, which makes it hot, then letting the compressed air lose energy by cooling to room temperature. I was going to use the ideal gas law to find the change in temperature when compressed/decompressed, and Newton's law of cooling to find the time it'd take to cool down. However, I don't think the ideal gas law can be used in this case. What equations are appropriate to find the temperature of a gas before and after it is compressed?", "label": 0}
+{"snippet": "Suppose we have two entangled particles, A and B. If we measure particle A and then subsequently entangle particle B with a third particle, C, would the state of particle A influence the combined states of particles B and C? Specifically, would there be any correlation between the combined spins of B and C and the measured spin of A? Have there been any experiments conducted to explore or validate this scenario?", "label": 0}
+{"snippet": "\"We understand that a set is a collection of objects, but not every collection qualifies as a set, as exemplified by the collection of all sets (consider Russell's Paradox). To define the collection of all sets, we employ the term 'proper class.' Now, I would like to confirm if my understanding here is accurate: A class is a collection of objects, and these objects can be sets. Classes are categorized into two groups, namely small classes, known as sets, and large classes, referred to as proper classes. Is this correct?\"", "label": 0}
+{"snippet": "I am studying a rotating cylinder model in general relativity. The interior metric is given, but I am trying to express the exterior metric. It has to be practical and describe spacetime around a rotating cylinder. So far I have considered the Kerr metric, of course, the Janice-Newman-Winicour metric, and the Tomimatsu-Sato metric. For the Kerr metric, I am struggling to express it in cylindrical coordinates. Doing so will make it easier to match it to the interior metric. Any suggestions or inputs would be appreciated, thanks.", "label": 0}
+{"snippet": "As a high school student, I'm curious whether everything emits thermal radiation, including monatomic gases and substances composed of a single type of atom and no molecules. Can these objects emit radiation in all wavelengths, and if so, how is it possible in the absence of molecules?Is it necessary for an object to be a blackbody in order to emit thermal radiation across all wavelengths?", "label": 0}
+{"snippet": "I was watching this video where the English gentleman asks the Scottish MP to speak in \"Antipodean English\". From what I know, 'Antipodes' refers to the southern hemisphere and I am unable to understand why the gentleman would want the other person to speak a dialect from that broad region in particular. Because this seems unlikely, I want to know what the person meant by the term \"Antipodean English\".", "label": 0}
+{"snippet": "Assuming the earth is either at the perihelion or at the aphelion, it is easy to see the Runge-Lenz (RL) vector is directed along the line joining the perihelion and aphelion. Since the RL vector is a constant vector, its direction (and also magnitude) must remain the same at all points of the orbit. So if we want to draw this vector at other points of the orbits, it will be drawn as a vector parallel to the line joining the perihelion and aphelion. Is this right?", "label": 0}
+{"snippet": "I'm looking for where best to start on the following problem. I have a graph of N nodes and each node as a weight. I need to group all nodes into X groups such that the sum of weights in each group are approximately even and that each group is a connected component of the original graph. After some simple searching I came across the lukes partitioning algorithm implemented in python. https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.community.lukes.lukes_partitioning.html#networkx.algorithms.community.lukes.lukes_partitioning This is approximately what I am looking for but performance feels slow for the size of the graph I am working with. Do you have any potentially better ideas that worked for you?", "label": 0}
+{"snippet": "It's a common myth (especially in popsci) that a black hole contains a singularity. However, I cannot find an explanation for what we think a black hole actually does contain. The best I've seen is \"in order to answer this question, we have to unify GR and quantum mechanics.\" So there are no attempts to answer this question despite our incomplete picture of physics? Let's say Schwarzschild black hole to start with.", "label": 0}
+{"snippet": "I am writing a research paper where I want to say The rest of the paper is organized as follows. in the introduction of the paper. However, the word \"rest\" doesn't sound good as it is perceived as if I am explaining about an unimportant part of the paper. I checked some synonyms on Grammarly, but nothing really fits well. I thought about the following: The remaining paper It also sounds odd as it sounds like \"leftover\" to me. I can be wrong as well. The remnant of the paper This is used mostly for historical events as far as I know. Any advice is appreciated.", "label": 0}
+{"snippet": "I'm not very well-versed in topology, but I know the basic concept of topological equivalence can be approximated by \"counting the holes\" in objects, in the sense that a sphere is different from a torus, but a torus is the same as a coffee mug because they have the same number of holes. I know this roughly approximates being able to smoothly deform one object into another. Can this be applied to interior \"holes\" as well, such as a hollowed-out sphere? Does the hollow center count as a \"hole\"? Is there a way to smoothly deform a hollow sphere into a torus or a sphere? If not, is a hollow sphere in a different topological equivalence class from both a sphere and a torus?", "label": 0}
+{"snippet": "I have read that projectile motion is parabolic in nature. I know that the equation of projectile motion represents a parabola. But when do we get a parabolic curve? Does it happen when there is downward acceleration and horizontal velocity? What condition results in a parabolic shape? Is there any possibility of elliptical motion or any other curve? What would be the determining factors in that case?", "label": 0}
+{"snippet": "It's clear to me that when an object is in free fall in a uniform gravitational field (\"Einstein's Elevator\") it feels no tug of gravity. However if it is in free fall in a nonuniform gravitational field does the object (or more specifically an accelerometer) feel a tug as gravity pulls in one direction and then another? Asked another way, is an object in free fall in a nonuniform gravitational field considered to be in an inertial reference system?", "label": 0}
+{"snippet": "I was recently studying a paragraph in which I came across a sentence, which was below: The British king, Charles I, had inherited a very difficult financial situation from his father. However, I don't understand why 'had' is being used here. My understanding is that had is used only in past perfect tense, where there are two events in past and we use had to signify that event that finished before the second event started. So I modified the above sentence like below: The British king, Charles I, inherited a very difficult financial situation from his father. Is the modified sentence correct? Please help me to understand.", "label": 0}
+{"snippet": "My uncle is a retired math professor. He has had some serious health issues in the past year, but he is still mentally sharp. For both fun and a distraction, he has been working on a textbook. However, I believe it is hard for him since he has trouble sitting at a desk and typing. Does anyone have any recommendations for good voice-to-text software that he could use? Latex and math formatting would be very helpful, obviously, although I could possibly help here.", "label": 0}
+{"snippet": "I have a set theoretic question. I don't understand why the collection of open balls of a metric space is a well-defined set. From my understanding of sets, a set is well-defined in Naive set theory if we can check whether an element is in it or not. But how can we check whether a subset is either an open ball or not? It seems very difficult to check. Maybe my view of a set is too rigid. Is there a better view of whether a set is well-defined? Thank you.", "label": 0}
+{"snippet": "I came across the following sentence while reading \"A Clash of Kings\" book by George R. R. Martin: Whitetree was the fourth village they had passed, and it had been the same in all of them. The people were gone, vanished with their scant possessions and whatever animals they may have had. None of the villages showed any signs of having been attacked Why is the \"may\" word used here instead of \"might\"? I thought that \"may\" can be used only in the present tense and have never seen it used in the past context", "label": 0}
+{"snippet": "I recently saw a video from a passenger of Concorde after it goes supersonic. Inside the aircraft, there is still a loud roar similar to what we hear in aircraft today. However, since the aircraft is supersonic, shouldn't the noise be left behind? Why is the roar present? I was expecting the aircraft to be nearly silent due to being supersonic, and it appears that is far from the reality.", "label": 0}
+{"snippet": "So I know that the statement \"If two random variables are independent, then the two random variables are uncorrelated\" is true. Does that mean its contraposition \"If two random variables are correlated, then the two random variables are dependent.\" also true? In terms of the theory of logic, the contrapositive statement should also be true, but then again, I learned \"correlation does not imply causation\". So I'm a bit confused. Can someone clarify this? Is the contrapositive statement really true? If so, what is the difference between that statement and the statement \"correlation does not imply causation\"??", "label": 0}
+{"snippet": "Suppose a person is using an electrical appliance and suddenly there is a power outage- would it be correct if that person immediately said to their family members that 'the power is out'? Or would it be better to say 'power has gone out'? In what way are they different? Are both idiomatic? (And similarly, is there a distinction between 'the power has come back' and 'the power is back on'?)", "label": 0}
+{"snippet": "I was reading about how reflection and refraction work at a quantum scale. What I understood was that the photon \"can\" take multiple paths to reach the end point and when we consider all these possibilities, most of them cancel out as they interfere destructively, while there's constructive interference around a certain direction. That is what we observe is the the sum of all the probabilities of the possibile paths the photon could take. Please correct me if I'm wrong. My question is how do we calculate that probability of each path? Or do we only calculate the sum of the probabilities directly?", "label": 0}
+{"snippet": "When @anna v explained why the planetary model of the atom does not make sense in this post, she said the electron in an orbit is accelerating continuously and would thus radiate away its energy and fall into the nucleus. However, when the Earth orbits the Sun, isn't it accelerating continuously toward the Sun? If this is the case, should the Earth radiate away its energy via gravitons and fall into the Sun eventually? I also checked questions about Why doesn't the Moon fall onto the Earth?, but the answers didn't talk about radiating away gravitons.", "label": 0}
+{"snippet": "From Beauville's book on complex algebraic surface, in Chapter IV, we know each Hirzebruch surface contains a unique irreducible curve with negative self-intersection. If we remove this curve from the Hirzebruch surface, different from contraction, it will result in a non-compact surface. I'm wondering what we can say about this non-compact surface. For example, what kind of symmetry does it have, will it still be toric? More generally, what if we remove an irreducible curve different from the one with negative self-intersection instead, how will it affect the situation above? I'd appreciate any relevant discussions or comments, thank you in advance!", "label": 0}
+{"snippet": "I'm trying to represent a company as a feature vector. The vector has multiple stats describing the company such as earnings growth, capital expenditures, gross margin, etc. The goal is to represent companies with these vectors and find the most similar companies based on some similarity measure (ie euclidean or cosine). My questions are: Would this be an accurate way to represent companies? Is there some normalization I have to do to the vectors before finding similarity? And what is the best measure of similarity for these vectors?", "label": 0}
+{"snippet": "According to Introduction to Solid State Physics by C. Kittel, An ideal crystal is constructed by the infinite repetition of identical groups of atoms. A group is called the basis. The set of mathematical points to which the basis is attached is called the lattice. The crystal structure of copper is face-centered cubic (fcc). So we can say the lattice is fcc, and the basis is composed of one single copper atom. I was wondering if it is wrong to say, instead, that the lattice is simple cubic (sc), and the basis is composed of four copper atoms. Both give the same arrangement of atoms in space, but in the second there are fewer lattice points.", "label": 0}
+{"snippet": "Examples of solutions to linear differential equation are (from Wikipedia): exponential function, logarithm, sine, cosine, inverse trigonometric functions, error function, Bessel functions and hypergeometric functions. So in this sense these are linear functions (for some generalized notion of \"linear\"). But I wonder if there are examples of functions that are \"strictly nonlinear\", in the sense that they are the solution of some nonlinear differential equation but not of any linear differential equation.", "label": 0}
+{"snippet": "I have an application I'm trying to model that involves using superconducting coils to produce a steerable dipole. To some degree, the problem is easier if I can modulate the current through the coil, but I have read in a few places that there can be practical challenges related to the superconducting coils being \"perfect inductors.\" Can someone help me get a better understanding of how to mathematically model a superconducting coil in both a DC and AC circuit? Specifically, I'd be curious if trying to vary the current quickly produces operational challenges like excess heat which makes it more difficult to keep the coil in a superconducting state. Thanks!", "label": 0}
+{"snippet": "Bicycle's brakes generally fall into two broad categories: rim brakes where the braking pads pinch against the wheel's rim, and disk brakes where the pads press against a disk (rotor) that is rigidly attached to the wheel's hub. General wisdom is that disk brakes are higher quality and offer better stopping power. But disk brake pads are much closer to the center of the wheel, which means that they have to exert more force to produce the same amount of torque. Wouldn't this be less stopping power?", "label": 0}
+{"snippet": "I noticed that dew only falls on horizontal surfaces, while vertical surfaces remain dry. But dew is the condensation of water vapor contained in the air. And for the condensation process, the direction of the surface does not matter. If you bring a smooth cold object into a warm room, it will be covered with condensate evenly on all sides. Why do vertical surfaces stay dry?", "label": 0}
+{"snippet": "I have a idea I'd like to explore: If a black hole can bend light due to its immense gravitational attraction, could we imagine an 'inverted black hole'? In this hypothetical scenario, this object would behave similarly to a black hole but with a force of repulsion instead of attraction. This repulsion would cause light to curve away from it, making it impossible for light to reach the white hole. I'm also curious about whether there are software or codes available that could help me visualize this concept, similar to how software like 'Space Engine' visualizes regular black holes. Right now, to keep things simple, I wish only to explore how this hypotetical object would affect light and images.", "label": 0}
+{"snippet": "Using a triangular glass prism to disperse white light into a rainbow works because different wavelengths/colours of light have different refractive indices in glass, doesn't it? The different refractive indices apply regardless of the shape of the glass. Therefore, wouldn't a simple rectangular slab of glass also disperse white light? The different wavelengths would be differently refracted and emerge separated from the other end. Why is a triangular prism always used to demonstrate dispersion? Is there something I'm missing?", "label": 0}
+{"snippet": "Mine is a very basic question yet I haven't got a satisfactory answer so I turn to you. Special Relativity is based on two assumptions, one of which is that the speed of light is constant for all inertial frames. While I know the disprove of universal reference frame, Aether, I want to know how we came to the conclusion that the speed of light REALLY is constant for all inertial frames (light traveling in vacuum).", "label": 0}
+{"snippet": "The gravitational binding energy or self-energy of a system is the minimum energy which must be added to it in order for the system to cease being in a gravitationally bound state. Equivalently, the gravitational self-energy of a body is defined as the work done by an external agent in assembling the body from the infinitesimal elements that are initially at an infinite distance apart. A gravitationally bound system has a lower (i.e., more negative) gravitational potential energy than the sum of the energies of its parts when these are completely separated. Is this type of energy a source for gravity? In order words, does a star have a smaller gravitational field due to its negative gravitational self-energy?", "label": 0}
+{"snippet": "I'm wondering which of the following sentences is correct: They realized that if the threat WAS not contained, it could endanger the nation.\" They realized that if the threat WERE not contained, it could endanger the nation.\" My understanding is that the subjunctive \"If X were\" is used for a counterfactual to a present situation. But here, the threat not being contained is a real possibility being considered in the past. If the main clause were written in the present tense, \"to be\" would be present indicative: \"If the threat IS not contained.\" So I'd think it should be past indicative when the main clause is past tense. Am I right?", "label": 0}
+{"snippet": "I just read an article describing the project Scorpius. The aim is to use explosives to compress and heat microscopic quantities of Plutonium in order to study the states of the matter in extreme conditions. I wondered why they needed to recreate those conditions with explosions. Couldn't they achieve the same states with a Diamond anvil cell? With such apparatus they could compress a microscopic quantity to more than a million atmospheres and by passing some laser pulses trough the diamond anvils they could heat the matter. Am I missing something about the project purpose?", "label": 0}
+{"snippet": "During the Electroweak era, the Higgs mechanism had not yet distinguished particles such as electrons and muons by mass. Is there a conceivable experiment, or a hypothetical cosmological observation we could make today, that could have identified electrons and muons as distinct particles during that era? Alternatively, might there be features in the Cosmic Microwave Background or the distribution of matter in the early Universe that could reflect the distinction between the electron and muon fields prior to the onset of the Higgs mechanism?", "label": 0}
+{"snippet": "Why do charges placed inside a metallic cavity have no effect on outer charges and vice versa? My teacher explained it by electrostatic shielding. He said that the conductor does not allow the electric field to pass through it. I agree that inside a conductor the electric field is zero, because free electrons of the conductor move opposite to the external electric field to create an equal and opposite electric field. But what about inside the cavity? There is nothing like free electrons in the cavity, so an external electric field should reach there.", "label": 0}
+{"snippet": "I am wondering if the physical shape of a current carrying conductor will have any effect on the shape of its magnetic field or is it that the magnetic field surrounding any current carrying conductor will always be perfectly round. For example, let's say that current is passed down a long L-shaped metal bracket, such as the one shown in the drawing below. Will the magnetic field follow the path drawn around the L-bracket, or instead will the magnetic field be perfectly round and will encompass the entire L-shaped bracket? Does the physical shape of a current carrying conductor affect the shape of its magnetic field?", "label": 0}
+{"snippet": "I was fairly convinced that usual QM formalism didn't necessitate the use of complex numbers and that ultimately they're just a matter of convenience and utility rather than anything fundamental. This paper claims that isn't the case. But their demonstration doesn't satisfy me because it's muddled up in this Bell-like experiment. Can anyone explain what's going on in a simplified manner? Their argument does not make it clear to me why splitting the wave function into its real and imaginary portions and treating them as two quantities which are coupled via Schrodinger evolution isn't always possible---even in the case of multipartite states.", "label": 0}
+{"snippet": "I've seen several sources stating that Einstein was partially inspired by the Ehrenfest paradox when thinking about general relativity. However in the Ehrenfest paradox the non-Euclidean nature of the space in the rotating frame of reference is linked to Lorentz contraction rather than gravitational forces like in GR. Is the link simply that the rotating disk question got Einstein thinking about non-Euclidean geometry as a way to treat non-inertial reference frames?", "label": 0}
+{"snippet": "Forward and reverse synchronization between the TeX source and the PDF output using SyncTeX is an immensely useful tool when writing larger documents. Sometimes, especially when the synchronization is not working as expected, I would like to see the synchronization anchors in the PDF file. I know that the information is stored in .synctex.gz file in some form, but this is hardly transparent for a human reader. Some graphical indication over the PDF output would be great. Does this exist? I am working on Windows. Solutions for other systems are of course welcome, though they won't help me.", "label": 0}
+{"snippet": "Two generalizations of graphs have been described in a number of articles: multigraphs and hypergraphs. A multigraph is a graph in which multiple or parallel edges between nodes are allowed. These edges have the same end nodes. A hypergraph is a graph in which an edge can join any number of vertices. An edge can therefore connect sets of multiple nodes to one another. Both concepts allow one to model relations among objects with more detail and precision than with 'ordinairy' graphs. However, I have yet to find an account in which a combination of both structures is described: the hyper-multigraph. Such a graph would allow for parallel edges between the sets of nodes. Question: are there any references on such hyper-multigraphs?", "label": 0}
+{"snippet": "Yesterday in my English class, I tried to say 'I hadn't got that book' and my teacher told me my sentence was incorrect, she said I should say 'I didn't have that book'. I bought Grammarly, and it shows me my sentence is correct. Or maybe there is a difference between 'I didn't have that book' and 'I hadn't got that book'. I would like to know the opinion of a British person.", "label": 0}
+{"snippet": "Fraternal twins is what you call a set of twins who look different, but the word fraternal also has the meaning 'of or relating to brothers', and comes from a Latin root meaning 'brother'. The question is, how do I refer to a set of twins who look different but are both girls? May I use the phrase sororal twins to describe them? Or can fraternal be used here, too?", "label": 0}
+{"snippet": "I'm trying to prove that the covering space X of a manifold Y is a manifold of the same dimension. I was stuck on proving X is second countable, more specifically, on proving the fiber of any element in Y is at most countable. I find a proof at Is a covering space of a manifold second countable?, but that proof is based on the countability of the fundamental group of a manifold. Could there be a more elementary approach without using this fact?", "label": 0}
+{"snippet": "I imagine the following thought experiment: Let us prepare two identical neutral fermions with identical spin and antisymmetric spatial wave function in one spatial dimension. Let the initial state be two Gaussian wave packets which start at some large distance and have identical speed, but opposite direction. Since the particles are neutral, the wave packages should move through each other undisturbed. But at the time, where the particles are at the same place, the antisymmetrized wave function adds up to zero, so you cannot normalize the state. The exchange interaction should be zero because the particles are not charged. For the same reason there should be no magnetic moment. Where is the error in the argument?", "label": 0}
+{"snippet": "In my notes regarding entanglement and CHSH inequality it says: Further, this is the case even for incompatible observables: measurements on one system allow us to predict with certainty the outcomes of measurement of incompatible observables on the other system. However, the uncertainty principle tells us that we cannot predict with arbitrary accuracy the results of measurement of incompatible observables. How is the first sentence allowed. My understanding was that if you measure one set of observable, then the other incompatible observables are still in superposition.", "label": 0}
+{"snippet": "Given the following Bayesian belief network, what is the probability that a non-smoking patient with a smoking parent will develop lung tumor? In this question, isn't the answer already provided within the question itself? As I understand it, I required to calculate the probability of developing a lung tumor given that the patient does not smoke, but their parent does. However, this information is already provided in the table at the bottom right. Am I missing something?", "label": 0}
+{"snippet": "Suppose I have a \"moving\" frame of reference where I send a light beam from point A to two equidistant points B and C (equidistant in the moving frame of reference). From a \"stationary\" frame of reference, A to B and A to C are different distances because they have different diagonal components. But the stationary observer still sees light travel from A to B and A to C at the same time. How is it possible given constant speed of light? Just started learning about time dilation. Any help would be appreciated!", "label": 0}
+{"snippet": "I am an engineering student who is slowly branching into applied mathematics. While I can find plenty of good textbooks on the rigorous treatment of the Fourier Transform itself (including functional analysis and the Schwartz space and the result of this for the Fourier Transform) but I am having difficulty in finding an equivalent for the Discrete Time Fourier Transform (DTFT). Does anyone know of books that rigorously handle the DTFT, particularly on the convergence of functions that are not absolutely summable and its DTFT?", "label": 0}
+{"snippet": "I tried to prove that the centers of two tangent circles are colinear with the point of tangency. If I just assume they have a common tangent at their point of tangency then it's pretty easy. However, how do we prove that two circles do indeed have a common tangent at their point of tangency? (without using the collinearity of the centers and the point of tangency to avoid circular logic)", "label": 0}
+{"snippet": "In the Spanish language there is a word that is used to describe a person that has been tagged as a deadbeat; it is Largo. Largo in Spanish means Long as in the measurement of the distance between two points or places, etc. If you loan any money to this person, it will be a long time before you get paid back, if you get paid back at all, or if you receive any kind of payment. They can also be known as a Largo if they are sly, tricky, or conniving with bad intentions.", "label": 0}
+{"snippet": "I'm looking for a formal language that has the following properties: Contains finitely many words (and you can prove it). Decidable/recursive (there's a Turing machine that always halts, that can determine whether any given word belongs to the language). It's impossible to compute the exact number of words it contains. Meaning, even if you've already found all the words in the language, you can never know if there's another word that you just didn't try yet. Such a language feels \"illegal\", but I didn't manage to disprove its existence.", "label": 0}
+{"snippet": "A Chinese teacher of English asked me about the following, taken from an English test for Chinese people. It's quite tricky I think. I would like to know three things: Which answer or answers do you consider to be correct? If you consider an answer to be wrong, why do you think it is wrong? How would you reword these answers to make them acceptable? Nanjing is a popular city with a long history. Could you tell me ______ . A. where can visitors enjoy delicious Nanjing snacks? B. when is the best time to visit the Confucious Temple? C. how will people get to the Zhongshan Hill Scenic Area? D. why was the city also called Jianye in ancient times?", "label": 0}
+{"snippet": "I am pretty proficient till Calculus II, but I want to learn about more advanced methods of computing integrals like Gamma function, Elliptic integrals and Leibniz integral rule. I also want to improve my mathematical problem solving ability with this. Should I read Advanced Calculus by Frederick S. Woods or Inside Interesting Integrals by Paul J. Nahi? Or would it be better to first learn multivariable calculus? (any other book suggestions are welcome)", "label": 0}
+{"snippet": "A group action on a set is said to be transitive if it has only one orbit. Now, a group action on the same set is said to be regular if all the stabilizers of the elements of the set are trivial. My doubt is, if there is only one orbit, then, by orbit-stabilizer, all stabilizers must be trivial right? What am I missing here? Any hints? Thanks beforehand.", "label": 0}
+{"snippet": "From my understanding, the frequency and wavelength of a mechanical wave can be observed by the motion of the particles (i.e., as the particles oscillate from their state of equilibrium, the wave propagates through the medium). But, with electromagnetic waves, how do we measure its frequency and wavelength? If an electromagnetic wave travels across a vacuum, isn't it pretty much invisible to the naked eye?", "label": 0}
+{"snippet": "I am tasked to simplify this circuit to one source and one resistor, which is equivalent to the original but obviously easier to solve. My problem is the fact, that I don't know how the nodes A and B affect the process. I'm more used to the circuits where the A and B nodes are on one end of the circuit, but these are in the middle. Not sure how this is supposed to be interpreted.", "label": 0}
+{"snippet": "I am wondering if this statement about parallel circuits and conservative fields is true?: The voltage drop over resistors in parallel is the same because the electric field is conservative, so the work done on a charge only depends on the start and end point. The field is conservative because the force it generates consists of the electrostatic force (Coloumb) and a magnetic force. We can show that the electrostatic force is conservative, and the magnetic force on moving charges is perpendicular to the velocity vector, so it does not do any work on the charge. So the only force that does work on the charge is the electrostatic force. Is this statement correct?", "label": 0}
+{"snippet": "I'm playing around with modeling an archway of a building using a solid modeler, and have come to a problem that exceeds my mathematical ability. Given an ellipse that has a known major radius, and is tangential to a line of a known length, angle, and offset on the Y-axis, can I find the ellipse's minor axis? It's been decades since I took a math class. I can handle basic trig, but I can't figure out how to get started on this one. Edit: Thanks everyone! You can see your solution in the flying buttresses of this (very preliminary) render.", "label": 0}
+{"snippet": "The company \"Fluke\" makes a DMM that they claim can measure AC voltage by simply clamping the connector around a live wire, and using the E-field to induce a voltage/current into the capacitor. I can understand the concept if we assume the person holding the DMM is grounded and the measuring loop is sufficiently sensitive. But what if the person holding the DMM is not grounded, or is in a vacuum, etc. Some people on the internet claim it works even if the DMM is hanging from the wire in open air. I have my doubts... So, I am wondering if someone can explain to me if current can flow in a capacitor that has no path to ground. It seems like an obvious \"no.\"", "label": 0}
+{"snippet": "I am trying to understand the Von Neumann decomposition, according to which every Von Neumann Algebra can be uniquely decomposed as integral (or direct sum) of factors. More specifically, I am trying to connect (if possible) the Von Neumann decomposition to the GNS theorem. Can someone please help me answer the following questions? Given a normal state, is it true that its GNS representation is always a factor? The answer would be different if the dimension of the algebra is either finite or infinite? Is it possible that the algebra obtained by applying GNS theorem on a irreducible state is not a factor? From the quantum mechanics point of view, why is the Von Neumann decomposition important?", "label": 0}
+{"snippet": "There's a clip going around on the internet of the driver Ross Chastain, 'wall riding' in a race that allowed him to pass many opponents on one turn. Here is the clip. What I do not understand is how did this work? The only explanation I can think of is that the normal force of the wall acted like a centripetal force, which meant he didn't have to brake on the turn, but this doesn't make too much sense to me since the frictional force of the wall on the car would slow him down quite a lot.", "label": 0}
+{"snippet": "I'm working on a project involving non-standard dice where each face can have a different size, but the overall shape and weight distribution of the die are uniform. I'm interested in finding out how to calculate the probability of the die landing on a particular face based on the size of its faces. Assumptions: The die maintains a uniform shape and weight distribution. The die has 'n' number of faces, each potentially with a different area. We ignore the complexities of rolling dynamics and assume the die lands flat on its faces. I am looking for an equation or a model that can accurately calculate the probability of landing on a face, given the area/dimensions of each face.", "label": 0}
+{"snippet": "Does anyone know where I could find a copy of Ron Graham's PhD dissertation, titled \"On Finite Sums of Rational Numbers\"? I found this paper, with a similar title, but I could not find Professor Graham's dissertation. I need to double-check some detail(s) in Professor Graham's dissertation which may not be in the published version. This is in consideration of my (current) approach to odd perfect numbers via Egyptian fractions.", "label": 0}
+{"snippet": "I am not a pure mathematician but an engineering professor. Right now I am going through the first chapter of Topology without Tears by Morrison. One of the questions is as follows. A set T consists of a set of real numbers, the null set and the closed interval [-r,r] where r is irrational. The question is whether (T,R) form a topology where R is the set of real numbers. The answer seems to be an obvious Yes irrespective of whether r is rational or irrational since both intervals can be infinitely large and can contain arbitrarily large numbers. But I am suspicious as it seems to be too obvious and I think the actual answer is No.", "label": 0}
+{"snippet": "I am new to linguistics and am currently learning how to figure out phrase markers for sentences. I am unsure about this sentence: She went off in search for her hedgehog. I know that \"she\" is a noun phrase, but I am unsure about the VP. Is the VP \"went off in search for her hedgehog\"? And does that split again into the three phrases: went off, in search and for her hedgehog? Does it look like this?", "label": 0}
+{"snippet": "I am trying to find the directional vector to hit a moving target. For example, as seen in my drawing, Lets say a space ship at position Sxy needs to fire a projectile to hit the moving asteroid (currently at position Axy). The asteroid is moving with a linear velocity vector Av. The projectile has a constant speed (magnitude) of Ps. How can I solve for the projectile directional vector Pv? Both the asteroid and the projectile have a radius.", "label": 0}
+{"snippet": "I am studying simplicial homology and I am a bit confused about the definition of an orientation of a (finite) geometric simplex. The definition says that two orderings of a simplex are equivalent if they differ by an even permutation, and so we get two equivalence classes - two orientations. My question is, what is an ordering of a simplex? Is it just a permutation of the vertices or does it have to satisfy some other rules? If it's defined to be a permutation of vertices, then we draw paths between vertices indicated by the permutation of vertices (I am thinking geometrically), then my lines might cross each other. Is it that this will not happen because vertices of a simplex are in general position? Thank you!", "label": 0}
+{"snippet": "I've been studying the Lax equivalence theorem . I've learned that it allows you to establish the convergence of a scheme through proof of stability. The Wikipedia article says that the method it's important because \"it is ordinarily difficult to establish [convergence] because the numerical method is defined by a recurrence relation while the differential equation involves a differentiable function\". I used the equivalence theorem to establish the convergence of the Crank-Nicholson method in an assignment. I was wondering what a direct proof would look like (I'm assuming it depends on the scheme). Can you please provide any references for this? Thank you in advance!", "label": 0}
+{"snippet": "With some formal systems, it's possible to enumerate all the theorems. This is the case for instance in propositional calculus or in some first-order theories with a recursively enumerable set of axioms (e.g. group theory, field theory, Peano arithmetic, etc.). I'm looking for a software that would implement such an enumeration. Or more basically, a software that would produce random theorems (which may or may not be of interest). A software doing that in any of the formal systems listed previously would be acceptable.", "label": 0}
+{"snippet": "My teacher taught us that a square matrix is called a diagonal matrix only if all the entries besides the ones on the principal diagonal are zero. He further cautioned that there is no restriction on the entries of the principal diagonal and that they may be zero or non-zero, BUT there must be atleast one entry on the principal diagonal that is non-zero. We were specifically told that null matrix is not a diagonal matrix as there simply is no entry along the diagonal. However, most if not all sources on the internet say that null matrix is also a diagonal matrix as all the non-principal diagonal entries are zero. Which one of the above definitions is correct?", "label": 0}
+{"snippet": "Imagine the following conditional: If washing machines are humans, washing machines are quadrupeds. It seems to me that the truth value of the conditional as a whole is ambiguous. Since its antecedent is false, logic tells us that the conditional is (vacuously) true. But in fact, the conditional as a whole does seem false: if we grant that washing machines are humans, then washing machines are clearly bipeds. But how can the same conditional be both vacuously true and (at least intuitively) false?", "label": 0}
+{"snippet": "I just read this answer to \"What exactly is a Photon?\" which has me a bit confused. It seems to be arguing that \"photon\" is just a catch-all term for any sort of interaction with the EM field and the implication is that it's not even a particularly useful concept, in contrast to the fundamental particles of other fields. But how is that any different from other elementary particles, when all particles are just excitations in quantized fields? I also found several threads talking about whether photons have wavefunctions or not, such as this one: Wave function of a photon? and I'm seeing conflicting information. If photons don't have wavefunctions, are they even particles at all, in the sense of being localized disturbances in a field?", "label": 0}
+{"snippet": "I am doing some interactive plots about cosmological horizons and in my research I stumbled upon the sound horizon, the baryonic acoustic oscillations and how it had an impact on the formation of the first structures in the universe. Some people have calculated the radius of the sound horizon at the time of recombination using the same equation used in the particle horizon but with the speed of \"sound\", which itself is a function of the density of matter and radiation. But I've never seen anyone actually plot the radius into the future like some have done with other cosmological horizons. Is there a reason for that? Does it not play an important role in the universe anymore? Was it only important at the time of recombination?", "label": 0}
+{"snippet": "The nlab claims that the maximal ideal theorem in Heyting Algebras (i.e. for every proper ideal in a Heyting Algebra, there is a maximal ideal that contains it) implies the axiom of choice. Sadly, it does not cite any proofs and I've been unable to prove this, I'd appreciate any proofs/references. I find this particularly interesting as it's known that the maximal ideal theorem for Boolean Algebras is strictly weaker than the axiom of choice. Yet, the same theorem applied to the apparently slightly bigger class of Heyting Algebras suffices to prove choice.", "label": 0}
+{"snippet": "I have difficulty understanding when we use \"an analogy\", \"a metaphor\" and \"a figure of speech\". I feel like in a casual conversation, people just use any of these words to say something that is different from its normal use. Does a native English speaker distinguish the difference between them in a casual conversation?. Is it correct to say: \"I am like a bee in a bottle is an analogy\" or \"I am like a bee in a bottle is a metaphor\" or \"I am like a bee in a bottle is a figure of speech\"", "label": 0}
+{"snippet": "In the study of the geomagnetic field, an expansion in spherical harmonics is used to represent the scalar magnetic potential: the first terms give the dipole approximation, then the quadrupole, etc. For instance, we can find here (International Geomagnetic Reference Field) reference data for the magnetic field, given as coefficients of a spherical harmonics expansion. My question is: how are those coefficients calculated? I was thinking of the Monte Carlo method, but I couldn't find any information on that. Note that I would also accept answers related to the gravitational field as the question also applies there.", "label": 0}
+{"snippet": "I'm an English learner, and sometimes I cannot understand why some words are used to express a meaning. For example, the word \"Down\". What's the difference between \"I walked on the street\" and \"I walked down the street\" or \"Alan drove down the street\" and \"Alan drove on the street\" ?? As far as I know, these verbs are not phrasal verbs, so how can I know when to add this \"adverb particle-like\" with a verb ?", "label": 0}
+{"snippet": "I saw this in a textbook and I want to confirm if it's true If a body of mass m rolls down an inclined plane of height h and length l (hypotenuse), the work done is mgh. It is the vertical height of the inclined plane that is used in the calculation, not the length (hypotenuse) of the inclined plane. Please how true is this because I believe we should be using a little bit of trigonometry since the object also moved a horizontal distance. Please if true, how?", "label": 0}
+{"snippet": "I'm trying to understand how car wheels work. In a perfect world the bottom of the wheel has no velocity. The wheels are in a state of pure rolling, which means there is no static or kinetic friction because the bottom contact point is not in motion. This would mean that in a world without air resistance a driver wouldn't have to push on the gas pedal, as there aren't any forces opposing the cars forward velocity. Is this right?", "label": 0}
+{"snippet": "I have a question about the EPR phenomenon of the quantum-mechanics. When you observe the EPR phenomenon, you separate two spins in the singlet state. Then, you and your fellow independently observe the direction of each spin, and you compare the directions. If one spin is in New York, and another is, for example, in Tokyo, how do you assign the directions? Because the earth is round, I do not know which direction is opposite to another. In reality, it is difficult to make such a large separation without losing correlation. However, in principle, it is irrelevant how large the distance is. Thank you for your attention.", "label": 0}
+{"snippet": "I found this problem online somewhere (cannot remember the exact source, sorry) and initially I thought it looked fairly simple and fun to solve. I've now sat for several hours and even asked some friends to help, but none of us can actually solve it (without complex algebraic equations). I am by no means an expert on geometry or trigonometric (or mathematics for that case), so I would assume there are some identities or theorems that would make this problem easier to solve that I just don't know. Can anyone help please. The problem is to solve for x in the below diagram (excuse the bad drawing in Paint):", "label": 0}
+{"snippet": "Generally speaking, the universe is electrically neutral and the universe abhors an unbalanced charge. Wherever there is a positively charged object, you can bet there is a negatively charged object not far away. However, no laws of physics prevent the accumulation of positive charge, say, so long as the negative charge is sent somewhere else. This must be true on a cosmic scale as well. Hence my question: What is the most electrically charged celestial body in the universe, and what is its charge, i.e. positive or negative? Dipoles don't count.", "label": 0}
+{"snippet": "From many papers I've read in condensed matter physics, it seems \"breaking time reversal symmetry\" is often equivalent to \"applying an external B field\", while \"breaking inversion symmetry\" can be done (but not limited to) by \"applying an electric field\". Is this true in general? A side question: if a perturbation breaks the inversion symmetry of the original Hamiltonian, does that imply it mixes states of opposite parity? Similarly, if a perturbation breaks time-reversal symmetry, does that mixes time-reversal pairs? Looking forward to any counter-examples. Thanks!", "label": 0}
+{"snippet": "At first glance, it seems like the \"many\" in \"There are as many A's as B's\" is an adjective. However, we can't substitute an arbitrary adjective in this sentence. Compare: \"There are as many A's as B's.\" (correct) \"The A's are as many as the B's.\" (incorrect) \"There are as numerous A's as B's.\" (incorrect) \"The A's are as numerous as the B's.\" (correct) I'm curious about how to describe the reason why two of these feel 'correct' (to me, as a native speaker) and two of them do not. Is 'many' here a different part of speech than an adjective? Or is \"as many as\" just its own grammatical construction with its own rules?", "label": 0}
+{"snippet": "David Cameron, the previous Prime Minister that has been away from politics for many years, has just come back as the Foreign Secretary. The BBC refers to him as the \"old new face\". Politics aside, just as an English grammar question, I wonder why it's \"old new face\" instead of \"new old face\": is there some convention/rule to determine the order of the two adjectives? Or is it just slang? I did some searching but was overwhelmed by face recognition AI links...", "label": 0}
+{"snippet": "I have an anodizing rack that has hundreds of prongs. These prongs are made of titanium and need to be squeezed together in order to place the parts on the rack. I am wondering how I would calculate the force needed to make the prongs touch so that parts can be added? I have seen some people saying to use F=kx treating the prongs as a spring, would this be the best way? Any help is appreciated.", "label": 0}
+{"snippet": "I was at a jewelry workshop today and saw somebody place a gold ring under an intense flame. Weirdly, the ring looked normal when underneath the flame, but glowed \"red-hot\" as soon as the flame was removed. The latter behavior is what I expect of a hot object emitting blackbody radiation. It makes no sense to me why the ring would not look like a blackbody object in the presence of the flame (where it could only be hotter). Maybe ions in the flame are affecting the physics at the surface and making it effectively opaque? I didn't capture the effect on camera, but this video sort of shows the same thing happening, though not nearly as clearly as what I saw in person.", "label": 0}
+{"snippet": "I'm trying to construct a table that looks like the following: I know I need to use multirow package in the tabular environment, but I can't figure out how since I couldn't find examples that are similar to my need. It seems like I need to use a multicolumn environment inside multirow for the 'Experiment' cells. Can someone guide me in the right direction? Thank you!", "label": 0}
+{"snippet": "As I read on Wikipedia, a phosphor coating of a CRT screen lights up because an electron in one of the phosphor atoms emits light when it goes down from its excited state. When a single electron hits a phosphor coating, is it the case that exactly one atom of the screen will glow? If not, what is the shape of the spot on the screen for a single electron?", "label": 0}
+{"snippet": "If we create a pair of rotary wings like those on a helicopter, and spin them in a vacuum, would it be possible for a virtual particle and anti particle pair to spawn, be split by an approaching wing, and take opposing paths around the wing, before re-combining and annihilating? Would this create a pressure differential as it does on macro scales in fluid dynamics? Does the particle and anti particle pair even need to be split or is it sufficient for multiple such pairs to spawn and move around the wing before annihilation? If we rotate the wings at relativistic speeds, does this increase the rate at which this occurs and the pressure difference generated?", "label": 0}
+{"snippet": "Given that our best models so far suggest that the universe has been expanding a lot ever since the time the CMB was emitted, I'm wondering: How large was the (visible) universe back at the time it became opaque and emitted the CMB? Specifically, I'm curious as to the (\"original\") circumference of the spherical shell we \"see\" out there, in comparison to how far the light from it has traveled to reach us.", "label": 0}
+{"snippet": "I was trying to figure out some details about a specific decay channel for a generic particle accelerator experiment. For instance if I have a proton proton collider with fixed energy, I would like to figure out what is the average decay length of a B meson, what would be the energy of its decay products (for a chosen channel) and similar things. I know there is a lot of MC software used in high energy physics but I was just wondering if someone had a recommendation for one which is free and is not hard to use and configure when doing such simple things.", "label": 0}
+{"snippet": "In his classic poem which pretty much everyone knows by heart, Edgar Allan Poe writes as follows: Ah, distinctly I remember It was in the bleak December, And each separate dying ember Wrought its ghost upon the floor. Why? \"... a bleak December\" would have sounded (or would it?) more logical: not all Decembers are bleak. Or: \"This occurred in bleak December\" would have scanned just as well. What gives?", "label": 0}
+{"snippet": "I have recently moved to an institution run by the British government where staff use the term \"indent\" as a noun to refer to an inventory exercise done to work out what they need to buy. This is consistent with several dictionaries, such as Merriam Webster: chiefly British a : an official requisition b : a purchase order for goods especially when sent from a foreign country Does anybody know where this usage comes from?", "label": 0}
+{"snippet": "I was reading a book, the author described the scenery of a certain place, and then said: \"You're hooked for life.\" The search engine told me it means, you have been fascinated by this scenery all your life, \"for life\" represents the duration of the action of fascination. My questions are: Can this sentence only be used after the previous sentence describes the charm of something? If I want to express people's obsession with life itself, can I use \"hooked on life\"? Your reply will be greatly appreciated!", "label": 0}
+{"snippet": "I've recently read about a subject field called \"Boolean differential calculus\", which discusses changes of Boolean variables and functions. This subject defines the derivative of a Boolean function, its minimum/maximum, etc. While the field sounds very interesting, I couldn't find much about its applications. I found a book by Steinbach and Posthoff called \"Boolean Differential Calculus\" which describes applications, but it's under a paywall. For any of you familiar with the subject, what are some interesting applications that can be done with it? I would also be interested in sources that are open-access. Thank you in advance!", "label": 0}
+{"snippet": "I don't have any physics background aside from intro physics so apologies if my question sounds very shallow. If lens power is based on focal length, but our eyes adjust its focal length based on the distance of the object we are observing, how do we know that our lens prescription is correct for all distances? Most eye tests I have done involve focusing on objects at a far distance. If our lens prescription is based on focal length when we focus on objects at a far distance, is it incorrect to be using this prescription when doing near distance work?", "label": 0}
+{"snippet": "I'm curious, if based on what we know with Newton's law, can we determine if a random planet, knowing it's mass and gravitational pull, can hold a moon in it's orbit. Or to phrase it another way, is there a gravitational force \"range\" in universe where if a planet has a force less than that range, a moon won't stay in orbit and just escapes and if the planet has a force more than that range, the moon is pulled into the planet.", "label": 0}
+{"snippet": "Let's say we have an undirected graph G, where V = number of nodes and E = number of edges. In this graph, there are vertices with odd degrees as well as even degrees, but I have to transform the graph to one with only even degree nodes and I can do that by removing some edges. How do we find the number of ways to remove the edges so that there are no nodes with odd degrees left (this could also mean removing all edges altogether)? Thanks a lot!", "label": 0}
+{"snippet": "The elongation of light waves occurs not because galaxies are moving away from each other, but because light waves are stretching along with the fabric of expanding space (cosmological redshift). Although the Milky Way is held together by gravity, space expansion occurs everywhere, including within the Milky Way. Since space expansion occurs in the Milky Way and light stretches due to space expansion, why don't we observe cosmological redshift within the Milky Way?", "label": 0}
+{"snippet": "In the derivation of potential energy of two-point charge system, we define the potential energy of the system as the work done in giving both charges to their present configuration, and while doing the derivation, we assume the work done in bringing the first charge to its desired configuration to be zero, but I think it shouldn't be like that. Why is the force = qE acting on the first charge due to the second charge being ignored while calculating the work done in bringing the first charge to the desired configuration?", "label": 0}
+{"snippet": "How can I learn General Relativity? Am a undergrad student, who happens to be interested in general relativity. I want to learn it by heart. What are the prerequisites for it? As a fresher who just got into undergrad, what resources are best for me? Feel free to suggest any YouTube playlist which can help me understand the math of relativity and any book that teaches me from scratch presuming I know nothing.", "label": 0}
+{"snippet": "I'm doing 'longitudinal' qualitative research, and to avoid continually being accused of assuming that I will find change, I need a term that covers both change and stasis - so I can say that I'm looking for instances of [change-or-stasis] in particular areas of experience over a particular period of time. One researcher gets round this by saying that stasis is a type of change, but I'm not sure that works. Any thoughts gratefully received!", "label": 0}
+{"snippet": "I have been curious about intuitionistic logic for some time and I want to know about it and I have a question, the law of the excluded middle and double negation elimination seem completely logical to me and I think they are always correct. But intuitionistic logic does not accept these two laws. What is the cause of this? Are there really propositions in mathematics for which these two principles do not hold? If so, please give examples of propositions that are examined in intuitionistic logic and the law of the excluded middle and double negation elimination does not work in them.", "label": 0}
+{"snippet": "I have been trying to get my head around this proof, but i just don't manage to do so. I am ok with the first two lines, it is just the definition. But on the next line, how is Cauchy-Schwartz inequality exaclty applied? And on the next line, I also don't understand how is Taylor's Theorem used. Update: I just managed to figure out the usage of Cauchy-Schwartz. But I still don't understand how Taylor's Theorem was used.", "label": 0}
+{"snippet": "The Nyquist limit for interpolation by trig functions states that one must give at least two data points per wavelength, because data just above and just below this \"folding frequency\" cannot be distinguished. I am currently playing with Hermite interpolation, providing the first few derivatives as well as the function values, and find that the Nyquist limit no longer applies. This cannot be a new observation, but I don't find anything about it online. Maybe I have not got the appropriate vocabulary?", "label": 0}
+{"snippet": "I've been reading a lot of various classic literature, and at times there is the sort of casual misogyny or racism that was commonplace and (within certain cultures) the social norm at that time. Such things are no longer so commonplace and generally aren't tolerated. I wish to have a concise adjective or noun to describe those things when discussing them that isn't so oblique and timid as \"outmoded\" or \"archaic\", but I cannot recall one nor find it with my (perhaps feeble) attempts to search for it online. Has anyone come across such a word? If not, I'm open to a suggested synthesized word or a potential loanword that might one day make it into a dictionary if we use it enough.", "label": 0}
+{"snippet": "I wonder how can I constuct a sphere inscribed in a tetrahedron using GeoGebra? I've thought I can construct it using the intersection of three planes bisecting angles between some pairs of faces in a tetrahedron, but when I contructed it, it didn't seem to work. Is this construction valid and I made some mistake while constructing the planes, or is it not a proper construction? If it is the latter, what is the proper way?", "label": 0}
+{"snippet": "If amber and cloth are rubbed together, it is known that some electrons are transfered from cloth to amber. In this case, cloth acquires a positive charge and amber a negative charge. If these two have opposite charge, shouldn't there be electrostatic force between these two ? So, the next time you rub these two items, shouldn't the electrons be transferred from amber to cloth?", "label": 0}
+{"snippet": "A solid sphere rolls without slipping up and then down an incline. Why does the static friction force point up the incline both when the object is rolling up and also when it's rolling down? I know it's necessary for the force to point up when the object is rolling up, because then it's the only source of torque on the object, and for the object to roll back down the incline, there must be a torque which acts in the opposite direction of the initial angular velocity. However, I don't understand why this is the case. Why does the force need to point up the incline to create the necessary torque, particularly when the object is rolling back down the ramp?", "label": 0}
+{"snippet": "\"Mill\" is usually used to describe the process of making flour (grinding), to describe a wind or water mill, or a factory. Since the process of milling or grinding consists of making small pieces or powder out of objects, I was wondering if the word \"mill\" can be used figuratively as in kill, destroy, obliterate or tear to pieces? For instance, in the context of a competitive computer game, would it make sense to say something like \"I was milled\" as in \"I was obliterated\" when losing a game as a kind of way to add a bit of color to the expression?", "label": 0}
+{"snippet": "According to the S-B Law, an area of mass will radiate out heat energy equal to the fourth power of its temperature in degrees Kelvin. If energy cannot be created nor destroyed, how can a body give off more heat than it receives? I understand how a magician seems to make a pigeon appear from nowhere, but I can't understand how so much more heat is being radiated out than was absorbed by the mass. How is this possible?", "label": 0}
+{"snippet": "I'm going to take an introductory class on dynamical systems at the level of Guckenheimer & Holmes, or Arnold's ODEs book, but I don't have any topology background. I know analysis at the level of Stein's Fourier and Complex analysis, but have not had exposure to full-blown measure theory or manifolds. Is there a book that covers basic point-set topology in an accessible manner but perhaps without unneeded generality? Thanks!", "label": 0}
+{"snippet": "I'm reading through the paper \"Lagrangian Intersection and the Cauchy Problem\" by Melrose and Uhlmann, and I'm having trouble with the definition of intersecting pair of Lagrangian manifolds. I am aware of the definition of conic Lagrangian manifold, but what is a conic Lagrangian manifold with boundary? Do we require the boundary to be isotropic or is it that if a conic Lagrangian submanifold has boundary then the boundary is always isotropic, or do we just define it to be such that the interior is a conic Lagrangian submanifold?", "label": 0}
+{"snippet": "I have a circle and a line with the length of its circumference. One end of the line is attached to a point on the circle circumference, forming the shape of the lowercase 'b'. Now, the line begins to wrap the circle clockwise, until it completes one revolution around the circle, where there's no more \"line\". What is the path created by the free end of the line?", "label": 0}
+{"snippet": "I've always thought of a transformation as \"the movement of a mathematical object through space\", but I found this definition that seems to be better: \"An operation that changes the status of a (mathematical) object to another state.\" Does anyone have a better definition that works for both dilations and isometries and also with more advanced math like linear transformations? Or, what would be the best way to combine these definitions? Is the \"space\" part important?", "label": 0}
+{"snippet": "The proof is quite obvious but how do you write it down nicely? I have this problem a lot with graph theory proofs where I don't know how to write them down so that they are rigorous enough. The proof itself would go something like this: Let C be a cycle in G.If we remove the edge e = {u, v} from C then C becomes a path between u and v. C is still connected so G is also still connected.", "label": 0}
+{"snippet": "I am looking for a word that describes advice that is too obvious to be helpful. Imagine asking for advice, and someone responds with simply saying to \"do what is desirable\" or \"avoid what is undesirable\" in the context of the advice. For example, if you asked someone for exam prep advice, and they simply said \"don't fail\", or if you asked for advice in marathon preparation and someone said \"don't get tired\". One might use the adjective as follows: \"Please spare your ____ advice\"", "label": 0}
+{"snippet": "I'm not a physicist so I'm asking you guys. We have been told that a device (\"medical\"...) uses a laser to irradiate a biological body (human, animal,...). The laser should apparently penetrates through metal and concrete (without destroying it). Can a laser penetrate through metal, concrete, ... without destroying the material? I don't believe that. After all, laser is light and light does not penetrate through steel or concrete. Except it's super thin, so the density would not be enough. Am I right with that? Thanks!", "label": 0}
+{"snippet": "I've only started my own studies on grammar recently and as I was reading CoGEL by Randolph Quirk, I came across this category called 'Catenative verb constructions'. According to the analysis used in the book, catenative verb constructions cannot be interpreted as verbs followed by a nonfinite clause acting as a direct or prepositional object. However, 'manage to' is also included yet when I look up the dictionary, 'manage' can be transitive even when used with the meaning 'to succeed in doing something, especially something difficult' like in these examples: In spite of his disappointment, he managed a weak smile. I don't know exactly how we'll manage it, but we will, somehow. Shouldn't 'manage to' be listed elsewhere then ? Or am I misinterpreting something ?", "label": 0}
+{"snippet": "I am trying to use the Poisson process for BLE(Blueetooth Low Energy) neighbor discovery. In this context, there are two devices called Advertiser and Scanner. The advertiser and scanner emit and listen to beacons in a duty-cycled fashion. This leads to longer discovery latency sometimes and I want to use the poisson process for the scanning and advertising patterns and prove the discovery is going to happen. Basically I want to merge two poisson processes and make sure there are two events within a small interval delta.", "label": 0}
+{"snippet": "I recently used a shear interferometer for aligning two lenses in an optical setup (a Galilean beam expander to be precise). I was able to align the lenses such that the vertical stripes were perfectly vertical (i.e. the beam is collimated). But I noticed that the image showed slight fanning: With fanning I mean that the stripes seem to be expanding when going to the right. Does anyone know which type of aberration causes this? I'm using this shear interferometer:", "label": 0}
+{"snippet": "Is it possible to find the highest \"noise\" value along a line segment defined by two endpoints within a Simplex (or Perlin) function by using an equation? The reason I ask is to avoid expensive ray marching. It's fine if there are multiple points along the segment with the maximum value. It would be preferred if it could work with multiple octaves of Fractional Brownian Motion as well. I'm fairly certain it's possible but it might be too difficult to derive. Corresponding code for the simplex (snoise) function can be found here. I've added a rudimentary image to show what I'm trying to do here :P", "label": 0}
+{"snippet": "I have a background in acoustics and do more and more of quantum mechanics. I wonder why don't we use more often the bra-ket notation in acoustics and vibrations like in quantum mechanics? In modal analysis, we deal everyday with Hilbert spaces, inner products and linear algebra so I think that it would make sens to use the notation in the same manner. Is it because the notion of state vector is less important in those contexts?", "label": 0}
+{"snippet": "Reading through wikipedia's page on international law, I noticed that there is never a definite article \"the\" before the phrase. It is a set of rules, norms, and standards generally recognised as binding between states, so it should be quite a definitive thing, right? So why is there no definite article? Compare: the constitution, the second amendment, the Bill of Rights, the Defense of Marriage Act, the Non-Proliferation Treaty.", "label": 0}
+{"snippet": "Is there more than one definition to \"polarization\" in the context of waves? In some cases, I've seen the term \"direction of polarization\", which I presume it refers to the direction of oscillation. In other context, I see this word use as a process of turning unpolarized waves into polarized waves. Also, there are times whereby people say that \"polarization only occurs in transverse waves\", which implies that polarization is a property/phenomenon of transverse wave. So is polarization a property, a process, an adjective to describe the direction of oscillation, or is it all of the above? Is there any other definition of polarization I'm missing here in the context of waves?", "label": 0}
+{"snippet": "I am studying about fibre bundles. If a fibre bundle is locally trivial then I understand the fibres are locally isomorphic. Also I understand that any compact Hausdorff base space cannot have a disjoint finite open cover for if I have a disjoint finite open cover then base space is disconnected. My question is, if my base space is connected, then are all the fibres isomorphic to each other?", "label": 0}
+{"snippet": "I have been watching videos of WIMP's and have a simple question.. The larger the particles, the shorter their lifetime. A top quark is so massive that it cannot form a \"stable\" bond with any other particle to form a meson or baryon. If WIMPS are too massive to make in a particle accelerator, how can they still be around today to affect gravity of galaxies? Wouldn't they have decayed by now into things we could see or detect?", "label": 0}
+{"snippet": "I have an enclosure mounted to the chassis of a vehicle. There are multiple points where the enclosure is fastened to the chassis as well as areas where it rests on the chassis without being fastened. Is there any point in putting vibration pads on the areas where the enclosure rests on the chassis? Logically I feel like anything fastened rigidly to the chassis would vibrate the same as the chassis.", "label": 0}
+{"snippet": "Could anyone help me to understand the difference between the usage for and to in the below sentences. They will be more interested in the struggles of the downtrodden, in those who are fighting to obtain the title deeds for respectable humanity. They will be more interested in the struggles of the downtrodden, in those who are fighting to obtain the title deeds to respectable humanity. Ideally, both the sentences are correct, however the preposition for is mostly followed by a noun whereas the preposition To is mostly followed by verbs. So, why is \"To\" correct in the second sentence in comparison with the first sentence?", "label": 0}
+{"snippet": "On plotting the angle of deviation vs the angle of incidence for a prism, we find that the graph dips only at one point. It is this result that is later used to prove that for minimum deviation to occur in a prism, the angle of incidence must be equal to the angle of emergence. But why exactly does the graph have only one minima? Are there any mathematical or physical reasons behind this phenomenon, or is it a purely empirical result?", "label": 0}
+{"snippet": "In his famous hit Working Class Man, Jimmy Barnes sings: He believes in God and Elvis He gets out when he can He did his time in Vietnam Still mad at Uncle Sam I can't make sense of the second line. What could it mean? What does he get out of? I thought that the line in question might be some idiom or slang known among workers, so I looked in dictionaries, but found no idiom or slang that would fit the context. Maybe it's something obvious to native speakers, but I am not one. I humbly hope that users of this SE can shed light on this mystery.", "label": 0}
+{"snippet": "I am a beginner to Lie groups and Lie algebra. Recently, I learnt that the dimension of the Lie algebra generated by a Lie group is the same as that of the Lie group. I have known for a long time that the space of vector fields on a manifold (even when not considered a Lie group), forms a Lie algebra. Is there any conclusion that can be made about the dimension of this Lie algebra? It seems to me that the Lie algebra generated a Lie Group (space of left-invariant vector fields) is the subalgebra of the Lie algebra generated by the underlying manifold (space of all vector fields), so their dimensions should not be the same. Any enlightenment is greatly appreciated!", "label": 0}
+{"snippet": "While scrolling through an online document, I came across the statement, \"If charges carried by the black hole are large, the curvature at the horizon is small.\" How is this so? I tried to think of an answer to this. My thinking goes this way: I know curvature is related to mass. If an object is more massive, it bends the spacetime fabric more, producing large curvature. So curvature small means mass small. So how does a large charge mean a small mass for a black hole? What is the relationship between the charge and mass of a black hole?", "label": 0}
+{"snippet": "Is there, or has there ever been, an unambiguous word for \"the leftmost extreme\" or \"the rightmost extreme\"? Such words exist for the other two dimensions. Imagine you are floating in a cube in space. You can go up until you hit the top. You can go down until you hit the bottom. You can go forward until you hit the front. You can go backward until you hit the (back/rear). You can go left until you hit the _______? You can go right until you hit the _______?", "label": 0}
+{"snippet": "In an acute-angled triangle ABC, let us denote H as its orthocenter and I as its incenter. Let D be the perpendicular projection of I on the line BC, and E be the image of point A in symmetry with center I. Furthermore, F is the perpendicular projection of the point H on the line ED. Prove that the points B, H, F, C lie on a circle. I think the idea here is the circumcircle BHC is the reflection of circumcircle ABC respect to BC. But I don't know how to proceed, can anybody help?", "label": 0}
+{"snippet": "So, the uncertainty principle states that one can not measure momentum and position with accuracy simultaneously. However, we know from relativity that simultaneously is something frame dependent in nature, so how can we reconcile these two in relativistic quantum mechanics or even QFT? I know that in QFT we define observables in different points in spacetime such that their Lie bracket is zero, but I'm not really sure how to go from this to an answer.", "label": 0}
+{"snippet": "I noticed that whenever I bunch up aluminum foil (into a ball), it becomes extremely hard to compress. If I use another piece of the same amount of aluminum foil, and keep folding it in, I arrive at a much smaller volume. It is full of air and much lighter than the same shape of solid aluminum, though, it is still extremely hard to compress. Question: Why does bunched up aluminum foil become so extremely hard to compress?", "label": 0}
+{"snippet": "I am a graduate student in mathematics studying algebraic logic. For quite some time now, I have been meaning to study physics -- it turns out that some ideas in foundations of mathematics have found promising applications in theoretical physics (topos quantum theory and quantum logic come to mind). I want to get a somewhat rigorous picture of classical and quantum mechanics, so that I can contextualize some of the things I will be reading later on. Is there a good resource that I can use for this? I would prefer to read something that has a careful development of ideas starting with classical mechanics, eventually culminating in a broad formulation of quantum mechanics. All suggestions are welcome!", "label": 0}
+{"snippet": "I came across some interesting dialogue in a tense scene in a novel, Salvation Lost by Peter F Hamilton: \"We'll know exactly what the other [people] are seeing and doing.\" \"Doing and seeing,\" \"What?\" \"Better grammar.\" \"Jesus, man; keep it relevant\" Though this is intended as comic relief, it has me wondering if there is any reason why \"doing and seeing\" is preferable to the reverse. Is there any actual guideline/grammar or does it just sound better to have the more active verb first?", "label": 0}
+{"snippet": "We recently attended a concert in a protestant church in England that was advertised as \"free admission with retiring donations\". The concert was indeed free with a voluntary (optional) donation. What is the meaning of retiring in this context? Googling without quotes gives results for people retiring from work, which is obviously not meant here, and googling with quotes returned similar events being advertised as such.", "label": 0}
+{"snippet": "A friend has pointed out that in an Oxford comma separated list, either every clause needs a verb, or each clause must be the object of the first verb. This seems to make sense to me, but would this mean that this sentence is a comma splice? \"Next week, I will go to the gym, beach, and get a haircut.\" The above sentence might be ambiguous, but are there any strict grammatical rules that this is violating? Does each clause have to have a verb, like so: \"Next week, I will go to the gym, go to the beach, and get a haircut?\"", "label": 0}
+{"snippet": "Everyone knows this experiment: You mix salt and pepper and use a charged balloon to separate the pepper from the salt. I never really understood how this works. In school (long time ago) we learned that unlike charges attract each other while like charges distract each other. In the experiment the negatively charged balloon attracts the pepper. Does this mean the pepper has a positive charge? Why is pepper charged? How can I predict for given particle if the balloon will attract, distract or not interact with it?", "label": 0}
+{"snippet": "I have often read that our universe was once small enough to be subjected to quantum mechanical effects, potentially altering how our universe turned out. This is a large theme in Laura Mersini-Houghton's Before the Big Bang. Michio Kaku also mentions this in his book Parallel Worlds. What exactly are they referring to? The initial singularity? The observable universe shortly after the big bang? The inflaton particle that inflated space giving rise to our universe? It is my understanding that the universe might have always been spatially infinite after emerging from the initial singularity so I'm not quite understanding what aspect of the universe was subject to QM.", "label": 0}
+{"snippet": "I have started to study formal languages, especially finite automata and regular languages and I encountered some difficulties, i.e. Is this true: Automata will be called isomorphic if, by changing the names of the states, one moves from one automaton to the second. Let be a regular language. How can I Prove that all minimal automata for the language are isomorphic? Thank you for any hints and answers!", "label": 0}
+{"snippet": "I am dealing with a PDE and I am trying to characterize the solutions: Galois differential theory might be of help, but I can only find books about this theory applied to ODE. Are there resources, books or papers, on the application of Galois differential theory to partial differential equations? I know the basis of the Galois differential theory applied to ODE as explained in Magid's Lectures on differential Galois Theory and Galois theory of linear differential equations by van der Put and Singer, and I am looking for something along the same lines, but maybe with more examples and at least at the graduate level.", "label": 0}
+{"snippet": "If I have two identical magnets of equal strengths producing equal repulsive forces between them, and if I replace one of the magnets with a stronger magnet (everything else remaining the same), how would the forces on both of them change, i.e. will they exert equal repulsive force on each other or not? Why? Also, does the size or strength of the magnet affect this conclusion? In other words, replacing one of the magnets with a significantly larger or stronger magnet will produce uneven/unequal forces on both the magnets?", "label": 0}
+{"snippet": "Lately, I observed a rainbow-like ring forming in my window during nighttime when the light enters from a street lamp. Interestingly, the sequence of colors in the rainbow seems to be reversed from what I anticipated. Normally, I would expect the inner part to be red and the outer part to be blue due to the greater refraction of blue light (like a sun halo). What could be the reason behind this color reversal phenomenon? Edit: To clarify, the window has a decorative film on it which causes the rainbow. The core question is still the same: Why would blue be on the inside and red on the outside?", "label": 0}
+{"snippet": "I am trying to understand the logic of negative exponents and I stumbled upon the video \"Negative Exponents\" by YouTuber JLC. He says negative exponents are \"defined\". But why is it defined the way it is? Is there some kind of international agreement or some kind of international organization that maintains this definition of negative exponents? What if I make my own definition of negative exponents? Please enlighten me, many thanks.", "label": 0}
+{"snippet": "I am trying to figure out what this phrase deconstructs to. Does it imply a logical OR, like: \"attention-deficit disorder\" OR \"hyperactivity disorder\"? For additional context, there are different types mentioned here: There are three main types of ADHD: Predominantly inattentive presentation. Predominantly hyperactive/impulsive presentation. Combined presentation. ...which seems to indicate that it is always both, but a little more of one than the other. If this is the case, does the grammar check out? Also when it is spoken as: \"attention deficit hyperactivity disorder\", or abbreviated as \"ADHD\", the slash is dropped, which loses meaning and adds confusion. Would there be a better way to phrase it? Would there be a better way to say it?", "label": 0}
+{"snippet": "Does anyone know a simple and accurate way to measure the size of an iron core using a magnetic sensor? Imagine having a collection of identical iron plates. I expect the strength of the magnetic field around the core to increase with its size. Would it be possible to determine the number of stacked plates by measuring the magnetic field strength using e.g. a Hall effect sensor placed on top of the staple? Are there better sensors/methods?", "label": 0}
+{"snippet": "This sentence is an excerpt from The Economist website. The Kremlin denied the advance, saying that Russian troops had repelled Ukrainian attacks in the region. What is the grammatical rule that's governing the \"saying that Russian troops had repelled Ukrainian attacks in the region\" in the sentence above? I've been looking into the types of clauses to find any applications that match this, but I think I'm lost.", "label": 0}
+{"snippet": "I am wondering if anyone happens to know the computational methods - and hence the computational complexity - of simulating the distribution of an electric charge (how electrons distribute) over a surface. In particular, I am curious about the computational difficulty in simulating the distribution of electrons over a highly asymmetric and non-uniform surface (like the surface of a rough rock). How does the simulation complexity scale with the complexity of the surface and the precision/accuracy of measurement?", "label": 0}
+{"snippet": "I am trying to write a proof regarding the following question and am stumped on this particular version of the problem. I believe that I have written a correct proof when asked if the columns of A are linearly dependent. That is solved by showing that the non-zero vector y can be used as a nontrivial solution of linear dependence. But I don't really know how this information translates when analyzing the rows of A instead. I tried to look for a counterexample that IS linearly independent but cant find one.", "label": 0}
+{"snippet": "I've recently read that what most people learned to think of as the 'speed of light' is actually the 'speed of causality', and that light just happens to travel at that speed (through free-space.) I'm also aware that light travels measurably slower through transparent materials such as water or glass. This leads me to ask: is light traveling slower through such materials, because the speed of causality is reduced in such materials? And if so, what does this tell us about how the speed of causality is determined by permittivity and permeability of various materials?", "label": 0}
+{"snippet": "I'm trying to reconcile two seemingly conflicting sources of information about Lorenz force. Let's consider a solenoid in proximity to a permanent magnet with the field pointing in the same direction as the axis of the solenoid. From the right hand rule I conclude that the wire should either be pushed towards the center of the solenoid or outside. However, the solenoid also acts as a magnet with poles on each sides and will attract/repel other magnets. How does one reconcile the two explanations ? Is the solenoid both contracting on itself and moving towards the other magnet at the same time ? If yes which force/equations describe the movement of the electromagnet towards a permanent magnet. Thank you!", "label": 0}
+{"snippet": "I am aware there are similar questions already asked, however, I find none of the answers satisfactory, they either do not contain any mathematics at all, or mathematics of a level I am not capable of comprehending. My doubt is that, if the change in kinetic energy is dependent on frame, then how is the law of conservation of energy valid in all frames? One possible explanation I have thought of is that the change of potential energy is also frame dependent, but I cannot think of a suitable example to justify the same. Please answer only using newtonian mechanics I do not know statistical or lagrangian mechanics.", "label": 0}
+{"snippet": "I have recently started to study integrals and faced some difficulties of understanding why we need antiderivatives to calculate area under curve. I am trying to visualize it using graphs but it just doesn't make sense to me. If anyone can explain me if it's even possible to understand them the way I try. here is the image: enter image description here Thank you :)", "label": 0}
+{"snippet": "I was curious if anyone knows the font used by the Desmos graphing calculator. All the formulas are formatted as LaTeX, so I wanted to know if there was a way to use this font in my own documents. It seems at first glance like standard Computer Modern, but upon closer inspection as you can see the \"w\" and \"v\" characters are rendered in a style that makes them pointier so that they are much easier to distinguish from omega and u respectively (and imo they just look a bit more pleasant). Here is a side-by-side comparison for context. Computer Modern: Desmos Font: (This is my first time making a post on the site, so apologies if I have made any mistakes!)", "label": 0}
+{"snippet": "What is the interpretation of temperature in the Ising model? Can one describe a theoretical thermometer for the Ising model? As far as I know, in the theory of gases, temperature is interpreted as a quantity proportional to the mean kinetic energy. A thermometer is a device capable of converting the average collisions of particles into the movement of a dial. The higher the mean kinetic energy, the more movement the device registers, and the dial goes up. I can't grasp a similar idea for the Ising model.", "label": 0}
+{"snippet": "I already know the term anaphora exists for repeating the same word for emphasis. I'm specifically interested in a term for repeating a word twice without additional clarification to express that something is especially strong or genuine. Examples \"Do you like her, or do you like like her?\" \"Are you making quick bread, or are you making bread bread? \"I'm so excited, I got a promotion promotion, with a pay raise and everything!\" I don't know that I've ever seen this in formal prose; it seems unique to spoken English, but if anyone knows of any written examples please add them. If no term already exists, I'd like to coin the term \"duplication duplication,\" to distinguish it from ordinary duplication.", "label": 0}
+{"snippet": "Imagine that Alice is the President of Arstotzka. Alice has a lot of enemies but she's generally an upstanding President so her critics have a hard time building a campaign against her. Instead, the critics are patiently waiting in the shadows until Alice makes a minor mistake - perhaps she misspeaks at a conference or her car driver skips a stop sign. The critics then blow this incident out of proportion and use it to smear Alice before the next election. What's a word or expression specifically describing the act/strategy of waiting for a small transgression to happen?", "label": 0}
+{"snippet": "Can you compute geodesics by treating it as a problem where you want to minimize the length of a curve through two points on a specified surface while having the constraint that the curve must reside on the specified surface? If so, can you explain how one could do so for a cylinder? Or is the calculus of variations the only method by which to do so? I tried setting up the constrained optimization problem for a cylinder but was unable to make any progress, leading me to think that maybe it's impossible to solve the problem without the calculus of variations.", "label": 0}
+{"snippet": "I am working on my thesis and need to convert my paper to a different format. I'm new to using latex, only having started using it for this project, and am struggling to get the base version of this template working. No error occurs, but compilation appears to halt, judging by the fact that main.log log ceases to update after a certain point. The repository hasn't been updated in a while, so I am guessing that the setup may be outdated. I've tried removing some of the references to other sections, but that doesn't appear to make a difference. If someone could help me get this working, or point me in the right direction, I would greatly appreciate it. https://github.com/davidanastasiu/thesis_template-SJSU_CMPE", "label": 0}
+{"snippet": "Show that, given four coplanar points, we can always draw two intersecting circles coplanar with the points, such that two of the given points are diameter endpoints of one circle, and the other two given points are diameter endpoints of the other circle. In this question, \"intersecting\" means that the circles share at least one common point. Example: I will post my answer. Alternative solutions are welcome. This question and answer serve to provide ideas that might help answer a harder question about five points and two non-intersecting circles.", "label": 0}
+{"snippet": "Ive recently been introducing myself to Gaussian Processes. In Bayesian linear regression, one would expect that when adding new features, the likelihood on the training set would weakly increase due to the larger degree of freedom, of course leading to overfitting most likely. I was wondering if this is true in general for marginal likelihood for GPs, regardless of the choice of kernel/specific hyperparameters? If so, what is formal explanation for this? Can we prove it mathematically? Thanks :)", "label": 0}
+{"snippet": "I heard that natives use Present Cont. to describe things in the future. As I understood, we use Present Cont. when we have arranged an action or there is at least one person with whom we agreed to have plans. But I saw this: I am teaching English tomorrow. I will be teaching English tomorrow. What is the difference and when I should use Present Cont. to describe action in the future?", "label": 0}
+{"snippet": "I work in an office where the airconditioning is not working, so I brought a small mobile airconditioning device: it's a small machine, emitting cooled air. It looks like this: However, according to the laws of thermodynamics, the total amount of heat should always increase in a closed system. Therefore, regular airconditioning systems vent their waste heat to the outside, but this little mobile machine does not have any connection to the outside, so it has no means to discard its waste heat. So my question is: how can such a machine even exist?", "label": 0}
+{"snippet": "Two congruent circles that touch at point H are given. Let the line p be their common tangent that doesn't pass through the point H. Construct a circle that touches both given circles and the line p. The most intuitive thing was to construct an equilateral triangle NOL (such that L is on p, and N and O are on the given circles) and find its circumscribed circle. However, the obtained circle intersects given circles at N and O, instead of just touching them. What am I doing wrong?", "label": 0}
+{"snippet": "If a set is equipped with total order (reflexive, transitive, antisymmetric, strongly connected), does this necessarily mean there exists an injective mapping from that set to the reals? Alternatively, if a set has larger cardinality than the reals can it not be well-ordered? I'm struggling to think of a counter example. Most of the canonical examples of sets with larger cardinality than the reals (all functions, power set of reals) cannot be equipped with total order.", "label": 0}
+{"snippet": "This question is bugging me from a very long time and I don't know whether it can be answered or not but still I am posting to get other's opinions. Is there any inherent property among all the uncountable sets which make them uncountable ? Or more precisely:- If I ever wanted to \"make\" an uncountable set, what ingredient should I put in so that I am guaranteed of the set being uncountable ? Edit :- My apologies for the wrong terminology used. By \"ingredient\" , I was just trying to refer to some property which is common to all the well known uncountable sets (e.g. the irrational set, set if real numbers) that I should keep in mind while forming a new set of numbers.", "label": 0}
+{"snippet": "Imagine a uniform thin layer of a viscous gel sticking on a vertical wall. A small sphere is submerged in this gel. The gel has a yield stress (Bingham model). How can I calculate the yield stress that will cause the sphere to start sliding with the fluid on the wall? This yield stress will obviously depend on the weight and dimensions of the sphere.", "label": 0}
+{"snippet": "I'm having a problem with the second part of the question, which shows that the sum of the vectors equals zero. I came up with a geometric proof, but I wondered how to prove it by using complex numbers and maybe links to the first part of the question. I was thinking about the equally distributed roots of unity, but don't know how to move on.", "label": 0}
+{"snippet": "I understand how we can have three coin tosses (or three events if you prefer) such that all three tosses are pairwise independent, but not mutually independent. One trivial example of this would be to just have the third coin be the xor of the first two coins. My question is whether it's possible to have four or more coin tosses such that any two coin tosses are pairwise independent, but any three coin tosses are not independent. If this is not possible, what would a proof be like showing that it isn't?", "label": 0}
+{"snippet": "I am a PhD student working on observational cosmology. My research is based on the experimental side of it (receiver design, etc.) but I would like to get deep into the CMB and CMB statistics. I have found several resources and have read some of the papers but I feel like they are a bit \"unconnected\". Does anyone know where I could start? I thought of just studying Ruth Durrer's (The Cosmic Microwave Background) book, but I am not sure if it will be complete enough.", "label": 0}
+{"snippet": "I am studying blackbody radiation and modelling a cavity as a blackbody. However, I am encountering a number of confusions in this description: Many textbooks mention that the cavity consists of metallic walls that act as perfect reflectors. Light entering through the hole, after multiple reflections, get absorbed. However, if the cavity walls are perfectly reflecting, how is the radiation getting absorbed by the walls? For studying the radiation emitted by the blackbody, the textbooks model the radiation inside (emitted by walls due to heating) as standing waves. But how are standing waves being emitted by the cavity? Because standing waves are supposed to be confined inside. Can anyone please explain in simple terms?", "label": 0}
+{"snippet": "For example, a carpenter works in carpentry and a plumber works in plumbing. So what trade does an electrician work in? Electrical? I searched the definition for \"electrical\" and found that it gives the part of speech as an adjective and not a noun like the dictionary does with carpentry or plumbing. This is confusing to me. I would like to understand and know how to talk about the trade for an electrician. I would appreciate it if someone could help clarify and explain this to me.", "label": 0}
+{"snippet": "Imagine a mass hanging from a string attached to the ceiling of a lift and the lift descends with a certain acceleration. From the reference frame of the ground the tension in the string would be smaller than when the lift remained stationery. However, let's say your friend was inside the lift and when asked about the tension would say that the tension was same, regardless of the list ascending, descending or stationery. Isn't that really counterintuitive? Isn't the force not relative and the same, regardless of the reference frame?", "label": 0}
+{"snippet": "For example: It is a thing that works producing stuff. This feels wrong to me, but I can't quite put my finger on what exactly is wrong about it. It seems like it's trying to be a participle phrase, but it's not necessarily modifying the current state of \"it\", and is, instead, describing what \"it\" is -- i.e. by working, \"it\" produces stuff. If it is, indeed, a participle phrase, then it should be able to be written as Producing stuff, it is a thing that works. But, to me, this doesn't seem correct either, so it leads me to believe that the very structure of the sentence is incorrect.", "label": 0}
+{"snippet": "I have been taught that path difference and phase difference are essentially the same thing, except phase difference is measured in an angle unit while path difference is measured in multiples of wavelength. This seems incorrect. I think they are rather different concepts, with path difference representing the difference in distance a wave needs to travel in order to reach a point. Are they really the same thing like I have been taught?", "label": 0}
+{"snippet": "For example, when referencing a webpage: Visit the \"The Performers\" page to learn about our musical lineup. In this case, I want to tell someone to visit a webpage entitled \"The Performers\" to find more information, but the repetition is throwing me off. If I were to remove the first \"the\" before \"The Performers,\" though, then it would essentially read as \"Visit page\" without an article. So, is it okay to use the article of the webpage title as the article for the sentence, or must I include the first \"the\" before the webpage title? The two iterations: Visit the \"The Performers\" page to learn about our musical lineup. Visit \"The Performers\" page to learn about our musical lineup.", "label": 0}
+{"snippet": "I think something is missing in the definition of homeomorphism I saw. It just said it maps the collection of open sets to the collection of open sets in a bijective way. What exactly makes this preserve topology? I can think of weird situations where each individual open set is mapped to totally disjoint open sets in a bijective way, throwing the topological structure out the window.", "label": 0}
+{"snippet": "The definition of optical path length is the distance that light could have travelled in the same time, in vacuum. So, can we define something analogous for sound waves, like an \"acoustical path length\", with respect to a specific medium, say air? And if we were to define something similar, how far would it's applications reach? For example, can we use it in doppler effect in cases when the observer and source are in a different media? Or interference, when there is a change of medium in between? If so, kindly guide me on how to do it.", "label": 0}
+{"snippet": "I know foliations as a particular topic in differential geometry. I understand the definition and basic properties of a foliation from the DG point of view, including the Frobenius theorem. While trying to understand why this concept is important I came across this Wikipedia page on integrability conditions for differential systems, but couldn't understand much of it. I do not want to too diverge from my other studies now, yet want to understand this association quickly and completely. Can you suggest me a source that is solely focused on the relation between foliations and systems of PDEs?", "label": 0}
+{"snippet": "I was going through this paper in which the authors state that : In Landau theory, a continuous phase transition is associated with a broken symmetry. The phase transition in a black hole system can also be characterized by the symmetry and order degrees as in a conventional thermodynamic system. The authors don't explicitly state which symmetry is broken for the black hole phase transition. Also, would such symmetry breaking lead to any chaotic effects? Any explanation in this regard would be truly beneficial.", "label": 0}
+{"snippet": "I am attaching the solution of a school question asking to calculate the inverse of a matrix. However, the solution proposed does not fit in anything I ever seen about calculating inverse matrices. I did not found any property that fits the final part of the solution (the one I highlighted in the image below) although the solution is correct, I would like to know which property or reasoning supports the final solution of such a problem. Thanks.", "label": 0}
+{"snippet": "I read an article that referred to the idea that a double slit experiment near the event horizon of a black hole observed by someone inside the black hole creates a paradox because the inside observer can break the interference pattern, thereby bringing information of their presence out of the black hole. This seems odd to me. The significant part of \"observation\" here, as far as I understand, is that it requires interaction. The inside observer can't interact with the particle to measure it's position. He can only detect it's position if something outside the black hole interacted with the particle, which means the superposition would have collapsed whether or not he was there. Am I missing something? Edit: Link: https://www.sciencenews.org/article/black-hole-paradoxes-quantum-states", "label": 0}
+{"snippet": "I have often heard that two physically distinguishable mixed quantum states produce different density matrices. However, how would I prove it? I know that they have to differ on the main diagonal, because these elements correspond to measurement probabilities in the standard basis. Moreover, I have seen someone using density matrices to show that two mixed states are physically indistinguishable. Does this process always work? In other words, is it true that for any two physically indistinguishable quantum mixed states, the density matrix is the same? And how to prove it?", "label": 0}
+{"snippet": "I'm learning some math by myself and I thought of this question that has to do with how useful complex numbers are: I'm looking for a specific example of an equation that has the following properties: The equation is true, i.e., its LHS and RHS are always equal, no matter the values of its variables, if any. The LHS and the RHS are algebraic expressions (no limits, derivatives, integrals, sin, cos, etc...) The equation only involves real numbers. Its shortest equality proof involves complex numbers. The proof ends with no complex numbers. It has a longer equality proof that doesn't involve complex numbers. It's a short equation (this property is subjective). Please, let me know if my question is wrong or if no such equation can exist.", "label": 0}
+{"snippet": "I want to understand in some detail why superconducting qubits need periodic calibration. The usual, hand wavy explanation is environmental effects that tend to vary from time to time. However, I suspect that the actual picture is more complex than that. I want to understand in particular which effects are purely external, like the earth magnetic field (in lack of a better example) and which are internal to the superconducting device. I am especially interested in those factors that are internal to the qubit itself, like manufacturing defects and physical characteristics that may change in time. A good reference on this subject would be appreciated.", "label": 0}
+{"snippet": "A spanning tree of a graph is a subgraph obtained by deleting only edges of the graph and which is also a tree. Why does one study \"spanning tree\" in graph theory? What are \"spanning trees\" real life application? We know the number of spanning trees of a graph is equal to any cofactor of the Laplacian matrix of the graph. Why is one interested in knowing number of spanning trees of a given graph? I would like to know enough in order to motivate a undergraduate or graduate student.", "label": 0}
+{"snippet": "Hi I was trying to determine the basis of the topology on the following collection in R {[a,b), a <b}. Here is what I tried : Knowing that the basis for a subspace topology is equal to the set of all intersections of {[a,b), a <b} with the basis of the topology it is a subspace to. Now I also know that the basis for the euclidean topology on R is {(a,b), a <b}. Can I just take the intersection of {[a,b), a <b} and {(a,b), a <b} to get the basis? If so what does this equal? Or am I totally wrong? Thanks in advance.", "label": 0}
+{"snippet": "I understand that Berry curvature sinks and sources correspond to Weyl points. However, I'm curious about the identity of points exhibiting a Berry curvature spiral, highlighted by red circles in the figure below. Could these be Dirac points? Is it possible to differentiate between Dirac and Weyl points based on the direction of the Berry curvature rotation? It's worth noting that these two spirals exhibit opposite rotation directions.", "label": 0}
+{"snippet": "I read that a sound wave (a scalar wave) produces monopole radiation, an eletromagnetic wave (a vector wave) produces dipole radiation, and a gravitational wave (a second order tensor wave) produces quadrupole radiation. How do I make sense of multipole radiation physically? The Wikipedia article on multipole radiation is informative on the mathematics, but I can't seem to get a physical picture. Note: my question is different from this post, which asks about the pattern of lowest order multipole radiation produced.", "label": 0}
+{"snippet": "first post here. I've been looking into acoustics a bit recently and I'm wondering if for a compressed solid, acoustic impedance should change along different axis in certain cases. Consider a cubic lattice of atoms with pressure being applied to the top and bottom, compressing the lattice. Atoms would be spaced further apart in planes parallel to the applied pressure. I'm hypothesizing that acoustic impedance would be higher for a sound wave travelling through the lattice perpendicular to the plane of applied pressure and lower for a sound wave travelling through the lattice parallel to the plane of applied pressure. Could we consider density as a vector to solve our impedance equation if the above holds true?", "label": 0}
+{"snippet": "We know that Maxwell's electromagnetic theory was originally an ether theory. Later, the ether was denied. But Maxwell's electromagnetic theory can be transformed into a theory of \"field\". The theory opposite to Maxwell's theory is the theory of action and reaction. Or it could be the theory of action-at-a-distance (Wheeler-Feynman absorber theory). According to Maxwell's electromagnetic theory, electromagnetic waves can exist independently of their source or have their own degrees of freedom. According to the theory of action-at-a-distance, electromagnetic waves cannot exist independently of their source. Electromagnetic waves do not have their own degrees of freedom. These two theories have been debated for hundreds of years. Is there a formula that can distinguish which of these two theories is right or wrong. Just like Bell's formula?", "label": 0}
+{"snippet": "Consider a few sentences: I read a lot. ?I read much. I don't read a lot. I don't read much. Do you read much? This seems to suggest \"much\" is a negative polarity item, but then we can say things like \"Much of it has to do with you not being here.\" So how much of a negative polarity item is \"much\"? I am particularly interested in existing literature on this.", "label": 0}
+{"snippet": "While reading the CMU FLAC overview, I stumbled upon the above image. While I have seen Greek numerals before, I had no idea that there was an entire algebraic symbology developed in Greek (though this isn't too surprising). To try and find more about this particular notation, I reverse Google Image searched it and found nothing (well, I was greeted to snippets written in the Tengwar, but that's besides the point). What is this notation? Can you direct me to an overview of the system?", "label": 0}
+{"snippet": "As a thought experiment, say, for the sake of simplicity, we have a meson. This meson, which is traveling near light speed, is traveling towards a black hole. And skirts the event horizon in such a way where the anti-quark ends up inside it's event horizon, but the quark does not. What would happen? Would this create a free quark? That seems like the only logical thing to happen, but I know that would also break color confinement.", "label": 0}
+{"snippet": "The operational principle of frequency combs is that you generate very short pulses (in time domain), and that in the frequency domain (due to Fourier's transform) the spectrum of such pulses is a comb. But this is just maths. And how it works from the physics perspective? Let's say I have a monochromatic continuous laser pointer that outputs only ONE wavelength. In front of the pointer I place a shutter that chops the beam into short pulses. How can those pulses have multiple optical frequencies (with many different wavelengths)? Or is my idea too simplistic and I'm forgetting something?", "label": 0}
+{"snippet": "If so, then why? We know that a current carrying closed loop in a uniform magnetic field experiences no force but when it's suddenly pulled by an external force, according to Lenz law a magnetic force will start acting on it to oppose the external force and eventually reach steady state at infinity. How can this be? Edit: Iam sorry for not specifying the doubt clearly, here is the question in which I was confused as to how there can be a magnetic force acting on the ring", "label": 0}
+{"snippet": "What does the Stark-Lo Surdo effect consist of in the interaction of the electromagnetic field and the active medium in a laser? I thank those who want to give a clear and concise answer. In my student notes from the seventies, I found the topic I was looking for, the calculation for which I attach. But what happens in practice (since I don't have an optics laboratory available)?", "label": 0}
+{"snippet": "Am getting the following error when I try to do tlmgr install package: tlmgr.pl: package repository http://mirrors.rit.edu/CTAN/systems/texlive/tlnet (not verified: pubkey missing) It appears I need to get the keys somewhere, but I haven't been able to find them on CTAN. Where else can I find them? If it's any use, I just updated my system on Arch, so maybe some other fellow Arch users had a similar problem?", "label": 0}
+{"snippet": "Any regular curve may be parametrized by the arc length (the natural parametrization or the unit speed parametrization). But I haven't seen an analogous development for regular parametric surfaces. I hope we can do this at least for orientable surfaces with no umbilical points. For such a surface, there will be two orthogonal lines of curvature through each point, and I suspect that there is a parametrization whose parametric curves coincide with lines of curvature. But I'm not sure how I should approach showing the existence of such a re-parametrization. Is there a such parametrization? If not, what are the conditions that we should impose to have such a parametrization?", "label": 0}
+{"snippet": "When talking about black holes and singularities, most books say that combining relativity and quantum mechanics gives the answer of infinity in some equations. They also say that: Infinity is the answer you get when the universe is trying to tell you that you have made a mistake. Why can't equations have answers of infinity? For example, a singularity is infinitely dense, so why can't other things about it be infinite?", "label": 0}
+{"snippet": "In the original version of Sequent Calculus by Gentzen for classical and intuitionistic propositional logic there is a structural difference: the classical version admits succedents with multiple formulas but the intuitionistic version admits only succedents with one formula. I'm searching for another formulation of Sequent Calculus in with succedents are restricted to one formula both for classical and intuitionistic logic. In particular I'm searching for a formulation in which Sequent Calculus for classical logic is obtained by Sequent Calculus for intuitionistic logic by adding some rule (i.e. excluded middle). Can someone suggest me some reference?", "label": 0}
+{"snippet": "It is often said that the achievability proof for Shannon's coding theorem relies on the channel being discrete and memoryless. At the same time, following the classical proof (using random coding and AEP), I can't find any part of the proof that explicitly uses the fact that the channel is memoryless (except arguably perhaps the guaranteed existence of a supremum of the mutual information?), as AEP has been shown to work for any stationary and ergodic channel. Further, Shannon's original paper does not seem to make any mention of memory in the proof as far as I can tell. Is it true that the classical achievability proof relies explicitly on the channel being memoryless? If so, where in the proof is the memoryless assumption used?", "label": 0}
+{"snippet": "Quick question with probably a simple answer. For context, I am currently in undergraduate classical mechanics studying potential energy. My question is, if a conservative force is one in which is only a function of position, can radioactivity be a conservative force? The example I thought of was if we take two identical particles which are undergoing radioactive decay, and we put one in the upper bound regions of the atmosphere, and the other at sea level, can we say that radiation is a function of position? I guess this also poses the question, can atmospheric pressure/temperature affect radioactivity? Feel free to slaughter my logic/understanding. Thanks :)", "label": 0}
+{"snippet": "I know work done is equal to product of force, displacement and cosine of angle between them. But that formula works only when we assume that the force is constant during displacement and it acts so long the body moves and also when the direction of force and displacement is constant. But how should I calculate work done if the direction of force or displacement is changing. So in this case there would be no constant angle between them and so dot product won't work as I don't know the cosine value and at this point I have got stuck.", "label": 0}
+{"snippet": "I have an object that takes a shape similar to a catenoid, which is known for its zero mean curvature. According to Laplace's law, the pressure difference is proportional to the mean curvature. This implies that if the mean curvature is zero, then the pressure difference is also zero. However, I am aware that when there is a non-zero pressure difference between the inside and outside of the object, which has left me puzzled. Is it possible to have a shape resembling a catenoid but with a constant pressure difference? Furthermore, how can I relate the curvature to the distance, r(z), from the z-axis to any point z on the boundary of this shape?", "label": 0}
+{"snippet": "Reading through Einstein's Brownian motion paper \"On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat\", it seems the final argument is that he can calculate the Avogadro's constant by using data on the diffusion rates, particle size and fluid viscosity. But its hard to see the connection that ultimately atoms must exist. Can someone lay out a flowchart of step-by-step reasoning leading to that conclusion? I see all the math steps, but need a more philosophical type of breakdown. Also can't the random movement and diffusion law movement of the particles be just as well explained by fluctuations of pressure and density of continuous matter?", "label": 0}
+{"snippet": "Is it correct to say: for any family of bounded operators (proper subset of B(H)) acting on a non-separable Hilbert space there is a non-trivial subspace of the Hilbert space that reduces the family? I know that this is true for any operator on the space so, I assume that it holds also for the von Neumann algebra generated by this operator. Can we generalize to non-commutative families? If the answers is positive (or positive with certain restriction imposed on the family) how can we show it? Is there any reference?", "label": 0}
+{"snippet": "If you were to measure a regular hexagon, is there a way to rotate the hexagon so that if there were two lines bisecting the center of the hexagon, both lines would be the same length? Can we then use the lengths of those lines to determine the area of the hexagon? Edit: To clarify, I mean that I intend for the lines to be perpendicular.", "label": 0}
+{"snippet": "There are four concepts which are studied in Calculus and Analysis: Convergence, Continuity, Differentiability and Integrability. In Calculus, you can define the latter three in terms of the first, but also you can define integrability without convergence using Darboux approach. In topology, you can define convergence and continuity in terms of neighborhoods, and in measure theory you can define integrability in terms of measurable functions. I wonder if there is a definition of differentiability without making any reference to the concept of limit or convergence, thank you so much by your help.", "label": 0}
+{"snippet": "Consider the following diagram Here, the diode is in forward bias, and allows current to flow. However, I am slightly confused why this is the case. A diode is defined to only allow current to flow from the anode ( Positive ) to the cathode ( Negative ). When drawing a diode, the cathode is the line and the anode the base of the triangle. Conventional current flows from the positive terminal to negative terminal, but in reality the electrons flow vice versa. Hence, considering the above diagram, shouldn't the electrons not be able to flow through the diode? The only way I can see around this, is that diodes are also drawn, considering conventional current. Is this correct?", "label": 0}
+{"snippet": "In the derivation of Torriceli's law it is assumed that the pressure at the tank hole is equal to atmospheric pressure. I believe this is true when the water starts flowing through the hole but I do not understand why this should hold during the whole purge procedure. Do you have ideas about the explanation? CFD calculations showing this behavior would be great. Many thanks.", "label": 0}
+{"snippet": "The second law of thermodynamics states, that entropy (of the universe) always increases. Entropy can, however, be (locally) reduced when energy is provided. At the phase transition from a relatively unordered to a more ordered state (e.g. condensation of vapor to a liquid), the entropy is lowered. At the same time, energy is released from the system (thanks to the enthalpy of condensation). Naively, I would expect that I need to provide energy (instead of gaining some) to the system to lower the entropy. Why does this not contradict the second law of thermodynamics?", "label": 0}
+{"snippet": "I know that the Heisenberg Uncertainty principle states that the position of an electron is uncertain, however, if an electron is created due to beta decay, then at what location is it more likely to begin its movement? Is it right inside the proton? Is it the outer edge of the proton? Is it adjacent to the proton? Is it near the proton? I mean is there a possibility of a beta particle from a nuclear decay to come into existence at the far end of the galaxy for example? What is the limiting condition for its position?", "label": 0}
+{"snippet": "According to Fermat's principle, light should take the least time between two points. Therefore, is it correct to say that the angle of refraction is solely dependent on the difference between speed of light in two mediums? Surely the the position of the observer is a key factor too, given the findings of the double-slit experiment that show a photon is only actualised on measurement/observation. Does this not imply the necessity of an observer for the existence of an angle of refraction?", "label": 0}
+{"snippet": "I've been reading more category theory as a prerequisite to understanding some more complicated theorems, and for the first time I'm running into arrows that are distinctly colored. Examples include these diagrams from Wikipedia for natural transformations and universal morphisms: The Wikipedia articles do not readily show me a link to where the coloring for these diagrams is explained, and I have not seen these colored diagrams in the textbook I have been reading for Category theory. Why are these arrows (and objects) colored blue and red? Better yet, (if possible) can someone give me a link/source/textbook that explains this coloring procedure? Thanks in advance.", "label": 0}
+{"snippet": "I understand that the word spook is a racial slur that rose in usage during WWII; I also know Germans called black gunners Spookwaffe. What I don't understand is why. Spook seems to also mean 'ghost' in German. Did the Americans call them spooks because the Germans did? If so, why did the Germans call them that? Or, if the Germans called them that because Americans called them spooks, then why did the Americans call them that? And how did Americans know the Germans had a nickname for black gunners?", "label": 0}
+{"snippet": "When researching the reflexive, symmetric, transitive, addition, subtraction, multiplication, division, and substitution properties of equality, the sources I found said they were true \"for all real numbers\". Are any or all of them not true for complex numbers? i.e., is the \"for all real numbers\" a necessary caveat, or should it say \"for all numbers\"? Also, I know the reflexive property applies to mathematical objects as well (any mathematical object is congruent to itself). Do the other properties of equality apply to all mathematical objects as well?", "label": 0}
+{"snippet": "I am trying to calculate the determinant of the following matrix. I literally have no idea if there's a general approach for solving such strange looking determinants, but I decided to subtract the first row from each row after the second. I don't know what to do next... May you show me what we're supposed to do and how do we find the determinant? Thanks!", "label": 0}
+{"snippet": "Assume a Gaussian surface in a non-uniform electric field that is directed along X-axis. Say the field is getting weaker as we go along positive X direction and it's constant along Y and Z directions. Then, if the Gaussian surface is a cube and charge enclosed is zero, the electric flux coming into the surface is more than that flowing out. So, shouldn't the net electric flux be non-zero contradicting Gauss's law? Does it mean such an electric field is impossible without a charge being distributed along the path?", "label": 0}
+{"snippet": "The usual semantics of first-order theories involves models who have a structure-set. Hence it is required to use some sort of set theory as the metatheory. However it is also widely known that one can do logic with a minimal metatheory, say a fragment of Peano. If we are using such a metatheory, what will the semantics become ? What will replace the notion of \"set-model\" ?", "label": 0}
+{"snippet": "Here is the problem, I thought it the I've been thinking for a long time, but I still don't have any ideas. Problem: Let A(S) be the group of all bijective functions on S with composition as its binary operation. then A(S) is finitely generated if and only if S is finite set. I know that proving from the right to the left is relatively easier, but when it comes to proving from the left to the right, I really don't have any ideas. I hope someone can help.", "label": 0}
+{"snippet": "I am typesetting my thesis in latex overleaf. I am struggling with one issue. I want to highlight my section with blue rectangular background with white color for heading as can be seen in picture. For subsection I don't want a background rectangle I simply want subsection of a blue color as can be seen in attached picture. I will really appreciate it if someone help me regarding this. Thanks.", "label": 0}
+{"snippet": "I was given an honors project to solve for the equations of motions of a pendulum with an oscillating fulcrum. I (somewhat) understand the procedure on how to solve it with lagrangian mechanics and the Euler-Lagrange equation, but I am stuck at a question. How do we know this cannot be solved with Newtonian mechanics? I tried to look up the answer on Google and even tried to solve for it myself but I obtained an equation with theta, acceleration in the x and y direction so Im not sure what to make of it. Does anyone know? Or are there any resources to understand the precise limitations of Newtonian mechanics? I am a physics undergrad who just finished electromagnetism and linear algebra, thank you!", "label": 0}
+{"snippet": "I am having trouble understanding why is temperature coefficient for avalanche breakdown is positive? The explanation I found online says as the temperature increase the mean free path decreases making collision and generation of carrier pair easier. But the electric field require to accelerate charge carriers to point of collision remains constant . So why does avalanche breakdown voltage increases with temperature if the electric field remains same? Doesn't increase in voltage indicate it is slightly harder to obtain avalanche breakdown? If the mean free path is decreasing and charge carrier generation is getting easier shouldn't occur at same voltage and not increase further", "label": 0}
+{"snippet": "The Coriolis force predicts that winds in the northern hemisphere should be deflected in a clockwise pattern and winds in the southern hemisphere should be deflected in an anti-clockwise pattern. Why is it that in the case of cyclones however, the cyclones spin anti-clockwise in the northern hemisphere and clockwise in the southern hemisphere? If it's indeed true then what is clockwise and anti-clockwise direction?!", "label": 0}
+{"snippet": "What is it called when someone says no, but actually doesn't mean that? Imagine this situation: when two lovers have had an argument then one of them is trying to apologise but the other one (usually the girl) says \"no, I don't forgive you.\" but she isn't really angry. She just want him to insist more. She says no in a some kind of seductive or cute way. What is this behavior called?", "label": 0}
+{"snippet": "I understand why all non-degenerate energy states can be chosen to be real up to an overall phase (as is highlighted here Is a non-degenerate wavefunction real or complex?). However I've been told the argument holds in the opposite direction -- (that all energy eigenstates that can be represented as purely real are non-degenerate). Is this true? I'm having trouble finding a proof of this.", "label": 0}
+{"snippet": "I know that as the kernel parameter for the RBF kernel increases, the Gaussian function becomes less peaked and broader. The reach of the points become larger meaning that farther datapoints have more weight. Intuitively, it makes sense that a larger reach means a smoother decision boundary. However, since I don't have an extensive background in mathematics, I find it difficult to come up with a more mathematical explanation. I was wondering whether anyone could help me with that?", "label": 0}
+{"snippet": "I came across this question while studying for the SAT. What the humanities teach are valuable skills. These include the ability to think critically; to construct, analyze, and respond to arguments; to see both sides of an issue; and to understand the processes that have brought us to where we are today. (A) NO CHANGE (B) skills: these The answer sheet says that (A) is correct, but it does not specify why. I thought the answer is (B) as what follows correctly elaborates on the previous information.", "label": 0}
+{"snippet": "This stems out of my personal curiosity and it's not related to any homework of sort. Suppose I have a table made of some uniform substance (like plastic), and then I strike some point of the table with a hammer. Will the disturbance/wave I produce travel always the speed of sound in that medium, or will there be cases in which the wave travels at a different speeds?", "label": 0}
+{"snippet": "I have a weighted directed graph representing the intensity of movements of individuals between locations, with weights representing the mobility flow. I have another dataset consisting of particular paths that are taken by specific individuals. For example, for a person named Alice, I know how she moved from node A to node B, potentially via some intermediate stops through other nodes. What I want to evaluate is how likely this is given the mobility network (the weighted directed graph). Essentially, can I compute some kind of distance/statistical measure that tells me how \"deviant\" or how \"consistent\" these observed paths are, given the mobility network (taking into account the edge weights)?", "label": 0}
+{"snippet": "I just discovered Lean and using computers for stating and proving theorems. The first question that came to my mind, can we write any proof with Lean? Or are there limitations (something that you can write a proof for on paper but not in Lean)? I'm not talking about practicality or feasibility. But does the Lean system have the capability? Edit: I posted the same question on proofassistants.stackexchange.", "label": 0}
+{"snippet": "So I'm confused with The Second Law of Thermodynamics. It says that heat flows from the high temperature to low temperature. For example, if we put a glass of cold water on the dining room, the cold water will eventually have the same temperature as the dining room, because heat will flow from the air in the dining room into the cold water. The cold water \"gains\" heat and the air in the dining room \"looses\" heat. But, why does the temperature in the dining room remain the same? Shouldn't it become colder? The same goes for a thermometer when someone that has a fever uses it. Will their body temperature loose heat because the heat will flow from their body to the thermometer?", "label": 0}
+{"snippet": "Geometrically, what is the difference between a diagonizable matrix and an orthogonally diagonizable matrix? I understand the difference algebraically, as explained here and many other places. But I'm struggling to see the difference geometrically: both will not rotate (assuming the field is the reals), but will stretch by different amounts along different axes (Wikipedia calls this a inhomogenous dilation). Graphically, I can't see the difference between, say, a circle or ellipse dilated inhomogenously along orthogonal axes versus non-orthogonal axes: in either case, it will remain an ellipse.", "label": 0}
+{"snippet": "I'm a physics graduate that is joining the master degree program of my University. One of the areas of research that i'm very interested is Quantum Field Theory over curved surfaces, but the point is that i don't know how to begin to start studying these subjects. I imagine that i should star from classical field theory and go all through until reach in the quantum field theory over curved spaces. So, do you have suggestions of literature to start those subjects?", "label": 0}
+{"snippet": "There is a word for animals like horses and cows that defecate wherever they happen to be when the need strikes them, versus animals like dogs and cats that seek out one place or another to do their business. It may be that all such animals are herbivores but \"herbivore\" is not the word I'm looking for as it relates to eating habits rather than pooping habits.", "label": 0}
+{"snippet": "I am getting confused as I study the AdS/CFT correspondence, so I ask this question. CFT is given on the conformal boundary of AdS, which can be derived from Poincare coordinate patch to AdS. Would this mean that CFT has its AdS dual only on the subspace covered by this Poincare coordinate patch? Or does CFT has its AdS dual on the entire AdS space?", "label": 0}
+{"snippet": "This Wikipedia's page says that: David Hume's problem of induction demonstrates that one must appeal to the principle of the uniformity of nature if they seek to justify their implicit assumption that laws which held true in the past will also hold true in the future. For which I'm confused about how to interpret the meaning of appeal in this sentence. Most of the dictionaries I consulted suggest that the phrase appeal to can only be followed by one or more people or organizations but here it is followed by to some law. So how should I interpret that sentence?", "label": 0}
+{"snippet": "I just came across this sentence while studying for the SAT and wonder if it makes sense. The women soon disperse, SOME entering the shallow waters at the beach, OTHERS venturing out onto the rocks to access deeper waters. My first question is, it sounds a little awkward to add some additional fragments beginning with SOME and OTHERS here. Are they participial phrases? Can they be added like this beginning with SOME and OTHERS? My second question is, can they be added with just a comma? SOME ... , OTHERS ... I feel there should be some conjunctions to make it more natural. This makes me so confused. I'd really appreciate it if you could enlighten me. Thank you.", "label": 0}
+{"snippet": "I am taking a graduate-level mechanics course right now, and we are working with the continuous limit of coupled harmonic oscillators. My professor mentioned that he prefers the \"bloch wave method\" to the determinant method for finding the wave equation, but I do not know what this is. There is no mention of it in Goldstein, to my knowledge. Does anyone know how this works?", "label": 0}
+{"snippet": "For measuring the electric potential difference between two oppositely charged plates A and B, a test charge q is moved from plate A to plate B. My textbook says that the charge is kept in electrostatic equilibrium such that an equal and opposite force to the electrostatic force is applied on the charge to move it opposite to the electric field. However, I don't understand how it is possible for a charge to move if it is acted upon by two equal and opposite forces. My teacher said that the charge moves due to inertia, but I did not understand how, since the charge was initally moving towards the negative plate A.", "label": 0}
+{"snippet": "One of the postulates of Copenhagen interpretation of quantum mechanics is that every observable has a Hermitian operator A. With these operators we can then find eigenvalues of observables, make a time-evolution of a wave function and, in general, calculate the properties of the system. However we also introduce anti-Hermitian operators. My question is: What is the use for anti-Hermitian operators, if observables are described with Hermitian operators? NOTE: I am just diving into the subject of Quantum mechanics, so I hope this question makes sense and is not \"too basic\".", "label": 0}
+{"snippet": "I've used both Polish and Reverse Polish (RPN) notation. I get that using them one doesn't have to deal with varying evaluation order. While the benefits to automatic computation (as in software) is clear, it's unclear how this aided human reasoning. Can anyone explain how Polish Notation (or even RPN) simplified reasoning by people over infix notation? I'll be happy with any examples or even references to additional reading.", "label": 0}
+{"snippet": "I have a Hotwheels track set. It has a looped structure such that at some point in the car's trajectory, it becomes upside down. But in such a situation, it doesn't fall to the ground. I understand this has something to do with its fast speed. Can someone please explain as to why exactly this happens? Why it doesn't fall down? Something like this. (arrow indicates the position I was talking about) I was wondering what kind of forces were acting on the car at that point. A theory based (and not mathematical) explanation would be helpful since I am not accustomed with mathematical explanations", "label": 0}
+{"snippet": "A decimal representation of a rational number is necessarily either terminating or non-terminating and repetitive. This comes from the fact that when you are dividing there are only a finite set of possible remainders (remainder is always less than the divisor). As you go on dividing for decimal representation, the remainder has to repeat. Similarly, in finite fields, as you go on raising the power of an element, the product has to repeat because there are finite number of possible answers. This leads to Fermat's little theorem. In both cases, the finiteness of the possible set of answers is leading to these important and beautiful results. Can you suggest some more examples of this kind - understandable by school and junior college students?", "label": 0}
+{"snippet": "(Disclaimer: I'm not all that familiar with any of the two topics) Consider the Ising model on some graph with, lets say, two heavily inter-connected components that are sparsely connected between each other. This \"bottleneck\" would imply (or would be implied by?) that the Cheeger constant of the graph (and thus the first eigenvalue of the Laplacian matrix) is small and also that it would be very difficult for the spins in one component to interact with the spins in the other component. My question then is: is there any result linking the Cheeger constant with the \"magnetization\" properties of the graph? Something like a bound on the temperature at which the phase transition occurs that depends on the Cheeger constant or vice versa? Thanks in advance!", "label": 0}
+{"snippet": "I'm trying to compile a document which needs the package minted, but it throws the same error over and over: ! Package minted Error: You must have `pygmentize' installed to use this package I can't seem to make it work. Other forums say to install the package \"Pygments,\" which is a Python package, but MikTeX doesn't seem to have that package in its repositories. Am I missing something? Do I have to install another LaTeX motor or something? Edit: Before anybody asks, yes I'm using the \"-shell-escape\" flag to compile the document which minted requieres.", "label": 0}
+{"snippet": "So, when we solve the optimization problem using Lagrange Multiplier method, I know that lambda can be positive or negative. Lambda is simply the rate of change in the optimal value when the constraint changes. So, I understand that lambda can be positive or negative. Now, my question is when we have inequality constraints. In that case, why do we have the requirement that lambda should be non-negative? I could understand the math behind it. But I am not able to follow up the intuition. Simply put, if Lambda is still the rate of change with respect to the change in the constraint, then why THEORETICALLY SPEAKING can't it be negative?", "label": 0}
+{"snippet": "I have the following list of points : I'm trying to find the best regression model to fit these points. The logistic regression is not close enough to the points : I guess I need something closer to a spline, but I don't know how to compute a regression model based on a spline, all I can find are interpolation models. Also, I would like to be able to compute the derivative of the regression. With a spline interpolation, I don't know how to compute the derivative over x so that it appears as a function of one-variable. For context, this is in order to build a tool for acid-base titration for chemistry. Thanks !", "label": 0}
+{"snippet": "How to punctuate a quotation which is an exclamation, at the end of a sentence which is a question? The quotation is \"Fire!\" The sentence is: Did he really shout \"Fire!\"? OK, this is simply the shortest example I can think of to illustrate the question, the actual quotation of concern is longer, and so is the question sentence. But if it is improper to use both the exclamation point and the question mark, I'd like to know why. Searching has only resulted in lots of hits regarding whether to put a single mark inside or outside the quotation.", "label": 0}
+{"snippet": "Suppose I have a principal bundle, and some group G acting on the principal bundle. Is it always possible to find a G-invariant connection on the principle bundle? If G is compact, then I can imagine one can find such a connection by picking any connection to start with and then 'averaging' this connection over the group G. But what is G is not compact? Does an invariant connection still exist, in general? If not, what conditions do I need on G?", "label": 0}
+{"snippet": "I recently asked this question about whether or not profinite groups admit maximal subgroups: And indeed, profinite groups admit subgroups of finite index, so taking any minimum index subgroup containing the finite index subgroup gives a maximal subgroup of the profinite group. Now I wonder if it's true that all subgroups of a profinite group are contained in a maximal subgroup, i.e., can you have infinite chains of infinite index subgroups which do not split off to maximal subgroups periodically as you go up the chain?", "label": 0}
+{"snippet": "(There are a lot of questions about entanglement shown in the Similar Questions box. If there's already something about what I'm about to ask, please refer me there.) Suppose the particle paths are arranged to be of different length (e.g., detector A is close to the emitter but detector B is many miles away). And suppose that both detectors provide an exact time stamp of the detection event. Upon reading the logs of the two detectors, would you find that both detections registered at the same time, indicating that one particle got \"stuck\" in detector A until the other particle was detected at B?", "label": 0}
+{"snippet": "I learned that the possessive apostrophe -s is used for living beings and the \"of\" form for non living things: The dog's name is Sherlock The color of the flower is yellow However, I have noticed that these rules are often ignored in spoken language: The road's name is Privet Drive The name of the dog is Sherlock Are these mistakes made by non-native speakers or are these just theoretical grammatical rules that are not really strictly applied by native speakers in their spoken language as well? Does one stand out directly as a non-native speaker with these errors?", "label": 0}
+{"snippet": "I'm wondering if 'calls have grown for X to be Y-ed' is an acceptable substitute for 'there have been growing calls for X to be Y-ed'? To clarify, these are examples of the latter from the first page of Google search results: 'There have been growing calls by some eco-activists and developing countries for powerhouse states to foot the bill for climate change.' or 'There have been growing calls for St David's Day to be made a bank holiday in Wales'", "label": 0}
+{"snippet": "I know that loop-level three-photon vertex in QED is zero since the contribution from fermion and antifermion cancel each other. Also, from what I know this has something to do with gauge invariance of the QED. However, my question is \"is this true even when the gauge invariance is broken?\". If the gauge invariance is broken, I guess the photon will not only get a mass, but also there will be additional contribution from longitudinal mode of the photon which I am not sure whether this will change the story.", "label": 0}
+{"snippet": "I need a verb that describes asking someone to stop helping you, even though you know they mean well, because it's not helpful. So you ask them in a way that is almost pleading. It's stronger than just asking, but it's not quite pleading. I'm doing an analysis of a play, and one aspect of this analysis is that I have to categorize, line by line, what each character is trying to do in one action verb. It is proving to be harder than I thought.", "label": 0}
+{"snippet": "When a capacitor is charged, electrons flow from the battery terminal to the plate of the capacitor, as the electrons flow through the wire, they must be having some kinetic energy? So, when the electrons finally stop at the plates of the capacitor, what happens to their kinetic energy? We don't normally assume the kinetic energy to get stored in the capacitor, we only consider the energy stored in the capacitor to be due to the decrease in potential energy of the charge as it flows from one terminal of battery to the other, then where does the kinetic energy go?", "label": 0}
+{"snippet": "In the case of elastic scattering or absorption between photons and electrons, the incident light is either fully reflected or fully absorbed and hence it either retains its wavelength or ceases to exist. But how does inelastic scattering between them work? Specifically, if light has a wavelength, how exactly does that wavelength change in such a way that the light transfers only some of its energy and hence its wavelength increases?", "label": 0}
+{"snippet": "Let A and B be solenoids with the same pole facing each other. Then will their repulsion cause the set up to jump upwards? Please correct me if I am wrong: Solenoid A exerts a downward force on Solenoid B, which in turn exerts the same force on the ground. Then due to newton's third law, the ground exerts the same force and the whole thing is pushed upwards. If this force is greater than gravity, the set up will jump upwards. The connecting material makes sure the solenoid B is also carried upwards with Solenoid A.", "label": 0}
+{"snippet": "I am trying to find the minimum energy point of a catenary curve. Can anyone please let me know whether there is a potential energy or energy formula for a catenary curve ? Especially I would like to know when the end points of a catenary changes it's position, I would like to know how the energy of a particular point on a catenary changes and where that particular point will reach in position.", "label": 0}
+{"snippet": "I am confused in which category to put this sentence. It's a polite request, so it looks like it's an example of Imperative Sentence. But it does express the desire to have mango (even though not directly with the use of \"I wish\" or \"I desire\"), so feels like it may be Optative Sentence as well. And the listener of this sentence will most likely respond in \"yes\" or \"no\", that makes it a question.", "label": 0}
+{"snippet": "We know that thermal radiation is one of the ways energy can be transferred from one object to another. And we know, objects at any temperature emit electromagnetic radiation. So does that mean molecules and atoms are constantly losing energy? And why isn't this considered in the first law of thermodynamics? How can we even calculate the amount of thermal energy converted into electromagnetic energy (radiation).", "label": 0}
+{"snippet": "I searched a lot on the internet but I couldn't find any helpful answers, so here I am. I'm trying to create a chessboard figure, using xskak package that contains a label for each square. An example of what I'm trying to achieve is shown in the xskak tutorial on overleaf, linked here. I'll also add a screenshot of the image I'm referring to: Thanks!", "label": 0}
+{"snippet": "I've heard three seemingly contradictory facts, so apparently I'm not understanding at least one of them correctly. \"Proper time along a path is the time elapsed for a clock that travels along that path.\" \"Proper time along a null path is zero.\" \"There are no preferred inertial reference frames, so if I travel at the speed of light, my own clock that I take with me will tick like normal for me.\" So how can it tick like normal but then not tick at all? Which of these three statements is incorrect?", "label": 0}
+{"snippet": "A jack of all trades is a master of none, but oftentimes better than a master of one is apparently accredited to William Shakespeare. Just to clarify - I mean the FULL quote, not just 'Jack of all trades' part. Is there a book, poem, or work by Shakespeare that proves he is the author? I have searched through the complete works of Shakespeare and couldn't find any phrase like this.", "label": 0}
+{"snippet": "Monoids represent maps from some mathematical object to itself. Groups represent the automorphisms of some mathematical object. What do abelian groups represent? One unsatisfying answer would be that they just represent automorphisms of nice enough mathematical objects. However it seems rather uncommon for the automorphisms of some object to form an abelian group unless they have very few automorphisms. Furthermore, the theory of abelian groups is very different from the theory of groups in general, and abelian groups appear frequently in other applications where they are not the automorphisms of some object in an obvious way, like homology groups. This suggests that maybe its just a coincidence that abelian groups are groups, and that they represent something else. What do they represent?", "label": 0}
+{"snippet": "Consider the following: \"Saranghe\" not only means \"I love you,\" but it also means \"Let's be together till we die.\" In Telugu, \"Intiki veltunnava?\" means \"Are you going home?\" What I'm wondering is whether I should capitalize the i in the transliteration of \"intiki veltunnava? In other words, which one should it be? In Telugu, \"intiki veltunnava?\" means... In Telugu, \"Intiki veltunnava?\" means... If Telugu had a distinction between uppercase and lowercase letters, I could just use the equivalent version in the English transliteration, but Telugu is written in an abugida script, so that isn't really applicable. The transliteration introduces a new element that I can't figure out how to resolve.", "label": 0}
+{"snippet": "The Novikov self-consistency principle prevents a paradox in which a billiard ball is sent to its past through a closed timelike curve (allowed under general relativity) such that it collides with its past self and prevents it from entering. Imagine a setup where the ball, as soon as it exits in the past, hits a switch that closes a gate across the entrance. What's to stop that from creating a paradox? There's no alternate trajectory for the ball; the switch can be a plate that covers the exit so that the ball can't avoid hitting it.", "label": 0}
+{"snippet": "Momentum is the defined as the product of mass and velocity and can be thought as measuring how much motion something has. However, it is not clear to me why we need momentum and why force is not sufficient to explain nearly all the phenomena. Consider a larger mass moving at the same speed as an object of smaller mass. We say the object of larger mass is harder to stop, as it has more momentum. However, could we not just say the object of larger mass exerts more force, so it requires a greater force to stop it? The use of momentum is not entirely clear to me.", "label": 0}
+{"snippet": "I got a mouse which has wireless charging capabilities a while back. I would like to take advantage of this. However, I currently have an extremely nice mousemat from grovemade I grabbed in a sale a while back https://grovemade.com/mouse-pads/ which I would like to keep using. My idea is simply place a wireless charging mousemat below it. However, the grovemade mousemat has an aluminium plate in it and so the wireless charing will induce eddy currents. If you know how strong these eddy currents will be and/or whether that will make wireless charging impossible. I would appreciate any help. Thanks, Pioneer", "label": 0}
+{"snippet": "This post, currently closed, asks for the intuition behind Liouville's theorem, which states that every bounded entire function is constant; I find the answers unsatisfactory and hand-wavy. I am looking for a more focused, precise description of what is going on. Is there a geometrical understanding of what is going on? I try to visualize a non-constant analytic function, to understand why unboundedness is necessary along some direction, but it isn't working for me.", "label": 0}
+{"snippet": "There has been some recent buzz around generalized/higher form/categorical(?) symmetries in the physics community. I understand Seiberg's papers are a popular resource, and I am aware of McGreevy's review on the subject in the context of condensed matter. Nonetheless, what are some other resources I might look at if I want to learn about the subject? Specifically, where might I find problems on the subject (e.g., Andrew Lucas's lecture notes include one fairly introductory problem on the topic)?", "label": 0}
+{"snippet": "I'm reading Billingsley's Probability and measure. I'm reading about extremal distributions, and I'm at where he is proving that Gumbel is one of the extremal distributions. I'm having a hard time understanding the proof and I'll appreciate it if someone helps me figure out the proof. The text highlighted in yellow is what i don't understand (it is quite half of the proof). Thank you in advance.", "label": 0}
+{"snippet": "I'm new to optimization and I'm reading a paper that they reformulate an ILP problem into QUBO using penalty method. Let's say we use a solver to solve above QUBO, and the global optima of QUBO obtained from the solver is infeasible to the original ILP. (infeasible from my understanding is the QUBO solution does not satisfy all constraints of the ILP). My dumb question is: Can the local optima of QUBO obtained from the solver still be feasible to the original ILP? I don't have much background in optimization, so it would be nice if you guys can suggest some materials mentioning my question. Thank you in advance!", "label": 0}
+{"snippet": "If someone sets up a table at the edge of a conference room selling their wares, it could be described as a \"stall\" or maybe a \"kiosk\". But what if someone instead sets up something like a few chess boards that people can play on? The word \"stall\" doesn't really seem appropriate to describe this (\"a chess stall\"?) but is there any word that would be more appropriate? I thought of \"sideshow\" but that doesn't seem right either because it's not really a show, it's an interactive game activity.", "label": 0}
+{"snippet": "When using \"too much\", it is put after the verb & before the uncountable noun e.g. I drink too much coffee. However, this sounds strange in the sentence: I use too much social media. Instead I use social media too much sounds more natural. Can anyone explain why this one doesn't fit the rule? So far it seems that it only happens with the verb use. (Another e.g. would be I use my phone too much).", "label": 0}
+{"snippet": "The Gauss-Bonnet theorem for compact regular surfaces is often only enunciated for totally regular surfaces, with no singular points. But what if I wanted to state it on a surface with a finite number of singular points but otherwise regular, like a cube? How is the Gauss-Bonnet modified? I know somehow the curvature has to be concentrated on the vertices, but I'd like some help in making that notion precise. Thank you.", "label": 0}
+{"snippet": "Assuming \"phreak\" is a portmanteau of \"phone\" and \"freak,\" giving us the term \"phreaking\" to describe the illicit act of hacking telephone networks, and \"Phishing\" pays homage to it by misspelling \"fishing\" to describe the practice of tricking someone into revealing sensitive information on computer networks, now we have \"Vishing\" (voice call phishing), \"Smishing\" (SMS text message phishing), and \"Qishing\" (QR code phishing) being used in the security industry. Is there a better term (besides \"annoying\") than \"jargon\" to describe these words?", "label": 0}
+{"snippet": "In one of his lectures, L Susskind stated that he cannot make sense of a metric with more than one timelike dimension. I also have trouble imagining it, but is there a good mathematical or physical reason why this is not possible? Let us assume all extra timelike dimensions are compactified, so we cannot directly observe them. What kind of trouble or unphysical problems would this create? I am not asking for non-standard physics here, but just a more formal reason than intuition as to why we assume the extra dimensions are necessarily spatial (I have a basic understanding of why string theory needs extra spatial dimensions, but I do not understand if it forbides extra time dimensions). The question is not limited to string theory though.", "label": 0}
+{"snippet": "I have seen several questions regarding the size of the absolute smallest black hole, the smallest stable black hole and similar. These made me wonder; what is the smallest stable black hole if it is immersed in a standard atmosphere? I assume there is some maximum rate at which the black hole can consume matter, and that this is related to its size. Therefore, since its Hawking radiation is inversely related to its size, logically there should be an unstable equilibrium point when these two equal each other. I could, of course, be completely wrong - however I'm afraid my knowledge of how to calculate anything regarding black holes is limited to working out the Schwarzschild radius.", "label": 0}
+{"snippet": "Imagine, there is a truck of mass 'm' accelerating with an acceleration 'a', this means that the truck definately carries some force 'F'(let). Now, imagine the truck collides with a man standing stationary on the middle of the road. So, the truck will hit the man with force 'F' and due to Newton's third law the man also exerts a force 'F' on the truck, then my question is that, why don't the truck's net force becomes zero, and why it continues accelerating? Kindly explain, where am I going wrong. Note- there is no external force other than 'F' acting on the system.", "label": 0}
+{"snippet": "We know that nothing including light can escape the gravitational pull of black hole. Now special relativity says that nothing travels faster than speed of light. Then how can effects of gravity due to the black hole be felt outside the black hole as nothing can escape black hole? This seems contradictory as anything is pulled inside the black hole due to gravity whereas nothing can escape a black hole.", "label": 0}
+{"snippet": "I've seen that the Leibniz formula of determinants can be reduced to the Laplace expansion through consolidating terms. What I haven't been able to find online is a connection between any of those and the geometric interpretation of determinants, which is the volume (or measure) contained between the parallelopiped formed from the column (or row) vectors. How do I prove that the Leibniz formula, which is based on terms composed of permutations has anything to do with geometric measures?", "label": 0}
+{"snippet": "I have just learned that linear frame dragging exists in General Relativity. I have also seen simulations where a periodically accelerated and decelerated mass causes a sort of gravitational dipole radiation, dragging nearby masses in the direction of the acceleration. My problem with this is that in my whole life I was taught that the leading order in gravitational radiation is quadrupole; dipole radiation can't exist because of conservation of linear and angular momentum. Is dipole radiation forbidden only in linearized General Relativity? What is the full picture here / what am I missing?", "label": 0}
+{"snippet": "I am trying to understand the jump operators in the Lindblad equation. Specifically, if there is any condition of boundedness we need to impose on them. I ask this because, as was pointed out in this post, there should be no assumption on the norm of the jump operators. But for example in this review, the jump operators live in the space of bounded operators. So is boundedness of the jump operators a necessary condition? In Preskill's notes, there is a derivation of the Lindbladian in terms of the operator-sum representation which gives some normalization condition that the jump-operator should fulfill in terms of the Kraus operators but I am not sure if this is relevant to my question.", "label": 0}
+{"snippet": "I think my formulation in the title may be a bit confusing. I mean a behaviour similar to \"gaslighting\" yourself into seeing/perceiving your own opinion from someone/something, even though that person/thing doesn't actually share your opinion. I've witnessed this a few times on social media when people interpreted satirical videos of political topics to match their own opinions/believes, even though the videos themselves were neutral/not actually picking a side in the political topic. Would be cool if there were a word for that.", "label": 0}
+{"snippet": "In textbooks on Category Theory, monoids pop-up all over the place, we several easy examples such as integers, lists and so on. I was then wondering about comonoids. What are some \"simple\" examples of comonoids appearing in mathematics? I've tried searching, but most texts either only mentions the concept of a comonoid, or provide some convoluted example. I'm trying to get a better feel for what a comonoid is, thus I'm searching for easy to grasp examples.", "label": 0}
+{"snippet": "A few days ago was the first time I ran into the word \"Nigerien\" meant to mean \"something related to the African country of Niger\" as opposed to \"Nigerian\" meaning \"something related to the African country of Nigeria\". Since this is very easily confused, for example by my spelling checker which didn't like \"Nigerien\" at all, and especially in spoken English, is that use actually correct, or is there a better word? And how would you pronounce it so that it doesn't get confused? (With the countries themselves, I thought NIger has an emphasis on the first syllable, and NiGERia on the second, but for Nigerien this sounds just wrong to me).", "label": 0}
+{"snippet": "If there is a circular metal loop and a changing magnetic field perpendicular to the loop, there is an induced electric field that causes the electrons to move and cause a current. But my question is why is there even a current? Why don't the electrons just move and rearrange themselves to cancel out the induced electric field, just as they do in case of electrostatic shielding?", "label": 0}
+{"snippet": "I am looking to replace the idiom \"kangaroo court\" in the following sentence: Class followed its usual script. The professor took center stage, exposing the deep racism, sexism, colonialism and homophobia of a previous generation and like well-rehearsed actors, us students assumed our roles as moral arbiters in a kangaroo court. I want the replacement to communicate the idea that the verdict or judgement is a forgone conclusion and that the trial/classroom is just a pretence of debate/justice as everyone already knows what the answer/verdict must be before discussion ensues. If no good replacement can be found you could rewrite the sentence entirely to help communicate the above point. Thanks a bunch.", "label": 0}
+{"snippet": "We know that a capacitor and an inductor both offer some opposition to the flow of current through an AC circuit and their reactance is a measure of the amount of Ohmic opposition due to these circuit components. I am aware of how these quantities arise mathematically. However, my question is, physically why do these circuit components provide a type of opposition to current flow in the case of AC circuits? What is the actual cause for this reactance to appear?", "label": 0}
+{"snippet": "Suppose you have a faucet that expels water at a rate r Liters/second. Will the rate at which water flows through some ring beneath the faucet be greater than r or equal to r? On one hand, if the rate at which water flows through the ring were greater than the flow rate of the faucet, wouldn't that violate conservation of mass? On the other hand, shouldn't water be traveling faster through the lower hoop, so it should have a higher flow rate? I've asked some people about this, and I've been told that the water column will inevitably become thinner as it falls such that the flow rate through the hoop will be the same as r. Is this true?", "label": 0}
+{"snippet": "I hope my question does not break the rules. I can't understand how this statement can be true in the book which I've mentioned: I cannot undestand why it's true because if I have two point charges with same sign and same magnitude then the electric field should be zero at point P: But according to gauss's law it's not zero and it equal to electric field due to one of these point charges. So this electric field is only caused by the charge inside the closed surface, not the charges outside it!", "label": 0}
+{"snippet": "I am doing a lab experiment (Franck-Hertz) at uni and am supposed to find the temperature, at which electrons are emitted from a barium oxide cathode (without the necessity of an external E-field that provides additional energy). I am attempting to calculate the temperature T = W/kB from the work function W (i.e. the ionization energy). Is there any source, that contains such data? I tried NIST Chemistry WebBook, but they only have data for BaO in the gas phase. I need some value for solid BaO.", "label": 0}
+{"snippet": "I am interested to see a derivation of Kepler's laws from Newtonian mechanics, which would be a suitable exercise or demonstration for a first-semester course in calculus. Therefore I'd like to avoid any use of the cross-product since this is usually only introduced much later in a calculus curriculum. I've looked at Newton's original derivations. They don't use any objects or theories which a first-semester calculus course couldn't use. But they do involve enough geometry that it seems \"a bit much\" for a first-semester calculus student. So I recognize that any such derivation will probably be hairy in one way or another. But in the off chance that there is some known elementary and simpler derivation, I wanted to ask. Thanks!", "label": 0}
+{"snippet": "Given a container filled with identical objects, how could I find the number of objects in the container accurately purely by analyzing the sound produced on shaking? More specifically, which acoustic parameter should I focus on? Some ideas I have had so far are: Looking at the number of amplitude \"spikes\" since the more objects there are, the more collisions there are Using Fourier Transform to break down the combined sound into its constituent frequencies, finding the number of distinct frequencies. Unfortunately, I am not sure if the frequencies will be measured for each object, since the objects are identical", "label": 0}
+{"snippet": "I have just switched to writing in LaTeX from markdown. I like to proofread by hand, and so in the past I used a template that increased the line spacing and changed the typeface to something monospaced just for proofreading. Now I cannot figure out how to change an entire document to being monospaced. I found several solutions that seem to only work on LuaLaTeX, but I would prefer to use pdfLaTeX.", "label": 0}
+{"snippet": "Circle k and a line p that intersect at points R and Q are given. Inside the circle point A is given. Construct all the circles that touch the line p and the circle k and pass through the point A. I tried to solve this problem using homothety, but it didn't work out so I guess that's not the proper way to solve it. I would appreciate any ideas.", "label": 0}
+{"snippet": "In the double-slit experiment, the interference pattern shows the probability of finding the particle (photon or electron) at a given volume. In a given experimental setting, this probability distribution doesn't change with time, so this probability distribution belongs to a stationary quantum state. I think that this doesn't mean that the Hamilton operator belonging to an experimental setting has only one eigenvalue and a single state that belongs to this eigenvalue because the pattern depends on the wavelength of the photon. If we used the superposition of two photons of different wavelengths, we would get a non-stationary interference pattern. Is there such a thing as \"the superposition of two photons of different wavelengths\"? Or the double-slit experiment can't produce non-stationary states?", "label": 0}
+{"snippet": "Phonons are typically used to describe quantised vibrations in solids. However, is it legitimate to talk about phonons for e.g. a sound wave propagating in air? Contrary to photons that are particles that can exist both in free space as well as inside an optical cavity, it seems like phonons are quasiparticles defined only in a solid (i.e. a cavity for sound). Is this the case?", "label": 0}
+{"snippet": "I've heard that because light takes time to travel from one place to another, we see objects in distant galaxies as they were when they released the light. new and advanced telescopes are able to see further and further into space, and therefore closer back in time to when the big bang happened. I've also heard that the laws of physics are slowly changing over time and that they might have been different in the early seconds of the big bang. In the future, could an advanced telescope be used to observe the light released by distant galaxies and other cosmic structures at the time of the big bang and observe physical laws that were different from the ones that we have in the present day?", "label": 0}
+{"snippet": "what would happen if I took a toroidal core, generated a static toroidal magnetic field in the core and then rotated the core around it's symmetry axis within a larger stationary toroidal winding around the same core? Just for simplicity imagine a toroidal transformer with a rotating core inside. Would I get DC current generated in the stationary coil? If yes can anyone explain by what law and formula?", "label": 0}
+{"snippet": "I haven't found satisfying answer yet. Beside those typical examples like how many colourings of a cube is there up to rotations or how many graphs are there on n vertices up to isomorphism etc., is there any \"real\" usage of Burnside's lemma in advanced math? All examples I could find seem to me more like funny riddles you can impress your friends with but they are not quite useful for anything.", "label": 0}
+{"snippet": "If I have n cards and n stacks of cards, how many ways can I split the cards between the stacks if the order of the cards in the stack is significant but the order of the stacks is insignificant and stacks are allowed to be empty. And is there an algorithm to find them. So for example, with two cards (a, b) and two stacks the possible arrangements are: [ab][],[ba][], [a][b]. ([b][a] is equivalent to [a][b]) this might seem like a silly problem but I am very much stuck and very much desperate", "label": 0}
+{"snippet": "Suppose I filled a bucket of water with a hose, now when it's filled, I remove the hose from the tap's end, while the other end is still submerged in water. Now if I throw the other end on the ground, it sucks all the water from inside the bucket spilling it out the ground till it's empty. Why does this happen? I assume there's something really simple about pressure and stuff going on which someone like me, who hasn't studied fluids in detail, can understand...", "label": 0}
+{"snippet": "I am trying to first construct a fractional linear transformation, to map the sector to a half or full circle. From there it seems straightforward using rotations, translations, and standard mappings between circles to half-planes to create a map that takes the sector to the right-half plane. My question is, how do I construct the fractional linear transformation? Lang's Complex Analysis shows how to construction fractional linear transformations to map a triplet of points to another triplet of points, but I don't see how that would be useful here.", "label": 0}
+{"snippet": "Good day all, I am looking for a way to estimate the composition of a thermal plasma formed by flowing gas between two charged electrodes. I understand that when plasma is formed this way, it would be composed of a number of species. Please is anyone able to point me in the right direction of finding an equation/correlation/data to allow me estimate the composition of the plasma for any gas? Thank you", "label": 0}
+{"snippet": "I remember my high school teacher explicitly saying that it took me a long time to do x was the correct form and I took a long time to do x was not. In recent years, I seem to remember hearing the latter quite often in common language, though. How applicable is the latter phrase compared to the former (a) in everyday speech and (b) in essay writing?", "label": 0}
+{"snippet": "I was discussing with some friends about English grammar, and we ended up confused about the accuracy of the sentences below \"I know the motive for your rescheduling the class\" \"I know the motive for your rescheduling of the class\" \"I know the motive for you rescheduling the class\" \"I know your motive for rescheduling the class\" Are all of them correct? Which one would be the most idiomatic?", "label": 0}
+{"snippet": "When I was young, a workmate convinced me that there was indeed a word which described the behaviour of someone who would congratulate themselves for behaving the way a person normally ought to, anyway. I don't want to write that word here, because some people might think part of it seems racist. So instead, I'll ask as plainly as I can: Is there a word that means \"Congratulating oneself or others, for behaving the way one ought to behave?\"", "label": 0}
+{"snippet": "Imagine a bicycle wheel level with the ground able to rotate around its center. Centered on one of the wheel \"spokes\" is a heavy marble which can slide from the center of the wheel to rim of the wheel and vice-versa. If the wheel is spun once very hard by hand, the marble will move from the center to the rim and return to the center as the wheel stops spinning. Question: Does the wheel spin longer with the heavy marble at the rim then if there was no marble on the spoke? I suspect it does spin longer. Please no formulas or highly technical discussion; a yes or no answer and a simple explanation would be appreciated. Thank you for sharing your knowledge of physics.", "label": 0}
+{"snippet": "This is a screenshot from a Khan Academy video on friction at the nanoscale. I understand how the force of friction on the purple block acts opposite to the direction of the force applied explained by the nanoscale diagram, but I don't understand how the Newton third law pair is explained by the diagram. Wouldn't the movement of the top layer of atoms move the bottom layer as well? In that case wouldn't the two layers move in the same direction?", "label": 0}
+{"snippet": "The motivation I was given for algebraic topology is to assign some algebraic objects as invariants to topological spaces. This way we can show that two spaces are not homeomorphic if they are assigned a different invariant. However it seems to me like in algebraic topology the invariants are always up to homotopy equivalence or maybe even only weak homotopy equivalence. This seems strange to me. Is there a reason why other kinds of algebraic invariants that can distinguish homotopy equivalent but not homeomorphic spaces not more widely studied? What is it about weak homotopy equivalence that is so special that seems to be the main focus of all algebraic topology?", "label": 0}
+{"snippet": "In the book General Relativity by M.P Hoson, the author tries to calculate the velocity of a particle radially infalling in Schwarzschild spacetime. The velocity is measured by the observer sitting at rest at infinity. For the same, he takes the ratio of proper distance and proper time of the particle, both measured by the observer. To calculate the proper distance, the path traveled by the particle should be spacelike, whereas, to calculate the proper time, the path traveled should be timelike. Since the particle can travel with only one of the paths, how does the observer simultaneously calculate the proper time and proper distance along the particle geodesic", "label": 0}
+{"snippet": "Provided everything remains constant, does the fringe separation, that is the distance between adjacent fringes become further apart for higher order maxima? Consider the above diagram. From the diagram it appears that the distance between adjacent maxima is getting larger with distance from the central maxima. My intuition agrees with this. However, I have heard that the distance between adjacent fringes is constant. Assume this is true. How so? Double slit interference pattern: Fringes are equally spaced and of equal widths. The above statement seems highly unintuitive. Shouldn't the spacing between adjacent fringes get larger, as the wave spreads out. How do I satisfy myself with the above statement? Proof?", "label": 0}
+{"snippet": "The below question was asked in national English exam in Turkey: Choose the best word or expression to fill the spaces in the passage. As Henry Hill, the actor Ray Liotta gives a complex portrayal of an Irish-Italian kid who succeeds in his youthful ambition ....... popularity as a wealthy gangster, only to have his position slowly eroded until it almost destroys him. A) to gain B)gaining C) to have gained D)having gained E) to be gaining My choice was b (gaining). But the correct answer is A (to gain). I thought the phrase \"succeed in \" takes gerund not infinitive. Why am I wrong for the answer.", "label": 0}
+{"snippet": "I'm studying X-Ray reflectivity at interfaces and the book I'm reading reads: ... The ideally flat, but graded interface, and the ideally sharp, but roughened interface, will be considered... I'm struggling to understand the difference between the two kinds of interfaces mentioned. Please consider that English is not my first language. Exactly speaking, what do they mean with graded and sharp? How do these two surfaces differ from each other?", "label": 0}
+{"snippet": "Imagine a system with a parallel plate capacitor with holes in the middle where the plates are charged before being disconnected and insulated. Neutral atoms are introduced between the plates and are subsequently ionized in some way. The created ions will gain momentum and travel through the hole after which their kinetic energy can be collected. As long as the kinetic energy gained by the ions is higher than the ionization energy we just gained energy. I know that this should not be possible so where am I wrong?", "label": 0}
+{"snippet": "Assuming we can't block neutrinos, and most of them pass through the earth, how do we know that the change in the neutrino detector is not just happened randomly? Is the detection of neutrinos more frequent when earth is closer to the sun, or are we just always seeing the same amount of neutrinos in the detectors because we have no way to block them?", "label": 0}
+{"snippet": "I'm doing mathematical analysis and I'm stuck with the following question: Give an example of a nowhere dense closed set of irrational numbers with no isolated points (that is, a perfect set of irrational numbers) I read this: Is this a perfect set? so apparently we can find such a set through specific enumeration of rational numbers, taking their vicinities union and taking its complement, but I struggle to find such enumeration that would not create isolated points.", "label": 0}
+{"snippet": "I came across this interview question online: Suppose you sit on the road side and observe cars driving by. Assume the distribution of cars driving by is according to an exponential distribution. Now you observe a first car after sitting for x mins, a second car after sitting for y min. Given those observations, can you estimate the parameter in the distribution? I don't see how I am able to solve it without additional information. Thanks", "label": 0}
+{"snippet": "I begin a PhD in coding theory next fall, and it concerns coding over certain types of rings (e.g. finite chain rings) instead of fields, and in consequence submodule codes. I have a fair amount of knowledge in comm. algebra and have had a standard undergraduate coding theory over finite fields course, so I was wondering: Is there a well-respected graduate text, or a good set of notes, covering more advanced tools in algebraic coding theory? Thanks, and let me know if I need to clarify anything.", "label": 0}
+{"snippet": "If I understand correctly, massive objects cause time dilation, and so time seems to pass more slowly for observers closer to a massive object than those who are farther away. Do cosmologists take the local gravitational effects of earth, the sun, and the Milky Way into account when calculating the expected speeds of stars orbiting distant galaxies? Do galaxies that are more distant rotate faster, by our observations, than those closer to us, even if comparing galaxies of similar mass?", "label": 0}
+{"snippet": "I am an undergraduate, studying physics. I have studied maths courses like Groups, Linear Algebra, Real analysis, Differential geometry and probability. I wish to get into mathematical physics, similar to what Arnold's book has to teach. But i find it a really difficult read since it's a graduate text in mathematics. Can anyone suggest me what stuff do i need to study before getting a good intuitive picture of Arnold's book. Or any resources that provide a road map, intuitive picture of the maths used in physics.", "label": 0}
+{"snippet": "Now I am studying elementary number theory, I am interested in arithmetic function, I have studied Burton's Number Theory but I can't find Dirichlet Convolution as a particular topic, I will be highly glad if anyone suggest some good book to study arithmetic function where I can find Dirichlet Convolution in details with some theorem like 'the set of all arithmetic function forms integral domain under pointwise addition and Dirichlet Convolution'. Thank you.", "label": 0}
+{"snippet": "I am trying to understand the concept of regular conditional distribution. I found the definition quit difficult to grasp . This is what i understood . A regular conditional distribution also called a probability kernel is a two variable function (x,A) -> K(x,A) x a scalar and A a set that verifies the following. when we fix x, we have a probability measure, when we fix A we get a measurable function. Can someone confirm this definition ? and give me an example of a non regular conditional distribution .", "label": 0}
+{"snippet": "The uncertainty principle holds for pairs of certain observables, such as position and momentum. All these observables have a relation to spacetime. Other particle properties, by contrast, such as mass or electric charge can be measured at arbitrary precision. Quantum theories do not even model them as observables, but as parameters to the field. So, what is the philosophical argument for why there is a uncertainty principle for some quantities, but not for others?", "label": 0}
+{"snippet": "I am currently using a software called \"SCOUT\" to thin film interference simulation, and I would like to know if there is a better software to do this type of simulations. My goal is to vary the thickness of a thin film in a multilayer, in order to create interference between the various thin films, and then create a specific color. So I want to freely change the thickness and get a graph of reflectance or transmittance corresponding to that change. The software should allow me to put my own materials with the respective reflectance and transmittance properties. I know some softwares, like \"zemax\" and \"lumerical\" but there are no videos doing what I intend. Does anyone have suggestions? Thank you!", "label": 0}
+{"snippet": "I've got a Literate Agda document, which contains a large number of unicode characters. It builds nicely with XeLaTeX and life is good. The problem is that arxiv only supports pdflatex, and I'd like to upload the file to arxiv. Are there any tools/scripts that can process a latex document written for xelatex and add the necessary commands to compile it with pdflatex? Things like declareUnicodeCharacter for each used character. Basically, I'm just looking for a better way than \"start compiling with pdflatex, get an error, add the unicode character, repeat\". Most of the unicode symbols are math symbols, so it shouldn't be too hard to map from the characters to TeX commands automatically.", "label": 0}
+{"snippet": "Hi, I'm taking a course of Electrical and Computer Engineering in my university. I don't understand why the partial circuit on the right side of the switch is ignored after the switch is closed. As you can see, the book says the network becomes (c) from (a) via the short circuit. What happens to the short circuit and the circuit on the right side? I think the resistor and the voltage source can still affect the network but it seems not..", "label": 0}
+{"snippet": "I have two non-orthonormal basis vectors, and I want to represent a third vector as a pair of coordinates using the aformentioned basis vectors. How would I do that? The dot product, which usually transforms a vector into coordinates in each basis vector, doesn't work for non-orthonormal bases. How would I get coordinates in terms of my non-orthonormal basis vectors? I should also mention that I am coding, and so all my vectors are currently represented as pairs of numbers on an (x, y) plane. Please ask if you need any clarification, I explained it really poorly here. Also, I do not know very much linear algebra, so it would be appreciated if you answer in simpler terms :)", "label": 0}
+{"snippet": "If Alice is located just beyond the event horizon of a black hole, and Bob is at some other point in space with de minimis gravitiational effect, what, if any, effect would it have on the \"spooky action at a distance\" between these two entangled entities? I'm a wannabe sci-fi writer looking to exploit untested but possibly plausible concepts derived from my own madness and admittedly poor understanding of the universe.", "label": 0}
+{"snippet": "I am struggling with prooving convergence for an optimizer which uses adaptive step-size with heavy ball algorithm for convex and non-convex functions. In some literature, I could find a regret bound analysis/proof for convex functions and proving that the estimated gradient at t -> inf goes to zero. Could anyone please guide me through the process of convergence proof for non-convex functions or give me literature recommendations for the same. Thank you very much in advance.", "label": 0}
+{"snippet": "I need help understanding how particles do what they do and maintain the structures they maintain if so many of them exist for such a short time? In the case of the nucleus and pions, pions only exist for mere nanoseconds. So if they decay, and their properties change, what is holding that nucleus together? Are the nucleons continually exchanging a stream of pions that perpetuates the interaction that holds the nucleus together? Like I said... Explain like I'm five.", "label": 0}
+{"snippet": "I really like the greek letters of the default LaTeX font but I want the rest of the characters to be in Times New Roman using the Mathptmx font. I find the greek letters of the mathptmx package rather ugly since they're disproportionately bolder than the usual text. So may I know how can I change the greek characters only and retain the times new roman text? I have tried many suggestions from countless websites but to no avail. Alternatively, can I ask if there's a way to change the greek letters somewhat more similar to the greek letters in the books like those in University Physics by Young and Freedman?", "label": 0}
+{"snippet": "When observing interference fringes one often uses a lens after the diffraction grating to focus the fringes on a screen like this: At first sight, one might think that after the lens the path difference between the rays is altered. I think this is not the case, but don't see a clear argument why. Maybe one could apply Fermat's principle, but this - as far as I know - is restricted to the situation that we compare the path from a point A to a point B (in this case P). But here we start with parallel rays and not from a single point A. So, is it right, that it doesn't alter the optical path difference and how to explain exactly why?", "label": 0}
+{"snippet": "I had a debate with a buddy about this. He said you could get a chord by drawing the triangle formed by the two points and the center of the sphere and that chord corresponds to a single great circle arc. I can get to the chord but then projecting that chord on to a path on the surface of the sphere seems non obvious. So is it true that two points not colinear with the spheres center on the surface of a sphere have a unique great circle connecting them and if so how does one prove it?", "label": 0}
+{"snippet": "As the diagrams of categories can be represented as graphs of objects and morphisms, I was wondering if (the diagrams of) higher-dimensional categories could be represented as hypergraphs, and if not why? And in the more general sense, what would be the best west to represent higher-dimensional categories (thinking of diagrams, but also data structures to represent them in programming languages)? And if we reverse the question, are there classes of categories whose diagrams would be best encoded as hypergraphs?", "label": 0}
+{"snippet": "We know a way of measuring energy of a electromagnetic wave is the Poynting vector, which is independent of the frequency. But let's say we want to make two different electromagnetic waves, with different wavelengths and so different frequency, but with the same amplitude (so same Poynting vector). In my opinion the guy in the image is spending more energy for the wave with higher frequency. But the Poynting vector, doesn't care. So is there another property of Electromagnetic Waves that accounts for the energy that the guy used to make the wave?", "label": 0}
+{"snippet": "Two people, A and B, starts from two different points and move in a perfectly straight line in an infinite plane. When they move they leave a visible trace after them. Question: What is the probability that their path (of traces) will intersect at some point regardless of where they start? What I've tried so far is to draw two circles and split it in quadrants. That helped a little bit but didn't really solve the problem, just got an overview. Here's some examples of interesecting paths (first row) and non intersecting paths (second row) which gives you an idea of the criterias for when they intersect and don't intersect: How would you approach and solve this problem?", "label": 0}
+{"snippet": "I don't see why or how this could be argued against or if it really matters, but that's why I ask the forum. I am just trying to understand the nature of the fields in the universe. Am I correct in thinking that the entire universe is just a few fundamental fields laid over each other, getting influenced by the different particles that happen to interact with them?", "label": 0}
+{"snippet": "In a nuclear reaction, protons and neutrons are exchanged and the resulting elements have a number of different protons and neutrons that uniquely define the element that we are studying. However, can we say that a hydrogen atom without any electrons (what we would usually call an ionised atom of hydrogen) is really hydrogen? Or do electrons fundamentally indicate the element that results from the reaction? Can we really say that an atom of hydrogen without electrons is actually hydrogen?", "label": 0}
+{"snippet": "My textbook says: Similarly, non-polar (i.e., covalent or organic) compounds like naphthalene, anthracene etc. are soluble in non-polar (i.e., covalent or organic) solvents like benzene, ether, carbon tetrachloride, etc. and are very little soluble in water. My question is that if we have a non polar compound, then it seems as if it should not dissolve to any extent. However, the quote says that non polar molecules are a little soluble in water. Thus I want to know why non polar solutes dissolve in water at all, even if it is only to a very lesser extent?", "label": 0}
+{"snippet": "What is a word to describe how a cat looks when it's groomed? My husband described it as nappy, which I don't think would be the correct word. To give an image of what I am trying to describe, think of a medium-haired cat that licked its fur and looks messy, with wet fur sticking up a bit. It's a weird request and may be too specific, but I hope there's some kind of answer to what I am asking.", "label": 0}
+{"snippet": "I just read a quote in which someone, on behalf of herself and her spouse, wrote \"Our heart goes out for ....\". I Googled to know if when it comes to speaking about heart not as a body organ, is it possible to use it in the singular form, but I could not find any reliable source for that. So, what is the correct form for such situations and does it apply for other organs, specifically brain?", "label": 0}
+{"snippet": "If I shred a book into numerous pieces, and scatter them, so that the original text is completely unreadable, then for me, as a reader, the book has lost all its information. Its entropy has greatly increased. As a reader, the book's information rested upon a state of minimal entropy. However, my (limited) understanding of Shannon's information theory is that the 'information' in the shredded book has increased along with its entropy. Is there a way of reconciling the conventional/layperson's understanding of information as an ordered presentation of knowledge (like a well-written book) with the Shannon equation of information with entropy/disorder? Apologies if I have failed to grasp something fundamental.", "label": 0}
+{"snippet": "In the image above, we have the principle of induction cooking. An alternating current is run through the coil, which causes a change in flux. This change in flux induces eddy currents in the conductive pan, and by Joule heating/resistive heating (P=VI), this causes the pan to heat up. So the only thing that you need is a pan that can conduct electricity/the eddy currents right? As long as the pan does not have a too low or a too high resistance. However, why is the effect specifically optimal for ferromagnetic materials/conductors? How does the ability to magnetize somehow enhance the effect of induction heating? Does the magnetization of the pan itself somehow enhance the eddy currents or something?", "label": 0}
+{"snippet": "Often charge is defined as a measure of interaction with the electromagnetic field. However, electromagnetic field is often defined as a field produced by moving electrical charges, or relates to charges in some way or the other. Due to this circular definition, I am not able to understand what really is charge and its influence on electromagnetism, or any interaction. So what exactly is charge and what does it have to do with electromagnetism, or any other interaction?", "label": 0}
+{"snippet": "There is a word in German, ausgezeichnet which vaguely sounds like the English phrase \"out of sight\" but that is usually translated as \"excellent\". I could see some non-German speaker hearing it and, knowing that it meant \"very good\" from context, deciding to use it and approximating its sound with \"out of sight\". Note that I am interested in whether the German word and the phrase are related, not the general history of \"Out of Sight\" Is there any evidence to support this etymology?", "label": 0}
+{"snippet": "Assume I have a hemispherical container of water and an eyedropper. Is it possible to add water to the container one drop at a time, such that each drop continues to add kinetic energy to the water? When a water drop is added, it creates waves. I am wondering if it is possible to keep adding water drops in time with the waves, so that it acts like constructive interference, and adds more energy into the waves. I think this could be a very interesting sculpture, to have a computer-controlled eyedropper which slowly builds up the amplitude of the waves.", "label": 0}
+{"snippet": "(I'm South Korean, so non-native question here.) I saw the sentence 'that looks about it'. Does it mean that something is seemingly almost done? I searched this expression on google but I couldn't find the exactly same pattern of the expression but I found at the Cambridge dictionary: that's (about) it : there's no more to be said or done So I guess the sentence 'that looks about it' means something like 'I think it's almost done'. Is my interpretation right? How often is this expression used?", "label": 0}
+{"snippet": "In quantum field theory we often hear that particles sometimes behave like waves and sometimes behave like particles. In quantum field theory we say particles are fundamentally fields. Is it correct to say that particles and waves are limits of quantum fields? For example, if we take a quantum field and apply the limits appropriate for a double-slit set-up, would the field come out a wave?", "label": 0}
+{"snippet": "I am no expert in the calculus of variations but I had some lectures about it and attended some talks. I noticed that searching for minima of functionals seems way more popular than searching for saddles. I know about some MiniMax theory or mountain pass theorems that can be used to search for saddles aswell but especially in the context of actual variational problems it seems to me that people are more often looking for minima. From a PDE point of view that seems kind of odd, because saddles could solve corresponding EL-equations aswell. Question: Are people actually more interested in minima? If yes, why? If you got any literature recommendations on saddles or similar topics, I would be very thankful aswell. Thanks in advance.", "label": 0}
+{"snippet": "I am once again asking more software-related questions, but I am happy to learn a general answer as well. I'm curious about how the is_infinite function works in SageMath (or in GAP). Does it simply check whether we input something that is already known to be infinite or not? Or does it print \"infinite\" after a specific number of elements? Or does it actually check if the group is infinite? I assume it's not a numerical answer to check if the group is infinite or not since the program can't count until infinity. So, I'm wondering what the method is for checking if a group is infinite or not (in SageMath and in general). Thank you for your answer.", "label": 0}
+{"snippet": "Can you refer me to books that are at the same advanced level of real analysis via measure theory as Folland's and Royden's books? I want to have a solid foundation and I've been referred to books like Cohn's and Axler's, but I don't have deep knowledge of real analysis (I'm still going to start studying introduction to analysis) and I don't know if these books combine measure theory and real analysis like the ones I mentioned in the title or whether they are purely measure theory. If possible it was a Dover book because they have affordable prices here in Brazil. Thanks to everyone who can help me.", "label": 0}
+{"snippet": "I've always been taught that vectors that form a closed polygon represent an object being at equilibirium, that is there is no resultant force on the object. However, this has never been intuitive to me. How does one prove, that if the vectors form a closed polygon, the resultant force has to be zero? Furthermore why must the arrows form a closed loop, why is it not enough for the lines themselves to form a closed loop?", "label": 0}
+{"snippet": "When reading about the notion of affine connection, the Levi-Civita connection appears naturally as the unique affine connection that preserve the metric and is torsion free. In this case, it is possible to express the connection coefficients analytically as a function of the metric and its derivatives. What I am curious of are alternative affine connections, possibly admitting explicit formulas for the Christoffel symbols. In other terms, what are other connections that agree with the definition, but are not necessarily compatible with the metric and do rather reflect some other underlying structure? Thanks", "label": 0}
+{"snippet": "I know what a collocation method is and how it can be useful for the direct transcription of optional control problems, using specific collocation points. I also know what a quadrature rule is and how it can be used to solve integrals numerically, using specific quadrature points. But I'm struggling to see the mathematical connections between these two concepts, that are obviously related (for example: the trapezoidal collocation method has to be related to the trapezoidal quadrature rule somehow). So basically I'm wondering: is there a one-to-one correspondence between one collocation method and the related quadrature rule? If so, is it possibile to show how they are reciprocally related, in general, from a mathematical point of view?", "label": 0}
+{"snippet": "I am writing to ask for references. I have been trying for hours to find some paper/ book containing information on cycles in cubic graphs. It is known that to determine whether a given cubic graph contains a Hamiltonian cycle is NP-hard, but since it is not a tree we know that it must contain at least one cycle. But do we know we can find such cycles in cubic graphs in polynomial time? Do we know an upper/ lower bound on the size of the cycles in cubic graphs? I would be grateful if you share any references or any information on this topic.", "label": 0}
+{"snippet": "In some parts of my document math environments, such as \"align\", are not recognized, e.g. there is no arrow on the left to hide it, there is no automatic indent, and the theme colors are not applied properly. The same happens with \"subsection\", \"section\", etc. However, in other parts of the document the environments work. What could be the reason and how do I fix this? I am using pdfLaTeX compiler. Here is an example of how it looks in the editor:", "label": 0}
+{"snippet": "For example, prove that if A AND B and A AND C are logically equivalent. How would I go doing this? I thought of using two truth tables: A | B | A AND B T T T T F F F T T F F T A | C | A AND C T T T T F F F T T F F T Then concluding they are logically equivalent. However, they are from two seperate truth tables. Would that be correct? Or do I have to combine the truth tables?", "label": 0}
+{"snippet": "Can you recommend me some papers or lectures on finding the solution of elliptic PDE which is the saddle point of its energy functional. I glance over some methods including mountain pass theorem and min-max scheme, but it's hard to select one paper or lecture to do some intensive readings, so I wonder if you can recommend me some classical papers or lectures on this topic?", "label": 0}
+{"snippet": "I am currently working through the book Mathematical Logic by Mileti (online version) and just finished the second chapter (induction and recursion). I have to admit that it is quite challenging and whereas I think I can follow through, it really takes a lot of effort and time to thoroughly understand the ideas since they are so abstract for me. Has anyone worked through it and could let me know if the density and difficulty will continue in that rate or if one quickly gets used to it? Thanks", "label": 0}
+{"snippet": "I was always fascinated with pure math, but lately I've been increasingly more interested on applications of math (preferably algebra/topology but other fields would be interesting too) in the real world. I am wondering if there are any books that discuss such applications, as I wasn't able to find any. To be clear, I'm not looking for detailed books at the research level. I'm looking for books that I can read in my leisure time just out of curiosity to see how concepts from algebra/toplogy/etc are related to the real world.", "label": 0}
+{"snippet": "I am working on a user manual, compiling it from .rst source files with the pdflatex engine. My user manual has two versions: in English and in Russian. The issue that I have is connected with tables that take more than one page. I have 'continues on next page' and 'continued from the previous page' captions added automatically. These captions are not a problem in English. However, they are partially translated to Russian (the 'continues on next page' caption is left unchanged, see the images). Is it possible to edit them or to remove them finally? I guess it might be defined in the preamble but I have no idea how to do this.", "label": 0}
+{"snippet": "This is a question I came across on Instagram today, and here's the diagram: (Note: The image is NOT to scale) I attempted to solve it first by amending the quadrilateral in various ways, but each of those methods lead to a strange contradiction, likely because the diagram is not to scale. I'm going to post my successful approach as an answer below, please let me know if my answer is correct or if there's something wrong with the method (the correct answer wasn't revealed, and if there are any other ways to approach this that I missed!)", "label": 0}
+{"snippet": "Blum proved that any mathematical theorem can be converted into a graph such that the proof of that theorem is equivalent to proving a Hamiltonian cycle in the graph from Applied Cryptography by Bruce Schneier I'm struggling to understand what the statement means, and I was unable to find anything on it after a few quick google searches. Can someone point me in the right direction, to what this statement is even talking about?", "label": 0}
+{"snippet": "Antennas work by accelerating electrons to emit EM radiation. In fact, my understanding is that any accelerating electron will emit EM radiation. But in relativity, no frame of reference is preferred. Therefore, an electron in an antenna can claim that every other electron in the universe is moving around it. So does that mean that when an antenna creates a signal, every other electron in the universe sends the same signal back to it?", "label": 0}
+{"snippet": "I am trying to recreate this diagram in a standalone PDF using TikZ or PSTricks. Two extra requirements: I have to be able to alter the viewing angle arbitrarily I want to use relative coordinates rather than hard-coding the absolute coordinates of every cube. I'd like to be able to define cubes relative to nearby cubes using nodes since it will be easy to generalise this code to other shapes. I'm fairly experienced with TikZ, but just looking for a more elegant solution.", "label": 0}
+{"snippet": "I will use an example to explain my question... Transphobia is an irrational fear of, aversion to, or discrimination against transgender people. In the above sentence, is the true definition that only the fear is irrational, or is the aversion and discrimination also irrational? Is the true meaning: Transphobia is an irrational fear of transgender people. Transphobia is an irrational aversion to transgender people. Transphobia is an irrational discrimination against transgender people. Or: Transphobia is an irrational fear of transgender people. Transphobia is an aversion to transgender people. Transphobia is discrimination against transgender people.", "label": 0}
+{"snippet": "I've been shown an Out of Office template, and one of the sentences in it asks the sender to contact someone else within the company \"in case of need\", as the email will not be forwarded. I've never come across that phrasing before. Is it British English? Usually, personally, I'd go with \"if/as required\", although that might be a tad too strong in this context...", "label": 0}
+{"snippet": "I have one cylindrical coordinate system attached with a laboratory device and another cylindrical coordinate system that is attached with an object in it. The object is symmetric about the z-axis in its own coordinate system, which is both displaced and tilted with respect to the laboratory system. How do I express the unit vectors in the object coordinate system in terms of unit vectors in the laboratory coordinate system? I can write the coordinate transformation in Cartesian coordinates and then convert the Cartesian coordinates into cylindrical coordinates but do not see how to do that with unit vectors.", "label": 0}
+{"snippet": "hello, hello. I am reading the book \"Geometry\" by Tatiana Alekseyevskaya (Gelfand) and found myself having the question below. An external angle is defined in Wikipedia as an angle formed by one side of a simple polygon and a line extended from an adjacent side. How does that definition applies to the following polygon (delimited by the green line)? If I extend one side of it, the angle will end inside the polygon. I also have found similar questions have been asked over this forum, but I suppose mine is more related to the definition itself being applied, unless this polygon doesn't qualify as \"simple\" polygon as the Wikipedia definition states. Thanks! -- Caleb", "label": 0}
+{"snippet": "Is it possible to have one master .cls file in Overleaf that works across different projects? For example, if I make a change in the .cls file while working in one project, it will be updated in all of the other projects that use that .cls file? I know that I could import the .cls file from another project, but I cannot update it within the project that has imported it.", "label": 0}
+{"snippet": "I have a particular model with two couplings, let's call it model A, for which I have the set of beta functions and fixed points. Now I am interested in a model where I have two copies of model A, each with a different fundamental field, let's call that model B. So, model B has two couplings for each field plus a fifth interaction that couples the two fields. I know this might highly depend on the specific scenario, but is there a general strategy as to how one would obtain the beta functions of model B from the beta functions of model A?", "label": 0}
+{"snippet": "I am wondering that whether Kolmogorov spectrum, which describes the energy distribution in turbulence be used to describe the plasma fluctuation in the atmosphere of neutron star. As I know, Kolmogorov spectrum has been used in solar physics to model the small scale fluctuations, and there is also research on the turbulence in the core of neutron star and used Kolmogorov spectrum. However, I haven't found references concerning describing the fluctuation in the atomosphere of neutron star, can it use Kolmogorov spectrum or other methods?", "label": 0}
+{"snippet": "I know the evolution of a main sequence star to a giant is a process that takes millions and millions of years, but how fast is the VISIBLE change? Basically, will our sun, for example, slowly grow to envelope the orbits of the inner planets, or will there be a sudden inflation of that star to a new much greater volume on a timescale of seconds or minutes or hours etc.?", "label": 0}
+{"snippet": "All the sources I have read from say that radial component of acceleration of a body in circular motion only accounts for the change in direction . I do not understand how this is possible. Another thing I do not understand is what provides the torque for such a body to rotate. Could you please explain to me the forces and accelerations involved using the classic ball-and-rope example?", "label": 0}
+{"snippet": "Calculus invention happened only few hundred years ago. So I assume that differential equations are being discovered and solved since that time. When I was in school I learnt that most differential equations cannot be solved analytically and are thus solved using numerical methods. The question in my mind is, what difference does it make if we can't solve a differential equation analytically? Is that bad? Are people doing research to find analytical solutions to old differential equations? Also, before computers existed, were people still able to use numerical methods to solve differential equations numerically? That would be quite a lot of work.", "label": 0}
+{"snippet": "We have a compactness result, where the \"flat limit\" of an integral current is itself an integral current. (with some conditions) Now I am curious about submanifolds. I am expecting that an equivalent result does not hold for submanifolds in general. However I am having trouble finding a resource to verify this. Does anyone know of an example, book or article I could check out?", "label": 0}
+{"snippet": "so I recently came across the term 'virtual mass' and when I looked up more about it, it just gave me some stuff about fluid mechanics that I dont understand properly. My understanding of virtual mass is that when a body is pushed through a fluid (let's say water) it moves slower than usual and behaves like hoe a big object with more mass would behave on land but then I realized that what I was thinking of is just upthrust/buoyancy so can somebody please explain virtual mass in simple (layman terms) words. (I just cant wrap my head around it)", "label": 0}
+{"snippet": "The harmonics of a theoretically infinitely small diameter string are pure integer multiples of the fundamental frequency. However, a real string has a thickness, and when vibrating in a harmonic, the additional node or nodes should be taken into account when considering the string's length. This should mean that higher harmonics would have frequencies higher than the corresponding integer multiple of the fundamental frequency. What is the formula that allows for this calculation, and what effect might it have on the quality of the sound an instrument might produce?", "label": 0}
+{"snippet": "In documentation for electrical vehicles there is a common acronym for \"state of charge\" that is written as \"SoC\" or \"SOC\". Are both versions equally ok, or are there rules guiding when to mix case, and when not to mix case? I hope this question doesn't fall under the category \"Questions that are primarily opinion-based\", which I learned are not be asked here (I just signed up).", "label": 0}
+{"snippet": "I am a self learner and I just finished calculus books (Thomas calculus , Larson book ) and I want to learn further topics in integration so I searched for good books on integrals and I heard that the book A Treatise on the Integral Calculus by Joseph Edwards is very good but this book seems very old , so my question is this book still worth reading today or there are modern better books this ?", "label": 0}
+{"snippet": "I have been trying to understand how to calculate the kinetic energy of a rotating rod that also has translational movement. I have written my question down on paper because I think it is more clear this way. In case B, I think I have miscalculated the kinetic energy when dividing it as the sum of the rotational and translational energy. I have been days trying to understand this high school level problem. I would be very thankful if someone can point out my error.", "label": 0}
+{"snippet": "Let's say the original source says: \"They were at the loud, busy, fair. They played many games there.\" My adaptation is: \"They played many games [at the loud, busy, fair]. Since \"at the loud, busy, fair\" is taken verbatim from the original source, do I need to write my adaptation as: \"They played many games ['at the loud busy fair'].\" to indicate that I have taken it verbatim?", "label": 0}
+{"snippet": "Specifically in relation to meteorology. I was wondering if the angular momentum an object, lets say a parcel of air has due to the roation about the earths axis. Is it conserved if moved to a different lattitude. According to my understanding the conservation of angular momentum applies as long as there is no torque on it. Is moving an object in latitudinal direction a torque in this case?", "label": 0}
+{"snippet": "Hi been trying to solve this question : Show that the following classes are not closed under ultraproducts: (a) the class of torsion groups; (b) the class of simple groups; Thought about showing that they are closed under isomorphism and to show that they are not axiomatizable hence they are not closed under ultraproducts, couldn't really proof that tho, so I would like some help! Thanks!", "label": 0}
+{"snippet": "I am looking for resources treating the problem of simultaneous DC Stark and Zeeman Effects for arbitrary directions of the magnetic and electric fields (not necessarily orthogonal or parallel). I am in particular interested in the effect of such simultaneous fields on atoms with hyperfine structure such as alkali. Of course feel free to write an answer if you yourself know how to treat this problem.", "label": 0}
+{"snippet": "You pull cards out of a shuffled deck until you get a jack and a queen. Given see the jack first, what is the expected number of cards between the jack and the queen? I believe this is a conditional expectation problem. Our goal is to subtract the expected position of the jack from the expected position of the queen. However, I am lost on how to find this other than writing out all possible combinations which isn't feasible. I know how to find the expected position of either card without the condition. Do I use this and compute variance in some way? Kind of lost, any guidance is appreciated.", "label": 0}
+{"snippet": "Abbot et al. \"Experimentally probing the algorithmic randomness and incomputability of quantum randomness\" remark that \"incomputability is a weaker property than Kolmogorov randomness\". I understand that a Kolmogorov random infinite sequence is incomputable. The statement implies that there are incomputable sequences that are not Kolmogorov random. Why? (It's difficult for me to imagine what such a sequence would be like. If the answer is complicated, pointers to textbooks or literature at a similar level would be welcome.)", "label": 0}
+{"snippet": "On a fire extinguisher's cover, \"In case of fire, break glass\" may be written. As you see, in short, instructional contexts, one often finds articles being omitted. Is this grammatically correct? Is there a name for this kind of writing? Must it instead be written as \"In case of a fire, break the glass\"? This omission of articles is very common in instruction manuals and tutorials.", "label": 0}
+{"snippet": "This is a less concrete question I was just curious about. We always talk about straight lines of symmetry and reflections but can non-straight lines of symmetry exist when reflecting something, and if so what would they look like? Logically, I'm not sure if it makes too much sense to ask something like this since I guess for some reflections, the reflection of an object could overlap with its own reflection but I'm asking just for the sake of maybe discovering something new. I guess it's also difficult to visualise what that would look like for example, what would the following circle look like when reflected across the red curve? Any insight into this would be greatly appreciated!", "label": 0}
+{"snippet": "I've been playing a game and after completing a mission, one character ask to another the following: How you doing on the feddy? From the context, I assume that it's somehow related to money, but I'm not sure-it's an odd word! The only site I found it was on Urban Dictionary. My question is, what does feddy really mean here, and how did it come to take on that meaning? (Here's the video that shows some more context.)", "label": 0}
+{"snippet": "Would a high-pitched unhearable frequency be heard whilst the doppler effect is in play? For example, when a car uses its horn whilst travelling by, the pitch shifts as it passes - which is the Doppler effect. What would happen if someone were to play a frequency so high that humans couldn't hear it and went past a bystander? Would the bystander be able to hear the frequency as the pitch shifts? or would it not affect it? Just a random shower thought that was playing on my mind...", "label": 0}
+{"snippet": "Does there exist a continuous function defined on an open interval and being differentiable in a unique point? I have found examples of real-valued functions which are differentiable in a unique point of their sources, but all of them are not continuous at the points where they are not differentiable. I would like to know if there are examples of these kind of functions in the continuous case.", "label": 0}
+{"snippet": "Why are pressure hulls machined to be nearly spherical? According to Wikipedia, https://en.wikipedia.org/wiki/DSV_Limiting_Factor has a hull that is machined to be nearly spherical \"for enhanced buckling stability\". Is this really superior to an unmachined hull in terms of pressure resistance? I can see why it might be useful to trim any excess weight from a diving vehicle, but I don't see how removing material can ever improve pressure resistance. Does anyone have any insights?", "label": 0}
+{"snippet": "So I'm learning data science concepts for analysis of stock price data and I've gone into a rabbit hole. I first came across numpy.triu() in the Numpy library which calculates the Triangle Matrix for a dataset to find large movements in stock price points over a range of time. Then I learned more about the concept and how values in the set are calculated. But now I'm wondering what the practical uses for this concept? I'm especially interested in uses in analyzing stock price data.", "label": 0}
+{"snippet": "I was reading the paper on the Hall Effect and found that the initial experiment was performed on a metal strip. The experiment on the metal failed to provide any useful results, and then it was stated that Owing probably to the fact that the metal disk used had considerable thickness, the experiment at that time failed to give any positive result. Later when the same experiment was performed with a gold leaf, the experiment gave satisfactory results. So, I wanted to know how thickness impacted the results of the Hall Effect Experiment.", "label": 0}
+{"snippet": "Spatial gradients in the refractive index of a medium have an impact on the wavelength, frequency, and direction of waves propagating through them. What about media whose refractive index changes (spatially uniformly) with time? Is it correct to say that there will be no changes to wavelength or direction of propagating waves? What equations should be used to model wave propagation in a medium with time-varying refractive index? As a bonus, how would we model propagation if the index is changing non-uniformly in both time and space?", "label": 0}
+{"snippet": "I was invited to review an article by one of the IOP journals (Journal of Physics Communications) a few months ago in which the author claimed that the EM fields, similar to photons, bend in a gravitational field. The calculations were slightly hard and I had not enough time to follow the calculations, and thus I had to decline to review the article. However, the article inspired me to consider that every single electric (or magnetic) field may have a photon-like behavior and it bends inside a gravitational field. Is this a rational deduction?", "label": 0}
+{"snippet": "I want to design new characters (mainly ornaments but also mathematical symbols) for the CM modern font family using METAFONT. What is the best way to achieve consistency with the rest of the family? The first idea that came to my mind was to copy paste the cmbase.mf file from https://ctan.org/tex-archive/fonts/cm/mf but that's a lot of duplication and I am not sure I am legally allowed to do so.", "label": 0}
+{"snippet": "I'm aware that in sentences using neither-nor constructions, the verb must agree with the subject closest to it. E.g.: Neither the dog nor the cats have been fed. Neither the cats nor the dog has been fed. However, when it comes to question forms, what should the verb agree with? Does the rule still apply? Has/have neither the dog nor cats been fed yet? To make it grammatically sound, should has or have be used in that sentence? Edit: The question should be \"Has/have neither the dog nor THE cats been fed yet?\", with the definite article \"the\" before \"cats\", which preserves the structure of the example I provided.", "label": 0}
+{"snippet": "For a phonon mode to be able to emit electromagnetic radiation, it must have a dipole moment. However, it is not intuitive to me why the LA phonon does not have a dipole moment: suppose all atoms in a unit cell are oscillating in phase back and forth relative to the electronic background, isn't this itself a dipole moment? The radiation should came out perpendicular to the oscillatrion direction. Mathematically, when we determine whether a mode \"has a dipole moment\", what quantity are we actually talking about? Thanks.", "label": 0}
+{"snippet": "I am confused about how to understand the sheaf on empty set (as an open subset) of the Zariski Topology over the Spec(Z), which is generated by the additive identity zero in Z. The sheaf I have in mind is the structure sheaf sending open sets to local rings. I read related pages and I cannot understand how sheaf over empty set is a terminal object. Is this terminal object an additive/multiplicative identity of the ring? Is terminal object an element of the local ring?", "label": 0}
+{"snippet": "I've seen these words both used but not interchangeably. My guess is that fascistic refers to 'fascist in nature', e.g if a building is fascistic it is reflective of fascist ideology but not necessarily a product of a fascist regime while fascist means relating to actual instances of fascisism e.g, saying a building is fascist means it was a Nazi building or otherwise. I'm not sure though...", "label": 0}
+{"snippet": "I have read that the Einstein-Cartan theory introduces torsion into general relativity in a way that produces coupling between gravity and the spin of particles. Then, the gravitational field is able cause the precession of this spin axis. But what about spinless particles? Wouldn't there be a difference between the way gravity acts on particles with spin vs no spin? I guess that even for particles with nonequal nonzero spin there would be a difference If gravity acts differently on the varied kinds of particles, the equivalence principle goes out the window. Plus, I don't know how to make the spin coupling disappear with a simple coordinate change", "label": 0}
+{"snippet": "Strictly speaking, a stochastic process can characterize a collection of random variables whose index is not time-related. Please, are there examples in the literature where this has been considered? Otherwise, should we refer to those processes as random fields as opposed to stochastic processes, reserving the term \"stochastic process\" for the case wherein time is involved? I'm particularly curious about the case wherein there is a process over space as opposed to process over time.", "label": 0}
+{"snippet": "I watched a video lecture that talked a bit about when proof by contradiction is and isn't a useful approach. This was useful, but it was from a heuristic approach which caused me to wonder is it the case that \"P is provable\" implies \"there is a proof by contradiction of P\"? I suspect this may vary by logic system. If that is the case I would still be interested in know what major systems do/don't have this property.", "label": 0}
+{"snippet": "I am helping a friend edit a manuscript for an informal reference book about music. There are several instances where I am perceiving a mixture of tense but I'm not sure how or whether to correct it. Here is an example sentence: If we begin on the first note of the C major scale and skip every other note, the following chords get created: I suggested changing \"get created\" to \"are created.\" The verbs begin and skip are clearly present tense, and I believe get created and are created are present perfect tense, so my analysis of mixed tense seems incorrect. Why does \"get\" seem like incorrect usage in this example?", "label": 0}
+{"snippet": "I read the following text on This Page: Does every polynomial have at least one imaginary zero? No. Real numbers are a subset of complex numbers, but not the other way around. A complex number is not necessarily imaginary. Real numbers are also complex numbers. Now, FTA states that: every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero. my understanding is that, unless \"Complex Root\" means something different than \"Imaginary Zero\", the former page statement is wrong. Please clarify the situation. Thanks. Edit: After reading the good comments below, I came across this diagram which helps: Diagram-Classifying Numbers", "label": 0}
+{"snippet": "Recently I saw two interviews, one with Victoria Beckham, the other one with Elton John. They were talking about their past experiences and that's the phrasing they used: But it wouldn't have happened if we HADN'T HAVE GONE to the Ukraine. (Elton) And I probably would still be that way if I HADN'T HAVE MET the girls. (Victoria) Is there any explanation behind the grammar written in capital letters?", "label": 0}
+{"snippet": "This is a silly question, but can it be done safely? My friend wanted to have a soup with electrolysis causing it to taste differently on each side of the bowl. I think this is dangerous, because there is table salt in the soup and I suspect that during electrolysis chlorine gas is made. Maybe someone can clarify the soup example or provide an alternative?", "label": 0}
+{"snippet": "I am studying some results about existence and uniqueness of solutions to some PDEs and many times Banach fixed point Theorem is used. I saw that the ideia is to consider the integral formulation and use the Theorem to prove existence and uniqueness in a ball but I can't understant how the uniquess extends to all the space. Any one can explain how to get uniquess in all the space and how existence and uniquess of solution to the integral formulation garantees the same for the PDE? Any help is appreciated.", "label": 0}
+{"snippet": "I have seen that there exists an intimate relationship between electric and magnetic properties. From what I know is that electric field creates electric potential around the source's space which can allow a charged particle to gain some PE and makes it possible for that particle to have translational and rotational motion. I have searched quite a bit and could see that magnetic potential energy can only cause rotational motion, why not translational motion?", "label": 0}
+{"snippet": "I've recently found a really old \"Philosophy of Math\" book in my University library, and in the book it says that the it has been proven that : if non-euclidean geometry is inconsistent, then so is euclidean geometry, and the reverse is also valid. But the book wasn't as helpful as it doesn't prove, or give some reference or name to this result. Does anyone have a proof for this or for something similar? Even a definition of what exactly \"inconsistency\" means in this geometric context would be welcome.", "label": 0}
+{"snippet": "I am competing in the American Computer Science League (ACSL), and I get problems similar to the following. Look at this directed graph. Now tell me the number of cycles in said graph. These questions need to be completed quickly and by hand. Unfortunately, the ACSL wiki (which provides help and study resources for the test) says to find all cycles by inspection. This obviously is slow and possible erroneous. I want to be able to complete these questions with the utmost accuracy. Is there a method to, given a graph, calculate the number of cycles by hand?", "label": 0}
+{"snippet": "The energy of photons is reduced by the expansion of space. Since the photons have been decoupled from matter their wavelengths have decreased from the visible range to the radio range. The same should hold for the neutrinos that emerged from the big bang. They still travel at a speed that's close to the speed of light. Almost all their energy is kinetic. Will their speed be reduced to, say, half the speed of light in the far future? If so, how long will that take?", "label": 0}
+{"snippet": "Every number theory book seems to start with divisibility, congruency, the division algorithm, etc., while completely ignoring the rigorous construction of the natural numbers. It seems like a wasted opportunity to explain to the reader what's actually happening. I feel the same about combinatorics. Permutations, combinations, and the rule of product are derived heuristically rather than through rigorous arguments from set theory. Is there a particular reason why number theory books take this approach rather than a rigorous from first principles approach?", "label": 0}
+{"snippet": "I am writing a an essay comparing The Great Gatsby and Pride and Prejudice in English (Australian English style), and to save on word count I wondered if it would be appropriate to refer to them, after the first few uses of the names, as Pride and Gatsby respectively. Is this acceptable to do in a relatively formal context, and if so, is there any procedure for first introducing the contracted names?", "label": 0}
+{"snippet": "I just built Lyx on Manjaro linux from pamac (there is an entry from the AUR, see https://aur.archlinux.org/packages/lyx). When I try to view a document in pdf using pdflatex an window pops up saying an error has occured in the external program \"pdflatex\" and that I should see the logs. Unfortunately I can't find the logs for pdflatex... If I type pdflatex in a terminal, it is up and running. Also all of the document classes and modules required by the Help - Introduction, Tutorial, ... are missing. I wonder if I missed a package to install. Thank you for your answers !", "label": 0}
+{"snippet": "I need to quote and excerpt a lot of the same passages from a diverse library in my work. I'd like to find an app that's basically a purpose-built database for this kind of thing -- where I can store the excerpted text, the BibTeX source, the page number, a brief description, maybe some keywords/tags/categories. Basically something like Jabref, but where elements are passages not sources. I found an app called TextCite, but it looks like it's no longer being updated and I had some trouble installing it. Any help is most appreciated.", "label": 0}
+{"snippet": "In a nuclear fission reaction the total energy and thus the mass of the products are lower than the total energy of the reactants. I understand the the difference in this energy can be used in a nuclear reactor/atomic bomb. But in the physical sense how does this energy manifest, is the kinetic energy of the reactants or some EM wave emission or combination of both. Also if it is the kinetic energy of reactants, wouldn't that energy be already included in the total energy of reactants?", "label": 0}
+{"snippet": "When observed from the ground frame (assuming no friction is present), the only forces that act on the rotating bead are weight and the normal force exerted by the loop towards the center of the loop. I suppose there is no component of the normal force in the direction of the bead's movement, so it shouldn't move upwards. I am unable to comprehend why the bead does move upward.", "label": 0}
+{"snippet": "In Tao's Fourier Transform preprint, https://www.math.ucla.edu/~tao/preprints/fourier.pdf, they show explicitly that the Laplacian can be viewed as a Fourier multiplier. In the same paragraph, they write ...This identity shows that the Fourier transform diagonalizes the Laplacian Why is the word \"diagonalizes\" used in this context? I know it from a Linear Algebra context, in which we diagonalize some matrix, but in this context it seems out of place. Am I missing something?", "label": 0}
+{"snippet": "Just a naive question about univalent foundations. As far as I understand, we want to define our mathematical types like sets, groups, categories, etc. such that structurally identical objects are equal in the sense of internal equality. But are we free to choose what kind of isomorphisms we are interested in? For example, can we define both, the type of categories with ismorphisms as equality, and the type of categories with equivalences as equality? Or the type of topological spaces with homotopy equivalences as equality, and the type of topological spaces with homeomorphisms as equality? How would these differences actually look like in the definition?", "label": 0}
+{"snippet": "I was just thinking about this studying for a biology test as for cells a greater surface area to volume ratio is desirable, so I wondered if there was a theoretically optimal shape that would maximize this ratio. I thought it might be that there is no such shape as you could just add folds to the surface indefinitely but I don't know if that is truly the case.", "label": 0}
+{"snippet": "This question is similar to this post, but in my case the actual numbers do not matter, I'm interested in the equations. I have an arbitrary triangle, of which only angle BAC and side AB are known. The sum of sides BC and AC (therefore the perimeter) is known and fixed. I am looking for an equation that gives me the value of angle ABC. Here's a screenshot, please remember that the exact dimensions are arbitrary, and are only there to show which parts are known. Triangle drawn in CAD This is really driving me crazy, I would appreciate any help! Thank you!", "label": 0}
+{"snippet": "I've mostly used and seen \"utilitarian\" in a negative sense: something that only exists for its function, and specifically for those functions. In other words, something that is single-purpose. utilitarian designed to be useful rather than decorative: But what if I wanted to describe something positively, could utilitarian be an apt adjective? I often see phrases like \"utility focused\" or \"utility oriented\" as positive, but utilitarian as negative. Aren't they the same? For example: \"I worked at Big Tech Company where I designed and developed utility focused modules\" sounds positive or neutral. \"I worked at Big Tech Company where I designed and developed utilitarian modules\" sounds pretty bad.", "label": 0}
+{"snippet": "I am looking into uses of Fourier series. I learned that it can be used to approximate functions (link). However, I think there are ways to approximate functions with polynomials (not limited to Taylor series). What advantage does the Fourier series have over polynomials in approximation? I think there is a disadvantage to the Fourier series. While the way to compute the values of polynomials is obvious, computing the values of Fourier series needs approximate values of the trigonometric functions.", "label": 0}
+{"snippet": "I was thinking of the trading of kinetic energy during a gravitational slingshot maneuver and wondered if the kinetic energy lost during that process makes any noticeable impact on the orbit of the planet. Since the planet we are performing this maneuver on loses kinetic energy, it is realistically possible to do enough slingshots that we noticeably change the orbit of the planet? And what would be the consequences of changing the orbit?", "label": 0}
+{"snippet": "Taka a standard spinning bicycle wheel with its spokes and place it in a magnetic field that is parallel with the axle. I know that if the spokes were not made of metal but some insulating rods there would be an emf and a corresponding current induced in the rim. My question is what happens when the spokes are made of some conducting metal, will there be an emf induced across the spokes and what will the current be in the rim and spokes?", "label": 0}
+{"snippet": "Do Boltzmann brain thought experiments suggest literally anything can form randomly? What are the limitations to what random fluctuations can form? Literally any physical, material object? Lastly, I am curious as to how this compares to an object with a high degree of complexity always existing. For example, is a bike more likely to always exist for no reason than it being created by random fluctuations? Or is it less likely?", "label": 0}
+{"snippet": "In a scientific abstract, I have a sentence like this: Yet, numerous capture-mark-recapture data sets, across wide taxonomic range, feature transient individuals. I want to emphasize that there are numerous capture-mark-recapture data sets, and that they all together cover a wide taxonomic range. Not each one of them; each of those data sets is covering only few very specific taxa; but all together they cover the wide taxonomic range. I don't want the expression to be too ambiguous in this direction. Is this sentence correct and unambiguous, or could it be written better? It shouldn't be much longer since I am very close to the word limit. EDIT: would this one be better? Yet, numerous capture-mark-recapture data sets, from a wide taxonomic range, feature transient individuals.", "label": 0}
+{"snippet": "I am very new to semiconductors and I'm trying to understand how photodiodes work for imaging sensors. If I am not wrong, a PN junction is required to detect electron/hole pairs that are photo-generated. The electric field in the depletion zone will move the charge carriers and create a current that can be exploited. Why not only use a semiconductor without doping? And then apply an electric field to the semiconductor: when light is emitted, it slightly improves the material's conductivity, and a current is detected. Why is it not that simple? Thanks", "label": 0}
+{"snippet": "The statement reads as follows \"If is invertible, there are no special solutions in the null space.\" According to me, its actually true because if the matrix is invertible, it means that it has full rank, and its null space contains only the zero vector. However, the questions asks you to explain why the statement is false. Is there a way for this to be false? Or, is the question wrong and the statement is true?", "label": 0}
+{"snippet": "Not that I work in this field, but I have heard the discourse from several people that string field theory is useless. So I would like to ask two simple questions? What makes SFT so difficult? Especially, it seems to me that one can construct an action that satisfies general coordinate transformation invariance and gauge symmetry (more precisely BRST symmetry) by using the BV formalism, as shown by Witten, but why is this useless? When moving from QM to QFT has several practical benefits, for example, one can easily construct relativistic scattering problems in Lorentz-covariant form, but in what way is SFT superior to string theory?", "label": 0}
+{"snippet": "A devout Christian, she plays tennis every weekend. The most beautiful of villages, Ullapool has hosted a food festival for the last twenty years. I see this kind of thing a lot in non-fiction writing, particularly things like short bios/blurbs and tourist writing, where people are trying to convey information but also make it attractive/enjoyable to read. The part before the comma feels like it's introducing the part after the comma, but actually the two things have no relation. Like One of the most infamous mass murderers of his generation, his favourite colour is red. Is it a recognised 'thing' and does it have a name?", "label": 0}
+{"snippet": "I'm aware that a semantically complete theory can be undecidable. (I believe it's because only logically valid sentences need be provable for a theory to be semantically complete.) But is it possible for a syntactically/negation complete theory to be undecidable? And do \"syntactically complete\" and \"negation complete\" mean the same thing? I've heard that: Any consistent, negation-complete, effectively axiomatized formal theory T is decidable. So for a negation complete theory to be undecidable, it'd have to be either inconsistent or not effectively axiomatized. But I have no idea how a theory could be negation-complete without those two other criteria in the first place.", "label": 0}
+{"snippet": "I am having a hard time understanding what eigenvectors and values intuitively represent in an adjacency matrix in a graph problem. I understand in a linear transformation, eigenvectors are vectors that are only scaled after the transform is applied and that the eigenvalues are those scale factors. Is it strictly for computational efficiency that we are so interested in the eigenvalues in graph theory, so we can utilize the eigenbasis for computations?", "label": 0}
+{"snippet": "I have these two graphs here: I wish to determine if they are Isomorphic. I know that I need to find a one to one and onto function, however I can't find a way to do it. My questions are: I know that these two are isomorphic. What is the function f ? In general, is there a way to find these functions ? Maybe using matrices ?", "label": 0}
+{"snippet": "I've seen diagrams for projectors where condenser lenses focus light directly onto the pupil of the projector lens, after going through the image source. Am I misunderstanding the diagram? If not, why does it focus directly onto the projector lens? I was under the impression that you'd want the condenser lens to form a real image somewhere before the projector lens - that way, the projector lens can image it, like this:", "label": 0}
+{"snippet": "Being impressed by Barr and Diaconescu paper entitled \"Atomic Toposes\" (https://www.math.mcgill.ca/barr/papers/atom.top.pdf), I would like to ask whether it makes sense to investigate \"Atomistic Categories\", namely categories such that for any object the corresponding poset of subobject is atomistic (namely every element is arbitrary join of atoms). Have these categories been studied, are there non-trivial exaples (the category of sets is an example, but I'm searching for other examples!)", "label": 0}
+{"snippet": "I am rather rusty and am reading Topology by Graham and Greene. One of the problems refers to a countable complete metric space. The rationals don't seem to be such a space, because the irrationals are adherent to them and one can form a Cauchy sequence of rationals that converges to an irrational. Thus, the rationals are not complete. Could someone please offer an example or two of countable complete metric spaces?", "label": 0}
+{"snippet": "I want to say something along the lines of \"We must protect everyone, especially children\". But this doesn't exactly work for what I want to say. Because I do not mean that children are MORE deserving of protection in this instance. How can I exemplify a group without raising them up to an elevated status? I thought of \"in particular\" but this has the same problem.", "label": 0}
+{"snippet": "In most material I can find on the cosmic distance ladder for a lay-level reader like myself, it never seems to explicitly say what distance its talking about. There is the proper distance when the light was emitted, and the comoving distance, where the light source is now. The light we are receiving however has traveled a different distance, the light travel time distance, which is less than the comoving distance and greater than the proper distance at emission time. What does the distance ladder actually measure? How could it be less than or greater than the distance light actually traveled?", "label": 0}
+{"snippet": "Lenz's law was explained to my class using an example wherein there is a bar magnet passing through a current carrying loop in a gravity free space. Our professor told us that the induced magnetic force is repulsive in nature in order to perform negative work on the bar magnet. The kinetic energy lost by the bar magnet as a result of the repulsive force would be lost in the form of heat in the wires of some internal resistance. If the induced repulsion is because of the heating effect of current, won't Lenz's Law be invalid for resistance free wires, where resistance is zero ? If it is valid, why ?", "label": 0}
+{"snippet": "In Landau's book of fluid mechanics, the most general formula for stress looks like this: let's call the eta in picture the first viscosity coefficient, call the zeta in the picture the second viscosity coefficient. I would like to know what are the typical values for these two coefficients for air. I am not sure if my memory is correct, but it seems that the second viscosity coefficient is often neglected. By the way, I am not sure if questions regarding fluid mechanics and CFD are appropriate to ask here, or if there is a more suitable place to ask these questions, if you know, please recommend some to me, thanks.", "label": 0}
+{"snippet": "As an Electrical Engineer, I have been studying convex optimization for a while. During my study, I see that most textbook claim that both second order cone programming and geometric programming can be solved effectively with modern solver. However, I cannot find any document that compare them together. So my question is does second order cone programming harder to solve than geometric programming ? Futhermore, is there anyway to come up with a Big O complexity to measure the difficulty of solving them in terms of the number of variables and constraints ? Thank you for your enthusiam !", "label": 0}
+{"snippet": "I was wondering if we could use background radiation to produce electricity (even a tiny amount). However, I've read somewhere that solar panels absorbing infrared (and lower frequencies photons) wouldn't be very efficient, as they are limited by the laws of thermodynamics. The arguments states that the panel needs to be cooler than the temperature of the body emitting the photon. How is this true? I cannot explain why it would be that way with the traditional band diagrams I've learned. As far as I understand it, the only limiting factor would be the band gap of the material that is used, and it needs to be low enough to capture low energy photons.", "label": 0}
+{"snippet": "Recently, I find an interesting paper that mentioned the Definition of curvature of an affine optimal control system. It suddenly reminded me that many textbooks on Riemannian geometry only tell us about metrics, geodesics, parallel transport, and curvature tensors and son on, using some special surfaces with constant curvature as examples. So for a general control system, how do we calculate its curvature tensor? Is this a problem worth studying? Are there any more examples? Thank you all for your comments and help!", "label": 0}
+{"snippet": "I have learnt that the intuitive idea behind inner product space is finding angles between vectors. But what does inner product actually mean physically or intuitively when it comes to matrices.Can I link inner product of matrices to concept of angles?.I can't imagine angles between matrices as I do for vectors. I really want to learn visually and not just theoretically. As I am amateur in this area my understanding might be wrong. So please do correct me.", "label": 0}
+{"snippet": "I have a .pdf file, in which I have to embed all the fonts. I found out that I should use this command: gs -q -dNOPAUSE -dBATCH -dPDFSETTINGS=/prepress -dPrinted=false -sDEVICE=pdfwrite -sOutputFile=edited_file.pdf myfile.pdf but the pdf file loses its interactiveness. For example, I have hyperlinks that jump to references, or clickable table of contents that becomes not clickable anymore after executing this command. Can you please help me to find a solution.... I have only linux, so everything Windows-related is not an option.", "label": 0}
+{"snippet": "If neutrino has mass, then it can change it's helicity. But all registered neutrinos have negative helicity while all anti-neutrinos have positive. Does it stands for all registered neutrinos including cosmic ones? I.e. does it mean that cosmic neutrinos had not enough time to switch their helicity? Or it was checked only for neutrinos in accelerator experiments, i.e. only for \"young\" neutrinos? What about solar neutrinos? Is their helicity known?", "label": 0}
+{"snippet": "I keep coming across the term storying in articles on narrative research. The authors however do not explain how the term storying is different in meaning and connotation from the term storytelling or story. I am keen to understand the various theoretical angles that I need to explore to understand the term Storying? Should I connect the concept of reflexivity to the concept of Storying?", "label": 0}
+{"snippet": "I'm working on a project that aims to discriminate semi-visible jets (SVJs) in a QCD background, through learning from simulated data in the context of the LHC. I know that these are related to hidden valley models, and probably also to dark matter. Can someone provide an intuitive explanation (even with some technicality) of why SVJs are important, and how these are originated? Also providing some insights about dark sectors, and potential implications for the discovery of dark matter. (sorry if I'm using an improper language, but I'm not a physicist.)", "label": 0}
+{"snippet": "The problem I'm working on has a region that's largely accurately modeled by a GP model using a squared exponential kernel. However, there is a large region in the \"truth\" model that is uniformly zero, with all samples taken from this region being zero as well. However, the GP model in this region oscillates from positive to negative when it's necessary for the problem I'm working on that this region is accurately modeled as uniformly zero, or at least negative when the remainder of the data is positive. Adding a dot product kernel to the squared exponential kernel to create a custom kernel helps somewhat but can't eliminate the spurious oscillations.", "label": 0}
+{"snippet": "this is my first post on Stack Exchange. I need a study guide for linear algebraic expressions. I am good at vector analysis and calculus, but not so good at linear algebra. Image : In the image above, is the part I have colored in blue a linear algebraic expression? I am having trouble searching and learning this. I can't type expressions by math symbols into the Google search bar. I can't find a proper interpretation of the formula and just figure out what it means from the context. I'm not even sure if that's a linear algebraic expression. Is my only option to take my time and study a linear algebra textbook sequentially? I apologize if this question doesn't fit into the Stack Exchange.", "label": 0}
+{"snippet": "If we place a point charge in a grounded metal box and view a slice of the box, the lines of equipotential deform from circular (immediately around the point charge, as we'd expect) to square at around the perimeter of the box where it is grounded. Is there a mathematical relationship we can derive for the morphing of the field lines from circular to square? I am unsure if the change is a linear combination of the two functions.", "label": 0}
+{"snippet": "For some reason, TexShop started autocompleting any ampersand & by adding a period/full stop, which is not a feature that I consider desirable, given that I almost exclusively use the symbol for tabular and align environments. I feel that there is probably a simple way to turn this behavior off in the preferences, but I couldn't see how to do so. How do I change the default behavior?", "label": 0}
+{"snippet": "When we think of functions, we refer to their oscillations or periodic components in terms of frequencies. The Fourier transform allows us to decompose a function into its constituent frequencies, providing a way to analyze the function in the frequency domain. For operators that act on infinite-dimensional function spaces, is there an analog of the frequency concept? Is there a transform or methodology that lets us analyze operators in a similar \"frequency-centric\" manner? I'm curious about both theoretical constructs and any potential applications such a perspective might offer.", "label": 0}
+{"snippet": "From what I have read and seen online. The explanation of why there is a net reduction in the speed of EM waves through a medium is due to the interference with the oscillating EM fields produced by charged particles caused by the EM wave passing close by. I hope my understanding, if at least a base level, is correct so far. But would there be any reduction in the speed of light passing through matter made up entirely of neutrons? Either a neutron gas or possibly neutron degenerate matter in the cores of neutron stars. Thank you for your time.", "label": 0}
+{"snippet": "I was wondering if there is an easy way to create diagrams like the following: where a, b, c are colors and strings connect like colors. In the paper I am reading, they don't allow crossings, but I would like to allow crossings between different colors. So something like this would be allowed (two colors red and blue) I tried to do this with the braid package, but the problem is that I don't know how to make those semi-circles Thanks in advance!", "label": 0}
+{"snippet": "I'm writing an online game, and I want to tell users what their highscore is since the beginning of the hour. But I don't want to say something wordy like: Your highscore since the beginning of the hour is... At the moment I've got: Your highscore this hour is... I have 'today' and 'this week' for the other timeframes, but it still feels very unnatural. Is there any pithy phrase I'm overlooking? Many thanks!", "label": 0}
+{"snippet": "Is there a ready-made LaTeX package that produces a calendar in a format known as Familienplaner in German speaking countries: Each month is set as a table on one sheet of paper. There is one row per day, and there are additional empty columns to be filled in (between one and five, typically). Sundays are specially marked (e.g., by red colour of the date, or by a grey row instead of a white one). Nice-to-have features: German language support for day-of-week and month names, week numbers, German holidays. P.S. Searching the net for \"Familienplaner\" results in a lot of free pdf offers for such calendars. P.P.S. The Familienplaner layout is different from the monthly calendar layout of this question: Calendar in LaTeX", "label": 0}
+{"snippet": "I was wondering if the book Contemporary abstract algebra was suitable for self study. I've heard from people that the level is somewhat low and that things such as polynomials in several variables, particularly theorems on symmetric ones. Also,ive heard that applications from abstract algebra to linear algebra are lacking as well. Is this true? if so, which books would you reccomend for abstract algebra self study?", "label": 0}
+{"snippet": "I am currently working on a BSM model for unification where I am adding scalars for unification. I add many scalars, so finding the most general gauge invariant lagrangian is becoming difficult. Is there a tool kit where I can enter the particle content, and under what representation of the gauge group they transform and get out the most general gauge invariant lagrangian? I have heard SARAH can do it, but I am unsuccessful with it. If anyone knows how to implement this in SARAH, that would be helpful, too.", "label": 0}
+{"snippet": "Recently, I watched small dominoes toppling over, until they push over a massive one. However, I am slightly confused why this doesn't violate conservation of energy. Consider supplying some amount of energy to a small domino, eventually when it topples over the large domino, that large domino can do significantly more work, and should have more energy. This clearly cannot violate the laws of physics. So what is wrong with my logic?", "label": 0}
+{"snippet": "Googling and Wikipedia, gives only the following construction A golden rectangle can be constructed with only a straightedge and compass in four simple steps: Draw a square. Draw a line from the midpoint of one side of the square to an opposite corner. Use that line as the radius to draw an arc that defines the height of the rectangle. Complete the golden rectangle. Question: What are the other known methods of constructing a golden rectangle with a ruler and compass?", "label": 0}
+{"snippet": "I saw this solution to a problem on twitter, and the solution seems to of used the direct comparison test for the improper integral. I asked my professor about it, but they replied with \"yes, just make sure to follow the given conditions.\" However, they didn't mention what conditions we would need to follow. If we can use Series Tests for Improper Integrals, how would we go about using them?enter image description here", "label": 0}
+{"snippet": "I want to make a commutative diagram in the tikz (or tikz-cd) environment to demonstrate the universal property of the pullback. To be precise, I want to make the following diagram in LaTeX (the arrows on top need NOT be curved): I am not sure how to draw this. I know how to make general commutative diagrams, and there are answers to making pushouts with universal property diagrams (How to do the pushout with universal property?) but I can't figure out how to make the above pullback diagram. Any help will be appreciated.", "label": 0}
+{"snippet": "I came across this question while studying for the SAT. After World War I, Percy Spencer was hired to work in the research _____ later known as Raytheon Manufacturing. A) lab of American Applicance Company: (a colon) B) lab of American Appliance Company-- (em dash) Though the answer choice states that B) is the correct answer, it does not specify the reason why A) is not preferable over B). I wonder if the usage of the colon in this sentence is correct. (As it sounds, to me, a little awkward to place a phrase like 'later known as --' after a colon.) I'd appreciate it if you could enlighten me. Thank you.", "label": 0}
+{"snippet": "As in the picture, we have a room with vents at the bottom to let cold air in and at the top to let hot air out. Normally the air flow is limited by the temperature gradient (correct me if I'm wrong). If we place a hot object in the vent on top, won't that create a faster draft? That way we could get very high \"wind\" speed indoors to replace fans. Is this possible, and if yes, what's the limit for air flow per second?", "label": 0}
+{"snippet": "Consider the following sentence Your time is limited, so don't waste it living someone else's. When I put it into a few grammar checkers like Grammarly, I get no errors. But I feel that there should be an error - like a word following \"else's\" (e.g., \"Your time is limited, so don't waste it living someone else's life.\", a quote due to Steve Jobs) Is there some sort of grammar error here, and if so what is it called?", "label": 0}
+{"snippet": "Is Aristotelian categorical syllogism (as in Copi's Introduction to Logic) a special case of the first-order logic? (This is my thought after making efforts.) Is it exactly the specialization of the first-order logic without any function symbol (but only predicate symbols)? (This is my thought after making efforts.) If it is still a specialization of the above specialization, what kind of specialization is it exactly? How would you define it as a formal logic system? Thanks.", "label": 0}
+{"snippet": "When a nucleus decays it is finding a more stable configuration, as all nature is. But is there a way of finding whether a specific configuration will decay? I know that there is a specific proton-to-neutron ratio range, of which outside nucleus decay. This can also be seen on the nuclides chart. I have also looked into concepts like nuclear binding energy and gluons. However, I never found a definitive answer to my question. My question: Is there a way, given the number of protons and neutrons (and electrons if need be), to find if the nucleus in this configuration will decay? (Please don't hesitate to use math to explain the concepts. In fact, I'd prefer it if I ended up with a formula.)", "label": 0}
+{"snippet": "Today I was explaining to my friend about opposite categories, and how the definition of monomorphism leads to defintion of epimorphism in opposite category. He asked me quite an interesting question. If we have a morphism in a category, how does that relate to the morphism in the opposite category? For example, let's consider that category Top, and a homomorphism between two topological spaces. What would be exact expression for arrow in the opposite category? I think it'd be something like the inverse function but I am not sure.", "label": 0}
+{"snippet": "This might be a very simple question, but the answer is not entirely obvious to me and I've been unable to find it stated anywhere. Consider two sets of generators (vectors), which are reduced in the sense that no two generators are parallel to each other (if one starts with two parallel generators, reduce that set by adding them together to make a single one). Then, if these two sets are not identical, can they possibly represent the same zonotope? I believe the answer is no. Am I wrong? A proof one way or the other would be appreciated.", "label": 0}
+{"snippet": "Outlook is questioning \"equipment register\" and asking me to double check if I am using singular or plural (error underline on the word register). This has me really confused and I can't find any information about what could be wrong with this phrase. For context, the phrase is part of a list of other items and I am using it to mean a register of equipment, like you would have a register of users, or a register of stock...etc. I get no grammar errors if I replace \"equipment\" with other words (although obviously I haven't exhausted all possible words!) If I write \"An equipment register\" the error remains. If I write \"One equipment register\" it goes away. Thanks!", "label": 0}
+{"snippet": "It is well-known the notion of weak limit in category theory. To obtain it, just take the notion of a limit and drop out the uniqueness property in the universal property. Now, as the universal property is crucial when proving the uniqueness (up to isomorphisms) of a limit, I expect the non-uniqueness of weak limits, in general. Well, it is possible to find an explicit example of category that admits weak pullbacks, where a cospan diagram admits two non-isomorphic weak pullbacks?", "label": 0}
+{"snippet": "While starting out on Lang's Algebra I have encountered the term \"exact\" sequence of homomorphisms. And I understand its definition and all the demonstrated examples but I would like to know more on this, like what are the things we get to know out of an exact sequence and does it aid in any kind of constructions or whatsoever. Is it possible to generalize them and how does that look like ?. For my background, I have only been introduced to Groups, Rings and Fields in my introductory algebra course but I would be delighted in seeing a bigger picture on these structures.", "label": 0}
+{"snippet": "I understand the fact that if there was no metallic ball in it, then when the ice melts, the level of water would neither rise nor fall. Now let us consider the case where there is a metallic ball in it. When the ice melts, the volume of water added to the vessel would be less than the volume displaced by the ice structure when it was floating. This should mean that the water level will fall if i am not mistaken, further which the metallic ball would sink. When that happens, it is displacing the same amount of volume as it did when it was within the ice. So shouldn't it mean that the water level would fall ?", "label": 0}
+{"snippet": "My intuition: In a system without air resistance, I would expect an arrow shot at an angle with its head pointing upwards to follow a ballistic trajectory without rotating around the horizon - because gravity can't induce torque on the body. So the arrow will impact the ground on its tail - not its head. Is this correct? If yes, what causes the same arrow to impact the ground on its head when there is air resistance?", "label": 0}
+{"snippet": "I don't think I understand correctly what it means for a Boolean formula to be reversible. By my current understanding, if a Boolean formula is satisfiable, then there exists a setting of variables such that the formula evaluates to true. If you were to reverse said formula, simply flipping each variable in the setting would also satisfy the reverse formula. You can similarly show that the reverse formula is satisfiable if the original formula. Overall, the reversible formula is satisfiable if and only if the original Boolean expression is. Since the author claims that determining reversibility is NP-complete, I think I'm missing something here. This is from the paper: On the Complexity of Polyhedral Separability", "label": 0}
+{"snippet": "Working on a thesis, I was wondering how to correctly hyphenate (if at all) the term \"high data rate\" in the following sentence: High data rate ECUs are connected directly to the backbone. The term \"data rate\" as such is not hyphenated. But compounds with \"high\" are hyphenated, e.g. as in \"high-income\", \"high-stress\". However, writing \"high-data rate\" doesn't seem right to me. What would be the correct hyphenation in this case?", "label": 0}
+{"snippet": "I've been reading a bit about how it is necessary to consider anharmonic effects in crystals if one wants to properly understand things like thermal expansion etc. So for example here: So the cubic term is said to represent 'asymmetry of mutual repulsion' and the fourth-order one 'large amplitude weakening' of vibrations. How could one come to understand these intuitively? How does one look at a cubic etc. term and come up with this explanation?", "label": 0}
+{"snippet": "I heard a while ago that the negation of the axiom of choice leads to the existence of a partition of the real numbers, into more partitions then there are real numbers. I found this post which says You don't want non-measurable sets? This means that you can partition the real numbers into strictly more parts than real numbers, but no part is empty. Yes, let that sink for a moment: you can partition the reals into more parts than numbers! I looked for a proof of this online, but could only find the result mentioned. A couple referenced this link, but it's locked behind a paywall. So, why does the axiom of choice lead to this counterintuitive result?", "label": 0}
+{"snippet": "So I was searching online for methods to approximate Pi and found this continued fraction that supposedly approximates to Pi when continued infinitely. I've tried searching all over the internet for how this was derived or why this works but could only find something similar but not close enough. I've got some basic knowledge of continued fractions but do not have experience with numbers that change throughout, how would one derive this equation? Thanks", "label": 0}
+{"snippet": "To compile my document (even a little one), my computer needs to load a lot of packages. During compilation (with pdflatex) I can see in the terminal that most of the compiling time is used to load the packages. It would save me lot of time (and ressources) if it was possible to keep the loaded packages in memory and resume compiling operations after that step when I don't modify the preamble. Is this feasible?", "label": 0}
+{"snippet": "Suppose one measures the position, then momentum, then position of a particle, and that all these measurements are done in quick succession of one another (ie. arbitrarily close to zero-time as possible). After the momentum measurement, the particles position is very uncertain. Therefore, the second measurement of the particles position can be quite different from the first. But does this not violate causality, since the particle can move a great distance in practically no time?", "label": 0}
+{"snippet": "The energy that an electromagnetic field can deliver to a system is proportional to the square of the field. However, we use the terminology watts per meter square to represent the amount of energy going past to represent the intensity of EM waves. How do you give a physical meaning to the 'amount of energy that the field carries past us per second' if you are only given the amount of energy that an EM field can deliver to a system? Why is it necessary to adopt watts per meter square for intensity, whereas I believe the energy that can be delivered to a system is perfectly fine for defining intensity", "label": 0}
+{"snippet": "In the case of a direct bandgap semiconductor, the recombination of an electron and a hole generates a photon that has energy equal to the bandgap of the semiconductor, accounting for energy conservation. But in this case, as the electron and hole have the same momentum, 'K' there is no difference. But the generated photon does have a momentum. So how is the momentum conserved in the radiative recombination in the case of direct band gap semiconductors?", "label": 0}
+{"snippet": "There is a Spanish joke, Ella es mi amiga vieja, disculpe, mi vieja amiga. The joke basically says, \"She is my friend that is old, excuse me, my old friend\", making fun of the person's age. Would there be a way to translate this into English? Of course, saying something like \"She is my friend old...\" doesn't work in English, though the joke does also work in languages like French. The translation I wrote may be considered to work, but I was looking for something smoother. Edit: my attempt: She is my old af friend, I mean my extremely old friend, I mean my old pal.", "label": 0}
+{"snippet": "I would like to be able to understand what the fission process is like (ideally, from total ignorance). What references could I read? Would it be more convenient to read chemistry books than physics books? From what I understand, the fission process involves \"breaking\" the nucleus of an atom. Regarding this: Is any atom fissile? Is there some non-fissile atom? Can this process be understood mathematically? Thank you so much.", "label": 0}
+{"snippet": "I couldn't find any similar topics and was curious if anyone had thoughts on the following: Could a magnet (ceramic and/or neodymium etc.) have an adverse affect on a Police Taser, if held to the Taser or held in proximity to the Taser. If yes, is there a material that the magnet could be covered in, to insulate those effects? (i.e. by effect, meaning unintentional discharge of the Taser, or causing the electronics on board to malfunction.) Thanks for any color you may have on this, much appreciated.", "label": 0}
+{"snippet": "What I was wondering is this. If I had a tube with water in it, with one end open and the other with a piston-like device attached to it, I can imagine that if I was to give the water a pulse, this would transmit down the tube as a mechanical wave as particles collide with each other - something like sound. But if we picture a scenario where instead of a pulse, I begin moving the piston down the tube at a constant velocity, what would the motion of the particles look like? Also what would this look like with air?", "label": 0}
+{"snippet": "I think I understand Ampere's law in the way it was taught to me by my instructor. But as the idea was given that how Gauss's Law in Electrostatics relates to electric field lines produced by charges inside the gaussian surface under consideration. We weren't given any idea that how magnetic field lines even relate to Ampere's law. I have already searched for it on the internet including the posts present here but found nothing. All I ask for is idea that how Ampere's law relates to Magnetic field lines?. Thank you", "label": 0}
+{"snippet": "I imagine that people will instinctively say, \"There is no masculine or feminine speech in English,\" but I am not so sure. For instance, the stereotype is that men speak roughly and women speak softly. Then there is the usage of tag questions, fillers, and raising one's voice pitch so that the sentence sounds like a question. Then again, it may be a question of assertiveness. I hope someone knows what I am talking about!", "label": 0}
+{"snippet": "Suppose we have a causal curve and we can cover the causal curve by convex normal neighborhoods. We also know that, in convex normal neighborhood there will exist a unique geodesic inside the neighborhood, connecting any two points in the neighborhood. So, my question is: Are we making the curve piecewise geodesic? If a curve is piecewise geodesic, can we say that the whole curve is a geodesic?", "label": 0}
+{"snippet": "I have been trying to prove the stability of a queuing system (stochastic), and the state-space I have obtained is uncountable. I am aware of the Foster-Laypunov criterion, but as far as I know, it applies to systems with a countable state-space. I want to enquire of stability conditions for the case with an uncountable state-space, and also if Foster's criterion can be extended to this case. Please let me know! Thank you.", "label": 0}
+{"snippet": "I recently stumbled upon the word biggety, meaning conceited or vain, and when I went to look it up, it seems the word is regional, which might explain why I'd never heard of it, except for one region it's supposedly used (Southern US) in is the region I've lived for over four decades. So, how common is it in the Southern US? How common is it in Midland US?", "label": 0}
+{"snippet": "According to https://en.wikipedia.org/wiki/Closed_manifold \"In mathematics, a closed manifold is a manifold without boundary that is compact. In comparison, an open manifold is a manifold without boundary that has only non-compact components.\" Closed manifold is a compact manifold without boundary. Open manifold is a manifold without boundary that has only non-compact components. Questions: Is open manifold opposite or antonym of closed manifold? (It seems not, but why not?) How do we call \"compact manifold with boundary\"? What are the differences between open manifold and non-compact manifold? How is the concept \"open\" in open manifold compared with the \"open\" in open set in set theory with topology, and open cover in topology? These open seem to mean different things.", "label": 0}
+{"snippet": "Godel's incompleteness theorem says that in mathematics there will be always true statements that cannot be proved and that adding that statement as a axiom generates other unprovable true statements. So, mathematics clearly has logical inconsistencies. I was wondering if it it is possible to find a language that doesn't satisfy Godel's incompleteness theorem or, to put it more simply, such that all its true statements are provable?", "label": 0}
+{"snippet": "A thin charged wire conductor, with a semidiameter of a is placed into a vacuum at height h (h >> a) above a big grounded conducting plate. The wire is placed parallel to the x axis, and the area of the plate lies in Oxy-plane. The potential of the conductor compared to the plate is V. Find the equation for the areal charge density in the coordinate system (O). I tried solving this problem, I could find the equation for V using method of images but I don't know how to find the areal density. Can you help?", "label": 0}
+{"snippet": "Is the Heisenberg's microscope gedanken experiment valid when considering spacetime kinematics? That is, if we consider a small region of space and try to measure its curvature, then we may use photons and see how the trajectory changes. On the other hand, the photon's energy changes the very curvature that we are about to measure. Here I assume that a high energy photon \"maps\" curvature more accurately. The ultimate goal would be to find an uncertainty principle that connects curvature and the rate at which the curvature changes.", "label": 0}
+{"snippet": "I've gone to Wikipedia and watched a few videos regarding Linear Codes, and from what I see, the Parity Check Matrix is always given, and because of that the Generator Matrix (consisting of Identity Matrix, Parity Matrix) can be made. But what if the Parity Matrix isn't given, and instead, only k and n? I understand the general layout, but I do not see how to figure out the actual contents (or identity, I believe its called) of the Parity Matrix. I should add that the specific scenario I am asking about is in binary, so maybe its only doable there?", "label": 0}
+{"snippet": "I've recently started learning about the physics of fluids and I've found that euler's equations exist and that I can use them to compute the flow of fluids with zero viscosity. But I have a problem that I don't see any easy way of adding an obstacle to a compessible flow as shown in this gif How should I do it? Is something similar possible also with navier-stokes equations? (I am aware that this questions is probably a duplicate of some older question, because this sounds as a really basic problem, but I've search for the anwer for some time and I even asked on the physics discord server and I found nothing)", "label": 0}
+{"snippet": "Is there a way in TeX (preferably plain XeTeX, but other engines are fine) to automatically choose between different options (e.g. between \"and\" and \"&\") so that the badness of a paragraph is minimal? For example, for a small hsize, the following is fine | I read a book by Smith & John. | But if we increase the value of hsize, we have to add space: | I read a book by Smith & John. | So we prefer to use the other variant: | I read a book by Smith and John. | If I remember correctly, the first printers used this kind of trick to avoid line breaks.", "label": 0}
+{"snippet": "I've heard about solitons in dense mediums (water), sparse mediums (acoustic) and optical fiber. But I can't find a good overview work on solitons in radio spectrum. Something like generating EM solitons with a peculiar antenna setup. It seems like an obvious thing for people to be working on, but looks like I just lack proper terminology to google it. Is there something that can be recommended, preferably with an experimental setup described?", "label": 0}
+{"snippet": "Davisson and Germer's experiment confirmed the wave-particle duality of matter. In this experiment a slowed down electron beam is reflected by the surface of a nickel crystal, which is able to split the electron beam into several parts, each of which is characterized by a reflection angle, rising a diffraction pattern quite similar to that of the X-rays. Is what I'm about to write right? This phenomenon is possible because the surface of the nickel crystal is not regular, but is formed by microscopic grooves capable of rising to the phenomenon of diffraction.", "label": 0}
+{"snippet": "I understand it is possible to find the shortest distance from a point to a straight line, but how do we extend this to any function. For a straight line it is simply the equation of the perpendicular which intersects the point of interest. If we have a cubic or a quartic function how would I model the shortest (straight line) distance to that function from somewhere on the plane? I anxiously wait a response.", "label": 0}
+{"snippet": "Is there a way to make meaning of it? I was thinking that maybe because the covariance is divided by the percentile rank of std dev of A, the magnitude of A is to a degree bounded. But how does it change the covariance, as covariance is about the co-directions of A and B rather than the magnitude in the first place. Essentially, what does \"covariance(A,B) divided by percentile rank of std dev(A)\" reveal? Any thoughts would be greatly appreciated!", "label": 0}
+{"snippet": "I have learnt that a planar graph is a graph which can be drawn on the plane without any of its edges crossing. What exactly is \"the plane\"? In plane geometry, we define a plane to be a flat surface of two dimensions; however here the use of \"the\" suggests we have a particular instance of a plane in mind, not just any plane. Is there a certain specific type of plane which is meant here, other than the general plane from plane geometry?", "label": 0}
+{"snippet": "I am reading the paper \"REPRESENTATION AND INDEX THEORY FOR TOEPLITZ OPERATORS\" by Gerald Murphy and came across this passage: I was wondering why we care about the strict topology or why is it important for multiplier algebra. So I know how these are defined but I've never understood why we should use it. Am I supposed to assume we are talking about the strict topology every time I see the multiplier algebra? Now for this specific example given below for the Toeplitz matrix, why is it better to identify the operators on Hardy space with the multiplier algebra when talking about convergence?", "label": 0}
+{"snippet": "Based on my intuition, once light is monochromatic it will stay that way unless you actively try to change its frequency. My intuition stems from the intricate optical laser setups in my lab that sometimes (often?) work with monochromatic light. Sound, on the other hand, seems to change its frequency easily when it interacts with the environment. Again, this is based on intuition so I'm not sure if its true. So my questions are Does light stay monochromatic once it is created? Does sound stay monochromatic once it is created? Why? Under what conditions do waves stay monochromatic?", "label": 0}
+{"snippet": "Considering no air resistance, the acceleration time graph for a free falling object would be a horizontal line as the acceleration remains unchanged. When we do take into account air resistance, the graph becomes a curve with negative gradient. However, to me, this is unclear. I understand why this must be a negative relationship, but why can it not be a negative sloping line. When we graph acceleration against air resistance, we see this is a negative sloping line. Why must this be the case? I am looking for both an intuitive and mathematical answer.", "label": 0}
+{"snippet": "We have a sentence like this: Transients are individuals just passing through, not contributing to the local population and its demographic rates, and they are thus very unlikely to be recaptured. Is it possible to remove \"they are\" behind the comma? So it would sound like this: Transients are individuals just passing through, not contributing to the local population and its demographic rates, and thus very unlikely to be recaptured. It would be much more elegant. But the catch also is that the \"thus\" doesn't refer to the most proximate sentence \"not contributing to the local ....\", but to the one at the beginning - \"just passing through\". Is that a problem somehow?", "label": 0}
+{"snippet": "In this quote (from this essay), Russell talks about a theorem showing that \"three or more lines meet in a point\". \"In geometry, instead of the tedious apparatus of fallacious proofs for obvious truisms which constitutes the beginning of Euclid, the learner should be allowed at first to assume the truth of everything obvious, and should be instructed in the demonstrations of theorems which are at once startling and easily verifiable by actual drawing, such as those in which it is shown that three or more lines meet in a point. \" What theorem is he talking about, and what is its proof?", "label": 0}
+{"snippet": "I'm new to manifolds and in my Computer Graphics class, we briefly explored the topic superficially through visual examples. From my intuitive understanding, we should be able to place a Euclidean grid on a manifold's surface or it should appear flat locally. However, I'm puzzled by how a pyramid with sharp edges and corners can still be a manifold. When we zoom in on the edges or corners, we only see flat areas along the faces of the pyramid, in any other direction it doesn't look flat. What is the difference between this case and two pyramids sharing a vertex (as an hourglass shape), which we classified as non-manifold? I'd appreciate if someone can explain what I'm missing in my intuitive understanding.", "label": 0}
+{"snippet": "I've been looking into profinite groups, their topological subgroup lattices, etc. I asked the question does every profinite group admit maximal subgroups? I can't find an example of a profinite group which does not admit maximal subgroups, though I also cannot prove that each must have one. I think that if this is true, then it is related to profinite groups being residually finite, something about being able to tell apart elements using a projection onto a finite group, which must admit maximal subgroups. Can someone answer this question with the affirmative, or give a counterexample of a profinite group which has no maximal subgroups?", "label": 0}
+{"snippet": "I know how to perform the double slit experiment in high school: a dark room, a source of light like a consumer electronics laser, a black board, and a card board with double slits. Is there way to extend this experiment to the one where we observe from which slit the photons pass (and causes them to not create the interference pattern anymore) without sophisticated measurement devices? Something that we can perform at home or at a typical high school? I have searched a bit but haven't found the answer. Does observing which slit the photons pass through require sophisticated measurement devices?", "label": 0}
+{"snippet": "I recently found that a rope suspended from two points forms the shape of a catenary curve, which brought me to another question: What is the shape made by a rod of uniform density when only one of its ends is held horizontally? Obviously the material and width would affect the strength of the rod and thus the shape it makes, however I assume they must all resemble the same curve. (similar to how all shapes and sizes of ropes will resemble a catenary curve when held at two points) I would love any help with this question!", "label": 0}
+{"snippet": "Suppose light from a laser passes through a single vertical slit. The width of the slit is certainly a factor how the light scatters after it goes through the slit; the thinner the slit, the wider the scattering. But my question is about the material surrounding the slit. How does the depth of the material influence the scattering pattern? And how does the composition of the material itself influence the scattering pattern? Does the nature of material around the slit significantly affect the scattering pattern?", "label": 0}
+{"snippet": "I know that slope is the tangent of angle of inclination. But are they just two ways of defining the same thing? Or do they have any significant differences regarding what purpose they serve in mathematics? The way angles are defined as arc divided by radius, while slope the height divided by the base, doesn't show much difference. I only have a basic understanding of calculus.", "label": 0}
+{"snippet": "So on the german wikipedia page of topological vector spaces it is written that, if a topological vector space is a Hausdorff space, then translation by a vector and dilation by a scalar are homeomorphisms. However, I have looked at several lecture notes and it is always stated (and proofed) that these two mappings are homeomorphism for general topological vector spaces (even those that are not Hausdorff). So I wanted to confirm that it is true that for any - possibly non Hausdorff - topological vector space the translation and dilation are homeomorhpisms. Also, can anybody think of a reason why on the german wikipedia they have restricted that statement to topological vector spaces with the Hausdroff property?", "label": 0}
+{"snippet": "I have heard that light is a transverse wave which is necessary for effects like polarisation, but I am unsure of what exactly this means. Is this saying that light's electric and magnetic components oscillate in perpendicular directions of three dimensional space? i.e could the electric (or magnetic) component literally oscillate say 'up' and 'down' making the electric field strength of points in space above or below the wave stronger or weaker according to the light's phase? If not, then what could it mean for light to be a transverse wave, and how does polarisation work in this context? Thanks in advance for any help with understanding this.", "label": 0}
+{"snippet": "Where do the electrons in a lightning bolt come from? There are problems with the explanations given up to at least two years ago. The explanation that the electrons come from inside the thunder cloud or are derived from cosmic rays are inadequate. There are a lot more electrons in a lightning bolt than those that come from these sources. Is there research which shows were the electrons actually come from ? Thanks.", "label": 0}
+{"snippet": "So I know that the main trig functions are sine, cosine and tangent, while cosecant, secant and cotangent are simply known as the \"reciporicals\", but wouldn't it make more sense for sine, SECANT and tangent be the main trig functions while COsine, COsecant and COtan be the secondary ones? After all, secant is just the reciprocal of cosine, so everything you can do with cosine you can do with secant.", "label": 0}
+{"snippet": "I was reading geometric optics when I came across the concept of virtual objects. I found the concept counter-intuitive, as far as reflection goes. (I perfectly understand the formation of such an object when the light ray is refracted through a glass slab.) Attaching the definition provided in my book: My confusion: A mirror forms an image when the rays originate from a certain object. So, how can an image of a virtual object form if the rays do not diverge from a particular point in the first place? What are some real-life examples of such a situation, as depicted by the figure below: I have checked answers to similar questions but my doubt is not cleared.", "label": 0}
+{"snippet": "I don't know exactly how boomerangs work, but I imagine that the fact that they are less symmetric than a sphere is part of the reason they can be thrown in such a way that they return to whomever threw them. Eggs also appear to lack some symmetry, because one side is usually pointier than the other. Of course eggs aren't ass aerodynamic as boomerangs and here it is claimed that aerodynamics plays a vital role for how boomerangs work, so probably the answer to my question is no: Will boomerang work in vacuum chamber on Earth? But I am still curious as to what would happen if you did throw an egg (shaped object) really fast like a boomerang. Does anybody know?", "label": 0}
+{"snippet": "Please correct me if I am wrong. Almost all materials are made up of atoms with electrons. If we rub two different materials, like plastic scale and oily hair on the head, then static charge develops on the surface of scale. This charge can attract tiny bits of paper. Also during lightening tiny droplets of water and ice crystals rub against each other to create static electricity. However if I rub my hands on the wall then no static charge develops on the hand. I checked it, as my hand did not attract tiny bits of paper , which means no charge developed on my hand due to rubbing. My question is : On which atomic factors of the materials does the phenomena of static charge depends ?", "label": 0}
+{"snippet": "In mathematics, scalars are defined as elements of a field. Are scalars in mathematics invariant under coordinate transformation? In physics, the way they are defined, I know they are. Since in physics, they are defined to be quantities having only magnitude and no direction, they are invariant under rotations or translation. Some sources say that in mathematics, scalars are, by definition, invariant under coordinate transformations. Can anyone please explain how defining scalars as elements of a field would intrinsically assume invariance under coordinate transformation? If not, can you give an example of a field whose elements may not be invariant under coordinate transformation?", "label": 0}
+{"snippet": "I am currently studying Analysis on manifolds for my thesis. I am looking for some references about the McKean-Singer conjecture and Patodi's proof. I read with much attention to detail his paper: Curvature and the eigenforms of the laplace operator. However I am having difficulty over some of the arguments. I would like to kindly request some references about this specific paper, for example some extra details or maybe if this is contained in a book. Thanks in advance.", "label": 0}
+{"snippet": "I am a chemist currently trying to dive in to details of random motions. I have been studying Einstein-Smoluchowski treatment, and want to learn further (Fokker-Plank's equation and Langevin treatment etc). Although I am comfortable with mathematics some of the textbooks I came across include lot of symbols I am not aware of, and hence it gets overwhelming. Could someone please recommend me textbooks which provide detailed conceptual and mathematical treatments, assuming I am not aware of all the symbols or denotations?", "label": 0}
+{"snippet": "Most objects in the universe cycle around their centre of mass: earth, sun, galaxies. Even galaxy clusters. However, the whole universe doesn't possess an angular momentum. It can't: If it had one, the centre would be a special point (which isn't allowed) and the velocities of the outer regions would easily become infinite. How does the angular momentum vanish with increasing scale? Shouldn't the laws of nature that lead to cycling for smaller objects also hold for larger objects?", "label": 0}
+{"snippet": "The Doves Press was one of the major players in the early British private press movement, hand-printing books in Hammersmith that were known for the absence of any illustrations and a focus on the aesthetics of beautiful type. Below is the famous first page from the Doves Press Bible. Can anyone provide some guidance on how to replicate this \"I\" that extends downwards to the height of the text? I find this quite interesting because there are several letters that could elegantly be extended vertically by stretching the vertical strokes of the letterform while leaving the proportions of other parts unstretched (I, J, H, E, P, L, F, T, Y, U, M).", "label": 0}
+{"snippet": "I read the paper Example of indeterminacy in classical dynamics. I understand the paper: Because the differential equation does not satisfy the Lipschitz condition, its solution is not unique, and thus there is indeterminacy. But is it really possible in physics, as in the example described in the paper, for the ball to rest at the origin to suddenly deviate to the left or right from the origin, which violates the law of causality? Or does the physical world not follow the law of causality?", "label": 0}
+{"snippet": "Are electric and magnetic multipole transitions are classified based on the nature of change in angular momentum of an electron during a transition between two states? In electric multipole transitions, the electron changes its orbital angular momentum, leading to transitions between different electron shells or orbitals within the same shell. In magnetic multipole transitions, the electron changes its spin angular momentum, resulting in transitions between different spin states.", "label": 0}
+{"snippet": "I'm looking for examples of dramatic typos - where a minor edit can dramatically change the meaning of a phrase, and would like to know if there's a name for this phenomenon. Paronyms are a similar concept, but seems to incorporate pronunciation - \"love\" and \"loathe\" might be paronyms but they're not especially similar in spelling. For example, \"symptomatic\" and \"asymptomatic\" are one letter apart but have opposite meaning, \"heroin\" and \"heroine\" have very different meanings. By edit distance, I mean the similarity of the two words - the number of single-letter additions or substitutions to turn one into the other.", "label": 0}
+{"snippet": "I did find the proof of pseudo torque about the center of mass of a body in combined rotation and translation being zero, and thus I'm convinced that in this frame of reference, we can conserve angular momentum. However, although the net torque about the point of contact in rolling is zero, I don't understand how we can conserve angular momentum about the point of contact in rolling motion, even though this axis itself is not fixed and constantly translating. Any help is appreciated.", "label": 0}
+{"snippet": "I have a question which asks me to compute the mapping matrix, but I have no idea how to do this. I understand the concept, but I am unable to understand how I actually solve problems. Would appreciate if someone gave me a step by step explanation of how I would tackle problems like these. Would it be the same method for finding a change of basis matrix as well? Here is the image of the question: Mapping matrix question", "label": 0}
+{"snippet": "If the axis of rotation is not passing through the centre of mass but some other point of a rigid body then how do we define the direction of angular parameters that is angular velocity, angular acceleration and angular displacement. For example : This is a sphere with a void in between rolling on a flat surface.C is the centre of mass and O is the axis of rotation. So basically my question is, will the angular velocity of the point A be perpendicular to OA or CA? Also will the angular acceleration of A be parallel or antiparallel to the angular velocity and correspondingly the centripetal acceleration would be perpendicular to the angular velocity right? I am confused about this.", "label": 0}
+{"snippet": "In the article about Coulomb's law There is following sentence: Coulomb's law is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. However in the Griffith's Introduction to electrodynamics Introduction before explaining Coulomb's Law, there is following sentence: To begin with, we shall consider the special case of electrostatics in which all the source charges are stationary (though the test charge may be moving). What i'm confusing is: Wikipedia applies to two charges at rest but Griffith's book applies to stationary source charge. They collide with each other. Which is correct one?", "label": 0}
+{"snippet": "I tried to implement Kruskal's minimal spanning tree algorithm and I found that the output is essentially a set of the edges... The output is not a tree at all. In my opinion, a tree can be represented by a parents array, and each node associates a key which is its parent. For a tree we need to know which node is its root at least I think. But the output of Kruskal's algorithm are just edges. How to fill this gap?", "label": 0}
+{"snippet": "All ferromagnets have domains in which the magnetic atomic dipoles are alligned. However, soft ferromagnets like iron respond quickly to the external magnetic fields while the hard ferromagnets(permanent ferromagnets) don't. In atomic view, what causes this difference? My fist guess is that in the hard ferromagnets the atomic dipoles are stronger and their density is higher so that their greater interaction keeps them more alligned compared to the soft ferromagnets. So,the hard ferromagnets are not affected by external magnetic field as easily as soft ferromagnets? I would appreciate if anyone please help me with that.", "label": 0}
+{"snippet": "Given two positive semidefinite matrices X, and Y. My question is, can we use von Neumann or the log-Determinant divergences to measure the distance between the two matrices. Most Manifold measure distance require two positive definite (PD) matrices. In this paper, the authors used the log-Determinant divergence with two positive semidefinite matrices (PSD). However, from what I know, the two divergences are for measures involving positive definite matrices (PD). Any insight please.", "label": 0}
+{"snippet": "Consider a mass rotating in a plane around a fixed point O at constant speed. In such case the angular momentum with respect to O is constant and its time variation is zero according to the fact the torque is zero.But if you change the point to which you evaluate torque and angular momentum, the time derivative of angular momentum is not necessarily zero. So?", "label": 0}
+{"snippet": "I have been brushing up on real analysis recently and, knowing nothing about topology but having seen some very general YT videos on the subject, I have developed a vague feeling that it somehow is very closely related to real analysis. For instance they both seem very concerned with continuity and continuous maps. Could someone please elaborate on the contact points between these branches of math?", "label": 0}
+{"snippet": "I was taught in my image processing class that when a mean filter is applied infinite times on a given image, the intensity of each pixel reaches the same value. I understood this that time entirely on intuition. But looking back, I tried to come up with the formal proof of this result but couldn't make any progress. So is there a way to actually proof this notion. Any help would be appreciated.", "label": 0}
+{"snippet": "My question is on the nature of oscillating electric field. From Maxwells equation, we know that the solution of the electric and magnetic field for an empty space are always oscillating fields. I learned that oscillating fields are connected to oscillating charges. However, what about the case when the the charge is not oscillating but rather, lets say, just linearly accelerating over a given distance. The field gets disturbed once the particle accelerate suddenly but what I don't understand is why this would still cause an oscillating field rather than just a locally distribution of the field. Hope my question is clear.", "label": 0}
+{"snippet": "I would like to know whether bounded linear integral operators (defined on a separable Hilbert space of functions) always have a countable point-spectrum. Or if not, what would be a practical counterexample. The following situations for instance already lead to a countable point spectrum: self-adjoint (or symmetrizable) operator kernel integral operator with bounded kernel But what about bounded integral operators in general? I couldn't find any helpful theorem.", "label": 0}
+{"snippet": "I'm trying to ad some probabilities on my model and I'm wondering which conditions are needed on my initial space. I'm starting with a metric space X and consider the set of operators from X to itself equipped with the topology of compact convergence. Let's consider the Borel sigma algebra of this space. Does there always exists a Probability on this measurable space ? Do I need some stronger assumptions on X ? EDIT : I forgot to specify that I'm asking about the existence of a probability with a \"large support\", equal to the space or infinite Thanks !", "label": 0}
+{"snippet": "I'm trying to find models that allow me to calculate dropped objects, specifically, a model where I can consider lateral displacement due to wind force and vary the weight and resistance force of the object. This is crucial because I'm trying to calculate with utmost precision the point of impact of a tool falling from a height at a construction site, to determine the safety zone that must be established below to prevent injury to anyone. I appreciate any information in advance.", "label": 0}
+{"snippet": "It is my understanding that sets are said to contain their elements but also a set is said to contain its subsets. However, I feel like this might lead to a confusion since while a set contains its subsets, its subsets are not necessarily elements of it. It seems to me the word \"contain\" must be restricted to only one of these meanings and there must be another word for the other. Am I missing something here or is this supposed to be understood from the given context?", "label": 0}
+{"snippet": "As far as I understand a material is a better thermal conductor if its thermal diffusivity is higher. The thermal diffusivity is inversely proportional to density, thus denser materials have higher thermal diffusivity all else being equal. Intuitively I would have expected the opposite to be true! Atoms close together interact more often with each other, transporting thermal energy more easily. In my mind that would explain why gases (and 'zero density' vacuum) are good insulators. Why exactly low density improve thermal diffusivity?", "label": 0}
+{"snippet": "I believe anyone who has driven a car without power steering has noticed this effect. I am not able to find a justifiable argument online. My thought process suggested it must have to do something with the static friction in the case of a moving car which provides it a centripetal acceleration, but I am not sure. A reasonable and complete argument will be much appreciated.", "label": 0}
+{"snippet": "It is easily shown that in proving compactness, we can assume the arbitrary open cover is given by a basic open cover. However, the same proof does not work when proving countable compactness. The reason is that not every open set can be written as a countable union of basic open sets. So my question is: in proving countable compactness, is there a counterexample showing that we cannot assume the cover is by basic elements? Note that such a space cannot be second countable. The trivial example of a discrete uncountable space is not a counterexample.", "label": 0}
+{"snippet": "In A_Treatise_of_Human_Nature, of David Hume, it is written: For if truth be at all within the reach of human capacity, it is certain it must lie very deep and abstruse: and to hope we shall arrive at it without pains, while the greatest geniuses have failed with the utmost pains, must certainly be esteemed sufficiently vain and presumptuous. I gathered that the usage seems to be to lie deep instead of to lie deeply. Why does an adjective follow the verb lie instead of an adverb? Is lie here a linking verb? Would the phrase It is certain it must lie very deeply and abstrusely. be incorrect?", "label": 0}
+{"snippet": "There is a book that is called embeddings in manifolds that studies topological embeddings and how they relate to each other (by homeomorphisms). I was wondering if there is a study of isometrically embedded polytopes in manifolds. \"Isometric\" here would probably mean conservation of the metric (as in metric spaces) rather than the Riemannian structure. So I would like to ask if there is anything I can find on the topic, if there is such topic, preferably a book but papers will do as well?", "label": 0}
+{"snippet": "I understand that the steady-state Kalman filter is more computationally efficient because the noise in a measurement equation and the shock in a state equation have a constant variance over the time period. However, what model should I use if I want to study the effect of a noise shock, which refers to a large shock that was not imaginable? Should I use a time-varying Kalman filter that allows for the variance of noise to vary? I am faced with this question because I cannot exactly tell the differences between these models and their respective advantages and disadvantages. Please help me out.", "label": 0}
+{"snippet": "I need to know the grammar and syntactical explanation of a phrase in the following sentence: The protest was reportedly linked to members of the group objecting to the replacement of the group leader. Is this phrase \"members of the group objecting to the replacement of the group leader\" an absolute phrase? If so, can absolute phrases act as the objects (noun clauses) of verbs?", "label": 0}
+{"snippet": "The back side of a coin is called reverse, the left or back side of a bound manuscript is the verso, but what is the back of a piece of paper such as a letter (not the envelope) called? Dictionaries give a wide selection of options (rear, back, reverse, backside, flipside, back page, etc.), and I don't understand which of these a native speaker would most likely use here. I would like to direct the reader of a formal letter (which in this case is a legal document) to further information on its back, e.g. \"bla bla (see the back of this letter)\".", "label": 0}
+{"snippet": "I found this https://en.wikipedia.org/wiki/Harmonic_oscillator in my search results when I search for \"electrical oscillator Hamiltonian\" and some other things too. But none of them answer my question about the form of the kinetic and potential energies of an electrical oscillator. Searching for the kinetic energy and potential energy does not show up fruitful either such as here. I am specifically looking for an electrical oscillator Hamiltonian. Any help would be appreciated.", "label": 0}
+{"snippet": "We are learning the rational root theorem right now. It is pretty clear how to prove a number is irrational when we know how to construct a polynomial that only includes integer and has the irrational number as a root (rational root theorem). However, if it comes to sum of two number with different power, it is pretty hard to construct the polynomial. Is there a general way to construct polynomial? Or is there any alternative ways to prove this question?", "label": 0}
+{"snippet": "If we have a smooth and frictionless pulley with two different masses attached at the ends of the rope (meaning they will accelerate) and the pulley is attached to the roof by a string, why cant we consider everything as one closed system and calculate the wieght of the that system to find the tension on the string attaching the pulley to the roof. After thinking for some time I feel that somehow allowing the masses to accelerate in one direction is relieving some of the force on the pulley. But why? Why can't we consider it a single system and find its wieght?", "label": 0}
+{"snippet": "I think it is computing the fine-grained entropy. However, I am confused by the case that when there is a black hole in the bulk. The Ryu-Takayanagi surface may include the horizon of the black hole in this case. However, the Bekenstein-Hawking entropy is a coarsed-grain entropy. I have also heard that the RT formula is computing the coarse-grained entropy of the complementary region. What does this mean?", "label": 0}
+{"snippet": "I am working on a model of a Fe square planar complex with nitrogen and oxygen given below is a monomer of that polymer. While constructing the hamiltonian matrix of this monomer I'm confused as to if I should take the orbitals of Nitrogen and Oxygen as normal atomic orbitals or hybridised orbitals? I tried to search up about it but couldn't find any method that used hybridized orbitals", "label": 0}
+{"snippet": "While solving this problem, we arrived at the solution in a form of discontinuous function of electric field. Intuitively it doesn't seem right. What is a physics explanation behind this discontinuity? Or is the mathematical approach wrong? Or is it just so idealised problem that it doesn't exist in reality anyway, so discontinuity doesn't have any physics meaning? Tried solution (electric field as sum of electric fields of all thin rings):", "label": 0}
+{"snippet": "I am a mathematician and a while ago I started studying quantum physics. I know the concept of superposition mathematically, but my question is regarding a famous experiment that Aaron O'Connell performed. Link to the TED talk that describes the experiment: https://youtu.be/dvYYYlgVAao He says in this video, \"The small piece of metal was vibrating and not vibrating at the same time.\" I did not understand this phrase because it seems illogical. Can this be explained in the experiment and is his statement correct or is it just to stir up the audience?", "label": 0}
+{"snippet": "I a m a high school student who has spent a lot of time learning about limits but still do not understand how they work completely. What I have understood is that sometimes a function does not have a y-value/s for one/(or more?) x-value/s however, since we know the y-values of the x-values close to the x-value with an undefined y-value we can approximate where the y-value for that x-value will be. To express this we use a concept called limits. My question is, can we use limits for functions where there is a y-value for every X-value? If yes,why would we do that? To show the behaviour of the points of a function as they get closer to a certain point? Thank you in advance!", "label": 0}
+{"snippet": "(I know this is going to sound odd just please consider it) What if you were to throw an indestructible ring straight into a black hole with a hole larger than it's singularity? Would its trajectory be straight through the black hole missing the singularity? If this is the case then wouldn't it reach escape velocity and as result break the speed of light? Think of it like a ball rolling down a hill and being able to speed up enough to roll back up a hill of the same height. I understand that a black hole achieves it's event horizon through distortion of space time so what I am truly pondering is if it would have a straight and un-impeded trajectory through the black hole.", "label": 0}
+{"snippet": "I found this problem on Facebook from a Mathematics group. Apparently it had appeared as one of the problems on a college entrance exam. The person who shared it on Facebook did not disclose the correct answer. I'm going to post my own approach below, please let me know if my answer is correct or if there are any other methods possible. (I even encourage solutions that may typically go beyond pre-college level mathematics.)", "label": 0}
+{"snippet": "Every well-ordered set is linearly ordered. However, is there a notion of well-orders that generalizes to partial orders? Maybe, the generalized definition will be that every non-empty subset has a minimal element, not necessarily a least element. I would be very interested to hear about such a definition, and more importantly, I would like to know about research on this topic about these \"generalized\" well-orders.", "label": 0}
+{"snippet": "I use VS code with the Latex workshop on Mac and it works perfectly fine when writing a paper. But I don't understand \"pdflatex\", \"mactex\", \"texlive\" or something other people are saying What are the essential components to compile a paper using Mac? How can I check what is working behind my VS code? (I don't remember what I installed so far to make my environment possible )", "label": 0}
+{"snippet": "I was reading in a patent that a rotating spherical body in space will experience a curvilinear translation, due to the conservation of angular momentum. This confuses me, as per my understanding if there is no friction, or any other force applied, conservation of angular momentum will keep the same rotating speed but I do not see why it will make it move/translate from its location. On the other hand, I have seen a video of a spinning object in the ISS changing direction alternatively, and I also do not know how it happens, in that case there is no translation that can be observed, but there is still friction with the air. Anyone can give some insights? Thanks!", "label": 0}
+{"snippet": "I am just wondering how do we transfer IMU readings to Body frame? Especially, linear speed and acceleration. In following diagram, the IMU is mounted on one of the surfaces of the body (you can imaging it to be a bot, vehicle, drone, or etc.). The center of the vehicle is at Body (green) point in this diagram, and it is on a different surface of the body. Both IMU and Body point are on a rigid body which moving in an inertial frame. Any hint is highly appreciated. I'd really appreciate if there are some references. Thanks!", "label": 0}
+{"snippet": "I am wondering about the correct verb form to use here: This article limits itself to consider... or This article limits itself to considering... For this example both sound dubious to me (possibly because of the presence of 'to'), and those I have asked are also unsure, including a native English speaker. And what about the passive counterpart: This article is limited to consider... This article is limited to considering...", "label": 0}
+{"snippet": "Earlier I was using texstudio with MikTex. In MikTex, I am facing some issue with its updates. So, I downloaded MacTex. How to configure texstudio with MacTex? When I am running texstudio, it is taking MikTex compiler. The error is shown below. Sorry, but /usr/local/bin/pdflatex did not succeed. The log file hopefully contains the information to get MiKTeX going again: /Users/bp/Library/Application Support/MiKTeX/texmfs/data/miktex/log/pdflatex.log pdflatex: major issue: So far, you have not checked for MiKTeX updates.", "label": 0}
+{"snippet": "I am confused by the definitions of a gauge transformation, a coordinate transformation and a diffeomorphism. In particular, should observables in GR be fundamentally invariant under gauge transformations, coordinate transformations or diffeomorphisms? For example, in these notes by Bertschinger, observables should be gauge invariant, and he defines a gauge transformation as an infinitesimal diffeomorphism. This appears standard and in line with e.g. Sean Carroll's GR textbook. On the other hand, there is this paper by Yoo and Durrer, which claims that cosmological observables are invariant under diffeomorphisms but not gauge transformations in general. Their definition of a gauge transformation appears to refer to simply \"an equivalent\" coordinate transformation - the sort which Carroll disagrees with being strictly correct in his textbook.", "label": 0}
+{"snippet": "Is it correct to say \"None can stop me?\" I feel like \"No one can stop me\" is the one I've seen used most often, but I'm not sure if \"none\" works too? Does there have to be a specific context where there are several people: e.g. \"There are many who will try, but none can stop me.\" And in other contexts (without specifically mentioning other people) \"none\" doesn't work?", "label": 0}
+{"snippet": "I'm having trouble reading documentation from packages. It seems like there's something wrong with the way I'm reading them. How should I read them, in order to learn how to use the packages correctly and efficiently? Also is there a place where you can learn typography related topics in LaTeX like glue and boxes? I don't find it talk all that much, and if they do they don't teach me why that's necessary. I haven't learn the details of typography other than fiddling with MS Word. And I would like to learn how to make is so that the fonts and font size aren't too long for the average characters per line.", "label": 0}
+{"snippet": "On the average Semi-trailer truck, assuming an average load, can the engine overcome the brakes and continue spinning the wheels despite the operator applying the brakes fully? This would be assuming the brakes are in good operating condition, and are not overheated or failing in some way. Additionally, would this also be the case if the tractor unit had no trailer on it, and no weight? How about fully loaded?", "label": 0}
+{"snippet": "I am having a conceptual difficulty understanding the following issue regarding space-time: it is clear to me why a full description of coordinates requires three spatial dimensions plus time. However, Linear Algebra also teaches that dimensions needs to be independent from one other, such that my movement along one dimension has no bearing on my movement along another dimension. This does not seem to hold in space-time, given the effects of time dilation and space contraction, which is essentially a rescaling transformation of one dimension based on the object's velocity along another. This seems to preclude such independence between said dimensions. Can somebody clear up my confusion?", "label": 0}
+{"snippet": "In the case of big freeze, space expansion will be accelerating and there appears to be a lot of different phenomena occurring. However, in the case of big rip, the expansion is super-accelerating so that light speed will be reached, ripping apart every structure. How come this speed is not reached in the case of big freeze. If the speed of expansion is accelerating, it should reach light speed at some moment. How does the evolution of scale factor in this case look like?", "label": 0}
+{"snippet": "So far I have not needed to insert jpg images in my LaTex files, but now I want to write a text that will include some pictures. I would like a format where the picture doesn't take the full width of the page but be rather set to the right or the left and the remaining space on its side filled with text. I have tried to use the figure environment from the graphicx package together with a minipage environment, but failed. What would be the best way to proceed? Is it safe (or even possible) to change from a one column format to a two columns format in the middle of a page?", "label": 0}
+{"snippet": "It's on the tip of my tongue. The great thing about this word is that there's a connotation that a person it describes is not just smart or curious, but that they find a childlike joy in learning. This word is paired with the word \"intellectually\", as in \"intellectually curious.\" But when it's on its own, it's more likely to be describing someone who's cheeky or sassy, particularly a child. But in that usage, there's the connotation that their cheekiness or sassiness belies gifted intelligence. I am pretty sure it starts with a p, or even maybe 'pro,' but I could be wrong about that.", "label": 0}
+{"snippet": "In indirect speech some modal verbs usually change. can -> could He said \"I can ride a bike\" = He said that he could ride a bike may -> might/could He asked \"May I use the bathroom?\" = He asked whether he could use the bathroom But what about dare? It can be a modal verb. \"No one dare go there\" he whispered = He whispered ...", "label": 0}
+{"snippet": "I'm from South America and I've been fluent (at least in my opinion) in English for several years as of now. With this in mind it has really called my attention lately that I've heard Afro-American people say, for example, \"I don't like no cats\" instead of \"I don't like cats\". With double negation. And the other one is, for example, \"Look at them kids\" instead of \"Look at the kids\". With them instead of the. It is not really confusing tbh but I'm just curious about why this happens?", "label": 0}
+{"snippet": "Would it be feasible to extend the range of an EV using a generator? I would guess that F=ma and perhaps a myriad of other factors would make a generator placed on an EV not work very well. I think of things like a wind generator to capture the wind power but the drag would slow the car down thus canceling the added energy. Or how about a generator in the rear wheels of the car to add back some of the loss? I could imagine something like that working in a downhill scenario but i can't see it adding much if any in the whole driving scheme. Seems Elon would have figured this out by now if any such thing would be feasible. What you guys think?", "label": 0}
+{"snippet": "This question is not similar to what I have read so far in this site. I am just trying to understand what electricity actually is. I have come to know that when charges move or vibrate in a wire by the supplied voltage, the electrons drift velocity is very slow. And the bulb glows instantly because energy travels through EM field, which is perpendicular to electric and magnetic field. Now, comes the question, suppose if I create a circuit, and connect it to the battery. So, the bulb will glow, but what if I put another unconnected wire near the circuit connected with another bulb. Will the bulb glow? Because electricity travels through EM field. Shouldn't the bulb glow? Which actually doesn't happen. I am just confused.", "label": 0}
+{"snippet": "Let's assume a galaxy has super massive black hole in it's center. We can't see what's inside the black hole because light cannot escape from it. In simple terms, black hole is a hole in the space and also assume that this black hole goes down all the way somewhere, like a straw/pipe that we cannot see. So now imagine a a spaceship is traveling exactly beneath the supermassive blackhole (but far away from event horizon where the blackhole can't pull it inside). And now what happens if the spaceship hits the blackhole straw/pipe? Just trying to understand is there any science that we can use to see where this blackhole straw/pipe goes to from outside. Or what happens if a spaceship or a planet hits this pipe?", "label": 0}
+{"snippet": "The s-procedure or s-lemma tries to solve a system of quadratic inequalities via a linear matrix inequality (LMI) relaxation. There are many different enunciations and if you are not sure what i mean you can check here. I have seen it be used in papers where the inequalities are not quadratic, for example here, but I cannot find a form of the theorem that seems to apply. Can anyone help me? Thanks in advance.", "label": 0}
+{"snippet": "I remember hearing at some point that pertubation QFT using Feynman diagrams can be thought of as certain limits of lattice QFT. Is there a precise statement of this fact? Or is it just a heuristic with no mathematical formulation/justification? Alternatively, is there a way to do calculation on lattices, that gives the same result as calculating Feynman diagrams, taking into account things like Pauli Villars/dimensional regularizations and renormalizations?", "label": 0}
+{"snippet": "I have read so many posts about the implication, but I am still confused. The statement \"if A, then B\" is always true when A is false. But I think that when A is false, nothing can be concluded. Moreover, I do not understand the example, \"If today is Saturday, then tomorrow is Monday.\" As today is Wednesday, both sentences are false so the implication should be true, but it seems in daily life that this implication is false.", "label": 0}
+{"snippet": "In the Vlasov variant of Boltzmann equation, the Coulomb pair forces are included via the force term that appears as the prefactor of the derivative of the density with respect to velocity. In that case, one is effectively calculating a mean force or a \"force field\" by averaging over all the pair forces. The average is obtained by an integral over the pair potential weighted with the density. Since this Vlasov approach allows to have good analytical insight into systems mainly governed by Coulomb forces (i.e Landau damping and other), is it possible to apply the same approach for Lennard Jones pair forces ? I could not find references and I do not understand why this is the case.", "label": 0}
+{"snippet": "I'm junior student in physics major, and i didn't study QFT or other graduate course yet, just undergraduated QM. Recently I take brief explanation class about SUSY, and in the class I heard that simple harmonic oscillation (SHO) is important because it is unique potential which is invariant under some gauge transform therefore it doesn't change some kinds of scattering properties (reflection coefficient, etc). Is SHO only example which is invariant under the gauge transform in SUSY QM? In the description, what kind of gauge transform is meant? How does the gauge transform relate to SUSY?", "label": 0}
+{"snippet": "I have a bit confusion of understanding. The central limit theorem in statistics states that, given a sufficiently large sample size, the sampling distribution of the mean for a variable will approximate a normal distribution. But the definition of sampling distribution is the probability distribution of a statistic that is obtained from many random samples of a specific population. I don't get it and see a contradiction of how getting a sample distribution from one large sample as CLT states while sampling distribution definition says it needs more than one sample?", "label": 0}
+{"snippet": "I am trying to understand the hall effects and have a few problems with them. So let's consider the classical Hall effect. We know that we consider a sample, where the electrons flow, we apply the perpendicular magnetic field, and the electron's motion is curved so they reach the sample's edge. There appears a \"new\" electric field. On the other hand, the quantum Hall effect sometimes showed that electrons move in a closed circular orbit, but not in the edge where they can go through \"skipping orbits\". So my question is, why in classical hall effect the electrons teachers the sample's edge and don't just move in a circle? What is more, do they move also along the edge like in the quantum hall effect?", "label": 0}
+{"snippet": "I want to say that a particular painting never gets old because you notice something new each time you look at it. What is a noun to describe this quality? An example sentence would be: \"Due to the xxxx of the painting, you see something new each time you look at it.\" An example to the opposite of this word would be a pop song that you get bored of after a few listens. Compound words are fine as long as they are nouns. The answers to this question come close to what I'm looking for but don't fit exactly since in my situation it's not the object that changes but it's so complex that your perception of it is different each time.", "label": 0}
+{"snippet": "Leaving school seems like such a huge event in our lives. There's this single summer where you have more freedom than you've ever had before with a group of people you've grown up with before you all go off in different directions in life: work, uni, travel, whatever. It might be the last chance to spend time with these people before you ever see them again, and so people want to make the most of this time, moreso than other summer breaks. It therefore seems strange to me that I've never heard that summer be given a special name, even in slang. Whether it's a formal term, colloquialism, slang, or TikTok hashtag, has anyone ever heard a name for this liminal period straight after compulsory education?", "label": 0}
+{"snippet": "In my understanding, light works as follows: every point in space where there is light, this light works as a point source. When we progress in time, the light spreads out from there in all directions (spherically). The new locations where the light is now, act as new point sources. From this it follows that the light from a laser beam would go in all directions, not just in the direction of a laser. However, we see in practice that (most of) the light only goes in the direction of the laser. How is this possible?", "label": 0}
+{"snippet": "I'm studying about method of undetermined coefficient. But i can't make sure when method of undetermined coefficient can be used. I know that the differential equation need to be non-homogeneous and the non-homogeneous terms need to speical form such as polynomials, trigonometric functions, or exponential functions. what I'm wandering is following: To use the method of undetermined coefficient, the coefficient need to be constant? and the differential equation need to be linear??", "label": 0}
+{"snippet": "According to the dictionary, the \"e\" is optional when a word ends in \"-dg(e)ment\". Dictionary examples: oxfordlearnersdictionaries.com: \"acknowledgement\" (also \"acknowledgment\") oxfordlearnersdictionaries.com: \"judgement\" (also \"judgment\", especially in North American English) oxfordlearnersdictionaries.com: \"abridgement\" (also \"abridgment\") ...And some other similar examples from the internet: ledg(e)ment, lodg(e)ment, grudg(e)ment. Of these, only judgment is explicitly said to be found \"especially in North American English\"; regional distinctions don't seem to play a role in any of the other options. Is this statement verifiable? What is the evidence, and how widespread is the variation? Is there a historical reason for judgment being unique in this sense? (If it even is unique...)", "label": 0}
+{"snippet": "Given two points and a line in the plane, is it possible to construct a circle tangent to the line which passes through the two points using ruler and compass? For those who don't know, these are the rules of ruler and compass constructions: you start with a set of initial objects (points, lines, etc.), at every step you can do one of the following: Construct a line or segment between two points in the set Construct a circle with a segment within the set being its radius Intersect two curves within the set Each of these moves add the outcoming curve/point to the set.", "label": 0}
+{"snippet": "If I understand correctly, the intensity of light is proportional to the number of photons hitting a certain area. If we then look at a single photon when described as a transverse wave, is its own energy equal to the square of the amplitude of that photon's wave? If we have a high energy photon this would mean the amplitude would be large, and the converse for a low energy wave.", "label": 0}
+{"snippet": "For example a car with a known speed and mass crashes with a completely unyielding wall. The car has a crumple zone, (and you know the modulus of the crumple zone) so it doesn't stop immediately, but how can you calculate the time it takes for it to stop? I've been reading a relevant article (Analytical approach for vehicle body structures behavior under crash at aspects of overloading and crumple zone length) but their equations are beyond me. First question, had a hard time finding any help with this. Thanks! The journal article in question: Analytical Approach for Vehicle Body Structures Behaviour Under Crash at Aspects of Overloading and Crumple Zone Length", "label": 0}
+{"snippet": "I am a Physics Major. I have done an undergraduate level course of differential geometry. I want to get into symplectic and Riemannian geometry, but I would like to start over from differential one again. I found this book that seems to cover what I want, but I am not sure if it is a good book or not. Can someone recommend a book or other sources (or even roadmap of multiple books) that start from differential geometry and teaches till (or gives proper introduction to) Riemannian and symplectic geometry (physics perspective is preferred but not necessary).", "label": 0}
+{"snippet": "Consider that I have a piece of paper, and I do a drawing on such paper. Now, consider the set of all possible \"transformations\" I can apply to this piece of paper that do not tear it. For example, I can rotate it, I can do an origami, I can make it into a cylinder... Is there a name for the set of all of such transformations? Could I say that all these transformations are within the conformal transformations, i.e. since conformal transformations also have scaling, could I say that the set of such transformations that do not tear the paper are within the set of conformal transformations?", "label": 0}
+{"snippet": "I've known that the distance between a compact set and a closed set is zero if and only if they are not disjoint, and I can also find counterexamples in which two disjoint closed set has zero distance. But how about a closed set and a bounded closed set? Does there exist a closed set and a bounded closed set with zero distance between them, and they are disjoint? The counterexample should not be found in Euclidean spaces though.", "label": 0}
+{"snippet": "I use xsim to create exams and it works very well. I kove the way it handles exercises and solutions. Now I'm starting to create a script and I was wondering if there is a way to hide the numbering in exercises so I can just write an unnumbered exercise and hide the solution for the students but leave a blank space for them to write in.", "label": 0}
+{"snippet": "I have an experiment where I have to find the damping coefficient of a compound pendulum situated in a clock. It swings at a very low amplitude, so I think I can make a small angle approximation. Because if I assume it has SHM, I can simply use logarithmic decrement to find the coefficient, which would make my work a lot easier. I cannot find much literature on whether a compound pendulum can even display SHM.", "label": 0}
+{"snippet": "This is a naive question. I am studying the surface-adsorbate systems using DFT calculations implemented in VASP. By setting LVHAR = True, I obtain LOCPOT which contains information about the ionic and electrostatic potential. I would like to clarify whether this information is actually the electrostatic potential or the electrostatic potential energy. My source of confusion is that VaspWiki states that the electrostatic potential is written in terms of eV, which indicates it should be an energetic quantity.", "label": 0}
+{"snippet": "The first pair of these sentences with perfect participles, shows a reason while the second shows a time, and this is how the teacher taught me their meaning, so I want to know why one is reason and the other is time. How can I know that one describes reason and the other time? Please convince me. He has failed four times already, he doesn't want to appear in the examination again. (Reason) Having failed four times, he doesn't want to appear in the examination again. (Reason) He has a lot of money in business, he doesn't want to risk his money any more. (Time) Having lost a lot of money in business, he doesn't want to risk his money any more. (Time)", "label": 0}
+{"snippet": "I am a person who gets bored all the time, so I found that counting something in my head helps occupy my time. I started counting in binary, but after a while this started getting old as I was doing it in the back of my mind, so I got bored again. So, my question is, can you count up prime numbers in your head using a \"mind-friendly\" formula, or is there something different you can count that keeps your mind busy?", "label": 0}
+{"snippet": "In the adjoining table, a dot indicates the combination of chemicals that cannot be placed in the same location as the other because of safety issues. If a company is dealing with the chemicals a,b,c,d,e,f,g,h,i,j listed in the table, what is the minimum number of storage locations needed by the company? My idea of the solution is something like this: I start with 'a'. I can collocate it with c,d,f,g,h,i, but not with b,e,j. But then, I note that d and f cannot be collocated. How/where do I go from here?", "label": 0}
+{"snippet": "I'm learning the grammar of relative pronouns; I thought all relative pronouns should be at the start of a clause, and then I learned that pronouns can be put after a preposition, as in \"The bed on which I was lying...\", but again, I came across some other examples that showed that we can put more words before the relative pronoun, as in \"The bed, the owner of which we had seen previously, ...\", or \"The bed, lying on which was a small cat, ...\" Does anyone know what are the rules? Can we put the relative pronoun anywhere in a clause? What about these sentences: \"The bed, we had seen the owner of which previously, ...\"?, are they grammatically correct?", "label": 0}
+{"snippet": "A ball is bouncing elastically after its collision from ground so can we call it SHM as it is oscillating and also it is periodic and it seems similar to other cases of SHM? If yes then where is it's mean position? But the thing is in SHM force always opposes direction of motion but here it is always in the same direction that is downward force(due to g). Also in SHM force is zero at the mean position but here force is never zero. There can be some flaws in my understanding of SHM as I am new to this. But all the answers are welcome!!", "label": 0}
+{"snippet": "I have generators for my group in GAP. Additionally, I possess a specific unitary element and wish to determine whether this unitary element arises from the Lie algebra of my group's generators. Initially, I considered a brute-force approach, intending to compute the matrix exponential of a particular generator of the group. However, I couldn't find any matrix exponential function in GAP (e.g., expm, ExpMat, MatExp, etc.). Now, I have two questions: How can I compute the matrix exponential in GAP? Is there a systematic method to compute the Lie algebra of the group generators, allowing me to identify my specific unitary element, and subsequently terminate the computation in GAP?", "label": 0}
+{"snippet": "I am doing a review for an article where I need to write some equations myself and want/have to stay anonymous. So far I plan to just LaTeX my notes, compile them with latexmk -view=pdf and send them in. My fear is that latexmk/pdflatex adds metadata that will break the anonymity of the review process. I checked the result with pdfinfo, and could not find info that would identify me in this case. But in general I would like to not only rely on some defaults of pdflatex, but to know if there is a cheap way (preferably via CLI options) to guarantee, that there is no identifying metadata.", "label": 0}
+{"snippet": "I'm making a roster in a spreadsheet of all the current employees, volunteers, sports coaches, and other workers at a school. What is the best way to label the column showing if someone is Full-time, Part-time, Volunteer, or On-call (like substitute teachers)? What word represents this? I already have a Status field denoting Current vs. Former. Should I just merge this unnamed field so that Current becomes more precise as Full-time/Part-time and then Former? It's in the same logical realm, I think.", "label": 0}
+{"snippet": "I am looking for an algorithm that could determine adjacent extreme rays of a polyhedral cone (extreme rays that share a face), given the set of inequalities defining the cone and an extreme ray for which the adjacent rays are to be determined. I was hoping there exist a python library that might already have coded up, but I could only find pycddlib, which seems to need to determine all extreme rays first. This seems inefficient to me: I was hoping there would be a method that doesn't neccesitate computing all extreme rays first. Thank you for help!", "label": 0}
+{"snippet": "I want a certain path that I generate to remain hidden (so I use the path command without actually drawing it), so that I can use that path to compute other points of interest such as intersections, but I don't want that hidden path to affect the overall scaling of my shown figure. Is there a way to generate such a path that does not affect the overall figure scaling?", "label": 0}
+{"snippet": "I am writing an article about data mapping, and discussing the various types of challenges in mapping data elements from one system to another. One of these challenges is assuming that a data element called X in one system is the same as a data element named X in a different system, simply because they are named the same. I am looking for a classification for words that have multiple, disparate meanings. My mind keeps jumping to polynomial, but I need that type of word that would relate to the meaning of words. Poly-meaning-al?", "label": 0}
+{"snippet": "I am trying to understand the following to defintions of being \"intrinsic\". They are from Differential Geometry of Curves and Surfaces by Tapp. Question: In what way are these defintions consistent? To call quantity intrinsic if it can be expressed completely in terms of the first fundamental form makes sense. To me it seems that requiering invariance w.r.t. isometries captures different properties that I would expect from intrinisc properties. For example that deforming a surfaces should not alter the length of a curve on that surfaces. It seems to me that there are two types of intrinisc properties and that the \"intrinisic geometry\" consists out of these. Many thanks in advance for any hints or explanations!", "label": 0}
+{"snippet": "If we consider a charge in space then we can draw infinite number of spheres (taking the distance between the spheres equal) around the charge and these spheres act as equipotential surfaces. Now, As the distance of all points on the sphere are same from the charge then why does equipotential surface gets farther apart when electric field decreases??i mean my questions is what is the problem with taking the distance between equipotential surface equal??", "label": 0}
+{"snippet": "When someone tends to hesitate to acknowledge a problem and avoid involving trouble even if needed, is it ok to say in a negative nuance that He/She always has a \"don't rock the boat\" attitude. I found the below definition at Collins Dictionary and considering that, it seems that not rocking the boat doesn't necessarily have a negative meaning: If you say that someone is rocking the boat, you mean that they are upsetting a calm situation and causing trouble. (www.collinsdictionary.com I'd like to describe a person who usually avoids troubles and never speaks up regarding existing issues such as social issues with a negative implication. I'd appreciate it if you tell me appropriate phrases to describe such a person.", "label": 0}
+{"snippet": "I'm struggling to explain it, but some examples are (mention does not imply endorsement!): Sir Keir Starmer -> Sir Kid Starver (criticism of his stance on child benefits) Benedict Cumberbatch -> Butterscotch Candybatch (surreal humour) Financial Conduct Authority -> Fundamentally Complicit Authority (critical of regulatory capture) Saddam Hussein -> Sadman Insane (general derision) These are nicknames, i suppose, but they are a specific kind of nickname.", "label": 0}
+{"snippet": "I was attending lectures om holography where the lecturer kept on mentioning that a QFT lives on a Cauchy slice. What does that mean? Is it such that each point of the slice is associated to a unique vector in the Hilbert space? Can this be generalized to QM? Does that mean that the harmonic oscillator lives on an integer lattice? Is this geometric correspondence the motivation behind the operator state correspondence?", "label": 0}
+{"snippet": "I am just a high school student. I had already heard that we can't determine the exact location of big bang. So now i have a question can't we approximate it? Like say divide the observable universe in many grids and you take the Average age of each grid and do this for all the grids. I assume intuitively that on average the parts of the observable universe which were formed earlier would be closer to the point of origin of the big bang right? I know that there are other effects to consider such as expansion of space but still it is not possible so my question is why?", "label": 0}
+{"snippet": "Let (B, S) a multi period binomial model that is arbitrage free. Prove that the unique time for an American call is the maturity T. I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My idea is to prove this result by contradiction. I want to find an exercise time t<T, such that there exists an arbitrage opportunity, so that the value of the portfolio at time t is greater than zero, starting with an initial value equal to zero. Is this a good idea, and how can I find such strategy explicitely?", "label": 0}
+{"snippet": "Let's say a small magnet is attached with its South pole on to the north pole of a bigger magnet vertically.There is no friction between the magnets so this means the normal force increased due to the attraction doesn't have any effect on its tendency to fall.My question is that : Does the small magnet slide down OR Do the magnetic field lines have such a property to pull the magnet up. Also, what changes are seen if the small magnet is attached vertically to a iron bar (frictionless again).", "label": 0}
+{"snippet": "I'm attempting to self-study real analysis and was looking at the popular textbook recommendations. So far, I've seen Abbott and Cummings for beginners. With Rudin, Stein, Bartle, and Zorich for more advanced books. My question is : What book is the sort of \"Bible of Real Analysis\" or reference book, where if one knows the book from cover to cover he would have a colossal grasp on the subject. To clarify my question, I mean a textbook that would cover the whole surface of analysis after learning it from a more elementary book such as Abbott or Zorich.", "label": 0}
+{"snippet": "I understand that if there are different capacitors of different capacitance then they can store same charge at different voltage differences only. But I wanted to understand that why the above happens when the capacitors are arranged in series...I want to know the mechanism behind that if we arrange different capacitors in series then they store same charge at different potential differences.....why they store same charge only that is flowing in the whole circuit due to net potential difference of the circuit....why they don't store different charges whose sum is equal to the net charge flowing in the circuit?", "label": 0}
+{"snippet": "I am currently studying the method of characteristics. So far I understand what I read in literature. The problem is that I didn't find a good explanation for imposing boundary conditions anywhere. Also, in the textbook problems, only the initial conditions are given. Please recommend me some literature where I can study how to impose boundary conditions on the solutions obtained using this method. A hyperlink to the literature would be of great help.", "label": 0}
+{"snippet": "Are there any public stats that demonstrate how much literature is produced in LaTeX as opposed to Microsoft Word, Adobe InDesign, etc? When I search \"latex market share\" every single result talks about rubber/pillow/mattress companies and not the typesetter. From what I have heard LaTeX is heavily used in Math & Science theses, and I would like to find specific numbers to back that claim. Does LaTeX stand a chance against other software outside the Natural Sciences, its stronghold?", "label": 0}
+{"snippet": "I have read a recently published paper on arXiv where the scientists claim to have developed a superconductor material working at room temperature and pressure. While it is clear that the results - if proven true - are preliminary, and that a lot of refinement would be necessary anyway, I am wondering what technological advances can we expect from such a discovery? Or, what technologies are currently impractical, impossible or unexplored due to the impracticality of currently industrially available superconductors?", "label": 0}
+{"snippet": "Our teacher told us that objects store potential energy in them according the position of the object above the ground because of gravitational force. Like we are holding a box up and it stores potential energy, and if we drop it, its potential energy gets converted to kinetic energy. My doubt is, If, we send a rocket outside the Earth, then after some point, the influence of Earth's gravitational field nearly comes to an end, Then where does the potential energy of the rocket go if we stop providing it velocity (Like dropping the box)?", "label": 0}
+{"snippet": "I'm studying a math book. There is a definition as seen below. A category is a class C of objects (denoted a,b,c ...) together with (i) a class of disjoint sets, denoted hom(a,b), one for each pair of objects in C... (ii) ... I want to ask which one of the following meanings should be deduced from this statement regarding the grammer rules; hom(a,b) is one of the sets of a class. hom(a,b) is a class of disjoint sets. The whole thing may confuse you so please just consider the part saying: \" a class of disjoint sets, denoted hom(a,b), one for each pair of objects in C...\"", "label": 0}
+{"snippet": "Please see here to see question & my solution Here are question & solutions I tried. How should one approach problems where both s-shifting and t-shifting are required? Is there a specific method or sequence that is recommended? I have attempted to solve these problems by applying the first shifting theorem (s-shifting) followed by the second shifting theorem (t-shifting). However, this method seems to lead to incorrect results. Answer said that t-shifting first, s-shifting later. Could you explain why this approach fails? What is the significance of the sequence in which the first and second shifting theorems are applied? When both shifting theorems are necessary, which should be applied first, and how does the order affect the final result? Thank you for your time and assistance.", "label": 0}
+{"snippet": "I have read about wave propagation and dipole antennas here. I do not understand how a single electromagnetic wave (i.e. the electric field in particular - I can come up with the magnetic field later) propagates when its electric field of a dipole antenna is shown below. For example, the iconic picture of an electric field of an electromagnetic wave looks like the figure in the bottom left corner in red below. How does it look in the bottom right diagram? I tried to plot it below again in red, but it doesn't make sense to me. For example, the amplitude of the wave would get bigger. So, I would like to know how a single electromagnetic wave propagates in this field.", "label": 0}
+{"snippet": "In the following sentence is \"painted\" being used transitively or intransitively? The sunset painted the sky with a tapestry of fiery colors. I asked ChatGPT about this and it gives reasons for both... For intransitive that it's being used metaphorically or poetically; the focus is on the action of sunset creating a visual effect, not the application of paint. When I reminded it that \"the sky\" certainly seemed to be the direct object it agreed at first that it was actually transitive. Yet when asked to confirm, it stated it was intransitive. Then it finally stated it's a matter of interpretation. Personally, I think it's transitive. Am I right?", "label": 0}
+{"snippet": "I want to make a program that will solve polynomials, but I don't want to just look at another program that already works as I think that would defeat the purpose of the exercise. And that's why I'm asking the question here instead of on Stack Overflow. I think it would be very difficult to implement Alpha-Beta Theory/Veita's Formula, and guessing using Factoring doesn't seem like a neat solution to me, so I'm wondering if there is in fact an easier implementation. I would also like this to be scalable for higher degree polynomials if possible. Thanks.", "label": 0}
+{"snippet": "I'm reading the famous paper by Haah: Local stabilizer codes in three dimensions without string logical operators. In the last sentence of the introduction, he wrote: A logical operator is a Pauli operator possibly with infinite support that commutes with every generator. Since each generator is local, the commutation relation between the generator and an arbitrary Pauli operator is well-defined. Why the locality guarantees the commutation relation is well-defined? Are there examples where removing the locality condition yields a not well-defined commutation relation between the logical operators and the generators of the Hamiltonian?", "label": 0}
+{"snippet": "I'm studying nonlinear control systems and I have some questions about the nature of this optimal control given by PMP: Traditionally, control methods based on Pontryagin's Minimum Principle (PMP) and Euler's method (or Runge Kutta) have been extensively used to address nonlinear system control problems. Is there a potential to get trapped in local minima resulting in suboptimal control outcomes? If there is one, why do we call it \"optimal\"?", "label": 0}
+{"snippet": "Solving Fresnel integral for vortex beam diffraction is necessary and difficult. Without the necessary integral formula, this isn't easy to derive. Therefore, I need some means to calculate it numerically quickly. I have learned some methods, such as angular spectrum method, fast Fourier algorithm. But I still can't understand its principle and implement it through matlab programs. I think I may need some correct codes or related books to learn, and I also hope to get a good explanation so that I can understand them better.", "label": 0}
+{"snippet": "Just a quick informal Question. I was wondering if the boundary of an LCF Manifold is also LCF ? By definition a LCF manifold is one in which, for each point, there exists a neighborhood around that point that can be conformally transformed to a flat Euclidean space. Since the boundary is a submanifold the answer to the above question should be, yes ! Do I have to be careful to which EUclidean Space i send the conformal transformation? i.e should boundary points only be conformally mapped to an euclidean half space? Thanks for clarification!", "label": 0}
+{"snippet": "Most articles show the plural form of equivalence as equivalences. The wikipedia on logical equivalence uses this form. However, I feel like I have seen equivalencies used in contexts like mathematics as well, like in this paper Equivalencies in Mathematical Structures: An Exploration through Model Theory and Groups Is the choice region specific (American vs European), domain specific (mathematics versus general conversation or other technical fields), or just whatever the writers preferred?", "label": 0}
+{"snippet": "Let's consider a glass slab ABCD. Now a light ray is incident on the near end of the air-glass interface AB and is emerging from the glass-air interface BD. In such a manner: Is there something wrong how I have made my figure. Can light emerge in such a manner from a glass slab. This is my first question and English is not my first language I hope you understood my doubt. I feel like the figure I have drawn does not look like the conventional ray diagram of light entering a glass slab. Also I am not an expert I am just a student who wants to know the answer to my question.", "label": 0}
+{"snippet": "I have a huge .bib file that contains all my references. Very few of them currently have a doi field. Given access to an online database that includes many of the same references, is capable of generating .bib entries, and includes dois, is there any more or less automatic way of using the database to add dois to as many of the references in the .bib file as possible? Note that the citation keys in my .bib file and those generated by the database are not identical, so matching would have to be done by e.g. title and author. Answers using e.g. Jabref or Zotero are fine. It feels like one of those tools ought to be able to do this. I just don't know how.", "label": 0}
+{"snippet": "A cumulative distribution function (cdf) has a countable set of discontinuity points. They need not be isolated. Let us call non-isolated points 'accumulation points' of this set of discontinuity points. Is it possible that a cdf admits also countably infinite accumulation points in its set of discontinuity points? If so, is this something as pathological as requiring a singular distribution or it can also happen with discrete distributions? Thanks for any clarification, it would be nice to have concrete examples.", "label": 0}
+{"snippet": "A long time ago, I had a teacher who said you could write \"lit.\" to mean \"read this as\". The typical example is to provide a tongue-in-cheek translation from English to English, such as: The power company charges an administrative (lit. bogus) fee on every bill. The author of the sentence is telling the reader to read past the euphemism (\"administrative\") and understand the subtext that the power company really just wants to take their money for made-up reasons. I just looked this up now, and couldn't find any reference material saying this was an accepted usage of \"lit.\". Maybe my memory isn't completely accurate?", "label": 0}
+{"snippet": "Given a table with x and f(x) values, g(x) a non-linear least squares approximation, and p(x) the Lagrange interpolating polynomial that passes through all of the points in the given table. What would be the best approximation on f, for a point x = k by only using p(x) and g(x)? Intuitively I thought about calculating p(k) and g(k), then taking the middle point of both, however I have no idea if this is reasonable to think of, nor if it is the best approximation for f(k). Is there a visual way to think of this problem? Or will I have to use the properties of both p and g to find the optimal approximation?", "label": 0}
+{"snippet": "Suppose there are two seeds kept at equal distance from a light source which emits a photon each on either directions. Seed germinates when a photon falls on it. According to rest frame both the seeds receive photons simultaneously but according to moving frame one of the seeds receive a photon earlier than the other seed. The second seed dies off due to delay, so there is only one plant in the moving frame but two plants in the rest frame. Is my line of reasoning correct? What happens when I bring the moving observer to rest so that he should agree with whatever observations made by the observer who was at rest?", "label": 0}
+{"snippet": "I've been asked by a friend taking a TOEIC exam to get an explanation of why \"wipe\" should be used in the following sentence, as opposed to \"wipes\": It was mandatory that each person wipe[s] off equipment after use with provided spray and wiping towel. Is it because there is an implied (should) before \"wipe\"? Or is it related to the fact that it is \"each person\" - meaning, of course, multiple people and perhaps substitutable with \"they\" - i.e. you couldn't say \"It was mandatory that they wipes\"? Or is it something completely different? This one has got me extremely curious, really looking forward to some of your insightful responses.", "label": 0}
+{"snippet": "Is there a word for a decision that's already been made despite the relevant processes not having been followed / analysis done. Foregone conclusion feels similar to what I'm after; but that implies that the facts are so obvious as to make the decision process moot; whilst I'm after a word for where the conclusion is based on one person's perspective without them having consulted relevant stakeholders / investigated the various options / collected evidence to support or dispute their arguments / etc.", "label": 0}
+{"snippet": "Assume that we have positively charged two solid conducting spheres of the same radius and material. It is evident that the surface charge is uniform on them to eliminate the internal electric field everywhere inside the spheres. However, how does the charge distribution change if we bring them close to each other? Recall that we place them close (not in contact) to each other. Does the exerted Coulomb's force upset the uniformity of the surface charges on both spheres? How can we find the new charge distribution so that the internal electric fields remain zero?", "label": 0}
+{"snippet": "I understand it's not possible to transmit information using entangled particles due to the randomness of the measure results. But what if the act of measuring itself IS the information? Let's say there's a constant flow of entangled particles received either side by Alice and Bob Bob measures every other particle. Is it possible for Alice to know which particle has been measured on the other side, and which didn't? I'm assuming unmeasured particles with superposition can show an interference pattern and measured ones don't Sorry if this is a silly question, I'm not a physicist and I fell in the quantum rabbit hole quite recently :)", "label": 0}
+{"snippet": "I was reading about the Pascal barrel bursting experiment, and it almost makes sense to me, save for one bit. I know that pressure corresponds to the number of collisions in the fluid. So my q is: why does adding water in the tall, narrow pipe in the experiment increase the number of collisions down in the barrel drastically? What is actually going on if we zoom in on a molecule of water in the barrel when we add all the extra water at the top? Thank you!", "label": 0}
+{"snippet": "I am not an expert in languages and this is my first question here... To my understanding, most of the languages were spoken before writing was discovered/evolved. What would cause a language to have same/similar sounding words with different meanings when the language was spoken? Wouldn't it cause more confusion when spelling could not distinguish the different words as there was no writing? I can think of some other examples such prey/pray or ate/eight which sound similar but their meanings aren't related. Did these words evolve/change in pronunciation over time, or were they used with similar meanings even a long time back, since before writing was a thing?", "label": 0}
+{"snippet": "For the operation of the transistor, the base-emitter junction is forward-biased and the Base collector junction is reversed-biased. Due to the concentration gradient, electrons from the N side (Emitter) go towards the P side (Base). Since the base is lightly doped and thin and due to the reverse biasing of the base-collector junction(electric field exits between the base and collector), the electrons coming from the N side (Emitter) go towards the N side (Collector) without much recombining with the hole in the P region (Base). Since we have a concentration gradient for electrons to flow from emitter to base then why do we need the base supply voltage in a transistor circuit?", "label": 0}
+{"snippet": "I would like to know some tips or hints to find a way to recognize whether \"as\" is using a meaning of \"when\" or a meaning of \"because\" when \"as\" connects two sentences. For example, the sentence below which currently confuses me. The third point, where it is in our interests to engage directly with China in a constructive and positive way to shape China's actions and behaviors as they impact on the wider world. In the above sentence, does \"as\" mean \"because\"? addtion: this sentence was from an interview script, so I cannot know if there is komma before \"as\". But thanks for all comments.It seems this \"as\" doesn't mean \"because\".", "label": 0}
+{"snippet": "Trying to work out whether to use 'is' or 'are' in the following sentences (aware they might differ): How many grams of flour is/are on the scale? How many centilitres of cough syrup are/is in the measuring cup? How many kilograms of fruit are/is on the scale? 'Are' seems most natural to me when speaking, but have read that units of measurement are usually counted as singular amongst the scientific community. Looking for UK English rules :)", "label": 0}
+{"snippet": "I was reading a preprint on archives (not yet published), and in the introduction the authors say \"Following X in [ref]...\" and go on to set up the problem. When I went to [ref], it turns out the authors of the preprint actually take three paragraphs word for word from X and include them in their introduction. Is this appropriate? Just saying \"Following X....\" makes it okay? To me, it still looks like plagiarism.", "label": 0}
+{"snippet": "Suppose we have a finite group G, and we had a configuration of points, lines etc. and lets say that the group acts faithfully and primitively on the set of points. Will the group be guaranteed to be flag-transitive on the entire figure or can G fix some proper subset of lines, for instance? My intuition says that shouldn't be possible, but I can't figure out how to prove it.", "label": 0}
+{"snippet": "Electromagnetic radiation phenomena exhibit a temporal asymmetry: we observe radiation coherently diverging from a radiating source, such the light emitted by a star, but we do not observe radiation coherently converging into a source, unless we delicately set up such a system. What can explain this asymmetry? And how is the asymmetry related to the causal asymmetry, on the one hand, and the thermodynamic asymmetry, on the other?", "label": 0}
+{"snippet": "Next year I have choose a few optative courses from a big list, but syllabi are not available yet, so I have to make a choice based on names only. I am thinking about taking one titled \"Groups and representations\". I have really enjoyed my Abstract Algebra courses so far, specially the part that covered Group theory. However, we never got into Representation theory, and I ignore what mathematical interest it might have. I was wondering if someone could provide me with a text explaining what is representation theory about and what is the mathematical interest or motivation behind it. I have found some books on the topic, but they all just start giving definitions and theorems and never give a good introduction.", "label": 0}
+{"snippet": "What makes quantum computers faster in certain problems than normal computers? Does quantum computing means that many solutions are explored simultaneously instead of one at a time due to quantum superposition of qubits? Is the complexity of solutions explored proportional to the number of qubits? That's my impression and my understanding of quantum computing. Any books or articles that exactly pinpoint how superposition or any other quantum phenomenon makes computation faster?", "label": 0}
+{"snippet": "A grammatically correct way to ask someone a question would be: Why are you still here? If I want to make a statement (instead of a true question), such as, You've been here too long or Your comments are annoying, or You're either a troll or a quarrelsome person, would \"Why you are still here\" (meaning- why do you continue arguing with everyone) be acceptable in a conversational English? Do you know why you're still here? is grammatically correct, but I don't want to know if he knows, I just want to express an annoyance with the person.", "label": 0}
+{"snippet": "Has anyone (in general) experimented with simulating moon lighting? It means the following. A gray ball is illuminated with light with a brightness equal to that of the sun. And at the corresponding angular distance from it, the level of illumination by the light reflected from the ball surface is measured and visually assessed. The goal is to compare the illumination intensity of real moonlight and that simulated in the experiment and to check the reliability of the calculated values.", "label": 0}
+{"snippet": "Cambridge says that the idiom home and dry is British English, which explains why I hear it used around me. It means: to have successfully finished something but I have heard it used also literally. Then I understand it as meaning to return home safe and sound after a travel/adventure of some sort. I wonder if this idiom has originated among sailors. I understand home but why dry? Is dry here a synonym of safe (and sound)?", "label": 0}
+{"snippet": "I'd like to know a word to describe a person who loves celebrities, gossips, trends or anything that is popular and is easily affected by them. She said she had moved to Paris because she loved \"Emily in Paris\" on Netflix. It seems that she is such a \" \"! I came up with \"sheep\"(https://www.urbandictionary.com/define.php?term=sheep), but I'd appreciate it if you could tell me other words to describe such a person better or more accurately.", "label": 0}
+{"snippet": "I'm trying to get a deeper understanding of the classification problem for finite groups and in particular the extension problem. I'm looking for some advanced books on the theory of finite group extensions which extensively and deeply covers the topic. Maybe an all-in-one book doesn't exist, in case I'd like also suggestions on books covering related and more specific topics such as Shur's multiplier and Group cohomology.", "label": 0}
+{"snippet": "Is there any book for a Mathematics student who can learn Machine learning in the aspect of Banach space geometry? Or, one can understand the connection between Geometry of Banach spaces and Machine learning? Any suggestions in terms of article, note, book regarding the development of such study is always welcomed. It will be very much helpful if anyone can suggest a good book which contains the discussion about the topic of Geometry of banach spaces that is required for Machine learning, Neural network such things. Thank you in advance.", "label": 0}
+{"snippet": "The professor asked me to write a small computer program that takes double integrals of rapidly varying functions. He did not mention which functions should be integrated but he said that I must use a numerical method with variable step size. I hope someone can recommend me a method that will do the job. It would be nice to have a link where this method is adequately described.", "label": 0}
+{"snippet": "There are many ways to draw a simple flowchart, using packages like tikz. But recently I read a paper and it seems that their complex flowchart is not a picture, but actually generated by latex. Here is what it looks like: I really would like to know how to make a chart like this, if there is a minimal example. EDIT: From what I can see on this picture, it is a combination of table and flowchart, which I don't know how to. So my actual question is, how could we combine a table with a flowchart? Or maybe is it just a complex Tikz (or other packages) implementation?", "label": 0}
+{"snippet": "If the expansion of the universe happens uniformly, how does this affect small objects? For example, are the distances between protons and neutrons inside a nucleus actually expanding? Is the nucleus constantly pulling itself together so its diameter stays constant? What about say between the carbon atoms in a diamond? If I can observe said diamond forever, will its atoms eventually disassociate with each other or will it stay in one piece due to its covalent bonds counteracting the expansion of space?", "label": 0}
+{"snippet": "I have a problem concerning a cylinder, cut by an arbitrary plane which is perpendicular to an axis, z. I know dz, the distance from centre of the cylinder to the plane. I know all dimensions of the cylinder. I know theta, the angle of rotation from the axis z. My poor drawing How do I calculate the volume of the cylinder above the plane? Is it possible? I've tried some trigonometry to get an integral based on the changing size of a circle segment... but it's getting very convoluted.", "label": 0}
+{"snippet": "Say I have some random variables X,Y that are jointly distributed according to some probability distribution (not necessarily independent). Is it possible to construct a Z = f(X,Y) (i.e. Z is solely dependent on both X and Y with no other source of randomness) such that X is independent of Y given Z? I believe this holds for all Z : Z = g(Y) or Z = g(x) for some deterministic function g, although I struggle to prove this formally. One straight forward example is in the binary case with Z = not Y. However, is there any formulation on how the conditional independence requirement restricts the function f?", "label": 0}
+{"snippet": "As far as I understand, the branes of brane cosmology are lower-dimensional \"sub-manifolds\" of some space. It was hard to imagine for me how such structure could exist and be physical. But then I learned of topological defects, which are essentially that. So my question is: Question: Are the branes of brane cosmology supposed to be topological defects of some sort? If not, how else could a \"sub-manifold\" be something physical? I also posed a related question which received little attention. Please note that I have only an undergraduate understanding of physics, but are fine with advanced mathematics.", "label": 0}
+{"snippet": "i'm taking a qft theory class, and we are doing a little bit of group theory, today the professor introduced us to Lie groups, but his definition is a little be weird he said that lie groups are groups whose elements are function of n parameters. This kinda confuses me and i can not see how this definition is equivalent to the one where a Lie Group is defined as smooth manifold with some other proprieties like the operation of the group be differentiable. Anyone can help me to clarify and get how these two definitions are equivalent? Thanks", "label": 0}
+{"snippet": "I am struggling to answer this question, and I was hoping for some assistance and/or help, it would be greatly appreciated. This link is a screenshot of the question because it does include diagrams: https://i.stack.imgur.com/wMVod.png The question includes a definition that is used to answer the question; if anyone knows how to answer or go about this, you would be helping me out a lot.", "label": 0}
+{"snippet": "I have some simulated data from a model of an IMU's gyroscopes. I am trying to use Allan deviation to verify that we have correctly modelled various sources of error in the sensor data. I was able to verify angular random walk, and have now moved on to bias instability. I'm following a tutorial on mathworks which describes finding a critical point in the Allan deviation curve, depicted as such: However, my sensors do not output this single, easily spotted critical point. My simulated data looks like so: Is this normal? If so, are there any techniques to choose the best critical point to get an instability reading? If not, what might cause it?", "label": 0}
+{"snippet": "By equivalence principle, one can find a local inertial frame at every point of spacetime. Then this is usually used to introduce the general spacetime metric, as a back-transform of the Minkowski metric. The transformation from Minkowski to general metric depends only on the first derivatives of the coordinate transformation. This means that locally we can get an inertial frame by applying a linear coordinate transform. It is puzzling because in motivating examples we always get accelerating transforms, such as a falling elevator. However, it seems that the acceleration does not play role in the final formula. What is happening? Is this because linear transform is enough to diagonalize the metric, but the quadratic part (i.e., the acceleration) is needed to make the Christoffel symbols vanish?", "label": 0}
+{"snippet": "I understand Thomson scattering as: When an EM wave is incident upon a charge causes it to oscillate in turn releasing energy as another electromagnetic wave. In an Electrodynamics lecture we took a different approach by assuming the far-field limit. The EM wave makes the charge oscillate causing it to emulate an oscillating dipole and hence releasing energy as another electromagnetic wave. I understand that these two present the same behaviour in the far field limit. However, I do not intuitively understand how the oscillating charge emulates an oscillating dipole.", "label": 0}
+{"snippet": "i'm writing my first document using LaTex. I want to include good-quality figures, so i opted to use the PDF format. i saved the images from the plots in Matlab as pdf files, and when i included the figure in my document it showed up with extra white borders, i'm not sure how to fix that. Cropping the pdf can be done, but i have many images to include so that would be tedious. any suggestions? or something else i can do? thank you", "label": 0}
+{"snippet": "We use Past Perfect to speak about actions before some moment in the past. What if my speaking partner doesn't know about a moment in the past? I had done everything. (I don't mention it, but in the mind I mean, I had done before some moment, which I know). What if i don't mention an moment, but it's obvious? I had written all documents. (It can be either obvious or unobvious, that I had written all documents before a deadline).", "label": 0}
+{"snippet": "Suppose I have an infinite wire and close by I place a loop which has increasing current. The wire and the loop is fixed . Now an emf will be induced in the infinite wire which in turn induces a current to oppose the changing magnetic field . My question is why this emf is induced in the infinite wire even though the wire is stationary( in order for motional emf to be induced) and also there is no loop formed by the infinite wire? How to define the flux change in this condition for the infinite wire in order to apply faraday's law to calculate emf?", "label": 0}
+{"snippet": "I am currently reading a book about numerical optimization and have reached line search methods. In a section studying the convergence rate of the gradient descent method, I am really struggling to understand how alfa is determined (see below). I really do not understand at all how to even differentiate with regards to alfa, when dealing with vectors and matrices, and I also am very confused as to how the b-vector can just completely disappear in the result. Can anyone explain how the derivative with respect to alfa is determined, and how alfa is isolated from there? Thank you to anyone who may be able to help. Explanation of how alfa is determined", "label": 0}
+{"snippet": "It is common knowledge that submodules of finitely generated modules need not be finitely generated. One can see this by considering a non-Notherian ring and extending this as a module. My question is, how does one think about this intuitively? The way that I think about is: When I restrict myself to a subspace, there is a chance I no longer have access to the elements that finitely generate the whole module. In contrast with Linear Algebra, this can occur when the subspace is non-empty. Could someone let me know if this is a correct way to view this or if there is a more intuitive way of viewing this result?", "label": 0}
+{"snippet": "Suppose I want to cover a whole circle of with hexagons. See the attached photo where coloured hexagons are those required to cover a whole circle. Given the length of the side of the hexagons and the radius of the circle, what's the minimum number of hexagons required to cover such circle? I notice that there are three ways of inscribing a circle in the hexagon tile: the center of the circle lies at the center of a hexagon, at the center of a hexagon side, and at the vertex between three hexagons. Attachment", "label": 0}
+{"snippet": "I know that in the pure algebraic context, connected groupoids are equivalent to groups. Moreover, connected groupoids can be seen as action groupoids. Consequently, any abstract groupoid is essentially a disjoint union of action groupoids. Therefore, is it not more natural to study group actions than study groupoids? Since group actions seems to have a richer structure than groupoids. So, why study groupoids? Does this also hold in a continuous context?", "label": 0}
+{"snippet": "In Information Technology, we often see something that looks like a compound adjective, pairing a number and a noum. Some examples are two-factor authentication, two-step verification and twelve-factor app. I always found it amusing that the noun itself is not plural. Why isn't it named, for example, \"two-factors authentication?\" Is there a rule for that construct? If so, what's its name? (My theory is that it probably came from multi-factor authentication, for example, in which there is some sense in the format, but I don't know for sure.)", "label": 0}
+{"snippet": "I have the simplistic image of a photon being a disturbance in the photon field caused by the loss of energy of an electron. In this image, I see that the disturbance is essentially a harmonic oscillation and it 'traces out a wave' as it propagates through the field. Also, given this image, it seems that the 'larger' the amplitude of this disturbance, the longer the wavelength and thus the 'lesser' the energy of the photon. This seems counterintuitive. Alternatively, is the 'amplitude' of the disturbance the same for all photons?", "label": 0}
+{"snippet": "While writing a fantasy narration I created this sentence: High among the clouds a castle floated. My American friend tells me it sounds bad to a native ear. I think he sees a problem with the unusual word order. At the same time the Hobbit starts with: In a hole in the ground there lived a hobbit. ...which seems a similar sentence. What is the science behind the word order in an English sentence? UPDATE: The original sentence was actually High among the clouds a castle floated, disregarding the force of gravity. I removed the ending phrase to simplify the problem, but from some of the responses I infer that the phrase may actually matter.", "label": 0}
+{"snippet": "I was just studying statics when I realized that a body can be in both static or dynamic equilibrium at the same time but I am not so sure. My textbook says that an object at rest is in static equilibrium while an object moving with zero acceleration i.e constant velocity is in dynamic equilibrium But.... Motion is relative so if two objects were moving with the same uniform velocity, they would be at rest relative to one another and therefore be at static equilibrium but since they are in motion relative to someone outside the system so they should be in dynamic equilibrium. Can anyone confirm this?", "label": 0}
+{"snippet": "A noon cannon usually has a single convex lens which focuses sunlight onto a fuse. The cannon contains gunpowder. The fuse ignites and the gun discharges at noon. https://en.wikipedia.org/wiki/Sundial_cannon A query has arisen about a noon cannon with TWO lenses -- what is the benefit of having two lenses? Does it provide more heat to ignite the fuse? The noon cannon with two lenses might be larger than usual, therefore needing a lens with a longer focal length. Images below. Thank you for any suggestions. I know quite a lot about sundials but I am not a physicist.", "label": 0}
+{"snippet": "I'm using CircuiTikZ and I came across this issue frequently: every time I want to tweak some options using tikzset, there is no documentation for the available key-value pairs. For example, if I want to change the voltage direction, in the documentation, only value (i.e., RPvoltages) is provided. However, I prefer to use key-value pair in my code for future reference so I was wondering how can I find the respective key name given value name or the other way around.", "label": 0}
+{"snippet": "Sorry if this sounds like a silly question, but what would happen if a scientist observes Schrodinger's cat alive, but is then thrown into a black hole before he has leaked any information to the environment. Then later a second scientist observes the cat - can he observe it as dead this time, since the first scientist and his information can't leave the black hole to contradict? That is, is a wavefunction allowed to show two different faces to two observers so long as they are never allowed to compare notes because of an event horizon? Is exiling information behind an event horizon the same as erasing it?", "label": 0}
+{"snippet": "So bound states have continuous position representation, yet countable discrete energy levels. Doesn't this imply that one of the following operations is invalid: <x|> or <E|>. Because |> cannot simultaneously have countable and uncountable number of elements. And the number of elements in the bra and the ket need to match otherwise the operation doesn't make sense. The ket |> exists independently of whatever representation we choose. So what's going on here?", "label": 0}
+{"snippet": "There are a couple of sentences: The water froze and caused the pipe to burst. If it is a succession of past events it should be Past Simple. But if the first part happened earlier, it should be : The water had frozen and caused the pipe to burst.So, can it be Past Perfect, or this sentence must be written in Past Simple? Year by year the population of the West increased. Should it be increased (Past Simple) or was increasing(Past Continuous) ? Because, I guess, Past Simple does not belong here . I don't know which tense to choose. There is no extra context, just sentences on their own.", "label": 0}
+{"snippet": "Suppose a piston enclosing an amount of air-fuel mixture and then this piston compresses the mixture to the point of auto ignition, if every part of the mixture ignite simultaneously is it safe to say that there isn't a flame front because it can't move because there is no longer a combustible mixture? If there is a flame front are they multiple flame fronts? Also if my reasoning is correct does that type of combustion have a name?", "label": 0}
+{"snippet": "In Arabic, the idiom \"You made my neck as small as a sesame seed\" is used to mean that someone related to you or a friend, put you in an embarassing situation with others. This idiom is usually used by parents when their children make them anything but proud. People who have long necks are assumed to be proud; hence, 'a neck as small as a sesame seed' in this idiom. Is there an idiom anywhere close to this meaning in English?", "label": 0}
+{"snippet": "I am currently reading electrodynamics from Feynman. When talking about the energy of the electromagnetic fields, he says that the location of the field energy could be known at least theoretically since all energy is a source of gravitational attraction, and if we could measure the gravitational attraction we could comment on the location of the energy in the fields. I have come across formulations where gravitational field is associated with an energy density and is said to be always negative. I wanted to know whether this energy can have an associated gravitational field.", "label": 0}
+{"snippet": "Suppose that, in a homogeneous linear system, the coefficients of one of the unknowns are all equal to zero. Show that the system has a nontrivial solution. Attempt: Note that the rank must be less than or equal to the number of columns in the coefficient matrix. If we had all columns of the augmented matrix different from zero, then, after being reduced to row-echelon form, we would have at most rank = number of columns. As we have a null column, then surely the rank is less than the number of columns. Therefore, we will have at least one free variable. Am I right? Furthermore, is there any way the solution could be more formal than that? (using the same approach)", "label": 0}
+{"snippet": "What comes after \"pair\"? Maybe \"quad\" for four? In cards it's \"three/four of a kind\" but what about contexts beyond cards (like science)? For example, in physics there's a \"pair-flip model,\" but what is the extension of this model to flipping three things? I've also tried the internet, see also: https://en.wikipedia.org/wiki/Tuple Not to be confused with: single, duo, trio, quartet, quintet, ... monad, dyad, triad, tetrad, ... single, couple, triple, quadruple, ... single, twin, triplet, quadruplet, ... Or does \"pair\" secretly belong in one or more of the categories above? Or is it just an isolated word for, e.g., trousers? Thanks for helping me solve this mystery!", "label": 0}
+{"snippet": "There's a word people around me used to use a lot, phonetically it would spell 'stercus' or 'stircus', I think. It was used in a context meaning excitable, frenzied, frenetic, that kind of thing. Like, you could say that: Kids who eat lots of sugar tend to go stercus. I don't know if it's an actual word and I can't find it because I'm butchering the spelling or misremembering how it was said. I'm a native speaker from Australia, if that helps.", "label": 0}
+{"snippet": "In the double slit experiment, an interaction with a detecting mechanism is needed to know which slit was the one the photon or electron passed through. I read in other questions that polarized filters are placed in the slits, how is it exactly that this helps us know which slit the photon passed through? Do experiments using electrons also use polarized filters? If not, what do they use and how does it work? Are there other types of detecting devices? Is there a detecting device that truly does not change any properties of the photon or electron when interacting with it?", "label": 0}
+{"snippet": "I am using sagemath to compute Einstein tensors of a non-standard spacetime. The output is something horrid and non-diagonal. I need to find the Eigenvalues of this tensor... which is represented as a symbolic matrix. This is proving to be non-trivial with the sagemath documentation. Is there a way to convert my tensor output into a matrix that sagemath can find the eigenvalues for? If a worked example is required, please let me know as I can provide an update easily. Thanks in advance...", "label": 0}
+{"snippet": "uh I'm curious again regarding the theories of reflection. This is known that Metals contain free electrons that absorb energy and vibrate when they come in contact with light. Later, they release the energy back in the form of light. But what if we polish a transparent conductive oxide glass (transparent glass which is electrically conductive). It doesn't seem to be acting like a mirror. So is it really just the electrons which decide the reflection? Do correct me if I'm wrong. I'm just a stupid kid :) My previous post", "label": 0}
+{"snippet": "I know for abelian group, there is a Kronecker decomposition theorem. It said any finite abelian group can be factored as direct sum of cyclic group of prime power order. I want to know is there anything similar with this for the abelian semigroup with identity? As for semigroup, we don't need the inversion, so it seems like it can also support some kind f factorization.", "label": 0}
+{"snippet": "When a spinning top slowly advances and hit a surface (a wall), intuitively one would expect that the top gets bounced mostly along the wall, due to the friction between the top and the wall. But the observed phenomenon is that the top gets bounced mostly in the norm direction of the wall, and in a much higher velocity than when it hits the wall.", "label": 0}
+{"snippet": "Looking for alternative to \"opened a can of worms\" in the following sentence... It needs to be graphical enough for a young readership to grasp, a readership that won't have heard of Pandora's box or even know what a can of worms is. Having fixed one friend's laptop I wondered if I may have opened a can of worms and now all my friends will expect the same service. Any suggestions?", "label": 0}
+{"snippet": "I have read a book saying that \"... backward induction cannot be applied to games of imperfect or incomplete information because this entails cutting through non-singleton information sets.\" However, in another textbook, it says that backward induction can be applied to games of imperfect information, and we can derive the equilibrium by starting at a historical point and show the subgame perfect equilibrium in that subgame is a equilibrium in the Nash equilibrium. I wonder what are the contexts to use backward induction in a game with imperfect information but complete information?", "label": 0}
+{"snippet": "From what I know, current flows across two points only if there is some potential difference across those two points. If that is the case, why does the current flow through a wire then? See the picture for clarity: As one can see, the potential is same on the left side of the wire. The current should not flow, yet it still does. Why?(I have the same question if the resistor was replaced by a capacitor.)", "label": 0}
+{"snippet": "I know that electric current is a scalar quantity and hence it should not follow vector addition. But I have read that equal currents in opposite directions will cancel out each other so is this kind of addition not a kind of vector addition?... where while adding we are including their directions also. So please explain that even when current doesn't follow vector addition then why the currents which are equal and opposite in direction will cancel out each other?", "label": 0}
+{"snippet": "Is it possible to arrange a set of massive objects such as stars in orbit around a black hole such that objects of lesser mass cannot physically reach and fall into the event horizon of the black hole? This could be similar to how Jupiter may protect the Earth from long period comets. In other words, could there be several star systems with the black hole in their center, such that any possible object on approach to the black hole would be gravitationally deflected away from the black hole?", "label": 0}
+{"snippet": "I need to find the X-coordinate of a vertex in a right triangle. It's been a while since I used trigonometry and I can't seem to wrap my head around it. Image with coordinates The Y-coordinate is always the same as the Y-coordinate of the vertex on the left, under the radius. I've tried using line intersection, but I don't know how to use that here since I don't know where to put the X coordinate of the diagonal line. What method can I use to solve this?", "label": 0}
+{"snippet": "We know that the Mandelbrot fractal contains a countable number of copies of itself. See : Does the Mandelbrot fractal contain countably or uncountably many copies of itself? Where that is explained. Notice that polynomials have a finite amount of zero's and entire functions have a countable amount of zero's. So I started to wonder : Is there a Julia fractal that contains uncountable many copies of itself ? And if so, can they be iterations of entire functions ? What are typical examples ?", "label": 0}
+{"snippet": "During the recent merger of two Neutron stars the lead up to the merger was detected as gravitation waves. This was the merger of two spinning bodies that had very strong magnetic fields and they were orbiting each other. How sure is the community of physicists that the signals detected were not ULF radio waves? Radio waves would have had the same frequency and arrived within the same time frame.", "label": 0}
+{"snippet": "I am not sure why, but when I am working on a multi-file project in TeX with a latexmain file, the compiler included with VIM-LaTeX does not compile multiple times to include newly added citations in my bibliography. This only occurs for multi-file projects. If I work on a project that has only one TeX file the file is compiled multiple times to include new citations. Does anyone have any clue what may be causing this?", "label": 0}
+{"snippet": "Take these sentences: I felt he was mean to do that. We'd be stupid to do something like that. I feel like the \"to do that\" part in them functions differently syntactically than in sentences like \"It is mean to do that\" where \"to do that\" seems to be an infinitive clause functioning as the subject. Is \"to do that\" a complement to the adjectives \"mean\"/\"stupid\"? Comparing \"he was mean to do that\" and \"he was mean for doing that\", I think semantically the two sentences seem close but still different, but I can't put my finger on how exactly they are different in meaning. So how are they different? Also do \"to do that\" and \"for doing that\" function the same way syntactically? Are they both complements?", "label": 0}
+{"snippet": "In general, knowing the mass distribution of two colliding objects and the exact point of contact, how would one take into account angular motion in the analysis of the dynamics of the individual mechanical energy of the objects and the total energy of the mechanical system? That is, each object may be rotating about it's own axis and in addition moving with some linear momentum. I've looked through my mechanics notes, but I don't quite think I know what happens. Around which point is there going to be torque? Or some angular impulse, I guess. Thanks!", "label": 0}
+{"snippet": "I'm looking for some interesting operators for which I can find invariant subspaces by hand. As most subspaces had some connections to eigenvectors, I'm currently searching for \"non-trivial\" / interesting (linear) bounded operators on Banach spaces, preferably Hilbert spaces, which do not have any eigenvalues. I know about Volterra and multiplication operators but I can't seem to come up with any of my own. In regards to Lomonosov's theorem, operators without eigenvalues, which commute with compact operators would be even better.", "label": 0}
+{"snippet": "When I jump off of something, even with eyes closed I can be pretty certain that I'm falling due to the associated sensation of falling. However, as gravity should be affecting each of my internal organs equally, surely the sensation must be due only to the air resistance, which causes my outer body to accelerate slower than my organs? As a follow up, assuming the above is correct, would the best way to minimise the sensation of falling be to keep as narrow a profile as possible I.e. keep pencil shape rather than spread arms and legs out flat?", "label": 0}
+{"snippet": "Take a cupboard or just a large wooden box. When pushed it a point above its center of mass, the cupboard topples because there is a net torque due to the friction and the force you apply. When pushed at a point below the center of mass, the cupboard does not as the torque due to the friction and the torque due to the force you apply are in opposite directions (they cancel). Now my question is if the force you apply is equal to the maximum value of static friction, then the box is at rest. However, since the friction applied is at a larger distance from the center of mass than your force, shouldn't there be a net torque?", "label": 0}
+{"snippet": "I asked a similar question before, but it did not give the answer I was looking for, so I will clarify what I actually want in this question. H. Andreka created a formal first-order logic theory that was meant to axiomatize special relativity. I very much enjoyed reading his paper and other papers that axiomatized special relativity. However, I have yet to find a similar text for Newtonian mechanics. What I am looking for is a paper or papers that give a formal first-order theory that axiomatize Newtonian mechanics.", "label": 0}
+{"snippet": "I am reading about monoidal categories and I am not able to think of categories which are non-monoidal. Am I thinking in the wrong direction? Is being monoidal, an additional property like topology? For example, given a set you define a topology on it making it a topological space. Similarly, given a category, you define a tensor product map making it into a monoidal category? Also, given a category does product of two objects from that category always exist? ( I know about the uniqueness but I am not sure about existence). If yes, can a map sending two objects to their product be considered as a tensor product map?", "label": 0}
+{"snippet": "Are all wormholes gravitational instantons in the context of General Relativity? My question concerns also the topology of spacetime in such case. A full Wick rotation of the metric, seems to change the geometry from that of Pseudo-Riemannian to Riemannian one. So given that topology of the Pseudo-Riemannian manifold in most general case does not match the topology with respect to the Riemannian metric, I want to know in the case of gravitational instantons, how is this situation interpreted? There's a Euclidean hole, but there's no Lorenzian hole at the same time?", "label": 0}
+{"snippet": "I was wondering how one might write down an expression which estimates the force experienced if a person were to be hit by a tidal wave (perhaps assuming the person could be modelled as a sphere). I guess you could also use Wagner theory to find the instantaneous force on impact, but this becomes complicated. I assume that similar to the analytic expression for Stokes drag for a low Reynolds number flow the force would depend on the viscosity and speed of the liquid, since being hit with water would not be as bad as being hit with a more viscous liquid.", "label": 0}
+{"snippet": "I was looking at my bathroom tiles, which were an interesting sort of repeating pattern of different squares and rectangles, and wondering how to model them as a recursion formula. Does anyone know any good or interesting books on recursion? Advanced level is fine with me. For my level of background, I just wrapped up Calculus II and am taking up to Calculus IV and Linear Algebra later this year. Also, I come from a software engineering background so I'm familiar with writing recursive graphics, but I feel like the way I write it is not that elegant and sophisticated. Thank you!", "label": 0}
+{"snippet": "I am currently studying the Lagrangian mechanics, and as far as I've understood, forces of constraint are the forces that are perpendicular to the surface of the movement of the object, thus do not cause any change in the velocity of, and constrain the trajectory of the object, (e.g. force due to the tension, the normal force). The magnetic Lorentz force fulfills all of those I mentioned above, so is it also a type of force of constraint?", "label": 0}
+{"snippet": "TLDR: Do observations of larger galaxies favour 'cuspy' dark matter halo distributions, as predicted by N-body simulations? I've been trying to understand the 'core-cusp' problem for dark matter halos and I understand that observations of dwarf galaxies don't agree with the results of N-body CDM simulations. What I don't understand is that, can it be taken by implication that larger galaxies do agree with these simulations, and if so, is there an expected 'cut-off' in terms of mass or radius where one would only expect to observe a 'cuspy' profile?", "label": 0}
+{"snippet": "The class of Eberlein compacts (those compacts spaces homeomorphic to a weakly compact subset of a Banach space) is well known and well studied; one of the many properties it enjoys is that every set in this class is also sequentially compact, thanks to Eberlein-Smulian. This led me to wonder: Eberlein-Smulian also holds in greater generality than for Banach spaces (as long as the Mackey topology in the space in question is quasicomplete, for example, the result holds). What is then known about the class of compact spaces that are homeomorphic to a weakly compact subset of, say, a Mackey quasicomplete space? Does it coincide with the class of Eberlein compacta?", "label": 0}
+{"snippet": "I am recently studying some chiral algebra from physics perspective. I found many chiral algebras have nice coset realization of current algebra. However, most of the literatures are very algebraic. And I have questions about the generators of chiral algebra at the level of OPE. One confusing thing for me is that many fermionic generators can appear in the coset construction. This is counter-intuitive to me as the current algebra generators are all bosonic. Is there a way to understand this?", "label": 0}
+{"snippet": "I mean open up a book on QFT and I know things like path integrals still don't have a fully worked formalism but then you see Fourier transforms and residues from complex analysis being applied to integrals of \"field operators\". I don't mean the functional analysis of quantum mechanics, I mean mathematically speaking are field operators as studied under functional analysis? Or do they need another formalism. Maybe there is no formalism and it is just hoped there is some way that the math works right and that it makes sense.", "label": 0}
+{"snippet": "Once an entangled particle is measured, it's wave function collapses. From my understanding, any sort of information exchanged to the particles can be considered a mistaken measurement. So how do researchers entangle particles, move them apart and then measure them? I assume they are held in vacuum and are maintained within a specified volume of space through magnetic confinement, but I would think that the magnetic fields holding them would also consequentially be a measurement on them. So I am at a loss as how they keep them entangled until an actual measurement is performed. I assume it's because my understanding of what is considered a measurement is flawed since I've read that even energy can be delivered to entangled particles even without collapsing their wave functions.", "label": 0}
+{"snippet": "In Birrell and Davies, the author says in the Introduction that If the gravitational field is treated as a small perturbation, and attempts are made to quantize it along the lines of quantum electrodynamics (Q.E.D.), then the square of the Planck length appears in the role of coupling constant. But why does the square of the Planck length comes in as a coupling constant here? How does one determine what the coupling constant should be?", "label": 0}
+{"snippet": "He promised that he will help me with my homework. He promised [that] he would help me with my homework. Which sentence is grammatically correct? I saw this debate and I genuinely don't know the answer since English isn't my first language. But I feel like the second sentence is more pleasing to hear. Can someone help? If you have an answer can I know why that was your answer?", "label": 0}
+{"snippet": "Could the following sentence be considered correct when comparing two or more subjects? It's visually more distinct. I'm aware that you can rewrite the sentence like this: It's, visually, more distinct. But, the pauses feel unnatural. There's also: It's more visually distinct. This just feels wrong, even if it's technically not. And lastly: It's more distinct, visually. However, 'distinct' can be ambiguous; so, I'd rather have the adjective 'visually' come before it. I'd also be interested in if there's a particular rule I can read more about that determines whether the first use ('visually more distinct') is correct or not.", "label": 0}
+{"snippet": "I usually have trouble trying to read huge tomes without any proper motivation - there's no feeling that I'm \"working\" towards something. Perhaps I've been spoiled by \"Abel's Theorem through Problems and Solutions\" by V.B Alekseev which builds up group theory solely to prove the insolubility of the quintic, but it was nice knowing there was something \"big\" at the end of it all. I'm looking for books in a similar vein, that might focus on a single question and build a story around it.", "label": 0}
+{"snippet": "Can any periodic set of integers be realized as the zero-set of a linear recurrence relation? It's stated on the OEIS page for eventually periodic sequences that \"all eventually periodic sequences with period N are linear recurrence relations of order at most N\" but if you interpret \"are linear recurrence relations\" as being the zero set of a linear recurrence relation this statement can't be true because Skolem-Mahler-Lech gives a stronger characterization than just eventually periodic (the zero-set must include every earlier member of the residue classes in the periodic part too). At the moment I don't see an obvious way to do it for periodic sets and can't find any other mention online", "label": 0}
+{"snippet": "I have a question pertaining to Penrose's ideas about cyclic cosmology. As predicted therein, the end of each cycle comes about when massive particles are extinct and time is no longer measured. What I don't understand is why this state is not an eternal one; what could possibly give rise to a new period of inflation, is it that energy is somehow bound in time as a dimension?", "label": 0}
+{"snippet": "Imagine a permanent magnet suspended in the air with an iron disc below it. Inbetween these a thick aluminium barrier. Attached to the disc at an angle is an air spring (or air shock). The magnet attracts the disc which hits the barrier but some of the force is absorbed by the air spring. The equation of the force the magnet produces is non-linear as it depends on displacement. The equation for the force the air spring absorbs is also non-linear because it depends on compression. How can I combine the two equations and any others necessary to find the force the barrier experiences?", "label": 0}
+{"snippet": "Can someone please reconcile the difference between the two common integrals below? They are almost identical except what's inside the natural log function. The denominator signs are switched depending on whether it's the variable x or u. I understand u represents a function where as x represents a variable but I'm not sure how it affects the outcome within the natural log function. Please explain Two similar common integrals", "label": 0}
+{"snippet": "Length of a curve can be defined for an arbitrary rectifiable curve(even in an arbitrary metric space). As is shown in this answer we can define line integral over any such curve(even in an arbitrary metric space). When it comes to surfaces and higher-dimensional cases it seems that there are no constructions of such generality. Wherever \"surface area\" and \"surface integrals\" are defined, some kind of smoothness is required for the surface in question. Are there any definitions of \"n-dimensional surface area\" and \"n-dimensional surface integral\"(which resemble the definitions of length and line integral over an arbitrary rectifiable curve) with much weaker conditions on the \"surface\" (in the same way as \"being rectifiable\" is weaker than \"being smooth\" for a curve) ?", "label": 0}
+{"snippet": "For me it is counter-intuitive: I should be hearing more low frequency sounds (bass) at a greater distance from a headphone speaker (like I hear only the bass when standing outside a club), because the bass travels further and high frequency sounds get absorbed easier on the way to the ear. But of course it sounds like the bass is completely absent when headphones are located far from the ear, and it sounds like only the very high frequency sounds survive. What is the physics behind this - why do headphones sound more 'tinny' when distance from the ear is increased?", "label": 0}
+{"snippet": "According to me we will apply a force on the charge and it will do a certain displacement to reach that point from infinity where we wanted to bring it and at that point there is no electric field. But still we applied force and displacement also occurred therefore work done should not be zero. Please explain me the concept and please tell me where am i going wrong?", "label": 0}
+{"snippet": "There's an idiom in Argentina translated roughly as \"to sleep someone\" (dormir a alguien), which is used when someone frustrates the plans of someone else by taking what the other person wanted in the first place and who obtains the benefit knows it. This may cover different situations, for example: If you walk ahead in the street to hail the taxi another person was about to hail. If you start dating someone another person you know was eager to ask for a date and you knew it. If you take the last slice of a pizza someone who went for a drink said was going to take. I'm looking for an idiom in English which describes this kind of behavior or situations.", "label": 0}
+{"snippet": "I am having a partcular issue with several pairs of glasses and wish to understand the physics of it. The problem is that the right arm of the frame is too tight against my temple, and at the same time the left nosepad is too tight on my nose. This seems rather unintuitive at first, as one might think if the right arm is too tight, then so should the right nosepad. My grasp of physics is poor but I think I can begin to see why this is not the case, and that the law that every action has an equal and opposite reaction might be applied. Any help with this would be greatly appreciated. I have taken them to an optometrists who were puzzled.", "label": 0}
+{"snippet": "There are many wonderful illustrations of parametric curves with b-splines and control points, but I mostly use splines for uni-variate functions. So I have a vector of control values, but not really points--at least not ones I can easily plot. If we take the three examples in the definition section of the wikipedia article on B-Splines: https://en.wikipedia.org/wiki/B-spline How could I determine the control point positions in each example in order to visualize them on the graphs?", "label": 0}
+{"snippet": "tl;dr If I'd introduce you to someone with \"Say hi to my cousin Harry.\", would you be surprised to later learn that it's my seventh second cousin twice removed because I used the word cousin and not specified it's not my first cousin? I'm used to using it one way, and someone else (also a native English speaker) uses it the other way. So I searched and found conflicting answers here and here. So are there really two customs, or is one of the sources wrong? Obviously \"cousin\" can mean second cousin as in the expression \"second cousin\". But what about when used without any qualifiers, such as \"my cousin said\", can that mean second cousin or not?", "label": 0}
+{"snippet": "As you know, it is expected that the velocity of stars and gas should slow down the further they are from a galaxy's center. However, in many cases, it does not slow down as expected, and this discrepancy is often attributed to the presence of dark matter. How can I obtain the expected radius - velocity plot for certain galaxies? What informations or data should I have about those galaxies to plot it? Can you provide me some links about it? I need to plot the observed rotation cuves and expected ones like in the image that Ihave added to this post .", "label": 0}
+{"snippet": "Let's assume that I have an ideal conductor(straight wire(, as we know that potential at any point on the ideal conductor is the same, if i place that ideal conductor in a region where magnetic field is increasing, so according to faradays law a potential difference will exist across the ends of the conductor, but how is that possible if we know that for an ideal conductor potential at any point is the same", "label": 0}
+{"snippet": "I have heard one meaning of it in the context of a personal goal is to set a too-easy goal (i.e., that you know you can easily achieve). I also heard it is coming from golf. Can someone shed more light on this? To be clear, I was not referring to computer science or computing area where it means to separate a piece of software on a computer system so it can only use particular programs, files, etc. Thanks!", "label": 0}
+{"snippet": "It's a very general question. Black hole paradox is an interesting problem but why is it something that physicists are so worried about? As neither can it be directly experimentally tested nor do I see any indirect proof of it, then what relevance does it have? I might have upset some of folks here, but I've got no hard feelings here. But as far as I've seen, people doing Quantum Gravity or related fields, always have their eyes on this paradox. I'm just curious to know why is it so important?", "label": 0}
+{"snippet": "This question is with regards to a polarimetric approach in analysing the concentration of a substance in solution such as sugar in water. I have been trying to find an answer to it through a little browsing but I could not really find anything useful. Most websites and books use dm for path-length of the solution in dm and concentration of the solution in g/ml. Why is this done? Why wasn't specific optical rotation of a substance in solution defined in terms of S.I. units rather than an awkward combination of c.g.s and other units?", "label": 0}
+{"snippet": "I was told that this sentence is so wrong, and after reading some related threads here, I now understand that \"earlier\" should be used with past tense. So is it okay if I change the sentence to \"As Puss has told them to, they all say the Marquis.\" Is this sentence natural? It's from a simplified reader \"Puss in Boots\". The context is that Puss shows the King around, making him believe that his master, Henry, is an important man. He tells the king that Henry is a Marquis. He also asks some people to lie to the king, having them say that they all work for the Marquis.", "label": 0}
+{"snippet": "From a Library of Congress article about Freud: ...patients tended to perform for the camera and doctors to record the most photogenic. This sentence seems to reuse the verb tended between the subjects patients and doctors. I think this is an instance of gapping. I have seen it in simpler cases like: Alice cooked the rice, and Bob the beans. I can't imagine anyone speaking like this casually, but it feels OK in writing. However, the more complex Freud sentence feels wrong. Is it? The object of the reused verb is an infinitive instead of a plain noun -- is that the problem? Or maybe that \"tended to ____\" behaves like a single compound verb, and the tended part cannot be reused?", "label": 0}
+{"snippet": "What is the subject of \"making\" in the following sentence? It seems that it is the most reasonable grammatically to think \"Yakkleman Skin Care\" is the hidden subject of making. This is because the subject of the participle needs to agree with the subject of the main clause grammatically. Yakkleman Skin Care has signed a deal with NutriSpark Online Shopping, making them the only retailer with access to our products. If \"Yakkleman Skin Care has signed a deal with NutriSpark Online Shopping\" is the subject of making, \"making ---\" seems to be a dangling participle. If so, is this kind of usage of participles treated as correct in authoritative English grammar books?", "label": 0}
+{"snippet": "In Continuous Variable -Quantum Key Distribution (CVQKD), usually Gaussian modulated coherent states are sent. This means both quadratures of a coherent state are chosen from two normal distribution. So do we can prepare a state with well-known quadratures on the phase space? My main question is, how someone can successfully create a coherent state with exactly well-known phase and amplitude quadratures. I think even if experimental devices are perfect, he/she can not make a quantum state with exact known quadratures. I think making quantum coherent states is limited by the Heisenberg uncertainty. Am I right? In other words, do these uncertainties happened not only during measurement but also during state preparation? Sorry if my question is simple but I really need to learn it.", "label": 0}
+{"snippet": "I have finished some courses on analytic number theory and wanted to learn about versions of Goldbach so I can pick a topic for my master thesis. I have seen a proof for an asymptotic formula for the tenary Goldbach conjecture in the lecture. I can not find the paper where the version of Goldbach for a prime and an almost prime was proven.I hope someone here can help.", "label": 0}
+{"snippet": "Gravitational waves have been very much in the news recently and I would like to understand them better. I know vaguely that they cause transverse changes to the geometry of matter as they pass by. For many classical wave systems there are integral solutions to the IVP for small disturbances, showing how the wave is driven by gradients, divergences and curls in the initial fields. Are there similar formulas for gravitational waves?", "label": 0}
+{"snippet": "As we all know, Subatomic particles show dual-nature when observed but why? why does this happen? also I am genuinely confused as to how does the particle know when to change its nature, I mean i know that it changes when it gets observed(detected by a detector) But how does it know that it is being detected and now it has to change its nature", "label": 0}
+{"snippet": "I am working on a non-linear optimization problem, containing bounds and constraints for the variables. Very complex problem involving networks and logical functions. I have been switching a tool from the Matlab language in which I originally implemented it, to Python. In the Matlab version, I used the 'interior-point' method of estimating the Hessian to perform gradient descent. I tested several options for the function scipy.minimize(), and the best result is obtained for the Nedler-Mead method. I read the paper but it seems that this method cannot incorporate bounds and constraints directly. I would like to understand exactly what it does with my constraints before I set up to use this method in the research project. Thanks in advance", "label": 0}
+{"snippet": "As a keen fan of Terry Pratchett and Jasper Fforde, I'm fascinated with words that logically should exist, but don't. A subset of these are referred to as \"lost positives\", such as \"ebriated\" referring to someone who is sober. However, there are other types of theoretical words, such as ones where you apply a prefix which isn't normally used, such as \"postcarious\", which logically means the unfortunate consequence of something being left in a precarious state. Is there a word/phrase which is used for these words which only exist in theoretical word-space (preferably in British English)?", "label": 0}
+{"snippet": "A superfluid has a property that makes it creep up the walls of its container and escape it until it's empty. How is it possible that the fluid performs work (against the force of gravity)? I can imagine setting it up so that after dripping to the larger container, there is an indentation on the ceiling so that when it climbs the larger container, it drips back to the smaller one, and keeps moving in a loop. Is it possible?", "label": 0}
+{"snippet": "We know that the comoving Hubble radius decreases during inflation when the universe is exponentially expanding and then increases during matter and radius domination. What is the reason behind this? I can see it mathematically. However, intuitively it's not so obvious. The universe is expanding during both the eras, accelerating during one while decelerating during the other, but expanding. I would imagine the Hubble radius decreasing during both since if the universe expands light (and causal physics) would have difficult keeping up.", "label": 0}
+{"snippet": "For a quadratic polynomial the polynomial discriminant appears in the quadratic formula however, I found this was not the case for cubic and quartic polynomials. The expressions used in the cubic and quartic formulae are different from the polynomial discriminants or at least they seem different to me. So is it just a coincidence that the polynomial discriminant of a quadratic polynomial appears in the quadratic formula or I have made a mistake somewhere and an alternate form of the discriminant is used in the cubic and quartic formulae. If the discriminants do exist in the cubic and quartic formulae then, is there a relation between them.", "label": 0}
+{"snippet": "Does one pee-pee with his wee-wee, or does he wee-wee with his pee-pee? Is one phrasing more typical than the other? That is to say: How is pee-pee used more commonly- as \"to urinate\" or as \"penis\"? And vice-versa for wee-wee. I'm curious if there are widespread or regional customs. Both are informally correct in American English. Pee-pee and wee-wee are both used as nouns/verbs for urination (\"I went pee-pee\", \"He pee-peed next to the wall\") and both are used as euphemisms to refer to the penis. This likely doesn't apply to UK or Australian English, at least based on this post about \"pee\" vs. \"wee\" and part of speech.", "label": 0}
+{"snippet": "My question may seem CS-related at first, but it's essentially mathematical, so, please, bear with me. I'm doing Neural Architecture Search (NAS) by varying the number of layers and neurons per layer for a neural network (connections are feed-forward, throughout), and then training it on a fixed task to test its performance. The end goal is to perform topological data analysis (TDA) on the best and worst architectures (graphs) to spot the persistent structures in a good/bad architecture. My question is: am I right in my assumption that TDA could spot such persistent structures? If so, which metric should I use? Just the connection weights? P.S.: My background in (computational) topology is quite minimal.", "label": 0}
+{"snippet": "I am a graduate student studying wireless perception, and recently I want to carry out liquid recognition. I want to use a speaker as a sound source to generate vibrations (by playing sounds of different frequencies). My idea is that different liquids have different resonant frequencies. When the frequency of the external force is close to the resonant frequency of the liquid itself, the liquid's The amplitude will be larger, so different liquids can be identified. I would like to ask you if my idea is reliable and can you tell me some theoretical knowledge, such as whether the amount of liquid also affects the resonant frequency?", "label": 0}
+{"snippet": "I have been doing some deeper reading on optics out of my interest and one of the most important differences between ray and Gaussian optics is the existence of a non-zero beam waist when a laser beam is focused using a field lens. Most literatures that I have read go over this fact as if it's a common knowledge, but doesn't exactly over why this phenomenon occurs. I understand that focusing to a single point would result in singularity which is physically impossible, but I was hoping if someone could explain what cause the beam waist behavior. Some literatures attribute it to diffraction, but I don't understand what causes this while a Gaussian beam is propagating in vacuum.", "label": 0}
+{"snippet": "I know it happens when the elements on both sides are identical, the more you remove asperities, the more they become like a single substance. But does this happen to the same extent if I take two different substances and start removing asperities? Or maybe close to that... My textbook doesn't explain much about this, it says \"By making the surfaces extra smooth, frictional force increases as actual area of contact increases and two bodies in contact act like a single body.\" Doesn't say anything about the substances taken. Thanks for your precious time.", "label": 0}
+{"snippet": "An example of a non-associative ring R whose non-zero elements form commutative quasigroup (with regard to multiplication in R) without identity is easy to find. I'm looking for examples of a non-associative ring S whose non-zero elements form a non-commutative quasigroup without unity. Put another way: A non-associative non-commutative division ring without unity. 'division ring' in the spirit of 'ring R (associative or not) whose non-zero elements form non-empty quasigroup by means of multiplication in R'. Can you help me ?", "label": 0}
+{"snippet": "In many (biological and living systems) physics courses I encountered the notion that systems operating far from equilibrium are related with more efficiency with regard to their specific tasks. One example I vaguely remember is the comparison of the energy efficiency of ATP to ADP convertion reaction with the efficiency of combustion engines. Unfortunately, I can not think of many specific examples and can only recall this abstract notion of efficiency of systems far from equilibrium. Could someone break this notion down by using many specific examples of simple physical systems, and in each case clearly defining the notion of far from equilibrium and the notion of efficiency ? You could start with the example I mentioned.", "label": 0}
+{"snippet": "I have a camera that gives Azimuth and Elevation of an object with respect to itself (camera). The camera doesn't send image but Azimuth and Elevation data (in float format). The camera doesn't provide range. Is their a mathematical way for me to calculate the range of the said object using Azimuth and Elevation. I wish to use this data received for camera in sensor fusion algorithm along with LIDAR data. For this I need range of the object.", "label": 0}
+{"snippet": "I am currently studying electromigration in liquid metals. According to studies that have been done for electromigration in liquid metals, the metal ions are affected by the electrostatic force and therefore can move to the cathode/anode. The force that moves the metal atoms to the electrode is affected by the charge of the metal ion. However, my professor told me that in liquid state metal atoms should be neutral/not ionized. So how exactly does an electrostatic field affect the metal atoms or cause atomic movement in this case?", "label": 0}
+{"snippet": "Free space is a region in which there is no matter and no electromagnetic or gravitational field. Which means that the resistance in free space is zero, because there is no resisting force and as far as I know, free space is a synonym for \"vacuum\" and there is no resistive force in a vacuum. So, how is the permittivity of free space, not zero? Permittivity is a property that measures the opposition against an electric field, but there is no resistance in free space, no opposition?", "label": 0}
+{"snippet": "This question relates to the Michelson-Morley experiment and whether anyone has so far proposed an equivalent experiment using aqueous waves instead of optical waves. If it is true that (i) The properties of optical waves and aqueous waves are approximately equivalent and (ii) Nature is consistent in her implementation of traveling waves, then, I believe such an experiment should manifest every characteristic of the Michelson-Morley experiment to some degree of approximation including relativistic effects such as relativity of simultaneity, lorentz contraction and time dilation. Is this a valid assertion? If not, why?", "label": 0}
+{"snippet": "Please forgive me for not having the best grasp on graph theory terminology. I am doing my best. I have a large connected subgraph of a large graph where I want to find, what I am terming the \"weak points,\" of the graph. A \"Weak point\" exists, in my conception, when given a vertex, there exists at least one single edge among the vertex's edges that can be deleted to create two independent distinct subgraphs. Does this character of a vertex have a name? I can imagine if one must delete two edges to create two independent subgrpahs this vertex would be a \"stronger\" vertex. Thanks", "label": 0}
+{"snippet": "In an inelastic collision where mechanical energy is not conserved, momentum is still conserved. Should the Earth or the ground be considered as part of the system in order to account for the conservation of momentum? Since there is friction in a collision, is it appropriate to include the ground as part of the system to analyze the conservation of momentum? Are air particles considered to be a part of this isolated system? To clarify I am specifically talking about two vertically-moving objects colliding.", "label": 0}
+{"snippet": "How does a common base transistor amplify current if a small part of its emitter current gets divided into base current and the rest goes to collector current? If the input signal is applied to the emitter part of the transistor then the output current in the collector part should be less than the input one. Then how is the current amplified where the current flow actually decreases rather than increasing?", "label": 0}
+{"snippet": "Is there a notion of a singularity of a real \"algebraic variety\" which looks locally like a double cone but with a countable infinite number of cones which meet in the same point? A short example or reference would be highly appreciated. I am self-studying algebraic geometry at the moment and the literature/videos do not treat this topic and I am lacking the necessary intuition.", "label": 0}
+{"snippet": "I am very confused about this, are they an excited state of a particle where an electron is excited to an upper energy level, which seems less likely to be the case since the resonant states of particles have different names; or are they the constructive interferences of the wave functions of two different particles, which again doesn't seem likely since as far as I know, one wave function is used to describe a system of particles instead of different wave functions. I am aware of the question, but the answer there doesn't satisfy me", "label": 0}
+{"snippet": "I am beginner to optimization and my question is fundamental. We all know that Static optimization means the design variables/objective function does not vary with respect to time. Dynamic optimization means the design variables vary with time. I need help in organizing the below algorithms/concepts into static and dynamic optimization categories. Ordinary calculus Dynamic Programming Convex Optimization Tabu Search Lagrange multiplier Genetic Algorithm Calculus of Variations Simulated Annealing Linear/Non-Linear Programming Particle Swarm Optimization Ant Colony Optimization First and Second Order Algorithms", "label": 0}
+{"snippet": "Why doesn't a pressure cooker reach a state of equilibrium where the steam passed is constant (assuming the contents of the cooker are maintained throughout the cooking process), but rather, it accumulates pressure until it releases it in the form of a whistle every so often? I don't understand why the pressure \"overshoots\" and releases more than what would keep the weight open, and then releases more than is needed for the weight to lower. I suspect this has to do with the static friction which needs to be overcome for the whistle to rise being greater than the dynamic friction, or something along those lines.", "label": 0}
+{"snippet": "As the title says, I'm trying to determine numerically when an n-DOF oscillating system (linear or nonlinear) subjected to forced base oscillation reaches the steady state solution. Is there an energy component (or another global parameter) that converges to a single value when the steady state is reached? I have the time series of the position and velocity of every mass and the base oscillation.", "label": 0}
+{"snippet": "Recently while experimenting with force experienced by current carrying conductor, I came across a abnormality in the horse shoe magnet, due to which the direction of force on the current carrying conductor by the Flemings Left Hand Rule was false. I noticed that when i kept a compass near the heads of the horse shoe magnet, the needle pointed from North Pole to South Pole of the magnet. But when it was kept between the two hands, it pointed from South Pole to North Pole. I dont think it is theoretically possiblle that magnetic field is going from North to South outside the horse shoe whereas it is going from South to North between the two ends of the horse shoe. Please explain this.", "label": 0}
+{"snippet": "There are certain complex functions which lack a proper denominator corresponding to which poles can be found for the given function. For example , the gaussian function, the frenel functions are some of the popular functions lacking any denominator, in the complex plane . So , as a result of those function lacking any pole , I am wondering how to evaluate their corresponding improper integrals using contour integration (complex analysis). Is there any way by which a denominator can be generated assuming certain conditions for those functions lacking denominator? I really want to clear the doubt regarding this ...All of yours opinions would be highly appreciabble in my regard. Thanks a lot in advance .", "label": 0}
+{"snippet": "I have a question about degenerate electrons in white dwarfs. So, as far as I know, when the gas contained in stars is compressed so much, the electrons start to fill the lowest energy level and then, for Pauli's Principle, they continue to fill up incresing energy levels up to a certain level. As you can read here http://astro.vaporia.com/start/electrondegeneracy.html, \"During compression, as electrons take on momentum, they gain too much to maintain a nucleus orbit, and they travel freely through the material rather than remain with a single nucleus.\" I did not understand this last statement. Does this mean that the electron become free? Or they are still bounded to the nuclei? Thanks for the answers", "label": 0}
+{"snippet": "It is well known that the method of image charges is not always applicable, so I was wondering: is there an analytic way to calculate the electric potential for a point charge interacting with a perfectly conducting, neutral (edited) metallic disk using image charges? If it can be calculated or not, for what reason? Even if it could be solved, I don't think the method conforms to that of a conducting sphere, so I would like to know (if there is one) an analytical method that would allow it to be calculated.", "label": 0}
+{"snippet": "When a satellite is revolving around a planet with an orbital velocity in presence of air resistance, the satellite's Kinetic Energy keeps on increasing as it falls down. The resistive force is trying to decrease the speed and the gravitational force cannot change the speed (or Kinetic Energy) as it's perpendicular to the velocity. Or, am I wrong and gravity can actually change K.E. even if it's always perpendicular to velocity. In the Free Body Diagram, I see no force acting along the velocity that can increase the speed of the satellite.", "label": 0}
+{"snippet": "I and some classmates are recently teaching ourselves the famous book Foundations of Perturbative QCD by John Collins via a form of regular peer reading group. We find that exercises in this book are really worth working on. But, as a group of relatively junior students, we are hesitating to go deeper before finding a way to verify our answers. One obvious solution must be to consult some more senior researchers. But, other than that we want to know whether there exists a document of solutions to this book, so that at least we can self-verify even if we fail to find such a senior mentor.", "label": 0}
+{"snippet": "The tangent plane at a point of a hyperboloid meets the hyperboloid in the two generators through that point. However, a tangent plane is defined as the locus of all tangent lines at a point on the hyperboloid. Now, since generators lie completely on the surface they can't be tangent lines to the hyperboloid. Then how is it possible that the tangent plane contains the generators that intersect at that point?", "label": 0}
+{"snippet": "What's a safe, easily executable experiment to confirm that quantization of light occurs directly to the retina. We know that light is quantized when projected on to a surface, or on to an inanimate detector, then the surface or the detector observed. An eye can detect a single photon. This means we should be able to quantize light such that a single photon lands on the retina of the left eye or of the right, and the observer confirm it is seen in only one eye. What's a design for this experiment?", "label": 0}
+{"snippet": "From my understanding self-energy is the energy required to put charges in a certain charge distribution and interaction energy is the potential energy caused by the interactions between particles, but to me it seems like there isn't really a big difference between them and this post What does electrostatic self-energy mean? basically talks about them like they are the same thing. My book says the total energy is the sum between the interaction energy and self-energy. I'm very confused.", "label": 0}
+{"snippet": "From what I understand relativity predicts that outside observers would never observe external objects actually crossing into the event horizon, due to time dilation. How does that can reconciled with the fact that the Schwarzschild radius is largely dependent on black hole mass? Then, does this imply that one can never observe an increase in the radius of the event horizon? This seems wrong to me, as there are different size black holes, and I'd like to know what I am missing.", "label": 0}
+{"snippet": "I am trying to say in good quality English that a certain idea which was implemented is currently used way beyond the scope it was intended for. It was a gap-filler which we are now basing our entire solution and this is going to be unsustainable. I am trying to write something like \"This architecture has exceeded it's original ____ and needs major refactoring\" I know there's a word exactly for this... I keep coming up with \"premise\" or \"precinct\" (I know the word I am looking for sounds something like these, not saying they are applicable). I've already used \"purpose\" a lot, in a different context, and I need to avoid using purpose for this statement to prevent confusion.", "label": 0}
+{"snippet": "Suppose a car is at rest and you apply the accelerator, then the wheels are applying a horizontal force on the road so according to Newton's third law an opposite force (friction) pushes you forward. From what I understand no matter how much force you apply (hit the accelerator) the maximum force that can push you forward is the limiting friction. But then since the car is going with an acceleration forward friction should again act backward and there will be no net force, so the car doesn't move. How is this possible?", "label": 0}
+{"snippet": "It's well-known that given a sentence independent of a system of axioms, we can consistently extend the system by appending either the sentence or its negation. However, if a given theorem can be deduced in each of the two systems, then we have a proof of that theorem. We don't even need to prove independence, because given any sentence, either it or its negation is consistent with a given system, provided that the original axiom system is consistent. I'm simply wondering whether there's a specific example of that proof technique having been used.", "label": 0}
+{"snippet": "An observer near the event horizon of a black hole will experience an extremely strong gravitational field. Due to the principle of equivalence, this observer cannot locally distinguish between this strong gravitational field and the experience of being in a highly accelerated frame. As a result, the observer will detect radiation or temperature in the seemingly empty space around them, as predicted by the Unruh effect. This radiation can escape to infinity being near the event horizon not inside the black hole, and is what we refer to as Hawking radiation.", "label": 0}
+{"snippet": "I tried to understand the physical interpretation of uniform continuity, and saw different graphical interpreation in Wikipedia. At the end, I have concluded that functions which are uniform continous in a set, also have finite derivative in all the set and its boundary. Is this interpretation right? I don't want to be rigourous at all, but if you can provide some proff or counterexample, it will be great. Thanks!", "label": 0}
+{"snippet": "Normal measurements of compressive strength work by compressing a sample with an hydraulic press and see when the sample deforms plastically or cracks. Now if pressure is applied on the surfaces of the sample that aren't in contact with the hydraulic press, will the compressive strength (as seen by the hydraulic press) increase ? If yes, will that increase be exactly the external pressure or lower or higher? I feel like the compressive strength as seen by the press must be higher because the pressure on the \"sides\" will prevent the material from going outwards thus deforming or cracking. (Imagine a cylindrical sample is being pressed) Am I missing something ?", "label": 0}
+{"snippet": "I was wondering if someone can explain simply why phase changes are isothermal processes? I am studying hydrology and some of our material about snowmelt has to do with phase changes and in this example, water retains a constant temperature when melting/freezing, or boiling/vaporizing. I was wondering why, as the ice melts, why does the temperature not increase as it is changing phase? I am just wondering if there is a chemical/molecular reason that better explains why the heat energy is no longer warming the ice as it changes phase. Like, is all the energy directed to separating the bonds and cannot go to heating? My background is aerospace/mechanical engineering so I have some thermo experience but the more simple the explanation the better. :)", "label": 0}
+{"snippet": "Consider a piston such that it is in mechanical equilibrium with its surroundings. If I pull the piston (reversible work) then the work done by me would be positive. If I push the piston, again work is done by me. However, in one case positive work is considered to be done on the gas inside piston, while it is negative in the other case. If I pull the piston, negative reversible work will be done on the gas -- does it mean that the gas is working on me? I know that I must be making a mistake, but what?", "label": 0}
+{"snippet": "What are some good entry points into physics? I'm wanting to eventually be able to understand some more abstract concepts like quantum physics but understand that is a very long way away. Just been spending far too long trying to understand things above my pay grade. I'm pretty sure I remember linear algebra being something I should read up on, what are some good books on that subject? What are some other good books that would be entry points? I'm wanting to eventually be able to understand some things like Planck area and a lot of concepts related to entropy. I would consider myself intelligent but not well read as I've slacked on learning since high school. Any help is much appreciated!", "label": 0}
+{"snippet": "I am working through Srednicki's \"Quantum Field Theory\" and am at the chapter on the Minimal Supersymmetric Standard Model (MSSM). In answer to why two higgs superfields are needed in the MSSM model, Srednicki's solutions say that \"...the superpotential cannot depend on hermitian conjugates of [super]fields.\" In trying to think through why this is, the best I could come up with is that any Yukawa term in the superpotential with a hermitian conjugate could either ... make a vector superfield and thus not something that would be in the superpotential and/or it would be a term that wouldn't be holomorphic (though I have to be honest, that my knowledge of holomorphism is very limited and shaky at best).", "label": 0}
+{"snippet": "Using induction on the complexity of formulas, let's assume that in every proper non-empty initial segment of a propositional formula, the number of left parentheses is greater than or equal to the number of right parentheses. Note: A proper initial segment of a propositional formula is an expression that starts and continues with the same symbols as but does not include all symbols of . Any thoughts?", "label": 0}
+{"snippet": "When a capillary tube is inserted into a large body of water, there is an increase in potential energy (PE) of the system. This is because the increase in PE of the rising water in the capillary is greater than the loss of PE of the body of the water. The increase in height of the capillary water is greater than the loss of height of the body of water, and the same mass is involved. Is an empty capillary tube really a source of potential energy?", "label": 0}
+{"snippet": "Simple question, but I can't find any answer around. If a pipe turns, aka is not straight, the length of the pipe (in order to calculate the resonance frequency) is given by the length of the imaginary line connecting the centers of the circular section of the pipe, by an imaginary string of zero width that connects the two extreme of the pipe, or by which other measure? For a straight pipe is easy, but I can't find any information on what happens when it bends. Silly question for the standard here, but I don't know where else to ask Thanks a lot", "label": 0}
+{"snippet": "I've come across the expression \"head(s) and tails above\" (the rest, the competition etc; different from something like \"can't make head or tail of something\" i.e. can't figure it out/understand). I can't find information about this. It seemingly means completely. Could you confirm its meaning and explain it a bit? Is it rare, is this expression recent and is it restricted to or typical of specific regions (Canada?)?", "label": 0}
+{"snippet": "I have been thinking about how physics has evolved since the time of Galileo . Back then physical laws could be describe using axioms which could be comprehended by anyone who reads them. But currently physics is done in a whole different manner. The laws are written mathematically. The language of mathematics is deeply encrypted in the study of physics. For example, the theory of general relativity requires the idea of tensors, black holes are deeply mathematical and so on. I just wanted to know why physics is done using mathematics? Cant it be done without mathematics - for instance, by only doing only experiments?", "label": 0}
+{"snippet": "Vogel's method selects the corresponding variable through a penalty. There is a penalty for each row and column and is the subtraction between the two lowest costs (in absolute value). We must select the highest penalty and then the lowest cost in the row or column of this penalty. I understand the second step (if you want to reduce the cost of the problem, you select the lowest cost of the row or the column), but not the first. I don't understand why we have to do the subtraction between the two lowest costs and, then, select the highest penalty. Can someone tell me what the explanation is?", "label": 0}
+{"snippet": "Does water vapor generate electromagnetic radiation/photons when it condenses into water droplets? I know that gas water molecules need a condensation particle to combine into water droplets. A pair of molecules combine on the surface and in the process transfer their binding energy into the kinetic energy of the condensation particle. Are any photons emitted during this transition? I'm guessing that the answer is no. By analogy, in the gas state a water molecule can be excited into a an unstable radiative state by colliding with an air molecule like nitrogen. Similarly it can be de-exited without radiation by a collision as well.", "label": 0}
+{"snippet": "The twin paradox is resolved as the twin who moves through at least two inertial frames has a shorter worldline (therefore less time elapsed in their frame) than the twin who remains in one. I know the crucial aspect is the multiple frames not the acceleration, since you can have variations of the twin paradox with no acceleration. Besides calculating the proper time for each twin's path, is there a (perhaps more intuitive) reason that changing inertial frames will lower the time elapsed on your watch?", "label": 0}
+{"snippet": "If an isosceles triangle is inscribed in a circle, then is it's altitude always greater than the radius? If yes, then why? My sir said that if an isosceles triangle is inscribed in a circle then its altitude is always greater than the radius and passes through the centre of circle but I don't understand why it is so and is it not possible if any other triangle is possible that is isosceles and has its altitude less than the radius of circle in which it's inscribed.", "label": 0}
+{"snippet": "The question was to transform this sentence from positive to comparative degree: She is not so young as I expected. Following the solutions of other sentences of this kind (the photo shows a similar kind of problem from where I adopted the solution) it can be written that: She is not younger than my expectation. I want to know why ...I expected has been changed to ...my expectation. What is the grammatical rule here? I don't get it what's wrong with ...I expected ? Is it wrong not to use possessive pronoun? The sentence transformation is from the past exam question of my student which she couldn't solve. I am her private tutor and want to teach her the correct things. Please don't misunderstand it as a homework.", "label": 0}
+{"snippet": "In the current approach of QFT, we model the process of creation of a particle (say a photon or a gluon out of a quark) as \"instantaneous\", meaning happening at a moment in time without any neighborhood (modeled via a delta function). To what extent is this an idealization of the real behavior of nature? Do we have any experimental evidence that this process happens with a certain duration? Can nature behave in a way which is more similar to a 'spike' rather than a smearing function? If this process have a certain duration - what properties does a particle has during the time it is 'in the making'?", "label": 0}
+{"snippet": "My teacher gave us the assignment to find the moment of inertia of any shape you want. So I decided to find the moment of inertia of our milky way galaxy. I found out that our galaxy is shaped like a warped disk, not a flat. After I knew about that, I looked for the equation of the Milky Way's shape. But, to me, Nasa's and some high university papers had so many big wards that I could bearly understand what they were talking about(I'm Korean.. ^^). I'm sure that I can understand the equation if I had it, but I just can't find any information about them. I would really appreciate it if someone could tell me what you know about these equations (shape). Thank you!", "label": 0}
+{"snippet": "I've a box with know width (W) and height (H) It has been rotated around an origin point O at a known angle The rotated box is enclosed in a bounding box for which the top-left point (Bx, By) and dimensions (Bw, Bh) are known Given the origin point, the angle, and the resulting bounding box, is it possible to determine the X coordinate of the original box (Ux)? I tried illustrating this in the following diagram.", "label": 0}
+{"snippet": "Hi :) What properties of triangles should I use to solve this problem? I can work out the size of the large triangle and all of its angles, but how do I apply this to the circle? What am I missing? This problem is from the first chapter of a trig book, so the methods needed can't be that advanced. Just need some pointers. Thanks! https://i.stack.imgur.com/BEXKX.jpg", "label": 0}
+{"snippet": "I created my lecture notes using the CambridgeUS theme. My students cannot get the .pdf file to print from Adobe. I tried printing my notes from Adobe on two different printers and I get the following message: \"The document could not be printed, kindly use our help page to troubleshoot.\" Adobe's help page didn't solve my problem. Other pdf files print fine to these same printers, and I have had no issues so it isn't the printers. I have tried every theme in beamer and have no trouble printing the same notes if I use Boatilla or the default theme. Thankfully, I have a work around. However, I am still wondering what I am getting wrong or missing when I use CambridgeUS theme. And advice, insight? TIA.", "label": 0}
+{"snippet": "is there a computable algorithm which lists all the finite subsets of natural numbers ?... i know that such a set is atleast countable... but can't determine if we can list every such subset in a computable manner ..... the set of all infinite sequences of the subsets of natural numbers is obviously uncomputable i think this problem should be computable, since any finite set is computable... but i need some sort of proof or reference , any site etc... thanks", "label": 0}
+{"snippet": "Is the measure of a simple closed curve consisting of two arcs transversal to a foliation equal to the sum of the measures of these arcs? Let A be an arc that is the union of arcs B and C, where arc B is transversal to the foliation and arc C is contained in a leaf of the foliation. Is the measure of arc A equal to the measure of arc B? Is the measure of open arc equal to its closure? Thanks.", "label": 0}
+{"snippet": "what I have been told is that present participles are used in active reduced relative clauses. considering present participle of \"be\", which is being, I was wondering can we use the same pattern? Another example in Longman dictionary is: who heard of a grown man being scared of the dark? or who heard of a grown man who is scared of the dark? Aren't they possibly equivalent of each other? Thanks in advance", "label": 0}
+{"snippet": "In Kittel's book of Solid State Physics, it is said that, whenever an electron passes the positive ion core in the lattice, it has the ability to distort the lattice s.t by attracting the positive ion cores. Does the attraction has to do anything to the mass of an electron, as being small, does it posses the attractive power to make the nearby positive ion cores to pull toward that electron, as positive ion cores are much heavier.", "label": 0}
+{"snippet": "I am reducing a block diagram manually and am not sure whether the following step is a valid step? I am using the rule of moving a summing ahead of a block in reverse. Reduction Step in Question I've checked the resulting transfer function before and after this step using MATLAB (connect function and Linear Analysis in Simulink) and they aren't the same, leading me to believe this isn't a valid step. Any help is greatly appreciated.", "label": 0}
+{"snippet": "In a uniaxial crystal there is an optic axis, an extraordinary axis, and an ordinary axis. The optic axis is not the direction in which we plan to propagate light. The light is propagating in a direction such that the electric field might oscillate parallel to the optic axis. I have included a hand-drawn diagram below. What about the crystal determines how the optic axis is oriented? Is one of the principal axes (ordinary / extraordinary) always parallel to the optic axis? How is the ordinary axis distinguished from the extraordinary? What happens if I propagate light along the optic axis? In a uniaxial crystal, is there a third refractive index that comes into play?", "label": 0}
+{"snippet": "Consider approximating a binomial distribution with normal. Originally, my binomial distribution is discrete, where the heights of the bars represent the probability. However, after approximating this distribution with a normal one, we find the probabilities using the area beneath the normal curve. How have the probabilities just changed from being heights to area? It seems unintuitive how these probabilities are more or less the same.", "label": 0}
+{"snippet": "I accidently deleted a large part of my work on a .tex file. Unknowingly, i saved the file , ran the typeset once and closed it. Hence the content is deleted from the pdf too. Is there any way to retrieve the deleted content. I check the previous version of the file too but it is not available either. Somebody please help. I am desperate.", "label": 0}
+{"snippet": "As we know that Euclidean geometry deals with triangles, quadrilateral,... and circles. Later in college we learn projective geometry but in quite modern language (vector spaces, equivalent relations). My question is, is there any roadmap or any book to learn projective geometry from high school Euclidean geometry which would be easier for high school student to learn projective geometry. I think it would be really helpful if our student could have some intuition with projective geometry before learning sth more modern like algebraic geometry.", "label": 0}
+{"snippet": "Work done in an isentropic process does not cause dissipation but leads to change in temperature of a system. But temperature allows wider range kinetic energy to be accessible leading to more microstates. This should lead to increase in entropy, but this doesn't seem to happen here. Does this mean that increase in entropy is compensated by something else? Or am I making some mistake here.", "label": 0}
+{"snippet": "I have a rotated retangle and a rectangle. Both are defined by their corners (however, for the non-rotated ones I also have access to topLeft, topRight, etc). Is there a way I can check if they intersect? (It would be enough to know if they intersect, even without knowing the extent of their intersection). I found solutions for two non-rotated rectangles and two rotated rectangles . Technically the solutions for two rotated rectangles could work in this case but I think that, since i know one of them is axis-aligned, there might be a faster way..", "label": 0}
+{"snippet": "I recently read that neutrinos have a polarization property---their polarization is opposite to antineutrinos. Is it possible to determine the polarization of a neutrino? For example, we can determine the polarization of a photon using a polarizing beamsplitter, V-polarizations will be reflected into detector A, and H-polarized photons will pass through into detector B. Can we do something similar with neutrinos, something like a neutrino beamsplitter? (Of course, neutrino detectors are huge, but in theory?)", "label": 0}
+{"snippet": "Using the GeoGebra program a few days ago, I came up with a wonderful feature about the parabola and the circle kissing its peak. I don't know if it is new or previously discovered. Please, if it was discovered previously, put a reference mentioning it in the comments, and in any case, can anyone prove it I don't think a lot of words are needed, this picture includes intuition", "label": 0}
+{"snippet": "I was reading Ali Omar text on solid state course and it said about the fact that electrons in a lattice or in a periodic lattice never scatters or make collisions with the positive ion cores, as the eigen functions of the solution of Bloch's theorem have infinite lifetime and eigen functions do not gets scattered? I do not understand as why eigen functions never scatters and what does scattering of eigen functions means and also what does it mean by saying eigen functions has infinite life time?", "label": 0}
+{"snippet": "I am trying to format a line of text that has two different sized fonts such that the vertical alignment of the smaller sized text is based off the larger sized text. In one instance I'd like the smaller text to be vertically centered on the larger text, and in another I'd like the smaller text topline to be aligned with the larger text topline. To my admittedly very limited understanding, this should translate to to changing a paragraph parameter to change the paragraphs vertical alignment to either \"center\" or \"topline\".", "label": 0}
+{"snippet": "Data rates are higher in X-band, but considering free space path loss and atmospheric attenuation(diffraction I'm assuming is significant here), won't lower frequencies stand a better chance? Again, cost and weight is a factor, but I want to understand the physics that goes behind these selections. Additionally, why do uplink and downlink frequencies differ in which one is higher?(Uplink is higher in the case of C and X band whereas it's lower in S band)", "label": 0}
+{"snippet": "Hello fellow grammar lovers! I need some help. I'm working on HR resources and have run into a bit of a conundrum about how to write about PTO. I know that I \"would like to take time off.\" But how do I go about \"initializing a time-off request?\" My question: Is it appropriate to hyphenate time off when used as an adjectival noun to modify request? My first thought is to use the hyphenated version to describe the noun (request), as nouns used to modify other nouns become adjectival nouns/noun modifiers/attributive nouns. Thoughts? Thanks! J", "label": 0}
+{"snippet": "Both mass and entropy behave differently for black holes than for normal matter. For simple Schwarzschild black holes, mass is proportional to their radius. The Bekenstein-Hawing entropy is proportional to their surface. Of course, the calculations for the two results can be found in the textbooks. Is there a simple explanation for why the dependencies on the radius differ? For example, fourfold surface implies fourfold entropy - but only twice the mass. In contrast, in normal matter, fourfold entropy implies fourfold mass. What is the best way to explain that in black holes, entropy increases more than mass? Somehow, mass and entropy are decoupled. What is the best way to explain this?", "label": 0}
+{"snippet": "I understand that according to Collins Dictionary, a suffix is an affix that follows the stem to which it is attached, as for example -s and -ness in dogs and softness. It has, however, a second definition: anything that is added at the end of something else. Would I then be right if I say that the following sentences have the same suffix \" is a vehicle.\"? An airplane is a vehicle. A car is a vehicle.", "label": 0}
+{"snippet": "When a magnet is moved into solenoid, it induces a current. And, when it is moved out of the solenoid, it induces a current. But what about in the example below. When a very long magnet, that has its whole body within the solenoid, is moved in some direction. The magnetic flux experienced by the coil from the magnet, should be very similar even if the magnet as a whole was moved a few centimeter.", "label": 0}
+{"snippet": "I searched for it but couldn't find any answer for this. For a light source is it simply the average of the full spectrum power? And how do you compute it for an image? How can you tell the difference between a yellow object lighted by a brighter light and a white object lighted by a yellowish light? Or maybe you can accurately compute it in front of a white sheet? Edit: I am talking about a lighting Kelvin temperature (for example of a bulb) rather than the actual temperature of the light source.", "label": 0}
+{"snippet": "Approximating the Earth by a circle with West facing in the theta-hat direction and East in the opposite, when a person jumps up, the Coriolis force faces West according to the right-hand rule. Upon descent, the Coriolis force faces East. Since you spend an equal amount of time rising and falling, shouldn't the effects of the Coriolis force cancel out? Why is this not the case? Why does a person end up falling slightly West?", "label": 0}
+{"snippet": "I'm helping edit a piece of fiction, which has a sentence that begins so: In another smaller kitchen... How is this to be punctuated? One choice is to leave it as it is. Another is using two commas: \"In another, smaller, kitchen...\" Since 'another' isn't an adjective or adverb, the usual rule(s) about grouped modifiers don't apply. (Note that there is a different kitchen several paragraphs before the line in question.) So--commas, no commas? (I can't see 'one comma' being right)", "label": 0}
+{"snippet": "So in flrw metric it's quite reasonable to take eigenvalue of the time-like component of the stress energy tensor and identify it with mass density. Now, if someone argues the cosmological constant comes from the stress energy tensor. Wouldn't they also have to account for the change in mass density? In the Newtonian limit I'm pretty sure this is a change in mass density. How do people who argue it doesn't matter where (stress energy or Einstein tensor) the cosmological constant comes from explain this discrepancy?", "label": 0}
+{"snippet": "Wagon-wheel effect is a well-known optical illusion due to the persistence of vision. It happens when the spoke of a wheel rotates to a certain position after the duration of persistent vision. Depending on such position, the apparent wheel motion can have many appearances. However, is it possible to design a certain pattern of wheel entirely free from such an effect? Except for the trivial solution (no pattern or spokes at all).", "label": 0}
+{"snippet": "I'm looking for a word that describes that feeling you get when somebody (of a group typically thought of having more power in society) brings up a group (typically thought of having less power in society: minority groups, women, LGBTQ) and you are hesitant to agree with them even though they are right (Like, in this hypothetical scenario they factually are, they're not twisting the facts or anything). It's kind of the same kinda gross feeling you probably got when you read \"even though they are right\" in a post loosely about racism from a stranger on the internet. This is the best explanation I can come up with. Is there such a word?", "label": 0}
+{"snippet": "Inspired by a youtube video, i was trying to do the double slit experiment at home using a single hair and saw the interference pattern. Then i wondered what would happens with many hairs and when i shine the laser trough a bunch of them, these kind of patterns emerge. Here you can see a video: https://www.youtube.com/watch?v=utJyBEfwugE Sorry if the question is too generic, i'm not a physics student.", "label": 0}
+{"snippet": "I want to confirm if I understand something correctly. We call the \"high potential terminal\" the positive side (cathode). Though, electrons move from negative to positive. Logically, electrons' potential energy is decreasing so the high potential terminal should be the negative side. In my opinion, from the electrons' perspective, the high potential terminal is the negative side, but since the current flows in the opposite direction, we always talk from the current's perspective, hence why we call the high potential terminal the positive side. Is this the correct logic?", "label": 0}
+{"snippet": "I want to minimize the amount of unused space in a binpacking problem. I keep seeing binpacking being described as using the least amount of bins possible. Example (emphasis mine): assign each item to a bin such that number of total used bins is minimized https://www.geeksforgeeks.org/bin-packing-problem-minimize-number-of-used-bins/ Would minimizing the amount of bins guarantee the least amount of waste? And if so, is there a minimum amount of bins (based on the algorithm used, not necessarily the one from the above link) that we need to use before it is efficient? Or is binpacking \"by default\" efficient in minimizing waste?", "label": 0}
+{"snippet": "I am building a database of sorts and came across this question. I am looking for a word that includes every region that is declared and made up by humans. So no natural regions like forests or continents, but regions that are generally associated with the people residing within its borders and other human-related stuff (laws, culture, goals...). Like Estonia, Tokio, EU... I found this similar question (Generic name for places like village, town and cities). But it's only about towns, cities etc.", "label": 0}
+{"snippet": "In the sentence below, Greenland may not be as \"green\" as the name suggests. The verb \"suggest\" should preceed an object as it is a transitive verb, but in the sentence, there is none. In this case, should the second \"as\" be understood as some sort of relative pronoun though there is no noun? Or should it be understood as a comparative conjunction? If it is a comparative conjunction, is it ok to not have a direct object for \"suggests\"? And if something is omitted, what is it?", "label": 0}
+{"snippet": "What would be the best books covering topics like Algebra, Geometry (Euclidean geometry) and Calculus? Which classics can be recommended (classics in the sense of historical works that have been widely disseminated throughout the history of mathematics, for example: Euclid's Elements)? I would like to have an overview of the main classics that influenced paradigms and changes in the history of mathematics (I understand that reading can be considered difficult, but I am willing to risk it). Objective: Historical Curiosity.", "label": 0}
+{"snippet": "A sphere with a radius of one is put inside a cubical box with circular holes cut out such that the ball fits perfectly. The box and the sphere share the same volume; find the surface area of the box. I tried cutting the cube down the middle to get a square and a circle. I then tried to find the distance between the two points of intersection between the circle and square on one side of the square but hit a dead end. I then tried to find the volume of empty space in the box since that could help me find the volume of the protruding parts of the sphere and maybe lead to the answer but it led to no avail.", "label": 0}
+{"snippet": "I was watching this video. It Showed that light ( green ) changes its color to red after incidence of light. I couldn't think of how this happens because light's color is dependent on frequency rather than wavelength and only the wavelength changes when light enters a new medium , according to these answers on whether light is depended on wavelength or frequency. So what explanation can be given for the change in color in a prism.", "label": 0}
+{"snippet": "A student asked how to integrate tan x and he was trying while using integration by parts. I taught him the substitution method but he then asked why we can't use integration by parts. My immediate thought was it is possible just much more complicated but in trying it out, I can't seem to do so. Is it simply not possible to integrate tan x by parts? Attached are my workings for the substitution method and the failed attempt at avoiding substitution. Integration by substitution Trial of integration by parts", "label": 0}
+{"snippet": "I am doing some work on the topic \"Adjunction\" and my current interest is to give some examples. I've wanted to provide some examples connected to some basic concepts from analysis on manifolds if such exists. What I thought maybe would work is the following: Tangent space functor and cotangent space functor Tensor product functor and multilinear form functor Pushforward and pullback of differential form I am not sure if any of these are indeed adjoint functors, so if they are I would appreciate any help in proving such a thing.", "label": 0}
+{"snippet": "If you take an axiomatic view of Classical Mechanics and the concept mass as primitive in this context, you could derive from Newton's laws an operational way of determining masses simply by arbitrarily assigning a mass to an object and demanding momentum conservation in its interactions with other objects. But if there are interactions that increase as a function of distance, this method ceases to be practical. Does this imply that an axiomatic theory should include the prescription that forces decay with distance?", "label": 0}
+{"snippet": "I'm trying to connect the calculations for the determinant I'm seeing and the idea that the determinant is a signed measure of the factor by which the volume bounded by the basis vectors of a vector space changes when those basis basis vectors are acted on by a linear transformation. Does anyone have a good way of connecting this geometric intuition with the way matrix determinants are computed, specifically with the \"product of pivots\" method I refer to in the title to this post? Thanks.", "label": 0}
+{"snippet": "In a PhD thesis we have to write a preface wherein some significant theorems from the main body of the thesis are needed to be restated. The amstools or thm-restate package does not help me in this regard. In this package the restated theorem must appear after the original theorem is stated. Till date I am doing it manually. But then the problem is if I change something in the original theorem then the same change must be done in the restated theorem also but manually. Is there any efficient method to do it?", "label": 0}
+{"snippet": "In quantum field theory, it seems that when we consider a massive particle's spin degree of freedom, we usually do in the particle's rest frame. And I know the little group will only change spin DOF and leave the momentum unchanged. My question is: If there is a Lorentz transformation that only change the momentum of the particle and leave spin DOF unchanged? And how to determine that transformation? Or in other words, can we compare spin of particles in different momentum? I think there should have, because when we transform a particle to its rest frame, the transformation operator is not unique since we can always do a more little group transformation, so there should be a unique one to leave the spin unchanged.", "label": 0}
+{"snippet": "I'm trying to calculate body trajectory that launched by some impulse. I have two points: start position and finish position which can be located on different heights (points is not symmetric). I know the height that body will reach, so parabola's vertex located that height higher of first point. Vertex located between points but we don't know it's X coordinate (if points on same height it will be in the middle between them). Is it possible to find parabola's equation in this case?", "label": 0}
+{"snippet": "If time measured by one observer moving at a greater velocity than another observer is observed to be passing more slowly, does this imply that there's such a thing as \"absolute time\" or \"base time\" which would be the passage of time as measured by a completely static observer of the universe? Basically time as measured from the universe's inertial frame of reference. I mean given the speed with which the milky way is hurtling through space, doesn't that mean we on earth are experiencing a dramatically slowed down version of this \"true time\" or \"base time\" or whatever you would call it?", "label": 0}
+{"snippet": "The pressure at a point inside a static fluid is same in all directions because the the collisions of particles take place isotropically. However, at the same time pressure increases with depth. So downward pressure must not be equal to upward pressure at that point. This two statements are contradictory and I am really confused. What is the problem in my understanding of the topic?", "label": 0}
+{"snippet": "I am finding very hard to understand how convexity works and why a correlated strategy if a convex linear combination of Nashes is a correlated equilibrium. (Both concepts of Correlated strat. and correlated equilibrium are clear) The following is the problem I can't grasp: problem Please feel free to modify my post I haven't been posting in a while and writing LateX feels very hard, also the question isn't well posed but I am trying to solve this on my own and this post is just another attempt to find a solution Thanks to anyone helping", "label": 0}
+{"snippet": "tried to submit my thesis to my school. However they told me that my fonts were not embedded, which they need for archival purposes. I thought I took the necessary steps to make sure they were. I think my .pdf figures in the document are likely the culprit.... But they're telling me that it's because in adobe document viewer there are fonts that say \"Embedded\" instead of \"Embedded Subset\". They say this means the fonts are not actually embedded. Are they correct? I'm surprised how much trouble I'm finding online on if a font labeled as \"Embedded\" really is embedded or not. From my reading I feel like Embedded is everything Embedded Subset is and then some (the characters not used in the pdf).", "label": 0}
+{"snippet": "Consider the single-hole diffraction of an electron. We can make the hole as small as we like and determine the electron's position with arbitrary accuracy. When it is in the hole, we can hit it with a low-energy photon, and measure its momentum. There is no guarantee that the photon will strike the electron. But it \"could\". It seems that we can measure the position and momentum simultaneously if we are lucky. Does it mean UP has nothing to do with simultaneous measurements but only with statistical uncertainty?", "label": 0}
+{"snippet": "I know that the derivative exists when the two sided limit at one point exists and at most of the discontinuities the two sided limit doesn't exist. But at point discontinuities, the two sided limit does exist, right? So it should have a derivative, i.e. it should be differentiable. But I read some of the answers for similar past questions and they say the derivate doesn't exist. Where am i wrong?", "label": 0}
+{"snippet": "As I understand it, sound needs a medium to travel and more often than not, the medium is the atmosphere, however sound can also travel through solid objects. And even we can hear our own voice talking (though less loud) even if we cover our ears since sound travels through our body. So, in case we are on the moon where the atmosphere is non-existent, would we be able to hear sound (say clapping or walking) due to sound waves being propagated through our own body or is that a stretch?", "label": 0}
+{"snippet": "Description Hi, I'm looking for an adjective that can be used to describe someone who is skilled at easily identifying the thoughts, abilities, and perspectives of another. The first sample sentence provided effectively captures the effect that I'm trying to convey. Sample Sentences e.g. Chloe is a _____ manager, she always appoints each individual, the tasks that fit them best. e.g. Mothers are typically _____ when it comes to their children; they always know what they need. e.g. Peter is a _____ friend. I never have to worry that he won't understand me. Potential Words Words that come to mind, include \"perceptive\", \"intuitive\", and perhaps even \"keen\" too.", "label": 0}
+{"snippet": "This question is very related with software development. I would like to know if there is a word to refer the way that a word is written. For example somebody has written \"HasChildren\" for a variable name while the correct way should be \"hasChildren\". I could tell this person: \"you should write hasChildren instead of HasChildren\". But if I want to be more polite I would say something like \"the way you use the lower and capital letters in HasChildren is incorrect, it should be hasChildren\". What I want is to have a term to replace \"the way you use the lower and capital letters\". Does that word exist? I am not sure if capitalization would work.", "label": 0}
+{"snippet": "How can I start from a Hamiltonian with electron-phonon coupling and show that a kink should show up in the energy dispersion relationship? In a brief communication called \"Universal Nodal Fermi Velocity\" there is a graph showing a kink in data collected from Angle Resolved Photo-Emission Spectrometry. After looking around a bit I found a review that convinced me that this is due to electron-phonon coupling and am now trying to convince myself with the math.", "label": 0}
+{"snippet": "I do not know if this is physics or engineering, but it is complex engineering I think at least. (In the implosion fission bomb first tested at Trinity and used in Nagasaki. Not the gun type.) A big problem with the implosion design was uneven compression and a member of the British team named Tuck suggested explosive lenses (which had been employed in anti-tank weapons, I think). Somehow the lenses were supposed to even out the explosive wave but were there not multiple shaped charges in the form of the lenses? And if so, how to ensure the lenses went off at the same time anyway? Basically, I would like to understand how explosive lenses fixed the implosion problem.", "label": 0}
+{"snippet": "I am seeing many reels on Instagram where they ask a person \"Can you spell Y, E, S\". The person says \"Yes\". Then they ask him \"Can you spell E, Y, E, S\". The person says \"E-Yes\" instead of \"Eyes\". Until today I thought that they should be using \"pronounce\" instead of \"spell\". Isn't spell the opposite? You ask a person how you spell \"Yes\" and they would answer Y, E, S. I saw so many reels from English speaking countries and now I am terribly confused if I don't understand what spell means.", "label": 0}
+{"snippet": "I want to know whether alternating current will hold you to stick to the socket or throw you away and why? In my textbook it is written that alternating current is attractive in nature but when i researched a bit i found that it will contract your muscles and make you stick to the socket. So i want to know which of the fact is correct and why? Please i want a complete explanation as I am totally confused.", "label": 0}
+{"snippet": "The question says it all. Simply stated: Can one prove grand unification from string theory? What is the argument chain of such a proof? The textbooks I read so far only appear to give hand-waving arguments. The question is not about deducing the standard model. The question is about deducing grand unification. This means that there is a single large Lie group. Can one prove somehow that string theory produces a unique (large) Lie group?", "label": 0}
+{"snippet": "Are there good reasons to use, e.g., \"customer relationship management solution\" over \"solution for customer relationship management\"? I understand that in certain contexts clusters of nouns, such as in the first example, can increase ambiguity if the adjectives aren't compounded accordingly. The preposition in the latter example reduces the ambiguity by expressing the relationship the subject, the solution, and its modifiers, customer relationship management. Are there other reasons that one might want to use a prepositional phrase over stacking, and hyphenating, adjectives?", "label": 0}
+{"snippet": "XeLaTeX and LuaLaTeX support Unicode, and are perhaps also in some other ways better than pdfLaTeX. However, are mathematical and logical journals prepared for submissions prepared with XeLaTeX or LuaLaTeX? Perhaps it is more prudent to prepare one's work with standard pdfLaTeX? I am a bit wary about these things, as I one time when finishing an essay for a book was suddenly told that they just accepted word-submissions. What is a prudent strategy if one wants to have an essay published in a good logic journal?", "label": 0}
+{"snippet": "I've been investigating this problem: Given some straight line planar embedding of a simple connected graph with a simple dual graph, does there exist a straight line planar embedding of that dual graph with each vertex lying in its corresponding face in the original embedding? What if we ignore the infinite face? I believe I have found a few complicated counterexamples to the main problem, but have no clue how I would go about proving the less restrictive case or finding a counterexample. I would also appreciate smaller counterexample to the initial case. Here is a graph that I believe is a counterexample.", "label": 0}
+{"snippet": "I believe I have heard the expression when someone did an analogy about nuclear war, comparing the danger to a game where the opposite player's objective is not to win but to make you lose. This was apparently called, in game theory, \"a scorpion player\". I thought they were called the \"scorpion player\" but I can not find any proof or anything close to this. Have I remembered wrong ? Is it an other name ? Or have hallucinated the whole thing ? If anyone has any information on if there is a name for such player, I would be thankfull. Many thanks.", "label": 0}
+{"snippet": "Suppose we have a hollow conducting sphere having a charge Q residing on it's surface. Then we take another such sphere which is bigger than the one mentioned before and surround the smaller one with it, would this cause the charge on the inner sphere to appear on the outer surface of the bigger sphere? If yes, then how can a spherical capacitor even work if all the charge on the inner sphere goes to the outer sphere's outside surface I have added an image below for reference", "label": 0}
+{"snippet": "In Halmos'book on naive set theory, Halmos introduced the idea of a \"family of sets\". He explicitly defined a family to be a function from some indexing set to an indexed set. However, whenever he talks about a family, what he seems to always be refering to is actually the range of the family. I get so confused whenever he speaks of families in his text, whether he is speaking about the function or the range of the function is very ambiguous. Does \"family\" then formally mean the indexing function itself, or perhaps the range of the function? Thank you in advance.", "label": 0}
+{"snippet": "Is there an adjective/expression that conveys the meaning that this something fills a role/place that should have been filled long ago because of its high added value? For example: \"The ____ exhibition on female figures in the development of modern design...\" Perhaps \"long-awaited\" is something similar but I was hoping to find one that doesn't imply that people were expecting this change to happen. Thanks!", "label": 0}
+{"snippet": "Google says just that \"toothless wonder\" is an individual in the public who is lacking a single front tooth. Well, that's logical. But what's the purpose of word \"wonder\" then? If this is a slang form I can't get it, please, explain it to me. And I really want to know where it came from. All I could find out is that there were some child books named Junie B. Jones: The Toothless Wonder, although I am not sure that they were the origin.", "label": 0}
+{"snippet": "In linear algebra, to convert the linear transformation or operator into matrix form, it's not hard, get the standard basis of domain and substitute in the transformation and write the image of the standard basis as a linear combination of standard basis of codomain and finally get the constants (c i's) and write that in column wise in the matrix format, we will get the matrix format of the linear transformation with respect to the standard basis of the domain and codomain. My question here is why can't we arrange constants row wise? Why it is fixed to arrange constants always column wise? Thank you so much for your response", "label": 0}
+{"snippet": "I use latex workshop on VS code combined with okular, but I would not mind using the internal viewer. I use forward search and backward search. My question is, whether there is a way to make the editor follow the viewer and the other way round: If i scroll in the editor, that the viewer shows the according segment and also if i scroll the viewer that the editor follows? This would be very convenient. In the long run, I maybe use latex to create html or what. Is it possible to do the same with a browser as a viewer?", "label": 0}
+{"snippet": "I want to know what the zero electrical resistance of a superconductor means. Does it mean when we connect the terminals of a battery with a superconducting wire, the electrons move within specific tunnels inside the superconductor for which the net Coulomb's force due to the nearby nuclei and the electron clouds are zero everywhere in these tunnels? Do Cooper pairs form to justify these neutral paths? If there are such paths, are they curved or straight? Do these tunnels, if exist, make the superconductor anisotropic?", "label": 0}
+{"snippet": "As far as I understand it, dark energy can affect bound systems at cosmological scales (How does dark energy affect the dynamics of galaxy clusters?) effectively modifying their orbits. This phenomenon and this thesis dissertation made me wonder... Could dark energy make a bound system (like a large galaxy or a satellite galaxy orbiting a bigger one) be \"less bound\" so that the orbits respective to the central point of mass are larger? And if dark energy would help to make orbits be further away from the central point of mass, does it mean that dark energy could add orbital energy to bodies orbiting the center of the galaxy at the outskirts of it?", "label": 0}
+{"snippet": "What is the basis of the believe that there should be a unified theory which simultaneously gives quantum physics (the regime small things moving very fast) and gravity (the regime of big things moving very slowly)? Is this just wishful thinking? Are there any people who make a strong case of the possibility that no such theory can exist? This is a sincere question. Please don't throw stones at me.", "label": 0}
+{"snippet": "I was studying Newton's Laws of Motion and my book gives a diagram in order to explain what components together can or cannot be considered a system in the figure given below. Now it says we cannot consider D and E together as a system as they don't travel the same distance because the disc D slides over a string but I'm having a hard time getting how exactly is it sliding over the string. Is the string wound up on the disc?", "label": 0}
+{"snippet": "We are aware that Microsoft Word has a feature called ink Equation that allows the user to write a formula with a light pen, even if the formula is complex, and then convert it into a real equation with an acceptable font. Obviously, this is an excellent option, since it is not necessary to use multiple commands to write a lengthy equation; instead, one can simply write the equation as seen. My query is: Is there a latex editor that includes this feature? If the answer is affirmative, which editor has this capability?", "label": 0}
+{"snippet": "When we put a circular hole of radius R on an infinite sheet of uniformly disturbed charge we do have an electrical field on a distance z (perpendicular to the sheet) from the center of the circular hole. But if we were to pick a gaussian surface such as a cylinder of radius R there would be no flux according to the gauss theorem. Because there would be no charge in the hole. I am having a difficult time understanding what i did wrong.", "label": 0}
+{"snippet": "I am trying to compile the most basic file of the Kaobook template as provided here and it does not work. Now, on my TeXLive, it doesn't because it gives me in the report that it is missing an options.sty file (an issue that I do not really know how to fix). What is more peculiar is that this is not compiling on Overleaf either (and I am literally opening the file there from the option provided on the page linked above without modifying anything). Is there any specific reason? Any feedback will be most welcome!", "label": 0}
+{"snippet": "Background: Masters in CS/Math. I'm brushing up on statistics I see mean squared error everywhere. As a student I took it for granted, but now when I tried to find the reasons for why it's so prevalent I am told: simplicity, emphasis on outliers and mathematical properties like differentiability. So what? It's not the only function with those properties. So why is it used so widely? Are there situations where it's provably the best function to use? Are there situations where there are other functions that are provably better to use? Say I am designing my own heuristic, and I have an error I want to minimize on. How do I know that squaring the error is the best way forward?", "label": 0}
+{"snippet": "I understand that every function is equal to some graph, while not every graph corresponds to a function; so that sets aside the difference between functions and graphs. However, I understand that any relation can be represented with a graph, and every graph coresponds to some relation. Therefore, are the set-theoretic structures of \"relations\" and \"graphs\" exactly identical? Are they just different names of the same set?", "label": 0}
+{"snippet": "Once a body \"crosses\" the limit where dark energy wins over gravitational forces (Is there a distance from a gravitational source where the influence of gravity and dark energy are balanced out?) would there be any way to make it return to the zone where gravity overwhelms the influence from dark energy? For example, if a body is orbiting a massive point and begins to slowly recede from it due to the expansion of the universe, could some kind of slingshot effect caused by a passing external object make that body get closer to the source of gravity to the point that it gets \"trapped\" in the zone where gravity wins over dark energy and therefore does not recede forever?", "label": 0}
+{"snippet": "It seems like homotopy pullback is pullback for the case of D(CW) (derived category of CW-complexes). Is this true? In general, I want to say that homotopy pullback satisfies the universal property of pullback in a derived category. What I know for sure is that the pullback of fibrations is homotopy pullback. In a derived category such as D(CW/X), weak equivalences are isomorphisms, and each map can be replaced by a fibration. Hence, up to isomorphism, everything is a fibration, on which the homotopy pullback is the pullback. I wanted someone to confirm that this homotopy pullback (which coincides with the pullback after replacement) satisfies the universal property of pullback.", "label": 0}
+{"snippet": "Why not explain the apparent attraction of masses by a repulsion coming from all directions in space (perhaps the dark force)? I.e. there is no gravitational force, just a repulsive force. A point in midspace would be receiving repulsive forces equally from all directions and appear to not accelerate. Mass near the outer reaches of our universe would have more repulsive forces coming from behind, and therefore accelerate outwards. An object near a large mass would be receiving less repulsion from the direction of the large mass (because that mass has absorbed some of the force) and therefore be pushed towards the large mass.", "label": 0}
+{"snippet": "This question was inspired by the very first exercise in Thurston's Three Dimensional Geometry and Topology, where he gives a picture of a very tangled up loop and asks what manifold it depicts. I understand there are several knot invariants and algorithms that can be used to detect the unknot. But where are the practical implementations? Are there programs into which one can feed an actual picture of a knot (as opposed to more directly computational representations) and have it at least recognize unknots? One test would be whether it would accept the above picture as input and give the correct answer.", "label": 0}
+{"snippet": "I have noticed when I view a hose pouring water the color of water slightly changes when looking from above compared to when looking from the front. Also, the same thing applies when you pour water from your mouth. If you look at it from above there's a color I can't describe very good (but I think there's a yellowish in it). But when you look at yourself in a mirror pouring water from your mouth, the water is colorless. To see the phenomenon better do it immediately after you've finished brushing your teeth. Just put a little water in your mouth and pour it down (looking from above). Why do I perceive this color change?", "label": 0}
+{"snippet": "What is the proof for this (assuming that we draw infinite field lines). I understand why flux through some area is proportional to the number of field lines through that area only in the case of an isolated singular point charge. However, I dont understand why this would be true in other cases, like two unequal charges. To make it clear, when an area has twice the amount of field lines going through it than another area, why is the flux through it exactly twice the other area. Why not thrice or half? Also, why do field lines that originate isotropically from one charge always end isotropically at another charge.", "label": 0}
+{"snippet": "I want to strap down a big heavy cylinder on a flatbed truck. The strap is attached to the truck bed as shown in the picture and also behind. Will the strap slip off as in the next picture? PS. This is a purely geometrical question about the length of the strap and the shape of the cylinder. Please consider that the block cannot move sideways and is blocked in place by some metal \"foot\" at the bottom.", "label": 0}
+{"snippet": "I've read that the equatorial radius of the ergosphere of a rotating black hole is the Schwarzschild radius. But in this animation made in natural units by Yukterez it doesn't apply. I then used Yukterez equations in Geogebra and I observed the same thing. No surface scales accordingly. In the extremal case, the event horizon at the equator should be half the Schwarzschild radius, but it isn't. Is this a consecuence of using natural units? How could I \"fix\" this?", "label": 0}
+{"snippet": "An FTIR spectrum was measured for me (device from Alignment and MCT Detector) and since I'm not very familiar with FTIR I'm looking for some advice. The absorbance spectrum was obtained by measuring the reflectance of a reference sample and the actual sample. The reference sample was stainless steel and the actual sample was probably stainless steel coated with dopamine and a peptide. The spectrum shows some kind of oscillations. It was suggested that the oscillation is due to interference caused by the dopamine coating. The coating could act like a thin film. Unfortunately, I haven't found anything paper/ literature supporting the suggestion. Have you seen something similar?", "label": 0}
+{"snippet": "I have a question. I have a problem that when I learn science, I like to think 'how do they know this is right?'. When we learn physics or science from a textbook, we read and understand it, and then we have exam. But how do you know what is given in a textbook or said in research is correct? Because we didn't do this experiment, or we don't know what the process is to get this scientific result by ourselves? So, should I trust it and accept it? If not, what should I do?", "label": 0}
+{"snippet": "Suppose a body is kept in space and is not fixed about any point (i.e, not hinged). If an external force is applied, the body rotates about the centre of mass. I saw one answer pointing out that moment of inertia is minimum about the centre of mass, and thus motion around any other axis is unstable. Is this view correct? And if true, how do we go about proving that it indeed is the most stable?", "label": 0}
+{"snippet": "Both nematic transition and Jahn-Teller distortion distorts the lattice and reduces the symmetry of a crystal; both of the structure transition can take place at higher temperature than the magnetic transition. Why in iron-based superconductors it is called nematic transition, while in molecular system it is called Jahn-Teller effect? (Particularly in the papers talk about iron-based superconductor they never talk about Jahn-Teller effect.) Is there a deterministic experimental fact to distinguish the two? Thanks.", "label": 0}
+{"snippet": "I'm writing a report. In the report we refer to program participants as either dedicated or auxiliary. Each has a unique situation in which they enter the program. Since they are a particular type of participant, I have been capitalizing them to avoid confusion, but I'm not sure if this is correct. For example: When Dedicated participants submit an application they must... Is this correct? I understand it as a proper noun. I'm confused about the rule as this comes up many times in reports I need to write.", "label": 0}
+{"snippet": "What is the synonym/counterpart for the word \"Default\" in NON-IT WORLD? We use the word in computer programs/apps, meaning that there is a pre-specified/pre-defined setting or situation. The word has also different meanings in Law and Banking. But I want an alternative to use in our daily life: for instance, a physician may choose a \"default\" treatment for a common disease, or one can have a default position/view on a particular topic .... I want a counterpart meaning of the same word for everyday uses (non-IT world).", "label": 0}
+{"snippet": "Could the gravitational effects of exotic matter be replicated by using something like a torus of mass around a point? Because spacetime is relative (I'm pretty sure), for observers on the torus, or just any celestial object i guess, would they not see the other points in spacetime around them having a negative energy, and repelling objects instead of attracting them? I know I've made some sort of misconception about this, but I can't figure out what it would be, except maybe spacetime not being relative. Edit: I drew an amazing picture to demonstrate what i was thinking", "label": 0}
+{"snippet": "This is a snap of a textbook while describing Uniform Circular Motion. For all the diagrams, and by the vector law, the directions of the del(v) vector is perfectly fine. But I am confused why this del(v) vector will always be pointing towards the center. As it is stated here, just because v is perpendicular to r and v' is perpendicular to r', therefore del(v) is perpendicular to del(r) does not sound satisfactory. Any other logical reason why del(v) vector will point towards center only when del(t) is long enough as in diagram a and b.", "label": 0}
+{"snippet": "Just wanted to question how Hilbert space dimensions work. From what I've seen, they're used to generalize the mathematics of finite-dimensional Euclidean spaces into infinite-dimensional vectors. I've seen them used in quantum mechanics, and in some cases stated to \"inherit finite dimensional space-time\" despite the Hilbert space having infinite dimensions. So I'm basically asking how Hilbert spaces correlate to the physical spatial dimensions they represent. Are there Hilbert spaces that represent topological spaces with infinite spatial dimensions? same question for any function spaces with infinite dimensions.", "label": 0}
+{"snippet": "I'm not sure if this is the right community I could ask to, but I'm looking for a reference in business calculus that has challenging problems. The ones that I found so far have easy problems and can be solved within a day. I'm looking for problems that will probably take time to solve and will use a lot of thinking (and not just copy the methods/insert some formulas to solve). I would appreciate it if someone can recommend to me a reference that I'm looking for.", "label": 0}
+{"snippet": "I'm trying to modelise the ping pong and water cup experiment. They were already questions on stackexchange about this: Why does a ping pong ball bounce higher when it is dropped together with a cup of water? but I would try an approach with Archimede Force and superficial tension. I want to apply Newton's law on the ping pong ball, but the water and the cup are moving too and I don't know how it works in that case or how to modelise it... What do you think about it?", "label": 0}
+{"snippet": "I have some powder in a container with one side open. If I then compress it from that open side, does the powder evenly compress, or will the side closer to the opening (or furthest from the opening) compress more, and end up with a gradient of compression? For example, when tamping ground coffee in an espresso portafilter - is the coffee density even distributed through the portafilter, or will it be denser at the top or bottom? And what factors (if any) affect this? Regarding individual particles - shape? size? texture? uniformity? compressibility (of each particle)?", "label": 0}
+{"snippet": "I recently delved into the topic about the reality of the Dirac string. Although several authors show how this object should not be real, this article \"Field momentum and the reality of the Dirac String\" proves they're wrong. I think the thesis of the article is very strong and I would like your opinion. I am writing my bachelor thesis on this study, I am learning both the Lagrangian and Hamiltonian formulation of the system to understand if I can find a solution, however the authors of the article seem to me to use only classical arguments. Any ideas?", "label": 0}
+{"snippet": "I read about the 'Method of undetermined' in the wikipedia and it said as following: In order to find the particular integral, we need to 'guess' its form, with some coefficients left as variables to be solved for. This takes the form of the first derivative of the complementary function. Below is a table of some typical functions and the solution to guess for them. I can't understand the sentence \"This takes the form of the first derivative of the complementary function\" what does it mean? Is there any relation between particular integral's form and derivative of the complementary function?", "label": 0}
+{"snippet": "I see the statement that: Similar to how a car needs fuel to run, a computer needs electricity to power it. In this case, I comprehend its meaning. However, I don't really get why \"similar\" is used at the top of the sentence here. If \"similar to how\" is an adveribial clause, my searches don't find any results or any envidence. Likewise, I can't figure out clearly any type of reduced relative clause.", "label": 0}
+{"snippet": "I have read that if helicopter's engine fails, you set the pitch to minimum but not reverse pitch. The rotor would have to be tilted back to provide an angle of attack on the blades so it glides like a fixed wing aircraft but with the rotor spinning to keep the blades from buckling under the weight of the craft. I think it would have to go into a slight reverse pitch to spin the same way. That would also provide more angle of attack on the receding blades where it is needed because of the lower air speed over those blades. How does it keep rotating in the same direction with the air going up through it if it can't go into a slight reverse pitch?", "label": 0}
+{"snippet": "I know that we have to use 'the' when it comes to groups of people, for example: The French are good at cooking. When nouns and adjectives are the same, we can omit 'the' Americans are good at sport. However, I do not know what to do with a word \"Brit\". I'd like to know Brits more OR I'd like to know THE Brits more? Can I omit the definite article?", "label": 0}
+{"snippet": "In an electric circuit, electron flows from the negative terminal of a voltage source to the positive terminal, which in turn, gives us the the conventional direction of electric current. So, the first question that arise in my mind is: On moving to the positive terminal, does the electron gain stability? If it does, then we know that an electron moves from a higher energy level to a lower energy level it releases a photon of a frequency dependent upon the energy gap, to gain stability. The second question is: Why does an electron move towards a region of lower energy but in a circuit, towards higher energy (positive potential is obviously a higher energy level)", "label": 0}
+{"snippet": "Suppose I have a rhombus based penrose tiling like the following: Is there some coordinate system that allows me to easily uniquely refer to a specific tile, and also from the coordinates efficiently calculate the coordinates of the tiles that border it? I also need to be able to easily tell what tile is on the \"opposite side\" edge of a tile with respect to a different tile that also borders it. Basically my end goal is, if I have some instruction like \"Straight, Straight, Left, Straight, Right\" and follow them on the grid to calculate if I ever cross my own path and when.", "label": 0}
+{"snippet": "I am attempting to apply the Grubler formula (which can be found here: https://learnmech.com/how-to-calculate-degree-of-freedom-of/) to determine the number of degree of freedom, but it does not seem to yield the expected in some cases. Is it correct that there are some cases where the Grubler formula should be avoided? If yes, how can I recognize these cases and what method could I use instead? EDIT: I've edited it to only ask about the underlying concept as required. Now, one might say that it lacks an example where it doesn't work ... tell me if that is the case, I'm just trying to comply.", "label": 0}
+{"snippet": "Interference is explained by showing a diagram of two parallel waves of light that are in phase or out of phase and showing the result of the fields constructively or destructively interfering. Implicitly it seems to be the case that they are polarised in the same plane as well. What I wanted to know is what this picture looks like when we're talking about unpolarised light. I'm reading about XRD and Bragg's, and can't seem to find any indication that polarised X-rays are used. And if that isn't the case, then even if two waves are in phase, the net E fields are polarised in random directions to each other and wouldn't undergo constructive interference. Where am I going wrong here?", "label": 0}
+{"snippet": "The wavelength or frequency of light determines its color. Photons seen as particles are said to have a frequency, determined by its energy, so I assume that 'is' the same color. But being quantum particles, photons also have a probability wave, determining how likely it is to detect it in a certain state (like, a position). How do these waves relate to each other, if at all ? Iow, would the double slit experiment have a different result when performed with 'red photons' instead of 'green photons', and if so, how would it differ ? Sorry if I get things wrong, I'm just grappling with the nature of these things.", "label": 0}
+{"snippet": "How strong of a gravitational field do you need for a projectile to make a full loop? By full loop I mean it curves once around the by dot, and then it ends up on the same trajectory as it was one before it approached. How many times the Schwarzwald radius would the projectile have to get for this to be possible? I know the limit in Newtonian gravity is half a loop.", "label": 0}
+{"snippet": "I had the feeling that physics has moved on from the idea that spacially bounded objects located in spacetime (such as particles) can be fundamental. Instead, QFT describes everything by quantum fields which are better considered as an everywhere present property of spacetime rather than embedded in it. From this perspective, it always felt to me like string theory is a step back, talking again about bounded objects located in spacetime (i.e. \"free floating strings\", as this answer states). Question: Is there a flaw in my understanding? How can free floating bounded strings give rise to spacially extended quantum fields? I am a mathematician and fine with advanced mathematics, but am a layperson when it comes to physics (you might consider me as an undergrad in this respect).", "label": 0}
+{"snippet": "I want to know the mean first passage time (MFPT) on a unit interval for two boundary conditions (please see attached figures a and b for your reference). This is in the context of the hydrodynamic dispersion of a particle. In case a) the b.c switch from reflection to absorbing whereas in case b) the b.c is reflective. Can anyone help me to figure out the mean first passage time in this problem?", "label": 0}
+{"snippet": "I am currently looking for a cyrillic font (for russian typewritting). It must be an opentype font usable with lualatex and fontspec, and must be complete : roman, italic, bold, small caps, superiors letters and figures, in serif and sans serif. For all I know, Libertinus is very close, but it lacks cyrillic small caps and superior cyrillic letters. Does a more complete font exist?", "label": 0}
+{"snippet": "I have a knot about the \"secondary\" colours and its spectra. So If I look the spectra of white light, I can see that yellow, which is between R and G, has some wavelength. If I do an addition of light of Red and Green, I get yellow. Ok. Now If I do an addition of light of Red and Blue, I get Magenta. But how come that Magenta is only a perception and has no wavelength, as Yellow for example ? I understand that some colours physically do not exist, but I dont understand why yellow exists as a real physical wavelength but not magenta. Can someone help please", "label": 0}
+{"snippet": "According to Stephen Boyd's textbook on ADMM, the global variable consensus ADMM updates are given as the following, which is pretty straightforward to understand: However, I've recently seen another variation of the consensus-ADMM updates from this work I tried very hard to derive the primal updates shown above but I just cannot arrive at the same equation. I wonder if this is the same as global variable consensus ADMM at all?", "label": 0}
+{"snippet": "So, I'm trying to make a basic shooter game in desmos, and I have a list of points that act as bullets. The (current) enemies right now are only some triangular jets that fly in a linear manner. My current goal is: Make it so when the point hits the triangle, it deletes itself from the list, and thus itself from the screen as well. The Triangle, upon getting hit, moves downwards in a curved path and stops when it hits the ground (a line). https://www.desmos.com/calculator/sjezpkhhxl Here is the graph itself. The lines for the bullets themselves are in the folder titled bullet and the lines for the triangle are labelled as enemy: fighter jets. If any more details are needed, please do let me know.", "label": 0}
+{"snippet": "My wife mentioned today that she would love to know more about 'how the world is made up'. She stopped learning science at a young age and finds most stuff meaningless or incomprehensible. She is not a child - so the challenge is, how to introduce the history and development of atomic physics with minimal specialist vocabulary, in a manner that reliably explains how physics got to the standard model. Pictures are good, waffle is bad, mathematics and equations is a no, hand-waving or similar patronising (eg '...for idiots!') statements are a no. Her wish is aspirational - so the presentation needs to be reasonably effortless... Any thoughts or suggestions?", "label": 0}
+{"snippet": "I remembered this really corny phrase today when I was on a walk but I forgot later before I could write it down. It's kind of like \"You are what you eat\" but with different words. It's not: You reap what you sow. You're the sum of your actions. Easier said than done. (It is a different one but they're both about contiguity. I don't remember what it is.)", "label": 0}
+{"snippet": "Why does she try and pull the stunt? This is probably an elliptic sentence - Why does she try the stunt and why does she pull the stunt (off)? - but it still seems like very bad style to me. Why does she (even) try to pull the stunt (off)? I am aware that it is not clear that the attempt was successful, however the to-infinitive comes much more naturally to me, for whatever reason. From context, it is clear that it was successful. So, would you consider it weak style to use an ellipse like this?", "label": 0}
+{"snippet": "I am trying to determine a statistical test to run. My dependent variables is employee retention. The independent variables are exam score and interview score. Unfortunately because employees who failed the the exam did not moved onto the interview, I do not have interview scores for all cases. Do I run a logistic regression? Is there any other test I can run to be able to use exam and interview scores to predict employee retention?", "label": 0}
+{"snippet": "To my understanding, the curvature of spacetime is determined by the stress-energy tensor. I was wondering if we could calculate some of those components using radiation. Is it possible that objects that possess immense electromagnetic radiation, for example, will follow with a strong gravitational pull? Does radiation occupy physical space? Just had a thought experiment where I visualize spacetime like water that engulfs any solid object and doesn't go through it. But in my visualization, the actual spacetime didn't touch the solid object since the solid object occupies more space than its physicality. It engulfs the radiation and interacts with it. Just thoughts :).", "label": 0}
+{"snippet": "So in my course of quantum computation i came across this question that \"What guarantees a quantum gate to be unitary?\" i was specially curious about photonic quantum gate. At first i thought that maybe unitary is not something that is guaranteed by any special phenomena but its inherited by the math behind quantum physics and that we use to describe any physical operation with an unitary operator but is it really the answer?", "label": 0}
+{"snippet": "We need to solve this problem without using trigonometry. KLMN square is inside ABCD square. Prove that midpoints of the segments AK, BL, CM, and DN are vertices of a square. KLMN can be situated anywhere inside ABCD. I think that we are going to use congruent triangles. I tried to draw so that the intersection point of diagonals of ABCD and KLMN coincide, I also tried the opposite to consider the general case, because KLMN can take an arbitrary position. So, I would like to see approaches, how to prove.", "label": 0}
+{"snippet": "I wonder if above some energies (or diagram level?) the virtual particles would rather behave (or become) like a micro black hole. Does that make sense? Could this somehow introduce a cut off above which Feynman diagrams would be unnecessary (the micro black holes would always evaporate in perhaps a few different ways), and in doing so avoid renormalization? This are speculations from a freshman, so please don't be hard on me.", "label": 0}
+{"snippet": "An oxymoron is a figure of speech in which contradictory terms appear in conjunction with one another. Can there be a figure of speech in which similar compatible terms appear in conjunction with one another? For example, how would I describe the following sentence? Nice should be great. Nice being the location, but also a compliment. Play on words? Comedic effect? Feel like there isn't one and idiom or a proverb doesn't quite fit.", "label": 0}
+{"snippet": "As my title says, is a \"change in scenery\" as correct as a \"change of scenery\"? I am self-conscious of how a \"change in\" might sound odd or off or be even absolutely incorrect. Are both forms of this sort of expression truly correct? I know the latter one is (a \"change of scenery\" makes full sense), but what about the former version of this idea with \"in\" as its preposition instead of \"of\"?", "label": 0}
+{"snippet": "So there's this debate ongoing on one post that this phrase is incorrect. People are getting confused and wondering how can Adele take a divorce from her own son. The sentence is: Adele says new album will explain her divorce to her young son. Is the above sentence correct? I always thought a divorce was taken from someone and not to someone. For context, the sentence is being used a headline caption for an image.", "label": 0}
+{"snippet": "If all bodies emit thermal radiation, does it mean that it's impossible to build something that can retain all of its energy - and last indefinitely? i.e. is everything in our world, including a dynamic, living system that can self-repair, eventually gonna collapse? OR - there is something in Thermodynamics similar to Superconductivity in Electromagnetism that would help prevent this? OR if there is no such effect, is there, even theoretically, a way to mitigate the effects? I can only think of creating new energy within a system faster than the system can lose it due to thermal radiation, but doesn't this violate conservation law(s)?", "label": 0}
+{"snippet": "I'm looking at an example system which has a very large number of microstates (effectively infinite - not possible to enumerate exhaustively, but possible to sample from). The energies of the microstates however are drawn from a normal distribution with some average energy and standard deviation of the energy. What is the partition function for a system like this expressed in terms of the average energy and standard deviation of the energy? What is the entropy?", "label": 0}
+{"snippet": "If the vacuum energy of the universe is not at its minimum, that is, the universe is at a false/metastable vacuum state, then it could decay into the true vacuum state. However, if our universe is already at the true vacuum state, then, this decay would not take place. However, in the far future, if we would wait enough time, could the true vacuum transition into a false vacuum level somehow? Or is this utterly impossible?", "label": 0}
+{"snippet": "I was thinking of converting a disused chimney into a static periscope, using long focal length lenses at top end of the chimney. A static design would be easier, so I was wondering how one would design the mirror shape such that it converted a cylindrical view onto the lens, which could then be processed at the other end of the chimney to generate a cylindrical view once more. Is it even possible?", "label": 0}
+{"snippet": "Assuming right to be positive, in this question, is the work done by the boy positive or negative? I would think it is negative because the force that the boy exerts is towards the left while the movement of the boy is towards the right. I would think that work done ON the boy is postive because the force that the string exerts on the boat is towards the right which is the same direction as the motion of the boy. Am I correct? I don't quite understand how to think about the idea of work done BY the boy in this context. What does it mean for work done BY the boy to be negative?", "label": 0}
+{"snippet": "I'm looking for open books on abstract algebra, other than Judson's AATA. I want one with a good number of exercises (and solutions, preferably), this one covers the rest. Does anyone know of one? This and this are similar questions. The first one has many answers and the second is markedly different, but answers specific to abstract algebra, with brief descriptions of each book (too much to expect in the first) might help someone someday.", "label": 0}
+{"snippet": "So I was wondering if it was possible to prolong the \"entropy\" of the bottle by making sure the heat of the contents of the inside of the bottle doesn't escape by first having a secondary bottle on the inside of the existing container. Then there would be a vacuum. So would the heat stay trapped if there were mirrors on the inside of the outer container bouncing infared radiation as it gets radiated from the inner container. Is this a means of preventing entropy increase in the universe, so could be used with dyson spheres to trap heat preventing it from escaping in the distant universe to preserve more energy? Are there any issues with this approach?", "label": 0}
+{"snippet": "According to numerous questions (e.g Is it recommended to use \"we\" in research papers?), one should use \"we\" instead of \"I\" while writing a scientific paper. However, it's unclear to me if, for example, \"In the following image you can see...\" should be replaced with \"In the following image we can see...\"? Personally I think, that the latter sounds better and also includes the reader together with the authors in the discussion at hand, as already mentioned in the above question. But it's still unknown for me, if it could or should be mentioned while reviewing another paper.", "label": 0}
+{"snippet": "Superdeterminism is one wild conjecture which is an alternative to the standard quantum mechanical interpretation and preserves local realism Superdeterminism seems to be too much of a stretch. If experimental results are pre decided it simply renders the experiments useless. Is there any alternative in the academia where something like minimal determinism is discussed? Like just the minimal amount of determinism needed to retain local realism. For eg: In the classic Bell's test, if the entangled electron pair generator knows the direction of measurement of spin beforehand for even one of the electrons while generating the entangled pair of electrons, hidden variable theory can violate Bell inequality. Instead of the entire system being superdeterministic, only one pair of entangled electron pair generator and electron spin detectors are determined.", "label": 0}
+{"snippet": "I'm looking for a single word that means \"to bring within reach\"/\"make possible\" for a technology or promising development. For example Mobile phones _____ photography for the common person. \"Facilitate\"/\"make accessible\" isn't quite right - I want to convey a step change, a paradigm shift. In particular, I'm naming a business. I work in robotics. Robotics has long been touted as a way to give people mobility, automate the mundane, and facilitate humans focusing on what matters to them. My goal is to build tools for other companies to accelerate them and _____ the promises of robotics for humanity.", "label": 0}
+{"snippet": "I work in STEM and a problem I often face with is the use of \"by\" or \"through\". Let me explain it with an example. I have a quantity named \"variance\" that is derived after a certain number of tests (called Monte Carlo simulations). So, I write it like the following: The performance of the estimator is evaluated by comparing its numerical variance with other estimators obtained by/through Monte Carlo simulations.", "label": 0}
+{"snippet": "this was my first question here and I asked it before I knew anything about this site like the dup questions I want resources (books) for studying Euclidean geometry beyond the high school level. I have been searching for good books on this topic but haven't found any. Could you please provide me with recommendations or suggest good books for this subject to study it in more depth than high school geometry?", "label": 0}
+{"snippet": "So, back in my school, our teacher was teaching structure of an atom. I had some doubts, like why do hot objects emit radiations and so many. I noticed that every question I had asked had an answer. If I added a why to it, thats another question. It mostly came to a conclusion that all atoms want to attain stability. My question is why atoms want to attain stability and can I relate it to entropy?", "label": 0}
+{"snippet": "How is this construction correct? The drawing-room began to look empty: the baccarat was discontinued for lack of a banker; more than one person said goodnight of his own accord, and was suffered to depart without expostulation; and in the meanwhile Mr. Morris redoubled in agreeable attentions to those who stayed behind. (Robert Louis Stevenson) In my humble opinion, the correct sentence should be: ... banker; more than one person said goodnight of his own accord and was suffered to depart without expostulation; .... We are not supposed to use commas when a second verb (was) has the same subject as an earlier one (more than one person). Of course, my problem lies only in that part of the brief.", "label": 0}
+{"snippet": "I am looking for a word for an environment where people feel choked. For example, the environment in medieval Europe (or in communist era) was far from free. One felt choked/strangulated. Is there is word to describe such an environment? For eg, for happiness, one could say An era/regime of happiness. What would that be for choked? Update: I was trying to say that the age of Enlightenment was a response to a 'choking kind of environment' where the church had too much control over people's lives.", "label": 0}
+{"snippet": "Whenever there is contact between objects, there exists a normal force. If we apply force on an object, our hands are in contact with the block, so there will be a normal force on my hand and normal force on the block, so the net force acting on the block will be the applied force plus the normal force. Why don't we include the normal force acting between our hand and object?", "label": 0}
+{"snippet": "I've seen a lot of proofs of the convergence properties for the Fourier series of continuous periodic functions that use the assumption that the function's derivative and second derivatives exist and are also continuous. I was wondering is the stipulation that the derivatives exist considered not that restrictive of an assumption because we can consider the Stone-Wierstrass polynomial approximation of the function instead which converges uniformly to any continuous function on an interval and does have continuous derivatives?", "label": 0}
+{"snippet": "According to Transformation of the energy-momentum tensor under conformal transformations The schwartzian term in the transformation properties arises due to the stress tensor being defined as the normal ordered classical expression, where the normal ordering happens with respect to the given coordinate frame. However, the infinitesimal transformation properties of the stress tensor can also be derived in terms of conformal Ward identities. I think it is kind of magical, that apparently the derivation in terms of the path integral \"knows\" about the appropriate change in normal ordering under coordinate transformations and I wanted to know, why the path integral implements the right normal ordering procedure, without having somehow incorporated it explicitly?", "label": 0}
+{"snippet": "I'm writing a book using the book document class and, for whatever reason, one of my chapters has its contents start on the next page rather than the current page. I have no idea why this is; I looked for manual page breaks or anything that might be causing an issue to no avail. Each chapter is broken up into a .tex file that inputs other sub-chapter .tex files. So, I'm not really sure what to post as far as a MWE since this issue plagues exactly one chapter. Is there some arbitrary setting or command that I accidentally enabled that does this? \"Broken\" chapter: Example of a \"correct\" chapter:", "label": 0}
+{"snippet": "In The Symmetric Group the author, Bruce Sagan, uses the terms degree and dimension of a matrix representation synonymously to mean the number of columns of the matrices. However, I have also seen elsewhere that the degree has been defined as the number of columns in the matrices, whereas dimension refers to the dimension of the vector space on which the group acts. I guess the author can define the terms how he wants, but is there a convention for what these terms mean more precisely?", "label": 0}
+{"snippet": "For an animation with TikZ and Asymptote (that I am somehow familiar with), its size is accumulative with the number of steps. I am mimicking animation for From Random Polygon to Ellipse, take a polygon with random vertices, find the mid-points of its sides, and use these to create a new polygon, replacing the original. Do this repeatedly and an ellipse will eventually form. See here for more explanation. In this situation, the number of steps/frames is large or extremely large, and only last step/frame is needed. Can we do it with TikZ or Asymptote? Do you have any other recommendation? PS: I can add a MWE with TikZ/Asymptote, but as said above, I think it is useless.", "label": 0}
+{"snippet": "I am creating fill-in the blank notes for my class using the Censor package, a solution I found on this forum here. What I can't figure out is how to make the blanks for my students to fill in longer -- ie, I don't want text to be ____ but more like ____________ since most people don't have tiny, perfect handwriting. Is there a way to add a multiplier to the length of the blank or replace a character with, say, two or three underscores instead of one so that normal people can fit their handwriting in one of the blanks? If someone has a different, cleaner solution that would be great too; the post explains the gist of what I need to do.", "label": 0}
+{"snippet": "I am searching for the title and author of a book once lent to me. I cannot recall much about it other than the color scheme used on the cover. The cover was black with orange lettering. Perhaps there was a gray strip at the very top. It looks somewhat like this cover. However, as I recall, the book had some depiction of a matrix on the front cover. The title had Matrix or Matrices in it. Perhaps Theory or Applications. If anyone knows what book I may be thinking of, a citation would be very appreciated.", "label": 0}
+{"snippet": "Consider the above diagram. I am currently learning about standing waves in an open and closed tube. To me, it is trivial why at a closed end, there must be a node, as particles are not free to move around back and forth. However, to me an open end is not so trivial. Why must it be an antinode rather than some other part in the wave?", "label": 0}
+{"snippet": "Could someone help me constructing such segment AB in Geogebra that would satisfy such properties: by moving the point A the segment moves as a solid body but does not rotate by moving the point B the segment changes its orientation and size the segment should be able to move like a solid body even if one of its edge points is attached to a line I have already tried to use vectors but got the result that don't satisfy those properties above.", "label": 0}
+{"snippet": "I am wondering if an incident gamma could compton scatter from the delocalised pi-electrons in an aromatic compound (e.g. liquid scintillator). I understand that compton scattering is valid for free electrons, and is usually described in terms of the outer most atomic energy levels where incident photon energy >> binding energy. However, how about compton scattering from molecules, and particularly delocalised electrons in aromatics? Furthermore, if it is possible, would the scintillator be excited and scintillate after a pi electron is removed? Thanks!", "label": 0}
+{"snippet": "The following are the formatting guidelines for citation call-outs and formatted bibliographic entries provided by the journal International Economic Review: Unfortunately, the journal does not provide a BibTeX bibliography style file that would implement these guidelines, and no template is avaibable in https://www.overleaf.com/learn/latex/Bibtex_bibliography_styles. I was wondering whether there is an encyclopedia of bibliography styles that I could choose from. Or, how shall I customize it by myself?", "label": 0}
+{"snippet": "basically the problem is the same as in a question i previously asked: Draw shaded region using tikz and pgfplots Now the problem is that the region i want to draw is more complicated, mainly because of the functions involved: This is what i want to obtain, but i don't know how to change the code in the answer in order to draw the graph showed in the image, also because tikz does not really get along with sqrt function. Does anyone know how to solve my problem?", "label": 0}
+{"snippet": "There are many methods for diagonalizing matrices; probably the most widely used is the combination of household transformations and the QR algorithm. Is there any superior method for diagonalizing large, non-sparse real symmetric matrices? Superiority can be a bit muddy, so I define it as fast, numerically stable, does not require large amounts of extra memory, and lends itself to parallelization and vectorization. Crosspost: SciComp.SE", "label": 0}
+{"snippet": "If a stationary charge is kept in front of current carrying wire , from charge's perspective the protons are at rest with it and electrons are moving , so shouldnt there be a lenght contraction in electrons and there density increase and stationary charge should feel a force , but it is seen that it doesnt?? please answer the question in stationary charge's frame of reference when electrons are flowing in the wire", "label": 0}
+{"snippet": "It doesn't have to be a MacBook exactly, other switched power supply powered metal case devices are good enough, but MacBook is the most common. It must be AC powered; the effect disappears when unplugged. Your other hand (which doesn't slide on the surface) must not touch the surface; the effect disappears when touching the surface with the other hand. You must move your finger; the effect disappears when you stop. The same effect can be felt by sliding on someone else who touches such a device. It's definitely not a potential difference. I suppose it's mechanical resonance, but can't explain.", "label": 0}
+{"snippet": "True or false question! Conduction is the slowest mode of heat transfer - true (given in internet) Now my question is, let's say you want to boil some water, in this case should not be the conduction mode be faster than convection? I mean within seconds, we can feel the heat energy if we touch that beaker, where we need some time to feel the same amount of heat energy from water. Kindly elaborate on this.", "label": 0}
+{"snippet": "Let there be some air contained in a vessel whose walls are elastic. The vessel is closed and we impart some velocity to it. Please note that the gas inside the container is stationary w.r.t. the container. But the container, itself, is moving with some acceleration. The gas particles should press against the walls in a direction opposite to the direction of motion. My question is can we say whether the internal pressure created by the gas particles increase or decrease with increase in the acceleration of the vessel?", "label": 0}
+{"snippet": "The electrons in the hydrogen molecule experience the same potential and are thus in the same state, so the Pauli exclusion forces them to have opposite spins. Since the protons are identical by symmetry, are these in the same state too? If they were, then the spins would be forced opposite and orthohydrogen would not exist. So in what way am I thinking about this wrong? Is it that the ground state for the protons is degenerate?", "label": 0}
+{"snippet": "Aperiodic tilings for the plane are quite popular. I can't find any papers on aperiodic tilings on infinite surfaces like a cylinder. One reason might be that these are no longer called tiles but something else (a curved finite surface). Do references for this exist? Periodic tilings of cylinder can easily be accomplished with a machine: https://en.wikipedia.org/wiki/Knurling A lathe machine has parts that rotate and easily create a periodic pattern that has one tile type. Not sure if there exists a machine that would do it with multiple tile types. My end goal is to find a similar method to aperiodically tile a cylinder. At least one part of rotation would have to exhibit aperiodic behavior, but I leave that outside of the scope of this question.", "label": 0}
+{"snippet": "If we have a set of sentences S in first order logic. We know that we can create a first order theory Th(S) from S, which is the \"set S\" union \"the sentences which we can prove them from S\" . Also as first order theory, this theory follow the rules (axioms and rules of inferences) of first order logic. Does it has sense to define the Th(S) as above but with an extra union with \"axioms of first order logic\" ? Also can i consider the Th(S) as formal system which has \"intersection\" with the formal system First Order Logic?", "label": 0}
+{"snippet": "In Bell's Spaceship Paradox, are there any direct observations that the stationary observer can make that would justify the breaking of the string without taking into consideration as to what's taking place in the frames of the ships? In other words, can it observe any changes in the string's properties that would justify the break without having to switch or calculate in other frames? If the string is replaced by a bar that can stretch a bit before it breaks, in the rocket's frame it would appear that the stripes become broader before the bar breaks. What would the stationary observer observe?", "label": 0}
+{"snippet": "Can the longest length of a regular icosahedron be equal to the longest width and the longest height? Since the icosahedron is regular, this would mean its faces would still have to remain as equilateral triangles. If this is not possible, are there any ratios between length, width, and height? As a follow up question, can we use edge lengths to determine the length, width, or height? Are there any possible equations?", "label": 0}
+{"snippet": "Example: She ate one or more apples, and each apple of the one-or-more apples was either red or green. In the example, if \"one or more apples\" is the antecedent, should the reference back (i.e., \"the one-or-more apples\") be hyphenated? My thinking is that \"one-or-more\" in \"the one-or-more apples\" works as a compound adjective or \"compound quantifier\" when referring back to the antecedent of the example, and hyphenation of the compound adjective or quantifier improves readability. Readability is not an issue in the example, but repeated references back to such an antecedent with the hyphenation seem to be easier to read in longer forms of writing.", "label": 0}
+{"snippet": "I understand \"what (a) nerve!\" means \"how rude\". I somehow always thought \"what a nerve\" is more common and was surprised at the exchange made in this question. Apparently American English speakers feel \"what a nerve\" is strange. My questions: Is it correct to think that the difference is regional? More specifically US/UK? If there are native speakers from other countries, how do you feel about \"what a nerve\"?", "label": 0}
+{"snippet": "A vertex is defined as a 'meeting point of two lines that form an angle'. When I increment the circumference of a circle into infinitesimal small increments I get something like shown below in the picture. This infinitesimal small increment of the circumference can then be divided into left and right which is shown by the black arrows in the picture. My question is, if the part of the circumference is infinitesimal small, the left and right part of it would not be curved and therefor the above mentioned description of a vertex would be true.", "label": 0}
+{"snippet": "I have heard of definitions along the line of saying that a transformation T of something with respect to a certain property p is symmetric if, after T is applied, p remains unchanged. Is there a way of refining this definition? How could you use this definition to show that fractals are symmetric? What are T and p? If something satisfies a recurrence relationship, is that a type of symmetry? ################################################## From the comments, I am getting the impression that there is no specific definition of mathematical symmetry. Fractals are frequently described as being highly symmetric. The idea is that you can uniformly contract or expand a fractal and lay it on top of itself.", "label": 0}
+{"snippet": "Given a stochastic differential equation SDE the mathematical definitions are clear to me, i.e. we want to find a filtered probability space, a BM and a process which satisfy the SDE. However in the real world we are given a probability space and a BM on it (e.g. the uncertainty on the stock market). Why constructing these weak solutions which are purely mathematical objects would help?", "label": 0}
+{"snippet": "When two black holes are merging, one of them can be ejected if it has less mass than the other black hole, so the gravitational waves emitted by both of them is unbalanced, and the more strong ones would \"kick\" the smaller black hole out of the merger, sometimes even kicking it out of the galaxy. This is known as gravitational recoil. Can this also happen with other objects like stars or planets so that they can get ejected to very high speeds? If not by the same mechanism, maybe through a similar one?", "label": 0}
+{"snippet": "Newb here. When I look up how to create two columns, I get a bunch of tutorials that assume one text will run from the bottom of column A to the top of column B, like a newspaper article that spans two columns. That's not what I want to do. I want to put one text in the left column, a different text in the right column. Like two separate newspaper columns. When the text reaches the bottom of column A, instead of picking up at the top of column B, it should start at the top of column A on the next page.", "label": 0}
+{"snippet": "This is not a hint-to-solve-exercise question, but just mathematical curiosity involving one my favorites branches of this beautiful science: group theory. Having done some research in databases like this one, I came across with some different ways to construct groups of a given order. Since I don't know about extensions, my knowledge is more limited but I have a question: how many \"different\" group/subgroup products are there? In the database I wrote, I found things like \"central product\", \"wreath product\" (apart from the typical direct or semidirect ones), etc, but, are these products the only constructions? Am I missing other types of products?", "label": 0}
+{"snippet": "As I wrote in the question, what is thermodynamic equilibrium? From what I understand is a state where the thermal, chemical properties don't change with respect of the time and there is a mechanical equilibrium as well. But can this be true for example, in a body with a temperature field with gradients? I was reviewing this concept because thermodynamic equilibrium is critical in defining a reversible process and I want to understand it well.", "label": 0}
+{"snippet": "I have a presentation with one of the slides titled Results: limited-data in-the-wild semantic segmentation What would be the correct way to capitalise this title? https://capitalizemytitle.com/style/APA/ recommends either Results: Limited-Data In-The-Wild Semantic Segmentation or Results: Limited-Data In-the-Wild Semantic Segmentation with the latter of the two being the one I originally used. However, this seems to be in conflict with the recommendations from this question, which say words like \"in\" or \"the\" should never be capitalised.", "label": 0}
+{"snippet": "Imagine if a box tied on string is swirl around a rough surface. The centripetal force might be contributed by both tension and friction. Since the surface of the object is flat instead of spherical surface, it might not rotate along its motion (rolling like a tyre). So, what type of friction should we consider that contribute to centripetal force?Is it static friction or kinetic friction", "label": 0}
+{"snippet": "I know that: At this time tomorrow, I will be playing cricket. is used since the so-called future continuous is used to talk about a continuous activity at a specific time in the future. Even present continuous is used to talk about a planned activity in the future. So my question is can we say this? At this time tomorrow, I am playing cricket. I am eagerly waiting for the scholars' or experts' comments on this.", "label": 0}
+{"snippet": "I was looking at the modeling of ttW production (but the question is general) and came upon an off-shell corrections paper. As I am no expert on MC generators, I am not sure if these off-shell corrections can lead to different amounts of radiation compared to an on-shell sample. My intuition says that maybe a Sudakov factor contribution might shift slightly and because of the Pt shift of jets the PS might differ but I do not expect large differences in number of jets as I can't think of an off-shell channel diagram that would differ significantly in extra radiation. Is this the case or are there examples where one does see noticeable differences (only in the modeling/in data as well)?", "label": 0}
+{"snippet": "The narrator in this video has a very clear native English accent. What caught my attention is near the end of the clip when he said: They spend so much time in the tree and they sleep while hanging upside down like a bat. Though I know that it's grammatically correct to compare a plural noun with a singular noun, such as: They are much slower than him. Or: They ran as slow as a turtle. However, I am still wondering how often (or rare) for native speakers to compare many \"lemurs\" with plural \"bats\" instead of a single \"bat\" in the first sentence, or at least isn't it abnormal to do so?", "label": 0}
+{"snippet": "In an attempt to understands some basic concepts about manifolds and differential geometry I encountered a concept of a parallel transport. This perhaps may be very naive question, but could one consider an analogy to the parallel transport (as defined in this Wikipedia article) being a ball rolling on a flat table surface? If so, is then such an example also an example of holonomy or not?", "label": 0}
+{"snippet": "Recently, I was attempting to describe the experience of traveling with strangers on one of those pedal trolleys which serve beer - how producing physical effort with others towards a shared goal inspires fraternity or camaraderie. I did some googling for inspire synonyms and a few searches along the lines of inspiring fraternity, but haven't been able to find the word I'm looking for. It would be a synonym of inspire, with this added connotation of specifically inspiring fraternity. Example sentence: Digging a ditch with another man ____ between the two of you. Any clever linguists know a single word to describe this?", "label": 0}
+{"snippet": "I understand that a taylor series is used to approximate a given function at a point to any required degree of accuracy, I have not however understood why when we take the taylor series of a function at point, expanding to infinite terms it perfectly represents the function over the entire domain of the function. Is there a mathematical proof for why this results from approximating a function and its infinite derivatives at a single point", "label": 0}
+{"snippet": "If you have a point mass moving with some velocity 'v' and then a force is applied perpendicular to 'v', physics/mathematics claims no change in the magnitude of 'v' , just a change in direction. But that doesn't make intuitive sense to me because wouldn't a force cause an instantaneous change in the point mass velocity perpendicular to 'v'? Therefore, wouldn't there be instantaneous velocity vectors perpendicular to each other and a resultant vector with a greater magnitude than 'v'?", "label": 0}
+{"snippet": "My professor was discussing this question. After finding out that CR equations are satisified at origin for the function he used the definition of derivative to check for differentiabilty. Also, he mentioned that we can't compute partial derivatives of u(x,y) and v(x,y), and for example one of them turns out to be discontinious at origin then say that the function is bot differentiable. I couldn't understand his reasoning. Isn't that the sufficient condition for differentiabilty?Thoughts? Click here for question", "label": 0}
+{"snippet": "I'm trying to write a book (documentclass \"memoir\") and I would like each chapter to begin alternatively with a greek or arabic letter. I have no problem with greek thanks to the package \"babel\", by contrast whatever attempt to write a-single-arabic-letter creates big conflicts in my template, such as compiling errors, and other problems (such as, the letter is automatically written on the right hand side: and it makes sense, of course, but I just need it as a symbol). I've looked through many other questions, which usually concern writing sentences, and I wonder if there is a simpler method that fits my case.", "label": 0}
+{"snippet": "The way I have it is: the Observable Universe looks as follows. In some ball, all the galaxy clusters exist, then in a bigger concentric ball the dark ages exist (no galaxies), then on the surface of this larger ball at the edge of the observable Universe the Cosmic Microwave Background exists. This leaves no room for an infinite or curled back on itself Universe, so it must be a wrong picture. How do you picture it? It would be advantageous to get a correct picture.", "label": 0}
+{"snippet": "When submitting a memorandum request for approval of something and providing options of for the signer... what is the best way to word the denial option ? Disapproved? Denied? Unapproved? This is intended to allow the approver to circle their response. Approved / Denied Approved / Disapproved Approved / Unapproved I feel disapproved is not the correct word... since they may disapprove of the request in theory but that doesn't mean they're saying no to the action. Denied seems to be more definitive. Unapproved works but seems lackluster in some way and may indicate the action was taken without prior approval or something similar to that.", "label": 0}
+{"snippet": "I am writing my Doctorate thesis in Latex. I am using book class, which by default is twoside and openright. But for the preliminary pages, specifically for page number ii, certificate, it needs to be printed on a new page, but the result is coming out as a larger right-side margin page for being an even-numbered page. The same problem arises for the list of figures and tables also, they are also starting on an even page and the output is a bigger right margin. Please help to overcome the situation. Thanks in advance.", "label": 0}
+{"snippet": "I'm doing undergraduate research on the history of Abstract Algebra (specifically permutation groups) and the notion of symmetric groups in indigenous artwork has come up several times. Is anyone aware of evidence of this 'intrinsic' human desire to construct groups I could point to? Or maybe some natural phenomena that conform to the definition of group? I'd like to have specific examples I can explain (and possibly map some ideas of formalized group theory onto). Thanks!", "label": 0}
+{"snippet": "So I had taken a course on BEC and Cold Atoms. I have read about the properties of non-interacting Bose gas and I was a little concerned about what we mean by two wave functions (of bosons) being the same. Does it mean that they are physically located at the same point in space? I understand that they have the same spatial probability distribution. But it is more than that. I basically want to know given two wave functions how do I say they are the same? A more physical meaning of two wave functions being the \"same\". P.S. This is my first time posting. So please be kind.", "label": 0}
+{"snippet": "Regarding an acceleration in an empty universe, from the special relativity we feel an acceleration in an empty universe since there is still the presence of an space-time with respect to which an acceleration is measured and the equivalence principle says that locally the effect of gravity and acceleration is indistinguishable i.e we feel the gravity whenever we are acceleration and conversely we feel acceleration when there is gravity that means according to equivalence principle we can't feel an acceleration in an empty universe since there is no gravity but special relativity says that we can feel an acceleration in an empty universe ,for me there seems a contradiction between special relativity and equivalence principle. Does anybody make clear this doubt?", "label": 0}
+{"snippet": "I imagine a swinging pendulum being held outside a black hole supported by the normal foce of a jet propelled rocket. The rocket's velocity is approaching light speed, therefore hovering the swinging pendulum right above the event horizon in the strong gravitational potential outside of the black hole. My first question is: what would the frequency be of this pendulum and would this be the natural limit to swinging frequencies? How could the frequency possibly increase more in potential in nature (besides by shortening length)? And following the consequences of this: I believe photons and pendulums behave identically under the influence of a gravitational potential; does this then imply photons also have a natural cut-off limit for their frequency?", "label": 0}
+{"snippet": "If I have an action that is not invariant under a change of coordinates. Does this effect the renormalizability of the theory? The procedure of renormalizing a field theory essentially boils down to carefully keeping track of observables while changing the length scale of the theory. If I have an action that is not diffeomorphism invariant changing the scaling of the action has physical meaning and also has consequences on the parameterization of the theory. How does the renormalization process differ between actions with and without coordinate invariance?", "label": 0}
+{"snippet": "My electromagnetic waves professor said any time an electromagnetic signal is received by an antenna, a transmission also occurs. I have not independently verified this, but I believe it is likely true. Does someone know if this is true, and can the basic physics be explained, please? Note: This question was inspired by my own comment on Antennas and relativity. I'm thinking of this more from a Maxwell's equation POV then relativity, however. ANOTHER NOTE: Per comments below, transmission is usually called \"scattering\" when unintentional.", "label": 0}
+{"snippet": "As an example, why does glass tend to break by means of intergranular fracture? My analysis so far led me to believe that the tendency can be related to the intermolecular bond strength in a given crystal grain and the intergranular bond strength. A stronger bond means that better load bearing. If the intermolecular bond is stronger than the intergranular bond, then a material is more likely to experience intergranular fracture. But is this correct?", "label": 0}
+{"snippet": "So, I know the proof for Halting Problem is not recursive using diagonalization. We prove it using proof by contradiction. First we assume HP is recursive which implies there is a Total Turing Machine. And prove it is not possible by contradiction. But the proof just says Halting Problem is not recursive. It doesn't say Halting Problem is recursive enumerable. So how to prove Halting Problem is recursive enumerable", "label": 0}
+{"snippet": "So in math, analysis in particular, divergent series are not particularly interesting since most sequences are divergent. However convergent series are interesting and they are useful. However, mathematicians have realized they had to be careful and define two types of convergence. Most of the theorems rely on absolute convergence. Therefore my question is, if your series turns out to be conditionally convergent, are you stuck? That is, can you not conclude anything further or can you still work with a conditionally convergent series?", "label": 0}
+{"snippet": "Consider how the wizarding world is hidden from the muggle world in the Harry Potter/ Wizarding World universe. Or in Hell Boy II. The troll market is hidden under a bridge. Red can see it but it's veiled from the human eye. Shadow Hunters. Clary can see the runes outside of the nightclub but Simon can't see them. I have been referring to it as a troll market concept but I feel like there is a better word(s) for it.", "label": 0}
+{"snippet": "So , I will be completing S.L Loney Coordinate geometry book very soon and I feel like I need more practice in Conics especially in Ellipse and Hyperbolae section , Can anyone suggest me a problem solving book in Conics (Not theory, Because S.L loney has a very vast theory and sufficient for my preparation) and the level of the book must up to a competitive level exam or Olympiad. Thank you:)", "label": 0}
+{"snippet": "From Boston Legal (or your everyday conversation): \"He and I will be going on a little vacation.\" \"Where?\" \"Probably best you don't know.\" Being short for \"It would probably be best if you didn't know,\" the spoken version changes the past tense to the present in the second half of the sentence. Is this something a grammarian would find fault with? Or dismiss it as colloquial?", "label": 0}
+{"snippet": "From how I've learned it in school the magnetic vector potential is used as a mathematical tool to simplify problems with current-carrying wires in classical electromagnetism, but is never treated as bearing any physical meaning. After doing some research on it myself, I found Feynman's lecture on the subject, which outlines how this vector potential actually takes center-stage in QED, not only featuring in its primary equations for concepts like phase change but also as capable of producing physical changes such the Aharonov-Bohm effect that can't be explained by the magnetic field alone. Are there any comparable physical effects the vector potential has in classical electromagnetism?", "label": 0}
+{"snippet": "I understand that thunder clouds are a congregation of millions of water droplets. As water evaporates from the ground, these water molecules rise up and collide with water molecules of the cloud, sometimes ripping off electrons. This creates a seperation between positively charged water droplets moving up inside the cloud, leaving electrons behind. Why do the electrons stay at the bottom of the cloud and not move up due to attraction to the positively charged water droplets?", "label": 0}
+{"snippet": "I'm new to fractals and especially the Mandelbrot Set. I've noticed these never ending and self-similar spirals all around the Mandelbrot set, just like the one below: At lower max-iterations, there is a black point in the middle of the spiral, which suggests me that there could be a minibrot there. I've read that minibrots are centered on c values with super-attractive orbits. However, since the spiral never ends, I cannot precisely get the middle point and calculate its orbit. Is there really a minibrot infinitely small at the end of the spiral?", "label": 0}
+{"snippet": "I've been learning about set theory and have heard of something called a \"group\". I didn't understand what it was, even after researching it, but I did find out one piece of information: All groups are sets but not all sets are groups My question is: what is an example of a set that is not a group? That would help me better understand it.", "label": 0}
+{"snippet": "More precisely, \"to\" is banned in the active form: The headmaster makes us honor our teachers but required in the passive (with no agent stated): We are made to honor our teachers I can just say it's something -- for lack of a better term -- mechanical: \"to\" is required to mark the infinitive in the passive voice. But then, why does \"mechanics\" matter in the passive voice but not in the active voice? More puzzling is that this phenomenon seems to apply to causative make, but not to causative force: The storm forced me to seek shelter I was forced (by the storm) to seek shelter Unlike make, \"to\" is required in the active voice of force. Thank you.", "label": 0}
+{"snippet": "Imagine a stationary transmitter which vibrates the surface of the balloon and a stationary receiver half way around the balloon that can pick up these waves. Let the balloon expand. Will the frequency of the received waves change due to a Doppler effect? As the balloon expands, the tension in the surface will increase which could alter the velocity of the waves. This is not a Doppler effect and could be allowed for. I ask the question because the motion of both the source and the receiver due to the expansion is perpendicular to the direction the waves are travelling in, though there is also a velocity of recession, which is different to the velocity of expansion.", "label": 0}
+{"snippet": "In the same context as of \"Trendy names\", why is \"Brandy names\" not used? Brandy comes naturally/intuitively as an adjective to brand in the minds of a new English speaker, instead of the commonly used words like brandworthy, brandable, branded. I want to understand the reason behind such usage. If we assume the word brandy does not denote a specific alcoholic beverage, is it grammatically correct to use \"brandy\" as an adjective of brand?", "label": 0}
+{"snippet": "What are the different methods using contour integration that can be used to count the non-trivial zeros of the zeta function? I know of Backlund's exact formula which is similar to Riemann-von Mangoldt formula. What are the other ways? If there aren't many other different methods, then where can I find the exact derivation, like from scratch to end of Riemann-von Mangoldt formula? I have managed half of it till the point I can derive Backlund's exact formula. Also an evaluation of the limitations would be nice. I know Titchmarsh's works are useful but what other resources can help me?", "label": 0}
+{"snippet": "In the sentence: \"There were people everywhere. They thronged the streets, choking the alleys. They had come in their thousands to see the light show\" I would group the infinitive of purpose and past perfect together, so that the sentence refers to a plan formed prior to the events of the story. At the same time, the arrival itself takes place before the crowds assemble and begin 'thronging'. Is my analysis off? EDIT: I apologise. I had to cut this short before clarifying. The sentence seems to be referring both to the arrival and a preformed plan.", "label": 0}
+{"snippet": "I'm trying to prove the above statement, and I had a look at this site. This ends the proof with the following statement the rank is the number of non-zero eigenvalues But, this is what makes me confusing, because it's not all the case that rank of a matrix equals the number of non zero eigenvalues as far as I know. This shows a counter example of this. Any comment about the rank of idempotent matrix would be grateful.", "label": 0}
+{"snippet": "I understand the general notion of twist like that of a mobius band(like a cylinder cut open and the glue the edges together with a \"twist\") , and the torsion in the context of algebraic structures like groups, in which a modulo-n torsion indicate when we multiply some element with n, we get the identity(please correct me if there is an error in my understanding). So in the context of topological groups, can these ideas be related, like in the case of a lie group, where we can talk about both twist and torsion and whether these ideas turn out to be related?", "label": 0}
+{"snippet": "I want to add a citation inside a pdf figure, and would like the citation to be a link to the bibliography. I know embedding a pdf with includegraphics normally mangles the link, but I have found a solution (in pdflatex), using the pax package. But am open to any other solution. pax preserves the hyperlink, and I tested it is working with a www address. But for the internal link to bibliography, I am not sure what link address should I use. At the moment, I insert this link in the pdf figure \"cite.citation_key\" But the result is that the hyperlink points to /home/user/cite.citation_key instead of the bibliography. Does anyone know how to achieve this.", "label": 0}
+{"snippet": "We were happy before. There was a market next to the school before. I saw a whale before. These are from a grammar book for kids that I'm proofreading, and this part is about \"past simple tense\". I would like to ask if these sentences are grammatically correct regarding the use of \"before.\" It seems that \"before\" should be used with perfect tense? Should I make the following changes? Thank you! We were happy then. There was a market next to the school (sometime ago). I saw a whale (sometime ago).", "label": 0}
+{"snippet": "We have the adjective \"facial\" for the noun \"face\", and I am wondering what the counterpart for the noun \"head\" is. I could not find it on Google, and ChatGPT told me \"cranial\" which seems a bit different from what I expected. Thank @Stuart F for the comment! My original thought was to make a joke on myself who can have some kind of \"head expressions\" (corresponding to \"facial expressions\") because I am a bit bald. And I am also happy to see that the vocabulary can be different in different contexts!", "label": 0}
+{"snippet": "Newton's globe experiment: two globes that share all their features are connected with a rope in an otherwise empty universe. Newton introduced this experiment to show that even though the cases where the globes don't move and where they rotate are not distinguishable relationally (i.e. considering their distance to each other), we can nevertheless distinguish them due to inertial forces that only occur in the rotation case (tension on the rope between the two globes). My question: could Newton also have chosen an example using linear accelerated motion instead of angular accelerated motion? Inertial forces should occur there as well. If not, why does he need circular motion to make his point?", "label": 0}
+{"snippet": "I know that \"soliton\" waves can consist of a crest without a trough. One would expect the reverse to be true as well. However, this Wikipedia excerpt says, So for this nonlinear gravity wave it is the total water depth under the wave crest that determines the speed, with higher waves traveling faster than lower waves. Note that solitary wave solutions only exist for positive values of H, solitary gravity waves of depression do not exist. Is this true, and if so, why?", "label": 0}
+{"snippet": "I'm still introducing myself in derivation, antiderivation and integrals, because I haven't studied it in class yet (I will study it next year and derivation in some months), but well, about my question I have seen that integrals and antiderivatives, at least, looks like the same, so, is that true? and also I didn't understand at all why the integration gives you the area, I mean, realize that derivation gives you the value of the slope is easy, but why the antiderivation gives you the area is a bit harder for me to understand, thanks!", "label": 0}
+{"snippet": "Alright so I am confused somewhat about Neutron Heavy Nuclei not decaying, or more specifically why it is that Neutron Heavy Nuclei sometimes decay by emitting Neutrons. Someone has already answered why neutron-heavy nuclei decay in general, weak force beta decay basically happens until it can't, but I do not understand why neutron heavy nuclei can, sometimes, emit Neutrons. I am talking about the light elements that have neutron upon neutron upon neutron. Hydrogen Isotopes beyond Tritium decay by Neutron Emission, why? Why doesn't it decay by beta decay? Why do other neutron heavy light elements perform neutron emission?", "label": 0}
+{"snippet": "We know that flowing water remains liquid even in the below-zero temperatures (a good example is rivers in arctic regions). Of course water doesn't remain liquid forever if temperature goes down constantly. Also, I know water freezes from surface. But that's for stationary waters like lakes. Not for flowing waters like a dam output which is so fast. I think it depends on a sort of things, like the speed of molecules, the viscosity of water, etc. Can we formulate it to find the answer? Perhaps with such a formula we can find the freezing temperature of other flowing liquids as well. And a minor question: How does the density of flowing water behave in below-zero temperatures?", "label": 0}
+{"snippet": "Consider a one dimensional chain of N classical point masses interacting with harmonic neighbor forces (with periodic boundaries for specificity). If the positions and velocities are prepared in a configuration corresponding to a specific oscillation mode, can the energy be transferred to other modes ? Or does the chain oscillate in that prepared mode forever ? Intuitively I do not see a reason why the energy should be transferred to other modes, but I am not sure. However supposing that is the case, does the chain return to that mode if small random disturbance is added at some time ? How is the stability of this mode to perturbations ?", "label": 0}
+{"snippet": "I was planning on using whipping boy but it seems that means more like a scapegoat (ie someone who is innocent but made to take the blame for others). Moreover, I want something that means that everyone seems to point to one particular person as the bad example and turn a blind eye to the same behavior in others. The issue is more with reputation or perception from an outside group than guilt per se, but I don't want to suggest that the example person is innocent. The context is history.", "label": 0}
+{"snippet": "I would like to calculate the repulsive force between two permanent magnets in a different variations of distance between the two polarity faces. Can the different distances associated to different repulsive forces be related to the magnetic field? Can the magnetic field have a variation when the distance between the magnets change? Can a tesla meter measure the magnetic field in the space between the two magnets? Can the repulsive magnetic flux between two permanent magnets be measured with a tesla meter? Thank you!", "label": 0}
+{"snippet": "I was writing a Statement of Purpose letter and I am stuck with this dilemma. Here is what I wrote: I pray that this letter attains your approval. I first used \"gains\" but my mind instantly switched it to \"attains\", as the word seems more formal...and then I thought of \"obtains\", which only got me more confused. All I know is that these words have the same meaning of getting something but I'm still struggling with the context/condition it should be used on. Which one should I use?", "label": 0}
+{"snippet": "I found that the definition of coherent phonon: A femtosecond laser pulse can initiate collective, in-phase atomic motions in solids called coherent phonons. My question is: what is the difference between coherent phonons and acoustic phonons? Acoustic phonons also mean the displacement of atoms has the same amplitude, direction and phase. Does it mean atoms move in phase and collectively for acoustic phonons? Thanks in advance.", "label": 0}
+{"snippet": "Is there a word that symbolize a status of either unstarted, started or completed ? For example a football match can be either unstarted, started or completed. I would like another word than \"status\" to indicate those lifecycle adjective, as we have a lot of other \"status\" in this context. Something like \"completionStatus\" : but this is not really it, as this is just about completion. I thought about lifecycle but that's too biology oriented.", "label": 0}
+{"snippet": "Throwing a small stone on the surface of a calm pond of water creates concentric ripples on the water surface starting from the point of impact and travelling outwards like transverse waves. At the same time the momentum of the sinking stone creates longitudinal underwater pressure waves that propagate outwards with the speed of sound in water. I am interested for an equation that describes the propagation speed relation of these two different types of waves created. Will the surface transverse waves have the same propagation speed with the underwater longitudinal pressure waves and if not how can the propagation speed of each type of wave calculated for water?", "label": 0}
+{"snippet": "How do you find the area of the highlighted subsection of a circle? Linked Below. The circle has a known radius from A-O and a trapezoid that lays inside it. The trapezoids longest edges contact the circle circumference at points D and E. All edge lengths of the trapezoid are known. The shortest distance from the center of the circle to the inner most edge of the trapezoid is also known, O-F. I'm trying to design a lid with these dimensions and need to know the area to get the lids weight. The trapezoid portion with the highlighted area will float on top of a fluid. Unfortunately, I don't remember much from my High School geometry class. Thanks for the help in advance.", "label": 0}
+{"snippet": "I'm curious about pendulums and their behavior during a solar eclipse. I also wonder about gyroscopes and if their behavior during stellar events has been observed. I wonder about the both of them, and of their relationships to each other. I wonder about Mobius loops and gyroscopes; what if a gyroscope was a Mobius loop in rotation, would it precess in a traditional manner? What if you lined the outer rim of a gyroscope with a plurality of strong magnets, all spinning the same way outwards? What would happen next? I wonder endlessly.", "label": 0}
+{"snippet": "Suppose, I have a sample from an unknown distribution. I want to prove/disprove (mathematically!) the following statement: The maximum likelihood (ML) estimator for the (unknown) population mean will always be equal to the sample mean irrespective of the likelihood function. We suppose that, the likelihood function is twice differentiable with respect to its parameters and the mean and variance is finite under the inverse likelihood function (pdf). I believe for symmetric distributions it is straightforward. To maximize the likelihood the center of the mass should be placed at the mean. So, sample mean should be the best estimator to maximize the likelihood of the observed data. But I can not relate to it mathematically.", "label": 0}
+{"snippet": "I have a question about contact force and normal force. whenever two bodies are in contact and one body tries to push another body there will be a normal force acting between them. like when we push or pull a body, when we hit a ball by a bat, when we lift a body from ground, like pushing a wall at horizontally or at an angle etc... these all are contact forces does that mean that all contact forces are normal force?", "label": 0}
+{"snippet": "Basically something that starts with the substitution principles, definition of an equation, of subtraction and division, axiom of opposites, your usual commutative, associative, distributive axioms, and covers all the way up to the end of high school trigonometry. Dolciani's two volume \"Algebra: Structure and Method\" was good but I need another similar work. Serge Lang's \"Basic Mathematics\" wasn't good enough. Reading the first few chapter of abstract algebra books wasn't that helpful as they were too broad in scope. Any other suggestions?", "label": 0}
+{"snippet": "Lately I've been approaching problems with conservation of momentum of systems, I was wondering, if I draw the free body diagram, then write the equations and then add them togheter; if momentum is conserved along an axis I will always get that the sum of the forces must be equal to zero in the equations of the dynamic along the axis where momentum is conserved, is that right?", "label": 0}
+{"snippet": "I see that the Oxford dictionary has a plural dice for \"a small cube with a different number of spots on each of its sides, used in games of chance\". However, there is no plural listed for \"a block with a special shape that is used for shaping pieces of metal\" (both definitions summarized). Researchgate has a photograph of \"Two dies arranged side-by-side\". Is dies the correct plural of this meaning of die? Why do the two meanings have different plurals? Which was in use first?", "label": 0}
+{"snippet": "For a new book I am writing with two friends, I like to include three biographies (mine as well as the other two friends) after the preface. Ideally, we like to keep three photos (A.jpg, B.jpg and C.jpg) on the left and our biographies on the right.. The book is in single column format, and I don't know how this biographies page can be done in double column format. Also, the biographies need to be aligned with our photos. We are OK with any format or style in a professional way as long as we can post our biographies along with the photos. Your suggestions are most welcome. Thank you.", "label": 0}
+{"snippet": "I have a pretty strict requirement for a document (I'm currently using memoir), which must: use biber/biblatex in the usual way based on a primary bib file (e.g., main.bib), and sort the resulting list of refs by author then year. at some other point in the text, I want to print out a list of all the refs of type article from a secondary bib file (e.g., extra.bib), sorted by youngest to oldest. Is there some biblatex voodoo that would make this easy-ish?", "label": 0}
+{"snippet": "This particular example comes from a peer-reviewed publication with authors who seem to be native speakers: This trend is both popular and has presented a variety of challenges I wonder if this is grammatical? If this sentence didn't have \"both\", we would parse it as follows: This trend ((is popular) and (has presented a variety of challenges)) But with \"both\", what do we have? This trend is both ((popular) and (has presented a variety of challenges)) but this gives us \"is has presented\", so this parsing is incorrect. Alternatively, we could try This trend ((is both popular) and (has presented a variety of challenges)). but then \"both\" goes inside the first coordinate. This is different from, say, You and me both where it's at the end.", "label": 0}
+{"snippet": "How or where can I find the Absorption cross-section of Gaseous Ions? I have looked over the internet and can only find it for neutral atoms. Does it increase or decrease for ions? I have found formulas but they include the imaginary part of the refractive index of the specific medium and I can't find how to calculate or get a relative order of magnitude for it even for plasmas. Scattering cross section will do too Please help.", "label": 0}
+{"snippet": "Let ABCD be a convex quadrilateral with AD = BC. Show that AD and BC determine congruent angles with the line passing through the midpoints of sides AB and CD... MY IDEAS MY DRAWING As you can see i noted some points. Okey, so, i thought of similar or congruent triangles. But i don't know where to start. Hope one of you cn help me! Thank you!", "label": 0}
+{"snippet": "There is literature on the lie symmetries of quantum harmonic oscillator differential equation. The generators satisfy certain lie algebra. On the other hand, we have ladder operator method. The relevant operators satisfy some lie algebra. I was interested in knowing if there might be some connection with the two approaches. Is there some relation between the two lie algebras. Cause if there is, it might help me explain ladder operator method better.", "label": 0}
+{"snippet": "In the Einstein field equations, the only tensor that shows up is the Ricci tensor and the metric tensor, together with the Ricci scalar. The Weyl tensor though is a tensor that is a part of the Riemann curvature tensor as well (the off-diagonal part). It represents tidal forces, which are non-local. Why doesn\"t the Weyl tensor show itself in the Einstein field equations? Is it because gravity is based on the equivalence principle, which is a first-order equivalence?", "label": 0}
+{"snippet": "I had recently come across \"Russian for the Mathematician\" by S.H. Gould, and saw it as a wonderfully useful resource. I have very little experience in Russian (only skill is ability to read Cyrillic), but I saw it as a useful introduction to the language, in the sense that I would be able to decipher Russian language math literature without the need to be entirely fluent or understand every word. Reading through a preview, I like how it breaks apart the words piece by piece to I was wondering if there were any resources for other languages in this similar vein, e.g. learning French or German with the main focus of reading scientific or mathematical literature. Downloadable here", "label": 0}
+{"snippet": "I hear this kind of false implications pretty often, e.g.: If you're smart you'd agree with me People who understand the situation would all agree that ... Anyone who says something else must be trying to confused us These often come up in social deduction board games, where the good team is trying to gain information and the evil team is trying to spread misinformation. If someone says one of these lines and I disagree, they can say \"see, he disagreed, so he must be on the evil team\". Is there a term for this kind of faulty logic trap?", "label": 0}
+{"snippet": "Is it possible to use magnets to lessen the force of a pull that is associated with Cervical Dystonia (spasmodic torticollis) which is causing an involuntary pull of the head over one shoulder. Having the magnets attached to clothing on one side such as a shoulder pad and more on a collar. Would the strength of magnets keep the head from pulling to other side ? As a person with Dystonia I'm trying to find a way of creating some sort of \"crutch\" to allow the head to look straight :)", "label": 0}
+{"snippet": "Imagine a tank that accelerates towards a relativistic speed. As the caterpillars are at rest with respect to the ground, the caterpillars will show no length contraction there. But the tank body above it will. The upper part of the caterpillars, on the other hand, will show more contraction than the tank body does. What will happen? Will the lower parts of the caterpillars slide along the tank body to \"deliver\" an extra piece of caterpillar for the upper part which contracts more than the tank body? Will the caterpillars snap? I'm not sure.", "label": 0}
+{"snippet": "This question may have been asked a bunch of times, but I have not found exactly what I was looking for. I say calculus, but mathematical/real analysis works as well as long as it does not have calculus as a prequisite. I have been looking for books that take an inquiry based approach, where the theory and everything else is build by solving problems with minimal explanations from the Author aside from introducing some definitions (Bogart's \"Combinatorics Through Guided Discovery\" is exactly what I am looking for, but for calculus/analysis). I am aware of jiblm, but I was wondering if there are published books on calculus/analysis using this approach that may be more suitable for independent learners?", "label": 0}
+{"snippet": "According to MathWorld, the probability distribution of the length of lines between randomly selected pairs of points inside a cube has a very complicated form. In particular it is not uniform. This distribution relies on the fact that the pairs are chosen uniformly and independently. My question is - is there a way to do a reverse engineering and enforce uniform line lengths density? Namely, say I want the probability distribution of the length of lines between randomly selected pairs of points inside a cube to be uniform, from what probability distribution should I sample my pairs? In particular, I want this sampling to still be independent, but not uniform.", "label": 0}
+{"snippet": "If I use a transformer the get a high voltage, the power of the transformer remains the same, as the current is reduced proportionally. However, according to ohms law, the current through a resistor connected to that secondary side of the transformer will be the voltage divided by the impedance of the resistor. But that is impossible, because this way both the voltage and the current felt by the resistor will increase, meaning an increase of power, while the power of the transformer remained the same, compared to the first side of it. Please sort out my confusion over it.", "label": 0}
+{"snippet": "Yesterday I heard this: suppose you have a rubber hose, in which you inject helium, which replaces the air which was there before. Now, because there is no helium in air, so the partial pressure is zero there, the helium escapes through the rubber into the surrounding air and creates vacuum in the hose (insofar it is possible in a rubber hose, effectively you'll get substantially lower pressure than before). Is this correct? If so, se can create vacuum using a solid membrane, which permits the gas (that we used to replace the air inside) to escape to the outside world, where its partial pressure was zero/low?", "label": 0}
+{"snippet": "I have found a sentence that goes like this: \"Serenity may be the name of the company, but it doesn't describe the company.\" Someone translated this sentence to my language as if \"may be\" meant there was a possibility that Serenity was the name of the company (and a possibility that it wasn't), but I feel like the sentence really means \"While Serenity is the name of the company, it doesn't describe the company\". Is there a specific name (akin to \"non-continuous verb\" or \"inclusive or\") for this usage of \"may be\"? I want to be able to say \"This sentence is using a [...], so the correct translation would be...\", chere [...] might be something like \"comparative may\" or \"comparative auxiliary\".", "label": 0}
+{"snippet": "[A partial groupoid (half-magma) is a set S equipped with a (single-valued) partial binary operation, as in Bruck's Survey of Binary Systems.] This question may be nonsensical, given that the duality between Cayley graphs and groups is deeply related to the mutual complete-ness of each structure. If that is the case, perhaps what I am really asking for is a common diagrammatic representation of partial groupoids. Here is a crappy mock-up of what I'd expect from diagrams of half-magmas in the latter case. If Cayley graphs encode the abstract structure of group, is there a similar type of graphs that encode the abstract structure of a partial groupoid? If there is not, is there some other commonly used diagrammatic representation used for partial groupoids? Thanks!", "label": 0}
+{"snippet": "There is a medical specialty called obstetrics and gynecology. In the UK I have only heard this truncated to something like the first syllables separated by a truncated \"and\". This could perhaps be written as \"obs 'n gy-nee\". I have multiple times recently heard this specialty referred to by Americans by spelling out prominent early letters, an initialism. This could perhaps be written as \"oh bee gee why en\" (as in one spelling out OB GYN). Is this a UK/US difference? Is there a \"right\" way to abbreviate this specialty? I am particularly interested in how it is said, as opposed to how it is written.", "label": 0}
+{"snippet": "While solving inverse function problems, I got confused in a part, like for any Inverse function to be defined, it must be one-one and onto, then in many questions why the codomain is given more than the Range as if we know that the codomain must needs to be equivalent to the Range for the Inverse function to be valid or defined, then why does they gave us the codomain different from the range? Kindly help me solving this doubt.", "label": 0}
+{"snippet": "So I understand that matter emits EM waves when hot. And that the higher the temperature, the shorter the wavelength, so cooler flames start off orange and the hotter flames reach light blue and white. What I'm wondering is if, hypothetically, you could take that blue-white flame and could make it considerably hotter, would the emitted wavelength reach UV thus making it invisible to the human eye? If so what temperature would need to be reached?", "label": 0}
+{"snippet": "I am interested in modeling the populations of low-lying, long-lived \"dark\" electronic states after excitation of an atom in the ground state with a laser. Using just a regular rate equation solver, I get nonsensical results. Provided there are no interactions between the low-lying states and the branching ratios to these states are known, is something like an Optical Bloch Equation solver needed to determine their population as the laser irradiates the atom?", "label": 0}
+{"snippet": "I downloaded a nice latex class, but I'm having trouble with one aspect of it - every page's header gets marked with either the chapter name or section name. As you can see, it makes the page look really cluttered. The code for the class is here. I've tried for a really long time to solve this, but I can't. I searched online and found that some commands containing mark have that info, and I've tried commenting out lines containing such commands. Still no luck and could use some help on this - I just want the page numbers to show in the header.", "label": 0}
+{"snippet": "If a block of mass m is attached to one free end of a spring and is performing simple harmonic motion of some amplitude A . Now if a wall is placed at some distance x (x < A ) from its mean position . It collides elastically, how is its amplitude going to change ? [ Will it be different in the side with the wall or uniform throughout? ]", "label": 0}
+{"snippet": "We know that sound travels through a medium through vibrations in the form of longitudinal waves. An example of it is here: We also know that particles of any medium vibrate when we give them more energy in the form of heat which gives them more kinetic energy. From this a logical inference can be drawn: heating the medium might disrupt the propagation of longitudinal sound waves. Consequently, should the disruption occur, would sound production be inhibited altogether?", "label": 0}
+{"snippet": "I am taking the second law of thermodynamics in the 'useful energy minimized' sense, although I am not sure if that is necessarily the most correct. Take the example of two electrons: electron A and electron B. Electron B has a wavefunction. Can we say that electron B's wavefunction will not have high probabilities close to electron A because that would lead to there being more useful energy than otherwise? Otherwise, is there a similar type of 'wasted energy maximized' or 'entropy maximized' for singular wavefunctions rather than groups of particles? Instead of treating entropy as an outcome of different particles, perhaps the wavefunction's different possible positions of particles can do a similar job?", "label": 0}
+{"snippet": "I know that the work done by gravity in going from A to C, and from A to B to C is the same. I also know that the work done by an applied force in going from A to C is the same as negative of the work done by gravity if there is no change in kinetic energy. But what is the work done by an applied force in going from A to B to C if there is no change in kinetic energy?", "label": 0}
+{"snippet": "It is assumed that a valid QFT, must have states/observables in a Hilbert space, transform according to the projective unitary representations of the Poincare group. I can understand why the observables must transform according to unitary representations of the Poincare group, but don't see any compelling reason for that symmetries must be projective as well. Some have explained it, as it is required for dealing with the phase factor redundancy in the wavefunction,but I guess this redundancy is dealt by the unitary representation itself, as the phase factors cancels out. I don't see why a phase factor redundancy demands the symmetry be projective.", "label": 0}
+{"snippet": "Exactly the question above. I've recently posted a question, and the more I look at it, the more it seems like a bug to me. The upstream code base on GitHub seems pretty inactive too (for about two years), having many open issues. I'm missing some experts who could help me or even the maintainer. Do you know whether there are good alternatives for PGFPlots which I can integrate easily into LaTeX and are quick to learn?", "label": 0}
+{"snippet": "Imagine spreading double-sticky tape all over the surface of a car or a plane. Would there more significantly more aerodynamic drag as a result of the adhesive 'sticking' to air molecules and slowing down? This would certainly cause more resistance in solid mediums but would this cause more resistance in air or water? If an adhesive surface can drastically increase friction with solid surfaces, could one also increase friction with the air?", "label": 0}
+{"snippet": "In finding this article, I questioned my understanding of the word 'gadget'. My current understanding is the word is (and please let me know in your answer if I'm right or wrong on this one) synonymous with 'accessory'. The only difference really being that accessory somewhat precedes the technological age. Hence, 'gadget' carries a sort of electronic/technological connotation (but not necessarily?). The article enumerates a 'backpack' as a gadget. Is that correct?", "label": 0}
+{"snippet": "A lever and a fulcrum is able to to multiply the input force to the output force and trade moving distance for increased force. The same happens in automobile transmissions, taking advantage of high motor RPMs. What exactly is the physical mechanism behind this? I am very aware you can mathematically prove it, for instance via an energy approach where energy in roughly equals energy out. Still, is it possible to explain the phenomena down to atomic level? That is, how is it in qualitative terms, that the force on the other side of the lever is amplified?", "label": 0}
+{"snippet": "I will have to teach a first course in differential equations. A good motivator might be to promulgate modelling with differential equations but I have seen some teachers have made polemic against modelling. Are there any really good resources on modelling with differential equations? I want something which will have an impact and motivate the learner. I am not really looking for artificial engineering examples but some bona fide real applications. Also, would like to bring in some history of differential equations to motivate the learner.", "label": 0}
+{"snippet": "What are local laws? I was reading this line in a book... Newtons second law is a local law. This means that it applies to a particle at a particular instant without taking into consideration any history of the particle or it's motion. What does this mean in simpler terms? Are their non local laws as well? Please explain with an example. I'm a high school student.", "label": 0}
+{"snippet": "It might well be that universal constants, say the speed of light, are only constant as far as we can tell in our chunk of the universe - in the same way that the Earth looks flat in the area you live. Are there any ways to tell that the speed of light is actually the same not just in our \"neighbourhood\" but in all the observable universe?", "label": 0}
+{"snippet": "Take a deck of cards, cut it in three, and rearrange the three packs in any order (for instance, the middle goes on top, the top in the middle, and the bottom stays). Repeat as many times as you want with different (and possibly uneven) cuts. What permutations can you generate? Motivation: given a set of symmetric matrices, the trace of their product does not change if they are subject to a permutation generated in the way above.", "label": 0}
+{"snippet": "I may be misunderstanding the general idea and the following specific example, but I was told that Dirac predicted the existence of the positron based on a formula for the motion of the electron(?) and then feeding in a negative value or imaginary value and somehow this suggested antimatter being a real thing. Sure enough the particle was soon discovered; perhaps the discoverers were guided by Dirac's work. But just why would anyone expect this? Could it not be that an equation works in many cases but not all? Was Dirac surprised by the discovery of the positron or would not finding such a particle have been more of a surprise?", "label": 0}
+{"snippet": "If we consider the addition of orbital sngular momentum L and spin angular momentum S to produce the total angular momentum vector J, then J is a member of the vector space that is constructed by taking the tensor product of the vector spaces associated with L and S. Why don't we take direct sum of the vector spaces of L and S instead to construct the J-space? Why are we particularly using tensor product to combine the spaces?", "label": 0}
+{"snippet": "From my textbook, A noun phrase is headed by a noun. Modifiers include articles, adjectives and demonstratives. Qualifiers include prepositional phrases and relative/adjectival clauses. Given the following: Your bag is in your locker What is the grammatical name? I know that its grammatical/syntactic function is the complement of the preposition . The problem is that I suspect it is a noun clause because \"your\" is neither an article, adjective nor a demonstrative. It is a determiner. Also, a noun clause can be perform every function that a noun phrase can, or so I think.", "label": 0}
+{"snippet": "Recently I learned about Markov chains. Consider a simple two-state Markov chain: This looks like a categorical diagram, with states as objects, transition probabilities as morphisms/arrows, and of course, identities as the same state transition probabilities. Although I don't know much, I also came across connections between two separate Markov chains, implying a functor equivalence. I wonder if there is such treatment in literature. Is there any benefit in approaching it this way?", "label": 0}
+{"snippet": "Today i studied about mirror formula, its derivation and sign convention used while deriving it, a question which i have is, why do i have to use sign convention while doing the derivation ? focal length, object and image distance all are distance so what is the point of using sign convention ? and while solving problems based on mirror formula why we use the sign convention again ? I have seen some answers on internet, they say that we use sign convention two times to cancel the effect of sign convention, but if want to cancel the effect of sign convention in the end then why do we use it, can't we solve without it ?", "label": 0}
+{"snippet": "When thinking about a \"random\" atom in space (say a Hydrogen atom), should I assume that the electron is in a ground state (or any particular excited eigenstate) or is it in a superposition of all energy levels before I measure the energy of the atom? On the one hand, If the latter is the case that would mean that there is a nonzero probability to measure any arbitrarily large energy for the system, which seems weird. On the other hand, should not any quantum system be assumed to be in a superposition of all the eigenstates before making a measurement, then is there any mechanism by which the superposition of such atom is collapsed even before measurement?", "label": 0}
+{"snippet": "I'm not sure where else to ask this since I'm not very familiar with this area. What is the backdrop of a theatre play act called? Like when the actors are behind the curtains and their silhouettes are instead flashed on the white screens or curtains. The play or act is all going on in the background just like a puppet play... What's it called? May I please know if this really is a thing or not?", "label": 0}
+{"snippet": "Baum-Welch is an instantiation of the more general Expectation-Maximization (EM) algorithm. But recently when I learned about it I couldn't figure out where the Maximization step is used. Because the Baum-Welch algorithm give me a sense of just iterating between computing some intermediate variables according to old parameters and updating parameters according to computed intermediate variables. Out of the reason, I searched this problem online, but I only find this article useful to me. My problem is a step in the derivative process troubled me(it's shown in the figure below). Could you please explain it to me? I asked my professor and she couldn't help me. enter image description here", "label": 0}
+{"snippet": "Consider a vessel completely filled with water and a vertically oriented capillary. If the water vessel was open at the top, you would expect capillary action to occur, lowering the water level in the vessel until a force equilibrium is reached. However, if we seal the vessel, the water would have to increase its volume/reduce its density for capillary action to take place, as no air can enter the vessel to fill up the volume. Does the (high) bulk modulus of water also apply here, as this expansion is nothing else than negative compression, i. e. would the hydrogen bridge bonds mostly suppress capillary action?", "label": 0}
+{"snippet": "Order the following functions in terms of little oh notation: where: Im actually confused on how to do it. I think its the functions that confuse me not the method on how to do it. I know that: But either my mathematical skills are failing me or there's a different way to do it, that I don't know. Any help is appreciated. Thanks a lot in advance.", "label": 0}
+{"snippet": "I just wanted to bring up some discussion about an apparently essential concept for some fields in mathematics as so as for some in physics, as already mentioned in the title, I'm referring to the word \"symmetry\". I'm currently studying about Lie symmetry method to search for first integrals of ODE's, and already saw that the main problem would be, exactly, to compute the symmetries, which involves a PDE. In adition, I constantly hear \"symmetry breaking\" from some working with QFT. It sounds like a joke but, are we trying to find those symmetries for you guys to \"break'em\"? Despite the kidding, could these two contexts be related in some degree?", "label": 0}
+{"snippet": "In an infinite universe composed of single point masses which can be simplified as a uniformly distributed mass density, what is the equation for the gravitational field intensity in Newtonian gravity? I assume that: The gravitational field intensity is constant through space since the matter density is constant. The net force on any test particle must be zero, because all forces must cancel out due to symmetry. The gravitational field intensity is infinite since the its the sum the gravitational field intensity of each mass point, and there are endless mass points at infinite distance. But it must converge to a specific value since contributions of far away point masses contribute less and less with the square of distance.", "label": 0}
+{"snippet": "Is there a word that means \"lost thing\"? Ir perhaps a word for \"forgotten thing/ something that has been forgotten\"? Similar to how requirement means \"that which is required\" or necessity is \"something necessary\"? I'm ideally looking for a noun or other words that are constructed to from an adjective describing something to the noun that stands for it. Here are two sample sentences: This book contains a list of major [lost things] throughout history. The [forgotten things] inspire many mythological stories. I am also okay if there's an archaic or uncommon word for this!", "label": 0}
+{"snippet": "I don't know much about this topic, but I read something saying that gravity is not a force using an example of inertial observation. I started thinking about the topic again when I was researching photon spheres and thought why does gravity (if it is a force) curve light when photons have no mass. The only possible answer would be that gravity is not a force but rather the warp of space around mass. Would this be right?", "label": 0}
+{"snippet": "I don't understand why you can't invert a hessian matrix using gauss jordan method. Can't you integrate or differentiate an entire row (because they are linear operators) and then subtract/add/swap? To clarify, I mean inverting the generic hessian formulation before it is applied to any function. In this way, I can get the hessian inverse so I can apply it to other functions. otherwise, I'd need to calculate hessian of a function and then invert, which takes a larger time complexity.", "label": 0}
+{"snippet": "Can we calculate the total observed time dilation on a spaceship and a planet by combining the planet's relativistic spin velocity and the spaceship's approach or recession velocity from the planet it came from and where it's heading? Would the spaceship see both planets as time-dilated due to their combined relativistic spin and approach/recession velocities? Should we consider both the spin velocity and the apparent recession/approach velocity, or just one of them, in such calculations?", "label": 0}
+{"snippet": "As I understand, it is perfectly possible to explain the standard double slit experiment with a laser beam using only classical physics. On the other hand, this experiment is one of those experiments which is mentioned the most when quantum theory is introduced. So at what point of the experiment -- or through which variation -- does quantum theory come in where classical physics fails ?", "label": 0}
+{"snippet": "In Baby Rudin a subset E of a metric space X is defined to be connected if \"E is not a union of two nonempty separated sets.\" This may be nit picking, but should this not be E is not a union of two or more seperated sets ? Wikipedia agrees. To be super nit picking, by Rudin's definition (and taking it super literally) a set that is the union of three nonempty separated sets would be connected since... two is not equal to three.", "label": 0}
+{"snippet": "According to the argument in this post, a theory of Quantum Gravity should not be compatible with the notion of time evolution. This is also called \"The Problem of time\". However, the target spacetime formulation of string theory does have a notion of universal background time given by the target spacetime. So it seems like it does not address the problem of time. The CFT part of AdS/CFT is also a QFT with a well-defined universal time. So does String theory not address this problem? If no, then what does it say about it?", "label": 0}
+{"snippet": "I heard this dialog in a Western film: Ruffian: Are you Josey Wales? Josey: That['d] be me. Methinks Josey responded That be me and not That'd be me. Is the former even correct? Is That be me. also a sentence in subjunctive mood, just as That'd be me is. If That be me is correct, what would be the difference in meaning between That'd be me and That be me? Please, take note that this question is not a duplicate.", "label": 0}
+{"snippet": "The intended meaning is that 'it', described simply, is 'everything'. Would I write: It is in short...everything. Or: It is, in short...everthing. Instinctively, I believe that a comma is needed before \"in short\". But the confusion arises here: Is it a common enough phrase that the comma is not needed? Is it a publisher's preference situation? Author's preference? I've seen the phrase 'in short' both with and without commas. Normally two commas are used, as it's a parenthetical, but the ellipsis makes the second one unnecessary.", "label": 0}
+{"snippet": "In one of our informal math research club sessions we are thinking of hosting a math meme making competition. Our idea is that math memes will trigger curiosity and interest among the participants. This would not only help in questioning and understanding the mathematical ideas behind the meme but the participants will also have fun doing it. Lets say that I go ahead with this idea. What could be a possible way achieve best results?", "label": 0}
+{"snippet": "What is the meaning of the phrase, 'as thus construed'? I was writing an essay and felt that phrase was appropriate, but I looked it up with quotes on google and found only references in some legal documents and academic papers. Is there a similar phrase that I am thinking of, or does this make sense by itself? For example, suppose I just described x a certain way. I then say, \"x, as thus construed, is Y.\" Does this make sense? Or is there a phrase that is more accurate here?", "label": 0}
+{"snippet": "so I am looking for good text books that treat signed measures, integration thereof and total variation etc. In particular also for finitely additive signed measures. I have found Dunford and Schwartz a little bit too general in that they dont necessarily consider (signed) measures but more generally set functions. I would also like the book to be as standard in notation and the used concepts as possible. So can you give me any suggestions for text books?", "label": 0}
+{"snippet": "I am in charge of deciding the name of a skill in a role-playing game that serves as a catch-all for abilities/skills that are otherwise unlisted in our handbook (think skills that will help players flesh-out their character's personality, quirks, and life). Such a skill could be a profession type, a craft (e.g.,whittling), or something more exotic like hyperlexia. Profession and Craft do not capture the spirit well enough. Ability seems too generic, as are its multi-word variants, e.g. Unlisted Ability. Knack seems closer to the mark but open to suggestions.", "label": 0}
+{"snippet": "I am currently studying a paper on Wasserstein Fair Classification. Several places they mention the Wasserstein barycenter, weighted barycenter distribution or the Wasserstein barycenter distribution. What is it? How is it defined? I can only find very deep measure-theoretic explanations, which are both a bit out of my league as a statistician, who never enjoyed analysis very much, but they simply also lack an intuition behind.", "label": 0}
+{"snippet": "I was wondering is it possible to try and do optimisation of an ellipsoid given the formulae for its volume and surface area? I would be trying to keep the volume constant whilst minimising SA. This is for one of my maths investigations, basically trying to minimise packaging of a kinder egg, so if this is somewhat of a dead end, what are some alternative approaches I can take forwards? Any help would be really appreciated! Update: Ive derived the equations for the SA and Volumes of an egg shape Would the Lagrangian Multiplier Method work here", "label": 0}
+{"snippet": "I happened upon this video purportedly showing a coin on a horizontal table receding away from a lens would disappear from bottom up. The explanation via diffraction resolution limit is wrong. However, I would like to find the correct explanation of the phenomenon. When the camera zooms in and focuses on the coin, the coin appears clearly. This can be explain by the fact that part of the light from the coin still enters the aperture of the lens. However, how would one explain the abrupt disappearance of the bottom of the coin below the table upper edge when the focus of the lens is on the table edge?", "label": 0}
+{"snippet": "My question is this: Why can't electric potential energy be defined at one point. Surely a point charge has some inherent electric potential energy cause by force applied by the source field. The applied force would cause the charge to accelerate. The acceleration approaches zero as you get farther from the field, so the velocity could also approach a known limit (depending on the function). That velocity can be used to calculate the maximum kinetic energy, which would equal the original electric potential energy imparted on the charge by the field. I know this is a classical treatment of the situation, but what's wrong with this line of thinking?", "label": 0}
+{"snippet": "I have questions about the inner product and coordinate transformation matrix. For F inner product space V, consider vector a and b in V and its inner product <a,b> then the inner product is invariant about changing the Basis of V? And let B and B' be Basiss of V. Then can I think that the coordinate transformation matrix from B to B', denoted by R is a unitary matrix because it preserves the inner product <a,b>?", "label": 0}
+{"snippet": "Electrons have an e-field, and a moving e-field causes a b-field. These fields are defined in such a way that it makes calculating things like forces much simpler. Is this just a model and there aren't actual 'waves' traversing around us, but rather mere forces caused by a movement of an electron? If the force caused by a charge wasn't viewed as a wave, would electromagnetism only be a model for calculating the effects of the charge, utilizing waves as a tool? If so, is it fine to propose that visible light is simply our brain's reaction to certain forces caused by moving electrons in a certain frequency?", "label": 0}
+{"snippet": "I have always been told that if you press the brake pedal fully and fast it can make the wheels lock themselves, and that you shouldn't do so because it would take longer to stop the car than if you push the brake pedal progressively, why so? I can imagine that when done progressively the car won't start doing jumps due to the wheels block as if you would brake immediately but I can't see why.", "label": 0}
+{"snippet": "The existence of dark energy leads negative pressure. Is the pressure can be anisotropic? What situation can cause anisotropy of pressure? Further, Is the pressure can be negative in some directions and be positive in other directions? Such as in spherical coordinates, the radial pressure is negative and the tangential pressure is positive. Will this happen when matter and Dark energy exist at the same time?", "label": 0}
+{"snippet": "I want to determine the largest area ellipse inscribed in a rectangle, in order to write a code that can determine the lengths c and d given a and b (see image here). I know the obvious answer would be c and d are halves of a and b, but I want the derivation (and also the maximum area) so I can stop thinking about this, saddly I can't seem to figure this one out. I remember doing the opposite in school (rectangle inside ellipse) but can't do it properly now. Hope you can help me.", "label": 0}
+{"snippet": "I'm quite close to release my first game, and I can't decide which is grammatically correct on my first user facing screen. My game will surely have some grammatical mistakes but I would appreciate it if the first screen would be more or less accurate ;P So the title wants to welcome the user into my game but I dunno which way I should go. Welcome to {Game Title} or Welcome in {Game Title} Any feedback is appreciated!", "label": 0}
+{"snippet": "i would like to find a way to study physics online and get academic credentials in it and be able to contribute to the research and publish. I know some topics are experimental and require physical attendance, however there must some subfields in physics that can be studied online. Now there are many online masters in STEM fields like computer science from reputable universities. Is it the same for physics?", "label": 0}
+{"snippet": "The Wikipedia page for locally constant function says that a locally constant function is constant on each connected component, but that the converse only holds if the space is locally connected. What would be an example of a function that is constant on each connected component but not locally constant? I first thought of the topologist's sine curve, which is not locally connected, but since this is a connected space, such a function would be constant on the entire space and therefore automatically locally constant.", "label": 0}
+{"snippet": "I need to prove in graph theory that if L(G)=G then G is a combination if simple cycles. I already did it assuming G is connected, so feel free to use this fact as given. My only issue is that it may be possible that in a non-connected graph not every one of the connected components will satisfy L(G)=G. For example, if the Connected components in G are A,B,C it may be possible that L(A)=B, L(B)=C, L(C)=A.", "label": 0}
+{"snippet": "Suppose there is constant diameter pipe where a liquid flows through it, and if pressure of a liquid is due to external force or its weight when it is constrained or semi constrained (according to the accepted answer on this question), how can someone visualize how does pressure drop occur due to frictional losses? Does the force on the liquid decrease somehow or does it become less constrained so it has lower pressure?", "label": 0}
+{"snippet": "I am studying the spontaneous symmetry breaking in the mean-field Ising model and it's clear to me the necessity of taking first the thermodynamic limit and then the zero-field limit to see the phase transition, otherwise we only see zero magnetisation even under Tc. I was wondering if there was a phase space approach underlying this result and if the spontaneous symmetry breaking implied and ergodicity breaking as well, as I imagine that the ensemble average is anyway zero, but this is not what we observe physically. Can someone give me a hint?", "label": 0}
+{"snippet": "I went through a quite a lot of posts here but did not find the information I wanted. I'm looking for a beginner / introductory (yet mathematically rigorous) book recommendation for differential geometry / topology required for General Relativity. I'm perfectly fine (in-fact I like) the so-called dry mathematics books (theorem-proof-theorem). What I need is - Very clear definition of Mathematical objects used in GR Crisp / rigorous proof in modern notation I need the book at advanced undergraduate or beginner graduate level. Thanks in advance.", "label": 0}
+{"snippet": "Is there any way one can modify a known functional so as to get a solution for another quantity related to it? Because this is too general I would like to make it more clear with an example. Given the classical EM Lagrangian, we acquire the equations of motion for a particle in an EM field. Starting from this, is there anyway one can find a functional that when varied will give the solution for, let us say, the electric potential, for a given charge distribution and known boundary conditions?", "label": 0}
+{"snippet": "To understand the attractive and repulsive force between two currents, I am looking at two electrons moving parallel and antiparallel to each other. How can an attractive (or less repulsive) Lorentz force between two charges and its directional dependence be explained? I would like to understand this in terms of dynamical effects of the electric field and not in terms of a magnetic field which is the common approach for correctly treating and not further looking at such details.", "label": 0}
+{"snippet": "Pramod Achar's book on perverse sheaves has a quick reference in the back that looks like this. How can I achieve something similar? The important things to me are: the general spacing (although maybe I would enjoy less margins on the outside), the two columns, the numbering and labeling, the horizontal line separators. For language, I only care about English. I don't have any font preference.", "label": 0}
+{"snippet": "Consider this fact that we all know from school mathematics: There is a one to one correspondence between real numbers and points of a line. But the problem is I have never seen a rigorous proof of this fact. This is what Apostol writes. And similar is the case with other modern analysis books. So my question is, where can I find the proof of this one to one correspondence. I don't care if geometry is in Hilbert's axioms or Tarski's or anyone else all I care about is correspondence.", "label": 0}
+{"snippet": "I'm bit confused about the current flow in capacitors. My question is, let's assume those two electric circuits: As shown in the picture, the only difference is only the capacitance. I'm wondering about the current flow magnitude. In which of the circuits the current flow will be bigger? or will it be the same? To start, I assume both plates of the capacitor are uncharged. My guess is that right at the moment of closing the switch before the capacitors are charged from the voltage source, the current flow will be even. Once they are fully charged, of course, the current will be bigger in the system with the bigger capacitor. But till this point, what will be the current flow? thanks", "label": 0}
+{"snippet": "it is said that the time period of a simple pendulum in space is infinite. it is because the gravity in space is zero and anything divided by zero is equal to infinity.how can time period be infinite? also, in space, everything just floats around. how can a pendulum in space do oscillations if there is no restoring force to bring the mass back to mean position. how can a simple pendulum exhibit SHM in space? if it cannot exhibit SHM , how is the time period formula for the simple pendulum applicable to the pendulum in space and what is the meaning of infinite time period. why do the time period of pendulum in space even exists?", "label": 0}
+{"snippet": "I was wondering if it is posssible to write my own environment for writing redox equations in form of: O: ... R: ... ___________________________ S: ... O stands for oxidation, R for reduction and S for the summary equation. Also, there is line that should separate O and R from S. I have never written any environment in LaTeX, so could anyone just help me start? I've seen that there are some packages that are about chemistry, but none help me about this problem.", "label": 0}
+{"snippet": "In surface integrals the process is to use the dot product of the vector field with the unit normal vector first and multiply that with the area element. In the line integral the process is to use the dot product of the vector field with the length element. Why isn't the unit tangent vector used in the line integral computations while in the surface integral computations the unit normal vector is used?", "label": 0}
+{"snippet": "While deriving the Planck's radiation formula, why do we use MB statistics when we calculate the average energy of oscillators? Shouldn't we use BE? Is this because temperatures concerned are very high and quantum stat goes to classical at high temperatures? But again, in a similar calculation, while calculating the lattice specific heat of the solid using Einstein's model or the Debye model, I have seen books calculate the average energy of oscillators using MB distribution only, but we use this formula to predict specific heats at very low temperatures also. So I don't understand, what is the reason?", "label": 0}
+{"snippet": "The sentence is as follows: \"Isn't it evident who/whom they have in mind for the position?\" Depending on how you try to reword it to figure it out, the answer seems different. --Is it not evident that he is the one they have in mind for the position? (This seems to be a case for \"who\" here.) --Is it not evident that they have him in mind for the new position? (This seems to be a case for \"whom\" here.) Should it be who or whom? Why?", "label": 0}
+{"snippet": "I know multiple singular subjects have been addressed here and singular compound subjects here. However, I came across a sentence with multiple subjects, one single paired with one plural. I could not find this question addressed. For example Does a table and four chairs sound like sufficient furniture for a breakfast room? That doesn't quite sound right to me, but then Do a table and four chairs sound like sufficient furniture for a breakfast room? also sounds a bit off. Which would be correct? Or are both incorrect? Purdue uni subject-verb agreement is confusing.", "label": 0}
+{"snippet": "An intuition that I thought of about a year ago, but my level does not allow me to prove it. I think it needs advanced tools to prove it, or just a counterexample to refute it. Who can help, please, thank you. The locus of the point of intersection of the perpendicular tangents of a convex curve is the convex curve Of course, the intuition is only in this direction and does not constitute an obligation, as the cardioid is a concave curve. Despite this, tracing the perpendicular tangents to it gives a circle", "label": 0}
+{"snippet": "Using Hugyen's principle and wave nature of light, refraction, diffraction are relatively simple to explain but I have been visualing a mental model for a couple of days where the photons on reach the boundary of two media, experience a difference in the structure of the medium of propagation and hence some sort of collision or change in the overall velocity vector of each photon occurs which leads to refraction. Can someone help me understand these phenomenon using particle nature?", "label": 0}
+{"snippet": "how one would know that the given frame of reference will be inertial or non inertial, without the use of 'accelerometers'. earlier physicst has defined this concept and I am sure that they define it without the help of accelerometers. I just want to know about the logic behind the whole concept. And I will be not getting any accelerometers in my exam and not able to conduct any experiment in the frame. i want to know how teachers just say that this frame will be inertial or not without any accelerometer.", "label": 0}
+{"snippet": "How come there is no loss due to coupling between the superconducting channel and the single particle channel? I imaging the two channels being two parallel wires, so the magnetic field from the current running in the superconducting state, should fully inclose the single particle channel generating a electric field, that at least would create a displacement current and introduce a loss. Why is that not so? Also is there no current fluctuation due to the current being carried by discrete charge quanta? I would assume that, that would also create a electric field fluctuation in the single particle channel causing a loss?", "label": 0}
+{"snippet": "I posted about monoid coproduct to try to understand the correct way for constructing them. In the process and from the answer I got, I am further confused whether the product and coproduct of plain monoids compare free monoids, what are the subtle differences in terms of what they look like. I understand in both coproduct of monoids and free monoids, the process of word reduction to strings are applied. I don't know anything beyond that. I am hoping someone can explain to me their subtle differences. Thank you in advance.", "label": 0}
+{"snippet": "If we add a constant to both sides of an equation, we will get a new equation with identical solutions. This is mostly true for multiplication and square roots, but there are some minor complications/exceptions. Taking the derivative of both sides will result in entirely different solutions. Is there a formal way to show how performing some operation/action on both sides of an equation will affect the solutions of the resulting equation?", "label": 0}
+{"snippet": "This is a question about grammar, in particular about a specific language syntax. In the german langage it's legit to write negative prefixes in braces like \"Die JSON (De-)Serialisation wurde implementiert.\" Is this valid in english? \"The JSON (de-)serialization has been implemented.\" As a software developer I need to document the work I've done and the software functionality itself. I often have a lot of language constructs similar to the one above. And if it's legit to use this syntax of negative prefixes it would save me a lot of time.", "label": 0}
+{"snippet": "I wonder whether there is a space filling curve that looks like the following if the width of the domain has an odd number of cells and looks like the following if the width of the domain has an even number of cells. I would like to fill a three dimensional grid none of whose sides (lengths) are guaranteed to be a power of two or even.", "label": 0}
+{"snippet": "How is it paradoxal that a set of all sets exists in set theory? Russel's paradox is about the set of all sets that do not contain themselves cannot exist, that I understand. But what about the set of all sets, in a unrestricted manner? Is it the fact that it contains itself (which may be what allows to define the paradoxal set of Russel's paradox) that is problematic?", "label": 0}
+{"snippet": "Is the result of a contour integral around a closed loop path unique? I'd think it'd be similar to a definite integral, which is unique. This came up regarding the proof of uniqueness of a Laurent Series - if the contour integral is unique, then the definition of the Laurent Series can be used to prove its uniqueness. Edit - as pointed out below, the Laurent Series aspect may be a limiting case, as it's within a specified annulus, so for any of the Cauchy coefficients, the same analytic annulus is used, so the same number of poles will always be within the inner radius.", "label": 0}
+{"snippet": "Is it true that if a curve is increasing, Euler's method will always underestimate an actual solution? So if a curve is either increasing and concave down, or increasing and concave up, we can simply ignore concavity and justify the answer based on the fact that it's increasing? Euler's method will therefore underestimate whenever the function is concave down and increasing, or concave up and increasing?", "label": 0}
+{"snippet": "There are two machine learning models, A and B. Model A classifies samples into 'O' and 'G'. Model B classifies the samples determined to be 'O' into 'S' and 'C'. Each model shows the probabilties of classification. Input samples pass through model A first, and if the result is O, then they enter model B. (If not they don't) In this case, how could I get the probabilities of classifications, G, S or C?", "label": 0}
+{"snippet": "What is a good, up-to-date, well-regarded text on writing physics solvers for (e.g.) game engines or realtime simulations? In particular, treatment of numerical stability, convergence, asymptotic complexity and performance, contact forces, and the handling of constraints are relevant to me. I have solid familiarity of university level physics, calculus, PDEs and ODEs, and linear algebra; and these can be assumed as prerequisites. (An ideal book would be the analogue of Pharr and Humphreys, but for simulation) What text(s) should I consult?", "label": 0}
+{"snippet": "In a Euronews headline I saw the following: Frontex: What would happen if the EU border agency quit Greece?. Shouldn't it be \"quits Greece\"? As far as I understood EU border agency is singular. Reopen note: Although the original close vote as a duplicate was accepted, Stuart F has since pointed out that the real issue here is that quit is probably past tense. I agree. The 'duplicate'tag here might wrongly lead readers to assume that the issue here is simply about singular/plural subjects.", "label": 0}
+{"snippet": "When I'm not writing a math paper, I write way faster by typing directly into a word processor. I form and revise sentences faster on the screen then I can on paper. But typesetting math is slower than handwriting, and I think better with a pen. I already know it's best to handwrite symbol-heavy text before typing, but what about text that's symbol-light, like an abstract or introduction? Should I write almost the entire paper by hand, or only the math dense portions?", "label": 0}
+{"snippet": "For no reason other than my own curiosity, I have been trying to figure out the solution to the following question: Given a bag of x marbles, what is the probability of having seen every different marble at least once after y draws with replacement? I am interested in making different graphs for specific values of x just to know what it would look like but I can only figure it out when x=y. The moment y>x, I do not know how to approach it. I have scribbled on more pages than is reasonable, so I hope I can find an answer here. Thanks!", "label": 0}
+{"snippet": "We could say it was painted beautifully to convey that the way it was painted was beautiful. \"beautifully\" being the adverbal form of beautiful (an adjective). What if the adjective is \"lovely\": How would you convey that the way it was painted was lovely? Is it: it was painted lovelyly This sounds/feels weird and I have never heard/seen it used. Furtherm \"it was painted lovely\" seems an error of grammar. Is there a rule/guideline that adjectives ending in \"ly\" have no adverbal form and can't be used as adverbs? Or should we just use the adjectival form for the adverb even if it is grammatically incorrect?", "label": 0}
+{"snippet": "I'm studying instability in Stellar Dynamics (in particular globular clusters instabilities). I have not understood clearly the definition of these concept. Dynamical instability is the study of the instability considering an adiabatic process: we perturb the system and see what happens. Thermal instability happens at much larger timescale than the dynamical one and is due to the exchange of energy between single stars (and since the thermal capacity of the system is negative, this process brings phenomena like the gravothermal catastrophe). Am I missing something?", "label": 0}
+{"snippet": "I want to make a robot that solves a hand-made maze, so that I want to provide it a LIDAR component to measure the distance to read the environment. Before buying a component I want to know if it's capable of measuring distance to a rotated surface. Under rotated surface I mean a wall that is not perfectly aligned with the LIDAR emitter, see the image Is it even possible that the light beam ever reach the LIDAR's receiver and how accurate the measurement can be?", "label": 0}
+{"snippet": "I have read everywhere that the gold foil experiment performed by Rutherford was done hoping that the alpha particles face only a little deflection/no deflection however this doesn't sit right with me, the old model of Thomson clearly shows that atom is a positive sphere with electrons embedded in it, what made him think that positively charged alpha particles moving through this atom wont face a repulsive force from the positively charged cloud?", "label": 0}
+{"snippet": "What exactly would happen if we sent a frequency that was not one of the harmonics into a closed and open pipe? What would happen if we gradually increased this frequency? From my understanding, I think if we were to send down this frequency, a standing wave could not form, so when we gradually increase this frequency, as soon as it matches the harmonic a standing wave is produced and max amplitude creates a loud sound. Would this be correct?", "label": 0}
+{"snippet": "In principle, the comparative form of polysyllabic adjectives has \"more\" before the word, rather than taking a suffix \"-er\". But why do adjectives ending in \"-y\" often take the suffix \"-er\"? For example, \"luckier\". (and the same for superlative) Regardless of which from \"more lucky\" and \"luckier\" is considered correct, many people use the latter anyway, and it also applies to other words that end with \"-y\". So why are polysyllabic words ending in \"-y\" an exception?", "label": 0}
+{"snippet": "In first-order logic, one has a way of constructing all sentences out of some logical symbols, as well as function and relation symbols pertaining to a special kind of signature one is in. Now in the book of Mac Lane on category theory, there is a similar construction, where the atomic statements (instead of only being things like equality over a single structure) involve also things like the domain of an arrow, where there are both objects and arrows, for instance. I would like to ask whether there is some widely used general construction that generalises both.", "label": 0}
+{"snippet": "What do you call it when someone is being back-handed in a way that looks and sounds nice outrightly but is intended to be mean? Passive-aggressive is too obvious. The equivalent to Bless her heart. The rudeness would be hard to tell to anyone who wasn't there to see or wasn't aware of the person's dislike for someone. Typically the person believes it goes unnoticed by the \"victim.\"", "label": 0}
+{"snippet": "A large regular hexagon is cut out of a triangular grid and tiled with diamonds (pairs of triangles glued together along an edge). Diamonds come in three varieties, depending on orientation; prove that precisely the same number of each variety must appear in the tiling. This puzzle is from Gurmeet.net's Tiling with Calissons puzzle page. The \"Proof without Words\" solution is accompanied by this image: My approach: I tried reading through the solution but it simply blows my mind. The proof without words, how did they even come up with that? Any clue how to start/proceed will help.", "label": 0}
+{"snippet": "I have come across them in a thrift shop and completely fell in love with the method employed by her. Almost nothing is taken for granted and everything from the definition of subtraction to the addition propert of equality is first demonstrated (or proved) before being employed. I have picked up Serge Lang's Basic Mathematics with the hope of reviewing Dolciani's exposition of high school algebra through someone else's words but the book failed me as it doesn't go deeper than your usual half-baked modern algebra book. I don't want to move on to reading the first chapters of some abstract algebra books as I don't know the notation much. Do you guys know of any other book similar to Dolciani's in method of exposition?", "label": 0}
+{"snippet": "On high slopes and rugged terrains, riding a bicycle while standing on the pedals is easier. Even though I cannot physically define what is \"easy\"; since it is a feeling that my body generates based on the ratio of work output to the energy expenditure and degree of tiredness of my muscles, I am pretty sure a humanoid robot moving exactly like us would also spend much less energy standing and cycling. Why is it so?", "label": 0}
+{"snippet": "Is there a word for people you like but are a pain in the ass? Nothing too vulgar. I am not looking to call someone it, but affectionately think about them \"that person is a complete [word]\". It's for a friend (of the opposite sex, though I don't necessarily want to signal that here). oh God Debbie, can you stop being a [word] I was thinking of 'frienemy' but that may be the opposite. I was also thinking of 'difficult' but it's potentially offensive and patronizing.", "label": 0}
+{"snippet": "I am studying trigonometry and have wondered if there are generalized power-reduction formulae for sin^n(x) and cos^n(x) yet the best that I found was formulae for odd and even powers on Wikipedia without any proof. Could you write a formula for sin^n(x) or cos^n(x)(if there are any) and a proof if it is possible? I will be thankful! (Also sorry for the wrong tags ) : . I just could not find five accurate tags for the question, my excuses.)", "label": 0}
+{"snippet": "Does spacial coherence mean that if I took a cross section of the laser beam beam, then I can find a relation between the phase of the electric field between any two points across the cross section even after the elapse of a very long time? Whereas the highly temporal coherence means that I can predict the phase of the electric field at any point across the cross section even after let's say a big amount of time?", "label": 0}
+{"snippet": "I have three scenarios: The following setup will experience an induced EMF since the area covered increases with time. (Shaded in orange) If instead of a wire/rod,we had a coil moving within the field, there would be no induced EMF for a constant magnetic flux density since area covered by coil is fixed and does not vary with time. The question is if I have something similar to the first scenario (in that a rod is used) but without borders, such that entire rod lies within the field (like the second scenario), would I get an induced EMF? If yes, what would be the change in area?", "label": 0}
+{"snippet": "Essentially what the title asks-- are matrix models, such as BFSS, believed to capture in any way the large possible space of false string vacua, for instance as saddles in the action with nonminimal energy, in such a way that the dynamics of settling into a false vacuum/metastable state could in principle be probed with such models? This would be from the perspective of answering questions about the \"cosmological prior\" that people sometimes gesture to in the context of anthropic arguments for the values of certain couplings.", "label": 0}
+{"snippet": "Let's take a hypothetical an experimental scenario where a stream of high-energy photons from a powerful source is directed via a system of mirrors and lenses in a two coherent rays to a vacuum camera. The photons collide in the vacuum camera, producing positron-electron pairs. The pairs are promptly separated before the annihilation by two coils, which lead into two vacuum tubes, that serve as entrances to electromagnetic toroidal containment units that \"speed up\" the particles, and prevent them from touching the walls of the units. What kind of problems would prevent such a setup from working as intended?", "label": 0}
+{"snippet": "I'm studying method of undetermined coefficients and i can understant what is its idea. But i'm ambiguous when we can use it. Of course, it is obvious that the differential equation is nonhomogeneous. And wikipidia says as following: Undetermined coefficients is not as general a method as variation of parameters, since it only works for differential equations that follow certain forms. But my book or wikipidia don't say the equation need to be linear or non linear To apply the method of undetermined coefficients, the differential equation have to be linear? or non-linear or both?", "label": 0}
+{"snippet": "So, I happened to be reading a grammar book in which I came across this weird looking sentence. This is the car of which parts are not available now. I think it should have been something like this: This is the car, parts of which are not available now. If the improvised version is correct, I do not know why. Can you guys help me with such constructions?", "label": 0}
+{"snippet": "I need some advice on the use of these two words - update and refresh. I am currently working on the desktop app and I need to give a button a correct name. There is a big number of objects that an app stores in the database and multiple users can work with them simultaneously. If one user changes an object, it gets changed for all the other users. And this button can disable or enable this function. I consider two names. Data Auto Refresh and Data Auto Update. Which sounds more native? And is there any significant difference between these words?", "label": 0}
+{"snippet": "I have a theorem in the form : if A is verified and B is verified and C is verified then D is verified. I'd like to show that we can't do without hypothesis C. How can I do this? Do I need to find an example where I have A, B and non(C) which are verified such that D is unverified? If I do this, what will I have shown?", "label": 0}
+{"snippet": "I am not well-versed in the research on topological solitons but am interested to make a good sense of its implication. The highly interesting point in this new talk by Nick Manton was where he is noting that multiple vacua can be modeled using solitons. But are these multiple vacua simply degenerate in energy? Or we can consider non-degenerate multiple vacua in different regions of space?", "label": 0}
+{"snippet": "I am reading Hiroshi Kunita's lecture Stochastic Differential Equations Based on Levy Processes and Stochastic Flows of Diffeomorphisms.It proves Ito's formula for cadlag semimartingale. Kunita's proof The proof is concise, but I doubt that it is not correct. Right in this picture, it constructs a function r(x,y)(in the first highlight), and claims that it suffices the identity(in the second highlight), but I just found the identidy is not valid since we can not get F by the integraton of the second order derivative F'' (this will only get F' instead of F). So I think this is proof is incorrect. Did I make some mistake?", "label": 0}
+{"snippet": "In modern day PV cells you usually have a silver-based grid on the upper end of the cell where it's exposed to the sun creating the optimization game of how thin/thick you can make your busbars and fingers so that maximum current can be passed without covering too much of the silicone surface blocking the sun's exposure to the n-type surface. In the early silicon cells they used to design the cells in the following way: Source: https://www.pveducation.org/pvcdrom/manufacturing-si-cells/early-silicon-cells Why did they stop with this approach? Was it just fabrication costs? This seems more intuitive as you're maximizing the surface area of the layer exposed to the sun?", "label": 0}
+{"snippet": "Following this post, I did this: [Options] --> [Adv. Editor] --> [Special options] panel --> [Go to error when displaying log] which however doesn't resolve my issue; after compiling, the cursor is always stuck at the same place. I'm suspecting some part of my code is colliding with this functionality, but cannot figure which. Edit: I tried unmarking the checkbox for \"Go to error when displaying log\" and it is now working! I thought it should be marked, but it seems not.", "label": 0}
+{"snippet": "A recent paper \"Gravitational Pair Production and Black Hole Evaporation\" (discussed in short here) says that any spacetime curvature would produce Hawking radiation, no need for event horizon. If this is correct then a question arises - how negative energy would take energy from observable object? Fermion cannot be partially annihilated and full annihilation is way more energetic then Hawking photon. So the only source of energy would be object's heat. But would that mean that object with temperature near absolute zero would stop radiating? There is nothing about temperature in equation. Does it mean that the paper is wrong? Or is there any mechanism to provide Hawking energy from object's mass? P.S. \"Black holes are white hot\" Hawkins:", "label": 0}
+{"snippet": "Here are two sentences that sort of mean the same thing, but need your help in identifying which one would be more appropriate. I do already have an idea as to which phrase would be more appropriate but I still chose to go with the other one. His mind pushed back, but he kept willing it to do all that it still could. His mind pushed back, but he kept wanting it to do all that it still could. Does using 'wanting' instead of 'willing' drastically change the meaning here? Since will is more of a statement of commitment, 'willing' might seem more appropriate here. But in some cases using want in its place doesn't change the meaning.", "label": 0}
+{"snippet": "Inspired by Are the visible matter and dark matter separately segregated? I wonder if the constituents (I don't say particles, as we don't know) have actions and forces among themselves, that we cannot detect directly from our observable matter. Might it be that there is a mirror world with the same forces as in our observable world, but just within themselves? Maybe even more than one, given that the dark matter has more mass than the observable one. As of now, we can \"observe\" the dark matter only by interpreting gravitational effects. If there should be any internal forces in dark matter, there should be a difference in clustering. Unfortunately, this is hard to detect. Is there any theory about that, or experimentation going on, or even results?", "label": 0}
+{"snippet": "Imagine there is no EM or Nuclear Force, and Gravity is the only force. Can gravity alone produce an atomic structure similar to a basic atom? In this scenario, the nucleus is just a single particle. The electron is another particle with only mass and angular momentum, like a planet orbiting a star. How feasible is it for Gravity alone to produce such a structure and hold it together, with energy and mass equivelent to those of simple hydrogen nuclei, electrons and matching speed/energy of orbits and angular momentum", "label": 0}
+{"snippet": "Let's assume we have two charged free particles with the same energy coming toward each other. What will be the time-dependent perturbation in this case? More precisely, I am asking what will be the change in Hamiltonian due to which perturbation is happening? Is it the Columbian potential only which will change? If yes, then how will it change as a function of time? Am I missing something very basic here? To provide more context to this question, I am trying to figure out how the Hamiltonian changes in a muon production process through electron-positron scattering. That is The form of scattering amplitude M .", "label": 0}
+{"snippet": "The matrix is not necessarily symmetric. The highest eigenvalue is positive and real (per Frobenius). Assume there is another eigenvalue with real part less than or equal to highest eigenvalue, real part positive, and higher than any other real part of any other eigenvalues. By \"semidefinite\" eigenvector I mean that the signs of the real part of all non-zero components are equal, since an eigenvector is invariant upon multiplication by a scalar.", "label": 0}
+{"snippet": "\"Export settings\" disambiguation and meaning. The aforementioned quotation is ambiguous. As I see it, it could mean either of the following: Export (verb) settings ---> Action of exporting the settings Export (adjectival noun) settings ---> Settings of export Is there a way to disambiguate \"export settings\" or is the English language, in such cases, inherently ambiguous and the actual meaning has to be inferred from context?", "label": 0}
+{"snippet": "The sentence: This essay will analyse this topic from both points of view and express my opinion. I think might be grammatically incorrect because it combines two separate actions while the coordination sounds ambiguous to me. Alternatively, are these the more correction versions? This essay will analyze this topic from both points of view and then express my opinion. This essay will analyze this topic from both points of view, offering an analysis, and conclude with my opinion.", "label": 0}
+{"snippet": "In the case of a particle system the wave function or state vector is in a superposition of possibilities before measurement. But does this rule apply in the case of vacuum state? Is it in a superposition of (energy) possibilities before measurement? We might say that nothing is there to measure in the vacuum. In particular virtual particles in the vacuum are non observable by definition. But with gravity, the effect of vacuum on curvature, can be measured and we can get information about it. Does \"before measurement\" make sense here at all?", "label": 0}
+{"snippet": "In the book: Logical Foundations of Proof Complexity (S.Cook), we have a proof for the Derivational Soundness and Completeness of LK assuming that the underlying vocabulary does not contain =. In this proof is said that the soundness direction holds also when he underlying vocabulary contains =. Theorem in the mentioned book My question is, why the soundness holds with = and completeness does not?", "label": 0}
+{"snippet": "Is there a single word to describe all the elements in a list, except the last item? The head of a list refers to the first item in the list and the tail refers to the last item. In mathematics and computer science, the tail can also refer to all the elements after the first; I'm not sure if that carries over into other domains. (chatGPT suggested \"penultimates\", which made me chuckle)", "label": 0}
+{"snippet": "I Would like to know a place (book, paper) that discuss thorougly the problem of degenerate elements in singular homology. I know that they are not a problem with simplices but you need to explicity deal with them in cubic homology (Massey for instance) I have read an terse old paper by Tucker (degenerate cycles bound) that address the problem in simplicial homology but I would like further details. In fact I am puzzled because all the standard texts tiptoe this matter (Hatcher, Munkres, Rotman, Vick). Thank you very much. To further clarify Is there any result that allows to forget degeneracy at once or should we check that is not a problem in any theorem (Hurewicz for instance", "label": 0}
+{"snippet": "Considering, the phenomenon of surface tension, is the interface of the liquid more dense than the bulk phase? Considering, if it were more dense, the phenomenon of surface tension would be explained, more dense, would result in greater strength at the surface. However, i've found various answers that state the interface is of higher density, while answers that state the interface is of lower density. Which one is the definite correct one?", "label": 0}
+{"snippet": "So imagine this situation. An object is experiencing two forces, one due to gravity in downward direction and other applied by us in upward direction such that our force is less than gravitational force. So the object will accelerate downward and its potential energy will decrease. Will the change in potential energy equals to negative of the work done by gravity? And If so then how, isn't it should be less than that because of our force, but then the change in potential energy will be negative of the work done by resultant force. Thanks if you answer it.", "label": 0}
+{"snippet": "When using Set heading in the margin to the left of text this method to place paragraph headings in the margin, this works for single-column documents. But when the twocolumn option of geometry is used (in report class), the second column's heading overlaps into the first column's text. Is there a way to have the left column's headings in the left margin, and right column's headings in the right margin?", "label": 0}
+{"snippet": "Is there a Hilbert curve for every space? as I understanding it in layman terms, it's a way to order a space sequentially which visits every place once. Does it work with continuous spaces, or just discrete? Are there certain limitations of dimensionality that you cannot use a Hilbert curve to explore? I guess I'm asking if everything can be serialized? What must I understand to understand the boundary of the Hilbert Curve concept?", "label": 0}
+{"snippet": "Why after Big Bang it is not going to Heat Death in the easiest path, actually the energy can get distributed uniformly to all directions. Instead we see the energy in Big Bang is being converted to atoms, then the stars, galaxy etc. are formed. Isn't these formations making the path to Heat Death more distant? Any natural law explain these formation of concentrated energy structures like atoms, stars, galaxy etc.", "label": 0}
+{"snippet": "As we know, a star that is too massive to become a white dwarf becomes either a neutron star or if it is even more massive, a black hole: neutron stars form with great gravity that comes with great mass, the gravity pushing down on its core, merging protons and electrons into neutrons making the core consist only of neutrons. Take this into consideration, is it possible that the same thing happens to stars that become black holes, since their mass (and thus gravity) is so large that even light can't escape?", "label": 0}
+{"snippet": "The interaction (of an electron with an external electromagnetic field) is because of the electron's charge, but charge causes an electric field, so, by Syllogism one can say the interaction is because of the electron's electric field. Now we can say that, by linearity, the external field and the field of the electron sums together. So how does a force arise from this summing process?", "label": 0}
+{"snippet": "We know for a fact that if an electron absorbs a photon with enough energy it gets excited to a higher energy level, which increases that electron's total energy and we know that energy can present itself either with rest mass energy, kinetic energy and potential energy. And we know from Bohr equations that the higher the r(radius) is lower the linear velocity is, so its kinetic energy should decrease and be converted into potential energy? If so , if it is just a matter of energy conversion between kinetic and potential energies how does the total energy of an excited electron increase? How does the photon energy that excites an electron to a higher energy level shared between the potential and kinetic energy of that electron?", "label": 0}
+{"snippet": "\"Inclusion\" means for something to be part of a group \"Exclusion\" means for something to not be part of a group Whether something is in the group or out of the group is obviously modified be the \"in\" or \"ex\" prefix, so the root word should be \"Clusion\" to mean \"part of a group?\", but I can't find any references to the word \"Clusion\" and im trying to come up with something that isn't super esoteric.", "label": 0}
+{"snippet": "Say you want to wear a shirt: it would be odd to say, \"I'm going topful\". Is the reason due to topless being more out of the norm, and thus requiring a term? Maybe in places where not wearing a shirt is more normal, topful may be a more likely word to exist. Or maybe topful sounds like it would be totally covered, so the term isn't used. Or maybe the suffix 'less' often isn't paired with a converse version with 'ful'. Or maybe it's a combination of these things. In any case, any ideas why topful is not said? Topful is indeed a word, but that doesn't seem to apply here: Full to the top, or brim; brimfull. (Webster)", "label": 0}
+{"snippet": "I want to understand what are the techniques one can explore to debug linear programming related optimization problem which is turning out to be infeasible. It turns out infeasible saying so and so equations lead to infeasibility but the problem is that the equation is formed using multiple inputs and has a logic behind it. How do I know which exact input caused the resultant equation to be such that it leads to infeasibility", "label": 0}
+{"snippet": "A Device independent test is a procedure used to characterise quantum resources with the minimal level of trust. If one wants to test correlations like entanglement in a device-independent way, we get non-local correlations. Then my question is: given that Quantum Discord is considered as a form of quantum correlation that has no classical analogous, is it possible to test in a device-independent way? Has anybody addressed this question in the past years? If the answer is no, then a second question comes: is quantum discord really a notion about \"correlations\", if it can not be tested in a device-independent experiment?", "label": 0}
+{"snippet": "I'm writing some text, with a float at some point. I don't mind where my float is placed exactly, but - I do mind if it breaks up individual paragraphs into two pieces, before and after the float. I just read this: How to protect text from being split by a float? where the (single and accepted) answer suggests some measure of clearing floats, or postponing the presentation of any floats (using placeins or flafter). But - that's not what I want; I'm ok with floats either appearing or not-appearing after or earlier than this point - I just want paragraphs to remain intact. What should I use instead?", "label": 0}
+{"snippet": "I need advice on the statistical method, and I've included some preliminary findings from my dataset, which includes mean, standard deviation, and variance. To distinguish between artifact-related and non-artifact-related data, I would like to receive the results from the mean, standard deviation, and variance formulation. Can someone provide me with a statistical formula that will enable me to distinguish between artifact-free findings and those that are not?", "label": 0}
+{"snippet": "At the moment I am trying to simulate charged droplets and their berakup in an homogeneous electrical field in vacuum. I am using a VoF-Method, but as the droplets get smaller and smaller I would need a finer mesh and smaller timestep. So I was thinking of using an Eulerian-Lagrangian approach by identifying droplets below a certain size and turn them into Lagrangian particles. The question then becomes how will I handle breakups for the Lagrangian particles. From what I gatthered there exist droplet breakup models between fluids like KH-RT, TAB, or PilchErdmann. Is there something similar for just electrostatic breakup?", "label": 0}
+{"snippet": "Say we want to inscribe a cicle with a regular polygon: The circumradius is is the distance to the vertices of the regular n-ngon. We can see on the image, this circumradius of a regular n-gon is greater at lower n. And as n goes to infinity, the circumradius should approach the radius of the inscribed circle. But what is the equation of the radius? I've tried calculating it and google it, and the condition must be, the apothem of the regular n-ngon should equal the radius of the inscribed circle. I would love your help on this.", "label": 0}
+{"snippet": "If the eigenvalues of two matrices are known is there any (generalized) way to tell the eigenvalues of the sum of the two matrices? I have come to hear that no such theorem exists that can handle the general case. I want to ask if it is possible to find and prove such a theorem. If yes, what background in linear algebra is required for it?", "label": 0}
+{"snippet": "Specifically, this is for the context of hydrodynamic levitation. Below is what I believe the forces acting on the ball are: What equation would be used to calculate R, the force from the Coanda effect? My logic above, by the way, is that since the ball exerts a force on the water that causes it to go to the right and downward, the water must be exerting an equal and opposite reaction force that causes the ball to be pushed upward and toward the left.", "label": 0}
+{"snippet": "From my understanding, but please correct me if I am wrong, this equation is implicit (See the attached screenshot). However, the goal is to create an identical (or similar) shape that is defined using \"parametric equations\". Is there any good way to do that please? Thank you for the help. In addition, if it is possible to configure this shape to be in the direct \"center\" of the graph (instead of being on the side), that would be even better. In summary: Define this shape (does not have to be identical, just needs to be similar) using parametric equations Plot the equation/shape to be in the center of the graph (symmetrical by the y-axis) Thank you for any advice or help. A bean-shaped equation modelled in Desmos", "label": 0}
+{"snippet": "The Coulomb's law is an expertimental law which calcuates the electrostatic force between distinct two electrically charged point particles (point charge) at rest. And Point particle doesn't take up space. However, there is following sentence in Content 'Limitation' in an the article in wikipedia: There are three conditions to be fulfilled for the validity of Coulomb's inverse square law: The charges must have a spherically symmetric distribution (e.g. be point charges, or a charged metal sphere). In here, i can't understand this sentence. Why charges must have a spherically symmetric distribution?", "label": 0}
+{"snippet": "What happens to the temperature of a body (not in the body frame) as it approaches the speed of light? My thinking is that the molecules will necessarily 'prefer' (as a natural consequence of the basic effects of SR - yes, I am handwaving at the moment and not giving detail just to avoid extra text) a direction of movement, rendering the conventional notion of temperature less adequate.", "label": 0}
+{"snippet": "I found this sentence in Oxford Dictionary in an entry for \"draw up\": Sarah drew herself up, full of indignation that he should presume to judge her. Also this one in the entry for \"sully\": They were outraged that anyone should sully their good name. My guess here is that \"should\" in the first example really means \"should not\", i.e, he should not judge her but I am not sure maybe some extreme meaning or pun is being used here beyond my pay grade in English grammar?", "label": 0}
+{"snippet": "I have found a similar question here. However, my reputation is too low to append comment for requiring more information. As a result, I have to post a question. I read Pandas documentation and I encountered the following sentence: The axis labeling information in Pandas objects serves many purposes. I could catch the general idea of this sentence, except the \"axis labeling information\" part. If I was the writer, I would write as \"the information of axis label ...\". So, I have mainly two points to ask about: Is it OK to write \"the information of axis label\"? Why use \"labeling\" not \"label\"?", "label": 0}
+{"snippet": "I am a computer science PhD student, and I need statistical manifolds theory for my work. I am currently reading Differential Geometry of Curves and Surface by Kristopher Tapp and Carmo. I plan to study Lee's smooth Manifold next. (My supervisor's recommendations.) Unfortunately I do not have the topology background to the depth I would like to have to; I studied Topology without Tears in my second year (not completely) but I do not remember all of what I read either. But I am keeping it alongside. Can anyone suggest a self-readable set of books to get to Stat. Manifold? I might end up needing quite a bit of Discrete Differential Geometry as well. Other suggestions about alternate study plans are also welcome.", "label": 0}
+{"snippet": "I am currently conducting complex simulation involving deformation of a solid object ( which is a surface, or a shell using the vocabulary of structural mechanics) and some fluid discretized using a particle method ( namely SPH). I am used to look at theoritical results to understand a bit a behavior of the solutions ( existence, unicity, rate of convergence, potential numerical issues, ...) but for this case I could not find anything. Is anyone aware of some literature on the topic ? Thanks, Quentin", "label": 0}
+{"snippet": "I have found answers to similar, much simpler questions on this site before (such as here How do you calculate probability of rolling all faces of a die after n number of rolls?), but can't find anything that deals with this exact generalization. After thinking about it some, this seems headache-inducingly more complicated to solve than these simpler variants, because the combinatorics are more nested and interfere with the simpler approaches used to solve those simpler problems (e.g. the fact that you want to roll each number b times instead of just once as in the linked question means that you can't use such a simple expression for not rolling that number in c rolls).", "label": 0}
+{"snippet": "I can't seem to prove this but I also cannot find a counter example. I am dealing with the idea of a function that is constant on the imaginary axis and is defined through an unbound domain. Is it a constant function?If so, why? And if it isn't, can you show me such function? I would like to note that this is not a function with ImF being constant, but F is constant when fed imaginary numbers. Thank aplenty.", "label": 0}
+{"snippet": "I know that in metric spaces sequentially compact is equivalent to compact. I also know that compact and sequentially compact for general topologies there is no relation between them. But I wanted to know if there is the same implication for Hausdorff I-countable spaces. The only thing I have found is that for Hausdorff spaces with the B-W property implies countably compact. Any books where I can research more on the subject?", "label": 0}
+{"snippet": "I have learned that a blackbody object only absorbs light and thus does not reflect any light. The blackbody object will, however, emit light, and none of this light is due to reflection. Where does this light/energy come from? I assume, given an atom, that the light emitted is due to excitation and decay of electron states. Is this correctly understood, and can there be other methods of emission?", "label": 0}
+{"snippet": "When capacitors are connected in series in a DC circuit, the voltage drop across individual capacitors at and immediately after the initial charging period is inversely proportional to the individual capacitance of each capacitor. But afterwards, this began to change due to leakage current. How does this affect individual voltages across each capacitor? Will this process eventually result in the capacitor with the lowest leakage current gaining a voltage drop nearly equal to the voltage drop across all of the capacitors in series?", "label": 0}
+{"snippet": "I am trying to translate a book from English and am confused about the meaning of the word \"block\" as it is used in this context. We attempted to block for local spatial variation in the landscape immediately adjacent to stands (landscape patches) that were sampled by comparing the abundances of small mammals in the stands to a single type of habitat that is immediately adjacent to the target stand. [Landscape Ecology of Small Mammals] What is the intended meaning?", "label": 0}
+{"snippet": "I am looking at GKP and cat states. Wigner plots are newish to me, and I'm trying to get an intuitive feel for the imformation they impart. Just by looking at a Wigner plot, can one discern whether the state shown would make a good qubit? What does one look for? Are certain, say, symmetries, important? E.g., I know the grid-like pattern of a GKP state means some error-correction is inherent. (Asking here too as well as on the quantum computing stack)", "label": 0}
+{"snippet": "Suppose the left lead, right lead and the scattering region are all the same metallic system; such as iron. Why is the charge transimission coefficient must be a positive integer number at any fermi energy level? How is the charge transimission coefficient related to the number of corssing points between the fermi energy level and the eigen state in the band structure? Would anyone please give me some suggestions? Thank you in advance.", "label": 0}
+{"snippet": "I am told many time that nothing can escape black-hole because black-holes escape velocity is more than speed of light. But we know object don't necessarily have to exceed speed of light to escape a gravitational body. Rockets can escape earth with lower than escape velocity if constantly thrusted. In the same way would it be possible to make an object cross event horizon from inside by constantly pushing?", "label": 0}
+{"snippet": "I have some questions about the motion of the simple pulley system illustrated in the book Machinae novae. Are the following conclusion about the system correct? Since the length of the rope is constant, the carriage will move to right by the same amount, passenger is pulling the rope to the left, irrespective of the mass of carriage? The carriage will never toppel, irrespective of the amount of pulling force or location of the carriage along the path. Basically, only the angle of the pulling rope will change but the angle of rope supporting the carriage will always be perpendicular. The mass of the carriage will be limited by the breaking strength of the rope?", "label": 0}
+{"snippet": "While we understand the universe to have had a beginning in the big bang theory, if gravity is quantum in nature yet still has an infinite range then surely once the distance between galaxies becomes great enough, pair production will begin in between those galaxies as a result of the gravitational potential energy being converted to stable particles? This is assuming that the expansion of the universe eventually reaches a steady rate and that dark energy is infinite. Am I missing something here? If so, what? I propose such a fate to the universe be named the \"steady-state fate\" if it is worthy of serious consideration.", "label": 0}
+{"snippet": "I want to know when a vehicle is drifting, assuming it's rear wheel drive and has enough torque to give it some good grip but also has a fairly high steering angle, so the rear tires only slip or do they also roll? Does this change by the radius of the turn? I'm doing an analysis on differential stresses that's why I need to know if I should consider tire and ground friction a force in calculating the differential output or not.", "label": 0}
+{"snippet": "I am a native English speaker but have never found a comfortable approach to requesting help. Would you please is more commanding/ authoritative in tone than I am looking for typically. Can you [please] is not actually grammatically correct: it literally is asking \"Do you have the capacity to do X - as opposed to the actual intent of requesting their assistance (and not doubting their actual skills to perform). What might be other way(s) to lightly/tactfully/carefully request assistance?", "label": 0}
+{"snippet": "In the lyrics of song Sorry by Halsey there's this line: I've missed your calls for months it seems Don't realise how mean I can be 'Cause I can sometimes treat the people that I love like jewelry Jewelry is a good and prestigious thing. Why does someone say I am a mean person for treating loved people like jewelry? My thought is that since jewelry makes the wearer more beautiful the wearer loves it for srlfish reasons. So I think the same applies here. It means they love people for selfish reasons, not for the sake of those people. Am I right or I'm missing something here?", "label": 0}
+{"snippet": "When we have a set, is it correct to refer to another set as 'itself' when this other set is merely equal to it? More formally, I am asking whether or not two sets with the same elements can be considered to be two separate mathematical objects. I am a programmer so I am used to the \"same object\" being a distinct notion to \"the object to which this object is equal\". Therefore, this has led me to consider whether or not this concept is true within mathematics.", "label": 0}
+{"snippet": "If I were to take a particle, moving at a non relativistic velocity, it will have a wavelength (according to De Broglie). However, If I were to change the referance frame of the motion, I know that the wavelength will change because the momentum changes. But will the change be synonymous with the shift of wavelength, if I did the same problem, just considering it wave and applying doppler's shift. If so, why? And if not so, then also, why? What would be the changes if I were to take a relativistic frame instead of a non relativistic one? PS: Due be noted that I am a high school students, who just has a surface level understanding of lorentz transformations and relativity.", "label": 0}
+{"snippet": "I know that we call a quantity a vector if it has magnitude and direction and follows vector laws of addition(the triangle law and parallelogram law). But why only it should only follow addition laws and not other laws like cross product or dot product and why they are not given in its definition. Is it like that if a quantity follows vector laws of addition it also surely follows laws of cross product or dot product or etc.", "label": 0}
+{"snippet": "I have been told that Quantum fields are the real \"fundamental\" of reality and particles are excitations in these omnipresent fields. I have also been told by no less credible sources that Quantum fields are instead simply a good mathematical \"abstraction\" and a fine way to quantum mechanically \"describe\" reality, namely elementary particles - as excitations in the Fock states of their respective quantum fields. I am not sure if this is a controversy, or even a debate in the scientific community, but I would like someone to elaborate as to whether or not those two views contradict each other, and if the do, to understand why.", "label": 0}
+{"snippet": "I am working on a package that could be use in different languages. I'd like to delegate the standard language settings to babel, mainly the spacing around punctuation and the writing of dates. Is it a bad idea to impose the loading of babel to manage local settings? The user could load babel before mine, such as to use babel fine-tuning before working with my package?", "label": 0}
+{"snippet": "It is quite easy to demonstrate that an object at rest that has balanced forces doesn't move. All the Internet examples of things that have balanced forced moving are large scale objects - cars and airplanes. I thought of something like a deployable parachute on a light object but it sounds complicated to set up. What is a good demonstation of balanced forces producing a roughly constant velocity?", "label": 0}
+{"snippet": "In a p-type semiconductor there are always free electrons due to thermal generation allowing for conduction. But If such an electron falls to a hole, it can no longer conduct. So shouldn't more holes slow down conduction? If intrinsic semiconductors have many more electrons in the conductive band at any one point in time, I don't understand why a p-type semiconductor should be more conductive. (My humble guess is that, when there are less holes, an electron jumping to the conductive band due to thermal generation is far more likely to jump back to the same place, because the other holes are too far away)", "label": 0}
+{"snippet": "For full context: I'm looking to categorize adults succinctly into binary categories: those with children, and those without So we could say there are two buckets of Adults here: \"Childless\" and ... \"Childfilled\"? Antonyms of \"Childless\" appear to just be fruitful, fertile, or around the ability to have a child I know an option would be to say that there are two buckets of Adults: \"Those with Children\" and \"Those without Children\", but it's too wordy for the system that we are trying to build Similarly, it could be that there are two buckets of adults: \"Parents\", and \"Childless\", but we found that to be too confusing to read. \"Parents\" is a noun while \"Childless\" is an adjective. Ideally, we are looking for two adjectives.", "label": 0}
+{"snippet": "When writing the equations for center of mass we assume as it to be the point where all the forces act and write the corresponding kinematic equations, and in doing so we dont assume any distribution of forces (like constant or linear wrt length or any dimension of the body) But when we consider the case of a rod lying on a surface with a force acting as F(x) = Kx where x is the distance from one end of the rod, we see that the force is more concentrated above the center of mass and the net force doesnt necessarily pass through the com. I am unable to wrap my head around this difference in result. Need some help understanding where im going wrong in my thinking", "label": 0}
+{"snippet": "The original Computer Modern Math Italic font has a modest amount of kerning listed in its TFM metrics (largely for punctuation, but also for some exceptions like lower case d). But when I use Latin Modern Math as a replacement using unicode-math in either of xelatex or lualatex, those kerns seem to be AWOL. The GPOS table in all of the unicode math fonts I've looked at has no kern tables. Is it really the case that OpenType math fonts don't have pair-based kerns? There's italic correction information in the MATH tables, of course, but I didn't see anything in the MATH table that corresponds to the kerns that seem to be missing.", "label": 0}
+{"snippet": "I produced a set of lecture handouts using .cls files (ndjflart and dupart) that I'd previously used in the past for a paper I published in a journal . I've now been asked to convert those notes into a book. Is there a straightforward way to generate a memoir class file from them, so that I can have chapters, left/right page margins etc? Thanks a lot.", "label": 0}
+{"snippet": "Is it possible to extract equivalent current sources from the partial measurements? I am specifically thinking of a scenario where we have a radiating source inside a closed surface and we measured radiated fields from that source. In principle, according to equivalence theorem or inverse source reconstruction method, if I can somehow measure all tangential fields over that closed surface, underlying current sources can be accurately extracted. But what if, only fields are measured over a part of a surface, is it still possible to extract equivalent sources correctly? What conditions do I need to enforce? Thank you", "label": 0}
+{"snippet": "I am using Cascadia Code font as my tt font, and I wish to use Light series as upright font, LightItalic as italic font, Regular as bold font, and Italic as bold italic font. I am not considering using setmonofont from fontspec package since it's annoying to carry ttf files. Instead, I am using casacdia-code package. How to change default series only for ttfamily using cascadia-code package?", "label": 0}
+{"snippet": "For context: This term or phrase is what it's called when a person (very often used in political debates) will try to take the rarest occurrence of any particular topic and present it as if it's the common practice in order to drive or support their argument. I would liken it to something like \"anomaly argument\" (except, not completely made up lol). I'll know it when I hear it but for the life of me, I just can't think of it. I hope my poor context helps just a little bit.", "label": 0}
+{"snippet": "Is there a term/words to describe that you lost intrest in doing something because you have repeated it so many times? Examples for these scenarios: You liked hamburgers a lot, but because you have eaten them throughout the years so many times, you dislike them now That song you once listened to the first time sounded really good, but after listening to it for many hours, it becomes a pain in the ears or just a boring song", "label": 0}
+{"snippet": "I kept a cold standing water in a glass for a while to warm it up. After a while I returned to see that small minute bubbles have formed in the glass. On closer inspection, the bubbles seem to not float to surface like fizzy drink but they have sticked to surface (mostly at bottom) while some but lesser bubbles have sticked to vertical surface of glass. I haven't seen or paid attention to this phenomenon, and also water is drinking water so it shouldn't be contaminated. I can't think of any physical phenomenon for this? So can anyone try to figure the root cause for this?", "label": 0}
+{"snippet": "If relativity is symmetrical (triplets moving away and returning to the center) then what happens to the Doppler effect as seen by the moving triplets? A B C A should see C moving (Doppler) away/to faster than B C should see A moving (Doppler) away/to faster than B B should see A and C moving (Doppler) away/to at the same rate. Note that the clocks (long term) in each case should match the Doppler (short term).", "label": 0}
+{"snippet": "Accoring to this question and a linked duplicate, it's been verified empirically up to some number that all twin prime averages greater than six, are the sum of two smaller twin prime averages. I was curious whether or not these formed a tree (with twin prime pairs at the vertices and the sum relation the edges). In order for these to form a tree, for every twin prime average, we would only be able to find one pair of smaller twin prime averages which summed to it. Can you find a counterexample, namely any twin prime average which is a sum of two smaller twin prime averages, more than one way?", "label": 0}
+{"snippet": "When I was learning photoelectric effect, It was told that Photons incident on metallic plate in vacuum causes electron to emit if the energy of photon is greater than work function of metal, In this case to me, The emitted electrons in vacuum seemed like a similar condition like that of cathode ray tube, can these emitted electrons be called cathode rays and will they have all properties similar to cathode rays?", "label": 0}
+{"snippet": "The two most popular ways to generate a topological manifold from others are picking a subspace of a topological space and computing the quotient space of a topological space. In differential geometry, it seems that looking at a subspace becomes far more popular than computing a quotient; an exemplary method is the preimage of a regular value of a differentiable function between manifolds. Is there an analogue result/ theorem for under which conditions a quotient space of some (differentiable) manifold is itself a (differentiable) manifold, the same way the regular value theorem spells out some conditions for which a subset of a differentiable manifold is itself a differentiable manifold?", "label": 0}
+{"snippet": "For the converse, while I agree that the point will be on the pependicular bisector, we can't assume the line drawn is actually the perpendicular bisector... yet the above textbook example assumes it is. I don't see why, based only on XA=XB, we're allowed to conclude that XY is perpendicular to AB and YA is congruent to YB? Surely to make the given conclusions we'd need to state that if two points are equidistance from the endpoints of a segment, those points determine the perpendicular bisector - what am I missing?", "label": 0}
+{"snippet": "I have been told that galaxies will never stop rotating because conservation of angular momentum But, there are planets inside of it can travel through dense nebulae and bodies of gas that would cause friction (and probably brake their travel speed through the Galaxy). Wouldn't that brake the galaxy's rotation? Also, gravitational waves can be emitted by rotating massive objects that have uneven mass distributions by so called quadrupoles or higher poles in their angular momentum. Also, in this study (https://www.space.com/dark-matter-slows-milky-way-rotation) they showed evidence that the galaxy rotational speed is decreasing due to dark matter. Then, would galaxies (and all their contents: nebulae, stars, planets...) ever stop rotating? Or they would only decrease their velocity but it would stabilize at some point?", "label": 0}
+{"snippet": "I want to write a formula and put on its right side the description of its variables. Here I just screenshoted the two parts and put them side to side with figure environment but I want to write some \"code\" that puts it like that but not with screenshots or pictures or anything like that. Is it possible ? And if yes, how can I do that ?", "label": 0}
+{"snippet": "I'm reading a textbook that gives both a \"weak\" and \"strong\" formulation of optimal control (first is a control function, second is the whole space, filtration, Brownian motion, and function etc). The textbook has a theorem about existence of optimal controls for the weak formulation and makes explicit that the strong formulation is not equivalent to a classical control problem. However, no existence theorem is present for the strong formulation.", "label": 0}
+{"snippet": "Let us consider a metal clamp which is placed rigidy and is placed parallel eto the ground. Now on the both ends the plates of a capacitor are kept such that they are parallel to the ground. A dielectric is kept in between and slowly released from the clamp. Also a battery is connected to the circuit so as to always keep the voltage constant. So the question is that we had to prove that the dielectric executes periodic motion. My approach We can find the change in capacitance and hence change in work done by the battery. But i am confused so as to how a restoring force could act? I s it due to the battery?", "label": 0}
+{"snippet": "If you have a square two-dimensional grid, that are lots of ways it could be triangulated -- for an individual square one could add an edge from upper-right to lower-left, or from lower-right to upper-left. For an ensemble of squares, a choice of extra-edge direction for each square, so lots of choices. I can think of a couple of reasons to triangulate a grid, to perform a linear interpolation on simplicies, and I read that algorithms for finding sinks and sources generally assume a triangular mesh. For these (and possibly for other) applications, are there better choices of square-grid triangulations? Pointers to the literature on this would be much appreciated.", "label": 0}
+{"snippet": "I was studying duality maps in my Advanced Stat. Mech. class and it was told that all self-dual points need not correspond to critical point. I understand that critical points are points where analyticity of the partition function breaks down. If this point is unique then it can be given by the duality relationship between the constants which appear in the theory. But what happens if this point is not unique?", "label": 0}
+{"snippet": "The system I am trying to model is essentially moving water interacts with ferrofluid. The ferrofluid is in a box that contains air and ferrofluid, such that the setup is buoyant. The ferrofluid chamber has outlets so that it can interact with water. Here's an example image of the system: I need confirmation in these aspects: That the right choice here is to model it like two phase flow not single phase or mixing model. That it can be modelled by either level set method or moving mesh method without compromises in results. If I do not want the fluids to mix, is there a way to still maintain pressure balance between them? Would a semi-permeable membrane work here? If not, is there any other way?", "label": 0}
+{"snippet": "I have been having this doubt when applying the Divergence of a Electrical Potential evaluated in a point, and then doing the Divergence to get the Electric Field in that point. But is this valid? or I have to do the Divergence first and then evaluate? Because when I do the first thing I get the correct result, but the process of which I get the solution is triggering me a little", "label": 0}
+{"snippet": "Is it possible to use punctuation marks such as commas, periods, and question marks just before colons or semi-colons? The error appears when accessing some URLs, e.g.: List items ... Can I set additional parameters for the following tasks?: List items ... I occasionally come up with such sentences due to perhaps my mother tongue (Japanese). However, I realised that such usages can't find anywhere so it might not be natural usage for native speakers. Any natural alternative ways to write it?", "label": 0}
+{"snippet": "It is well known that a convex function is minimised over a convex set, if and only if there is a subgradient which is inwards normal to the set at that point. i.e the negative subgradient (direction of steepest decrease) points directly out of the set. Is there a corresponding rule for maximising a convex function? i.e is beig maximised at a point equivalent to having a subgradient that is normal outwardsto the set at that point. i.e the direction of steepest increase points directly out of the set.", "label": 0}
+{"snippet": "A neutron is udd, then an u-anti-u starts to exist close to the neutron. Then the one d and u change places forming an uud (proton) and anti-ud which decays to an electron and electron-antineutrino. Now it is my reasoning that since this process exists the process can be sidestepped so that a udd decays directly to a uud and electron and electron-antineutrino. Is this true?", "label": 0}
+{"snippet": "I wonder how would we go about to calculate centripetal/centrifugal acceleration for relativistic objects moving at near the speed of light , do we use the original acceleration = force/mass, or input gamma factor for it to be , Acceleration = (gamma) force / mass , Acceleration = Force / (gamma) mass Which one is valid ? If both aren't is there a particular way and/or equation to calculate centripetal and centrifugal acceleration for relativistic objects ? How ?", "label": 0}
+{"snippet": "Is there a package or option that starts alternating row colors from within a table, so that no matter how many manually-colored rows are inserted, the alternating can be started again with the same color each time? (In a single table, I want to manually color a few \"heading\" rows, each followed by an undetermined number of alternating gray/white rows -- always starting with gray.)", "label": 0}
+{"snippet": "This is something I have noticed on a fairly regular basis, and this is a recent example, where the questioner starts by saying \"I'm working on\" and ends up asking \"How do we...?\" Can someone help me with this circuitry? I am not an electrical engineer. I'm working on a brain/organoid computer interface system . . . How do we connect the cyclone . . . Is it some cultural thing? Is there a mechanism to it, like that if others are included they feel more inclined to help?", "label": 0}
+{"snippet": "I'm writing math notes, and I would like to use the symbol for the letter T that appears in this picture (seen in a TeX.StackExchange post): click The symbol I want is in the line \"Calligraphic: UPRIGHT: euler (Euler script)\". How can I load it? Note that I'm not interested in changing all symbols in my document. I just want to use that T perhaps once in the entire document.", "label": 0}
+{"snippet": "Elliptic Integrals and Jacobean Elliptic functions I know it is easy to determine u =F(x,k) where F is elliptic integral of the first kind knowing both x and k. I know it is also possible to determine x = sn(u,k) where sn is the Jacobean Elliptic function knowing only both u and k. Is there a function to determine the modulus k only knowing u and x?", "label": 0}
+{"snippet": "Fox's Trapezoidal Conjecture asserts that the coefficients of the Alexander polynomial of an alternating knot alternate and the sequence of their absolute values forms a trapezoidal shape. The same is true for the Jones polynomial for some alternating knots that I checked. However, since I didn't find an analogous conjecture for the Jones polynomial, I expect that it is not true for some known knot. Which one? Was there proposed perhaps some more narrow version above conjecture for the Jones polynomial of alternating knots? (Either with stricter assumptions or with relaxed conclusions.)", "label": 0}
+{"snippet": "What word describes someone who is extremely carefree to the point of risking their lives. The person is not even bad or annoying; in fact, they are vibrant & outgoing. Except they don't extremely carefree to the point of risking their lives. I was thinking of \"extremely carefree\" or even \"unhinged\". For example, That girl who got stabbed at the club was______; She was outgoing but extremely carefree to a scary point.", "label": 0}
+{"snippet": "Here is the situation. Let's say I have have a mass of a given liquid and I heat it to create a gas. The gas has a lower density than air, so it will move higher and higer in the atmosphere. Then, I recondensate this gas into liquid. Suppose both process are ideal, so the energy I put in the system to cause evaporation is the same energy released by the system from the condensation. We now have the same liquid as before, but since it moved up in the atmosphere, it now has a muche bigger gravitationnal potential energy than it previously had. Of course, the energy is conserved, so this additionnal potential energy must come from somewhere, but where?", "label": 0}
+{"snippet": "I am writing an application in which I complain that every time I point out to the cooks or their supervisor that the meal is not up to the mark,and actually show them how it is, they say that no body else complains, only I complain. However, whenever I ask my colleagues about this, they tell me that what I am saying is valid, and they also point it out all the time. So this is a habit of this staff to gaslight women employees like this. We have put up with this for years. Therefore, I'll really appreciate if someone can help in this. I need a synonym of gas-lighting which conveys the intent properly.", "label": 0}
+{"snippet": "There is no scenario where we can use Coulomb's law. There is no static charge. Even if we consider the local charge density to be constant for a system of charges, the individual charges are still moving, and as we know they are not quite the same. Moving charges show different effects. Even if we think about putting a frame with the particle so that we can consider the charged particle as static that also does not help because there is no single frame for a system of charge Also we want to measure the effect in our lab frame. So, how is Coulomb's law still relevant?", "label": 0}
+{"snippet": "Often you have to adjust the table of contents manually. With very large documents, it is then very time-consuming to compile the entire document each time just to be able to look at small adjustments to the table of contents. Is there any way to tell LaTeX to compile only the toc and not the document? Or maybe you can copy the toc file of the actual document, rename it to the jobname of a small test file and then let it compile, sort of without the associated document?", "label": 0}
+{"snippet": "Say we have a hot cup of coffee that is giving off steam. It is releasing heat into the environment through radiation and conduction. The steam is from certain particles reaching a high enough kinetic energy as to escape the attractive, intermolecular forces that bind them intrinsically. If we physically inhaled steam, thereby increasing the rate of heat loss through steam, would it effectively cool the coffee?", "label": 0}
+{"snippet": "In steady state condition of a conductor under normal temperature, we find that the derivative of drift velocity is zero by setting electric field equal to zero, and one concludes that current density is proportional to the electric field. But in case of superconductor, why don't we have such a steady state condition like thing or in other words, why cant we have a unique solution by setting electric field equal to zero, as in two fluid model of superconductor, one finds that the derivative of current density of super electron is proportional to electric field and not the current density.", "label": 0}
+{"snippet": "Why are there two interior regions in this diagram? There seems to be two inner horizons, and two wormhole regions. Where do the two such regions comes from? What determines which reason someone falls into? Could a composite body fall into \"both regions\" with part of it going into one region and part into the other. The diagram seems to indicate that if you're precise enough you can fall almost directly from the Black hole to the white hole while spending an arbitrarily small amount of time in either of the Wormhole regions.", "label": 0}
+{"snippet": "I would like to consider the sound incident to a water filled pipe wall. I think the pipe wall is typically considered as a rigid wall boundary, it means all the incident wave is reflected. Is this assumption is correct in real world? I think if the sound inside the pipe is large, we can hear the sound from outside the pipe. In practical, what kind of boundary condition should be assumed for the pipe wall?", "label": 0}
+{"snippet": "Using thesisdown to write my Masterthesis I was wondering about the default indentations of the package: If you check the pictures below, all the pages (of the default 'knitted' thesisdown rmd-files) have different indentations (holds also for the toc). On a first glance my guess was that pages with a heading have a certain indentation, whereas the following pages don't have any indentation. This theory also holds for the toc. But imo it doesn't hold for the first picture. So I ask myself: is this indentation behaviour intended or is it an 'unwanted' side-effect? And is there a way to unify the indentations for all pages?", "label": 0}
+{"snippet": "I am reading Middlemarch by George Eliot. I encountered this long sentence and only understood the gist of it. I can't figure out the grammar style and I am looking for the verb of the subject \"he\". Here is the sentence: Thus, the mind of Frisk was exactly of the sort for Mr. Solomon Featherstone to work upon, he having more plenteous ideas of the same order with a suspicion of heaven and earth which was better fed and more entirely at leisure. Why does the sentence have \"he?\"", "label": 0}
+{"snippet": "There are projective sets in descriptive set theory. For them, the axiom of determinacy is not contradicting the axiom of choice. Given the axiom of choice, every set is a projective object. But in a world without AC, is any projective set a projective object in the sense of category theory? Or did those terms happen to use the same word and there is any counterexample?", "label": 0}
+{"snippet": "Assuming the object positioned in front of the mirror at some point on the principal axis before the focus, each point of that object emanates light in all directions, so what happens to the rays of light that do not fall parallel to the principal axis and those that pass through the focus, do they not converge at some point in space? Do they diverge, not forming a sharp image? Why is a real image formed in a concave mirror considered only the two rays of light, the one that falls parallel to the principal axis and the one that passes through the focus?", "label": 0}
+{"snippet": "During the rotation of the Earth, a centrifugal force is formed, according to the actions of which ocean water should be collected at the Equator, forming a \"hump\" hundreds of meters high. However, there is no water hump on the Equator. The depth of the ocean does not depend on latitude, although there should be such a dependence. at the same time, the centrifugal force is sufficient to deform the shape of the earth from a regular sphere to a geoid!", "label": 0}
+{"snippet": "For a given game, is there any relationship between the computational complexity of weakly solving the game and strongly solving it? I ask because a weakly, but not strongly solved game with simple strategies to guarantee at least a draw could still be interesting to play if the players place little value on a draw, and do not know how to win if their opponent is also trying to achieve more than just a draw. However, if simple strategies weakly solving a game guaranteed simple strategies strongly solving it, then this point would be moot. So, if for a given game, as some parameter scales up we have a weak solution of a particular complexity class, can we bound the complexity class of a strong solution?", "label": 0}
+{"snippet": "When I saw factorials, I immediately thought about Wilson's theorem. However, I didn't succeed at all. I also thought about cyclic groups, but with such amount of information I haven't find the use of them. How can I prove it, where to start at least? Source of the problem: practice for exam made by my teacher in the university. Motivation is simple - I want to see more abstract algebra ideas since I don't even know how to start correctly.", "label": 0}
+{"snippet": "As a non-native speaker I currently have a doubt about something. I am writing a technical note about units of measurements (kilogram, meter, second...) and physical quantities (mass, length, time) for software (and I am talking about abstractions in software architecture) and I am note entirely sure whether I should write : Unit and quantity abstractions Units and quantities abstractions when talking about \"the software abstractions of units and quantities\". Is only one of them grammatically correct? Or if both of them can be correct, what is the difference and which one should I pick?", "label": 0}
+{"snippet": "Is there an adjective or shortish expression for an item that is \"not known to be needed\". Context: at the beginning of a process, all items are \"unknown as to whether they will be needed or not\", so all items are \"X\". As I progress through my process, at any point in time I may realize that some item is now or will be needed for sure. At that point, the item moves from \"X\" to \"needed\". Chat gives \"discretionary\" :) , good but not quite...", "label": 0}
+{"snippet": "Magnetic field lines are loops, so at the surface of a magnet pole they look like this? there is a dead zone at the center where there is no lines/magnetic field present? Or lines converge in the middle to a single line or point? like so? Which picture is correct? also on some googled pictures I can see a single straight line coming from the center of the pole that goes nowhere... I know that lines are really an mathematical artifact, I just want to know how the field is shaped near the surface at middle of the magnetic pole.", "label": 0}
+{"snippet": "I believe that Star Trek has advisors so that their science has at least a tenuous theoretical basis. The latest episode is based on interacting with an \"improbability field\". Is this just gibberish or is there some conceptual basis in quantum field theory? The only reference I can find is in this book that says which entails the process that allows for the development of Multidimensional Geometry through its use of Vibrations, the actual nature of Numbers and Math as a whole, the formation of Particles and Fields, and how Quantum Entanglement is instrumental to that", "label": 0}
+{"snippet": "So I came across this game called \"Getting over it\". It is a game where you propell yourself upwards with a hammer, sticking it into various places to keep it in place. My question is, if you were to do the same thing in real life, how would the force applied by you onto the wall above you lift you up? You can check the game if you want to understand what I mean.", "label": 0}
+{"snippet": "I am writing lecture notes for a course I am teaching. A Module on Matrix Computations involves a special mathematical expression and I have no clue how to typeset in LaTeX. I have enclosed an image of this calculation and I request your kind help how to typeset it. There is a special type of arrow in this image, and I have never seen it listed in the standard list of arrow commands in LaTeX. I thank you for the kind help!", "label": 0}
+{"snippet": "Is Point O called the center of the half disk (informally, semicircle)? It's not the centroid since it's not at the center of mass. I'm not sure if it should be called the center if it lies on an edge of the shape and it's only the center of the full disk. I've never seen an official term for it for just a half disk. Does anyone have an answer for this?", "label": 0}
+{"snippet": "I have a game in which pieces normally get tiled in an arrangement like this (which can be shortened or extended arbitrarily): But in special circumstances a piece may be permitted to be placed in between and on top of the other pieces, like this (red circle shows the one piece placed on the corner of four other pieces): I'd like to briefly describe this placement something like this: A red piece may be placed _____ in relation to normal pieces. What the best, short, clear way to describe this placement?", "label": 0}
+{"snippet": "A pipe with a pump and two open ends is placed under water. When the pump is initially turned on, will the pressure at P_out and P_in initially rise/fall, but then stabilize as a flow of water V_flux develops (and the suction pressure is equal to the pushing pressure at all points)? The assumption is that the pressure from the pump first travels as a compression and rarefaction wave, and then once those meet and a flow forms, they cancel out to some extent.", "label": 0}
+{"snippet": "Can anyone tell me what are the relevant pieces of information that are required to find the amplitude of a speaker membrane for a particular input ac signal frequency and voltage amplitude? Could you also show the method by which I can achieve that? Do I need to do an energy balance? Does that mean I would require to know the elastic modulus of the material of the membrane? Or is there any other predefined parameter of the speaker usually provided that I can use to get around that kind of calculation approach?", "label": 0}
+{"snippet": "As Photons do not experience time or space, then according to my thought experiment, all photons must occupy some kind of singularity as well as what WE observe from earth. I was also thinking that the faster you travel the smaller the universe becomes and although you experience time, that time is dependent on the observer. I'm trying to get my head round this (I have no science background) It appears to me that the universe is at the big bang all the way to what we observe at the same instance", "label": 0}
+{"snippet": "The text defines the torque of a particle system as being connected with the axis of rotation. \"Taken two particles of masses m connected to a thin rod of negligible mass etc\", but later when the text explains the torque due to gravity defines the torque of a body as the point of origin (I assume that the axis of rotation is orthogonal to that point, right?), but should I guess this body is connected to the axis of rotation or not? However, in the case of a torque due to gravity, how should I imagine point O? Because in the end the axis of rotation passes through the point O and belongs to the body, right?", "label": 0}
+{"snippet": "It is clear that infinitesimal strains are obtained from finite strains (e.g. Green-Langragian or Eulerian-Almansi tensor) by removing nonlinear terms which smallness order is greater than that of linear terms. But it is not clear for me whether such a procedure is justified, if we bear in mind that finite strains are subject to differentiation when plugging their into the equilibrium equation. After all, the contribution of nonlinear terms in equilibrium equation can be significant, as the derivative of function can be much greater than function itself, even if that function is considered to be sufficiently small.", "label": 0}
+{"snippet": "I found a metal rod lying on the floor and I found out that it sticks when brought closer to a steel sphere like a magnet, but, neither the sphere nor the rod is a magnet. More astonishing is that the sphere sticks to the rod to only a single side of the rod and not the other side as if it was a uni-directional magnet, but none of those two objects interact with any other metal objects and the rod and the sphere are not repelled by a permanent magnet either. Please can anybody explain this anomaly.", "label": 0}
+{"snippet": "I recently came across this document which I am trying to recreate, and this is what I'm dealing with: I have no clue where to start in trying to replicate a header and footer like that, I new to LaTeX classes so I'm not really sure where to start. Youtube is pretty plain on this topic and Overleaf learn section doesn't help me much either. I really want to create a .cls file in order to adapt it to other related documentation... If anyone could point me in any direction it would be great, or if you already have some experience and easily recreate it yourself, that would be awesome! Thanks in advance!", "label": 0}
+{"snippet": "I understand numbers to be defined as objects defined to have certain convenient properties in relation to certain operations. It is very surprising that the exact same group objects should be applicable to the modelling of such seemingly disparate concepts as length, area, degree, cardinality, time, wavefunction, etc. I also find it surprising that the qualities of numbers, which appear quite contrived, should correspond to anything real in the first place. How can I make the relationship between these concepts and the concept of number more intuitive and expected?", "label": 0}
+{"snippet": "A signal in additive noise is sampled by a receiver with an unstable clock. Maybe the clock has absolute bounds on its frequency drift and sample time aperiodicity, or maybe the clock has some statistical characterization (maybe an Allan variance). Maybe the signal being sampled was also produced by such a system. Can anyone recommend any brief treatments on this situation's signal model, its spectral analysis, and efficient (or typical) signal processing approaches in this domain? I notice there is a brief Wikipedia article for \"Coherence theory (optics)\" which is closely related, if not more general.", "label": 0}
+{"snippet": "For example, suppose a spaceship explodes. The sound of the explosion will travel in the expanding cloud of escaping gas. I gather that it should rapidly weaken and the pitch should drop, but I'd like to get more specific than that. Are there any models that suitably describe precisely this sort of situation? Additionally, is it feasible for there to be a relatively safe distance away from such an exploding spaceship where the expanding gas cloud isn't yet extremely rarified and an audible sound might actually be heard through your space helmet?", "label": 0}
+{"snippet": "There are two facts about elementary row operations and column/row spaces: Column space is affected by elementary row operation, whereas row space is not. (the issue of finding a spanning set of column/row space) Linear dependence relations between columns are preserved over elementary row operations, whereas the same between rows is not. (the issue of finding linear independence between columns/rows) In finding the column space or row space, we lose and gain something in either case. I am not sure why this is possible intuitively: the issue of finding a span is linked to having linear independence between the vectors. Therefore, my question is a more conceptual one: why are the two above statements intuitively consistent (at least to an amateur like me, they seem opposing)?", "label": 0}
+{"snippet": "What is the exact difference between a moment and a couple? In some YouTube channels and books, they say the moment of a force produces a translational as well as rotational motion whereas the concept of couple produces a pure rotation. How and why is it so? I am not convinced about this yet. Once you fix your point of axis or rotation axis. How come when you apply a force the body would make a translational motion?", "label": 0}
+{"snippet": "My objective at this point is not to learn all and advanced mathematical proof concepts/techniques. At this point my objective is to get basic understanding of what is mathematical proof and learn only basic concepts/techniques behind them. Also, I need it to have as minimal prerequisites as possible. Best variant will be some article or tutorial or a small part of a big book. Can you please provide such material?", "label": 0}
+{"snippet": "My goal is to implement a mathematically correct multivariate normal distribution using Sobol QRNG sequence as a source of randomness. The implementation should NOT produce the whole set of a given size at once, but instead it should reveal next values one by one, also depending on getting new values out of the Sobol sequence. So the algorithm should be streaming the data with minimum memory requirements. This guy claims he implemented MVN out of Sobol, which is officially endorsed on the MATLAB website. However, he has another call to rand() in the middle of his code, so it feels he does not fully understand what he is doing. That's why I hope for your help with a strictly mathematically and statistically valid approach here on Math.", "label": 0}
+{"snippet": "For example, if you say New Orleans like \"New Orleens\" it's considered wrong, instead of \"New Orlins\" (Orleans is pronounced different in France though), or Iran like \"I ran\" is wrong, instead of \"Ear on\". But then people have names for other places all over, like Germany or Allemagne, instead of Deutschland, which would have their own pronunciation. An even closer example would be France, pronounced like \"Fronce\" for the locals, and closer to \"Frants\" for Americans. Maybe this is protested in France, I'm not sure. Or Greenwich, UK vs. USA (I wonder if each says the other should be pronounced like their own). But when does pronunciation of somewhere else become wrong instead of their own way of saying it?", "label": 0}
+{"snippet": "I read that the standard depiction of covalent bonding is misleading. It gives the impression that the valence electron exists at that bond site. But really it exists as a wave throughout the crystal. So is it a standing wavefunction that has a peak at the bond site? From this can we infer that conduction electrons have propagating wavefunctions? Furthermore, how is it that an electron can mantain its wave characterictics in a crystal? We know that oberservations (more accurately interactions) collapse the wave function. Certainly the electron is interacting with many potentials and forces in a crystal.", "label": 0}
+{"snippet": "Let us assume that the classical spacetime describes relative positions of mass particles, and the relative positions are in fact described by quantum entanglement. That is, the stronger the entanglement, the shorter the classical distance. If a group of mass particles are being pulled very close together by classical gravity, then can we argue that interactions behind entanglement become fuzzy and that infact weakens the entanglement, hence the classical distance can't be arbitrary small and gravitational singularities don't exist?", "label": 0}
+{"snippet": "I study the magnetic trapping recently. I met a problem. I consider the original quadruple magnetic trap. In the original quadruple magnetic trap, the magnetic vanishes at the center. The Majorana flips happens at the center. If we want atoms move in the trap adiabatically, the Lamor frequency must be larger than the trapping frequency of the trap. What does the 'adiabatically' mean and how come is the condition? I saw this statement in my lecture note and other prof.'s lecture note but I have no idea why it is.", "label": 0}
+{"snippet": "I have read the related discussion and some text and get some basic ideas. Geometrical interpretations of SVD Visualization of Singular Value decomposition of a Symmetric Matrix What I don't understand is why are we rotating twice? I imagine we only need to rotate once, and scale once? Is there any significance in the angle we rotate? One answer did say \"the value of this is not too important as long as you pick a sensible number as the rotation matrices are not unique\" which makes it more confusing to me ...", "label": 0}
+{"snippet": "I am confused about the curve carried by the train track. I am using two references: Mosher's note (via arcs) and Johnson's blog (via bands). By Mosher's definition, I wonder if or not, in the following picture, the blue arc is carried by the train track determined by the red and green arc (we can make the blue arc arbitrarily close to the train track). Similarly, by Johnson's definition, I wonder if or not the blue arc is carried by the train track determined by the bands from the red and green arc.", "label": 0}
+{"snippet": "We know that displacement is change in an object's position (here position means 'position vector'). Then velocity will be change in position of the object with respect to time, simply displacement/time taken. But I was taught that velocity is change in displacement with respect to time, then it means velocity will be equal to change of (change in object position =displacement) with respect to time. So, which one definition is correct?", "label": 0}
+{"snippet": "I want to understand something: when someone measure the pressure, temperature and specific volume of a material, I think the pressure is applied in all directions of the material. This can be understandable for liquids and gases because the pressure in a closed container and for instance, you can used a piston to increase the pressure in this system. What about in a solid? the pressure or normal stress applied in this solid doesn't mean that the stress in other directions exists, so what kind of equipment is usually used to measure and control this thermodynamic property (oressure) ? Or is my assumption wrong and is not necessary that all direction of the body to be applied the same pressure?", "label": 0}
+{"snippet": "I am not sure if I understand the energy band diagram correctly. In a pn junction situation below, before the p type material come into contact with the n type material as in figure a), an electron at the conduction band minimum in the p material has the same(or roughly the same) energy level as an electron at the conduction band minimum in the n material. Is it still true after they are fused together? If so, how come it is showing on the band diagram there is an energy difference as in figure b)?", "label": 0}
+{"snippet": "Many textbooks on tensors start with a sentence like \"An equation written in tensor form is valid in any coordinate system.\" The second sentence is often \"Closely associated with tensor calculus is the index notation.\" According to me, this seems contradictory. The first sentence seems to state that coordinate systems should be avoided while the second one emphasizes the need of a coordinate system. How far can we go in tensor (calculus) without relying on index notation? Are there books specifically following this approach?", "label": 0}
+{"snippet": "Consider no air resistance. If we throw a ball vertically upward from my point of view it goes vertically up and down and moving along straight line. But from point of view observer in outer space it is parabolic because of rotation of the earth. We know vertical acceleration/deceleration is due to earth gravity. But where component of velocity parallel to the Earth's surface come from to make parabolic path?", "label": 0}
+{"snippet": "In the book Then I'm trying to understand the reasoning behind constructing the matrix, I get the unique scalars P_ij part, representing the one basis's vectors with another basis vector's linear combination. But then he uses same matrix for getting another basis's vectors. I'm confused about this kind of reasoning and it appears in other proofs too. How these scalars i's and j's satisfy these equations? At this part, he uses same matrix but using j's and i's at the same time. Sorry this question is not clear but in general i am confused about constructing matrix P, can someone explain the reasoning?", "label": 0}
+{"snippet": "I thought about the question in the title for a ring that is not a Dedekind domain (here, the unique decomposition is a well-known theorem and also characterizes Dedekind domains!) but only a one-dimensional noetherian integral domain. The following is the motivation: In a Dedekind domain, every fractional ideal is invertible. Therefore, my idea is that actually the invertibility of such a fractional ideal makes a unique prime decomposition possible. Is this true? If yes, how could one proof this?", "label": 0}
+{"snippet": "I'm going to study plasma characteristics by using Particle-In-Cell (PIC) method and I know that plasma has fluid behaviour and can also consider as particle behaviour also. To understand a basic of PIC simulation, I would like to understand an origin of the PIC that why it used differential equation to describe plasma properties from Eulerian method? and what is the difference between Lagrangian and Eulerian method for plasma physics?", "label": 0}
+{"snippet": "When one says light comes on immediately when you turn on the switch of a flashlight cause the electric field is set up in the wire with a speed approaching the speed of light, what does exactly this sentence mean \"electric field is set up in the wire with a speed approaching the speed of light\" does the electric field travels from the source? If it doesn't how can it has a speed to begin with? Is there any sort of electromagnetic wave that originates upon turning the switch on that signals the farthest electron to move?", "label": 0}
+{"snippet": "How to cut the square which tessellates to octagon using straightedge and compass? What are the exact measures of colored sides? What is the angle marked with red color? Edit (I added vertices): Edit. Acknowledgement after answers. Thanks to Jean Marie, Blue and Daniel Mathias for tackling the problem. I accepted Blue's answer for its breakthrough, but I also weighed Daniel Mathias' solution for its geometric simplicity. Initially, I didn't expect the problem to be so laborious. I invite you to my puzzle in a similar flavor of dissections, which after many years still has no answer nor proof that the solution does not exist. Variation of Haberdasher problem of Henry Dudeney - dissection of equilateral triangle into square with flipping pieces", "label": 0}
+{"snippet": "What is the difference between the two sentences below? And what does the first sentence express exactly? Also, could you provide a grammatical analysis of the structure of the first sentence naming each of the parts of the sentence (which one is the subject/object, etc) and parts of speech (noun, verb, etc.)? We were here for a search of what the first sentence was in comparison with. We were here for a search of what we were comparing the first sentence to. P.S. We had an argument with a friend and we tried to present as objectively both sides as possible and refrain from showing any sides.", "label": 0}
+{"snippet": "Is the word multiperspectively (sometimes polyperspectively) only used to describe literature, as in narrative perspectives? Could I use it to describe a personal trait? For example: In debates people despise that I multiperspectively argue.... I did see a post asking what the word was for \"seeing from multiple points of view\" and this word didn't come up. Also, I understand this is a serious English site, my question is not for any scholarly reason. I am trying to write to a person and I got stuck while trying to find an adverb that means this.", "label": 0}
+{"snippet": "I have a Kalman filter that uses location as part of its internal state. This location is expressed as x, y coordinates in meters north and west from a fixed point (the home location). Part of my measurements for the filter are GPS coordinates. Can I translate the measurements back to the state space using the H matrix? The range of movement for the tracked object is small enough that I can use a fixed multiplier to scale the longitude to meters. But how do I add the transpose to the matrix, so that the GPS coordinates use the home location as the origin?", "label": 0}
+{"snippet": "I am self studying algebraic topology, the fundamental groups and covering spaces and homologous groups. I have read the topological properties of classical matrix groups like connectedness, path connectedness and compactness. Now I want to study the algebraic topological properties of these groups. In particular what are the fundmental groups of patnconnected components of the matrix groups? Does there exists any relation among the matrix groups via covering spaces? If anyone provide some referances regarding these questions that will be very much helpful. Thanks in advance.", "label": 0}
+{"snippet": "When an electromagnetic wave interacts with a free electron the electron starts to oscillate in the direction perpendicular to the propagation of the wave meanwhile when a photon interacts with a free electron what will the electron do? Will it oscillate in the direction perpendicular to the momentum of the photon? or will it travel in the direction of the momentum of photon? How can someone describe this interaction in photons form so that the electrons oscillates?", "label": 0}
+{"snippet": "In present tense or past tense, subject and verb can be omitted after conjunction. For example People tend to laugh when (they are) imagining pleasant things When (I was) going home, I met my father Then could it be possible to omit subject and verb in case of the past perfect tense as well? For example, As it had been written in a hurry, the report showed many errors. As written in a hurry, the report showed many errors. Or, because this case is of the past perfect tense is changing this way only correct? (Having been) written in a hurry (without conjunction 'as'), the report showed many errors.", "label": 0}
+{"snippet": "I live in this region and is studying to retake the national test and I need a big amount of tough exercises to practice but I can't find good documents/ textbooks over here. Any appropriate textbooks help me greatly. The topics are: calculus, algebra (especially logarithm), complex numbers, Oxyz algebra(?) (I really don't know what to call this one. It includes the equations of lines, planes, spheres, etc. And vector formulas. No matrices.). Thanks for your help.", "label": 0}
+{"snippet": "From the perspective of an electron in the double slit experiment, does the \"rest of the universe\" that it is disconnected from behave in the same manner as the electron does in our view? As in, is the world around it, from the electrons point of view, as a closed, separate system to be interpreted the way we see the electron? Is the effect relative? From the electrons perspective, could it be in a \"collapsed\"-state and consider only the universe around it to be in a superposition? I hope the question makes any sense, because I am really curious and a little confused about the whole thing. Thanks in advance!", "label": 0}
+{"snippet": "I was reading Lazarsfeld's Positivity in Algebraic Geometry, and I realize that Cartier divisor can have torsion elements, but I can't find such an example. I know for the Noetherian scheme that is locally factorial, the Cartier divisor is isomorphic to Weil Divisor and we know Weil Divisor group is free therefore it's torsion-free. So this can only happen when the Weil Divisor do not isomorphic to Cartier divisor is there any example that the Cartier divisor has a torsion element.", "label": 0}
+{"snippet": "Okay, apart from the American slang term, or the reference to a male chicken, what is the meaning of the syllable \"cock\"? For example, shuttlecock ... in badminton. Or, as I'm doing housework and learning about plumbing, a \"ballcock\" valve in a toilet, or a \"sillcock\" valve in pipes? Does it refer to a specific shape, or a mechanism or something? Which might make sense for the valves, but then what about the shuttlecock?", "label": 0}
+{"snippet": "I can't decide what I prefer - having empty space at the end of a page or a split box. For example: Should I be aiming to make sure the page is full with no need to break boxes? Like, I can add more text I probably don't need further up the page so that the last box starts on a new page, is this something people do for aesthetics? Or should I be happy enough with a break like this? Or the empty space?", "label": 0}
+{"snippet": "Consider the small weight is attached to a big diameter wheel and the big weight is attached to a smaller diameter cilinder. I've read that if you ignore friction and all the forces are balanced perfectly, you could consider the possibility of this machine lowering the lighter weight through the distance of one wheel circumference at uniform speed while the heavier weight is raised by the smaller distance of one circumference of the cylinder. In this situation, what would be the forces that balance out the differences in the gravitational forces that act on each mass?", "label": 0}
+{"snippet": "I know the restatable environment from the packages thm-restate combined with thmtools, which allows to formulate theorems that can be restated later in the document. Now I am wondering, if there is a similar solution for equations like equation, align, etc.. I have already tried to just reuse that restatable environment for equations, but as expected I got an error. I have already found \"solutions\" that suggestion to copy the content and tag the reference number. However, this seems to be a stopgap.", "label": 0}
+{"snippet": "I would really like to create these pictures to help with fractions. I know how to begin using tikz package. I am not sure how to go about setting it up so that I do not have to draw it separately each time. I would love to show something that I have started with but have no idea. And what if I wanted to make the rectangle horizontal and not vertical? Thank you so much for any responses!", "label": 0}
+{"snippet": "Suppose that I have two electrons in a box that were originally spread by a infinite potential wall. The two electrons are in their ground state wave function (sine function). Now I removed the barrier for the two electrons to interact. How is the Pauli antisymmetrical pair formed? Do I have to impose them to become the antisymmetrical pair in the beginning, or can I derive the antisymmetrical form from the original sine functions?", "label": 0}
+{"snippet": "If I were to have asked this question about local systems, it would be extremely easy to give examples from physics/biology, etc. I can give example if people want, but this should be easy to Google. Question: What examples of perverse sheaves naturally show up in nature? More specifically, I mean examples which are not local systems, and the example only applies to perverse sheaves (or constructible complexes of sheaves) and not sheaves of vector spaces in general.", "label": 0}
+{"snippet": "I am not sure why the following configuration can not be a configuration of a electromagnetic wave. I mean, i am sure it can not be the configuration of the fields in a plane perpendicular to a wave, but i can't explain the reason in a satisfactory way. Look, it seems there are souces propagating with it, since these configurations are the configurations of a point electri ccharge and a infinite line with current. But i would like i better way to explain why we can't have it.", "label": 0}
+{"snippet": "At a weight m, a plane is acceleration upwards at rate of a. We also remember the value of g. From my understanding, we have two opposite forces that we care about. The force due the gravitational acceleration, which points in the negative y-direction, The force of the upwards acceleration, which points in the positive y-direction. The first force must be equal to m times g, while the second would be equal to m times a. However, that is not the case with the upwards acceleration. My physics book gives this reasoning for calculating the upwards force: I don't understand why we would add g, since it points in the opposite direction?", "label": 0}
+{"snippet": "The question is simple. Could analog computers (for example, electrical analog computers) in effect avoid traditional numerical instability problems that come from solving a set of PDEs over a discretized domain? Progress on significant physical problems (the computational aspects at least) are often substantially delayed because of time spent figuring out how to avoiding numerical instabilities, and often the solution ultimately utilized is just to hit the problem with lots of artificial diffusion, which seems unrigorous at best. Also, since many physical theories are often significant approximations themselves, maybe some accuracy could be sacrificed (in moving to analog computers) for the greater benefit of avoiding numerical instabilities.", "label": 0}
+{"snippet": "To my understanding, normal reaction is a force that pushes in the opposite direction of gravity, in order to keep the object from falling, or phasing through the surface. Though, what happens when we enter a circular rail? In this case, the guide book is saying that the normal reaction is pushing alongside gravity. Then, shouldn't it fall down? I thought the normal reaction was supposed to be pushing upwards in this case. If not, then is the normal reaction always bound to the center of the circle? I can provide the exercise with the answers, in case there's not much details in there.", "label": 0}
+{"snippet": "A grad school problem has been haunting me for years and I have never been able to find it on the google machine nor was the professor who assigned the problem able to describe how to actually solve the problem... How do you find the surface area of an ellipse projected onto a sphere? The real world application is what is the footprint area of a satellite transmission signal so you know how long a ground station will be in contact with the satellite?", "label": 0}
+{"snippet": "Say a spaceship is traveling at a certain velocity v (>>c) and it emits light from the nose of my spaceship in the direction of travel. The speed of light is finite and hence there should be a change of wavelength of light. How does the speed affect the momentum transfer does my light have lower momentum thanks to the direction in which it has been emitted?", "label": 0}
+{"snippet": "My math professor told us that the upper and lower bounds theorem of polynomials (pictured) applies not only to rational roots, but also to the modulus of complex zeroes. They were unable to come up with an explanation for why this works, and I do not grasp this concept at all. Why/how does the bounds theorem apply just as well to to complex zeroes as it does to rational zeroes? How does the modulus come into play at all for that matter? Bounds Theorem", "label": 0}
+{"snippet": "I heard that if Universal Expansion continues at some point galaxies will be so separated that a future civilization would have no way to know there are other galaxies, for them the Galaxy they live in is alone in the universe. (I'm planning to write a sci-fi story about it). Thus more or less in what time frame would that expansion would cause that effect? Thank you in advance.", "label": 0}
+{"snippet": "I am new to it, so please help. As I know, AC current is back and forth motion of electrons, which radiates electromagnetic waves, so there is energy radiation from power line to our home. But in case of DC, if the magnetic field and electric field are static then how does energy radiate. I have searched that drift velocity of electron is slow, so DC flows at the same speed as of AC which is C. So, how does this happen if there is no radiation of DC? Please answer.", "label": 0}
+{"snippet": "I have a body on a horizontal surface with friction. My thermodynamics system is only the body and I want to describe this with the first law of Thermodynamics. Suppose the body has a start kinetic energy and for the friction in the final state it has no more kinetic energy. For this problem there isn't a heat exchange but only a work exchange caused from the friction. How can i write the fist law with this system?", "label": 0}
+{"snippet": "I have Two parallel lines, I want to create from one line to another using a cubic Bezier curve (S shaped basically), I'm free to pick any start point and end point. But the constraint is this path should be optimally shortest, also another constraint is I don't want the curves with too much curvature, I just want to switch to the other parallel line smoothly without creating too much curvy path. My question is how to pick start and end point? for having such a curve? I'm considering Bezier curve would be best for this with my very little research Thanks :)", "label": 0}
+{"snippet": "I was thinking about the definition of reversibility but there is something that I cannot understand. In real life the surrounding of a system (anything else in the universe) is always changing making impossible a reversible process even if the process is slow enough to guaranteed the lack of friction heat loss and this surrounding are not in thermodynamic equilibrium so I cannot understand how people calculated entropy under such conditions, am I wrong in the assumption of choosing the surrounding as everything outside the system or it is enough to choose the immediate surrounding that is in thermodynamic equilibrium?", "label": 0}
+{"snippet": "My question is whether there are some books on chess mathematics with theorems and their proofs concerning winning strategies for classes of initial positions. Despite there being a lot of books on chess theory and surveys on the use of AI in chess, it seems there is no purely mathematic chess theory that may use the results of game or group theory. If this is the case, then someone has to start it (despite obvious combinatorial difficulties).", "label": 0}
+{"snippet": "What is the best way (as in most efficient) way of writing pseudocode like below? In particular I like that it is well-structured but gives enough freedom in writing (in reality it it is just standard inline text aligned in a specific way). If a library was used I would be grateful if anyone can spot if. In case there isn't such library, how can I achieve the result?", "label": 0}
+{"snippet": "The following graph is a sensor measurement. Scatter plot The data points are also available in this excel file. I want to do some offset correction/scaling to make the measured points match the actual points. What is the simplest algorithm to do computationally by programming language like Python or MATLAB. These data are acquired in MATLAB continuously point by point, and I have to apply these offset to each point. Will something like finding a linear fit for all possible points and multiplying it with a polynomial work? or if there are any better methods, please suggest.", "label": 0}
+{"snippet": "I am wondering if a vertex can lie on an edge in a planar graph- I am not sure if an edge of this vertex is regarded as crossing the edge on which the vertex lies. I have two questions here: Is the actual edge from the vertex tangent to the edge on which the vertex lies? Even if it only is tangent, does it still fit the definition of a planar graph that edges don't cross- as crossing would mean it would have to go through the edge and out of the edge, rather than just touching it at a single point? Is a vertex simply a point and an edge a line segment in the sense in which these terms are defined in plane geometry?", "label": 0}
+{"snippet": "I'm not scientifically adept, so bear with me. Would it be feasible to retain enough fuel on new satellites/space stations, etc., that we could dispose of them when obsolete by sending them to the sun where they would likely incinerate before they came close to the \"surface.\" How would we ensure burn up rather orbiting the sun? Already in earth orbit, how much speed would be needed to \"hit\" the sun? Impractical because of fuel needs? We could use the space station as an example. It would seem to me that eventually the gravity of the Sun would pull it lessening the need for fuel, it's getting way from the rest of solar system's gravities that would require fuel.", "label": 0}
+{"snippet": "according to my book the perpendicular component of reaction force is called normal force when there is contact between two bodies. I can not understand that how for example when we jump we pushes the ground downward(action) and the ground pushes us upward(reaction) how this reaction is normal force? or for example if someone jumps to the shore from a boat, the boat moves in the opposite direction we push boat in backward direction and boat pushes us in forward direction(reaction) is this also normal force or friction force plz someone explain i dont understand.", "label": 0}
+{"snippet": "Countable atomic structures are homogeneous, i.e., all finite tuple of the same first-order type are conjugate under automorphisms. While this is classical, I can't think of an example of a countable structure whose homogeneity is best proved via atomicity. Competing proof strategies include construction of that structure as a Fraisse limit possibly in an expanded language. Is there a countable structure whose homogeneity is proved via atomicity in a manner at least as good (whatever that means) as via Fraisse theory?", "label": 0}
+{"snippet": "here is a vague question: I recognized that adjoints of operators and commutants of non-degenerate self-adjoint algebras share similar features, e.g. the double adjoint of a closable, densely defined operator is the closure of this operator. The double commutant of an non-degenerate self-adjoint algebra is the strong/weak closure of it (double commutant theorem). It seems to me, that this property of double(something) implies closure is a recurring feature and I was wondering whether they are somehow related in a maybe category-theory kind of sense? Thanks", "label": 0}
+{"snippet": "When is a category of sets and spans just a category of sets and kleisli morphisms? There is a link between spans and kleisli morphisms, but I feel like they are the same things. I guess I am assuming that the base category for the monad is Set. Is this only true for the multiset monad? To see how we can have a category of sets and spans, just see the nlab article here:", "label": 0}
+{"snippet": "We know that a pair of scissors is hard to use at maximum opening angle, because the force from the blades pushes the object away from the scissors and the actual cutting force is reduced. If we would design a pair of (simple, two-piece, with one point of rotation) scissors whose blades have a limited maximum incident angle, or even better, a constant incident angle, then what shape does it look like? Does it have a mathematical form? image source amazon.com", "label": 0}
+{"snippet": "If the large space voids between galaxies had uniformly-distributed \"negative\" gravitational lensing, would its presence be obvious from photos in the same way that the presence of Einstein crosses and Einstein rings make clear the existence of positive gravitational lensing? Or would it only cause subtle distortions, such as reducing the angular diameters of distant galaxies as a function of their distance from us or by distorting how light transitions into and out of a positive gravitational lens? If it would only cause the subtle effects (not obvious ones involving the inversion of images), is it possible for this effect to exist given what Hubble, Planck, etc. has received?", "label": 0}
+{"snippet": "I have a question about article usage. I have two sentences and I'm struggling with the articles in the second sentence: There may be invoices on each table. When (?) invoices lying on (?) table disappear, it's a problem. I would guess the invoices and a table. My reasoning is that I'm not talking about specific table so it should be indefinite article. But definite article for invoices because we talk about specific invoices on that table.", "label": 0}
+{"snippet": "If we get magnetic field lines on a piece of cardboard, shouldn't it form a gradient of metal pieces across the board (thick layer of metal pieces near the magnet and thin layer of metal away from magnet) rather than forming lines of metal pieces leaving crevices between them. Like in the red areas it is somewhat evenly distributed on board. But in the blue area they forms pattern of lines. Why do they forms lines? Why don't they form a gradient of metal pieces? According to me there are infinite field lines, and only the magnitude of magnetic field decreases as we go away from the magnet.", "label": 0}
+{"snippet": "Lately I've encountered a few situations in discussions where I feel like there may be a word that is either more succinct and/or perhaps more wry than just 'ethically convenient'. An example sentence would be: You can only say you wont be involved in unethical thing because it so happens that you cant be because reasons unrelated to your ethics. You are being/You are _______. Basically something just fell on your lap with no personal effort, but you then take advantage of that to further your moral standing. Often it is done willingly, but it could be done with less awareness, perhaps through a form of delusion. 'Casuistic' from the answer here is interesting, but not quite right.", "label": 0}
+{"snippet": "A dude has the power to split a nucleus. But this nucleus doesn't hit anything, it just explodes, and that's that. He explodes the atom. He can let the nucleus explode, or he can absorb it. I was making this character thinking he could just split an nucleus, and it would make a nuke-level explosion, and then he could absorb the power of a nuke. But is ONE SINGULAR nucleus splitting, with NO help whatsoever, would that ONE singular nucleus explode with the force of a nuke?", "label": 0}
+{"snippet": "What bugs me the most is that since there is net charge, i dont know two things, how would that charge distribute across the surface (even though my intuition says that one of the sides will have more charge than the other) and how would one calculate the dipole moment since the distribution wouldn't be symmetrical about the X-axis (in this problem the equator of the sphere), i've found the potential around it via legendre polynomials which i guess could help, but i just... dont really have a good idea of what to do neither the confidence", "label": 0}
+{"snippet": "To clarify with a made-up example: When you address the nation state ... Above, 'state' could be taken as either a part of an open compound noun ('nation state', see footnote), or a verb ('to state'). As a non-native speaker I notice that such ambiguous interpretations do briefly hinder my reading flow, as I have to retract a bit. Also, similar ambiguous cases don't seem that rare. Hence, must, or at least may, one use a comma to disambiguate such cases? In the running example, is this allowed (or even required)? When you address the nation, state ....", "label": 0}
+{"snippet": "In piezoelectricity, the piezoelectric tensor is of rank three and its a reason why piezoelectricity is not present in all materials whereas for electrostriction, it is present for all crystal symmetries because the electrostriction tensor is of rank four. So, I think the presence of the electromechanical phenomenon is related to the rank of the related tensor because the rank is related to the crystal structure ?", "label": 0}
+{"snippet": "I've always curious about one interesting fact. I will explain it with example. Currently, I'm watching an example which shows the following picture and says that box at the left is the speaker and it produces a sound wave. I wonder why it's being drawn like the above. since it's a longitudinal wave, which actually doesn't have the shape like that. Since particles move in the same direction as wave, their motion is right and left back-and-forth. On the graph though, I get why they end up drawing sin/cos functions, but in the real motion, they don't have the shape as on the above picture. Transverse waves do though which I get why. Thoughts?", "label": 0}
+{"snippet": "I am learning multivariate regression, with matrix equations and heavy use of: Transposes Inverses Identity, idempotent matrices Can anyone refer some books where I can learn the properties of matrix equations. Practice problems would be a great help. (I looked up some standard books on Linear Algebra - for example, Anton - but the topics are different from what I need. For example, Anton has Vector spaces, subspaces, eigenvectors, which is not really what I need).", "label": 0}
+{"snippet": "I have a question about the potential and wave functions of discrete energy levels of quantum point contacts. Assuming one has a rectengular potential well: Can the potential of the QPC be assumed to be infinite or is it finite and the charge carriers also have a probability of being outside the potential well? Is it also necessary for the wave functions to drop to zero at the edges so that the quantized conductance can be observed?", "label": 0}
+{"snippet": "On looking upon the process of penetration of radiation. I came upon this: \"If the particle has enough energy, it can deposit its energy to break the molecular bonds displacing the electrons, hence it can penetrate the object. So, if the same thing is done in a large scale with higher concentration of radioactive particle hitting an object per unit area, would it be possible to break nearly every single molecular bonds, and resulting into the object breaking apart in dust?", "label": 0}
+{"snippet": "I'd just like to enquire on how this sort of chapter style is done. I am aware it is some permutation of the memoir class with hansen style chapter headings, however the number seems to be in sans-serif, the text in CMU serif, and the document to be in a different font to what I typically find on hansen templates. If anyone could replicate this for me, it would be greatly appreciated.", "label": 0}
+{"snippet": "Is the wire in the figure below homotopic to a wire between the two points that just go straight above the pipe? My knowledge of topology is very basic, and it seems to me that the pipe can be seen as some kind of hole, so the wire seems to really be impossible to untie. However, there is a youtube video that seems to untie it. Is it a trick or is my intuition wrong, and if so is it easy and evident to tell why they are homotopic without having to watch the video? Or something else that I am misunderstanding? enter image description here", "label": 0}
+{"snippet": "In the Wikipedia entry associated with the Kahn-Kalai conjecture, there is the following assertion This conjecture concerns the general problem of estimating when phase transitions occur in systems. As this entry notes, the conjecture (technically \"theorem\", as is recently proved) is in the field of graph theory and statistical mechanics I am particularly interested in the consequences of this conjecture in view of statistical mechanics and (even if possible) its implications and applications to formation of complex networks in engineering fields. The main article, as far as I can see, heavily focuses on graph-theoretic facets of the conjecture. So, is there any applied exposition of this conjecture?", "label": 0}
+{"snippet": "For example: Should the free market then only capture that which is beyond necessity? I'm not sure if \"then\" is accomplishing anything, or if it is even correct in this sentence. Perhaps it should be written more like Should the free market only capture that which is beyond necessity? But this sentence doesn't sound like it is referencing any contextual information. Perhaps this Then should the free market only capture that which is beyond necessity?", "label": 0}
+{"snippet": "So some authors consider (sigma additive) signed measures on algebras (that are closed only under finite unions) instead of on sigma algebras. This happens for instance when considering the subset of finitely additive signed measures that are sigma additive. So my questions is what can I do with these a sigma additive measure on an algebra? I.e., do the usual convergence theorems hold? What kind of restrictions arise?", "label": 0}
+{"snippet": "When firing single photons and letting and interference pattern occur. If you were to draw a straight line from one of the slits to a particular interference gap on the screen, and continued this line through the screen, when you moved the screen to different distances from the slits, would an interference gap be present along the lines trajectory at all screen distances? Or would the interference alternative between gap/no gap along the lines trajectory at different screen distances?", "label": 0}
+{"snippet": "I'm using the FrontiersinHavard Latex class provided by the author guidelines of the Frontiers Media. Strangely enough, even though their guidelines specifically state table captions should be placed above the table, the class forces the captions under the tables. There is also little to no documentation on that document class itself. Are there any options to disable this behavior when declaring the document class, or does one need some other workaround to override the document class?", "label": 0}
+{"snippet": "When water molecule is cooled, it is well known that it expands: That's the reason the rocks in the desert explode in the cold of the night: the rocks have water inside that expands with cold and breaks the rock. Other molecules compress when cooled. Could this effect (expansion/contraction when heated) be used to moved an electron as a POC of doing work? For example, water is a polar molecule, so it's mere expansion/contraction seems to point that it can move electrons. Given there are random temperature fluctuations everywhere, it seems possible to use these micro contractions/expansions. Does this break any known rules? If we manage to use a diode equivalent, it would move electrons in only one direction.", "label": 0}
+{"snippet": "We consider an electron \"Bob\" trying to escape from a metal surface as shown (blue circles represent electrons, red circles represent ions). I know that Bob can't leave the metal surface is because the attraction due to the ions is greater than the repulsion due to the electrons below. My question is: why F(attraction, by ions near the surface) is greater than F(repulse, by electrons)? Thank you!", "label": 0}
+{"snippet": "Suppose I have N unique objects, where N is known, but I have a subsample of only M of them in a bag, where M is unknown. I draw X from the bag with replacement (where X is known) and observe A unique objects (where A is known). If I next draw Y from the bag with replacement (where Y is known) what is the distribution for B, where B is the number of unique objects I will observe?", "label": 0}
+{"snippet": "In one of our class discussions about the origins of the word Bank (Money), a guy guessed that maybe it comes from the Bank (the land alongside a river) since the sand gets deposited there, as an equivalent to Bank being a money depositing place. It felt right, except Bank comes from Banque, a Latin word for table, as that's how the financial transactions used to happen, over a table. Now, what I want to know is could it be that Bank and Bank are related? One coming from the other? If so, which one came first?", "label": 0}
+{"snippet": "Is there any difference between an axiom and a postulate? I would say that while an axiom is any proposition fixed as true without premises in a theory, a postulate is (also according with its etymology postulatum = something that is requested) something that is necessary to assume to make a theory fit (also in a consequential way) with some kind of experimental measurement. Is there any convention about it?", "label": 0}
+{"snippet": "Although inertial forces are just our mathematical creation to help apply Newton's law even in non-inertial frames, can we assume or is it (mathematical proof) that inertial forces also create its field. I think it does so, because when we say that we cannot distinguish between gravity and accelerated motion, we assume them to be same. Is it just as assumption or a correct assumption?", "label": 0}
+{"snippet": "Im currently a math masters student. Im doing good and i obtain good grades. Im interested to pursue PHD. At a masters level course i have never been able to solve all exercises which a lecturer has given. This really bothers me and i feel like i need to solve every single exercise problem easily if i want to pursue PHD since these problems in most cases have known solution, hence how i should be able to do research in mathematics if im not able to solve these known problem? My way of thinking might be too black and white in this sense. So my question: people who have completed a phd or a fellow masters student; were you able to solve every single exercise at classes?", "label": 0}
+{"snippet": "I know that if a wire is carrying current, the force is F= iBl sinc But what if the wire does not have current, and rather the magnetic field around it varies. Will there still be a force? If so, what will be it's magnitude. You may consider magnetic field direction as required to get a value of force if possible. Note: This is not repeated question. Other similar questions are regarding wires carrying current. Mine is for wires with no current.", "label": 0}
+{"snippet": "Why are terrestrial planets like the Earth so much smaller in size than the gas giants? Why can't they be the larger ones? Why are there no stars made up of something solid(/rocky)?(To generate energy, it could maybe use fission in place of fusion)But anyways, Is it because that would violate some laws of physics or mathematics or is it just the way the universe formed? If it is due to the former then what fundamental laws does it break?", "label": 0}
+{"snippet": "Is there a general book of mathematics which starts from first order logic, treats set theory (in ZF setting) in which first order logic is used, then abstract algebra (in which set theory is heavily used), topology (at least point set topology) and finally mathematical analysis (in which all the previous concepts are used). In all these parts most important results should be covered. In this way one can study mathematical analysis having solid foundations of mathematics? Am I dreaming or a book of this kind exists?", "label": 0}
+{"snippet": "I know from calculus that Riemann Integrals are Riemann sums. We use such integrals to calculate areas under curves. But why does adding an infinite amount of small terms give a finite result for non divergent curves? I know the obvious answer would be to just look at the graph of the function and we can see there is a finite area. But I keep thinking of the Harmonic series and how adding an infinite amount of smaller and smaller terms has as a result infinity. How can we be sure the small terms if the Riemann sum also don't add up to infinity?", "label": 0}
+{"snippet": "I have read yesterday the following statement: An initial object when it exists is the colimit of the empty diagram. A terminal object when it exists is the limit of the empty diagram. And I found some justification of the second statement here: What means an empty diagram? but still the justification is not very clear to me, I am wondering if someone can explain this to me in a simpler way please?", "label": 0}
+{"snippet": "Using a magnifying lens with the sun as the source, one can focus the light in a single point. Is it possible to use just lenses, or any number of transparent materials of any particular shapes, to focus sunlight into a line and not just a point, and turning it into what I think is called a \"focused beam of light\"? Is it possible to do with just transparent materials?", "label": 0}
+{"snippet": "In a recent chat conversation, I asked someone quite high up in my global organization but not belonging to my regional org setup - \"Shall I send an email copying my supervisor\", and he replied in the chat window with a \"I am good\". What does it mean? I wanted an opportunity to introduce my supervisor to him through email, but what should I make of his response? Is he asking me to send the email (OR) is he asking me not to send the email?", "label": 0}
+{"snippet": "According to several dictionaries I have, \"validate\" is a transitive verb. But both Grammarly and ChatGPT judge the following (imperative) sentence as correct: Ensure feature quality by validating with the UI team before release. I would use: Ensure feature quality by validating it with the UI team before release. Is the sentence without it correct? If yes, is it because the verb can be intransitive or because of something else? Edit: corrected them to it.", "label": 0}
+{"snippet": "It is well known that the electric field by a ring on a point charge can be easily calculated by integrating the each infinitesimal electric field by each infinitesimal charge. However if one were to attempt to calculate the contrary, that is, electric field exerted by a point charge on a ring, how can one integrate each infinitesimal electric field by the point charge on the ring, since unlike the former, the electric field in the latter case is not generated by an infinitesimal charge, rather by a well defined, let's consider, Q charge?", "label": 0}
+{"snippet": "After learning about progressive waves, I struggle to understand what physically causes particles to move up and down in such a wave. What mechanism is actually transferring energy as these particles move up and down? Only longitudinal waves seem intuitive to me. Furthermore, consider water waves. Do we still consider this transverse, even though the particles move in circles rather than up and down. What causes this movement? Is it true water can only be transversal due to the attraction and interactions between water molecules?", "label": 0}
+{"snippet": "In all the textbooks that I've seen complex numbers were presented as a given (from history - Cardano's formula etc.). Fundamental theorem of algebra, Frobenius theorem and others use complex numbers as some answer. But is there a way to deduce complex numbers constructively from some (algebraic) reasons without any knowledge about its existence? I'm looking for questions where the only best answer would be complex numbers. Something like \"what is algebraic closure of the field of real numbers?\", but without any a priory reference to complex numbers. Maybe someone can tell me where I can read about this?", "label": 0}
+{"snippet": "I'm currently learning Latex and using Overleaf plus documentation. Sometimes I want to quickly see what other options a package has to offer. Since Overleaf shows a PDF preview, I would like to know if there is a way to quickly list that package's options. Basically what I'm looking for is a page like TeX_primitives_listed_by_TeX_engine that shows each primitive but with a link that explains watch each one does. Like the docs for any programming language, for example.", "label": 0}
+{"snippet": "Imagine if you have a molecule with a large size, e.g. proteins. Anything that rotates experiences pseudoforces if my understanding is correct (e.g. coriolis, centrifugal etc). Since every molecule rotates, does this have any effect on these molecules that we could measure? Or properties that arise because of these pseudoforces? My guess would be more smeared out electron clouds, or weaker covalent bonds or something. Or a clustering of more heavy atoms in the centre point since farther from the centre would mean weaker bonds. My guess could also be that the effect is so small that it is negligble. Probably only really big molecules that spin very fast could have an effect (if any).", "label": 0}
+{"snippet": "I hope I can ask this question here. I have downloaded Asymptote from windows-binaries and want to run an asy-program that contains the row (it has worked a long time ago) import gsl; But that seems not to be included in the distribution. The manual says something about If asymptote is compiled with... you have access to the gsl-library. Obviously the version I downloaded from the webpage is not compiled with gsl. How do I find a version that is, och how do I add it to the version I have? -anders", "label": 0}
+{"snippet": "I'd like to achieve the following using Latex: I'm open to still-better ways of formatting such block matrices. But the above is what I'm thinking towards, right now. I'll be doing a lot of these and I'd like to beautify the stuff I've been posting before. Especially since directed graphs, column and row spaces, the left and right nullspaces, modified network analysis, and the Schur complement method can figure prominently in analysis. I'm not very familiar with using tikz packages. But I'll learn more, if needed. The following is an example of the above that I do not want to produce: It's sad-looking and I'm hoping for something significantly better, more in the direction of the first image above.", "label": 0}
+{"snippet": "We know that inside solenoid the magnetic field are same at all point's and are parallel to each other My question is why they are parallel as my teacher explained it as solenoid is set of multiple circular loops and one face coil form North pole while other will form South pole and magnetic field lines from both poles will join in parallel I think this explanation is not correct Any response would be appreciated", "label": 0}
+{"snippet": "A long rectangular cardboard thrown in air starts spinning automatically on its way down. Few observations in this experiment: Long rectangular cardboard pieces spin well Doesn't work well with square / circular pieces Long ellipsoid pieces seems to spins the most Also note the spin axis on the way down. Even if you give a little torque to it spin it vertically upwards, eventually on way down the spin stabilizes so the body starts spinning around the horizontal axis This doesn't work with paper / foam as they start floating. Higher density materials like iron / glass of the same size/shape also don't spin A small demonstration can be seen in this video. Can someone explain the exact physics/aerodynamics behind this?", "label": 0}
+{"snippet": "In a system, the total energy is composed of Electronic >> Vibrational > Rotational >> Translational. As far as I understand, temperature is only related to the average kinetic energy, which includes Vibrational, Rotational, and Translational components and not electronic energy (excitement states)?? If theoretically, so much energy is added to the system that initially, the temperature increases due to these first three degrees of freedom, but then more and more electronic excited states are populated because the molecules kinetic energy provides enough that electronic excitation occurs, which, of course, takes up that kinetic energy, wouldn't this lead to brief drops in temperature with energy input?", "label": 0}
+{"snippet": "I wonder about the Hmiltonian form fo the Potts model and would like to know about its matrix form using the generalized Pauli matrix. I believe it might be possible in a smiliar way applied to the Ising model, as you can see in the website below: How can I explicitly express the Ising Hamiltonian in matrix form? I'm not sure if it's just changing the Pauli matrix into generalized form from the Ising model.", "label": 0}
+{"snippet": "I try to apply the replica trick in a two-dimensional gravitational model. I interesting for the case where the semiclassical geometry is an evaporating black hole. These geometries have no time-reflection symmetry. In many related articles they say that the geometries must have time-reflection symmetry, but I can't find why. It seems to me that the method can generalize to geometries with no time-reflection symmetry.", "label": 0}
+{"snippet": "I am organizing an algorithmic lecture at my university, which is more theoretical. Regarding Landau-notation and runtime analysis, using algorithms that implement mathematical formulas is great. In my opinion, it helps the students see the connection. Of course, I also want some difficult exercises, and I am searching for mathematical functions that have a very algorithimal touch, if you know what I mean. Because it is hard to describe, here are two examples of such functions: nth prime number and nth Dedekind number. Can you provide me with similar formulas?", "label": 0}
+{"snippet": "Force acting on person when jumping from boat is denoted by red colour and force acting on boat is denoted by yellow colour. I have not included the buoyant force and boat weight force on the boat. Coming back to my question:- The force applied by the person on the boat(F)can I Say it friction force which moves the boat in backwards direction and in reaction force acts on person feet can also be called friction force?? Or it some other kind of force like muscular force which moves the boat in backwards and person in forward??", "label": 0}
+{"snippet": "The force repulsing two protons never goes away, meaning that there is a constant force pushing the protons apart forever. Firstly, where are these protons getting the energy to constant apply this force, and where is the nucleus getting the energy to continue to hold them together? Is it the binding energy? If so does it eventually run out of energy to hold them together?", "label": 0}
+{"snippet": "I'm writing an academic article title, and, for matter of capitalizations, I would like to know: if \"-based\" is appended to a word, is \"-based\" treated as another word and should be written with capitalized \"B\", or is \"-based\" treated like a suffix that became one with the word, and thus is written with a non-capitalized \"b\"? Title example: \"Computer-Based Strategies For Asking About Title Capitalization On Stack Exchange\"; \"Computer-based Strategies For Asking About Title Capitalization On Stack Exchange\".", "label": 0}
+{"snippet": "I need a reference for this elementary result which I assume to be true and known. Adding a citation in the paper I'm writing (even to a problem in a textbook) would be faster and more elegant than adding the proof itself (which may elude my decaying brain): Given a finite set S of real closed intervals, if each pair of intervals has an overlap (intersection) of length at least k, then the intersection of all the intervals in S has length at least k. Thanks.", "label": 0}
+{"snippet": "Which could exhume a response like, \"Lul, nice term for this type of pun subgenre.\" A pun is the humorous use of a word or phrase so as to emphasize or suggest its different meanings or applications, or the use of words that are alike or nearly alike in sound but different in meaning; a play on words. But I'm not sure of this type of subgenre. Edit: If it's not a pun (the jury seems out on whether it counts, I didn't think it was myself until I saw it included any play on words), an answer on what type of joke it is would then suffice.", "label": 0}
+{"snippet": "How do we define radius in quantum mechanics. A particle has wave-particle duality, so do we define the radius as Compton wavelength or Bohr radius or some sort of superposition of both? I don't think that either of it works, because of the Heisenberg uncertainity principle, the Bohr radius would vary because the electron shell is probabilistic and requires a wave function. Also we have defined classical electron radius, but as the name says it is classical rather than quantum mechanical. I was curious about this because as I was estimating the Kugilblitz Swarzchild Radius that is required to produce a Micro Kugilblitz with LHC at it's maximum energy, I got the result but I was unable to find the particle at the same or below size Thanks!", "label": 0}
+{"snippet": "I've been having a little bit of a debate with one of my friends about the correct use of a word. I hope the native English speakers can help me put an end to this :) I know the word \"bold\" is mostly used as in brave and courageous, but is it right to use it as prominent, too? This aspect of this issue seems bolder than the rest. Can it be used like this or is it meaningless?", "label": 0}
+{"snippet": "I have seen in this link that there is a way to calculate the rolled material length and the number of turns based on: the material thickness inner diameter of the roll external diameter of the roll Is there a way to calculate the length of a material roll (in my case fabric) without knowing its thickness but with knowing its number of turns? So calculate the length by knowing: the number of roll turns inner diameter of the roll external diameter of the roll", "label": 0}
+{"snippet": "\"Norton's Dome is a thought experiment that exhibits a non-deterministic system within the bounds of Newtonian mechanics. \" A ball rolled to the top can reach it in finite time with zero energy at the end, which means if you time reverse it the ball appears to star moving for no reason. By don't use just use an inverted cone with a point at the top? Whouldn't this be much simpler?", "label": 0}
+{"snippet": "We see only stars whose light is not older than the age of universe. This is understood. If a star is too far away that currently we don't see it then possibly we will see it later, then the age of the universe will grow. What I don't understand is how a star that we see now can move away out of visible universe in future.", "label": 0}
+{"snippet": "I have created some otf files of fonts for symbols and I'd like to write a package from them and then upload it to CTAN. But I have no experience in writing a package. So is there any reference to write a package from otf files? Please give some advice on the references which should be very basic. Specifically, with otf files of some fonts for symbols in hand, how to write a package like MnSymbol?", "label": 0}
+{"snippet": "I'm a beginner in the subject & my question can be meaningless, so I'm sorry from start if that's the case. I just don't understand why all of the image f(L) can be a sublattice of L' when f is a homomorphism from L to L'. I learned that all subsets of a lattice don't have to be a sublattice at all. If I don't understand wrong, it's not about the elements of the lattices actually but about the operator differences between them. So why there is not a possibility of a non-inherited operator of f(L), or a non-sublattice lattice of the L' as f(L)?", "label": 0}
+{"snippet": "Like the multiple pronunciations of \"ough\" or different spellings for the same sounds in English I've read come from mixing different dialects into one language. Whereas with French, they imposed on centralized set of rules. Or in Spanish, there are multiple languages/dialects in Spain (though I think at least Franco did try to impose Castellano for all). And other countries have their own histories of language homo/heterogeneity routes taken. What made English turn out the way it did, as opposed to others? In other words, did England ever try to impose one set of rules on how to say written letter combinations (e.g. 'ough'), like other languages have done, one way or another?", "label": 0}
+{"snippet": "Suppose a square table. You are shooting from a corner. A ball ends its path upon landing in a corner. At what angles can you shoot a ball from your corner such that the ball will never come back to your corner? Edit: seemingly my question would be how can you prove that if the trajectory is periodic, how can you prove that it will encounter another \"corner\" point before it returns to itself?", "label": 0}
+{"snippet": "I have a matrix, if I apply inverse function from existing softwares, I get an inverse matrix for every non singular matrix. I would like to know if there is a measure that tells that how close the approximation to check weather to consider the inverse matrix not. In my application, there is a possibility to discard an inverse matrix that's not well approximated. I am looking for few hints, keywords to look for or an advice in calculating the measure. I really appreciate any kind of help.", "label": 0}
+{"snippet": "I know that particles don't go from one end to the other, they just vibrate and transfer sound energy to next particle. How do they return to equilibrium again? Do they return just after collision with next particle in the medium or do they return as a consequence of reflecting off objects like a slinky? And if they return after reaching objects and reflecting back, is that how we hear our own sound. What will happen if you levitate in the atmosphere arbitrarily at one place (assumption), will you be able to hear your sound provided there are no objects around?", "label": 0}
+{"snippet": "Is it important to understand the concept of a universal 'now', to explain that time is a local phenomenon, and the rate of time varies throughout the universe, always dependent on the local distribution of mass, and within passing particles dependent on their relative velocity? I currently think that there is a universal now, but each point in space 'thinks' that it is a different age. I understand that photons don't age (relative to us) because of their relative speed, and they see their entire path since they were formed, (perhaps in a primordial star) as all squished into a single instant, including my retina as I see it.", "label": 0}
+{"snippet": "Couldn't we just assume that waves have mass and momentum and can become localized? Dirac Deltas can be given a rigorous mathematical foundation but physicist do not use the Gelfand triple. Why not just assume that electrons, photons, etc., have the same dimension as space? I know string theory does this but are there reformulations of QFT that use this idea that together with the insight that renormalization has a connection with scale invariance gets rid of all the problems that plague QFT? It just seems to me that the concept of a particle is a very unphysical idea.", "label": 0}
+{"snippet": "This is the answer. My question is why the integral of E is not zero if there is positive charge on the inner surface when the field lines end on the shell. And why the integral of E is zero when all charges is negative on the inner surface, the field lines also ends on the shell. What is the difference between these two situations?", "label": 0}
+{"snippet": "Molecules in solids get polarized and the resulting dipoles align with the external bias field. Can this be done with lightweight spheres that are oppositely charge on their surfaces? Like surfaces that are contact electrified. If a powder made of such oppositely charged fused spheres is placed in a bias field, will each individual particle (two oppositely charged fused spheres) align themselves? If clumping becomes an issue, I guess we could vibrate them lightly while in the bias field.", "label": 0}
+{"snippet": "How do they calculate the line of sight of a galaxy or binary star system from an observer's point of view. the velocity of a star in a binary star system depends on the line of sight so how do they measure that crucial parameter with precise values? but in case of unresolvable binary star system like spectrometric and astrometric binaries how do they take the (sin i) parameter", "label": 0}
+{"snippet": "I know this may sound very weird, but I'm curious on what makes the water be like water? Like why, when we get into a pool, we are like in a \"lower gravity\" pull? All our movements are slowed down in water in comparison to air? I very much know it is a strange question, but I've really never thought of it this way, I've always assumed water is like that, but never actually started to think why we move like that underwater. I'm guessing, it has to do with the properties of the water, but if someone can shed some more light on this, I'd appreciate it?", "label": 0}
+{"snippet": "Apparently, the special relativity theory is based on analyzing the motion of a point particle with relative speed near the speed of light. However, if I apply and combine this theory with a collection of particles with Newton's third law acting, is it correct to analyze the mass as a whole, whose dynamics equation is still modeled by F(net)=dmv/dt, where F(net) is the sum of all forces experienced by sub-particles within the system, and that m is modeled by Is this correct? If so, please provide reasonable reasons.", "label": 0}
+{"snippet": "Suppose a bunch of micron sized particles are charged positively on one half of their surface, and negative on the other. If they are arranged randomly, I understand they will have high entropy, as the system is in disorder. If under the influence of an electric field, we shake these particles such that they align themselves (they will, right?), the dipoles are now in the state of least energy and the system is more ordered, so I understand the entropy must have decreased? Yes, not the total entropy, just the particles themselves. Is my understanding correct, and if yes, will this bring a decrease in temperature of the particles? Before: After applying electric field and shaking:", "label": 0}
+{"snippet": "The white line is a flexible conducting foil suspended on the metal wire. I think the external DC circuit will induce a charge on the flexible part and the other charges move to ground. The charged flexible part will incline towards the oppositely charged electrode from the AC circuit and once the voltage reaches peak, the air breaks down and the charge is transferred. When the current switches, the flexible part moves towards the other electrode and a spark transfers the charge in the same direction as before. Am I hideously mistaken?", "label": 0}
+{"snippet": "In Arabic, this idiom is used to refer to the fact that when your survival, basic, or primitive needs are not met, you can't think of arts, music, your ambitions, or luxury. e.g. A: \"Why is he not planning with us for the vacation? It will be a once in a life time tour around the world!\" - \"He has a trial next month and could lose half of his savings to his wife, a hungry man can't enjoy the sunset\" In the example, the primitive need for the feeling of safety blocks the way of planning for luxarious vacation.", "label": 0}
+{"snippet": "I am doing competetive programming task called \"Ptaszki\" Its easy dfs with some observations. But i came across the following problem: I have two sequances of size n and m respectively and i want to count the number of ways to insert x different elements into this sequances You can choose for every element to which sequance it will go. You can also insert every element to the start or the end of the sequance. I dont have any idea how to solve it. Could you please help me?", "label": 0}
+{"snippet": "I see some textbooks showing how Hubbard model with Mean field approximation can explain ferromagnetism of band electrons(stoner theory), but intuitively I can't understand why an on-site Hubbard repulsion term (rather than say Heisenberg term which correlate neighboring sites) can lead to a long-range ferromagnetic correlation. Although hubbard U seems to prefer non-zero spin at a certain site, whether one site's spin is up or down will not have any influence on another site's spin direction, so by what means are different sites correlated?", "label": 0}
+{"snippet": "Now (hypothesis) -- And the Physics of Time In this page the author talks about (find in page) (in the context of LIGO Observatories-->) \"In their most powerful event, reported just this past February, the combination of two massive black holes should, according to general relativity theory, have resulted in a massive amount of new space in the vicinity of the final star\" Please explain my question. I don't get this!!!", "label": 0}
+{"snippet": "I came across this sentence: But I craved it so hard at the time, didn't I just? The author appears to be a native speaker. The part that confuses me is the \"just\" at the end of the question. Is it meant to lessen the guilt of \"craving it\"? If so, can question tags be ended with other words than \"just\" to slightly alter the meaning of the question?", "label": 0}
+{"snippet": "Dark matter is believed to be a substance of unknown origin with mass that is distributed in space. Can the same observed effects be explained by an intrinsic curvature of regions of space without presence of any mass energy in them? Say during big ban the space got randomly curved such that there are areas with curvature that is just the property of space, like valleys and hills in a landscape. If so, it might be that there are no dark matter particles or any baryonic matter to explain visible effects.", "label": 0}
+{"snippet": "What is the correct way to describe people inheriting a castle? (American and British English) Castle heirs or Heirs of the castle or Heirs to the castle It's just a phrase I've heard, but I've seen it written in various ways and I want to know which is the correct way. \"heirs to the kingdom, heirs to the castle, heirs to blah blah\". Sometimes they put, example, \"heirs of the crown\" or \"crown heirs\".", "label": 0}
+{"snippet": "I have three doubts regarding the magnetic field due to the charge:- Is a magnetic field generated when a charged particle moves with constant velocity or it only generated when the charge particle is accelerated or both? Why and how does movement of charge result in the creation of a magnetic field around the particle? We also know that motion is relative so if we observe in frame of moving charged particle then its magnetic field should not be there, then what we do in this case? Note (related to third question): as we use pseudo force in non-inertial frame then what do we use in this case?", "label": 0}
+{"snippet": "I was studying various cryptographic encryption schemes and why modular arithmetic is being used so much while encrypting messages. Why don't we use simple multiplication with a large known prime with the message, as factorizing large numbers takes exponential time complexity, so it would be hard for an intruder to decrypt the message? So, simply using an encryption scheme that multiplies a large prime on the message to be encrypted is also hard to decrypt for an intruder without knowledge of the prime number multiplied. Why was there a need felt for modular arithmetic-based encryption schemes? wanted just a motivation why we should study modular arithmetic...", "label": 0}
+{"snippet": "Can modular exponentiation be used to shuffle a list? I have noticed that modular exponentiation sometimes repeats every number only once, and therefore works like a shuffle mechanism for a list. I do not exactly know within what constraints it does this. I am interested in modular exponentiation for shuffling lists to reduce the computation needed to know the new position of any given object (that each object can know its new position, without knowing the position of every other object or the list as a whole).", "label": 0}
+{"snippet": "A transgender colleague requires being referred to as \"they\" and not \"he /she\" In what number do I use verbs with this pronoun when it refers to a single person: they is/ are(?) a transgender ? Anther example: When a person is elected the chair of the committee, they give(s?) an inaugural speech. I know I could say \"he or she\" gives, but this sounds to me too formal or too long. With a transgender, this option does not work; So, back to the transgender example: Do(es ?) they require being referred to as \"they\" ?", "label": 0}
+{"snippet": "Here contains a template for a thesis. In style_sheets there's a template.tex file. The template works by editing that file and compiling. When one does so there is an appendix A and appendix B at the end of the pdf. I have used this write my thesis, but still am not able to remove appendix A and B. Erasing the appendix code in template.tex makes it where the file won't compile. How can I remove the appendix chapters?", "label": 0}
+{"snippet": "The above is one of the four two-dimensional lattice systems. See this article for some info. The parallelogram is the primitive unit cell, because it can be translated in order to recreate the entire lattice. So, what is the hexagon then? The conventional unit cell, whatever that means? Is it shown because the symmetry operations that can be performed spans a greater part of the lattice than that which is provided by the primitive unit cell?", "label": 0}
+{"snippet": "In very long wires, such as hundreds of kilometers, when we flip a switch and turn on the electricity, does the magnetic field (that iron filings organize around) start to form in one direction and then move through the conductor to the other end? Such that iron filings around the whole wire, would start to react to the magnetic field at different times, with delay the further from the start we get? If yes, does the magnetic field forming propagate in the opposite direction to conventional current, the direction that the electrons travel in?", "label": 0}
+{"snippet": "Assuming that light travels as photons that can interfere with themselves while also only being detected as specific localized points, the results of the Elitzur-Vaidman quantum bomb tester experiment demonstrate that the interference of a photon can be affected without the photon itself being absorbed/affected by the object which affects the photon's interference. Does this mean that events that could have happened but did not (\"counterfactual\"), e.g. the photon being absorbed by the \"bomb\", are what determine what actually is observed, e.g. the photon being detected at Ddark? If so, how can this occur -- is the explanation for this, for now, strictly dependent on interpretation?", "label": 0}
+{"snippet": "In the above question , there will be induction of charge on inner sphere , hence on its surface there must be non zero value of electric potential . But in the solution , the electric potential on the surface of inner sphere has been taken as zero. Inner sphere is connected to earth does it mean that electric potential on its surface is zero despite of charge on the sphere ? Does it mean that any conductor even if it has charge is connected to earth will have zero electric potential? I can't digest this , pls provide some useful insights", "label": 0}
+{"snippet": "Suppose event H is a subset of G, where everything in the event H is contained in G but not vise-versa, the probability that H occurs is r and the probability G occurs is s, what's the probability that either G or H will occur, but not both occurring? The probability that G will occur but H will not occur is (s-r). The probability that H will occur while G not occurring is zero.", "label": 0}
+{"snippet": "I am curious to know if the relatively newly developed melanin-based semiconductor materials made with polydopachrome have been able to create films or crystals which visually reflect blue, purple or green hues (translated in to nm). If so, was the form of synthesized polydopachrome utilized in creating those outcomes more resembling that found in in the plant/fungi or more represententative of those found in the animal/insect kingdoms? If blues, greens and purple light reflecting melanin based semiconductors exist, are the structures associated with concentrated or unusual copper bonds? Zinc? Manganese?", "label": 0}
+{"snippet": "Considering the probabilistic relationship between the momentum and position of an electron, are the pictures that show the interaction between electrons and positrons an accurate description of particle motion? We often see visuals that represent the probabilistic nature of particles as probability clouds. How can this converge to well-defined paths? (I never studied this subject, this is just knowledge from general physics books and videos.)", "label": 0}
+{"snippet": "By this I mean say you had and entire galaxy to work with, and you could measure the exact wavelengths of the waves you send out and record it. You would shoot this light beam across the galaxy and measure the exact wavelength of the light you are transmitting, and receiving. Could you compare the difference in the wavelengths between the same light and calculate the one way speed of light from it?", "label": 0}
+{"snippet": "Since value of electric field decreases as we go from surface to the centre for a solid insulating uniformly charged sphere then why does the potential increases as we go from surface to the centre?According to me we will need to do less work against weak electric field therefore the potential will be less as we go inside the sphere from the surface since electric field is decreasing as we go from the surface to the centre.", "label": 0}
+{"snippet": "i think the title speaks for itself, since the defining trait for NP class is that - they are the set of decision problems verifiable in polynomial time by a deterministic Turing machine. thus it shouldn't matter if the algorithm computing the function belongs to any particular class - exp or factorial, even non-PR , as long as they are computable, but i am unable to find any specific example. if there aren't any known such algorithms or problems, can it be proven that they atleast should exist ?", "label": 0}
+{"snippet": "Just as underwhelm/overwhelm exist without any usage of 'whelmed' (generally speaking) I'm wondering if there's any adverb ending in -ly without an adjectival counterpart (or that has dropped out of usage). For example where 'he walked XYZly' is recognisable, correct, or common for this or some other time period; whilst 'his walk was XYZ' is not. NB: I've found no other answers for this question elsewhere, and search engines usually lead to explanations of 'flat adverbs' not ending in -ly which is not what I'm asking.", "label": 0}
+{"snippet": "I can't make out clearly what could be defined as a \"topic element\". In \"A Communicative Grammar of English\", Geoffrey Leech has written: Fronting is often accompanied by inversion; that is, not only the topic element, but the verb phrase, or part of it, is moved before the subject. Accompanied by this diagram: Now, \"x\" in the above diagram is stated to be \"the topic element\". However, from what I've learned, the topic is usually either \"given info\" or used to link statements. Moreover, they are usually subjects. Yet here \"down\" and \"never\" are considered to be \"the topic element\"? I'm truly desperate for an answer here.", "label": 0}
+{"snippet": "Reflective is obvious, but what about the other properties? It's weird when we check the symmetric property of the identity relation. The symmetric property happens when (in a matrix representation) the upper triangle and the lower triangle that exists in a matrix that's divided by the matrix's diagonal get mirrored. Also, you can make a graph representation of the relation and see that it's just loops. So is it symmetric or not? (also, check out if it's antisymmetric or not because I think the matrix representation shows that it's antisymmetric)", "label": 0}
+{"snippet": "\"Underpinned by left-wing perspective,the defence gains in significance,based as it is on the development of critical art of inheritance,of combing past and present and establishing links to shape a better world.\" In this sentence how the word \"based\" is used as i have read based on but here is nothing such.please reply correct should have been \"Underpinned by a progressive left-wing perspective, the defense gains in significance, as it is based on the development of critical art of inheritance, combing past and present and establishing links to shape a better world.\". so how it is used?", "label": 0}
+{"snippet": "How rare or how common are the analytic (differentiable infinitly many times) functions in real applied math? Is it like a \"this almost never happens\" or is it \"most of the time you can approximate a physics experiment with analitic functions (and if you failed, you are bad at math)\"? I ask because there are so many nice properties of analytic functions in complex analysis. But are they relevant? Seems like \"differentiable forever\" is too strong of a limitation.", "label": 0}
+{"snippet": "So - I know that when we observe galaxies, we are observing their past. And that if the same past-them were to be looking at us, they would see our past. But when we look at their past - that is a moment in time that would, to them, be the present. So, what I cannot find an answer to (possibly because I don't know how best to search for it) is: does it then make sense to say that it is possible that a galaxy that is future to us, could be observing our present - but as past to them? (if that is so then that opens up a whole can of worms that all time is occurring at all times, yes?)", "label": 0}
+{"snippet": "Hypothetically speaking if you had a satellite going near the speed of light in a straight line towards an exoplanet light years away and that satellite had a telescope pointed at the surface of an exoplanet. What could a year long journey look like, while traveling near the speed of light, through the lens of that telescope that what light years away pointed directly at the surface of the exoplanet? would the telescope capture the planet in fast forward as the light information would be entering the telescope faster? Would it be slower as time dilates for exoplanet because it not moving the sleed of light?", "label": 0}
+{"snippet": "I have to prove that if the dimension of vector spaces V and W is the same then T: V->W is injective if it is surjective. My idea is as such: know that all elements in W have corresponding element in V (surjective) Know that all elements in V correspond to some element in W (map) I want to use that I know that V and W must be over the same field (by homogeneity) and generalize that since the dimension is the same then the number of elements must be the same, thus proving injection. Is this valid?", "label": 0}
+{"snippet": "one day I kept my phone in my pant pocket, I haven't opened it for a long time. My phone is covered with a plastic case. So why the phone is getting wet when I observed it after some time even though plastics are non conductive towards heat. When I kept my phone in pant pocket without the case then no wet has been observed by me on the phone Whether it is due to heat of the phone or the sweat of mine due to the heat released by the phone or the heat is mainly due to heat from the screen of the phone (as some background apps were running at the time) which is open and it is not close by any non-conductive material", "label": 0}
+{"snippet": "The normal force may be unevenly distributed on the surface of contact between two bodies. I had a discussion with my friend but was unable to prove whether this assertion is true or false under two RIGID bodies. I know it is a unreal question. Therefore, I am seeking a mathematical solution to this question. (If this question is independent from classical mechanics, how to prove?)", "label": 0}
+{"snippet": "In India, most educated People say that \" my exams have been preponed\" As an English teacher I know that Americans say moved up and Britishers say that advanced in the context. One of the best English professors I know in India says that prepone is the right word in the context.Even some native speakers said that the word prepone could be accepted. I would like to know the opinion of the experts in the group.", "label": 0}
+{"snippet": "When we work with rational numbers, our continued fraction will have a finite number of elements. Are there ways to estimate the number of elements of a continued fraction when expanding a rational number? For example, in the following form: \"For the chosen rational number N, continued fraction will contain at least/at most/strictly M elements\" The obvious way is to implement the continued fraction decomposition algorithm and simply count the number of elements each time the loop passes. But this method can be quite time-consuming if there are a large number of elements of the continued fraction. I tried to find the answer and the only thing I found was this thread: Nth number of continued fraction But it ultimately came down to what I said above.", "label": 0}
+{"snippet": "Like how Taylor Swift fans say that she needs to take private jets because fans would make her taking public transport untenable. So it's the fans themselves that are the reason for her behaviour, which they are making excuses for. Is there a term for such people, or for what they are doing? An example of how it could be used: Fans are (creating the exceptional need for an excuse they are making) Taylor Swift's use of private jets' or something like that.", "label": 0}
+{"snippet": "I need to write an equation to determine how rotating a digital balls path with the ball as the center of rotation effects the amount it moves on the x&y axis each frame. I made a table of points on the equation to help me write it, but I'm unable to convert the equation into points. I linked an image of the table here. Does anyone know the answer? I think it's a helix. It's fine if you need to switch which axis each column corresponds to in the equation, as long as you mention which ones you switched. Click here to see the table", "label": 0}
+{"snippet": "I'm looking for an interesting application of Sequences and Series (theory from mathematical analysis) in the field of Operational Research, in particular involving combinatorics or linear optimization problems. I have tried only chat GPT for now and all I could get is an application of Dynamic programming to solve the knapsack problem where series and sequences are defined for recurrence. I was wondering if there is another one or maybe an interesting application not from the Operation Research fields. Thanks in advance.", "label": 0}
+{"snippet": "The definition of exegesis is Bible leaning and thus is not a word many outside of the church are familiar with. And yet people can understand the idea of trying to interpret a text as the author or authors meant it to be understood. This applies to the US Constitution. Is there a familiar word that is used by secular society that means to understand what the authors meant when they wrote a text?", "label": 0}
+{"snippet": "Recently, I've been solving problems involving Burnside's Lemma. The question often says: \"Find all different colorings if we identify colorings when they transform into each other under some rotation/symmetry/isometry/isomorphism.\" I get confused about in which cases I need to consider the figure being \"turned inside out\" like for example tetrahedron can be. It seems to me that: rotation - no symmetry - yes isometry - yes isomorphism - yes Assuming it is possible for a given shape. Is this true? Or it depends?", "label": 0}
+{"snippet": "@JonathanZ Thanks for going all the way to help me out. An oil-pipe has to connect the oil-well O and the factory F, between which there is a river whose banks are parallel. The pipe must cross the river perpendicular to the banks. Find the position and nature of the shortest such pipe and justify your answer. I tried out this problem with some numbers and got the idea of path of minimum pipe length. How can I do it more rigorously? This is what I got through my intuition. I think blue one is the minimal path.", "label": 0}
+{"snippet": "Example: a close friend died of cancer, so you feel very bad. Yet they were old and no longer suffering, so you also feel glad. Both feelings are strong and truthful, yet the emotions about the same object or situation equally oppose each other. Ambivalent comes close, but I was looking for another word to more exactly describe the situation. Ambivalent would describe a struggle where you might not like something about someone, yet still like other characteristics, hence you are uncertain how to balance the situation (be their friend or walk away). What word describes when you are not struggling to balance two truths, but accept both opposing feelings? I ask because we are helping someone who is grieving.", "label": 0}
+{"snippet": "In the literature and comments, I have met two pieces of jargon: Low energy SUSY, High energy SUSY I'm confused about the technical and well-defined conceptual differences between the two type of Supersymmetry? Of course one such difference should be the scale at which SUSY is broken, but I have no idea how high and low are distingushed formally and how they differ fundamentally from each other? For example, I read a comment due to Peter West: that LHC can only rule out low energy SUSY which is different matter from high energy SUSY.", "label": 0}
+{"snippet": "I pasted the whole fragment from the book \"Teaching Physics by Laurance Viennot\". I generally understand this fragment. However, I am not sure if I understand what author means by the phase at each of those points then has to be readjusted in order for a geometrical optical treatment to be applied to that \"object\". I circled that fragment with blue. Can you give me more guidance how to understand that?", "label": 0}
+{"snippet": "So during our numerics course we learned a few interpolation methods Aitken/Neville, divided differences,Lagrange and the Vandermonde matrix. How these work is clear to me for the most part, I'm just wondering what are the advantages and disadvantages of the respective methods compared to each other? I know about a few things here and there like some methods being easier to expand when gaining new points but our script seems a bit sparse on that info and I'd like a more holistic picture.", "label": 0}
+{"snippet": "Do two mechanical transverse waves traveling in the same medium have the same speed whatever the source might be? If the answer to this question is yes, can I generalize and say \"all waves of the same EXACT category traveling in same medium have the same wave speed\" and by the same exact category I meant to specify the exact type of the wave, that is to state its both kinds; mechanical and traverse, or mechanical and longitudinal. That being said, I can't say that two mechanical waves one is transverse while the other is longitudinal have the same speed in the same medium, they could have the same speed though, but its not a general statement, is that right?", "label": 0}
+{"snippet": "I was looking At a couple different replies to some questions on here and I kept seeing people saying that larger mass black holes have a lower gravitaional strength on their surface than lower mass black holes. I am no expert by any stretch of the imagination but I would of assumed that the larger the mass the more powerful the gravity. Does anyone know why this is", "label": 0}
+{"snippet": "I've been playing with this problem for a long time, but I don't see a solution yet. Consider the sides of a trapezoid of lengths a and b, a > b (not heights) ( see edition (and the bases major \"a\" and minor \"b\"). Determine the height of this trapezoid using two different methods. Don't use trigonometry Can you help me EDIT Typing error: a and b sides, a and b are not heights, a>b, the bases greatest \"p\" and least \"q\" There is also the image that refers to the data", "label": 0}
+{"snippet": "I must learn tons of identities for vector calculus for Electromagnetism, but they were taught as a list of items to memorize. Some of them are reasonable to follow (such as gradient or curl acting on sum or product of vectors), but I'm lost with curl and vector product. I lack any formal math background, so I'd like a book/ page where these expressions are justified/ derived in an understandable way. Thanks in advance!", "label": 0}
+{"snippet": "In the photo I added,there is a question as you can see and its given solution. When the switch S was open, charge on each capacitor was calculated and the voltage was taken as the net voltage of the two connected batteries. But for calculating charges on the two capacitors when the switch S is closed, only the voltage of one battery was taken for the corresponding capacitor. Why is it so. Why the effect/voltage of other battery is ignored.Either I am lacking some concept clarity or the charge must have flown through other sides( A and C) as well. What will be the new charge on the two capacitors after closing the switch S if the charge flowing through each section (A,B and C) is considered?", "label": 0}
+{"snippet": "As we try to refine our spectrometer better and better each day, like first we observed doublets in Hydrogen atom, then we observed fine structure's in hydrogen like and in many heavy elements. Then we saw hyper fine splitting too where atomic nucleus takes part too. My question is what will happen in the case where we have a spectrometer and we are observing one single line of a particular spectrum which is so sharp that (till my knowledge I know splitting till hyper-fine level) will we observe a single a infinite sharp line or what. Or there will be some error like Doppler broadening etc. kind of situation.", "label": 0}
+{"snippet": "I wonder if there is a tex library that can create an equation like this (found in this paper and the authors actually create a figure for this, not in tex) With some research, I see that the arrows can be made using witharrows but I am not sure about the colored part, specifically the I_i(D) part where the two colors (dark green & light green) overlap. Any pointer will be highly appreciated! Thanks!", "label": 0}
+{"snippet": "I was looking through some old documents and pitching them from my time at uni. In there, I found some materials handling notes, and one regarding the handling Uranium metal bars. Basically, it said that they didn't require any special handling. As a thought experiment, this makes sense as the bars are just purified ore and thereby very dense and the radiation would be just surface emission. Is this true?", "label": 0}
+{"snippet": "I read this sentence earlier, and it struck me as incorrect: A number of parameters is associated with an open connection. My first thought was the is should be an are, but talked myself out of that because number is singular. Then I asked my wife (family grammarian), and she says that the sentence is incorrect; it should read as follows: A number of parameters are associated with an open connection. We checked out some examples using an online dictionary, and it seems she may be correct. What's the answer - which is correct?", "label": 0}
+{"snippet": "I was reading a USACO Guide Page on data types and I came across two formulas for the absolute and relative difference in the desired answer and the actual answer that is outputted. This is meant to be calculate the absolute and relative errors but what really is the difference between them? I tried to read this question but could not understand it. From a mathematical standpoint what is this exactly and what are its true applications in programming? Where would I need each type? Here is an image of the text I was reading: Image of text from USACO", "label": 0}
+{"snippet": "I am trying to learn contour integration, for the purpose of learning another technique I can apply to computing definite (real) integrals. Although I can apply the process well enough, ( with some issues in contour selection, but that's a different question). The problem i am dealing with, is how can a person tell if a particular real integrand is a good candidate for contour integration? I've read something about \"five cases\" where it can be used but it felt weird for such an arcane technique to be limited to precisely five situations so I came here to ask instead.", "label": 0}
+{"snippet": "In many contexts we have the concept of mapping one element to another. Is the mapping itself an object which has a lifecycle? What makes the mapping come into existence? I may not be asking this very articulately but when it is stated that there is a mapping, what causes this? Where is the information that says the mapping exists stored? Is this related perhaps to Axiom of Choice?", "label": 0}
+{"snippet": "I have been trying to solve this question from twitter for like two days could anyone help me with this? All the credits go to the name mentioned in the image My attempt to solve: I think it's harder to understand my messy diagram. But all I have done here is drawing a parallel line from a vertice to the opposite side of the square and with that I have find the lengths of the mentioned segments in terms of x Thank u in advance for looking into this problem", "label": 0}
+{"snippet": "First, I know it \"worked\", in physics sense. My question is what happened in the math sense. When promoting something, such as a field, to an operator, am I essentially mapping the field to (infinitely dimension) operator that depends on spacetime? And the canonical commutator just somehow followed from this map (my guess is that the map somehow preserve the Poisson bracket and somehow map the bracket to commutator.. or maybe we can just get it somehow from operator's dependence on spacetime?)? Alternatively, could it be that I am mapping the field to a more intricate mathematical object that encompasses canonical commutator (as well as other symmetry and their generator? as the operator version of the charge just somehow works quite well as a generator)?", "label": 0}
+{"snippet": "I am in the process of writing a research paper that compares my Methods A and B against a commonly accepted gold standard (reference) method. All methods produce objects that are identical in the ideal case. I am now in the search for a noun to refer to the objects which are not the reference objects, i.e. objects produced by A and B, in the context of the comparison. Example sentence: The ______ are smaller compared to the reference objects. So far I have tried working with test objects and input objects and sample, but they appear wrong to my intuition. Ideally it would be a term familiar to other academics.", "label": 0}
+{"snippet": "Huygens and Maxwell have wave theories about light. On the other hand Planck and Einstein have theories about particle nature of light and could explain blackbody radiation and photoelectric effect which theories of Huygens and Maxwell unable to explain. What about Newton's particle theory of light? Does it have advantage of explaining a phenomenon that all wave theories unable to explain? Is Newton theory of light could be considered as root for \"essential need\" for particle imagination of light or it is merely a non-essential theory when we could have wave theories?", "label": 0}
+{"snippet": "I'm not a mathematician, but I've read alot about QFT theory. The way it is visualized are different levels of energy and the fields interacting with one another. Am I correct that these fields overlap each other in the same point in space? What if each point in space has exactly the same amount of energy, and in order to create higher levels of energy, that energy has to be drawn from the points around it which would pull and twist space as it absorbs the surrounding energy to produce the known subparticles. Do we consider QFT fields as more energy in a single space? Or do we consider each field as just a description of a higher energy state?", "label": 0}
+{"snippet": "So here's something I was wondering about. Let's say I have to have boundary conditions in flrw metric which does not leave the universe isotropic and homogeneous. This would go against observations. Thus the boundary condition too must respect this. But I know how to apply killing vectors on tensors not boundary conditions. How does one then proceed to find all possible boundary conditions which leave preserve isotropy and homogeneity?", "label": 0}
+{"snippet": "Today, someone asked me if the pronunciation of the \"c\" in \"exacerbate\" is an /s/ or a /z/. In fast speech, it seems indistinguishable if I substitute /z/ for the /s/ , which is the standard dictionary pronunciation). Are both pronunciations acceptable? I did some digging and discovered that between two vowel sounds, the phoneme is voiced (reason, cousin, teasing) , but I'm not sure if this is a hard and fast rule.", "label": 0}
+{"snippet": "According to the special theory of relativity, in moving body all physical processes are slower than they should be for a stationary body according to the time counts of a fixed (laboratory) frame of reference. In the case of moving mechanical clock we have changes in rate of the clock (according to mentioned above mechanical clock ticks slowly). In other case (for other types of clocks) we have the same changes too. But what changes do we have in the case of moving light clock if speed of light is constant? Thanks.", "label": 0}
+{"snippet": "Another weird question, I know, and may sound simple but I'm now trying to see why a lot of the things that we usually do without thinking, have some sense in physics, like this one. Let's say you are in a deep pool, and you are covered with water entirely but, you raise your hand above the water, what happens in the water is that your body actually goes down and sinks. Why is that? Like why by putting some parts of our body outside of the water level makes us to go down in the water? I know it may be simple but I want to know, is it because we are like \"lifting\" in some sense, our own arm, so it makes us to go down?", "label": 0}
+{"snippet": "When it comes to the reciprocal space of twist bilayer graphene, there is a very typical picture: In this picutre it shows the hoppings bewteen the nearest Dirac point between two layers. And there are six hoppings since there are six Dirac points. And these two Dirac points then form the new moire first brillouin zone of the twisted bilayer graphene, as the picture show: But I don't understand how the brillouin zone of the twisted bilayer graphene is derived. Because the reciprocal space is not even derived since the moire sublattice is not clear in the arbitrary angle. So how to derive the first brillion in formal for arbitrary angles for twisted bilayer graphene and what the reasonibility of the above picture with respect to TBG?", "label": 0}
+{"snippet": "Is it right to say diffraction is a geometrical optics phenomena and scattering a wave physical effect? I am considering a finite-length conducting plane and supposing a wave hitting the surface and reflected upon. In my opinion in addition incident wave should excite current sources on the plane resulting in a traveling surface wave. Upon reaching the edge wave they should scatter; if I assume very thin edge, but in many literature its said diffraction of waves is occurring at the edges. What will be correct from a physics point of view? Thanks", "label": 0}
+{"snippet": "When we try to form a real image on a screen by a convex lens, we place the screen at a distance where the image is focused. But if we try to place the screen at a distance less than the distance where the image is focused(refracted rays still fall on the screen) so will the image appear on the screen or will screen be blank? If image does appear how will we calculate its magnification and position?", "label": 0}
+{"snippet": "I am interested to see if anyone can direct me to a text on using limits and integration in the \"Error-Accumulating Real Numbers\" field structure. This field consists of the real numbers, but the accuracy of a value diminishes as the reported precision increases, so the error associated with a particular value increases as the precision of reporting on that value becomes greater. How would one go about taking limits and performing integration on such a field? Is it possible?", "label": 0}
+{"snippet": "The classic plate experiment highlights how omitted wavelengths of light create an energy differential and pressure. This pressure is dependent on the distance between the plates, including how this distance determines the omitted wavelengths of light. Could the equation be generalized for any case where wavelengths differ and an energy differential exists? E.g., redshifted cosmological objects being acted on by light sources from our local frame of reference?", "label": 0}
+{"snippet": "When we see an object in a spherical mirror, the different parts of the object has different pictures which are also at different locations compared to each other. The lights that go from the tip of the object reflect and intersect at a point. But the lights that go from the middle of the object reflect and intersect at a different point. We can emit lights from each part of the object, and all of them reflect and intersect at different points. So how do we see the picture of an object as a whole thing in a spherical mirror while the different parts of the object have different pictures?", "label": 0}
+{"snippet": "among the elementary function sets: Polynomial Trigonometric function Exponential Function Hyperbolic Function I don't see the development of algebraic identities, and then the detailed construction of various problems of solving equations, proving identities and simplification for any of their inverse algebras except for the exponentials, in the case of logarithms. What makes logarithms more deserving of this treatment than say, the inverse hyperbolics? I read on wikipedia and actually found some obscure, but few inverse hyperbolic algebraic identities, same for trig. But I've never seen an algebra problem on them, especially in standardised tests, whereas everybody is familiar with logarithmic algebra. Why is it that out of the set of elementary functions, logarithmic algebra occupies a special place out of all the elementary inverse algebras?", "label": 0}
+{"snippet": "If visible photons don't interact with the valence electrons in glass due to large band gap, then how do you explain the slower speed of light in glass the way classical em wave explanation does? Does the interaction (non-orbit shifting) take finite time to complete and thus slowing down the photons? Or is it just phase speed that's retarded, not the individual photons? We can test these two theories with for example a laser pulse through glass rod.", "label": 0}
+{"snippet": "if we have two electrons with their spins entangled like this: And if we measure the spin on the left electron, then right electron spin also change like this: So, my question is, do this spin change on the right electron can cause a chain reaction in other particles near to it?. And what forces will be involved in that chain?. I'm curious on why stimulus in the brain are localized when we aren't aware and propagated when we are.", "label": 0}
+{"snippet": "I have been provided with question in Functional analysis which is stated as below: I also have been provided with a solution which is given by the below picture. Now what they have essentially proved is that all the p norms are equivalent to each other by trying to make it bounded by some constants. My question is that how does it prove that convergence with respect to p-norm is equivalent to the convergence of individual components. Note I have posted image as I am new to math stackexchange. I know we are supposed to write latex. Please ignore for this time and provide me with proper argument instaed of downvoting the question", "label": 0}
+{"snippet": "Can we join two sentences with a comma if written in a conservational tone? Is this sentence grammatically correct? We also need to remember that donations need not be strictly only in cash, they can also be in kind such as making aircraft or helicopters booked in the name of some company or individual, being provided to a political party for its use. Source: Is There Life After Electoral Bonds?", "label": 0}
+{"snippet": "I wanted to know if there is a general formula to figure out the amplitude of an image formed if the object performing SHM about the principal axis or perpendicular to it at some position of a simple, Concave, Convex and all lenses (biconcave & convex,plano concave & convex, concavo-convex and convexo-concave). One numerical I have solved only involved axial SHM (about the principal axis) and involves a simple multiplication of the image's magnification and the objects oscillate along the principal axis with some amplitude. Why would we use its magnification, why wouldn't the image just have the same amplitude?", "label": 0}
+{"snippet": "I'm interested in how people just generate a question from scratch,(i'm preparing for indian highschool level competitive exam \"iitjee\"), i think people don't just start writing random stuff and label that as a question but, there are only four things i can think of they are using geometry some sort of inequalities complex numbers somehow algebra But i don't know how to generate trig questions from it, if anyone could help in giving some examples and thought processes it would be much appreciated. (Seen my teacher creating questions from Jensens inequality, mth power theorem,am-gm-hm-qm inequality,complex number) (It was my first time asking questions please ignore if any mistakes are made) Thank you!", "label": 0}
+{"snippet": "Consider a free body, not hinged about any point. If a force is applied to one end of the body, the body has a net nonzero torque about many points in space. About which will it rotate? Am I wrong in thinking that it will rotate at all? Note that I am not asking about a couple, but a single force. I asked a similar question a few days before, but it got closed, with links not at all answering my question.", "label": 0}
+{"snippet": "Jordan rolls eight fair dice, computing the sum of the numbers on the top of the dice after the first three rolls. What is the probability that Jordan is able to find at least one way to pick exactly three of the latter five dice in such a way that the sum of these three dice is the same sum as that of the first three dice?", "label": 0}
+{"snippet": "I would like to know if there is a relation between bounded variation of functions and bounded variation in sequences. I know one can not directly correlate the concepts but if we consider the Fourier series of the function of bounded variation, what can be said about Fourier coefficients, would they be of bounded variation (sequence definition) and what about the vice versa case? Are there any articles or books related to interlinking these concepts?", "label": 0}
+{"snippet": "A frame of reference is the perspective you have on a happenstance. But isn't it a viewpoint or point of view? As in, a literal point, from which something is observed? If so, why is it called a frame and not a point? Does frame of reference literally crops a section of existence as the perspective of observation? Why is it one phrasing over another?", "label": 0}
+{"snippet": "If a photon has a wavelength and a frequency and we depict a graph with multiple hills and valleys like done in basically every explanation regarding photons and their wave/particle behavior, like in this one. is it correct to say that one photon (as simplified as it is) is stretched from one hill to the next? And multiple of those sections are either multiple photons behind each other (when the sun emits them) or the trail of one photon as a record in space or time(depending on what one wants to depict). Or is one photon the entirety of those many hills and valleys? My understanding is, that one photon is one part from hill to hill or valley to valley, depending on how you look at it.", "label": 0}
+{"snippet": "For a set A, we are incrementally building a basis for A. Suppose some oracle keeps giving us new vectors from A that are not spanned by our partially-built basis. There must be some theorem that tells us this constructive procedure of adding new linearly independent vectors will always terminate after the same number of vectors are added (no matter what vectors that oracle gives us), and all sets constructed this way must form a basis for A. What is the theorem? Is it in Axler?", "label": 0}
+{"snippet": "I am no scientist, but I do love science as well as the unknown. Are there laws of creation for biological life? Would it be safe to assume that our bodies are made up from things that came directly out of the big bang and over time made connections through atoms and adjustments through evolution to achieve consciousness? I have much more but I'll keep it as simple as I can for now.", "label": 0}
+{"snippet": "A small circle is tangent to the lower right quarter of a larger ellipse. The ellipse is straight (not rotated), and its lowest point is centered at origo. The following is given: \"a\", the axis of the ellipse along the x axis. \"b\", the axis of the ellipse along the y axis. \"r\", the radius of the circle. \"h\", the top y coordinate of the circle. I am seeking the x coordinate of the tangent point between the ellipse and the circle as a function of a, b, r and h.", "label": 0}
+{"snippet": "Dirac's initial interpretation of antimatter is the existence of Dirac Sea. However, it doesn't work for bosons since we can't invoke Fermi's exclusion principle. Goldstone boson can be emergent but it's neutral. Xiaogang Wen's work also revealed the possibility of an emergent QED structure from string-net condensation which shows fermi statistics and gauge interactions can be emergent. We also see emergent Lorentz Invariance in the low energy area of condensed matter system. W bosons are charged bosons. It seems impossible to me for charged boson to fit into Xiaogang Wen's \"it from qubit\" fantasy. Does anyone know the approach to this or related literature?", "label": 0}
+{"snippet": "So if our eye is considered a lens, a parallel beam (sort of like collimated light from a flash light) should converge to a single point, the focal point. So does that mean our eye will see a finite parallel beam as a single dot? That seems contradict real life experience, where I still see the parallel beam as a beam with finite width. What gives?", "label": 0}
+{"snippet": "After reading the paper On the Expressive Power of Homomorphism Count, I was wondering if there were some nice material I could read trying to study graphs from a categorical point of view. Stuff like trying to make it in an abelian category, looking at exact sequences of graphs (maybe you'd need to consider some kind of pointed graphs category), maybe defining stuff like Ext groups and studying them. I hope my question makes sens. Thanks in advance for any answer.", "label": 0}
+{"snippet": "Whether it is Orion or Sagittarius, the speed relative to me is clearly faster than the speed of light. These are not inertial systems, so they are not subject to the constraints of special relativity, but does the fact that their apparent velocity is a circular motion exceeding the speed of light cause any kind of apparent change in time for celestial objects if the argument is based on a celestial coordinate system? They at least don't seem to be unable to follow, unlike the laser beams I shot at the moon or something.", "label": 0}
+{"snippet": "When I was reading the calculus of Variations chapter in Classical Mechanics by John R. Taylor, he mentioned that cart rolling back and forth on cycloid-shaped track are exactly isochronous (period perfectly independent of amplitude). As I was trying to solve this by the original integral, I find it hard to compute and the normal Casio type calculator cannot solve it as well, also I sought help from websites like Integral Calculator, the result function is not independent of the starting angle I set. Can someone help me, great great thanks!", "label": 0}
+{"snippet": "I'm trying to make a comprehensive decision tree for finding integral/improper integral convergence. The goal would be a comprehensive \"guide\" or list to follow in order to determine the convergence without having these automatisms already learned. Here is what I have made currently: Decision tree Are they any better ways of doing this? More optimized ? How can I make this tree more complete, more accurate ? Apologies if language is off in the image, I'm not great at this.", "label": 0}
+{"snippet": "Aero is not my speciality at all so apologies if missed anything. But when looking at potential flows, i thought the whole point is for there to be no rotation at any point and its that reason the velocity can be described by a scalar fuction at any point, yet the vortex flow has a point of curl in the center and hence circulation. I noticed in J.D Andersons aero book that it is this particular flow that allows for lift in invicid flow which greatly confuses me further. Is there some hidden explination behing the vortex element? Appreciate the comments.", "label": 0}
+{"snippet": "I am not getting the following sattements related to contact force and normal force which are: If the direction of contact force cannot be determined, it should be shown as two components. If perpendicular to the surface of contact cannot be drawn, the normal force will act perpendicular to the surface of the body. If neither can be done, normal force has to be drawn as two components- one in the X- direction and one in the Y-direction. The forces acting along the X and Y directions are independent of each other. What does these following satements are trying to explain?", "label": 0}
+{"snippet": "So I think I understand what binomial coefficients are, \"K number of combinations that can be made from set N\". However, I keep seeing examples demonstrating K being the number of successes against the number of outcomes. However, my thinking is by the logic of the first example I gave, when finding the number of combinations Tails Tails would be included as it is a combination that can be made from set N. However, this does not feature a heads and is not a success.", "label": 0}
+{"snippet": "I would like to reference addresses throughout a document and as an appendix generate a list with all the address entries used and the link to the places in the document where they were used. Just like it is done with a bibliography. I'm actually thinking it'd be the easiest to use a special kind of entry and store them in a bib file, and then use it as a list of citations. How would you do it? Many thanks!", "label": 0}
+{"snippet": "Suppose We have a charged rotating cylinder such that the magnetic field inside it is the same as a solenoid of the exact same dimensions. Obviously, the current per-unit length for both will be the same. Now, what can we say about the magnetic flux in the cylinder since there is no n (turns per unit length)? What can we comment about inductance? It depends on n and not current.", "label": 0}
+{"snippet": "I want to know if the verb seem can be used only for observable things? For example, if I guess the computer hard disk is failed doing some action and has some logical issues can I say: \"It seems the hard disk has logical errors.\"? In this case, no physical failure is not observed on the disk but I know something is wrong with it. In case the \"seem\" is not suitable, what alternative verb do you suggest?", "label": 0}
+{"snippet": "I am about to compile a number of different published articles into a single thesis. While each document on its own can compile and produce a PDF, there are several macros files (shorthands for various formulas) that are inconsistent between them. Is there any way to do this with the least amount of change to each latex document? In particular, is there a way to include the macros \"locally\" for each article so that they don't conflict?", "label": 0}
+{"snippet": "As the name suggests, I am trying tio draw in TikZ the following figure for a surface current distribution (I am used to drawing with hand, so I find the switch to the digital a bit tough): The striped region is a urface that is covered with current densities J, and the second image is a representation that gives an idea on the relation of all the vectors involved. The dashed line between A and B is an \"cross-section\" that helps to calculate a line integral with the element being dl, and the vector n is a normal vector to the surface with u a vector orthogonal to it. Thanks immensly, and have a wonderful day.", "label": 0}
+{"snippet": "Is there an easy way to list all appearances of all words in the text of a LaTeX document that occur before a makeindex entry for that word arises in that document? When we move text around in a document, we can find that we have moved the definition of a technical term later in the document than one of the instances of that term being invoked. We cannot completely automate the task of eliminating these errors, because the same term might have a technical meaning defined somewhere, but also a common meaning, and the common meaning might be the meaning intended in an instance occurring before the definition. Still, TeX could help by making a list of these, so we could check.", "label": 0}
+{"snippet": "In a theory that predicts gravitons, shouldn't the background be flat and gravitational interaction then be modeled as a scattering event? Answer included below. Credit to /u/broguetrain on Reddit for providing the answer when I asked on there some time ago. I wanted to post this Q&A here (with some edits for clarity) due to recent drama on Reddit so as to assure my ability to reference it in the future. I do encourage additional answers on this that might provide further useful details. For example: elucidating on how specific metrics can be described as the coherent state of strings in the graviton state.", "label": 0}
+{"snippet": "their reasoning was that when the bike lean towards horizontal the reaction acting on the bike by surface will act in an angle through the center of gravity of the slanted bike(not perpendicular to the surface). therefore the horizontal component of that angled reaction will provide the centripetal force even though friction is not present. they also said that if the friction is present this component will be added to the friction and their resultant will act as centripetal force. i find this hard to believe.i think it is impossible to turn on a frictionless horizontal surface. can someone please help me find the correct answer?", "label": 0}
+{"snippet": "Or at least I think it was Pratchett taking a potshot at religion (exact wording unknown either): \"When you got them by the balls, you, uhm, got them by the balls.\" Note that both parts of the sentence are metaphorical, meaning about \"When you control their sexuality, you control them totally\". Which rhetoric figures are involved here (is the one metapher more, uhm, metaphorous than the other since the first part involves actual balls, at least pars pro toto or so)? Seems to be quite a lot...", "label": 0}
+{"snippet": "There is a misconception that electrons push each other from their mutual repulsion within a circuit. Rather they are pushed by the electric field. I also understand that the electric has the energy rather than the electrons being charged carriers. However, I can't seem to understand why we need wires at all when energy is in the fields rather than the electrons. What is flawed with my logic?", "label": 0}
+{"snippet": "Basically I know how \"a\" and \"an\" are used: a member an adult member but how is the same handled when the middle word is inserted parenthetically or even in brackets: I met a member of the club. I met a/an - adult - member of the club. I met a/an (adult) member of the club. Should there be \"a\" used, because the main phrase is \"a member\" or should \"an\" be used because the adjective starts with a vowel? And is there a rule to quote?", "label": 0}
+{"snippet": "I want to drop a cup of water with a ping pong ball within it so that it falls straight (as much as possible) and that I can reiterate the experiment rigorously... I've seen someone using magnet and a specific system that sadly I cannot build at home. My idea is to hold the cup and trigger something that let fall the cup with the ping pong ball but nothing good comes in my mind. Do you have any ideas? Thanks for reading", "label": 0}
+{"snippet": "I was reading an article about high density housing and/or constantly being online and came across a single word I had to check the dictionary for and it was used to mean \"the absence of a community spirit\". e.g. \"The x caused by the complex housing situation.\" I have had no luck with antonyms for community or synonyms for diaspora. I can no longer remember the word or the article. It may mean the degradation of community or the circumstances preventing it. What word is used to define this asocial vacuum?", "label": 0}
+{"snippet": "I look how to implement the algorithm (program) for solving so called Zebra(Einstein) Puzzle. For that, i look for some formal or mathematical representation of conditions in this puzzle. Can you suggest possible ways to represent it, while this representation should makes easier to solve that? Of course, do not suggest the trivial forms, like list of all possible variants, this is not efficient if there are too many variants.", "label": 0}
+{"snippet": "I've been attempting to get a row of dots from the end of the equation right to the equation label, that allows the reader to easily trace along from, say, an equation on the right of the page, muuch like the format commonly used for contents pages; headings with a row of dots leading to the page number(s) so that the reader doesn't get lost, trying to trace along the \"line\" with no guide per se. Thanks", "label": 0}
+{"snippet": "The ant on rubber rope paradox says that an ant moving along a rubber rope that can infinitely expand will reach the other end of the rope regardless of how fast the rope expands and how slow the ant moves. Why then multiple sources say that there is cosmic event horizon, and two persons at some distance exceedidng Hubble limit would not be able to meet?", "label": 0}
+{"snippet": "Is there a way to calculate equivalent parameters of a few RL links for direct current circuit (like on the generalized example on the image below)? So far I've studied that known formulas for series/parallel connections of R and L elements cannot be used because it's not R and L elements, which are connected in parallel and series, but RL elements (as a single entity), which can connected in parallel or series.", "label": 0}
+{"snippet": "My former college is starting a departmental journal which I am editing and typesetting. I have edited and typeset every contributed article individually using the article class and initially tried to bring them all together using the combine class then individually tried the subfiles and standalone packages but none of it worked. So finally I decided to use pdfpages package and include all the articles as pdfs in my main document. Now, each included pdf article has a separate title and author BOTH of which I want to add to the main toc. How do I do this?", "label": 0}
+{"snippet": "A large part of the computational physics literature relies on solving Newtons equations for deriving phase diagrams and related properties of the LJ system. In many cases this approach does not require justification since one could be interested only in the dynamics of the system during a short time. But this is not the case if one is interested in caculating partition functions. So I have not found any established result to ensure that this approach is sufficient for sampling the phase space and calculating partition functions.", "label": 0}
+{"snippet": "The universal law of gravitation of Newton calculate the intensity of gravitational force by the radius and mass of an body.. so in a black hole there is very much small radius and a large amount of mass... So I think newtonian gravity would predict large amount of force.... That is similar to the great pull of black holes due to gigantic space time curvature...", "label": 0}
+{"snippet": "I now have a point located at x, and the value at that point is q(x). I want to discretize the point to the surrounding grid points and maintain a Gaussian distribution. A one-dimensional grid is fine. Is there any generally recognized good discrete method? Thank you. As far as I know, B-spline does not satisfy Gaussian distribution, so B-spline is excluded. One method I found is D.E.Shaw's Midtown-splins, but it can only reach the third order, which cannot meet my needs. What is a better discrete interpolation method?", "label": 0}
+{"snippet": "Can anyone suggest existing technologies that must account for electromagnetic momentum? I believe one example to be confinement in nuclear fusion; but momentum there appears in an averaged form, as pressure. Just to give an idea of what I mean with \"existing technologies\": general-relativistic time dilation has to be concretely taken into account in any phone's GPS. (Edit: many excellent answers have been given, it's really difficult and partly meaningless to choose one as \"the\" answer! I chose JEB's one mostly because it is about a macroscopic effect and about a directed form of electromagnetic momentum, rather than more \"averaged\" forms closer to electromagnetic pressure.)", "label": 0}
+{"snippet": "For many (!) years I have written papers in MS Word with numerous embedded equations generated by MathType software. MathType prior to its recent acquisition by Wiris was able to function as a standalone equation editor and save equations as pdf files that could be embedded in Word, and edited either within Word on independently in the saved pdf format. The new version of MathType is an absolute disaster: the interface is pathetic with many controls of sizing and fonts lost, the generated equations are bit-mapped (not vector graphics), etc, etc. I hope to switch to producing all equations in manuscripts with LaTeX, but wonder whether some version of LaTeX can generate Word-embeddable pdf files, and if so what version(s) of LaTeX are suitable. Thank you!", "label": 0}
+{"snippet": "I want to know the temperature of electron plasma whose data has been generated via particle in cell simulation. My professor said if I have histogram of electron density by kinetic energy, then I can get temperature of the electron plasma when I apply the log on density. He also mentioned slope of log applied histogram for calculation. I have tried to find out what is that method, but I couldn't find any reference from it. Does anybody know about this? I need to change my lab and advisor before the september ends so I need to organize what I have done as soon as possible for contancting other labs. And thank you for your helps.", "label": 0}
+{"snippet": "This question Sum of Countable Increasing Absolutely Continuous Functions is Absolutely Continuous says if the functions are all AC, then the sum is also AC. Then if the answer is not true for my question, we only need to consider the case of continuous singular functions. However, I have no clue how to deal with them since I only know the Contor function as an example of continuous singular function, and the summation of the varients of it seems cannot lead to a contradiction.", "label": 0}
+{"snippet": "The wave function collapses anyways whether I wanted to know which slit the electron passed through or not, the only difference there is that in the former case the wave function collapse for any electron at either of the two positions directly behind the slits, i mean the electron still in superposition of all possible locations on the screen, but upon watching the electron passing though which slit, the collapse magically favors only one of two possible location, i.e., the ones directly behind the slits, Is that right?", "label": 0}
+{"snippet": "Recently i have been reading \"A radical approach to real analysis\" by David Bressoud and this thing got stuck in my mind Here you might lose convergence at the end point is written in last paragraph what is this meant for an infinite trigonometric series .It has also some relation with derivatives somehow. This was written for the explanation of fourier series and crisis in mathematics but what means by phrase losing convergence and how it is related to trigonometric infinite series", "label": 0}
+{"snippet": "Let's say I put a neutral conducting sheet in front of a charge. What will happen to the sheet? If I place a plate with some thickness in front of the charge, charges will develop on the face of the plate to maintain the electric field inside the plate zero. There is no such thing inside the sheet, so how will it react to the charge in front of it?", "label": 0}
+{"snippet": "I'm using the article documentclass to write a simple document, but when i compile the code the tableofcontents look like this: From section \"Progetti\" there is no space between the number and the name. The code of the section is the following: I already tried to take out the subsubsection thinking it maybe was the cause, but the problem persist. I also tried this method but it add more space between number of section and name but it increase the space between all the sections, correct ones included. Can someone give me a solution? Thank you.", "label": 0}
+{"snippet": "In P Halmos measure theory book it written A Sigma ring S generated by C, the class of compact subsets of X where X is locally compact Hausdorff Space. Then S has open set and sets of S is called Borel Sets. I am very confused. How a sigma ring generated by the class of compact set has open set. P Halmos Measure theory book:", "label": 0}
+{"snippet": "For a new paper I am writing to IEEE journals (double-column formats), many important paragraphs suffer from the default hyphenation in LaTeX. Especially, I don't like the hyphenations given in the Funding Statement at the end of the paper. If I don't want hyphenations in some words such as \"under\", \"Programme\", \"Excellence\", \"Operational\" etc., how do I instruct LaTeX not to hyphenate these words in the IEEE LaTeX document? Thank you..", "label": 0}
+{"snippet": "I was given this problem in physics class. My teacher said that they reached the ground at the same time, but when I tested it out (video), I got drastically different results. I showed the professor and asked him why real life and theory did not match up, and he said to just accept it and would not explain what is going on in real life. Why is the experimental result so different from the theoretical answer?", "label": 0}
+{"snippet": "Pretty straight forward question. Which of the following sentences is/are \"correct\"? They are simping on Korean players They are simping in Korean players They are simping for Korean players What I want to express is that a group of people feeling extreme sympathy for Korean players in a online international game. I've always used for but I see a lot of people writing almost the same sentence using mostly on and rarely in", "label": 0}
+{"snippet": "I am learning the theory of large deviations. In so many results in the theory and from the very beginning in each book about this subject one starts by introducing a family of probability measures satisfying some properties and defined on some (Polish) space. I do not understand why one needs in some important context and any context of the theory of large deviations to introduce a sequence or family of probability measures. Can somebody explain and provide some example of why one needs many, i.e. a sequence, measures ? Many thanks.", "label": 0}
+{"snippet": "In the ideal quantum information version of metrology, a maximally entangled state is viewed as the best resource for quantum metrology. The optimal phase uncertainty of the NOON state reaches to the Heisenberg limit. Later we have seen that for same average particle number, an entangled coherent state (ECS) outperforms the phase enhancement achieved by NOON states for small number of photons. Can we say that ECS violates the standard Heisenberg limit? If Heisenberg limit is standard then hoe coherent states give better phase measurement?", "label": 0}
+{"snippet": "I can get a bit overwhelmed trying to find which frac or h symbol corresponds to the output of a complex expression. An easy way is to copy paste into lyx and edit there as you can edit the output directly by clicking on the right symbol but that can cause context switches and might lead to using the mouse which might break the flow and slow down the writing process.", "label": 0}
+{"snippet": "Imagine that a person is walking with a constant velocity along the horizontal plane and turns the fan on the filing into a circular motion. Then, after sometime the fan will achieve a constant velocity, Then derive a relation to know the relative velocity of the fan with respect to that person! Say the radius of the fan is r, the acceleration is a, and the constant velocity achieved by the fan is v in time t.", "label": 0}
+{"snippet": "I know partial derivatives should be used to solve this, but I'm wondering is there any to find the plane using the vector method of getting the Normal vector and a point on the plane. In this case, we already have a point, we just need to somehow find the Normal vector. Also, is there any connection between Normal vectors and partial derivatives in this case of finding equations for tangent planes?", "label": 0}
+{"snippet": "In the communication network given below, link failures are independent, and each link has a probability of failure p. (consider the physical situation). A can communicate with B as long as they are connected by at least one path which contains only in-service links. Given that exactly five links have failed, determine the probability that A can still communicate with B. Given that exactly five links have failed, determine the probability that either g or h (but not both) is still operating properly. Given that a, d, and h have failed (and no other information), determine the probability that A can communicate with B.", "label": 0}
+{"snippet": "Title says it all really. As is commonly known, the trace of the density matrix must be one and the trace over the density matrix times an operator is the expectation value of that operator. If you instead add up ALL the entries of the matrix (perhaps times some function related to the row/column indices) does this represent something OR does it equal some numerical value? Does it have some numerical relationship to the trace (strictly greater, or smaller, etc.?)", "label": 0}
+{"snippet": "I would like to know the structure of the sentence and also meaning. Is the vision subject? What in the sentence is what? The vision to do today what is needed for tomorrow. Can I understand.. like this? the vision we do today is what we need for tomorrow. The sentence was part of a speech as follow. Reject pessimism and fatalism. Refuse limits on our spirations. To do that, we need to have the imagination and confidence to do things differently and better. The vision to do today what is needed for tomorrow.", "label": 0}
+{"snippet": "Correct me if i am wrong but all circuits must follow the law of conservation of energy. And the energy is supplied by the action of source to create a potential difference by moving charges against electric field In a battery the energy of chemical reactions that create potential difference is equal to the energy used so the spin of an electric generator must have enough energy to equal it's usage in multiple homes. So all of heat energy that get's used in multiple homes and rotating fans they all get singled out by a spinning conductor in a magnetic field? Ik this might be stupid but to me it seems sorta impossible", "label": 0}
+{"snippet": "Since the only thing a computer can do is modify its machine state, and you can always change from one state into another state (there exists such a program) and so each program is invertible; and if all the programs are deterministic, then associativity also makes sense. Two programs are considered equivalent iff they do the same thing to the machine's state, given any starting state. So do I have the title right or not?", "label": 0}
+{"snippet": "I found one passage that I really cannot understand the grammar structure. The below is the problematic sentence. The crates feature voids, allowing large volumes of water sufficient surface area to seep back into the ground. - Source I think this sentence should be; The crates feature voids with sufficient surface are, allowing large volumes of water to seep back into the ground. I want ask why you can bring the words \"sufficient surface area\" suddenly between \"water\" and \"to\". Could someone explain this grammar structure ?", "label": 0}
+{"snippet": "I was going through the energy/mass equation and it is said that both of the said quantities are interconvertible. That made me think that if we try putting actual values into the equation, the interconversion is actually very large; speed of light itself is a large constant, and the product of its square and mass of a said object would be large. Putting our energy consumption into consideration then, why do we have energy problems in the world? Relative to our world's energy consumption, we should have infinite amount of energy for the world. Why is it that we still struggle with energy problems all over the world?", "label": 0}
+{"snippet": "A high voltage wire can either have an large excess of electrons (net negative charge density), or a large defect of electrons (net positive charge density). The voltage difference between the wire and the human can be positive or negative. Are both cases equally dangerous? Is there a difference between electric shock from a positive wire and from a negative wire? (In one case electrons will rush into my body, in the other electrons will rush out of my body)", "label": 0}
+{"snippet": "Suppose I have an equipotential surface S. Thus the electric field at each point on said surface is direction normal to the surface. Will the magnitude of this electric field be constant for all points on this surface? (This reasoning comes from the feeling that if the electric field strength were to differ, a closed loop path along such field lines may have work done by electric force as non zero) I may be wrong, so this is just a small thought. Thank you.", "label": 0}
+{"snippet": "Was is generally accepted as singular - 'a dog was in the garden', were, plural - 'some dogs were in the garden. So why is 'You was in the garden' so wrong, (you were in the garden) but have to be 'you were in the garden, singular and plural? It seems to be restricted to only the noun 'you', which could be singular or plural - and in a lot of cases, that fact remains hidden.", "label": 0}
+{"snippet": "In Quantum Mechanics conservation laws are fundamental, I was thinking about spin altering models of interaction such as the Ising Model and realized that it isn't at all clear how angular momentum conservation occurs in such a situation. If there is spin flipping occurring where does the contrary compensating angular momentum go as to have global angular momentum conservation? The interaction fields absorb this angular momentum?", "label": 0}
+{"snippet": "During JJ thomson experiment and similiar other experiments,they found that cathode rays were deflecting from its direction under magnetic fields and electric field,also the gold leaf attached to co-axial cylinders led to conclusion that the cathode rays are negatively charged,but later,By Putting a paddle wheel or fan in path of cathode,the wheel turned and moved,the fan also moved,This led them to conclusion that they must have mass,but is this the only criteria required for an unknown object to have mass,that they can perform mechanical work?The scientists at that time concluded that they have mass,and then went on to calcultate charge to mass ratio of it,assuming rays has mass?Can't any other particle now known do work as well as have no mass?", "label": 0}
+{"snippet": "Are there any experiments done to verify the absence of forces caused by complex structural organisations in systems? Afaik, experiments in QM and Standard model QFT talk about the validity of the interactions in individual particles that are not in any complex sturctures. Experiments in Condensed matter physics involve configurations with some structure. In these cases, there is no requirement of downward causation. Are there any experiments in more complex organizations which rule out downward causation? Is it even practically possible at our current experimental strength?", "label": 0}
+{"snippet": "When the size of the observable universe was small as a proton what was the physical content of it? Was there a limit of particles in such a tiny volume with enormous high density and energy? Can we find more than one proton inside such a volume, can we assume that because an electron, a quark, or a photon are point particles there was no maximum limit for the number of say electrons instide a volume the size of a proton?", "label": 0}
+{"snippet": "For example does a virtual electron have the same characteristic intrinsic values like mass, charge, magnetic moment etc. as a normal stable electron? Or can these range wildly and not having specific values for the case of the virtual particles and if yes don't you think that the term for example \"virtual electron\" is kinda of misleading? How can for example a virtual particle ten times the mass of its normal stable counterpart be the same particle? Wouldn't it be a less specific but nevertheless more correct description of these particles be the term virtual fermions in general or virtual bosons or virtual pairs without labeling them with a specific normal particle's name of the Standard Model of particles?", "label": 0}
+{"snippet": "While calculating electric flux through an uncharged ring kept near a charge, we tend to draw a spherical Gaussian surface that covers the ring by edges but while using the gauss law, we tend to take the entire circular region of ring as area bounded by it(just like we do for circular disk). However, the ring has electric field passing through it only in the ridges.So why are we taking the entire circular region in case of ring where in the middle there is actually no area?", "label": 0}
+{"snippet": "I decided to use the Maple software to help me solve dynamic optimization problems, and I found this final solution for T. (example in the picture). example What does the LambertW mean for the solution T? Can I get rid of this expression to express T in simple terms? Does theLambertW (including the expression inside it) have a solution or an equivalent expression? If this is the final form, I assume I can no longer proceed with symbolic/analytical solution, and I must move to computation?", "label": 0}
+{"snippet": "i just started my study in organic semiconductor. I realized to increase conductivity, polarons are formed in the polymer backbone. From what i read due to localised energy state level by polaron that can exist in the band gap, the band gap is narrowed. My question is if why is can polaron exist in band gap while electron can't though they are both almost identical. Also, do the formation polaron exist as somewhat of a 'bridge' to narrow the gap between conduction band and valence band? Helps or guides are really appreciated.", "label": 0}
+{"snippet": "The soundness of FOL is proved in meta-language(natural language) by proving every deduce rule is correct, so we feel peaceful using those rules to deduce. But the process of proving every deduce rule is correct also uses deduce rules in natural language. For example, proving the correctness of PC(Proof by Case) also uses PC in natural language, so we assume the PC rule exists and assume PC is correct in natural language. Do we need to construct another meta-language for the natural language to prove those assumptions like we are doing for FOL? Otherwise, how can we feel peaceful using those rules when deducing in FOL? Furthermore, is it possible to construct such a meta-language for an unrestricted language such as the natural language?", "label": 0}
+{"snippet": "At one time or another, you've probably inquired about something (perhaps online) and been met with the curt or critical response. It's meant to showcase their cleverness. It's more of a concealed boast than it is a help. Is there a word or phrase which calls out is the disingenuousness of the help, since it's not that at all? This word or phrase characterizes the response and not the person or the behavior.", "label": 0}
+{"snippet": "recently I was solving questions on uncertainty principle but never came across questions involving system of particles like combination of electron and alpha particle. I wanted to understand how to deal system of particles while solving uncertainty principle questions. My initial thought was to calculate total uncertainty in momentum of the system and then using the conservation of momentum, divide this uncertainty in momentum by the respective masses of electron and alpha particle to obtain their respective uncertainty in velocity. Is this approach right?", "label": 0}
+{"snippet": "Hi there my question is pretty much in the title. I have to create tables which are longer than one page. The caption needs to be above the table, it would also be a great extra option if i could rotate the text inside the cell and i would need an automatically adjustable cell width just like tabularX does. Do you have any recommendations? Thank you", "label": 0}
+{"snippet": "I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution probability for the possible values of the observable, which is better than only expectation values. So why do we claim that 'all we can get is expectation values'? Also, why cannot we model these uncertainties in the a priori knowledge of a measurement using random variables and probability language? Is it really necessary to go through this whole formalism?", "label": 0}
+{"snippet": "How the word livid came (according to Merriam-Webster) to have three different meanings (in addition to the default, 'furious', one)? As I see, it could mean blue-and-black pallid reddish. I mean, I know that all meanings are accepted, but is that so? If I say to someone My car is livid. won't they have any predisposition to favour one of the meanings? At least based on your experience, which option is the first you think of?", "label": 0}
+{"snippet": "I know that the search for Higgs would be quite pointless if there was no estimation of its mass. Namely the perturbative violation of unitatity, gave us an upper bound on its mass.Unitarity Constraints on Heavy Higgs Bosons I wonder if there are enough parameters in the Standard Model of particle physics, such that it introduces sharp bounds on SUSY parameters that cannot escape experiments? Is there in general any model independent prediction made by SUSY or it can always be rescued by means of introducing new fields and couplings phenomenologically?", "label": 0}
+{"snippet": "He brought some food to eat on the road. He found some beer to drink in the fridge. Is it only reality and sanity that keep us from taking the beer example to mean he would be squashed in the fridge like a contortionist, sipping a beer? Or do the verbs license, or if that is too strong, erect interpretive guide-rails for, adjunct phrases? Is meaning accruing as we parse, eliminating certain possibilities and bringing others to the fore? What is the real-time elimination of improbable meanings called in the linguistic literature?", "label": 0}
+{"snippet": "People say my idols are Messi and Ronaldo(no hate) but I dont know why I am attracted to Physics and Math.It always amazes me, this is just a dumb question which i suppose is gonna be closed by midnight today but can someone teach me physics? I would love to and also do questions he/she gives me, it will be like a free trial for me as a student and you as a teacher. Once again, even though this is closed, just know that I love you guys and you are what I aspire to be one day.", "label": 0}
+{"snippet": "Latex IEEE format color problem As you can see the text after the figure until the end of the paper became light blue. But, it supposed to be black. I don't know what happened! I utilized both 'color' and 'xcolor' package in my paper. When I remove the highlighted text inside the paper, the problem is solved. But, I think it is the figure problem in ieee latex format that cause the change of the text after it", "label": 0}
+{"snippet": "In accelerated pure rolling ,as we know velocity of the bottom most point is zero with respect to ground but what makes it to have zero tangential acceleration. If tangential acceleration is to be zero at that point ,it must have net force zero in horizontal direction.The ground applies friction on bottom most point, which in turn applies some internal force on oher points in the body(due to rigidity of body) causing the whole body to get angular acceleration ,the other points applies the same reaction force on the bottom most point .We don't know the magnitude of internal forces. So on what basis we say that these forces cancel each other to make the tangential acceleration or horizontal acceleration of the point zero?", "label": 0}
+{"snippet": "I want to write the i and j as one \"ij\", as can be seen in the Dutch language, in my LaTeX document, but can't figure out how to do it, even with ChatGPT! If someone knows more, please hit me up! It could be the case that this is just not possible as it is not that frequently used, especially not when actually typing it. If so, please let me know too. Thank you.", "label": 0}
+{"snippet": "I'm using xindy to create indeces. However, the default sort order is not sensible for uppercase and lowercase. Is there a way to create a .xdy file so that the uppercases are sorted in front of lowercases. Here is an example: A Abel....... Alex....... aboutism... account.... axis....... B Bible...... basics..... bigger..... I think the issue is, by default, uppercase letters are mapped to lowercase letters, thus cannot be distinguished former and sorted according to that. I wonder if anyone can help me create a .xdy that sorts alphabet case-sensitively.", "label": 0}
+{"snippet": "I read this thread of articles by Casher(quite marginal in terms of citation) where they show in certain realistic models SUSY is broken by non-perturbative effects. Explicit breaking of supersymmetry by non-perturbative effects The SUSY currents turn out anomalous. Now I want to add a twist: Does the anomaly survive even by addition of extra dimensions? If so, is the number of such dimensions the same as critical superstring theory? Or Super gravity?", "label": 0}
+{"snippet": "Construct a triangle ABC when angle A, length of angle bisector from A and circumradius are given. Since angle A and circumradius are given, we can find out the length of BC. I can elaborate on the same further if you're interested... This seems like a simple problem but I can't get it. Thank you! In a circle with a radius equal to circumradius, an angle equal to angle A constructed from any point will intersect the circle at two points, the distance between which will remain constant and equal, in fact, to side BC. This is how we can get length of side BC given angle opposite it and the circumradius.", "label": 0}
+{"snippet": "Hopefully my question is not out of order in this site. I am trying to weigh an object that is too wide/long for my weight scale. If just put it on top of it it tips over. So my solution is to place my hand on the 'short side' to prevent it from tipping over. Assuming I am not pushing (just holding my hand as an 'stopper'), does that change the weight the weight scale measures? why/why not?. I guess if I push the measured weight would increase (not sure either). details: I am trying to weigh a planter to know if it is safe to put in the balcony.", "label": 0}
+{"snippet": "The statement of class existence theorem includes \"F be a formula that quantifies only over sets\" then there exists a class A such that it contains only sets and a set x is in A iff F(x) is true. I am curious to see an example which breakz this requirement and have a quantifier over classes, and what kind of paradox it causes. I mean the requirement for the class A to contain only sets pretty much covers Russell's paradox of not belonging to itself. But why for quantifiers should be over sets only? What formula F will cause problems?", "label": 0}
+{"snippet": "If the circulation is negative and flux is clearly not zero then will the flux also be negative? If a curve C and its vector field are going in opposite directions (meaning C is going clockwise and the vector field is going counterclockwise), then circulation will be negative. If the vector field is pointing outwards from the curve meaning it is leaving the curve then will the flux remain positive?", "label": 0}
+{"snippet": "If I penetrate water's surface with needle (using hand) then Cohesive forces> Adhesive forces and water molecules climb up the needle (exactly like capillary action) and needle behaves hydrophilically and when I make it rest like mosquito's legs on water, it floats (mosquitos actually float on water due to surface tension and hydrophobic nature of legs), the needle behaves hydrophobically and Cohesive forces> Adhesive forces in this case. So, my questions is, Is hydrophobic and hydrophilic nature orientation and position dependent (like whether needle is in bulk after penetrating \"skin\" of water or at surface like mosquito's leg)?", "label": 0}
+{"snippet": "In PWT, the wave function depends on the positions of all the particles. Therefore the velocity of a given particle depends of the positions of the other, it's why the theory is non local. In the model why there is a single wave for all the particle and not a wave for each particle? So that the velocity of a given particle does not depend on the other.", "label": 0}
+{"snippet": "I want to know like for continuity of a function at a given point we can check the limit of the function at that point and the value of the function at that point but how to verify if a function is uniformly continuous or not over a given interval and all kind of interval that is for open , closed and semi open or closed interval", "label": 0}
+{"snippet": "This figure is taken from Wolfram MathWorld. The site classified the third region as not simply connected, and I get it, but it isn't also multiply connected, since multiply connected means that I can connect any two points in the region with a curve that lies entirely in the region. However, it is clear that I cant connect one point in the upper subregion with another one in the down subregion with a curve that lies totally in the region, correct? Note A multiply connected region is a connected region but not simply.", "label": 0}
+{"snippet": "the decision partition problem is Np-complete.Now I would like to proof that if a polynomial Algorithm exists for the decision Problem than another polynomial algorithm would exist too, that would give two sets A and B that fulfill the decision Problem.Clearly this problem is Np hard .I would like a hint or something to help me to approach this problem because I am lost.How can I use the decision partition problem to output the sets A and B", "label": 0}
+{"snippet": "Air can hold water in proportion to partial pressure of water vapor. This is affected by temperature. But is the water capacity of air also affected by ambient pressure? I did find some answers that water holding capacity of air decreases with increasing pressure. Quora link, UCAR link But I was unable to find any equations that would tell me exactly how much it changes. In this case we talk only about change in pressure. So temperature and volume would stay the same. I will be glad for any sources that can answer me this relationship.", "label": 0}
+{"snippet": "I have a man-in-the-street question that was probably \"predetermined\". If everything around us is co-interacting particles whose source is some infinite small point that started their expansion into nothing due to the Big Bang, how come those particles have any interactions? They should become further with every second, just as grenade fragments that can only meet each other after the explosion only if there are some external preexisting obstacles on their way that cause their bounce.", "label": 0}
+{"snippet": "Wikipedia asserts that The rays represent luminous intensity, which varies according to Lambert's cosine law for an ideal diffuse reflector. Describing this figure: I understand this is a perceptual phenomenon, and we are observing the light coming from an object that is diffusely - and isotropically - reflecting light. and that the Lambert Cosine has to do with how stretching a circle on one axis increase its area. However, I do not understand how or why this stretch happens, since (in my mental representation) we are always looking at small cylinders of light that come straight (normal) to the eye surface. Can you explain, or maybe include a simple draw of how you image this?", "label": 0}
+{"snippet": "I understand that our main supporting evidence for dark matter is the anomalous speed of objects orbiting around the edges of distant galaxies. Is there a reason why dark matter solves this problem better than say, the strength of gravity simply being stronger in the region? My idea is that maybe these galaxies don't seem to be large scale attractors, but it also seems to me that they could be attracted themselves to areas of space where gravity is EVEN stronger.", "label": 0}
+{"snippet": "With Compton scattering the total momentum and the total energy of the photon electron system is conserved, so it has to be ELASTIC Collision/Scattering. But an argument is that just because the kinetic energy of the incoming photon is different than the outgoing photon, it is INELASTIC Collision/Scattering. However, I thought we had to look at the system, which is the photon and electron interaction; not just the scattered photon itself. So, what is the real issue here?", "label": 0}
+{"snippet": "If one plate of an isolated charged parallel plate capacitor is earthed, then that plate must have a potential zero after being earthed as that is what earthing an isolated conductor does, but potential on each plate is only due to the charges on the other plate. Since the other plate(the one which is not earthed) is isolated and non-neutral, potential due to it on the earthed plate should not change. As surface charge density on the unearthed plate cannot be zero... how on earth will I manage to get the potential of the earthed plate to be zero without changing the charge on the other plate?", "label": 0}
+{"snippet": "In the dimensional analysis, relationship of dimensionless parameter is? Above is the previous question I asked. I kinda understand that relationship of dimensionless group can be more complex. However, I was taught using the above method to determine dimensionless groups. Then how should I interpret the last equation? It seems to me that the groups are related by multiplication. Is the method wrong or does the above equation doesn't actually mean equity but shows the fact that they are somewhat related?", "label": 0}
+{"snippet": "So I've heard that all finite abelian groups are isomorphic to direct sums of the integers or of integers modulo a power of a prime, then you get that all extensions of reals are basically the real numbers or the p-adic number. Is there any such theorem for the rationals? Any other way of creating numbers that is not some vector space or an algebra over the reals? The way the complex numbers are just two dimensional real numbers and the grassman algebra is just an algebra of the complex numbers. I gues what I am saying is, is there any other way to do multiplication that is really new? Not having a copy of the natural numbers embedded inside?", "label": 0}
+{"snippet": "Zenithal perspective projections are generated from a point P and carried through the sphere to the plane of projection as illustrated in the figure below. By a simple geometric relationship, we can show that the radius satisfies the following: with . The inverse equation is given by: where I could reproduce the first equation but not the second one. I think the derivation is purely based on algebraic operation of the first one but I have no idea how. Does anyone have any idea how to derive the second equation?", "label": 0}
+{"snippet": "Okay so by the definition of a wave i.e The osciallatory disturbance in a medium which propogates energy is called as wave..the stationary wave contradicts both the crieteria as it doesnt propogate nor does it transmit any energy. Now one may say that a stationary wave is made by two progressive waves with same phase, frequency and amplitude superimposing in opposite direction..and we know that compsition of two waves is also a new wave..by that conclusion the stationary wave must be a wave..but it contradicts the definition of a wave So what do we call the Stationary Wave as? this was asked to me by a physics proffessor and i am pondering since. wave", "label": 0}
+{"snippet": "In my physics high school lecture my teacher taught the concept of electromagnetic induction under diamagnetic materials (though not completely disregarded it in ferromagnetic substance but as a characteristic property of diamagnetic substance) but the typical high school numericals that are in my textbook consist of conducting ring (as resistance will be low so due to induced emf an induced current is easy to imagine). So is electromagnetic induction possible in ferromagnetic ,antiferromagnetic substances etc (ie it is a universal phenomenon, independent of magnetic properties of material) or is it dominant (or observable) only in diamagnetic substances (ie depending on the magnetic properties of material)??", "label": 0}
+{"snippet": "We know that volume is cubicly proportional to radius of a sphere. But if the radius is become half due to relativistic Length contraction, it's being reduced from only one dimension, not three. And the object is not a sphere any more . Does it mean that the volume in that case is directly proportional to radius? And is density inversely proportional to the square of radius? (Since the mass is increasing by same multiple as the radius decreasing?", "label": 0}
+{"snippet": "Usually, when we study algebraic topology, we learn a lot of theory with just a few examples, like compact surfaces (orientable or not), wedge product of many circles, and a combination of those. Are these any slightly more complicated but special examples which shows important facts about the truth/falsity of some interesting statements? I find that I need to know more examples, but I do not know where to start. Some reference would be helpful. To be more focused, I am mostly interested in just singular homology and spaces with \"low dimensions\". To give an example of something which is more specific, for instance, examples of spaces with homology different from the examples above would be interesting.", "label": 0}
+{"snippet": "Arrow orbit around point C like graph show. Is motion of arrow, rotation or curvelinear translation according to physics definition? What is definition and types of translation and rotation? I find this: \"When the paths of motion for any two points on the body are parallel lines, the motion is called rectilinear translation. If the paths of motion are along curved lines which are equidistant, the motion is called curvilinear translation\"", "label": 0}
+{"snippet": "Can anyone suggest a reasonably generalisable way to generate these marginal drop caps? The key features are that the drop cap may be more than one glyph long its width is scaled to fill the margin (minus a bit of white space for legibility) its height is scaled to a user-specified whole number of lines (nb. the first example spans five lines and the second four).", "label": 0}
+{"snippet": "Our pre calculus teacher told us to start our mathematical investigation and he gave us three topics to explore to formulate a problem, a title and a our own formula that is novel or cannot be found in the google. Our group decided to focus on the third topic that was given which is algebra. So I would like to ask for help if you could give me ideas on what to research and come up with a problem/situation involving algebra. Thankyou", "label": 0}
+{"snippet": "I made a guess two years ago. I have a strong feeling that there is a proof using the fixed point theorem with geometric visualization, but I couldn't do the proof. If you have a simple closed convex curve, thr line Perpendicular to the tangent on the curve at both ends must be present If this feature is already known, please point to a reference that mentions it If you can prove it would be appreciated, thanks", "label": 0}
+{"snippet": "Bases for vector spaces are non-unique. Also, new bases can be generated from other bases very easily and formulaically. Is there some \"prototype\" basis, which we could find for every vector space, that defines a specific relationship between the elements in and across the different vectors for every possible basis for the vector space? In the same vein, how generally can we specify what a basis looks like for some vector space?", "label": 0}
+{"snippet": "My sense is that it never means an actual physical defect as in, \"The quarterback's knees were shot -- he could still throw, but he knew that to management he was damaged goods.\" Or can it be used in the case of concrete damage to a person's body as the above example? It seems like for a simple medical issue, the term is too nebulous and indeed would be used when the extent or classification of the problem is not so clearcut, like some psychiatric problem that most people do not fully understand.", "label": 0}
+{"snippet": "I cannot simply know where to use \"port\" and \"interface\", because these two words translate into one same word in my native language. So, I wanna figure out the difference between \"port\" and \"interface\", and when and where to use which. In my understanding (please correct me if I were wrong), the physical things, such as the holes on the side of laptop into which you plug the power cable are called \"ports\", whereas the visual holes inside the laptop, such as the signals transmission connection are called \"interface\"?", "label": 0}
+{"snippet": "I'm Finding it hard to visualize how higher pressure makes the boiling point higher. I understand how pressure increases then temperature increases such that say air molecules compressed gives it energy and then the molecules move fast and average kinetic energy increases hence temperature increases. But When we can say pressure increasing the bonds between molecules can easily be broken with the external force , but it somehow takes more temperature to disassociate bonds such that it transfers into a gas?", "label": 0}
+{"snippet": "Let assume a metal tube open on one side having alpha emitter material on the other blocked side. Since alpha particles are blocked by the metal they will be emitted only through the open side and make thrust by the momentum of the alpha particles. Very small one, but continually accelerate the satellite. Partially depends on other question - how alpha particles are emitted from in depth of a chunk of material, aren't they blocked by the outer layer of this chunk?", "label": 0}
+{"snippet": "It seems like 'my sister and her' are both subjects so it should be 'my sister and she'... And it would be if they worked on something specific together (the obvious object). Eg: My sister and she work on this project. But the \"together\" at the end changes everything right? Unbundling the sentence it is clear that it is actually saying \"my sister works with her\", making 'her' the object. In this case should it be my sister and her work together? Does the together really change the object?", "label": 0}
+{"snippet": "I am given: Five points on the ellipse, The sharing center of the ellipse and the circle, And the circle. One of those five points is one of the intersections of a circle and an ellipse. Can we construct the three intersections of an ellipse and a circle that is not given? Blue ones are given, and greens are the points I want to find.", "label": 0}
+{"snippet": "For a conductor in an external field, I would like to know whether the electron clouds of each atom, just shift slightly (resulting in positive charges just on one edge, and negative charges just on the other with all internal area remaining neutral). Or, whether the electrons fully dissociate, leaving positive ions throughout the conductor volume but with all electrons on one side. If this second case, then how would the electric field work out as zero inside?", "label": 0}
+{"snippet": "Question: When we only listen to the sound of that machine (TV), not watching its screen, which is appropriate to say \"listen to the TV\" or \"listen to TV\"? Background: When we watch that machine, we say \"watch TV\"; and when we put it work, we say \"turn on the TV.\" I think these usage indicate that we use \"the\" when the object is material thing not function. But we say \"listen to the radio\" or \"listen to the music\", so I wonder about the question stated above.", "label": 0}
+{"snippet": "I had the following problem with the index: The alphabet order of the words in English: I have the order of capital letters come first then the order of small letters come next. I need the order to come according to the letters regardless of being capital or small. For example: Abed Dep Ced amid bned I need those words to be like: Abed amid bned Dep Ced The next issue is: I have one gap in the index as shown in the below picture", "label": 0}
+{"snippet": "I only recently thought about this, and I can't come to any conclusion. An explanation for ferromagnets is perhaps explainable, and my teacher said Quantum Mechanics complicates things since the magnetic behavior is distorted, given for ferromagnets their origin is the spin of the electrons. But what about materials that are magnets but are not ferromagnets, for whom the origin of magnetism is not spin? Any of my reasonings is too vague for any explanation. If anyone can lead me to a source where I can read about this, I would be very grateful.", "label": 0}
+{"snippet": "In my notes the axiom of extensionality is that 'two equal sets contain the same elements', this language suggests to me that there are two different sets that happen to be equal, which suggests there is an infinite number of sets with the same elements. I see this definition given many places and it causes me some confusion. This seems to defeat the point of equality, which usually defines the 'same value', the above seems incorrect then, is it just a choice of language and clearly there exists only one set with a certain group of elements, or can we have two seperate sets with the same elements?", "label": 0}
+{"snippet": "From school we know examples of energy conversions: from electromagnetic to electric, from electric to heat, from heat to electromagnetic, etc. However, obviously this almost has nothing to do with conversion, because as heat, as electricity, as friction, and so on are electromagnetic field energy. But what if there is some electrically charged and massive particle moving at constant velocity and being accelerated by gravitational field, and not electrical. Will it emit (scatter) gravitational wave (quants) instead of electromagnetic, or both? Also in opposite situation, same particle, accelerated by em field radiates photon, only because of electromagnetic interaction, or it emits photon (and gravitational waves) independently on the type of interaction?", "label": 0}
+{"snippet": "I recently learned that we always break components of force along and perp to direction of net acceleration (for simplification) So in problems involving circular motion.... We resolve forces along centripetal acc So in problems involving vertical circular motion...we break mg along centrifugal force(ofc working from non inertial frame) But in problems involving banking of road w friction....we break centrifugal force along and perp to mg ...Why so?? We should have broken Normal and friction along centrifugal force", "label": 0}
+{"snippet": "Huygens principle. can we accordingly define refraction to be diffraction from an infinitesimal length slit? According to Huygens principle, sticking to classical physics terms. as long as slit length is at most a wavelength, spherical form of waves is maintained. If we look at propagation inside a homogeneous medium the shape of waveforms is maintained and we can claim \"mono-refraction\". So is diffraction actually a mono-refraction through an infinitesimal length of slit? As a thought experiment...", "label": 0}
+{"snippet": "In PowerPoint, there are often nice three key point diagrams like (source: https://www.slideteam.net/performance-mapping-ppt-powerpoint-presentation-portfolio-graphics-pictures-cpb.html) or (source: https://www.slidegeeks.com/business/product/three-levels-relationship-marketing-examples-ppt-powerpoint-presentation-ideas-display) My question is, how do I best generate such diagrams in LaTeX for usage in beamer? I assume this will likely involve TikZ? Ideally, some guidance, if possible even a MWE could be given to create a similar nice diagram. That way, also LaTeX users can make use of such styles. One central node on the left, like in the first example Three (or even better, a flexible amount) of child nodes arranged around the central node (to the right of it) Text entries next to child nodes like in the second example Color style like in the second example", "label": 0}
+{"snippet": "From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we choose some point, around it in all directions, properties are the same throughout the end of the material from that point, but image taken from here, still says material is isotropic.", "label": 0}
+{"snippet": "I know about the conditional sentences that go as following: \"If I were he, I would have forgotten the whole lesson.\" In the sentence above, \"he\" is preferable to \"him,\" but can it also be preferred in the following case? Whom can I trust, if not ___. a) he b) him I pardon, if this is related to conditional sentences. Quora has similar question but with very short answers, as in: Edit: I don't think my example sentence is concerned with relative clause, rather the first part of the sentence looks independent: \"Whom can I trust, if not he\" contains comma between them. And how does following sentence is related to the above sentence: If I can't rebuke him, whom should I rebuke. (Does 'him' makes sense here?)", "label": 0}
+{"snippet": "the xelatex compile output will automatic write some output in content folder, when compile in the root of project, there contains a content folder and it works fine. Now I tweak my command and add the -output-directory parameter like this: xelatex -output-directory=/Users/xiaoqiangjiang/Downloads/cquthesis/out/ main.tex the out folder did not contains the sub-folder content make the compile failed. the error looks like: ! I can't write on file `content/introduction.aux'. Is it possible to make the xelatex compile command auto create the content folder in the output new out folder? because all the compile process was automatcially running by robot. I can not created the content folder by hand one by one.", "label": 0}
+{"snippet": "Is this grammatically defective? The rides were fast and long, as well as exciting, despite my apathy. Context: I often find myself writing sentences that I don't want to reorder but may contain an error, and am ignorant of grammar, if not absolutely naive; I have confused chat-gpt, asking it this. Background: I understand, I think, that it would be: You can either do \"The mayor, as well as his brothers, is going to prison\" or \"The mayor as well as his brothers are going to prison.\" but am reluctant to admit defeat yet.", "label": 0}
+{"snippet": "I am a student in robotic assocciation and I designed working spectrometer for UV-Vis emission spectrum. The issue is evoking emission spectrum. The spectrometer is designed to be working on board of martian rover. Can I evoke the emission by shining the rock samples with UV lamp or X-ray lamp? We can't use laser beams or burn the sample due to onboard safety. Are there any other methods of obtaining one?", "label": 0}
+{"snippet": "I had a sentence like this in my manuscript: [describing some limitation] .... Some studies worked it around by combining the results of two models ... in the sense that those studies made a workaround for the limitation. The native speaker changed the bold term to \"worked around it\", but I am almost sure I know the original form (from the IT world, where workarounds are a very common topic :)), and also can find it on the Internet. But I can find his version too, I just like the original one better. Are both acceptable? The result is supposed to be in US English, if it makes a difference. (Note that this paper is not in the IT area, but the statistical modelling methods in ecology).", "label": 0}
+{"snippet": "Suppose a straight current carring wire of finite length if kept in a external magnetic field (perpendicular to its length say dot). I know initially it would experience a magnetic force of magnitude ILB due to drift velocity of charges inside wire but now the wire would gain velocity , but if I use lorentz law to find magnetic force again what way the wire be doing motion.", "label": 0}
+{"snippet": "It is often recommended to the particular symbol from MnSymbol that you require instead of importing the package entirely such as the answer by @egreg. What is the general process of doing this? What if I need several symbols? Is there a difference, say, if I need an arrow vs. delimiters? Not really a question, just a complaint: seems crazy to me that I need to do this just to get a few symbols from a package that offers them.", "label": 0}
+{"snippet": "Wikipedia claims for the proof of Arrow's Impossibility Theorem that when Every voter in segment one ranks B above C and C above A. Pivotal voter ranks B above A and A above C. Every voter in segment two ranks A above B and B above C. (B and C may switch for segments one and two but not pivot) by IIA the societal outcome must rank A above C, as in the previous case Why is this true?", "label": 0}
+{"snippet": "In the light clocks, time ticks via the motion of light and since speed of light is constant therefore when the clock is in motion ,the photon has to cover a greater distance by the perspective of an object at rest . So in the perspective of object in rest time ticks at slow rate but in other clocks such as mechanical clocks .time ticks via the motion of different objects not light. and the speed of the objects are not constant.so from the perspective of an object at rest time ticks at the same rate. How can be this possible as time dilation affects all clocks?", "label": 0}
+{"snippet": "So this was a test question, I answered that both cars have the same acceleration. Since the graphs for A and B both are straight lines, therefore, the acceleration of both must be zero. But the answer given to us was that both are moving with same velocity. These graphs are not always to scale, so I thought that the d option would be more appropriate than c. The beginning of the test says to mark the most appropriate answer.", "label": 0}
+{"snippet": "In the solution to this question, they have first taken the component of downwards-acting gravity(g) along the incline which is the sin component then again they have taken the component of the gsin along the x-axis and y-axis. Now my question is how are we supposed to take the component of a component and why not just g in the downwards direction used for calculation of centre of mass?", "label": 0}
+{"snippet": "Say we have a plate full of soup, why to cool it down we move the spoon around in the plate? Is it to facilitate the thermal interchange between the air and the soup? Also why is the edge of the plate always cooler than the center of the plate? It may be because of how close it is to the plate so it exchanges heat with the plate?", "label": 0}
+{"snippet": "are modus ponens and tollens axioms if not how can they be derived or proved? if I am good at math then I am good at logic, I am good at math, therofe I am good at logic this seems evident but is there any proof for them? looking at the truth table for implication we see p->q is true when P is true and Q is true", "label": 0}
+{"snippet": "I'm trying to name categories on my online shop, I have a category for whimsical items, kids, etc. I'm trying to name a category for items that have actual day to day functionalities. For example, a suction cup used to fix car dents. Thus: Manual lint remover Manual fruit juicers Car back seat bag with pockets Scratch removal device for cars... These products, _____s, are mainly cool looking items, all with special functionalities.", "label": 0}
+{"snippet": "This question about how to choose a singular or plural verb for sentences with number as the subject has been asked a few times here. Nonetheless, will ask again for the following sentence: The number of each type of fruit (apples, oranges, and bananas) is chosen based on the published price. This answer The number of students is larger and this answer A number of questions have been asked describe that the definite article \"the\" indicates that a single number is chosen. In this case, three numbers are being chosen: one number for each type of fruit.", "label": 0}
+{"snippet": "For college, we are supposed to hand in uncompiled .tex files for the teacher to make the .pdf themselves. However, college computers have very few packages installed ; but I have heard somewhere that one can include the package along with the .tex source. I cannot find a guide on how to do this, can someone explain how or provide a link for me ? I am not asking how to normally use packages, rather how to include them for compilation on a system where installing packages directly is not possible.", "label": 0}
+{"snippet": "Good day, I am a lay person in this field So i am very sorry if my question Is dumb. I am wondering whether the Hypothesis H formulated by Schreiber and Sati stating that C-field is charge quantized in J-twisted Cohomotopy theory doesnt assume already existing spacetime manifold And a C-field which would together constitute the ontology of this theory? Doesnt this go against ideas of Nima Hamed And others who would like to create a deeper mathematical structure from which both spacetime And Quantum fields emerge?", "label": 0}
+{"snippet": "Premise: Verb 'want' is normally (?) stative We use adverbs when we have an action verb and adjectives when the verb is stative In sentence \"I want it bad(ly)\" we would use the adverb 'badly' and not adjective 'bad' --> \"I want it badly\" (correct) From that we can infer that the verb 'want' is then an action one. But is this really true? And what action does it describe here? Furthermore, where/when can we use 'want' as a stative verb then?", "label": 0}
+{"snippet": "By Definition Electric field vectors point in the same direction as the electric force that a (hypothetical) positive test charge would experience, if placed in the field. Electric Field Lines are generated by connecting all of electric field vectors together, forming continuous lines and curves. What does electric field line actually represent My search tells me it represents the path any charge would take but then force vector direction is tangent? but it is not a path taken? Fact ref what is paradox here. How is magnitude of the field, indicated by the field line density? ref seems that the this representation is the cause of my lack of understanding? What am i missing here?", "label": 0}
+{"snippet": "I am currently doing some writing, and constantly try to create smooth transition and ease of readability and linkage between sentences. This sentence feels like it kind of halts the reader a bit. Albeit although assemblers are not commonly discussed as much as the two language processors, they are, however, equally important in the pipeline. Replace 'are not commonly discussed as much as' with something that virtually means the exact same but, might be a single word.", "label": 0}
+{"snippet": "I have a bulleted list which describes how to write an effective bulleted list, and is itself an example of all the tips in the list. Terms in this area that I have found so far are: autological / homological self-referential recursive Is one of these best, or is there another term (single word or phrase) that I can use to describe this list? e.g. The ____ list above is...", "label": 0}
+{"snippet": "I know this question has been asked before, but I can't find an old reference on this subject, so feel free to point to my duplicate post if you have a link to an older post. Working with LaTeX, PDF and git is a real headache because at each compilation, the binary PDF file changes but not the visual PDF if no changes are made inside the associated LaTeX file. How do you produce the same PDF after compiling the same LaTeX file several times? Is this type of solution bad? (I have a worse solution for hiding the PDF in git, but I'd like to omit it).", "label": 0}
+{"snippet": "I just got a higher algebra book written by Barnard for a couple bucks. But as I was scrolling through, I found two things that did not make sense. Can anybody tell me the meaning of them (the pic is given below) ? What is that 'L' shaped symbol under the numbers and variables and why is there a limit with \"nothing approaching nothing\" ?", "label": 0}
+{"snippet": "Knowing the strength of concrete you can get the mass of an object put on a concrete block is able to withstand on given area. As for a falling object, kinetic energy itself doesn't translate to force, so the force decelerating the object while collision occurs is somehow defined by material properties of the block (for simplicity, the object does not deform). Is it possible to calculate fall height of the object at which the concrete block will not undergo permanent deformation? And what the coefficient of restitution would be?", "label": 0}
+{"snippet": "I am looking for a bell-shaped periodic function f(x) with parameters a and b, with following characteristics: ( not sure if such function already exists or one can formulate one ) : oscillating between zero and a constant non-negative number A. Width of bell can be modified through parameter b. customizable period of c. Preferably easy to calculate its integral Obviously such function should look like a spike with lower b numbers and conversely turn into square-like with larger b. I tried playing with Gaussian and normal distribution, it satisfies the first two requirements but fails to drop to zero at periodicals of x = c. something like the picture below any suggestions highly appreciated !", "label": 0}
+{"snippet": "Is there a way to avoid division through size n in ift (ifft) ? Performing the Inverse (Fast) Fourier Transform on the complexnumbers, you go with a for loop through every element dividing it through the sizeof (dimension) of the array, to complete the last step of the inverse fourier transform. Is there a (more efficient) way to go without it ? Division is computationally expensive.", "label": 0}
+{"snippet": "If you take empty space right next to a black hole once in awhile, you will get a positive particle being admitted in the opposite direction of the black hole. In the creation of the photon this demands that a negative energy is supplied in the opposite direction of the positive particle which would be into the black hole. But why can this not happen the other way around?", "label": 0}
+{"snippet": "is there already a technology that provides one-way viewing glass with no regard to whether the back side is lit or not? the case is: two rooms (A and B) side by side, people in room A want to see directly into room b without room b knowing, all the while room A must be lit all the time of viewing is there such a glazing solution for this problem?", "label": 0}
+{"snippet": "I've been reading various papers relating bounded gaps between Primes, sieve theory, Carmichael numbers and the like and Thomas wright's papers stood out to me as being very well written and yet proving non trivial results. I found his papers to be a good way to also get interested in a topic such as his paper on siegel zeroes and K tuples Conjecture. It like seeing math tools in action before finding out what they are. Are their any other authors who struck you as such? Maybe their papers taught you a lot or felt very deep in ideas or just very well written?", "label": 0}
+{"snippet": "enter image description here I calcultaed this integral in three different ways. contour integral, fourier TF and obvious way. I've seen this integral depends on distribution. if we just calculate this with normal way, apprently it diverges, but given (Schwartz) distribution, it's gonna be dirac-delta distribution. I also solved this integral with complex contour integral. but in this way, it concludes -i which contradicts above conclusions. so here are my questions I assumed that this integral just depends on how we tackle. Am I correct? Is the last way with complex integral correct? Thank you.", "label": 0}
+{"snippet": "The chorus of False Disposition begins with this line: When a boyish constitution gets to lead the revolution, everything about this seems a bad idea The definitions I have found for 'constitution' mean either: some sort of document or rules, or an attribute possessed by a person or thing. Neither makes much sense in the given context Is there another definition which fits this line better?", "label": 0}
+{"snippet": "If we think about inertial mass and gravitational mass as independent concepts and develop physics then we would know after a while they are only propotional (by precision we have by now). but it seem physicist say they are equal. when in history they became equal? two guesses: Newton himself says gravitional force is propotional to product of inertial masses and doesn't bring to play another thing such as gravitational mass. then this gravitional force itself acts on inertial masses and produces acceleration. this two masses were propotional and somewhere in history physicist changed units to coefficient of proportionality became one.", "label": 0}
+{"snippet": "The theory only deals with the local curvatures, not the global topology. Hence any manifold with an allowed metric is allowed. These can be infinitely many, especially for negative curvature space-times. From So I suppose for the same physical situation, there would be many manifolds from which it can be studied, then, how do we choose on which manifold that we actually do the calculations?/ find the manifold that fits for that scenario?", "label": 0}
+{"snippet": "When charge moves at a constant speed, it is said that it produces static magnetic and electric field. Why static ? If it moves, at every points, electric field and magnetic field change as they are dependent on a distance to the point. So even if charge moves at constant speed, we still should have electric and magnetic fields changing in every point in space.", "label": 0}
+{"snippet": "Assume that you are using the FAST algoritm for corner/feature detection. You pick an image and run the FAST algorithm. Question: All these green dots are actully coordinates in x and y direction. What type of rotational invariance information can I get from only knowing the coordinates that are created by the geometical shapes inside the image? For example: If we measure the angles between every point, the angles are going to be the same, no matter how we rotates the image. NOTE This is a feature detection algorithm, sometimes one or more coordinates can flicker e.g some green dots disapear and appears few milliseconds after.", "label": 0}
+{"snippet": "When a perturbation makes open and closed channels coupled and A closed channel's bound state energy is lower than an open channel's contiunum enrgy, a coupled state energy (e.g. spin triplet and singlet) is higher than the open one by Secondary perturbation. I think it is described as a repulsive interaction and it prevents atoms from creating a molecule. But moleculu is stable because of having lower energy. It confuses me. The open channnel is coupled with the state which has lower energy. Intuitively I feel like the energy is going down and the Molecule is easily formed.", "label": 0}
+{"snippet": "I am self reading textbook \"Visual Complex Analysis\" by Needham And I am unable to \"solve\" this part . Like in terms of understanding I have a good image of how these translations and rotations happen but I don't know how to actually like write it in mathematical form I got where this k come from but I have no idea where c comes out Similarly i am trying but i cannot figure out what p should be ? Similarly this v here makes no sense to me and i cannot interpret what this means ? So plz help?!", "label": 0}
+{"snippet": "Just a thought from a dream Since water expands so greatly when frozen could it be possible to freeze the water in a metal cylinder but one side is like a car piston with a very high gear ratio which would be no problem to turn because the pressure the ice builds up which generates electricity to freeze the water again and repeat (Would doing this test in a vacuum help or?) Please someone debunk me", "label": 0}
+{"snippet": "I'm writing a game theory book, and I've wrote something like this: As it can be seen, that mathematical expression has been splited into two lines. It surely can be fixed, by making some spaces' width more, and if needed, leaving a little space for the expression to appear in the next line, as latex sometimes does. How can I force it automatically do it when needed?", "label": 0}
+{"snippet": "So we know that EMF of the battery provides an electric field in the circuit and thus accelerating the electrons inside them, so my question is that lets say if there is a perfectly conducting wire, so there the electric field will continuously accelerate the electrons(as no resistance if there for them to collide and make them lose energy) and we know that nothing can go beyond speed of light, so will there be a current in the circuit or will the current be just too high? I looked for the explanation at many places, but everywhere people just say that such a wire is not possible, but what if it is?", "label": 0}
+{"snippet": "Can then resultant vector pass through the vectors being added? Does the order in which place vectors according to head to tail rule matter? let's suppose that vectors A and B are pointing east while C is pointing south. is it necessary that we place A and B first according to head to tail rule? because if place A first then C, then it gives a resultant vector that is passing through the vectors being added", "label": 0}
+{"snippet": "Can English have words that are both alliterations and also rhyme? is looking for the sets of words that I want to put a specific term to. Sets of words such as: divide, deride, decide alliance, appliance dusty, dirty I'm wanting the missing word in These words X with each other where 'X' is something more comprehensive than \"alliterate\" or \"rhyme\" because they don't encompass that the other pattern is occurring too. Minimal pair is close, but that allows single phoneme variation in any location, not just the middle, and wouldn't allow a hypothetical set of four-phoneme words that vary in their middle two.", "label": 0}
+{"snippet": "i have a question about numeral systems that use the place value concept , in the decimal system the position is a power of ten and it has set of ten unique digits, the binary system its position is a power of two and it has a set of two unique digits and so on for all systems that use the place value concept my question is why the position value depends in the number of digits ? why cant we have a system that has n unique digits and use a position value different than n let's say m for example ?", "label": 0}
+{"snippet": "if there is a block on top of an unfixed inline. and if the system is released from rest what is the acceleration of the block and the incline? can someone draw fbd and show? the difficulty in this problem is that you can't figure out the normal force and stuff like that. This is not an a= homework question, I'm genuinely curious about how to draw the fbd.", "label": 0}
+{"snippet": "Imagine we have a double walled sphere from an insulating material.(So like an outer shere with smaller sphere inside it) If we insert a fully ionized gas inside the space of the double wall could we theoretically \"trap\" inside the sphere protons for example? Will the electrostatic forces the electrons feel from the gas when near the wall of the sphere be enough to stop them or they need a classic electric or magnetic field to be contained?", "label": 0}
+{"snippet": "I would like to have a list of documents to read so that a newcomer can start working on Latex Programming. What would be a good material sequence to read (e.g. described by documentation section names) and study ? Naturally, on things that are freely available, no books to purchase. Some have suggested the question What is the best way to learn TeX? But I want to focus on the latest way to program; for LATEX.", "label": 0}
+{"snippet": "I need a reference for the proof of the bordered Hessian test. I know how to use it, but I kinda learned it \"in the wild\" and need a standard good reference for its proof to add to my references section. I tried to google for it, but I only found tons and tons of manuscripts teaching how to use it via computation examples, with no proofs/books.", "label": 0}
+{"snippet": "As we know there are two way test a hypothesis. One is critical value method and the other is p value method. I've discovered that its very difficult to calculate p value in hand besides there are some statistical tools to calculate p value instead. But my professor will not let me use statistical tool. If I follow critical value method instead to solve problems more efficiently and easily will it be wrong? As there are two methods available. And is there any shortcut way to calculate the p value in both t and z test please help me to find out. Thank you and apologize for making the this long.", "label": 0}
+{"snippet": "I'm working with ascelike-new journal template (located here). The editor asked me to remove figures from the submitted pdf. Since the journal uses an online system to compile the uploaded tex files, and I cannot manually delete the pages with the figures. I tried many existing solutions (examples here and here) and was unsuccessful (the tried solutions either put a frame or hide the figure and its text references). Is there any way I can remove the figures and list of figures and keep references in the text?", "label": 0}
+{"snippet": "I have read other threads. However they cannot solve my problem. Anyone has any firm knowledge about how could we do that? I have a limited time and I dont know why my supervisor insists on word file. Actually does anybody have any idea whether wiley accepts latex original file for the revision process? The editor asked for word file but I believe he forgot to mention latex. How come for initial submission they accept latex but for revision they mentioned just word? I might get answer here g ask editor. Please do not answer like that since we could not ask directly from editor for many reasons.", "label": 0}
+{"snippet": "Using an unnumbered ruler and a caliper you should Construction of two Focus for conic section with five points. The difficulty is that the conic is not drawn, only the five points must be used I was interested in this question in the past and I am asking it now for the sake of knowledge sharing because I think there are a lot of people who are interested in getting the build steps, I will not put the full details of the solutions because it will be too long but I will put simple signs and graphics, you can add more details in the other answers...", "label": 0}
+{"snippet": "If mass does not interact with charge, why does the mass of an electron move (means by which mechanism it moves) in an electromagnetic field? It is same like we stick ball on magnet with fevistic and than that magnet move due to magnetic force towards other magnet also that ball moved with that magnet it moves because of sticky force not magnetic force right ?? So there is some force in first place that bound charge with mass right?? so mass moves with charge in electromagnetic field due to that mustric force that bound charge with mass and not moving under electromagnetic field interaction .sir please tell am I right or wrong ??", "label": 0}
+{"snippet": "I have walked. I will walk. I walk. All of these immediate verbs have infinitive forms in to walk, to will, to have. Thus one can naturally say you seem to walk, you seem to will to walk, you seem to have walked. But what of the case of I would walk? The closest grammatically proper construction that I can think of would have to be you seem LIKE you would walk. See titular question", "label": 0}
+{"snippet": "Light exists with energy E = hf. That is supposed to be quantized and discrete but maybe \"f\" in the equation is continuous when not emitted specifically from an electron (moving through the g well). But light exiting a gravity well loses energy and is red shifted. What about light at the frequency of one in a decent gravity well? As it tries to exit, it would lose energy, but it may get to a point when that energy is zero. Is it reflected back into the well? Does it kick around within the energy well that it can exist in because it can't leave?", "label": 0}
+{"snippet": "In this Youtube Short it was mentioned a way of constructing a shape that followings any curve one could draw. Apparently the motivation to construct it is to do the following, roll a sphere of clay as it rolls on the curve (on a paper). The identations would cause it to exactly follow the curve. ...but...why? Why does the intendations cause it to follow exactly the curve that caused it's indentations?", "label": 0}
+{"snippet": "Suppose we work in GR, then space time is four dimensions, but, if we have a mechanical system with a high number of degree of freedoms, say five then how would we fit it into a four dimensional space time. Now that'd obviously be impossible, it'd suggest that the sense we talk about dimensions of physical system is different from that of the arena. But, how exactly?", "label": 0}
+{"snippet": "in our physics lessons we often learn how to calculate the time that sound of a plane that travels faster than sound takes to reach us using the Mach cone. But can we use the same method to calculate the same value for a plane that travels as fast as sound? Does it make a cone? I would be really grateful I f you could explain this with some examples.", "label": 0}
+{"snippet": "I would like to create a pack of graphics to highlight the simple interest rate gain like below. The blue, or any color available, would be the initial capital and the green the gain month by month. Hopefully coming from a math formula but not required to be, it can be static also. How can it be done? The pie chart is not big deal but the histogram with two colors is the hard one to me.", "label": 0}
+{"snippet": "I'm asking myself a question related to temperature integration. First is possible to integrate a temperature distribution over the time and over a certain volume? If yes, these resulting integrals which physical quantity are representing? For example, the integral of the temperature over a volume can represent the Internal heat energy divided by the specific heat and the density of the volume (assumed both constant)? While the temperature integral over time can be assumed as the opposite of the heat flux density?", "label": 0}
+{"snippet": "Say you have rising steam forming water on some surface and when the water accumulates, it forms a drop that falls because of (I suppose? Not sure) Mass exceeding the force of surface tension. Does the material on which the steam gathers influence the size of the drop when its mass is heavy enough to make it fall ? If yes (pretty sure it does), what criteria allows to calculate that specific point where a drop is too heavy to hold onto a surface ?", "label": 0}
+{"snippet": "I can understand, how it is constant after awhile, that due to the range of strong nuclear force the force is increasing linearly with the linear increase of the nucleon number, making it a constant. But At the beginning, shouldn't the same would have been take place, the energy required to bind the nucleons per nucleon be constant as it is still inside the range of nuclear force, only in the heavy elements the range is exceeded and the nucleons does not possess enough binding energy as before contributing to the decrease in binding energy per nucleon. Why is it in the start increasing?", "label": 0}
+{"snippet": "When building electronics to measure usually it is asked what the bandwidth of the signal is and what is the frequency range usually done to limit noise bandwidth and thus have more SNR. To me it seems like measurements are preconditioned, I know what I want to measure and I limit my equipment to that expectation. Why there is no paradox in the sense that I prepared the measurement to measure what I expected and then I measured what I expected?", "label": 0}
+{"snippet": "I am asking this question only because I want to figure out does space move in this case similarly to a fluid like water or oil are or even more better as speeds o planets around a star.. or this phenomena has a different formula describing a complex effect caused by the gravity as a force deriving from S-T curvature? Thanks in advance for an 'easy to understand' answer....", "label": 0}
+{"snippet": "This site has lots of similar questions like mine, there is force just instant strike after that object moves freely, so my question is not like these. Rocket engine produce continuous force at one end of rod in free space. Initial condition: rod is at rest, not rotate, not translate in relation to space station that is near him.(Neglect tiny gravitation due to mass of station and neglect rocket fuel mass loss) Will rod when RPM increase enough end up in pure rotation around CoM or CoM will orbit aorund center of smallest circle? Is this left trajectory of Euler spiral, path of rod CoM? Fersnel integral Like this?", "label": 0}
+{"snippet": "I want to illustrate overlaps in three sets, similar to how one of these standard color plots [do they have a name?] look like except that I want to choose my own colors and different text [not C, M, and Y]. (I want the inside most quasi-triangle to be a red, the area outside of the plot to be a green, and the partials [both three inner and three outers, though different] have some sort of mix colors. presumably a little bit lighter, because I need text in each intersection, too, that needs to be readable.). the idea is to show that when all three things come together, it's bad. a trifecta. maybe I need a graphical artist rather than latex...or is this somehow built in?", "label": 0}
+{"snippet": "If we draw a curve of a function without drop the pen then the function must be continuous or not?I am confused with it. If there is curve for which some portion of the curve parallel to y axis at any any x then there have many value for single x and we can draw this curve without drop the pen then the curve is continuous or not?", "label": 0}
+{"snippet": "If simple CFD softwear like XFoil and OpenVSP use the panel method to find an estimate of the drags and lifts/pressure distributions. How do they find drag and lift if the panel method works based on invicid flow? I thought that there can be no drag or lift created in a complete invicid flow which i think i do understand. (I am awear its obvious the panel method cant calculate purley from itself the skin friction) But it is not at all obvious to me regading any form/induced drag Im at university but we mostly just use the softwear/equations, but i recetly take the time to actually try understand the working/derivations so apologies theres something obvious missed.", "label": 0}
+{"snippet": "before I write the an article, I would like to roughly partition the text. The sections and images should be where they are in the final article, with white space where the text is supposed to be. For that, I would need placeholders that consists of a certain number of white spaces, which automatically reduce as soon as I add real text. (I load the single chapters as single files into the main file and maybe here \"filling up the text with white spaces\" is possible) One could hence compare it to a \"Latex-form\" for the text. Does a package or a method like this exists?", "label": 0}
+{"snippet": "Suppose we look at the surface of a lake and see a reflected image of high-altitude clouds in the sky. The distance of a cloud from the lake is far more than the depth of lake. So then how can an image be formed? I know that we see an image formed into the lake because still water surface of lake can be treated as a plane mirror. But in this case, how can object distance be equal to image distance that happens in a plane mirror? The height of cloud will be kilometres, but the depth of cloud will be a few metres.", "label": 0}
+{"snippet": "forward implication f is continuous therefore it is bounded hence u is bounded hence u is a continuous. Reverse implication: f is expressed as function of u(x) - i((uix)) u is continuous and hence real part is continuous imaginary part contains scalar I therefore it is also continuous. and hence f is continuous. f(x)=u(x)-iu(ix) u(x)=Re(f(x)) <= |f(x)| ||u(x)|| <= ||f(x)|| now define k(x)= bar of f(x) / mod of f(x) |F(x)|=k(x)f(x)= f(k(x)x) = Ref(k(x)x) = u(k(x)x) and ||kx|| <= ||x|| and I don't understand how to proceed ahead", "label": 0}
+{"snippet": "If we take two balls that change colours white and black, if we set that change in colours is always opposite one from another, for sure if we take one ball to the end of universe, if that ball will have black colour and second will have white colour.. How we know that spin (black and white balls) are not set from start when two entangled photos are made?", "label": 0}
+{"snippet": "I have been thinking about this situation, I have no idea how the normal force act of such a body. Here I have taken the point mass and ring of same mass m but please provide a general solution. So I will state it as a question: How will normal force of the floor act on the ring of mass m and radius R, with a point mass on it when released is the same position as I have given in the picture. And ofcourse gravity is acting on it, take it g.", "label": 0}
+{"snippet": "P= Pulling Any reference for the gradient of Normal Reaction. Will pushing the weight lead to reversal of gradient? Does this mean there is gradient of friction force (as it depends on normal reaction)? While it seems that based on irregularities the reaction developed should be different at each point of contact between surfaces which would lead to different friction & normal force magnitudes at each point as illustrated in which supports intuition.", "label": 0}
+{"snippet": "I am reading measure theory in Rudin Book and in one of the its proofs, it is derived from an equality which exists between four sequences that this equality should also exist on four Limits. I think it is resulted from this fact that sum (and so difference) of two convergent sequences converges to sum of limits But I feel somehow unsure in this case. Can some one describe equality on limit more for me? Thanks in advance This is the sequences and the limits:", "label": 0}
+{"snippet": "If we have any simple object like sheet,rod or sphere with uniform charge at them, is electric field at surface always finite? For sphere I read that it is finite because as test approaches the surface the area patch which can cause infinite field at a point is also getting smaller hence charge on patch is also getting smaller. So it is applicable for all case and if not why not?", "label": 0}
+{"snippet": "And what if the line that being fitted has an additional constraint of avoiding certain points while making the polygon? Is there some specific fields I need to be exploring? For instance, set theory. The points that forming a polygon can be a set, and points under constraint condition can be another set. Another thinking direction was convex optimization of set points with constraints. PS: I do not mean fitting of line as in machine learning.", "label": 0}
+{"snippet": "I think that would be a very helpful website where you could search for a theorem or topic and get instantly a list of proofs published by the users no matter where they come from books or made made by themselves and were each proof of the list will by ranked by votes so each user will ideally vote by the most accurate or easy to understand proof", "label": 0}