darklight03/StackMIAsub huggingface dataset:
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.
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?
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.
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?
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?
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?
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?
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.
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!
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
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?
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.
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.
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.
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?
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?
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?
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?
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?
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?
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.
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.
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.
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?
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?
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?
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?
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. ?
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.
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?
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.
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?
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?
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?
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?
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?
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.
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?
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."
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?
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?
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?
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.
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?
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?
I am currently setting up a portable LaTeX environment (TeX Live) with VisualStudio Code and the LaTeX Workshop extension as the editor. How do I specify in the LaTeX Workshop settings the path to the LaTeX environment? This is for Windows. Changing the environment variable on every computer used is not desirable. I also couldn't find something in the settings of the LaTeX Workshop.
I am currently reading Falconer's book on Hausdorff dimension. My question is whether Hausdorff dimension is invariant under local isometry between smooth Riemannian manifolds? I think it should be yes, but I am not sure how to choose the covering( needed for calculation of dimension) using the local charts explicitly to get the invariance. Any help would be very much beneficial for my understanding.
I have an html table like <table>...</table> with some css formatting and I'd like to put that table into latex document. I don't want to put it as a figure because I will not ba able to copy its content. How can I do that (preservig formatting and styling)?
I am learning general relativity by myself. I wonder if the equivalence principle is simply equivalent to, in geometrical terms, the statement that a Lorentzian manifold is locally flat, which is a somewhat trivial result from the point of view from math.
Many textbooks derive the single-particle excitation energy gap from the BCS mean-field hamiltonian, and then stop there, implying that this gap is sufficient for superconductivity. To be frank, I cannot see why a gap implies superconductivity. Superconductivity is a transport phenomenon. But the BCS mean-field hamiltonian is just a static hamiltonian; it is not directly connected to transport, right?
Everytime I approach any projectile motion/kinematics problem, I get confused. I don't know how to translate the problem into an operational method, and every time I complete a problem, the next one is a new mystery to me. How should I tackle this issue and master this problem type?
My super basic question is, the (magnetic) force between two steady current loops obeys Newton's third but the (magnetic) force between two charges doesn't. This is surprising given that the former is built out of the latter, so is there any significance to this fact?
I'm currently learning about Radiation in my Physics course, and so far i was interested in betavoltaic batteries that convert eletrons to photons and then eletricity. I'm confused about how to calculate the energy per second (W) produced by eletrons converted to photons. Can someone help me on that?
I am very confused and probably understanding the concepts of renormalization wrongly: If the running coupling constant is a real experimentally observable quantity and the change with scale has a physical interpretation as "vacuum polarization", how can it get independent of the scale if we could sum up all orders of perturbation theory?
Can you explain to me the reason why Thomson Scattering can not explain what happens when light meets an electron at low intensity, and what does that have to do with light being a wave or particle or relativistic/QM effects?
I cannot seem to find or come up with an answer to the following question: In mathematics, is it possible to prove that there is only one (shortest) proof of a given theorem (say, in ZFC)? Are there any (preferably natural) examples?
When you write a spline curve as a linear combination of b-spline basis functions, it's called a "b-spline". The basis functions are generated recursively by the deBoor-Cox algorithm, starting with degree zero and working upwards to higher degrees. These b-spline basis functions are thus written in terms of (i.e., as a linear combination of) other b-spline basis functions, so they are also b-splines?
I need to run an experiment on the effect of temperature on refractive index of a liquid, and in order to make the change most visible and have the lowest percent uncertainty I need the change in refractive index to be as high as possible. What are some liquid with high changes in refractive index with change in temp, higher change then water ideally.
I have seen some mathematical texts that use words like Lemma, Theorem, Corollary, etc. What would be the appropriate description of such terms? Do they fall under some linguistic category? Is there any general term associated with these kinds of premises?
I'm writing a bullet point in a presentation. I want to say: Our partner and customer commitment remains unchanged. However, it feels like it reads better if I change it to: Our partner and customer commitment remain unchanged. I know if I read them separately, remains is correct. I've searched Google, and "remains" is more common. Should I use remain or remains?
My textbook states that when the diffraction gap is smaller, there is more spreading of the waves. However, it seems unintuitive to me, since why would waves spread less if there is more space for it to spread? Is there an intuitive way of understanding it?
I came across a thesis which has a feature in its references. Each reference includes the page number(s) of which the reference is cited. Is this possible to do using Latex? I found it really interesting to use. Apologies for the image being in French.
Say, you have a complex number in standard form and another in trigonometric form, can you do operations with them, for example adding/subtracting, multiplying/diving the two numbers, just like that, or do you have to convert one of them to the other form to be able to do operations?
Is there a name for white noise that has non-constant variance? I have some examples from experimental data where the variance of the white noise increases with time. However, I am not sure how to model this.
For propositional logic, for every formula, there is an equivalent formula in the CNF and DNF. These normal forms have the advantage of being representable in a "tabular" form rather than a "tree" form, which may be more computationally friendly. Is there something similar for linear logic? I am mainly interested in the additive-multiplicative fragment.
I understand that an algebraic group may not be a topological group because the continuity of multiplication with respect to the Zariski topology is weaker than that with respect to product topology. But is there a nice example that helps to explain this. Many thanks!
I'm looking for a selection of problem books on probability theory, at the level of student olympiads in mathematics. I've already looked at Albert N. Shiryaev Problems in Probability, but maybe you can suggest some more interesting options. Many thanks!
Was just curious, is it possible to obtain the eigenvectors if you only know the eigenvalues and the dimensions of a square matrix? Or what further information from the matrix can you gain from only knowing the eigenvalues?
I know that mechanical computers have been used for a number of different calculations, the most famous (at least on the internet) seems to be the firing control computer used by the US Navy. But were there any entirely mechanical devices (other than a slide rule) that could calculate logarithms?
I am trying to understand Schmidt decomposition. I am stuck in one sentence here. See the example picture. Here, I can understand everything except the line "For both HA and HB the Schmidt basis is diagonal (Hadamard) basis." Can anyone help to understand what the author tried to tell here by using this line?
For example, during refraction, when photons pass through a glass slab, they change direction. Why does this happen? Is the reason for this not applicable when photons strike perpendicular to the glass slab?
Is there a TeXShop directive (something like % !TEX TS-program = lualatex) that I can place at the top of my document and can tell TeXShop to compile using LuaLaTeX with latexmk? That is, a TeXShop directive that does the equivalent of latexmk -lualatex file.tex.
We derive the formula of escape velocity by using conservation of mechanical energy, where we consider that work done by external force is neglected. But to provide the velocity to send an object to infinite distance from gravitational pull of Earth, don't we have to apply an external force?
Is it possible, with LuaTeX, to retrieve the textual content of a PDF (using lua code I imagine)? For my purposes, it doesn't have to be "clean" (for example, the order doesn't really have to be respected), it's for "statistics" on the words used.
So the context is this: I taught my friend how to play a video game and he's gotten to a point where he's passed all of my stats and records. I'm looking for a word to use like ronin (samurai without a lord or master) and I'm curious as to if that exists. Thank you ahead of time
As the title says: Is there a distance at which the Kerr metric looks like Schwarzschild metric? Edit: if there isn't any such distance (smaller than infinity), can we measure from the outside, with which speed a black hole rotates?
In complex analysis the term branch is used to designate a holomorphic function defined on a region. The most prominent example is the principal logarithm, which is a branch of the logarithm. Does anybody know the history of why the word branch used? I'm guessing branch, tree, decisions, choice.
In the context of optical tweezers, if used in a vacuum and a particle starts off slightly to the right from the center of a beam, would the particle eventually become perfectly centered or would it continuously slingshot from right to left? Does this depend on the strength of the laser?
Is this just an extension of the idea that with a small enough perturbation, the Principle of Least Action will still hold, and the system will continue to take the most optimal path?
Since light travels at the speed of light towards a target, the spatial distance to the target seems to be zero, owing to Lorentz transformation. It seems that there is a logical flaw here. Can someone explain that? Question is similar to this: Wouldn't a photon disappear because of length contraction?
I am using a convex lens in a wavefront-measuring interferometer for testing microscope objectives, where the lens images the exit-pupil of the objective onto my camera. It is my understanding that the effects of diffraction from the convex lens will have some influence on my interferogram, especially around its edges. How can I actually take these effects into consideration?
I came across the concept of topology of time and causality in Reichenbach book, "Philosophy of Space and Time". It would be nice to have list of references of recent developments of the same. It could be textbooks, research papers or published articles.
I am searching for optimal control examples in fluid mechanics in which only ordinary differential equations are considered (i.e., in system dynamics or model of optimal control problem) with exact or approximate state and control variable plots. So far, I am getting examples containing PDEs. Does anyone know of any sources (books, journal articles) containing such examples?
On Wikipedia (article:https://en.wikipedia.org/wiki/List_of_trigonometric_identities) I came across this trigonometric identity in the infinite sums section In the article no proof was provided and so I would like to know if anyone here knows a proof of the identity.
Given a pair of inversely similar triangles ABC and AB'C', as shown in the graph, CB and C'B' intersect at F. X, Y, Z are the midpoints of BB', CC', and AF respectively. Prove that X, Y, Z are co-linear. This is a very elegant result, and somewhat alike Newton's line. All proofs welcome, and a geometrical solution would be very nice!