Given an arbitrary set of Christoffel symbols for a spacetime. How does one identify the Euler, Coriolis force, centrifugal force and linear fictitious force? I suspect it should be possible to do it both from the metric and Christoffel symbols?


Does anyone know of any free and relatively easy-to-use math apps like Geogebra that can be programmed (or were explicitly designed) to draw the geodesic between any two selected points on a saddle surface like the one below? Thanks in advance.


I am interested in reference material for Physical Applications of Stochastic Processes. The playlist does have an associated book, but it is a litte dense, and the derivations are mostly left to the exercises. Is there any book/site that covers the same material (a different perspective), or even one on general stochastic processes.


I want to typeset a truth table where the truth values of a complex formula are aligned with the corresponding connectives as shown in the attachment. Would someone know a solution? Thanks in advance!


A TLDR summary is used to shorten a long detailed article. However, what if you have written a brief and concise summary, but would like to add further non-essential background details at the end?


In @UmbertoP's response to the question, "Partition of real numbers into dense subsets of positive measure," the answer is understandable to a advanced undergraduate; however, I have inadequate knowledge of measure and set theory. I tried to create a more explicit example here but it's too complicated. Question: Is there a more explicit version of Umberto P's answer that's understandable to an average undergraduate?


On the web, I have not found much concerning the argument which is convincing to me. I have then worked out a proof of Fatou's Lemma assuming convergence in measure. I ask you if it sounds fine. Thank you so much.


I know what real projective line is. But what is a formal definition of a projective line? Unfortunately there is nothing on Wikipedia about it. They are always talking about projective line as a part of projective plane. How would one describe projective line without any underlying space? Thanks.


I know latex, but new in xslt (learning now), I need to convert the tex to xml file through XSLT (one of my friend suggest, but i failed to convert). Please suggest or give example to convert the files.


Looking at the P-H diagram, the working fluid pressure drops when it goes through the expansion valve. Temperature drops at constant enthalpy due to Joule-Thompson effect. Therefore the system must be pushing the working fluid to lower pressures when there is not enough refrigerant, but why would it do that? Is the suction pump working harder?


what is the nature of force on electron in atom .Is it coulombic or electromagnetic force? As electron is in random motion so we cannot take it as electrostatic force. Please clear my confusion.


I am writing this document for HR at work and wish to outline what our staff should do to get reimbursed. The sentence should be something along the lines of... All incurred expenses/expenses incurred should be claimed within three months of their taking place. Is there a rule?


When light is refracted through little drops of water the rainbow is formed behind the water molecules. When light is refracted through a glass prism the rainbow is formed inside the prism. Then why when the light is refracted through a bubble the rainbow is formed on the surface of the bubble?


I can find some properties and characterizations of path algebras and its elements in representation theory books but I want some references that study and treat path algebras as invertible elements, idempotents, ideals, etc... without focusing on representation theory. Best regards.


I wonder about the possible influences of the continuum hypothesis or its negation on quantum theory. Could we think about a physical system for which Hilbert space would have dimension cardinality (cardinality of orthonormal basis set) between integers and reals (thus in favour of continuum hypothesis negation)? J.


I know the effect would be incredibly small if there is one. If I were to point a laser pointer at the moon and a gravitational wave were to pass by perpendicularly to the laser would it shift the point on the moon momentarily as the wave passed?


It is well-known that the Laplace-Beltrami operator for a Riemannian manifold takes a relatively simple form with the harmonic coordinates. This operator should be obtained as a product of Dirac operators. So, my question is: What should the form be for this Dirac operator? Does some literature exist about?


This has always bugged me. The energy levels are discrete, so an electron is said to only absorb photons with EXACTLY the energy of the jump between levels. Otherwise, the photon passes straight through right? But isn't photon energy on a continuous spectrum such that the energy match would have to be infinitely precise? How is that possible?


To what extent is the Ising model for the ferromagnetic transition experimentally relevant for real ferromagnets ? For example if one quantitatively compares the magnetization versus temprature data rescaled by the critical points, do the data match with Ising scaling ? Any hints to compilations of data or comparisons would be appreciated.


For example, the paper I am reading states that the current was "periodically interrupted without changing polarity" to "demonstrate that the peaking behavior is not due to a capacitive effect." They observe a standard voltage trace. What does "capacitive effect" mean in this context?


Is Anti de Sitter spacetime repulsive because of its negative scalar curvature? Will a fluid flowing radially inward experience an opposition that has a radially outward component? And how can one quantify this "opposition"?


It is known that it is impossible to have a non-singular vector potential for the monopole magnetic field. How about the monopole harmonics? Could the wave functions be made single-valued and finite on the sphere?


I have seen several suggestions on ways to indicate a person's middle name was preferred over their first name: Firstname "Middlename" Surname Firstname Middlename "Middlename" Surname Firstname Middlename Surname, aka Middlename Is there any consensus on the best approach in an obituary?


In wikipedia page of tensor product, there is a tensor product of mixed type tensors: I wonder exactly how the map works (it takes in ... and spits out ...). Can someone help me to find an explicit form of this map? I met this problem when looking at second covariant derivative of tensor fields. Thanks.


Consider an electron that is launched towards an atomic nucleus. As the electron gets closer to the nucleus, the electric potential energy between these particles changes, it decreases. According to energy conservation what follows is an increase of energy outside of this electron-nucleus system. Is it now correct to say that the emitted bremsstrahlung x-rays provide this increase in energy?


I am a maths hobbyist, and now I study books on differentiable manifolds and their geometry (tensors, connections). My question is : what is the use (or examples) of the linear connections ? Or later, the Levi-Civita connection, in Riemannian Geometry ? What calculus we can do with them ? Thank you very much !


I'm new to latex and this is my first time using it to write my report. I want to style my Table of contents and list of figure like the following images- table of contents- list of figures- I have no idea where to start and how to format toc and tof like this. I would greatly appreciate your guidance and expertise.


In atomic collisions,does the neutron fuse with the proton of hydrogen and release a photon which is absorbed by the electron which then gets excited to higher energy state? Or do the neutron and proton stay in contact like a deuterium nucleus without any release of photon. In the latter case how is the lost kinetic energy of the neutron absorbed by the electron?


Is it even possible to calculate a particle number of some field in lattice field theory? After all, it's implemented in the formalism of imaginary time path integrals, here's no such concepts as particle number operator, creation and annihilation operators. After searching the internet i didn't find anything useful. I'm interested in bosonic fields.


I am looking for an appropriate word for parking a car at the Workshop, for repair in the coming days. The word deposit gives an impression of a financial transaction. I put/deposited/parked my car in the workshop for repair. What can be the most appropriate word in this context?


It is commonly explained that semiconductors like silicon, germanium, GaAs... are opaque because all of the visible wavelengths are above the band gap so they get absorbed. However silicon and germanium have indirect bandgaps and require a phonon interaction which should be rare. Why are they not transparent to the human eye?


This appears in an Olympiad handout by Kevin Zhou. However I don't get where this result came at all. How would you prove it? I also don't see in what situations the right side of the expression can be more useful than the left side.


The image of things falling into a Black Hole stays frozen on the event horizon forever. So how is it that we don't see the image of a dying star where a Black Hole formed? We see the black, with an accretion disk.


It is well known that there are algorithms developed for asymmetric encryption that take advantage of the fact that the product of two prime numbers cannot be factored in polynomial time. Usually, prime numbers are not used in symmetric encryption. Do you know of any algorithm where prime numbers are used at any stage of symmetric encryption?


Is Shockley-Read-Hall recombination synonymous with all phonon-assisted nonradiative processes? In organic molecules, "internal conversion" is used to describe non-radiative decay from excited states. It seems like nonradiative recombination can take many forms (including Auger Recombination, recombination at defects and recombination at surfaces). Looking for clarification.


What ratio of final to initial mass of a rocket to achieves the highest energy efficiency - the highest ratio of final mass kinetic energy to chemical energy expended? And more generally the relation of efficiency to mass ratio. This is a bit hypothetical because we are not usually interested in efficiency in this sense, but the answer is curious none the less.


Bands and solo singers have discographies, (film) actors have filmographies, and so forth. Is there a similar term for television? I've come across "televisiography", but the article's author compared its usage to cinematography and not filmography.


As we all know that in a pn junction depletion layer is formed and due to immobile charges electric field is directed from n side to p side but why does this electric field acts as a barrier for diffusion rather than an enhancer for diffusion of charge carriers?


I keep coming across "quotes" on the internet that say things like "psychology says, if a person blah blah" I'm wondering what the term would be when someone 'mislabels' a field of study (psychology in this case) as a person, as if a field of knowledge is someone talking, I don't know how else to put this. Thanks for any help!


Are there actual equations for the Parton Distribution Functions for quarks and gluons? I've been looking high and low for theory-based papers about this and it seems like a wild goose chase at this point. If the answer to that question is no, are there any theoretical results that can be used to compare to experimental results? Hope to hear an answer soon.


I'm working on a class file in Overleaf, and would like to be able to have the editing tab for the class file and the main file open at the same time, rather than needing to repeatedly switch between them. Is there a way to do this?


I'm not sure how can the following formula be derived. Please explain step by step with reasons: Present value of constant cashflow at fixed rate: Future value of constant cashflow at fixed rate:


Are the most fundamental particles, e.g., bosons, fermions, etc., capable of further subdivision? Are they at their most fundamental? Or do we consider them so because we're just not capable of going any further? theoretically, couldn't any fundamental particle always have some smaller component on which it depends?


Recently, I got an internship as a Content Writer, and they issue a report for the work done using Grammarly for further corrections before finalizing. I have noticed that a lot of the suggested changes by Grammarly were of usage of passive voice. How do I avoid this to begin with and why is considered wrong?


"This is because of abrupt discontinuity of fields" I have read this or similar sentences in many papers. I am bit puzzled. How and under what conditions electric field can be discontinous? In my opinion this is unphysical, field lines start at one charge and end at opposite charge. Then how can fields be discontinous midway?


I found a tutorial on converting a PDF to SVG, but this method seems to only work on local devices. I wonder if it is possible to output images from LaTeX using online compilers like Overleaf.


According to the Wikipedia page here, a real, unsymmetric tridiagonal matrix can be brought to symmetric form by a similarity transform. Does anyone know if a generalization of the formula given there exists for unsymmetric tridiagonal matrices which are complex and Hermitian, and; contain nonzero elements in their upper-right and lower left corners (i.e. which are subject to periodic boundary conditions) Thank you!


If a spaceship approaches a rapidly spinning planet, would the planet's inhabitants , the inhabitants of the planet where the spaceship came from , and the spaceship's occupants observe time dilation between all each other due to their relative motion?


I plotted some simulated stellar emission spectrums from PHOENIX which also each came with their respective effective temperatures. With the effective temperatures, I used Wien's law to estimate the peaking wavelength of the spectrums. Why does Wien's law seem to underestimate the peak wavelength? Also, why is the error increasing with lower effective temperatures of the star that emits the spectrum?


I used Google Scholar to export the citations in Latex but they are not written in a correct and homogeneous form for all the references. How can I use Mendeley to reorganize my references already made by Google Scholar? I don't want to do this work manually because I have a lot of references.


I am working on a heavily mathematically project about plasma. In particular, I want to find references that treat the problem from microscopic models that include relativistic and magnetic effects (Coulomb forces, QFT, etc) and obtain kinetic models (BBGKY, Landau equation, Maxwells equation, etc). What are some state of the art papers/references?


Why doesn't the Hafele-Keating experiment settle the twin paradox? It is my understanding that clocks were used, and that the shifts matched the calculations. Doesn't this settle the twin paradox if we replace humans with clocks, implying that the travelling twin is the one who age less?


Given an undirected graph, denote N as the number of vertices and E as the number of edges in the Graph. The Graph consists of k connected components where k <= N. Assuming each connected component is complete, What is the minimum number of edges in G (as a function of N and k)?


"The phone is ringing" refers to an incoming call, so saying that is misleading when you've gotten a text/notification. Is there a different word to use in that sentence ("The phone is _______") to mean "the phone is making the sound of receiving text/notification"?


About a hundred people had already gathered, a guard rail the only thing separating them from the crater's edge. Is it not more proper to say "About a hundred people had already gathered, a guard rail was the only thing separating them from the crater's edge."? It naturally sounds more clear in my opinion when was is used.


Just realized the Japanese word Kawaii is pronounced Ka-wa-ii (three syllables). With that in mind those two last "i" in Hawaii look suspicious now. Shouldn't they be pronounced separate, making up a third syllable? Otherwise, what's the purpose of the double "i"?


Thinking of compound words or phrases where the order of the words can be swapped around and still make sense: Examples: Lighthouse - House Light Birdhouse - House BirdRacetrack - Track Race So far that's all I've been able to discover. Is there a word for this reversibility phenomenon?


In the formula of the law, we have to find the cross product of the distance(r) and the infinitely small part of the conductor dl. My doubt is why are these both considered as vectors ? Aren't they measurements of lengths ? I'm unable to relate vectors with this concept, kindly help me out :)


I need to plot this algebraic curve in tikz but I don't understand how to deal with these curves in tikz since it's not a function. Desmos tells that it should look something like this I only need a curve without axis or whatever and only in tikz.


I used the program R to calculate the values of the maximums and the points where the new function starts, however, I don't know how to use these points to graph the function I'm looking for. Image of the results I got from R


I came across (a pretty sad) poem by Meggie Royer. She writes: I stood by as strangers stroked her muzzle and she wilted beneath their touch like she did once for mine. For context: she writes about her dog here. I interpret 'wilting' as something positive in this case. Can someone shed some light on this for me?


I have recently been looking at random variables and did come upon the below matrix (in image form because it is too large to copy): I have been attempting to find the inverse of this matrix, and have only been able to find decimal approximations. Does anyone know of any software or site that could compute the exact inverse?


Can the word provenance be used in reference to a person, or should it only be used for objects? For example, would it be improper to ask someone for their provenance? Longman, and AHD, for instance, only mention it being used for 'things' / 'objects'.


I'm trying to trace back the etymology of 'palatable', but what I'm really looking for is the process of semantic expression over time. When did the word begin to be used to speak of things unrelated to food? I will be grateful for any leads, resources, or information.


I am wondering where can I find examples of explicit calculation of Bala-Carter correspondence for algebraic groups of classical types of small ranks. Would you please give me some clues? Thank you very much!


Consider the following (mock) sentence: We use a class of methods in which fruit (here: bananas) are combined with vegetables (here: pumpkins). An editor has proposed instead: We use a class of methods in which fruit (i.e., bananas) are combined with vegetables (i.e., pumpkins). The meaning strikes me as different however. Question: Are both sentences correct? Do they differ in their meaning?


When using the changes package, it highlights the changed text and adds a superscript denoting the author id. Is it possible to suppress this superscript? I use different colors for different authors. PS: This is a follow-up question to this question, but is also a stand-alone question.


Suppose a plane mirror is half-submerged in another medium (say water) and light rays are incident obliquely on mirror at the interface separating two media. My questions - (a)- Will reflected rays suffer refraction ? (b)- What angle will the reflected rays make with normal after reflection? Will angle of reflection be same as angle of incidence (as given by law of reflection) ?


So imagine you have a bottle of water or any type of liquid (like a bottle of milk that has just been opened)that is completely full or even three quarter of it is full,why does the water or milk come out of the bottle in waves when you pour it in a glass?


Can someone please show me the formalisms of the energy and the momentum conservation in the curved space-time for electromagnetic? I know it's going to be two equations. but I couldn't find them anywhere and I couldn't calculate them.


When resolving vectors into their horizontal and vertical components, why must the individual vectors form a closed triangle? I don't understand why vectors must form a closed triangle when one vector is the sum of the other two. Why is this true, and how do prove this?


I've seen in many places, including Weibel's excellent book, that the category of short exact sequences (in an abelian category) has kernels and cokernels, although it is not abelian. However, I cannot find any analogous information about the category of long exact sequences, so: Are there kernels and cokernels in this category? In other words, is it pre-abelian? Thank you!


I was reading this thread Exterior power of a tensor product and I found that the result cited in first answer is very useful to me, but I couldn't prove it myself and what's said there is not enough for me. Can you give me a good reference?


I was playing around with Desmos today and came up with this formula for finding global minima: It works by descending until it finds a negative value. The same method could work with multiple variables using nested products. Would that be a computationally feasible method to use in machine learning?


In our class today we spoke about the Einstein and Debye models. We associated the Einstein model with the optical phonons and the Debye one with the acoustic phonons. But I have a question: what is the argument made for associating acoustic phonons with the Debye model and the optical phonons with the Einstein model?


I understand that wavelength is inversely proportional to index of refraction, which causes dispersion of light (red visible light is deflected less than purple), and total internal reflection. Is there a way to explain, based on these concepts why red objects (as seen in white light) absorb most light other than red light, which gets reflected?


I'm trying refer to a node and its ancestors, but not its descendants. There's a decent discussion about this here but most of the suggestions would include descendants (kin, lineage, blood-line, etc.) Typically I'd just say "a node and its ancestors" but I'm trying name this variable in a computer program and I can't come up with anything good.


I would like an alternative way to write the following statement I accept that my brother is a terrorist and condemn his actions with the condition that you accept that your father is a war criminal and you condemn his war crimes. The obvious implication being, my condemnation is conditional. Or is the phrase "with the condition that" correct and sufficient in this statement?


My oven has the heating element in the bottom. So the bottom shelf is more directly exposed to it, and should be the hottest shelf. But hot air rises, so the top shelf should have the hottest air, and should be the hottest shelf. I don't know which logic to follow! What part of my oven should be the hottest?


Are these the same thing? I understand the marginal likelihood is the predictive likelihood over the prior, but since the GP the prior is defined on the training set, are these the same thing? Can we show it mathematically?


I don't want to reinvent new names when writing a paper. I want to ask if there is already a name for a "zero measure", or "null measure", which makes every measurable set measure zero.


Before the big bang, there was a point surrounded by nothing (no space or anything). Then the big bang happened and the universe expanded. so beyond the universe's limits, there is nothing? I don't understand this, can someone help me? I'm not a physicist I just wonder. and also the expanding rate of the universe affects the speed of time or not?


I am a physics undergraduate student currently taking a classical mechanics course, and I am not able to understand what conjugate/canonical momentum is (physically). It is sometimes equal to the linear momentum we know but not all the time. What exactly is potential momentum? It would be great if someone could explain it in simple words.


I find the word "meta" to have a unique meaning. People have begun using it as a standalone word, as in, "That movie was so meta." However, I think this is colloquial, and it often means "philosophical, mind-bending", not strictly "a self-referential system", in the precise sense. What could be a good adjectival form of "meta"? "Metalogical"? "Metaistic"?


I found a post that mentioned this problem where students get confused when interpreting mixed numbers: Avoiding confusion between mixed fractions and multiplication If a student ask "then when can I assume there is a multiplication sign between two numbers", what is the correct answer?


If energy exerted is a function of distance and force, the object would not move in this case. But would energy not still be exerted? Simplified the example for sake of clarity; but specifically asking with regards to a person doing something like a bicep curl and learning to only squeeze their bicep, rather than tensing their whole arm and fighting against themselves.


Anti-bumping granules are usually small stones. I presume that the principle of these granules ensuring smooth boiling, is that it blocks the upward motion of solution molecules. Usually the stones have an irregular shape. I am wondering, if the anti-bumping granules are in regular shapes, like a sphere, a cube, will there be some influences to the anti-bumping action of the granules?


I remember there is a term/saying for accidentally speaking something out loud about what you secretly wish for. For example: you like someone, but you aren't awared of it, but then accidentally say it out loud in a conversation.


If I am not mistaken, this video says that X-rays travel faster in glass than in a vacuum. Special Relativity says that information can not travel faster than the speed of light in a vacuum, so what is keeping us from making Tachyon Phones with glass and x-rays?


Since the time it takes for the earth to complete one rotation about itself (i.e., the time we call "day") is not constant, then the angular speed is also not constant, that is, there is a non-zero angular acceleration. What is the corresponding torque(s) causing this angular accelaration?


For example, if John has a bike. It's John's bike. It's John, a colleague of mine, 's bike. How do you really write that? I know I can just say "It's the bike of John, a colleague of mine," but that doesn't sound as clean as using 's.


I searched for some answers, but most answers discussed the meaning of torsion, instead of its definition. Not knowing how the torsion is defined (in cohomology) I couldn't understand those answers at all.


I am a non-native speaker and for this very special example I can't find any explicit rules in the literature: The paths, whose lengths are equal, have been created. Is "whose" the right word here? I can only find singular examples and wonder if the word must change for plurals.


After spending some time looking for different means and mediums to model blackholes, I came across sonic holes which are modeled through Bose-Einstein-Condensates. However I have not been able to find any other possible methods of modeling blackholes (other than computer simulations). This question addresses the issue only partially. Are there any other proposed or experimentally tested methods of modeling blackholes?


I was wondering if it was possible to have an infinite ray in a finite tree? This is impossible merely from the fact that an infinite ray goes through infinite vertices, contradicting the finiteness of the tree right? Is it fine if I just stated this as an obvious lemma? Thanks.


I understand that anywhere is an adverb in this sentence: We couldn't go anywhere nice to eat. However, I am a little confused about how nice to eat is explained. nice and to eat both modify the adverbial anywhere , but I'm not understanding how that works. I've always learned that adjectives don't modify adverbs. Could someone explain this sentence structure to me?


In quantum mechanics we know that every operator can be represented by a matrix.Being a beginner of quantum optics, my question is does there exist a matrix for squeezing operator also? If does, can the elements of the matrix be parameterized?


It is well known that a covering space of a graph is also a graph. It is also true that the image of a graph under a covering map is a graph? I'm not sure that this is true, but I cannot find a counterexample.


I would like to know the correct preposition for research when used with "any topic." Should it be: It enables us to research any topic with ease. Or: It enables us to research into any topic with ease.


I am struggling with analysing the sentence 'Y happens, benefitting patients with X'. I can see that 'Y benefits patients with X' uses the present tense simple form of the verb. But in the first example, is 'benefitting' functioning as a gerund or an adjective?


I know that in general, nearby paths in a chaotic system tend to diverge exponentially, but are there continuous systems where paths diverge at other rates? For example, is there a system where nearby paths diverge say double exponentially or at some rate determined by tetration? Or are there ones with slower divergence, for example only quadratic or cubic divergence instead of exponential?


I'm looking for a catch-all term. Do we say "intellectual property work" or "intellectual property content" or something else? For example, At the moment, the best solution is to file their work with intellectual property office in specific jurisdictions where the creators wish to protect their IPs. Could I say "their work?"


Is there "a categorical way" of speaking of objects in a monoidal category which can't be written as a tensor product? (We have to be careful with multiplication by the unit.) The same can asked for a cartesian category and there might be a smoother way of answering the question. Both questions seem interesting to me.


What's the difference between "wave" used with "to" and "wave" used with "at"? Two sentences as examples: She's waving at the person behind me. and The lookout man had waved to me as I approached. Could either choice be used in each sentence?


I'm finding everywhere this fact about this being the simplest knot which is not equivallent to its reverse (same knot, other orientation), but I can't find any proofs out there and I also don't know any invariants that can distinguish these two, so if anyone knows which invariant can do this or where to find the proof, I would be very grateful.


One teacher told me that the bare infinitive cannot be used as the direct object of a modal verb because it is not a noun. But, isn't infinitives with or without "to" infinitives?


Equilibrium position of a pendulum is defined as the position where no external force acts on the body and if no force is applied, it remains at rest. In the image, isn't gravity acting everywhere, then how will you define the middle point in the pendulum's motion as equilibrium position? Even if you remove gravity, initial push is required for it's motion.


Urbanization is at the stage when most people are aware of the central importance of infrastructure. Urbanization is at the stage where most people are aware of the central importance of infrastructure. Which is better to use 'when' or 'where' in both sentences and why? In my opinion, 'stage' indicates a period, i'm uncertain which word is more suitable.


This is puzzling to me because I have learnt that a charged sphere has the same electric field and electric potential at a point beyond its surface. So does it mean that a point charge is also inherently a sphere?


What is the current known record for the maximum number of ions that have been successfully trapped in a Paul trap? Could you also share a reference to the scientific article or any form of published research where this achievement has been documented?


I mean thermodynamic equilibrium implies mechanical equilibrium, but mechanical equilibrium doesn't mean to that the system to be in static equilibrium. For some reason, all the systems I have seen in thermodynamic equilibrium are at rest. Am I wrong with this thought?


I have read that moving ions generate a magnetic field as it moves. Similarly, is this also true regarding the nuclear magnetic moments of the atom? In other words, would a moving atom with a nuclear magnetic moment generate an electric field as it moves?


I read 'The Standard Model Effective Field Theory at Work' by Isidor, Wilsch, and Wyler. In a footnote, they say that, in principle, right-handed neutrinos could be included in the Standard Model by extending the fermion content. But these would be completely neutral under the Group of Standard Model. Why is that a problem? Why is the chiral fermion such a necessity?


When I pour dry lentils into a water bowl, I notice many of them form little clusters, with an air bubble in the center. Why does this happen? I'm guessing something about static electricity. But not sure bubbles or lentils have charge...


This perhaps may be very naive question, but could one consider an analogy to the parallel transport (as defined in this Wikipedia article) being a ball rolling on a flat table surface? If so, is then such an example also an example of holonomy or not?


I wasn't able to get a proper reason behind this and the only thing I could find were classical analogies for spin which (when I asked my prof) were not to be relied upon.


While seeing the derivations of the Rayleigh Jeans law and the Planck's Law for a Blackbody Radiation, I came across a fact that they assumed that Electromagnetic Radiation inside a cavity would form standing waves only. Why is it that the blackbody radiations inside the metal box should be a standing wave only in the derivation of Rayleigh Jeans law and Planck's law?


Could you give an intuition about why does MHD requires the following condition in time and spatial scales, please? Thanks. At scales much larger than the mean free path and gyroradius, and time scales much larger than the collision time and gyroperiod, the magnetohydrodynamics (MHD) model is good.


I have tried exploring different periodic functions combined with exponential growth rates, however, all my models fail to overshoot the carrying capacity. I have also examined piece-wise functions that could work, however something that is more elegant would be much more pleasing.


Do you know any trick for including rectangles around references, such as Figures, Tables, and url links, etc. in Texpad editor when the TexpadTeX typesetter is used? While I can manually change or hide these rectangles (or even alter their colors) using pdfLaTeX, etc. (i.e. manual typesetter) these commands seem to fail when using the TexpadTex typesetter. My goal:


I've noticed that "Diagnostic" can be used as a plural! Such as in some windows warning messages. What's the subtle difference between Diagnostic and Diagnosis? How do we use each of them in a correct way?


It is easy to see how primitive warfare might sometimes have beneficial environmental effects; it is not clear how they could amount to a cause of primitive warfare. Could you tell me, please, what grammatical tense is meant here, present or past tense?


How far apart do two vertical glass surfaces have to stand for a water droplet that is sticking to both of them to break into two? I apologize in advance for the question possibly being too imprecise .


That test particles travel along the geodesic is assumed in the context of GR. But does it apply to strongly gravitating object, such as black hole in an expanding universe, binary neutron star, etc.? How to justify if so?


I read about the classification theorem of finite simple groups, and I was wondering if there is a topological meaning to spaces that have a simple fundamental group? In addition, is there something that we can learn about spaces with finite simple fundamental groups, by using the classification theorem? Thank you in advance!


I'm in an argument with somebody, about this line. The number of customers increase vs The number of customers increases. We are focusing on the number, but the subject is plural. He's arguing that the subject is "number" I'm arguing that it's "customers" What would be grammatically correct? If there is a correct way, is there any references on it?


I'm new to LaTeX; is there a way to tell the TeX engine to generate the hyphenation of a given list of words as a text output file? For example: abdomen abduction aberrance ... What I want is something like: ab-domen ab-duc-tion aber-rance ... possibly as text.


I understand that the direction of the magnetic field lines at the equatorial plane is opposite to the direction of the magnetic moment by definition. Is there a reason of physical significance as to why that is the case?


The first post below provides examples of commutative non-cancellative Archimedean semigroups with no idempotents. Can anyone provide a reference to a characterization theorem for commutative non-cancellative Archimedean semigroups with no idempotents? (For example it is known that a commutative Archimedean semigroup with an idempotent is an ideal extension of a group by a nilsemigroup.)


I was just wondering what happens when you see a visible light, for example violet, and that light slowly increases/decreases until it's not visible to the human eye. Will it fade or just become instantly invisible? Could it even injure and cause blindness?


Do you have an example of a path-connected non-hausdorff space on which two points can't be injectively path-connected? (that is, any path between them is not injective). I tried to figure out what such a space should look like, and what its topological properties should be, but I failed. Thank you very much, AF


In Stephen King's The Jaunt, I found this sentence: Five Jaunt attendants circulate, speaking in low, cherry voices and offering glasses of milk. It's either a typo (was supposed to be 'cheery') or something I don't understand. Can anyone think of an idea?


What is the maximum possible rate of change of length-of-day (in units of minutes per day), on Earth? It is well known (and easy to observe) that it's larger near the equinoxes, and at higher latitudes, but how large can it be? (Perhaps we can use Seasonal changes in hours of daylight)


In an interview today, I was asked the definition of transformation group which I was unable to answer. I tried googling the same but I could not find a precise definition. Can someone please give precise definition or reference for the same? P.S: I am aware with groups of mobius transformations or orthogonal transformations etc.


For example, willingness to provide for someone is generosity and willingness to protect someone is bravery, but if we wanted to put both of these (an possibly other values) under an umbrella term, what would that word be?


Could you use me's as in something like this? The person behind me's phone keeps ringing. The person behind me's breathing sounds laboured. I've tried looking at other questions but I couldn't find anything about it in this context.


The correct way to cite an unpublished manuscript in apa is: Author. (Year). Title. [Unpublished manuscript] Department of blabla, University of blabla. However I can't get LaTeX to show me the "Department of blabla, University of blabla" part. Notes give parentheses such that: (Department of blabla, University of blabla)


When Hubble determined the distance to Andromeda he based his estimation on Cepheids. However, the result was less than half the current value. What was the cause of this error and could another adjustment happen in the future?


Some examples where we don't speak about abilities, but what is legally allowed: May I drive a car if I hold an international driver license? You may drive a car if you hold a driver license. I have never seen "may" in these contexts but I don't understand why I should use "can".


In the X-ray experiment, energy lost by the electron is released as a photon. When does this happen? If there is a single nucleus deflecting a single electron how many photons would be emitted? Does the photon emit when the electron is closest to the nucleus? Any links to reading material would be appreciated.


I would like to know what the rest of the sentences is. I would like to know what the rest of the sentences are. Can they both be correct depending on the context? The meaning I am aiming for is that some sentences are cut off mid-sentence, and so I cannot understand what is being said.


What are the best practices for having correct hyphenation in the bibliography section of documents when using Biblatex? Most times my bibliography seems wrongly formatted, especially in two-column documents. URLs and names with a hyphen are also difficult to deal with.


The word I'm looking for is similar to "claustrophobia"; it's to describe the feeling of being trapped in a place that feels too narrow, almost like you can't breathe properly in it. (A noun, preferably not a -phobia one.)


I just came across the words from the site "https://www.androidpolice.com/gmail-mark-all-messages-read/", which indicate, as for me the same thing but by using different words in the article "volume bar", "volume slider" and "volume rocker". So, my question is do these three indicate the same thing as the volume adjustment function on mobile phones? I've included a screenshot for your reference. Thanks


Do Canadians follow the American English pronunciation with the "eye" phoneme or do they tend to stick with the Commonwealth pronunciation, i.e. with the short "i" vowel? (Sorry, don't seem to be able to paste IPA.)


I understand magnets require cooling to achieve supermagnetivity. How much of liquid nitrogen do Maglevs carry with them? How much is required to keep them cool? What is liquid nitrogen consumption per distance traveled?


"Geometric median" seems like the obvious choice for "median (but for even number of values, take the geometric mean of the central two values instead of the arithmetic mean)", but this seems to have a different meaning. Is there a term for this type of median?


Usually a calculus or real analysis book has the following topics Convergence of sequences and functions Continuity Differentiability Integrability I am searching a book with those topics but such that each topic is developed in the most abstract way, i.e. convergence and continuity maybe from the perspective of topology or metric spaces and integrability from Lebesgue perspective. Thank you so much for your help.


Behold the joke in its original glory The judge looked down upon the counsel and said, Judge: Listen, counsel. I have been listening to you for three hours, and I am none the wiser. Barrister: I expected that, my lord, but I thought you might be better informed. How is "I thought you might be better informed" a jab at the judge?


I am writing a research paper and I have to write it in LaTeX but I am struggling to recreate the follow image into tikz code. Thank you in advance for your help


The pigeonhole principle seems self-evident, most people would accept it without evidence, but I wonder if we wanted to prove it, would we have to use the excluded middle principle? I would be grateful to provide a proof with or without the excluded middle principle, but I am curious as to which proof does not use the excluded middle principle.


Given a minimization optimization problem of a linear target function over the set of positive semidefinite matrices of some fixed maximal rank, subject to affine constraints, what are (analytical) methods to find lower bounds on the optimal value of that problem? If we had no rank constraints, the answer would be "convex optimization duality", but the rank constraint makes the problem non-convex.


I am using the latex workshop plugin in visual studio to write a tex file, everytime I save the document the background task will auto build the document, I have already find the auto compile in latex workshop but failed, is there any way to disable the auto compile process?


By measuring the energies of the emitted alpha particles, how can we say that they have energies less than the height of the nuclear potential well when they are inside the well? How can we be sure that alpha particles are not momentarily acquiring energies greater than the height of the nuclear potential well and coming out without requiring the mechanism of quantum tunneling?


What do you call the long straight pieces of metal, set into the ground, that you find at bus stops (at least in Canada)? People stand next to the post when waiting for the bus. They look like this: Do you call it a bus stop post?


We say that induced potential in a magnetic field is directly proportional to the rate of change of flux but when a wire moving perpendicularly in a uniform magnetic field at constant velocity it is said that a potential is induced.But there isn't any rate of change of flux . So how does it induce a potential?


If I released a giant cloud of Oxygen into space, would you be able to hear sound inside of it before it dissipated? From my understanding, the reason there is no sound in space is because there are no atoms for the sounds waves to interact with. So if you theoretically put atoms in space would they carry the sound?


I have read the neutrino mass problem. The unnatural smallness of neutrino mass implies the existence of new physics so the seesaw mechanism is introduced to solve this theoretical problem. I understand that Dirac neutrino has only the problem of its origin, however, is the possibility that neutrinos are Dirac particle ruled out by the current experimental observation?


I saw that true strain is a sum of strains over many increments. Why would this be more accurate than using engineering strain? Engineering Strain assumes the initial length to be constant which makes sense to me because strain is just a measure of deformation. What is wrong with the idea of assuming initial length to be constant?


Consider the following scenario: There is a wind blowing right above lake surface. This wind will induce a surface current in the lake. I am quite new to this topic, so I would be interested to know if there is a well-known model or perhaps some references that gives the relationship between the wind speed and the speed of the surface current. Thank you.


If a person or thing is the exemplar of a particular virtue, you might say that they or it is exemplary or ideal; but the word "paragon" has a particular, even mythical connotation that none of the adjectives I've seen has. Could you say that something is "paragonic?" Perhaps "paragonal?"


This question is from permutations and combinations i have no approaches it would be fine if someone could just give an approach to this problem. I am a high school student with basic knowledge of combinatorics


I have an antenna that is placed at a certain height over conducting ground plane. If it's measured, I could imagine ripples in a farfield pattern owing to reflection from the ground. Is it correct to use two-ray ground reflection models to predict the complexity of interference patterns (maxima/minima) in the far field?


After discussing this problem with multiple others, I've heard tons of different answers. I understand the explanations for both A and D. I've found differing sources on the web for this question as well, some supporting A and others D, even a few C. Can someone help explain what the answer is and why?


Theorem with Diagram I am taking a topology class, and my lecturer keeps using diagrams like these. I am capable of understanding the theorem, but I must admit that diagrams like these often go above my head. Is anyone able to explain this diagram to me, what the arrows represent in in context with the theorem?


The force exerted by the nucleus on the alpha particles is electrostatic in nature. So, why does mass has an effect? How do we conclude that the electrons don't effect the alpha particles from the fact that the mass of the electrons is negligible although they have the same charge as of the protons in the nucleus.


Q. The smoke ____ out from the chimney. a. left b. rose c. went This question was asked recently in an exam. So which one of the options is the most appropriate option to be filled in the blank ?


I want to write a legal memo using Latex. What class should I use in order to do this? Is there any other advice one could offer when formatting a legal memo to my company in Latex?


I believe I can prove that such a solid doesn't exist, because if it did it leads to perpetual, motion as the solid could not remain still in any position on a horizontal surface once it is set in motion, and that is against the first and second law of thermodinamics. My question is if there is a mathematical proof without resorting to physics


It is well known that steel grains tend to grow larger under heat treatment. Is it possible to enlarge grain size through any other means? I cannot seem to find anything via web search. If steel is too narrow a scope, the question can be generalized to all metals.


Let a vertically polarised beam of laser light pass, at right angles, through a horizontally polarised beam of laser light of much greater wavelength. Does the oscillating magnetic field of the one cause Faraday rotation in the other?


I've had my eye on properly understanding climate, climate change and the wide array of phenomena related. But, as a physics grad student, I'd fancy more exact, math-based bibliography, that treats all these interesting topics in a more formal manner, rather than with vague, high-school level explanations. Recommendations are very much appreciated.


The sentence in question is: Donuts are not a part of healthy eating. I'm debating between the following: Nothing wrong Donuts are not part of healthy eating (because "donuts" is plural, is it grammatical for "a part" to follow? Or does this not matter?)


When calculating "antenna element length" should we use the speed of light in the "medium between transmitter and receiver (antenna)" or the speed of light in the "element material"? (for example speed of light in air vs speed of light in Aluminum)


I'm looking for resources/references(books, websites, lectures) that cover everything Fourier: right from series(real, complex) to transforms, discrete transforms, and possibly modern topics like FFT. Particularly, I'm interested in the various applications in image and signal processing, so something that covers this contextually is also much appreciated.


The Wu experiment shows how parity symmetry does not hold for the weak force. However, how does this proof that parity conservation also doesn't hold? If my understanding is correct, the absence of parity conservation would mean that particles with odd parity can change to even parity and the other way around. But what changes parity in this beta decay via the weak interaction?


What is the rhetorical purpose of the phrase: "to be honest?" I think it has become a way to indicate that what came before was a lie but the speaker does not want to be direct. On LinkedIn, I see it used by Climate Crisis disinformers to smear posts about global warming.


I never use more than nine chapters, sections, subsections, or subsubsections. Therefore, I would like to remove the middle periods (but not the final period) in my section heading, as follows, both in the main text and the Table of Contents. Is this possible?


I am trying to submit to arxiv and facing this error. I have the .bbl file in my folder structure. I cannot seem to find the reason of this error. Also, what are .rels files, these are not created by me. I also saw this solution, and tried. It shows output.bbl in the logs. Do I add this in the main folder structure?


Imagine that a rocket is going up at a high speed and after some time its engine shuts off and it separates from the rocket. In such a situation, drag and gravity are both downwards. Does the same direction of drag and gravity cause weightlessness? If yes, why? If not why? And in general, what does this same orientation cause?


Suppose a particle is in time independent potential and NOT in any superposition of eigenstates. Then expectation value of position is time independent and expectation value of momentum should always be zero according to Ehrenfest theorem.Is this true?


What is a system described by a set of random variables for which there are distributions over subsets of these variables which are not marginal of a distribution over all random variables at once. That is, what is an example of contextual statistics in the real world. I would like an example that is not quantum mechanics please


In motion planning for quadrators the optimization goal is sometimes to minimize the (norm squared of the) jerk and more often the (norm squared of the) snap. Can someone provide an intuitive and theoretically explanation? What optimization goal is used for cars in general (i.e. velocity, acceleration, jerk)?


I recently learnt that more than two photons can be entangled. Are all the three photons are expected to have the same polarized angle due to entanglement? Does measuring one of the three photons collapse the entire entanglement or the other two photons continue to be entangled?


This question has been asked before (see this: Amoeba splitting probability), but I've recently come across this article which uses a biased random walk approach. Screenshots from article attached: What are the "usual arguments" being referenced here? Confused as to how he did this.


my friend and i have been debating the answer to this question could someone help me with this by explaining their answer please :) Is it possible to measure the energy of the particle if the wave function psi is not an eigenfunction of the hamiltonian?


Experiments that feature the creation of entangled photons through SPDC often make use of coincidence counters. How can one photon be accurately correlated with its entangled partner by a coincidence counter? Are there any methods or technologies that help decrease the error of coincidence counting methods that help validate the trust in their accuracy that so many experiments depend on?


The ejection of photoelectrons is independent of the intensity of radiation. But the quantity of electrons ejected depends on the intensity. So is there a limit to how much the intensity has to be, below which zero photoelectrons are ejected even if the frequency is sufficient for an emission?


In school we did this experiment. We impacted a laser beam through a solution of sodium bicarbonate and the path of laser was visible in it. Does it have anything to do with coloids? But is this solution a coloid?


This is a picture I found online: I have two questions about this. How do we know that over the power source and over the resistor, the electrical field is parallell to the power source or resistor. I highlighted this with the blue circles. Is the field symmetric around the power source and resistor if we rotate around it?


What metric determines the "geometry" of the gravitational field generated by the mass of the sun? Is there a general metric that incorporates arbitrary mass and devolves into the Schwarzchild metric for black holes that conforms with the Einstein Field Equations?


I was wondering if there was a one-word term for this. I suppose a classic example might be the "Door Close" button on an elevator. Essentially, a working feature that apparently does something, and the user can activate it but it will not actually play any meaningful role in the operation of the device.


Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? I imagine it should be absolutely massive so that tidal forces are minimal. And if all this is possible, are there any special effects on the Star apart from usual time dilation?


I have a small confusion, do conservative forces obey Newton's Second Law always? Because it depends on the end points and the path taken, the acceleration may vary path to path, but the force doesnt depend on it, so IDEALLY it should defy it.


Does it have connection to the physical act of squatting or is it coincidental? After all, people that occupy a property, may just lie or stand in there, instead of squatting. So this does not seem to be very logical. I can't find any etymology or origin story of the legal term...


I've recently been reviewing the Feynman Lectures. Caltech has posted Feynman's actual handouts from his lectures on the website below. https://www.feynmanlectures.caltech.edu/flphandouts.html Though they are helpful supplemental material, most handouts do not come with solutions. Does anybody happen to know how I can find solutions to them?


What is the formula to find the average value of this waveform? What is the relation between the peak to peak value and average value of this waveform? Note that it's not an alternating wave. It's positive but changing wave.


Can Fukui method be employed for the Chern number calculation in a low-energy continuum model? Let's consider the low-energy continuum version of the Kane-Mele model. If not what are some other ways one can try? Thanks.


Example: Once I click on the main text and press "Enter", the Outline Pane automatically switches back to "Table of Contents" (instead of sticking with "Labels and References", which is what I'd like). How do I stop this?


since its an open problem if NP = EXP, so i want to know the problems in exp for whom no polynomial certificates for output verification have been found so far . Any link or name would be nice


I have a problem getting the right template for IEEE Open Journal of Vehicular Technologies from IEEE Template Selector. I make the right choices but then i get the template for Open Journal of Instruments and Measurements. Where can I find the right template?


I read about time dilation and how to prove time dilation existence with light clock. But how to prove that time slow down on all other type of clocks (biological, mechanical, digital, electric, atomic, etc.)? Is it possible to test it on real experiments? Thanks.


I know that all vectors are contravariant because if we transform into another basis vector we find its components change inversely to its original components. But I don't know why gradient is a covariant. How the components changes same as basis vector changes?


Does "hash browns" refer to a countable thing? Or a substance? Have I had too many or too much "hash browns"? The word "browns" seems to imply a quantity. But, is there such a thing as a single hash brown? Or, are the strands just "pieces of hash browns"? (Or of "hash brown"!?) Why does this all sound wrong??


Gravity is non-linear, so if it is mediated by gravitons, gravitons must interact with each other. On the other hand, the effects of gravity moves with the speed of light, so if it is mediated by gravitons, gravitons must be massless. How can gravitons interact with gravitons if they are not charged under gravity?


I'm a physics teacher and I'm wondering if there's any game for physics elevator problems (weight in accelerating elevator) that the student can play with to better understand in what situations the weight is less or more


In logic, the completeness theorem in propositional logic consists in showing that a formula is provable if and only if it is a sentential tautology. Suppose now that I have a set of non-logical axioms on top of tautologies. Does it make sense to look for a weakest form of the completeness theorem in that case?


Supersymmetry is a model based on symmetry between bosons and fermions. Bosons carry force and they are described by potentials. Fermions are matter particle and they are described by wavefunctions. Does fermions carry force similary to bosons in supersymmetry? Can fermions be described by potentials instead wavefuctions?


Trying to discern correct use of prepositions. Here's the sentence as I have it: This was proof that he could stay steadfast under conditions in which other men could not! Should it be: "...under conditions which other men..." ? Or is there another way that's more correct?


See, it's a simple question.What exactly is stress? Is it the restoring force applied by the body in reaction to deformation force or is it the deformation force itself? I had this doubt because in some videos, they said that stress is the force applied whereas some others said that it's the distribution of internal forces. Please help me clarifying this doubt!!


The Wikipedia article on propagators mentions that the harmonic oscillator propagator can be derived from the free particle propagator using van Kortryk's identity. This is followed by the identity itself which appears formidable. It is not clear to me how to even begin with this. How is van Kortryk's identity used? https://en.wikipedia.org/wiki/Propagator


I believe the title contains all useful information for the problem. I tried to show that this map would have to be an isometry, but I can't seem to ensure that orthogonal vectors in the domain remain orthogonal in the image.


I'm looking for a word to describe the sensation of emptiness, an emptiness endured for so long that it has evolved into physical pain.: Like you cannot breathe but at the same time feel unable to move or speak or do something you once loved.


I am self studying general relativity and there is some especially hard problem (it is called bonus problem in book) I am currently working on it, but I am trully stuck, so I would appreaciate all the help I could get. Thanks!


This is a follow up question asked and answered (Radio-dating and the age of the earth) The answer was given that the mineral Zircon is formed under high pressures and temperatures. How do we know, for example, most of the Zircon on Earth wasn't formed in some extraterrestrial event before the Earth formed?


The verb for lying is "told","I told a lie." Occasionally I will hear, "I said a lie." The latter usage really is cringey to me although perhaps "said" is a common usage in some areas. Is "said" actually wrong? What do you call verbs that seem to go with specific nouns?


I'd like to create a weighted grid paper template. I'd like it to basically look like a sheet of lined paper, but with faint, equally spaced, vertical lines through it. I looked into the gridpapers template which has a set of templates but I could not figure out how to change the properties of the vertical/horizontal lines.


White holes are described by the time reversed Schwarzschild metric. A test particle which is gravitationally attracted to the black hole's event horizon in the Schwarzschild metric is also gravitationally attracted to the white hole's event horizon in time reversed Schwarzchild metric. Still, white holes are described as a region of "outward-flowing space time". How are both compatible?


Non-native English speaker here. Maybe this is easy for native speakers. Wiktionary clearly explaines, that surfaced roads (covered in gravel, stones or tar) are refered to as metalled roads. Why is metalled used as the overarching word? This seems counter-intuitive since all of the stated materials used for the surface-cover are thoroughly non-metallic.


As far as I understand, local OMP (optical model potential) depends only on the relative position, and non-local OMP depends on relative position and momentum. I am searching for more information so as to understand the difference more intuitively.


SPM and Raman scattering both cause spectral (frequency domain) broadening of ultrashort laser pulses. So I was wondering if what we know as SPM spectral broadening is dependent on Raman scattering at microscopic level. SPM is a nonlinear process. What about Raman scattering? If Raman is not nonlinear, then can a nonlinear process be dependent on a linear process?


Is this the correct term for words which are nouns when the first syllable is stressed, and verbs when the second syllable is stressed? Examples include PERmit and perMIT, and CONtract, and conTRACT. There are frequently-occurring suffixes such as '-ject' and '-tract', but are there any other relevant rules and patterns?


I wanted to extend the length of the last line in a minipage, so it touches the minipage margin (creates a perfect box of text). I doubt it has any practical use, but im trying to recreate a poem in LaTeX. Sorry if there is a simple answer, I learned LaTeX basics just today. I hope it's even possible.


I am wondering if a nonlinear map can be considered like a set of linear maps, with a different linear map for each element in the domain. And a linear map would then be the case where the offsets and scales are the same over the whole domain. Or does nonlinear map have more connotations to it?


This is a question about conservation of momentum. Will the inertia of the rotating pencil make the pencil bounce higher? Both cases the pencil is dropped from the same height but the spinning pencil is made to spin by a force couple besides being dropped.


At least, why not try with protons, they are much heavier and at the end, any deflection from Lorentz force will not overshadow the Stern- Gerlach phenomenon. But the question is still, was such experiment carried out or not?


Today the prof. a new sign and I don't know how to draw it. It is like overline, but on both ends of the line go down, so there is half of a rectangle above the letter. Does anyone know, how to make it in Latex?


My friends and family call me Tumbleweed because I'm tall and clumsy, but sometimes I wander if there's more to it when my "friends" call me Tumbleweed. I was wandering if Tumbleweed can be used as a nickname for such a person (clumsy and gangly)?


I was wondering...if entropy is a "state function" then why does going through an irreversible cycle give a negative value for entropy (Clausius inequality), I know it might be due to the fact that entropy is an unnatural transformation but I want to understand why? cause it is still a cycle... why it isn't a zero value?


I'm looking for a template (or a class) to write a systematic literature review in Public Health Sciences. I can use the article class, or a specific class as oup-contemporary; but I'm wondering if such a template exists? I didn't find any specific template for a systematic literature review. If I can't find it, I can create one with the article class.


In Linux when I want to install packages that are not provided by my distribution's repository, I can manually add entries to sources.list and download them. Are there any such alternative repositories for TeX that provide well-maintained packages unavailable in CTAN? Or is CTAN the one and only go-to for TeX packages?


If a point charge with q charge is brought near a conducting body(especially sphere) how much charge will be induced in the body? Also when will induced charge be equal to inducing charge? Edit:- I want to know when the conductor is earthed and as well as when it isn't, assuming a metallic body in vacuum or medium.


Which sentence is grammatically correct or sounds more native-like? Politicians tend to discuss their sources of income nontransparently, leaving the discussions surrounding them out. Politicians tend to discuss their sources of income nontransparently, leaving out the discussions surrounding them.


I have a picture that is a rectangle and has an open center. I want this image to be my page border. How would I go about doing this? If I try to make the picture fit the entire page then I can't have the text on the same page that the image is on.


This is a graph represents the number of times a week the students in a class walk to school A question asked is "In total, how many times do all the boys in the class walk to school per week?" I don't even understand the question to be honest. What is being asked and what is the answer?


Why is it impossible to determine a real inertial frame? We can determine the applied torque on a gyroscope by observing its precession. And thus we can evaluate the acceleration of our non-inertial frame. Is this acceleration relative to a real inertial frame? If so then it should be easy to determine a real inertial frame. Help me on this, IM really confused


How does the above circuit work? My textbook only has potential divider circuits such that there is only one output voltage. Such as this one. Could we replace the arrowed line in the uppermost diagram with two lines? This is the only way the above diagram would make sense to me.


Could someone provide references for a modern treatment of statistical manifolds? I have so far only found treatments that seem quite old, where the notation is somewhat dense to follow, to some extent probably because the font seem adapted to "old-school" typewriters.


When a potential explicitly depends on time, energy is not conserved. However, if we take into account what is causing this potential (for example, a machine moving some object(s)), would the total energy of the combined system be conserved? I'd like to know if there's any proof one way or the other in the most general case.


I saw in one place the phrase "A which means B" being used as "A is equivalent to B", and in another instance the same phrase being used to mean "A if only B". Which is the correct usage? My feeling is that it means "A is equivalent to B".


Here's the example: "They are first taught the basic procedures for scuba diving, including safety and communication with fellow divers, then familiarize themselves with the equipment before dipping their toes into the water." I could come up with simpler examples but this is the one that I'm struggling with. Is it odd either syntactically or semantically?


Simple question. How did the English word "possess" come to have a voiced "Z" sound for the first double-S? Are there any other words that have this? Doesn't double-S consistently mean an unvoiced S sound, across a number of Germanic languages, English included?


According to wikipedia page: https://en.wikipedia.org/wiki/Commuting_matrices, there is a characteristic for commuting matrices such that: If A has distinct eigenvalues, and A and B commute, then A's eigenvectors are B's eigenvectors. How to prove this statement?


It is possible to estimate the position and rotation of camara on xyz axis (both location and rotation) from vanishing points ? If so how ? I tried to search the web for an answer but i didn't found anything i could understand relatively easily (i am not at academic level in mathematics and English is not my mother tongue)


I recently learned that position vectors and spin vectors lie in different spaces, and the complete wave is the tensor product of both. I wanted to know that whether we can talk about commutation of spin and position operators. Can we talk about commutation of operators that act on different spaces? If so, how?


What I mean is that are there any elements which we can actually observe decaying into other elements, like a magical transmutation? Just like how a paper burns into ash.(or some other interesting chemical reaction) If yes, then please tell me about them.


The boy who will come to see you tomorrow will bring you that book. Can this sentence be changed to either of the following? a. The boy coming to see you tomorrow will bring you that book. or b. The boy to come to see you tomorrow will bring you that book. Which one would be the better choice?


I make my ice in those little round to-go containers that usually hold sauces/dressings. When using the clear containers, the ice sticks to it and requires heat or violence to get it out. When I use the black containers, the ice slides right out with no fuss. Any thoughts on why?


In the above text it is mentioned that the incident light ray travels along the principal section.But any ray which travels along the principal axis should not go through the double refraction. Then why the text says that the incident light ray split into two rays?


If two random variables does not have linear relationship then they are uncorrelated even if they might be dependent. I am unable to come up with an example where two random variables have linear relationship but are uncorrelated.


The following question probably philosophical and as a result maybe not fit here, but I consider it as a Mathematical logic question: "If there are no roads, then all roads lead to Rome." Is this sentence true or false?


I have studied science till school, but not in grad... so I might very much be wrong ... isn't the wavelength of sound waves larger than the dimensions of atoms? Won't sound waves skip over atoms?


Writing a differential equation for such a figure is an uncomplicated task. It can be accomplished by using snell's law. But the resulting equation probably isn't solvable. I put it in wolfram alpha and it didnt even show it's graph. May be not it's solution, but I'd like to see its graph at least.


I came across this in Khan Academy Integral Calculus. I am asked to find this integral... I did the substitution, and it made sense so far... Then, I was unable to figure how to solve the definite integral. This was their solution... Where did that sin expression come from? I am so confused!


In my thesis I have to cite the references in the style shown in the picture. I think it is more near to apa style, but not exactly same. Could anyone please guide how can I generate references in this format. I am using .bib file and working on overleaf.


If neutrinos are so easy to produce, but it rarely get absorbed or detected, doesn't that mean the universe will be full of neutrinos? Will its density ever reach a balance where its absorption events occur as frequently as emission events? Is the universe already reaching the balance or far from it?


I read some papers that study the global existence of a solution to a PDE. Sometimes, I found the notion of the "continuation principle". What do we mean by the continuation principle? any recommended references and thank you in advance.


Maybe this a dumb question, but, is the gravitational dilatation of time caused because a particle travelling through a geodesic in a curved space-time must cover a larger distance than the one travelling through empty space?


I'm interested in knowing if there is a name for a graph G where; Its vertices: Are a subset of the vertices of graph H. Are the terminal vertices of paths in H. Its edges: Are only incident to the terminal vertices of paths in H.


How would we use the phrase "under one's belt" if the subject is 'us'? Would it be "under our belts" or "under our belt" because it is an idiom? For example With a year of successfully running this company under our belt/belts...


I'm reading on Lie group and Lie algebras, but I am confused with the correspondence between them. Does any element in the Lie group correspond to an element in the Lie algebra (tangent space at identity)? If so (such as two-dimensional rotation), why is it only valid near the tangent point? Or is it just a convenience for the first-order approximation?


I am in a heated debate over whether to use "is" or "are" in the following sentence: "When I look into her eyes all I see is/are bright lights beaming energy through our path on eternity together." Please advise.


For progressive waves we define phase difference as difference in phase angle between two points. However for standing waves, the phase difference becomes something else. We say two points are in phase when they travel in the same direction and with the same amplitude. So why have the definitions changed here?


Diamond dust is a natural phenomenon that occurs when ice crystals form closer to Earth and interact with sunlight. Now diamond dust shimmers because of the reflection and refraction of sunlight. I know that the shimmering of light on water is formed due to specular reflection therefore I wanted to know if the same applies to ice crystals.


I was wondering if a graph existed because I used euler's inequality and it said that theres supposed to be a graph but im having a hard time figuring out what it is. Thank you!


The term is used throughout the literature but I was not able to find a definition or even a paper properly introducing the term. What does a Hamiltonian have to satisfy to be a parent Hamiltonian? An explanation or examples would be much appreciated!


I'm editing a flyer someone else wrote and I have the following sentence: Our storytelling series launches with featured speaker, Aloysius Firefly, professor of arts. I think ought to be "... speaker Aloysius Firefly, professor of arts." What do you think?


Does measuring the energy of the particle cause its wave function (psi) to change if psi isn't an eigenfunction of the Hamiltonian? quite confused about this one on when the wave function changes when taking a measurement and when it doesn't. please help :)


Why does it say "possibly empty" in the definition of bipartite graph? Wouldn't that mean that every graph is bipartite, moreover I don't think partitionins can have empty sets. Is this a mistake?


I want some good books recommendation on number theory. I self-studied a good chunk of calculus and I am self-studying analysis right now, and would like to start number theory. I also have a good understanding of mathematical proofs. So, any recommendations for good advanced books on the topic?


I would like to reference this fact (probability measures are closed under convex combination). I found this (for example, probability distributions are closed under convex combination) but I would rather want to cite a paper/textbook. I would be happy if someone could provide such a reference (ideally to a paper or a book for which a PDF is freely available).


I am writing a paper which I want to start with a literary quotation. How do I do this? It should probably appear above my name and the title. It is not "To be or not to be" but for the purposes of my question it might as well be.


I have been wondering about this little problem for a while now. Everyone understands that, in the binary, the opposite of 'man' is 'woman', and the opposite of 'gentleman' is, namely, 'gentlewoman'. However, from what I can tell, there seems to be no word that refers to the opposite gender of the word 'lady'. Any ideas?


i have already read carlo rovelli's 'reality is not what it seems' and lee smolin's three roads to quantum gravity, how should i proceed from here and what books do i read that balance theoretical approach with the mathematical approach, i was looking forward to a first course LQG and string theory should i go ahead with them?


Water at absolute zero is, I suppose, ice. At room temperature it's water. At a certain point steam. What happens to it as we approach infinite temperature? (what we might call "absolute" hot)


Does a charge moving freely in an electric field's direction, produce a magnetic field? If so, then why is energy conserved in cases of distance of closest approach? If there is a magnetic field it is non conservative, so how is this possible? I tried to find out but could not find the reason for it.


I have two different circles with their formulas, which intersect from different parts of themselves, how can I calculate the area of the intersection and the rest of the circles? Is there some way to do it without using calculus? And how to calculate that area, why? Here is the question, if you find a way, it doesn't matter the exact numbers:


How was the singular value decomposition (SVD) method originally derived? How might one discover decomposition this from first principles? Related Q&As that lend intuition to SVD but not derive or show how one might come up with such a decomposition: Understanding the singular value decomposition (SVD) What is the intuition behind SVD? (cross validated stack exchange)


Consider: "What are you up to right now?" "I hope to secure an appointment with her." As opposed to: "What were you up to just then?" "I was hoping to secure an appointment with her." Yes, I know it sounds "more natural." But: why does it?


What's a good way to make an interleaved layout having text blocks aligned to one side and images/graphics aligned to the opposite? Or in other words: Imagine a raster of a three column layout where the text spans over the left and center layout column and the images span over the center and right column.


There is the famous isomorphism theorem for measure spaces: All separable nonatomic normalized measure algebras are mutually isomorphic. what about an atomic normalized measure algebras? Is it possible to establish an isomorphism or a measure-preserving transformation from an atomic normalized measure algebra into the measure algebra of the unit interval? These theorems would be helpful in understanding my qeustion. Any help would be appreciated.


Simple question: what is the verb for the phase change from gas (or any other "regular" state of matter) to plasma? The best thing I can think of is "ionization into a plasma" but is there a nice, one-word equivalent counterpart to other phase change verbs like melting, boiling, subliming, etc?


The sun emits white light, which is a mixture of light from all frequencies. Instead, it should have emitted a beam of light of the same frequency, as the source is the same? So, can you please explain why the sun emits light in all frequencies?


Yes, I know this package can generate structure from .mol and SMILES files. I'd like to know: is it possible to follow the reverse path, i.e. once the structure has been drawn with chemfig, generate the .mol file and/or the SMILES?


Is it possible to draw a Braid like this? (with dots and vertical strands) I tried to use TikZ braids Package but on the documentation I don't see anything similar to this things. Thanks in advance


I recently wrote, on Stack Exchange, in regard to the books of the bible : ... Paul, Mark and Luke's contributions ... I did so instinctively and afterwards realised what I had done. Am I wrong to 'bracket' together without fully stating : ... Paul's, Mark's and Luke's contributions ...


Why doesn't water inside a glass enter a straw when you close the top of the straw before putting it inside the glass. Shouldn't the atmospheric and pressure of water push the water into the straw since I would assume that the pressure inside of the straw is the same as atmospheric pressure which is lesser.


I was reading my book and came across that sample median is unbiased estimate for symmetry distribution with finite expectation. I was able to proof this but is this true for Cauchy distribution? Since mean does not exist for Cauchy distribution. And how can I show that it's an unbiased or biased estimator depending on the result?


In this question here, it was asked whether a black hole could emit protons with energies exceeding the GZK limit via Hawking radiation, the answer given was yes. So I ask, what proportion if observed GZK exceeding cosmic rays could realistically have been produced by said process?


I am currently a physics and mathematics double major graduate student. Looking for a text book and problem sets on the topic of vector field analysis, would be best if the book is advanced and problems is difficult. Also with application to classical electrodynamics/


I'm studying Fourier series and i'm using Desmos to graph the results and it does look like its approximating towards a square wave but is there a way that i can just graph a square wave in desmos? and periodic functions in general?


I've been investigating book layouts for a project I'm working on and I found the title page and book layout from the art and practice of printing I have attempted to create this layout using memoir but to no success. How would I go about recreating this layout in Memoir?


It has been proved by the Red Shift that universe is expanding. But if the universe is actually expanding, it needs energy to do so. I also do not know that with expansion in universe if mass increases. My question is from where do the universe get the energy to expand? How does it not violate the law of conservation of energy?


I was trying to understand problem regarding finding the adiabatic modulus given the isothermal young's modulus. I'm still an amateur in thermodynamics. I just didn't understand the final step where the two adiabats are combined.


I'm in search of an online tool that can: Write both LaTeX equations, as well as normal text. Convert the document into an image and let the user download it Also the tool must be free, because why not!


I have been reading a lot of resources but it seems a little too difficult for me to grasp, I have no background in mathematical competitions and the activities in my college related to competitive math are really limited. Can anyone give me a list of books or pages to start from the very basics to build my way up to the real problems?


Relatively straight forward question I had after finishing a review of the ethereum yellow paper. How might one go about or is it even possible to formulate the general math behind a blockchain as a category with a set of objects (transactions, nonces, accounts), and a set of morphisms ( state change function, block validation function, etc).


Human Assets Development or Human Asset Development The second one has no "s" at the end of asset. Which is more natural, and is there a rule for this (for example, use a singular noun (human asset) when the noun is used in a phrase (human asset development)?


Today I learned several vocabs including "adhere to". Also the teacher said that "New rules are adhere to" is also grammatically correct and used normally. However, I think that it feels weird to me because it ends with preposition "to". Can anyone help?


The meme-y term "dummy thicc" uses "dummy" as an intensifier modifying "thicc" (meaning curvy). How common is this usage of "dummy"? How long has it been around? Is the etymology here related to the use of "stupid" or "crazy" as ironic intensifiers? (Wiktionary lists "Extremely" as an adverb definition of "dummy", but without quotes or other background.)


Is it correct to apply the word fellow to a thing, not a person? For example "fellow companies"? Definitions in M-W, Collins and Cambridge all point to fellow being applicable only to people.


I'm looking for ways to visually signify the links between turns in a transcript and found this which I think is a brilliant way to do it in a book by Erving Goffman. Is there any way to replicate this on LaTeX in a consistent way over a large corpus?


Here is a piece of text: But the historical pattern of warfare remains inconclusive, frustrating, endlessly cyclical. States persist in warfare because the mechanics of the balance of power rarely permit escape from it. [link] The first sentence confuses me (especially the words "inconclusive" and "frustrating"). Please tell me how you understand it? How can it be rephrased?


Can someone give a reference textbook, etc which explains / has examples for polar integration to calculate center of mass. (This is at the level of advanced pre-college physics, say for example the JEE entrance exam, so references that explain in detail are preferred. JEE does not have multivariable calculus. Will prefer refernces that use single integration. Simple shapes will do


Does the region surrounding a bar magnet have a greater abundance of virtual photons, or more energetic (but the same number) virtual photons when compared to a region further away from the bar magnet?


To show dilation in spatial relativity, is it accurate to do a "god's eye view" showing a top down view of both trains, or is dilation from one perspective alone (view from Train A or Train B)?


I am working on a heavily mathematically project about plasma. In particular, I want to find references that treat the problem from microscopic models that include relativistic and magnetic effects (Coulomb forces, QFT, etc) and obtain kinetic models (BBGKY, Landau equation, Maxwells equation, etc). What are some state of the art papers/references?


In the Blandford-Znajek Process (which is considered a potential mechanism to explain jets from AGN), the lorentz force is assumed to be vanishing (the force-free condition). But we see that the lorentz factor for the outflow is quite high. If there is no exchange of energy from the electromagnetic fields to the charged particles, how are these two facts reconciled?


Is the dual/opposite of a Heyting Algebra still a Heyting Algebra? What about locales? I don't see any obvious way to prove it but don't know enough examples either to test for counterexamples.


Is there a database or tool that gives all the STY and CLS files that are part of TeX Live or CTAN? I can do some basic web scrapping to retrieve this information, but I would like to avoid having to reprint the roll.


I am writing a stellar atlas and I am using the astronomy and astrophysics template in latex but when making a document the template makes an abstract without me asking. How do i delete the abstract ? (Template can be found on the website https://www.aanda.org/for-authors)


"The ample supplies have the government urging vaccinations not just for people at highest risk of dying from influenza, but for anyone who wants to avoid a week of aching misery." Original Posts Is "have the government urging" a causative structures like "I had John fix the car"? If so, why we use 'urging' here instead of 'urge' in bare infinitive form?


Is there an alternative description/characterization of the stable module category of Abelian groups? I guess that the category of torsion groups is a subcategory of it, but is it all of it? What is the structure of the image of torsionfree Abelian groups?


The context is to describe groups such as "Stop Oil" that claim to be environmentalists, but behave in such a way to garner disdain of environmentalists (like blocking traffic which forces cars to idle and pollute MORE while also pissing off the very people they should be trying to win over), and in turn, their cause.


I am trying to understand how to write the gravity-matter and gravity-gravity hamiltonians in terms of daggered/undaggered operators. Is there any pedagogic review paper on writing such hamiltonians in terms of combined annhilation/creation operators with corresponding coefficients.


I saw this many times but I don't understand why it is an improper subset. The power set has all the elements S has and more so they are not equal making them proper subsets and not improper ones no? Or it doesn't matter that much if I put proper subset or not here?


I was looking for a way to derive a fourth-order error formulation of a second-order derivative at the contact surface of two different materials. Say, solving a thermal diffusion equation with varying thermal conductivity and diffusivity. Thanks in advance!


In Russian, we say "to have one's bumps" when we mean that someone makes their own mistakes, thus getting experience and learning from their errors. Is there anything similar to that in English?


Here is an example: I have developed my ability to identify the factors that impact my physical, mental, and emotional health[,] and am beginning to apply this understanding to make informed decisions. Do you agree with the comma I would use (shown in brackets)? Why or why not?


It feels like the transition from a sea of probability of a droplet of precision (or wave, depending what you're looking for) would be a loss of entropy, if so wouldn't this violate the Second Law? Or does Heisenberg's insistence that we cannot ask questions about what happens before observation exempt it from such considerations?


I guess it's a straight line, which is the axis of a hyperboloid of one sheet, and the three straight lines on different surfaces given are a family of generatrix of this hyperboloid of one sheet


Obviously there is a limitation as to how well experimental configurations that depend on coincidence counting can efficiently remove the noise present at any given experiment. This leads me to wondering, how efficient are modern day coincidence counting techniques? A percentage of noise removed, signal to noise ratio, an evidenced estimation, or something of the like would suffice.


For the zeta function itself, I have been using the Riemann-Siegel Z formula implementation as written here: https://web.viu.ca/pughg/thesis.d/masters.thesis.pdf However, my searching skills have completely failed me on the derivative. Is there an algorithm that calculates the derivative that is relatively easy to understand, and/or doesn't involve too much computation?


I am completely new to ConTeXt and have just started to experiment with writing metapost directly within ConTeXt. In Latex , we use the tcolorbox macro package to achieve the effect of code on the left and output on the right, my question is, how can I achieve a similar effect in ConTeXt?


I'm starting to learn the memoir class to use it with a book I'm writing in LyX.I've read most of the memman docuement. When I create a new LyX document I can enter the title, but not a subtitle, half-title page, or the other front matter pages. Do I need to put all this in the LyX preamble? TIA, Rich


I am looking for books and papers that take a mathematical perspective on the physics topic of dimensional analysis. I am sure there are such texts out there. I would be very glad to know of any such texts.


It is not possible to have a process in which the entropy of an isolated system is decreased Does that mean, if we increase the volume of a gas, entropy of gas increases, now when we decrease the volume of gas to its original volume, the entropy of gas comes back to its original state, but the excess entropy is transferred to the surroundings?


Here's a Desargues Configuration with all points on a square lattice: Is there a more compact version, either on a square lattice or triangular lattice? Also, if there a less obvious Desargues configuration that's larger, but still with relatively simple coordinates?


I have proved that pseudocompact implies completeness in a metric space, which is, as I understand it, a step to proving pseudocompactness implies compactness. How do I show complete and pseudocompact implies (sequentially) compact?


Do I need to repeat the subject after a semicolon splitting two sentences that have the same subject in formal written English? For example: He talked to the owners, which was understandable; paid the bills, which was not expected; and, did not even ask for the money back, which was unbelievable. Should I add the subject "he" after each semicolon on the example above?


Gaia provides low resolution spectra from BP/RP filters and the values of equivalents width for hydrogen spectral lines are also provided in it's stellar database. How can there be negative equivalent widths of Halpha spectral lines values as shown in the picture below? Shouldn't they all be negative or positive?


I have read this title Pakistan top court orders immediate release of ex-PM Imran Khan. Why they have written "orders" in present simple? I mean why not in present perfect or simple past?


I've read in some sources that Entropy is a measure of how much energy is not available to do work but I'm not quite sure what this is getting at. The only thing that I could think of is perhaps that heat cannot be fully converted work in a cycle with a portion dumped out as entropy. Is my interpretation correct?


Is it not a misnomer to call in a non-perturbative setting an irrelevant direction irrelevant? I know that it comes from perturbation theory where an irrelevant direction is irrelevant for the IR dynamics but in a non-perturbative regime an irrelevant direction should have effects in the IR.


There is an idiom that says basically, "Better to go out in a blaze, than burn out like candle." I'm probably totally off, but it's something like that. The point of the cliche is not to let your objection or opposition die with you, but to make it the cause of your departure.


Do I need to make sure the gerunds match in the following sentence: There is not much attention paid to really examining what constitutes this notion, much less scrutinizing the received criteria for it.


Polarization in GWB should carry as much important information as in CMB. However, I've done some superfluous literature research and found little discussion. Is there any planned project for measuring the polarization? Or is there a method to extract the information from existing experiments?


Is there a specifically appropriate term to say "reading between the lines" or "to read between the lines"? Or to devise inferred meanings and unspoken things, and not necessarily something that's consciously implied but that the other person may be giving away without realising?


I just start learning Physics. The picture shows the ISS orbiting Earth. Suppose now we (or rather, God) put a baseball behind the ISS. The ball is not moving with the ISS, we just put it on the track of the ISS and let go of it. Will this ball fall directly to Earth while things in the ISS are floating?


I was using Latex to write my report and whene I open the pdf generated I had (equations, Notations, list of figures, list of tables...) marked in red or green as shown in the image. How can I get rid of these markers. Any help will be appreciated.


What's an adjective that describes cutting mats that also have grids drawn on them, and specifically distinguishes them from cutting mats that don't have grids on them? I guess if there's no cutting-mat-specific word, the word that means "this device has gradations marked on it" (that could also describe rulers, measuring cylinders) would also work. That is a ____ cutting mat


I want to say that I solved a programming bug and has been around for years in my resume. I currently have something like "Debugged long standing bug" but I don't think it conveys that point that this issue has persisted for many years. I could obviously say "Debugged bug that has been around for many years" but that doesn't sound like resume-language


For this particular diagram below, is there any reason why all the radii of the circles are in a geometric progression? I've tried using similar triangle to try and prove it, but was unsuccessful Any help would be much appreciated


There is a certain premise which I am unable to represent correctly as propositional logic: "When I play basketball, I wear my sneakers; otherwise, I never wear it." (PlayBasketBall -> WearSneakers) <-> (-PlayBasketBall -> -WearSneakers) What changes do I need to make in order to represent it correctly?