Just saw the definition of word miss from some web dictionary, which says "to fail to hit, catch, etc something." I suppose this could be written as "to fail to hit, catch, or do something alike something." Does that etc mean, technically, "or many other things alike"? How? Doesn't et mean "and" in Latin?


So the way I understand FG-modules is that it is analogous to a vector space defined over a field F with G a basis. However, I encountered a problem given the hypothesis that V is a possibly infinite dimensional FG-module where G is a finite group. I am confused how you can have a FG-module when your "basis" G is finite?


Hounds tend to "bay" rather than "bark". When a dog barks, you can say "he let out a loud bark". In a similar construction emphasizing the hound-ness of the creature, can you say "he emitted a loud bay that echoed through the chamber"? Or would it be a bark regardless?


Just a book problem I need help on: A letter is picked at random from the alphabet. Find the probability that the letter is contained in the word "house" or in the word "phone". I know this problem has something to do with mutually inclusive?? Would be great if someone could explain this to me Thanks!


There are quite a few modern sans-serif humanist fonts, slab-serif fonts and other interesting Google web fonts. How do we typeset in LaTeX/PDFTeX/LuaTeX/XeTeX using them? Is there a way in TeX to call fonts like the Google fonts directly from their CDN URI? Are there any packages like Michael Sharpe's package that covers these modern fonts?


Why do we feel tired while running as during running we are increasing our kinetic energy. I understand that the energy inside us(from food or something else) is being converted to KE while running but when we stop to which form is this KE converted???


I understand how to use the theorem environment in LaTex and would like to know if there is a similar environment for postulates or how I can make an environment for postulates on my own.


The title basically explains everything. The OP is an independent learner, who in the current stage sets S.S.Chern's proof of the generalised Gauss-Bonnet theorem as the goal. But what is the prerequisite knowledge of reading his two papers? I'm afraid basic Riemannian geometry would not suffice.


Show by a counterexample that the following "converse" of Theorem(A subgroup of a cyclic group is cyclic) is not a theorem : "If a group G is such that every proper subgroup is cyclic, then G is cyclic."


In a standard poker game (no wild cards), suppose you are dealt five cards and your hand contains exactly one pair. You trade in the three worthless cards for new ones. What is the probability that your hand improves? meaning that there is a substantive transformation from one "kind" of hand into another


Is it hard to calculate the coordinates and zoom factor that was used to generate a fractal image of, say, the Mandelbrot set? If you know the rest of the parameters, like how many iterations where used, in generating the image.


I'm reading Srednicki's QFT textbook. I'd like to do some projects that put the content learned into actual use. Is there any good project topic? I don't mind if it's already worked out some where. I just want to experience the process of actually putting QFT into use, or simply relating the textbook knowledge to more problem-oriented situation. The textbook problems are smaller drills.


I am a beginner of Fourier analysis, but my major is economics, I have not much of idea about frequency domain. My question is, since we have whole set of theory to work on time domain, such as time series analysis and stochastic process, why we need frequency domain.


Earlier I wrote a sentence that happened to end with a plural possessive. Is this OK to have? For example, "I got the guys' costumes, but not the girls'." looks odd to me. It would be easy to reword or simply add costumes at the end, but is it grammatically correct?


As we know, the Ky Fan norm is convex, and so is the Ky Fan k-norm. My question is, does this imply that the difference between them is a non-convex function, since it results from "difference between two convex" functions ?


We see Rainbows many times, but we always see them Horizontally or from Sideways. Why can't we see it from under it?/From the point where it starts or ends(end points)? I also want to stress on that, I am asking on viewing part and not about the formation, reason, causes of a rainbow.


Finite groups and finitely generated groups are intensively studied, but are there interesting investigations on non finitely generated groups? I already know some references for abelian groups, so I am rather interested by nonabelian groups; are they nice enough to hope general results? Maybe are there interesting links with set theory?


I have a current waveform from my circuit which goes up and down the x-axis. x-axis represents time and my y axis represents current. How should I calculate total area under the curve? Should I take the absolute for negative part of current or just waveform integral will work?


If you consider them as laws, then there must be independent definitions of force and mass but I don't think there's such definitions. If you consider them as definitions, then why are they still called laws?


Can someone please show me how this works, i'm going out of my mind I know the truth tables for the individual AND, OR AND NOT but when it comes to them being combined my understanding is shattered into pieces =/


Is there any group with the non-trivial frattini subgroup such that the intersection of the Frattini subgroup and the commutator subgroup is trivial? Expect the groups can be constructed by the direct product of two groups; an abelian group with the non-trivial Frattini subgroup and a group with the trivial Fratini subgroup?


With literary or historical references, what phrase would an English-speaking monarch have used to indicate to either their attendants or to their court that they were in need of using the toilet facilities?


Do these three words mean the same thing? From my understanding, discordant means not agreeing or out of tune. This is similar to non-concurring (as concurring would mean agreeing on something). Also, controversial means something which gives rise to disagreement. How do I understand the subtle difference in meaning when the wors are so similar?


Given this sentence: I look forward to learning new subjects and contributing to teaching them, (to?) facing new and diverse challenges, and (to?) producing outstanding work. My instinct is that I can omit the second and third to, but can someone please confirm and explain?


Which sentence is grammatically accurate or they both acceptable? "The main ingredient is blueberries" sounds better to me. "The main ingredient" is indicative of one type of ingredient, so does that mean that it doesn't matter if "blueberry" is in plural or singular form?


The sentence I am unsure about is: A rigid adherence to the doctrine of precedent would have resulted in a country where segregation was lawful but minimum wages were not. I'm confused by the subjunctive, and in particular the proper usages of 'was' and 'were'. Are they used properly above?


I am transferring a professor's .doc files to LaTeX so that we can do more sophisticated formatting and I ran across a problem. I would like to recreate this number line in LaTeX. Help with which package to use and which commands to study would be a great help.


Is there a word that names the sequence events were written about or described in, as opposed to the word chronologically? Example: Did you want us to present the events in the story chronologically or (in the sequence they were written)?


Is QFT being applied to quantum computing and control theory? I took yesteryear a basic course on quantum computing and if I remember correctly we didn't touch on any QFT (though I think that if it were a course with prequisites of QFT, not a lot of people would have attended the course).


im trying to find some sort of formula to calculate lines within a circle. I need to find the length of the various lines within the circle from which I only know the diameter. Is there some sort of formula that uses the dropoff of a circles side from the center? Thanks, Martijn


Are there simple alternative of these font sizes in ConTeXt? Or one needs to use some special module? I looked at this page here. It seems to be a lot of boilerplate of such a simple task.


Can I always find a Hamiltonian for any given Dynamical System such that the Hamiltons' equations are satisfied? The hamiltonian may be an extremely complicated function (Possibly containing complex terms) but in principle, is it always possible to find the hamiltonian for a given Dynamical System?


Given the principal directions (max and min), principal curvatures, and normal of a surface at point n, how would you go about looking for a point on the surface at a given vector distance from n? I'm trying to create a Solidworks Addin to map a spline to a surface and have limited mathematical knowledge (up to diff eq).


If I conduct an experiment and get results, and I can then relate those to real life in a way, what is the verb that this link to is doing? My first thought was validate, but that isn't correct.


With certain electronic devices if you make a mistake you can brick (used as a verb) the device, so that it ends up in a defunct state. So the device ends up being bricked. What is the correct term to recover from this bricked state? On the web one can find the terms debrick and unbrick, but which one is correct?


Possible Duplicate: Include < and > symbol Why when I create pdf in texlive with pdflatex, the characters < and > are displayed as inverted ! and ?, respectively. However, when I copy/past them, they are OK. What is the problem with PDF display. It's like the system does not have appropriate font, but aren't they common characters?


I'm not super solid on my linear algebra, so I am getting lost in the discussions of halfspaces. Can someone give me an intuitive explanation (possibly with a concrete toy problem) of Blackwell's Approachability Theorem, and the algorithm its proof constructs?


Is there any other word which can be used instead of something and some stuff, and how can the use of something and some stuff be avoided. For example: He saw her dwelling on something; it seemed more like she was trying to recall something. can it be written differently, without using something and/or some stuff?


I want to express that the sleeping time has no much relationship with the activity and ... But the following sentence looks very strange. Please help me paraphrase this one: No absolute relationship between sleep time and the activity, entertainment, and learning time.


How can I generate in xelatex a QR code with any given image inside, like so or better like this, using either pstricks or the new qrcode package? Note that the QR-code must still work after including the image.


I have a question on comparisons. I said no error first, and that was wrong. I don't see an error with B or D or A. Is it C "being"? Should it be switched to be?


Can someone illustrate the idea of "forcing" in set theory through some simple examples? The article on forcing on wikipedia goes straight to axiom of choice and continuum hypothesis, I wonder if there are simpler application that illustrates this so called technique.


What is entropy of the universe? What is the change in entropy of our universe? Is this change increases or decreases? If the entropy of universe keeps on increasing then what are the consequences? Is there any limiting factor to this increase? One practical application of entropy where it is applied in day to day life?


Now i doing the home work about Residue Integration and i doubt that "Can the direction of Contour Integral be affect to the result of integration?" I mean with the same shape of contour but direction of contour changes from clockwise to counterclockwise or counterclockwise to clockwise.


In Ion Optics, an immersion lens is composed of two planar apertured electrodes. My question is why it is called an 'Immersion" lens? I know that an Einzel lense has three or more electrodes. But physically for the ion optics, what is the difference between Immersion and Einzel lens? Or what is the advantage of Einzel over immersion lens?


I read Griffiths EM today and it says something very interesting but a little bothering to me. It states for an atom, the position of center of mass of an electron cloud lies in the center of the proton. But my question is why? What will happen if this is not true?


Are coproducts left exact or right exact functors in general? Let k be a commutative ring (unital assosiative). Specifically in the category of k-algebras is the tensor exact. (This is not the case in the category of k-modules, but then again the tensor is not a coproduct therein).


I have heard that phrase recently on this YouTube video "Why We Row (Inspirational)" and I can assume what it means, but I just don't understand it on the context of the speech. ... don't be suprised if someone decides to flip the script and take a pass on yelling uncle, and then suddenly as the old saying goes, we got ourselves a game.


For a transformation such as this, how does one determine the form of the kernel? Is it simply making the right side equal to zero, solving for each individual variable, and then creating a matrix with these 'new' a,b,c,d values?


I am often asked to prove properties of regular bipartite graphs, and beyond the two parts having equal size nothing seems obvious. Are these graphs more intuitive than they first seem? In particular, right now I can't work out why an r-regular bipartite graph is r-edge-colourable. Thanks


Where I can find a proof of self similarity of Grigorchuk group. I read it somewhere that Grig group follows this interesting property so I read about it but could not find a proof anywhere. It was not so trivial to me, so may be someone has any reference on it which one can provide. Thanks.


I know that -tight switch arranges the image size to include all the ink on the page. For this instance, however, I want to give a width of my choice and crop only in the vertical direction. Furthermore I only want to crop the space below the image. Is this possible without modifying the dvipng source code?


If you had a powerful electromagnet in the shape of a hollow sphere in which the top and bottom halves are the opposing poles, what can the magnetic filed at the center of the sphere be used for?


When reading grammar, I find the names of the tenses kind of weird to me; Present simple and not simple present past simple and not simple past present continuous and not continuous present etc Does this contradict with the "adjective noun" ordering rule or is it an exception (or something else)?


I know one should never use The reason is because, but does the same apply to The reason is so? It would make sense, because when someone asks you "Why (insert question here)?" , it's common to reply, "So that (reason here)." I'm not certain about this though and have not found anything online.


I'm using different fonts in XeLaTex. However, there are some fonts installed in the same name in my system. How can I change the name of the fonts to distinguish them in Linux System?


In the metatype FAQ, there's a section called "I have Metafont sources of some font. How could I convert it to TrueType using Metatype?" In that, he lays out a dozen steps that really should be scripted. Does anyone know of such a script? (I understand the result won't look very good at low font sizes.)


I was wondering if interchange and exchange are equivalent and can be used interchangeably or exchangeably (okay this is an example already)? What are the differences between their prefixes, inter- and ex-? It is common for XML to be used in interchanging data over the Internet.


I do not have a clue on how to solve out this type of question, and how to deal with integration with a combination of brownian motion and linear function. Can anyone help me out please?


I'm going to be studying this result for a dissertation this year, and I wondered what there were in the way of higher-dimensional analogues? Also, what are some standing research questions on this theme? I think the interplay of the different theories is fascinating.


I have learnt that a fraction with a surd in its most simplest form should have the surd in the numerator and not the denominator? Why is it convention not to leave the surd on the denominator? Is it just arbitrary convention or does it have an actual purpose?


If I toss a coin an infinite amount of times, can I be sure to get an infinite amount of heads? Is it possible for it to be tails every flip meaning I get no heads at all?


five friends including Bilyana and Bojana are sitting in a row in a theatre determine the probability that they are not sitting together. This is part of a homework assignment. I don't even know where to start with this.


To pluralise is to make plural, dog becomes dogs, conversely singularise. What is the generic term for such actions? The number of a verb is its singularity or plurality, so perhaps numberise? Is there a word for the concept or process of pluralisation and singularisation?


Lighter nuclei liberate energy when undergoing fusion, heavier nuclei when undergoing fission. What is it about the nucleus of an Iron atom that makes it so stable? Alternatively: Iron has the greatest nuclear binding energy - but why?


I'm looking for a word with the meaning that 'rapidise' sounds like it ought to have. The sentence: to make the process more rapid would be replaced with: to rapidise [sic] the process I have considered accelerate quicken or hasten expedite which work, but are not quite right for me. I'll use 'accelerate' in the absence of anything else, though.


In the quote, "He is to resist the vulgar prosperity that retrogrades ever to barbarism" What does resist mean? to tolerate to protest What does vulgar prosperity mean? obscene prosperity ill mannered prosperity What does ever mean? always occasionally What does retrogrades mean?


If I had a list of awards and wanted to organise that list by the organizations that gave out those awards, what would be a good word to use? I can only think of by awarder which doesn't sound great.


Something less roguish than "imp" or "wag." I'm thinking about a person who is perhaps a bit sullen or in need of some levity. The word or phrase would be better if it expressed how this person feels rather than labelling the type of person they are. Maybe a type of sentiment.


I hope I am not being pedantic; however, I could not come up with an answer on the internet. I wonder which is the letter which can be discriminated from the alphabet system on the basis of its myriad uses. Any suggestions?


I am using krantz-single.sty in which the environments example and theorem are already defined with its own fonts, numbering (according to chapter) etc. I would like to number examples and theorems consecutively. So, I cannot use amsthm.sty to define Example as a newtheorem. I need only the counter for numbering to change. How to do it?


In your opinion, what is the most cosmological or physics argument that may favor the existence of something like a god to produce a universe like ours and what is the most counter argument for that. Please don't drag this discussion into theology.


I want to write a sentence something like this - > I like to meet people of my native origin(country, city, town and so on). How can i write the things that are in bold in one word - > I like to meet ____


Can anyone show detailed proof of why radius of convergence of perturbation series in quantum electrodynamics is zero? And how is perturbation series constructed? So, as this argument requires imaginary electric charge of bispinor field (negative coupling constant), how is this argument considered valid?


W is the complex-valued transformation of the original signals x and y without selection of the window length with respect to time t. W is the complex-valued transformation of the original signals x and y without a selection of the window length with respect to time t. Which is correct?


I want to combine the following sentence: Relationship between son and mother, and relationship between daughter and mother Into one sentence for title of an article: Relationship between son, daughter and mother Is grammar and meaning correct?


Nouns can be used as adjectives modifying other nouns, like: The discussion was about supplier local content development. Can we rephrase the above to: The discussion was about local content development of supplier. In general, can we rephrase nouns acting as adjectives to "of" clause like the example cited above?


Assume that a charged particle accelerates/vibrates at a certain frequency and as a result produces e.g. red light. If every frequency has just a single wavelength associated with it, then the charge can never be a source of white light. So how do we get white light? What is the equation that relates the vibration frequency of a charge with the wavelength emitted?


i've just found out that EM stress energy tensor along with gravitational stress energy contribute to the curvature of space. So, does the electroweak field also contribute to the curvature of space? And what about another field like the higgs field? Sorry if my question is to speculative since i really curious with this kind of stuff


I think its something to do with acceleration but can't put my finger on it. Something about the most power needed as the greatest acceleration, as water flows up to full rate the accel and thus power decreases. Does that make sense?


I am not too sure just by reading the manual as to the subtle differences between the .initial and .default PGF key types. Can someone explain and demonstrate the differences with a minimal example?


Many spherical harmonics derivations start from finding a solution to Laplace's equation and the results are in fact what are called spherical harmonics. However, how's Laplace's equation really related to spheres? Particularly, Wikipedia says spherical harmonics being defined "on the surface of a sphere".


Say I have three kinds of items that I call A, B, and C. Now, I want to ask someone to create one. Which form is the correct one? Create an item A. or Create an A item. ?


My magnet seems to work independently of, and unaffected by, the Earth's magnetic field, yet the magnetic field of my magnet changes as I introduce some other similar magnets of varied sizes into its field. How would the magnetic field of this magnet differ at different locations on, orbiting around, and anywhere between, Earth and our other planets?


In my business communication over Internet text messengers, for example Google Talk or Skype, I see that many people often use shorten words like u instead of you, r instead of are and the like. How appropriate is usage of such words in contemporary communication? Is it used in emails also? Should we avoid it as much as possible?


I would like to contact my recruiter (via email) asking for updates on my application. What should I put in the title so it is informative, but also at the same time does not sound like I am too impatient? (I also would like to provide additional information about my accomplishments in the email) Thanks


If I'm attempting to be booked to do an event, and I'm saying: "we're now booking dates for such and such". Is that proper usage of booking? Or should I say, "we are being booked for dates in such and such"?


The Dold-Thom construction on a space is its free commutative monoid. Its homotopy groups are isomorphic to the integral homology groups of the original space. What are the integral homology groups of the Dold-Thom construction?


I have read that a wire contracts side ways on stretching it . But why? What happens at the atomic level when a string is stretched? When there is no force applied in the side ways direction, why does the wire contract sideways decreasing its cross section?


Let us pretend the 'one who hates his own image' is a 'selfie-loather'. If so, a sentence incorporating the term could be He always said he hated mirrors and I had assumed he was a 'selfie-loather' so I was shocked when I saw him apparently admiring his face in the glass!


I have read that pseudocapacitors are combined of a carbon electrode and a metal oxide one. On the carbon electrode simply a double layer is built up and on the other some chemical actions(redox) happens. I was wondering how the chemical reaction happens and how this is possible when we have just on electrode in the reaction?


We know Cauchy Residue theorem from the Complex analysis. however I wonder if there is a kind of Generalization of Cauchy integral and Residue theorem to the complex multidimensional holomorphic function too ? if such theorem exists, please mention any possible application of this theorem too. Can this theorem help in Iterative elimination of roots of a polynomial equations system ?


Is the difference purely stylistic, or is there a slight change of meaning in using one form of over the other? "It is the god-given given that must be accepted because it cannot be changed," as opposed to: "It is the god-given given that must be accepted: it cannot be changed."


I'll take one day leave for my family affair. I'll take one day leave for my family stuff. What's the different exactly? Or what situation is the best to use "affair", and "stuff" ?


we know that if R as a ring is left artinian then ring R has a minimal left ideal and left socle of R is nonempty. now i wanna know can we prove this: if R is left artinian ring then right socle of R is nonempty. how can i find a relation between them? tank you for your help


As the title says, does a polynomial with an infinite number of terms define algebraic numbers as roots? An algebraic number is defined as a solution to a polynomial with rational coefficients, but it is not usually specified whether this polynomial can have infinite terms.


If I remember correctly you cannot compress a liquid, but I know you can compress a gas. (usually to the point it becomes a liquid then no further) What happens if I were to compress soda water? A liquid with a gas trapped in it. Would the gas escape the liquid, then compress? Or compress within the liquid?


I have found this list of densities here: http://wiki.chemprime.chemeddl.org/index.php/Density_of_Black_Holes and I am looking for the density of quarks but I have not found it. I was wondering if Black Holes could be some kind of quark plasma (QGP). Is this possible?


Why does the second requirement of a basis, i.e. that a point in two sets must also be contained in a third set contained in the intersection of the two set, make sense? Why is that what we should think of as a basis?


There are people who keep their things in a prim and proper manner. They take good care of their stuff and use it with care. Is there a single word to describe them?


How does one correctly use the word "allegory" in a sentence? For example: This story is an allegory [for|of] pride. I have seen examples of both: the long poem is an allegory of love and jealousy [Merriam-Webster] To that extent, are his experiences an allegory for life? [Your Dictionary]


I am using pgfplots to create charts. How can I adjust the width of images of legend entries? I have adjusted plot coordinates in legend image code in the line legend style, but this not worked truely. Is there any way to do this?


I would like to define a maximum height and a maximum width for an image at same time. I suppose there must be a package to do this, but actually I'm unable to find it...


I am writing a research paper on quantum shuffle multiplication, and there is just one piece that I'm missing: I want to give one or several examples of its applications, and so far I have not been able to find any by searching online.


Please consider the following image: Now I'm just trying to understand how exactly this thing is rotated...I'm looking at it exactly like on the image of the car...So the normal force is slightly bent because of the angle, but the angle seems to be on the opposite side from where it should be, I'd think it would be the lower corner, not the upper.


"Indeed, whoever buys this needs to want a tablet and laptop in more or less equal measure." "Needs to want"? Isn't it a kind of unnecessary way around saying: "I think that people buy this if they want a tablet and laptop in more or less equal measure."? Or am I missing something?


Using a truth table I had no problems to proof, that this equation is correct. But how can I transform the first part to get to the second? I tried using de morgan but I never made it. Can anyone give me advice?


I want to change position of tufte-book(twoside) class in my thesis. In normal mode, margins for odd pages is on the right side and for evens, is on the left side of page. I want to change the position of margins. Normal: Reverse:


Are there meridians that effect cloud movement? While observing radar images of moisture bearing cloud movements (at my location in Florida), I've noticed a splitting of the cloud formations a majority of the time. It has become apparent and predictable.


Question is said in title.Suppose X is a separable topological space and S is a dense subspace of X,to prove S is separable or give a counter-example,and we may add what conditions to make this statement true?


If you have an asteroid for example and a planet, isolated from all other gravitational influence and initially at rest with respect to each other, how would you find a position vs time function for the asteroid and the planet falling toward each other?


I know this is true if F is infinite but don't know how to prove it. And is this still true if F is finite? I think The Primitive Element Theorem is the keypoint to prove this statement. Primitive Element Theorem: Let K/F be a finite extension of fields, if F(K/F) is finite, then there exists q in K such that K=F(q).


What's the most general way of obtaining the mean field theory of a microscopic Hamiltonian/action ? Is the Hubbard-Stratonovich transformation the only systematic method? If the answer is yes then what does necessitate our mean field parameter to be a Bosonic quantity ? Is the reason that all of directly physical observable quantities should commute?


Could be there material that begins melting/softening when it's temperature is lowered? I would say no, but I've seen enough physics to know that not always life is so easy. Moreover I think I've heard something about it, but can't remember a thing.


When a lamp or other luminous object is very bright, we cannot see clearly the things close to it. What we see is a whitish region that surrounds it. What do we call this? (Is it a perception or a phenomenon?) This picture features a lamp in the centre; half the image consists of the white region surrounding the lamp.


Which of the following questions are correct according to the grammar, and why? When will be the results declared? When will the results be declared? Does this hold to all future perfect tenses?


"Welcome to our store!" "We have the best hamburgers in the market which we have been cooking for generation after generation with no equal!" "The best prices around for such a complete piece of work" et cetra. Is there a good expression for such words?


How can we say Mike has an apple, and Jane has an apple in a single clause? Can I say Both Mike and Jane have an apple or Mike and Jane each have an apple? They sound fine to me but I am not sure. Is there any alternative? Each of Mike and Jane has an apple might sound too complicated.


Could you help me find the one-sided exact binomial test formula? I use this statistical test in R-language, but I can't find the formula for it. Eng Wikipedia (https://en.wikipedia.org/wiki/Binomial_test) and RLang help gives me only examples without needed math description. Thank you!


I'm using LyX and need to have the chapters to start soon after the end of the previous chapter. A LyX solution will be most appreciated. Document class report and I am not to change the document class.


I don't even know how to title my request. I am also not including any code, because I have absolutely no starting point. I'm writing a technical document and once in a while I need to put a notice/warning into the text. What I want to do is best described by seeing what I've done in Word: I'd be so grateful for any help!


I search all over the Internet for a proof of Descartes's rule of sign. Found a pdf file which has page-long proof that a high schooler has to no way to understand. Can somebody talented here give me a proof of the rule, in geometry preferably, or if impossible to be done in geometry in simple algebra or trigonometry.


I am reading a book that states the hero "knew himself to be among the dead". Does this means that he considered himself as good as dead, or that he understood that all the people around him were dead? Generally, what does "among the dead" means?


Can anyone describe to me one change to the electric field and one change to the magnetic field that MUST take place as particles gains energy in a synchrotron accelerator? This could also just be an in general question about particles gaining energy.


In Chinese, when we want to express the idea of "change A which is erroneous to B which is correct", we usually say "correct A to B"; very concise, right? But is it the proper way to express that meaning? If so, please cite a web page containing that expression; if not, present the correct way please and cite a web page too.


Water waves are dispersive ( longer wavelengths travel faster ) but sound waves in air are not, otherwise we would listen first the high frequencies and the low frequencies after. What decides if a wave will be dispersive or not? This question has been asked again. I am looking for an answer or a comment that explains the physical reasons behind the mathematics.


Most people know the classic committe style problems. I read this solution to one of the basic version of the committe problem and was impressed, but not sure why it works. I was hoping someone could explain why does it work.


Rolling implies rotation and translation. Cranking implies the motion people used to do before power windows and Sliding is what actually happens to the window. When and why did people start using the expression "roll the windows down," instead of something more descriptive?


If I form a sentence like: I could read the book if I hadn't wasted my time. Would it be considered a past perfect sentence with the part I could read the book being in simple past for context in the sentence or does it only show a possibility?


Is there a formula for generating a set of Coprime integers that every element of this set is coprime to the other elements in this set? I want to create a collection of this formulas!


I am new. I have a question about the icons in the texstudio IDE for tex: the icons in both the tool bar and in the left panel are pretty small. Is there a way to enlarge them a little bit? Thanks very much.


What is correct between "bests" & "best", when used in the context as per title. To clarify, there is no noun after this term. i.e. it's not "one of the best [XYZ]s". Example: I had been to that restaurant. It's indeed one of the best/bests (?)"


I'd like to create a new style in TikZ for nodes with transparent background, rounded corners, with labels oriented vertically on their left on a opaque fill (similar to a tabbed paper). A sample sketch is given below. The "Label" will be given to the style as parameter.


I know how to work from a chemical equation to an ODE, as described here: http://brunel.ac.uk/~cspgoop/uploads/ode_chemical_network.pdf How do I go the other way? I want to convert the Lotka-Volterra ODE system to chemical equations so I can use it in a cell simulation program.


I would like to create B-Lymphocyte picture (antigen) and i would like to know if someone could give me a start point (e.g. online examples, etc.). Here are some examples of what i would like to create: Regards


Which is the correct form when adding the -ify suffix to member? memberify membrify I know it's not a regular word, I want to use it in a context for something like "make me a member".


Are there any books specifically on collision processes between atoms and molecules and collision probability? I would like to get an overview of the factors that determine collision probability between particles, like number density, relative velocity, particle size and such.


I am in favour of compromises and I am glad that Gabriel also is. Is it okay here to end the sentence with "also is"? Is there a better/more proper way to express this?


I would like to ask a question about an abbreviation about for weighing silk and goatswool in a commercial manuscript. The abbreviation using like on the photos. Can you please help me what is the meaning of these abbreviations. Any suggestions are welcome.


If we place a small magnet between two wires carrying current in opposite direction separated by some distance r, will the magnet move or not? And if the magnet will move then in what direction will it move and how?


I am a bit lost how to proceed this integration (I got a recommendation to use substitution here) with goniometric functions in here. I know the correct result, but still can't determine it.


If I place a compass over a wire(such that the wire is positioned north-south) with charge flowing through it, and it points northeast, how can I determine the direction of the electron current flowing through the wire?


Sometimes we read books rather quickly and don't give them much (or any) thought, so the action 'reading' does not necessarily imply that we have given enough thoughts to any book we read. Is there a word that describes reading a book with great care; usually but necessarily slowly over a long period of time.


Usually a two-body nuclear problem is exactly solvable through quantum mechanics e.g. the deuteron nucleus having two particles a neutron and proton. As one goes over to three particle systems, say a triton or a neutron described as composed of three quarks, the equations get coupled. Is there a simple way out to get to calculate the ground state of three particle systems?


In this derivation is it necessary to write the triple integral, as I thought that if we are dealing with one fluid particle it only contains one "point" and hence we do not have to take a sum?


I am not understanding why gradient will show the direction in which the function value rises most quickly. It is just the vector of partial derivatives of the function. And why its magnitude will determine how fast the temperature rises in that direction.


I'm looking for a references / short book which discusses what is going on LHC collider - specific experiments, collision processes, analysis of data, how exactly the facility is operating (not professional level but for a high-energy Phd level). I would love to hear your recommendations.


How to visualise solenoidal vector field;I am thinking it as a solenoid going in a circular fashion with propagation in the z direction. I was solving a problem to check that field is solenoidal or not ?


Online resources describe a function as a correlation between domain and range values, while a sequence is just a bunch of numbers correlated with the term. Isn't this the same thing if you consider the term to be the domain and the sequence value at that term to be the range? What's the difference between a sequence and function?


I am interested in good integer approximation from below and from above for binary Log(N!). The question and the question provides only a general idea but not exact values. In other words I need integers A and B so that A <= Log(N!) <= B


I have done some integration in the past, but came across the following question: The question is simple, calculate the integral and give the final answer. I am really not sure what to do and how I fill in the infinite values. Could somebody give me some more insight in how to solve this question.


I want to use taint in a positive context, something along the lines of: I will have the opportunity to taint my life with the culture and experiences of others. What would be a better word for this purpose?


I want to use well-connected in the context of The James family was a well-connected family in ... Can someone suggest better ways to say it? I want it to mean that that particular family was well known in the area, was well respected, and had clout.


In ZF classes are used informally to resolve Russells Paradox, that is the collection of all sets that do not contain themselves does not form a set but a proper class. But doesn't the same paradox manifest itself when discussing the class of all classes that do not contain themselves?


In the latest South Park episode, I noticed a line: We have so many abandoned babies and not enough people like yourself who care. Which kinda struck me, because I'd expect it to be people like you. Is the original quote broken, or are both correct, representing a different meaning?


Is it important for a physicist to be good at math? Should he be on par with a mathematician? According to me physics and math are like English and biology we study them in the same language but they are not same.


What does "uncancellable" mean? Does it mean that something may be uncancelled, or that something may not be cancelled? [Edit:] How would one express each of those ideas? For bonus points, is there a way to be indicate that something may be not uncancelled? In-uncancellable?


Which of the following is grammatical? He had lollies be they red or blue? He had lollies be them red or blue? It seems as if it could be them as an object of be.


When I first see the following, it is the best theme that I've seen. I want to get theme like this. How can I use theme like this? Bayesian Nonparametrics Part II, Peter Orbanz


I was looking for a free PDF from which I can review MV calculus. Specifically: MV Limits, Continuity, Differentiation. Differentiation of vector and scalar fields Surface/Multiple Integrals A succinct book would be great, (coherent) course notes and presentations would do as well. I ran google searches with filetype:pdf but I couldn't find one which fits all my requirements.


Does anyone know which Latex environments that are supported in pandoc when converting Markdown to html? I have tested equation, align, alignat which seams to work, so is there e.g. a family/kind of environments that are supported, so I don't need to test by trial and error?


There are many problems involving, proving numbers are irrational or not an integer and so forth (e.g roots of polynomials, size of an angle) What are some general techniques/tricks that I can use in these types of olympiad problems?


Is there some well known and useful measures of non-linearity for functions? I know this is rather broad question (more precisely two questions), but I'm stuck with my problem and interested in all answers in hopes it will unlock my thinking process.


The nation and the world would be better off if Congress took a break from partisanship and finally debated a legal framework for the American military action .... Republican lawmakers prefer to simply blame President Obama rather than earn their paychecks.


I've noticed that during British lightning storms, I have only ever seen sheet lightning However, on holiday in other countries, I frequently see Forked Lightning Q) Is this just caused by cloud, or is it two distinct forms of lightning? Q) Is there a reason Britain only seems to get the sheet kind?


As the title states. Is there a way to insert a background picture for a beamercolorbox. I mean I can make two of them overlap or something, but can I insert a background picture somehow? Thanks.


I have seen a nice looking table of contents in a Beamer presentation. There were some formulas, pictures, graphs situated across the frame in a shadow background. Any idea how to do this?


? She cracked an egg into the frying pan. In this sentence, should cracked be replaced with broke? I take that to crack means to break, but without causing a complete separation of the parts. The windshield of this car was cracked.


I have two magnetic bars and when they are brought close sideway the two bars join where the two South poles are adjacent to each other, and so does the two North poles. If the magnetic field goes from South to North and repel when is the same pole, why doesn't the magnetic bar rotate and align itself to NSNS?


What is the difference between a) By then, you will have shown what you meant to do since the beginning. b) By then, you will show what you meant to do since the beginning.(Is this grammatically correct at all?) Thank you.


I m writing one article in which i need to write a paragraph full of medical terms. How can i wrap a text in a line without using line break (or hyphen)? Regards


I am having trouble coming up with a noun that is almost like an Easter egg. Is there any word that could be something someone intentionally leaves for another person to find at a later time?


There are commercial software that create the look of an analog page flipping effect from a PDF document. Is there a similar animation in TeX? (Not to be confused with flippdf package which gives a mirror image for printing machines.)


I am uncertain on how to approach this proof. For most everything I've encountered concerning symmetry, it has involved taking the transpose in order to show some property. Here, I'm not certain if and how that would be effective.


In a cylindrical chamber with a high diameter-to-height ratio; a fluid is tangentially injected. there is an axial exit to the cylinder. how do I determine if the vortex so formed is laminar or turbulent? what parameter will indicate this? (this is a simulation; so I can measure whichever velocity/turbulent KE that is needed.)


Can of course be used in technical writing? I heard that it is used typically in informal writing. I am not sure though. For example, The existing scheduling techniques work well on a mix of single threaded workloads where half of the threads are memory-intensive and half are CPU-intensive. Of course, these are not designed for scheduling multithreaded programs.


If airport security scanners of any kind (xray, thermal, whatever else they use) looked at two items: A printed paper textbook The same printed paper textbook into which we have inserted a regular folded US letter-sized paper with something written on it with a pencil, pen, marker, etc. Could the security be able to detect the difference between the two?


Two diagonal matrices each other's entries rearranged (same eigenvalues and multiplicities), are they similar? This seems like such a simple question, but I can't quite see a connection. I want to say that the two diagonal matrices can commute with each other, and this gives us the algebraic edge to show their similarity, but I'm generally bad with abstract algebra proofs.


If a group is finitely generated, then it is a quotient of the free group on the set of generators. Further if a subgroup of a group has some finite presentation, does it mean that it is normal, intuitively a presentation corresponds to idenitifying certain element (or words), so it might be in some sense a quotient, and therefore normal. Is this right?


I look for an advanced linear algebra (A complete book but wich deals indiferently with infinite/finite vector space). To give an idea i expect a book that (for exemple) would prove the existence of a base in any vector space by Zorn Lemma. Thanks PS: I found Bourbaki's book but the level is quite hard


Is the following conjecture true ? I am trying to collect some properties about box topology and product topology in order to study for topology exam. is the product of connected compact space connected in the box topology?


I don't know whether a semicolon or a comma should be used. For example: Now that GoT is done for the season what will James complain about besides Disney movies?Find out on a new episode of Off Time Radio; if he ever texts me back.


The designer prefers using mathptmx font for the book, but I really dislike its greek characters. They are larger and bolder than non-greek characters. Do you have any suggestion how to please both the designer and myself? :-) Maybe you could suggest another font that looks like Times (New) Roman and does not have this "problem" with greek characters'? Math support is essential.


When diagramming the sentence, "Simon, would you please sing now?", should I diagram Simon or you as the subject? Would you be diagrammed as pronoun and please as an interjection? I am trying to help my son diagram real-life sentences and am getting stuck myself.


I wanna ask why sequence is important in general topology. As far as i know, many theorem can be proved without using sequence. Does sequence make some proof easier than other way? or is there any other reason? If yes, can you give some example for references?


Similar to the Newton Raphson algorithm that has a (global) convergence property when we minimize a (strictly) convex function over Euclidean space (based on the second order Taylor serise expansion with a geometric or any other property), can we say that it also has a convergence property by replacing Euclidean space with a convex cone?


How can you add vertical space between the word "Proof" and the actual start of the proof? This question shows how to start the proof on a new line, but I can't add space properly.


I've heard that the cat which there may not be enough room to swing actually refers to a type of whip. Is that true? What is the actual origin of the phrase not/barely enough room to swing a cat?


I am digitizing a book and there is only a single page which has page border as shown in the attached image. How can I create border to a single page? Is there a library where I can choose a border from?


Is the Riemann sphere anything more than a simple visual tool to help students understand the complex planes, or the behavior of complex valued functions at infinity, limit points etc? Or is there a practical use in calculations of complex valued functions using the topology or geometry of the the sphere itself?


What are the conditions to be met by a LP that allows to infer that its optimum solution will be integral? Is total unimodularity a necessary and/or sufficient condition? What if all variables are binary?


I recently used a sentence similar to the following: Curiously, do you prefer black? Some people found it grammatically incorrect. That was a surprise, for I thought it was perfectly okay. Someone even came with an alternative: Out of curiosity, do you prefer black? Is the second sentence actually better? Is there a real difference (bar the number of characters)?


I have seen many popular accounts of simple magic squares but I would like to find a proper mathematical background to understanding magic squares. What background knowledge do I need. I am a retired senior school maths teacher.


The condition to get an interference pattern we must need coherent sources. After superposition, they produce interference. If we select a random photon in the superposition states, can I know the source it came from?


When there is a phrase like "the page of the book," is it correct to put both the in the sentence? What are the rules in general? What if we had more OF in the sentence? e.g. "the room of the department of the organization"


Is hydrostatic pressure independent of temperature? Why only the weight of overlaying liquid is taken into account for calculating hydrostatic pressure and not the collision forces due to temperature? In space (if temperature is not zero),will the liquid pressure on walls be zero?


Does anyone know how to make relatively simple diagrams like the images below? Is there a some sort of "template" I could use perhaps? I'd like to code my Calculus notes but I'm not sure how to make the diagrams. It's Left approximation, right approximation, and middle approximation, respectively. Alas...


I am looking for a singular word that categorizes this set of words: {forewords, preface, prologue, chapter, author's note, etc} The best I can come up with right now is Section Heading which is obviously not one word.


I am using latex editor LyX. I write a book with many authors. I want to list each author name in each chapter in table of content. How can I list author name in table of content?


That chair was very sturdy, or so I thought. "Or so I thought" means the previous phrase is wrong after a while of consideration. (or something similar) Is there any term/words that can replace "or so I thought" in the same/similar context? (Rephrasing is fine, but not just purely replacing the words, ie. "or so I presumed")


I sent my CV to get a job into one company. But they rejected it. The reason was: "Please do not send your CV without a cover note." English is not my native language and it is hard for me to understand what cover note means. What is it?


There are several question in this site comparing different basis functions including Schauder basis and others, but I could not connect the difference between the Schauder basis and Eigenbasis clearly. Would someone please point the best way to contrast between the two?


What is a word or concept that describes a situation where one person puts forth a point of view, and another person does not directly address the position, but instead responds with an obvious, basic fact whose implications cast doubt on the correctness or strength of the point of view? This is intended to belittle the point of view.


We recently had a discussion whether "Pay for play" or "Play for pay" is the correct term to describe that you get money when you play. Which one is correct to point out that you get paid for playing?


is there any function whose zero is singular point of function ? i.e. construct a complex valued function such that there is zero of function at which it fails to be analytic f: D to C is a function where D is subset of C


Graduation day is coming; when trying to send a card to a friend I have a difficulty to decide which preposition to use in this simple phrase. "Good luck with/in/on your journey!" My first thought is to use "on". However; a google search shows the three prepositions are often used. Thanks!


I want to understand the proof of how to estimate variance from the Normal distr, using the method of moments. It boils down to simple algebra. I can't understand why I tried to prove it like this but get an error in the end.


I'm writing a text and am confused about a word I knew before. The definition is : to Take away the property of someone (by government or bank or a legal institution). I have found seize or take over, but I know there is better word for it which I had used in my translations before. Can any one suggest a better word?


In describing electron states in hydrogen, we have a very "simple" picture, at least in intro-quantum. But this only has one electron! As we permit more electrons, we also have things like the exclusion principle, which comes from the spin-statistics theorem, but that relies on the electrons having some kind of coupled wave functions, right? Why do electrons always come in pairs?


We assume that distribution of electrons follows Fermi-Dirac distribution / statistics in semiconductor model which will help to find the concentrations of electron and holes and the relationship between them. Why is it that we use this distribution? Why in particular is this distribution used in such models?


What is the literary device used for the following quote from The Fellowship of the Ring : By light of moon and ray of star I think that it is an idiom.... I may be wrong!


I have a URL in my bibliography which line-breaks in an unpleasant way. The URL breaks as follows: http://www.mathworks.se/help/matlab/matlab_oop/(break) implementing-operators-for-your-class.html I want to allow breaks at "-" so that the URL would look something like: http://www.mathworks.se/help/matlab/matlab_oop/implementing-operators-(break) for-your-class.html I'm using a customized plainnat.bst file in order to get surnames first if that makes some difference.


After conferring with each other concerning the foregoing matters, if the parties do not reach an agreement upon any such matter, Petitioner shall have the descretion to make the decision and the provision hereinafter set forth concerning resolution of disputes shall not apply to her decision.


Right now I am taking an algorithms class. However my university does not provide a discrete math course. To make matters a little rougher, proofs and induction had barely been touched by any of my computer science courses. If possible, could you provide a few links to learn this concept from?


What is the coefficient of mass gained/lost by a star in its first phase transitioning into a blackhole. Does the blackhole have more or less mass than the star it was made from? Thank you Regards


How is Base emitter junction and collector emitter junction biased? How do we determine the value of potential difference between emitter and collector required to be maintained in order to determine input characteristic of transistor? Explanations covering nitty gritty are most welcome.


AFAIK the limit of a term does not exist if that term does not converge, but I haven't found a suiting question here yet. This probably is a double of a similar question.


Kuvio (Finnish for 'pattern') seems to be a very general tool for diagram making. Which are the major disadvantages? Why isn't it used more often (only one Q/A on the site seems to mention it)? Can it be used in papers sent to mathematical journals? About Kuvio and other packages on diagrams


"Do you think the children enjoyed their meal?" As you can see, this question started with the "Present Tense's auxiliary verb" which was "Do". Why can we still use Past Tense's verb (enjoyed) then? By the way, I'm a newbie. Named "David"


from the Wapshot Chronicle by John Cheever: For with his maturity, Moses had found in himself a taste for the grain and hair of life. The context doesn't really help so much in understanding.


I have the following sentence: I am a developer, thinker, and a strong advocate on micro-services, architecture and development of blah blah I am a strong advocate ON Or should it be: I am a strong advocate OF


How can we use a reduction to prove non membership of a class. Can we say if A is reducible to B they are in same class or if we can't reduce A to B. B is not same class as A. Regards,


We know that magnetic field arises due to relative velocity of charged particle . Electrons in wire move at very slow drift velocity but relativistic variation of magnetic field doesn't seem to apply on them because if observer also travels with drift velocity , magnetic forces on wire should vanish if its in external magnetic field but it doesn't ?


According to my teacher, an electron is point sized and it does not absorb or release energy. Moreover, my teacher says their orbital absorbs energy rather than the electron. If that is the case, then what about the photoelectric effect, in which electrons release energy after excitement?


A closed group in Facebook bash me for asking them if there's such word as "UNSWAPPING" I reached Google and Dictionaries of which I failed to find this word. Yes, there's an adjective "unswapped" but I never found "UNSWAPPING" please help me. I want to know the precise answer. Thank you!


I am writing my master's thesis now, and I got a small question on the two terms in the title. You probably noticed, my English sucks... I have a sentence like: "this model is needed", but I want to change the to sentence to "this model is in need". Is that correct?


Electromagnetic induction sounds quite analogous to inertia to me. Just like inertia it opposes the 'change'. So is this phenomenon has something to do with what we call inertia for macroscopic objects. And do electron has some inertia like property to create this phenomenon.


Take a video camera and crank up the frames per second rate. Disregarding current technological advancements, could a camera's FPS go so fast that any two captured images be identical? Would accomplishing this defy "time"?


It is tempting to switch to unicode-math. But there is (at least) one point that I still don't like. That are the double stroke characters. They look simply terrible in XITS Math. Just compare: with Are there any better options with unicode-math? At least they should be serif!


I have several full names in my rather large bibiography. Since I do not want to change all these I'd like to have the forename shortened to an initial. So "Lieschen Mueller" should get "Mueller L.". I use the standard authoryear style.


I'm trying to write a paper about US Invasion in Iraq is unjust morally, militarily, and legally. I can't think of words to explain when I'm trying to explain that I have moral "evidence" or ideas from the book that will help to support my moral argument. It is technically not evidence, but what word should I use to accurately explain it like evidence?


Often I read about "under-appreciated" books. Being an author myself, I am putting together my resume in English and I am unsure what word to use to describe a book that has had positive reviews and apparently was sucessful. Should I say "appreciated book dealing with.."? Also do I need to use articles? Title of the book (An) appreciated book dealing ..


Possible Duplicates: What is the correct possessive for nouns ending in s? Pronouncing possessive words that already end in s How do I pronounce possessives that end with the awkward "s's" and "'s"? Examples: I found the mistress's attitude ridiculous These are the eggs' shells. Which coat is Amos'?


Suppose in this moment the universe stopped expanding, how long would if take and how would we register the change? Since the bodies are still and it is space that is expanding in between, we wouldn't notice the change even if the expansion would completely stop in a short time?


I want to extend the implementations of the examples here to represent graphs with vertices simply represented as text as shown in the figure . I wasn't able to find similar templates/examples in the tikz manual. Could someone point me to a MWE?


A nurse is telling: There was a girl who was driving inside a tunnel and something just fell on her car and she died. That messes me up more than thinking about patients who are sick. I have a hard time understanding what is the meaning of the phrasal verb in the context.


I have Ellipse's center-points, minor-radius and major-radius. I can find, how to check if given point(x, y) exists in Ellipse or not. Now, I want to find given point(x,y) exists at which angle in Ellipse. Thanks in advance Vikram


If we have a solid conducting sphere with charges around it, then the electric field inside the sphere is zero, otherwise the electrons of the sphere would not be in equilibrium as there would be a net force acting on it. However, if its a hollow sphere, then why does the electric field inside the hollow sphere have to be zero?


In this sentence: "We would also accept an international transfer, but in that case we would ask you to pay your bank's charges at the time of the instruction to ensure that we received the full amount" is it correct to use "received" or should it be in present tense?


When must an edge for a connected simple graph appear in every spanning tree for this graph? I would have thought it was the midpoint of the longest simple path in the graph. However, there would then be another way to connect the graph, so location of vertices doesn't matter.


I'm editing a post that has the sentence: How much larger should it be to be secure? I've come across other situations where there are repetitions in a sentence (such as that that) and am hoping for a word to describe this occurrence and a generalized approach to rethink it so the sentence becomes clearer.


A question for "real" mathematicians who have become better acculturated to math-speak than this philosopher! If you read a phrase like ... the natural numbers equipped with the evens-before-odds order ... just what do you understand by equipped? [I have my suspicions, of course, but I won't prejudice the comments/answers by saying ...!]


I can't get this right, but I'm not sure which is the correct statement: We do not tolerate against pornography images. or is it We do not tolerate with pornography images. Which is the correct way of not agreeing with pornography images?


I approached this exam question the wrong way apparently, help please? Consider the word "mathematics". In how many ways can you rearrange all the letters so that the vowels are paired and always apart?


My desktop background rotates through a bunch of space and nature scenes, and this one came up. What would be the effect on people walking around down here, if another earth was looming overhead instead of our moon.


I have attempting to solve this using the infinite ramsey theorem, with colouring based on whether the sum of two vertices has an even or odd number of distinct prime factors. This is leading to an infinite recursion. Is this ok? At the end of all time I will be done.


Can we prove or disprove that : There exists for any given closed figure, a point which is equidistant from all of its vertices? Any closed figure means literally any closed figure? I am gonna instinctively say no, but How!?


The mainland counties of England form a graph with counties as vertices and edges as touching borders. Is there a Hamiltonian path one can take? This is not homework, I just have an idea for a holiday around England where I visit every county only once!


Say I have a laser. If I spin the laser so that the beam sweeps in an arc along a very distant object, could that dot travel faster than the speed of light? In Diagram form:


Question is as clear as stated in title. What is the maximum energy that can be stored in a gluon field flux tube without production of an quark anti-quark pair? And how much it usually store in a meson?


It would be [adjective] to dismiss president's new policy, as purely politic playing, it appears he has genuine intentions to improve the well being of the poor. What adjective would be correct to mean that things were dismissed too quickly?


This is a question just out of interest to know the power of integration by parts. There are various level of integration by parts. What are some of the most general form of integration by parts? I have encountered it very often in PDE's. I look forward to gaining more insights on it. Thank you for your ideas, help and discussions.


Is there any undergraduate textbook on graph theory using linear algebra? A request is a beginning with graph matrices that explain most concepts in graph theory? P.s. This thread has more specific requests than this thread What are good books to learn graph theory?.


Is there a package to produce syntax-colored blocks of source code in plain TeX ? A listings equivalent ? Or (maybe) some macro to produce a colored tex input for some given source code ? Is it possible to achieve something through LuaTeX ?


I am looking for a correct expression for an activity when a person is injured or in a bad leath condition for any reason and is doing special exercises to feel better. Is it reeducate? Rehabilitate? Vindicate? Thank you.


Is there a rule, which states that one must or must not use comma before "then" in a sentence like this: If you can read this, then you might want to answer this question.


I use the method described in this link for getting hyperlinks from different PDF files: Can you have hyperlinks to locations in different PDFs? I would like to remain with two open PDF files, source and destination. When I use the described method, the source PDF is replaced by the target PDF. Can I control how to display the PDF files?


are there any concrete rules that say wich words(parts of speech) in a title should start with a capital ? what would be a correct capitalization for the title of this question ?


He is not satisfied with her praise. He is rather satisfied with my praise. I am sure this "rather" modifies "with my praise." But the position of it doesn't have to be in front of "with?" Like only, as in "You only clean your room when it gets helplessly untidy."


I think there must be a good word for this, but can't think of what it might be. Harmony and Melody are pieces of it, beat seems simplistic, Instrumentation seems too scientific and dull. Any Ideas?


I know that you can construct a square root of a given segment through a certain construction, and I know that construction. What is the proof that this construction works to construct a square root?


What is the meaning and the accurate use of the word "Aura"? Does it mean literally " Atmosphere"? consider this example: " Heavy snow,, thunders... strong wind. What a lovely aura! " P.S: I meant by aura not the weather itself but the general atmosphere around me that i feel at that moment.. My feeling. Thanks in advance!


What are the different kinds of relations one can obtain between the elements of a finite Geometric progression other than the fact that one element upon the previous element gives the common ratio?


I would like to ask this question; A word that is used to describe someone who is very kind and likes most to help other people with their problems? (I need both a noun and an adjective; if they are all applied)


I liked the bar of the first answer in this question: Progress bar for latex-beamer so my question is if there is a way to put this progress bar in the right/left side of the slides. Thanks.


What is the type (adjective, noun, etc.) of the word atom in hydrogen atom? I think that atom here does not qualify hydrogen in any way and we can use it or not, and the meaning of the word hydrogen will not change. So, hydrogen atom and hydrogen are equivalent.


I use LyX. When I use the "Title" environment under article(hebrew), it uses very big spacings between it and the rest of the document. How do I control the spacing and make it use a compact title so my resume will all fit in one page?


I need to reply to an email and I wanted to clarify to the other person that: I understand exactly what needs to be done on the technical side but I'm not familiarized with the red tape involved in the process. Would that be, somehow, offensive?


If C is a collection of connected subsets of M, all having a point in common, prove that union of C is connected. I know a set is connected if it is not disconnected. Also, from the above, I know the intersection of all subsets C is nonempty. I am not sure where to go from there.


When two words are put together as in "heads up", "put down", "build out"... are they considered a phrase? And if so, do the term for these are "adjectival phrases" as they mention on this question: Is "put together" an adjectival phrase?.


Which is better? The protocol was signed last week after all punch list items were fixed up. or The protocol was signed last week after all punch list items had been fixed up.


I am using white colored font on black page and somehow I am losing my page numbers. I suppose the page number is still in black color. So How do we set the color of page number? And while on the topic, how about color of page runners etc.


I need sections included in the TOC, but not in the body text for a PDF output; so when I click the section at TOC, it will jump to the related page [where section header/title is not displayed]. How do I do this?


Is there any approach or mathematical formula using which we can predict the interarrival times for a Poisson distribution (not the expected interarrival time as it comes out to be same dependent only the rate parameter) ? Do we need require to know the probability distribution for finding the time interval for a a particular number of events to occur ?


Many resources state that light skin/pale skin absorbs more UV than dark-colour skin. Doesn't black absorb maximum radiation? For an example, see this article: Natural selection therefore favored a genetic solution to that problem by evolving to a pale skin that absorbs UV more efficiently.


You have a large house. Negative question= Don't you have a large house? Saying ''Haven't you a large house?'' is wrong am i correct? But is ''Haven't you got a large house?'' correct or wrong?


I found that net charge density in the interior of a conductor is zero.The charge resides only on the surface.Then can we say that there is no volume charge density of any uniformly charge conductor?


I will provide definitions for which I can't think of the word: as though not trying one's best having the appearance of little effort The word is used to describe something that you look at and think, "They're not really trying." I remember thinking this is a good vocab word, and darn it, I forgot it. This has been driving me crazy all day.


Now, shadows dawn as the twilight comes. Dawn has the meaning "come into existence". Does it work that way almost every time with words like, for example, shadows? Or, are there quite limited types of word that can be used with dawn? And, the sentence above, does it sound awkward to you?


Can a virtual image created by a concave lens create any image by the convex lens oriented parallel (at the same direction of refracted rays of the concave one) with the concave one? If not, can any other orientation of the convex lens can do the work? What is the effectiveness of a high powered convex lens to do the stuff?


Is it correct to say: At the time, circumstances arose such that I had to leave the city. in the meaning that situation got such that the speaker could not stay in the city anymore? Particularly, I am curious if one can say arise about circumstances or situation.


When I walked on the road, I happened to pass a pool of mud. Somebody had already set some blocks of stones and bricks on the mud from one end to other end in order to pass it. I could pass it by treading on the blocks of stones. What do you call such a temporary arrangement to walk on?


I recently encountered: vernal adj. of, in, or appropriate to spring And I truly wonder if there is also equivalents for the other seasons (summer, autumn, and winter). EDIT: I just found aestival n. relating to summer. Please feel free to contribute words that have the similar/same meaning to spring and summer even though I have found those.


What does the prefix atta mean? What is it trying to abbreviate? What a? Wiktionary claims that it stands for that's a or that's the, but I do not see the resemblance to atta.


On Wikipedia, I read, "A box can be thought of 'small boxes' infinitely repeating in all three dimensional directions" I don't understand what does Wikipedia wants to say with a box containing infinite numbers of similar small boxes. Why would it be infinite. I can have any integer however. Can any one explain it to me?


What actually elementary proof means ? If there is an elementary proof for a conjecture , then is it a theorem ? I saw papers on some conjectures proving stating as elementary proof. Then it means the conjecture is proved ? Is there any site that correctly tells about status of a conjecture ? thanks in advance .


I remember that there was one technique of English writing that writes down every single word what one thinks. I forgot what this type of writing is called, does anyone knows the word? "umm, I think yesterday was raining, eh.. but oh wait, no, It's incorrect. It was cloudy......."


I see commutivity used in contexts where the meaning appears to be the same as commutativity. Here are an example from physics and another example. Is commutivity incorrect? Does it differ from commutativity?


I have to take a talk of an hour and I have to talk about blow-up of toric varieties. Can you suggest me some interesting examples that I can present? How can I find a good reference for the theory needed? I'd like to do a talk rich of images and interesting examples. Thank you!


In case of identical particles we multiply the individual wave functions of the particles to get the system wave funtion. But why are we not adding? Or performing any other operation to get the system wave function. Can anyone show the math that what physics will be violated if i simply add the individual particle's wave function?


I found this phrase in The Adventures of Sherlock Holmes book; this is the full paragraph, with my emphasis: You will remember that I remarked the other day, just before we went into the very simple problem presented by Miss Mary Sutherland, that for strange effects and extraordinary combinations we must go to life itself, which is always far more daring than any effort of the imagination. Does it mean something like "more daring than we thought"?


Here's the quote (from The Tragedy of Macbeth, by William Shakespeare): This supernatural soliciting Cannot be ill, cannot be good. If ill, Why hath it given me earnest of success, Commencing in a truth? I am thane of Cawdor. If good, why do I yield to that suggestion Whose horrid image doth unfix my hair And make my seated heart knock at my ribs, Against the use of nature? The connotations may have changed since it was written, but doesn't the word "seated" evoke the image of the object under discussion being, to all intents, still? As in pretty much motionless? What am I missing?


Google defines paradox in three ways, the first two being: a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory. a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true. These are almost opposite definitions. My English book defined it as the second, but I've always understood it to mean the first. Which is the most common usage?


What happens to the energy when waves completely cancel each other out via destructive interference? It seems like the energy just disappears, but that would violate the law of energy conservation. My guess is that the kinetic energy is transformed into potential energy. Or maybe what happens to the energy depends on the specific interference scenario? Can someone elaborate on that or correct me if I'm wrong?


I'm studying Complex Analysis and everything up to this point has been pretty straightforward to visualise, but I can't get my head around residues, especially as they seem to have two very different definitions (as a Laurent series coefficient and as an expression involving an integral on a closed path) that I can't understand why they equate. Can anyone give a fairly simple explanation of residues? Thanks!


A paracompact space is a space in which every open cover has a locally finite refinement. A compact space is a space in which every open cover has a finite subcover. Why must the product of a compact and a paracompact space be paracompact? I really have very little intuition about how to go about this question, so any hints or a proof would be greatly appreciated.


Is there a word that is similar to "marketing" that doesn't imply the idea of commercialization or profit? For example, a non-profit that assists domestic abuse victims may run a campaign where they advertise their services. They may put up posters, buy billboard space, and so forth. While this is marketing, people in that industry may be very reluctant to call it a "marketing campaign". This is because marketing tends to carry the connotation of trying to sell something. Is there a more neutral word?


I'm currently working on an English project and I have chosen to rewrite a story (Heart of Darkness by Joseph Conrad) in a biblical, King James style. I have done a large amount of reading but I do sometimes get confused, especially on certain sentence structures. Do you have any tips on grammar, vocabulary, or sentence structure that will help me make my writing seem more authentic?


Can someone please explain why the van der Waals force is attractive instead of repulsive? My understanding is that is has to do with the electron cloud creating a dipole, but I can't seem to understand why the force isn't repulsive (since like charges repel.) Since the electron cloud is moving, I would think it would cause a force that is attractive sometimes and repulsive sometimes, with the average effect being more repulsive. Obviously I am missing something!


I'm really sorry if this question has been asked before, I looked but couldn't find anything. I'm going through an elementary number theory book and in the first chapter it introduces the least integer principle. There is no proof accompanied with it, it just states: "a nonempty set of integers that is bounded below contains a smallest element." Is the reason the book doesn't give a proof because we take this as an axiom? Or is the proof so trivial that it need not be written? Thanks!


I've been reading a Real Analysis textbook that my friend loaned to me. I have come across a proposition that says that a totally bounded set is bounded, but a bounded set is not always totally bounded. This makes sense, however I am having trouble thinking of an example of a set that is bounded but not totally bounded. Could anyone shed some light on this? Thanks!


I am working on some optimization problems, and I am aware of the method of proving that the "angle of incidence equals the angle of reflection" using Fermat's principle and calculus. However, my textbook suggests that there is a simple way to prove this without calculus, but I'm a little unsure about how to do this. I would appreciate any advice on how to proceed.


Here are the definitions of the two words: Hypocrisy: the practice of claiming to have moral standards or beliefs to which one's own behavior does not conform; pretense. Affectation: behavior, speech, or writing that is artificial and designed to impress. However, I'm not sure about the difference between the usage/connotation of these two words? Is there any example where you would use hypocrisy instead of affectation or the other way round?


Wikipedia says: In particle physics, supersymmetry (often abbreviated SUSY) is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners. In a theory with unbroken supersymmetry, for every type of boson there exists a corresponding type of fermion with the same mass and internal quantum numbers (other than spin), and vice-versa. There is only indirect evidence for the existence of supersymmetry [...] I want a mathematical explanation of SUSY.


I know that when I'm solving a linear equation of the form ax = b (mod n), the gcd(a,n) tells me how many solutions there are. I don't really understand why this is. More than a proof, I'm interested in an explanation that will help me understand the relation between the gcd and number of solutions. Also, why does the gcd need to divide b for there to exist solutions? Thanks


I'm trying to wrap my head around function spaces. I get that you can define the inner product as the integral the multiplication of two functions over the entire domain because it satisfies the properties of the inner product. What I don't understand is what makes this a complete space? I don't understand the concept how a complete space works with functions. Any insight would be appreciated.


When is it appropriate to use the terms Dear Sir or Madam and To whom it may concern? The rules I was taught state that Dear Sir or Madam should be used when you're writing a letter to a person about something that person has direct involvement in (e.g. returning a defective product to a customer service department). By the same rules, To whom it may concern would be used for situations in which the recipient is a third party to the topic of the letter (e.g. regarding a letter of reference or recommendation). Was I taught correctly? Is the rule actually something else? Or is this one of those situations where many people have an opinion but there is no real rule?


I've been trying to determine an explanation for the falsity of a logical statement for some time now and I've had no luck in figuring out exactly how to go about it. The statement in question goes as follows: Explain why the statement for any integers a, b, c, if ab = ac, then b = c is false. Perhaps I'm misunderstanding the way to determine the falsity of a logical statement? Any help is appreciated.


What is the difference between positive definite kernels and positive definite functions? As I understand it, a positive definite kernel is a positive definite function if it is translation invariant. Is this correct? If not, what is the actual relationship between these concepts? I'm reading Learning with Kernels and using this text, Wikipedia, and Google, haven't been able to find a good answer to this question. References are appreciated!


Often, I'll be driving down the road on a summer day, and as I look ahead toward the horizon, I notice that the road looks like there's a puddle of water on it, or that it was somehow wet. Of course, as I get closer, the effect disappears. I know that it is some kind of atmospheric effect. What is it called, and how does it work?


Just as there is a difference in meaning between "likely" and "liable" in terms of a desirable or undesirable outcome, is there any subtle diference between "apt" and "likely" ? Does the use of "apt to" and "likely to" in the following sentences convey the same degree of expectation ? "John is apt to call on us on Wednesday afternoon." "John is likely to call on us on Wednesday afternoon." My dog is apt to run away if I don't close the gate. My dog is likely to run away if I don't close the gate.


I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect. As I found them very interesting, I would appreciate if anyone could provide me with some good sources(books, internet links etc) to learn more about them. Please keep in mind that I am only an undergraduate student, so difficult graduate stuff might not be of very use to me.


I'm currently learning about local extrema in serveral variables and have come across the second derivative test for classifying critical points of multivariable functions. I have read and understood the test (see link below), however I don't understand the idea behind it. Why is the critical point of a function a minimum if the eigenvalues of the Hessian matrix are all positive? I understand the idea behind the single variable case, however I am confused about the role of eigenvalues in the case of several variables. http://en.wikipedia.org/wiki/Second_partial_derivative_test Any insight into this would be much appreciated. Thanks.


Wikipedia's page for Imperial Units does not list Fahrenheit. The corresponding page for SI Units lists Kelvin as an SI unit, and Celsius as a derived SI unit. This leads me to believe that Fahrenheit does not belong to the Imperial System. Fahrenheit is listed as a page belonging to the Imperial Units category, also on Wikipedia. I know that the US mostly uses the Imperial system and also uses Fahrenheit for temperature. Meanwhile, the UK mostly uses the metric system and also uses Celsius for temperature. Is this just a coincidence, or is Fahrenheit actually a part of the Imperial system?


I'd like to use "digitally challenged" to refer to someone who is missing part or all of a finger, but it sounds like I'm talking about someone who doesn't know how to use computers. Are there any phrases, ideally somewhat humorous in nature, that I can use to refer to people who are missing part or all of a finger? Example usage: Steer clear of that izakaya. I've heard some of the patrons are [alternative to "digitally challenged"].


I'm preparing some marketing materials for my boss, and one section contains the phrase "Here are a few examples:". The list that follows contains two items, which strikes me as being incorrect, though I can't find much evidence of this. Is it semantically correct to refer to two items as "a few"? Is there a solid rule for this, or is it just personal preference? Edit - As Armen correctly pointed out, this question is about semantics rather than grammar. I changed my phrasing to reflect this.


At the moment I am following a course on variational methods for mathematicians. Last week we derived the Euler-Lagrange equations for a functional under a constraint. In this derivation we found that the Lagrange multiplier may depend on time. However, I could not remember having ever seen an example of a Lagrange multiplier dependent on time during my physics courses. Does anyone have a nice (mechanical) example?


I know that it is technically impossible to reach the speed of light in vacuum since the mass of the object travelling would reach infinity. However in a medium, would there be some sort of theoretical equivalent to a sonic boom that would occur? Since sonic booms are formed when sound waves can't catch up with an object, could the same happen with light waves? Would it look like an immense burst of light in the sky?


I'm writing an essay for medical school applications. Both my parents were physicians, so it is what I was familiar with growing up. Instead of pursuing medicine in college, I decided to pursue something else and try a few different careers after college. Now I'm back on the medicine path and I'm trying to explain why I needed to try other stuff first. I'm hesitant to use the word "comfort zone" because I think it implies that medicine would be the comfortable (i.e., easy) path, when that is not the case. Any other phrases come to mind that explain this sentiment?


I have been learning more about Hilbert spaces in an effort to better understand quantum mechanics. Most of the properties of Hilbert spaces seem useful (e.g. vector space, inner product, complex numbers, etc), but I don't understand why we need the inner product space to form a complete metric space. My Questions: Why do we need the inner product space to form a metric space? Why does it have to be a complete metric space?


I've been studying random walks as part of a finance course and I'm starting to become really interested, and I'd like to start a study of them from a mathematics (i.e. more formal/rigorous) point of view. However, my knowledge of mathematics is quite limited (calculus, basic linear algebra and probability, a bit of (stochastic) differential equations). So I was wondering what fields I need to familiarise myself with before I can effectively study random walks. Maybe there's even a good self-contained book on random walks for beginners?


In Mendelson's book ("Introduction to mathematical logic") he defines truth values for sentences in the propositional calculus using truth tables. However, it seems to me he assumes implicitly that every well-formed sentence (what he calls "statement form") has a unique parsing; i.e. it is impossible for the same statement form to arise in two different ways. This is of course correct, but it requires a proof. The omission of such proof (or even mentioning it is needed) is somewhat surprising for me as Mendelson's book is otherwise very explicit about everything. Am I missing something?


I have been trying to work this problem out for a bit and am stuck. Does anybody have any ideas how to proceed or solve this? I think this has something to do with rings and fields but I can't seem to find the connection. EDIT: I know the other proof listed as a duplicate here, but it uses Cauchy's Theorem and we are not allowed to use that because we skipped that chapter.


Does it sound right to say "be successful" instead of "good luck" as a quick reply? For instance: A : I have a tough exam tomorrow. B : I hope you'll be successful in your exam. I suppose using "be successful" as a part of a sentence sounds right, but isn't it kind of awkward or unnatural to say "be successful" as a short reply instead of "good luck"?


Apologies if this question has been posted somewhere else, but I have not managed to find an answer that works for me. I am trying to create a bibliography using Harvard style, using BibDesk to create the .bib file, and Biber and BibLatex. However, the bibliography contains the DOI, the URL, the ISSN, a further e-print URL - all things I do not want. My question is: is there a way to delete these fields in BibDesk, so that they are absent in the .bib file?


I came across this problem in my textbook, and I don't understand why the answer is 'as' and not 'that'. "We are attracted to people who have a sense of humor, who can laugh at the same things ____ we laugh at." In the sentence above, the word that goes in the blank is 'as' according to the textbook. Could someone explain why? Thank you in advance.


I want to apply the Biot-Savart law to calculate the magnetic field at a point created by current flowing through a square/rectangular conductor. More specifically, a trace on a printed circuit board. To me, a trace on a circuit board is the summation of many infinitesimal rectangular conductors. I have seen lots of examples for a wire (circular conductor), but not rectangular. How should I go about getting started with this problem?


I just came across the following sentence in the book "The theory of everything": If one keeps traveling in a certain direction on the surface of the Earth, one never comes up against an impassable barrier or falls over the edge, but eventually comes back to where one started. Using multiple "one"s repeatedly in a sentence sounds odd to me. Since I found it in a reputable book, I am wondering whether it sounds good to the ears of a native English speaker. Wouldn't it be better to replace the second and third "one" with "he", "she" or "they"?


Definition: dilemma a situation in which a difficult choice has to be made between two or more alternatives, especially ones that are equally undesirable. a difficult situation or problem. Source: Google. Example sentence: The dilemma of modern life: trying to find an outlet outside of your house. I guess this sentence fits the second definition. So is it correct? (Or should I use another word instead?)


When someone has unreasonable expectations and feels that he is owed by others, this trait is described as a "sense of entitlement". But how do you refer to the person who has this trait other than calling him "a person with a sense of entitlement"? If there is no single word to describe this kind of character, can you suggest a few equivalent phrases for "a person with a sense of entitlement"?


Let's say I want to describe a habit in the past (something that happened many times over and over again) in the form of a conditional statement. Is the following sentence grammatically correct? If I forgot to do my homework, I would pretend the dog ate it. Or is it If I had forgotten to do my homework, I would pretend the dog ate it. Or is there another, more correct form?


I have been trying to understand the notion of parallel transport and covariant derivative. I am unable to see why the change in a vector when it is parallel transported from one point to another shouldn't be a vector. If it is, why isn't the Levi-Cevita connection not a tensor ? Hence my questions are : What is a connection geometrically ? What is parallel transport in a particular coordinate system geometrically ?


I need some help with the following question: In the game of "odd man out" each player tosses a fair coin. If all the coins turn up the same except for one, the player tossing the different coin is declared the odd man out and is eliminated from the contest. Suppose that three people are playing. What is the probability that someone will be eliminated on the first round? Hint: use the complement.


I've just switched from mac to windows and have just started using TeXworks. I like it, but I find that the default pdf viewer is difficult to use. For example, there doesn't seem to be a key command for going to the bottom or top of the current page; I can't view pages continuously; spacebar does nothing for navigation; and trackpad functionality appears to be broken (scrolling with the trackpad causes the pages to jump around in a seemingly random fashion). Is there a list of key commands somewhere? Or is there a way of using a different default pdf viewer?


What are the advantages and disadvantages of piecewise linear interpolation, cubic interpolation, and cubic spline interpolation? I know that piecewise linear interpolation is not smooth and may not be accurate for nonlinear functions. The other two are smooth. But I think my understanding is a little superficial. Especially the difference between the cubic interpolation and cubic spline though I know how to compute them. Could someone help me understanding the advantages and disadvantages of these three? Thanks so much!


While reading my copy of "Resnick and Halliday", I noticed that the book has made a distinction b/w the terms " degree celsius" and "celsius degree". When I googled this, I was able to find only one matching hit(on the first page), which stated that while degree celsius is the unit for the measured temperature, celsius degree is the unit of the difference in temperature. Is this correct? Please share your knowledge and help me.


A single toss of a fair coin cannot be predicted. But if we observe a large number of tosses, we can prove mathematically the law that roughly half of them will show up heads. The movements of individual molecules in a gas cannot be predicted and can be assumed to be random. But if we observe some macroscopic phenomena such as temperature or pressure, we can prove mathematically that some laws are satisfied. Individual quantum events are random. But if we observe a large number of such events, we discover experimentally that they satisfy the laws of quantum mechanics. Could the laws of quantum mechanics be proved mathematically as in the examples above?


Here's what I know about dark matter: Astrophysicists realized the movements of galaxies and other astronomical bodies cannot be explained by the gravitational effects of matter known to be there, so either there is a lot of matter missing that doesn't react with light or general relativity needs to be fixed. For the purpose of this question, assume the former. I've read that this "dark matter" can't be composed of baryons (quarks and leptons). My question is how do we know that it can't be baryonic? After all, air is invisible. Maybe that's a bad analogy, but you get my point: Why can't there be matter that is invisible, yet composed of baryons?