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Suppose I have a hose pipe connected to a tap. I turn on the tap and water flows out of the other end of the pipe. Now imagine I install two valves at different points along the pipe. Water will flow normally if both valves are open, but not if either one of them is shut. No doubt you can now see where this is going. I...
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I'm implementing physics for a computer game, and came accross something that looks unintuitive to me. Consider two bodies at rest: Let's say we momentarily apply the same amount of force to them, but in different locations: at the center of mass for one body, and off-center for the other. The second body will gain ang...
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I've got a few months to go before I enter in graduate school, but I have to say that my math background is not as good as I would like. Thus, I would like to take the opportunity to strengthen it and work on undergraduate analysis. I had in mind to work on the Rudin book I've heard so much about, the book is very conc...
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Let's assume we have a standard double-slit experiment, just for illustration's sake. When an electron collides with the detector, is its momentum parallel to the emitter's output, or is it something else? I know that the uncertainty principle forbids us from knowing too much about the momentum when we know the positio...
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I've been reading some category theory texts for my undergraduate monography, and I've found that one can talk about small and large categories using small/large sets, or do the same using sets/classes. Most introductory texts just shrug formalisms off, mention one of these formalizations and goes on. I've noticed that...
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I'm looking for a real analysis book that covers measure theory and I've been recommended Folland's or Royden's books, but their price is quite high and I was wondering if any of the books below would serve as a cheaper substitute. Theory of Functions of Real Variables by Lawrence M. Graves; Real Variables with Basic M...
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I'm having a little bit of a hard time understanding some concepts to do with self-inductance in class. I understand mutual inductance. That's when a loop has some time-dependent current going through it, and because the current is time-dependent, the magnetic field the loop produces is also time-dependent, and the mag...
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Given a mapping f: R->R, what properties must f have in order for its range to be countably infinite? I'm personally not sure, especially in terms of formalization, but ideas of non-monotonicity or some construction of countably infinite equivalence classes come to mind. For context, in quantum mechanics it's said that...
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I was solving this question in my coursebook and was not able to understand it conceptually. Though I did understand the mathematical approach to it. Now I understand that when the rod is given an initial velocity towards right, due to its motion an EMF is induced across it. Current starts flowing until it reaches a st...
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Consider a circular horizontal plane (like a round tabletop) rotating around its center. Consider a body A resting on this tabletop. Since the tabletop is rotating around its center, the body is moving along with it in a circular motion around the center of the circle. I understand that in circular motion, there's alwa...
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I'm wearing glasses with a sunglass clip-on. This means I have my regular glasses and, on top of them, I have a second pair of lenses that work as sunglasses and attach to my regular glasses using tiny magnets. I'm also in a car, and I'm looking through a window layered with Insulfilm. Curiously, when I look through th...
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This popular question got me wondering if there is a simpler way to reduce radon in homes. Our house has a fairly standard radon mitigation system. It has a lot of parts. There is a hole cut in the basement floor. There is a thick pipe which goes up through all the floors with lots of bends and turns, like the old Micr...
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I found a few questions that are similar to mine, but I do not think that either of them answers exactly what I want: Is there a Birkhoff-like theorem for stationary axisymmetric metrics? or Gravitational Collapse: Kerr solution is a vacuum solution but not for any rotating body? My question is this: When we look at si...
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My friend was sitting in a wheelchair, with a cup of coffee in one hand. That made me wonder, how would the wheelchair move if he turned only one rear wheel? He tried it, using his right hand to turn the right rear wheel. The wheelchair starting moving in a circle. No surprise. But I was interested in the radius of the...
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I apologize if this question has been asked before, but I haven't been able to find a post which covers this exact question. Let's say that we have a driving car which is moving forward. At some point, one of the rotating tires hit a stone on the road. Which way does the stone move, in relationship with the angle in wh...
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Suppose we have an isolated n-type semiconductor having varying concentrations of carriers over x. After some finite time, the concentration becomes uniform for a given constant temperature. We always say that this is because of diffusion which allows the movement of charge carriers to move from higher to lower concent...
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I'm trying to deepen my understanding of Von Neumann entropy (out of interest in the quantum Bekenstein bound) by learning more about the reduced density matrix (aka local density matrix), which is given by the modular Hamiltonians (aka entanglement Hamiltonian). As I understand it, modular Hamiltonians are only known ...
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Adjectives and adverbs can be formed by adding "y" or "ly" to e.g. a noun, such as: heart -> hearty, heartily However, sometimes these words are not in use, or make no logical sense, such as: chair -> chairy, chairly Although you could come up with a situation where you'd use "chairy", e.g. "this block of wood looks qu...
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I am teaching students at a high school about bending of a beam (the beam is clamped at one end and then an applied force acts downwards close to the end of the beam to bend it). I thought that it did not require further explanation that the deflection of the beam due to the force at the end is inversely proportional t...
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Compressive strength is how much inward force a given area of material can withstand before failure. The force tries to compress the atoms closer together. Mohs hardness is the difficulty of a material to be scratched. Abrasion resistance. However, when an object scratches another, there first is a point of contact whe...
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I really don't like the phrase "excited for" which seems to have become very common in recent years, as in "I'm excited for the weekend...". My sarcastic reply would be "I don't think the weekend cares or appreciates you being excited on its behalf". Anyway, I'm aware I have to accept that language changes, even though...
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"Longingly" is the adverb form of "longing". Depending on where you look, "longing" is described as an adjective, a verb, or a noun: Oxford defines it as either a noun or an adjective. Cambridge, Collins, and Merriam-Webster seem to define it exclusively as a noun. Wiktionary says it's either a noun or the present part...
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My question is closely related to the answer of this question: Why is general relativity background independent and electromagnetism is background dependent? General Relativity is often stated to be "background independent", because it calculates how spacetime is curved. That's in contrast to other theories like classi...
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Quite naturally, the observable Universe is the only bit of the Universe we can extract information from, as light from farther away has not reached us yet, and there are zones from which we'll never even be able to extract information, as they are causally disconnected from us due to their high speed. Therefore, how d...
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Recently I came across Normal matrices and their properties, one of which states that their eigenvectors are the same as their adjoint and are orthogonal. I've gone across some proofs and I understand it but when I tried to prove the same using the inner product, It somehow states that the above is true for any arbitra...
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In the English language there are many words where the letter "a" is pronounced as a short (continental European) "e". Or at least very close to it. However dictionaries point out that in these cases the correct pronunciation is more an "ae" sound. Several websites on English pronunciation take the same view. So I deci...
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In Photoshop (and many other computer graphics applications) there are are various ways that images/layers can be composited with their underlying background. These are sometimes called blending modes. One blending mode in particular is multiply, which has the convenient feature that it eliminates white backgrounds fro...
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I found this MC question that asks about a soft iron bar entering a solenoid: At first, my answer was (B) because the iron bar should increase the magnetic field induced by coil M and, according to Lenz's law, this magnetic field should oppose the original current, making the lamp dimmer. Also, the magnetic field creat...
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Given a path, how do the magnitude of the velocity and acceleration vector along the path correlate? I am confused due to the fact that the acceleration is the change of velocity over time and in general if you plot the velocity and acceleration over time, you can see a correlation (e.g. constant velocity means zero ac...
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Relativistically, the electric field of a moving charge is not purely radially directed, but is instead concentrated perpendicular to the line of motion. So, a current loop consisting of electrons as charge carriers should generate a "charge separation" effect, where the negative electric field is concentrated perpendi...
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A term in a Lagrangian is gauge invariant if one makes sure to use quantities which transform in proper representations of the group of gauge transformations. This means that one cannot write terms in the Lagrangian using a 'bare' gauge field, but one can use the associated field strength or act on a gauge field with a...
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This may be an amateur question, however here goes. I understand the double slit experiment creates a situation where detecting which slit the particle/wave goes through causes a collapse of the wave function and for the particle to act like a particle and not cause an interference pattern. What I want to know is this:...
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I'm considering to choose between "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe, and Yurii Nesterov's "Lectures on Convex Optimization" to supplement for my university course. I have had Calculus and Linear Algebra, my course covers constrained and unconstrained convex optimization, linear programming a...
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I often see "functional" used as an adjective in situations where I think that "function" would actually be the better choice. Specifically, I am referring to translations of German compound nouns. Here is an example: Funktionsarchitektur. This is the architecture of the function/functions. To be specific, we are talki...
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while working on problems related to fluid mechanics i came across a problem in which we were asked to find the kinetic energy of a sphere which is under pure rolling and has non viscous fluid filled inside it. here you can see the figure : so my initial thoughts were to write the moment of inertia of the whole body ab...
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I tried finding a decent book to study nonstandard analysis from and found Goldblatt's Lectures on the Hyperreals. However, I was very disappointed to find out that the text is not rigorous at all --- Goldblatt doesn't even prove the transfer principle. Are there any completely rigorous treatments of the hyperreals? Id...
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A popular misconception in the layman public is that the Big Bang was some sort "explosion" at a single point of space, where originally all matter was concentrated and then it "exploded" outwards. This is of course different from the modern general-relativity understanding of reality, which is that it is space itself ...
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You know how when you talk to someone about a bad time you're going through, and they feel the urge to one-up you to achieve some sort of imaginary victory point? E.g. School is challenging because I have to catch a bus early in the morning. Pfft, that's nothing, I used to have to WALK to school. I did the dishes and t...
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A sufficiently strong electromagnetic pulse can/will destroy smartphones and computers. I know somebody who went into MRI machine and forgot a Visa credit card in his pocket. The card was toast and he had to get a new one. A mobile phone in an MRI probably wouldn't fare better. But a big part of the human body itself i...
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Suppose there are two arbitrary side lengths of a right angled triangle that are known to us. There are two possible cases here that I can see: Either one of the side lengths given is the length of the hypotenuse. Both the sides lengths given are the lengths of the legs of the right angled triangle Now, additionally on...
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While the gravitational path integral is not a well-understood concept mathematically, a number of works (particularly in recent research connected to AdS/CFT) emphasize the importance of integrating over metrics on surfaces with nontrivial topologies as well as surfaces diffeomorphic to a flat spacetime. These metrics...
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I am new to algebraic geometry. I can't understand why an etale space is considered locally homeomorphic to its base space. The analogy I have heard is that etale space can be visualized as "stacked over" the base space, or that it is like a "puff pastry". I understand that we can (locally) map this stacked/pastry spac...
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I know that white light, upon entering another medium from air/ vacuum, disperses into its constituent colours. Essentially when travelling in the air, all of the constituent colours have the same speed but when entering another medium, they travel with different speeds and hence they are refracted by different amounts...
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We commonly anthropomorphise or personify non-living things by giving them human characteristics: "the angry storm". We zoomorphise things by giving them animal characteristics: "the storm roared". But what word would describe giving general (not necessarily animal) attributes of living things to non-living things: "th...
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Semantic consistency of a theory T is defined by there being a model M in which all theorems of T are true. Syntactic consistency of a theory T is defined by there being no formulas A such that both A and it's negation ~A are provable. So let's assume semantic consistency and then assume syntactic inconsistency. Since ...
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In classical mechanics , the Laplace-Runge-Lenz (LRL) vector is a characteristic feature of the Kepler problem. This enables a very simple discussion of the properties of the orbit for the problem. It is an extra conserved quantity besides the total energy and angular momentum for a particle moving under the influence ...
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So I've recently started taking maths seriously in hopes of doing physics at university and have gotten pretty good at algebra and learned some very basic calculus but I'm having trouble finding a good introductory geometry textbook. I know this question has already been asked at least twice before and I looked at the ...
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I am struggling to see the motivation behind Radon measures. In many places I see that they are described as measures that "interact nicely with the underlying topology", but without further elaboration. On Wikipedia it states A common problem is to find a good notion of a measure on a topological space that is compati...
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Background: My understanding is that model-theoretic semantics (MTS) and proof-theoretic semantics (PTS) differ in the following ways. In MTS, you first define the notion of truth in models and then having this notion you develop a "good" (sound, complete, decidable) proof system. In PTS, you just define a proof system...
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I'm confused by how thermometer works based on The Zeroth Law of Thermodynamics. The Zeroth Law of Thermodynamics said that "If a body, A, be in thermal equilibrium with two other bodies, B and C, then B and C are in thermal equilibrium with one another." Then, about thermal equilibrium, it said that "If when two bodie...
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Greetings fellow physicists. I have some questions about the ability of different electromagnetic waves to pass through materials that I hope you can clarify. It seems that microwaves can go through concrete, wood, etc. since we can listen to the radio inside houses. However, it doesn't make sense to put a TV antenna i...
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In Australia, we use the expression Tall poppy syndrome for a "social phenomenon that occurs when someone's success causes them to be envied, resented, criticized or discredited." https://en.wikipedia.org/wiki/Tall_poppy_syndrome Conversely, is there a term or expression that's used for a social phenomenon where succes...
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I would like to know of any techniques that can be used to measure the electric field strength precisely and accurately in both time and space. I know that there will be physical/ practical limitations to this and that it is not possible to measure at an infinitesimal position, but I would still be interested to know w...
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I've asked this question in Quora and the answers I got were: First answer: Using "more" and "less" helps maintain clarity and consistency in comparative forms. It provides a straightforward and predictable way to form comparatives and superlatives without relying on irregular or unpredictable suffixes. Second answer: ...
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I am actually having an introductory course in Special Relativity in which I was looking at the Michelson Morley experiment. And I have this silly confusion. The setup for the Michelson Morley experiment looks something like this in every textbook (assuming the observer is in the comoving frame) When this same setup is...
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I know that the tangents from a point to a conic section subtend equal angles on the focus. However, I have mostly studied conic sections from the perspective of coordinate geometry, so even when there are properties common to all conic, I have to prove them separately for parabola, ellipse, hyperbola, and circle. The ...
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The Leibniz formula for determinants starts with multi-linearity and the alternating property and builds from there. I asked a question about why we should start with multi-linearity: What's so special about multi-linearity?. And the response (which had an excellent alternate motivation for the determinant which I wasn...
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I just stumbled across this older video of a girl trying to "talk" to Alexa (the voice assistant). She says "I am trying to talk to you, hen". Now, I am not a native English speaker, but I am familiar with the endearing term "honey", also sometimes written "hunny" or even "hun" or "hon" depending on the pronunciation. ...
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Consider a metric space with a path between any two points, so a real line segment of some length between them, and the length of this line is the same as the distance between the two points in the metric. This is called a geodesic metric space. Any two points are connected with a shortest path. There could also be mul...
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Say that I have two long cylinders of material as shown that are in a region of oscillating magnetic field where the field direction is aligned with the long axis of the cylinders. I want to calculate the inductive heating of each cylinder (let's pretend for a moment that none of the parameters like resistivity are tem...
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I hope that this is the correct site to ask this question, but since I was unable to find one specifically for modeling, I decided to ask here (and please feel free to correct me, if any of my statements is bogus): There are tools which allow one to do parametric modeling like Rhino's Grasshopper or Blender's Geometry ...
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I have been interested in hyperbolic (negatively curved) space and I have been reading enough about it to feel that I understand it relatively well intuitively (e.g. the Poincare disc). But the problem is when I flip the curvature sign in my head to positive curvature and elliptic space nothing seems to make sense. For...
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I'm looking for the best BE substitute for the AmE word "ornery" in the phrase "an ornery bunch". Complicating the task for this second-language speaker of English is that according to the Oxford Dictionary of English, "ornery" means "bad-tempered and combative" in AmE whereas it means "bad-tempered or difficult to dea...
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When I compile my document with pdflatex with natbib and either the plainnat or the dinat style on my computer, the author list is translated to German. E.g., I get "und" between authors instead of "and" and instead of "et al" I get "u. a.". I am very puzzled, because I don't know why. In my bibliography file all refer...
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Consider two samples of visit lengths to two different Emergency Departments. We want to test whether or not the means of the samples are different. A basic requirement is independence between and within samples. However, while we know that there are no patients that had visits in both samples, there are patients who h...
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I started running a tabletop RPG campaign set in the distant future where mankind has degraded to a primitive hunter-gatherer society, and I'm looking for flavorful terms for NPCs to describe directions. As research, I started watching the show "See" which has a similar premise, and they use the term "sun grave" to ref...
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I saw this post which says: The way you do it is just a simple logic. Imagine a tennis ball and imagine you can't really see it, just like you can't see an electron. So the only way you can see where the tennis ball is is to hit it with another tennis ball or with an enormous amount of light that it will actually displ...
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I am doing some research into social interactions and the data is represented in a series of square matrices for analysis. I am interested if the grouping of matrix elements above/below off-diagonal, as highlighted by blue and green in the following diagram, are known by a specific name? These groupings of matrix eleme...
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I am trying to understand the basics of quantum mechanics and I am having some issues in understanding the main mathematical properties of quantum operators. In particular, it's clear to me that: Quantum operators must be Hermitian to guarantee: real eigenvalues, that can be measured an orthogonal basis, so that after ...
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Although neutron stars are mostly made of neutronium, the pressure at the surface is not very high which allows regular atomic matters to exist. Emission spectrum can reveal the chemical composition of distant stars. However, neutron stars are surrounded with extremely strong magnetic field which is enough to distort t...
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this is my first post, please excuse my non-technical language. I would like to simulate the return of a stock, that is correlated with other stocks, that meets the mean and variance of a given empirical time series. The usual way to do this is to set up a geometric brownian motion and to use a cholesky factorization o...
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Ok, this is my first question on this site. But it's one I've been thinking about for a while. Say through whatever means, we place a device capable of generating thrust/ kinetic energy on the surface of the Earth. The goal being to remove Earth from its orbit and exit the solar system. By "perfect conditions" I mean t...
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I'm a native English speaker, and I noticed that I sometimes use accusative pronouns (him, her, me) to replace actors in certain clauses. I have a feeling this is prescriptively considered incorrect usage, but I want to be able to describe it. "What does that have to do with me not coming to class?" "I want to hear abo...
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"Such" has many meanings, one of them being to refer to something of a particular kind/type (see "of this or that kind"). However, in many legal documents and laws in Malta, "such" is used instead of "this" or "that", or instead of "the said thing". For example, a legal document might read as follows: The following are...
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Not really sure if physics question or engineering question. If we can apply energy to make an object in space move faster, the reverse should be possible - we should be able to extract energy while causing the object to slow down. So in theory, if we use rail gun to launch a projectile in space, we should be able to e...
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I ordered a book online, unseen, and the invoice told me the book, or at least its pages, were 'foxed'. I had never come across the expression, did not know the word could be a verb and discovered : Foxing is the age related browning, or brown-yellowish spots, that can occur to book paper over time. When this aging pro...
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In condensed matter and materials physics it is often assumed that the response of a condensed phase to some perturbation is determined by the fluctuations of the system at equilibrium (without perturbations). For example, the electric resistance of a liquid (the response of the current to an applied field) is determin...
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In order to obtain phonon spectrum, we usually do Born-Oppenheimer approximation and assume that the electrons are always at the ground state when the atoms move, and by calculating the force on each atom (usually using DFT) we are able to assemble the dynamic matrix of the atoms and obtain the phonon modes. After this...
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In An Argument Against Abolishing Christianity it is written: Another advantage proposed by the abolishing of Christianity is the clear gain of one day in seven, which is now entirely lost, and consequently the kingdom one seventh less considerable in trade, business, and pleasure; besides the loss to the public of so ...
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In a power grid, the grid itself has a certain amount of inertia from all the spinning loads and generators. If at a given moment in time the production and consumption of active power does not match, the power mismatch will be provided/absorbed by the spinning energy stored in the grid, and the frequency of the whole ...
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Suppose there is a plank on a smooth surface and a man is standing on one end of it. The surface of plank is rough. Now the person starts to move towards the other end with some acceleration and the plank also starts to shift to keep the COM stationary as the only forces acting here are all internal. Now my question is...
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Note: this question is not a duplicate of the following questions: How to remove vertices from a graph that are not coverable by cliques? How to remove vertices from a graph while preserving clique coverage of specific vertices? This question is with respect to removing vertices that are not reachable from a set of ver...
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Let's say we entangle four electrons based on their spin. Now, let's say we measure the spin of electron A along the z-axis (up/down), and we observe a spin of 'up'. My understanding is that this means that the remaining three electrons would need to have some combination of spin which adds up to 'down'. Next, we measu...
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I need a word that describes someone who advocates for harmful laws or policies; it would describe someone who writes policy without listening to the people it affects or someone who doesn't pay attention to actual effects of that policy, kind of like politically or socially tone-deaf. They might continue to stand behi...
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I want to start learning model theory for my master's thesis, but I can't find the right book for me. For some context, last year as an undergrad I had a class on logic where we learned the following: So I already had contact with formal languages, structures, models, and both the semantic and syntactic aspects of firs...
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Whenever I get into a disagreement with an individual I notice that this phenomenon always occurs. (I either notice it during the argument or afterward.) Allow me to provide you with an instance to help describe exactly what I am talking about: I am having a disagreement with an individual regarding bottled water VS ta...
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I'm trying to understand how Newton's third law works with springs. If we hang a block on an ideal spring mounted to the ceiling, in equilibrium, the block is affected by gravity downwards and the spring force upwards. So according to Newton's third law the spring itself is affected by the spring force downwards. This ...
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My question may be simple but I'm curious, let's say I start bouncing a ball like a footballer with my foot on an elevator, and it starts moving upwards (with acceleration) and then it stabilises itself moving upwards with no acceleration at a constant velocity. My question is if the ball will or not start bouncing les...
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I am wondering how this sentence is to be paraphrased: At weekends they prefer to stay home and visit some friends. I am not sure which ones are close to the original: They like to remain in their house at weekends and they also like to go and see their friends. They like to remain in their house at weekends and to go ...
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The task is: The farmer has several sheep, each responding to one or more names, and several sheep may respond to the same name. Each sheep answers to at least one of the names, the farmer knows which sheep respond to which names. The farmer has two paddocks for food and a haircut. A farmer can say a name, and then all...
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I was talking to a colleague professor the other day and he said something that got me curious. The way I remember it, he said basically that in experiments a Bose-Einstein condensation is usually trapped by some external potential, which I imagine to be an electric or magnetic field. Then, the temperature is considera...
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If all matrices can represent a linear transformation, can I refer to some general notion of the transformation associated with the matrix to make conclusions about the matrix? For example, I want to prove a simple true/false statement, "If A and B are square matrices such that AB is invertible, then both A and B must ...
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I do not understand at all why, if an object is sitting on a spinning platform, the friction force is towards the center. I understand the need for a centripetal force during circular motion, but friction is only in opposition to a force being applied to an object / system, why does it act as centripetal? I understand ...
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A flat spiral in immersed in a homogeneous magnetic field. An electric current is flowing in the spiral. The directions of the B field, the spiral and the current can be seen in the picture. As the result of the electric current and the B field, Lorentz Force appears acting on the electrons, aka the Hall Effect. The el...
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It is stated that an object in motion acquires "kinetic energy" while an object under the influence of gravity when raised to a height acquires "potential energy" but I have a doubt that what leads to the object acquiring the energy in actual sense? What special is happening that an object in motion or an object at a h...
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I am doing an experiment with the overall research question of: To what extent does the amount of fluid within a hollow cylindrical can affect its dynamics while rolling down an inclined plane I was able to derive an equation for acceleration for the case of a fully solid cylindrical shell and then used law of conserva...
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Also, how do different sets of principles affect the results we can get in our meta-theory? The more concrete questions that lead me to ask the above two questions are stated below. If we are studying intuitionistic logic, should we also drop the excluded middle rule in our meta-theory? Besides, in classic logic, I see...
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I've been exploring the concept of gravitational wave (G-wave) emission from symmetrically accelerating systems and have encountered a puzzling question. Standard sources typically state that symmetrical systems, such as a perfectly rotating sphere, do not emit G waves. As they require a changing quadrupole moment, whi...
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Is the essential argument that these systems are microscopically chaotic enough that we can approximate their evolution as random (vastly simplifying calculations) and still make accurate experimental predictions? Or are there deeper physical/mathematical foundations? A related question: how does one interpret the dist...
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So, I have been studying thermodynamics, in it I read that state functions are those functions which depend only on one state of the system and are independent of the path taken, which is pretty easy to understand. And this clears why properties like enthalpy, pressure, volume etc are state functions. Then there was th...
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