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Both the Laplace transform and the Fourier transform in some sense decode the "spectrum" of a function. The Laplace transform gives a power-series decomposition whereas the Fourier transform gives a harmonic (or loop-based) decomposition. Are there deep connections between these two transforms? The formulaic connection is clear, but is there something deeper? (Maybe the answer will involve spectral theory?) | 1 |
How does our sun create positrons? And does the sun emit said positrons after their creation? I read that the sun creates positrons at it's center but I couldn't find how they form. Is it a byproduct of fusion or does it occur as our sun stars to die? | 1 |
I read that the following is ungrammatical: Because of the accident, he arrived at the dock an hour late. As such, he missed the boat and forfeited his deposit. Why? What is the correct usage of as such? | 1 |
Refraction: light changes direction of propagation when entering a material with a different refractive index. Does the direction of propagation of light change sharply and almost instantaneously (as shown in the diagram) or smoothly? | 1 |
I'm not a native English speaker, but sometimes I get the feeling that the pronunciation of English words is random. Why is "Yosemite" is pronounced as "Yoh-Sem-Ee-Tee" and written as "Yosemite" and not as "Yosemitee"? | 1 |
It is well known that any conformal mapping of the unit disk onto itself extends to the unit cirle. However, is there an homeomorphism of the unit disk onto itself which does not extend to a continuous function on the closed unit disk? If yes, can you give an explicit one? Thank you, Malik | 1 |
If I issued a payment to a company, and I wanted them to notify me when receiving the payment, could I say 'please acknowledge the payment when receiving it?' Is the word 'acknowledge' alright to be used here? | 1 |
Which of the following, if any, is correct? You answered the same questions as me. You answered the same questions as I did. You answered the same questions as I have. How can you tell? I tried Googling it, but I only get Breaking Bad references. I also saw this, but I don't know how it would apply in this context. | 1 |
I have this fragment: ... the experience and knowledge gained will be helpful in my career as a neuropathologist. Is the "as" here okay? It somehow does not sound right to me. Obviously I want to say that it will be helpful to me, during my career in neuropathology. | 1 |
Here are a few attributes that a text may have: "name", "length", "quality", etc. What's the name of the text attribute that refers to the text itself? Would that be the text's "content", the text's "body" or something else? | 1 |
Is there a way to convince LaTeX to automatically add tildes in front of one- and two-letter words, numbers and such simple things (in normal mode, not in math mode)? I know there are preprocessors for that, but manually launching them is tedious. What's the best way to achieve it automatically? | 1 |
I came across this sentence as I was reading a book: My clothes disintegrated, victims of the sea. I think saying: My clothes, victims of the sea, disintegrated. would be correct. Which one is the right one? | 1 |
When an object is heated a lot and then brutally cooled down or vice-versa, it can crack or even break spectacularly. What happens inside that makes it do that? Is it only because the hot core swells when the cold surface shrinks, which causes internal stresses? Bonus: Are certain materials more sensitive to thermal shocks (high CTE?)? | 1 |
I am working on a project involving the motion of rigid body. From the literatures, I found two main tools, namely the dual-quaternions and screw theory. May I ask what are the major differences between them? It is appreciated that if some documents can be suggested for beginners. | 1 |
I'm using the memoir class, and would like new chapters to begin on the left-hand page, unless the chapters in question are only one page long. Neither openleft nor openany give this behavior. I am not opposed to using another class, or using sections instead of chapters, if I can get this behavior by doing so. | 1 |
What is the third order term in the Taylor Series Expansion? I know it will just be third order partial derivatives but I want to know how is it expressed in a compact Matrix notation. For instance Jacobian for first order, Hessian for second order partial derivatives. In other words, what is the third order term in the equation below? Thanks for your help! | 1 |
I used "It's not fair", but someone told me "fair" is the "F" word, and they don't like it in their house. Should I avoid using it? ps: sorry if my question offended someone, I didn't mean to it. | 1 |
I need a prove that pumping lemma can't be used to prove regular language. Pumping lemma is only used for proving non-regular language, but I need to show that how it can't be used to prove regular languages? | 1 |
Are there any interesting theorems outside of set theory that use ordinals in their proofs? The only example I know of is Goodstein's theorem, and I haven't been able to find anything else. In other (more vague) words, what is the use of ordinals? (Other than Goodstein.) Theorems that use the word "ordinals" in their statement don't count; Goodstein is a good example. | 1 |
I remember there is a theorem that states that if you have more polynomials than the number of variables, there must be an algebraic relation between them, but I forget what the theorem is called. (I'd also appreciate if I could be directed to a proof of it.) Thanks. | 1 |
Are the finite dimensional comodules the compact objects in the category of comodules over a Hopf algebra? If yes, is there a reference? If no, which are the compact objects? Here by compact I mean that the Hom functor from the compact object preserves filtered colimits. Thank you! | 1 |
I have to build a simple electromotor in the following way: I attach a permanent magnet to a battery, connect some metal supports to the terminals of the battery, and place a coil of wire on the supports, suspended above the magnet. My question is, will it still work just as well (or at all) if the wire is insulated? Thanks! | 1 |
I tend to think of data structures of type Structure.Field.Subfield as analogous to file directories. I.e that Structure is a folder and Field is a folder inside the folder.. etc. Is this a good way to think about it? | 1 |
I'm having a brain cramp: if cookies should be avoided, and carrots are preferable instead, is it correct to say: Avoid cookies in favor of carrots. or if not, what's the correct way to phrase? | 1 |
I understand the mathematical definition of Uniform Continuity. But I was wondering that if there is a intuitive explanation for this concept similar to Continuity where we sometimes say that if I draw the graph of a continuous function I do not need to lift the chalk from the board. | 1 |
For the sake of argument, assume the LHC was able to accelerate / focus / collide neutron beams, with the same energy levels it runs at for p-p collision. Would the collisions produce any major differences vs the p-p collisions? | 1 |
Is there a simple, elegant solution to add footnotes in a table (tabular)? Preferably, the solution can also support the cleveref package. EDIT: My intended effect is that, the footnotes should be displayed at the bottom of the page, just as regular footnotes are. However, I've checked out ctable package but found no such feature. Am I missing something? | 1 |
We are given the lengths of all sides of a polygon. We need to determine if the given polygon is convex or concave. How can this be done? What is the propery applied to determine this? | 1 |
I'm starting to read Baby Rudin (Principles of mathematical analysis) now and I wonder whether you know of any companions to it. Another supplementary book would do too. I tried Silvia's notes, but I found them a bit too "logical" so to say. Are they good? What else do you recommend? | 1 |
I've exhausted the usual High School curriculum for Mathematics and i need some recommendations. I want to start a serious course in Mathematics at a local college, but that's simply too long to wait, i'd like to get started now. So right now i'm just looking for some fantastic books and some fantastic tips, any recommendations are appreciated. | 1 |
Consider the following examples: "And it is a bottle, too." "And it is a bottle too." Is there a semantic difference between these two sentences? Or do they mean the same thing, with or without the comma before "too"? If not, what is the correct usage of the comma in context of "too"? | 1 |
I have learned that the classical measurement of the speed of light with a rotating mirror does not work with a laser (as opposed to, say, a mercury-vapor lamp). Can you tell me if and how coherency of light is necessary/contraindicated for the success of this experiment? | 1 |
If we consider a balloon full of air submerged in water then we all know that it will rise rapidly. I am having trouble understanding this at the level of individual molecules of air and water. What is a molecular/microscopic explanation for this phenomenon? | 1 |
Is it correct to use "But" at the start of a sentence like this? You can afford it. But think twice before buying it. Won't using "But" instead of "However" mark me as a non-native speaker? | 1 |
I have read that the electric energy flows from the battery into the circuit through electric field created outside the wires into the light bulb (or any other resistor). I have also read that the friction caused in the movement of electrons cause light bulb to heat up. So which is the correct explanation? | 1 |
I am preparing my CV with moderncv and chose the casual style. Now, I would like to omit the icons for phone, email etc. How do I do this? Thank you very much in advance! | 1 |
I am trying to understand a statement of a problem. Wondering how can a striaght lines in three different planes meeting at one point. Does not it imply that all the three planes are also intersecting at some line?. Can three lines in parallel planes meet at some point?. | 1 |
I am compiling my document in Persian using XeLaTeX, but the references are all in English and I'm appending them using BibTeX. At the end of the document, the references are all unknown characters, how could I handle this problem? | 1 |
I want to simulate an impact between two bodies according to gravity, and eventually considering other forces to stick matter together. I'd like to use python to do this, but I am open to alternatives. What kind of tools or libraries can I use to perform this task ? | 1 |
The nebulae we see in the night sky are forming new stars. The stars are eating up the nebulae and there is no obvious process in which those nebulae are being created to compensate for that. Shouldn't the universe have run out of those nebulae a long time ago? | 1 |
Often when I want to say that something became clear, I may instead say that the thing "became lucid" or that the thing is "becoming lucid" is there a single word that I can substitute for this? | 1 |
Consider the following excerpt of the Liouville's theorem proof taken from "Arnold - mathematical methods of classical mechanics": In changing the variables in the integral, I don't understand why there is not the absolute value of the Jacobian determinant. Why the determinant of the Jacobian of the flow is positive? | 1 |
If one pays for transportation of oneself a fare has been paid. What is paid if the transportation is of a non-person object (a parcel, a letter, a vegetable, a box of rocks)? | 1 |
Why do people use "skies" instead of "sky" (when, indeed, we only have one sky)? Reach for the sky/skies! and I'm glad to finally see some blue skies. I'm glad to finally see a blue sky. | 1 |
So, I came to naming a variable in my PHP today. The variable was to contain information about the state of a switch, E.g - on and off. However, I couldn't, for the life of me, think of what to name it. I ended up settling for State. But for arguments sake, what other words could I have substituted for State? | 1 |
According to the Oxford English Dictionary, a diatribe is defined as a forceful and bitter verbal attack against someone or something. I had previously understood it to mean something more along the lines of drawn out, longer than it needs to be, impassioned persuasion. For example, in a friendly letter, My [diatribe] begins here. Any alternatives? | 1 |
I'm gluing the edges of a square together with the caveat that there's a "fold" down the middle. I think this produces sort of a sphere with four "pinches". I'm wondering if my intuition is correct and if someone could provide a more rigorous foundation for what I'm trying to do and elaborate on the nature of the singularities. | 1 |
There are n studio apartments in a building. Some of the apartments are connected with each other by direct phone line. Prove that it is possible to assign to each apartment a female or a male in such way that each person has direct connection with at least as many people of the opposite sex as he/she has with people the same sex. | 1 |
So the sentience is "It's hard to find a good path to taking this mission on", I wonder why it is "to taking it on" not "to take it on", is "taking" using as a gerund? Can I say "It's hard to find a good path to take this mission on"? What's the difference? | 1 |
I really like the nLab and its collaborative style of writing. Are there any other websites which follow the same philosophy, but on different topics, or with different points of view? For example, is there one more on the metric aspects of Riemannian Geometry, Geometric Analysis, Harmonic Analysis and the like? | 1 |
Intuitively to me it seems likes increasing compression ratio would require more work to compress the gasses before ignition, so you'd just end up getting back what you put in - like a spring. What am I missing? | 1 |
If yes, why don't they fill up with water, and can you breathe the air there? Like, it's not exactly atmosphere there, but an underwater cave with higher ceiling. P.S. Possible that it has a different name than air pocket, but due to my limited knowledge of English, I have no idea. Thanks in advance! | 1 |
Possible Duplicate: Calculating prime numbers The question is in the title. Is there a number that is divisible only by numbers greater than its square root? If not, why? I need this because it can speed up a calculation algorithm significantly if the answer is no. | 1 |
We often use "cool water". But can we use "cool water" or "cold water"? Which is correct? Examples: I drink cool water only. People always like cool water. In the above examples, instead of the word cool, can we use cold? | 1 |
If you want to fly a spaceship with human passengers as close to the Sun as possible, then what effects would the spaceship have to be designed to counteract in order to keep the passengers alive and how close to the Sun could you get before there would be no way to counteract the effects ? | 1 |
There is a book titled Running for Mortals. I didn't recognize word mortal. Then I looked up it and get the meaning as below. mortal N - A human being I wonder, is mortal widely used as human being or it is used only for special areas like sports, medical, etc? | 1 |
What is an uncommon synonym for the noun "motion" (movement)? I'm looking for cool sounding words like "twitter" that are synonyms or somehow relate to motion, the noun that means movement. Example: "I bought a motion detector to alert my household of criminals." | 1 |
There are many documentaries, forums, blogs and more dedicated to Dark Matter. I have been frantically searching for an answer to my question however none of my sources have clarity to the matter of hand. I would really love a clear explanation to: What exactly is Dark Matter? Please help me to have a clear understanding. | 1 |
I was wondering what happens to the electron after it leaves it's valence shell and strikes a stable valence shell; in an insulating material? I realize that the energy from the strike, is absorbed by the atom that was struck and that these electrons do not 'break free'...so what happens to the electron that struck them? | 1 |
I hold him in high regard. The court holds him responsible/liable. She held it dear. We hold these truths to be self evident. This construction only seems to work with certain adjectives. Are these examples all set phrases or can it be used freely? Can I say "I hold that crazy" and make sense? | 1 |
I have a question like how can we mathematically prove that for a general matrix Conjugate Gradient method will always converge within n steps in exact arithmetic ? where n is the size of the matrix. | 1 |
I'm writing a presentation using the Singapore theme. The dots in the navigation bar are appearing vertically (one below the other) rather than horizontally. This is consuming a lot of space of my frames and is even not looking good presentation wise. I have seen presentations using this theme where the dots appear horizontally. How can I do this? | 1 |
I have a maximum number of pixels that I can process in my app at one time. The user must be able to open any image and if it's bigger than the maximum number of pixels it should be scaled down to fit the maximum resolution size. Keeping the rectangle ratio. How can I calculate the new rectangle? | 1 |
I can't find the precise definition of what is the orientation of a GaAs lattice. Being the superposition of two fcc lattices (one of Ga, the other of As), I would think that it is the direction of the closest Ga atom to any As atom of the structure. Is it right? | 1 |
I am writing a chapter in a book and I want to say that "I believe that this researcher is right ....", in a more formal way. Can I say "The present author believes ....." | 1 |
In statistics one often hears the phrases "log likelihood" and "log error". Why is it natural to consider the logarithm of these guys? My wild guess is that the Gaussian is a pretty "normal" distribution, and it's natural to take the log of such a thing. But this is pretty sketchy. A pointer to a reference would be great. | 1 |
I wrote "How is conditions being unfair not an issue?" instead of "How are conditions being unfair not an issue?" as I believe the subject of the sentence is 'conditions being unfair' rather than 'conditions'. However, I'm not quite sure. Which is it? | 1 |
So I understand that the an inner product space basically uses pythagorean theorem because it is similar to a distance formula. I'm still having trouble with this proof. I am a bit confused about where to start. It could be notation that is throwing me off, so any breakdown would be great. | 1 |
I always find it very difficult to understand the notion of chemical potential physically/intuitively unlike pressure and temperature in statistical mechanics. Can some one suggest some nice references or briefly discuss about it intuitively. Actually I came across it again in the context of AdS/CFT. It will be really helpful if it is discussed in holographic context. | 1 |
There's a Polaroid photo in the album, and I want to ask the owner about the person in it. Can I ask him: "Who's that man in the snapshot (shot)?, or I should ask "Who's that man in the picture (photo)?" Thanks in advance, Victor. | 1 |
Is there a name for this manner of purposely speaking in double negatives, e.g. I wouldn't say no to a cup of tea! I've noticed it as a habit of some people, perhaps often going along with a particular type of sense of humour and British understatement. | 1 |
in a company bylaws document, I'm trying to describe situations in which a the term of a company director can be ended. These include death, as well as "going insane" or "losing his mind" - but I'm looking for a more "PC" or "legalese" way of saying this. Any ideas? | 1 |
Lady Macbeth has plotted this out carefully and diligently. Can I use the word "plot" in such a way? I know most people would want to replace that with "planned", but I don't want to keep using that word. | 1 |
Is there a more casual way to say "send me an email"? I'm going to put this at the bottom of the "contact" section of a website. "Pop me an email" is the only one I've managed to come up with. | 1 |
I'm wondering if an ordinary power series expansion of the floor function is possible, and what it is if it's possible. Additionally, I'm wondering what some of the most common uses of the floor function are in practice. Additionally, I'd like to know what use a series expansion of a floor function may be. So, again, what's the series expansion of the floor function? | 1 |
I'd like to say: The calm, balmy evening air showed no sign of the carnage that would ensue. My question is: should it be "no sign of" or "no signs of"? Obviously the word "sign" is countable noun in this context. One sign. Two signs. But NO SIGN means zero sign. Should I use sign in singular form "sign" or plural form "signs" here? | 1 |
According to wolfram a function is monotonic if its derivative never changes sign, but the derivative doesn't have to be continuous. So I feel the answer is Yes, tangent is monotonically increasing. Maybe not? | 1 |
We're a bunch of friends building an RC boat, this may sound stupid but I had an argument with a friend where he insisted that his design will work. Basically, he's saying that by putting a powerfull fan and a piece of tissue as a sail, when the fan will blow air into it, the boat will move. What do you think? | 1 |
I came across this line in a site: Can u make sth effective for a sports betting related product? I can't understand what is meant by sth effective here. I tried to google it but was unable to understand. Can anybody explain to me what is meant by this word? Is it an English word or is it from another language? | 1 |
Is there a word that describes a discussion that never gets to the core of the issue, but continuously lingers on the periphery? I was hoping to fit it into a sentence such as : "He derided his retainers for their _____." | 1 |
We know that multiplicity of least eigenvalue of laplacian matrix of graph gives us number of connected components in graph.What is intuition behind this theorem? How do we know that this works in reality?Is there any proof of that sort? | 1 |
I'm quite confused about this actually! In fact, I had always thought current flows from a region of higher potential to a lower one. Does it have anything to do with the fact that it's a source of emf instead? What significance does that have? | 1 |
So I'm trying to prove the validity of this formula and I am a bit lost, not sure how to start. I know generally speaking a valid formula is one where if all the premises are true, then the conclusion can not be false, but I don't know how to prove this really. any help is appreciated https://i.stack.imgur.com/Opmck.jpg | 1 |
I was writing an email, and I started off with I am writing to inform you of certain errors... However, is this use outdated or awkward in emails (assuming that I don't know the recipient)? What about formal correspondence (e.g. letters)? | 1 |
Are they two different phenomena or same phenomena having different properties in different situations? In what scenario should we consider induced emf and in what scenario should we consider motional emf? And which of the following does faraday's law and lenz law mention about? Are both caused due to induced electric field? | 1 |
I'm trying to represent some string conditions in terms of regex. One of those conditions I find hard to transform is that the string must have at least three different characters. So is there any plausible regex for that condition? Suppose the alphabet only contains English characters (a-z A-Z). Thank you, | 1 |
What's the exact term used to describe the "why" in some people's spoken English (somewhat rural or archaic by now, I suppose) as in "When I saw how much it cost, why, I knew I couldn't afford it".....or "When our family car broke down, why, we'd just walk, until we could fix it", etc....anybody recognize these? If so, why the "why"? | 1 |
I am doing documentation for a web application issue and I'm not sure how best to word what I'm trying to say: "This appears to work no longer in any web browser." "This appears no longer to work in any web browser." "This appears not to work any longer in any web browser." Which is most correct, or are they all equally correct? | 1 |
Sometimes, my supervisor writes emails to ask whether we can cancel or reschedule our meetings, or request me other things. The way he writes emails is very polite. And I usually reply him by: Yes, sure! Yes, it's fine! I wonder if these responses are considered polite? How do I politely (but not really formally) respond to my Professors' requests? Thank you very much! | 1 |
I am designing an algorithm that generates shapes of bezier curves. Each output are control points for a single curve. In some cases, it should return a circle. Which control points does the algorithm have to output for the shape to become a circle? | 1 |
It's an exercise of the book Linear Algebra Done Right. I'm not clear about how to prove these problems, would you please offer me some suggestion about how to improve this kind of ability, thanks a lot. | 1 |
A scammer got a hollow gold bar and fills it with a combination of lead and air, with the same average density as gold. What's the simplest way of discovering the fraud? I know that x-rays will see it, but are there simple means for analyzing it? (without destroying it) | 1 |
I'd like to have output an equals sign that has a small question mark over the top of it. (I'm proving an equation, but it is not obvious until the final step that the equation is true.) Do I need to create a special symbol myself (via a macro, etc.), or is there already one defined? | 1 |
If I have a friend that spreads their interests too thin, gathering a large body of superficial knowledge related to many topics, I'd probably use the phrase "jack of all trades, master of none" to describe them. Are there any phrases or idioms to describe the opposite? Someone suffering from an extreme overspecialisation, who is so singular in their expertise it perhaps damages effectiveness? | 1 |
Title says it all, I'm looking for the formula to get the bearing from one point to another on a number plane. I have found examples of this for lat/lon around the earth but that's not exactly what i need. Thanks | 1 |
Besides SVO, which are the word orders that can be found in English? Are there any that are peculiar to dialects such as Singlish or Indian English? Please provide an example sentence for each order along with pertinent information such as tense, mood, voice, etc. | 1 |
Question: Is it possible to start a grammatically-correct English sentence with the word "Than"? If no, what other English words share this property? Background: Trevor claimed that it is impossible. This is an attempt to verify or repudiate Trevor's claim. | 1 |
Example: "So," I said, after deciding on a topic of conversation, "do you like karaoke?" "So," I said, after having decided on a topic of conversation, "do you like karaoke?" What's the difference? Is having decided an uncommon usage? | 1 |
Suppose I have a weighted connected graph which is traversable (each vertex has even degree) and I wish to walk over all edges. Clearly any Eulerian path minimizes the total weight. What can be said about the case of non-traversable (weighted connected) graphs? Can a minimum-weight path still be found in polynomial time? | 1 |
Is there any word or phrase to describe a person who always feels rthat he has forgotten something even if he hasn't forgotten something really, while going out from somewhere? Example :- Peter is a xxx as he always feels that he has forgotten something, whenever he goes out of his house. What can be the replacement of xxx? | 1 |
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