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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. | 0 |
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", ...? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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! | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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. | 0 |
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 | 0 |
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. | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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. | 0 |
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 | 0 |
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)? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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). | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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 ? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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. | 0 |
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! | 0 |
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. | 0 |
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... | 0 |
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 | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
I'm not sure if the use of "easy to move" in this sentence is correct. They say that our uniform looks cool and easy to move. It sounds strange to me. I can use the word "comfortable", but are there other words or ways to say it? I'd really appreciate your help. Thank you. | 0 |
Quick question - if the formal name for the solid counterpart of a sphere is a ball, and the formal name for a "half-sphere" is a hemisphere, what is the formal name for the solid counterpart of a hemisphere? Half ball? Hemi-ball? Just "solid hemisphere"? Is there even an agreed-upon formal name for this solid? | 0 |
Does anyone know how such a matrix is referred to in the literature? Ultimately my goal is to look for an analytic expression for its determinant. But because I don't know what it's called, it's been very difficult to go through the literature... Thank you so much for your help. | 0 |
At least for German-language documents (and especially when using microtype) LaTeX, to my taste, puts too much emphasis on preventing hyphenation. Is there any parameter that can be changed so that, in favor of more consistent white spaces, more hyphenation is done? | 0 |
There is an unhappy colleague in our company and I want to talk about this issue in my next meeting. I want to mean "A bad apple ruins good apples" but this sounds so negative. I want to model it positively. How do I do it? | 0 |
I was learning basic statistics and I read a proof that the standard deviation is always less than or equal to the range. I don't understand how range can ever be equal to the standard deviation. I could only think of one case: when all data points have the same value. Is there any other case possible in which the equality holds? | 0 |
When doing palatography, one needs something to paint the tongue with. It is usually a mixture of olive/sunflower oil and powdered charcoal. The question is, what can this substance be called? Is it a colouring, paint or/and dye? What is the most suitable word? | 0 |
I'm seeing some results on Google but it seems quite an unusual word combination. Is it okay to use it or would it be considered "weird"? Context: Free for non-companies We believe Open Source should be free for individuals and non-profits. Only companies pay. The word "non-profit" isn't usable as it wouldn't convey the same message. | 0 |
Pretty much the question. Is there a line (figurative) that separates when you'd use one term and when you'd use the other? Is there a distinctive characteristic of one that is not found in the other? Please help me understand. Thanks! | 0 |
just a quick question about how to determine if a matrix has a JCF - I know that if the characteristic polynomial factorises as a product of linear factors it has one but what if you only know the minimal polynomial factorises as a product of linear factors? Is this enough to say the matrix has a JCF? Thanks | 0 |
NO SHADOW of the fork! A distinct black shadow can be observed at the bottom of a glass before and after the fork enters the water, but the shadow disappears at the instant of entry, is this a phenomenon of refraction of light? (as shown in the figure) How does it work? | 0 |
Could someone please tell me how we define CM modular form and non-CM modular forms in the most basic way?Also, could you provide the references to your definition? I have tried searching for the definition. But still the definition is not clear to me. | 0 |
In the image below, the expression is depicted as a result of multiplying a polynomial by an infinite series, which is represented as an exponential function. Could someone kindly elucidate how the final equality is derived? Thanks in advance. | 0 |
I'm reading an article where risk measures are defined on the space of random variable (not necessarily bounded), so I want to understand why risk measures are defined at first (for example in Follmer and Schied) for bounded r.v. | 0 |
If the Earth were perfectly isolated from the rest of the universe - with no exchange of matter, energy, radiation etc - would we be able to recycle all stuff on Earth perfectly? For example, simple processes like electrolysis and burning of hydrogen. If no energy or matter is lost during these events, what's preventing us from reversing and recycling them indefinitely? | 0 |
I know Pieri's formula for elementary symmetric polynomials and for complete homogeneous symmetric polynomials, but is there an analogue for power sum symmetric polynomial? It seems that it should be similar, but the summation should be carried out by other partitions. Maybe someone knows where to read about it? | 0 |
How do we judge if a certain ruler-and-compass construction is the shortest? For example "the shortest construction of a regular pentagon." Is there a software that can come up with a construction of a geometrical item given a collection of input data? | 0 |
Rotating a fluid filled cylinder and calculating the equation of it's free surface is an elementry problem in fluid mechanics. However I was wondering, if we rotate the same cylinder by an axis parallel to the main axis and passing through a point on it's circumference, what would be the equation of the free surface in this case, and what will it look like? | 0 |
In a cloud chamber, atoms of air are ionized by passing radiation, providing nucleation sites that enable droplets to form. When those atoms are de-excited, one would expect them to release light; does this happen, and if so is this radiation detectable? | 0 |
Which is correct? Is it, "Do you want your house painting" or "Do you want your house painted"? Examples of both can be found on the internet. Is there a difference between them? Can you use either? | 0 |
I would like to know how to write half integrals and generally integrals of nth order in LaTeX, for example in Cauchy's formula for repeated integration, because I didn't find how to do that on the whole internet. | 0 |
What does the MHD theory predict when two regions with magnetic field of opposed polarization interact? When we take in account the resistivity then we can observe a rearrangement of the topology due to magnetic reconnection but I am wondering what does the ideal MHD equations predict in that scenario. | 0 |
I was wondering, where I made a mistake in this attempt to disprove the four color map theorem. I hope that you smart folks can help me out. I already apologize, if the tags are wrong. I am not really a math specialist. | 0 |
I was wonder about following statement. "Harmonic function is radially symmetric." What is correct meaning about above statement? I think it means 'Harmonic function is invariant under rotation' i.e: Let u(x) is harmonic function and x is n-dimensional vector. If A is nxn orthogonal matrix, then u(Ax) is also harmonic function Is it correct? | 0 |
I have a confusion. At one hand, magnetic moment is forced to align with an external static magnetic field; on the other hand, a magnetic moment can precess around an an external static magnetic field with a fixed angle. Clearly these two phenomenon cannot happen simultaneously. So which is correct? | 0 |
I am reading again about Lie Algebra, and one main concept is that of the tangent space of a lie group. We consider it to be all the possible tangent vectors as a path crosses the identity element in the lie group... but why exactly the identity element? Why not consider tangent spaces at a generic point? | 0 |
If an object is projected towards east or west from the equator, we get the coriolis force to be vertical. If this projectile, say, miss its target from below, can this be attributed to the coriolis force? | 0 |
Can the definite article have two different meanings in front of identical words in one sentence? As in The bicycle is a vehicle but the bicycle in this room is just a decoration. Or perhaps this sentence should be better written as A bicycle is a vehicle but the bicycle in this room is just a decoration. ? | 0 |
Does anyone know of a relatively simple and easy-to-use graphics app (like GeoGebra) that can graph hyperbolic geodesics on a hyperbolic paraboloid? I'm trying to graph the geodesics on the top image to the surface on the bottom image, specifically to best visualize the hyperbolic case of the parallel postulate. I haven't found a way to do it on GeoGebra. | 0 |
I encountered this correction in IntelliJ, a tool for editing computer programs: Is this right? I feel like there is an implicit "that" in the sentence: I need to borrow some money so [that] I can buy some medicine for Tom. And therefore the second clause is really a dependent clause in disguise. What do the experts say? | 0 |
I have to do an exploration in maths. I was thinking to do it on how the angle of incidence and reflection vary with the eccentricity of the ellipse. Do you think could be interesting? Do you have any suggestions for the method? I was thinking to extend it on ellipsoid billiards. | 0 |
If electricity is the flow of electrons, how come it can flow at the speed of light? Shouldn't how fast it moves be limited to a speed lower than the speed of light because it has mass? | 0 |
I have several times seen stated the fact that the complex projective space with the Fubini-Study metric is isotropic, but i can't seem to find the proof anywhere, can anyone suggest a book or answer with a proof? | 0 |
I have been learning electrostatics, and I didn't quite understand why charges reside only on the surface. The charges are moved until they reach the surface after which they cannot move further and hence the field that had developed cancels the external electric field. How does this cancel the external electric field? | 0 |
Lorentz scalars are invariant under Lorentz transformations, which are a subset of linear transformations. I wanted to know if it is possible, for a Lorentz scalar, to NOT be invariant with respect to another kind of linear transformation (e.g. scaling or whatever linear map other than Lorentz). Can you mathematically prove your answer? | 0 |
x = f(a,b,c), y = g(a,b,c), and z = h(a,b,c) if a,b,c are sides of a triangle, then x,y,z are also sides of a triangle. How can you write sets of functions f,g and h? | 0 |
I'm wondering if its ever possible to find two non-isotopic knots which have identical jones polynomials but different seifert genus? Attempting to google for this I found this example of non-isotopic knots with identical jones polynomials. But in the first page of the paper its clearly stated that all the knots have identical genus. | 0 |
So, the thing is i was using this code on overleaf (it worked fine there) and i wanted to switch to texstudio because of the compiling limits on overleaf. So i copied the whole command from overleaf tex file and pasted in the texstudio. But it says "Error: File 'sn-jnl.cls' not found." when i run it. how do i fix it? | 0 |
Is there a name for the particular part of a circle shown in red? I know the white sections are segments. If the vertex was at the center of the circle it would be a sector. I don't suppose that any mathematician would have been brazen enough to call it the "ice-cream cone." | 0 |
Is it correct to say that if two parabolas touch, then tangents at the point of intersection have the same slope? If it is true, is there a neat geometric interpretation of the fact? | 0 |
If I had a pair of entangled particles that were both in superposition, and I put one of them through a interference experiment, such as the double slit experiment, would I see an absence of interference the moment I measure the other particle? And how would this change if both were in an interference experiment and I measure one of them? | 0 |
Why were multiple layers of absorbers and scintillators used in the CMS HCAL? Couldn't they have used just one absorber and one scintillator layer? Why was the choice made to have multiple layers? | 0 |
I read book "A primer of infinitesimal analysis" John Bell. I was confused when I saw example with area under curve. In that example author mentioned about nondegenerate triangle of zero area. But triangle of zero area is degenerate triangle. How is it possible? How to imagine what author meant in that example? Thanks. | 0 |
I have read that a net charge in a closed, finite universe would result in the electric field from the charge "winding" forever which would lead to infinite energy. However, wouldn't the electric field lines cancel out if they were winding around the surface of a sphere like in the diagram? | 0 |
I was scrolling through a wiki article on terminal velocity when I spotted an upside down delta. What does this symbol mean? How is it applied in other contexts? EDIT: If possible could someone expand upon "a covariant vector made of space derivatives?" I sort of understand how a vector can be made up of partial derivatives, but what does covariant mean? | 0 |
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