darklight03/StackMIAsub huggingface dataset:
Are all wormholes gravitational instantons in the context of General Relativity? My question concerns also the topology of spacetime in such case. A full Wick rotation of the metric, seems to change the geometry from that of Pseudo-Riemannian to Riemannian one. So given that topology of the Pseudo-Riemannian manifold in most general case does not match the topology with respect to the Riemannian metric, I want to know in the case of gravitational instantons, how is this situation interpreted? There's a Euclidean hole, but there's no Lorenzian hole at the same time?
I was wondering how one might write down an expression which estimates the force experienced if a person were to be hit by a tidal wave (perhaps assuming the person could be modelled as a sphere). I guess you could also use Wagner theory to find the instantaneous force on impact, but this becomes complicated. I assume that similar to the analytic expression for Stokes drag for a low Reynolds number flow the force would depend on the viscosity and speed of the liquid, since being hit with water would not be as bad as being hit with a more viscous liquid.
I was looking at my bathroom tiles, which were an interesting sort of repeating pattern of different squares and rectangles, and wondering how to model them as a recursion formula. Does anyone know any good or interesting books on recursion? Advanced level is fine with me. For my level of background, I just wrapped up Calculus II and am taking up to Calculus IV and Linear Algebra later this year. Also, I come from a software engineering background so I'm familiar with writing recursive graphics, but I feel like the way I write it is not that elegant and sophisticated. Thank you!
I am currently studying the Lagrangian mechanics, and as far as I've understood, forces of constraint are the forces that are perpendicular to the surface of the movement of the object, thus do not cause any change in the velocity of, and constrain the trajectory of the object, (e.g. force due to the tension, the normal force). The magnetic Lorentz force fulfills all of those I mentioned above, so is it also a type of force of constraint?
TLDR: Do observations of larger galaxies favour 'cuspy' dark matter halo distributions, as predicted by N-body simulations? I've been trying to understand the 'core-cusp' problem for dark matter halos and I understand that observations of dwarf galaxies don't agree with the results of N-body CDM simulations. What I don't understand is that, can it be taken by implication that larger galaxies do agree with these simulations, and if so, is there an expected 'cut-off' in terms of mass or radius where one would only expect to observe a 'cuspy' profile?
The class of Eberlein compacts (those compacts spaces homeomorphic to a weakly compact subset of a Banach space) is well known and well studied; one of the many properties it enjoys is that every set in this class is also sequentially compact, thanks to Eberlein-Smulian. This led me to wonder: Eberlein-Smulian also holds in greater generality than for Banach spaces (as long as the Mackey topology in the space in question is quasicomplete, for example, the result holds). What is then known about the class of compact spaces that are homeomorphic to a weakly compact subset of, say, a Mackey quasicomplete space? Does it coincide with the class of Eberlein compacta?
I am recently studying some chiral algebra from physics perspective. I found many chiral algebras have nice coset realization of current algebra. However, most of the literatures are very algebraic. And I have questions about the generators of chiral algebra at the level of OPE. One confusing thing for me is that many fermionic generators can appear in the coset construction. This is counter-intuitive to me as the current algebra generators are all bosonic. Is there a way to understand this?
I mean open up a book on QFT and I know things like path integrals still don't have a fully worked formalism but then you see Fourier transforms and residues from complex analysis being applied to integrals of "field operators". I don't mean the functional analysis of quantum mechanics, I mean mathematically speaking are field operators as studied under functional analysis? Or do they need another formalism. Maybe there is no formalism and it is just hoped there is some way that the math works right and that it makes sense.
Once an entangled particle is measured, it's wave function collapses. From my understanding, any sort of information exchanged to the particles can be considered a mistaken measurement. So how do researchers entangle particles, move them apart and then measure them? I assume they are held in vacuum and are maintained within a specified volume of space through magnetic confinement, but I would think that the magnetic fields holding them would also consequentially be a measurement on them. So I am at a loss as how they keep them entangled until an actual measurement is performed. I assume it's because my understanding of what is considered a measurement is flawed since I've read that even energy can be delivered to entangled particles even without collapsing their wave functions.
In Birrell and Davies, the author says in the Introduction that If the gravitational field is treated as a small perturbation, and attempts are made to quantize it along the lines of quantum electrodynamics (Q.E.D.), then the square of the Planck length appears in the role of coupling constant. But why does the square of the Planck length comes in as a coupling constant here? How does one determine what the coupling constant should be?
He promised that he will help me with my homework. He promised [that] he would help me with my homework. Which sentence is grammatically correct? I saw this debate and I genuinely don't know the answer since English isn't my first language. But I feel like the second sentence is more pleasing to hear. Can someone help? If you have an answer can I know why that was your answer?
Could the following sentence be considered correct when comparing two or more subjects? It's visually more distinct. I'm aware that you can rewrite the sentence like this: It's, visually, more distinct. But, the pauses feel unnatural. There's also: It's more visually distinct. This just feels wrong, even if it's technically not. And lastly: It's more distinct, visually. However, 'distinct' can be ambiguous; so, I'd rather have the adjective 'visually' come before it. I'd also be interested in if there's a particular rule I can read more about that determines whether the first use ('visually more distinct') is correct or not.
I usually have trouble trying to read huge tomes without any proper motivation - there's no feeling that I'm "working" towards something. Perhaps I've been spoiled by "Abel's Theorem through Problems and Solutions" by V.B Alekseev which builds up group theory solely to prove the insolubility of the quintic, but it was nice knowing there was something "big" at the end of it all. I'm looking for books in a similar vein, that might focus on a single question and build a story around it.
Can any periodic set of integers be realized as the zero-set of a linear recurrence relation? It's stated on the OEIS page for eventually periodic sequences that "all eventually periodic sequences with period N are linear recurrence relations of order at most N" but if you interpret "are linear recurrence relations" as being the zero set of a linear recurrence relation this statement can't be true because Skolem-Mahler-Lech gives a stronger characterization than just eventually periodic (the zero-set must include every earlier member of the residue classes in the periodic part too). At the moment I don't see an obvious way to do it for periodic sets and can't find any other mention online
I have a question pertaining to Penrose's ideas about cyclic cosmology. As predicted therein, the end of each cycle comes about when massive particles are extinct and time is no longer measured. What I don't understand is why this state is not an eternal one; what could possibly give rise to a new period of inflation, is it that energy is somehow bound in time as a dimension?
Imagine a permanent magnet suspended in the air with an iron disc below it. Inbetween these a thick aluminium barrier. Attached to the disc at an angle is an air spring (or air shock). The magnet attracts the disc which hits the barrier but some of the force is absorbed by the air spring. The equation of the force the magnet produces is non-linear as it depends on displacement. The equation for the force the air spring absorbs is also non-linear because it depends on compression. How can I combine the two equations and any others necessary to find the force the barrier experiences?
Can someone please reconcile the difference between the two common integrals below? They are almost identical except what's inside the natural log function. The denominator signs are switched depending on whether it's the variable x or u. I understand u represents a function where as x represents a variable but I'm not sure how it affects the outcome within the natural log function. Please explain Two similar common integrals
Length of a curve can be defined for an arbitrary rectifiable curve(even in an arbitrary metric space). As is shown in this answer we can define line integral over any such curve(even in an arbitrary metric space). When it comes to surfaces and higher-dimensional cases it seems that there are no constructions of such generality. Wherever "surface area" and "surface integrals" are defined, some kind of smoothness is required for the surface in question. Are there any definitions of "n-dimensional surface area" and "n-dimensional surface integral"(which resemble the definitions of length and line integral over an arbitrary rectifiable curve) with much weaker conditions on the "surface" (in the same way as "being rectifiable" is weaker than "being smooth" for a curve) ?
For me it is counter-intuitive: I should be hearing more low frequency sounds (bass) at a greater distance from a headphone speaker (like I hear only the bass when standing outside a club), because the bass travels further and high frequency sounds get absorbed easier on the way to the ear. But of course it sounds like the bass is completely absent when headphones are located far from the ear, and it sounds like only the very high frequency sounds survive. What is the physics behind this - why do headphones sound more 'tinny' when distance from the ear is increased?
According to me we will apply a force on the charge and it will do a certain displacement to reach that point from infinity where we wanted to bring it and at that point there is no electric field. But still we applied force and displacement also occurred therefore work done should not be zero. Please explain me the concept and please tell me where am i going wrong?
There's an idiom in Argentina translated roughly as "to sleep someone" (dormir a alguien), which is used when someone frustrates the plans of someone else by taking what the other person wanted in the first place and who obtains the benefit knows it. This may cover different situations, for example: If you walk ahead in the street to hail the taxi another person was about to hail. If you start dating someone another person you know was eager to ask for a date and you knew it. If you take the last slice of a pizza someone who went for a drink said was going to take. I'm looking for an idiom in English which describes this kind of behavior or situations.
I am having a partcular issue with several pairs of glasses and wish to understand the physics of it. The problem is that the right arm of the frame is too tight against my temple, and at the same time the left nosepad is too tight on my nose. This seems rather unintuitive at first, as one might think if the right arm is too tight, then so should the right nosepad. My grasp of physics is poor but I think I can begin to see why this is not the case, and that the law that every action has an equal and opposite reaction might be applied. Any help with this would be greatly appreciated. I have taken them to an optometrists who were puzzled.
There are many wonderful illustrations of parametric curves with b-splines and control points, but I mostly use splines for uni-variate functions. So I have a vector of control values, but not really points--at least not ones I can easily plot. If we take the three examples in the definition section of the wikipedia article on B-Splines: https://en.wikipedia.org/wiki/B-spline How could I determine the control point positions in each example in order to visualize them on the graphs?
tl;dr If I'd introduce you to someone with "Say hi to my cousin Harry.", would you be surprised to later learn that it's my seventh second cousin twice removed because I used the word cousin and not specified it's not my first cousin? I'm used to using it one way, and someone else (also a native English speaker) uses it the other way. So I searched and found conflicting answers here and here. So are there really two customs, or is one of the sources wrong? Obviously "cousin" can mean second cousin as in the expression "second cousin". But what about when used without any qualifiers, such as "my cousin said", can that mean second cousin or not?
As you know, it is expected that the velocity of stars and gas should slow down the further they are from a galaxy's center. However, in many cases, it does not slow down as expected, and this discrepancy is often attributed to the presence of dark matter. How can I obtain the expected radius - velocity plot for certain galaxies? What informations or data should I have about those galaxies to plot it? Can you provide me some links about it? I need to plot the observed rotation cuves and expected ones like in the image that Ihave added to this post .
Let's assume that I have an ideal conductor(straight wire(, as we know that potential at any point on the ideal conductor is the same, if i place that ideal conductor in a region where magnetic field is increasing, so according to faradays law a potential difference will exist across the ends of the conductor, but how is that possible if we know that for an ideal conductor potential at any point is the same
I have heard one meaning of it in the context of a personal goal is to set a too-easy goal (i.e., that you know you can easily achieve). I also heard it is coming from golf. Can someone shed more light on this? To be clear, I was not referring to computer science or computing area where it means to separate a piece of software on a computer system so it can only use particular programs, files, etc. Thanks!
It's a very general question. Black hole paradox is an interesting problem but why is it something that physicists are so worried about? As neither can it be directly experimentally tested nor do I see any indirect proof of it, then what relevance does it have? I might have upset some of folks here, but I've got no hard feelings here. But as far as I've seen, people doing Quantum Gravity or related fields, always have their eyes on this paradox. I'm just curious to know why is it so important?
This question is with regards to a polarimetric approach in analysing the concentration of a substance in solution such as sugar in water. I have been trying to find an answer to it through a little browsing but I could not really find anything useful. Most websites and books use dm for path-length of the solution in dm and concentration of the solution in g/ml. Why is this done? Why wasn't specific optical rotation of a substance in solution defined in terms of S.I. units rather than an awkward combination of c.g.s and other units?
I was told that this sentence is so wrong, and after reading some related threads here, I now understand that "earlier" should be used with past tense. So is it okay if I change the sentence to "As Puss has told them to, they all say the Marquis." Is this sentence natural? It's from a simplified reader "Puss in Boots". The context is that Puss shows the King around, making him believe that his master, Henry, is an important man. He tells the king that Henry is a Marquis. He also asks some people to lie to the king, having them say that they all work for the Marquis.
From a Library of Congress article about Freud: ...patients tended to perform for the camera and doctors to record the most photogenic. This sentence seems to reuse the verb tended between the subjects patients and doctors. I think this is an instance of gapping. I have seen it in simpler cases like: Alice cooked the rice, and Bob the beans. I can't imagine anyone speaking like this casually, but it feels OK in writing. However, the more complex Freud sentence feels wrong. Is it? The object of the reused verb is an infinitive instead of a plain noun -- is that the problem? Or maybe that "tended to ____" behaves like a single compound verb, and the tended part cannot be reused?
What is the subject of "making" in the following sentence? It seems that it is the most reasonable grammatically to think "Yakkleman Skin Care" is the hidden subject of making. This is because the subject of the participle needs to agree with the subject of the main clause grammatically. Yakkleman Skin Care has signed a deal with NutriSpark Online Shopping, making them the only retailer with access to our products. If "Yakkleman Skin Care has signed a deal with NutriSpark Online Shopping" is the subject of making, "making ---" seems to be a dangling participle. If so, is this kind of usage of participles treated as correct in authoritative English grammar books?
In Continuous Variable -Quantum Key Distribution (CVQKD), usually Gaussian modulated coherent states are sent. This means both quadratures of a coherent state are chosen from two normal distribution. So do we can prepare a state with well-known quadratures on the phase space? My main question is, how someone can successfully create a coherent state with exactly well-known phase and amplitude quadratures. I think even if experimental devices are perfect, he/she can not make a quantum state with exact known quadratures. I think making quantum coherent states is limited by the Heisenberg uncertainty. Am I right? In other words, do these uncertainties happened not only during measurement but also during state preparation? Sorry if my question is simple but I really need to learn it.
I have finished some courses on analytic number theory and wanted to learn about versions of Goldbach so I can pick a topic for my master thesis. I have seen a proof for an asymptotic formula for the tenary Goldbach conjecture in the lecture. I can not find the paper where the version of Goldbach for a prime and an almost prime was proven.I hope someone here can help.
Gravitational waves have been very much in the news recently and I would like to understand them better. I know vaguely that they cause transverse changes to the geometry of matter as they pass by. For many classical wave systems there are integral solutions to the IVP for small disturbances, showing how the wave is driven by gradients, divergences and curls in the initial fields. Are there similar formulas for gravitational waves?
As we all know, Subatomic particles show dual-nature when observed but why? why does this happen? also I am genuinely confused as to how does the particle know when to change its nature, I mean i know that it changes when it gets observed(detected by a detector) But how does it know that it is being detected and now it has to change its nature
I am working on a non-linear optimization problem, containing bounds and constraints for the variables. Very complex problem involving networks and logical functions. I have been switching a tool from the Matlab language in which I originally implemented it, to Python. In the Matlab version, I used the 'interior-point' method of estimating the Hessian to perform gradient descent. I tested several options for the function scipy.minimize(), and the best result is obtained for the Nedler-Mead method. I read the paper but it seems that this method cannot incorporate bounds and constraints directly. I would like to understand exactly what it does with my constraints before I set up to use this method in the research project. Thanks in advance
As a keen fan of Terry Pratchett and Jasper Fforde, I'm fascinated with words that logically should exist, but don't. A subset of these are referred to as "lost positives", such as "ebriated" referring to someone who is sober. However, there are other types of theoretical words, such as ones where you apply a prefix which isn't normally used, such as "postcarious", which logically means the unfortunate consequence of something being left in a precarious state. Is there a word/phrase which is used for these words which only exist in theoretical word-space (preferably in British English)?
A superfluid has a property that makes it creep up the walls of its container and escape it until it's empty. How is it possible that the fluid performs work (against the force of gravity)? I can imagine setting it up so that after dripping to the larger container, there is an indentation on the ceiling so that when it climbs the larger container, it drips back to the smaller one, and keeps moving in a loop. Is it possible?
We know that the comoving Hubble radius decreases during inflation when the universe is exponentially expanding and then increases during matter and radius domination. What is the reason behind this? I can see it mathematically. However, intuitively it's not so obvious. The universe is expanding during both the eras, accelerating during one while decelerating during the other, but expanding. I would imagine the Hubble radius decreasing during both since if the universe expands light (and causal physics) would have difficult keeping up.
For a quadratic polynomial the polynomial discriminant appears in the quadratic formula however, I found this was not the case for cubic and quartic polynomials. The expressions used in the cubic and quartic formulae are different from the polynomial discriminants or at least they seem different to me. So is it just a coincidence that the polynomial discriminant of a quadratic polynomial appears in the quadratic formula or I have made a mistake somewhere and an alternate form of the discriminant is used in the cubic and quartic formulae. If the discriminants do exist in the cubic and quartic formulae then, is there a relation between them.
Does one pee-pee with his wee-wee, or does he wee-wee with his pee-pee? Is one phrasing more typical than the other? That is to say: How is pee-pee used more commonly- as "to urinate" or as "penis"? And vice-versa for wee-wee. I'm curious if there are widespread or regional customs. Both are informally correct in American English. Pee-pee and wee-wee are both used as nouns/verbs for urination ("I went pee-pee", "He pee-peed next to the wall") and both are used as euphemisms to refer to the penis. This likely doesn't apply to UK or Australian English, at least based on this post about "pee" vs. "wee" and part of speech.
My question may seem CS-related at first, but it's essentially mathematical, so, please, bear with me. I'm doing Neural Architecture Search (NAS) by varying the number of layers and neurons per layer for a neural network (connections are feed-forward, throughout), and then training it on a fixed task to test its performance. The end goal is to perform topological data analysis (TDA) on the best and worst architectures (graphs) to spot the persistent structures in a good/bad architecture. My question is: am I right in my assumption that TDA could spot such persistent structures? If so, which metric should I use? Just the connection weights? P.S.: My background in (computational) topology is quite minimal.