darklight03/StackMIAsub huggingface dataset:
I'm a mathematician currently working on a problem involving splitting a square into two triangles, either by a line connecting top-left and bottom-right, or top-right and bottom left. I'm trying to think of natural names for these, but the only thing I could think of was acute and grave (after the directions of accents, originally Greek I believe). Are there other options?
I am currently studying X-ray-emitting plasma pervading clusters of galaxies, and I see many studies employ an ideal equation of state to infer the pressure of the plasma. Is this the correct thing to do? Apart from this, it seems like an ideal equation of state is thrown around in astrophysics many times without proper justification. What do you think?
A "stable" is the compartment where an individual horse is housed. A "stables" is the building which contains multiple stables/horses. So the stables is a singular building, but the word "stables" is clearly plural, not singular... Example sentence: "Where else would you buy a horse other than a stables?" she said. Is this sentence grammatically correct? If not, how would you correct it?
I'm looking for different criteria of identity for the notion of 'set'. I know that the standard criterion of identity is extensionality but I was wondering if there are others. I looked around but couldn't find any literature on other criteria. I thought you could help me find some material on that topic? Thanks for taking the time. All the best, David
In one study, for instance, bar codes were placed on bees, tracking their activities. Is this correct? Or do we say... In one study, for instance, bar codes were placed on bees to track their activities.
If i have an electron and an antimuon is it possible that they could annihilate into a electron neutrino and antimuon neutrino? Am i correct in saying both spin and charge are conserved in this reaction.
We've been learning in class that when approaching a perturbed Hamiltonian with degeneracies you should try to choose a basis made of eigenstates of both the unperturbed Hamiltonian and the perturbation. But at that point, why do you need perturbation theory? Don't you now have the exact solutions to the Schrodinger equation?
I understand that superconductors have zero resistivity, however, I wonder if there is a relation between resistivity and the work function of a specific material so that a superconductor has zero (or a low value) work function. If so, photons with very long wavelengths can release electrons from the surface of a superconductor. Am I right?
Phonetic spelling is when one spells a word according to how it is pronounced (e.g.; knight => nite). What word would be used to describe the pronunciation of a word based on how it is spelled, ignoring silent letters (e.g.; knife => cuh-nife)?
I understand that a graph is connected if there is a path between any two vertices. However, I am unsure about the number of components of a graph. Is a single vertex considered a component? If yes, is it connected? In particular, what is the number of components in the below graph? Is it one or three?
I wonder how to best phrase this. The idea was to ask someone about their time zone. "Where do you live that it's morning for you?" The 'that' feels off / like a literal translation from Czech. "Where do you live where it's morning for you?" The double 'where' feels weird too. Are these sentences correct / do they feel natural for native speakers?
This is probably a very naive question, but is there something about Godel encoding that is essentially arithmetical, or is it possible to construct analogous mappings between the objects studied in a theory and statements in the theory itself for non-arithmetical theories (i.e, theories whose objects of study are not numbers). Are there any notable examples of this being done?
I was wondering if the word normal is redundant in the definition of a simple group. I strongly feel that there must be a simple group with at least three subgroups. However, I'm unable to find any. Any help?
I used to use Microsoft Word to draw this type of graphs, but it is not so convenient and it is difficult to be precise and accurate in details. Is there any better tool?
I heard my teacher stating that the base form of a verb is not an infinitive itself, but it is used to construct one of the two forms of infinitives. Edit note This question has been linked to a previous one of mine. However, in that question I was asking about the difference between infinitives and bare infinitives. This is a different question altogether.
I've been looking to understand linear algebra(vector spaces and subspaces) from different sources, then I came across the statement " the union of x-axis and y-axis" to the question "Give a set that is closed under scalar multiplication but not addition". I don't really understand how
I was wondering what's the order between mode, median, arithmetic mean, geometric mean and harmonic mean in a distribution with positive skewness and in another with negative skewness. Which are the theorems used to prove their relationship?
I am looking for books and papers that treat the physics theory of classical mechanics in a rigorous, mathematical manner. I would love to read such a text. Are there even such texts out there? I have already read physics books on classical mechanics, I am now looking for a rigorous mathematical text on it.
In Baldwin's "Model Theory and the Philosophy of Mathematical Practice" I read this phrase. The interaction between the syntactically definable properties of theories and the Boolean algebra of definable sets in their models is crucial. I was wondering what is meant by this "interaction", to me it is not evident that there should be such relation.
I just started going through this http://www.damtp.cam.ac.uk/user/tong/qft.html of QFT and I got stuck at the very beginning. The Lagrangian for the field is derived by: I think that the second step in this derivation is integration by parts, however after trying multiple times I still don't get what I need to get. Could someone explain what I'm doing wrong and provide step-by-step derivation?
I was watching a Lecture by Douglas Hofstadter on "Albert Einstein on Light; Light on Albert Einstein". And there was a slide which said that Einstein had idea that All periodic phenomena should have quantized energy levels. Can some one explain such idea? Thanks.
Recently I saw a video saying that due to the Pauli's exclusion principle there can only be a fixed number of electrons in a place but for photons it doesn't hold true as it's spin is different. So then is the number of electrons in an unit volume is fixed ?
I want to select a finite number of points on compact Lie groups that maximally cover the manifold in some sense. I have heard that some related aspects are Voronoi diagrams on manifolds and lattice structures on Lie groups. Any relevant literature on these topics would be appreciated.
How does a blackbody actually heat up and change temperature if it emits all the radiation that it absorbs by definition? And by extension, if the absorptivity and emissivity of a body are equal, then how is the temperature actually changing?
Does anyone know any good resources on the the Poisson kernel? I'm really looking for a measure theoretic approach to harmonic boundary problems. If anyone knows any such books, that would be much appreciated.
I have an assignment that requires us to make a continuous rollercoaster. we have to find the derivative of the functions we us and show that the gradients match. I have part of my rollercoaster done but I was wondering whether or not you can somehow connect an exponential function to the rollercoaster. Heres what my graph looks like atm.
For some strange reason, all the figures in a LaTeX document that I'm preparing are being put right at the end. This is despite me specifying precisely the figure placement in the figure arguments (with a ! too). How do I stop this from happening?
I was told the framing of a knot is the linking number of the push-off. But I don't understand why the framing does not depend on the knot but only on the parallel copy. How about a Legendrian knot? (I heard this is more rigid than a topological knot)
I have once heard that the definition of energy is "the ability to do work". However, that is a counterfactual definition, because a physical system can have that ability without actually doing work. So, has someone proposed a non-counterfactual, non-modal definition of energy? I want a rigorous definition.
Russians often use the formulation "take an integral". Now I noticed it in an article, written by a Russian and I can't recall I have ever encountered it in English. Is it a possible alternative to the basic "calculate an integral"? What other options are there? "Evaluate", "find", ...?
Hello Physics StackExchange Team, I want to know whether it is possible to experimentally determine the velocity at which the free liquid surface is moving/rotating in a cylinder with a rotating disk. The velocity at the free surface will be lower (in comparison to the disc speed) but is there any way to experimentally capture/calculate it? Please help. Thanks.
I've read many definitions for a transcendental number and some of them say that a transcendental number is a number that is not the root of any integer polynomial, while other say is a number that is not the root of any rational polynomial. My question is why such restrictions? Can't we just give algebraic polynomial instead?
I've read that if a state is a product state, the reduced density matrices are pure and if the state is entangled, the reduced density matrices are both mixed. What would it mean if you had a system of two particles, and when you calculated the reduced density matrices, one was pure and one was mixed?
What might cause the pdflatex output from a memoir class book to have two columns per page rather than one? Multiple columns can be used in some articles but not in a book.
In school, I was taught that a line segment must be finite. But a fractal has an infinite perimeter. If you just took two points along that perimeter, and "stretched it out" wouldn't you have an infinite line segment?
It is my understanding that the way cosmologists formulate theories like big bang theory, steady state universe theory, heliocentrism, etc, is by observing the sky using telescopes and imagining explanations for what they see. Are there any good books that I can read to learn more about these theories and the scientific processes that lead to them, that go into details?
How do I use LaTeX on an Android device? Can I make animations using it? If yes, how? I am new to stuff like this. What are some good sources and app for using LaTeX on Android?
I have two circular coils facing each other in parallel. Through one coil current flows. I move the second coil in a parallel fashion. What is the direction of current induced on the moving coil? Acc. to me, there should be no induced current as in parallel movement, the flux doesn't change.
Could you please help me to know why transfinite induction only works on well-ordered set and not arbitrary set ? Why the fact that every susbset has a least element is necessary for transfinite induction principle ? Thank you very much!
In software engineering, I sometimes see "first cut" in a context where it could mean "first version". Is it some idiom? Where does it come from? Does it mean literally "first version", or is there any emotional subtext, or did I misunderstand its meaning completely?
In an article of wikipedia, it is stated that : Charge is the fundamental property of matter that exhibits electrostatic attraction or repulsion in the presence of other matter with charge. I can't understand why there is "electrostatic" mentioned in this statement. Isn't there attraction or repulsion between two moving charge too?
There is a well known algorithm (Bhaskara-Brouncker) to compute the continued fraction expansion of the square root of an integer, using integer arithmetic only, no floating point. Is such an algorithm known also for square roots of fractions of integers?
A word for when an artist builds up their ability to paint, but over time their art starts regressing. Or perhaps a child, once magnificent at playing the guitar, begins to pluck the wrong string and slur the notes, eventually becoming mediocre.
Why is the construction 'I would love to' so commonly used, and is it grammatically correct? If the word 'would' cannot be used with state verbs like love, think, etc, then isn't this technically wrong? And why is it used so often?
In logic, why do we talk of universal closure of a formula, and don't consider its "existential closure" (as far as I know)? I guess that one of the reasons may be that interesting systems like PA are written down much more succinctly and naturally without the universal quantifiers. I think there might be more to it than that, though.
I don't know if this is true or not, I tried to prove and I didn't succeed and the I tried to give a counter example and I also failed. so can someone please help
I have a latex file and a website. On the website I have an input field, in which you can write text. Then when you click a download-button on the website I want that it automatically creates a pdf (with latex) with the value of the input field.
I've been reviewing the double slit experiment lately and I believe it is missing a few crucial things. Thickness of the wall is my primary focus. How could I add thickness into the equation? I'm interested in seeing the effect on a model.
Suppose that I were to jump on the surface of the Earth. The moment I hit the surface, shouldn't the force Earth is applying on me be greater than the force I am applying to it so that I stop completely? If the forces were equal, wouldn't I still be moving?
I hear about "The Graph Isomorphism Problem", and am a bit confused as to where the issue is. Isn't the adjacency matrix ( up to permutation ) unique for a graph up to isomorphism? Can't the problem be solved as easily as checking if two graphs have the same matrix up to permutations?
Is there a concept of induced subgraphs for directed graphs? I would intuitively think it is nearly the same as for undirected graphs. I was just thinking that it would be a subset of the vertices such that all arcs from the original graph from one vertex in the subset to another in the subset exists in the induced subgraph edge set.
From my understanding, within the context of the Standard Model, charged lepton flavor conservation is an accidental symmetry due to some renormalization condition. How does this work in the case of pair production? Would the result be different if instead the photon pair produced to an electeon neutrino and a muon anti-neutrino?
Suppose you have a closed differentiable plane curve. Are the tangent lines to the curve at the most distant points on the curve always parallel? What if we assume that the curve is convex? I don't see why this should be the case, but it also seems like it might be the kind of weird geometric property that unexpectedly turns out to be true.
In any path-connected metric space, can we connect any two points with an injective path? This seems possible, for instance by "removing" the points where the loop is not injective, but I cannot prove it. Is it true? If yes, how to prove it? If not, do you have a counterexample? Thank you very much, AF
If a quadratic form is represented as a matrix, it may not be symmetric, but there must exist a representation that is symmetric (or Hermitian if complex). But is the reverse true? That is, do all symmetric and Hermitian matrices represent a quadratic form (except maybe in the case where matrices are all zeros)?
As the question states, how would you calculate the t-statistics in GLS? Is it just the same as in OLS? And are these results still reliable? I have heteroskedastic data and so am using GLS, but I'm not sure if the calculations for t-statistics change or the values are less reliable?
What is the difference between "a memoir" and "a biography"? According to my study, "a biography of a person A" is normally written by someone else not A and "a memoir of a person A" is normally written by A himself. Also, "a biography" is quite detailed from birth to death while "a memoir" is not too detailed.
I'm curious as to the purpose of relativity and why the universe would function this way as opposed to a universe with an aether. So what would be different if we had an aether?
The product of two matrices A and B with dimensions (n,k) and (k,m) results in a matrix C (n,m). I remember that my professor used to call this rule after a specific person (I guess the inventor of that rule). Do you know how the name of the person is? Or how do you call that rule in general?
I know that Galois groups let us determine when polynomials are solvable by radicals, and that Lie groups can be used to solve some differential equations. Does there exist an analogous group theory method that tells something about the solutions of recurrence relations? I am interested in both existence/Galois type results and symmetry methods of solution.
I just learnt about Feynman Diagrams, and I've been going through many examples to practice the reading of Feynman Diagrams myself. I have already found diagrams for Positron Emission, Electron Capture, and Beta Emission decays but yet have not seen one on Alpha emission or Gamma decays. Can these decay mechanisms be expressed through Feynman diagrams, or am I just missing something here?
Assuming a charged particle moves at speeds near the speed of the light. Will the electric field generated by that particle get affected by length contraction and time dilation? In other words, will this cause a more dense field closer to the particle which declines faster with distance compared to a stationary charged particle?
I'm trying to optimize plasma cleaning process to be signal driven instead of fixed time. I have a vacuum chamber with hydrocarbon contaminants, I use air plasma for cleaning. Is there an option to terminate plasma, based on the amount of contaminants left in the chamber?
I would like to know if the thermal motion of molecules stays constant if the pressure is increased at constant temperature or not. The viscosity increases with pressure, thus the friction between the molecules also. If the thermal energy is constant, will the motion of the molecules decrease due to higher friction?
I have a question about whether or not to use the plural for a noun in the following sentence: Men, woman, and horses grew smaller as they moved on. Since there was only one woman in the group, I think it is neither necessary nor correct to match the plural nouns with "women". Am I right? I appreciate any assistance you can provide.
I've heard that very massive stars can sometimes collapse into black holes without creating supernovae. How does this happen? (I suspect it's something to do with the relative lack of Urca process neutrinos which are active in the cooling of neutron stars).
I am trying to develop a more intuitive understanding of the field produced by magnetization and polarization. I have the following image, and I can derive it from Maxwell's equations what the fields inside and outside are given uniform polarization, but is there a way to understand them more intuitively?
I would like to use the QT Deuce font in overleaf. It is in the LaTeX font catalogue, but the instructions for usage on that site use the fontspec package which requires XeTeX or LuaTeX rather than the pdflatex that Overleaf uses. Is it possible to use QT fonts in overleaf?
In the book entitled "Algorithmic and Combinatorial Algebra" written by Bukot and Kukin and they showed that there exists a finitely presented Lie algebra with unsolvable word problem. Can we conclude same result for the case of Lie superalgebras?
According to Birkhoff's Theorem, any spherically symmetric body will not emit gravitational waves. I can understand this for an object that is contracting and expanding because from far away the gravitational force is the same. But now imagine, we have a spherically symmetric body that is linearly accelerating through free space. In this case, would gravitational waves be emitted ?
Cayley graphs are necessarily vertex transitive, but the converse is not true in general. Is there any general/asymptotic result that discusses the percentage of Cayley graphs in vertex-transitive graphs? Or would this be a hard problem?
Fix a finite-dimensional real inner product space. Does a self-adjoint operator have a symmetric matrix with respect to all bases, or just with respect to orthonormal bases? Also, does this change at all when one admits a pseudo-Euclidean inner product, rather than the (standard) Euclidean inner product?
How the slang word "jacked" (having well-developed muscles) is formed? The word jack itself may be related to drugs, however I don't think that the meaning comes from there. There is a theory that it has formed from the word jagged (having low body fat), but I cannot find a proof to that.
When reverse bias is applied, why can't electrons from p region that are currently occupying the holes jump into the conduction band of the n region, which according to the image (taken from hyperphysics) would not require extra energy, thus completing the circuit? But this doesn't seem to happen since the current is negligible during reverse bias,why?
Prove that for any finite collection of points in the plane, not all collinear, there is a triangle having three of the points as its vertices, which contains none of the other points in its interior.
my professor asked me to read about Tate's Thesis, but I have looked everywhere and I couldn't find the thesis itself. I found lecture notes and introductions on the the thesis. I am confused. Is Tate's Thesis a thesis? If so, where would I be able to find it? I really appreciate your help!
They thought that the general would lead them to victory. vs. They thought that the general would have led them to victory. Is there a difference between the two sentences above? Is one grammatically incorrect? There is no particular context. I am more interested in learning the difference between the two (if any) and how the subtlety in wording affects the overall meaning.
I'm trying to understand the nature of polar molecules. Have there been experiments where we can say to have actually measured the dipole electric field generated by a polar molecule such as hydrogen fluoride HF? The idealized experiment I have in mind for example is tracking the deflection angle of a free test particle (electron) as it passes near a single HF molecule...
I would appreciate if someone could help me with this problem. I have tried to find a general expression for the multiplication of three matrices but wasn't successful in my pursuit. enter image description here
John Taylor's Classical Mechanics says this... I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the second condition is not? And if so, how are the forces in that situation non-conservative even if they satisfy the second condition?
In an infinite-dimension space, the relative interior of a non-empty convex set may be empty. I was wondering whether there is a concept (as a generalization of relative interior) with the following properties: for any non-empty convex set, Its "concept" is non-empty. Whenever the relative interior of this set is non-empty, its "concept" is the same as the relative interior.
What is the motivation for studying D-modules? All I know is that they are some algebraic way of discussing differential equations. They are showing up in seminars, and I haven't yet been able to convince myself that D-modules are useful. So what kind of questions were D-modules made to answer, and how is it useful to view differential equations in this way?
I coded a small example of RSA in Python. When filling p and q, I mistakenly put in two numbers that were not prime numbers. And it worked fine anyway. My question is, why is it so important for RSA to take prime number as inputs?