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I have a subtle doubt about the physical interpretation of the mathematical definition of vector field as a derivation. In basic physics we understand a vector quantity as a quantity that needs more than magnitude to be fully specified, in other words, quantities with the notion of direction. This goes very well with t...
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I have a question about the appropriate usage the possessive personal pronoun "mine" over the possessive determiner "my". I have done some research and understood the differences between them, but my questions isn't quite about that. One of the main purposes of pronouns is to eliminate repetitions, yet I cannot be sure...
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When I used to play video games, "all in" meant that you were devoting your army to a "do or die" effort. In other words, you were either going to win or lose in the next battle. The "all in" meant that you typically brought all of your soldiers to fight, holding none back. But years ago I was doing the Daily Jumble, a...
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In this sentence, would you use "to inform" or "for informing"? These findings are critical ______ future research Likewise, would you use "to understand" or "for understanding" in the following? These results provide a powerful framework _____ existing patterns. This is a question that comes up a lot in science writin...
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I don't get this joke: It smells like up dog in here, What's up dog? Nuuthin dog, what's up with you? (source) I understand that the person asking "What's up dog" is tricked into asking a question they didn't intend to ask. I also understand the meaning of the "What's up?" question. I don't understand why this exact qu...
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How common is it for native English speakers to actively replace the past tense 'did' with the past participle 'done'? I used to think it was only really done in rather vulgar dialects, but I have increasingly heard this usage now by people who speak otherwise normal Received Pronunciation, or Standard American English...
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In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with. First of all, the S-matrix is a scattering matrix which comes from scattering processes. In the context of quantum mechanics and quantum field...
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I am confused about the usage of the words like and unlike in sentences. Like and unlike make me confused because I see them being used everywhere almost interchangeably, and to make matters worse I even saw commas making difference in meaning. Which of the following sentences is most correct, and least ambiguous? Unli...
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I'm new to finite fields - I have been watching various lectures and reading about them, but I'm missing a step. I can understand what a group, ring field and prime field is, no problem. But when we have a prime extension field, suddenly the elements are no longer numbers, they are polynomials. I'm sure there is some g...
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There are many books, written by highly decorated academics, which feature proofs that I can hardly comprehend in an acceptable amount of time. Roughly each week, it happens that I find myself having spent around three hours to convince myself of a single proof - usually, the proofs are from textbooks for undergraduate...
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I want to typeset diagrams describing functions which take multiple inputs and return multiple outputs. These should look like boxes with labels in them like "f" or "g" and with some input wires coming in and some output wires going out. The diagrams I'd like to typeset will involve several such boxes with some output ...
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Suppose I was standing in the sea, and touched an electric fence; I would receive an electric shock, because both my body and the sea are conductors, and create a path for the electricity to flow. The sea is so big that it has the capacity to draw and dissipate a great quantity of charge. However, if the sea was draine...
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I will be writing a report in which I analyse the performance of a piece of software. I would like to show my data using PGFPlot. My plan of attack is to schedule a script to run on the machine I am using, which will run the program a number of time with a variety of parameters (the main one being the number of process...
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I dont get why a forward gear allows sliding a car backwards. Any ideas? So this is a car with an automatic transmission. The transmission is in the drive mode (move forward). Car is at the slope facing the hill up. I am in the car pushing the gas pedal very gently. The car is supposed to move forward going up the hill...
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I am simultaneously taking courses in functional analysis and commutative algebra. In doing so, I found that there is, at least heuristically, some similarity between the notion of an algebraic variety (essentially, the zero locus of a family of polynomials) and the annihilator of a subspace of a Banach space (the coll...
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The following is a GRE sentence completion question. The most striking thing about the politician is how often his politics have been (i)_____rather than ideological, as he adapts his political positions at any particular moment to the political realities that constrain him. He does not, however, piously (ii)_____polit...
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While studying Faraday rotation (linear magneto-optic rotation) I came across a fact that Faraday rotation can be enhanced. Verdet constant which depends on the wavelength can be enhanced as change in refractive index with change in wavelength is maximum near resonant light. Now if the incident light frequency is reson...
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I had previously asked about how useful everyday solar physics data is to other astronomers ... But about a year from now, we will have another Venus transit, where Venus will pass between the sun and the earth ... I was just in a meeting with some EPO (education and public outreach) folks about trying to prepare somet...
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(Please note: I've seen some other questions asked like the one I myself am asking, I realize that I am indeed late to the party, but I am genuinely curious and none of the previous answers have satiated me as of yet. Note that this is a highly hypothetical question, asked by somebody who isn't even a college student s...
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A BibTeX question (using BibDesk). I am having trouble working out how to make BibTeX handle the new Digital Library of Mathematical Functions (DLMF) web page. No authors or editors are listed. DLMF itself suggests (http://dlmf.nist.gov/help/cite) When referring to the web site from a print publication, it is recommend...
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Sometimes I see something like "a mapping preserves the structures of its domain and of its codomain". From Wiki about morphisms in category theory: a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathemat...
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We tried my electrolyzer with a friend today, we filled a small bottle with HHO gas, and set it on fire. It was loud but not a big deal, like a firecracker. Then we added some soapy water and created HHO bubbles instead of filling the bottle with HHO underwater. Then we lit the bubbles and it exploded so loud that for ...
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Sometimes in quantum cosmology, when we are thinking about 'wave functions of the universe' we have in mind some sort of formal path integral, where we include not just the variations in the dynamical fields (metric and so forth), but also possibly some sort of prescription for summing over all possible topologies. At ...
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When I'm pushing a tall, cylindrical object stood on its end (like a Pringles can) I can push it near its bottom, and it will slide forwards, or push it near the top, and it will topple over. So, there must obviously be a point somewhere on the side of the cylinder where it stops moving forwards and begins falling forw...
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This image from Wikipedia shows how a black hole would look like: A black circle that acts as a gravitational lens for light rays coming from behind. How would a rotating black hole look like? How would it look like when viewed from side and when viewed from the top (along its axis of rotation)? If I understand it corr...
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I've began learning LaTeX for the expressive purpose of eventually creating a resume template of my own. A business school friend of mine showed a very professionally-looking resume he created from a workshop, and I would like to turn it into a LaTeX template. I know there are already many existing resume templates, bu...
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I am currently a math major in college and my main problem is that it feels directionless. My college offers little in term of variety in undergraduate math so I moved on into taking graduate courses and I am actually loving it. But at this point I am just randomly taking courses that looks interesting and was wonderin...
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When creating a presentation, I sometimes create extra slides that contain additional information, a more thorough explanation, or an extra plot pertaining to certain parts of my talk. These extra slides are usually in a separate PDF and the document is usually only opened if an audience member asks a question or reque...
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Some time ago I learned the difference between a present participle and a gerund, so today I decided to pass any online test to make sure I understand it. I passed it having made only one mistake, which asked the difference between the two in this sentence: Nobody was surprised at John being absent. One needed to choos...
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Background: I was cooking eggs (very difficult) with a plastic spatula which was not very good, so when I set it on the border of the pan it began melting. In order to keep cooking, I reached for a wooden spoon which can touch the pan without melting. This led me to wonder about the behaviors of the materials. For exam...
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I think everyone should have seen a bowl of hot water moving by itself on a flat surface such as glass(seems like it is moving by itself but maybe there are some external force applied to it when it moves). What is the explanation of this phenomenon? Hypotheses : Since the bowl is heavy, for it to move the friction bet...
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For the absolute life of me, I cannot seem to wrap my head around the proofs given in my number theory and cryptography class. Maybe it's the teacher, or the textbook, both or neither, but this is causing me great concern for two reasons. First is obvious, since I hate solving math without a full comprehensive understa...
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"It is also my favorite quotation. " Does this sentence mean that this is my favorite quotation in addition to other quotations which are my favorites, or does it mean that I am a person who has this quotation as a favorite, in addition to the persons who have this quotation as a favorite? Does "also" indicate the pres...
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I am trying to prepare a paper for submission to a journal that is not an AAS publication, but I would still like to use the AASTeX package for the tools it provides and stylistic reasons. The journal does not have its own LaTeX package, so I can use the AASTeX package as long as I make sure to conform to the few given...
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This question actually came about from a discussion of another question posed here The neutron is known to be comprised of an electron and a proton, and there are observations that the neutron can be created by these particles or alternately decay into these particles. Furthermore the stability of the neutron is vastly...
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I have been performing an experiment at school in which I test the force on an iron surface from the magnetic field of an electromagnet. The electromagnet has a rectangular iron core. The theory predicts that the force increases linear with the surface area of the iron plate. This is because the volume between the plat...
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I would like some help with what the word it in the paragraph below (with emphasis added; the word is not emphasized in this way in the original). Does it refer to the TV or the antenna outlet? The passage is taken from Haruki Murakami's TV People. Everything gets removed from the sideboard to make room for the televis...
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I was finding the are the of hypocycloids. Then it struck me that apart from integration, there could be another method of finding the area of the hypocycloid with different curves. But the problem is I am not getting my answer right. So could somebody please help me tell if my logic is wrong altogether or if I am doin...
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Materials in quantum information often emphasize that one and two bit classical reversible gates cannot achieve universality for the classical reversible computation, whereas universal quantum computing can be achieved only using one or two qubits gates. I want to understand why classical reversible computing cannot be...
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If you make a straight cut through a square, one part can always be made to cover the other. (This is true by symmetry if the cut goes through the centre, and if it doesn't, you can shift it to the centre while taking from one part and giving to the other.) However, if you cut an equilateral triangle, it may or may not...
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I'm looking for an adjective that describes an object that, rather than is just the outside, is instead just the inside. Searching for antonyms of hollow, I have only found the word solid, which suggests both the inside and outside of an object. I really need a way to describe something as being just the inside of some...
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I've long wondered about the future of our species. Taking the long view, I find it very amusing to consider the challenges that humans will face and (hopefully) overcome on our journey to the end of time. The most vexing problem is the apparently insurmountable issue of Proton Decay and how this could put a premature ...
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My aim is to produce an html-file with the same text as the pdf produced by LaTeX- The html shall represent the pagination and line-break structure of the pdf: When there is a linebreak in the pdf I want to produce a <br> in html, when there is a paragraph I want to produce a <p> in html, when there is a newpage in the...
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I've been searching the internet all day for this particular case and can't find a single word on the subject - whether that's my poor searching or the subject is obscure, I do not know. I am also not particularly fluent with mathematical jargon, so forgive my fumbling explanation. Hopefully one of you may re-phrase my...
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I have long found the Simulation Hypothesis to be better-able to answer questions that I have regarding the universe than the string theory and the quantum field theory. What I believe is that the notion of our universe being a simulation, especially in the last few years, has developed to the point where it should be ...
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An off-topic question posed at Mathoverflow by Andrew Stacey, but one which fits here: One thing that came out of Terry Tao's recent blog posts on this matter (first post and follow up) is that it's hard to get an overview of all the different ways of getting one's amazing mathematics onto the web. I thought it'd be us...
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To move charge from one point to another in an electric field, the force which we must apply is equal and opposite to the force due to the field. (Quoted from Engineering Electromagnetics by Hayt.) Here is my concern: To move a charge, shouldn't the force that we must apply be just a little higher than the force exrted...
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I've come across a book that has this general questions about lines and planes. I can't agree with some of the answers it presents, for the reasons that I'll state below: True or False: Three distinct points form a plane - BOOK ANSWER: True - MY ANSWER: False, they cannot belong to the same line Two intersecting lines ...
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This question concerns the residual heat (if any) contained within the Earth's moon. At the time of the Apollo moon landings, it was widely reported that the boot marks left by the astronauts would last "forever", as there is no atmosphere to disturb them and because the moon was geologically "dead." Ignoring cosmic du...
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As you know the active noise cancellation technology used in many application such as protection of aircraft cabins and car interiors to reduce engine noise also some headphones use this feature to reduce unwanted ambient sounds. Actually I don't know the details of how this feature works, but I do know that it has inp...
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I am an undergraduate CS student but I love mathematics and spend most of my time doing and reading math books. I realize that it's important to get into the habit of reading papers and journals so it will be easier to think of ideas for projects and research. I'd like to know how I should start reading papers and what...
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I am trying to make a computer game, which involve radioactive hazard. The game is still in its early stage, and I want to add mechanisms which are as realistic and as fun as possible. So I'm trying to understand how radioactivity is "absorbed" in the air. For example (please excuse any physic mistake), if you have som...
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I have a basic enough question. Assume that one has one of those ideal see saws, i.e. the teeter-totter pivots on point source, the balance is of uniform mass etc. Now assume that one places an object of mass m on one end. This will force the balance to tilt on side. Now suppose that one adds another mass of m on the o...
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In a previous question, I learned that in order to detect an object in space, what matters is how much electromagnetic radiation it is giving off, and what sources of EM radiation the sensor can pick up. Given that the sensitivity of the sensor over the spectrum is a parameter for detectability, I would like to learn i...
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Good evening, I'm writing my thesis in Latex, with which I already had the pleasure to work for some other projects, but I'm now facing a problem I don't know how to solve. I'll try to get to the point as straight as possible: let's say I have a chapter of simulation results, which includes a huge set of images. This c...
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This is kind of a big squooshy question (or series of questions), which I will try to cast in a more precise form. Apologies if I don't succeed. Context: I'm an amateur set theory/category theory enthusiast with special interest in stratified set theories. My knowledge is substantial in odd spots, but not very well rou...
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Looking at Cohen's success at proving independence of the Axiom of Choice and the Continuum Hypothesis, I was wondering if it was possible to mechanize forcing techniques for the purpose of proving independence (and hence undecidability) of conjectures. It would seem to be useful to test any sentence you're trying to p...
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If I write My car can go pretty far and it gets good mileage I have combined two independent clauses to create a compound sentence. I might just as easily write My car can go pretty far. And it gets good mileage. But if I write Surprisingly, my car can go pretty far and it gets good mileage, meaning that it is a surpri...
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I was watching a BBC sitcom. The scene is set in a wedding ceremony. In the opening of the speech of the father of the bride, he tends to be humorous, and thus he says: "Welcome to the wedding of Laura and Paul, whether you're friends, family or freeloaders, loved ones or loathed ones, people we like or people we had t...
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If a conformal mapping, e.g., a Schwarz-Christoffel mapping, maps the real line (from left to right) to a polygon, which is traced out from left to right, why is the upper half plane mapped to the interior of the polygon? Is it a preservation of orientation argument? I.e., since the upper half plane was to the "left" o...
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So, I know that this question may be tough to answer, but I am asking this question in all seriousness, and I don't consider myself a newbie... Lately, I am trying to find a way to "generalize" my approach classical mechanics. Specifically, I need a system that can always guarantee a solution to any problem. In a sense...
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Today my laptop battery died while I was finishing off a sticky note and so naturally I just went 'Oh, bollocks!'. After all, it didn't warrant one of the "big six"; it was more a "damn" moment. So I opted for "bollocks". I didn't think it was rude; it was just fun to say. I was around a colleague at the time and they ...
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I understand the phrase when it is used literally in this example. He's ill and doesn't know what he's saying. I perceive it to mean that a person is struggling with an illness that prevents him from thinking clearly and understanding his words. However, there have been times where the usage seems more vague to me, par...
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Nearly four years ago, upon hearing of the observation of time dilation in two optical atomic clocks at an elevation one metre apart, due to acceleration towards earths centre of gravity by Chou, C. W.; Hume, D. B.; Rosenband, T.; Wineland, D. J. I wondered where the point would be, at which time dilation caused by acc...
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While studying for my thesis (in dynamical systems) I've encountered multiple times with the concept of nuclear operators and nuclear spaces, often linked with the works of Grothendieck. For example, when studying the generalized transfer operator (or Ruelle operator) for the Gauss Map, Dieter Mayer points out that thi...
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I don't really understand the reason why wave theory of light fails to explain the blackbody radiation. My textbook says the Planck's quantum theory explains blackbody radiation. It says "If we assume, he said, that radiation is emitted in packets of energy instead of continuously as in a wave, then we can explain the ...
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Not all questions start with Wh- words, so why don't we start a question with a question mark to make it more obvious that it is actually a question? For instance, when I'm reading a book which has a long interrogative sentence at the bottom of the right-hand page, it often isn't until I turn to the next page that I re...
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We are regularly taught in high-schools and universities that, according to General Relativity (GR), gravity is nothing but a manifestation of space-time curvature (which, in its turn, is caused by matter and energy). However, GR is still only a model, which hasn't been challenged by experimental evidence/precision thu...
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Suppose the big bang did create equal portions of matter and antimatter and they exist right over top of each other, such that there is a constant inversion going on. Since a matter and antimatter universe would be identical, we wouldn't know whether we're living in one or the other; therefore, isn't it possible that a...
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My daughter is in high school and is working on a science project. She has really enjoyed writing the paper in LaTeX. Now, she has to make a tri-fold presentation of the major points. In the past, that has meant PowerPoint printed onto letter-size paper then pasting those pages (one slide per page) onto the board. How ...
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There are a few tools that will automatically retrieve BibTeX-formatted references from MathSciNet. BibDesk is offered with TeXShop, but only works on a Mac. Are there similar tools that work for Unix/Linux or for Windows? There are a few applications written as stand-alones that get the job done: mscget (requires pyth...
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I have previously done a course on group theory and now I am doing a reading course on category theory. So as an interesting exercise I have been asked to write an exposition of group theory for someone who already knows category theory but doesn't know any group theory. I have been given the liberty to decide how I bu...
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I often have problems with article words referencing to its correct referent. In the following statement for example: The touching scenes in the film leaves the audience a heavy feeling, encouraging them to consider charitable acts and the role it plays in our society. My intention is to have the word "them" linked to ...
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I am currently studying English and as such enjoy reading English books from time to time; for instance I have recently been reading the fifth book of A Song of Ice and Fire since the French version was not to be released anytime soon. As I read it I often came across a grammatical form I had never encountered previous...
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I am discussing with a friend (over email) the pros and cons of various interview styles. At some point in the email I write: "Ideally the candidate will demonstrate X." Then in the next sentence I want to describe, by comparison, what action by the candidate would not be ideal. I was initially tempted to write: "What ...
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My question is basically this, if I am only able to measure the total electric field and the magnetic field at a few discrete points in space and time, is it possible to separate the convective and the inductive electric field? Here is the background. Consider the geomagnetosphere. There is a background geomagnetic fie...
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The Boltzman approach to statistical mechanics explains the fact that systems equilibriate by the idea that the equillibrium macrostate is associated with an overwhelming number of microstates, so that, given sufficiently ergotic dynamics, the system is overwhelmingly likely to move into a microstate associated with eq...
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After having switched computer I had to reinstall TeXLive and TeXMaker on my Mac OS X Yosemite, however, after having done this I whenever I try to compile with (pdflatex) TeXMaker I get the error: log file not found. I am aware that this means that TeXMaker is not able to find my TeX distribution, but what baffles me ...
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I am searching for the "most natural" definition of a (geometrical/space) point as an element of "something" in mathematics (I am trying to design a small computational geometry library on strong mathematical basis). For example, for a vector, it's easy: a vector is an element of a vector space, end of story. Same for ...
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This is a question I have been wondering about the last few days, and I'm still not sure if it should be posted here on in the music section, so please excuse me if it's misposted. Hatsune Miku is a world-wide popstar, taking news and filling concert halls. What makes her unique is that she is not a human person. She i...
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It'd be nice to be able to style words or sentences or subsections based on arbitrary metrics. For example, it might be useful to highlight words based on their length - bolder highlighting for longer words, so that you can zoom out of the document, and get a quick picture of where it is getting complex. Another exampl...
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I've read questions like this one, this one, and this one which ask why we use complex numbers instead of real numbers, and that's one half of the question, but the other half, which I've never seen conclusively explained, is why we use complex numbers as a wrapper at all. From what I understand, there's nothing specia...
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Reading this explanation, I've understood that the divergence in computation of Casimir force on two parallel conducting plates is because of an unphysical model of ideal conductor, which makes EM field vanish on its boundaries. This looks much like unphysical model of rigid body in relativistic mechanics. Still, zeta ...
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Why isn't this possible? I've seen the ducted fans, it works (even if it is very rough). I've also seen the magnetic boards that hover above a special magnetic-reactive surface. But that isn't true hovering in the sense of usability as you cannot leave that surface and you cannot surely expect a proper surface to be ev...
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If I have an X amount of randomly generated positive numbers, what type of algorithm could I run to find the following: Precisely where the largest difference exists between two of the numbers? How much is that difference? Where does the smallest gap exist? How much is that difference? Generate a list of all difference...
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I am writing a story with a character who was a prince born albino in a very superstitious country. His Uncle intensely feared killing him, as he believed it would release a demon inside of him. This myth becomes the only thing that saves his life when his kingdom is overthrown as a child. He learned that having people...
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I am in a bind, trying to wrap up my thesis in two weeks time. My university requires me to use their citation style, which they only provide for endnote or zotero. Since all my citations are in bibtex (which I know, and I have no time to experiment with other bibliographic formats or programs, trying to make them coll...
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I am just going to give an example of what I mean using Skolem's Paradox. I don't want to get into Skolem;s Paradox itself or its "resolution." Skolem's showed that in first-order formulations of ZFC, whether some set A is countable depends on what is in the model. For example, take a model M of ZFC (assuming there is ...
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I decided to study Euclid for fun. I have Oliver Bryne's edition. I also want, as much as possible, to construct the figures myself, to get a deeper understanding. How did people traditionally do this? I have a compass, and a ruler. So far I've constructed the first three propositions from book one. However, it's not c...
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From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is grueling. However I'm certain that there are things that one could do to prepare in advance for the rigours of such a degree. What i'd like to know is what foundations mus...
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I was thinking deeply about figurative language today, and I read a sentence that must be an example of a specific type of figurative language, but I didn't remember learning about it and couldn't find it on a reference I use. The sentence, from Street Love by Walter Dean Myers, is: Could it even withstand the voltage ...
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As I understand it, there is a large contingent of physicists who believe that the measurement problem is "solved" by decoherence, without, for example, needing to postulate the existence of "many worlds." Yet at the same time my understanding is that in the decoherence picture there is only unitary evolution of the wa...
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My colleague and I are working on our style used in communications, and we have a question around whether it's acceptable to use "you're" or if we should always write "you are". Our style guide says: Our tone is conversational, honest, thoughtful, but never familiar or using slang terms The specific example we're looki...
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I cannot hear the distinction between certain sets of vowel sounds. Normally the words in each of these sets (and of several others) all sound identical to me: Don, Dawn; marry, merry, Mary; ah, awe; cot, caught; ferry, fairy. If the speaker's accent heightens the differences between them I might be able to tell them a...
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In any sizable system, the number of equilibrium states are much, much greater then the number of non-equilibrium states. Since each accessible micro state is equally probably, it is overwhelmingly likely that we will find the system in an equilibrium state. However, for a closed system, one that does not interact with...
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There is a mother, Ann, who has a stereotypical 'good' personality: she is religious, a teacher, and a very generous lady. Her daughter, Emily, isn't the nicest lady: she whines a lot, insults people, and is ignorant to her family history. My professor asked to mention in my essay that Emily's personality was an 'un-im...
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When I've attended math competition discussions, I've often heard people remark "oh, this is a famous problem" or say that it's similar to one. Most of them I've actually never heard of before. Competition books tend to have a vast list of past problems, and I haven't been able to sift through and tell which ones are s...
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I was wondering if there are some general definitions for direct product and for direct sum, for example in category theory or in set theory, so that the concepts for vector spaces, Abelian groups, rings can be unified, or in other words, the common features of those specific concepts can be abstracted? In particular, ...
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I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest bid, and an ask that was slightly lower than the current lowest ask. Whenever anyone bought or sold, that would mean that I wo...
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Of course a lot of people misunderstand the primary meaning of the adjective "moot" -- "open to question" or "argued about but not possible to prove" -- using the word only in the expression "moot point", which rightly or wrongly is often taken to mean "not worth debating". As a result the word is apt to cause confusio...
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