darklight03/StackMIAsub huggingface dataset:
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".
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?
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?
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.
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.
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?
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?
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?
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.
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.
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.
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
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.
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"??
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'?)
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?
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.
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!
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?
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.
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.
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!
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?
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?
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.
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?
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).
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?
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?
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?
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?
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.
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?
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.
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?
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.
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?
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.
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?
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?
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?
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.
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?
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!
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?