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There are many wonderful illustrations of parametric curves with b-splines and control points, but I mostly use splines for uni-variate functions. So I have a vector of control values, but not really points--at least not ones I can easily plot. If we take the three examples in the definition section of the wikipedia ar...
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tl;dr If I'd introduce you to someone with "Say hi to my cousin Harry.", would you be surprised to later learn that it's my seventh second cousin twice removed because I used the word cousin and not specified it's not my first cousin? I'm used to using it one way, and someone else (also a native English speaker) uses i...
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As you know, it is expected that the velocity of stars and gas should slow down the further they are from a galaxy's center. However, in many cases, it does not slow down as expected, and this discrepancy is often attributed to the presence of dark matter. How can I obtain the expected radius - velocity plot for certai...
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Let's assume that I have an ideal conductor(straight wire(, as we know that potential at any point on the ideal conductor is the same, if i place that ideal conductor in a region where magnetic field is increasing, so according to faradays law a potential difference will exist across the ends of the conductor, but how ...
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I have heard one meaning of it in the context of a personal goal is to set a too-easy goal (i.e., that you know you can easily achieve). I also heard it is coming from golf. Can someone shed more light on this? To be clear, I was not referring to computer science or computing area where it means to separate a piece of ...
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It's a very general question. Black hole paradox is an interesting problem but why is it something that physicists are so worried about? As neither can it be directly experimentally tested nor do I see any indirect proof of it, then what relevance does it have? I might have upset some of folks here, but I've got no har...
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This question is with regards to a polarimetric approach in analysing the concentration of a substance in solution such as sugar in water. I have been trying to find an answer to it through a little browsing but I could not really find anything useful. Most websites and books use dm for path-length of the solution in d...
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I was told that this sentence is so wrong, and after reading some related threads here, I now understand that "earlier" should be used with past tense. So is it okay if I change the sentence to "As Puss has told them to, they all say the Marquis." Is this sentence natural? It's from a simplified reader "Puss in Boots"....
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From a Library of Congress article about Freud: ...patients tended to perform for the camera and doctors to record the most photogenic. This sentence seems to reuse the verb tended between the subjects patients and doctors. I think this is an instance of gapping. I have seen it in simpler cases like: Alice cooked the r...
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What is the subject of "making" in the following sentence? It seems that it is the most reasonable grammatically to think "Yakkleman Skin Care" is the hidden subject of making. This is because the subject of the participle needs to agree with the subject of the main clause grammatically. Yakkleman Skin Care has signed ...
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In Continuous Variable -Quantum Key Distribution (CVQKD), usually Gaussian modulated coherent states are sent. This means both quadratures of a coherent state are chosen from two normal distribution. So do we can prepare a state with well-known quadratures on the phase space? My main question is, how someone can succes...
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I have finished some courses on analytic number theory and wanted to learn about versions of Goldbach so I can pick a topic for my master thesis. I have seen a proof for an asymptotic formula for the tenary Goldbach conjecture in the lecture. I can not find the paper where the version of Goldbach for a prime and an alm...
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Gravitational waves have been very much in the news recently and I would like to understand them better. I know vaguely that they cause transverse changes to the geometry of matter as they pass by. For many classical wave systems there are integral solutions to the IVP for small disturbances, showing how the wave is dr...
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As we all know, Subatomic particles show dual-nature when observed but why? why does this happen? also I am genuinely confused as to how does the particle know when to change its nature, I mean i know that it changes when it gets observed(detected by a detector) But how does it know that it is being detected and now it...
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I am working on a non-linear optimization problem, containing bounds and constraints for the variables. Very complex problem involving networks and logical functions. I have been switching a tool from the Matlab language in which I originally implemented it, to Python. In the Matlab version, I used the 'interior-point'...
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As a keen fan of Terry Pratchett and Jasper Fforde, I'm fascinated with words that logically should exist, but don't. A subset of these are referred to as "lost positives", such as "ebriated" referring to someone who is sober. However, there are other types of theoretical words, such as ones where you apply a prefix wh...
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A superfluid has a property that makes it creep up the walls of its container and escape it until it's empty. How is it possible that the fluid performs work (against the force of gravity)? I can imagine setting it up so that after dripping to the larger container, there is an indentation on the ceiling so that when it...
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We know that the comoving Hubble radius decreases during inflation when the universe is exponentially expanding and then increases during matter and radius domination. What is the reason behind this? I can see it mathematically. However, intuitively it's not so obvious. The universe is expanding during both the eras, a...
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For a quadratic polynomial the polynomial discriminant appears in the quadratic formula however, I found this was not the case for cubic and quartic polynomials. The expressions used in the cubic and quartic formulae are different from the polynomial discriminants or at least they seem different to me. So is it just a ...
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Does one pee-pee with his wee-wee, or does he wee-wee with his pee-pee? Is one phrasing more typical than the other? That is to say: How is pee-pee used more commonly- as "to urinate" or as "penis"? And vice-versa for wee-wee. I'm curious if there are widespread or regional customs. Both are informally correct in Ameri...
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My question may seem CS-related at first, but it's essentially mathematical, so, please, bear with me. I'm doing Neural Architecture Search (NAS) by varying the number of layers and neurons per layer for a neural network (connections are feed-forward, throughout), and then training it on a fixed task to test its perfor...
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I am a graduate student studying wireless perception, and recently I want to carry out liquid recognition. I want to use a speaker as a sound source to generate vibrations (by playing sounds of different frequencies). My idea is that different liquids have different resonant frequencies. When the frequency of the exter...
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I have been doing some deeper reading on optics out of my interest and one of the most important differences between ray and Gaussian optics is the existence of a non-zero beam waist when a laser beam is focused using a field lens. Most literatures that I have read go over this fact as if it's a common knowledge, but d...
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I know it happens when the elements on both sides are identical, the more you remove asperities, the more they become like a single substance. But does this happen to the same extent if I take two different substances and start removing asperities? Or maybe close to that... My textbook doesn't explain much about this, ...
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An example of a non-associative ring R whose non-zero elements form commutative quasigroup (with regard to multiplication in R) without identity is easy to find. I'm looking for examples of a non-associative ring S whose non-zero elements form a non-commutative quasigroup without unity. Put another way: A non-associati...
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In many (biological and living systems) physics courses I encountered the notion that systems operating far from equilibrium are related with more efficiency with regard to their specific tasks. One example I vaguely remember is the comparison of the energy efficiency of ATP to ADP convertion reaction with the efficien...
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I have a camera that gives Azimuth and Elevation of an object with respect to itself (camera). The camera doesn't send image but Azimuth and Elevation data (in float format). The camera doesn't provide range. Is their a mathematical way for me to calculate the range of the said object using Azimuth and Elevation. I wis...
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I am currently studying electromigration in liquid metals. According to studies that have been done for electromigration in liquid metals, the metal ions are affected by the electrostatic force and therefore can move to the cathode/anode. The force that moves the metal atoms to the electrode is affected by the charge o...
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Free space is a region in which there is no matter and no electromagnetic or gravitational field. Which means that the resistance in free space is zero, because there is no resisting force and as far as I know, free space is a synonym for "vacuum" and there is no resistive force in a vacuum. So, how is the permittivity...
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This question relates to the Michelson-Morley experiment and whether anyone has so far proposed an equivalent experiment using aqueous waves instead of optical waves. If it is true that (i) The properties of optical waves and aqueous waves are approximately equivalent and (ii) Nature is consistent in her implementation...
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Please forgive me for not having the best grasp on graph theory terminology. I am doing my best. I have a large connected subgraph of a large graph where I want to find, what I am terming the "weak points," of the graph. A "Weak point" exists, in my conception, when given a vertex, there exists at least one single edge...
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In an inelastic collision where mechanical energy is not conserved, momentum is still conserved. Should the Earth or the ground be considered as part of the system in order to account for the conservation of momentum? Since there is friction in a collision, is it appropriate to include the ground as part of the system ...
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How does a common base transistor amplify current if a small part of its emitter current gets divided into base current and the rest goes to collector current? If the input signal is applied to the emitter part of the transistor then the output current in the collector part should be less than the input one. Then how i...
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Is there a notion of a singularity of a real "algebraic variety" which looks locally like a double cone but with a countable infinite number of cones which meet in the same point? A short example or reference would be highly appreciated. I am self-studying algebraic geometry at the moment and the literature/videos do n...
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I am very confused about this, are they an excited state of a particle where an electron is excited to an upper energy level, which seems less likely to be the case since the resonant states of particles have different names; or are they the constructive interferences of the wave functions of two different particles, w...
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I am beginner to optimization and my question is fundamental. We all know that Static optimization means the design variables/objective function does not vary with respect to time. Dynamic optimization means the design variables vary with time. I need help in organizing the below algorithms/concepts into static and dyn...
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Why doesn't a pressure cooker reach a state of equilibrium where the steam passed is constant (assuming the contents of the cooker are maintained throughout the cooking process), but rather, it accumulates pressure until it releases it in the form of a whistle every so often? I don't understand why the pressure "oversh...
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As the title says, I'm trying to determine numerically when an n-DOF oscillating system (linear or nonlinear) subjected to forced base oscillation reaches the steady state solution. Is there an energy component (or another global parameter) that converges to a single value when the steady state is reached? I have the t...
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Recently while experimenting with force experienced by current carrying conductor, I came across a abnormality in the horse shoe magnet, due to which the direction of force on the current carrying conductor by the Flemings Left Hand Rule was false. I noticed that when i kept a compass near the heads of the horse shoe m...
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There are certain complex functions which lack a proper denominator corresponding to which poles can be found for the given function. For example , the gaussian function, the frenel functions are some of the popular functions lacking any denominator, in the complex plane . So , as a result of those function lacking any...
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I have a question about degenerate electrons in white dwarfs. So, as far as I know, when the gas contained in stars is compressed so much, the electrons start to fill the lowest energy level and then, for Pauli's Principle, they continue to fill up incresing energy levels up to a certain level. As you can read here htt...
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It is well known that the method of image charges is not always applicable, so I was wondering: is there an analytic way to calculate the electric potential for a point charge interacting with a perfectly conducting, neutral (edited) metallic disk using image charges? If it can be calculated or not, for what reason? Ev...
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When a satellite is revolving around a planet with an orbital velocity in presence of air resistance, the satellite's Kinetic Energy keeps on increasing as it falls down. The resistive force is trying to decrease the speed and the gravitational force cannot change the speed (or Kinetic Energy) as it's perpendicular to ...
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I and some classmates are recently teaching ourselves the famous book Foundations of Perturbative QCD by John Collins via a form of regular peer reading group. We find that exercises in this book are really worth working on. But, as a group of relatively junior students, we are hesitating to go deeper before finding a ...
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The tangent plane at a point of a hyperboloid meets the hyperboloid in the two generators through that point. However, a tangent plane is defined as the locus of all tangent lines at a point on the hyperboloid. Now, since generators lie completely on the surface they can't be tangent lines to the hyperboloid. Then how ...
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What's a safe, easily executable experiment to confirm that quantization of light occurs directly to the retina. We know that light is quantized when projected on to a surface, or on to an inanimate detector, then the surface or the detector observed. An eye can detect a single photon. This means we should be able to q...
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From my understanding self-energy is the energy required to put charges in a certain charge distribution and interaction energy is the potential energy caused by the interactions between particles, but to me it seems like there isn't really a big difference between them and this post What does electrostatic self-energy...
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From what I understand relativity predicts that outside observers would never observe external objects actually crossing into the event horizon, due to time dilation. How does that can reconciled with the fact that the Schwarzschild radius is largely dependent on black hole mass? Then, does this imply that one can neve...
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I am trying to say in good quality English that a certain idea which was implemented is currently used way beyond the scope it was intended for. It was a gap-filler which we are now basing our entire solution and this is going to be unsustainable. I am trying to write something like "This architecture has exceeded it's...
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Suppose a car is at rest and you apply the accelerator, then the wheels are applying a horizontal force on the road so according to Newton's third law an opposite force (friction) pushes you forward. From what I understand no matter how much force you apply (hit the accelerator) the maximum force that can push you forw...
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It's well-known that given a sentence independent of a system of axioms, we can consistently extend the system by appending either the sentence or its negation. However, if a given theorem can be deduced in each of the two systems, then we have a proof of that theorem. We don't even need to prove independence, because ...
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An observer near the event horizon of a black hole will experience an extremely strong gravitational field. Due to the principle of equivalence, this observer cannot locally distinguish between this strong gravitational field and the experience of being in a highly accelerated frame. As a result, the observer will dete...
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I tried to understand the physical interpretation of uniform continuity, and saw different graphical interpreation in Wikipedia. At the end, I have concluded that functions which are uniform continous in a set, also have finite derivative in all the set and its boundary. Is this interpretation right? I don't want to be...
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Normal measurements of compressive strength work by compressing a sample with an hydraulic press and see when the sample deforms plastically or cracks. Now if pressure is applied on the surfaces of the sample that aren't in contact with the hydraulic press, will the compressive strength (as seen by the hydraulic press)...
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I was wondering if someone can explain simply why phase changes are isothermal processes? I am studying hydrology and some of our material about snowmelt has to do with phase changes and in this example, water retains a constant temperature when melting/freezing, or boiling/vaporizing. I was wondering why, as the ice m...
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Consider a piston such that it is in mechanical equilibrium with its surroundings. If I pull the piston (reversible work) then the work done by me would be positive. If I push the piston, again work is done by me. However, in one case positive work is considered to be done on the gas inside piston, while it is negative...
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What are some good entry points into physics? I'm wanting to eventually be able to understand some more abstract concepts like quantum physics but understand that is a very long way away. Just been spending far too long trying to understand things above my pay grade. I'm pretty sure I remember linear algebra being some...
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I am working through Srednicki's "Quantum Field Theory" and am at the chapter on the Minimal Supersymmetric Standard Model (MSSM). In answer to why two higgs superfields are needed in the MSSM model, Srednicki's solutions say that "...the superpotential cannot depend on hermitian conjugates of [super]fields." In trying...
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Using induction on the complexity of formulas, let's assume that in every proper non-empty initial segment of a propositional formula, the number of left parentheses is greater than or equal to the number of right parentheses. Note: A proper initial segment of a propositional formula is an expression that starts and co...
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When a capillary tube is inserted into a large body of water, there is an increase in potential energy (PE) of the system. This is because the increase in PE of the rising water in the capillary is greater than the loss of PE of the body of the water. The increase in height of the capillary water is greater than the lo...
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Simple question, but I can't find any answer around. If a pipe turns, aka is not straight, the length of the pipe (in order to calculate the resonance frequency) is given by the length of the imaginary line connecting the centers of the circular section of the pipe, by an imaginary string of zero width that connects th...
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I've come across the expression "head(s) and tails above" (the rest, the competition etc; different from something like "can't make head or tail of something" i.e. can't figure it out/understand). I can't find information about this. It seemingly means completely. Could you confirm its meaning and explain it a bit? Is ...
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I have been thinking about how physics has evolved since the time of Galileo . Back then physical laws could be describe using axioms which could be comprehended by anyone who reads them. But currently physics is done in a whole different manner. The laws are written mathematically. The language of mathematics is deepl...
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Vogel's method selects the corresponding variable through a penalty. There is a penalty for each row and column and is the subtraction between the two lowest costs (in absolute value). We must select the highest penalty and then the lowest cost in the row or column of this penalty. I understand the second step (if you ...
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Does water vapor generate electromagnetic radiation/photons when it condenses into water droplets? I know that gas water molecules need a condensation particle to combine into water droplets. A pair of molecules combine on the surface and in the process transfer their binding energy into the kinetic energy of the conde...
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The twin paradox is resolved as the twin who moves through at least two inertial frames has a shorter worldline (therefore less time elapsed in their frame) than the twin who remains in one. I know the crucial aspect is the multiple frames not the acceleration, since you can have variations of the twin paradox with no ...
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If an isosceles triangle is inscribed in a circle, then is it's altitude always greater than the radius? If yes, then why? My sir said that if an isosceles triangle is inscribed in a circle then its altitude is always greater than the radius and passes through the centre of circle but I don't understand why it is so an...
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The question was to transform this sentence from positive to comparative degree: She is not so young as I expected. Following the solutions of other sentences of this kind (the photo shows a similar kind of problem from where I adopted the solution) it can be written that: She is not younger than my expectation. I want...
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In the current approach of QFT, we model the process of creation of a particle (say a photon or a gluon out of a quark) as "instantaneous", meaning happening at a moment in time without any neighborhood (modeled via a delta function). To what extent is this an idealization of the real behavior of nature? Do we have any...
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My teacher gave us the assignment to find the moment of inertia of any shape you want. So I decided to find the moment of inertia of our milky way galaxy. I found out that our galaxy is shaped like a warped disk, not a flat. After I knew about that, I looked for the equation of the Milky Way's shape. But, to me, Nasa's...
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I've a box with know width (W) and height (H) It has been rotated around an origin point O at a known angle The rotated box is enclosed in a bounding box for which the top-left point (Bx, By) and dimensions (Bw, Bh) are known Given the origin point, the angle, and the resulting bounding box, is it possible to determine...
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Hi :) What properties of triangles should I use to solve this problem? I can work out the size of the large triangle and all of its angles, but how do I apply this to the circle? What am I missing? This problem is from the first chapter of a trig book, so the methods needed can't be that advanced. Just need some pointe...
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I created my lecture notes using the CambridgeUS theme. My students cannot get the .pdf file to print from Adobe. I tried printing my notes from Adobe on two different printers and I get the following message: "The document could not be printed, kindly use our help page to troubleshoot." Adobe's help page didn't solve ...
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is there a computable algorithm which lists all the finite subsets of natural numbers ?... i know that such a set is atleast countable... but can't determine if we can list every such subset in a computable manner ..... the set of all infinite sequences of the subsets of natural numbers is obviously uncomputable i thin...
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Is the measure of a simple closed curve consisting of two arcs transversal to a foliation equal to the sum of the measures of these arcs? Let A be an arc that is the union of arcs B and C, where arc B is transversal to the foliation and arc C is contained in a leaf of the foliation. Is the measure of arc A equal to the...
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what I have been told is that present participles are used in active reduced relative clauses. considering present participle of "be", which is being, I was wondering can we use the same pattern? Another example in Longman dictionary is: who heard of a grown man being scared of the dark? or who heard of a grown man who...
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In Kittel's book of Solid State Physics, it is said that, whenever an electron passes the positive ion core in the lattice, it has the ability to distort the lattice s.t by attracting the positive ion cores. Does the attraction has to do anything to the mass of an electron, as being small, does it posses the attractive...
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I am reducing a block diagram manually and am not sure whether the following step is a valid step? I am using the rule of moving a summing ahead of a block in reverse. Reduction Step in Question I've checked the resulting transfer function before and after this step using MATLAB (connect function and Linear Analysis in...
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In a uniaxial crystal there is an optic axis, an extraordinary axis, and an ordinary axis. The optic axis is not the direction in which we plan to propagate light. The light is propagating in a direction such that the electric field might oscillate parallel to the optic axis. I have included a hand-drawn diagram below....
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Consider approximating a binomial distribution with normal. Originally, my binomial distribution is discrete, where the heights of the bars represent the probability. However, after approximating this distribution with a normal one, we find the probabilities using the area beneath the normal curve. How have the probabi...
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I accidently deleted a large part of my work on a .tex file. Unknowingly, i saved the file , ran the typeset once and closed it. Hence the content is deleted from the pdf too. Is there any way to retrieve the deleted content. I check the previous version of the file too but it is not available either. Somebody please h...
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As we know that Euclidean geometry deals with triangles, quadrilateral,... and circles. Later in college we learn projective geometry but in quite modern language (vector spaces, equivalent relations). My question is, is there any roadmap or any book to learn projective geometry from high school Euclidean geometry whic...
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Work done in an isentropic process does not cause dissipation but leads to change in temperature of a system. But temperature allows wider range kinetic energy to be accessible leading to more microstates. This should lead to increase in entropy, but this doesn't seem to happen here. Does this mean that increase in ent...
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I have a rotated retangle and a rectangle. Both are defined by their corners (however, for the non-rotated ones I also have access to topLeft, topRight, etc). Is there a way I can check if they intersect? (It would be enough to know if they intersect, even without knowing the extent of their intersection). I found solu...
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I recently read that neutrinos have a polarization property---their polarization is opposite to antineutrinos. Is it possible to determine the polarization of a neutrino? For example, we can determine the polarization of a photon using a polarizing beamsplitter, V-polarizations will be reflected into detector A, and H-...
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Using the GeoGebra program a few days ago, I came up with a wonderful feature about the parabola and the circle kissing its peak. I don't know if it is new or previously discovered. Please, if it was discovered previously, put a reference mentioning it in the comments, and in any case, can anyone prove it I don't think...
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I was reading Ali Omar text on solid state course and it said about the fact that electrons in a lattice or in a periodic lattice never scatters or make collisions with the positive ion cores, as the eigen functions of the solution of Bloch's theorem have infinite lifetime and eigen functions do not gets scattered? I d...
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I am trying to format a line of text that has two different sized fonts such that the vertical alignment of the smaller sized text is based off the larger sized text. In one instance I'd like the smaller text to be vertically centered on the larger text, and in another I'd like the smaller text topline to be aligned wi...
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Data rates are higher in X-band, but considering free space path loss and atmospheric attenuation(diffraction I'm assuming is significant here), won't lower frequencies stand a better chance? Again, cost and weight is a factor, but I want to understand the physics that goes behind these selections. Additionally, why do...
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Hello fellow grammar lovers! I need some help. I'm working on HR resources and have run into a bit of a conundrum about how to write about PTO. I know that I "would like to take time off." But how do I go about "initializing a time-off request?" My question: Is it appropriate to hyphenate time off when used as an adjec...
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Both mass and entropy behave differently for black holes than for normal matter. For simple Schwarzschild black holes, mass is proportional to their radius. The Bekenstein-Hawing entropy is proportional to their surface. Of course, the calculations for the two results can be found in the textbooks. Is there a simple ex...
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I understand that according to Collins Dictionary, a suffix is an affix that follows the stem to which it is attached, as for example -s and -ness in dogs and softness. It has, however, a second definition: anything that is added at the end of something else. Would I then be right if I say that the following sentences ...
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When a magnet is moved into solenoid, it induces a current. And, when it is moved out of the solenoid, it induces a current. But what about in the example below. When a very long magnet, that has its whole body within the solenoid, is moved in some direction. The magnetic flux experienced by the coil from the magnet, s...
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I searched for it but couldn't find any answer for this. For a light source is it simply the average of the full spectrum power? And how do you compute it for an image? How can you tell the difference between a yellow object lighted by a brighter light and a white object lighted by a yellowish light? Or maybe you can a...
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Approximating the Earth by a circle with West facing in the theta-hat direction and East in the opposite, when a person jumps up, the Coriolis force faces West according to the right-hand rule. Upon descent, the Coriolis force faces East. Since you spend an equal amount of time rising and falling, shouldn't the effects...
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I'm helping edit a piece of fiction, which has a sentence that begins so: In another smaller kitchen... How is this to be punctuated? One choice is to leave it as it is. Another is using two commas: "In another, smaller, kitchen..." Since 'another' isn't an adjective or adverb, the usual rule(s) about grouped modifiers...
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So in flrw metric it's quite reasonable to take eigenvalue of the time-like component of the stress energy tensor and identify it with mass density. Now, if someone argues the cosmological constant comes from the stress energy tensor. Wouldn't they also have to account for the change in mass density? In the Newtonian l...
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Wagon-wheel effect is a well-known optical illusion due to the persistence of vision. It happens when the spoke of a wheel rotates to a certain position after the duration of persistent vision. Depending on such position, the apparent wheel motion can have many appearances. However, is it possible to design a certain p...
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I'm looking for a word that describes that feeling you get when somebody (of a group typically thought of having more power in society) brings up a group (typically thought of having less power in society: minority groups, women, LGBTQ) and you are hesitant to agree with them even though they are right (Like, in this h...
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Inspired by a youtube video, i was trying to do the double slit experiment at home using a single hair and saw the interference pattern. Then i wondered what would happens with many hairs and when i shine the laser trough a bunch of them, these kind of patterns emerge. Here you can see a video: https://www.youtube.com/...
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