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For the converse, while I agree that the point will be on the pependicular bisector, we can't assume the line drawn is actually the perpendicular bisector... yet the above textbook example assumes it is. I don't see why, based only on XA=XB, we're allowed to conclude that XY is perpendicular to AB and YA is congruent to YB? Surely to make the given conclusions we'd need to state that if two points are equidistance from the endpoints of a segment, those points determine the perpendicular bisector - what am I missing? | 0 |
I have been told that galaxies will never stop rotating because conservation of angular momentum But, there are planets inside of it can travel through dense nebulae and bodies of gas that would cause friction (and probably brake their travel speed through the Galaxy). Wouldn't that brake the galaxy's rotation? Also, gravitational waves can be emitted by rotating massive objects that have uneven mass distributions by so called quadrupoles or higher poles in their angular momentum. Also, in this study (https://www.space.com/dark-matter-slows-milky-way-rotation) they showed evidence that the galaxy rotational speed is decreasing due to dark matter. Then, would galaxies (and all their contents: nebulae, stars, planets...) ever stop rotating? Or they would only decrease their velocity but it would stabilize at some point? | 0 |
I want to write a formula and put on its right side the description of its variables. Here I just screenshoted the two parts and put them side to side with figure environment but I want to write some "code" that puts it like that but not with screenshots or pictures or anything like that. Is it possible ? And if yes, how can I do that ? | 0 |
I'm reading a textbook that gives both a "weak" and "strong" formulation of optimal control (first is a control function, second is the whole space, filtration, Brownian motion, and function etc). The textbook has a theorem about existence of optimal controls for the weak formulation and makes explicit that the strong formulation is not equivalent to a classical control problem. However, no existence theorem is present for the strong formulation. | 0 |
Let us consider a metal clamp which is placed rigidy and is placed parallel eto the ground. Now on the both ends the plates of a capacitor are kept such that they are parallel to the ground. A dielectric is kept in between and slowly released from the clamp. Also a battery is connected to the circuit so as to always keep the voltage constant. So the question is that we had to prove that the dielectric executes periodic motion. My approach We can find the change in capacitance and hence change in work done by the battery. But i am confused so as to how a restoring force could act? I s it due to the battery? | 0 |
If you have a square two-dimensional grid, that are lots of ways it could be triangulated -- for an individual square one could add an edge from upper-right to lower-left, or from lower-right to upper-left. For an ensemble of squares, a choice of extra-edge direction for each square, so lots of choices. I can think of a couple of reasons to triangulate a grid, to perform a linear interpolation on simplicies, and I read that algorithms for finding sinks and sources generally assume a triangular mesh. For these (and possibly for other) applications, are there better choices of square-grid triangulations? Pointers to the literature on this would be much appreciated. | 0 |
I was studying duality maps in my Advanced Stat. Mech. class and it was told that all self-dual points need not correspond to critical point. I understand that critical points are points where analyticity of the partition function breaks down. If this point is unique then it can be given by the duality relationship between the constants which appear in the theory. But what happens if this point is not unique? | 0 |
The system I am trying to model is essentially moving water interacts with ferrofluid. The ferrofluid is in a box that contains air and ferrofluid, such that the setup is buoyant. The ferrofluid chamber has outlets so that it can interact with water. Here's an example image of the system: I need confirmation in these aspects: That the right choice here is to model it like two phase flow not single phase or mixing model. That it can be modelled by either level set method or moving mesh method without compromises in results. If I do not want the fluids to mix, is there a way to still maintain pressure balance between them? Would a semi-permeable membrane work here? If not, is there any other way? | 0 |
I have been having this doubt when applying the Divergence of a Electrical Potential evaluated in a point, and then doing the Divergence to get the Electric Field in that point. But is this valid? or I have to do the Divergence first and then evaluate? Because when I do the first thing I get the correct result, but the process of which I get the solution is triggering me a little | 0 |
Is it possible to use punctuation marks such as commas, periods, and question marks just before colons or semi-colons? The error appears when accessing some URLs, e.g.: List items ... Can I set additional parameters for the following tasks?: List items ... I occasionally come up with such sentences due to perhaps my mother tongue (Japanese). However, I realised that such usages can't find anywhere so it might not be natural usage for native speakers. Any natural alternative ways to write it? | 0 |
It is well known that a convex function is minimised over a convex set, if and only if there is a subgradient which is inwards normal to the set at that point. i.e the negative subgradient (direction of steepest decrease) points directly out of the set. Is there a corresponding rule for maximising a convex function? i.e is beig maximised at a point equivalent to having a subgradient that is normal outwardsto the set at that point. i.e the direction of steepest increase points directly out of the set. | 0 |
A neutron is udd, then an u-anti-u starts to exist close to the neutron. Then the one d and u change places forming an uud (proton) and anti-ud which decays to an electron and electron-antineutrino. Now it is my reasoning that since this process exists the process can be sidestepped so that a udd decays directly to a uud and electron and electron-antineutrino. Is this true? | 0 |
I wonder how would we go about to calculate centripetal/centrifugal acceleration for relativistic objects moving at near the speed of light , do we use the original acceleration = force/mass, or input gamma factor for it to be , Acceleration = (gamma) force / mass , Acceleration = Force / (gamma) mass Which one is valid ? If both aren't is there a particular way and/or equation to calculate centripetal and centrifugal acceleration for relativistic objects ? How ? | 0 |
Is there a package or option that starts alternating row colors from within a table, so that no matter how many manually-colored rows are inserted, the alternating can be started again with the same color each time? (In a single table, I want to manually color a few "heading" rows, each followed by an undetermined number of alternating gray/white rows -- always starting with gray.) | 0 |
This is something I have noticed on a fairly regular basis, and this is a recent example, where the questioner starts by saying "I'm working on" and ends up asking "How do we...?" Can someone help me with this circuitry? I am not an electrical engineer. I'm working on a brain/organoid computer interface system . . . How do we connect the cyclone . . . Is it some cultural thing? Is there a mechanism to it, like that if others are included they feel more inclined to help? | 0 |
I'm writing math notes, and I would like to use the symbol for the letter T that appears in this picture (seen in a TeX.StackExchange post): click The symbol I want is in the line "Calligraphic: UPRIGHT: euler (Euler script)". How can I load it? Note that I'm not interested in changing all symbols in my document. I just want to use that T perhaps once in the entire document. | 0 |
Elliptic Integrals and Jacobean Elliptic functions I know it is easy to determine u =F(x,k) where F is elliptic integral of the first kind knowing both x and k. I know it is also possible to determine x = sn(u,k) where sn is the Jacobean Elliptic function knowing only both u and k. Is there a function to determine the modulus k only knowing u and x? | 0 |
Fox's Trapezoidal Conjecture asserts that the coefficients of the Alexander polynomial of an alternating knot alternate and the sequence of their absolute values forms a trapezoidal shape. The same is true for the Jones polynomial for some alternating knots that I checked. However, since I didn't find an analogous conjecture for the Jones polynomial, I expect that it is not true for some known knot. Which one? Was there proposed perhaps some more narrow version above conjecture for the Jones polynomial of alternating knots? (Either with stricter assumptions or with relaxed conclusions.) | 0 |
What word describes someone who is extremely carefree to the point of risking their lives. The person is not even bad or annoying; in fact, they are vibrant & outgoing. Except they don't extremely carefree to the point of risking their lives. I was thinking of "extremely carefree" or even "unhinged". For example, That girl who got stabbed at the club was______; She was outgoing but extremely carefree to a scary point. | 0 |
Here is the situation. Let's say I have have a mass of a given liquid and I heat it to create a gas. The gas has a lower density than air, so it will move higher and higer in the atmosphere. Then, I recondensate this gas into liquid. Suppose both process are ideal, so the energy I put in the system to cause evaporation is the same energy released by the system from the condensation. We now have the same liquid as before, but since it moved up in the atmosphere, it now has a muche bigger gravitationnal potential energy than it previously had. Of course, the energy is conserved, so this additionnal potential energy must come from somewhere, but where? | 0 |
I am writing an application in which I complain that every time I point out to the cooks or their supervisor that the meal is not up to the mark,and actually show them how it is, they say that no body else complains, only I complain. However, whenever I ask my colleagues about this, they tell me that what I am saying is valid, and they also point it out all the time. So this is a habit of this staff to gaslight women employees like this. We have put up with this for years. Therefore, I'll really appreciate if someone can help in this. I need a synonym of gas-lighting which conveys the intent properly. | 0 |
There is no scenario where we can use Coulomb's law. There is no static charge. Even if we consider the local charge density to be constant for a system of charges, the individual charges are still moving, and as we know they are not quite the same. Moving charges show different effects. Even if we think about putting a frame with the particle so that we can consider the charged particle as static that also does not help because there is no single frame for a system of charge Also we want to measure the effect in our lab frame. So, how is Coulomb's law still relevant? | 0 |
Often you have to adjust the table of contents manually. With very large documents, it is then very time-consuming to compile the entire document each time just to be able to look at small adjustments to the table of contents. Is there any way to tell LaTeX to compile only the toc and not the document? Or maybe you can copy the toc file of the actual document, rename it to the jobname of a small test file and then let it compile, sort of without the associated document? | 0 |
Say we have a hot cup of coffee that is giving off steam. It is releasing heat into the environment through radiation and conduction. The steam is from certain particles reaching a high enough kinetic energy as to escape the attractive, intermolecular forces that bind them intrinsically. If we physically inhaled steam, thereby increasing the rate of heat loss through steam, would it effectively cool the coffee? | 0 |
In steady state condition of a conductor under normal temperature, we find that the derivative of drift velocity is zero by setting electric field equal to zero, and one concludes that current density is proportional to the electric field. But in case of superconductor, why don't we have such a steady state condition like thing or in other words, why cant we have a unique solution by setting electric field equal to zero, as in two fluid model of superconductor, one finds that the derivative of current density of super electron is proportional to electric field and not the current density. | 0 |
Why are there two interior regions in this diagram? There seems to be two inner horizons, and two wormhole regions. Where do the two such regions comes from? What determines which reason someone falls into? Could a composite body fall into "both regions" with part of it going into one region and part into the other. The diagram seems to indicate that if you're precise enough you can fall almost directly from the Black hole to the white hole while spending an arbitrarily small amount of time in either of the Wormhole regions. | 0 |
I would like to consider the sound incident to a water filled pipe wall. I think the pipe wall is typically considered as a rigid wall boundary, it means all the incident wave is reflected. Is this assumption is correct in real world? I think if the sound inside the pipe is large, we can hear the sound from outside the pipe. In practical, what kind of boundary condition should be assumed for the pipe wall? | 0 |
Using thesisdown to write my Masterthesis I was wondering about the default indentations of the package: If you check the pictures below, all the pages (of the default 'knitted' thesisdown rmd-files) have different indentations (holds also for the toc). On a first glance my guess was that pages with a heading have a certain indentation, whereas the following pages don't have any indentation. This theory also holds for the toc. But imo it doesn't hold for the first picture. So I ask myself: is this indentation behaviour intended or is it an 'unwanted' side-effect? And is there a way to unify the indentations for all pages? | 0 |
I am reading Middlemarch by George Eliot. I encountered this long sentence and only understood the gist of it. I can't figure out the grammar style and I am looking for the verb of the subject "he". Here is the sentence: Thus, the mind of Frisk was exactly of the sort for Mr. Solomon Featherstone to work upon, he having more plenteous ideas of the same order with a suspicion of heaven and earth which was better fed and more entirely at leisure. Why does the sentence have "he?" | 0 |
There are projective sets in descriptive set theory. For them, the axiom of determinacy is not contradicting the axiom of choice. Given the axiom of choice, every set is a projective object. But in a world without AC, is any projective set a projective object in the sense of category theory? Or did those terms happen to use the same word and there is any counterexample? | 0 |
Assuming the object positioned in front of the mirror at some point on the principal axis before the focus, each point of that object emanates light in all directions, so what happens to the rays of light that do not fall parallel to the principal axis and those that pass through the focus, do they not converge at some point in space? Do they diverge, not forming a sharp image? Why is a real image formed in a concave mirror considered only the two rays of light, the one that falls parallel to the principal axis and the one that passes through the focus? | 0 |
During the rotation of the Earth, a centrifugal force is formed, according to the actions of which ocean water should be collected at the Equator, forming a "hump" hundreds of meters high. However, there is no water hump on the Equator. The depth of the ocean does not depend on latitude, although there should be such a dependence. at the same time, the centrifugal force is sufficient to deform the shape of the earth from a regular sphere to a geoid! | 0 |
For a given game, is there any relationship between the computational complexity of weakly solving the game and strongly solving it? I ask because a weakly, but not strongly solved game with simple strategies to guarantee at least a draw could still be interesting to play if the players place little value on a draw, and do not know how to win if their opponent is also trying to achieve more than just a draw. However, if simple strategies weakly solving a game guaranteed simple strategies strongly solving it, then this point would be moot. So, if for a given game, as some parameter scales up we have a weak solution of a particular complexity class, can we bound the complexity class of a strong solution? | 0 |
When I saw factorials, I immediately thought about Wilson's theorem. However, I didn't succeed at all. I also thought about cyclic groups, but with such amount of information I haven't find the use of them. How can I prove it, where to start at least? Source of the problem: practice for exam made by my teacher in the university. Motivation is simple - I want to see more abstract algebra ideas since I don't even know how to start correctly. | 0 |
As a non-native speaker I currently have a doubt about something. I am writing a technical note about units of measurements (kilogram, meter, second...) and physical quantities (mass, length, time) for software (and I am talking about abstractions in software architecture) and I am note entirely sure whether I should write : Unit and quantity abstractions Units and quantities abstractions when talking about "the software abstractions of units and quantities". Is only one of them grammatically correct? Or if both of them can be correct, what is the difference and which one should I pick? | 0 |
Is there an adjective or shortish expression for an item that is "not known to be needed". Context: at the beginning of a process, all items are "unknown as to whether they will be needed or not", so all items are "X". As I progress through my process, at any point in time I may realize that some item is now or will be needed for sure. At that point, the item moves from "X" to "needed". Chat gives "discretionary" :) , good but not quite... | 0 |
Magnetic field lines are loops, so at the surface of a magnet pole they look like this? there is a dead zone at the center where there is no lines/magnetic field present? Or lines converge in the middle to a single line or point? like so? Which picture is correct? also on some googled pictures I can see a single straight line coming from the center of the pole that goes nowhere... I know that lines are really an mathematical artifact, I just want to know how the field is shaped near the surface at middle of the magnetic pole. | 0 |
I believe that Star Trek has advisors so that their science has at least a tenuous theoretical basis. The latest episode is based on interacting with an "improbability field". Is this just gibberish or is there some conceptual basis in quantum field theory? The only reference I can find is in this book that says which entails the process that allows for the development of Multidimensional Geometry through its use of Vibrations, the actual nature of Numbers and Math as a whole, the formation of Particles and Fields, and how Quantum Entanglement is instrumental to that | 0 |
So I came across this game called "Getting over it". It is a game where you propell yourself upwards with a hammer, sticking it into various places to keep it in place. My question is, if you were to do the same thing in real life, how would the force applied by you onto the wall above you lift you up? You can check the game if you want to understand what I mean. | 0 |
I am writing lecture notes for a course I am teaching. A Module on Matrix Computations involves a special mathematical expression and I have no clue how to typeset in LaTeX. I have enclosed an image of this calculation and I request your kind help how to typeset it. There is a special type of arrow in this image, and I have never seen it listed in the standard list of arrow commands in LaTeX. I thank you for the kind help! | 0 |
Is Point O called the center of the half disk (informally, semicircle)? It's not the centroid since it's not at the center of mass. I'm not sure if it should be called the center if it lies on an edge of the shape and it's only the center of the full disk. I've never seen an official term for it for just a half disk. Does anyone have an answer for this? | 0 |
I have a game in which pieces normally get tiled in an arrangement like this (which can be shortened or extended arbitrarily): But in special circumstances a piece may be permitted to be placed in between and on top of the other pieces, like this (red circle shows the one piece placed on the corner of four other pieces): I'd like to briefly describe this placement something like this: A red piece may be placed _____ in relation to normal pieces. What the best, short, clear way to describe this placement? | 0 |
A pipe with a pump and two open ends is placed under water. When the pump is initially turned on, will the pressure at P_out and P_in initially rise/fall, but then stabilize as a flow of water V_flux develops (and the suction pressure is equal to the pushing pressure at all points)? The assumption is that the pressure from the pump first travels as a compression and rarefaction wave, and then once those meet and a flow forms, they cancel out to some extent. | 0 |
Can anyone tell me what are the relevant pieces of information that are required to find the amplitude of a speaker membrane for a particular input ac signal frequency and voltage amplitude? Could you also show the method by which I can achieve that? Do I need to do an energy balance? Does that mean I would require to know the elastic modulus of the material of the membrane? Or is there any other predefined parameter of the speaker usually provided that I can use to get around that kind of calculation approach? | 0 |
As Photons do not experience time or space, then according to my thought experiment, all photons must occupy some kind of singularity as well as what WE observe from earth. I was also thinking that the faster you travel the smaller the universe becomes and although you experience time, that time is dependent on the observer. I'm trying to get my head round this (I have no science background) It appears to me that the universe is at the big bang all the way to what we observe at the same instance | 0 |
The text defines the torque of a particle system as being connected with the axis of rotation. "Taken two particles of masses m connected to a thin rod of negligible mass etc", but later when the text explains the torque due to gravity defines the torque of a body as the point of origin (I assume that the axis of rotation is orthogonal to that point, right?), but should I guess this body is connected to the axis of rotation or not? However, in the case of a torque due to gravity, how should I imagine point O? Because in the end the axis of rotation passes through the point O and belongs to the body, right? | 0 |
It is clear that infinitesimal strains are obtained from finite strains (e.g. Green-Langragian or Eulerian-Almansi tensor) by removing nonlinear terms which smallness order is greater than that of linear terms. But it is not clear for me whether such a procedure is justified, if we bear in mind that finite strains are subject to differentiation when plugging their into the equilibrium equation. After all, the contribution of nonlinear terms in equilibrium equation can be significant, as the derivative of function can be much greater than function itself, even if that function is considered to be sufficiently small. | 0 |
I found a metal rod lying on the floor and I found out that it sticks when brought closer to a steel sphere like a magnet, but, neither the sphere nor the rod is a magnet. More astonishing is that the sphere sticks to the rod to only a single side of the rod and not the other side as if it was a uni-directional magnet, but none of those two objects interact with any other metal objects and the rod and the sphere are not repelled by a permanent magnet either. Please can anybody explain this anomaly. | 0 |
I recently came across this document which I am trying to recreate, and this is what I'm dealing with: I have no clue where to start in trying to replicate a header and footer like that, I new to LaTeX classes so I'm not really sure where to start. Youtube is pretty plain on this topic and Overleaf learn section doesn't help me much either. I really want to create a .cls file in order to adapt it to other related documentation... If anyone could point me in any direction it would be great, or if you already have some experience and easily recreate it yourself, that would be awesome! Thanks in advance! | 0 |
I understand numbers to be defined as objects defined to have certain convenient properties in relation to certain operations. It is very surprising that the exact same group objects should be applicable to the modelling of such seemingly disparate concepts as length, area, degree, cardinality, time, wavefunction, etc. I also find it surprising that the qualities of numbers, which appear quite contrived, should correspond to anything real in the first place. How can I make the relationship between these concepts and the concept of number more intuitive and expected? | 0 |
A signal in additive noise is sampled by a receiver with an unstable clock. Maybe the clock has absolute bounds on its frequency drift and sample time aperiodicity, or maybe the clock has some statistical characterization (maybe an Allan variance). Maybe the signal being sampled was also produced by such a system. Can anyone recommend any brief treatments on this situation's signal model, its spectral analysis, and efficient (or typical) signal processing approaches in this domain? I notice there is a brief Wikipedia article for "Coherence theory (optics)" which is closely related, if not more general. | 0 |
For example, suppose a spaceship explodes. The sound of the explosion will travel in the expanding cloud of escaping gas. I gather that it should rapidly weaken and the pitch should drop, but I'd like to get more specific than that. Are there any models that suitably describe precisely this sort of situation? Additionally, is it feasible for there to be a relatively safe distance away from such an exploding spaceship where the expanding gas cloud isn't yet extremely rarified and an audible sound might actually be heard through your space helmet? | 0 |
There are two facts about elementary row operations and column/row spaces: Column space is affected by elementary row operation, whereas row space is not. (the issue of finding a spanning set of column/row space) Linear dependence relations between columns are preserved over elementary row operations, whereas the same between rows is not. (the issue of finding linear independence between columns/rows) In finding the column space or row space, we lose and gain something in either case. I am not sure why this is possible intuitively: the issue of finding a span is linked to having linear independence between the vectors. Therefore, my question is a more conceptual one: why are the two above statements intuitively consistent (at least to an amateur like me, they seem opposing)? | 0 |
What is the exact difference between a moment and a couple? In some YouTube channels and books, they say the moment of a force produces a translational as well as rotational motion whereas the concept of couple produces a pure rotation. How and why is it so? I am not convinced about this yet. Once you fix your point of axis or rotation axis. How come when you apply a force the body would make a translational motion? | 0 |
My objective at this point is not to learn all and advanced mathematical proof concepts/techniques. At this point my objective is to get basic understanding of what is mathematical proof and learn only basic concepts/techniques behind them. Also, I need it to have as minimal prerequisites as possible. Best variant will be some article or tutorial or a small part of a big book. Can you please provide such material? | 0 |
My goal is to implement a mathematically correct multivariate normal distribution using Sobol QRNG sequence as a source of randomness. The implementation should NOT produce the whole set of a given size at once, but instead it should reveal next values one by one, also depending on getting new values out of the Sobol sequence. So the algorithm should be streaming the data with minimum memory requirements. This guy claims he implemented MVN out of Sobol, which is officially endorsed on the MATLAB website. However, he has another call to rand() in the middle of his code, so it feels he does not fully understand what he is doing. That's why I hope for your help with a strictly mathematically and statistically valid approach here on Math. | 0 |
For example, if you say New Orleans like "New Orleens" it's considered wrong, instead of "New Orlins" (Orleans is pronounced different in France though), or Iran like "I ran" is wrong, instead of "Ear on". But then people have names for other places all over, like Germany or Allemagne, instead of Deutschland, which would have their own pronunciation. An even closer example would be France, pronounced like "Fronce" for the locals, and closer to "Frants" for Americans. Maybe this is protested in France, I'm not sure. Or Greenwich, UK vs. USA (I wonder if each says the other should be pronounced like their own). But when does pronunciation of somewhere else become wrong instead of their own way of saying it? | 0 |
I read that the standard depiction of covalent bonding is misleading. It gives the impression that the valence electron exists at that bond site. But really it exists as a wave throughout the crystal. So is it a standing wavefunction that has a peak at the bond site? From this can we infer that conduction electrons have propagating wavefunctions? Furthermore, how is it that an electron can mantain its wave characterictics in a crystal? We know that oberservations (more accurately interactions) collapse the wave function. Certainly the electron is interacting with many potentials and forces in a crystal. | 0 |
Let us assume that the classical spacetime describes relative positions of mass particles, and the relative positions are in fact described by quantum entanglement. That is, the stronger the entanglement, the shorter the classical distance. If a group of mass particles are being pulled very close together by classical gravity, then can we argue that interactions behind entanglement become fuzzy and that infact weakens the entanglement, hence the classical distance can't be arbitrary small and gravitational singularities don't exist? | 0 |
I study the magnetic trapping recently. I met a problem. I consider the original quadruple magnetic trap. In the original quadruple magnetic trap, the magnetic vanishes at the center. The Majorana flips happens at the center. If we want atoms move in the trap adiabatically, the Lamor frequency must be larger than the trapping frequency of the trap. What does the 'adiabatically' mean and how come is the condition? I saw this statement in my lecture note and other prof.'s lecture note but I have no idea why it is. | 0 |
I have read the related discussion and some text and get some basic ideas. Geometrical interpretations of SVD Visualization of Singular Value decomposition of a Symmetric Matrix What I don't understand is why are we rotating twice? I imagine we only need to rotate once, and scale once? Is there any significance in the angle we rotate? One answer did say "the value of this is not too important as long as you pick a sensible number as the rotation matrices are not unique" which makes it more confusing to me ... | 0 |
I am confused about the curve carried by the train track. I am using two references: Mosher's note (via arcs) and Johnson's blog (via bands). By Mosher's definition, I wonder if or not, in the following picture, the blue arc is carried by the train track determined by the red and green arc (we can make the blue arc arbitrarily close to the train track). Similarly, by Johnson's definition, I wonder if or not the blue arc is carried by the train track determined by the bands from the red and green arc. | 0 |
We know that displacement is change in an object's position (here position means 'position vector'). Then velocity will be change in position of the object with respect to time, simply displacement/time taken. But I was taught that velocity is change in displacement with respect to time, then it means velocity will be equal to change of (change in object position =displacement) with respect to time. So, which one definition is correct? | 0 |
I want to understand something: when someone measure the pressure, temperature and specific volume of a material, I think the pressure is applied in all directions of the material. This can be understandable for liquids and gases because the pressure in a closed container and for instance, you can used a piston to increase the pressure in this system. What about in a solid? the pressure or normal stress applied in this solid doesn't mean that the stress in other directions exists, so what kind of equipment is usually used to measure and control this thermodynamic property (oressure) ? Or is my assumption wrong and is not necessary that all direction of the body to be applied the same pressure? | 0 |
I am not sure if I understand the energy band diagram correctly. In a pn junction situation below, before the p type material come into contact with the n type material as in figure a), an electron at the conduction band minimum in the p material has the same(or roughly the same) energy level as an electron at the conduction band minimum in the n material. Is it still true after they are fused together? If so, how come it is showing on the band diagram there is an energy difference as in figure b)? | 0 |
Many textbooks on tensors start with a sentence like "An equation written in tensor form is valid in any coordinate system." The second sentence is often "Closely associated with tensor calculus is the index notation." According to me, this seems contradictory. The first sentence seems to state that coordinate systems should be avoided while the second one emphasizes the need of a coordinate system. How far can we go in tensor (calculus) without relying on index notation? Are there books specifically following this approach? | 0 |
Consider no air resistance. If we throw a ball vertically upward from my point of view it goes vertically up and down and moving along straight line. But from point of view observer in outer space it is parabolic because of rotation of the earth. We know vertical acceleration/deceleration is due to earth gravity. But where component of velocity parallel to the Earth's surface come from to make parabolic path? | 0 |
In the book Then I'm trying to understand the reasoning behind constructing the matrix, I get the unique scalars P_ij part, representing the one basis's vectors with another basis vector's linear combination. But then he uses same matrix for getting another basis's vectors. I'm confused about this kind of reasoning and it appears in other proofs too. How these scalars i's and j's satisfy these equations? At this part, he uses same matrix but using j's and i's at the same time. Sorry this question is not clear but in general i am confused about constructing matrix P, can someone explain the reasoning? | 0 |
I thought about the question in the title for a ring that is not a Dedekind domain (here, the unique decomposition is a well-known theorem and also characterizes Dedekind domains!) but only a one-dimensional noetherian integral domain. The following is the motivation: In a Dedekind domain, every fractional ideal is invertible. Therefore, my idea is that actually the invertibility of such a fractional ideal makes a unique prime decomposition possible. Is this true? If yes, how could one proof this? | 0 |
I'm going to study plasma characteristics by using Particle-In-Cell (PIC) method and I know that plasma has fluid behaviour and can also consider as particle behaviour also. To understand a basic of PIC simulation, I would like to understand an origin of the PIC that why it used differential equation to describe plasma properties from Eulerian method? and what is the difference between Lagrangian and Eulerian method for plasma physics? | 0 |
When one says light comes on immediately when you turn on the switch of a flashlight cause the electric field is set up in the wire with a speed approaching the speed of light, what does exactly this sentence mean "electric field is set up in the wire with a speed approaching the speed of light" does the electric field travels from the source? If it doesn't how can it has a speed to begin with? Is there any sort of electromagnetic wave that originates upon turning the switch on that signals the farthest electron to move? | 0 |
How to cut the square which tessellates to octagon using straightedge and compass? What are the exact measures of colored sides? What is the angle marked with red color? Edit (I added vertices): Edit. Acknowledgement after answers. Thanks to Jean Marie, Blue and Daniel Mathias for tackling the problem. I accepted Blue's answer for its breakthrough, but I also weighed Daniel Mathias' solution for its geometric simplicity. Initially, I didn't expect the problem to be so laborious. I invite you to my puzzle in a similar flavor of dissections, which after many years still has no answer nor proof that the solution does not exist. Variation of Haberdasher problem of Henry Dudeney - dissection of equilateral triangle into square with flipping pieces | 0 |
What is the difference between the two sentences below? And what does the first sentence express exactly? Also, could you provide a grammatical analysis of the structure of the first sentence naming each of the parts of the sentence (which one is the subject/object, etc) and parts of speech (noun, verb, etc.)? We were here for a search of what the first sentence was in comparison with. We were here for a search of what we were comparing the first sentence to. P.S. We had an argument with a friend and we tried to present as objectively both sides as possible and refrain from showing any sides. | 0 |
Is the word multiperspectively (sometimes polyperspectively) only used to describe literature, as in narrative perspectives? Could I use it to describe a personal trait? For example: In debates people despise that I multiperspectively argue.... I did see a post asking what the word was for "seeing from multiple points of view" and this word didn't come up. Also, I understand this is a serious English site, my question is not for any scholarly reason. I am trying to write to a person and I got stuck while trying to find an adverb that means this. | 0 |
I have a Kalman filter that uses location as part of its internal state. This location is expressed as x, y coordinates in meters north and west from a fixed point (the home location). Part of my measurements for the filter are GPS coordinates. Can I translate the measurements back to the state space using the H matrix? The range of movement for the tracked object is small enough that I can use a fixed multiplier to scale the longitude to meters. But how do I add the transpose to the matrix, so that the GPS coordinates use the home location as the origin? | 0 |
I am self studying algebraic topology, the fundamental groups and covering spaces and homologous groups. I have read the topological properties of classical matrix groups like connectedness, path connectedness and compactness. Now I want to study the algebraic topological properties of these groups. In particular what are the fundmental groups of patnconnected components of the matrix groups? Does there exists any relation among the matrix groups via covering spaces? If anyone provide some referances regarding these questions that will be very much helpful. Thanks in advance. | 0 |
When an electromagnetic wave interacts with a free electron the electron starts to oscillate in the direction perpendicular to the propagation of the wave meanwhile when a photon interacts with a free electron what will the electron do? Will it oscillate in the direction perpendicular to the momentum of the photon? or will it travel in the direction of the momentum of photon? How can someone describe this interaction in photons form so that the electrons oscillates? | 0 |
In present tense or past tense, subject and verb can be omitted after conjunction. For example People tend to laugh when (they are) imagining pleasant things When (I was) going home, I met my father Then could it be possible to omit subject and verb in case of the past perfect tense as well? For example, As it had been written in a hurry, the report showed many errors. As written in a hurry, the report showed many errors. Or, because this case is of the past perfect tense is changing this way only correct? (Having been) written in a hurry (without conjunction 'as'), the report showed many errors. | 0 |
I live in this region and is studying to retake the national test and I need a big amount of tough exercises to practice but I can't find good documents/ textbooks over here. Any appropriate textbooks help me greatly. The topics are: calculus, algebra (especially logarithm), complex numbers, Oxyz algebra(?) (I really don't know what to call this one. It includes the equations of lines, planes, spheres, etc. And vector formulas. No matrices.). Thanks for your help. | 0 |
From the perspective of an electron in the double slit experiment, does the "rest of the universe" that it is disconnected from behave in the same manner as the electron does in our view? As in, is the world around it, from the electrons point of view, as a closed, separate system to be interpreted the way we see the electron? Is the effect relative? From the electrons perspective, could it be in a "collapsed"-state and consider only the universe around it to be in a superposition? I hope the question makes any sense, because I am really curious and a little confused about the whole thing. Thanks in advance! | 0 |
I was reading Lazarsfeld's Positivity in Algebraic Geometry, and I realize that Cartier divisor can have torsion elements, but I can't find such an example. I know for the Noetherian scheme that is locally factorial, the Cartier divisor is isomorphic to Weil Divisor and we know Weil Divisor group is free therefore it's torsion-free. So this can only happen when the Weil Divisor do not isomorphic to Cartier divisor is there any example that the Cartier divisor has a torsion element. | 0 |
Okay, apart from the American slang term, or the reference to a male chicken, what is the meaning of the syllable "cock"? For example, shuttlecock ... in badminton. Or, as I'm doing housework and learning about plumbing, a "ballcock" valve in a toilet, or a "sillcock" valve in pipes? Does it refer to a specific shape, or a mechanism or something? Which might make sense for the valves, but then what about the shuttlecock? | 0 |
I can't decide what I prefer - having empty space at the end of a page or a split box. For example: Should I be aiming to make sure the page is full with no need to break boxes? Like, I can add more text I probably don't need further up the page so that the last box starts on a new page, is this something people do for aesthetics? Or should I be happy enough with a break like this? Or the empty space? | 0 |
Consider the small weight is attached to a big diameter wheel and the big weight is attached to a smaller diameter cilinder. I've read that if you ignore friction and all the forces are balanced perfectly, you could consider the possibility of this machine lowering the lighter weight through the distance of one wheel circumference at uniform speed while the heavier weight is raised by the smaller distance of one circumference of the cylinder. In this situation, what would be the forces that balance out the differences in the gravitational forces that act on each mass? | 0 |
I know the restatable environment from the packages thm-restate combined with thmtools, which allows to formulate theorems that can be restated later in the document. Now I am wondering, if there is a similar solution for equations like equation, align, etc.. I have already tried to just reuse that restatable environment for equations, but as expected I got an error. I have already found "solutions" that suggestion to copy the content and tag the reference number. However, this seems to be a stopgap. | 0 |
I would really like to create these pictures to help with fractions. I know how to begin using tikz package. I am not sure how to go about setting it up so that I do not have to draw it separately each time. I would love to show something that I have started with but have no idea. And what if I wanted to make the rectangle horizontal and not vertical? Thank you so much for any responses! | 0 |
Suppose that I have two electrons in a box that were originally spread by a infinite potential wall. The two electrons are in their ground state wave function (sine function). Now I removed the barrier for the two electrons to interact. How is the Pauli antisymmetrical pair formed? Do I have to impose them to become the antisymmetrical pair in the beginning, or can I derive the antisymmetrical form from the original sine functions? | 0 |
If I were to have asked this question about local systems, it would be extremely easy to give examples from physics/biology, etc. I can give example if people want, but this should be easy to Google. Question: What examples of perverse sheaves naturally show up in nature? More specifically, I mean examples which are not local systems, and the example only applies to perverse sheaves (or constructible complexes of sheaves) and not sheaves of vector spaces in general. | 0 |
I am not sure why the following configuration can not be a configuration of a electromagnetic wave. I mean, i am sure it can not be the configuration of the fields in a plane perpendicular to a wave, but i can't explain the reason in a satisfactory way. Look, it seems there are souces propagating with it, since these configurations are the configurations of a point electri ccharge and a infinite line with current. But i would like i better way to explain why we can't have it. | 0 |
At a weight m, a plane is acceleration upwards at rate of a. We also remember the value of g. From my understanding, we have two opposite forces that we care about. The force due the gravitational acceleration, which points in the negative y-direction, The force of the upwards acceleration, which points in the positive y-direction. The first force must be equal to m times g, while the second would be equal to m times a. However, that is not the case with the upwards acceleration. My physics book gives this reasoning for calculating the upwards force: I don't understand why we would add g, since it points in the opposite direction? | 0 |
The question is simple. Could analog computers (for example, electrical analog computers) in effect avoid traditional numerical instability problems that come from solving a set of PDEs over a discretized domain? Progress on significant physical problems (the computational aspects at least) are often substantially delayed because of time spent figuring out how to avoiding numerical instabilities, and often the solution ultimately utilized is just to hit the problem with lots of artificial diffusion, which seems unrigorous at best. Also, since many physical theories are often significant approximations themselves, maybe some accuracy could be sacrificed (in moving to analog computers) for the greater benefit of avoiding numerical instabilities. | 0 |
To my understanding, normal reaction is a force that pushes in the opposite direction of gravity, in order to keep the object from falling, or phasing through the surface. Though, what happens when we enter a circular rail? In this case, the guide book is saying that the normal reaction is pushing alongside gravity. Then, shouldn't it fall down? I thought the normal reaction was supposed to be pushing upwards in this case. If not, then is the normal reaction always bound to the center of the circle? I can provide the exercise with the answers, in case there's not much details in there. | 0 |
A grad school problem has been haunting me for years and I have never been able to find it on the google machine nor was the professor who assigned the problem able to describe how to actually solve the problem... How do you find the surface area of an ellipse projected onto a sphere? The real world application is what is the footprint area of a satellite transmission signal so you know how long a ground station will be in contact with the satellite? | 0 |
Say a spaceship is traveling at a certain velocity v (>>c) and it emits light from the nose of my spaceship in the direction of travel. The speed of light is finite and hence there should be a change of wavelength of light. How does the speed affect the momentum transfer does my light have lower momentum thanks to the direction in which it has been emitted? | 0 |
My math professor told us that the upper and lower bounds theorem of polynomials (pictured) applies not only to rational roots, but also to the modulus of complex zeroes. They were unable to come up with an explanation for why this works, and I do not grasp this concept at all. Why/how does the bounds theorem apply just as well to to complex zeroes as it does to rational zeroes? How does the modulus come into play at all for that matter? Bounds Theorem | 0 |
I heard that if Universal Expansion continues at some point galaxies will be so separated that a future civilization would have no way to know there are other galaxies, for them the Galaxy they live in is alone in the universe. (I'm planning to write a sci-fi story about it). Thus more or less in what time frame would that expansion would cause that effect? Thank you in advance. | 0 |
I am new to it, so please help. As I know, AC current is back and forth motion of electrons, which radiates electromagnetic waves, so there is energy radiation from power line to our home. But in case of DC, if the magnetic field and electric field are static then how does energy radiate. I have searched that drift velocity of electron is slow, so DC flows at the same speed as of AC which is C. So, how does this happen if there is no radiation of DC? Please answer. | 0 |
I have a body on a horizontal surface with friction. My thermodynamics system is only the body and I want to describe this with the first law of Thermodynamics. Suppose the body has a start kinetic energy and for the friction in the final state it has no more kinetic energy. For this problem there isn't a heat exchange but only a work exchange caused from the friction. How can i write the fist law with this system? | 0 |
I have Two parallel lines, I want to create from one line to another using a cubic Bezier curve (S shaped basically), I'm free to pick any start point and end point. But the constraint is this path should be optimally shortest, also another constraint is I don't want the curves with too much curvature, I just want to switch to the other parallel line smoothly without creating too much curvy path. My question is how to pick start and end point? for having such a curve? I'm considering Bezier curve would be best for this with my very little research Thanks :) | 0 |
I was thinking about the definition of reversibility but there is something that I cannot understand. In real life the surrounding of a system (anything else in the universe) is always changing making impossible a reversible process even if the process is slow enough to guaranteed the lack of friction heat loss and this surrounding are not in thermodynamic equilibrium so I cannot understand how people calculated entropy under such conditions, am I wrong in the assumption of choosing the surrounding as everything outside the system or it is enough to choose the immediate surrounding that is in thermodynamic equilibrium? | 0 |
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