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A cumulative distribution function (cdf) has a countable set of discontinuity points. They need not be isolated. Let us call non-isolated points 'accumulation points' of this set of discontinuity points. Is it possible that a cdf admits also countably infinite accumulation points in its set of discontinuity points? If so, is this something as pathological as requiring a singular distribution or it can also happen with discrete distributions? Thanks for any clarification, it would be nice to have concrete examples. | 0 |
A long time ago, I had a teacher who said you could write "lit." to mean "read this as". The typical example is to provide a tongue-in-cheek translation from English to English, such as: The power company charges an administrative (lit. bogus) fee on every bill. The author of the sentence is telling the reader to read past the euphemism ("administrative") and understand the subtext that the power company really just wants to take their money for made-up reasons. I just looked this up now, and couldn't find any reference material saying this was an accepted usage of "lit.". Maybe my memory isn't completely accurate? | 0 |
Given a table with x and f(x) values, g(x) a non-linear least squares approximation, and p(x) the Lagrange interpolating polynomial that passes through all of the points in the given table. What would be the best approximation on f, for a point x = k by only using p(x) and g(x)? Intuitively I thought about calculating p(k) and g(k), then taking the middle point of both, however I have no idea if this is reasonable to think of, nor if it is the best approximation for f(k). Is there a visual way to think of this problem? Or will I have to use the properties of both p and g to find the optimal approximation? | 0 |
Suppose there are two seeds kept at equal distance from a light source which emits a photon each on either directions. Seed germinates when a photon falls on it. According to rest frame both the seeds receive photons simultaneously but according to moving frame one of the seeds receive a photon earlier than the other seed. The second seed dies off due to delay, so there is only one plant in the moving frame but two plants in the rest frame. Is my line of reasoning correct? What happens when I bring the moving observer to rest so that he should agree with whatever observations made by the observer who was at rest? | 0 |
I've been asked by a friend taking a TOEIC exam to get an explanation of why "wipe" should be used in the following sentence, as opposed to "wipes": It was mandatory that each person wipe[s] off equipment after use with provided spray and wiping towel. Is it because there is an implied (should) before "wipe"? Or is it related to the fact that it is "each person" - meaning, of course, multiple people and perhaps substitutable with "they" - i.e. you couldn't say "It was mandatory that they wipes"? Or is it something completely different? This one has got me extremely curious, really looking forward to some of your insightful responses. | 0 |
Is there a word for a decision that's already been made despite the relevant processes not having been followed / analysis done. Foregone conclusion feels similar to what I'm after; but that implies that the facts are so obvious as to make the decision process moot; whilst I'm after a word for where the conclusion is based on one person's perspective without them having consulted relevant stakeholders / investigated the various options / collected evidence to support or dispute their arguments / etc. | 0 |
Assume that we have positively charged two solid conducting spheres of the same radius and material. It is evident that the surface charge is uniform on them to eliminate the internal electric field everywhere inside the spheres. However, how does the charge distribution change if we bring them close to each other? Recall that we place them close (not in contact) to each other. Does the exerted Coulomb's force upset the uniformity of the surface charges on both spheres? How can we find the new charge distribution so that the internal electric fields remain zero? | 0 |
I understand it's not possible to transmit information using entangled particles due to the randomness of the measure results. But what if the act of measuring itself IS the information? Let's say there's a constant flow of entangled particles received either side by Alice and Bob Bob measures every other particle. Is it possible for Alice to know which particle has been measured on the other side, and which didn't? I'm assuming unmeasured particles with superposition can show an interference pattern and measured ones don't Sorry if this is a silly question, I'm not a physicist and I fell in the quantum rabbit hole quite recently :) | 0 |
I was reading about the Pascal barrel bursting experiment, and it almost makes sense to me, save for one bit. I know that pressure corresponds to the number of collisions in the fluid. So my q is: why does adding water in the tall, narrow pipe in the experiment increase the number of collisions down in the barrel drastically? What is actually going on if we zoom in on a molecule of water in the barrel when we add all the extra water at the top? Thank you! | 0 |
I am not an expert in languages and this is my first question here... To my understanding, most of the languages were spoken before writing was discovered/evolved. What would cause a language to have same/similar sounding words with different meanings when the language was spoken? Wouldn't it cause more confusion when spelling could not distinguish the different words as there was no writing? I can think of some other examples such prey/pray or ate/eight which sound similar but their meanings aren't related. Did these words evolve/change in pronunciation over time, or were they used with similar meanings even a long time back, since before writing was a thing? | 0 |
For the operation of the transistor, the base-emitter junction is forward-biased and the Base collector junction is reversed-biased. Due to the concentration gradient, electrons from the N side (Emitter) go towards the P side (Base). Since the base is lightly doped and thin and due to the reverse biasing of the base-collector junction(electric field exits between the base and collector), the electrons coming from the N side (Emitter) go towards the N side (Collector) without much recombining with the hole in the P region (Base). Since we have a concentration gradient for electrons to flow from emitter to base then why do we need the base supply voltage in a transistor circuit? | 0 |
I would like to know some tips or hints to find a way to recognize whether "as" is using a meaning of "when" or a meaning of "because" when "as" connects two sentences. For example, the sentence below which currently confuses me. The third point, where it is in our interests to engage directly with China in a constructive and positive way to shape China's actions and behaviors as they impact on the wider world. In the above sentence, does "as" mean "because"? addtion: this sentence was from an interview script, so I cannot know if there is komma before "as". But thanks for all comments.It seems this "as" doesn't mean "because". | 0 |
Trying to work out whether to use 'is' or 'are' in the following sentences (aware they might differ): How many grams of flour is/are on the scale? How many centilitres of cough syrup are/is in the measuring cup? How many kilograms of fruit are/is on the scale? 'Are' seems most natural to me when speaking, but have read that units of measurement are usually counted as singular amongst the scientific community. Looking for UK English rules :) | 0 |
I was reading a preprint on archives (not yet published), and in the introduction the authors say "Following X in [ref]..." and go on to set up the problem. When I went to [ref], it turns out the authors of the preprint actually take three paragraphs word for word from X and include them in their introduction. Is this appropriate? Just saying "Following X...." makes it okay? To me, it still looks like plagiarism. | 0 |
Suppose we have a finite group G, and we had a configuration of points, lines etc. and lets say that the group acts faithfully and primitively on the set of points. Will the group be guaranteed to be flag-transitive on the entire figure or can G fix some proper subset of lines, for instance? My intuition says that shouldn't be possible, but I can't figure out how to prove it. | 0 |
Electromagnetic radiation phenomena exhibit a temporal asymmetry: we observe radiation coherently diverging from a radiating source, such the light emitted by a star, but we do not observe radiation coherently converging into a source, unless we delicately set up such a system. What can explain this asymmetry? And how is the asymmetry related to the causal asymmetry, on the one hand, and the thermodynamic asymmetry, on the other? | 0 |
Next year I have choose a few optative courses from a big list, but syllabi are not available yet, so I have to make a choice based on names only. I am thinking about taking one titled "Groups and representations". I have really enjoyed my Abstract Algebra courses so far, specially the part that covered Group theory. However, we never got into Representation theory, and I ignore what mathematical interest it might have. I was wondering if someone could provide me with a text explaining what is representation theory about and what is the mathematical interest or motivation behind it. I have found some books on the topic, but they all just start giving definitions and theorems and never give a good introduction. | 0 |
What makes quantum computers faster in certain problems than normal computers? Does quantum computing means that many solutions are explored simultaneously instead of one at a time due to quantum superposition of qubits? Is the complexity of solutions explored proportional to the number of qubits? That's my impression and my understanding of quantum computing. Any books or articles that exactly pinpoint how superposition or any other quantum phenomenon makes computation faster? | 0 |
A grammatically correct way to ask someone a question would be: Why are you still here? If I want to make a statement (instead of a true question), such as, You've been here too long or Your comments are annoying, or You're either a troll or a quarrelsome person, would "Why you are still here" (meaning- why do you continue arguing with everyone) be acceptable in a conversational English? Do you know why you're still here? is grammatically correct, but I don't want to know if he knows, I just want to express an annoyance with the person. | 0 |
Has anyone (in general) experimented with simulating moon lighting? It means the following. A gray ball is illuminated with light with a brightness equal to that of the sun. And at the corresponding angular distance from it, the level of illumination by the light reflected from the ball surface is measured and visually assessed. The goal is to compare the illumination intensity of real moonlight and that simulated in the experiment and to check the reliability of the calculated values. | 0 |
Cambridge says that the idiom home and dry is British English, which explains why I hear it used around me. It means: to have successfully finished something but I have heard it used also literally. Then I understand it as meaning to return home safe and sound after a travel/adventure of some sort. I wonder if this idiom has originated among sailors. I understand home but why dry? Is dry here a synonym of safe (and sound)? | 0 |
I'd like to know a word to describe a person who loves celebrities, gossips, trends or anything that is popular and is easily affected by them. She said she had moved to Paris because she loved "Emily in Paris" on Netflix. It seems that she is such a " "! I came up with "sheep"(https://www.urbandictionary.com/define.php?term=sheep), but I'd appreciate it if you could tell me other words to describe such a person better or more accurately. | 0 |
I'm trying to get a deeper understanding of the classification problem for finite groups and in particular the extension problem. I'm looking for some advanced books on the theory of finite group extensions which extensively and deeply covers the topic. Maybe an all-in-one book doesn't exist, in case I'd like also suggestions on books covering related and more specific topics such as Shur's multiplier and Group cohomology. | 0 |
Is there any book for a Mathematics student who can learn Machine learning in the aspect of Banach space geometry? Or, one can understand the connection between Geometry of Banach spaces and Machine learning? Any suggestions in terms of article, note, book regarding the development of such study is always welcomed. It will be very much helpful if anyone can suggest a good book which contains the discussion about the topic of Geometry of banach spaces that is required for Machine learning, Neural network such things. Thank you in advance. | 0 |
The professor asked me to write a small computer program that takes double integrals of rapidly varying functions. He did not mention which functions should be integrated but he said that I must use a numerical method with variable step size. I hope someone can recommend me a method that will do the job. It would be nice to have a link where this method is adequately described. | 0 |
There are many ways to draw a simple flowchart, using packages like tikz. But recently I read a paper and it seems that their complex flowchart is not a picture, but actually generated by latex. Here is what it looks like: I really would like to know how to make a chart like this, if there is a minimal example. EDIT: From what I can see on this picture, it is a combination of table and flowchart, which I don't know how to. So my actual question is, how could we combine a table with a flowchart? Or maybe is it just a complex Tikz (or other packages) implementation? | 0 |
If the expansion of the universe happens uniformly, how does this affect small objects? For example, are the distances between protons and neutrons inside a nucleus actually expanding? Is the nucleus constantly pulling itself together so its diameter stays constant? What about say between the carbon atoms in a diamond? If I can observe said diamond forever, will its atoms eventually disassociate with each other or will it stay in one piece due to its covalent bonds counteracting the expansion of space? | 0 |
I have a problem concerning a cylinder, cut by an arbitrary plane which is perpendicular to an axis, z. I know dz, the distance from centre of the cylinder to the plane. I know all dimensions of the cylinder. I know theta, the angle of rotation from the axis z. My poor drawing How do I calculate the volume of the cylinder above the plane? Is it possible? I've tried some trigonometry to get an integral based on the changing size of a circle segment... but it's getting very convoluted. | 0 |
Say I have some random variables X,Y that are jointly distributed according to some probability distribution (not necessarily independent). Is it possible to construct a Z = f(X,Y) (i.e. Z is solely dependent on both X and Y with no other source of randomness) such that X is independent of Y given Z? I believe this holds for all Z : Z = g(Y) or Z = g(x) for some deterministic function g, although I struggle to prove this formally. One straight forward example is in the binary case with Z = not Y. However, is there any formulation on how the conditional independence requirement restricts the function f? | 0 |
As far as I understand, the branes of brane cosmology are lower-dimensional "sub-manifolds" of some space. It was hard to imagine for me how such structure could exist and be physical. But then I learned of topological defects, which are essentially that. So my question is: Question: Are the branes of brane cosmology supposed to be topological defects of some sort? If not, how else could a "sub-manifold" be something physical? I also posed a related question which received little attention. Please note that I have only an undergraduate understanding of physics, but are fine with advanced mathematics. | 0 |
i'm taking a qft theory class, and we are doing a little bit of group theory, today the professor introduced us to Lie groups, but his definition is a little be weird he said that lie groups are groups whose elements are function of n parameters. This kinda confuses me and i can not see how this definition is equivalent to the one where a Lie Group is defined as smooth manifold with some other proprieties like the operation of the group be differentiable. Anyone can help me to clarify and get how these two definitions are equivalent? Thanks | 0 |
I am struggling to answer this question, and I was hoping for some assistance and/or help, it would be greatly appreciated. This link is a screenshot of the question because it does include diagrams: https://i.stack.imgur.com/wMVod.png The question includes a definition that is used to answer the question; if anyone knows how to answer or go about this, you would be helping me out a lot. | 0 |
I have some simulated data from a model of an IMU's gyroscopes. I am trying to use Allan deviation to verify that we have correctly modelled various sources of error in the sensor data. I was able to verify angular random walk, and have now moved on to bias instability. I'm following a tutorial on mathworks which describes finding a critical point in the Allan deviation curve, depicted as such: However, my sensors do not output this single, easily spotted critical point. My simulated data looks like so: Is this normal? If so, are there any techniques to choose the best critical point to get an instability reading? If not, what might cause it? | 0 |
By equivalence principle, one can find a local inertial frame at every point of spacetime. Then this is usually used to introduce the general spacetime metric, as a back-transform of the Minkowski metric. The transformation from Minkowski to general metric depends only on the first derivatives of the coordinate transformation. This means that locally we can get an inertial frame by applying a linear coordinate transform. It is puzzling because in motivating examples we always get accelerating transforms, such as a falling elevator. However, it seems that the acceleration does not play role in the final formula. What is happening? Is this because linear transform is enough to diagonalize the metric, but the quadratic part (i.e., the acceleration) is needed to make the Christoffel symbols vanish? | 0 |
I understand Thomson scattering as: When an EM wave is incident upon a charge causes it to oscillate in turn releasing energy as another electromagnetic wave. In an Electrodynamics lecture we took a different approach by assuming the far-field limit. The EM wave makes the charge oscillate causing it to emulate an oscillating dipole and hence releasing energy as another electromagnetic wave. I understand that these two present the same behaviour in the far field limit. However, I do not intuitively understand how the oscillating charge emulates an oscillating dipole. | 0 |
i'm writing my first document using LaTex. I want to include good-quality figures, so i opted to use the PDF format. i saved the images from the plots in Matlab as pdf files, and when i included the figure in my document it showed up with extra white borders, i'm not sure how to fix that. Cropping the pdf can be done, but i have many images to include so that would be tedious. any suggestions? or something else i can do? thank you | 0 |
We use Past Perfect to speak about actions before some moment in the past. What if my speaking partner doesn't know about a moment in the past? I had done everything. (I don't mention it, but in the mind I mean, I had done before some moment, which I know). What if i don't mention an moment, but it's obvious? I had written all documents. (It can be either obvious or unobvious, that I had written all documents before a deadline). | 0 |
Suppose I have an infinite wire and close by I place a loop which has increasing current. The wire and the loop is fixed . Now an emf will be induced in the infinite wire which in turn induces a current to oppose the changing magnetic field . My question is why this emf is induced in the infinite wire even though the wire is stationary( in order for motional emf to be induced) and also there is no loop formed by the infinite wire? How to define the flux change in this condition for the infinite wire in order to apply faraday's law to calculate emf? | 0 |
I am currently reading a book about numerical optimization and have reached line search methods. In a section studying the convergence rate of the gradient descent method, I am really struggling to understand how alfa is determined (see below). I really do not understand at all how to even differentiate with regards to alfa, when dealing with vectors and matrices, and I also am very confused as to how the b-vector can just completely disappear in the result. Can anyone explain how the derivative with respect to alfa is determined, and how alfa is isolated from there? Thank you to anyone who may be able to help. Explanation of how alfa is determined | 0 |
It is common knowledge that submodules of finitely generated modules need not be finitely generated. One can see this by considering a non-Notherian ring and extending this as a module. My question is, how does one think about this intuitively? The way that I think about is: When I restrict myself to a subspace, there is a chance I no longer have access to the elements that finitely generate the whole module. In contrast with Linear Algebra, this can occur when the subspace is non-empty. Could someone let me know if this is a correct way to view this or if there is a more intuitive way of viewing this result? | 0 |
Suppose I want to cover a whole circle of with hexagons. See the attached photo where coloured hexagons are those required to cover a whole circle. Given the length of the side of the hexagons and the radius of the circle, what's the minimum number of hexagons required to cover such circle? I notice that there are three ways of inscribing a circle in the hexagon tile: the center of the circle lies at the center of a hexagon, at the center of a hexagon side, and at the vertex between three hexagons. Attachment | 0 |
I know that in the pure algebraic context, connected groupoids are equivalent to groups. Moreover, connected groupoids can be seen as action groupoids. Consequently, any abstract groupoid is essentially a disjoint union of action groupoids. Therefore, is it not more natural to study group actions than study groupoids? Since group actions seems to have a richer structure than groupoids. So, why study groupoids? Does this also hold in a continuous context? | 0 |
In Information Technology, we often see something that looks like a compound adjective, pairing a number and a noum. Some examples are two-factor authentication, two-step verification and twelve-factor app. I always found it amusing that the noun itself is not plural. Why isn't it named, for example, "two-factors authentication?" Is there a rule for that construct? If so, what's its name? (My theory is that it probably came from multi-factor authentication, for example, in which there is some sense in the format, but I don't know for sure.) | 0 |
I have the simplistic image of a photon being a disturbance in the photon field caused by the loss of energy of an electron. In this image, I see that the disturbance is essentially a harmonic oscillation and it 'traces out a wave' as it propagates through the field. Also, given this image, it seems that the 'larger' the amplitude of this disturbance, the longer the wavelength and thus the 'lesser' the energy of the photon. This seems counterintuitive. Alternatively, is the 'amplitude' of the disturbance the same for all photons? | 0 |
While writing a fantasy narration I created this sentence: High among the clouds a castle floated. My American friend tells me it sounds bad to a native ear. I think he sees a problem with the unusual word order. At the same time the Hobbit starts with: In a hole in the ground there lived a hobbit. ...which seems a similar sentence. What is the science behind the word order in an English sentence? UPDATE: The original sentence was actually High among the clouds a castle floated, disregarding the force of gravity. I removed the ending phrase to simplify the problem, but from some of the responses I infer that the phrase may actually matter. | 0 |
I was just studying statics when I realized that a body can be in both static or dynamic equilibrium at the same time but I am not so sure. My textbook says that an object at rest is in static equilibrium while an object moving with zero acceleration i.e constant velocity is in dynamic equilibrium But.... Motion is relative so if two objects were moving with the same uniform velocity, they would be at rest relative to one another and therefore be at static equilibrium but since they are in motion relative to someone outside the system so they should be in dynamic equilibrium. Can anyone confirm this? | 0 |
A noon cannon usually has a single convex lens which focuses sunlight onto a fuse. The cannon contains gunpowder. The fuse ignites and the gun discharges at noon. https://en.wikipedia.org/wiki/Sundial_cannon A query has arisen about a noon cannon with TWO lenses -- what is the benefit of having two lenses? Does it provide more heat to ignite the fuse? The noon cannon with two lenses might be larger than usual, therefore needing a lens with a longer focal length. Images below. Thank you for any suggestions. I know quite a lot about sundials but I am not a physicist. | 0 |
I'm using CircuiTikZ and I came across this issue frequently: every time I want to tweak some options using tikzset, there is no documentation for the available key-value pairs. For example, if I want to change the voltage direction, in the documentation, only value (i.e., RPvoltages) is provided. However, I prefer to use key-value pair in my code for future reference so I was wondering how can I find the respective key name given value name or the other way around. | 0 |
Sorry if this sounds like a silly question, but what would happen if a scientist observes Schrodinger's cat alive, but is then thrown into a black hole before he has leaked any information to the environment. Then later a second scientist observes the cat - can he observe it as dead this time, since the first scientist and his information can't leave the black hole to contradict? That is, is a wavefunction allowed to show two different faces to two observers so long as they are never allowed to compare notes because of an event horizon? Is exiling information behind an event horizon the same as erasing it? | 0 |
So bound states have continuous position representation, yet countable discrete energy levels. Doesn't this imply that one of the following operations is invalid: <x|> or <E|>. Because |> cannot simultaneously have countable and uncountable number of elements. And the number of elements in the bra and the ket need to match otherwise the operation doesn't make sense. The ket |> exists independently of whatever representation we choose. So what's going on here? | 0 |
There are a couple of sentences: The water froze and caused the pipe to burst. If it is a succession of past events it should be Past Simple. But if the first part happened earlier, it should be : The water had frozen and caused the pipe to burst.So, can it be Past Perfect, or this sentence must be written in Past Simple? Year by year the population of the West increased. Should it be increased (Past Simple) or was increasing(Past Continuous) ? Because, I guess, Past Simple does not belong here . I don't know which tense to choose. There is no extra context, just sentences on their own. | 0 |
Suppose a piston enclosing an amount of air-fuel mixture and then this piston compresses the mixture to the point of auto ignition, if every part of the mixture ignite simultaneously is it safe to say that there isn't a flame front because it can't move because there is no longer a combustible mixture? If there is a flame front are they multiple flame fronts? Also if my reasoning is correct does that type of combustion have a name? | 0 |
In Arabic, the idiom "You made my neck as small as a sesame seed" is used to mean that someone related to you or a friend, put you in an embarassing situation with others. This idiom is usually used by parents when their children make them anything but proud. People who have long necks are assumed to be proud; hence, 'a neck as small as a sesame seed' in this idiom. Is there an idiom anywhere close to this meaning in English? | 0 |
I am currently reading electrodynamics from Feynman. When talking about the energy of the electromagnetic fields, he says that the location of the field energy could be known at least theoretically since all energy is a source of gravitational attraction, and if we could measure the gravitational attraction we could comment on the location of the energy in the fields. I have come across formulations where gravitational field is associated with an energy density and is said to be always negative. I wanted to know whether this energy can have an associated gravitational field. | 0 |
Suppose that, in a homogeneous linear system, the coefficients of one of the unknowns are all equal to zero. Show that the system has a nontrivial solution. Attempt: Note that the rank must be less than or equal to the number of columns in the coefficient matrix. If we had all columns of the augmented matrix different from zero, then, after being reduced to row-echelon form, we would have at most rank = number of columns. As we have a null column, then surely the rank is less than the number of columns. Therefore, we will have at least one free variable. Am I right? Furthermore, is there any way the solution could be more formal than that? (using the same approach) | 0 |
What comes after "pair"? Maybe "quad" for four? In cards it's "three/four of a kind" but what about contexts beyond cards (like science)? For example, in physics there's a "pair-flip model," but what is the extension of this model to flipping three things? I've also tried the internet, see also: https://en.wikipedia.org/wiki/Tuple Not to be confused with: single, duo, trio, quartet, quintet, ... monad, dyad, triad, tetrad, ... single, couple, triple, quadruple, ... single, twin, triplet, quadruplet, ... Or does "pair" secretly belong in one or more of the categories above? Or is it just an isolated word for, e.g., trousers? Thanks for helping me solve this mystery! | 0 |
There's a word people around me used to use a lot, phonetically it would spell 'stercus' or 'stircus', I think. It was used in a context meaning excitable, frenzied, frenetic, that kind of thing. Like, you could say that: Kids who eat lots of sugar tend to go stercus. I don't know if it's an actual word and I can't find it because I'm butchering the spelling or misremembering how it was said. I'm a native speaker from Australia, if that helps. | 0 |
In the double slit experiment, an interaction with a detecting mechanism is needed to know which slit was the one the photon or electron passed through. I read in other questions that polarized filters are placed in the slits, how is it exactly that this helps us know which slit the photon passed through? Do experiments using electrons also use polarized filters? If not, what do they use and how does it work? Are there other types of detecting devices? Is there a detecting device that truly does not change any properties of the photon or electron when interacting with it? | 0 |
I am using sagemath to compute Einstein tensors of a non-standard spacetime. The output is something horrid and non-diagonal. I need to find the Eigenvalues of this tensor... which is represented as a symbolic matrix. This is proving to be non-trivial with the sagemath documentation. Is there a way to convert my tensor output into a matrix that sagemath can find the eigenvalues for? If a worked example is required, please let me know as I can provide an update easily. Thanks in advance... | 0 |
uh I'm curious again regarding the theories of reflection. This is known that Metals contain free electrons that absorb energy and vibrate when they come in contact with light. Later, they release the energy back in the form of light. But what if we polish a transparent conductive oxide glass (transparent glass which is electrically conductive). It doesn't seem to be acting like a mirror. So is it really just the electrons which decide the reflection? Do correct me if I'm wrong. I'm just a stupid kid :) My previous post | 0 |
I know for abelian group, there is a Kronecker decomposition theorem. It said any finite abelian group can be factored as direct sum of cyclic group of prime power order. I want to know is there anything similar with this for the abelian semigroup with identity? As for semigroup, we don't need the inversion, so it seems like it can also support some kind f factorization. | 0 |
When a spinning top slowly advances and hit a surface (a wall), intuitively one would expect that the top gets bounced mostly along the wall, due to the friction between the top and the wall. But the observed phenomenon is that the top gets bounced mostly in the norm direction of the wall, and in a much higher velocity than when it hits the wall. | 0 |
Looking for alternative to "opened a can of worms" in the following sentence... It needs to be graphical enough for a young readership to grasp, a readership that won't have heard of Pandora's box or even know what a can of worms is. Having fixed one friend's laptop I wondered if I may have opened a can of worms and now all my friends will expect the same service. Any suggestions? | 0 |
I have read a book saying that "... backward induction cannot be applied to games of imperfect or incomplete information because this entails cutting through non-singleton information sets." However, in another textbook, it says that backward induction can be applied to games of imperfect information, and we can derive the equilibrium by starting at a historical point and show the subgame perfect equilibrium in that subgame is a equilibrium in the Nash equilibrium. I wonder what are the contexts to use backward induction in a game with imperfect information but complete information? | 0 |
From what I know, current flows across two points only if there is some potential difference across those two points. If that is the case, why does the current flow through a wire then? See the picture for clarity: As one can see, the potential is same on the left side of the wire. The current should not flow, yet it still does. Why?(I have the same question if the resistor was replaced by a capacitor.) | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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 ? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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! | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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! | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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. | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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. | 0 |
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 | 0 |
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? | 0 |
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? | 0 |
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 | 0 |
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) ? | 0 |
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? | 0 |
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? | 0 |
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. | 0 |
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. | 0 |
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