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So this is my second query about the photovoltaic effect. I've looked into it more and understood it for the most part, but there's still something I don't completely get. After the electrons are excited into the conduction band, some sources say that they can't cross into the opposite material due to an electric field...
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I've been reading up on nuclear reactors, and understand explanations of how it works, how water is heated to steam, which turns the turbines, etc.. I understand all of the safety features, and how control rods are used, and what they do with spent fuel. However, what I can't figure out (after lookin at many websites a...
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I'm not much informed about manifold but I should answer some questions about it. Based on the definition I have written an answer for the following question but I feel there is something wrong with it! Could you please help me? Q: Let M be a smooth manifold and suppose that we have an open cover for that. If S is a su...
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I hope it is appropriate to ask this type of question. I'm in my second year as an undergraduate right now. While my problem solving skills have improved tremendously, I almost never tried to actually remember what I learned. I always had the attitude: "If I don't remember it, I will simply look it up." While this migh...
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Timothy Gowers asks What is so wrong with thinking of real numbers as infinite decimals? One of the early objectives of almost any university mathematics course is to teach people to stop thinking of the real numbers as infinite decimals and to regard them instead as elements of the unique complete ordered field, which...
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In the last assignment given to me by my professor, there is a question which asks: In classical theory, it says that in presence of air friction, a pendulum continuously loses energy with time and its amplitude also decreases with time. However according to quantum theory, the pendulum loses energy only in discrete pa...
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In a laser interferometry experiment, we project a pattern of interference fringes onto a CCD sensor. For best results, we want good contrast between the bright and dark fringes, and we carefully compensate for various sources of noise - for example, by taking camera images with no fringes present, and with the laser t...
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I was reading a physics book by some author and I got a little too confused with the explanation he stated about magnetic fields. A magnetic field is a field of force produced by current-carrying conductors or by permanent magnets. Correct me if I'm wrong: A magnetic field is basically a region / space where magnetic l...
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First of all, I'm genuinely sorry if this question isn't "serious" enough for this forum! A common cliche in movies and tv is that a very tough object (eg the villain) is frozen, and then hit with something, shattering into a million pieces. I've seen a demo of a flower being put into liquid nitrogen, then being crumbl...
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I'm sure his has a general form and welcome a link to a duplicate, but as I don't quite know what to search for, here goes. Whilst answering a question on the Mathematics Stack Exchange, I found myself needing to say the mid point of one diagonal of a rectangle is coincidental with the mid point of the other and that t...
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Possible Duplicate: What is the correct way to pluralize an acronym? I am helping a former intern ready their resume for distribution. The candidate used an abbreviation I was unfamiliar with: B.S.s in Physics, Computer Science, and Mathematics I am familiar with the student's educational background so after a moment o...
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I have only taken a basic quantum mechanics course (this book, so you know where I'm coming from), but I've been wondering about something. If we set up a quantum system in a known state and take a measurement of two incompatible observables, we will get two real numbers. If we repeat this experiment multiple times, th...
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I'm teaching a geometry course this semester, involving mainly Euclidean geometry and introducing non-Euclidean geometry. In discussing the importance of deductive proof, I'd like to present some examples of statements that may appear to be true (perhaps based on a common student misconception or over-generalisation), ...
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According to Wikipedia: For most radioactive nuclides, the half-life depends solely on nuclear properties and is essentially a constant. It is not affected by external factors such as temperature, pressure, chemical environment, or presence of a magnetic or electric field. Have any experiments been done to test what ef...
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About two years ago I watched some old Monty Python interviews. In one of them, Graham Chapman, a Brit, makes fun of Terry Gilliam (the only American) for his lack of vocabulary. He specifically cited a moment when the group flew over the great lakes and Gilliam said "there's a bunch of water". I found this amusing. Bu...
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In these forums and elsewhere it is routinely agreed that "we do not have a theory of quantum gravity." My question is, how do we know that canonical quantum gravity is "wrong"? I understand that the theory is perturbatively nonrenormalizable, but doesn't that just mean that we can't apply perturbation theory to it? It...
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First let me introduce my terminology: A "Mechanical theory": A theory which describes time-evolution of a particle or a system of particles regardless of the fields affecting the particle/system. e.g. Classical mechanics, Quantum mechanics, etc. A "Field theory": A theory which describes time-evolution of a particle o...
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I'm a high school student and I'm trying to understand the concept of the Higgs boson. So I apologize ahead of time for any incoherence I may say. As per my understanding bosons are force carrying particle that are excitations of their respective fields. For example the photon is the boson of the electromagnetic field ...
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I'm looking for an alternative way of saying "You can't run before you can walk." This is equivalent to saying "you can't take on higher level things before you have mastered the basics". I am looking for either a rewording of the original phrase or a whole new phrase with the same meaning. I prefer that this not have ...
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I have a question related to already shortened words and their plural forms. As I have seen on this site and have found in the dictionary, words like mas and pas are the plural form of the shortened words ma and pa (as in mother and father). However, it occurs to me that were I to write this, in order to clarify the me...
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I'd like to know what franchise meas as a verb in the following sentence: Catering in this school has been franchised to the company. The native speakers I consulted, both American, don't seem very sure of its meaning. I know the verb typically means (of a large company like McDonald's) to permit an individual or a sma...
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As an applied mathematics student coming from a small university, I have not had an adequate course in writing/formulating proofs for problems in advanced calculus/real analysis (my university has an advanced calculus course, not a real analysis course). In the fall I will take the first of a two part course in advance...
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I'm trying to translate this text to Polish and everything seems pretty clear to me, apart from the usage of the words "within" and "without". I presume it's some kind of technical vocabulary referring to the subject of jousting. Could someone explain to me what these words mean? Here are three excerpts from the text: ...
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"Crack The Whip" is a game played on ice skating rinks where several individuals line up all facing the opposite end of the rink, and skate forward. When the group reaches the opposite end of the rink, the "point man" or the person on one end of the line stops, and everyone else pivots around him. Supposedly, the perso...
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Even though I don't work at Google, the Google Styleguides have been very helpful for me in adopting consistent, readable style conventions for my code. Unfortunately, there is no Google Styleguide for LaTeX. Q: For LaTeX, does anyone know of something equivalent to the Google Styleguides? Quick searches of the web for...
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I'm trying to figure out a kind of taxonomy of quantum phenomena. So far the categories I've come up with are (in historical order, with example phenomena): discrete quantities where continuous ones are expected (black-body spectrum, atomic spectra, Stern-Gerlach [spin spectra]), interference phenomena where trajectori...
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In the following statement, I am confused with the meaning of "whether" in the second sentence. Could you please advise which one is the meaning of this statement? a or b? The statement: "For the grant of the permanent Partner visa, you can be either in or outside Australia. This is the case whether you lodged your ori...
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An inertial frame of reference is described as being a frame of reference in which the first law of Newton (the law of inertia) holds. This means that all events as described with respect to this frame of reference must have a zero net force acting on it and therefore traces a straight line with a uniform non-translato...
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I am currently a senior in high school, and I have been studying mathematics for about nine or ten years now in my personal time outside of school. I am not familiar with academia or in general higher education, but I do know that I want to continue studying mathematics or something in a related area. I am having a lot...
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What would be an idiom or word or name for someone that is an initial tester (like a beta tester). I am writing a speech for my younger brother's engagement and want to say how I have always been the first to try everything in my family--schooling, learning to drive, college applications, etc.--because I was the oldest...
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Possible Duplicate: When is it okay to end a sentence in a preposition? So we've all heard the admonishments from our teachers not to end a clause with a preposition A plumber visits a wealthy estate to fix a clogged toilet. As the butler opens the door, the plumber barks out,"I'm here to fix the toilet. Where's your b...
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Background: I am an upper level undergraduate physics student who just completed a course in classical mechanics, concluding with Lagrangian Mechanics and Hamilton's Variational Principle. My professor gave a lecture on the material, and his explanation struck me as a truism. Essentially, he argued that the difference ...
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I am a high school senior and I am interested in doing a math research. I hope someone can recommend areas or topics of research that are challenging, rewarding, and yet do not exceed my capability. (I acknowledge this is quite hard) My math background: a. I have done competition math (Elementary number theory and comb...
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I am planning to take a graduate Geometry course next semester. The preliminary syllabus does not specify any textbook but has the following descriptions: Catalog Course Description: This course studies higher geometry including triangulations of polygons, Voronoi diagrams and Delaunay triangulation, algorithms in comp...
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Fluid dynamical instabilities are present in many different everyday things. The famous tears in wine for example are a classical example of a Marangoni effect, where surface tension gradients due to evaporation cause an instability. I recently came across an instability that occurs when you have just emptied a glass w...
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There's an old debate going on in the guitar community about how much does wood choice and body shape affect the sound of an electric guitar. No one denies that there's a difference acoustically (how the guitar sounds unplugged) because in this situation it's the wood and body shape that amplify the sound made by strin...
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Let's say I am at the train station and I missed the train, I still see it driving off. I would naturally say to myself: 'Damn, that was the train I was hoping to get.' Would that be wrong? If not, why is the past progressive used here? I have been taught that you use the past progressive when you are either talking......
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My friends and I were playing a game where you roll dice and you bet money on what picture it's going to land on and I began reasoning with myself that if I tallied up what pictures the dice landed on that the ones it has not landed on were more likely to come up in the next roll of the dice. So I began a process of ob...
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Is "family" both plural and singular? or would I have to say families for the plural form? For example, which of these is the best option: "A majority of those whose family were unaware of their sexuality..." "A majority of those whose families were unaware of their sexuality..." "A majority of those whose family was u...
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I'm reading Chris Hecker's third article on rigid body dynamics http://chrishecker.com/Rigid_body_dynamics Quoting... "More importantly, if our collision detector supplies us with a 'normal vector' for the collision (denoted by n, and pointing toward body A by convention), we can define the 'relative normal velocity' a...
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I would like to better understand how neutrino oscillations are consistent with conservation of momentum because I'm encountering some conceptual difficulties when thinking about it. I do have a background in standard QM but only rudimentary knowledge of particle physics. If the velocity expectation value of a neutrino...
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I've recently learned about ultraproducts, but the source I learned from almost immediately after the definitions restricted to talking about countably incomplete ultrafilters. I know that the existence of countably complete ultrafilters is a large cardinal issue, but aside from this, is there a reason to focus on the ...
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While my physics teacher was explaining pseudo forces to us he gave the following example : An elevator is accelerating upwards. In it there is a bob strung up by a rope. There are two observers, A in the elevator and B outside of the elevator, on the ground and not accelerating. Due to the action of gravity and the li...
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Is there a word to describe someone who uses complaints to indirectly brag about themselves? An example would be "I hate going to concerts because people start singing and because I have perfect pitch it irritates me." Perhaps another example might be "I don't like that video game. It's too easy and I get bored." The c...
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I think prejudice is too general. The definition Google gives me for prejudice is: "preconceived opinion that is not based on reason or actual experience." - it doesn't specify that this preconceived opinion is due to membership in some group (or, more specifically, perceived membership in a group), although it seems t...
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In one of the books on algebraic topology (I don't remember exactly which one) there was an exercise to build an example of two topological spaces having two continuous bijections between them which are not homotopy equivalent. To be honest, this exercise confuses me a little because, as I understand, each pair of home...
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One quality or trait that many employer looks for in a leader is the ability to not only perform well yourself but to also elevate the performance of others around you. For example, Steve Nash was an elite point guard and an all-star that made the people around him better. He made Shawn Marion and Amare Stoudemire all-...
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I was driving to work this morning when this question occurred to me. I was going up a clover-leaf entrance ramp to the highway. The person in front of me was lazily floating the outside of the curve, whereas I always tend to hug the inside of the curve. Hugging the inside of the curve tends to lead to an apparently hi...
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Given the equations of two spheres, how would I find the equation of any plane tangent to the two spheres? I tried something, but I realized that it failed, and I am not sure where to go from here. I have only basic knowledge of cross product, dot product, etc. and have not yet taken calculus. My attempt: I know the ce...
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Back when I studying the time independent perturbation theory of the Hamiltonian in quantum mechanics, I remember reading that there are only three problems in physics with exact solutions: the free particle, the harmonic oscillator and the hydrogen atom. It was further stated that any given problem (even a simple pend...
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I'm a little out of my depth here... I'm trying to understand quasiparticle tunnelling in superconductor-insulator-superconductor junctions. Many books use the "semiconductor model" to explain this: (source: wikimedia.org) These diagrams show the available quasiparticle states (with a large band gap due to the formatio...
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I was working on a lab in class drawing Free Body Diagrams. The problem required we drew an FBD of a ball that is in the motion of being thrown. I drew a slightly diagonal line labelled Applied Force, a vertical line straight down labelled Gravity, and a line opposite of Gravity labelled Normal Force. I was told that t...
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I'm a huge Pulp Fiction fan, and the following is one of my favorite scenes, but it also irks me. (source: IMDB) Jules: [Jules shoots the man on the couch] I'm sorry, did I break your concentration? I didn't mean to do that. Please, continue, you were saying something about best intentions. What's the matter? Oh, you w...
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Break comes to a close, and you, a renowned mathematics professor, step into a grand lecture hall to deliver the first lecture of the semester on topology. This is an introductory course. Half of the students cannot even pronounce homeomorphism. As you look around the room, a bead of sweat works its way across your bro...
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Can a sentence like this: "I don't know who the first man that made such and such thing in such and such place was," be grammatically correct if we don't put "was" at the end of the long phrase, that is, if we write: "I don't know who was the first man that made such and such thing in such and such place"? I can see in...
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I'm writing a paper about an algorithm that I have developed. Just for illustration, I will say that the method name is "quicksort". My question is about the usage of the in the following context: This paper proposes quicksort, a novel and fast algorithm. The advantage of quicksort is that... My question is whether I s...
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I'm entering my second year of undergrad (majoring in mathematics), and I've found that I am really bad at Linear Algebra, but very good at Calculus and Differential Equations. I'm hoping to venture onto Sci. Computing/Applied Maths, but I'm worried my inadequacy (as quite personally, unfortunate lack of interest) for ...
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I was looking for a synonym of spontaneous, and voluntary naturally came to my mind. In an attempt to understand the difference between them, I tried to google spontaneous vs voluntary. To my surprise, nothing really interesting popped up from search results. Then I decided to look them up respectively. As expected, vo...
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Suppose we have a contact process on a finite lattice. I'm asked to give a heuristic argument for the fact that the extinction time for the contact process is exponential in the size of the lattice when it is in the supercritical phase, and logarithmic in the size of the lattice when it is subcritical. The supercritica...
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Motivation: If I start with the group axioms and drop the requirement that I have inverses, I get the monoid axioms. If I proceed to drop the requirement that I have an identity, I get the semigroup axioms. If I then drop the requirement of associativity, I get the magma axioms. If I drop the operation, I get the set a...
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There is a challenge involving a lemon floating in a jug of water which seems impossible to beat. I've noticed it in several pubs of Edinburgh. The challenge is as follows: There is a jug half filled with water. Floating in the water, there's a lemon. The lemon doesn't touch either the bottom nor the edges of the jug. ...
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I've been using OpenOffice and/or MS Word to do my college assignments, but since I started this new discrete math course, I'm finding myself very annoyed with the math formula options in those programs. I learned about LaTeX and figured it would be my best option. Since I really just want to get my college assignments...
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My wife was discussing pudding consistency this morning and used a sentence along the lines of, "I only like the pudding you make". I blinked and asked if she really liked the pudding I make and she replied, "No, I mean the pudding you make, you know, like if I were to make some pudding". She was using the "you" in a s...
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I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the lecturer just drew a picture of a solid wall with two slits and then showed pictures of the interference patterns generat...
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I'm trying to understand the connection between the wave model and the particle model for light. It's understood that the energy of a photon is given by E=hf, but from my understanding of fourier analysis, the only kind of wave that has a precise frequency is a plane wave. The plane wave is an idealization, since no re...
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Whenever I add milk to my morning coffee I often enjoy watching the patterns which are created. These patterns have a striking resemblance to certain fractals and my question is, "Why?" Oh dear, that is never a good question, so let's try "Why shouldn't they?" The obvious observations are that the water is very hot whe...
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I read about this law / property a couple of months back, but I've forgotten what it's name was and I can't seem to find it by Googling. I was hoping someone could give me the name for this property. If I recall correctly, it was named after same famous mathematician like Gauss or something... More detail: This site wa...
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I am familiar with basic quantum mechanics and I know that there is no concept of 'force' in quantum mechanics, unlike in classical mechanics. Problems in quantum mechanics are solved by writing down the Hamiltonian for a system, and trying to solve for the various eigenvalues. Some of the first problems that are taugh...
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I'm in doubt in the application of Gauss' Law to find electric fields when the charge distribution is symmetric. Well, first of all: I know how to find the magnitude of the field - we just enclose the charge distribution with a gaussian surface on which the electric field will not change it's magnitude, and then using ...
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Good afternoon, I'm trying to learn about Fuzzy alone, I was using some texts on the Internet about it, but it was very difficult to learn. I want to learn about Fuzzy set as shaper of uncertainty. Operations with fuzzy sets. Characterization and properties of fuzzy sets. The Zadeh extension principle. Fuzzy numbers. F...
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After spending almost one year on this site, I've realized that my knowledge of mathematics is not deep enough. I love mathematics, i mean I am obsessed with it. I have a masters degree in mathematics from a reputed university in India and now I want to pursue PhD in this subject. It's been one year since completion of...
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I'm writing a paper about classes of formal languages, and I'd like to have a diagram showing their heirarchy. Something similar to this (from Wikipedia:) Is there a LaTeX package which, I can give the relationship between the classes to, and have automatically generate and lay-out a venn-diagram for me? The idea is th...
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This sounds like a daft question, but I'm serious. Translation and rotation are clearly different -- the symmetry between them is broken by Newton's Laws. But in the Lagrangian/Hamiltonian frameworks, they look extremely similar! The Lagrangians for free rotation and free translation are exactly the same, up to the rep...
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It's my first time to write latex with Mac os (or in fact, using Mac os in general) and unlike with Windows I'm having some trouble viewing my output files. I'm using texmaker. I would like to have either dvi or pdf viewer constantly open and auto-refreshing when I save changes or convert them to latex. I was told that...
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Basic books dealing with the interaction of X-rays with matter ussually don't mention anything about the polarisation, but I read somewhere that X-rays scattered in matter are linearly polarized, specially those scattered at right angles of the incident rays. If I remember well, the reason was discussed considering the...
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This was explained to me many years ago, by a physics teacher, with the following analogy: "If someone on the beach wants to reach someone else that is in the water, they will try to travel as much as they can on the beach and as little as possible on the water, because this way they will get there faster." I'm paraphr...
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I am attempting to write a program that will compute the average amount of a particular product produced when randomness is involved. Let's say that I am trying to produce some widget. Whenever the production process for this widget is started, it is not guaranteed that the process will be successful. So let's say that...
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Starting from tomorrow, I will be tutoring some undergraduate students following a course in general topology. I am looking for examples motivating the importance of topology in mathematics which can be explained without too much difficulty using concepts of other areas of mathematics (or physics) they have already tre...
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I have this sentence: I strongly believe that the first step in making the most efficient solution for any problem is analyzing it well. Would it be better to use either of the following? I strongly believe that the first step on making the most efficient solution for any problem is analyzing it well. I strongly believ...
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I was watching a show on the science channel about gas giants; there is something I do not understand. I am not a scientist, so this may be obvious to some. I learned that there a three states of an given physical object; solid, liquid, and gas depending on how cold or hot the object is. An easy example is ice, water a...
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I've recently discovered that the following theorems require the axiom of choice to be proven: every surjective function has a right inverse. a real-valued function that is sequentially continuous at a point is necessarily continuous in the neighbourhood sense at that point. every vector space has a basis. When I revis...
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I've used 'extraterrestrial' twice in a paragraph already, so it's starting to get repetitive... Edit: The sentence I'm hoping to prove is 'Humans have reached [insert word] scales', referring to the furthest we've went in the universe. By reaching I mean actual physical human presence, which excludes anything discover...
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I am trying to describe the evolution of a motion which is composed of smooth parts called "free flights" and instantaneous impacts. For example, consider a bouncing ball: its motion is a succession of free flights, separated with impacts (when the ball touches the ground). I would like to refer to two time-related qua...
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Based on the following example: Local Area Network (LAN) You can say that LAN is the short form and the Local Area Network is the long form. What is the another word for "short form"? (Is 'acronym' a better word for replacing 'short term'? or 'abbreviation' would be a better choice?) What is the another word for "long ...
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I was wondering if the cardinality of a set is a well defined function, more specifically, does it have a well defined domain and range? One would say you could assign a number to every finite set, and a cardinality for an infinite set. So the range would be clear, the set of cardinal numbers. But what about the domain...
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I'm struggling to find the words to convey the concept even now, but perhaps it would make more sense to illustrate by example. Certain communities like Reddit and Quora tend to be liberal-leaning and have other attitudes and opinions not entirely reflective of the population as a whole, in large part simply because th...
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Suppose someone (like a boss, friend, cousin,.., to whom you can not say "no" easily) has a personal request for you which you find difficult to decline, but you cannot bring yourself to say no, because you feel embarrassed or too shy to say no (i.e. you do not feel free to say no), or just simply don't like them to fe...
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I'm a software developer (although math isn't my strong point). I've developed a device to monitor/control my clothes dryer by monitoring the intake air's humidity & temperature, and the exhaust's humidity and temperature. The plan was to compare the exhaust air's humidity against the intake air. Once the humidity in b...
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My school requires that dissertations follow a set of sometimes odd formatting requirements. We have a latex class file which does a reasonable job at bringing documents into compliance with their requirements. There is, however, one requirement that I have't got a clue how to make happen: Footnote are supposed to be a...
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On a chat channel today I was reading two people talk about some of the more popular movie formats and movie players available. One of the interlocutors said something that got me thinking. I will cut quick to my question. Is there a semantic difference between the following two phrases: ... the last movie I played ......
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Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about that same line. Now, Euler's Theorem simply says that any rigid body displacement can be decomposed into a rotation plus tra...
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Lets say I have the following sentences... Cake is really bad for you. It contains a large amount of sugar. It contains common allergens. It looks silly. Additionally, lets say I wanted to connect all three of these thoughts together in a similar manner... Cake is really bad for you. It contains a large amount of sugar...
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I'm taking a very computational course in partial differential equations. Because of this emphasis, I'm feeling very underwhelmed by the course, and have a lot of questions that really aren't answerable in the current state of affairs. My professor basically tells me to take an advanced course in real analysis for a ri...
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When using the interrogative pronoun, 'who', what would the possessive form be? 'Who checks X letterbox every day?'. I feel it ought to be 'his' but some people I know claim it should be 'their', which to me seems to contradict the singular form of the verb 'check'. 'Who checks his letterbox every day?' is what I would...
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I would be tempted to rephrase my question as : why do people seem to care only about the curvature of a connection on fiber bundles ? Indeed, the curvature gives the vertical part of the commutator of horizontal fields (the horizontal part is the lift of base commutator), while the commutator of vertical fields has no...
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My understanding right now is that an example of conditional independence would be: If two people live in the same city, the probability that person A gets home in time for dinner, and the probability that person B gets home in time for dinner are independent; that is, we wouldn't expect one to have an effect on the ot...
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In Afrikaans, it is considered very disrespectful to use "you" ( "jy") when referring to someone who is above the level of a peer. Instead, it is expected that you use "u", which is a very respectful form of "you". Also you can talk in the third person "How is ma'am today" would be the equivalent. I cringe internally w...
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In a modern nuclear reactor for example a PWR there are multiple containment systems which prevent the release of radioactive material into the environment and shield the environment from the radiation. Here is a quote from the wikipedia article about this: The reactor vessel is the first layer of shielding around the ...
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My brain immediately suggested the non-word "promisand", but I doubt I would be understood if I said that. What's a good word (or failing that, phrase) for the action or thing that was promised? This reminds me of Latin expressions like Carthaginem esse delendam (Carthage must be destroyed, lit., 'Carthage is a thing-w...
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"One way mirrors" are used in interrogation rooms etc. The wikipedia article states that: A true one way mirror does not, and cannot, exist. Light always passes exactly equally in both directions. However, when one side is brightly lit and the other kept dark, the darker side becomes difficult to see from the brightly ...
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