I need a very much physical explanation for the phenomenon of Resonance associated with forced oscillations (damped). I have gone through HRW and Concepts of Physics by H C Verma, but that wasn't of much use for me. I got some mathematical idea of the thing, but still I'm not confident.


If tidal power plants are slowing down Earth's rotation then is it theoretically possible to build a power plant that would drain energy from Earth's angular momentum (thus slowing down it's rotation)? What would such machine look like?


What's the word for the condition in which you have a unusually high body temperature after being exposed to harmful winds without proper clothing protection? It's as if the winds somehow got through your pores and made you sick.


When I spin a penny, I spin it on its "edge" (circumference). So why is it that when the penny inevitably stops spinning, it never comes to rest on its edge, instead falling onto one of its faces? It is not a problem with the "thinness" of the penny; its possible to balance a penny on its edge in a couple of seconds.


So I was writing a lab report for Physics I, where I was describing projectile motion. I had written Since gravity on Earth does not have a horizontal force, the object will not lose horizontal velocity (velocity in the x direction). Then this made me think, is there any gravitational force found in nature that has both vertical and horizontal components?


Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in the sense that if a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system).


It is known that there are no diproton or dineutron nuclei. Does this mean that two protons or neutrons are not actually attracted to each other? Even if the attraction was weak, wouldn't it cause bound states anyway? Related: What do we know about the interactions between the protons and neutrons in a nucleus?


I have recently heard the term "Acme developer of IPhone." I was just wondering what it stands for? I think I know the meaning: Is it when a developer goes to a client and presents his/her ideas for the app?


Anthony Martin, assistant accountant, PwC, and associate editor, Washington Post. The commas above look a little too much. Are they technically all correct? Which would you recommend removed? I was thinking of removing the one before "and" since it looks the most clunky, but feel that comma is necessary here.


Like charges repel. What keeps an electron's charge from repelling itself? This problem would come up if an electron was divisible and its parts had fractional charge. A related question is, what keeps an electron from being divisible?


I got that words from novel. I've been looking for the meaning but still can't get what it means. Is that kind of slang? "Hi, Mr.Tushman! I see you're running a little behind today! Did your car get rear-ended again? What a bum rap!"


I have gps trackings that I know they fall into a certain pattern - a line with a known angle. How do I find the line that minimizes the distances of the points from it but is in the correct angle? Unfortunately, I can't post an image for example.


I have a question about the following: Texas is only one of the states that still have sizable wheat production. Texas is the only one of states that still has sizable wheat production. I want to know whether the above construction is true. If so, what is the rule?


Can guilty be used as a noun? For example, as in the title of Chase's novel: The guilty are afraid. Is it that people or folks is understood after guilty and in effect an ellipsis? I do not find guilty marked as a noun in Webster or Wikitionary.


I know you can draw a protractor with TikZ. The problem is that my students use the triangular shaped one like this. So in order to make it a little bit more familiar to them, I am wondering if there is also a predefined one like this one?


Is there a particular word for a joke or a humorous story which has a moral to it? In a way, something that is similar to a fable, but with the humour implied.


I have read several explanations of standard deviation and z-score, I know how to it calculate them but I am not sure what is differences betwen them. Can someone explain it to me? When is suitable to use stdev and when z-score?


I want to have an answer with that question above for my physics lesson. I really don't have an idea about it, so, I ask help from you guys and hope that someone can help me with it.


I would like a way to convert a document from HTML to LaTeX, on a Windows platform. A main motivation of mine is for ways to display books from Project Gutenberg. such as, Wells' The Invisible Man. What is my best option?


I am trying draw a line of distinction between these three events. As I understand it: Ritual is somewhat related to a religion. Festival is associated with a group of people and that brings happiness. Ceremony is something that is followed by a group of individuals before performing a task. Can someone please tell me if I am wrong, and also provide some examples?


In one of his lectures Richard Feynman, a great genius and a 'naughty Bronx kid', refers to to the Coulomb force, electricity as "the screwing force". Apart from the obvious joke and double entendre, can you explain that original definition and in what way it is different from other forces or from an EM wave?


Could somebody suggest a single word for 'I think it is right but not exactly sure about it'. I can say 'I am almost sure' but wondering if a word exists with same meaning.


Does present perfect in conditional only mean future situations? Can it be used for hypothetical future? When I went to Africa, I thought as if I have already been there. If you have studied, you would pass the exam.


I was wondering why you would say "There is people coming" as you can hear in the last trailer of Game of Thrones. English is not my native language but I'd think that you have to use plural in this sentence such as "There are people coming". Is this "urban"-talk or am I missing something?


I am not very good at speaking and listening English. Can someone please suggest some songs, which have clear pronunciation of English words, to listen and understand the songs too and also I can use them to improve my vocabulary. Actually very fast music, especially those with too many and loud musical instruments never helped me understanding the lyrics.


What is the physics behind welding iron? It is obviously the electricity that causes the two metal parts to fuse but what is the role of the welding rod and why is it said to damage your eyes when you look at the spark. Is it just the brightness, or does it radiate a specific wavelength that is more damaging, such as UV rays?


The universe is believed to have originated from absolutely nothing, and we know it is still expanding. Physics says "something can arise from nothing". I understand how mass and energy are related and one can take the form of other. But, how can everything arise from absolutely nothing?


I am pretty new to Turing Machines and I am trying to understand the basic things first...so my question is , would this machine accept all words ending in 'a' ? if that's the case would the REJECT state be all string without 'a' and ending with 'b' ?


Is this sentence correct? She will grow up hating what she sees in the mirror. Or should it be: She will grow up hating what she will see in the mirror. I think first one is correct, I just want to know why and the rule.


"packet" and "package" are synonyms when we refer to mailings, but does the same apply to "network packet"? My co-worker frequently says: "network package". It's like nails on a chalkboard to me, but is it correct?


Which one is more proper to use: 'allocable' or 'allocatable'? Sources say the former is derived from the original Latin word 'allocare', while the latter is a part-of-speech-variant of the English word 'allocate'. Also, is there a standard rule in English to form able-ending adjective of words terminating in 'ate'? Thank you.


I need to find uses and interesting questions by using jacobian matrix for a project work ,can any one help me. I found jacobian matrix is used in dynamical systems, but i didn't understand it.Is there is any question in dynamical systems which is connected to jacobian matrix


I have the same problem like here: How to create custom section titles with a "<title> <number>" format in ConTeXt? But I would like to solve it in LaTeX. Is there a simple way to adapt code from the @phg's answer?


If I tell you the real and imaginary parts of the index of refraction for all frequencies, name a property that can't be predicted based on that information. If you're assuming this is a gas, specify your answers to properties measured in gases. Likewise for solid, etc. edit: I see my question is not a good fit for this site: https://physics.stackexchange.com/help/dont-ask My apologies!


I am making a small book and I want to put a phrase in both pages like the picture above, I want to keep the chapter title and page numbers. Could you give me a hand on this?


Well, our professor in class posed a question to all of us: Is frequency a scalar quantity? The obvious answer, of course, is yes, it is, because it does not have a direction associated with it. But then, a scalar is defined as a coordinate invariant quantity. In the case of frequency this obviously fails (the Doppler shift). So how do we classify it?


Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc): For any given set, the intersection with the empty set results in the empty set. For any real number, multiplication with zero results in zero.


I have a question that is short and sweet: Are spectra (both fluorescence and absorbance) of any molecule dependent on temperature? In particular, is the spectral lineshape function of any molecule dependent on the temperature (so, kinetic energy) of the surroundings and possibly itself?


Why is this a wrong Triangulation ? I have to say, we had triangulation at the end of the topology course, so not in details. And the professor only mentioned the basic rules for the triangulation, but in this case, idon't know why it fails.


I was reading the book "Theories of Integration" by Douglas Kurtz, and I have a question about the following proof from the book. Specifically, would it be valid to replace the argument that follows "It remains to show that A satisfies the Definition [of Riemann Integral]" by: Thanks!


If it's infinite, is it countable or uncountable infinite? I am a newbie to this topic... I don't know what modular arithmetic for polynomials means. Can someone please give me a link where I can learn?


I have problem with sentences structures. I have sentences: I specialize in design wireless and wired network infrastructure, configure devices company's Cisco Systems and MikroTik, and security and techniques used successfully to protect IT resources. Additionally, I have knowledge of voice over IP (VoIP) technology. I am not sure, is this sentence grammatically correct? Thank you in advance for your help.


If one rotates a function such as the sine function about the origin, is there a general method to find the taylor series for the rotated function? Assuming of course that the rotated function is still a single valued function.


I would like to find a mathematical function like the one I sketched below. My first idea was to rotate a sin function, but now I don't think that would work because I would like the function to be well-defined so that for one x, there is only one y.


I understand that the quadratic equation can solve any second order polynomial. Furthermore, equations exist for polynomials up to fourth order. However, without a graduate level degree and a deep understanding of mathematics, is there an explanation of how we can prove that the equations for solutions to a fifth order and above don't exist? Thanks in advance.


Suppose you met a famous person, and you were shy and anxious and almost overwhelmed by them. Is there a word for describing that? Similar to getting stage fright, or "choking", except in this case for a person? When he said hello to me, I couldn't respond. I (was) __________.


When two nouns come together like taxi driver, the role of the first noun is noun adjunct. Now the question is what is the second noun's role. I mean the role of driver in taxi driver. Thanks


I feel like it could mean either "what you are capable of doing," or "what you are willing to do." Do one of those better represent the meaning of this phrase or are they both right?


I've been trying to look at stopping times and continuous time change in martingales but have trouble understanding without some concrete examples. Anyone knows of any good references that might be helpful? Thanks!


A wire has cylindrical symmetry, therefore we should consider the possibility of the induced by field in the p,phi and z directions. I know from the right hand rule that we only get a field in the phi direction but I'm not sure how we show that there is no field radially or along the length of the wire.


I wrote the following sentences: Eyed closed, he imagined the moment disintegrating, returning to the stars, and continue existing there for eternity. Eyed closed, he imagined the moment disintegrating, and returning to the stars to continue existing there for eternity. Now, I'm not sure if I should say continue existing there or continuing existing there.


Suppose I somehow know propagator for a given quantum mechanical system but I don't happen to know either the Lagrangian or Hamiltonian. (For simplicity, assume that this is non-relativistic.) Is there a procedure by which I can recover the original Lagrangian?


I used to say cleats but found it uncommon for some people, though I had no trouble with soccer shoes. I have always lived in a Spanish-speaking country (Nicaragua) so I find it hard to know why that is. Are cleats only used in some places? Wikipedia also mentions football boots.


Which is a good book to refresh discrete maths fundamentals for a grad student? It would be great if the book has short and terse explanations of concepts with lots of worked out examples(/to be worked out exercises) to set the brain rolling. Can someone suggest a similar refresher for graduate level algorithms?


Given two latitude and longitude points, the bearing with respect to north of a great-circle path starting at each point, and the distance between the two points, how can I calculate the latitude and longitude of the intersection of the two paths if it exists?


Can anything be stated about the distribution of the digits of Pi, i.e., if I were to sample n digits of Pi, can anything be said about the probability to observe certain digits, or is there any reason to assume that they would not be evenly distributed? This is purely a curiosity question.


Recently I have considered the following question: for a sequence of i.i.d. random variables(maybe normal distribution), the expectation of the maximum of n such kind of variables is dependent on n, so if n goes to infinity, will the expectation of the maximum of infinite i.i.d random variables be infinite? What is the upper bound of it?


What is a polite way to describe a person as "white-washed", i.e. a person of visible color who acts and talks and cultured the way a white Western person is. Or is white-washed OK ?


So I am filling out a CV and answering about my education, when it comes up 'year obtained' I have never come across this on a CV before and if I have it hasn't been worded this way. Could someone help me? I am confused about whether it asking me the year I started or left, Thank you.


What would be a good term for the subject of a requirement? If one has a requirement applied to them, they would be the [word] of that requirement. I'm looking for something more descriptive than subject or target. Constrained seems like a good fit, but it feels a bit unwieldy?


Is there a non-collective noun for an "instance" of publicity? In other words, a restaurant receives publicity every time a local newspaper publishes a review or an article about it. Each of those articles or reviews are examples of a [blank] for the restaurant?


We know that the ring of analytic function on a connected open set is a Bezout domain. Do we know what happens if we remove the hypothesis of connectedness? It is no longer a domain, but does the ring share the same nice properties like: every finitely generated ideal is principal?


The other day I was talking to a friend about when to use "middle" or "center". I was using it in the context of top, middle, bottom, as a listing, and he suggested it should be top, center, bottom. I want to know whether it should be middle or center.


I have a feeling that this usage - which I personally find highly irritating, because it suggests either that the initiator of a conversation is helping a person who is in dire straits or that they themselves are in trouble and seeking help from a lifeguard figure - became popular in California, but is that correct?


Recently, I am studying Chinese Zodiac Compatibility. They said "Snake (one born in Snake year) and Rat (one born in Rat year) are a volatile pair". I am not sure what "volatile pair" mean? like each person can go to different direction in their life or something like that? or they just do not like to each other See the website here http://www.travelchinaguide.com/intro/social_customs/zodiac/compatibility.htm


What are the Ishibashi states and Cardy states in CFTs? I am familiar with conformal field theory language. It would be great if someone can discuss about the basic idea of these states and their applications.


If a rubber ball is red, I know that it is absorbing all colours except for red, which it is reflecting. So there is not actually a part of the object that contains any red. But what tells an object to reflect the light that it does? Is it something in the surface that does not let that wavelength enter it? Thanks.


I have always wondered and once I even got it, but then completely forgot. I understand that gravity causes high and low tides in oceans, but why does it occur on the other side of Earth?


Which of the following is correct when addressing an audience or more than one person? Or are both equally valid? I hope you have all had wonderful summers! OR I hope you have all had a wonderful summer!


Please forgive my stupidity. So many years after my undergraduate study and so many years after dealing with various concrete ODEs and PDEs, I still cannot tell the essential difference between them. What specific belongs to PDEs but not to ODEs? What conclusion for ODEs cannot be generalized to PDEs? At the moment, my understanding is simply that PDEs have more than one variables.


Is it okay to use ain't in formal conversation? I know ain't can be used for am not, is not, are not, have not, has not. So if I can use it in day-to-day life, it will be easier for me I guess.


As an ESL I'm not sure if I can use the following sentences: You can take no other directions. I'm using it on giving indications to a foreigner. Should I use instead: You can't take other directions. Which one do you think it is the most natural/idiomatic?


Can someone give me some information about this area? PDEs on non-cylindrical domains I take to mean parabolic (let's fixed parabolic) PDEs on domains which evolve in time. What is the state of the art on this topic? What kind of problems do people consider? What tools are used for existence and uniqueness? Any recommended papers?


Sometimes I feel uncomfortable to say "How do you spell xxx ?". It sounds like asking his or her own way of spelling a word implicating that I am not necessarily expecting the correct answer. Is "How do you ... ?" a polite question to ask the right way to do things ?


I'll take the sky diver example. Right when a sky diver jumps out of the plane the net force of the diver is greatest. Then the diver begins to reach terminal velocity where the force of resistance = the force of gravity. So while the force of air resistance increases to equal the force of gravity is the sky diver decelerating?


I am looking for exact or perturbative solution realistic lotka-volterra (the one with logistic term in one of the equations) equations in population dynamics. Any reference where they have done it will be useful.


I'd like to know whether the phrase "where I be" is grammatically incorrect or whether it is correct if in the subjunctive mood. If it is in the subjunctive mood, what exactly would it mean? The entire example sentence is: I look for a place where I be free.


Idiomatically we do say "a strong will". But can we say "strong wills"? The context is The optimism and (the) strong will(s) of the handicapped children touched me deeply. Also, do I need a "the" before "strong will(s)" in this sentence? Thanks.


Does a direct limit of projective need to be projective? And is the inverse limit of injectives injective? I guess they need not, but I can't find an example. Can you help please?


Is this sentence grammatically correct? [This method] binds a handler to one or more events to be executed once for each matched element. source Is it just a contraction of the following sentence? This method binds a handler to one or more events, that is (supposed) to be executed once for each matched element.


Did Feyman suggest even though Q.M. has great predictive power no one will ever really understand it ? Some people have said there may be hidden variables that explain underlying principles of Q.M. but has this been ruled out? Has Q.M. been put in an axiomatic framework?


I have difficulties in using each. Which would be correct in the following sentences? They are each connected to a hydrogen atom/hydrogen atoms. They each are connected to a hydrogen atom/hydrogen atoms. They are connected to each hydrogen atom/atoms. [Assuming that each of them is connected to one H atom.] We each have our own car/cars. [Assuming that each of us has one car.]


After reading the Wikipedia article about procuration, I'm still confused. Here's what I want to know: What does the author mean by "the phrase per procurationem is ambiguous if used with undeclinable English names"? If I sign a letter on behalf of someone, is this protocol acceptable? Sincerely, Secretary's Signature p.p. Account Owner's Name The author implies this method is debatable. What's the debate?


How is the meaning of a sentences affected by chosing one of those words? For instance, what's the different between The screech cicadas reverberated through the forest. and The screech cicadas reverberated throughout the forest.


This is the word problem. If they work together, John and Vince can finish their project in Biology in two days. If they worked individually, it will take John three days longer than Vince to complete the task. How long will it take each to do the job alone? Thanks in advance ;)


In soccer, if a player waits for another player to get into a proper position before passing the ball to him then can I say "That was a nicely waited pass" or would that be grammatically correct?


I see the British normally use plural form of the verbs associated with collective nouns. An example, "The team have fired its coach" versus "The team has fired its coach". I have been told this is slang that has become mainstream. Any idea as to its real origin?


I understand the nature of light can be complex and has extensive theories/experimental data. We hear light can be both a wave and particle, so why can't it be both, a wave of particles?


By this, I mean someone who is not extremely religious, but, in a time of crisis, will turn to religion for hope. An example would be a mother who prays if her daughter is kidnapped, but does not pray on a daily basis. Is there a word for this?


Here are two sentences patterns: Have you ever been to the opera when you lived in Milan? and Did you ever go to the opera when you lived in Milan? What is the difference between them? How can we say, which is right sentence?


My native language has a word for that process hence I am curious to find out if English has one. I searched for it on the Internet without success. Apart from "removing stem", I found "removing leaves" from cilantro.


Assuming inter-universal (see here) travel is possible, can a perfectly mathematically describable universe exist inside a multiverse? If it could, would that mean that the multiverse is mathematically describable as well? (A perfectly mathematically describable universe would be perfectly predictable as well. Can one predict the future of such a universe when inter-universal travel is possible and the multiverse is not perfectly mathematically describable?)


And if so, then why does everybody keep asserting nothing can go faster than light speed (I'm implicitly assuming there could be something which we do not observe, which goes faster than light)?


Consider a solid yogurt. Can we assign a specific state of matter to it? I mean, it behaves like solid. However, if we "mix" it with a spoon, it becomes liquid, or at least in the usual sense. It is also quite plastic, which complicates. My current guess is that it is either a glass or a gel, but I'm quite unsure about it.


Is open mapping theorem true for a analytic function in several variable ? I've encountered a problem, which can be solved easily if that's true. But I couldn't find that after doing some Googling


I am looking for a expression, phrase or word that describes a person or behavior that pretends a mistake made was intentionally done so as to save face. There is a phrase in my language saying "To pretend that the fall was a technique/stunt". I am looking for an equivalent for this in English.


And you may not really expect an answer or want/need an answer. Not quite rhetorical. For example you may be talking about something that happened and wondering who did it and everyone knows who did it including yourself but you ask, 'I wonder who that was.'


Sorry for the daft question, but, is the following a correct thing to say? "The preimage of a function f is a function iff for any element b in the range, there exists exactly one a in the domain such that f(a) = b" "A function is injective iff its pre-image is a function." Thank you.


While showing my work to my adviser, he uttered a sentence, "You could do it better!". Is it analogous to: You could have done better OR You can do it better (so improve it)? It seems to me this sentence can mean both of these.


Is it possible to create a certain design of a conductor to reduce eddy currents greatly? So that the magnetic "breaking" can be reduced? Is it even possible for the force generated by the eddy currents to become negligible?


I know that when some of the previously unsolved problems were solved they created new fields in mathematics. May someone explain to me what would be the result of a major problem like the Hodge Conjecture being solved vs a "smaller" problem like "Do quasiperfect numbers exist?" in today's society. Thank you in advance.


What exactly does a phrase 'we need to take contingency on them' mean? This is an expression I heard from a project manager so I presume it has to do smth with risk mitigation. However, I'd rather not guess. Thanks.


I know there're various types of rhyme in English, such as slant rhyme. There're also things called assonance and consonance. I plan to rhyme "pan" with "screen". Essentially two monosyllabic words ending with "n". Obviously this is imperfect rhyme at best. Is there a linguistic term to describe this type of pairing? If so, what is it called? Thank you.


How would I indicate, for example, that I am going to use "toms" to mean "tomatoes". Something like: Tomatoes (toms) are red. This is false as some toms are green. I like toms.


Is the usage of "though" in the following sentence correct? It's said that it is a picture of a rabbit, but I'm sure enough that what I see is, though, a fish. Don't mind the contents. What I want to ask is whether I can use "though" that way or not. If not, why?


"Small initial discrepancies may not be seen as meet for a federal case, particularly when the employee, trying to succeed in a nontraditional environment, is averse to making waves." Is there a legalistic meaning for meet or did the author mean to use the word meat in the text quoted above?


I dont think so, because then the rays will intersect and the image will be real. Please let me know if you know a case in which a virtual image is formed in front of the mirror.


I ask a question about "What is a wavefront?" which follows the question "What makes the radiation behind a slit coherent". For the wavefront it was answered, that "In electromagnetics ...(that are) the points that are at the same height." Now I'm wondering, are the wavefronts moving?


A lemma in my lecture notes claims, as in the title, given a surjective ring homoromorphism from R to S, ideals in S are the R submodules of S (in the first paragraph - picture attached), but I can't see why this is true. Note that we are assuming all rings are commutative. . Any help very much appreciated


What is (if any) the name of the operation of changing the root of a rooted tree? Picking a vertex which is not the root, then reorienting the edges in such a way that the vertex becomes the root?


I know that through the Abel Ruffini Theorem the general solution to a polynomial of degree five or more cannot be found explicitly. But are there are any other ways to find the roots of such a polynomial besides exhaustive methods like Newton's Method? The question of finding such roots arose when trying to find the the y maximum of the unit lemniscate.


What would you call a triangular object with two sloping, concave sides? See the following image. Consider object A, object B and the entire structure as a whole; object C. What do we call object C? It is related to architecture. I'm trying to describe the structure of an opera house design proposal.


Is it the same as the space of all possible descriptions of a single electron? If not, how do they differ? Please give the mathematical name or specification of this space or these spaces.


What I want to know is: the preimage of an integer by a valuation map is an open set? Otherwise: Can we cover a valuation field by open sets with elements with fixed valuation?


When you say "I had it coming", does it always mean "I caused it to happen to me"? Can it also mean in an appropriate context "it just happened to me"? Also, does it always have to be "coming" and not base form "come" like "I had it come"?


It is preferred to use ipad to create and edit TeX files and use LaTeX. I know some applications to use TeX but they need Internet and are not complete. Is it possible to use texlive on Ipad (IOS)?


A. "John gave the slogan". Make it an interrogative sentence with WH-word. Which one is correct? Who did give the slogan? Who gave the slogan? B. "Grandfather came to meet John". Make it an interrogative sentence with WH-word. Which one is correct? Who came to meet John? Who did come to meet John?


I found this sentence in Collins COBUILD English Grammar. "Was the Colonel waved his paper yet?" I have no clue about what it could mean. Grammar-wise, it looks totally messed up. Is it me not getting something here or might that be an odd sort of error on the publisher's side?


Possible Duplicate: Differences among words describing someone who is expert in many things I just wondered, what could we call a person with deep knowledge in various fields? For example, computers, music, sports, etc. I think I could use sage, but it wouldn't be appropriate if someone is experienced in multiple fields.


Is it the case that for a harmonic function on a graph any value of the interior point is the weighted average of the boundary points? I know that for a harmonic function each point is the weighted average of its adjacent neighbors, but can you extend that to the boundary points?


I'm very curious about how light is created. I'm trying to get back to some type of real understanding about why everything on the sub-atomic level vibrates and the implications for the preservation of both the conservation of energy and conservation of momentum. How is light created at the atomic level?


My primary and most common example is to read something and say (or write) that it "sounds familiar". Text has no sound. I'm sure there is a technical term for this practice or phenomenon. What is it?


I'm doing a small research project into these but their Wiki page and other pages I've looked at just detail what they are, and their properties. Does anyone know of any real world applications or some interesting facts besides their properties?


What is the equivalent word for a person who doesn't want to hear/listen others' personal feelings/information. If not, the equivalent word for a person who are stubborn in listening to others' feelings/information. Opposite to the meaning of the word reticent.


Actually, I was seeking for top universities, which has mathematics depart, in Pakistan and I found one, namely Quaid-i-Azam University. Which is known for its Education in "Natural Science". Then I apprehend what is Natural Science. So, I started to read the article on Wikipedia about it but I didn't find mathematics in their context. Is not mathematics a branch of "Natural Science"?


I'm wanting to make a logic tree using forest that looks something like the picture below: I'm struggling to list the premises of the argument at the first node of the tree in the way that is done in the picture. Any help would be much appreciated!


I understand how spinning tops don't tip over, cf. e.g. this and this Phys.SE questions. What I'm more interested is in identifying the factors that determine the direction the spinning top moves to?


In the same way as when they surround a nucleus? How about when electrons go through wires or are ejected as beta particles? Do they still only have probabilities of being somewhere, or...?


My student wrote in his essay it gives her face a peculiar charm? I tried all the dictionaries at hand (hard-copy and electronic ones) but did not find a definite answer whether this phrase sounds English. Could you please help me?


I am reading about zeta function from book by Ingham. In that book the following theorem is given. I am unable to understand what does he mean by finite part of plane in the statement.


As I decided to use LaTeX to make a presentation and I'm a newbie, I would like a not-very-long tutorial that introduces all features of the beamer class package one can use along with its output. Is there any other package which is preferred over beamer?


Can anyone please help me understand the symmetries of G, where G is the group of the symmetries of the circle. Prove that G has elements of order n for all positive n integers, as as elements of infinitive order. Thank you


I would like to know which fields in physics have seen growth or benefited by applying QFT? I know that approaches to quantum gravity such as string theory use QFT, HEP and also some branches of condensed matter physics. Where is it applied in condensed matter physics exactly? And in what other areas of theoretical physics, has QFT been applied?


In constructing the trace space on a subset of a measurable space, it seems one has to assume that the subset is an element of the original measure space's sigma algebra, i.e., measurable in the original measure space. This is not explicitly given in the problem statement. I have not found a list of errata for this book anywhere.


I've heard in many places, educated people saying "but nevertheless...". I think both but and nevertheless have the play the same role. Is their combination, as to emphasize that what follows is opposes to the previous statement(s), allowed? Is it considered redundant or uneducated?


When we put a little pin on the surface of water, it floats; is this because of surface tension or buoyancy? Can somebody also draw a force diagram for me to explain how surface tension of water supports an object. And anybody has any advise for me that I can do any simple experiment to demonstrate water-surface tension?


I'd like to include in my LaTeX code some form of indication that certain words are keywords, or that a phrase is a quote, or that another phrase is an example, etc. Where can I find a list of inbuilt semantic indications like these?


In my search for the definition for the poetry term "doggerel," which I still do not understand, I came across the term "irregular rhyme." Can someone explain the definition of these terms, and how they are used in the literary sense?


I found something called "Cervantex" here on this plattform. I tried to Google it, but I have one problem - I don't speak Spanish. So are there anyone who please could tell me, what Cervantex is, and what it could be used to? Thank you in advance.


On Wikipedia we read: dirty money: (idiomatic) Money that is illegally gained, illegally transferred or illegally utilized. Especially money gained through forgery, bribery, or thievery. Is there a precise origin of the idiom "dirty money"? Why has the word "dirty" replaced "illegal"? (perhaps because an author has used it an important novel?)


what does it mean "to be in receipt of something"? I have checked the meaning but have not figured it out fully, since I am a translator I need a literal translation for me to build out a meaningful, usable sentence in my own language. Thanks in advance


what will be happen if we put asynchronous generator in vacuum chamber & run it above its synchronous speed. After reaching its over synchronous speed we will cut off electrical supply. Can it run continuously? Can we generate electricity from it?


Blogs and websites typically provide an index page of entries where they show an excerpt of the post. Excerpts usually include title, author, post date, and a blurb. What is the term for these sorts of excerpt?


The text I am studying from seems to suggest that the rank of a quadratic form q on a vector space V is equal to n=dim(V), and I'm confused as to why this is the case.


Is there single word that means "all seeing"? From what I can tell, omniscient is often used to cover this, but that more accurately means "all knowing". It likely stems from a presumption that if you can see all, you know all. Nevertheless, I'm looking for a word that means specifically "all seeing". Would it be something like omnivisient?


QUESTION: Compare and contrast the following distributions giving examples Geometric and Negative Binomial distributions Exponential and Gamma distributions I don't understand how I would answer this had it come in an exam... Do I derive one distribution from the other? Or simply state in the simplest of terms what makes each pair of distributions similar...?


I am about to collect information from multiple sources and transform them into one language/terminology. I wonder what would be the correct term for this process? Maybe a different word would fit even better? Thanks!


Why does each individual photon have such a low amount of energy? I am hit by photons all day and I find it amazing that I am not vaporized. Am I simply too physically big for the photons to harm me much, or perhaps the Earth's magnetic field filters out enough harmful causes such as gamma rays?


I understand the meaning of this word in general, but there's just one question. Here are two examples: We painted even the floor. AND We even painted the floor. Are they correct and if so, do they have the same meaning?


Consider the name John J Doe Jr. If John is the first name, J is the middle initial, & Doe is the last name, what is Jr.? I checked with Webster years ago and they could not find a specific name.


Why each sphere admits an orientation reversing diffeomorphism onto itself? (For even dimensional ones can we take conjugation map?) And why complex projective spaces do not admit? Is there a geometric way to see this without using characteristic classes?


I would like to be able to draw a box that shows up on in the PDF but does not print, just like the boxes around links that are made using the hyperref package. I would like to put a minipage environment with multiple paragraphs inside the box.


I know that we now have telescopes which can capture the images of the stars and galaxies millions of light-years away from us. Does the telescope capture the past image of the star, i.e. the light which it emitted centuries ago? What guarantee is there that the star is still alive? What basis do organizations like NASA plan missions for evading such stars?


If a civilization could build a strong , lightweight tube, hundreds of thousands of kilometers long , could theoretically use it to communicate faster than light, simply by rotating it at one end , the other rotates at the same time , or not ?


Of triangle ABC, I am given the coordinates of two points (A and B) and the angles between the side AB and each of the two other sides. How can I get the coordinates of point C?


I'm writing a project and I am stuck on the last part which I have to explain the usage of mixed and scalar product of vectors, where are they useful, what could be done with them in the future and so on. Where can I find information about this?


From Wikipedia, "In Norwegian and Swedish, Kraken is the definite form of krake." Since "Kraken" is already the definite form, why do we add a "the" prior to "Kraken"? Or "Kraken" is a word taken from another language, therefore its grammatical property was dropped?


From etymonline, ingenious, ingenuous, indigenous all share the same roots: in- and indu- mean "in", and "gen" means "produce". But the meanings of the words are not the same. So do you have some ways to remember the differences between their meanings?


We are looking to use this text, as a headline on our sustainability page, on our website. As coworker asked if "sustainably" was grammatically correct. I am unsure. TCS believes that thinking sustainably will make our future stronger, to think globally and act locally through a variety of green initiatives Is the word sustainable used correctly, is it even a word?


If you take a look at WolframAlpha, or other computer algebraic system, you will find that it is able to do symbolic manipulation like real humans. For example, if you type in an integral, it can show you step by step on how to solve the integration. What are the algorithms behind all this?


In the textbooks that I read (namely Ashcroft/Mermin , Marder, etc.) it seems that a distinction is made between the correlations in electron gas and a Couloumb interaction between the electrons. What is exactly meant by the concept of correlations? How is that connected to the interactions in electron gas, and how does the screening enters the picture?


Albert Einstein is often considered the most original scientist of the modern age. Even he, though, acknowledged his reliance on the work of others, such Emmy Noether. I have trouble understanding why is it correct to have "though" in this sentence.


Want to know if there is a collective word to describe these kind of words that change their meanings in an opposite way (rather than irrelevantly) when a single letter is added/removed/changed so that I can look them up. Otherwise can you provide some examples here? e.g. appeal <> appal


I often read sentences where the idea is "I would say" but it starts with "I guess". For example: I would say he is not coming. I guess he is not coming. Do both have the same meaning?


Are proton, antiproton, electron, positron the only subatomic particles that can freely exist (i.e. I don't want particles that only exist in bound state as constituents such as quarks) and don't decay, i.e. are stable? What about muons? Are there other particles/hadrons that can exist freely (i.e. not in some bound states) and don't decay?


i want to ask what's the difference between these sentences. Because Can't is present tense and happened is past tense. Could anyone explain it to me thank you! She Can't believe what happened to her. She Couldn't believe what happened to her.


I'd like to have some boxes colored differently from others in a baposter. It seems like a natural way to do this is to allow a specification of some parameters (boxColorOne, borderColor, etc) in the options for headerbox, but I don't know how to make this happen.


A: do you have any questions? B: None so far. Is "none so far" a strange English and was it correct to use it in the dialogue above?.I was told by a native speaker that it is strange to use it this way in the dialogue.


What is the origin or history of using "skin" to refer to "money?" For example, a golf competition called a "skins game" or, referring to an investor who, "has some skin in the game."


The arrow of time is usually defined by the direction in which entropy increases. In a closed system, if there's a max entropy that the system can reach, does that mean time stops or at least become undefined at the max entropy state? See also: For an isolated system, can the entropy decrease or increase?


A graph, a chart, and a plot can all refer to the same thing. Is there any even somewhat consistent distinction in these three words? (I mean, in this particular sense of the words; it is not relevant that a chart is also a nautical map, a plot is also a scheme, and a graph is also an unrelated mathematical object.)


I have zero idea what this construction is called. Here are a few examples that I've just whipped up: He was fired, and his friend punished. He was robbed, and his brother kidnapped. The idea is that the second part of the sentence takes the same verb as the first. Kind of like continuity of the sentence.


A Hamilton circuit (or path) is a path that visits each vertex exactly once (except the start/end point) and ends at the starting point. I've stared at this for quite a while and cannot find a Hamilton circuit yet my guide says that one exists. Where is the path?


I need to cite as an endnote (with the endnotes package) twice in the same chapter of a document. How do I do it without introducing twice the reference? That is, how do I refer to the same endnote in different parts of the chapter? Thanks


In how many ways can you break a off a rectangular piece of chocolate from a chocolate bar with m x n squares. [We must respect the structure of the chocolate bar, that is break only along horizontal or vertical lines.


What is an example of a situation where AB is not subgroup of G, when A, B are subgroups of G? My first instinct is always to go for some dihedral group or other...But I could not find an example of a case when the above is true. Maybe I am doing it wrong...


Which of the following is correct: Supplier of tile, stone, tools and equipment or Supplier of tiles, stones, tools and equipment If you could provide an English rule to know that would also be very much appreciated. Thanks!


Is it possible to determine a triangle given its three perpendicular bisectors (meeting at a point which will be the circumcenter) and, say, a point of an edge, or any condition that can make the solution unique, using compass and straightedge? Of course I could put a system of equations, but I'm looking for a graphical procedure.


I came across this symbol on page xix of the book Universal Artificial Intelligence by Hutter: (link to full text of book) It is used for the Solomonoff-Levin universal semi-measure. I've never seen it before, and wondering if anyone can help me understand. Thanks.


I'd like to design a chapter heading similar to the one in the picture below. I like to put a line between the number and the chapter name and also align the the chapter name to the left. I'm using the document class book. Any ideas how to do it?


Is there a word that means "outdated name"? For example: Record, although very little music is on vinyl Film, although most movies are digital Horsepower, although no one uses horses as a metric anymore Phone, although it's mostly used to access the web and so on.


In a quad. ABCD with AB=CD, P and Q are mid points of diagonals AC and BD.P and Q joined and extended hits both sides AB and CD at S and T respectively. How can I prove that angle AST=angle DTS?


What are the prerequisites to prove the central limit theorem? In my statistics textbook it is stated without a complete proof, so I guess I need more than calculus. However, do I need more than undergraduate real and complex analysis? In what book can I find a complete proof of the central limit theorem?


I'm at university and I learned linear algebra, set theory, logic, and other kind of mathematics that use functions a lot. Now, I know that function is very important and useful in mathematics but I never asked why we need to define the domain and co-domain of a function? How is it useful? Thank you in advance.


I have this written down in my notes, but cannot seem to find verification of it. How can I see this fact? I believe there is a theorem, something along the lines of if a group G is isomorphic to H then, H is a group. Can anybody verify this or point me to the direction I am looking for? Thanks.


I've been learning homology (and hence Category Theory) and have been interested in groupoids for some time. I've gotten to localization in categories, and that has sparked the following question: Is the localization of a category a groupoid? So going further, isn't localization a functor from Cat (the category of categories) to groupoids (which can be seen as a sub-category of Cat)?


Here is the question: and here is the solution: Can someone please explain it to me - the second line in particular. I don't understand where the limits for the series' come from.


What is the adjectival form of Plato? "Platonistic"? For example, in the following sentence: He made the Platonistic statement that there are truths, but there is also the Truth. Or is it incorrect to turn a proper noun into an adjective?


Can anybody explain for me how this structure "is at its highest level" is correct. Example : Confidence in the British economy is at its highest level since the Coalition came to power amid signs the recovery is gathering pace


Speaker A: "You lived in Hawaii? Cool! How was it? Tell me, tell me. Speaker B: "Haha, it wasn't as interesting as you/you'd think. What's the correct option in this case? Or should I have written as you might think instead?


When did the word 'want' stop meaning "in need of" or 'lacking' and begin to refer to desire? (Evidence old phrases with the original meaning like: "want for nothing" or "waste not, want not".)


How much of a difference would it make if every roof, road and vehicle were painted white? This would certainly reduce the urban heat island effect but how much of a difference would it make to total scattered insolation? Apologies in advance for this the bizarre question.


I'd like to ask if these following sentences have the same meaning ? Hong Kong had been ruled at the whim of its colonial overlords. Hong Kong had been ruled by arbitrary colonial overlords. And what should we infer from the sentences, ruler changes often and randomly or the way of their rule changes often and randomly?


How would I prove that a span of certain vectors is equal to the span of their scalar multiples. The proof would include proving both sets are subsets of one another? Span{x,y,z} = Span{ax,by,cx} where x,y,z are vectors and a,b,c are non-zero scalars.


I use colour diagrams (saved as pdf files) which I include in my LaTeX file. Is there any options in pdflatex to create a gray scale document or a pdf viewer where you can view the document in gray scale? Enabling you to view the document and fix any problems before it gets printed on a non-colour printer.


What are the ways electrostatic charged objects leak charge in humid conditions? Can airborne particles pick up charge by contact, then be repelled hence removing charge? If so would it be a significant factor?


I always get the doubt about this. I know that a bike measures its speed based on the motion of its front wheel. So what is the case with train? Is it same principle? Then what about an airplane? Is it by radars?


In the novel A Day Among The Liars by Edward Page Mitchell, there is this sentence: "My rod creaked and bent double," a stout, red-faced gentleman was saying, "and the birch spun like a testotum." Please can anyone explain the meaning of "birch spun like a testotum"?


Have we as of yet been able to calculate the space-time curvature around a galactic (or idealized) disk? I have not heard of or been able to find this. Is it even possible to calculate anything meaningful, either analytically or numerically? What I'm curious about is the shape near the disk itself, either ignoring dark matter or including some halo configuration


What is good dictionary software? I am asking about the ones that can be downloaded and used on Windows machines, and not online websites. I thought Word Web is a good one, but are there any advanced and good dictionaries?


When somebody talks in a way where they swallow parts of a word, talk very fast or talk in a way that is difficult for most listeners to comprehend, what do you call the way this person speaks? I'm looking for an adverb that conveys the meaning "unclearly", "mangled" or just "ununderstandbly" (yeah I know it's not a word).


Which degree of 'less' is correct in the following sentence - "Seats in this room are much less/lesser in comparison to the adjacent one." Also please state any general rule of English if it is being applied here. Thanks.


Is the phrase ... because of my current educational and residential situation a correct way to refer to where and why I study what I do and why I live where I do? Or should it be "education and residence situation"?


Recently, I was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the idea was silly. But I then googled it and found this article. Is this idea really compatible with other theories as the article mentions? Is there any chance of this proposition being true?


Does anyone have suggestions for books, or lecture notes, (or videos) for studying pullback rings? I know definition; and a few facts about it (for example when it is Noetherian). Now I want to start for learning it. I'm not good at category theory, so please consider this in your answer. I've read Bruns-Herzog's book an I'm familiar with homological algebra. Thanks a lot!


Is the comma used correctly in these two sentences? In order to sign and return the documents to us with EchoSign, the two initial boxes marked in red will require your initials. In any case, there are two initial boxes marked in red which will require initials, in order to sign and return the documents to us with EchoSign.


Write the best verb-form for the blank. A: Who have you worked with? B: I ________ with people from all over the world. The intended answer is 'have worked'. One of my students answered, 'have been working'. Of course it makes sense. But do you think 'have been working' can be called the best form for that blank above?


I almost hesitate to ask this, because it is hard to believe no one else asked it; but it isn't showing up in the "similar titles" list. What is special about 'C' that switches the 'IE' immediately following it?


When two systems are in thermal equilibrium, this means that there is no heat flow between them. What is the analogous definition for mechanical equilibrium? (I know that in mechanical equilibrium the pressure of the two systems must be the same, like temperature in thermal equilibrium, and this is not the definition I am after)


Let's imagine, I'm speaking about someone's three specific cars, which are over there, there, and there. Now I'm saying that I have installed a new sound system in all of them. Which is right: [...] I have installed a new sound system in all the three cars. [...] I have installed a new sound system in all three cars.


There is well known gravitational redshift of real photons. What about gravitational redshift of virtual photons of charged neutron star? Is electrostatic force become weaker while mass of charged neutron star is growing? How can electrostatic field of a charged particle swallowed by a black hole escape from the event horizon? How can charged black holes exist at all?


Here I have some basic questions about max-plus algebra. How this is useful? Why we need to define a different algebra? What aspects are highlighted in this which were untouched in conventional algebra?


The computational algebra system MAGMA has a function called Order. What it does is find the multiplicative order of its argument, which must be a nonzero element of a field. This question is asking about how this order is calculated. Can anyone point me to a reference explaining that or explain that to me in an answer?


When light passes from a more dense to a less dense substance, (for example passing from water into air), the light is refracted (or bent) away from the normal. My question, is there any theory that i can say precisely why light go away from normal or get closed to the normal.


I want to draw Hermite-Gaussian modes using tikz, all that is really needed is a blurred circle and blurred lines that overlay splitting it into different sections as shown in this picture: I am not even able to find a proper way of doing the first one, since all blurring options i have found so far are not smooth enough.


I am having trouble coming up with an example of spaces where there exists a weak homotopy equivalence in one direction but not the other. Any hints or references are greatly appreciated! Note: This is an instance of stagnating autodidactic studying, hence no home-work tag.


I'm writing a story for my English class. Does the following sentence effectively mean that she had a good figure behind her dress? She hid quite a figure behind the Wardrobe. Does it apply to both male and female?


I wanted to convey that a university degree is true and valid, but I am not sure if the word "established" can be used for the degree itself. Any suggestions on which words I can use to convey that same meaning for a "degree"? Can I check if it is the word "established" can be used for an educational program?


I am trying to write a class based on the book class (a thesis class for my department). My question is: is it bad for some reason (or, is it considered bad) to use packages in the class files instead of more primitive TeX / LaTeX commands? For example, should I use the geometry package or the relevant primitive commands?


I understand that playing a square wave from speakers cannot produce a PERFECTLY sharp division between compression and rarefaction. But it's sharp enough to sound distinctly different from a sine wave. As it travels, does the wave "smoosh out" even further as it travels, changing from a square wave into something closer to a sine wave?


Is rate of change of velocity wrt distance and rate of change of velocity wrt time the same thing?If both are same can we define acceleration in the former way? Please explain using calculus.


I want to know the difference between already and yet in this example: I was surprised that they had __ to decide what to do. My answer on this question was already and my teacher marked it as a wrong answer in the test. What's the difference between already and yet in that sentence?


Can you help me explain the meaning of the phrase "ascend to rule the heavens on" in the sentence below? Myth was born in Thebes of Geb and Nut who ascended to rule the heavens on their death.


Usually from books, Rayleigh scattering only refers to the light scattering by neutral atoms or molecules. For example if I want to measure temperature or number density in combustion using Rayleigh scattering, and a lot of combustion intermediate species are not really neutral, do I have to take care of the scattering signal from ions? Same question to plasma measurement because of ionization. Thanks.


I thought during this transition only the potential energy increases as energy is used to weaken the van Der Waal forces between the molecules. And that the internal energy is only dependent on the change in kinetic energy . So why does internal energy increase? Thankyou for the help.


Ex. He threw the grenade, but it blew off part of his leg. He wasn't expecting any case of _______ damage, but that's what you get when you're reckless. Is it "collateral" damage?


The diagonal entries of a triangular matrix are the Eigen values of the matrix as per the theorm. My question is why not convert the given ordinary matrix into a triangular one by row reducing it and now the diagonal entries will be the Eigen values of the matrix


These words are all more or less interchangeable, but I'm wondering which is most distinguished. If I have a group of representatives, but some are the leaders of their groups and others are just regular members of their groups, or some are from influential groups and some are from uninfluential groups, which terms would I use to hint at who is most important?


Are there any significant differences in meaning or usage between "everyone" and "everybody", or "anybody" and "anyone"? As far as I know, there are some grammatical points involving "everyone" and "everybody", or "anybody" and "anyone", but books/internet/professors cannot identify any differences of meaning or usage between these two pronouns.


Impossible to automatically generate BibTex keys using Ctrl-G as I did it with the previous version of JabRef. It seems that there is a bug in this issue of Jabref. Please help me...


I am reading some lecture notes (completed with exercises and competition-like problems) provided by my college professor, but I would like to study probability from a proper book. Can you suggest one with good problems and clear rigorous style?


Is there a non-gendered term for manning a station, as in manning the desk? The only ideas I can come up with are "stationed at" the desk or other clunky things. Finding the right gerund would make my day.


I have a vague idea of the three words kill, murder and slay, but I am not sure exactly what makes the verbs different (as well as the nouns killer, murderer and slayer). When do we use each of them?


Possible Duplicate: Typesetting algorithms in LaTeX like Knuth Does anyone know if there is a style that mimics Knuth's The Art of Computer Programming? Baring that, would anyone know how to customize the memoir class to get an analogous result?


Using natbib, how can I obtain a full reference inline in the body of a document? I need to include the full reference, not just the citation, at the beginning of a chapter.


I know that there is a noun for cancer as an area of medicine: oncology. But is there a word for things under the umbrella of the art and science of cancer treatment? I was thinking of something other than "cancer therapy." Something like "oncologics", although that's not actually a word.


Are there contra variant and covariant vectors or are there only contra variant and covariant basis for vectors and these basis transform into further contra variant and covariant basis respectively according to certain co-ordinate transformation laws, keeping the vector as it is, which can be viewed as an arrow ?


I have a beamer template provided by my university. I want to edit it such that there is a table of content in all slides at the left side. For simplicity, we can consider a plain template and if anyone helps me on this template, I can build it according to my template. Thanks in advance.


While reading one of the technical books I encountered "the remainder of the text will explore how the .NET framework...". From the context I understood it means "the remaining text of the book will explore ...". Is there any difference between them or why is one used over the other?


I recently heard an American presenter using the phrase "discover what it is that is important to you." What is the linguistic difference between saying "what it is that is," rather than "what is"?


Given that the atmosphere of Titan is mostly methane, and from a comment on this TED talk... Would it blow up from a lighted match-stick? Seems like it's at least plausible. But, wouldn't the lack of oxygen hinder this event? Or perhaps I'm confusing the blow up with combustion?


Shall I use do or make together with statistical inference? Refering to this site, do is used "when someone performs an action, activity or task" and make for "constructing, building or creating". In my understanding of "statistical inference" it can be both: the action of drawing conclusions and the results of this process. So which one shall I use?


I want to refer to a report available on a particular site. Although some human being must have compiled the report, but there isn't any reference to any specific name. Which BibTeX attribute should I choose for such citing.


In the song Tonight Again, there's a line going They may be right but only maybe I understand that "maybe" is an adverb, while "may be" is a combination of the verbs "may" and "be", as mentioned in this question. However, is there any difference in the degree of certainty between the two, as might be suggested by the "but only"?


I'm looking for a way of creating glossaries, with the help of glossaries package, per chapter or section. In a particular glossary for section should be only the terms used in this section. If term is used in multiple section - appear in correspondent glossaries. Example (done with the help of description environment, just for an example): How can I achieve this?


I'm looking for the word that means certain words when placed together sound bad. Example: Mary is sad because she had bad luck. Better wording: Sadness engulfed Mary after she experienced misfortune. What is the word that means example numer one SOUNDS awkward?


As you probably know, electrical current and magnetic fields are close friends. In an iPhone there is a compass, however there are also lots of cables and in all of them, or at least in most of them passes a current. How come the current doesn't drive the compass away (and far) from the real north?


For people who go an extra mile to make others comfortable, be it friends, family, etc. I need an adjective or a noun, most probably one word, that can describe people who always keep others above or ahead of themselves.


Given these two versions of a sentence: For many people, dogs are the best friends. To many people, dogs are the best friends. I have following questions: What is the difference between using for and using to for this sentence? Are both versions grammatical? If not, which one should be used and why?


I want to create epub document, but I only have a tex file (unfortunately, mathematical formulas, and drawing diagrams). I tried pandoc: tex to html, tex to xhtml, to xml, but nothing works properly. I use tikz. You can do the epub file with png or svg? Some ideas?


We have an idea to post short ads like "our company is hiring" in company blog posts. The company develops software and one of duties of people we want to hire will be finding, locating and fixing bugs in programs. Can we refer to such people as "bug assassins"? Won't "assassin" word have some negative meaning?


I have a general question about the applications of mathematics. What are some applications of mathematics that are not scientific, perhaps maybe literary or philosophical, or political. I am basically asking for the scope of mathematics, and looking for concrete examples.


How are the external magnetic field intensity H, magnetisation M and the entropy related to each other? i.e. if I change the magnetic field intensity by dH what will be the change in entropy dS in terms of M.


If repeatedly picking a random element from a set, what is the expected number of times I'd have to pick before seeing all the elements of the set? Edit: when picking an element, it is simply counted and not removed from the set, so it can be picked again.


After the spontaneous breakdown of local symmetry in presence of gauge fields (Higgs Mechanism), we can always choose a gauge where the Goldstone bosons are eaten up by the gauge field (also called unitary gauge). Which Lagrangian should be used for physical calculations-(i) the one in which goldstone excitations are present or (ii) the one in which they disappear?


I'm working on an optics project that I'm using Fresnel Equation for Intensity. but I've got a question, is copper a non-magnetic ? You know because in Fresnel Equation, for non-magnetic materials which their refractive index is a real number, the formula is more simple. Thanks in advance


What is the perfect word for the clicking sound which happens when you stretch your bones? When chiropractors try to do adjustments, we can hear a clicking sound on the bones. What is that sound called?


I'm writing a CV and in one section I'd like to enumerate the activities I did. Should I write I proved ... I participated ... I mentored ... ... or Proved ... Participated ... Mentored ... ... or Prove ... Participate ... Mentor ... ... or any other better form for the verbs?


I've solved a bi-objective optimization problem by means of NOMAD solver from OPTI Toolbox and as a result I've obtained a Pareto frontier: How to interpret the visible "gap" in the Pareto frontier?


I am looking for a proof of the next theorem: "If the higher order time derivative Lagrangian is non-degenerate, there is at least one linear instability in the Hamiltonian of this system." Where Non-degeneracy means that the highest time derivative term can be expressed in terms of canonical variables.


Every source I look at online says something vague about Church's notion being equivalent to Turing's, but what exactly is the Church-Turing thesis? As I understand, it attempts to precisely define the term "algorithm," but my understanding is not very strong of this concept.


What do you call nature words ending in -land? For example, moorland, wetland, marshland, woodland...You get the picture. Is there a name for such things? And is there one for a place that is surrounded by water/made up of shores of lakes/rivers/streams besides wetland?


What is the difference between prevention and avoidance? Can you give generic examples? The reason for my question is, that I want to know the difference between preventing and avoiding a threat against a (technical) system.


I often say What is an idiom? When I read Longman Pocket Idioms Dictionary Cased, I saw the sentence What are idioms? Are there any differences between the two forms? Which one is preferred?


I'm aware of this question, where most answers point out how to externalise the TikZ parts in some way. I want to know which journals actually accept TikZ in submissions, and possibly which versions.


If a body A needs to be charged by a charged body B by process of induction, then why it's necessary that A must be a conducting body or must have a free electron. Also what is major difference between Induction & Polarization of a body. Experts please explain me it in detail.


Where in the analytic hierarchy is the theory of all true sentences in ZFC? In higher-order ZFC? In ZFC plus large cardinal axioms? Edit: It seems that this is ill-defined. Why is this ill-defined for ZFC, but true for weaker theories like Peano arithmetic and higher-order arithmetic?


I had read that light does slow down in glass because photons interact with atoms in glass. They are absorbed and re-emitted and during this phenomenon it's speed decreases. See also this and this Phys.SE post and links therein. But then why does it bend? It has confused me a lot! Furthermore i have very little knowledge of Optics or Physics as a whole.


I need a word to say to the person that apologizes for something that they didn't do but feel responsible for. The word word mean: "I accept your apology, but it is not needed. (you, are entirely fine!)"


My significant other tells me that I'm not "going to go" to the shops, I'm "going to" the shops, and beats me mercilessly when I say that. Is this not correct? I might not be going to the shops until later, is my point!


Derive the MLE for Bernoulli distribution? Just need help studying for a test tomorrow and this is a question on the practice exam. I think I will get a question on this just with a different distribution so can someone help me?


The defining property of the A series paper is that when a sheet of paper (represented by a rectangle) is cut in half, both of the resulting rectangles are similar to the original one. Are there any other shapes or solids that have this property? Google is silent.


This famously known fractal has infinitely many circles, however I find it hard to find a rigid proof that confirms how or why this fractal is composed of infinitely many circles (and only circles). What if, at one point inside the circle, there comes a point where no proper circle that is tangential to the other circles in the fractal can be constructed?


Is it "superior of" or "superior to"? In a sentence: We conclude that our proposed model is superior to the base case. or We conclude that our proposed model is superior of the base case.


Yes, we can easily explain to all intelligent adults why the Earth looks flat, when it is actually round. But my question is, how can we explain this fact, that the Earth is round, to those people who will not accept new data, which contradicts their knowledge, by providing them with some proper facts?


Is there an adjective meaning attainable through aural practice? As in "This language skill is more easily attainable through aural practice." That is, the more you listen, the more that skill develops. Is there a single word you could put in the blank in "This is a/an ...... skill"


If time moves more slowly on Earth (due to our proximity to a gravitational body) than for someone orbiting Earth in a spaceship, yet the opposite occurs in the frequently cited "twin paradox" of the earth-bound twin vs. the twin in the fast-moving spacecraft, then my question would be this--is the slowing of "time" the same as the slowing of molecular/atomic motion?


If gravity is this "unexplainable force" that pulls everything to the center of a planet or stellar remnant you stand upon, why doesn't gravity pull itself? If gravity affects anything with energy, why doesn't gravity affect itself? Gravity is energy, right?


Wikipedia give this answer "Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes "the theory of groups" as an object of study." Can someone please explain the difference in more specific terms.


What does a rotating hoop, with each point moving at a velocity close to the speed of light, appear like with respect from a stationary observers perspective. For example how does the shape of the hoop change? (Note, I'm not intending to ask about optical effects, but rather what physically happens, analogous to length contraction of a moving train.)


I am doing homework and I got confused about this phrase when I was writing. I am not a native English speaker. (...) and the only way to do this was taking control of everything and being authoritarian towards the people who/that could not do anything about it. I would be grateful if you help me clarify which word should I use.


I would like to know if there is any global command that would prevent any page-breaks inside sections. All my sections are short enough. I read some solutions, such as Absolutely, definitely, preventing page break, but I would like an automatic solution.


I was at an Model UN conference and often notes like the following get passed. As I'm not a native speaker, I assume that this has to do with some pronunciational issue. Can you please explain what's so funny about this sentence? (Djibouti seemed to be often used in such context.) If Bangkok invaded Djibouti would Greece help?


This is an exercise following a discussion of fibrations. preceding that there was a discussion of cofibrations and the long exact sequence of homotopy groups of a pair. Any hints would be greatly appreciated. Thanks for your time.


Is there a simple term for the question this one was closed as a dupe of other than "the question this one was closed as a dupe of", because "the question this one was closed as a dupe of" is pretty long and unwieldy and much in need of a simpler term than "the question this one was closed as a dupe of".


For an event, I would like to add next to the name of some participants, that they "will be there". For example, Mr. AAA Mr. BBB (will be there) Ms. CCC Can any one suggest a better, professional replacement for "will be there". Thanks in advance.


I need to copy (with small editions) the shown definition in my own document. I don't have the source code of this pdf, so I don't have any idea which environment/package/etc. should be used to create the definition in same style.


Can we write down a generic expression for propagator for any arbitrary spin? At the least, about the ultraviolet behavior of these propagator. Especially, I would like to know whether there is a specific dependence on spin of the field.


What is the idiom for a guy/situation who/where has his own lacking but still mocks others? Like you are poor but you laugh at a rich man who has just become bankrupt. For example, suppose like this "A drainer mocks at a needle". Explanation: A drainer has hundreds of pores, but he is mocking at needle's only one hole.


At the temperature range of ordinary fire or maybe even ordinary boiling water, is the Coulomb potential between light atomic nuclei occasionally overcome to give way to fusion? Basically, how are the nuclear fusion cross sections calculated and are they a function of temperature?


When am I supposed to use the terminology of EM "wavenumber", instead of "wavelength" (or frequency)? The concepts of wavelength and frequency are no problem for me, but wavenumber (number of wavelengths per unit length) seems redundant to me as a student engineer and proto-physicist. And then there's use of energy levels at higher frequencies.


There is a nine digit number . If you delete the digit at its unit place the remaining number would be divisible by nine, if you delete the digit at its tenth place the remaining number would be divisible by eight and the process continues. all the digits of the number are unique...what is the required number?


LatexDraw is a PSTricks code generator for Latex. LatexDraw generates PSTricks codes of any fugure are drawn. Are there any such tools that will generate pgf-tikz code of any figure for latex? If yes please suggest me. Thank you in advance.


I considered 'self-proclaimed' but that, I believe, suggests an element of self-promotion (the proclamation aspect) whereas soi-disant, at least as I think of it, is more about self-presentation and in some contexts self-deceit.


I'm writing a document where I had to change all instances of the variable i to x and the document is already considerably long. Is there a editor that will allow me to do this, or in general, replace text inside math environments?


This is a follow-up to Do Lipschitz/Hurwitz quaternions satisfy the Ore condition? Jyrki Lahtonen answered the question in the positive by noticing that every right principal ideal in either ring has a non-empty intersection with the center. Does this property have a name? Has it been studied? Are there Ore domains without it? Are there cancellative Ore monoids that don't have this property?


Backlog/noun an accumulation of uncompleted work waiting for you when you return from vacation . It's a pity that we don't have "forelog" as a word for work that is done to clear one's desk before a vacation. What are the some alternatives to define all the work that is done to clear one's desk before a vacation?


I keep hearing about big bang, but there are no white holes and no black hole has been observed exploding. So is there a point in which a black hole reaches critical mass?


I'm writing my PhD thesis in latex and learned a lot from this forum. However, I could not find an answer to the question how do I put an decorative hook before the chapter title. I think that it looks rather nice to have this but thats personal.


What is the covariance matrix of the product of a random scalar and a random vector in general (if any) and in all special cases, in terms of the variance of the scalar and the covariance matrix of the vector?


What is the currect research status of solving Navier-Stokes Equation, any up-to-date review/good paper on this topic? Or direct numerical simulation is still the best way to understand the complexity of turbulence? Thanks


"I touched their forehead[s] with my fingertip." I'm not certaint whether or not forehead in this example should be singular or plural. There's a group of people, so obviously, multiple foreheads are being touched. However each individual person only has one forehead.


Wikipedia says: Having an eigenvalue is an accidental property of a real matrix (since it may fail to have an eigenvalue), but every complex matrix has an eigenvalue. Yet, IMO, real matrices are subclass of complex ones. So, even without having any mathematical degree I see that this cannot be true.


(I'm new to latex and don't know the right keywords to search.) I would like to put a header and footer lines to my figures (floats), instead a framebox, since they sometimes takes longer than a whole page. Any suggestions? I want the result to look like:


The pulley is with a finite mass. The two blocks, hence, have different tensions exerted on the rope. My question is do the two blocks have the same acceleration ? I would like a reason for the same.


In a recent question, it was stated that particles in high pressure air always flow to lower pressure. In a pipe with a constriction, fluid flows from from low to high pressure after the constriction. (From here.) How are these concepts related?


let f:R->R What is the range of the function f I think it is(-infinity to infinity). But i am confused because p/q is in their lowest term. Can Someone please help me, Thanks in advance


I'm looking for a word that means: bigotry against, or disdain for, uncouth people. ('Misanthropy' is too general, I think.) This would sort of be the converse of anti-intellectualism. By 'uncouth people', I mean people who (example) might casually toss litter into the street and not give it a second thought, etc.


I asked a similar question about bubbles making less friction on a mass moving through water, now I'm wondering of sound waves could do the same thing as supercavitation or possibly create it's own propulsion with the right combination of frequencies.


I was working in products of structures and I am trying to find a counterexample to the following: "the product of totally ordered sets is a totally ordered set." Unfortunately I could not find one. Can someone provide me with a counterexample?


Should I use You are granted the choice to either be my friend or my enemy. or You are granted the choice of either being my friend or my enemy. ? It's for my poem and I want to double-check.


I think the expectation is a function of random variables. I also know that a function of a random variable is a random variable. So the expectation is a random variable? But I also know the expectation is a constant. I am confused about this.


Do all the planets in our solar system have the same angular speed? Physics teacher says yes, my research is not crystal clear. I want to make sure I have the right information for future reference.


To explain the matter-antimatter assymmetry, CP should be violated according to Sakharov conditions. Charge conjugation is required as matter and antimatter have opposite charges but why Parity Violation? Is it because they have opposite chirality as well? Isn't it model dependent?


Is there a term for a person who by local standards is normal in his/her behaviour? I mean a person who tends to like the same sports, same teams, same music, and same hobbies. Because in El Salvador people are like that, and I call them (in my mind) very generic, trivial, and boring.


Let M be a surface M, i am concerned with Abelian covers. These are the covering spaces for which the deck group is Abelian. The largest such cover corresponds to the commutator subgroup of the fundamental group , in which case the deck group is the homology group. I would like to know how to construct it for a genus two surface.


For as long as I can remember, I've only used the word 'delete' in a technological context. I'm fairly certain, most kids--or the generation before them--know exactly what the word means. Did this word get much use in other literary works?


Is there an idiom or word for describing the moment or situation when governments blame some unknown power(s) for bad results caused by their own actions? These governments try to acquit themselves by blaming these nonexistent, external powers.


I'm not sure, but I'm being asked to describe the set of points that are in this neighborhood of a circle with radius r. here is the only thing I can think of ...which is the equation of a circle with epsilons added to the y...It seems incorrect.


In the context of the following sentence: "This report gives an overview of x, which took place between the second and final year of my degree from xmonth to ymonth." Should I be using the word year or years? I'm inclined to choose the latter, as I am referring to two years and not one.


Why does "used to" mean "accustomed to"? Why is "used to" used to indicate a recurring past event? In I used to be used to using it. there are three meanings of "use". I ask about the etymologies of the two bolded meanings.


What's that word meaning 'thus more strongly'? As in X applies to Y, and thus even more strongly to Z. E.g.: The body's immune system needs warmth, so adequate heating is good for you (and [this conclusion follows with even more force] for sick people) I seem to remember that there is such a word, and it's Latin, though I could be wrong.


The Wikipedia article describing the electromagnetic stress energy tensor seems to suggest that this tensor can only be defined in flat space-time. How is it possible to define an electromagnetic stress energy tensor this way since any available electromagnetic energy/momentum must render the space-time curvature nonzero? How in practice would someone extract useful information with this stress energy tensor?


What is the negation of this statement ? "The equation has real distinct roots" Is it "The equation has no real distinct roots " or "The equation has no real roots " or Is it "The equation has no real roots, but it can have real repeated roots"


When I write something like this: I am a man that is doing these things. Is it correct to shorten it like this? I am a man doing these things. And does it require commas?


So while I was solving this, I marked the correct answer as D, though the correct answer is claimed to be C. What I have read from different books is do not assume anything from the figures. So the solution assumes that the triangle formed would be a right-angled triangle, but it would be wrong to assume that, right?


If you are applying to a school you are an "applicant". What is the word for the thing you're applying to? Similar to the sentence "the stalker stalks the stalkee", what would be in the blank in the sentence The applicant applies to the ______?


I read this question in the sample questions section. It hasn't been asked yet, now I'd like to know. I have heard that regional dialects of English are often more closely related to provincial dialects because the comparatively well-to-do Londoner did not need or want to move to a strange new land and instead people from the countryside went abroad.


I have to purchase some items. We have to tell how many ways are there to select N items of K types. However, the constraint here is we need to have at least one item of each type. How many ways exist?


I know that a cone isn't a regular surface because I can't construct a chart with cts partial derivatives at its tip. But can anyone show me this last step rigorously? Why would any chart for the tip have a discontinuous partial derivative?


Possible Duplicate: Put legend (pgfplots) below the plot I'm trying to set correctly the right position of the legend of my plot. I would have the legend just bottom right of my plot. Any idea? Using this code I got error legend style={ cells={anchor=south}, legend pos=outer south east, },


Is is acceptable to use "different" as a preposition, as you would use "unlike" or "in contrast to", like in the following example? Thus, different from previous work, we aim to answer those questions.


Hurry up and get ready for school. Don't be a slowcoach! Be a ______ ! What fits in the _____ ? Hopefully something other than fastcoach! I found some old discussion but nothing there seem to fit. Slowcoach (BrE) = Slowpoke (US).


I'm going blank here, so forgive me for what should be simple. The search engines weren't helpful. I tried to search. Example: The finicky felines finished their food. I'm drawing a serious blank here, so go easy on me.


I'm currently struggling which of the following two versions (I anononymized them) is the correct grammatical form for the title of a publication: Evaluating Safety, Cleverness and Fastness of Masking Systems Evaluating the Safety, Cleverness and Fastness of Masking Systems We are currently using the first version. Is it missing "the"?


I'm doing some maintenance work on some software - whose original developers are unknown. There is a report called the "All Zingo Report", which basically dumps all the data for the primary "entity" in the database (the primary entity represents a person that has been referred to a government-associated medical program). Why would the word "zingo" be used to describe such a report?


As far as I understand Everett's Many-Worlds Interpretation, he makes the case for a realist theory of QM at the enormous cost of many-worlds. Are there any arguments in favour of Everett's interpretation that makes the case for his theory one a purely instrumental or operational view - in that certain calculation look easier or more 'elegant'?


OK, this is an attempt: I remained there, gazing at the sea. Its color was light green in the part closest to the shore, turned slightly darker in the middle, then abruptly changed to dark blue in deeper waters. Are those words commonly used? Or is there a better and simpler terminology to describe them?


Why doesn't the volume of water in a nuclear fuel pool become irradiated? Why wouldn't the water around the pool become radioactive and circulate around making the whole thing deadly? My question spawned from this cartoon from XKCD. The Spent Fuel Pool


I have some problem with "at the cost of" here. Does "light reveals itself at the expense of obscuring something else" mean: light reveals itself by lighting other things (because light itself has no physical presence and so is defined with its effects)? or light reveals itself by obscuring other things?


What can we say about the quantum state from the number of zero and non-zero eigenvalues of the corresponding density matrix? Anything related to entanglement or any other properties? Does they vary with the nature of states such as it is pure or mixed? Please add some references.


If one brings a fluorescent bulb close to a plasma ball, why does the touch of a finger cause the bulb to become brighter when touched? Why, when you hold the metal portion of the bulb, as opposed to the glass, does it NOT turn on at all?


I was recently looking at automatic differentiation. Does something like automatic differentiation exist for integration? Would the integral be equivalent to something like Euler's method? (or am I thinking about it wrong?) edit: I am looking at some inherited code that includes https://projects.coin-or.org/ADOL-C as a black box.


I want to use brackets similar to lceil, rceil and lfoor, rfloor, but with the vertical lines on both sides at an angle. Does anything like this already exist? If not, would it be difficult to create them?


In manifolds and complex geometry there is this thing called the pullback. Usually when I see it, its going backwards on maps that are going forwards. I've been told that it is just a composition of functions. I just need help understanding this concept.


Could you give examples where one is better suited than the other one? Or are they completely synonymous? (I'm not a native speaker.) Update: I'm writing a piece software documentation and I wonder if it's better to use choose or opt: ... Note that these components can receive input themselves (although they may opt/choose not to). ...


I am writing my M.Sc. thesis in biochemistry, which has mathematics. I am new to latex, but I am greatly interested in it. I am watching/reading tutorials but was wondering if the community could recommend a good set of video lectures/pdf to write a document such as a thesis? Thank you very much for your time!


I used the code from here to get text to wrap around images, but whenever I have a long image near the end of the page, it runs off the page and gets cut off. How do I fix this?


My navigation bar at the top of each slide (that links to each section) has too many sections. I would like to keep the bar and keep each section but I would like to wrap it i.e. have it on two lines. Is that possible? I am using compress and I am using progressbar as a theme.


The moon shone on his face as he spoke, and the girl was pleased to watch it, it seemed to breathe such an innocent and old-world kindness of disposition, yet with something high too, as of a well-founded self-content. What does this "as of" mean here? I would need a sentence structure explanation.


Someone just told me that writing "it makes me happy" is incorrect in its sense not in grammatical aspect because "it" is "not human" please help me, is it okay to write "it" with "happy"? I am learning English so please help me.


I am looking for a similar solution as here Description list with aligned descriptions except that I want to use it with beamer. If I use enumitem with beamer, inner theme is replaced by enumitem. I do not want to use enumitem because of this problem. Is there any alternative package or solution which works only with description? Kindly suggest.


during a lab experiment, i noticed that a metal ball has a much harder time rolling on metal rails when their is a current passing through it and the rails. I was wondering why and if there was a name for this force. Does the fact that a current passes "pull " the balls towards the rails and increases friction? Thanks


this may look like a duplicate question to this one and many, but really I had a hardtime in finding the desired solution. The breaklines=true didn't work as it breaks the long command. Hence simple copy and paste doesn't work, because when the code is pasted in terminal it gets split over many lines with preceding angle brackets > .


I've read anything getting close to a regular black hole would experience spaghettification but not when you get close to super-massive black hole. Is there a point of "peak spaghettification" where the mass of the black hole exerts the greatest tidal force? Or, have I misunderstood something along the way?


Do quantum probability and free probability mean the same thing - that is, they deal with noncommutative random variables? What about quantum measure theory? Is quantum measure theory the foundation of quantum probability (kind of like measure theory is the foundation of the classical probability theory)?


A father's age is now five times that of his first born son. Six year from now, the old man's age will be only three times that his first born son. Find age of each.


This is my sentence, and I was hoping to make it sound more academic: The aim is to ascertain whether or not the actors from the two films analysed can be considered to be heroes Is there a better, more academic way of saying 'whether or not'?


Imagine that you would like to write down your passwords or other critical information into a sheet of paper. Could an algorithms without using a computer be so good as to avoid people of cracking it? There seems to exists some secret code messages that weren't discovered for centuries. So, theoretically it sound plausible, but how would I proceed?


It is remarked by some text book that according to definition of absolutely continuous functions if the finite sums in the definition are replaced by the sums of (infinite) countable items, the assertion still holds. But I don't know why, even I understand that the number of the finite items is arbitrary. Any comments are welcomed. S.C.Liu


let say that we can detect the wavelength and frequency of radio wave then can we detect that from where these radio waves are coming or from how much distance these waves are coming?


If I am given the position vector of a particle at any time, how can I know if the particle spins clockwise or counterclockwise? UPDATE: Maybe I should have said that the particle is moving in cirlces.


Would a switch of the word 'assistant' and 'manager' cause differences in a universal corporate context? In my opinion, assistant manager is just a rank below a manager. This seems to apply to manager assistant.


The name of the city of Sodom is the etymon of sodomy. Question: Are there words in English for which Gomorrah is an etymon? According to Online Etymology Dictionary the unit omer is related to Gomorrah. Beyond this I haven't found other words that are, at least, related. It would be interesting to know.


This is the only similar spelling mix-up in English that gets me every freakin' time. I can never remember which is which. One is a mathematical notion; the other is a nice thing to say. Does anyone know of any clever mnemonics for complement / compliment to get this one straight?


Compact Linear Operator is defined such that the operator will map any bounded set into a relatively compact set. Why is this property so special that it can be named as "compact"? Does it share some similar properties as compact sets? What is the motivation to define and study such a set?