I know that electric current is a scalar quantity and hence it should not follow vector addition. But I have read that equal currents in opposite directions will cancel out each other so is this kind of addition not a kind of vector addition?... where while adding we are including their directions also. So please explain that even when current doesn't follow vector addition then why the currents which are equal and opposite in direction will cancel out each other?


Is it possible to arrange a set of massive objects such as stars in orbit around a black hole such that objects of lesser mass cannot physically reach and fall into the event horizon of the black hole? This could be similar to how Jupiter may protect the Earth from long period comets. In other words, could there be several star systems with the black hole in their center, such that any possible object on approach to the black hole would be gravitationally deflected away from the black hole?


I need to find the X-coordinate of a vertex in a right triangle. It's been a while since I used trigonometry and I can't seem to wrap my head around it. Image with coordinates The Y-coordinate is always the same as the Y-coordinate of the vertex on the left, under the radius. I've tried using line intersection, but I don't know how to use that here since I don't know where to put the X coordinate of the diagonal line. What method can I use to solve this?


We know that the Mandelbrot fractal contains a countable number of copies of itself. See : Does the Mandelbrot fractal contain countably or uncountably many copies of itself? Where that is explained. Notice that polynomials have a finite amount of zero's and entire functions have a countable amount of zero's. So I started to wonder : Is there a Julia fractal that contains uncountable many copies of itself ? And if so, can they be iterations of entire functions ? What are typical examples ?


During the recent merger of two Neutron stars the lead up to the merger was detected as gravitation waves. This was the merger of two spinning bodies that had very strong magnetic fields and they were orbiting each other. How sure is the community of physicists that the signals detected were not ULF radio waves? Radio waves would have had the same frequency and arrived within the same time frame.


I am not sure why, but when I am working on a multi-file project in TeX with a latexmain file, the compiler included with VIM-LaTeX does not compile multiple times to include newly added citations in my bibliography. This only occurs for multi-file projects. If I work on a project that has only one TeX file the file is compiled multiple times to include new citations. Does anyone have any clue what may be causing this?


Take these sentences: I felt he was mean to do that. We'd be stupid to do something like that. I feel like the "to do that" part in them functions differently syntactically than in sentences like "It is mean to do that" where "to do that" seems to be an infinitive clause functioning as the subject. Is "to do that" a complement to the adjectives "mean"/"stupid"? Comparing "he was mean to do that" and "he was mean for doing that", I think semantically the two sentences seem close but still different, but I can't put my finger on how exactly they are different in meaning. So how are they different? Also do "to do that" and "for doing that" function the same way syntactically? Are they both complements?


In general, knowing the mass distribution of two colliding objects and the exact point of contact, how would one take into account angular motion in the analysis of the dynamics of the individual mechanical energy of the objects and the total energy of the mechanical system? That is, each object may be rotating about it's own axis and in addition moving with some linear momentum. I've looked through my mechanics notes, but I don't quite think I know what happens. Around which point is there going to be torque? Or some angular impulse, I guess. Thanks!


I'm looking for some interesting operators for which I can find invariant subspaces by hand. As most subspaces had some connections to eigenvectors, I'm currently searching for "non-trivial" / interesting (linear) bounded operators on Banach spaces, preferably Hilbert spaces, which do not have any eigenvalues. I know about Volterra and multiplication operators but I can't seem to come up with any of my own. In regards to Lomonosov's theorem, operators without eigenvalues, which commute with compact operators would be even better.


When I jump off of something, even with eyes closed I can be pretty certain that I'm falling due to the associated sensation of falling. However, as gravity should be affecting each of my internal organs equally, surely the sensation must be due only to the air resistance, which causes my outer body to accelerate slower than my organs? As a follow up, assuming the above is correct, would the best way to minimise the sensation of falling be to keep as narrow a profile as possible I.e. keep pencil shape rather than spread arms and legs out flat?


Take a cupboard or just a large wooden box. When pushed it a point above its center of mass, the cupboard topples because there is a net torque due to the friction and the force you apply. When pushed at a point below the center of mass, the cupboard does not as the torque due to the friction and the torque due to the force you apply are in opposite directions (they cancel). Now my question is if the force you apply is equal to the maximum value of static friction, then the box is at rest. However, since the friction applied is at a larger distance from the center of mass than your force, shouldn't there be a net torque?


I asked a similar question before, but it did not give the answer I was looking for, so I will clarify what I actually want in this question. H. Andreka created a formal first-order logic theory that was meant to axiomatize special relativity. I very much enjoyed reading his paper and other papers that axiomatized special relativity. However, I have yet to find a similar text for Newtonian mechanics. What I am looking for is a paper or papers that give a formal first-order theory that axiomatize Newtonian mechanics.


I am reading about monoidal categories and I am not able to think of categories which are non-monoidal. Am I thinking in the wrong direction? Is being monoidal, an additional property like topology? For example, given a set you define a topology on it making it a topological space. Similarly, given a category, you define a tensor product map making it into a monoidal category? Also, given a category does product of two objects from that category always exist? ( I know about the uniqueness but I am not sure about existence). If yes, can a map sending two objects to their product be considered as a tensor product map?


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.


I am a graduate student studying wireless perception, and recently I want to carry out liquid recognition. I want to use a speaker as a sound source to generate vibrations (by playing sounds of different frequencies). My idea is that different liquids have different resonant frequencies. When the frequency of the external force is close to the resonant frequency of the liquid itself, the liquid's The amplitude will be larger, so different liquids can be identified. I would like to ask you if my idea is reliable and can you tell me some theoretical knowledge, such as whether the amount of liquid also affects the resonant frequency?


I have been doing some deeper reading on optics out of my interest and one of the most important differences between ray and Gaussian optics is the existence of a non-zero beam waist when a laser beam is focused using a field lens. Most literatures that I have read go over this fact as if it's a common knowledge, but doesn't exactly over why this phenomenon occurs. I understand that focusing to a single point would result in singularity which is physically impossible, but I was hoping if someone could explain what cause the beam waist behavior. Some literatures attribute it to diffraction, but I don't understand what causes this while a Gaussian beam is propagating in vacuum.


I know it happens when the elements on both sides are identical, the more you remove asperities, the more they become like a single substance. But does this happen to the same extent if I take two different substances and start removing asperities? Or maybe close to that... My textbook doesn't explain much about this, it says "By making the surfaces extra smooth, frictional force increases as actual area of contact increases and two bodies in contact act like a single body." Doesn't say anything about the substances taken. Thanks for your precious time.


An example of a non-associative ring R whose non-zero elements form commutative quasigroup (with regard to multiplication in R) without identity is easy to find. I'm looking for examples of a non-associative ring S whose non-zero elements form a non-commutative quasigroup without unity. Put another way: A non-associative non-commutative division ring without unity. 'division ring' in the spirit of 'ring R (associative or not) whose non-zero elements form non-empty quasigroup by means of multiplication in R'. Can you help me ?


In many (biological and living systems) physics courses I encountered the notion that systems operating far from equilibrium are related with more efficiency with regard to their specific tasks. One example I vaguely remember is the comparison of the energy efficiency of ATP to ADP convertion reaction with the efficiency of combustion engines. Unfortunately, I can not think of many specific examples and can only recall this abstract notion of efficiency of systems far from equilibrium. Could someone break this notion down by using many specific examples of simple physical systems, and in each case clearly defining the notion of far from equilibrium and the notion of efficiency ? You could start with the example I mentioned.


I have a camera that gives Azimuth and Elevation of an object with respect to itself (camera). The camera doesn't send image but Azimuth and Elevation data (in float format). The camera doesn't provide range. Is their a mathematical way for me to calculate the range of the said object using Azimuth and Elevation. I wish to use this data received for camera in sensor fusion algorithm along with LIDAR data. For this I need range of the object.


I am currently studying electromigration in liquid metals. According to studies that have been done for electromigration in liquid metals, the metal ions are affected by the electrostatic force and therefore can move to the cathode/anode. The force that moves the metal atoms to the electrode is affected by the charge of the metal ion. However, my professor told me that in liquid state metal atoms should be neutral/not ionized. So how exactly does an electrostatic field affect the metal atoms or cause atomic movement in this case?


Free space is a region in which there is no matter and no electromagnetic or gravitational field. Which means that the resistance in free space is zero, because there is no resisting force and as far as I know, free space is a synonym for "vacuum" and there is no resistive force in a vacuum. So, how is the permittivity of free space, not zero? Permittivity is a property that measures the opposition against an electric field, but there is no resistance in free space, no opposition?


This question relates to the Michelson-Morley experiment and whether anyone has so far proposed an equivalent experiment using aqueous waves instead of optical waves. If it is true that (i) The properties of optical waves and aqueous waves are approximately equivalent and (ii) Nature is consistent in her implementation of traveling waves, then, I believe such an experiment should manifest every characteristic of the Michelson-Morley experiment to some degree of approximation including relativistic effects such as relativity of simultaneity, lorentz contraction and time dilation. Is this a valid assertion? If not, why?


Please forgive me for not having the best grasp on graph theory terminology. I am doing my best. I have a large connected subgraph of a large graph where I want to find, what I am terming the "weak points," of the graph. A "Weak point" exists, in my conception, when given a vertex, there exists at least one single edge among the vertex's edges that can be deleted to create two independent distinct subgraphs. Does this character of a vertex have a name? I can imagine if one must delete two edges to create two independent subgrpahs this vertex would be a "stronger" vertex. Thanks


In an inelastic collision where mechanical energy is not conserved, momentum is still conserved. Should the Earth or the ground be considered as part of the system in order to account for the conservation of momentum? Since there is friction in a collision, is it appropriate to include the ground as part of the system to analyze the conservation of momentum? Are air particles considered to be a part of this isolated system? To clarify I am specifically talking about two vertically-moving objects colliding.


How does a common base transistor amplify current if a small part of its emitter current gets divided into base current and the rest goes to collector current? If the input signal is applied to the emitter part of the transistor then the output current in the collector part should be less than the input one. Then how is the current amplified where the current flow actually decreases rather than increasing?


Is there a notion of a singularity of a real "algebraic variety" which looks locally like a double cone but with a countable infinite number of cones which meet in the same point? A short example or reference would be highly appreciated. I am self-studying algebraic geometry at the moment and the literature/videos do not treat this topic and I am lacking the necessary intuition.


I am very confused about this, are they an excited state of a particle where an electron is excited to an upper energy level, which seems less likely to be the case since the resonant states of particles have different names; or are they the constructive interferences of the wave functions of two different particles, which again doesn't seem likely since as far as I know, one wave function is used to describe a system of particles instead of different wave functions. I am aware of the question, but the answer there doesn't satisfy me


I am beginner to optimization and my question is fundamental. We all know that Static optimization means the design variables/objective function does not vary with respect to time. Dynamic optimization means the design variables vary with time. I need help in organizing the below algorithms/concepts into static and dynamic optimization categories. Ordinary calculus Dynamic Programming Convex Optimization Tabu Search Lagrange multiplier Genetic Algorithm Calculus of Variations Simulated Annealing Linear/Non-Linear Programming Particle Swarm Optimization Ant Colony Optimization First and Second Order Algorithms


Why doesn't a pressure cooker reach a state of equilibrium where the steam passed is constant (assuming the contents of the cooker are maintained throughout the cooking process), but rather, it accumulates pressure until it releases it in the form of a whistle every so often? I don't understand why the pressure "overshoots" and releases more than what would keep the weight open, and then releases more than is needed for the weight to lower. I suspect this has to do with the static friction which needs to be overcome for the whistle to rise being greater than the dynamic friction, or something along those lines.


As the title says, I'm trying to determine numerically when an n-DOF oscillating system (linear or nonlinear) subjected to forced base oscillation reaches the steady state solution. Is there an energy component (or another global parameter) that converges to a single value when the steady state is reached? I have the time series of the position and velocity of every mass and the base oscillation.


Recently while experimenting with force experienced by current carrying conductor, I came across a abnormality in the horse shoe magnet, due to which the direction of force on the current carrying conductor by the Flemings Left Hand Rule was false. I noticed that when i kept a compass near the heads of the horse shoe magnet, the needle pointed from North Pole to South Pole of the magnet. But when it was kept between the two hands, it pointed from South Pole to North Pole. I dont think it is theoretically possiblle that magnetic field is going from North to South outside the horse shoe whereas it is going from South to North between the two ends of the horse shoe. Please explain this.


There are certain complex functions which lack a proper denominator corresponding to which poles can be found for the given function. For example , the gaussian function, the frenel functions are some of the popular functions lacking any denominator, in the complex plane . So , as a result of those function lacking any pole , I am wondering how to evaluate their corresponding improper integrals using contour integration (complex analysis). Is there any way by which a denominator can be generated assuming certain conditions for those functions lacking denominator? I really want to clear the doubt regarding this ...All of yours opinions would be highly appreciabble in my regard. Thanks a lot in advance .


I have a question about degenerate electrons in white dwarfs. So, as far as I know, when the gas contained in stars is compressed so much, the electrons start to fill the lowest energy level and then, for Pauli's Principle, they continue to fill up incresing energy levels up to a certain level. As you can read here http://astro.vaporia.com/start/electrondegeneracy.html, "During compression, as electrons take on momentum, they gain too much to maintain a nucleus orbit, and they travel freely through the material rather than remain with a single nucleus." I did not understand this last statement. Does this mean that the electron become free? Or they are still bounded to the nuclei? Thanks for the answers


It is well known that the method of image charges is not always applicable, so I was wondering: is there an analytic way to calculate the electric potential for a point charge interacting with a perfectly conducting, neutral (edited) metallic disk using image charges? If it can be calculated or not, for what reason? Even if it could be solved, I don't think the method conforms to that of a conducting sphere, so I would like to know (if there is one) an analytical method that would allow it to be calculated.


When a satellite is revolving around a planet with an orbital velocity in presence of air resistance, the satellite's Kinetic Energy keeps on increasing as it falls down. The resistive force is trying to decrease the speed and the gravitational force cannot change the speed (or Kinetic Energy) as it's perpendicular to the velocity. Or, am I wrong and gravity can actually change K.E. even if it's always perpendicular to velocity. In the Free Body Diagram, I see no force acting along the velocity that can increase the speed of the satellite.


I and some classmates are recently teaching ourselves the famous book Foundations of Perturbative QCD by John Collins via a form of regular peer reading group. We find that exercises in this book are really worth working on. But, as a group of relatively junior students, we are hesitating to go deeper before finding a way to verify our answers. One obvious solution must be to consult some more senior researchers. But, other than that we want to know whether there exists a document of solutions to this book, so that at least we can self-verify even if we fail to find such a senior mentor.


The tangent plane at a point of a hyperboloid meets the hyperboloid in the two generators through that point. However, a tangent plane is defined as the locus of all tangent lines at a point on the hyperboloid. Now, since generators lie completely on the surface they can't be tangent lines to the hyperboloid. Then how is it possible that the tangent plane contains the generators that intersect at that point?


What's a safe, easily executable experiment to confirm that quantization of light occurs directly to the retina. We know that light is quantized when projected on to a surface, or on to an inanimate detector, then the surface or the detector observed. An eye can detect a single photon. This means we should be able to quantize light such that a single photon lands on the retina of the left eye or of the right, and the observer confirm it is seen in only one eye. What's a design for this experiment?


From my understanding self-energy is the energy required to put charges in a certain charge distribution and interaction energy is the potential energy caused by the interactions between particles, but to me it seems like there isn't really a big difference between them and this post What does electrostatic self-energy mean? basically talks about them like they are the same thing. My book says the total energy is the sum between the interaction energy and self-energy. I'm very confused.


From what I understand relativity predicts that outside observers would never observe external objects actually crossing into the event horizon, due to time dilation. How does that can reconciled with the fact that the Schwarzschild radius is largely dependent on black hole mass? Then, does this imply that one can never observe an increase in the radius of the event horizon? This seems wrong to me, as there are different size black holes, and I'd like to know what I am missing.


I am trying to say in good quality English that a certain idea which was implemented is currently used way beyond the scope it was intended for. It was a gap-filler which we are now basing our entire solution and this is going to be unsustainable. I am trying to write something like "This architecture has exceeded it's original ____ and needs major refactoring" I know there's a word exactly for this... I keep coming up with "premise" or "precinct" (I know the word I am looking for sounds something like these, not saying they are applicable). I've already used "purpose" a lot, in a different context, and I need to avoid using purpose for this statement to prevent confusion.


Suppose a car is at rest and you apply the accelerator, then the wheels are applying a horizontal force on the road so according to Newton's third law an opposite force (friction) pushes you forward. From what I understand no matter how much force you apply (hit the accelerator) the maximum force that can push you forward is the limiting friction. But then since the car is going with an acceleration forward friction should again act backward and there will be no net force, so the car doesn't move. How is this possible?


It's well-known that given a sentence independent of a system of axioms, we can consistently extend the system by appending either the sentence or its negation. However, if a given theorem can be deduced in each of the two systems, then we have a proof of that theorem. We don't even need to prove independence, because given any sentence, either it or its negation is consistent with a given system, provided that the original axiom system is consistent. I'm simply wondering whether there's a specific example of that proof technique having been used.


An observer near the event horizon of a black hole will experience an extremely strong gravitational field. Due to the principle of equivalence, this observer cannot locally distinguish between this strong gravitational field and the experience of being in a highly accelerated frame. As a result, the observer will detect radiation or temperature in the seemingly empty space around them, as predicted by the Unruh effect. This radiation can escape to infinity being near the event horizon not inside the black hole, and is what we refer to as Hawking radiation.


I tried to understand the physical interpretation of uniform continuity, and saw different graphical interpreation in Wikipedia. At the end, I have concluded that functions which are uniform continous in a set, also have finite derivative in all the set and its boundary. Is this interpretation right? I don't want to be rigourous at all, but if you can provide some proff or counterexample, it will be great. Thanks!


Normal measurements of compressive strength work by compressing a sample with an hydraulic press and see when the sample deforms plastically or cracks. Now if pressure is applied on the surfaces of the sample that aren't in contact with the hydraulic press, will the compressive strength (as seen by the hydraulic press) increase ? If yes, will that increase be exactly the external pressure or lower or higher? I feel like the compressive strength as seen by the press must be higher because the pressure on the "sides" will prevent the material from going outwards thus deforming or cracking. (Imagine a cylindrical sample is being pressed) Am I missing something ?


I was wondering if someone can explain simply why phase changes are isothermal processes? I am studying hydrology and some of our material about snowmelt has to do with phase changes and in this example, water retains a constant temperature when melting/freezing, or boiling/vaporizing. I was wondering why, as the ice melts, why does the temperature not increase as it is changing phase? I am just wondering if there is a chemical/molecular reason that better explains why the heat energy is no longer warming the ice as it changes phase. Like, is all the energy directed to separating the bonds and cannot go to heating? My background is aerospace/mechanical engineering so I have some thermo experience but the more simple the explanation the better. :)


Consider a piston such that it is in mechanical equilibrium with its surroundings. If I pull the piston (reversible work) then the work done by me would be positive. If I push the piston, again work is done by me. However, in one case positive work is considered to be done on the gas inside piston, while it is negative in the other case. If I pull the piston, negative reversible work will be done on the gas -- does it mean that the gas is working on me? I know that I must be making a mistake, but what?


What are some good entry points into physics? I'm wanting to eventually be able to understand some more abstract concepts like quantum physics but understand that is a very long way away. Just been spending far too long trying to understand things above my pay grade. I'm pretty sure I remember linear algebra being something I should read up on, what are some good books on that subject? What are some other good books that would be entry points? I'm wanting to eventually be able to understand some things like Planck area and a lot of concepts related to entropy. I would consider myself intelligent but not well read as I've slacked on learning since high school. Any help is much appreciated!


I am working through Srednicki's "Quantum Field Theory" and am at the chapter on the Minimal Supersymmetric Standard Model (MSSM). In answer to why two higgs superfields are needed in the MSSM model, Srednicki's solutions say that "...the superpotential cannot depend on hermitian conjugates of [super]fields." In trying to think through why this is, the best I could come up with is that any Yukawa term in the superpotential with a hermitian conjugate could either ... make a vector superfield and thus not something that would be in the superpotential and/or it would be a term that wouldn't be holomorphic (though I have to be honest, that my knowledge of holomorphism is very limited and shaky at best).


Using induction on the complexity of formulas, let's assume that in every proper non-empty initial segment of a propositional formula, the number of left parentheses is greater than or equal to the number of right parentheses. Note: A proper initial segment of a propositional formula is an expression that starts and continues with the same symbols as but does not include all symbols of . Any thoughts?


When a capillary tube is inserted into a large body of water, there is an increase in potential energy (PE) of the system. This is because the increase in PE of the rising water in the capillary is greater than the loss of PE of the body of the water. The increase in height of the capillary water is greater than the loss of height of the body of water, and the same mass is involved. Is an empty capillary tube really a source of potential energy?


Simple question, but I can't find any answer around. If a pipe turns, aka is not straight, the length of the pipe (in order to calculate the resonance frequency) is given by the length of the imaginary line connecting the centers of the circular section of the pipe, by an imaginary string of zero width that connects the two extreme of the pipe, or by which other measure? For a straight pipe is easy, but I can't find any information on what happens when it bends. Silly question for the standard here, but I don't know where else to ask Thanks a lot


I've come across the expression "head(s) and tails above" (the rest, the competition etc; different from something like "can't make head or tail of something" i.e. can't figure it out/understand). I can't find information about this. It seemingly means completely. Could you confirm its meaning and explain it a bit? Is it rare, is this expression recent and is it restricted to or typical of specific regions (Canada?)?


I have been thinking about how physics has evolved since the time of Galileo . Back then physical laws could be describe using axioms which could be comprehended by anyone who reads them. But currently physics is done in a whole different manner. The laws are written mathematically. The language of mathematics is deeply encrypted in the study of physics. For example, the theory of general relativity requires the idea of tensors, black holes are deeply mathematical and so on. I just wanted to know why physics is done using mathematics? Cant it be done without mathematics - for instance, by only doing only experiments?


Vogel's method selects the corresponding variable through a penalty. There is a penalty for each row and column and is the subtraction between the two lowest costs (in absolute value). We must select the highest penalty and then the lowest cost in the row or column of this penalty. I understand the second step (if you want to reduce the cost of the problem, you select the lowest cost of the row or the column), but not the first. I don't understand why we have to do the subtraction between the two lowest costs and, then, select the highest penalty. Can someone tell me what the explanation is?


Does water vapor generate electromagnetic radiation/photons when it condenses into water droplets? I know that gas water molecules need a condensation particle to combine into water droplets. A pair of molecules combine on the surface and in the process transfer their binding energy into the kinetic energy of the condensation particle. Are any photons emitted during this transition? I'm guessing that the answer is no. By analogy, in the gas state a water molecule can be excited into a an unstable radiative state by colliding with an air molecule like nitrogen. Similarly it can be de-exited without radiation by a collision as well.


The twin paradox is resolved as the twin who moves through at least two inertial frames has a shorter worldline (therefore less time elapsed in their frame) than the twin who remains in one. I know the crucial aspect is the multiple frames not the acceleration, since you can have variations of the twin paradox with no acceleration. Besides calculating the proper time for each twin's path, is there a (perhaps more intuitive) reason that changing inertial frames will lower the time elapsed on your watch?


If an isosceles triangle is inscribed in a circle, then is it's altitude always greater than the radius? If yes, then why? My sir said that if an isosceles triangle is inscribed in a circle then its altitude is always greater than the radius and passes through the centre of circle but I don't understand why it is so and is it not possible if any other triangle is possible that is isosceles and has its altitude less than the radius of circle in which it's inscribed.


The question was to transform this sentence from positive to comparative degree: She is not so young as I expected. Following the solutions of other sentences of this kind (the photo shows a similar kind of problem from where I adopted the solution) it can be written that: She is not younger than my expectation. I want to know why ...I expected has been changed to ...my expectation. What is the grammatical rule here? I don't get it what's wrong with ...I expected ? Is it wrong not to use possessive pronoun? The sentence transformation is from the past exam question of my student which she couldn't solve. I am her private tutor and want to teach her the correct things. Please don't misunderstand it as a homework.


In the current approach of QFT, we model the process of creation of a particle (say a photon or a gluon out of a quark) as "instantaneous", meaning happening at a moment in time without any neighborhood (modeled via a delta function). To what extent is this an idealization of the real behavior of nature? Do we have any experimental evidence that this process happens with a certain duration? Can nature behave in a way which is more similar to a 'spike' rather than a smearing function? If this process have a certain duration - what properties does a particle has during the time it is 'in the making'?


My teacher gave us the assignment to find the moment of inertia of any shape you want. So I decided to find the moment of inertia of our milky way galaxy. I found out that our galaxy is shaped like a warped disk, not a flat. After I knew about that, I looked for the equation of the Milky Way's shape. But, to me, Nasa's and some high university papers had so many big wards that I could bearly understand what they were talking about(I'm Korean.. ^^). I'm sure that I can understand the equation if I had it, but I just can't find any information about them. I would really appreciate it if someone could tell me what you know about these equations (shape). Thank you!


I've a box with know width (W) and height (H) It has been rotated around an origin point O at a known angle The rotated box is enclosed in a bounding box for which the top-left point (Bx, By) and dimensions (Bw, Bh) are known Given the origin point, the angle, and the resulting bounding box, is it possible to determine the X coordinate of the original box (Ux)? I tried illustrating this in the following diagram.


Hi :) What properties of triangles should I use to solve this problem? I can work out the size of the large triangle and all of its angles, but how do I apply this to the circle? What am I missing? This problem is from the first chapter of a trig book, so the methods needed can't be that advanced. Just need some pointers. Thanks! https://i.stack.imgur.com/BEXKX.jpg


I created my lecture notes using the CambridgeUS theme. My students cannot get the .pdf file to print from Adobe. I tried printing my notes from Adobe on two different printers and I get the following message: "The document could not be printed, kindly use our help page to troubleshoot." Adobe's help page didn't solve my problem. Other pdf files print fine to these same printers, and I have had no issues so it isn't the printers. I have tried every theme in beamer and have no trouble printing the same notes if I use Boatilla or the default theme. Thankfully, I have a work around. However, I am still wondering what I am getting wrong or missing when I use CambridgeUS theme. And advice, insight? TIA.


is there a computable algorithm which lists all the finite subsets of natural numbers ?... i know that such a set is atleast countable... but can't determine if we can list every such subset in a computable manner ..... the set of all infinite sequences of the subsets of natural numbers is obviously uncomputable i think this problem should be computable, since any finite set is computable... but i need some sort of proof or reference , any site etc... thanks


Is the measure of a simple closed curve consisting of two arcs transversal to a foliation equal to the sum of the measures of these arcs? Let A be an arc that is the union of arcs B and C, where arc B is transversal to the foliation and arc C is contained in a leaf of the foliation. Is the measure of arc A equal to the measure of arc B? Is the measure of open arc equal to its closure? Thanks.


what I have been told is that present participles are used in active reduced relative clauses. considering present participle of "be", which is being, I was wondering can we use the same pattern? Another example in Longman dictionary is: who heard of a grown man being scared of the dark? or who heard of a grown man who is scared of the dark? Aren't they possibly equivalent of each other? Thanks in advance


In Kittel's book of Solid State Physics, it is said that, whenever an electron passes the positive ion core in the lattice, it has the ability to distort the lattice s.t by attracting the positive ion cores. Does the attraction has to do anything to the mass of an electron, as being small, does it posses the attractive power to make the nearby positive ion cores to pull toward that electron, as positive ion cores are much heavier.


I am reducing a block diagram manually and am not sure whether the following step is a valid step? I am using the rule of moving a summing ahead of a block in reverse. Reduction Step in Question I've checked the resulting transfer function before and after this step using MATLAB (connect function and Linear Analysis in Simulink) and they aren't the same, leading me to believe this isn't a valid step. Any help is greatly appreciated.


In a uniaxial crystal there is an optic axis, an extraordinary axis, and an ordinary axis. The optic axis is not the direction in which we plan to propagate light. The light is propagating in a direction such that the electric field might oscillate parallel to the optic axis. I have included a hand-drawn diagram below. What about the crystal determines how the optic axis is oriented? Is one of the principal axes (ordinary / extraordinary) always parallel to the optic axis? How is the ordinary axis distinguished from the extraordinary? What happens if I propagate light along the optic axis? In a uniaxial crystal, is there a third refractive index that comes into play?


Consider approximating a binomial distribution with normal. Originally, my binomial distribution is discrete, where the heights of the bars represent the probability. However, after approximating this distribution with a normal one, we find the probabilities using the area beneath the normal curve. How have the probabilities just changed from being heights to area? It seems unintuitive how these probabilities are more or less the same.


I accidently deleted a large part of my work on a .tex file. Unknowingly, i saved the file , ran the typeset once and closed it. Hence the content is deleted from the pdf too. Is there any way to retrieve the deleted content. I check the previous version of the file too but it is not available either. Somebody please help. I am desperate.


As we know that Euclidean geometry deals with triangles, quadrilateral,... and circles. Later in college we learn projective geometry but in quite modern language (vector spaces, equivalent relations). My question is, is there any roadmap or any book to learn projective geometry from high school Euclidean geometry which would be easier for high school student to learn projective geometry. I think it would be really helpful if our student could have some intuition with projective geometry before learning sth more modern like algebraic geometry.


Work done in an isentropic process does not cause dissipation but leads to change in temperature of a system. But temperature allows wider range kinetic energy to be accessible leading to more microstates. This should lead to increase in entropy, but this doesn't seem to happen here. Does this mean that increase in entropy is compensated by something else? Or am I making some mistake here.


I have a rotated retangle and a rectangle. Both are defined by their corners (however, for the non-rotated ones I also have access to topLeft, topRight, etc). Is there a way I can check if they intersect? (It would be enough to know if they intersect, even without knowing the extent of their intersection). I found solutions for two non-rotated rectangles and two rotated rectangles . Technically the solutions for two rotated rectangles could work in this case but I think that, since i know one of them is axis-aligned, there might be a faster way..


I recently read that neutrinos have a polarization property---their polarization is opposite to antineutrinos. Is it possible to determine the polarization of a neutrino? For example, we can determine the polarization of a photon using a polarizing beamsplitter, V-polarizations will be reflected into detector A, and H-polarized photons will pass through into detector B. Can we do something similar with neutrinos, something like a neutrino beamsplitter? (Of course, neutrino detectors are huge, but in theory?)


Using the GeoGebra program a few days ago, I came up with a wonderful feature about the parabola and the circle kissing its peak. I don't know if it is new or previously discovered. Please, if it was discovered previously, put a reference mentioning it in the comments, and in any case, can anyone prove it I don't think a lot of words are needed, this picture includes intuition


I was reading Ali Omar text on solid state course and it said about the fact that electrons in a lattice or in a periodic lattice never scatters or make collisions with the positive ion cores, as the eigen functions of the solution of Bloch's theorem have infinite lifetime and eigen functions do not gets scattered? I do not understand as why eigen functions never scatters and what does scattering of eigen functions means and also what does it mean by saying eigen functions has infinite life time?


I am trying to format a line of text that has two different sized fonts such that the vertical alignment of the smaller sized text is based off the larger sized text. In one instance I'd like the smaller text to be vertically centered on the larger text, and in another I'd like the smaller text topline to be aligned with the larger text topline. To my admittedly very limited understanding, this should translate to to changing a paragraph parameter to change the paragraphs vertical alignment to either "center" or "topline".


Data rates are higher in X-band, but considering free space path loss and atmospheric attenuation(diffraction I'm assuming is significant here), won't lower frequencies stand a better chance? Again, cost and weight is a factor, but I want to understand the physics that goes behind these selections. Additionally, why do uplink and downlink frequencies differ in which one is higher?(Uplink is higher in the case of C and X band whereas it's lower in S band)


Hello fellow grammar lovers! I need some help. I'm working on HR resources and have run into a bit of a conundrum about how to write about PTO. I know that I "would like to take time off." But how do I go about "initializing a time-off request?" My question: Is it appropriate to hyphenate time off when used as an adjectival noun to modify request? My first thought is to use the hyphenated version to describe the noun (request), as nouns used to modify other nouns become adjectival nouns/noun modifiers/attributive nouns. Thoughts? Thanks! J


Both mass and entropy behave differently for black holes than for normal matter. For simple Schwarzschild black holes, mass is proportional to their radius. The Bekenstein-Hawing entropy is proportional to their surface. Of course, the calculations for the two results can be found in the textbooks. Is there a simple explanation for why the dependencies on the radius differ? For example, fourfold surface implies fourfold entropy - but only twice the mass. In contrast, in normal matter, fourfold entropy implies fourfold mass. What is the best way to explain that in black holes, entropy increases more than mass? Somehow, mass and entropy are decoupled. What is the best way to explain this?


I understand that according to Collins Dictionary, a suffix is an affix that follows the stem to which it is attached, as for example -s and -ness in dogs and softness. It has, however, a second definition: anything that is added at the end of something else. Would I then be right if I say that the following sentences have the same suffix " is a vehicle."? An airplane is a vehicle. A car is a vehicle.


When a magnet is moved into solenoid, it induces a current. And, when it is moved out of the solenoid, it induces a current. But what about in the example below. When a very long magnet, that has its whole body within the solenoid, is moved in some direction. The magnetic flux experienced by the coil from the magnet, should be very similar even if the magnet as a whole was moved a few centimeter.


I searched for it but couldn't find any answer for this. For a light source is it simply the average of the full spectrum power? And how do you compute it for an image? How can you tell the difference between a yellow object lighted by a brighter light and a white object lighted by a yellowish light? Or maybe you can accurately compute it in front of a white sheet? Edit: I am talking about a lighting Kelvin temperature (for example of a bulb) rather than the actual temperature of the light source.


Approximating the Earth by a circle with West facing in the theta-hat direction and East in the opposite, when a person jumps up, the Coriolis force faces West according to the right-hand rule. Upon descent, the Coriolis force faces East. Since you spend an equal amount of time rising and falling, shouldn't the effects of the Coriolis force cancel out? Why is this not the case? Why does a person end up falling slightly West?


I'm helping edit a piece of fiction, which has a sentence that begins so: In another smaller kitchen... How is this to be punctuated? One choice is to leave it as it is. Another is using two commas: "In another, smaller, kitchen..." Since 'another' isn't an adjective or adverb, the usual rule(s) about grouped modifiers don't apply. (Note that there is a different kitchen several paragraphs before the line in question.) So--commas, no commas? (I can't see 'one comma' being right)


So in flrw metric it's quite reasonable to take eigenvalue of the time-like component of the stress energy tensor and identify it with mass density. Now, if someone argues the cosmological constant comes from the stress energy tensor. Wouldn't they also have to account for the change in mass density? In the Newtonian limit I'm pretty sure this is a change in mass density. How do people who argue it doesn't matter where (stress energy or Einstein tensor) the cosmological constant comes from explain this discrepancy?


Wagon-wheel effect is a well-known optical illusion due to the persistence of vision. It happens when the spoke of a wheel rotates to a certain position after the duration of persistent vision. Depending on such position, the apparent wheel motion can have many appearances. However, is it possible to design a certain pattern of wheel entirely free from such an effect? Except for the trivial solution (no pattern or spokes at all).


I'm looking for a word that describes that feeling you get when somebody (of a group typically thought of having more power in society) brings up a group (typically thought of having less power in society: minority groups, women, LGBTQ) and you are hesitant to agree with them even though they are right (Like, in this hypothetical scenario they factually are, they're not twisting the facts or anything). It's kind of the same kinda gross feeling you probably got when you read "even though they are right" in a post loosely about racism from a stranger on the internet. This is the best explanation I can come up with. Is there such a word?


Inspired by a youtube video, i was trying to do the double slit experiment at home using a single hair and saw the interference pattern. Then i wondered what would happens with many hairs and when i shine the laser trough a bunch of them, these kind of patterns emerge. Here you can see a video: https://www.youtube.com/watch?v=utJyBEfwugE Sorry if the question is too generic, i'm not a physics student.


I want to confirm if I understand something correctly. We call the "high potential terminal" the positive side (cathode). Though, electrons move from negative to positive. Logically, electrons' potential energy is decreasing so the high potential terminal should be the negative side. In my opinion, from the electrons' perspective, the high potential terminal is the negative side, but since the current flows in the opposite direction, we always talk from the current's perspective, hence why we call the high potential terminal the positive side. Is this the correct logic?


I want to minimize the amount of unused space in a binpacking problem. I keep seeing binpacking being described as using the least amount of bins possible. Example (emphasis mine): assign each item to a bin such that number of total used bins is minimized https://www.geeksforgeeks.org/bin-packing-problem-minimize-number-of-used-bins/ Would minimizing the amount of bins guarantee the least amount of waste? And if so, is there a minimum amount of bins (based on the algorithm used, not necessarily the one from the above link) that we need to use before it is efficient? Or is binpacking "by default" efficient in minimizing waste?


I am building a database of sorts and came across this question. I am looking for a word that includes every region that is declared and made up by humans. So no natural regions like forests or continents, but regions that are generally associated with the people residing within its borders and other human-related stuff (laws, culture, goals...). Like Estonia, Tokio, EU... I found this similar question (Generic name for places like village, town and cities). But it's only about towns, cities etc.


In the sentence below, Greenland may not be as "green" as the name suggests. The verb "suggest" should preceed an object as it is a transitive verb, but in the sentence, there is none. In this case, should the second "as" be understood as some sort of relative pronoun though there is no noun? Or should it be understood as a comparative conjunction? If it is a comparative conjunction, is it ok to not have a direct object for "suggests"? And if something is omitted, what is it?


What would be the best books covering topics like Algebra, Geometry (Euclidean geometry) and Calculus? Which classics can be recommended (classics in the sense of historical works that have been widely disseminated throughout the history of mathematics, for example: Euclid's Elements)? I would like to have an overview of the main classics that influenced paradigms and changes in the history of mathematics (I understand that reading can be considered difficult, but I am willing to risk it). Objective: Historical Curiosity.


A sphere with a radius of one is put inside a cubical box with circular holes cut out such that the ball fits perfectly. The box and the sphere share the same volume; find the surface area of the box. I tried cutting the cube down the middle to get a square and a circle. I then tried to find the distance between the two points of intersection between the circle and square on one side of the square but hit a dead end. I then tried to find the volume of empty space in the box since that could help me find the volume of the protruding parts of the sphere and maybe lead to the answer but it led to no avail.


I was watching this video. It Showed that light ( green ) changes its color to red after incidence of light. I couldn't think of how this happens because light's color is dependent on frequency rather than wavelength and only the wavelength changes when light enters a new medium , according to these answers on whether light is depended on wavelength or frequency. So what explanation can be given for the change in color in a prism.


A student asked how to integrate tan x and he was trying while using integration by parts. I taught him the substitution method but he then asked why we can't use integration by parts. My immediate thought was it is possible just much more complicated but in trying it out, I can't seem to do so. Is it simply not possible to integrate tan x by parts? Attached are my workings for the substitution method and the failed attempt at avoiding substitution. Integration by substitution Trial of integration by parts


I am doing some work on the topic "Adjunction" and my current interest is to give some examples. I've wanted to provide some examples connected to some basic concepts from analysis on manifolds if such exists. What I thought maybe would work is the following: Tangent space functor and cotangent space functor Tensor product functor and multilinear form functor Pushforward and pullback of differential form I am not sure if any of these are indeed adjoint functors, so if they are I would appreciate any help in proving such a thing.


If you take an axiomatic view of Classical Mechanics and the concept mass as primitive in this context, you could derive from Newton's laws an operational way of determining masses simply by arbitrarily assigning a mass to an object and demanding momentum conservation in its interactions with other objects. But if there are interactions that increase as a function of distance, this method ceases to be practical. Does this imply that an axiomatic theory should include the prescription that forces decay with distance?


I'm trying to connect the calculations for the determinant I'm seeing and the idea that the determinant is a signed measure of the factor by which the volume bounded by the basis vectors of a vector space changes when those basis basis vectors are acted on by a linear transformation. Does anyone have a good way of connecting this geometric intuition with the way matrix determinants are computed, specifically with the "product of pivots" method I refer to in the title to this post? Thanks.


In a PhD thesis we have to write a preface wherein some significant theorems from the main body of the thesis are needed to be restated. The amstools or thm-restate package does not help me in this regard. In this package the restated theorem must appear after the original theorem is stated. Till date I am doing it manually. But then the problem is if I change something in the original theorem then the same change must be done in the restated theorem also but manually. Is there any efficient method to do it?


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.