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We know in pure translation force distributed evenly in each particle on rigid body, so in effect every particle of body moves with same velocity or acceleration in pure translation. What happened in pure rotation, how force is distributed in pure rotation particle by particle to moves a body in pure rotation? | 0 |
The question is as simple as that. This is the kind of thing I want to achieve: The idea is to make a symbol used for divided differences. It needs to be a true delta letter rather than a triangle, but actually it is not that easy. | 0 |
the graph of the function[The graph of the functionthe graph of the first derivative of the functionThe attached graph shows the existence of turning point but the first derivative of the graphed function is never zero anywhere within the domain of the function. What does this mean? | 0 |
In general spectral analysis, we have examples of unbounded from below hamiltonians with discrete spectrum. Is it okay to say that they have no sense in physical context, because for me it looks like particle can emmit infinite energy in some weird sense. | 0 |
I want to mark a fraction, which I shorten, with an arc. Haver anybody an idea how to start? I wish that it looks like the text in the picture. Is there a way to do it? | 0 |
i Know elementary and their applications and there is a theorem: "The inverse operation (function) of an elementary row operation exists and is a elementary row operation of the same type." i want to know the proof of this theorem! thanks :) | 0 |
I am looking to study more about electron impact ionization. I noticed that this topic or anything collision-related, is not present in Chen in detail. Is there another resource that I can use to understand this better? | 0 |
suppose we have a circle to which we make a target and rotate it without breaking the basic definition of a tangent how many tangents are drawn as rectangles strips i have tried with integrals but I really want to know the answer to this question | 0 |
I searched on the Internet for the answer and found none. How can one find it? Also, I write "SLITEX" because methinks every letter of the name is, even if small, raised or lowered, the capital one but feel free to groundedly correct. | 0 |
If still charges in a wire loop do not respond to a(or have their own) magnetic field, then how is current is generated by changing a magnetic field? And why only a changing magnetic field? What actually happens at the atomic level? | 0 |
Though both of these terms come from other languages, they are both said in English, depending on where one is. One (ay wey as a more English form) can mean holy crap!, and the other can mean something similar. Maybe it can be due to a related background? | 0 |
I have not got any solution after a few try. In latex, how we can comment out a single word from a line. I mean for example Hello %this is so on it comments out this and the rest of the line as well. Is there any way to comment out only this part, not the rest of the line ? | 0 |
When an ideal gas is compressed isobarically the given energy by the external source is let out as heat alongwith some more heat that comes from the decreement of internal energy. My question is why doesnt the energy given by the external source increases the internal energy and some lets out some heat?? Maybe I am missing something conceptually about so please help. | 0 |
While proving associative property of vector addition graphically, everything else appears symmetric except the fact that vector a do not have a derived line as part of the final graph. Is it due to a being considered base? | 0 |
Let the Zhegalkin polynomial for function consist of those and only those monomials that are not included in the polynomial for function . How different can the functions and be? (Write the maximum and minimum number of sets on which they different for each ). | 0 |
i used to substitute a value into the actual book prescribed answer and the into the answer i got to see if the equations yield the same answer. i now want to confirm if the method i am using is legitimate. this is my solution to the question this is the book solution | 0 |
This question looks like me value theorem by canceling of a way to apply it in the problem quite yet. An image I messed around with the given equation and tried to set it equal to the second derivative but it I came up with nothing. I'm suspecting that my method to solve this problem is incorrect. | 0 |
I asked a question a while a go what is a bound state and the question was closed because there is a similar question. Now since best description we have to describe nature in quantum field theory How we define bound states in quantum field theory? | 0 |
have you ever encountered works on set partition in which the principle of inclusion exclusion is used in the case of a single parameter and reused in the generalized case (with several parameters) ? | 0 |
Does there exist such a notation? It looks similar to old factorial notation, but its in upper right corner rather than lower left. I need it as math environment or with some simple code so as to achieve: These are made in ms word. | 0 |
If particles are excitations of fields: how does the field record the spin of a particular particle? There is no space to record the spin states of two particles, of opposite spin, in the field. | 0 |
I what taught that my last name which starts the Mc that the c should be above the symbol =, does anyone know what this means? I can not really type it out on a key board but if you write it out with a pencil you can see the M "lower case c with = under it". | 0 |
I have the following in my notes: I dont understand the statement 'simple model fails' Is the graph shown supposed to be theoretical model or is that the experimental data. This are equation derived before the graph: | 0 |
I feel that the reason to define thing like current density is that we want to use the directional nature of the current like a vector quantity and since electric current is not a vector so we define something which has same direction as current but a vector? is is true? | 0 |
my sir told me that he will get a shock, but why not bird then he replied bird has legs acting as insulators i am in confusion what is the right explanation to this | 0 |
I make reference at this question: Package pgfkeys: I do not know the key '/tcb/O' and I am going to ignore it and to accepted answer. If the text of question and or of the answer span on the next page, like here: the left arrow dont span on the next page (with both tcoloboxes breckables). Can we solve this problem? | 0 |
I was at a complexity optimization class and they said all constant sheaves are a twist of a perverse sheaf; is it specifically in complexity optimization or is it true for all constant sheaves?! | 0 |
I'm using the Overleaf documentation to produce a bibliography with in-text citations, using bibLaTeX (compiler is XeLaTeX, document class is article). I've tried all of the citation styles on the overleaf webpage, and none produce superscript in-text citations (i.e. numbers as superscripts). The closest I can get is numbers in square parentheses. Is there no citation style that has superscript numbers? Or does this indicate that something else is going wrong? | 0 |
I have seen that the notion of affine scheme is a generalization of the notion of affine varieties where the coordinate ring is replaced by any commutative unit ring, and the variety with the Zariski topology is replaced by any topological space. Does this mean that every affine variety is an affine scheme? I think that if we have an affine variety X and we construct its structure sheaf then the affine variety is a locally ringed space but how we conclude that it is isomorphic to a spectrum of a ring? Or there is another proof of this statement? | 0 |
Is there any expression in English that refers to the situation when someone who is just an acquaintance (not a close friend) happens to be present around you at a social gathering (be it at a house party, a club ...), and you are debating whether to show them that you have seen them out of being shy or to avoid an awkward greeting? I'm seeking anything that fits the bill, whether it's a single word, or a phrase. | 0 |
A directed graph G=(V,E) is given and I am asked to prove if there is a tree of shortest path of this graph that cannot be returned using BFS. Meaning to say if it is true or not that for every tree of shortest path a BFS can return it. I thought that the answer is true, for every tree of shortest path there is a way of arranging the adjacency lists of G such that a BFS can return this tree, but I cannot find a mathematical way of proving it. Or maybe it is false, meaning there is a counter example of a tree of shortest path that cannot be returned by BFS but I can't find this example either. I would appreciate some help, thanks! | 0 |
Airplanes traveling at supersonic speeds produce sonic booms because the pressure waves they create converge to produce an extra high intensity wave. But what about planes traveling at slower speeds? These create pressure waves too (although they do not converge). Are these pressure waves the sound you hear from an ordinary plane in the sky? I always thought the sound of an aircraft came from its engine noise. | 0 |
Chess is an incredibly intricate game, offering an immense number of moves and combinations. Due to this complexity, determining the precise count of legal chess games poses a significant challenge. As of my knowledge, the total number of possible legal chess games remains unknown due to the vast array of potential moves and positions that can emerge during gameplay. However, I've been pondering an intriguing question: Can we establish whether the total number of legal chess games is odd or even? It's a captivating puzzle that has captured my attention. I've given it considerable thought, but I must admit that I'm still uncertain about the parity of the total number of games. Can anyone direct me how to approach this? | 0 |
The Hills mechanism postulates that when a stellar binary system is perturbed by a supermassive black hole (SMBH), the tidal forces at play result in the capture of one star while simultaneously ejecting the other. My question is as follows: Why does one star become captured while the other is ejected? Is it not possible for the SMBH to capture both stars and maintain the binary system within its orbit, or alternatively, eject the entire binary system? | 0 |
A graph is homogeneous when every isomorphism between two finite induced subgraphs can be extended to an automorphism of the whole graph. I was reading Diestel's graph theory where he describes the following graph and says its clearly homogeneous. It's not immediately apparent to me why. If I have an isomorphism between two finite induced subgraphs, and map every other vertex outside the subgraphs to itself, does it become an automorphism of the entire graph? But wouldn't that make almost anything homogeneous? What is special about this one? | 0 |
Most eye floaters are caused by age-related changes that occur as the jelly-like substance (vitreous) inside your eyes liquifies and contracts. Scattered clumps of collagen fibers form within the vitreous and can cast tiny shadows on your retina. The shadows you see are called floaters. If you look in a mirror while getting floaters would you see an image of the floaters in the mirror? Since they are basically shadows on the retina, I think we should theoretically be able to see an image but practically not because the shadow image would be very small. | 0 |
I have been trying to find the proof of the derangement theorem, and have checked out some materials on them (since its proof has not been taught to us). But I have not been able to understand much of it. So, I was thinking, is the inclusion-exclusion principle used? Since the expression seems somewhat familiar. If not, then could someone please explain the proof in a slightly simplified manner? | 0 |
I am trying to understand what fugacity really is. I asked a related question on chemistry stack exchange but am not satisfied with the answer. In many books, such as Physical Chemistry by Engel and Reid, Physical chemistry bh Castellan, etc. fugacity is called as effective pressure. My questions are a)What does the word 'effective' is trying to say? and b) If we already have various equation of states that have already accounted for intermolecular forces, then why is there a need for fugacity? I'm sorry if this is a stupid question but english is not my first language and maybe I am not interpreting fugacity correctly. So any help is appreciated! | 0 |
Objects appear in different colours because they absorb some colours (wavelengths) and reflect or transmit other colours. The colours we see are the wavelengths that are reflected or transmitted. As far as I understand, when an atom absorbs a photon, one of its electrons gets excited (and unstable). So it drops back to ground state, emitting that energy in the form of photons of a specific colour. This means that we should find objects to be in certain colours, but, for example, hydrogen gas is colourless. How is this possible? Shouldn't Hydrogen gas have a specific colour related to its emission spectra? I was reading an article on this topic today (https://www.khanacademy.org/science/chemistry/electronic-structure-of-atoms/bohr-model-hydrogen/a/spectroscopy-interaction-of-light-and-matter), and this came into my mind. Can anyone please help in clearing my understanding? | 0 |
What I mean is how the shape of an object affects it's physical properties. I've been studying Marine Biology and there's constant talk of how a fish's shape determines how well it can swim but no explanation of why, say, "Stream lining" reduces water resistance outside of it "just making sense" and I'd like something more in-depth. Similar phenomena would be: How a blade's shape determines how it cuts, Why certain shapes are more structurally sound, What determines a shape's aerodynamics. Is there a field of research dealing with this? It's been driving me mad. | 0 |
An excerpt from my grammar lesson: In a formal context, 'due' should always be treated as an adjective, and 'due to' must therefore follow or refer back to a noun, as in: his success was due to hard work. In this case, how is 'hard work' considered a noun? In a prior lesson, a noun was defined as a word that names a person, place or thing. by this definition, isn't 'hard work' more appropriate to be a verb? Am I missing something? | 0 |
I recently engaged in a lively debate with a friend about whether the term "hot dog" qualifies as a misnomer. My argument stemmed from the fact that a hot dog doesn't actually contain dog meat. Instead, it's typically made from beef, pork, or a combination of meats. My friend argues that the term "hot dog" supposedly originates from a playful association with the dachshund sausage, given its resemblance to the dog breed and therefore, it shouldn't qualify as a misnomer. While this may be true due to the term's roots in historical references, it still inaccurately portrays the contents of this food today with the lack of any canine involvement. | 0 |
The connection between Markov processes and Potential Theory is well known, as is conformal invariance of Brownian motion which allows probabilistic proofs of statements in Complex Analysis, like Picard's theorem. What are some results in these areas (Potential Theory, Complex Analysis, maybe Complex or Differential Geometry) that admit probabilistic proofs, and possibly for which no other proof is known? To what extent are probabilistic methods in these areas actually crucial in proving new theory and to what extent are they more of an interpretation of facts that are already known? It would be great if there were some survey about this. Thanks in advance for your answers. | 0 |
My friend is working on a snow gun, which involves using compressed air to blow apart water coming out of a pressure washer. I read that you can cool air by compressing it, which makes it hot, then letting the compressed air lose energy by cooling to room temperature. I was going to use the ideal gas law to find the change in temperature when compressed/decompressed, and Newton's law of cooling to find the time it'd take to cool down. However, I don't think the ideal gas law can be used in this case. What equations are appropriate to find the temperature of a gas before and after it is compressed? | 0 |
Suppose we have two entangled particles, A and B. If we measure particle A and then subsequently entangle particle B with a third particle, C, would the state of particle A influence the combined states of particles B and C? Specifically, would there be any correlation between the combined spins of B and C and the measured spin of A? Have there been any experiments conducted to explore or validate this scenario? | 0 |
"We understand that a set is a collection of objects, but not every collection qualifies as a set, as exemplified by the collection of all sets (consider Russell's Paradox). To define the collection of all sets, we employ the term 'proper class.' Now, I would like to confirm if my understanding here is accurate: A class is a collection of objects, and these objects can be sets. Classes are categorized into two groups, namely small classes, known as sets, and large classes, referred to as proper classes. Is this correct?" | 0 |
I am studying a rotating cylinder model in general relativity. The interior metric is given, but I am trying to express the exterior metric. It has to be practical and describe spacetime around a rotating cylinder. So far I have considered the Kerr metric, of course, the Janice-Newman-Winicour metric, and the Tomimatsu-Sato metric. For the Kerr metric, I am struggling to express it in cylindrical coordinates. Doing so will make it easier to match it to the interior metric. Any suggestions or inputs would be appreciated, thanks. | 0 |
As a high school student, I'm curious whether everything emits thermal radiation, including monatomic gases and substances composed of a single type of atom and no molecules. Can these objects emit radiation in all wavelengths, and if so, how is it possible in the absence of molecules?Is it necessary for an object to be a blackbody in order to emit thermal radiation across all wavelengths? | 0 |
I was watching this video where the English gentleman asks the Scottish MP to speak in "Antipodean English". From what I know, 'Antipodes' refers to the southern hemisphere and I am unable to understand why the gentleman would want the other person to speak a dialect from that broad region in particular. Because this seems unlikely, I want to know what the person meant by the term "Antipodean English". | 0 |
Assuming the earth is either at the perihelion or at the aphelion, it is easy to see the Runge-Lenz (RL) vector is directed along the line joining the perihelion and aphelion. Since the RL vector is a constant vector, its direction (and also magnitude) must remain the same at all points of the orbit. So if we want to draw this vector at other points of the orbits, it will be drawn as a vector parallel to the line joining the perihelion and aphelion. Is this right? | 0 |
I'm looking for where best to start on the following problem. I have a graph of N nodes and each node as a weight. I need to group all nodes into X groups such that the sum of weights in each group are approximately even and that each group is a connected component of the original graph. After some simple searching I came across the lukes partitioning algorithm implemented in python. https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.community.lukes.lukes_partitioning.html#networkx.algorithms.community.lukes.lukes_partitioning This is approximately what I am looking for but performance feels slow for the size of the graph I am working with. Do you have any potentially better ideas that worked for you? | 0 |
It's a common myth (especially in popsci) that a black hole contains a singularity. However, I cannot find an explanation for what we think a black hole actually does contain. The best I've seen is "in order to answer this question, we have to unify GR and quantum mechanics." So there are no attempts to answer this question despite our incomplete picture of physics? Let's say Schwarzschild black hole to start with. | 0 |
I am writing a research paper where I want to say The rest of the paper is organized as follows. in the introduction of the paper. However, the word "rest" doesn't sound good as it is perceived as if I am explaining about an unimportant part of the paper. I checked some synonyms on Grammarly, but nothing really fits well. I thought about the following: The remaining paper It also sounds odd as it sounds like "leftover" to me. I can be wrong as well. The remnant of the paper This is used mostly for historical events as far as I know. Any advice is appreciated. | 0 |
I'm not very well-versed in topology, but I know the basic concept of topological equivalence can be approximated by "counting the holes" in objects, in the sense that a sphere is different from a torus, but a torus is the same as a coffee mug because they have the same number of holes. I know this roughly approximates being able to smoothly deform one object into another. Can this be applied to interior "holes" as well, such as a hollowed-out sphere? Does the hollow center count as a "hole"? Is there a way to smoothly deform a hollow sphere into a torus or a sphere? If not, is a hollow sphere in a different topological equivalence class from both a sphere and a torus? | 0 |
I have read that projectile motion is parabolic in nature. I know that the equation of projectile motion represents a parabola. But when do we get a parabolic curve? Does it happen when there is downward acceleration and horizontal velocity? What condition results in a parabolic shape? Is there any possibility of elliptical motion or any other curve? What would be the determining factors in that case? | 0 |
It's clear to me that when an object is in free fall in a uniform gravitational field ("Einstein's Elevator") it feels no tug of gravity. However if it is in free fall in a nonuniform gravitational field does the object (or more specifically an accelerometer) feel a tug as gravity pulls in one direction and then another? Asked another way, is an object in free fall in a nonuniform gravitational field considered to be in an inertial reference system? | 0 |
I was recently studying a paragraph in which I came across a sentence, which was below: The British king, Charles I, had inherited a very difficult financial situation from his father. However, I don't understand why 'had' is being used here. My understanding is that had is used only in past perfect tense, where there are two events in past and we use had to signify that event that finished before the second event started. So I modified the above sentence like below: The British king, Charles I, inherited a very difficult financial situation from his father. Is the modified sentence correct? Please help me to understand. | 0 |
My uncle is a retired math professor. He has had some serious health issues in the past year, but he is still mentally sharp. For both fun and a distraction, he has been working on a textbook. However, I believe it is hard for him since he has trouble sitting at a desk and typing. Does anyone have any recommendations for good voice-to-text software that he could use? Latex and math formatting would be very helpful, obviously, although I could possibly help here. | 0 |
I have a set theoretic question. I don't understand why the collection of open balls of a metric space is a well-defined set. From my understanding of sets, a set is well-defined in Naive set theory if we can check whether an element is in it or not. But how can we check whether a subset is either an open ball or not? It seems very difficult to check. Maybe my view of a set is too rigid. Is there a better view of whether a set is well-defined? Thank you. | 0 |
I came across the following sentence while reading "A Clash of Kings" book by George R. R. Martin: Whitetree was the fourth village they had passed, and it had been the same in all of them. The people were gone, vanished with their scant possessions and whatever animals they may have had. None of the villages showed any signs of having been attacked Why is the "may" word used here instead of "might"? I thought that "may" can be used only in the present tense and have never seen it used in the past context | 0 |
I recently saw a video from a passenger of Concorde after it goes supersonic. Inside the aircraft, there is still a loud roar similar to what we hear in aircraft today. However, since the aircraft is supersonic, shouldn't the noise be left behind? Why is the roar present? I was expecting the aircraft to be nearly silent due to being supersonic, and it appears that is far from the reality. | 0 |
So I know that the statement "If two random variables are independent, then the two random variables are uncorrelated" is true. Does that mean its contraposition "If two random variables are correlated, then the two random variables are dependent." also true? In terms of the theory of logic, the contrapositive statement should also be true, but then again, I learned "correlation does not imply causation". So I'm a bit confused. Can someone clarify this? Is the contrapositive statement really true? If so, what is the difference between that statement and the statement "correlation does not imply causation"?? | 0 |
Suppose a person is using an electrical appliance and suddenly there is a power outage- would it be correct if that person immediately said to their family members that 'the power is out'? Or would it be better to say 'power has gone out'? In what way are they different? Are both idiomatic? (And similarly, is there a distinction between 'the power has come back' and 'the power is back on'?) | 0 |
I was reading about how reflection and refraction work at a quantum scale. What I understood was that the photon "can" take multiple paths to reach the end point and when we consider all these possibilities, most of them cancel out as they interfere destructively, while there's constructive interference around a certain direction. That is what we observe is the the sum of all the probabilities of the possibile paths the photon could take. Please correct me if I'm wrong. My question is how do we calculate that probability of each path? Or do we only calculate the sum of the probabilities directly? | 0 |
When @anna v explained why the planetary model of the atom does not make sense in this post, she said the electron in an orbit is accelerating continuously and would thus radiate away its energy and fall into the nucleus. However, when the Earth orbits the Sun, isn't it accelerating continuously toward the Sun? If this is the case, should the Earth radiate away its energy via gravitons and fall into the Sun eventually? I also checked questions about Why doesn't the Moon fall onto the Earth?, but the answers didn't talk about radiating away gravitons. | 0 |
From Beauville's book on complex algebraic surface, in Chapter IV, we know each Hirzebruch surface contains a unique irreducible curve with negative self-intersection. If we remove this curve from the Hirzebruch surface, different from contraction, it will result in a non-compact surface. I'm wondering what we can say about this non-compact surface. For example, what kind of symmetry does it have, will it still be toric? More generally, what if we remove an irreducible curve different from the one with negative self-intersection instead, how will it affect the situation above? I'd appreciate any relevant discussions or comments, thank you in advance! | 0 |
I'm trying to represent a company as a feature vector. The vector has multiple stats describing the company such as earnings growth, capital expenditures, gross margin, etc. The goal is to represent companies with these vectors and find the most similar companies based on some similarity measure (ie euclidean or cosine). My questions are: Would this be an accurate way to represent companies? Is there some normalization I have to do to the vectors before finding similarity? And what is the best measure of similarity for these vectors? | 0 |
According to Introduction to Solid State Physics by C. Kittel, An ideal crystal is constructed by the infinite repetition of identical groups of atoms. A group is called the basis. The set of mathematical points to which the basis is attached is called the lattice. The crystal structure of copper is face-centered cubic (fcc). So we can say the lattice is fcc, and the basis is composed of one single copper atom. I was wondering if it is wrong to say, instead, that the lattice is simple cubic (sc), and the basis is composed of four copper atoms. Both give the same arrangement of atoms in space, but in the second there are fewer lattice points. | 0 |
Examples of solutions to linear differential equation are (from Wikipedia): exponential function, logarithm, sine, cosine, inverse trigonometric functions, error function, Bessel functions and hypergeometric functions. So in this sense these are linear functions (for some generalized notion of "linear"). But I wonder if there are examples of functions that are "strictly nonlinear", in the sense that they are the solution of some nonlinear differential equation but not of any linear differential equation. | 0 |
I have an application I'm trying to model that involves using superconducting coils to produce a steerable dipole. To some degree, the problem is easier if I can modulate the current through the coil, but I have read in a few places that there can be practical challenges related to the superconducting coils being "perfect inductors." Can someone help me get a better understanding of how to mathematically model a superconducting coil in both a DC and AC circuit? Specifically, I'd be curious if trying to vary the current quickly produces operational challenges like excess heat which makes it more difficult to keep the coil in a superconducting state. Thanks! | 0 |
Bicycle's brakes generally fall into two broad categories: rim brakes where the braking pads pinch against the wheel's rim, and disk brakes where the pads press against a disk (rotor) that is rigidly attached to the wheel's hub. General wisdom is that disk brakes are higher quality and offer better stopping power. But disk brake pads are much closer to the center of the wheel, which means that they have to exert more force to produce the same amount of torque. Wouldn't this be less stopping power? | 0 |
I noticed that dew only falls on horizontal surfaces, while vertical surfaces remain dry. But dew is the condensation of water vapor contained in the air. And for the condensation process, the direction of the surface does not matter. If you bring a smooth cold object into a warm room, it will be covered with condensate evenly on all sides. Why do vertical surfaces stay dry? | 0 |
I have a idea I'd like to explore: If a black hole can bend light due to its immense gravitational attraction, could we imagine an 'inverted black hole'? In this hypothetical scenario, this object would behave similarly to a black hole but with a force of repulsion instead of attraction. This repulsion would cause light to curve away from it, making it impossible for light to reach the white hole. I'm also curious about whether there are software or codes available that could help me visualize this concept, similar to how software like 'Space Engine' visualizes regular black holes. Right now, to keep things simple, I wish only to explore how this hypotetical object would affect light and images. | 0 |
Using a triangular glass prism to disperse white light into a rainbow works because different wavelengths/colours of light have different refractive indices in glass, doesn't it? The different refractive indices apply regardless of the shape of the glass. Therefore, wouldn't a simple rectangular slab of glass also disperse white light? The different wavelengths would be differently refracted and emerge separated from the other end. Why is a triangular prism always used to demonstrate dispersion? Is there something I'm missing? | 0 |
Mine is a very basic question yet I haven't got a satisfactory answer so I turn to you. Special Relativity is based on two assumptions, one of which is that the speed of light is constant for all inertial frames. While I know the disprove of universal reference frame, Aether, I want to know how we came to the conclusion that the speed of light REALLY is constant for all inertial frames (light traveling in vacuum). | 0 |
The gravitational binding energy or self-energy of a system is the minimum energy which must be added to it in order for the system to cease being in a gravitationally bound state. Equivalently, the gravitational self-energy of a body is defined as the work done by an external agent in assembling the body from the infinitesimal elements that are initially at an infinite distance apart. A gravitationally bound system has a lower (i.e., more negative) gravitational potential energy than the sum of the energies of its parts when these are completely separated. Is this type of energy a source for gravity? In order words, does a star have a smaller gravitational field due to its negative gravitational self-energy? | 0 |
I'm wondering which of the following sentences is correct: They realized that if the threat WAS not contained, it could endanger the nation." They realized that if the threat WERE not contained, it could endanger the nation." My understanding is that the subjunctive "If X were" is used for a counterfactual to a present situation. But here, the threat not being contained is a real possibility being considered in the past. If the main clause were written in the present tense, "to be" would be present indicative: "If the threat IS not contained." So I'd think it should be past indicative when the main clause is past tense. Am I right? | 0 |
I just read an article describing the project Scorpius. The aim is to use explosives to compress and heat microscopic quantities of Plutonium in order to study the states of the matter in extreme conditions. I wondered why they needed to recreate those conditions with explosions. Couldn't they achieve the same states with a Diamond anvil cell? With such apparatus they could compress a microscopic quantity to more than a million atmospheres and by passing some laser pulses trough the diamond anvils they could heat the matter. Am I missing something about the project purpose? | 0 |
During the Electroweak era, the Higgs mechanism had not yet distinguished particles such as electrons and muons by mass. Is there a conceivable experiment, or a hypothetical cosmological observation we could make today, that could have identified electrons and muons as distinct particles during that era? Alternatively, might there be features in the Cosmic Microwave Background or the distribution of matter in the early Universe that could reflect the distinction between the electron and muon fields prior to the onset of the Higgs mechanism? | 0 |
Why do charges placed inside a metallic cavity have no effect on outer charges and vice versa? My teacher explained it by electrostatic shielding. He said that the conductor does not allow the electric field to pass through it. I agree that inside a conductor the electric field is zero, because free electrons of the conductor move opposite to the external electric field to create an equal and opposite electric field. But what about inside the cavity? There is nothing like free electrons in the cavity, so an external electric field should reach there. | 0 |
I am wondering if the physical shape of a current carrying conductor will have any effect on the shape of its magnetic field or is it that the magnetic field surrounding any current carrying conductor will always be perfectly round. For example, let's say that current is passed down a long L-shaped metal bracket, such as the one shown in the drawing below. Will the magnetic field follow the path drawn around the L-bracket, or instead will the magnetic field be perfectly round and will encompass the entire L-shaped bracket? Does the physical shape of a current carrying conductor affect the shape of its magnetic field? | 0 |
I was fairly convinced that usual QM formalism didn't necessitate the use of complex numbers and that ultimately they're just a matter of convenience and utility rather than anything fundamental. This paper claims that isn't the case. But their demonstration doesn't satisfy me because it's muddled up in this Bell-like experiment. Can anyone explain what's going on in a simplified manner? Their argument does not make it clear to me why splitting the wave function into its real and imaginary portions and treating them as two quantities which are coupled via Schrodinger evolution isn't always possible---even in the case of multipartite states. | 0 |
I've seen several sources stating that Einstein was partially inspired by the Ehrenfest paradox when thinking about general relativity. However in the Ehrenfest paradox the non-Euclidean nature of the space in the rotating frame of reference is linked to Lorentz contraction rather than gravitational forces like in GR. Is the link simply that the rotating disk question got Einstein thinking about non-Euclidean geometry as a way to treat non-inertial reference frames? | 0 |
Forward and reverse synchronization between the TeX source and the PDF output using SyncTeX is an immensely useful tool when writing larger documents. Sometimes, especially when the synchronization is not working as expected, I would like to see the synchronization anchors in the PDF file. I know that the information is stored in .synctex.gz file in some form, but this is hardly transparent for a human reader. Some graphical indication over the PDF output would be great. Does this exist? I am working on Windows. Solutions for other systems are of course welcome, though they won't help me. | 0 |
Two generalizations of graphs have been described in a number of articles: multigraphs and hypergraphs. A multigraph is a graph in which multiple or parallel edges between nodes are allowed. These edges have the same end nodes. A hypergraph is a graph in which an edge can join any number of vertices. An edge can therefore connect sets of multiple nodes to one another. Both concepts allow one to model relations among objects with more detail and precision than with 'ordinairy' graphs. However, I have yet to find an account in which a combination of both structures is described: the hyper-multigraph. Such a graph would allow for parallel edges between the sets of nodes. Question: are there any references on such hyper-multigraphs? | 0 |
Yesterday in my English class, I tried to say 'I hadn't got that book' and my teacher told me my sentence was incorrect, she said I should say 'I didn't have that book'. I bought Grammarly, and it shows me my sentence is correct. Or maybe there is a difference between 'I didn't have that book' and 'I hadn't got that book'. I would like to know the opinion of a British person. | 0 |
Fraternal twins is what you call a set of twins who look different, but the word fraternal also has the meaning 'of or relating to brothers', and comes from a Latin root meaning 'brother'. The question is, how do I refer to a set of twins who look different but are both girls? May I use the phrase sororal twins to describe them? Or can fraternal be used here, too? | 0 |
I'm trying to prove that the covering space X of a manifold Y is a manifold of the same dimension. I was stuck on proving X is second countable, more specifically, on proving the fiber of any element in Y is at most countable. I find a proof at Is a covering space of a manifold second countable?, but that proof is based on the countability of the fundamental group of a manifold. Could there be a more elementary approach without using this fact? | 0 |
I imagine the following thought experiment: Let us prepare two identical neutral fermions with identical spin and antisymmetric spatial wave function in one spatial dimension. Let the initial state be two Gaussian wave packets which start at some large distance and have identical speed, but opposite direction. Since the particles are neutral, the wave packages should move through each other undisturbed. But at the time, where the particles are at the same place, the antisymmetrized wave function adds up to zero, so you cannot normalize the state. The exchange interaction should be zero because the particles are not charged. For the same reason there should be no magnetic moment. Where is the error in the argument? | 0 |
In my notes regarding entanglement and CHSH inequality it says: Further, this is the case even for incompatible observables: measurements on one system allow us to predict with certainty the outcomes of measurement of incompatible observables on the other system. However, the uncertainty principle tells us that we cannot predict with arbitrary accuracy the results of measurement of incompatible observables. How is the first sentence allowed. My understanding was that if you measure one set of observable, then the other incompatible observables are still in superposition. | 0 |
Given the following Bayesian belief network, what is the probability that a non-smoking patient with a smoking parent will develop lung tumor? In this question, isn't the answer already provided within the question itself? As I understand it, I required to calculate the probability of developing a lung tumor given that the patient does not smoke, but their parent does. However, this information is already provided in the table at the bottom right. Am I missing something? | 0 |
Suppose I have a "moving" frame of reference where I send a light beam from point A to two equidistant points B and C (equidistant in the moving frame of reference). From a "stationary" frame of reference, A to B and A to C are different distances because they have different diagonal components. But the stationary observer still sees light travel from A to B and A to C at the same time. How is it possible given constant speed of light? Just started learning about time dilation. Any help would be appreciated! | 0 |
I am an engineering student who is slowly branching into applied mathematics. While I can find plenty of good textbooks on the rigorous treatment of the Fourier Transform itself (including functional analysis and the Schwartz space and the result of this for the Fourier Transform) but I am having difficulty in finding an equivalent for the Discrete Time Fourier Transform (DTFT). Does anyone know of books that rigorously handle the DTFT, particularly on the convergence of functions that are not absolutely summable and its DTFT? | 0 |
I tried to prove that the centers of two tangent circles are colinear with the point of tangency. If I just assume they have a common tangent at their point of tangency then it's pretty easy. However, how do we prove that two circles do indeed have a common tangent at their point of tangency? (without using the collinearity of the centers and the point of tangency to avoid circular logic) | 0 |
In the Spanish language there is a word that is used to describe a person that has been tagged as a deadbeat; it is Largo. Largo in Spanish means Long as in the measurement of the distance between two points or places, etc. If you loan any money to this person, it will be a long time before you get paid back, if you get paid back at all, or if you receive any kind of payment. They can also be known as a Largo if they are sly, tricky, or conniving with bad intentions. | 0 |
I'm looking for a formal language that has the following properties: Contains finitely many words (and you can prove it). Decidable/recursive (there's a Turing machine that always halts, that can determine whether any given word belongs to the language). It's impossible to compute the exact number of words it contains. Meaning, even if you've already found all the words in the language, you can never know if there's another word that you just didn't try yet. Such a language feels "illegal", but I didn't manage to disprove its existence. | 0 |
A Chinese teacher of English asked me about the following, taken from an English test for Chinese people. It's quite tricky I think. I would like to know three things: Which answer or answers do you consider to be correct? If you consider an answer to be wrong, why do you think it is wrong? How would you reword these answers to make them acceptable? Nanjing is a popular city with a long history. Could you tell me ______ . A. where can visitors enjoy delicious Nanjing snacks? B. when is the best time to visit the Confucious Temple? C. how will people get to the Zhongshan Hill Scenic Area? D. why was the city also called Jianye in ancient times? | 0 |
I am pretty proficient till Calculus II, but I want to learn about more advanced methods of computing integrals like Gamma function, Elliptic integrals and Leibniz integral rule. I also want to improve my mathematical problem solving ability with this. Should I read Advanced Calculus by Frederick S. Woods or Inside Interesting Integrals by Paul J. Nahi? Or would it be better to first learn multivariable calculus? (any other book suggestions are welcome) | 0 |
A group action on a set is said to be transitive if it has only one orbit. Now, a group action on the same set is said to be regular if all the stabilizers of the elements of the set are trivial. My doubt is, if there is only one orbit, then, by orbit-stabilizer, all stabilizers must be trivial right? What am I missing here? Any hints? Thanks beforehand. | 0 |
From my understanding, the frequency and wavelength of a mechanical wave can be observed by the motion of the particles (i.e., as the particles oscillate from their state of equilibrium, the wave propagates through the medium). But, with electromagnetic waves, how do we measure its frequency and wavelength? If an electromagnetic wave travels across a vacuum, isn't it pretty much invisible to the naked eye? | 0 |
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