What is a verb for illusion? I want to use it in a sentence like the following: The optical effect [illudes] my perception of its real shape. But illude does not exist. But I cannot find illude in my Dictionary (OS X Dictionary.app). I want to find a verb that is somewhere between deceive and confuse.


In the fourth episode of Sons of Anarchy's second season, there is a scene where Bobby is wearing chaps and all the guys are making fun of him. Then he says: Cowhide can take the man-hide. I can't figure what it means! I would appreciate it if someone would explain the meaning.


If you have a sequence of real analytic functions that converge on every compact subset in your domain, do their derivatives necessarily converge to the derivatives of the function that they converge to?


Suppose you drop an object which has two ends, of which one is heavy and the other is pretty light. Will the object fall with its heavier end downward or with the lighter one? Why does it happen?


The expression "It's all up hill from here!" and "It's all down hill from here!" mean that things will only get better or things will only get worst. Metaphorically going uphill can provide for a better position, while going down hill is easier. Which expression represents which way?


Theoretically, if a black hole grew to a huge scale such that the effect of dark energy was large, could the black hole become 'normal' space again (i.e. no horizon or singularity)? What I'm trying to understand is, does dark energy 'uncurve' space-time?


An electron and a proton are moving on straight parallel path with same velocity. They enter a region of semi infinite magnetic field perpendicular to velocity. What will happen there? Will both of them never come out of the field? Or they come out with same velocity at same time?


How to determine the ground state of a classical field, for example an electromagnetic field? What is the difference between the the ground state of a classical field and that of a quantum field?


What is the opposite of "abbreviation"? For example, if "ELL" is an abbreviation for "English Language Learners", then "English Language Learners" is a(n) _______________ for "ELL". I'm looking for a word that will work for all abbreviations, not just acronyms, so another example would be: if "abbr." is an abbreviation for "abbreviation", then "abbreviation" is a(n) _______________ for "abbr."


This question was asked by one of my Professor during the class. I'm getting intuition that these functions should be one-one (I'm wrong maybe). But, I'm unable to classify all such functions. Please help in this!!


As I understand, we do not have yet a unified theory covering at once both general relativity and quantum mechanics. However, do we have a theoretical framework completely covering both classical Newtonian gravitation (i.e. without space-time curvature or for not so massive gravitational sources) and quantum mechanics? Is there any reference on this question?


Silly thought. A transducer, by definition, is a device that converts variations in one form of energy to another. An electric lamp converts electricity into visible light - the brightness may vary depending upon the electric potential applied. Is it correct to state an Electric Lamp is a transducer?


This is part of a CNN news article I need to translate. I am not quite sure about what situation the phrase describes. Here is the part the expression comes from: "When did the light switch go off for you to say, oh, my goodness, things have really drastically changed and I'm in trouble if I don't change with them?"


How to tell if a particular EPS figure has a TIFF preview and how to remove this preview? For some reason the Journal of Mathematical Physics don't want these preview to be there when uploading files.


In Mathematics, often a theory becomes popular because it tells us something new or gives different proof for already established facts. For example, I have read that algebraic number theory is helpful because it helped us to solve some diaphontine equations (most notably, Fermat's last theorem). I want to know what kind of questions are answered by Galois Representations.


I know most primality tests are probabilistic, but doesn't that pose a major problem to security like RSA that depend on the prime numbers always having no smaller factors? And if you can repeat the tests enough times to ensure that the number is prime, then would it be correct to say it's not probabilistic anymore?


I heard the saying, "life of Riley" when someone was talking about my cat, and I wondered what the origin of the expression is. The only thing I can think of is that it comes from the name of someone who was pampered and lazy, a king for example.


For example an electron radiates when accelerated. So does a positron. But is the radiation emitted by accelerated positronium the sum of the radiation emitted by each separately? If not, why not? If so, does this provide a way of testing whether a given neutral particle is composite? For example, does a neutron bremsstrahlung when decelerated?


It's always puzzled me how objects with properties like rest mass and charge (and color) could really be geometric points. Is this just a fiction needed for the math to work? Could quantum field theory work with spherical electrons and quarks?


Which of the following is grammatical? He wants to remain a cool kid for the rest of his life. He wants to remain as a cool kid for the rest of his life.


I know how to calculate mean and variance of some given numbers but I have trouble computing them for probability distributions especially when it is a continuous probability distribution. For example, can you show me how to calculate mean and variance of Gaussian distribution?


Can somebody provide an example of a network with a high clustering coefficient and a large average path length? A visual representation of such a network would be great. No reason for asking, besides that I think it would be interesting.


Why do we need a weak convergence for the sequence in a Hilbert space to be convergent? A Hilbert space is a complete pre-Hilbert space, so, every sequence converges in a given space. Where is my confusion? Many thanks.


I'm looking to find the width and height of a rectangle without rotation within a rotated bounding rectangle. I have rotation in degrees and the width and height of the bounding rectangle. Basically I'm looking to find the largest ( largest area ) un-rotated rectangle that will fit inside a rotated rectangle of any given size.


I am looking for an example (with proof) of two norms defined on the same vector space, such that the norms on the two spaces are NOT equivalent, but such that one norm dominates the other...


I am coming across the term: non-convex optimization problem. What exactly is this non-convex structure, and how do I know by only looking at the structure of the problem, I could tell it is non-convex and thus difficult to solve?


Is there a word for the situation when someone takes something said in the most negative possible way, basically stretching what is said to fit the negative meaning that they desire it to mean. Example: "Maybe we shouldn't hang out." to mean: "I never want to talk to you again, you are cut from my life."


when the sound barrier is broken, a series of concentric waves of sound is produced.Does it mean when the speed of light barrier is broken, a ripple of photons are created in the space-time fabric?


This is purely a curiosity, but I'm fascinated by mid-word pluralization, even if the word in question is a compound word. For example, passersby or standersby. No others have occurred to me. Can you provide other examples, or a link to a resource that enumerates them? I'm particularly interested in compounds that do not include spaces or hyphens.


After six months of looking for jobs, she got a reply from a job application she posted online from Macy's asking her to come to a interview. The sentence does not sound right to me, what would be the correct way to say this?


I am trying to figure out how to solve the questions above for the given PDF but im not sure how to do the steps. I'm not looking for answers here as I want to know how to do it, just looking for the equations and steps for each part. I know the standard deviation is the square root of the variance correct?


An essential part of a guitar is its hollow body. Without it, the strings wouldn't be very loud; as far as I know, the purpose of the body is to set up some sort of resonance and make the sound louder. How does this work? How can an isolated system amplify sound? Where is the energy coming from?


For programming purpose, I'd like to compare the entropy of two Poisson distributions to the entropy of a single Skellam distribution. The entropy of a Poisson distribution is given in this wiki article. What is the entropy of a Skellam distribution?


I am writing a sentence like so: "I bought the Dell laptop because not only did I find the price appealing but I also liked the the fact that the laptop had an integrated webcam." Is my use of ".. not only .. but also ..." appropriate? Is there a better way to phrase such a sentence?


I know that 'Jutland', a part of Denmark, comes from the Danish 'Jylland', which describes the same region. But was that name just invented at random, or does it come from the verb 'jut', as the land juts out into the ocean?


I have read that accelerating or oscillating electron emits photons. But why and how does it so? And why only photons? There are other bosons like gluons, W and Z bosons, so why does electron emit only photons? And what is the mechanism ?


When we write a business email and want some information from the mail recipient, then which is the most professional way to ask for information? Does using "please" in a sentence make it look bad?


I recently went through some important numbers like the Stirling and Bell number for calculation of partitions /equivalence relations. I was wondering if someone can help me get a list of important numbers and their applications in Combinatorics ; like Catalan , Fibonacci , Stirling etc.???


For example, the word "jihad." Translated, the word means "struggle" or "strive" and I am sure there are others. The word "jihad," is just taking the pronunciation of the word in the native tongue, and spelling it phonetically in English. Is there a specific word for that?


Why do some pressure cookers initially leak steam from the sides and after a while settle down and don't leak? Is it a positive feedback mechanism from the building steam which makes the sealing tighter and vice versa?


I have a distance matrix M and have used multidimensional scaling and it gives me some eigenvalues. How should I interpret such eigenvalues? Do they show some sort of variability or what? More practically, I really cannot understand the real meaning of eigenvalue. For example I can understand |M|, but I have no sense about the eigenvalue.


I heard that If we travel for long distances in the direction of the rotation of the earth, we can gain some extra hours in the journey. Is it true? What if we travel in the opposite direction?


The multline environment does exactly what I want in splitting a long formula between lines by utilizing the horizontal space to the fullest. (I don't want the alignment features of the align environment.) The problem is, I want to vertically center the equation number, as opposed to making it appear on the second line (as it does by default). How do I do this?


Is it possible to create a head-mounted optical device that allows the user to see the wind, by means of thermal imaging / infrared detection, variations in the light's refractive index, or something similar?


I wanted to ask about the exact meaning of pathology. Is it just for disease or can we use it for other things? I mean, for example, if I want to talk about the determination of harms in culture or technology, can I use the term "technology pathology" or "culture pathology"?


I am writing a paper on a dystopia and how the leader came to be. I need a term to describe how he wasn't elected into power but he just assumed the role of instigator and no one questioned him.


Caroline wondered whether there were coffee shops and restaurants in other galaxies. She imagined them installed on floating asteroids, or in the rest area of cosmic highways. Since the universe was so infinitely large, how couldn't there be at least one or two? Is installed a good term to use in this case? If not, are there other better options?


Why in adiabatic compression and expansion small volumetric change occurs while in isothermic compression or expansion very small pressure is applied and volume changes very significantly i am referring to PV diagram of Carnot engine?


This question is about font in Tex. I want to make my Tex output have the font as in this book https://www.math.wisc.edu/~boston/ddt.pdf but I do not know how. I have no idea where to begin. I appreciate your help!


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?)


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?


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?


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?


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"?


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


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?


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.


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.


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?


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?


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?


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?)?


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.


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.


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!


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.


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?


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.


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.


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!


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!


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?


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?


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.


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?


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?


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?


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?


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.


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"?


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?


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?


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?


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?


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!


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?.


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?


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 ?


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?


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?


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?


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)?


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.


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?


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?


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.


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.


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?


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?


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?


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!


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.


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?


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 ?


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?


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."


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.


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?


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?


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.


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?


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?


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?


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 ....."


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.


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?


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.


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.


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.


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.


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?


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.


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.


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?


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?


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?


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?


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?


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 _____."


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?


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?


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


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)?


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?


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,


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"?


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?


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!


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?


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.


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)


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?


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?


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


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.


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.


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?


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?


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?


The plural form of leaf is leaves, although according to Merriam-Webster leafs is also correct. Dwarf can be pluralized as either dwarfs or dwarves. Conversely, the words roof and safe are pluralized as roofs and safes. Is there any logic underpinning these variations? Is there a historical trend where words that were previously pluralized as -ves are now being increasingly pluralized as -fs?


If the question state: A connected and undirected graph, then does this graph allow loop or multiple edges? I searched over the internet, but some allow, some don't. It's so confusing. Any idea? Thank you.


I am doing Spivak's Calculus, and I find it EXTREMELY difficult. I usually ask questions here because I cannot do the problems on my own. How long should it take to do a Spivak problem? Is it preparatory for contest problems such as Putnam? Thanks!


For a long time I was wondering why there is I win instead of I won. I met such usage in a lot of games and movies. For me, it's logical to say I won, because this winning action is done already. I win for me seems like I'm winning right now. Can anyone clarify this for me?


Palindromes are words, sentences, numbers that are the same forwards and backwards. Is there a term for words that are one word forwards but a different word backwards? For example, star backwards is rats, or god is dog.


Are there any good books on musical theory from a mathematical standpoint? Is "Music theory and mathematics : chords, collections, and transformations", edited by Jack Douthett, Martha M. Hyde, and Charles J. Smith, one on them?


As far as I know, it is valid to say "they can produce music on their own terms" when you want to say that a group can produce music without having to answer to anybody but themselves. Is it also valid to say "they can produce music in their own terms"? Does this convey the same thing? If not, what does it really mean?


I've recently discovered a guy named Gary Vaynerchuk. At his Youtube channel he named himself as garyvee. Besides his last inital is V (spoken vee), does the double ee has any meaning ?


The proof featured at http://planetmath.org/newtonsmethodworksforconvexrealfunctions shows that, roughly speaking, Newton's method is unconditionally convergent for convex/concave functions. I am looking for a textbook or paper reference of this fact. I have found part of it in Michael Spivak's Calculus:


What is it called when a letter is within another letter? For example, the letter O within the letter L: Edit: Or the first C in the Coca-Cola logo: Does this arrangement of type have a name?


I am aware that the plural of metropolis is metropolises, but to me it sounds stilted and to be honest I cannot recall ever hearing it used. Is there an irregular plural of metropolis that would be in a less formal register. Any common mistaken pluralizations?


I have bought many books about vocabulary. Most of them by Cambridge Press. However, I don't know if it is the right way to learn vocabulary from a book like those or is it better to pick new words while reading! Any studies around this?


In LyX I accidentally clicked 'Version Control' -> 'Revert to Repository Version' as it's just below 'Check In changes' option. This resulted in loss of all work since last check in, and using 'redo' is not possible. Is it possible to undo a revert like this?


I'm in the process of purchasing a house and reading through the contract, I can't find a single instance of the comma. (As if legalese wasn't hard enough to read already!) This includes the segregation of sentence clauses, separating lists, following certain leading adverbs (however, therefore, etc.), etc. Are commas considered superfluous in legal documents? Perhaps just property documents?


The usual mantra of a quantum field theory is that real particles (as opposed to virtual ones) are excitations of a field. Is this a necessary property of all (operator-valued) quantum field theories? Are there any theories currently in existence whose fields do not or cannot produce real particles?


What do we mean when we talk about a topological space or a metric space? I see some people calling metric topologies metric spaces and I wonder if there is some synonymity between a topology and a space? What is it that the word means, and if there are multiple meanings how can one distinguish them?


Should it be "find your company's zen" or "find your companys' zen"? Or perhaps another? I am convinced it should be "find your company's zen" as it suggests ownership of said zen, but I want to be sure. What should it be?


I'm creating an application that has a checkbox to assist colorblind users. I'm not so fond of the term because it isn't accurate, but at the same time I don't want to seem overtly politically correct. A couple of options I'm juggling right now: Colorblind assistance Reduced color perception assistance Color perception assistance Problems perceiving colors?


Can someone help me understand what's going on here? This is for a problem involving moment generating functions, which is related to statistics and probability, but I figured it was more of a math questions. The whole expansion is below:


My first question here..sorry if I'm not very specific but I try to be. A T-tetromino has three connected blocks in a line and another one above the middle block. How many ways can one be painted on the grid if orientation matters? What about if it doesn't?


I thought that Empty was the word, that besides its original meaning, could be used when you refer to some abstract idea, like "I feel like my soul is empty today". However, recently I've encountered the word Vacuous in the same abstract contaxt "That idea is vacuous". So what's the difference between those two?


Does anyone have any suggestions as to what is a good topic for a short talk on theoretical physics to a bunch of Math and Physics undergrads that might make them "embrace" theoretical physics? Thanks. (Brain storm: String theory, quantum tunneling, etc...?) Also it would be great if someone could suggest some resources.


While the moon is certainly not a good reflector of solar radiation, surely the radiation it reflects back heats the Earth (even if it is a terribly small amount). How would one go about calculating (or estimating) this heating contribution on a night with a Full Moon?


I need to rewrite my article to fit in the format of Hindawi Special Issue Cloud-Oriented Data Center Networking. After searching their site, I can't really find any useful information about formatting, they only mention that pdfs and docs are accepted, nothing more, any LaTeX template is given. What should I do?


How would you say "I'd like to get off the medication" not using the colloquial phrasal verb "get off"? I.e., something that you'd hear someone well-versed in the English language say. For example, can someone fill in a word or phrase to complete the following sentence: I'd like to be ___ medication by next month.


I had a question on LCDs after noticing something interesting about its color. LCDs are black when they aren't used. But when we observe LCDs closely, we see they are made up of red, green, and blue dots. Therefore, since they reflect red, green, and blue, collectively, an LCD screen should look white. So why does it look black?


How can I create a blind footnote such as the one in the picture below? By blind I mean that there is no number in the text, or in the footnote. I would like to have this footnote on the bottom of the first page of my document and all the other footnotes in the document should be unaltered.


What is an example of a prevariety in which the intersection of some two open affines is not an open affine? My examples of prevarieties that are not varieties does not extend beyond the affine line with the origin doubled. My guess is that the plane with four origins might give an example but I don't see how. Thanks.


I used to read the term "pure energy" in the context of matter-antimatter annihilation. Is the "pure energy" spoken of photons? Is it some form of heat? Some kind of particles with mass? Basically, what does "pure energy" in the context of matter-antimatter annihilation refer to?


One thing I love about English is that verbs can be easily created just by adding the suffix "-ing" and adjectives by adding "-ly". How would you call this phenomenon? Examples: Googling, Youtubing Pants-shittingly


We have a scalene trapezoid. We know AB and CD bases and the diagonal AC. Be P the point of intersection of the two diagonals. Is it possible to find the general expression for AP? I would like to know the formula for AP, if it exists, depending on AB, CD, AC


I have a circular area, and I need to distribute a certain number of points in this circle in a Poisson Distribution. Functionally, how would I be able to distribute the points in a Poisson distribution? If I were to just place the points as 'randomly' as possible, would that be good enough?


Are there any simple "experiments" that can be done in a high school science lab that could demonstrate some sort of basic principals of wormholes or spacetime? Or sort of proving how long something would take to get through a wormhole or why you wouldn't be able to travel through them etc.


I'm not sure I understand the question. As far as I understand it when it says vector space of dimension n, it signifies that there will be n amount of vectors; right? So basically it wants you to prove that a set of two vectors can't span a set of three vectors?


If we have a smooth football in the shape of an ellipsoid, and that water runs down on its sides, can we trace the path of a water drop on it? For a sphere it seems easy because the force tangential to the surface is perpendicular to the radial vector whereas in the case of an ellipsoid it isn't. Any help?


Is it possible to create a picture that would look like this? I have solved a problem that also asks to draw a similar picture. Don't want to ruin my document by inserting a picture of the drawing by hand (see below). Any insight is greatly appreciated.


I downloaded both TeXnicCenter and MiKTeX on a new PC. When compiling a file (which was made on another pc), I get the error ctable.sty not found. Then I get the suggestion to download the correct package from the internet, but it does not work. How do I choose the correct "remote package repository" in the given list? Thanks for your help


I am not a native English speaker and there are some grammar mistakes I do a lot, especially have/has in conjunction with each/every, and so on. Q: Is there some way to highlight all occurrences of some words (from a list I specify) in a document automatically?


Can we reconstruct a polynomial with only Y values? What if the number of Y values are far more than the degree of the polynomial? Also can we obtain the root of this polynomial with this Y's value without interpolating?(i.e. without knowing the coefficients of the polynomial)


The potential for the Higgs field is a quartic one (Mexican hat). Is this done for simplicity or are there fundamental reasons for this choice? I can imagine further contributions to this potential without altering the essentials, which may lead to differences in the derived particle masses.


If photons don't interact directly, how can electromagnetic waves interfere? I know that photons can scatter via higher order mechanisms, but not directly. Does those mechanisms explain the classical phenomenon of wave interference?


Where do the formulas for reciprocal lattice vectors come from? I recently began studying tensors and the same formula's appeared yet again, this time called dual basis vectors! This reignited my interest in a derivation of the reciprocal lattice. Can someone provide some insight into this?


This question presumes that vanilla texlive is superior and thus deserves to be installed despite the troubles over Ubuntu apt-get. What exactly are these benefits? I'm considering going back to texlive via apt-get due to some issues in Rstudio and knitr, but want to fully understand the trade-offs.


We have the following graph: whose every line is colored either red or green. Prove that in every possible coloration there exists one red or/and one green triangle. This problem was introduced in reference to the Dirichlet's box principle.


I came across the word "cable" very often in http://www.guardian.co.uk. Like: WikiLeaks cables: Drive to tackle Islamists made 'little progress' US embassy cables: How the Guardian protects sources WikiLeaks embassy cables: the key points at a glance I know what a cable is, but what does "cable" here mean?


Is this what 'No good deed goes unpunished' means? No matter how good you are or how many good deeds you do (or favors you do) for someone, s/he will always find fault with (bitch about) them and will not be truly appreciative. Could someone please cite an example of this idiom's usage, please? Thank you.


I'm a postgraduate student in physics, but I have achieved interesting results in Cauchy equation. I found a reason why Adams method for solving differential equations gives rise to divergent solutions. I explained this phenomena and provided a new improved integration schema. Could anybody help me to choose a good mathematical journal where I can publish my results?


Is the minimal polynomial of a linear transformation equal to that of its matrix representation on some basis? One of my textbooks on linear algebra defines eigenvalues and eigenvectors in terms of minimal polynomials, while the other textbooks define them in terms of characteristic polynomials. What is good about defining them in terms of minimal polynomials? Why are minimal polynomials important?


I want to get a list of bib-keys from my .bib file which I don't actually use in my document. I have found "Unused bibliography entries - how to check which entries were not used?" but since I'm using biblatex I don't have the information in the .aux files, so I can't use checkcites. Is there a biblatex way to get such a list?


Are the odds of predicting that someone would win the lottery the same as just some random person winning the lottery, or are they different probabilities? Because to me, if I read that someone had won the lottery, I wouldn't be that amazed, but if someone predicted that a particular person would win and that prediction came true, I'd think that's far more far-fetch.


Question:Find the number of arrangements of all the letters in TALLAHASSEE. How many of these arrangements have no adjacent A's? I want to know why it is a combination prob and not permutation.


Why is polarized light used in microscopy for the analysis of rocks(for example)? Why not use unpolarized light? What is it with polarized light that makes the analysis of rocks better? Edit: please refer to the actual physics behind your answer


I make figures in powerpoint, export them as pngs, and include them in my document. I sometimes get strange borders around them, sometimes around indivual elements of the ppt file, like this (black boxes are just censoring): It doesn't print, but looks bad on the screen. Any tips to get rid of it?


In the dictionary, the words "convert" and "transform" both have the meaning of changing the form of something. So how should I distinguish them? In what situation they are of the same meaning, and in what situation they are different?


Do I need a comma before "particularly" in the case below? Thank you very much for your help! Vitamin D has properties against metabolic, neoplastic, and immune disorders particularly breast cancer, osteoporosis, and cardiovascular disease.


Recently I came across the word substantional. What's its definition, and how can it be used in a sentence? Are there any common synonyms? Where did this word come from? I suspect it's related to substantial, but it's not entirely clear. This was used in a context looking for reference back to an authority of some kind, but I'm unsure if this is relevant.


I read this term shave cream in NY Times today. According to the results in COCA (Corpus of Contemporary American English), shaving cream (I also found this word in the dictionary) is far more common than shave cream in American English. I would like to know if there's any difference between these two terms.


I was criticized the other day for using this word. It never occurred to me that it was offensive, but Wikipedia says it "may" be derogatory. Given Vancouver's hockey team, I tend to think it's benign, but I wouldn't want to get William Shatner angry. Please help me oot.


In a sentence beginning, "The head officer[,] or his designee[,] shall..." are the bracketed commas appropriate? If so, could you explain the formal grammar rule that would require them? I'm a legal proofreader; if I suggest commas, it must be ascribed to a formal grammar rule, rather than personal choice. (And as a bonus question, is the comma I placed before "rather" necessary?)


Is there a word to concisely say 'an unavoidable sin'? Or maybe just a better way to say it. This is in the context for example of someone who habitually does some particular activity and then regrets it afterwards.


In Mormon missionary culture, they use the word "trunky" to describe the feeling at the end of their two-year mission when they are tired, ready to go home, and are mentally packing their trunks to go home. They have mentally checked out from their mission at hand. I'm looking for a commonly used word or phrase that means generally the same thing as "trunky".


What's the word to describe someone who acts arrogantly and always disagrees with others unreasonably in order to upset people around him/her? [I'm not looking for adjectives like unpleasant, annoying, unfriendly, rude, I'm looking for a more specific term like opinionated, didactic, loquacious, gregarious ] I think I'd come across it before but I've forgotten what it is..


Which is your most favourite subject in school ? What is your most favourite subject in school ? Which one is acceptable? If both are acceptable, do they have any difference in meaning?


What is the exact meaning of the sentence below? We can't try to get away with something in an academic paper that we would abhor in a political debate (or worse yet, in a political advertisement). The sentence is from the first paragraph of the article 'Being Logical'. Especially, where does the something belong initially? In an academic paper or in a political debate?


I have existing .tex file and want to create similar one. I am doing this by saving the file with another name, I just click "save as", but it won't be saved as a .tex file. Instead it creates .bak file or something else that cannot be compiled any more. What is the problem and what I'm doing wrong?


I'm curious as to how to construct an infinite variable polynomial. Is there an nice formulation of such a thing? I've attempted using functions and functionals to construct one, but that didn't lead anywhere. I need it to find a separatrix for a functional-differential system of equations. I'm very appreciative of any help.


All I have to do is run the plastic comb through my hair and hover it over small pieces of paper, right? The comb should then be charged and attract the pieces of paper... but that doesn't seem to work. I've used the tiniest bits of paper too. What's happening?


How many elements are there in a total ordering T of a set A with |A| = n? I have no clue on how to do this problem. If someone could let me know how to start the problem, it would be much appreciated.thanks


Is there a way to construct lists by multiple instances of a field instead of using and or comma, respectively? E.g., instead of @article{FooBar, ... author = {John Doe and Richard Roe}, keywords={foo, bar}, ... } I would like to get the same result in the reference by @article{FooBar, ... author = {John Doe}, author = {Richard Roe}, keyword={foo}, keyword={bar}, ... }


I am using the tcolorbox package, and I want to use a gradient ellipse title box with border on the titlepage. It is possible somehow or I have to use another package to manage this?


I have heard someone say "As a consultant, Dave can charge orbital fees, so we would rather have you do it." I tried to look up "orbital" but did not find what I was expecting.


I am not a native speaker and yesterday someone told me that "She got her first child" would be misunderstood and "She had her first child" is correct. Now I wonder if this is a 'local' thing here in Wales or a general 'rule'.


The following is taken from a website: Sir, do you realize your wife fell out of the car several miles back? The expression fell out here, as I checked in the dictionary, doesn't make any sense. Does it mean fell off?


When a Force is applied on a body at rest, it produces Acceleration which is equal to change in Velocity. But due to the Force, we see that the Velocity is increasing consequently. So why don't we take both of them proportional to each other rather than Force and Acceleration?


I wanted to use a header which looks like the image attached below. At first I tried using a fbox with a parbox but I had issues with the right widths because the text wasn't properly aligned at all. What would be your attempt at mimicking the style of the first three lines in the sample?


I want to apolagize in advance if the questions are too easy but I tried on my own and apparently I didn't make it, so please help.Also write down every single step in the solutions without omitting anything that you may consider as obvious. First task:


I have two questions. The first question: What are the differences in meaning and grammar between "until you listen to me" and "until you start listening to me"? I'm hoping that someone can help me here. But there is another question: What are the differences between 'I'm hoping' and 'I hope'?


Would it be considered a malapropism to substitute a word or portion of a word in a phrase with another word or portion of a word, generally rhyming with the original word, and generally considered an offensive replacement? For example, the term "Election Day" substituted with "Erection Day" or the company name "Pizza Hut" to "Pizza Slut"?


Here, in the place where I am being hosted, almost every evening there is an event usually called "burlesque". Is "burlesque" normally used by Americans? How is the word used generally? In what context do we refer to this word?


If a function has countably infinite number of discontinuities, can it still be called piecewise continuous [say greatest integer function]? I read that a piecewise continuous has finitely many discontinuities. Thanks for the help in advance.


I have found increasingly that I am accidentally typing ctrl-d instead of ctrl-f only to silently comment out an entire paragraph I am working on. Is there a way to disable ctrl-d ? Ideally I would still like to be able to comment out paragraphs so if it can be mapped to some other keyboard shortcut that would be even better.


Imagine the 'Bishop' chess piece. The four directions that it can move can be called 'diagonal'. Similarly the 'Castle' moves in the horizontal and vertical directions. Is there a single word that describes this movement?


Can you please tell me if my comma in the following statement is correct? Should there be a comma after "questions" as it is below? Should you have any questions, please feel free to contact me at the number below.


The only meaning of "ass" I knew until today was the fleshy body part. But what I read today on a shopping receipt shocked me. One of the items mentioned there was Other ass. Surely that shop doesn't sell body parts. So does this word have some other meaning or is it just a spelling mistake?


I would like to know whether there are mathematical models for the processes of melting (like an ice-cream melting on the biscuit rather than snow) and weaving (or interweaving). If so, of what kind? If you need more specification, please tell me. Thanks in advance.


From the common English grammar lesson, the past perfect tense with had is usually followed by dependent clause. For example: He had studied English before he moved to New York. Now, if I want to say something like this: Yes, I had turned off the lamp. or I had made two mistakes: ... ... Is it allowed in English grammar?


Is it true that the number of arbitrary constants in the solution (if solutions exist) always equal to the order of an ordinary differential equation? If yes, how to "prove" such a statement, if it can be proved at all? If no, what are typical counterexamples?


A haven is a place that is safe. So, "safe haven" is redundant. Shockingly, several state legislatures have even passed laws for dropping off babies with no penalty; these laws are usually referred to as "safe haven" laws.


There are lots of good apps for teaching mathematics to children but I would like to learn about apps for undergraduate/graduate/research levels. Helper questions Any algebra system (like Maple, Sage)? Interactive geometry (like GeoGebra, Cabri, etc)? What else?


I'd like to put am image in a certain position on the title page in beamer. I also don't want it to interrupt the text flow, i.. I want the image to appear "behind" the text. Any ideas?


"There is no man outside the house" "There is not a man outside the house" "There was no solution to the problem" "There was not a solution to the problem" Can I use both of them? Are the sentences equivalent? Which one is more idiomatic?


Is it possible to have a clickable "copy to clipboard" feature in a PDF document generated by LaTeX? Ideally in the form of a macro that also allows for graphical elements to be embedded inside it (to make, say, a custom button that, when clicked, copies something to the clipboard). Edit: An Acrobat only solution will work too.


I am looking for a phrase that compares two characters that share very similar attributes and characteristics. Prufrock and Hamlet truly are [ ... ] I don't want something like "very much alike" or "similar"or anything like that. Rather, I'm looking for a distinct phrase to describe this.


I know we use normal linear regression for modeling functions on datasets, but can someone explain how neural networks help in approximating more complex functions, especially when they are nonlinear? Intuitively, what does each layer adds to the whole process of approximation? What I am looking for is an explanation of how neural networks approximate functions, and not a comparison with the biological neurons.


We know the values of the coordinates (Xa,Ya), (Xb,Yb), and (Xc,Yc). We also know the lengths of A, B, and C. Is there a way (equation) to figure out the exact coordinates where the three lines A, B, and C intersect (the x? and y?). I assume you could rotate all three of the lines until eventually they matched up.


Deal all, I am looking for a gentle introduction to algebraic invariant theory (for a Bachelor project) with some simple (but interesting) applications in representation theory (of finite groups, of Lie algebras). Thanks for your help!


Is there a single word or a couple single words that would describe the situation of not being able to fully express/explain your feelings or emotions to someone so that you can get them to understand your situation or point of view? This doesn't quite include feelings.


I am looking for a word or an idiom about showing respect to someone superior in work because you are afraid of him. I'm not talking about real respect or showing respect to him or his works, just getting scared by his ruthless actions. Is there a word or an idiom for respecting someone because you are afraid of him?


There is a sentence: I am grateful to Mr. White for A and B[,] and to Mr. Black for C and D. Should I put a comma before "and to Mr. Black" or not?


Has anyone proved or disproved that there are a finite number of minor-closed graph families? If not, what is the general belief in the math community? Alternately, is there another approach (not using minors) to classifying undirected graphs?


I've just learned about removable discontinuities. So, when we have such a function we redefine it, making a new function that is defined at the point the first isn't. What is the point of this? What advantages do we get? Wouldn't making it continuous cause problems when we use it instead of the old one?


We all know that we can see anything because of Light Absorption and all. We can hear things because of caused vibrations. But what makes an object smell? I read somewhere about the presence of odorous chemical compounds in the objects which makes them smell. Then, What gives smell to those odorous chemical compounds?


If a hypothetical cylinder was infinitely long, could it vibrate at any frequency, since any frequency would be a harmonic of it? And (less hypothetically) if a cylinder was only really long, would it have a similar effect? I'm talking specifically about sound waves (and more specifically, trumpets).


Is it possible to use the character set available in the "Webdings" OpenType font which is installed on my PC using XeLaTeX? Other non-symbol fonts seem to work fine, but I just get boxes for every character I try in this font, and other symbol fonts like Wingdings etc.


When are two natural transformations between two functors considered the same? When are two morphisms in a category considered the same? Do we have such a notion like we have in Set theory? Thanks


Does the adjective Machiavellian always have a capital letter? For example: The Machiavellian Iago manipulates Othello into believing his wife, Desdemona, had an affair. Not sure if this is anything to go by but, Microsoft Word corrects the word to have a capital. I am not sure if this is also the case when it is an adjective.


Does a diagonal matrix commute with every other matrix of the same size? I'm stuck on one line of a proof that I am writing, and I would like to switch order between a non-diagonal and a diagonal matrix. Thanks,


I'm trying to find a simple and easy to understand example of a free module that has bases of differing sizes. We were told about the existence of them in class but no example was given.


The name of our research center is Southeastern Transportation Center, STC is the acronym, of course. In writing, I use STC, not 'the STC' but our director says 'the' is needed so that it reads well. For example, I write: STC supports graduate education.; director says it should be The STC supports graduate education. Ruling?


I'm confused by this sentence: "Lakesha hopes to win the approval of her mother by switching her major from fine arts to med." I think that in this case hope is intransitive, and I think the part "to win....mother" is working as an adverbial infinitive phrase. Is it the object?


I can't clearly get this phrase. Is it related to the "kick out the jams"? Or "jam" means the song/jazz improvisation, so what does "kick out" mean in that case? The context is "they are kicking out the last jam of their set".


Okay, so everywhere I've read, I hear the main difference is the requirement of a medium. But for example, if you take the case of heat 'radiating' from a red-hot iron, isn't that actually convection and not radiation? I mean, isn't the temperature difference between the surrounding air and the iron causing the air to gain heat?


I'd like to use tikz to shade an isosceles triangle with points A B C and length of AB and AC are equal. Shading should go from AB (red) to AC (green) where the color on a line through A always stays the same. I have found such a shading for circles but unfortunately not yet for triangles... Thanks in advance Jan


My teacher gave me an error identification question, which is : "An itch resulting when a nerve that can carry pain is only slightly stimulated". I have a feeling the word "resulting" is a fault but don't know how to use it properly or if it needs change. Please help me.


Is it possible to use the phrase: "We are meeting at last" when two people meet for the first time? For example, in a movie one person said: "We meet at last". Why did he use the present simple instead of present continuous? I mean, this was an action, which was happening at the moment of speaking.


What is the physical meaning of the fractional integral and fractional derivative? And many researchers deal with the fractional boundary value problems, and what is the physical background? What is the applications of the fractional boundary value problem?


The question and my attempt can be found here: https://i.stack.imgur.com/WSkbv.jpg I don't quite understand what i'm suppose to do. It says to prove the inequality with whatever so I tried to substitute and then factor and I thought it would just work out, but it didn't. Thanks


Speaking of probability distribution, Can someone kindly tell how and when I use binomial distribution and uniform distribution in real life situations? I understand their mathematical formulas but I want to be able to choose the right one to perform when a certain problem is given to me to analyze. Thank you in advance.


I have seen lots of answers proving this theorem via induction. However, I'd like to know how to prove that every digraph such as all vertices have in degree equal to its out degree is Eulerian, using the concept of maximum trail. Does anyone have a clue?


I have a question in my text book that asks me to simplify the above expression. I reached the solution: However, the textbook gives the answer as: I appreciate that the value of these two expressions is the same. However, I am unsure as to how and why the answer above was reached instead of my answer.


I'd like to draw a partial arrow (i.e. with only "half" of the tip) but with a triangular tip shape (e.g. using >=latex), instead of the standard single line you get with "left to", "right to", etc. The result should be something like the following image: How can I achieve this? I haven't seen any such tip in the TikZ/PGF manual.


I would like to find a suitable word, that summarises data like different body parts' circumferences. What I could think of is 'Body Information', but it sounds bad at least for my non-native ears, and I don't know whether there is something better.


CERN recently stated that antimatter may be repelled by matter, much like the opposite effect of Gravity. So is it possible that antimatter is actually repelled to the edges of the Universe to create a sort of outer-shell, something that allows the expansion of the Universe into nothingness.


I am interested in having a local change to the default theme of beamer. I want every title in the beginning of a slide to be boldfaced, black (instead of purplish, black) with a horizontal line that stretches below it, with some margin between the line and the end points of the slide. Is that possible to do with beamer?


Dictionary.com lists plagiarist as the noun form of plagiarism and lists plagiarizer as the noun form of plagiarize. I do not see the distinction of the separate entries and expected both words to be listed as noun forms.


I was studying a photoelectric simulation (http://phet.colorado.edu/en/simulation/photoelectric) and I observed a really unusual thing. When I held intensity and potential at a constant value and then varied the frequency I observed that there was peak in photocurrent. That is, it first increased when moving towards ultraviolet and then decreased. Please try it yourself and explain.


I am a graduate student. I wanted to do computation on heat transfer problem mainly heat convection. I am working on turbulent regime. Can you kindly suggest some good books so that I can get introduced and then use a few as references for my research from a physics perspective.


How flexible is the measurement "a dozen"? If there are nine hundred and ninety-nine thousand people at a rally it is acceptable to say one million people attended, but if eleven people are arrested is it acceptable to round up to a dozen?


Offhand, I'd say it's a variation of the bouffant with a bun on top. It transcends generations. Here's a fairly famous painting by John Sloan: And, almost a hundred years later, here's Captain Janeway:


I am writing a paper on terrorism throughout social media, yet I cannot find a way to phrase the state of horror within a country. My sentence is as follows, "Terrorist attacks are detrimental to the families of its victims as well as the (state of horror/fear) within the country."


If I had bought insurance for the trip, I would have got a refund after I got sick and had to cancel. OR If I had bought insurance for the trip, I would have got a refund after I had got sick and (had) had to cancel. ?


Obviously experiment is the end-all-be-all of any science, but I'm curious if there's any a priori reason to model space as Euclidean three-space (from a pre-relativity viewpoint, of course; I'm ignoring the fact that space is only locally Euclidean). I'm comfortable with differential geometry if it's necessary.


Note this question is not a duplicate of this question because that question does not address the use of "far more". It sounds strange to me but it's probably perfectly fine. "Many more" or "far more people" sounds better. The example sentence: Much more people came to the party last time.


The situation is as shown above. Now, to explain why the bottom disk rises, I applied Bernoulli's Equation at a point just below and just above the disk.The pressure difference hence obtained should push the disk up. Even though this is definitely incorrect, as these two points are not on a streamline, I have no clue as to the correct explanation.


A line from William Golding's The Lord of the Flies: All round him the long scar smashed into the jungle was a bath of heat. Is it just me or does the sentence seem grammatically off?


Several species of fish have names that are both singular and plural form. These include cod, flounder, salmon, and trout, they are used to describe one fish or ten. Does this stem from fish being both singular and plural? Was the irregular plural form passed along to the species of fish?


According to OED, the most common use of "terse" is: Freed from verbal redundancy; neatly concise; compact and pithy in style or language. I've see some usage of terse conciseness, or terse brevity, or similar constructions. To me that seems redundant, even ironic. Am I wrong?


from my understanding,every set has at least two subsets; the null set and the original set itself. My question is, what is the power set of the null set? Shouldn't it be just itself?


Can I somehow use natbib with beamer now? When I try to load the natbib package the file does not compile. There is some old evidence that there is a conflict here: Beamer and Natbib. But maybe this is now rectified?


I am currently spending some time creating a (partial) Liferay translation for the Greek language, and I came upon this original English message text: Your request processed successfully. Can the verb "process" be used intransitively in this manner? Or would this be the correct form? Your request was processed successfully.


John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to Smith's fear about the method of characteristics. Did he mean that with experience and practice, one obtains understanding?


What is the word to describe the phenomenon where at first nobody has the intension to clap (after a performance, lecture, etc). But suddenly one person starts clapping loudly, breaking the silence, and there goes the applause! Everyone starts clapping!


I vaguely remember there is a notion of numbers rich in divisors, i.e. (number of divisors of N)/N is comparatively large. What's their name? Given a number M, how could I find such a number in its neighbourhood?


What does the following sentence mean? This menu will be shown to all users but John. Does it mean that the menu will be shown to all users except John or only to John?


"I gave him two dollars." This tacitly means "to him". Are there exceptions to the rule that an indirect object in English always means "to" or "for"? In English, "I stole him two dollars" does not mean "I stole two dollars from him", and one does not say "I withheld him that information" (either of those usages would be valid in German).


What is the word for the action of telling the horse you are on to move forward, turn left, turn right, or the like? I assume "driving" would be the easiest to understand, but it sounds like it does not fit a living thing like a horse. The word "controlling" seems most accurate, yet controlling an animal gives negative connotations, does it not?


I am not looking for a good book but an appropriate book that is suitable for my logic course. Currently the professor only offers lectures. (Not sure why, perhaps there is no universal approach to logic, so no suitable book?) Ideally, the book contains question similar to the question I asked here. Any suggestions would be very welcomed.


Is there a way to add a hyperlink to a reference from a bibliography (bib/bbl) in an image (created using IPE)? I want to create an image with text that when clicked directs to a reference in the bibliography in the document.


How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, for the photon Green function, for the phonon Green function)? Explanations and references for actual constructions would be greatly appreciated. What is the use of skeleton diagrams in qft and in many-body physics?


I guess the answer is NO, for polynomials. I know that there are more than one series expansion for every function. But I am talking about power series here. All Ideas are appreciated


What, if any, is the difference between the two? My best guess is that a 'roundel' is the traffic island or structure that you drive around, while the 'roundabout' also includes the road you're driving on.


Which one sounds better or is correct? I managed a number of challenging projects, such as / which included (...) designing new electronic devices (...) the design of new electronic devices (...) new electronic devices design


What can be said about the determinant of a matrix when its rows (or similarly, columns) are unit vectors? Do such determinants have a geometric interpretation? For example, in the two-dimensional case, the determinant of two unit length vectors is the sinus between them.


What insights does category theory offer in terms of grand unified theories? Any references to books or papers that give categorical descriptions of any of the common grand unified theories would be helpful.


I was told by a fellow student that sometimes one cannot represent certain functions by a taylor series. I was also told that sometimes using a taylor series in a proof is invalid. Is any of this true? When is it invalid to use taylor series expansion? Edit: By certain functions, I mean well behaved functions with nice properties, entire, countinuous, etc.


I was wondering how to get in my acronym list ":" (colon) after the short abbreviation, for example: I want to get UV: Ultra Violet but I keep getting UV Ultra Violet without the colon.


Two circles intersect in points B and A. Through the point A is drawn a line that intersects the circles in points C and D. Prove that the measure of angle CBD is a constant value for any line that is drawn through the point A. Thanks a lot for your possible help!


Is there a more formal synonym for "doing one's best"? For example, as a formal document title: "Is the government [doing its best] to..." Or is it suitable (i.e., sufficiently formal) as it is?


One which is influenced and steered by pressures from a government which itself is corrupt. Doesn't sound too unfamiliar today, does it? Anyway, it is to help me translate a German word "die Systempresse".


It's widely known that the name "JavaScript" is trademarked by Oracle (formerly a trademark of Sun, formerly a trademark of Netscape). What was formerly a trademark of Netscape? Sun? Oracle? JavaScript? How would one recast the sentence to unambiguously give each of the alternate meanings? [EDIT] The sentence is merely an example. The question relates to correctly structuring a sentence for clarity.


(ignoring the air resistance that causes the bottle to take positions in mid air. Let's say it is dropped in a vacuum with earth's gravity accelerating it downwards) I just cannot catch what happens with the bubble with my bare eye, and I thought I should better ask some experts :)


What is a formal word/phrase that describes a person who always searches to benefit from other people? It is hard to recall the word in my own language to translate. So I decided to give it a try and ask here. I prefer adjective


I understand that torque is defined as the cross product of the difference vector between the point of impact and the center of mass and the force vector, but what happens when the impact is over an area? Do I just find the center of the area and use that as the impact point?


When would you use "expert in" and when would you use "expert on"? A quick google search yields about the same for both, but I have a feeling "expert in" can occur in sentences somehow with a different meaning altogether.


Given an acute triangle ABC with altitudes AH, BK. Let M be the midpoint of AB. The line through CM intersect HK at D. Draw AL perpendicular to BD at L. Prove that the circle containing C, K and L is tangent to the line going through BC


Is there a word that references someone's "humanness"? Something that one would posses, that would characterise them as human. I wouldn't say "human" in terms of morals, but "human" in the most literal sense. I'll give an example: "He demonstrates extreme physical ability, to the point where I question his __". What would be the most appropriate way to express this?


I don't have any knowledge of statistics beyond high school common sense. Why is the standard deviation usually seen in combinatorics textbooks, and why is the standard deviation defined intentionally? What is its purpose? Thanks in advance. I have checked in Wikipedia and many other websites to see what this is, but they are not very concise and clear.


Possible Duplicate: Proof that Pi is constant (the same for all circles), without using limits How can you prove that the ratio of the circumference to the radius is a constant (regardless of what the constant is) using elementary geometry. Thank you


Is the concatenation of two arbitrary alphabets is considered an alphabet ? Also Is the set of all Java reserved words is considered an alphabet ? I am inclined to say yes. We could take a string and consider it a symbol. What do you think ?


This might be too general question, but still, I think this may be some useful question. So, what math branches are there generally? (for example, one branch would be abstract algebra, differential geometry etc.) Or what math branches are recognized in undergraduate math programmes?


I have been trying to find a quick answer of this, but my google searches didn't get me anywhere. I'm confused about using in or on in the following sentence. We will return your call in the following business Day or We will return your call on the following business Day Thank you


I can't find a reference for a set of generating vectors for the Tetrahedral-octahedral honeycomb lattice. I would like to know the "canonical" set and if possible a more general set described by angles (I think it would take three angles to completely describe it but I'm not sure on this either.)


Is there a word that describes a concept which loses its power when put into words? EDIT: For example, the context could be a philosophical (or pseudo-philosophical) idea like "zen" attitude. When a monk can not tell his pupil directly how to achieve enlightenment because the idea is _____.


I used VerbTeX app in my Android phone. But this app does not support XeLaTeX and requires an internet connection to be used. Is there any distribution of TeX for Android? How I can install TeX on my Android phone?


Can anyone show me or direct me to a (free, online reference of a) FULL proof of Green's and Stokes' Theorems? I have been looking and all the proofs I've read prove the theorems for a certain class/type of surfaces/regions...but does anyone know of a general, complete proof?


I mean I will continue to work for this company for maybe some months or some years, so can I use "for some time" as I mentioned in the title. What would a native speaker say? Thanks in advance.


In The Econometrics of Financial Markets by Campbell, Lo and MacKinlay -- a beautifully typeset book -- I have found gorgeous cross correlation matrices of the style below. What is an elegant way to typeset these labels for the rows and columns in LaTeX (ideally in conjunction with the amsmath matrices)?


Is the concept of a field just a mathematical construct? Is there any way to realize its existence? For instance, the fact that moving a charge affects other charges in the surrounding not instantaneously is explained in terms of the existence of an electric field. Is there no other approach to this problem?


For example, If this van's a-rockin', don't come a-knockin' Here We Come A-caroling (song title) Come on-a My House (song title) I have a few related questions: What is the "a-" or "-a" called? Is there a function beyond a rhythmic one? Why is "a-" attached to a word at all -- and why attach to a word at all?


Shade-off and halo effect introduce distortion to phase contrast images. I am trying to utilize these features to write a program which could identify spherical cells from (positive) phase contrast images. Since cells are not necessarily of the same diameter, I want to figure out the theoretical intensity distribution. Could anybody give me some hints?


Say a rotating ball or neutron star gets completely annhilated to energy by meeting its anti-matter counterpart (also rotating in the same direction), what happens to the angular momentum? It cannot disappear due to conservation laws.


A polar coordinate function f(x) can be rotated around the axis by h with the shift f(x - h). However, this rotates the graph. Is there a way to shift a polar coordinate function by x and y measurements? If so, what is it? Can it be done for all functions or only a subset?


In what ways did the points made by the writer in the introduction contradicts her conclusion? (In the question listed above, shouldn't "contradicts" be written as "contradict" - since we are referring to the "points" made by the writer?)


Any idea how can I automatically invoke Mathtype from texstudio using macro (javascript) and put the formula back onto texstudio automatically. It can be done manually, but I want to know is it possible to do this in an automated manner like when invoking mathtype from word.


Usually, when we see two letters put together it is to define the pronunciation or to differentiate synonyms or just its foreign origins. But some words don't seem to have any reason to double up. Why does vacuum have two of the letter U? Why does aardvark have two of the letter A? Why does llama have two of the letter L?


In the following sentence, should I use 'who' or 'whom?: An Open Letter To Those [Who/Whom] I Have Hurt I googled the usage and it said to test by replacing with He/She or Him/Her representing Who and Whom respectively. I don't think that applies in this situation.


What is the difference between gain optimization and gains optimization in a financial context? I want to know in particular if one of those terms is better English, or if they have different meanings.


I've come across the phrase "take tea" in some sentences, and reckoned it is used as an idiom and not meant literally. For instance, "Children to compete for chance to take tea with the Mad Hatter." That sounds like an interesting pun. What does it mean, and what are its origins?


I'm considering two books to learn vector calculus at a level beyond that presented in standard calculus textbooks such as Thomas' or Stewart's, and more applied than a very rigorous text like Munkre's manifolds. Which one covers more advanced topics? Which one is more rigorous? Which one is more applied? Marsden's or Colley's Vector Calculus?


A person belongs to a different country than the one she is currently in. She is clearly a foreigner/alien. But what is the single word for the discrimination faced by her when the natives of this country constantly call her a foreigner in order to point out that she does not belong here? In other words, what's the word for domicile based discrimination?


Is there a derivation of the magnetic field from the electric field of a charge q moving with speed v? (I know that there are some online, but my limited knowledge in multivariable calculus does not help in understanding such derivations.) I understand conceptually how a changing electric field can produce a magnetic field but I do not understand it mathematically.


Call a set finite if there is a bijection of the set with some natural number, and call a set infinite if there is an injection of the set of natural numbers into that set. How do you prove that sets which are not finite are infinite? Does it require using the Axiom of Choice?


For example, if I wanted to know what the product/coproduct is in a certain category, I could find it on that site. I commonly come across websites (such as wikipedia) that give a few examples of some categorical concept. I would like a site with a large database which is constantly updated.


So I always hear that you can't disturb quantum computers because this will ruin the particles superstate. Well, how do we know WHEN to retrieve the result from the calculation? How can we determine when the calculation is finished, without observing it?


You go to a store and buy a product that sounds like it's the best deal. But then you get it home, and it doesn't deliver. What does deliver mean here? Does it mean It doesn't work as you expected?


Thanks for reading my question. I'm wonder why a symplectic form should be closed. I found many different answers in the internet, but it sounds like a technical requirement (if we omit this requisit, we obtain almost symplectic structures, insteresting as well). Why do yo think? I just want to have a fresh perspective. Thank you in advance.


I recently came across the term encampment. Although I could understand that the word must be very close related to camp, it bugs me that I don't understand why such a long word for the same thing exists. Is encampment a more sophisticated word than camp? The translation for both words refer to the same words in my mother tongue (german).


I'm self-studying now and I've found an exercise. Matt ... while we were having dinner. The correct answer is phoned. But I couldn't figure out why was phoning is not a right choice. There is some logic in this answer because Matt is doing a continuous action. Maybe there is something in usage of while I don't know yet?


Wolfram isn't helping me much so I am curious if there are other programs out there. I don't know what degree it is, but I have a series of numbers and I'd like to determine the linear recurrence function/coefficients so I can find any value I want via matrix exponentiation. Are there such programs for interpolating, and how would I do it?


According to reputable sources, sideburns is a corruption of burnsides, a reference to the Civil War General Ambrose E. Burnside. What was this style of facial hair called before that? I'm referring to side whiskers and a mustache with a clean-shaven chin. Also, is there any difference between the original sideburns and friendly mutton chops?


We know function and its inverse are mirror image about the line y=x and also that their composition is identity function (y=x again) So I was wondering if there is a link? I tried to look up for graphical interpretation of composition of functions but I couldn't fund any.


According to Wikipedia: In the form of a screw jack it is commonly used to lift moderately heavy weights, such as vehicles. More commonly it is used as an adjustable support for heavy loads, such as the foundations of houses, or large vehicles. These can support a heavy load, but not lift it. Insights into its mechanism is greatly appreciated .


Consider the task of extracting a cylindrical rod held by friction in a tightly fitting shaft. Instinctively one would tend to twist the rod around its axis while pulling. The question is, what is the physical basis for this? Does applying a torque reduce the axial force required?


I received an email suggesting that we do something: "next week, when we would have been" doing something else. Would you call this an example of future subjunctive? If not, then what? Perhaps it's a present perfect subjunctive? I have been searching for an answer and have found few sites with any reference to a counterfactual statement set in the future.


Let us say I have a single (converging lens) could I use the Abbe diffraction limit (for a microscope) to find its resolution or do I have to use the Rayleigh criterion. (i.e. Is the Abbe diffraction limit strictly for a microscope with more then one lens, or can it be used with only one lens?)


I want to make a cardboard lamp, but i want it to look like half a sphere. Given a cardboard thickness of x, and a circle width of y, how many elements do I need and what radius do the elements need to be? Anyone got a formula for that? thanks alot!


I'm looking for a synonym for the word "time card" or "clock card". I try to find a word for a card with which you can track your work times on a certain device your employe installs for its workers. I used the expression clock card but a native friend from uk said it is not a common expression. Can u help me?


What I wrote is: "However, just as any other data carrier, images not only contain important data, but also such of lesser significance to us. " I want to say that images not only contain important data, but they also contain data of lesser significance. How can I write it without repeating "contain" and make the whole sentence sound more natural?


The majority of definitions give the same meaning - "Pandora's box" is a synonym for "a source of extensive but unforeseen troubles or problems." Are there any other metaphors or phrases with the same meaning?


A book divided in several chapters/topics, can also be considered to be divided in categories (or have categories)? Not sure if category can be used in this case, or if it should only be used in the context of category theory.