Is it always true that projective objects are retracts of free objects? I know that retracts of projective objects are always projective, so in particular, retracts of free objects are projective. To prove the converse for modules, write your projecive module as a quotient of a free module, and then take its kernel to get a short exact sequence. This sequence splits because it ends with a projective object and so by the splitting lemma our module is a direct summand of the free module. How to generalize these to an arbitrary algebraic theory? I guess we should somehow look at the kernel pair of the quotient map?


A question regarding drawing checkers pieces and boards using TikZ has been asked here previously and I'm aware of the chessboard package. However I want to draw a Chinese checkers board: I want to draw it as opposed to using an image because I want to be able to edit the locations of pieces. The question is how I would go about drawing the board. Two options I see are: Draw the board as rows of circles and then draw the outline similar to the above. Draw the board as rows of equilateral triangles as seen here. Either way is fine, but drawing either one is a mystery to me. Any tips?


When a sensor registers electromagnetic radiation, such as that used for the transmission of communication like light or radio waves, does this radiation "abrade" or "erode" the material of the sensor? Are there any traces of the received radiation that can be detected, even if only theoretically? An example from a biological background would be that high energy light (such as that in the UV range) destroys the pigments in the eyes, which is why animals that live longer than a few years cannot see in the UV range. Maybe something similar happens with man made sensors for different wavelengths of electromagnetic radiation.


I was about to use this word in an email to refer to its recipient, as in: I was the guy who nabbed you as you were leaving to ask about ... I'm going for a friendly, familiar tone. Is my usage of 'nab' inappropriate? Looking it up in the Oxford Dictionary: verb (nabs, nabbing, nabbed) [with object] informal catch (someone) doing something wrong: the Feds nabbed a suspected terrorist take, grab, or steal (something): Dan nabbed the seat next to mine


I'm currently studying Action. I've been reading about how a particle has particular probabilities of ending at an infinite number of events. Say I have a free particle that isn't experiencing any external forces (no potential, or friction). I give it a particular kinetic energy, whilst it is at some arbitrary event A. Why doesn't the particle stay at position A, "lose" its kinetic energy and reduce the action to a minimum? Why does it travel in a particular straight line? You can't argue from conservation laws since they are dependent on the idea of the stationary action principle. I'm curious to know the answer, cheers!


Today, in the midst of chatting on other SE sites, the term "bum buddies" was used. Some other users took this to be offensive, saying that it was just a slightly less egregious version of "butt buddies". I was not offended by the term, but others informed me that it has homosexual connotations. I always remember using the term to refer to close friends, almost as a synonym of "bosom buddies". Can someone guide as the correct usage (so I can avoid using inappropriate terms in the future)? If there is any history on the term that could be useful as well, please include it.


This was said by one of my mates while retelling a story. The story runs that there was a court being held, and there was a recording-clerk as well. But this was a humor story, and the story continued that everybody was telling the recording-clerk to take out what was previously said, to the point that the clerk lost his temper and "dropped the pen and threw up the sponge." Does this saying mean that he resigned?


Let's say the objects are marble size or even single atoms or quarks. They are placed in an otherwise empty universe(expanding or non-expanding) at opposite ends of the universe with an arbitrarily large distance between them. With a combination of great enough distance and small enough mass will the gravitational pull between the two objects ever equal zero or merely approach it? Given an infinite amount of time would they ever meet?


I've come across many pages, articles and texts which say something like When X does Y, God kills a kitten When X happens, God kills an elephant Like here - God kills a pigeon here - God kills a kitten What does it exactly mean? Does it mean that something great was achieved, so a sacrifice was made? or Does it mean that a particular action/event is bad and should be avoided?


Two non antipodal points on a sphere have a geodetic which is a segment of a great circle on that sphere. I'm trying to calculate the Euler angles that would rotate the "equator" great circle of the sphere (in my case, the normal to this plane is the y axis) into the great circle that intersects two points specified by two pairs of angles (theta and phi, latitude and longitude, whatever. Though, yes, latitude and theta aren't the same, I know.) I feel like I've made it way more complicated that it needs to be and I'm stuck.


I came up with this question when I received an email from a committee with a sentence 'We have decided not to publish it', which seems really strange to me because the grammar I learned in English classes is 'decide not to do something' and 'decide to not do' was told incorrect. I searched for answers to this problem online, but did not find a clear as well as persuasive answer. In terms of grammar, is 'decide not to do' correct ? If it is incorrect, is there a reason why people say 'decide not to do' even in official letters ?


I was wondering if anyone knew how to make music notation that looks like the below: I'm not even sure where to start with this kind of thing, I've tried doing it by hand before in Inkscape, but I did not find that easy, algorithmic, or professional looking. I was hoping some kind of package might be available in TeX. This is another, similar example:


For a particle attached to a rope moving along a circle that has the length of rope as radius, the tension provides centripetal force and work done by tension is zero since velocity of particle is perpendicular to tension at any instant. But I am thinking about this case: Here, a particle is tied to a vertical cylinder and is given a velocity perpendicular to rope. My doubt is the work done by tension. The length of rope decreases and the particle moves towards P which is along the direction of tension. So the work done is non zero. Am I correct? (Let the particle move in a frictionless surface)


I am wondering if there is a word to describe a person who likes chaos. By this I mean a few specific things: The person is pleased to hear when chaos is created, or confusion emerges The person will take opportunities to create chaos or confusion The person enjoys taking part in chaotic or disorganized situations. I can't seem to think of a word to describe the type of person who would act in this way. I hope this question is clear. EDIT: Below gbutters sums up nicely: What I wonder is if there is a word for a generally good-natured person who just likes some good old-fashioned chaos. It seems like any person that thrives on chaos would have to have some extra baggage.


I need a good book containing many challenging exercises (or problems) on Convergence Concepts in Probability. The topics I have covered are: Borel-Cantelli Lemmas Modes of Convergence and individual properties Laws of Large Numbers Central Limit Theorem Levy Convergence Theorem and Kolmogorov's Maximal Inequality Expectation and Limit Theorems like MCT, DCT and Fatou's Lemma. I know that there are several books offering enough theory but I am in no need of those. I would want a book containing stimulating problems because just by studying theory, I cannot be sure that I can apply those concepts in relevant areas. Thank you.


What does the noun "lucker" mean? It's not in the Webster, but Google does give search results for such key phrases as "I am a lucker" or "He is a lucker" (and those are not misspellings like "luckier" or "lurker"). So people DO use that word. I myself heard it a number of times. And if they use it, it should have some meaning. So, here is my question: what does the noun "lucker" mean?


I am being told that "sports" is a singular noun. This is creating a problem for me (as a teacher) because it sounds 'odd' even if it is correct (i.e. one of the exceptions to the rule). e.g. Sports has (rather than sports have)... I always thought sports referred to more than one team activity (e.g. football, rugby, golf, bowls etc.); hence, it was plural. For example, I like playing sports. Sports have always been of interest to me. QUESTIONS Is sports a collective noun? Which usage is correct?


A busy intersection sees two traffic accident per month on average. Suppose the number of accidents follow a Poisson distribution. Starting from January next year, which month do you expect to be the first one in which there is no accident? I figured it would be the same for every month (as in every month is equally likely to have no traffic accidents), and can't figure out why a particular month would be expected as the first one to have no accidents. Any reason a single month is more likely than others?


I'm looking for the appropriate term to use for what gets "used up" as potential energy is converted to heat and work. For example, some of the the energy in solar radiation is converted by photosynthesis to chemical energy; much of the rest is lost as waste heat. The bio-chemical energy is used to power various biological functions until it has all been lost to waste heat. At the various steps along this path what term would you use for what there is less and less of? It can't be "energy" since that's conserved. It's potential energy, but is that really a standard term for what's lost when potential energy is converted to waste heat?


What would happen if an object (like a space ship) was to stop its orbit around the sun. would time slow down with that object (the same way time sped up for the characters in that great film Interstellar). Or even more so, if that object was to stop its orbit around the galaxy so to speak. And so on and so on. At what point is an object considered motionless? Could it be that the finite origin of the big bang has no time?


If the mass of A is greater of the two, and if air resistance is the same on both, which ball will reach the ground first/simultaneously? I thought that since the acceleration acting on them is same, both will reach the ground simultaneously. But the answer in the book says that ball A (the one having greater mass) will reach first. I mean, isn't this what people thought before (I guess it's true) Galileo performed his experiment, until they were proven wrong?!


Which would be correct? What is your favorite song, and explain why? (I'm thinking this is right.) What is your favorite song, and explain why. This could be written as, "What is your favorite song? Explain why." But that seems kind of clunky. Looking at similar questions on this site I see that maybe there isn't a great answer to this (or maybe that this question is more straight forward than what I was looking at). I dislike the Chicago Manual of Style format, so ideally one of the two choices above would be correct.


I want to create a separate file for tables so that the main latex file doesn't get cluttered. I know I can define tables in new file and add the same file in the main file using input{Tables.tex}. However, I am not sure how can I ask for/produce (not refer) the tables using the labels of tables in the main document? Any suggestions would be appreciated. Thanks.


I want to make someone a present by subscribing for him to a mathematical journal. (It should appear every month or every two months). The contents should be comprehensible to an undergraduate in mathematics, and be about a broad selection of topics (for example not only analysis). I expect the content to be something like proposing interesting problems and then giving solutions with some references for further study. Are there some famous journals you could suggest me?


I have seen that sometimes, in particular in number theory and combinatorial commutative algebra, our questions are somehow related to finding the number of points with integer components in a region/shape. Since this seems to be related to some open problems and conjectures, does there exist a branch of mathematics that specifically study such questions? If yes, what it's called and what prerequisites one must know to study it.


I think it may not be possible. Given all the pair correlation functions (e.g. calculated from Ornstein Zernike theory), it seems possible to obtain the internal energy (assuming different species interact through pair-potentials (i.e. potentials that do not involve more than two bodies)). To obtain the free energy, the "naive" way is to obtain the partition function and take logarithm. Yet it seems not easy (except possibly through cluster expansions? which is not exact.) Any help will be much appreciated.


Assume an airtight bag occupied by air such that the pressure inside the bag is equal to the atmospheric pressure. Assume the surface tension of the bag is negligible. What is the change in air pressure inside the bag relative to a weight placed on it? Is it possible to approximate the weight of the object on top of the bag by the air pressure inside the bag, without knowing the volume of the bag or the area of the object?


Ionization energies/Electron affinities are well mapped. I wonder about opposite processes... I imagine for anion the necessary energy will be equal to the electron affinity (energy released when the anion was created). What about cations? If I had an cation and free electron (both with low kinetic energies) will it automatically recombine? Or if I had let's say grounded metal surface and near it a cation of some gas, will it do the same (and how would react an anion in this case)? Thank you for answers. If you could direct me to the proper literature I would be grateful :) (I know it requires QM for any decent description).


The American convention in quotations is (typically) to place punctuation inside quoted text. But I always run into situations where the punctuation of the quote interferes with the punctuation of the sentence. How would you punctuate this (American, non technical)? When my friends ask, "What do you want for your birthday?", I never know how to respond. It seems odd to place the last comma outside the quote simply because of the question mark. Is that the preferred (i.e. most often accepted) standard?


I have heard that in my next semester, our quantum mechanics teacher will be giving a great emphasis on difficult integrals with the most of them having to do with gamma functions. Does anybody know a book(or any other source) that I can learn about and practice gamma functions integration (with applications to physics and more preferably quantum mechanics if possible)? The only thing I have found are books that just list the integrals of gamma functions in tables rather than having a few examples and them some practice problems.


Hullo, Im just starting up with LaTeX. I keep getting error messages even though I feel as though everything has been done correctly. I am just doing the intro exercise which is shown from the help tab from my MikTeX install. I am getting errors like article.cls not found. Can I download a LaTeX editor from somewhere, or is the MikTeX which I installed mising some files. Can someone please help me?


I've heard this phrase used many times. e.g. -Got a completion date back on your new conservatory? -Ha! Chance'd be a fine thing. I think I have a general idea of what it must mean from its context. But I just don't see how it makes sense. What does it actually literally mean, and why? It doesn't seem to make sense to me. What does "chance" have to do with anything?


So, in the field of metallurgy, there are a few varieties of phase diagram that are used to predict the post-processing characteristics of alloys. These include Time-Temperature Transformation diagrams and Continuous Cooling diagrams. Currently, I've found myself working with metal oxides, and I'm trying to find what the equivalents are in this field. It looks like so-call Oxidation Curves are a commonly used tool, but this doesn't give me any information on the microstructure or properties I can expect out of bulk materials. Are there such references?


Dual spaces are home to bras in quantum mechanics; cotangent spaces are home to linear maps in the tensor formalism of general relativity. After taking courses in these two subjects, I've still never really understood the physical significance of these "dual spaces," or why they should need to exist. What is a dual / cotangent space? Could someone explain why they are necessary, and what their physical significance is?


I'm working on a collaborative project and I like to organize all the supporting files for my tex documents (rather than just having everything in one flat folder). This involves referencing figures/files/etc. by a (relative) path. The difference in slash convention between linux/windows means that collaboration between users on different systems becomes annoying. Is there any easy way of dealing with path references between systems?


Suppose I take a vacuum tube and accelerate electrons in it by electric fields then collide it on a copper plate. Will the electrons then go inside it and generate an electric current by putting a positively charged panel on the opposite end to create a potential difference? If yes how can I extract the electrons from the positive plate back into the vacuum tube? Thanks! Also you can see a diagram I made for what I am trying to say,


I have three questions: (i)Does rank of a square matrix same as the degree of its characterstic equation. (ii)Do elementary row transformations of a given square matrix result in a characterstic equation different from that of given square matrix (iii)Geometrically speaking what do cofactors of a square matrix mean. What is significance of some of them becoming zeros or all becoming zeros. These are theoretical questions and so if you could refer to me some book or online resource which can explain these concepts it would be a great help. Also it would be nice to know what other members think about these topics. Thanks in advance


I have a few issues to discuss linked to the Future Subjunctive. Can "If I were you." mean the same as "If I were to be you." In other words, can "If I were you." have the reference to the future which "If I were to be you." has? If I were you at tomorrow's competition I would win. ? = ? If I were to be you at tomorrow's competition I would win. Would you understand, if told, that "If I be you" means "If I were to be you"? Is this construction still used in contemporary English or is it totally obsolete? If I be you at tomorrow's competition I will win. Is this construction possible? If I am happy at tomorrow's competition I will win.


Equation of continuity says us that if we insert some fluid in a tube, the same amount of fluid will come out from the other end. If we make a small hole in a hose pipe, water will come out with a great speed. The bigger the hole, the slower the speed. This is a direct consequence of the equation of continuity. But at the case of water tap, when we start to turn on the tap slightly, the velocity of water is slow. As we turn on the tap more, the speed increases. This is contradictory with equation of continuity.


I'm TeXing a course for a teacher of mine, and he wants me to have the section titles in the headers (I use fancyhdr to achieve this). He also wants me to retain the section titles he gave me in the original (word) file. Since some of these section titles are too long to fit in the header title, is there a way to define a shorter version that is to be used in the header? Enabling multiple header lines would also do. I'm using the book class.


So I've been reading a section about energy levels and came across this statement: "As the atoms of a material are brought closer together to form the crystal lattice structure, there is an interaction between atoms that will result in the electrons in a particular orbit of one atom having slightly different energy levels from electrons in the same orbit of an adjoining atom." What I don't understand is that how could be an interaction of atoms of the same material occur, if they have the same potential, number of e- and structure. And why would they have a difference in energy levels??


Is there really a difference between using "allows for" and just simply "allows" as in this scenario? To me, both of these sentences mean exactly the same thing. Does having the 'for' make the sentence mean something even slightly different at all? I have searched all over but have not encountered anything that is similar to this scenario. Any help is much appreciated. Music allows me to express myself. Music allows for me to express myself.


Taking into account gravity, air resistance, and wind velocity and direction. (And also temperature if it's actually relevant.) I know the muzzle velocity, the total distance the bullet traveled, its diameter, mass, length, and the angle from which it was fired at. Now, I do not know its drag coefficient, so how do I calculate it? (The muzzle velocity is supersonic.) The question is, what is the velocity of the bullet by the time it traveled the total distance? What are the formulae that I would need to use to calculate that? Much obliged.


The gist of my problem is that Slovene isn't supported in babelbib. I've got a half-done .bst file which translates some of the needed words, but not all of them. I also noted there exists a slovene.mbs file in miktex. However, when I tried creating a new bibliography style with makebst, I still didn't get the words translated. Since my bibliography is pretty simple - the only thing I'm missing is translation for 'edition' - I felt it would be best if I edited the existing .bst. How do I go about that?


I say that "whoever" is the correct grammatical choice in the following sentence: Give the raise to the hardest-working employee, whoever/whomever that may be. I say "whoever" is correct. The reason is that, when we isolate the "whoever/whomever" clause ("whomever that may be"), the phrase converts to "It may be he". "It may be he who is the hardest-working employee", not "It may be him who is the hardest-working employee". Thus, I believe "whoever" is the correct choice here. Am I right? And is my explanation in determining "whoever" on point? This question is different because the "whoever" clause is at the end of the sentence.


Yesterday, I told an Indian my English name is 'Melao', he smiled and asked me if there's any special meaning. In fact, I get this name from a song with Latin style -- 'Corazon De Melao', I think it's legibly. So, I wonder if there's any special meaning in English-speaking countries when it is used as a name? Or what's your feeling when you hear a boy with a name 'melao'? Thx in advance.


I am trying to solve the following problem using proof by strong induction. the problem is: Assume that a chocolate bar consists of n squares arranged in a rectangular pattern. The entire bar, or any smaller rectangular piece of the bar, can be broken along a vertical or a horizontal line separating the squares. Assuming that only one piece can be broken at a time, determine how many breaks you must successively make to break the bar into n separate squares The farthest i have gotten is the basis step, but i dont even know if that is correct Potential basis step that i got it is P(n), but besides that i am clueless


I am writing a research paper in which my thesis concerns how a character matures through his merging of characteristic traits in his relationships with other characters. How can I introduce this topic with an analogy "attention-getter" that demonstrates this idea of merging things together to form something new? In another words, I'm looking for an analogy that compares how an individual who combines attributes that he acquires from his relationships can actually create a new, and better, identity for himself.


What's the difference between pronunciation and enunciation? I learned this a long time ago in English class but forgot what it was. Clarification For example, Wikipedia says: Good enunciation is the act of speaking clearly and concisely. The opposite of good enunciation is mumbling or slurring. See also pronunciation which is a component of enunciation. Pronunciation is to pronounce sounds of words correctly I can't tell from this what the specific difference is. When is it correct to say someone's pronunciation is off versus when their enunciation is off? Merriam Webster's definition defines enunciate as : articulate, pronounce That would seem to say it's the same as to pronounce. Is there a specific example of incorrect pronunciation verses enunciation?


It''s quite common for academic papers and such to have a short title intended to catch the casual browsers's interest, followed by colon and a longer more explanatory alternative. I know this is a lousy example (I couldn't easily find a better/shorter one), but even so I'm sure this Catchy Title : Longer version conveying more information about the work format is also used in fictional works. Is there a standard name for that secondary title. It's not really an "alternative title". The only thing that comes to mind for me is byline, but I know that's not right either.


I have seen several proofs that there exist nonstandard models of arithmetic, but they all seem to rely on the compactness theorem, which is not implied by ZF. So are there any proofs in ZF that there's exists a nonstandard model of PA? Tennenbaum's theorem, which states that every nonstandard model is uncomputable seems to hint at the possibility that there are models of ZF that contain no nonstandard models of PA.


I'm attempting to document a change that will make two things more congruent. I'd like to use a word in this way: This change [makes similar] the two items. The best I've been able to find by searching is "assimilate"; however, I feel that this word has unpleasant connotations in some cases and could be misconstrued. Is there a better word? For a little more context on this specific situation: I'm making the interfaces of two different software libraries more similar. They're remaining separate libraries, but they do nearly the same thing and are now more similar in their behavior.


This is a follow-up of my previous question regarding loading image using latex command. @erik kindly informed me that latex only supports images in eps format. I converted my JPG file to an eps file using bmeps.exe in the miktex/bin directory. I can see the image in the dvi file generated by latex. But the original color image in the JPG file becomes a black-white or gray scale image in the eps file. Is it possible to get a color image in eps format using bmeps.exe? Does latex support color image? A minimum woking example can be found here.


English is used all over Europe in (more or less) academic papers and books that are not necessarily related to reviews and publishing houses based in UK or US, and that are not necessarily intended for UK or US markets. English is largely used between non-English speaking areas as lingua franca. What is the main trend in this field concerning the use of British vs American English? Are there certain guidelines (or even EU directives) on the matter?


I read a quote somewhere and it seemed flawed in its language and word usage. Take a look at it: "Trust a person to that extent, that he feels guilty to cheat you & care for a person to that extent, that he fears to lose you." The letters in bold are the clauses that I found flawed in particular. Shouldn't it be: "Trust a person to the extent, that...." At the same time I find "care for a person to that extent, that..." sounds alright.


I have a problem regarding supply distribution. I distribute widgets on a monthly basis; I have many customers and each of them request a different quantity each month. My monthly supply is limited and I cannot fill every order. How do I distribute fairly, across the board? There must be some sort proportional way to do it. Let me know if I need to provide additional information. Thanks


A friend uses this ____-whore construction all the time. I challenged her to find a better way to say it. I suggested addict, enthusiast, devotee, and several other words. She said none of these convey her meaning the way whore does. She says she'll watch anything. I told her she's not being paid to watch, and whore would imply that she is. Can anyone suggest a better alternative?


I am a freshman in high school who needs a math related project, so I decided on the topic of fractals. Being an avid developer, I thought it would be awesome to write a Ruby program that can calculate a fractal. The only problem is that I am not some programming god, and I have not worked on any huge projects (yet). So I need a basic-ish fractal 'type' to do the project on. I am a very quick learner, and my math skills greatly outdo that of my peers (I was working on derivatives by myself last year). So does anybody have any good ideas? Thanks!!!! :) PS: my school requires a live resource for every project we do, so would anybody be interested in helping? :)


Is there a theory of constrained optimization with complex variables, do you know any textbook on that topic? The typical textbooks on constrained optimization deal with real variables. I actually found some references which loosely explain the procedure of derivating w.r.t. the complex conjugate to obtain optimality conditions but could not find a rigorous mathematical justification. In particular I am interested in using a Lagrangian, and couldn't find any reference on that. Thanks.


At a homecoming dance, no boy dances with every girl, but each girl dances with at least one boy. Prove that there are two couples, gb and g'b', who dance, such that g doesn't dance with b' and g' doesn't dance with b. I'm not sure where to start. Hints only please, NO SOLUTIONS. I will most likely reply back to your hint to ask you more, so please stay online :)


People in London, who live in the suburbs, may tell you they work 'up town', meaning in the City or the West End. In other large cities in Britain, Birmingham, Manchester, Leeds etc., I think people who earn their living in the City Centre (equivalent to Downtown with capital D) will say casually that they work 'in town'. I think I'm right when I say that only Londoners go 'up town'. So where did the idea of 'Downtown' come from?


To complete college (or what the equivalent in Denmark would be) I will have to write a text about a topic that I choose. I have chosen to write about mathematics in business economics, and specifically, I want it to be about investment analysis and risk assessment. I am seeking some inspiration for possible mathematical topics to include. My knowledge in math is at bachelor degree, but I am up for a challenge. I already have a few ideas, e.g. I am pretty sure I will include something about the poisson distribution. Any answer is appreciated. Thank you in advance.


Someone else asked Are camp followers prostitutes? and the answer seems to be that while not every one who follows a military camp is a prostitute, if you aren't referring to a prostitute, you should probably pick another label for the person. A similar effect can be seen with sexually themed words like "mistress", "madam", "ejaculate", and "escort". I assume this linguistic process has been studied and I'm curious what its name is.


I'm looking for reading assignment ideas for my students. I'd like them to read up on results in mathematics in layman's terms. For example, the Monty Hall problem, or Borsuk Ulam as the "Ham Sandwich Theorem". I feel a good source for the types of things I'd like them to read is this post. I would have each (group) student do a write up on a particular subject. Does anyone know of any books that give a list of results that are understandable for a calculus student?


During review of an article I found an erroneous sentence: The known predators of the plant are sheep, donkeys ... I am an engineer, with not so much knowledge in ecology. Based on my earlier studies I suggested to change predators to consumers. I checked it with a search on the net. Surprisingly I found too few hits in my search. Consumers of a plant is acceptable? Can you recommend alternatives?


I understand that structures with the properties of the real and complex numbers can be defined and derived from the axioms of ZFC set theory. But can a structure with the properties of a (possibly uncountably infinite dimensional) vector space be derived from ZFC or is it axiomatic statement that a vector space is a set (and that therefore the axioms of set theory apply to it) ? I think the question becomes relevant in the proof that every vector space has a basis (from Zorn's lemma = axiom of choice). It's not just a matter of whether one accepts the axiom of choice in set theory, but how one gets to believe that a vector space complies with set theory axioms.


Most physics textbooks and even questions in stack exchange answer the question why there exists a charge buildup in the bends of a current carrying conductor. But what I am unable to understand is: why a surface charge gets developed in the straight region of a current carrying conductor? why there is a gradient of the surface charge density along the length of the wire?


I managed to install some english dictionaries as shown on https://github.com/TeXworks/texworks/wiki/SpellingDictionaries#mac-os-x. Then I was able to select Edit->Spelling->English-UnitedStates(en_US). At that point, all misspelled words were underlined in red. However, I would like to ask, once you finish writing your document, is there a way to search for any red-undefined misspelled word? The reason I am asking is to help my students, who will be writing projects in Texworks during the fall semester. When they are done, how can they check the spelling in their full document?


A condensate of open strings with both ends attached to the same D-brane can be equivalent to a displacement of the D-brane with no open string condensate. A solution to the D-brane Born-Infeld action gives rise to a semi-infinite string extension which is entirely equivalent to an open string with one end attached to the D-brane. Why aren't D-branes and strings independent degrees of freedom?


When I first learned algebraic geometry, I naturally wiki-ed the subject and there was a line there that said the old school Italians used the notion "generic points without any precise definition." Now that I know what a generic point is, I am curious as to how did the Italians think about a generic point and/or what their intuition about it was and what kind of results did they prove using this notion. Any answer would be greatly appreciated!


As I was familiarizing myself with different methods of computing complexities of recurrences, I stumbled upon the Akra-Bazzi method. Seeing such a beautiful result literally made my day. I was able to come up with a proof that makes use of an inductive argument, but induction alone isn't all that satisfactory. Does anyone know of a material that illustrates a constructive proof of this wonderful result?


Let's say you have a spherical charge distribution of radius R. This distribution has some charge density as a function of radius. I know that I can determine the electric field outside of the charge density by forming a spherical gaussian surface around the charge distribution and apply gauss' law. But what if I want to find the field directly on the surface. That requires that my surface intersects some of the charge of the distribution. In that case, when I apply Guass' Law. How do I determine the charge enclosed by the sphere. Do I discount the charge which exists on the surface or is that counted as enclosed by the sphere?


This is quoted from an U.S. TV series. Warden: Brad. Brad (Captain): Any updates? Warden: None. They were last seen at that cemetery in Oswego. Brad: They'll get them. They'll get them. Warden: It's been handed over to the FBI. Brad: Well, that doesn't mean we can't work it. Warden: It does, actually. You and I have been pulled off the pursuit. Brad: Why? Warden: We're going to find out shortly. We have to report to the DOC headquarters. I will meet you there. Brad: Sir, we can get these guys. Just give me a couple more days and I swear I'll get them. Warden: Brad! We've got to go.


I have several items of clothing for which their dark colours could run on washing. Some have a warning label in that says 'wash dark colours together'. Some have a label that says 'wash dark colours separately'. These apparently contradictory labels actually tell me to do the same thing, when context is taken into account. What other examples are there, either out in the wild, or that could be constructed, of opposite messages meaning the same thing?


I am writing up a paper on magic squares, and I would like to include the lo shu magic square, but I'd like to do this using XeLaTeX as opposed to just including a picture. The following picture is what I want to produce: Does someone know how to produce what's above? I thought something like tikz would probably have to be used, but I'm not very advanced with LaTeX just yet.


What is the best word to refer to the person that I (directly) supervise, in the context of a corporate workplace? The closest I can think of is employee, but that doesn't directly convey a direct supervisor relationship. Other options I can think of are apprentice (usually used to refer exclusively to someone who is still learning where I come from), underling (patronizing), and worker (again not specific). For example when describing a project: My employee designed the front-end of the system while I worked on the critical business logic.


(Quantum) integrable systems, that belong to solutions to the Yang-Baxter-equation, are often solved by the (algebraic) Bethe Ansatz. Solutions to the Bethe-equations lead to the eigenvalues of the transfermatrix and in that way also to the spectrum of the hamiltonian. However, suppose you already knew an eigenvalue of the transfermatrix, is there a way to construct the Bethe-roots, that would have lead to it? If any additional explanations are needed to answer the question, just let me know. I think the answer to the question is in general no. If there are however some specific exactly solvable models, where it is possible, that would be also of interest.


What is the meaning of the phrase " you rolled them sevens with nothing to lose " ? In the song entitled " The weary kind " which is a sound track of the "Crazy heart" movie , there is a line that i can't understand. Your heart's on the loose You rolled them sevens with nothing to lose, there's ain't no place for the weary kind Could you please help me to understand that phrase ?


Do predation and predating share a common etymology? Predation seems to imply that one species holds precedence over another species in the food chain, whereas predating seems to imply that one event holds precedence over another in the linear progression of time. Both words obviously share the prefix pre, but my question is more about the dat part of each word. What is the origin of dat in early English or in Latin or the Romance languages Latin gave birth to? And how does that origin explain the meaning of the modern words predation and predating?


I want to prove that a certain metric space is totally disconnected. In a metric space context this is the same as saying that every connected component is a singleton. I think another way of proving that a space is TD is proving that there is a proper, nonempty open and closed set. Is that right? Please let me know any alternative equivalent definitions you might now. Cheers!


I have this problem where I have two lines given and I have to find a transversal. However, it also has to be perpendicular to a given plane (lines are not necessarily in the given plane). My guess was that I would have to find perpendicular lines to the plane and then see if they are also transversals of those lines. But I've been stuck. Is this the right approach? Or should I start working from the lines and then tend to the plane and transversal being perpendicular?


I'm referring to this one: Any man who is his own translator has a fool for an editor. The resemblance that this expression bears to the one about any individual who chooses to represent himself/herself in a legal case is undeniable. Yet, even when the meaning of the latter expression is pretty clear to me, I'm not sure I get the point which whoever made up the translator/editor variant of the proverb was trying to make... I would be really glad if, in addition of getting an answer for the question in the title, you could help me unravel the meaning of the expression under consideration. Let me thank you in advance for your learned replies.


I know this on our hands/in our hands discrepancy has been discussed here in a broad way, but since it's idiomatic, I think it would be helpful to consider a few specific examples, like the one here. Would you use "on our hands" or "in our hands" here, and why? It refers to something you invented and produced, and you're guessing it will do well on the market. So you're not having anything literally in your hands. You don't know if it's a top-seller yet, you just think it will become one. That's why "on our hands" seems right to me. Am I wrong?


Is there a word to describe the competitive advantage gained from sabotaging a competitor, or more generally the advantage gained from dishonesty? An example: Your office receives pamphlets advertising an office cleaning service. Your current office cleaning service steals and hides that pamphlet before an employee at the office can see it. What words can one use to concisely describe the advantage that your current cleaning service has gained?


I recently installed AucTex on a new computer, and am having an issue that I do not recall with regards to accessing environments. Using C-c C-e, auto-complete etc., I am only able to access a handful of environments. Auctex does not detect align, matrix, or any other math environments. It is possible to simply enter the environments by hand, or create custom environments, but this seems tedious for something that I wouldn't expect to be happening. Perhaps there is something I am missing.


It seems Optimal Estimation/Control Theory requires a lot more than undergraduate maths. Any good book that would help me get started? I have so far referred the following books but found them quite difficult. Is it just me? is it the subject? or are there better books? Extra points for someone who gives a detailed road map of how to go about learning Optimal Estimation/Control Theory H.W Sorenson - Parameter Estimation Dan Simon - Optimal Estimation Theory Arthur Gelb - Applied Optimal Estimation


I am working on the lyrics for one of my songs and english is not my first language. Here's the question - which of these sentences is correct? No thorns to prick your heart No thorns to prick your heart with (Meaning that the character of the song has no 'thorns' (figuratively) he/she could use to prick the heart of the one he/she addresses to) Thanks in advance


When someone says, I barely understand that. Does he mean: He almost doesn't understand [which means he understands a bit] He almost understands [which means he doesn't understand] Or if someone says: Your brain is barely used. Does he mean: Your brain is almost not used [which means, it is used, but very rarely] Your brain is almost used [which means it isn't] I used to think that it was the first option. But a friend, out of the blue, said it was the second one. Which one is it? Or have my friend and I got it entirely wrong? Are there other words with similar meanings to barely? Is nearly one of them?


So a stage whisper is defined as (American Heritage Dictionary): The conventional whisper of an actor, intended to be heard by the audience but supposedly inaudible to others on stage. A whisper that can be or is intended to be overheard. Is there any good description of the opposite? For example, if I'm in a crowded place, and I mock-yell under my breath so that only I or a single friend am actually aware of it, how could we describe that?


I noticed that her eyes had been dancing as she looked out at the scenery. It appeared in a state-sponsored high school leaving examination in Slovakia last week and it seems to have been adapted from a short story by a native speaker, so it really ought to be correct, but I don't see how or why. Past continuous seems the obvious choice, this just seems wrong as it's all happening at the same time.


I have read that electromagnetic waves carry momentum because they carry energy, while energy is equivalent to mass. So they carry momentum. But this explanation is in the context of special relativity. I don't know whether mass energy equivalence is necessary for wave momentum. So I hope you can discuss in the contexts of both Newtonian or special relativity. A quantitative definition like the Maxwell stress tensor of electromagnetic wave is better.


I find that when learning more abstract concepts, it helps to have a 'simple' example tied to every theorem in order to fully appreciate the theorem or property. However, the course notes I am currently using for my studies of Measure Theory (this is a first course for me) do not have many examples. It is highly rigorous and detailed, but lacks examples. Are you aware of any introductory books on Measure Theory that has a good number of examples tied to each theorem? In other words I guess, do you know of very 'gentle' books on this topic?


Claim A directed graph has an Eulerian cycle if and only if every vertex has equal in degree and out degree, and all of its vertices with nonzero degree belong to a single strongly connected component. I was looking for this proof in the Internet, but all i have found are the proofs for undirected graphs. I would be glad, if someone can give a link or name of the book, where i can find proof for this claim.


The last few years I've noticed a trend of people posting articles or news stories on facebook that had offended them, and commenting with a sense of outrage they seemed also to relish on some level. Today I heard the term outrage porn for the first time, and felt delight in hearing this phenomenon succinctly and accurately named. I got to wondering if there was a word that described the surprise and satisfaction of hearing a concept captured by name for the first time... I'm not looking for general words describing the satisfaction of insight or clarity -- but a word or phrase that applies specifically to hearing a concept named for the first time.


In high school we learned to say "than I" and "as I" because you could potentially add an "am" to the end of the sentence. Examples: "She is smarter than I." (Think: "...than I am.") "He is as tall as I." (Think "...as I am.") So analogously, shouldn't it be "like I" as well: "He is sincere, just like I." (Think: "... like I am.") But universally, it seems that we use "like me". Where does this reasoning break down? Is there history here?


When I use the word "sorry" for something I did wrong I'm sorry I bumped into you. I would be apologizing. However, when I used the word "sorry" to express pity for something that is not actually my fault, I'm sorry you couldn't figure that out. I'm sorry for your loss. is it still called an "apology" in English? In Chinese, we wouldn't use the same word in these different sentences. I would love to know what this type of sentence is called.


I've been asking myself this and other questions in the field of philosophy of mathematics. Could we, if we were isolated from any kind of sensory experience, be able to learn mathematics? Also, what does it take to learn math?, is there a 'module' or a 'structure' (like the one theorized by Noam Chomsky in his studies on linguistics) in our brain that lets us apprehend mathematics?, do we need a language (be it natural, be it symbolic) to learn mathematics? PD: I'm a beginner to SE, if this question if off topic please do tell and do recommend me where should I ask it.


I'm looking for command to use in one terminal so as to know the following facts. Is there one LaTeX distribution installed ? What is the path where to put local classes or packages ? In my Mac, I know that it is '/usr/local/texlive/texmf-local/tex/latex'. The command will be used by one Python script so as to automate the installation of my personnal little classes or packages. The solutions given in the following comments work well on Mac, and I think that this works also under Linux, but I don't know how to do under Windows...


I have some TikZ code in my LaTeX document. Whenever I edit other parts in the LaTeX document, I recompile it. But repeating recompiling unmodified TikZ code can be time-consuming. I was wondering if there is some way to avoid re-compilation of unmodified part of LaTeX document? If such methods exist, do they apply not just to unchanged TikZ code but also unchanged non-TikZ code? Thanks and regards!


I am in need of help figuring this out-- If the only straight lines in hyperbolic geometry are those that pass through the center, then isn't there a right angle? (horizontal and vertical) Which fulfills that requirement of the definition of a rectangle. That leaves the other two sides as hyperbolic lines with negative curve and extending infinitely, resulting in three acute angles, right? Aren't the two straight lines passing through the center parallel to their opposite hyperbolic line? Which also fulfills the definition of a rectangle. I'm sure I am overlooking something or have gotten myself very confused. Please help.


Slightly tongue-in-cheek this one but written in good faith... I am a competent user of LaTeX and use it with Eclipse as IDE, MacTexlive as install, and XeTeX as engine to author my PhD. However, there are times when I like to procrastinate and love LaTeX as an end in itself not just as a means to an end. What would you recommend as a good way of procrastinating whilst usefully extending my capabilities and abilities to use LaTeX? In the past SVN, biber and beamer have served to distract me from my thesis. Any more potentially fruitful areas?


Can fusion and fission happen at the same time, in the same place? I was talking with a friend, and he thinks that fission and fusion happen at the same time at the sun, is that true? I guess this would cause perpetual motion, then I speculated that they could happen, but in different proportions and I believed that fusion is happening in a higher proportion than fission. What do you think? I've searched on wikipidia, and I still found no mention to fission happening in the sun.


This Batman equation thing got me thinking: for an arbitrary curve drawn on the Cartesian plane, can you write a corresponding equation which is not piecewise? What about closed shapes, a la the Batman symbol? I assume that there are limitations, such as that the curve would have to be differentiable and/or continuous everywhere, but is this possible for any random squiggle? Or is it not?


The English wikipedia page for Nothing starts with the sentence: Nothing is a pronoun denoting the absence of anything. I was expecting Nothing is a pronoun denoting the absence of everything. since in the context a positive answer is expected. Googles: N-gram viewer shows that anything is more common than everything in this context, so I assume that anything is the natural choice here. But why is that?


I am in a situation where i am expecting some data from my client. I want to write the same in a very polite manner that "i am expecting the data, even after my repeated intimations." Here i wanted to use a sentence as I'm just sending this mail to remind you that, currently i am awaiting for data. I am confused i should use wait or await in this context.


I would like to know if there is a common abbreviation for days of the week in a two letter form. I mean: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; can be abbreviated as Su, Mo, Tu, We, Th, Fr, Sa? Is this the common form? Note that I have also seen Sn for Sunday, and some times St for Saturday (but I think less frequently). It will be used in a tabular data program to show information about free work days of employed and each column can't have enought space to include full week day name. For "common form" I mean, what are the abbreviations that is more used in programs.


Are there any (mathematical) puzzles that are still unresolved? I only mean questions that are accessible to and understandable by the complete layman and which have not been solved, despite serious efforts, by mathematicians (or laymen for that matter)? My question does not ask for puzzles that have been shown to have either no solution or multiple solutions (or have been shown to be ambiguously formulated).


If a couple are having a romantic or sexy get away where they're staying in bed and having sex and otherwise hanging out - is there a term use for the periods where they're not actually in the act of having sex? Perhaps pillow talk is the closest term I can think of here - but this seems to refer to the act of just talking, whereas I'd like to encompass anything else they might do - like eating, watching TV etc. eg. During [something period] we had a tickle fight, I organised my to do list, and she knitted some socks. I'm looking for something you might use in a romance or sexy novel.


I'm not a native english speaker (so forgive me for my poor language skills in general :) ) and I'm puzzled by this "whose / which / of which" issue. I have a sentence like this: "BLAA is a project whose purpose is to build and...". To me it sounds that it should have which instead of whose. I was always tought that whose refers to a person and which to a matter, and based on that I would use which but all the articles I read about it seem to say that whose is the way to go. What to do? And please keep the explanations in KISS form ;) Thanks! -Heidi


I intend to study linear algebra during my summer vacation.I will be thankful if anyone could please point me to a good text.I do not care about the difficulty as long as the book is self contained.I do have some experience with problem solving and proof-writing. Edit:I don't care about applications.I prefer one which is quite theoretical. Secondly,here is a book I came across.I request comments on that book too.I will make a choice after some deliberations.


I was wondering if there was any way to flip a transistor or similar node component around in the circuitikz package? For the bipoles it's fairly simple as you just reverse the start and end, but for more advanced circuits I'm having trouble (things such as current mirrors or what have you). I've seen various solutions on scaling up and down, but none on flipping.


I was aked to solve the following problem: Guiven three lenghts and a triangle ABC, from every vertex whe draw one of the three lenghts, find the conditions such that the three lenghts meet in one point. Then I suposed that at least two lenghts and a side makes a triangle, supose that the side is AB and the two lenghts meets at P, then using the cosine theorem to the triangle ABC and tha traingle ABP and I get a very large expression involving only lenghts, but it was very complex, and I think it can be simplified. Then my question is, if there is a synthetic solution to the problem. Please I don't want a full solution. Thanks.


I've seen constraint and restriction used quite often in scientific literature. For example, This algorithm needs to be further improved due to severe space constraint and restriction. I simply can't figure out the subtle difference between constraint and restriction. They seem to be circularly defined according to each other. I assume that they must be different in some way. Otherwise, they wouldn't have been used together so often. If they were really close enough in meaning, why not just drop one and use the other? Or are they used in combination to place an emphasis?


I am looking for a high school/ pre-college level Algebra book that is self contained for self-study. Nothing special, I don't want a book about number theory, but a book in preparation of high school geometry, trigonometry and calculus. I have noticed that recommendations for Algebra books on this site, start with books that are really advanced (for my level) and overshoot the mark with suggestions for abstract Algebra or number theory. I am someone that is rebuilding my math skills and need to get a strong foundations before I move up in intellectual weight.


In my report, I am defining/describing some terms. What is a proper way to start and format a sentences like: The term crawling denotes the practice of ... Should I put the word/term crawling in quotes, bold, italic, or something else? I think The term "crawling" denotes the practice of ... looks a bit ugly but is probably easier to read. On Wikipedia, most terms seem to be formatted in bold font.


This might seems off topic or something, but I am a middle school student and i'm really into Quantum Field Theory and String theory and every video on youtube or article on the internet shows only the concept and Intro to these theories but I want to know about the maths envolved and do the maths myself as well , so i would love it if you guys would be suggest me a site or anything else where i can learn from scratch all the maths involved in Quantum Mechanics and maybe Einstein's Relativity as well.


So the category of affine schemes is dual to the category of commutative rings, Stone spaces are dual to Boolean algebras, localizable measurable spaces are dual to commutative Von Neumann algebras, and I'm sure there are many more examples. In general, a category of algebraic structures is going to be dual to some related category of geometric structures. My question is, then: is there an analogous story for coalgbraic things? If I take a category of coalgebras for some comonad and flip the arrows around, will I get something interesting? Are there any good examples of this over familiar comonads (say, the costate comonad)?


I've been trying to find one single word that covers knowledge concerning both the properties and cultivation of plants, but have come short with some words. Here are some of the words I thought of, but eventually found lacking: Botany: I feel this implies purely scientific research on plants, ignoring the cultivation of plants and things like crop rotations and irrigation techniques. Agriculture: I think this word only covers food crops and plants commonly grown for decoration. I feel it misses out on the more thorough knowledge of all (not just commonly cultivated) plants, including currently unknown ones. Ultimately, I'm looking for a word that encompasses the subjects of both Botany and Agriculture, but have come short for now.


I'm trying to come up with a better word to describe a "driver" or "conditional"; basically, the name of an object or event which is a trigger for something else. Would it be appropriate to say that a button which turns on a light is an affector? If I believe I understand its usage in this context, it would only be an affector while triggering the event (the button is pressed). I've been unable to find support to convince me that this is the appropriate use of the word.


I just need to know what exactly happens when charging/discharging a capacitor. Is there any heat transfer between the capacitor and the surroundings? Is there a heat transfer between other parts of the surroundings (wires, the battery)? Another thing I don't understand generally... How do we know if a process is reversible or irreversible? Should we take the third law of thermodynamics as a principle and calculate the change in the entropy of the Universe through the formula given for entropy? If so, how about a process like the free expansion of a gas in which there is no heat transfer but the entropy increases? What about an adiabatic process? Where is the start point for calculating the change in entropy of the Universe for charging/discharging a capacitor?


Me and my dad are having a dispute over if this is is a run on sentence or not: From making silly pictures on Photoshop to playing a game that brought me to another world, and even being dubbed as the IT guy in elementary school. He argues that it's a run on, and the ending can't stand on it's own. I think otherwise. May anyone help settle this debate?


I was wondering if there is a method for finding primitive idempotents of a finite dimensional algebra (over a field)? or in other words is there any way to build the complete set of primitive idempotents from one (idempotent)? Or if it is impassible to find a method, I believe a good reference or some tricks (general notes) on idempotents is also going to be very useful to me.


Sometimes, I forget to use the proper form when an adverb is required. Or sometimes it simply doesn't appear to me one is required, unless I actually consider the grammar of my sentence. I suppose that's mostly because in my native language (German), there is no morphological difference between an adverb and an adjective. This led me to wonder: Is this distinction in English merely an idiosyncrasy or can I really semantically convey something other than intended, if I omit the suffix by mistake?


I'm doing an analysis, of client contracts that contain the following factors: The per-unit license price (A) The initial order quantity (B) The recommended retail price (C) What I'd like is a single figure that represents "How good of a deal" the client got, with the quality of the deal being a low license price in comparison to both the initial order quantity and recommended retail price. Generally speaking, The per-unit price decreases as the initial order quantity increases. The per-unit price increases as the recommended retail price increases However, as the contracts were often negotiated, there is a lot of deviation between the individual contracts. How can I go about this? My math is embarrassingly super rusty.


This is perhaps a beginner/simple question, but how does includegraphics determine the "box" encapsulating a vector graphic embedded on, say, a letter-size paper? When I read my EPS files (generated with Matlab) using GhostView, they appear in some corner of a full-size, otherwise blank page. Do the various page properties (like orientation, type, etc.) matter? And why does there need to be some blank page underneath the saved graphic for that matter? I'm trying to understand how best to prepare figures for publication. Thanks in advance.


What is the principle behind centrifugation? I understand the idea that you spin something around the centripetal force will cause an apparent force on the spinning system. However I don't quite grasp how particles (in the non subatomic sense) with different density should be affected differently. Quite coarsely, I would expect to write down Newton's second law, but then the mass would simplify and the acceleration of every particle would be the same, regardless of mass. Is friction the answer? Or am I missing something silly?


For a long time I have been investigating this question on my own, but it seems impenetrable. The question is this: To find a method whereby it becomes possible to convert proof A into proof B, where the proofs A,B can be of anything, e.g. a lemma, theorem, etc. For example, it is possibly in geometry to solve something by means of coordinates or by means of euclidean geometry. However, these proofs are usually found one after the other, independently, and not derived one from the other. I am asking if it is possible to derive the euclidean geometry proof directly from the coordinate proof, or vice versa. I would really appreciate any insights regarding this from experts, or papers/articles that touch on this topic. Thanks.


I have some confusion over the ER=EPR conjecture. In what way does entanglement in the laboratory lead to black holes? I must not be reading the literature correctly. Perhaps it should read " It's possible to entangle particles near an Einstein-Rosen Bridge in a way to effectively show ER=EPR by appropriate measurements. Perhaps some confusion on my part on what the target of the conjecture is so I can image what sort of measurement would be used. It's difficult for me to think of physics without a measurement.


Here is an example from Murphy's grammar textbook: You are in a restaurant. You and your friend are looking at the menu. Maybe your friend has decided what to have. You ask her/him. You: What ...? The correct answer is "What are you going to have?" My question is: the decision is being made at the moment of speaking, so shouldn't it be "What WILL you have?"


So everybody says the gravitational field has no curl, and is not comparable to a liquid swirling around a drain. Observationally, of course, there are many examples of vector fields (which I think are gravitational fields) which look like they have some curl. A pair of stars, for example, one being slowly devoured by the other. The path of the swirling gas seems to trace out a field with a lot of curl in it. Just as if you were to pour dye into water that is swirling around a drain. How do you reconcile the observed vector field with the gravitational field which is not supposed to have curl? Is there some way to work them into a single model?


I am looking for a book (or article, or notes...) explaining details about the link between integral points on varieties defined as complement of certain divisors and integral solutions to the equation(s) defining the divisor itself. Namely, if I have a projective space defined over a number field and a divisor defined on it by a polynomial, I can define integral points on the complement of such divisor (quasi-S-integral points, following Serre). I know I could do (and I have done) the work by myself, but I am pretty sure that an expert review could give me examples, insights and references I am missing. Thanks!


It's common to say that a pregnant woman is expecting, but is it acceptable to say that her husband is expecting? I ask because my male teacher's wife is expecting in a week. In case you didn't know, to be expecting means (for a pregnant woman, at least) that one will be giving birth soon, but it could generalize to males as meaning "will have a new child soon."


I was reading about function and I came across this text, If A and B have same number of elements and particularly if A = B then we only need to prove one of either onto or everywhere defined to prove that it is a bijection. Now I don't get this point. I will be thankful if someone can elaborate this with an example. Thanks in advance.


I have found out that using the verb be in passive constructions such as: I had my house be burned down is incorrect, therefore it should be I had my house burned down. But is it possible instead of be to use get? E.g. The wire is passed through the pliers in a specific way to avoid having it get bent. The rope had its surface wear. The rope had its surface get worn. The rope had its surface worn. The first two sound very odd to me, but just for clarification could you please point out the errors and which ones are correct? Or is using get, be it in -ing or the to infinitive, in any situation along with have incorrect?


Serre's Duality Theorem is well known and well studied and, as far as I know, there is a "big" algebraic proof for the general case, which is now kind of standard, and can be found in Hartshorne and other references done pretty much in the same way. On the other hand, there is an analytical proof for the small case of complex algebraic curves (compact Riemann surfaces), which makes use of differential forms, meromorphic functions, residue Theorem and so on. Since the curve case looks special, I was wondering if anyone knows of the existence of a more simple algebraic proof of Serre's Duality Theorem and can give me references. Thank you very much in advance.


In layman's terms, how do you determine the resistivity constant of a non-ohmic material having measured voltage and current? I understand that non-ohmic materials don't follow Ohm's Law, but will this still be able to be used to determine the resistance? Otherwise how can I determine an initial resistivity in order to use R=[rho]l/A to figure out the resistivity? Is there a different formula for this circumstance, or will I need to collect more data? (Yeah, even I know it's a totally dumb question)


Suppose there's a box with one face cold, and the opposite face hot. So when the air molecules hit the cooler face, it will transfer its momentum and energy to the wall, bouncing back with less momentum. And when molecules hit the hotter face, it will bounce back faster. And the hotter side will be hit more frequently by air molecules. So will the box feel any force due to the temperature difference?


If I place two positive charges of different magnitudes on the x-axis (one at the origin, one at the some position x), as the two charges repel each other are the forces that they impart on each other the same? Why? Edit: I'm working on a problem that has that situation, and the problem asks for me to find the position of one of the charges if the other one is at a given position. Why can't I just set the two forces equal to each other and use that to find the position of the other charge?


I have to do an experiment about light. I preferred to measure the speed of light by the experiment of Michelson and Morley. When you do the experiment, it will result in an interference pattern by changing the distance of one of the mirrors. I know they had the intention to measure the speed of light relative to the ether and the earth. But how could they derive the speed of light with the resulted interference pattern?


If I call my mother when I am done shopping in the morning, I might tell her "I am coming home" if she is at home, but "I am going home" if she is not. That afternoon at home, discussing the day's events with my father, I could say "I had already planned to come home after shopping," or "I had already planned to go home after shopping." Which is preferred, and why?


A pattern that begins a word is generally denoted as "prefix", one that ends a word is generally denoted as "suffix". Is there a word that indicates a pattern that surrounds a word. For instance (hello), is there a word that indicates the parentheses? So if I have several patterns i.e.: "hello" (hello) {hello} [hello] etc. What word do I use for the surrounding pattern?


I am not a native speaker of English and I am now reading a Sci-Fi book called Dune. I am unable to grasp all the sentences but I do get the overall meaning of paragraphs. But this sentence is completely puzzling me. One of the slave-concubines permitted my father under the Bene Gesserit-Guild agreement could not, of course,bear a Royal Successor, but the intrigues were constant and oppressive in their similarity. Here are my doubts: The "could not" refers to the agreement or the permission by the slave-concubine? The "intrigues" refer the details of the permission or the agreement? Could someone please help. I really enjoy the book and would love to understand it better.


A person repents to God. Then God responds to their prayer and (v) their repentance. What verb goes here? What is the correct collocation? The only examples I can find on the internet are : 'I was earnestly begging of God to give me repentance.' and 'Then hath God also to the Gentiles granted repentance unto life.' However, the meanings of these sentences are unclear. Does 'give/grant repentance mean that they were given the chance to repent? That's not the meaning I'm looking for.


I've just lost a word I use frequently whenever talking about the reasons for punishments. The word should (I think) fill the blank: Punishments, such as jail time, __ people from doing crime. The word is related to stopping, hindrance, incentive, restrict, etc. In this usage, it should also imply that it stops people from committing crime because they don't want to go to jail. Jail also stops people from committing crimes because they can't leave jail. It should fit both of these simultaneously. I hope this isn't too far of a stretch.


I'm using TextMaker. This is my first time using bibtex. I tried a simple example found in forums where I created a .bib file and ofcourse a .tex file. Problem occurred when I tried to run my bib file. It says "Log File not found!". My .tex file runs fine. I know this is not supposed to be that complicated. As I just want to create a simple bibliography using bibtex.


I have seen some similar questions but I admit I'm a newbie when it comes to cgi and general server setup and need some direction. I have a personal domain hosted on yahoo.com that I would like to install LaTeX on. I would like it so that it works in the following (or similar) way. Typing <img src="www.mysite.com/latex.cgi?{my formula}"> will create a rendered gif that I may post on other websites, mainly forums without LaTeX support where I like to help others. Only basic packages are required for my uses (at least for now), things such as Tikz are not needed. So is this very difficult to do?


In many religious calendars, the day goes from sunset to sunset. When translating to the civil calendar, you can divide that day into two parts: from sunset to midnight (A), and from midnight to the following sunset (B). For terminology, "eve" works well for part A. Is there a term for part B? The closest I've found are "day", "morning" and "morrow". Is there another term that could be used?


Do you think that the following sentence structure is correct? "Attach any material you need included". I meant to say "Attach any material that you need to include". I agree it may not be formal but I don't think it is wrong or difficult to understand. Do you think that the sentence is wrong? If yes, where do you think the problem is? Could anyone help me with this?


I'm trying to understand the symmetry content of the conductivity matrix: one information is, presence of time-reversal symmetry causes the off-diagonal terms to vanish. When this is broken (e.g. in Hall effect) off-diagonal terms become finite. (A side question is, why is the conductivity matrix always anti-symmetric?!) Apart from that, does it contain any information about the spin of the charge carriers. My guess would be it should not, as one computes conductivity using classical theory. If I take a spin-orbit coupled (SOC) system (where inversion symmetry is broken), will the SOC information be present in the conductivity matrix? If it is, then how? What other symmetries in the system are relevant for the conductivity matrix?


I have heard that in America, and likely elsewhere as well, we are beginning to be more gratuitous with our use of extreme words when not entirely accurate, such as the words "awesome", "always", "never", "crazy", etc. Is there a word or phrase to name this phenomenon? What are the implications of this behavior with respect to our use of language and its effect on our lives?


In the photocurrent experiment, if the intensity of light is kept constant, but the frequency is slightly increased, what's the effect on the saturation current? I think saturation current should decrease because the number of photons should decrease. But, all my reference books say that the saturation current depends only on intensity, and since it is constant, hence there will be no change. Can you please tell me which reasoning is correct? And why? EDIT: Another confusing factor is the energy of electrons. If the electrons have more energy due to the increased frequency then I would take less time to get to the anode and that should increase the current. Now, which factor is more dominant? And how do i know that?


I couldn't help but wonder every time I saw such a noun phrase. I've seen both forms used equally often, so I guess both of them can be used interchangeably. But do I guess right? Some examples: Here is a frequently used compound nouns list. Here is a frequently used compound noun list. I usually rephrase them into something like this. Here is a reference list of compound nouns.


I think I understand both the centrepedal effect and Einsteins curved space time. However I am confused about which best describes the motion of a planet ( or other orbiting body ). Simply put, does the earth experience any centrepedal effect or does it just follow the geodesic line and therefore not experience any centrepedal forces. Can someone please explain or let me know that science has yet to answer this question.


So I have to write a report paper for a course and I would like to prove that the q-Gaussian is the distribution which arises once one maximizes the Tsallis entropy. But I face difficulties in proving it. Actually I am quite new to the field of Statistical Mechanics and not really familiar with the methods of going through a proof like that. Could it be possible that someone providess a reference which provides the proof or show me how to actually maximize a distribution, so that I am able to start at least from that? Thank you!


Every word I say is true; this I promise you. I think the pronoun 'this' is the direct object of the verb 'promise' and 'this' should be be placed after 'you', but it is placed at the beginning of the sentence. Because this sentence is on a web page about English grammar at http://grammar.yourdictionary.com , I believe this is not grammatically wrong. Is this an exception? Then, how can it?


Is it theoretically possible for an object or particle to change to the opposite direction without making a complete stop first? Lets say I have a fictional hammer swing setup like this: I fire an electron to the hammer and the hammer smashes it back, is it possible for the electron (or any other particle or body) to change direction without slowing down and making a complete stop? If not, which law defines that? Note: the question isn't about the hammer part but that was just the first thing that came up in my mind.


I have recently been reading about Quantum Electrodynamics which I found very interesting, but even more confusing. I understand photons mediate the electromagnetic force and interactions between charges can be described by virtual photon exchange. And that in Quantum Mechanics particles paths can be evaluated by sum over all paths... An electron travelling from one point to another will take all paths, emitting and reabsorbing virtual photons. Does the electrons take all paths including those that involve faster than light velocities? Is this question null, Does it mean anything to ask about properties of virtual particles? Do I have the wrong idea about what virtual particles are?


Lets consider the following: The book doesn't explain, "What's the wisdom behind education?" Changing this to an indirect question becomes the following: The book doesn't explain what the wisdom behind education is. Now, I found many instances on Google where structures like this weren't really converted to indirect questions. For example: The book doesn't explain what's the wisdom behind education. "[She] doesn't say what's really on her mind." Edit: And consider the following: What's the logic behind it. (a) I wonder what's the logic behind it vs. (b)I wonder what the logic behind it is. (a) sounds better but why? And are these constructions acceptable?


I vaguely remember seeing something like a "picture" of various groups a while back. It was as if the elements of the group were each associated with a point and many points had segments connecting them, but not all were connected. Does anyone know what I am talking about? If so, would you care to take the time to explain the basics (or point me to a resource, if you think google won't help)? Thanks.


Is it possible for a black hole to be ejected from a galaxy after an encounter with the central supermassive black hole? What would be the impact of the passage of the hyperV-BH through the galaxy? Is it observable? Have we observed any hypervelocity black holes? What experimental techniques do we need to be sure (how should current methods to discover gravitational lensing be modified)? Please note that arXiv papers and articles out there mostly talk about hypervelocity stars.


I'm thinking of writing a paper on a new way of deriving the conservation of energy from symmetry principles and the Galilean transformations, but I'm not sure where to publish. Taking a look at AJP, it tends to be there for teachers at universities writing papers on how best to teach a certain topic, and to clear up misunderstandings. On the other hand, my paper certainly isn't to do with cutting edge physics, but merely another approach to something that is understood in other ways, and therefore not worthy of being published in Physics review, say. So where should I publish? More generally, how are the papers physicists publish mainly categorised, and which main journals publish papers in these areas?


Hmmm... You can definitely drop down the voltage, and ideal capacitors don't dissipate any power. So it seems, at first glance, that you could use a capacitor divider as a lossless voltage step-down device for AC. So you could use a cheaper variable cap divider as a replacement for a Variac? And it would be continuously variable, too, whereas the Variac is only variable in discrete windings. There has to be something wrong with this. What am I not thinking of?


I am stuck in this problem for a while, and the main idea will be important for some exercises, so I really want to know how to find an example like this I need an example of an proper ideal, let's say M, of C[x,y] (the ring of the complex polynomials in x and y) such that the quotient C[x,y]/M do not admit a homomorphism f(x,y) -> f(a, b) (for a, b complex numbers) from C[x,y]/M -> C.


I've been wondering if there is a word to express that something was current at the time of its creation. It (in bold) should plug-in into a sentence similar to: The results are based on an analyses that deal with the then-current methods. As far as I can tell, both "contemporary" and "current" refer to now, whereas I would like to express something was "current" in the past.


I am looking for a textbook in control theory (for a friend) that covers topics such as Pontryagin's maximum principle. My friend is not a mathematician by trade, but holds a degree in applied mathematics (and is thus not math-shy, but prefers to skip detailed discussions on regularity and prefers intuition). Recent aspects of control theory (e.g., viscosity solutions) need not be present. (I apologize for all the parameters)


What would you call someone who does things knowing specifically that his/her actions will cause pain and/or conflict or completes an action just to get someone in trouble or hurt them? For example, in Private Peaceful there are two people that are in love, but the Colonel goes out of his way to tell the father of the girl that the boy is a thief and would be bad for their reputation. What is a word that would describe him?


In the phrase "My dog wiggles it's butt" there seems to be a division of opinion as to whether the use of the apostrophe is grammatically correct. I suggest that as the dog in question is the owner of the butt in question and that said dog is an animate object replaced by the use of the word it then the apostrophe is a correct. Just as we use the apostrophe to show possession in the phrase "Mary's head."


To negate a participle phrase we use not at the beginning of it, as in "Not having heard the news, he had no idea what was going on." Can we also use the negative particle in some other porition in the sentence without it making any change in the meaning of the sentence? As in "Having not heard the news, he had no idea what was going on." Is it entirely wrong or is it used in spoken English by native speakers (even as a common mistake among native speakers of English)?


So I've been correcting an architectural piece translated into English, wherein a sentence befuddles me: ...A wooden table... marked the location of a previous bench. What the author tried to say is that a wooden table is now located where once stood a bench. This usage of previous simply doesn't feel right to me. Any advice? PS, what about location in that sentence? For me, if a noun has to be used, locality seems to work better in the sense of "the fact or condition of having a location or position in space" of the word. Or am I over-scrutinizing things here?


I would like to express that I fundamentally upgraded something in a concise way. That is, I did not create that something, but it is almost as if I completely redesigned it and made much better. The word would be used in the following way: I fundamentally upgraded the manufacturing process to allow for considerably higher modularity and efficiency. 'Improve' or any of its synonyms are too weak, whereas 'fundamentally upgrade' seems too clumsy to me. I guess 'revamp' is pretty close but it seems to me that this word might be too informal or not be appropriate in the given context. Do you see any alternatives?


Currently using BibDesk with TeXShop (for mac). The apalike bibliography style is pretty much perfect for how I like (and more importantly my advisor likes) to do my references. The only problem is that the citation that comes up in the text [Author, Year] is repeated before each entry in my reference list at the end of the document. Is there a way to remove this so I may just have the Author, Year, Title etc. as normal just without this extra square bracketed part at the beginning? Here's what it looks like: Many thanks for any contribution you may be able to give in advance!


If there is a mechanical device which is controlled by electronics, these electronics can be hidden inside the device itself or hang outside it and connected to it by wires. Is there a word which indicates the second option, without writing a lengthy sentence? Example: instead of: "... a device with a controller connected to it by wires" something like: "... a device with a controller _ wires". (in wires? on wires? by wires?) "on wires" would seem to be the logical choice to me, but I couldn't find a single relevant phrase on Google.


Not too long ago, someone began to discuss the thinking and motivation behind the Lagrangian and its formalism for the Newtonian framework and an intuitive understanding of such formalism. Somehow, it ended in the case that the Lagrangian can be understood in terms of conservation of information (largely) without having to rely on other laws. Is this line of argument correct? And, more importantly, would this mean that unitarity is a stronger statement than conservation of energy?


I would like to hack a new BibTeX style file based on plain.bst, in which I make it possible to display the value of a location field in the inproceedings entry type. I have started as follows: I have added location to the list of defined fields in the ENTRY block. In FUNCTION{inproceedings}, I have simply inserted the line location output right after where it prints the booktitle. This works! However, now I would like simply to enclose the value of location in parentheses. I have tried defining a FUNCTION{format.location}, but I don't understand the BibTeX language well enough to get this right. Any suggestions for the function? And how do I call it in FUNCTION{inproceedings}?


I just don't get the concept behind why a lens or a mirror forms a reproduction of the object at present. Is it to do with the object blocking parts of the light source? I just don't understand why an image of that object is produced. The question is essentially trying to understand what causes the image to be produced from the object, in the first place.


I am rather puzzled and confused, I have been trying to get a clear understanding of how would spectral clustering work for an undirected weighted graph, I have used the normalized Laplacian, but I always get complex not strictly positive eigenvalues, all the resources I am finding build on the results that the Laplacian is real symmetric positive semi-definite matrix, hence real non-negative eigenvalues. Any guidance is greatly appreciated, specially in the answer to the question if I take the norm of the normalized Laplacian would spectral clustering algorithms be still valid with same results.


Is there any "second-countable" theorem ? With this i mean if there is any result like Nagata-Smirnov Theorem (that states necessary and sufficient condition for a space be metrizable), but for second-countable spaces. Also, with Urysohn Metrization Theorem it's straightforward to prove that if a space is compact and Hausdorff, then is secound countable iff is metrizable. Is there any result like this but with the hypothesis that the space is only Hausdorff (i mean, something like : Let X be a Hausdorff space. Then X is second-countable iff [something]) ? Thanks a lot !


As an external observer at infinity, I observe a star collapsing. But because the surface of the star will be infinitely redshifted, I will never see the formation of the black hole. For me, there will be always some matter outside, it never crosses the event horizon. So, can I observe the Hawking radiation if I never observe the formation of the black hole ?


A finite presentation is a presentation where the set of generators and the set of relators are finite (Source) I'm studying for an exam where one of the "exam topics" is: The example of the infinite presentation. But what is an infinite presentation? From the finite presentation my first thought was a presentation where the set of generators and the set of relators are both infinite. But since I can't find any example on this in my notes, I suspect that the definition only requires that the set of relators is infinite.


So basically, you have three different types of 'things' (for lack of a better term): You have that which is necessary, that which is contingent (you have a choice), and that which is necessary but only because it must be so after a contingent choice has been made. So it's necessary, but not to begin with, and is necessary in a very different way. I guess you could call that which was necessary to begin with, necessarily necessary, and that which is necessary by choice, not necessarily necessary. But of course, am sure there's a better word, or at least term, to describe this phenomenon.


I took matrix computations course, our course book is Numerical Linear Algebra and Optimization. As a computer science student, sometimes I get the impression that I lack some fundamental background knowledge about it. It'd be great if you could introduce some useful but not very long elementary linear algebra sources (not very long, since I should get back to my course book ASAP). Please note that I've Googled the subject and got some cookbooks but I am looking for some sources which are specifically related to the above mentioned book and covers those topics.


I have see a lot of people said it is not possible to draw a circle by Bezier Curve. However, I want to know why? I did see somebody explain, but I am not quite sure what they mean. Like, Bezier curve is parabola, so it is impossible to draw a circle by it. But how can I proof it? proof that Bezier curve is only parabola and never be circle?


I know that demonstrating the Mandelbrot Set is connected requires a non-trivial proof, and that Mandelbrot himself was fooled at first. But can it be demonstrated visually that the set is connected? If the Set were known to be path-connected, I might hope for a computer program that would let me select two points in the set and demonstrate the path between them. Showing connectedness visually seems harder to me. Is there an intuitive way to do it? Perhaps allow the user to draw a region R and then identify at least one point on the boundary of R is in the Mandelbrot Set? Unfortunately that seems less satisfying than demonstrating a path.


I'm currently studying electricity on my own, and as I read in a metal electrons are moving across the metal freely (depending on the attraction of the nucleus). As we close the circuit, an electromagnetic waves spreads into the metal moving the electron from the minus pole to the plus pole. Can someone explain to me why is there an electromagnetic wave created when we close the circuit and why it forces the electrons to move like this? Thanks a lot


Which one should it be? One of the guys' One of the guy's EDIT: Never mind, I think I answered my own question. I realized it would probably be related to the object being possessed. E.g.: "One of the guys' swords" means "There are multiple guys. They own multiple swords. I am referring to one of those swords." "One of the guy's swords" means "There are multiple guys. One of them owns multiple swords. I am referring to one of those swords."


Can anyone please explain exactly how formulas like Tupper's self referential formula can be constructed? I'll like to see the reasoning behind the derivation of such formulas and the steps required to create a new one. NOTE: I know Tupper's self referential formula is not as 'self referential' as it is claimed but some form of 'universal' formula capable of producing any bitmap of a given size, given the value of N.


Imagine a structure that is held above the water by pylons that are grounded on the ocean floor. In between these pylons is a pontoon that, when tides are rising holds and lifts a heavy weight. When the tide is falling the weight is supported by the structure, which can gradually let the weight down, and in doing so create electricity. Would this be a practical or even viable way to create electricity? Why or why not?


I have a image in a beamer and I want to overlay a table on that image. How can I achieve that ? I have a figure that I created in powerpoint which is as follows: In the above figure, the statistical parameters such as RMSE and NSE are added later. Is it possible to add similar thing in latex beamer ? I want to show the text first on the upper panel and then on the bottom panel. Thanks.


I wonder what could be a good book to start learning in depth all aspects of the Fourier transform up to the FFT algorithm, and beyond. I am going to dedicate quite some time on the subject, so I expect something with a lot of exercises (calculus, demonstrations) and solutions, from the basics up to the most complex topics. Could be nice to also have some exercises (with solutions) with practical applications in Matlab or Python/Numpy. Any pointers? Tutorials, books, chapters, websites? thanks! :)


I was trying to measure the noise of a device with metal probes. I was not sure whether I should trust the results because I was told contact noise might contribute to some degree. I am a little confused about the notion of "contact noise". Is it because of the contact resistance (every resistor is a noise source)? Or is it something related to other factors such as probing materials or surface? Could anyone make a brief explanation? I am eager to know the origin of this "contact noise", and how I can evaluate such noise.


Usually, I think "have to" indicates obligation, which is pretty similar to "must". But today I found this sentence and its usage of "have to" confused me: (it is from NYTimes.com) Long-term forecasts seem to me rather like time capsules, designed more to provide retrospective amusement for those who eventually have to read them, than to be taken seriously as they are first uttered. It would be uncomfortable to interpret have to as must since we are not "compelled to read them". Can anybody explain this for me?


For Hausdorff spaces the following are equivalent: Every point admits a compact local base. Every point admits a compact neighborhood. Every point admits a precompact neighborhood. Every point admits a precompact open neighborhood. (Among these the local compactness is the usually applied one.) For non-Hausdorff spaces: What are examples where neither of them are equivalent? What situations make the latter two become important? (I'm just wondering as these are almost always taken as definition.)


In German, there's a term "Reizblase" which describes the bladder of someone who has to hit the bathroom every ten minutes. The dictionaries suggested "irritable bladder" as a translation which - seeing how other "Reiz-" organs are also called "irritable" - makes sense. The thing is, the German word holds up nicely in a highly colloquial sentence. I'll try to emulate that in English. Dude, again? WTF? You really got yourself one irritable bladder right there. I am not a native speaker but I feel like "irritable bladder" doesn't fit in with the rest of this sentence because it is a different register. Is there a more colloquial term? If not, would people say a sentence like the one in the example?


Basically a friend of mine and I have had this hot debate for a little too long, I contend that these two tools are not only logically unconnected but they require different assumptions (I believe one requires a continuously differentiable function and another requires it to simply be continuous). We've even gone through the proofs and disagree on how the assumptions are used. I don't see the connection... Maybe I'm wrong, maybe they are equivalent (you have one as a tool if and only if you have the other). Anyway, any fresh perspective would be welcomed and any deeper discussion on either appreciated, thanks.


There are many books, in which Yang-Mills theory is introduced "just like that". But I didn't find some book with set of historical arguments, which had led people to using it in quantum field theory. Can you tell me about this? Maybe, my question leads to the next question: how did people guess that they need to expand the group of local gauge invariance for describing, for example, quarks?


When saying a sentence like: Nikola Tesla __ famous because he was a genius. Should the blank be replaced by is or was? Or is it dependent on when the person is/was famous? If so, what exactly are the rules? I searched on Google and English.SE but didn't find an answer, even after using quotes to counter the amount of stop words in the question...