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According to the Bernoulli's equation, if velocity decreases, then pressure increases. I am trying to understand the Bernoulli's effect based on a situation. Suppose we have a stream of water. Let's assume it is an ideal fluid. Imagine the water flows out from a wider pipe to a narrower pipe. Since the area decreases, according to the Continuity equation, velocity of water molecules increase. This causes an decrease in pressure. I don't understand the last part. If water molecules' velocity increase, then their kinetic energy also increases. Wouldn't this causes more collision between pipe's wall and water molecules, thus giving higher pressure? | 1 |
I hope this isn't an inappropriate question here! I'd like to ask the following (perhaps slightly ill-posed) question: why do we study prime ideals in general (commutative or non-commutative) rings? The situation is somewhat clear to me in some nice cases such as Dedekind rings, but even in slightly more general settings (e.g. general commutative Noetherian rings) the theory becomes rather horrible. What benefit do we gain from an understanding of the prime ideals of a ring? Thank you! | 1 |
The following quote from Anthony Burgess has a comma after it: There is, in fact, not much point in writing a novel unless you can show the possibility of moral transformation, or an increase in wisdom, operating in your chief character or characters. But this quote from William S. Burroughs doesn't: There is in fact something obscene and sinister about photography, a desire to imprison, to incorporate, a sexual intensity of pursuit. When should you use a comma after "there is in fact"? Is it necessary to put a comma after "there is in fact"? | 1 |
While learning about shock waves in an introductory Gas Dynamics course, it was revealed that normal shocks are unstable if formed in a converging channel. Even if the local conditions ostensibly require the presence of a shock in the converging section, the flow instead chooses to reinvent itself, moving the shock wave to a diverging section while simultaneously altering the upstream conditions. I can verify that this is a genuine phenomenon, but is there any formal explanation in terms of the underlying flow physics? | 1 |
We are struggling to find the correct word(s) that describes a list of all messages in the system that are sorted by recency. Trending does not work because what we are displaying is not what is popular in the system, only the most recent. Recent does not work because it implies there is a limit to the number of messages we display. All does not work because it does not imply that they are sorted by recency. Any hints or suggestions are welcome. Thanks! | 1 |
In an electron gun, the heating filament heats the cathode, releasing electrons by thermionic emission. I've read that "electrons are negatively charged particles and the positively charged cylindrical anode develops a strong electric field that exerts a force on the electrons, accelerating them along the tube". However, I don't think that this explanation is very clear, and I was wondering specifically how the "strong electric field" inside the cylindrical anode is able to accelerate the electrons? | 1 |
My understanding is that in quantum mechanics the wavefunction may be expressed as a function or as a ket vector (composed of many orthogonal ket vectors). I'm not too sure about the further differences between these two approaches. For example, I am familiar with operating on the wavefunction as a function with the hamiltonian operator, but when you use ket vectors can you use the hamiltonian operator in the same way or do you have to find matrix representations of the operators? I would also be grateful for any links to websites or books explaining the different approaches. | 1 |
What is the English word for "collecting money for a special event from a group of people"? For example, say some friends are planing a party. Each one has to contribute some amount of money to the event. What is the word or phrase that can be used to explain this kind of activity? I have found "fund raising" to have a similar meaning, but I feel it's more along the lines of "collecting money for some charity event". Is that right, and is there a better word I can use? | 1 |
I'm trying to write a tagline for my live blogging service, and this is what I've come up with: Live blogs that are a breeze to write, a pleasure to read and are actually updated in real-time. Is that correct grammar or should it be Live blogs that are a breeze to write, a pleasure to read and actually updated in real-time. The completions 'a breeze to write' and 'a pleasure to read' both follow '... that are'. So why does 'are actually...' sound better to me? Doesn't that repeat the 'are'? | 1 |
Given any problem, how do I know whether it is solvable using Dynamic Programming? For example: consider the rod cutting problem. Now, how do I know whether dynamic programming will give me an optimal answer? Basically my question is: how do I check if a problem follows the "Principle of Optimality" - that optimal solution of every problem involves the optimal solution of a sub problem. And are there any problems that don't follow this principle? (If there aren't, my original question becomes redundant, of course!) | 1 |
In mathematics we often have statements like a x <= b, where a and b are constants and x is a variable. Now there may be variables satisfying the inequality (that is the statement is true) as well as variables violating it (in which case it's false). However I don't have any words in my vocabulary to express stricter statements: Is there a word to describe that the variable x satisfies the equality a x = b? What about the case that a x < b? I remember having read "x is a root of the inequality" meaning a x = b somewhere, but I can't remember where. | 1 |
Let's say me and a colleague are going to a meeting and I want to make sure his responses to the questions raised are similar to mine, that we are in agreement and we will responde in a similar manner. Can I say: "Let's make sure our responses are aligned" or, "Please let me know your views cause I want my responses to be aligned with yours." | 1 |
The words "opportunism" and "opportunist" suggest the ability to take advantage of situations -- but they assume that one is doing so for one's own benefit, which makes the terms pejorative. What is a non-pejorative word in English that means "have the skill and wisdom to recognize and seize opportunities that lead to broad gains"? I am looking for something that is part of the "art" of diplomacy and politics, for example. "Clever" is a somewhat helpful adjective, but there is no such thing as a "cleverist." "Entrepreneur" means is a person who is willing to take on risk and innovate, but lacks the sense of seizing opportunities as they emerge. It seems like an important concept that has no word. Any suggestions? | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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 | 1 |
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. | 1 |
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!! | 1 |
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. | 1 |
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. | 1 |
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"? | 1 |
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. | 1 |
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..."? | 1 |
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. | 1 |
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? | 1 |
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. | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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. | 1 |
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? | 1 |
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. | 1 |
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. | 1 |
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? | 1 |
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. | 1 |
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. | 1 |
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? | 1 |
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. | 1 |
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. | 1 |
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? | 1 |
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. | 1 |
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. | 1 |
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. | 1 |
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? | 1 |
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. | 1 |
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. | 1 |
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: | 1 |
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 | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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. | 1 |
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. | 1 |
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. | 1 |
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? | 1 |
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! | 1 |
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. | 1 |
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? | 1 |
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. | 1 |
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.) | 1 |
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 | 1 |
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? | 1 |
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 | 1 |
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. | 1 |
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! | 1 |
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! | 1 |
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? | 1 |
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 ? | 1 |
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. | 1 |
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? | 1 |
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? | 1 |
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. | 1 |
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! | 1 |
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) | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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. | 1 |
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! | 1 |
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? | 1 |
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. | 1 |
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. | 1 |
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? | 1 |
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. | 1 |
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. | 1 |
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? | 1 |
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." | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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? | 1 |
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"? | 1 |
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? | 1 |
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 | 1 |
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? | 1 |
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