darklight03/StackMIAsub huggingface dataset:
This post, currently closed, asks for the intuition behind Liouville's theorem, which states that every bounded entire function is constant; I find the answers unsatisfactory and hand-wavy. I am looking for a more focused, precise description of what is going on. Is there a geometrical understanding of what is going on? I try to visualize a non-constant analytic function, to understand why unboundedness is necessary along some direction, but it isn't working for me.
There has been some recent buzz around generalized/higher form/categorical(?) symmetries in the physics community. I understand Seiberg's papers are a popular resource, and I am aware of McGreevy's review on the subject in the context of condensed matter. Nonetheless, what are some other resources I might look at if I want to learn about the subject? Specifically, where might I find problems on the subject (e.g., Andrew Lucas's lecture notes include one fairly introductory problem on the topic)?
I'm reading Billingsley's Probability and measure. I'm reading about extremal distributions, and I'm at where he is proving that Gumbel is one of the extremal distributions. I'm having a hard time understanding the proof and I'll appreciate it if someone helps me figure out the proof. The text highlighted in yellow is what i don't understand (it is quite half of the proof). Thank you in advance.
I'm new to optimization and I'm reading a paper that they reformulate an ILP problem into QUBO using penalty method. Let's say we use a solver to solve above QUBO, and the global optima of QUBO obtained from the solver is infeasible to the original ILP. (infeasible from my understanding is the QUBO solution does not satisfy all constraints of the ILP). My dumb question is: Can the local optima of QUBO obtained from the solver still be feasible to the original ILP? I don't have much background in optimization, so it would be nice if you guys can suggest some materials mentioning my question. Thank you in advance!
If someone sets up a table at the edge of a conference room selling their wares, it could be described as a "stall" or maybe a "kiosk". But what if someone instead sets up something like a few chess boards that people can play on? The word "stall" doesn't really seem appropriate to describe this ("a chess stall"?) but is there any word that would be more appropriate? I thought of "sideshow" but that doesn't seem right either because it's not really a show, it's an interactive game activity.
When using "too much", it is put after the verb & before the uncountable noun e.g. I drink too much coffee. However, this sounds strange in the sentence: I use too much social media. Instead I use social media too much sounds more natural. Can anyone explain why this one doesn't fit the rule? So far it seems that it only happens with the verb use. (Another e.g. would be I use my phone too much).
The Gauss-Bonnet theorem for compact regular surfaces is often only enunciated for totally regular surfaces, with no singular points. But what if I wanted to state it on a surface with a finite number of singular points but otherwise regular, like a cube? How is the Gauss-Bonnet modified? I know somehow the curvature has to be concentrated on the vertices, but I'd like some help in making that notion precise. Thank you.
Assuming "phreak" is a portmanteau of "phone" and "freak," giving us the term "phreaking" to describe the illicit act of hacking telephone networks, and "Phishing" pays homage to it by misspelling "fishing" to describe the practice of tricking someone into revealing sensitive information on computer networks, now we have "Vishing" (voice call phishing), "Smishing" (SMS text message phishing), and "Qishing" (QR code phishing) being used in the security industry. Is there a better term (besides "annoying") than "jargon" to describe these words?
In one of his lectures, L Susskind stated that he cannot make sense of a metric with more than one timelike dimension. I also have trouble imagining it, but is there a good mathematical or physical reason why this is not possible? Let us assume all extra timelike dimensions are compactified, so we cannot directly observe them. What kind of trouble or unphysical problems would this create? I am not asking for non-standard physics here, but just a more formal reason than intuition as to why we assume the extra dimensions are necessarily spatial (I have a basic understanding of why string theory needs extra spatial dimensions, but I do not understand if it forbides extra time dimensions). The question is not limited to string theory though.
I have seen several questions regarding the size of the absolute smallest black hole, the smallest stable black hole and similar. These made me wonder; what is the smallest stable black hole if it is immersed in a standard atmosphere? I assume there is some maximum rate at which the black hole can consume matter, and that this is related to its size. Therefore, since its Hawking radiation is inversely related to its size, logically there should be an unstable equilibrium point when these two equal each other. I could, of course, be completely wrong - however I'm afraid my knowledge of how to calculate anything regarding black holes is limited to working out the Schwarzschild radius.
Imagine, there is a truck of mass 'm' accelerating with an acceleration 'a', this means that the truck definately carries some force 'F'(let). Now, imagine the truck collides with a man standing stationary on the middle of the road. So, the truck will hit the man with force 'F' and due to Newton's third law the man also exerts a force 'F' on the truck, then my question is that, why don't the truck's net force becomes zero, and why it continues accelerating? Kindly explain, where am I going wrong. Note- there is no external force other than 'F' acting on the system.
We know that nothing including light can escape the gravitational pull of black hole. Now special relativity says that nothing travels faster than speed of light. Then how can effects of gravity due to the black hole be felt outside the black hole as nothing can escape black hole? This seems contradictory as anything is pulled inside the black hole due to gravity whereas nothing can escape a black hole.
I've seen that the Leibniz formula of determinants can be reduced to the Laplace expansion through consolidating terms. What I haven't been able to find online is a connection between any of those and the geometric interpretation of determinants, which is the volume (or measure) contained between the parallelopiped formed from the column (or row) vectors. How do I prove that the Leibniz formula, which is based on terms composed of permutations has anything to do with geometric measures?
I have just learned that linear frame dragging exists in General Relativity. I have also seen simulations where a periodically accelerated and decelerated mass causes a sort of gravitational dipole radiation, dragging nearby masses in the direction of the acceleration. My problem with this is that in my whole life I was taught that the leading order in gravitational radiation is quadrupole; dipole radiation can't exist because of conservation of linear and angular momentum. Is dipole radiation forbidden only in linearized General Relativity? What is the full picture here / what am I missing?
I am trying to understand the jump operators in the Lindblad equation. Specifically, if there is any condition of boundedness we need to impose on them. I ask this because, as was pointed out in this post, there should be no assumption on the norm of the jump operators. But for example in this review, the jump operators live in the space of bounded operators. So is boundedness of the jump operators a necessary condition? In Preskill's notes, there is a derivation of the Lindbladian in terms of the operator-sum representation which gives some normalization condition that the jump-operator should fulfill in terms of the Kraus operators but I am not sure if this is relevant to my question.
I think my formulation in the title may be a bit confusing. I mean a behaviour similar to "gaslighting" yourself into seeing/perceiving your own opinion from someone/something, even though that person/thing doesn't actually share your opinion. I've witnessed this a few times on social media when people interpreted satirical videos of political topics to match their own opinions/believes, even though the videos themselves were neutral/not actually picking a side in the political topic. Would be cool if there were a word for that.
In textbooks on Category Theory, monoids pop-up all over the place, we several easy examples such as integers, lists and so on. I was then wondering about comonoids. What are some "simple" examples of comonoids appearing in mathematics? I've tried searching, but most texts either only mentions the concept of a comonoid, or provide some convoluted example. I'm trying to get a better feel for what a comonoid is, thus I'm searching for easy to grasp examples.
A few days ago was the first time I ran into the word "Nigerien" meant to mean "something related to the African country of Niger" as opposed to "Nigerian" meaning "something related to the African country of Nigeria". Since this is very easily confused, for example by my spelling checker which didn't like "Nigerien" at all, and especially in spoken English, is that use actually correct, or is there a better word? And how would you pronounce it so that it doesn't get confused? (With the countries themselves, I thought NIger has an emphasis on the first syllable, and NiGERia on the second, but for Nigerien this sounds just wrong to me).
If there is a circular metal loop and a changing magnetic field perpendicular to the loop, there is an induced electric field that causes the electrons to move and cause a current. But my question is why is there even a current? Why don't the electrons just move and rearrange themselves to cancel out the induced electric field, just as they do in case of electrostatic shielding?
I am looking to replace the idiom "kangaroo court" in the following sentence: Class followed its usual script. The professor took center stage, exposing the deep racism, sexism, colonialism and homophobia of a previous generation and like well-rehearsed actors, us students assumed our roles as moral arbiters in a kangaroo court. I want the replacement to communicate the idea that the verdict or judgement is a forgone conclusion and that the trial/classroom is just a pretence of debate/justice as everyone already knows what the answer/verdict must be before discussion ensues. If no good replacement can be found you could rewrite the sentence entirely to help communicate the above point. Thanks a bunch.
We know that a capacitor and an inductor both offer some opposition to the flow of current through an AC circuit and their reactance is a measure of the amount of Ohmic opposition due to these circuit components. I am aware of how these quantities arise mathematically. However, my question is, physically why do these circuit components provide a type of opposition to current flow in the case of AC circuits? What is the actual cause for this reactance to appear?
Suppose you have a faucet that expels water at a rate r Liters/second. Will the rate at which water flows through some ring beneath the faucet be greater than r or equal to r? On one hand, if the rate at which water flows through the ring were greater than the flow rate of the faucet, wouldn't that violate conservation of mass? On the other hand, shouldn't water be traveling faster through the lower hoop, so it should have a higher flow rate? I've asked some people about this, and I've been told that the water column will inevitably become thinner as it falls such that the flow rate through the hoop will be the same as r. Is this true?
I hope my question does not break the rules. I can't understand how this statement can be true in the book which I've mentioned: I cannot undestand why it's true because if I have two point charges with same sign and same magnitude then the electric field should be zero at point P: But according to gauss's law it's not zero and it equal to electric field due to one of these point charges. So this electric field is only caused by the charge inside the closed surface, not the charges outside it!
I am doing a lab experiment (Franck-Hertz) at uni and am supposed to find the temperature, at which electrons are emitted from a barium oxide cathode (without the necessity of an external E-field that provides additional energy). I am attempting to calculate the temperature T = W/kB from the work function W (i.e. the ionization energy). Is there any source, that contains such data? I tried NIST Chemistry WebBook, but they only have data for BaO in the gas phase. I need some value for solid BaO.
I am interested to see a derivation of Kepler's laws from Newtonian mechanics, which would be a suitable exercise or demonstration for a first-semester course in calculus. Therefore I'd like to avoid any use of the cross-product since this is usually only introduced much later in a calculus curriculum. I've looked at Newton's original derivations. They don't use any objects or theories which a first-semester calculus course couldn't use. But they do involve enough geometry that it seems "a bit much" for a first-semester calculus student. So I recognize that any such derivation will probably be hairy in one way or another. But in the off chance that there is some known elementary and simpler derivation, I wanted to ask. Thanks!
Given a container filled with identical objects, how could I find the number of objects in the container accurately purely by analyzing the sound produced on shaking? More specifically, which acoustic parameter should I focus on? Some ideas I have had so far are: Looking at the number of amplitude "spikes" since the more objects there are, the more collisions there are Using Fourier Transform to break down the combined sound into its constituent frequencies, finding the number of distinct frequencies. Unfortunately, I am not sure if the frequencies will be measured for each object, since the objects are identical
I have just switched to writing in LaTeX from markdown. I like to proofread by hand, and so in the past I used a template that increased the line spacing and changed the typeface to something monospaced just for proofreading. Now I cannot figure out how to change an entire document to being monospaced. I found several solutions that seem to only work on LuaLaTeX, but I would prefer to use pdfLaTeX.
Circle k and a line p that intersect at points R and Q are given. Inside the circle point A is given. Construct all the circles that touch the line p and the circle k and pass through the point A. I tried to solve this problem using homothety, but it didn't work out so I guess that's not the proper way to solve it. I would appreciate any ideas.
In the double-slit experiment, the interference pattern shows the probability of finding the particle (photon or electron) at a given volume. In a given experimental setting, this probability distribution doesn't change with time, so this probability distribution belongs to a stationary quantum state. I think that this doesn't mean that the Hamilton operator belonging to an experimental setting has only one eigenvalue and a single state that belongs to this eigenvalue because the pattern depends on the wavelength of the photon. If we used the superposition of two photons of different wavelengths, we would get a non-stationary interference pattern. Is there such a thing as "the superposition of two photons of different wavelengths"? Or the double-slit experiment can't produce non-stationary states?
Phonons are typically used to describe quantised vibrations in solids. However, is it legitimate to talk about phonons for e.g. a sound wave propagating in air? Contrary to photons that are particles that can exist both in free space as well as inside an optical cavity, it seems like phonons are quasiparticles defined only in a solid (i.e. a cavity for sound). Is this the case?
I've heard that because light takes time to travel from one place to another, we see objects in distant galaxies as they were when they released the light. new and advanced telescopes are able to see further and further into space, and therefore closer back in time to when the big bang happened. I've also heard that the laws of physics are slowly changing over time and that they might have been different in the early seconds of the big bang. In the future, could an advanced telescope be used to observe the light released by distant galaxies and other cosmic structures at the time of the big bang and observe physical laws that were different from the ones that we have in the present day?
what would happen if I took a toroidal core, generated a static toroidal magnetic field in the core and then rotated the core around it's symmetry axis within a larger stationary toroidal winding around the same core? Just for simplicity imagine a toroidal transformer with a rotating core inside. Would I get DC current generated in the stationary coil? If yes can anyone explain by what law and formula?
I haven't found satisfying answer yet. Beside those typical examples like how many colourings of a cube is there up to rotations or how many graphs are there on n vertices up to isomorphism etc., is there any "real" usage of Burnside's lemma in advanced math? All examples I could find seem to me more like funny riddles you can impress your friends with but they are not quite useful for anything.
If I have n cards and n stacks of cards, how many ways can I split the cards between the stacks if the order of the cards in the stack is significant but the order of the stacks is insignificant and stacks are allowed to be empty. And is there an algorithm to find them. So for example, with two cards (a, b) and two stacks the possible arrangements are: [ab][],[ba][], [a][b]. ([b][a] is equivalent to [a][b]) this might seem like a silly problem but I am very much stuck and very much desperate
Suppose I filled a bucket of water with a hose, now when it's filled, I remove the hose from the tap's end, while the other end is still submerged in water. Now if I throw the other end on the ground, it sucks all the water from inside the bucket spilling it out the ground till it's empty. Why does this happen? I assume there's something really simple about pressure and stuff going on which someone like me, who hasn't studied fluids in detail, can understand...
I am trying to first construct a fractional linear transformation, to map the sector to a half or full circle. From there it seems straightforward using rotations, translations, and standard mappings between circles to half-planes to create a map that takes the sector to the right-half plane. My question is, how do I construct the fractional linear transformation? Lang's Complex Analysis shows how to construction fractional linear transformations to map a triplet of points to another triplet of points, but I don't see how that would be useful here.
Good day all, I am looking for a way to estimate the composition of a thermal plasma formed by flowing gas between two charged electrodes. I understand that when plasma is formed this way, it would be composed of a number of species. Please is anyone able to point me in the right direction of finding an equation/correlation/data to allow me estimate the composition of the plasma for any gas? Thank you
I remember my high school teacher explicitly saying that it took me a long time to do x was the correct form and I took a long time to do x was not. In recent years, I seem to remember hearing the latter quite often in common language, though. How applicable is the latter phrase compared to the former (a) in everyday speech and (b) in essay writing?
I was discussing with some friends about English grammar, and we ended up confused about the accuracy of the sentences below "I know the motive for your rescheduling the class" "I know the motive for your rescheduling of the class" "I know the motive for you rescheduling the class" "I know your motive for rescheduling the class" Are all of them correct? Which one would be the most idiomatic?
When I was young, a workmate convinced me that there was indeed a word which described the behaviour of someone who would congratulate themselves for behaving the way a person normally ought to, anyway. I don't want to write that word here, because some people might think part of it seems racist. So instead, I'll ask as plainly as I can: Is there a word that means "Congratulating oneself or others, for behaving the way one ought to behave?"
Imagine a bicycle wheel level with the ground able to rotate around its center. Centered on one of the wheel "spokes" is a heavy marble which can slide from the center of the wheel to rim of the wheel and vice-versa. If the wheel is spun once very hard by hand, the marble will move from the center to the rim and return to the center as the wheel stops spinning. Question: Does the wheel spin longer with the heavy marble at the rim then if there was no marble on the spoke? I suspect it does spin longer. Please no formulas or highly technical discussion; a yes or no answer and a simple explanation would be appreciated. Thank you for sharing your knowledge of physics.
This is a screenshot from a Khan Academy video on friction at the nanoscale. I understand how the force of friction on the purple block acts opposite to the direction of the force applied explained by the nanoscale diagram, but I don't understand how the Newton third law pair is explained by the diagram. Wouldn't the movement of the top layer of atoms move the bottom layer as well? In that case wouldn't the two layers move in the same direction?
The motivation I was given for algebraic topology is to assign some algebraic objects as invariants to topological spaces. This way we can show that two spaces are not homeomorphic if they are assigned a different invariant. However it seems to me like in algebraic topology the invariants are always up to homotopy equivalence or maybe even only weak homotopy equivalence. This seems strange to me. Is there a reason why other kinds of algebraic invariants that can distinguish homotopy equivalent but not homeomorphic spaces not more widely studied? What is it about weak homotopy equivalence that is so special that seems to be the main focus of all algebraic topology?
In the book General Relativity by M.P Hoson, the author tries to calculate the velocity of a particle radially infalling in Schwarzschild spacetime. The velocity is measured by the observer sitting at rest at infinity. For the same, he takes the ratio of proper distance and proper time of the particle, both measured by the observer. To calculate the proper distance, the path traveled by the particle should be spacelike, whereas, to calculate the proper time, the path traveled should be timelike. Since the particle can travel with only one of the paths, how does the observer simultaneously calculate the proper time and proper distance along the particle geodesic
Provided everything remains constant, does the fringe separation, that is the distance between adjacent fringes become further apart for higher order maxima? Consider the above diagram. From the diagram it appears that the distance between adjacent maxima is getting larger with distance from the central maxima. My intuition agrees with this. However, I have heard that the distance between adjacent fringes is constant. Assume this is true. How so? Double slit interference pattern: Fringes are equally spaced and of equal widths. The above statement seems highly unintuitive. Shouldn't the spacing between adjacent fringes get larger, as the wave spreads out. How do I satisfy myself with the above statement? Proof?