This image from NASA illustrates drag coefficients for several shapes: It is generally accepted that some variation of the teardrop/airfoil shape has the lowest drag coefficient. I was wondering what shape has the highest drag coefficient. The image suggests that it is a flat plate, and that would seem to be an intuitively correct answer, but is that correct? Is there some other shape (perhaps with a concave front or back relative to motion) that has an even higher drag coefficient?


Clouds are made out of tiny droplets of water. These droplets, to my understanding, act like tiny prisms (which is why there are rainbows after rain). From my line of thinking, if we had a room with a bunch of prisms randomly placed about and had a light enter from one side, the walls would be quite colorful. Why, then are clouds white (and then darker shades of gray as they become filled with more rain)? Edit: I understand that white is all the colors together, but if that logic applies to clouds, then why not rainbows?


Question: Which of the following affect the frequency of a tuning fork? Tine stiffness Tine length The force with which it's struck Density of the surrounding air Temperature of the surrounding air Answer Attempt: Based on the formula for the frequency, I know that tine stiffness (or density) affects it, and so does the tine length. I believe the temperature and density of air can have a slight affect as well. What about the force with which it's struck?


We're releasing a website in which the users can submit and join video game competitions. The game can be League of Legends, FIFA, Counter Strike and so forth. We're not native english speakers so we're not sure whether we should use "tournament", "championship" or simply "game" to characterize an instance of these competitions. What is the difference between these terms? Which of them would be more suitable for one single instance of an eletronic sport competition?


This is possibly a silly question but when we derive the equations of motion of a particle using the principle of least action. We must assume that there is a single minimum (for a fixed choice of boundary conditions), right? What happens if we have two minimums? How do we decide what trajectory that particle took? Is it just a case of never creating a Lagrangian with that form?


I am documenting a piece of software that will be transferred to a customer. The customer will run the software continuously. They may choose to update and improve it, but this is optional. To keep the software running smoothly, there is a minimum set of upkeep tasks that must be done periodically. Things like checking error logs, testing server uptime, making backups, and so on. For the document, I want a recognizable term to describe this set of activities. Here are words I thought of so far, which I feel are inadequate: Minimum upkeep tasks Maintenance mode Life support activities Bare-bones operation


I am working on a barn door tracker for taking astro photos. My drive train has a small periodic error that I'm trying to eliminate and I was hoping someone might be able to suggest a formula that would approximate what is shown in the attached image. The image shows three cycles of the error. It appears to me to be similar to a sine wave but with the upper half stretched out. It doesn't need to be exact, just something so when I subtract it out, I'll get close to a straight line. I hope that makes sense. Any assistance would be greatly appreciated.


I am currently completing a maths project that aims to approximate the roots of functions using MATLAB. The two root finding methods that I have used are inverse quadratic interpolation and the secant method. I have written scripts for both methods and have obtained approximations to the roots of different functions. I was wondering if it was possible to graphically illustrate the various iterations for a specific function, on the same graph, to show the method converging to the actual root value? If this is possible I would like to be able to complete it on MATLAB if not then excel? Does anyone know if this is possible or even how to go about completing it? Thank you!!


Wikipedia gives the following definition of a formal proof: A formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language) each of which is an axiom, as assumption, or follows from the preceding sentences in the sequence by a rule of inference. Given this definition, a sequence whose final term is an axiom could qualify as being a formal proof. What would it be a proof of? The idea that an axiom can have a formal proof, seems anti-intuitive. I haven't been able to find a definition of 'formal proof' sufficiently detailed as to unequivocally answer the question posed within the title of this post.


I have heard of impulsive differential equations being used in some epidemiological models of infectious disease. I haven't heard of them before in my math education, and I was wondering how they might work. I presume there is some mechanism to introduce a step-wise/impulse discontinuity, but I'm not sure what a simple model might look light, or how it behaves. Any help would be appreciated.


In the foreword for a knitting book there's this passage: Knitting has become as ubiquitous as the humble sheep. Which is followed by a couple more sentences on how great it would be to learn how to knit etc. I've googled "the humble sheep", and haven't had any success. Is the phrase roughly equivalent to "Wool is everywhere nowadays, and wherever there's wool, there's knitting"?


I'm using the word subscription with the following meaning: subscription: an arrangement to receive something, typically a publication, regularly by paying in advance. (Definition taken from Google, I'm not sure how to link to the source) Basically, I'm looking for a word that is an arrangement to send something. Does anyone have any good suggestions for what that might be? I have thought about Producer & Publication, but they seem a little off to me. A 'Producer' can produce the something to send, but doesn't necessarily have to send them and a Publication seems like the something that is being sent.


Our company occasionally has to write letters to a third-party in response to a complaint. There are times when we only know the complainant's last name (usually with first initial). Typically, we would write something like "Mr. Jones signed up for service on..." or "Mrs. Smith contacted us on...". If we do not know the person's gender, what is the appropriate way to refer to the customer? Would we just use "complainant" or should we ensure that we use the customer's name? EX: "The complainant contacted us on..." vs. "J. Smith (the Complainant) contacted us on..."?


A Ponzi scheme is a fraudster uses money from new investors to pay old investors, so that it looks like he is doing something profitable. At some point, when all the investors want their money, he doesn't have it (because he took some of it). A key part of the definition of Ponzi scheme is fraud (the fraudster said he was making money when he wasn't). What's the word for a "Ponzi scheme", happening by accident. For example, a bunch of people may invest in a stock causing a bubble, and then the price crashes. This is like a Ponzi scheme because those who sold first got a profit at the expense of everyone else, but there wasn't any fraud since it happened by accident.


I am using Tikz externalize for the figures in a manuscript. The original files containing the Tikz/pgfplots code have been deleted (but will be regenerated in several hours when my simulations finish running). In the meantime, I would like to make a few changes to the text and give it to someone else to review. I still have the output files from the previous Tikz compilation. Is there a way to prevent Tikz from trying to rebuild these files and instead use them as is?


I'm wondering if there's a word or term for a person who looks for an opportunity to insult and berate other people. I'm sure you've all been there; you're using an online public forum, like Facebook, to voice an opinion. There's always that one person who gets completely offended, or they take things completely out of context. They then proceed to publicly scold and shame you - excessively, it seems. It makes you wonder if maybe they're just looking for something to complain about, or if they enjoy being abusive? Maybe they just get a kick out of making you look bad, and want everyone else to dislike you? "Troll" and "butthurt" seem to fit fairly well, but I was hoping to find a more traditional English equivalent.


First of all, I ain't a native speaker. And one of the most confusing sentences to me is I ain't going to this place no more. Ain't in this sentence basically means am not, so it translates to I am not going to this place no more. What exactly does no more in this sentence mean? Does it have the same meaning as any more?


I am facing an example that I am not able to understand at all. It says the the limit of a pointwise convergent sequence of positive semi-definite metrices is positive semi-definite. Basically, I do not understand how to use the pointwise convergence for a matrix, that is, I do not know a definition that is general enough to be applied to that case, and I was not able to find it anywhere. Can someone help me?


Here is the full question: Prove that every continuous function on a closed interval is Riemann integrable. Give an example of a continuous function on an open interval which is not integrable. I think he might be Riemann integrable for the second question because I'm pretty sure that every continuous function on an open interval is integrable just by definition. If that's not true, does anyone have any ideas for the answer?


I am brand new to lattices/partitions. Given that the set of all partitions of a finite set is a poset ordered by refinement, how does one prove that it is a lattice? I know you have to prove that the join and meet exist, but how does one construct them in this case? In other words, what are the join and meet of two partitions?


I have been reading about Jupiter as of late and reason I am asking is if Jupiter has strong enough gravity to pull hydrogen to itself then it should be only matter of time when it will acquire enough mass to ignite itself and become a star, same would apply to any other planet that is big enough to hold hydrogen (In other words if planet gains more matter than it looses it will become a star eventually). Or am I missing something here?


As I understand it (and admittedly it's a weak grasp), a computer processes information irreversibly (AND gates, for example), and therefore has some minimum entropy increase associated with its computations. The true entropy increase is much greater, and comes from the conversion of electrical energy to heat. How efficient is a typical desktop computer when viewed in this light? Make any assumptions you find useful about the energy use, computations per second, temperature of the room, etc.


In my mathematical writing in grad school there used to be sentences like "Whenever x is a fish, then x is an animal." (Yes, that's what my dissertation was on!) I am a native speaker of English and this seemed fine to me. My adviser (who is not a native speaker of English, though it's not entirely relevant) insisted that this was incorrect, so I stopped using it because he was pretty much the only one reading what I wrote. He suggested replacing "then" with "we must have that" (which I did). I still wonder, though...is it really incorrect?


I notice that a lot of researchers tend to have crappy-looking websites, often because they aren't willing to put in the time it takes to learn HTML, CSS, and design principles--they'd rather do research. I'm assuming that said researchers know LaTeX, as it's pretty much the standard for academic typesetting. So why not leverage that knowledge to make a kick-ass homepage? Are there any LaTeX packages or tools that are designed with the easy creation of a nice-looking website in mind? And, no, I don't mean just haphazardly turning a topology paper into a Web page.


I once asked some English people the following question: "At what time do you go to sleep?" They gave me a blank stare. You see, I tried to avoid the standard expression "At what time do you go to bed?" because it is ambiguous. I may get into my bed but may not fall asleep right away. I may be reading or emailing on my iPad or watch TV.


I'm looking for a mathematical treatment of mass action kinetics under the assumption of detailed balance. In particular, I'm interested in the proof that the free energy is a global Lyapunov function. There are many papers that prove this for the more general case of "complex balance". However, I'm not particularly interested in that generalisation, because I'm interested in applications to chemistry, which means making different generalisations that are not compatible with it. So my questions are: What is a nice, simple proof that assumes detailed balance and shows that the free energy is a global Lyapunov function? Is there a good overview paper that gives a concise mathematical treatment of the subject without making generalisations beyond what can be observed in a real (closed) chemical system?


This has been bugging me for a while, does anyone know what this word is? Maybe I imagined it. I thought it might have been "superfluous", but I don't think that is it, then I thought it might have been "hyperbole" but I do not think that is it either. Any thoughts? Here is some context. Person A: If a billion people view my web site, my server will crash. Person B: That is a ___ example. The difference between the word that I am looking for and "hyperbolic" is that a hyperbole is not meant to be taken literally and this is. Hope that helps.


Is there a term for the word that describes where a person is from or what nationality they are? For example, someone from America is an American, and someone from Finland is a Finn. Is there are term for the words American and Finn that denotes that they mean "someone from a particular place"? I could have sworn I stumbled upon such a word years ago, but I cannot for the life of me remember it.


To me "I must help her" sounds wrong. I feel that I would rarely say this. On one website they say that 'must' is more for personal obligations (e.g. I must help my mother.) and that 'have to' is for external obligations (e.g. my boss says I have to finish the report.) Is it that simple (and vague)? Or does anyone have a better explanation?


Is the sentence: "We felt we had let our coach down because we hadn't won the match" correct? I read a sentence "We felt we had let our coach down because we didn't win the match" in an English textbook. I wonder that, when we compare the happening time of the three things: A "feel" B "let our coach down" and C "did not win the match" it will be C> B> A. So is it possible to say: "We felt we had let our coach down because we hadn't won the match" also? If it is ok, too, are there any differences between the two sentences? Thank you very much in advance.


I'm interested in knowing the structure of a CNOT gate, in quantum computing. THe problem with that is, that I've read how the structure of a nuclear quantum computer works, but I still don't understand how that can be implemented to create a quantum CNOT gate. I've read the article of the original proposal of Cirac-Zoller, but it wasn't explained very good, I guess, so I want to ask, if someone has a link to some publication where it's explained better than there, possibly with more pictures rather then formulas. Thanks.


A: I can't understand why my parents keep me from buying fast food. B: Me, too. It's delicious. Does B's answer sound natural? In Korea, we usually teach that we should use 'me, neither' in a negative sentence, 'me, too' in a positive sentence. But I am not sure if this is always true. I think that 'me, too' is a valid response in this particular case, but one of my students said that 'me, too' is grammatically incorrect, so it is unnatural. Who is right?


While reading about linear algebra for math olympiads in these notes, I came across the following assertion: Remark. The set of invertible matrices form a Zariski (dense) open subset, and hence to verify a polynomial identity, it suffices to verify it on this dense subset. Could someone provide an explanation of what it means to be a "Zariski (dense) open subset"? A proof of this result is sketched in the notes, but I feel there is some deeper theory going on underneath. In case anyone is interested, the author has a similar set of notes here.


I'm in the process of learning about Matroid Theory (I'm reading Oxley's book). I came to this from combinatorics and topology. Now, I just read of connections between matroids and combinatorial optimization. Yet the only example I've seen so far is that of the greedy algorithm. So, I'm wondering if there is some astounding application of matroids to optimization. By that I mean either something that can be solved with matroids and for which no matroids-free solution is known, or something that can be solved much more easily using matroids.


The Free Dictionary defines it as "to start to accept and deal with a difficult situation," but I don't know what accept means in this expression. Does accept mean to welcome the difficult situation? That can't be right, as I've heard "come to terms with" pertain to one whose friend or family member died, and I doubt anyone would welcome that. Does accept mean tolerate, as in to allow the difficult thing to happen? That wouldn't work either, as going back to the death example, there's nothing one can do to make the dead individual stop being dead (for now, at least). So, I'd like some help understanding "come to terms with" given my trouble with the definition I've seen.


I was excited to learn that XeLaTeX finally has microtype support (I had asked about that earlier). However, after adding microtype to my document, I noticed that line breaks at hyphens now go wrong. Previously, the word foo-bar would be hyphenated as: foo- bar But with microtype enabled, I now get foo-bar and that runs over the right margin. Is this a known problem, and are there tuning parameters to fix this?


I'm working through Mumford's Red Book, and after introducing the definition of a sheaf, he says "Sheaves are almost standard nowadays, and we will not develop their properties in detail." So I guess I need another source to read about sheafs from. Does anybody know of any expository papers that cover them? I'd prefer to not have to dig deep into a separate textbook if possible.


As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates due to gravity. It can reach a point where its velocity is high enough to keep falling but also keep missing the object it is falling towards. What keeps it from accelerating (because of gravity) and eventually reaching escape velocity? I feel like I'm either looking at things the wrong way or I have the entire thing wrong.


I have a circle with a known center and radius. I have an arc with a known radius and two points on its edge, where one end is at the same position as the circle's center. Is there a way to find their point of intersection that's simpler than turning this into two circles and intersecting those (and somehow figuring out which of the two points of intersection to use)? In other words, the green bits of this diagram are known, and I'm trying to find the red:


I'm having trouble deciding whether the word 'name' can be used possessively. Currently I'm thinking it's correct to say: Patients' names have been altered to provide anonymity However it just doesn't look right to me. Is the above correct for a group of patients or would any of the following be better: Patients names have been altered to provide anonymity Patient names have been altered to provide anonymity


What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a convincing proof that it can be done at the level of path integral. How do we know for sure that Minkowski action and Euclidean action lead to the equivalent physical result? Is there an example where they differ by e.g. a contribution from a pole not taken into account while performing Wick rotation?


I have been studying the concept of transcedental numbers. Till now, I had taken it for granted that all important numbers like pi and e were transcedental. I have no reason for assuming this or for clustering them together. It's just my intuition had placed numbers like pi, e and the golden ratio together and for some reason assumed they are all transcedental. This was before I was aware of a rigorous definition of a transcedental number. I just remembered that the golden ratio is one less than it's square. So, it does satisfy an algebraic equation. Does this mean that the golden ratio is not a transcedental number?


I have a problem analysing this sentence from the point of finite/nonfinite clauses, clause elements and their functions: He does not want to destroy his parents' dream of him achieving a Cambridge degree. I am especially interested in the: dream of him achieving a Cambridge degree. I know that 'achieving a Cambridge degree' is a non-finite -ing participle clause. However what is its function? And what is the function of 'of him'? Is it a postmodification?


In a one dimensional lattice system with periodic boundary conditions, in which the last and the first site of the lattice are the same site, momentum is conserved modulo a vector of the reciprocal lattice. My question is if for a system with open boundary conditions, in which the single particle wave functions vanish in the two extremes of the chain, momentum or quasi-momentum is conserved. In principle, there is no discrete (nor continuous) translation symmetry, so momentum shouldn't be conserved. However, I wonder if momentum conservation is completely lost or if there are some remains.


When you put chopsticks (or any other object) in a glass cup of water, why do the chopsticks seem curved or bent? Is it because of the shape of the cup, the water, or the chopsticks itself? Note: I'm sorry I currently don't have an image of it. You can try this at home. Just put a pair of chopsticks in a glass of water. If you have an image, please edit this question and put an image in.


I am a first year student at varsity and I am new to Astronomy. A question came up in my tut asking about the Hubble constant and cosmological time. I couldn't answer it because I have not understood the relationship between the two. What I've heard is that H is constant for space(although I don't understand what that implies), and is not for time. What does this all mean?! Please help...and please keep things simple.


Consider the quote from "What is a Grantor Trust" article. This trust is revocable, which simply means it can be altered, modified, and otherwise changed or even terminated during the life of the grantor, provided that the grantor has full mental capacity. As far as I could figure out from other forums words "alter" and "modified" mean "to change slightly", and "change" is more generic word and may also mean "replace" or "exchange for something else". The text in bold sounds to me like "it can be slightly changed, slightly changed, and otherwise changed". Are there some differences in meaning between "alter" and "modify" in this context or in general? Are they generally interchangeable?


In the most basic sense, what is abstract algebra about? Wolfram Mathworld has the following definition: "Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields." I find this, however, to say the least, not very informative. What do they mean by abstract algebraic structures? Along these lines, what are groups, rings, and fields then? I've been told by a friend that groups, essentially, are sets of objects, although, this still leaves me wondering what he means by objects (explicitly). I don't need anything rigorous. Just some intuitive definitions to give me some direction. Thanks!


I'm a programmer and like to name my variables as accurately as possible (who knows who will be reading my code in a few years' time?) I've been thinking about sports video games recently, and have thought about the idea of a generic sports game engine. Most sports games have an arena, crowds, a playing surface and players. They also have a puck, ball, discus, javelin, etc. and this has me wondering: What is a generic term for this object? Something that could transcend all sports. Edit: Since it seems there may be no exact term for this type of object, I'd gladly settle for some sort of analog.


I think to answer this question we would have to fully understand the nature of black holes. It seems to me that the smaller black hole could have a lower density than the larger one. In this case the smaller black hole might be effected by the tidal forces of the larger black hole. But if the densities of the two black holes were the same, wouldn't the smaller black hole be immune to spaghettification?


Is it somehow possible to extend TexStudio to use dictionary words in autocompletion? For example, when I type "som", I want the autocompletion list to show me all words from the dictionary starting with "som". I know TexStudio uses autocompletion for words that already appear in the same document. I've tried to create a .CWL file, but apparently it is only for commands and plain words are not supported.


I'm trying to create my own ultrasonic humidifier. I ordered the misting part which works great but it only functions correctly in shallow water. So I'd like to feed from a large water reservoir to a smaller one. My question is how can I fill the smaller reservoir to a desired water level? Will I have to use a closing/opening valve or is there a simpler way? (I was thinking a small balloon hooked up to a pulley that opens and closes a latch much like a toilet but I am trying to avoid complexity.)


My assignment asks us to prove or provide a counter example for If R is symmetric, then Rc is symmetric. I know that if R is symmetric, then (x,y) and (y,x) are both in R, but what I do not understand is what is R^c, what does R^c do to the relation? I believe that complement basically means "not", so does that mean the complement of R is NOT symmetric? I can't seem to wrap my head around this concept, any help would be appreciated. Thanks


The metaphor of a surface (typically a pool table or a trampoline) distorted by a massive object is commonly used as a metaphor for illustrating gravitationally induced space-time curvature. But as has been pointed out here and elsewhere, this explanation seems (to a layman like me, at least), to be "hopelessly circular", and in the end contributes little to an understanding of how modern theories of gravitation work. Are there other (or additional) metaphors that might be helpful in illustrating to lay readers (a) what motivates modern gravitational theory and (b) why it has greater explanatory power than Newtonian gravitation?


A field F is algebraically closed if every non constant polynomial in F[x] has a root in F. Is this the right definition? I am wondering if only one root in F and the rest of the roots not in F can also be considered 'algebraically closed'? I remember reading somewhere that if a root is in F then all roots are in F. Is this a special case of something? If so, could someone enlighten me on what it is? Thank you


Assuming an object is moving in a straight line propelled by a force. How much energy would that force have to exert so that there are no known forces or objects that could stop it from moving in that straight line? I'd guess limits like the speed of light might come into play here, but it would be interesting to know what the values would be if those limits weren't there.


I am in sales and when I make a cold call I typically begin the conversation with, "I just wanted to..." Some common phrases are, "I just wanted to see if you might be interested..." or "I just wanted to follow up with you..." I hate this phrase as it shows a lack of confidence and it's not truthful. I want more than JUST to do something, I want to engage in a conversation so I feel disingenuous starting the conversation with this statement. Does anyone have any alternative ways of beginning these statements? Thanks!


I am a newbie to Mac OS X. I installed TeXmaker and found that the Chinese characters in the interface are garbled completely (see figure below). I tried a lot to fix this but nothing worked. Finally I realized that this is related to the "Interface fonts". However, on my mac there's no such setting option!!! (Previously I used ArchLinux and there was indeed such a button) Does someone happen to know how to modify "interface fonts" for mac TeXmaker? Many thanks in advance!


Sorry for the elementary question, but I am confused. Suppose I am telling someone about a conversation I had with a friend the previous day. Which would be correct? "I asked him if he were well" "I asked him if he is well" "I asked him if he was well" Am I right in saying that the third sentence would be "double past tense", as in referring to a previous conversation where I asked my friend if he was well at an even earlier point in time?


Apart from Cantor's diagonalization argument, there are a number of ways to show that cardinality of R is greater than that of N (eg: Baire Category theorem, path connectedness of R and so on). Are there any arguments outside Set Theory which naturally lead us to sets of higher cardinality than R ? In other words, if Set Theory never existed, would we be happy to conclude that there are only three types of cardinality - finite, countably infinite and uncountably infinite - or would we have gone beyond ?


In prime numbers, one has the sieve of Eratosthenes, which is a method of computing the next prime, once you have all previous primes: You just cross out the multiples of the previous primes on the number line, and the first remaining number is the next prime. I wonder whether there is such a method for prime gaps. Of course, one could add up the prime gaps and then apply the sieve of Eratosthenes, get the next prime, and then compute the next prime gap from it, but I wonder whether there is a more "direct" way.


I have a problem in Texmaker. I have divided a document into a number of subfiles. I would like to compile the whole document from the current subfile without running the master file. I tried to define the current file as a master file by changing the status of the current subfile to a master file in Options menu. However, I receive errors after running the subfile. Can you please give me some pieces of advice in this respect?


Let's look at an internal combustion engine (more precisely a standard gasoline car engine) as a black box (so without going too much into details about internal processes). The inputs of this system are throttle (gas pedal position), moment of inertia it sees and possibly external torque? And the outputs are torque and angular velocity. Can you provide me with a simple model of these relations? Or in other words, how do I know how throttle affects the movement of the car?


Could anyone briefly explain, or point me towards a resource explaining, the main differences between the main integration theories, namely: Riemann Integration Riemann-Stieltjes Integration Lebesgue Integration Lebesgue-Stieltjes Integration I understand that this a question with a potentially very long answer, since integration is no small theory. I can find information on these integrals separately, but I would really be interested in a comparison of these integrals with one another.


Recently, I have lost a great amount of work on a project in LaTeX because of unwittingly saving changes when cutting out a large chunk of text and copying the remaining part. I was wondering if there was any way to bring back a version of a LaTeX document from a previous time to this incident. I know such a function is available on Google Docs, but is it available here? If so, how? Thanks!


I'd like to ask how verbs 'to be riddled with something' (idiom) and 'to teem with something' (phrasal verb) overlap each other and can we replace with one another in the same sentence? For example: ...the judiciary are riddled with prejudices and the judicial system is filled with flaws, and innocent people will be executed. His body was riddled with cancer. Her typing was slow and riddled with mistakes. The woods are riddled with rabbit holes. The streets were teeming with tourists. A river teeming with fish ( The sentences were excerpted from Oxford Dictionary Online)


I am writing a large Sweave document that will be broken up into many chapters with the final output being a large pdf of everything and an individual pdf for each chapter (with the same page and caption numbering as in the large pdf). I found some great answers about working with multiple files but haven't seen how to also create the individual chapter pdfs with proper pagination. Is there a way to do that?


I am not a native English Speaker, but I work with English speakers on a daily basis and they have always troubles pronouncing my surname, so they will often ask me to tell them how they can pronounce it. My surname is Sulce. I also tried a pronouncing service and they said "Sorry, we can't pronounce that." So, I would like to ask native speakers to help on defining the most correct way to pronounce it. What's the first pronunciation that comes to your mind for the word Sulce?


I've read in books that one can't put one's hand through a table because the table offers a "Normal Reaction" to the hand. And it is also stated that this force is electromagnetic in nature. But what is this force? Can it be explained using classical electromagnetism "in terms of something I'm more familiar with"? Moreover, if it is this force that stops my hand from going through the table, why is it that certain other solid substances, like sand, don't produce the same result? Also, is there any limit to this Normal reaction? I mean on pushing too hard my hand might go through the table. Is there any upper limit to this force?


A location, A, is said to be equidistant from two other locations, B and C, if the distance from A to B is the same as the distance from A to C. What is the equivalent word to use in the context of time? That is, suppose that the distance from A to B is different from the distance from A to C, but it takes the same amount of time to get from A to B as it does from A to C.


i'm having a problem with the definition of open, closed and clopen sets. I have understood the basic definitions, but then the teacher today in class said that the normed space is limitless. A colleague of mine said then that the normed space is clopen, but i can't really see why. To me, a normed space, since it has no limits, it is impossible to find a ball that has points not belonging to the normed space, so it can't be a closed set, right? Then, it must be an open set. Or am I mixing everything up? Thanks in advance!


I'm looking for a word that describes the act of doing something without a real logical reason but just because they can. A example of what I'm talking about would be like this: The boy hacked the Pentagon just because he could. He didn't steal anything and he didn't want the attention; he just wanted to proclaim his own self-dignity. What would you call someone like that or the act of doing something like that?


I was looking at reviews for Sakurai's Quantum Mechanics textbook, and some mentioned it being outdated, specifically mentioning his use of imaginary time. Is this idea deliberately avoided in modern treatments? I can't see why a simple parameter change t->it, would be or not be an outdated concept. It doesn't make things significantly prettier, but it doesn't hurt anything either. With that said I've never before heard the specific phrase imaginary time so maybe it is outdated.


I am looking for a word or phrase regarding something that is "impossible". I can't seem to put my finger on it, but I am trying to think of the word to describe something that is the top of the top, and thus impossible to achieve? The only two words I have come up with are elusive and formidable, neither of which really mean what I want them to mean. I want something more clever to put it plainly.


According to Biber's Longman Student Grammar of Spoken and Written English, insterts are one of the three families of words (apart from lexical and functional words). At some point, the author explains that inserts generally carry emotional and discoursal meanings, such as oh, ah, wow, used to express a speaker's emotional response to a situation, or yeah, no, okay used to signal a response to what has just been said. Could someone,please, explain in simple words, what does the 'discoursal meaning' mean?


I believe the answer to this question is yes. I was hoping someone would critique my logic. Let X be a separable and metrizable space. Then it has a countable dense subset A. Let B be a basis for X. For every a in A, choose a basis element U in B such that a is in U (if such exists). This forms a countable collection V. Suppose, for a contradiction, there is an element x that is in no element of V. Then x is in a basis element U. U must contain an element of A since A is dense. But this U is not in our collection V, a contradiction.


I'm running into an issue with my dissertation. I'm using a template created to format my dissertation according to the University's guidelines. When I format it using the twoside argument for the class, I get my list of figures and List of Tables pages each with an extra page afterward saying List of Figures - Continued, but there is nothing else on the page. This only happens with the twoside argument.


For example, if I take a slap shot on a hockey puck, from what I understand, the forces acting on the puck are friction, the normal force, and the puck's weight. And, since I'm not constantly either pushing the puck, or pulling the puck there are no other forces acting on the puck, because me shooting the puck was just a one time force. Am I thinking about this correctly?


Which is the appropriate word to be used in the sentence: The system we were testing was determined to be insecure/unsecure. The usage is in the context of security, specifically a lack thereof. I've always said insecure, because I didn't believe unsecure was a word (although unsecured is). Even as I type this, I'm getting a spell check complaint about it. However, I was laughed at once when I called a particular device "insecure."


With reference to Black holes in particular, how can you approximate the luminosity of an accretion disk? It is possible to quantify the temperature at a given point, but as the disk is not a black body, and this temperature is at a specific point, I am unsure how to equate this to luminosity - surely you could not do so using the Stefan-Boltzmann constant?


I happened upon the following sentence in a textbook: 'An increase in the number and size of islets is characteristic of infants born to diabetic mothers. I get that, as the sentence is presented, the singular noun 'increase' is governing the singular verb 'is', but aren't two different 'increases' being described, one in size and one in number? On another note, I would probably see nothing wrong with 'The love of money and power was his undoing'. I'd imagine a single 'love' that embraces both 'money' and 'power'. So, what's the rule in matters like this?


The person at the desk next to me is writing his Ph.D. thesis, and is trying to decide how to lay out some tables. He has too much data for one table, but is not a fan of rotated tables. So we were talking and had the idea that he could make two tables, and place them on adjacent pages so you could see them at once. However, you'd have to make sure they didn't wind up on the front/back of a single page. Is there a way to do that, or is this sheer madness?


The sentence, "he took my toy away" can be rewritten as, "he took away my toy." However, "he took me away" cannot be rewitten as "he took away me." The second sentence sounds awkward at the very least, and I do not think it is grammatically correct, but I do not know any exact rule stating so. Is the last sentence valid, and if not, why?


I recently found myself in a situation where I wanted to use a line that went something like this: "...we must examine the effects these ideas had on their respective creators..." and I just couldn't find the right word in place of "creators". Something feels off about "creators". We don't create thoughts we have thoughts or we think thoughts. "Owners" doesn't really work as no one can "own" a thought, and "thinkers" sounds too childish. What other words are there that describe "the person who came up with an idea"?


In the book The Road to Reality by Roger Penrose, projective geometry as developed during the Renaissance is framed as (eventually) playing a pivotal role in quantum mechanics. (In fact, Penrose seems enamored with the idea that there is some connection between painting and physics, particularly where twistor theory is concerned. The book's epilogue is the most blatant example of this, though other examples abound.) Not having studied quantum mechanics, I can't really imagine how projective spaces would be used to formalize what I know intuitively about the way QM works. Can someone provide a very simple example?


Recently, I have had a debate with a friend that "brings all the boys to the yard" is an idiom and he refuses to accept it. Since this has been used as a part of a rapper's lyrics, he says this is not an idiom. All in all, is it an idiom and how to find out if some phrases are idioms or not? Is there a specific dictionary or a thesaurus? The lyrics go like this: My milkshake brings all the boys to the yard, And they're like It's better than yours, Damn right, It's better than yours, I can teach you, But I have to charge See full lyrics at AZLyrics.com


Recently I wanted to write an essay about the women in Jane Austin's time. I wrote the women at that time were concerned much about how to be engaged to a decent husband. Not like women nowadays, they want to be treated equally as men and realize their value in society. So I want to say the women back in Jane Austin's time, their viewpoint toward life was too vulgar. I am not sure if I use this word correctly or it will convey a totally different meaning. Could you please help me?


So according to my understanding, the free energy of the system should be a continuous function of temperature. This is because if the free energy is not continuous at temperature T, then at this temperature the free energy can have two values (i.e. two states) and the two states will mix to eliminate the difference in their free energies. Is that a reasonable explanation for the continuity of free energy? The free energy is a continuous function of temperature does not mean it is differentiable everywhere, because at the point where the phase coexistence start to occur the free energy is not differentiable. Is that the case?


I've been reading some Feynman's books. There's a point that intrigues me. It's the fact how we understand a physics equation, not only mathematically, but digging deeply into its roots as a physicist. I'm just a first- year- physics student, but I would like to understand the basic equations I'm studying through its physical meaning, but to be honest I don't really know what Feynman meant. I hope you can help me. For example a equation such as: F=ma Thanks!


Dark energy is introduced as a constant inside Einstein's equations. Its primary purpose, from what I understand, is to make Einstein's equations compatible with the accelerating expansion of the universe. As a consequence, of the "predictions" of dark energy is the expansion of the universe according to Hubble's law. I know there are numerous experiments that verify this expansion (and its acceleration), and thus indirectly support the dark energy theory. My question is: Are there other factors that give credit to the existence of dark energy? Are there any experiments that support this theory, but not only through the verification of Hubble expansion?


Consider the category of finite dimensional vector spaces with morphisms being linear transformations. Is it still true that monics and epics are actually injective and surjective linear maps, respectively? The converse is surely true since the category is concrete. I know this monics and epics are precisely the injective and surjective maps in the category of Sets and in the category of groups, but it is not necessarily true in the category of topological spaces, so I'm just curious if it is true or not in the category of f.d. vector spaces, and if so why?


We were learning about Boyle's law (pressure is inversely proportional to volume of a gas) and in the experiment to prove the law, we were told that we cannot change the volume of a gas too rapidly without affecting its temperature. I have two questions about this: Why does temperature of a gas change when its volume changes very rapidly? This process (rapid changes in volume) is used in the liquefaction of gases. How is this done?


In my Astronomy class, I learned that temperature results from the speed of air molecules colliding into your skin. Thus, if the air molecules in the room have a high kinetic energy and thus collide with you at high speeds, your temperature will increase. So how does a breeze of wind, in which I imagine air molecules would be moving very fast (or if they're not moving fast, YOU are moving fast relative to them), result in feeling cooler?


When I say "I cannot attend to it" it sounds like I'm saying "I'm not able to attend to it", while what I want to express is that I'm capable of doing it, but I just don't need to. In Slavic languages it's resolved by changing the negation particle position: [negation] [can] [do something] vs. [can] [negation] [do something]. In the first case I negate "can", while in the second I negate the "do" verb. How to achieve the same in English and not be ambiguous?


I'm studying basic topological, metric and normed spaces and I am curious why one of the axioms of both a metric and a norm is the triangle inequality. It makes some sense to me having the triangle inequality satisfied sometimes, but I don't quite understand why you necessarily need it for a general metric/norm, since there are still topologies arising from it. Could someone maybe elaborate a little bit?


I guess the title says it all. However, I have skimmed through several books, and while they all tell you how to use generating functions to find an expression for the n'th term of a recurrence relation, none of them say why it works. I think I have a somewhat intuitive understanding of what is going on, but I think I need a more definitive explanation.


Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form "gravity wells." Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing?


Let us assume that the standard model is correct up to Planck mass. (Yes, I know, this is a big assumption.) If we continue the running of quark masses with energy (due to renormalization), what are the mass values we get for the six quarks at Planck energy? Is the sequence of mass values the same at Planck energy or do some quarks "catch" up with others? Is there some literature on this issue?


I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary derivatives with covariant derivatives. But I have read somewhere that this generalization is not unique and it is just the simplest one. Can anyone introduce some resources about this subject and how electromagnetism and Maxwell's equations are generalized to curved spacetime?


Possible Duplicate: How does gravity escape a black hole? If nothing in the universe can travel faster than light, how come light can't escape a black hole? I mean, Einstein's relativity says nothing can travel faster than light, but yet, light can't escape a black hole. Does this mean that light really isn't the fastest thing? That the pull of the black hole is really faster than light? That Einstein was wrong, even though it's been backed up by scientific evidence? I'm very confused. If anyone would be able to answer my question, I would appreciate it: Why can't light escape a black hole if nothing can travel faster than light?


I am having trouble understanding this concept, and have not found any good resources on google that explain it in a straightforward manner: An adjacency matching in an undirected graph G is a collection of disjoint edge pairs in G such that if two edges e and e' are paired, then e and e' share a common endpoint. I am asking clarification of this as it is concept presented in homework, to which I will have to develop an algorithm to solve for - in other words, I am asking about the question itself and not the answer.


I would like to know if there is a technical term to cover both interpolation and extrapolation. The reason why I am asking is that I am writing a computer program to do interpolation and extrapolation using a functional-object language called Scala. In there, I would like to define a class/template that abstracts the notion of interpolation and extrapolation. At the moment it is called interpolation but that's not really reflecting all of what it really does since the same methods can be used to do extrapolation. Is there a general term that mathematicians use that cover both these areas?


Recently I wrote the following words. Age gives you the wisdom of experience while youth gives you the intelligence of mental flexibility. There is a horizon time when you have both of these things to a significant extent. Afterwards I looked up "horizon" in online dictionaries and I couldn't find a definition that matched this usage. I see it as similar to calling the point after which light cannot escape a black hole the "event horizon." Is this usage correct?


I was wondering if we could find a set of basis vectors that span the cone of positive semidefinite matrices? I know this question is hard, but I would really appreciate if even someone can share a related paper about this topic in the literature of Linear Algebra. I could not find any paper about this issue. I should mention that any answer to this question should be highly related to the topic of semidefinite programming in the area of mathematical optimization. Thanks


Parallelogram ABCD is bisected by diagonal AD, and produces two triangles ABD and ACD. Prove that triangles ABD and ACD are congruent. My proof (or at least attempt): note I am not a high school student and have yet to learn geometry, I'm attempting to familiar myself with proofs beforehand though. And yes, I know my spelling is atrocious and I should use LaTeX. Thank you!


When calculating the amount of time elapsed for an inertial reference frame over the course of its travel at constant velocity between two points, are the effects of both length contraction and time dilation taken into account (i.e. the distance seems shorter to the traveler and the time for the traveler seems to pass more slowly to a stationary observer), or is only one or the other effect used to calculate the amount of time elapsed in the inertial reference frame in motion? I believe the answer is only one or the other, since the effects are really two sides of the same coin, one applying to an observer within the frame and the other applying to an observer outside the frame.


Ferromagnetism depends on the arrangement of orbitals and spin in the valence electrons of an atom (below its Curie point). But what is so special about the orbitals of iron, nickel and cobalt, to make them the main ferromagnetic materials, and everything else more or less pale in comparison? Please note that I am not asking "how do magnets work?". I know about domains, EM and the like, but on a strictly atomic/QM level, I would like to understand what sets these materials so greatly apart from dozens of others with seemingly similar orbital arrangements.


What's the right word to indicate a type of education based on memorizing facts or a superficial understanding of things, without real insight or critical mind development? In my native language (Italian) we have expressions like "nozionismo" or "educazione nozionistica" or "didattica nozionistica". But, after I looked in the dictionary, it seems to me that the word "notion" in this case is a "false friend". In fact, "nozione" seems different from "notion", which is rather like an opinion.


Noncommutative algebraic geometry is a developing field. Things have not yet got the final form as in commutative geometry. But one might wonder whether things are any better in the case of skew-fields, ie division rings, ie possibly noncommutative rings in which each nonzero element has a multiplicative inverse. Algebraic geometry is much simpler in the case of fields. So are things better in the case of skew fields? For instance, is there any particularly nice geometry over the quaternions, like there is one over the complex numbers?


The definition of an inner product in Linear Algebra Done Right by Sheldon Axler assumes that the vector space is over either the real or complex field. PlanetMath makes the same assumption. Is there a definition of an inner product over, for example, finite fields? I sometimes find finite fields easier to reason about, so it would be nice to have a definition of an inner product for vector spaces over them.


I am a sophomore in high school. When I approach a math problem or concept, I normally try to determine a formula or systematic method of solving all similar problems. However, since I entered precalculus, I have found that this approach does not work. I really love math and find it interesting and exciting, but I find that I am unable to solve the kinds of conceptual problems that I have been doing more recently. For example, when I try to do a counting problem, it is often unclear how to approach it. How can I improve my problem-solving and critical thinking skills? Also, how can I approach problems logically to solve ones that are not clear at first?


Alright, so David Griffiths in his "Introduction to Electrodynamics" states that the Twin Paradox is not a paradox at all since the traveling twin returns to Earth. By returning to Earth, the twin had to reverse direction, thus undergoes acceleration, and therefore cannot claim to be a stationary observer. However, what if the traveling twin simply Skypes the twin that is on Earth. The twin on earth will still appear older, which would make no sense since in that case the rocket can be seen as the stationary frame of reference while the Earth "travels" at a speed close to the speed of light. No acceleration is undergone, yet the paradox remains. Is Griffiths just completely glossing over important nuance again?


Is there any case in classical (non relativistic) mechanics where the strong form of Newton's third law does not hold (that is, reaction forces are not collinear)? For example, if we consider a system of two point particles in equilibrium with each other upon which a constraint acts so that the reaction forces are directed in a direction that is not collinear. Is such a situation possible?


My professor in class went a little over chaos theory, and basically said that Newtonian determinism no longer applies, since as time goes to infinity, no matter how close together two initial points are, the distance between them will increase greatly. But why isn't this merely a matter of the imprecision of our measuring instruments? If we can somehow know our initial conditions exactly, wouldn't we still be able to calculate what the system will be like at some time t in the future?


Is there a word (other than asshole) to describe someone who always says things in a way that makes other people look incompetent in order to make themselves look better? A different word to describe their language would also suffice. Edit: for clarification, here are a few sentences they might use: "I wouldn't have done it that way" "Do you even know what you're talking about?" (Implying that they do and you don't.) "Well, it wouldn't have happened if you knew about such and such." Basically a kind of blame-passing system to cover up the fact that they are the actual problem.


I'm having a bit of trouble understanding the semiconductor band gap diagram on Wikipedia: (from Band gap article). Why is the size of the band gap increasing with the Density of States (DOS) in the semiconductor material? I would expect the opposite given the intuiton that more occupiable energy states would mean a higher probability of an electron moving from a valence band to a conduction band? Should the x-axis here maybe be something like "# electrons in the conducting band" to show the increasing amount of energy needed to promote electrons to the conduction band as a function of the electrons already promoted to the conduction band? And why the ovoid geometry, which I've seen elsewhere?


I am interested in finding out about the current status of the planned book: The Triangle Book by John H. Conway and Steve Sigur. I understand that Steve Sigur died some time back. I got no reply from Prof. Conway; is there someone who knows the fate of this project. Is it abandoned or is it still under preparation? Here is some information about the planned book.


It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero. What exactly is the reason behind this? Except for, of course, the mathematics behind it. Is there any logic why the field intensity should be zero within a sphere? For example, it is logical to say that the field intensity would be zero at the center, as all the intensities cancel out. However, this cannot be the case for any point within the sphere.


Let's say we have a multi-slit experiment with N slits.Since the central fringe has the most intensity, is there an equation to calculate the intensity of central fringe in terms of the intensity of the original light wave? I searched Fraunhofer Diffraction and Fraunhofer Diffraction Equation but neither of them helped me since they calculate the intensity of a fringe in terms of the intensity of the central fringe.Thanks.


I understand that one of the great things about LaTeX is that, as long as you're using the same source file, the output is guaranteed to be identical regardless of the platform that you're generating it on. I'm assuming this is the case because LaTeX is controlling everything from the typesetting to the fonts themselves. If I use XeTeX, do I get the same guarantee, even assuming the I use the same TrueType fonts on two different platforms?


Adiabatic approximation or the Born-Oppenheimer approximation is used whenever the electronic motion is too fast that the electrons effectively see static nuclei and the nuclei, in turn, see an averaged electronic cloud. My question is: As the word 'adiabatic' suggests no heat/energy transfer, does this mean that the energies associated with nuclear and electronic motions are non-transferable? If my understanding is right, the limiting criterion of the approximation is when transfer can no longer be neglected. My other question is how to judge when the transfer is significant?


I'm confused about the how the notion of distance is used in Conformal Field Theory. Let's take for example the Operator Product Expansion (OPE). In a conformal field theory, due to the scale invariance only angles - and not distances - matter. But in the very definition of the OPEs one speaks about two operators evaluated at nearby points. How can one make sense of this apparent contradiction?


I am developing a database application where a user should be able to store multiple ways of contacting someone in a database table. This database table can for e.g. contain: phone numbers mobile numbers email addresses twitter IDs facebook IDs whatsapp numbers Now I am looking for a table name. The obvious choice would be contacts. However, the term 'contacts' is used when referring to people and not ways of contacting this person. I am looking for a single word to describe all ways of contacting a person.


Im wrong about something here, but Im not sure what. As far as I know the product of two normal distributed variables is not normal distributed. However, if the joint distribution of Y and X is bivariate normal then Y given X is normal distributed as well as the marginal distribution of X. Furthermore, the joint distribution of Y and X is the product of the condtional distribution of Y given X and the marginal distribution of X which are both normal. If we define a new variable Z to be distributed as the condional distribution of Y given X, then the product of Z and X (which are both normal distributed) is bivariate normal. Am I on the right track or did I miss understand something somewhere?


Suppose you have a tetrahedron. It doesn't have to be regular. Now suppose you have another tetrahedron contained inside the first tetrahedron. Again do not assume it is regular and do not assume that both tetrahedrons are similar. Could it happen that the perimeter of the tetrahedron in the inside is larger then the tetrahedron on the outside? Whether it is or not prove it. Do a proof by contradiction. This one is tricky. I have been thinking about this problem for a long time now and do not see any way to come up with a reasonable solution. The help would be greatly appreciated!


Recently some of my colleagues has started using the phrase "touch space" a lot, for example in sentences like "I just called you to touch space", or "I will touch space with him tomorrow". I can deduce that it means something like "talk to" or "meet with", but what is the original meaning, what is the advantage of using "touch space", and where does it originate from ?


I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was Galois theory. I am interested in doing 'my own' research, if you catch my drift. That is, I would like to apply the Galois theory I will be studying to something, and do some research. My professor mentioned some possible applications within coding-theory and cryptography. Do you have any specifics in mind? I would be happy to hear your insights.


I want to tell someone the following: "I bring an e-reader with me on the bus every day so that I have something to do during my commute to work." Does the phrase "commute to work" clearly refer to the trip there and the trip back from work? Or is it more proper to say "commute to and from work" in order to ensure that it is clear that I mean both directions?


I want to get the density of a fluid going through a pipe. I can measure the flow and pressure with a flowmeter and the temperature using a thermometer. With this information, I want to calculate (or approximate) the instantaneous density of the fluid passing through my instruments. How would I go about doing this? I'm looking at a liquid (not a gas), mostly incompressible. Think water with varying amounts of solute (salt, sugar) in it.


Just wondering, what would happen in this experiment. In the experiment you would first have two entangled particles. Then you fire one of the particles, lets say "Particle A", at a double slit towards a detector. While in transit to the detector, what if the other entangled particle, lets call it "Particle B" was observed / had it's wave function collapsed? Would "Particle A" still generate a wave-like interference pattern or would the wave function for both be collapsed? In theory you cannot send classical data by entanglement, so this experiment must somehow fail, but I can't quite figure out why. If this experiment were to succeed, then you could read and send data about wave function states over entangled particles.


I am trying to remember the phrase that describes a particular kind of folly - trying to "beat the house", or willingness to play a rigged game. As I recall it has the form of "a fool's errand" - that is, the game is referred to as belonging to the person who is silly enough to play it. I'd appreciate knowing the origin of the phrase, too.


I believe that pigs can fly I think here "that" is being used as a conjunction to combine the independent clause (pigs can fly) with the dependent clause (I believe) That the boys painted the pig green annoyed the pig. This one I'm not so sure about. "The boys painted the pig green" is an independent clause, and "annoyed the pig" is a dependent clause; but in this case "that" doesn't join them. Any insight?


The critics against Copernicus and Galileo argued that, if the earth moved, then, a heavy body that was dropped from a very high tower should fall to the west of the foot of the tower. Galileo argued, however, that this body would fall slightly to the east. My first guess is that the body would fall directly under the point in which it was dropped. Who is right?


I'm attempting to build a regular expression that will accept only strings of the form: Begins with: /# Ends with: #/ Contains the following in between /# and #/: Any combination of {a, b, /, #} but not the combination #/ Bascially, a regular expression that determines whether a string is appropriately comment delimited. I've tried many expressions, but can't find anything that quite works. I'm not sure how to allow all other combinations of a,b,/,# but disallow #/. Any help putting me on the right track would be much appreciated.


I have been trying to approach this by finding the gravitational torque of the person on the merry-go-round, however I can't find a way to relate that to angular velocity in the given circumstances. If this problem requires angular momentum to solve, then I won't need to know the solution because it won't be on my final, however I still want to make sure that I'm not missing something.


I read this article where the title suggests the iPhone was dropped from space, but it looks more like it was dropped from an airplane I would think that if astronauts dropped an iPhone from space that it wouldn't land on Earth, but rather, float on for infinity (our Universe keeps expanding), or would the iPhone be captured in some planet's gravitational force and drop there. Help me understand this physics principle.


Please, take a look at the following: "Friends" and "foes" are, according to Carl Schmitt, defined in function of their capacity to respectively enhance or diminish the power of one's own state. Does "in function of" equal something along the line of "in relation to"? I'm aware that the "in function of" thing was once covered here, but I'm afraid there was no answer there I'm now looking for. EDIT: THANKS EVERYONE FOR THE ANSWERS.


I have been recently reading quite a little about Kaluza Klein theories. I am still far from mastering this but I am curious if any experiment that may disprove or give hints of the existence of extra spatial dimensions is to be expected to be performed relatively soon. This page of CERN, for example, says that the LHC might give some clues, but it doesn't really dive into much detail. So, in some detail, which experiments might say something about this, and when might they be expected?


I just finished reading Richard Feynman's lectures on Quantum Electrodynamics (QED: The Strange Theory of Light and Matter) and it fascinated me. However, there's an unanswered question I have from reading it. If, as Feynman argues, "light doesn't really travel only in a straight line; it 'smells' the neighboring paths around it and uses a small core of nearby space" (though it is overwhelmingly likely to appear to be traveling in a straight line over long distances), how does this not defy the law of conservation of momentum? My understanding is that this law applies to light as well, with a momentum defined by p = E/c. If so, light curving would clearly defy it, would it not?


I was wondering where the term 'button-down' comes from. I tried to do some research but I was not very successful... How was the word button-down formed? Is it a compound ? Does it originate from the noun "button", which then became the verb "to button" meaning to fasten? Then, how did it become an adjective ? If the adjective "button-down" originates from the verb "to button (stg) down", shouldn't the adjective be "buttoned-down"? If so, how did it change to become only "button-down" ? I looked up etymonline and the online merriam-webster but could not find any answer. Can anybody answer this ?


If I grant someone a Boon, I am granting them a temporary positive effect. If I were to grant someone a temporary negative effect, what would an adequate word to describe that be? I was initially drawn to Bane, as it's another four-letter B-word, with a negative connotation, but I'm not sure if the two terms are inherently equitable. Is this an appropriate usage of Bane? Is there a better word entirely?


A friend of me who is not studying mathematics now needs to deal with integrals, double integrals and triple integrals within his study of chemistry. He asked me to give him a suggestion for a basic book that explains basic facts, rules etc., about integrals. I think this means Riemann integral and that it should not be too complicated. I do not know such a book, do you know a book that deal with basic things concerning integrals for a non-mathematician? Thanks for your tips!


What word aptly describes a job or position that requires more than is reasonable from the person occupying it? An example of usage might be: "Today, John finally resigned his ___________ job." To clarify, John is fully qualified to perform his duties and genuinely enjoys his work. Unfortunately, John's job at Evil Corp is unreasonably demanding. John's superiors have been frequently forced to increase his workload while lowering his pay. Long term employees are leaving the company in alarming numbers. John has a very loyal personality that has urged him to stick it through, but alas, John has reached his limit and must resign.


Possible Duplicate: Are collective nouns always plural, or are certain ones singular? Which is correct: The rest of the staff is or are? The rest of my family is or are? I've done a bit of research and I understand that "family" should be preceded by singular or plural verb depending on how you want it to be treated. For example, His family is one of the oldest in the county. and His family are all doctors. These are apparently both correct. But in the following instance, could a grammar expert tell me which should be be? When his family are abducted or When his family is abducted ? Thanks.


I know that at the research level, it's common to use different areas of Mathematics to solve a problem. But my question is whether at the undergraduate level it is possible to have a problem or exercise in which to solve it, it is necessary to use subjects that are not normally seen together. For example, a problem involving at the same time Differential Geometry and Differential Equations, or Abstract Algebra and Calculus or Linear Algebra and Combinatorics... In short, is this possible? Could someone give me examples ? PS: I'm not talking about subjects that are pre-requisite to each other like Analytic Geometry and Calculus. And remember, I'm referring to the undergraduate level.


I have a data logger that is recording the temperature readings from thermocouples at a specific interval. This gives me data points that I can graph where the x-coordinate is time and the y-coordinate is temperature. For each set of data points that I graph, I can connect the points and make a line - usually curved. I need to find the derivative of each line and graph those as well. There is no known function that creates these curves, so I can't simply find the derivative of a function. All I have is a huge list of (x,y) coordinates. How do I take a derivative and graph it in this case?


Wasn't there a mathematician who was convinced that "god" was out to get him? When he was travelling by sea he would write a friend a letter claiming that he had finally proved a difficult theorem (even though he hadn't). His reasoning was that he would always reach his destination safely since god couldn't stand to let him die on the dangerous voyage while leaving the rest of the world thinking that he had actually come up with the proof... There was also some story about rainy days and sports games, but I can't remember. Who was this? I tried searching with Google, but couldn't find anything and didn't know exactly what to search for...


Can you suggest books/articles on Function approximation Let me quote from the above wiki: Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. Any books/articles dealing with the above mentioned problem.Preferably with examples.


I have checked OALD. I looked up "disinformation" which according to dictionary means "false information that is given deliberately, especially by government organizations" and "Misinform" as a verb means "to give somebody wrong information about something". However, there is no explanation of the word "Misinformation" as a noun. What exactly is the difference between these two? I would like to know if there is any nuance between these two words or if they can be used interchangeably.


The universe is expanding at an ever increasing rate. Thus the following three-part question. Are there any theories that suggest the expansion is a consequence of a pull from some unknown source rather than a push from the presumed dark energy? Regardless of the cause, and assuming the expansion continues at an ever-increasing wheee, when will the most distant parts reach the speed of light? And then what happens?


Possible Duplicate: Confused about the role of mass I know that two different masses fall at the same rate in the same gravitational field because the greater gravitational force of the heavier one is exactly offset by its greater inertial resistance. What I don't understand is why the larger mass wouldn't fall more slowly at first and then once the inertial resistance is overcome, it would then accelerate faster than the less massive one. It seems that the rate of acceleration (not velocity, which obviously does) would vary according to the distance of the fall


The concept of reversibility always gives me a hard time.In a reversible process the change of entropy is zero. On the other hand for irreversible process it is not.But there comes another topic which is 'internal reversibility'. I couldn't quite grasp the concept. Can any one simply explain the following topic in plain words for me? What is internal reversibility or internal reversible process? Difference between internal and external reversible process?


I added the hyperref package and got some errors. Thus I deleted the auxiliary files and compiled again. This time there were no errors, and the links work except in the cites (bibliography), where I get question marks and links that send me to the first page. Any ideas? In fact I don't need the links in the cites, so if there's a way I can solve the problem by having just the links in the figures and in the index it's welcome.


I am trying to decide on a symbol for a particular mathematical quantity, it has three different types of indices and I'm running out of places to put sub-scripts/super-scripts. I have a few ideas, but would like input on what looks best (or any additional ideas you may have). Since you are all typesetting experts, and anyone who uses TeX likely has some affinity for aesthetics, I figured this was a good place to ask. Here are my ideas so far: For context, the symbol is used in equations similar to this:


I know the difference between the two. Breath is a noun and breathe is a verb. It was taught to me that way and I've never mixed them up in any way because their different pronunciation reflects their difference in spelling. This is reflected in this NGram chart which shows extremely few documented cases of incorrectly using "to breath" as a verb. However, I've recently noticed many, many, many people on the internet using "breath" as a verb (e.g. "I need to breath"), and it is quite confusing and irritating. Is there any history behind this misuse?


I've just had a discussion about using "to separate" when relating to events in time. A colleague of mine used the word to describe that an event occurred between two other events while the events aren't necessarily continuous. For example, he'd say "Monday and Friday is separated by Wednesday". I think that the separator should be "thicker" to fill the gap between the two endpoints fully. So I'd say "Wednesday is between Monday and Friday" or "Monday is separated from Friday by Tuesday, Wednesday and Thursday". Which explanation sounds better? Would you use other words to describe that something happens after something else has already ended and the next thing hasn't started yet?


So tonight's Quatrantids shower got me thinking. Why does the debris from comets and former comets hang around so long? Each year the earth sweeps through the region of space that the comet went through. However, the comet doesn't come by each year, so the earth must be going through the same cloud numerous times. And each time we get a meteor shower as a result. I suspect an answer, but I'd rather hear from professionals.


After recently going through a short program of self-study in quantum mechanics, I was surprised to find a quote attributed to Feynman essentially saying he was extremely bothered by the computational process of renormalization. It's "dippy" that anyone should have to subtract one infinity by another in order to arrive at a finite answer. What's he referring to there, in rough terms? And what's the latest in attempts to replace this computational procedure with something more physically plausible, so that the theory can have more meaning and less dippiness?


I'm writing a Cover Letter and I'm including the following sentence: "Furthermore, I have a passion for dealing with- and meeting- new people." I recall an English professor suggesting something like this because, here, the "with" and the "meeting" both relate directly to "new people." Is this correct? Or should I just stick with commas and get on with my life (as below)? "Furthermore, I have a passion for dealing with, and meeting, new people." <-- seems weird. Thanks for your help!


Possible Duplicate: In what ways can TeX be used beyond document production? What else can we create in LaTeX besides aesthetically beautiful typeset documents? I know we can create theses, monographs, books, we can draw using PSTricks or TikZ and create slides with Beamer, but what else can we do? I do not know, but how to create mailers? How to create animations? These are just a few suggestions. What else can we create in LaTeX? How to go beyond LaTeX?


I have programmed a counter. It counts at one point per second until it reaches ten points, at which time it resets back to zero and begins to count at two points per second. Again, upon reaching ten points it resets again and begins counting again at three points per second... and so forth, continuing to increase the points per second by one each time it reaches ten points and resets back to zero. My question is, what is the process to construct the formula that will tell me how many resets have occurred after t seconds? Thank you.


I've read the textbook Groups and Their Graphs by Grossman, and I'm interested in learning more about graphs. I know about O. Ore's book in the same series (Graphs and Their Uses), but I'm interested in a book which will tell me more about the relation between graphs and groups. I don't know any advanced mathematics (I only about group theory and graph theory from Grossman's book), so please recommend books which are not too complicated. I would also be glad for recommendations of books which are about group theory but have a focus on graphs.


As far as I interpret it, the law of ever increasing entropy states that "a system will always move towards the most disordered state, never in the other direction". Now, I understand why it would be virtually impossible for a system to decrease it's entropy, just as it is virtually impossible for me to solve a Rubik's cube by making random twists. However the (ever so small) probability remains. Why does this law underpin so much of modern physics? Why is a theory that breaks this law useless, and why was Maxwell's demon such a problem? Does this law not just describe what is most likely to happen in complex systems, not what has to happen in all systems?


Here is the situation: Kids in a small yard are about to play soccer. There are no goalposts in that yard (or "goals" or whatever you call it, I mean those metal frames on each side of the soccer field that have nets on them. Once the ball is in the net, the score changes). So, one boy picks up some sticks from the ground and tries to mark out the goalposts for each team. While doing that he says: "This will be your team's goal and that will be our team's goal" Is the first goal that he mentioned the one that his team will be defending or trying to get the ball into?


The default twoside memoir document style makes the right margin really large on recto (odd) pages and the left margin really large on verso (even) pages. This seems counter-intuitive to me. It seems to me that you want the large margin against the spine of the book, to compensate for the part of the margin lost to the binding process. So is the default style really what one wants for publishing, or do I need to customize the margins to be the opposite of what they are by default?


As I was reading about the experimental arrangement for photoelectric effect, I saw a diagram that puzzled my knowledge of electrodes. I found that in the experimental setup the cathode of the photoelectric plate or emitter was connected to the positive terminal of the cell. Why is it so? How can a negative electrode be connected to positive terminal of a cell? I read Wikipedia article on cathode and it said " In a device which consumes power, the cathode is negative, and in a device which provides power, the cathode is positive". What does this mean?


I understand that for a set of vectors to be linearly independent, none of the vectors in the set should be a linear combination of some other vectors in that set. But why on earth should I care about it? How does it help me? For example imagine a simple situation - I have a system of inequalities, which defines a set of points (vectors) which satisfy all these inequalities. Why should I care whether this set of solutions to the system is linearly dependent or independent?


Being a mathematician with mathematician friends, my friends and I occasionally like to joke about the peculiarities of the English language. This one came up recently: Obviously, most English sentences and phrases cannot be read backwards and forwards and maintain the same meaning. For instance, "watch this" and "this watch" have clearly different meanings. In mathematics, we call this non-commutativity, and it is deeply interesting. So the question is, can anyone think of a phrase or sentence which has the same semantic meaning when the words are read from right to left?


The result of an imbalance of electrons between objects is called static electricity. It is called "static" because the displaced electrons tend to remain stationary after being moved from one insulating material to another. Please can any one explain to me what does it mean by the word stationary in the definition? Does it mean that the displaced electrons do not spin around the nucleus in another material's atom?


The vast majority of the time when I see the word "myriad" it is in a sentence like "He had a myriad of things." However I don't like the extraneous words so I normally use it like "He had myriad things." My boss corrected the latter usage while editing something I wrote. I averted an argument by simply changing the sentence to "He had various things." but was I incorrect?


I saw someone write the sentence "Of course they're". As a native English speaker, this instantly seemed wrong but I couldn't come up with a good reason as to why. I did a bit of research and there seems to be a rule called "stranding" where if there's an object before the clitic then it can't end like that but I don't entirely understand it.


I am trying to create a machine that moves on two points (Wheels or legs). Because of the extremely difficult nature of perfectly balancing the parts, I am wondering is there any way to create a mechanical mechanism to balance it. I know that it can be done with many different electric circuits, but I am wondering is it even theoretically possible to create such a system? And if it's possible, does anyone know of any systems that do that? P.S. Could someone retag this appropriately? I'm new to this SE, and I'm not sure how to tag it.


I frequently hear people quoting widely-used idioms or proverbs as if they are fact, simply because they are used frequently by many people. For example, "An apple a day keeps the doctor away." Can these be called a "truism" even if not true or must they be actually true to be called a "truism"? Are there more precise terms for the two meanings, "widely believed ideas, which really aren't true" and "widely believed ideas, which really are true"?


Sometimes, I feel that the term "first generation" is used sort of vaguely sometimes. So it confuses me (because my situation) is a little bit complicated. My dad, was an immigrant from a foreign country and lived here long enough to get a passport. That way, he has an American citizenship. My mom, wasn't born in the US and doesn't have a US citizenship. I wasn't born in the US, so am I a first generation American? Or do I just have a citizenship (because of my dad's American citizenship)?


I use TexStudio to create a tex file and save it in my DropBox in the Cloud. I then use CloudConvert to make a pdf file, which I then save on my Windows Pc. This works OK, but isn't there a simpler, more direct way? I'd like to execute a Windows program which inputs a tex file and outputs a pdf file. I have MiKTeX installed on my PC.


Let's say we have a normal circuit with a light bulb, with wires and a battery. When one places a capacitor in this circuit, how is the light bulb able to light up, even when the capacitor prevents the flow of charge? Also, why does it dim and then go out eventually? Then when the battery is removed from this circuit, how is the light bulb still able to light up? And what is happening when the light bulb dims and goes out in this situation as well?


My question is about the use of would in the following sentence. He grew up around cars that would later become classics. The use of would in this particular sense always looks confusing to me because it's so different from: I would like to know... I don't think he would agree to that... Would you mind.... Would it be alright if I... etc. The above sentence, as I see it, means "he grew up around cars which were going to become classics in the future". Is that correct? If yes, does it also mean that the cars actually became classics later?


I know that for rigid bodies only the work-energy theorem states that the net work done on the body equals the change in kinetic energy of the body since a rigid body has no internal degrees of freedom and hence no other forms of energy such as potential energy. Is there a most generalized form of work energy theorem that is valid for rigid as well as non rigid bodies and for conservative as well as non-conservative force? I would like a work-energy equation that would be valid for point particles, rigid bodies and non-rigid bodies.


Assuming that the earth is spherical, that its temperature is continuous, and that some other more or less realistic conditions hold, we might think that the Earth's core temperature should be about the average of its surface temperatures. This is not the case, as the core is hotter than all but a few spots on the surface. Can someone explain where the assumptions break down? Is it that the temperature is not static?


For introducing a field of science, usually we require a definition which summarizes the goal which is intended to be achieved by this field. Linear Algebra is one of the most important parts of mathematics which has not only interesting pure mathematical ideas but also a lot of applications in physics and engineering. So it seems reasonable to have a Complete, Clear, Brief, and Delicate definition for this important branch of mathematics. I am wondering that what is the best fit for such a definition. For example, the very first sentence that the Linear Algebra Done Right by Sheldon Axler starts with is Linear Algebra is the study of linear maps on finite dimensional vector spaces. What is your definition of Linear Algebra in few sentences?


We all know the "Inertia" of a particle is actually related to its "Mass". But when we talk about "Moment of inertia" of a body, we actually are talking about its "Mass distribution" about some point/axis. So depending on how the mass is distributed in the body (what shape a body has), its moment of inertia could be determined. So my question is can we do it vice-versa? I mean if we had the moment of inertia of a body about some axis, can we construct its shape?


I'm quite stuck with this problem. I know that I have an object in orbit. I know the eccentricity of that orbit, as well as the semi-major axis of the orbit. Giving a true anomaly, how do I find the speed and altitude of that object? The true anomaly is the angle between the line made with the focus of the ellipse and the position of the object. Thank you! P.S. I'm more looking for a general help, more than a specific answer. That's why I didn't give any numbers.


Imagine driving in a straight line on a ice lake, when you hit the brakes, if your goal is to stay in straight path with no spinout, which wheels would you choose to have locked: front or rear? Assuming the steering wheel is kept fixed in both cases, I learned that it's better to have front wheels locked in this case. But can someone explain in accurate terms why? Thanks.


Generally speaking, the rainy season is in the summer in tropical climates, and in the winter in mediterranean climates. (I admit that is a gross oversimplification) What is the cause for this difference? Purely speculatively, it seems intuitive that hot weather would lead to higher humidity, which in turn would lead to more spontaneous rain clouds. This would obviously be maximized by summer weather. But why is the rainy season in the winter in colder climates?


As I understand it, trans means "an individual whose gender identity is different than what they were designated at birth". However, I also hear the terms transgender and transsexual used for similar meanings. I know that personally I only refer to myself as trans or rarely transgender, and never transsexual, and the latter sounds very odd to me. I'm interested in why there are several words for roughly the same meaning, and if they do have different meanings or simply based on geography and time period.


I was playing a table-top rpg with a friend. It was set... well it was pretty weird, so I won't get into it. Suffice it to say the bad guy had a stick of dynamite and we were on a volcano. I hit the dynamite with my slingshot, knocking it into the lava directly behind the villain. My DM said the dynamite melts away. I said it should have blown him up. Needless to say, as a couple nerds (we were, after all, playing a fantasy game and then arguing about the physics of it) we were pretty upset with each other. What would have happened in this... totally realistic scenario? Would the stick of dynamite exploded? Or simply melt away?


I have a basic question regarding the ramifications of P vs NP. If P=NP, then SAT would be in P. If I understand the definitions correctly, this would imply that there is a Turing machine which decides SAT in polynomial time. However, does this mean that there would actually be a polynomial-time algorithm for producing a solution of SAT? For instance, what if there were some mysterious polynomial-time computation one could do to a given instance of SAT which would tell you whether or not it was satisfiable, without actually producing a solution (I'm thinking of primality-testing, where for arithmetic reasons it can be easier to verify prime-ness than to actually exhibit a factorization)


I'm in need to implement Monotone Cubic Interpolation for interpolate a sequence of points. The information I have about the points are x,y and timestamp. I'm much more an IT guy rather than a mathematical person, so I'm looking for an example of implementation. What I need to do with the resulting functions is store them for future analysis. My favorite syntax are PHP, Python, Java, Delphi, VB or a generic algorithmic language of your choice.


Lines and conics have clear geometric meanings that are coordinate-free, but cubics seem to rely entirely on cubic equations and coordinate systems. Are there ways to define cubic curves without cubic equations? I thought about this question by trying to generalize tangent lines and osculating circles. Since a tangent line is defined by taking the limit of two points on the curve, and an osculating circle is defined by taking the limit of two tangent lines on the curve, I thought about taking the limit of two osculating circles on the curve, but after playing around with evolutes and involutes, I couldn't come up with anything.


I'm an ESL teacher. Normally I teach lower intermediate but I also teach a mixed level grammar review class. I pride myself on being able to explain things clearly but today I found myself in THREE sticky situations all in the same class! I'll explain here the two problems involving conditionals. First Case: Is it better to say... If he knew that I WERE/WAS home now, he would call. OR If he knew that I AM home now, he would call. Does the second verb in the if clause also take the subjunctive form because it is in the if clause or should it take the present simple form because it is not a hypothetical (I am home now is not hypothetical, his knowledge of it is.)


I find it really amusing when other people misuse words but my sense of humor fails when it's me. I have always used "notwithstanding" to mean "assuming that A doesn't impact B". For example The delivery will be on time, notwithstanding the holiday. To me, this meant, the delivery should be on time, but you never know what impact the holiday will have on it. Turns out, notwithstanding means almost the opposite: in spite of, regardless of. So my question is, what word should I be using instead?


Suppose we look at the twin paradox where the twin traveling at high speed relative to an observer on earth has a clock which counts time by sending photons of light across a distance within the spaceship (perpendicular to the direction of motion) to a detector which counts off 'time' as the interval between photon detections. If the speed of light is constant in both frames, and the distance the photon travels is equal in both frames (no length contraction in the perpendicular direction), won't both observers say the same amount of time has passed in both frames at a later time (suppose the observer on earth uses an identical clock)? Wouldn't a difference in observed time intervals imply differences in the speed of light?


A guy walks into a bar. His buddy laughs and says, "Don't worry, I didn't see it either. What is the meaning of this joke? What makes it funny? (Is it supposed to be funny?) I saw this joke in the mood message of a British guy. It is a kind of bar joke but there is usually a connection. (For example: a guy with dyslexia walked into a bra). I didn't get this one. Can it be a meta-joke?


I'm trying to analyse the Ballad of Serenity Valley which is the theme song for the tv series Firefly: take my love take my land take me where I cannot stand I don't care I'm still free you can't take the sky from me My interpretation relies on the meaning of 'take' in the second line, being different from the third line, which are a rhyming pair. Is there a name for this scheme or pattern?


There is plenty of information about how to encode arithmetic given the lambda calculus. The wikipedia article on Church Encoding seems complete to my inexpert eye. My question is "how about the other direction?" What's a good way to encode the lambda calculus in ordinary real or integer (or even matrix) arithmetic? It would seem that an application of Godel Numbering would do it, but I have been unable to find any writing on Godel Numbering for the lambda calculus specifically. It also seems plausible to encode the lambda calculus in arithmetic in some way more efficient than Godel Numbering; perhaps someone has done that? I might settle for the SKI calculus or some other Turing-complete language that's easier to encode than the lambda calculus.


If you are using a word that normally wouldn't start with a capital letter, should it be lower case after an e.g.? Also should e.g. have a capital E at the start of a sentence? Example phrases: Should I always plug in electrical items? e.g. Electric hairdryer, phone charger... Should I always plug in electrical items? e.g. electric hairdryer, phone charger... Should I always plug in electrical items? E.g. Electric hairdryer, phone charger... Should I always plug in electrical items? E.g. electric hairdryer, phone charger...