darklight03/StackMIAsub huggingface dataset:
In quantum field theory, it seems that when we consider a massive particle's spin degree of freedom, we usually do in the particle's rest frame. And I know the little group will only change spin DOF and leave the momentum unchanged. My question is: If there is a Lorentz transformation that only change the momentum of the particle and leave spin DOF unchanged? And how to determine that transformation? Or in other words, can we compare spin of particles in different momentum? I think there should have, because when we transform a particle to its rest frame, the transformation operator is not unique since we can always do a more little group transformation, so there should be a unique one to leave the spin unchanged.
I'm trying to calculate body trajectory that launched by some impulse. I have two points: start position and finish position which can be located on different heights (points is not symmetric). I know the height that body will reach, so parabola's vertex located that height higher of first point. Vertex located between points but we don't know it's X coordinate (if points on same height it will be in the middle between them). Is it possible to find parabola's equation in this case?
If time measured by one observer moving at a greater velocity than another observer is observed to be passing more slowly, does this imply that there's such a thing as "absolute time" or "base time" which would be the passage of time as measured by a completely static observer of the universe? Basically time as measured from the universe's inertial frame of reference. I mean given the speed with which the milky way is hurtling through space, doesn't that mean we on earth are experiencing a dramatically slowed down version of this "true time" or "base time" or whatever you would call it?
The pressure at a point inside a static fluid is same in all directions because the the collisions of particles take place isotropically. However, at the same time pressure increases with depth. So downward pressure must not be equal to upward pressure at that point. This two statements are contradictory and I am really confused. What is the problem in my understanding of the topic?
I am finding very hard to understand how convexity works and why a correlated strategy if a convex linear combination of Nashes is a correlated equilibrium. (Both concepts of Correlated strat. and correlated equilibrium are clear) The following is the problem I can't grasp: problem Please feel free to modify my post I haven't been posting in a while and writing LateX feels very hard, also the question isn't well posed but I am trying to solve this on my own and this post is just another attempt to find a solution Thanks to anyone helping
tried to submit my thesis to my school. However they told me that my fonts were not embedded, which they need for archival purposes. I thought I took the necessary steps to make sure they were. I think my .pdf figures in the document are likely the culprit.... But they're telling me that it's because in adobe document viewer there are fonts that say "Embedded" instead of "Embedded Subset". They say this means the fonts are not actually embedded. Are they correct? I'm surprised how much trouble I'm finding online on if a font labeled as "Embedded" really is embedded or not. From my reading I feel like Embedded is everything Embedded Subset is and then some (the characters not used in the pdf).
Consider the single-hole diffraction of an electron. We can make the hole as small as we like and determine the electron's position with arbitrary accuracy. When it is in the hole, we can hit it with a low-energy photon, and measure its momentum. There is no guarantee that the photon will strike the electron. But it "could". It seems that we can measure the position and momentum simultaneously if we are lucky. Does it mean UP has nothing to do with simultaneous measurements but only with statistical uncertainty?
I know that the derivative exists when the two sided limit at one point exists and at most of the discontinuities the two sided limit doesn't exist. But at point discontinuities, the two sided limit does exist, right? So it should have a derivative, i.e. it should be differentiable. But I read some of the answers for similar past questions and they say the derivate doesn't exist. Where am i wrong?
As I understand it, sound needs a medium to travel and more often than not, the medium is the atmosphere, however sound can also travel through solid objects. And even we can hear our own voice talking (though less loud) even if we cover our ears since sound travels through our body. So, in case we are on the moon where the atmosphere is non-existent, would we be able to hear sound (say clapping or walking) due to sound waves being propagated through our own body or is that a stretch?
Description Hi, I'm looking for an adjective that can be used to describe someone who is skilled at easily identifying the thoughts, abilities, and perspectives of another. The first sample sentence provided effectively captures the effect that I'm trying to convey. Sample Sentences e.g. Chloe is a _____ manager, she always appoints each individual, the tasks that fit them best. e.g. Mothers are typically _____ when it comes to their children; they always know what they need. e.g. Peter is a _____ friend. I never have to worry that he won't understand me. Potential Words Words that come to mind, include "perceptive", "intuitive", and perhaps even "keen" too.
This question is very related with software development. I would like to know if there is a word to refer the way that a word is written. For example somebody has written "HasChildren" for a variable name while the correct way should be "hasChildren". I could tell this person: "you should write hasChildren instead of HasChildren". But if I want to be more polite I would say something like "the way you use the lower and capital letters in HasChildren is incorrect, it should be hasChildren". What I want is to have a term to replace "the way you use the lower and capital letters". Does that word exist? I am not sure if capitalization would work.
How can I start from a Hamiltonian with electron-phonon coupling and show that a kink should show up in the energy dispersion relationship? In a brief communication called "Universal Nodal Fermi Velocity" there is a graph showing a kink in data collected from Angle Resolved Photo-Emission Spectrometry. After looking around a bit I found a review that convinced me that this is due to electron-phonon coupling and am now trying to convince myself with the math.
I do not know if this is physics or engineering, but it is complex engineering I think at least. (In the implosion fission bomb first tested at Trinity and used in Nagasaki. Not the gun type.) A big problem with the implosion design was uneven compression and a member of the British team named Tuck suggested explosive lenses (which had been employed in anti-tank weapons, I think). Somehow the lenses were supposed to even out the explosive wave but were there not multiple shaped charges in the form of the lenses? And if so, how to ensure the lenses went off at the same time anyway? Basically, I would like to understand how explosive lenses fixed the implosion problem.
I am seeing many reels on Instagram where they ask a person "Can you spell Y, E, S". The person says "Yes". Then they ask him "Can you spell E, Y, E, S". The person says "E-Yes" instead of "Eyes". Until today I thought that they should be using "pronounce" instead of "spell". Isn't spell the opposite? You ask a person how you spell "Yes" and they would answer Y, E, S. I saw so many reels from English speaking countries and now I am terribly confused if I don't understand what spell means.
I want to know whether alternating current will hold you to stick to the socket or throw you away and why? In my textbook it is written that alternating current is attractive in nature but when i researched a bit i found that it will contract your muscles and make you stick to the socket. So i want to know which of the fact is correct and why? Please i want a complete explanation as I am totally confused.
The question says it all. Simply stated: Can one prove grand unification from string theory? What is the argument chain of such a proof? The textbooks I read so far only appear to give hand-waving arguments. The question is not about deducing the standard model. The question is about deducing grand unification. This means that there is a single large Lie group. Can one prove somehow that string theory produces a unique (large) Lie group?
Are there good reasons to use, e.g., "customer relationship management solution" over "solution for customer relationship management"? I understand that in certain contexts clusters of nouns, such as in the first example, can increase ambiguity if the adjectives aren't compounded accordingly. The preposition in the latter example reduces the ambiguity by expressing the relationship the subject, the solution, and its modifiers, customer relationship management. Are there other reasons that one might want to use a prepositional phrase over stacking, and hyphenating, adjectives?
XeLaTeX and LuaLaTeX support Unicode, and are perhaps also in some other ways better than pdfLaTeX. However, are mathematical and logical journals prepared for submissions prepared with XeLaTeX or LuaLaTeX? Perhaps it is more prudent to prepare one's work with standard pdfLaTeX? I am a bit wary about these things, as I one time when finishing an essay for a book was suddenly told that they just accepted word-submissions. What is a prudent strategy if one wants to have an essay published in a good logic journal?
I've been investigating this problem: Given some straight line planar embedding of a simple connected graph with a simple dual graph, does there exist a straight line planar embedding of that dual graph with each vertex lying in its corresponding face in the original embedding? What if we ignore the infinite face? I believe I have found a few complicated counterexamples to the main problem, but have no clue how I would go about proving the less restrictive case or finding a counterexample. I would also appreciate smaller counterexample to the initial case. Here is a graph that I believe is a counterexample.
I believe I have heard the expression when someone did an analogy about nuclear war, comparing the danger to a game where the opposite player's objective is not to win but to make you lose. This was apparently called, in game theory, "a scorpion player". I thought they were called the "scorpion player" but I can not find any proof or anything close to this. Have I remembered wrong ? Is it an other name ? Or have hallucinated the whole thing ? If anyone has any information on if there is a name for such player, I would be thankfull. Many thanks.
Suppose we have a hollow conducting sphere having a charge Q residing on it's surface. Then we take another such sphere which is bigger than the one mentioned before and surround the smaller one with it, would this cause the charge on the inner sphere to appear on the outer surface of the bigger sphere? If yes, then how can a spherical capacitor even work if all the charge on the inner sphere goes to the outer sphere's outside surface I have added an image below for reference
In Halmos'book on naive set theory, Halmos introduced the idea of a "family of sets". He explicitly defined a family to be a function from some indexing set to an indexed set. However, whenever he talks about a family, what he seems to always be refering to is actually the range of the family. I get so confused whenever he speaks of families in his text, whether he is speaking about the function or the range of the function is very ambiguous. Does "family" then formally mean the indexing function itself, or perhaps the range of the function? Thank you in advance.
Is there an adjective/expression that conveys the meaning that this something fills a role/place that should have been filled long ago because of its high added value? For example: "The ____ exhibition on female figures in the development of modern design..." Perhaps "long-awaited" is something similar but I was hoping to find one that doesn't imply that people were expecting this change to happen. Thanks!
Google says just that "toothless wonder" is an individual in the public who is lacking a single front tooth. Well, that's logical. But what's the purpose of word "wonder" then? If this is a slang form I can't get it, please, explain it to me. And I really want to know where it came from. All I could find out is that there were some child books named Junie B. Jones: The Toothless Wonder, although I am not sure that they were the origin.
In linear algebra, to convert the linear transformation or operator into matrix form, it's not hard, get the standard basis of domain and substitute in the transformation and write the image of the standard basis as a linear combination of standard basis of codomain and finally get the constants (c i's) and write that in column wise in the matrix format, we will get the matrix format of the linear transformation with respect to the standard basis of the domain and codomain. My question here is why can't we arrange constants row wise? Why it is fixed to arrange constants always column wise? Thank you so much for your response
I use latex workshop on VS code combined with okular, but I would not mind using the internal viewer. I use forward search and backward search. My question is, whether there is a way to make the editor follow the viewer and the other way round: If i scroll in the editor, that the viewer shows the according segment and also if i scroll the viewer that the editor follows? This would be very convenient. In the long run, I maybe use latex to create html or what. Is it possible to do the same with a browser as a viewer?
I want to know what the zero electrical resistance of a superconductor means. Does it mean when we connect the terminals of a battery with a superconducting wire, the electrons move within specific tunnels inside the superconductor for which the net Coulomb's force due to the nearby nuclei and the electron clouds are zero everywhere in these tunnels? Do Cooper pairs form to justify these neutral paths? If there are such paths, are they curved or straight? Do these tunnels, if exist, make the superconductor anisotropic?
As far as I understand it, dark energy can affect bound systems at cosmological scales (How does dark energy affect the dynamics of galaxy clusters?) effectively modifying their orbits. This phenomenon and this thesis dissertation made me wonder... Could dark energy make a bound system (like a large galaxy or a satellite galaxy orbiting a bigger one) be "less bound" so that the orbits respective to the central point of mass are larger? And if dark energy would help to make orbits be further away from the central point of mass, does it mean that dark energy could add orbital energy to bodies orbiting the center of the galaxy at the outskirts of it?
What is the basis of the believe that there should be a unified theory which simultaneously gives quantum physics (the regime small things moving very fast) and gravity (the regime of big things moving very slowly)? Is this just wishful thinking? Are there any people who make a strong case of the possibility that no such theory can exist? This is a sincere question. Please don't throw stones at me.
I was studying Newton's Laws of Motion and my book gives a diagram in order to explain what components together can or cannot be considered a system in the figure given below. Now it says we cannot consider D and E together as a system as they don't travel the same distance because the disc D slides over a string but I'm having a hard time getting how exactly is it sliding over the string. Is the string wound up on the disc?
We are aware that Microsoft Word has a feature called ink Equation that allows the user to write a formula with a light pen, even if the formula is complex, and then convert it into a real equation with an acceptable font. Obviously, this is an excellent option, since it is not necessary to use multiple commands to write a lengthy equation; instead, one can simply write the equation as seen. My query is: Is there a latex editor that includes this feature? If the answer is affirmative, which editor has this capability?
When we put a circular hole of radius R on an infinite sheet of uniformly disturbed charge we do have an electrical field on a distance z (perpendicular to the sheet) from the center of the circular hole. But if we were to pick a gaussian surface such as a cylinder of radius R there would be no flux according to the gauss theorem. Because there would be no charge in the hole. I am having a difficult time understanding what i did wrong.
I am trying to compile the most basic file of the Kaobook template as provided here and it does not work. Now, on my TeXLive, it doesn't because it gives me in the report that it is missing an options.sty file (an issue that I do not really know how to fix). What is more peculiar is that this is not compiling on Overleaf either (and I am literally opening the file there from the option provided on the page linked above without modifying anything). Is there any specific reason? Any feedback will be most welcome!
Background: Masters in CS/Math. I'm brushing up on statistics I see mean squared error everywhere. As a student I took it for granted, but now when I tried to find the reasons for why it's so prevalent I am told: simplicity, emphasis on outliers and mathematical properties like differentiability. So what? It's not the only function with those properties. So why is it used so widely? Are there situations where it's provably the best function to use? Are there situations where there are other functions that are provably better to use? Say I am designing my own heuristic, and I have an error I want to minimize on. How do I know that squaring the error is the best way forward?
I understand that every function is equal to some graph, while not every graph corresponds to a function; so that sets aside the difference between functions and graphs. However, I understand that any relation can be represented with a graph, and every graph coresponds to some relation. Therefore, are the set-theoretic structures of "relations" and "graphs" exactly identical? Are they just different names of the same set?
Once a body "crosses" the limit where dark energy wins over gravitational forces (Is there a distance from a gravitational source where the influence of gravity and dark energy are balanced out?) would there be any way to make it return to the zone where gravity overwhelms the influence from dark energy? For example, if a body is orbiting a massive point and begins to slowly recede from it due to the expansion of the universe, could some kind of slingshot effect caused by a passing external object make that body get closer to the source of gravity to the point that it gets "trapped" in the zone where gravity wins over dark energy and therefore does not recede forever?
It seems like homotopy pullback is pullback for the case of D(CW) (derived category of CW-complexes). Is this true? In general, I want to say that homotopy pullback satisfies the universal property of pullback in a derived category. What I know for sure is that the pullback of fibrations is homotopy pullback. In a derived category such as D(CW/X), weak equivalences are isomorphisms, and each map can be replaced by a fibration. Hence, up to isomorphism, everything is a fibration, on which the homotopy pullback is the pullback. I wanted someone to confirm that this homotopy pullback (which coincides with the pullback after replacement) satisfies the universal property of pullback.
Why not explain the apparent attraction of masses by a repulsion coming from all directions in space (perhaps the dark force)? I.e. there is no gravitational force, just a repulsive force. A point in midspace would be receiving repulsive forces equally from all directions and appear to not accelerate. Mass near the outer reaches of our universe would have more repulsive forces coming from behind, and therefore accelerate outwards. An object near a large mass would be receiving less repulsion from the direction of the large mass (because that mass has absorbed some of the force) and therefore be pushed towards the large mass.
This question was inspired by the very first exercise in Thurston's Three Dimensional Geometry and Topology, where he gives a picture of a very tangled up loop and asks what manifold it depicts. I understand there are several knot invariants and algorithms that can be used to detect the unknot. But where are the practical implementations? Are there programs into which one can feed an actual picture of a knot (as opposed to more directly computational representations) and have it at least recognize unknots? One test would be whether it would accept the above picture as input and give the correct answer.
I have noticed when I view a hose pouring water the color of water slightly changes when looking from above compared to when looking from the front. Also, the same thing applies when you pour water from your mouth. If you look at it from above there's a color I can't describe very good (but I think there's a yellowish in it). But when you look at yourself in a mirror pouring water from your mouth, the water is colorless. To see the phenomenon better do it immediately after you've finished brushing your teeth. Just put a little water in your mouth and pour it down (looking from above). Why do I perceive this color change?
What is the proof for this (assuming that we draw infinite field lines). I understand why flux through some area is proportional to the number of field lines through that area only in the case of an isolated singular point charge. However, I dont understand why this would be true in other cases, like two unequal charges. To make it clear, when an area has twice the amount of field lines going through it than another area, why is the flux through it exactly twice the other area. Why not thrice or half? Also, why do field lines that originate isotropically from one charge always end isotropically at another charge.
I want to strap down a big heavy cylinder on a flatbed truck. The strap is attached to the truck bed as shown in the picture and also behind. Will the strap slip off as in the next picture? PS. This is a purely geometrical question about the length of the strap and the shape of the cylinder. Please consider that the block cannot move sideways and is blocked in place by some metal "foot" at the bottom.
I've read that the equatorial radius of the ergosphere of a rotating black hole is the Schwarzschild radius. But in this animation made in natural units by Yukterez it doesn't apply. I then used Yukterez equations in Geogebra and I observed the same thing. No surface scales accordingly. In the extremal case, the event horizon at the equator should be half the Schwarzschild radius, but it isn't. Is this a consecuence of using natural units? How could I "fix" this?
An FTIR spectrum was measured for me (device from Alignment and MCT Detector) and since I'm not very familiar with FTIR I'm looking for some advice. The absorbance spectrum was obtained by measuring the reflectance of a reference sample and the actual sample. The reference sample was stainless steel and the actual sample was probably stainless steel coated with dopamine and a peptide. The spectrum shows some kind of oscillations. It was suggested that the oscillation is due to interference caused by the dopamine coating. The coating could act like a thin film. Unfortunately, I haven't found anything paper/ literature supporting the suggestion. Have you seen something similar?
I have a question. I have a problem that when I learn science, I like to think 'how do they know this is right?'. When we learn physics or science from a textbook, we read and understand it, and then we have exam. But how do you know what is given in a textbook or said in research is correct? Because we didn't do this experiment, or we don't know what the process is to get this scientific result by ourselves? So, should I trust it and accept it? If not, what should I do?