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 } and execute at end scope={} 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 \"