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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. | 0 |
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. | 0 |
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)? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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. | 0 |
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. | 0 |
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! | 0 |
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! | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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. | 0 |
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 | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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. | 0 |
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! | 0 |
Why doesn't the first line have an auxiliary to make it interrogative? These lines are from Sorry Seems To Be The Hardest Word, featuring Elton John: What I got to do to make you care? What do I do when lightning strikes me? | 0 |
I'm an undergraduate student and currently I'm approaching tensorial calculus. I was wondering: is there some geometric meaning to the operation of rising/lowering indices (and then if there was any geometric difference between vectors and covectors), or are they only mere formal operations? In case, why don't we simply use only vectors in the definition of tensors? | 0 |
What are the ways to center headers only without using the titlesec and sectsty packages? If we take the titlesec package, then the question is how to prevent this package from automatically changing header styles? | 0 |
What is the concept of hypersurface in general relativity? I know it could be characterized into three categories but how do we define hypersurface (in general) in physics? I didn't get what thing it is. | 0 |
I have always believed --- from somewhere --- that in archaic English, cats were always referred to using feminine pronouns, regardless of what sex they actually were. But I thought to go and find a reference for it and I can't find anything. Was this ever a real thing, or was I just hallucinating? | 0 |
If I lift a weight to a certain height, where does the gravitational potential energy at that height originate from? is kinetic energy converted into gravitational potential energy as the weight is decelarating as it approaches the maximum height? or is the chemical energy from my body (doing the work) shared between kinetic energy and gravitational potential energy? Hope this makes sense. thanks. | 0 |
Why do electrons have discrete energy states when they are bound to a nucleas and not when they are free for example in an electron beam. Why doesn't an electron beam have certain specified energies like bound electrons do. | 0 |
I have seen that a number of packages exist that define symbols. How can I find a list of just the core symbols provided by the Latex Team, but without the use of packages like amssymb, MnSymbol and so on. | 0 |
I am new, not have expert level knowledge. But I have studied about black hole information paradox. The black hole doesn't kept any information which passes event horizon. Which can break physics. Is there any theory about Information Paradox, to resolve it. | 0 |
What is a good term for plants whose parts, either as tubers, roots, or fruit/seeds are harvested and consumed? I exclude plants such as hemp and flax whose fibres are used, or, for example, poppies for opium. | 0 |
i.e. is the comma to signify the boundary between the instruction and the recipient of it (that is to say, "Hey, stupid! Keep it simple"), or is it serving the function of an "and" (as is sometimes used in US English but rare in British). | 0 |
I have tried to search a lot about the laws that predicted this behaviour of black body. But haven't really found out. And the ones I found like equipartition theorem, i find them contradicting with classical physics itself. How exactly it was predicted that with increase in temperature, there would be increase in intensity of radiation at each frequency. | 0 |
I've realized that there are many results in set theory rely on the theorem that states "the union of countably many countable sets is countable". However, all of the proofs of this theorem I've found so far, including ones on SE, rely on the axiom of choice. So, I'm wonder without AC is it still true or false or neither provable nor refutable? | 0 |
What's the difference between these? I will go to the bathroom and brush my teeth I will go to the bathroom and will brush my teeth Perhaps one of these sentences is grammatically incorrect. Which one is desirable to use in technical writing? | 0 |
I've noticed that both are used though "point in" is seemingly far more prevalent. Is there any difference or it's down to one's preferences? E.g. There's no point in talking to you. vs. There's no point talking to you. | 0 |
Is there a phrase with a similar meaning to the phrase Don't put all your eggs in one basket which doesn't make reference to eggs? I'm writing a story in which one character is a bird and I feel it doesn't make sense for them to use this specific phrase about eggs, given that eggs are essentially bird pregnancies | 0 |
If the activity involved only me and one other friend, e.g. playing tennis, I know "I played tennis with Jake" is correct. However, is it possible to also say something like "We played tennis with Jake"? If not, is there a slight adaptation in the structure which allows for the use of "We"? | 0 |
I've heard of the term escortee, but Googling it doesn't turn up any definition. If not that, then what could I use in this sentence: I escorted the girl through the school; she is a ________. | 0 |
I do not know exactly what shape is a spoon. I feel like it is an elliptical paraboloid but really I don't know. I really need to do this for my math project. Any help would be very appreciated! Image of a sample shape | 0 |
Is it possible to give an example of countable set, with uncountable derived set, such that intersection with this set and its derived set is empty? I know that if given set is uncountable, then it is impossible. But what if set is countable? | 0 |
Do internal forces of an atom lead it to move, or can an atom only move when an external force is applied to it? For example, if we had a perfect vacuum with the exception of one arbitrary atom, would it move due to internal forces? | 0 |
I am proofreading an article and have come across: "to a focus on a fulfilled (upper)middle-class life". At first I was simply going to put a space between the closing parenthesis and the "middle" but am now second-guessing myself. My question is, in keeping the parentheses, would it be: "(upper) middle-class" or "(upper-)middle-class" or some other form? | 0 |
When a railway is laid in a cold environment, should tensile or compressive force be applied? How does this work? I think the answer should be tensile. The railways expand while heated so applying tensile force would mean there is less extension and therefore less stress. Is this a correct explanation? | 0 |
I have a problem where I have to study "the geometric properties of the Brachistochrone curve in non-Euclidean spaces". But I am confused about the definition of the Brachistochrone Problem/curve in any non-Euclidean space. Please offer me some help. | 0 |
I considered the word "circumstantial" or phrase "circumstantially true" but I feel like there's another word that better describes this. In an example; if you step in a puddle and your feet get wet then that is the truth in your case, but it is not the case that anyone who steps in a puddle will get their feet wet. | 0 |
How would I go about drawing something that looks like this (please excuse the extremely lousy Paint image) I am sorry I cannot provide any exact code, but I am basically clueless as to how I'd do this. I hope you have understanding. Thanks in advance. | 0 |
I've been learning about the density wave theory of spiral arms, and also how the gravitational potential of galaxies is non-axisymmetric, resulting in a sinusoidal spiral potential. I've then learnt that the spiral arms/density waves occur at this spiral potential minima. Why is this? | 0 |
Is there any word for someone who doesn't accept others' favors? They have no reason for it, they just say no. Perhaps it's because they would feel insecure. Example: -Why does she always say no when I offer her snacks or drinks? -You know she is a [word] | 0 |
I've been learning spectral methods mainly through reading the book "spectral mehtods in matlab" by Trefethen. I have a simple question: Could spectral methods solve first-order differential equations? It seems using spectral methods requires two initial conditions. | 0 |
Recently, I was reading about a article which tells about something known as "Susskind Complexity". The article states that the interior volume of a black hole grows forever. How/why does the internal volume of a black hole grow forever? What is the mechanism/reason behind this? | 0 |
How to prove that a Hilbert space is the directed colimit of its finite-dimensional subspaces? Does this imply that the category of Hilbert spaces (and bounded linear maps) is the Ind-completion (see here) of that of finite-dimensional Hilbert spaces? | 0 |
I am looking for a distribution whose mean and median are different, preferably a distribution that share some properties with Gaussian distribution. I kinda know that there is something called skewed distribution or alike that probably would work but I have no idea how it is defined and/or how the expectation/median is estimated. Thanks a lot. | 0 |
I know "No, it can't be" can mean "It's impossible that it is", but I don't think "No, it may not be" can also mean "It's impossible that it is". I know that "No, it may not be" can mean "It's possible that it is not", but can't the sentence mean "It's impossible that it is" like the case of 'can'? | 0 |
So, I'm preparing for a PTE test and came across this problem in the Fill in the Blanks section. Gators can move through the water oh so silently, barely ___ (making/creating/adding/showing) a ripple. Why is the answer creating the ripple (not making the ripple) here? I just wanted to know the reasoning behind selecting the word "creating" instead of "making". | 0 |
Can I use parse as a verb in this example? The clouds began to parse and the day opened up. Meaning the clouds began to separate from one another and dissolve. Parse is commonly used to describe analyzing text or sentences but can also be defined as to resolve into its elements. | 0 |
If we have a beam of photons (high energy X-ray) and a beam of protons both with the same energy, which one will get further inside the human body and why? Can this be explaind due to LET (Linear energy transfer)? | 0 |
In a problem, I have the expression of acceleration and velocity in Cartesian coordinates , and it ask me to calculate the tangential and normal acceleration, so we don't know how I can do that, can any one help me? | 0 |
I have a problem, where I am asked to give a precise definition of the Sierpinski-triangle. The problem describes the usual algorithm to construct the triangle. However, I am clueless on how I should give a different definition. Is there some definition using the union of the points of the Sierpinski-triangle? | 0 |
From what I 'understand', Noether's second theorem applies to infinite-dimensional symmetry groups. A classic, even historical, example is the invariance group of Riemannian spacetimes, i.e. the set of spacetime diffeomorphisms of GR. Does Noether's second theorem also apply to quantum field theory (= the 'gauge groups')? Or is it confined to general relativity? | 0 |
I'm wondering what native English speakers call a person (man or woman) who is attracted to a no-make-up look and dislikes it when people wear a high amount of makeup. I can think of no-makeup lover or not into makeup. But is there a specific word being used? | 0 |
It is well known that the quaternions, octonions, and sedenions are well studied, but I don't find any articles or books in which other hypercomplex numbers are studied. Does anyone know a book or an article in which other hypercomplex numbers are studied? And if so, what is the usage of numbers like pathions, voudons, etc...? | 0 |
Looking for a reference for a textbook that discusses classical conditions for contraction mapping, such as diagonal dominance. It should contain theorems similar to the one in the picture (which I found on this post without a source). | 0 |
Basically it means that the vowels must come in the order - E, U, A, I, O and can be place anywhere in the word. I tried to do it by assuming that each of the vowels can come in five different spots. But I didn't get anywhere... | 0 |
We don't pronounce "th" in "pothead" as a single logical sound, or "ph" (as "f") in haphazard. They are consecutive letters pronounced individually. Is there a term to describe such a language phenomenon? I'm guessing no but it can lead to some humorous situations (I think on the Simpsons, policeman Lou said "poth-ead" which I found entertaining). | 0 |
What is the adverb that is commonly used when describing something rapidly/drastically increasing? It's on the tip of my tongue and I can't get it out. It's not tenfold, rapidly, drastically, dramatically, stratospherically, etc. but similar. I think it has a connotation of quickly multiplying. (It's a single word.) It's driving me insane--any idea what it is? | 0 |
My understanding is for a rigid body the angular velocity between two points fixed on the body is the same for all points. In other words the angular velocity vector would be the same. I can't find a proof of this. To be clear I'm talking translating the origin on the body, not relocating the secondary point you're computing the angular velocity of. | 0 |
I know that a charge moving parallel to a straight current carrying conductor experiences a force towards that wire due to magnetic lorentz force. I am more curious about the idea where the charge is stationary and the wire is moved parallel to it in the opposite direction at the same speed. Will there be a force on the charge this time? | 0 |
In Spanish there is a suffix, -udo, that's used for "in adjectives derived from nouns, it indicates abundance, big size, or intensity of the meaning of the root." Is there something like this in English? | 0 |
I'm thinking of doing a project with some undergraduates soon involving edge ideals, particularly binomial edge ideals. Do you have a gentle introductory reference to this topic suitable for undergraduates? We can assume that the students are comfortable with basic algebraic objects such as rings and ideals, as well as what graphs are and some of their basic theory. | 0 |
I'm not sure if there's a better way to say this: It would have been better if my brother had died rather than struck a bargain in the red desert. Am I using that right? Ugh! Help me please. This is the first line of my story and my critique group is arguing about which sentence is correct. | 0 |
I learnt that an optic fibre uses the concept of total internal reflection (TIR) to transmit data at high speed, but why do they not use just simple mirrors instead of using refractive medium and making a light incident at an angle more than the critical angle, so that total internal reflection can occur? | 0 |
I am currently studying intro to analytical number theory by Tom Apostol. It is a very def-thm-proof kind of textbook, and even after taking notes of definitions and theorems, i still struggle with exercises. Can someone please suggest a method for me to get more out of the book? Also, does anyone have lecture notes that can be paired with the book? | 0 |
I would like to learn what prerequisites are needed in order to be able to work on a postgraduate thesis on the topic: Invariant Einstein metrics on compact simple Lie groups and Stiefel manifolds. I have noted Lie groups, differentiable manifolds, general theory of relativity, and tensor analysis. | 0 |
Assuming that a sinusoidal wave with an amplitude a million times bigger than the diameter of a black hole enters a black hole, what happens to those parts of the amplitude that are not inside the black hole? The other question I have is, "Does the black hole change the amplitude of a frequency that enters it?" | 0 |
Sorry everyone. I do not really know if this belongs here, but I can't find a solution by myself, since I have no idea of what could be happening here! I have the fonts installed, but TexStudio says they are missing! How could I start solving this problem? | 0 |
According to wikipedia: https://en.wikipedia.org/wiki/Affinity_laws, when shaft speed is constant, the pressure is proportional to square of impeller diameter. I am wondering why this is true. Surely, for larger diameter, more air is pumped, so we need a stronger force. But why pressure also need to increase? | 0 |
Do we know absolutely nothing about what might be the state of matter-energy inside the black hole? Are there existing theories or research that explore the possibility of a metastable vacuum inside black holes? | 0 |
Say I have a bunch of colors in math mode. How do I remove all of these colors (reset to default or black) efficiently? (If the colors are in text i.e. not math mode, I can just do this: Select text > Text Style > Color > Default > Apply. But when the colors are in math mode, this doesn't work.) Related | 0 |
In programming it is rather the norm than the exception to have functions whose input are different data types. For example a function who produces a substring of a given string would have the following signature in Java: public static String substring(String s, int n) {..} Are there examples of such functions in Mathematics and what is their application? | 0 |
According to my understanding we get a lot of energy during nuclear reaction because mass transforms to energy. According to picture below total mass remains the same after reaction. Is the picture wrong? | 0 |
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