When I look in old mathematical textbooks from the seventies and before, mathematics is always upright. Their use of italic letters in other contexts, however, shows that this is not because of technical limits. On the other hand, all textbooks I have seen with italic math look very TeX-like. So I was wondering if this is a coincidence? could italic math be an invention by Knuth introduced in TeX? Does someone know the history of italic math?


In compton scattering, a photon may deliver only some of its energy to an electron. But when dealing with photon electron interaction in an atom, it's all or nothing. Why the difference? Also, within compton scattering, given the initial wavelength of the photon, we get a relationship between scattering angle, and wavelength of the scattered photon. But we can't know the scattering angle without knowing the wavelength of the scattered photon. So there's a free variable. What determines the wavelength of the scattered photon? Is it some type of random process? Thanks in advance.


Possible Duplicate: Is the word 'whose' referring to an inanimate object correct in this sentence? Is there a more appropriate word? Basically I'm wondering if a sentence like this is grammatically correct: "Meaning is thwarted by its delivery, whose poetry is relative to taste." I cannot avoid it with, "Meaning is thwarted by its delivery; its poetry is relative to taste" because 'its' seems to refer to 'meaning.' There needs to be a word like 'whichs' or something. Or is there? Please clarify my question if you know the proper grammatical labels for what I'm talking about; I know them not.


I was going to post a comment on my own theory about Mars and Jupiter colliding, but I just read the rules and it breaks it...badly. I was looking for informal peer review. So my question is, has there been any mainstream published work about the possibility of planets colliding or interacting greatly? (Velikovsky doesn't count obviously, I'm thinking an actual scientist) (besides the Earth-Moon of course) I can't seem to find any.


Question: Find a conformal map from the exterior of the closed unit disk to the unit disk. Also, prove that it is indeed a conformal map (bijective and holomorphic along with its inverse). I missed that the two days we covered conformal mapping due to chaos in my life. I have been trying to find worked out examples and have been reading up to get some insight, but I am lost since I can't find something that details a complete worked out problem. p.s. If anyone knows a great resource that would help me out to further my grasp of conformal maps in complex analysis it'd be much appreciated if you could disclose this.


Consider the following situation. You are standing in a room that is perfectly circular with mirrors for walls. You shine a light, a single ray of light, in a random direction. Will the light ever return to its original position (the single point where the light originated from)? If so, will it return to its position an infinite amount of times or a definite amount of times? Will it ever return to its original position in the original direction? I thought of this little teaser when reading about a problem concerning rays in a circle and wondered about this question. As for my attempts, this is well beyond my skill.


An proverbial anecdote I've heard for a problem solving deadlock is something along the lines of: A farmer needs to fix a bucket, which requires this, that then requires that and so on and so forth until it requires a bucket to fix the bucket. However I haven't been able to find this particular proverbial anecdote for a problem solving deadlock, so I'm wondering: What is the most common (folksy?) proverbial anecdote for describing a problem solving deadlock?


What does this phrase from The adventures of Tom Sawyer sentence mean: "True, the knife would not cut anything, but it was a "sure-enough" Barlow, and there was inconceivable grandeur in that -- though where the Western boys ever got the idea that such a weapon could possibly be counterfeited to its injury is an imposing mystery and will always remain so, perhaps." Thank you!


Given a Matroid (E,I), I is a set of independent subsets of E, right? And independent subsets means that no two of these subsets must have an element in common, right? Now according to the hereditary property of Matroids, if A is a subset of B which is a subset of E and if B belongs to I, then A also belongs to I. If A is a subset of B, then all the elements in A are in B, then how are these two independent? All the sets that are supposed to belong to I (i.e. A and B in this case) must be independent (i.e. must not have any common element) right?


I am currently reading about the subject given in the title of this thread. The definition they give for equivalence classes in my textbook is a rather ostentatious in its wording, so I just want to make certain that I am understanding it properly. They say to let R be an equivalence relation on a set A, meaning that this this particular relation is reflexive, symmetric, and transitive, right? Essentially the rest of it seems to say that you can partition off the elements that make the relation reflexive, thereby creating a subset of the relation R. Does that seem right? I could really use some help, thank you!


I am studying various crystals and the two-dimensional materials that could be potentially obtained by cleaving them (isolating a region bounded by two parallel planes). In elucidating the properties of these materials, it would be good to know what symmetries could the cleaved material possess given the symmetry of the original crystal. What is the best way to approach this problem? My question can be alternatively interpreted as follows: how to find all the layer subgroups of all the space groups? ("Look them up" is a legitimate answer for my purposes, if you can tell me where to look!)


Are there any resources online for astronomy experiments that I can perform myself? I am looking if anyone knows any measurements to take while looking for various objects during the evening particularly using a telescope/binoculars. A couple of examples would be determining the orbits of the moons of Jupiter through an evenings observations or trying to measure a stars parallax from measurements throughout the year. I can think of a handful of other ones but was wondering if there were any other resources to provide some more ideas.


So, I've noticed over time that I see both "afterward" and "afterwards" at different times. Having a pet peeve (though I'm not certain it's actually a well-founded prejudice, lexicographically speaking) against hearing "anyways", I've started to wonder recently about "afterwards". With a quick bit of web searching, I turned up this analysis, which I find to be somewhat helpful, I'm just wondering if there's more that people could say to help me get an intuitive understanding of when to use which, or otherwise why to use one versus the other. I suppose (as mentioned in the linked article) this question could also apply to forward, backward, toward, etc. Which shall I use? When? Why? Does the 's' indicate some sort of plural meaning, or something else?


I am an undergraduate in Mathematics writing his dissertation on General Relativity this year. The next couple of months will be dedicated to learning the math (geometry) and the physics, and to this end I am looking for must-read/must-watch material on the topic. General book recommendations are welcome, but keep in mind I can use Google! I am mainly looking for really good introductory content that I would have a hard time finding myself, whether it be videos, course notes, books or blog posts. My apologies if this is a duplicate!


I am trying to determine if the plane on which two triangles lie intersects for a collision-detection implementation. Unfortunately, I'm stuck at step one, which is finding the plane on which a triangle lies. I tried looking around on Google and what I can find seems to imply that I need to find the normal to the plane instead of the plane, and the direction of the normal. Can anyone explain why I just need to find those two?


You often hear that black holes are so strong in their gravitational pull that matter, even light cannot escape. But this seems to contradict the laws of conservation of energy. Is it possible that perhaps light (photons) are not themselves elementary particles, and within the immense gravity of black holes decompose into some other sub-particle or dark matter that we cannot yet measure/see? I know there is no way, yet, to measure or determine this, but it seems like there is a more simple explanation than matter just "disappearing". Thoughts?


If A is a closed set,then what can we say about closure of A^C ? It is a closed set.But my doubt is whether A and closure of A^C is disjoint or not? what i had tried is: if A is closed, A = closure of A. A and A^C is disjoint, so closure of A AND A^C is disjoint.Can anyone help me to understand whether they are disjoint or not..


In terms of dollars per watt, using theoretical efficiency limits, what technology holds the most promise to become the primary solar energy capture technology? My hunch is carbon-based modules, since materials are abundant and relatively easy to manufacture; however their efficiency currently is nowhere near silicon-based semiconductors. In the future, assuming that scientists will push very close to the theoretical limits, what will provide the most power for the lowest cost? If this is relevant at all, I am trying to decide where to focus my graduate studies in physics, and I want to contribute in getting the most promising technology to its limit. If you can at least point me in the right direction to figure out the answer myself, I would greatly appreciate it.


Possible Duplicate: How does gravity escape a black hole? How can gravity get out of a black hole? If a black hole is so powerful that even light does not travel fast enough to get out, and gravity, or rather, gravitational waves, travel at the speed of light, how does gravity get out? And please don't say that the black hole creates a "well" in space that other masses "slide" down. Such a well would be unstable and, if two black holes pass near each other, neither would be able to "slide" down the other since both are infinitely deep. These wells would make gravity selective.


If I have a cup of water filled with air at the bottom of a pool, then when the cup is "upside down" the air doesn't leave because the water pressure is pushing it up against the top of the container. But then when I flip the cup, such that it is no longer upside down, the air rushes upwards. But why on earth does this happen? I mean the water's pressure is pushing this air downwards against the bottom of the container. If I were to draw an FBD which force is causing this air bubble to rush upwards? Thanks


Many years ago I heard a radio broadcast featuring a beeping sound that always seemed to come from behind me. The announcer said that the sound would have this quality and it did, even when I turned around. It was a plain beep, and the radio only had one loudspeaker. It was a complete mystery to me then and it still is, so can anyone explain the effect? (Previously posted at https://www.newscientist.com/topic/lastword/its-behind-you/.)


I wrote a technical article in which I used (probably overused) constructions of the form "The main point is that...", "The problem is that...". As I am a native Italian speaker, these sentences have the natural form that I would use in my language. One of the reviewers suggested that a better way to formulate these sentences in English is "As the main point,...", "As the problem,...". I feel these sentences carry "less power" than my original ones since the main word is not the subject anymore. Any thoughts? Is the construction I used incorrect, inelegant, or good English? Thank you


What do echo and reverbation have in common? They are the reflection of sound waves, they are formed when sound waves meet a hard surface, they cause a repetition of the sound. The waves keep having the same frequency (the source doesn't change); They have the same speed and length as they had before the reflection, because the environment doesn't change. Is there anything else?


I am working (writing and typesetting) on a book for children. I have used the memoir class. The book looks good for an adult audience. But I had ideas of making it more interesting for the children. More specifically, how about adding little thumbnails to the table of contents page? These will be tiny images placed randomly and rotated randomly. Or a different pattern border around each page? Like bright colored zigzag pattern for one page and may be, colored crayon strips on another? With my limited experience and expertise in latex, I could not crack this one. Any ideas/ suggestions/ solutions?


"Working for the man". Does "Working" act as a noun, verb or something else in this case and why? If I said, "I am working for the man." Then clearly working is a verb. However, I'm confused by the colloquial phrase "working for the man." It seems to have a "poetic" tone if you will. Because the subject does not exist I wonder if "Working" is a state of being in this case? As "Peter Shor" pointed out Maybe the answer is that because this is not a complete sentence then we don't know what role "working" plays in the sentence. FWIW, I'm imaginging how I can translate the phrase into Japanese. Which word I use for "Working" depends on whether it is a noun or a verb.


Is there an intuitive way to understand the convex duality? If the primal problem is minimization, the dual is maximization over another set of variables - but I would love to have a geometric visualization of this and an intuitive way to understand why this ought to be true. I'd also want to see strong duality present in such an intuition. Textbooks are dense in the math, but I haven't come across a place where this could be imagined in our minds without variables and equations. Could someone here help me out?


If I have two points at different X/Y coordinates, I know that: They are vertically aligned if both are at the same X coordinate; They are horizontally aligned if both are at the same Y coordinate. Based on the X/Y coordinates of one in relation to the other I can also tell the distance between them, etc. Now, how can you tell that the points are diagonally aligned by following the same logic?


We still hang up the phone, even though we really only push a button, not suspend it in a cradle. Sometimes we tape a television series, even though the DVR does the heavy lifting, not the analogue insides of a VCR. Is there a term for these words and phrases? I'm not sure about using words like obsolete or archaic, because the methods they describe may be, but the phrases themselves are not.


Reading the article "Emergence of scaling in random network, by Barabasi and Albert" I faced a lot of results obtained by simulations of the A-B random graph model. I always wanted to do such simulations, but honestly I don't know how to start. There is a better programming language? There are packages? There is a special software to handle heavy data? To put everything in one question: how they do that kind of simulation?


As kind of a real-life example, I'm struggling to write a description of the Crusades from the point of view of a Catholic pope. I know that through the Crusades, the Christians basically "rescued" the city of Jerusalem from the so-called "filth" that inhabited it. (Note: Please do not be offended by my use of the word "filth") You might say there's a tip-of-the-tongue phenomenon going on here.


I'd say both of these uses of "he was shot" make sense: "How did he die?" -- "He was shot in the street" [meaning shot dead] "He was shot in the street, but luckily the bullet only hit his foot." [meaning shot at -- there was a bullet coming his way] Would you agree? And what would you think of a headline "He was shot in the street". Is the man dead or was he just 'shot at'?


As an American, a large part of my impoverished experience of British accents comes from ancient BBC comedy imports on PBS. I'd very much like to identify the regional accents the following actors are using: the farmer Maurice Moulterd in Are you being Served? Again! (aka Grace and Favour) (the second series where they're running a country inn). Alice Tinker and Owen Newitt in The Vicar of Dibley Onslow from Keeping Up Appearances All four have distinct ways of speaking (not necessarily the same, but then that's the problem, I can't tell). Which accent does each of these four use?


In this question different people understood different things when talking about topological manifolds. Some argued they they have to be Hausdorff, some that they have to be second countable and some, both. When I studied them, my teacher showed us examples of non-Hausdorff (the line with two origins) and non-second countable (the long line) manifolds. For me, a topological manifold is a locally Euclidean topological space. What are the different definitions of a topological manifold you know? What it depends on? What author you read when you studied them? Who was your teacher? EDIT: What properties have the topological manifolds if we define them as second-countable and Hausdorff that they don't have if they are only locally Euclidean?


The problem says "In a factory, m workers work h hours to do j jobs. If p new workers are hired, how many hours will the work force have to work to do j jobs?" I worked out the answer logically, but I'd like to know if there's a formula that I can go to to make it simpler and faster when this kind of question arises again. Also I'm really not sure what the type of problem is called, so sorry for any confusion in tagging/titling.


I was surprised to discover my dictionary had this entry for dilemma: a situation in which a difficult choice has to be made between two or more alternatives, esp. equally undesirable ones The notion of dilemma meaning two or more flies against what I was taught about the word. The very idea of a false dilemma is specifically based on the number two. Has my dictionary merely updated its definition to encapsulate the many people who use dilemma for more than two equal choices? Or was someone in my youth being unnecessarily pedantic?


What is the word a deep desire that some external force has kept you from gaining it? For instance in the movie Foxcatcher, the rich guy always wanted to be wrestler but his mother didn't let him because she thaught it was a low sport and it was beneath him and this made a 'deep desire' in him to be a wrestler. Is there a word for that? The word I'm looking has some kind of negative meaning. This 'deep desire' makes you do stupid things and kind of has a bad effect on your personality.


I am learning Mean value property (MVP) of the heat equation. MVP of Laplace equation was relatively easy to understand I think it is because of the spherical symmetry. But I am not able to appreciate the MVP of heat equation. It's not very easy to imagine the "heat ball" in the following theorem from a note: Here are questions: How do I define a heat ball? How does it actually look like?


I have read this is true for all hyperbolic triangles, but I am trying to find an extreme example, or a limit behavior, were the sum of the angels of a hyperbolic triangle are minimized. Is there a min/ inf? Also, why do all hyperbolic triangles have angles sum less than pi (if that is true)? To avoid ambiguity, I am referring to hyperbolic triangles in the open upper half complex plane.


Consider the examples from the Free Dictionary: That summer, she up and died. He had lived here for twenty years, and then one day, he up and left for good. Is this a contraction of a longer phrase, making "up" a particle (as in "get up")? Or is "up" meant as a verb, but mysteriously not inflected according to tense/person? (in which case, how did it end up not being inflected?)


If we can think about the universe as a wave function then many particles should be entangled with many other particles in the universe. The obvious question arises why we don't see those entanglements in everyday circumstances. One standard explanation given is those entanglements average out and cancel so we can ignore those. However, hardly any mathematical justification is given for them to cancel. My question is how much trust one should have on that particular assertion? Is there any mathematical arguments already put forward by anyone?


Do matter and antimatter eliminate each other or release their equivalent energies? I'm almost certain it's the latter as mass can't be destroyed, but when speaking of the big bang it's said if there were equal amounts of both matter and antimatter there would be nothing left. I wonder how that can be true if they don't destroy each other. It may have something to do with how energy decays into matter.


Got curious about polynomials and Galois theory the other day and realized I have no idea how current mathematics treats polynomials (or rather polynomial like expressions) that have arbitrary algebras for the exponents. A quick search yields polynomial extensions like Laurent polynomials but I couldn't find anything that uses any other groups for the exponent, like Gaussian integers, complex numbers, cyclotomic rings, hypercomplex numbers and other algebras. What are these structures called and how is their behavior similar and different with ordinary polynomials?


Let's consider a partition of the words in the english language according to respective use frequency. Looking at the frequency graph it should be easy to find classes of words with approximately the same frequency. Now I'm interested in the size of these classes. I know that the size depends on the relative cut-off points, but I'm more interested in a general classification, i.e. are there more common words, or more uncommon words?


I have recently come across two key concepts in quantum optics: shot noise and back-action noise. This is very important for me to know: first, are shot noise and back-action noise the same? Please let me know if there is any other equivalent term for back-action noise among the quantum optics community. I am also wondering whether back-action is the nature of light beam in vacuum, or is it related basically to measurement detector like homodyne? I really like to know exclusively the characteristics of back-action noise to be able to model it.


There are so many famous paradoxes which are examples of how humans are unable to intuitively understand probability -- there's a discrepancy between their supposed actual experience and the mathematical evidence. There's things like the birthday problem where what we would expect the probability to be is much less than the actual, but also the monty hall problem where the confusion comes in why the answer is what it is. My question is, what is the cause of this? Why are we biased into thinking things are more or less likely than they really are? Why do we find it so difficult to accept and understand the correct probability in the case of the monty hall problem, burnt pancake problem, etc.?


Recently I was proof reading an email that a coworker was going to send to a superior and I pointed out that the valediction wasn't capitalized. He said it didn't need to be because it was the start of a phrase or clause and not a sentence, and that people only do it because other people do it. But in the back recesses of my mind I'm thinking that there is a rule that says that it should be capitalized. Is my coworker right and capitalization is unnecessary in this case? If I'm correct, what rule or guide can I point to, to prove my stance? (T/t)hanks, Jeremy


I've been thinking about this, I want to use this as my science project. The two viable solutions I've thought of so far are magnet or rotary based. Pendulum clocks could be powered once a day and run the clock for the whole day. From the rotary motion, could I easily generate electricity? A magnet on the pendulum could generate energy through coils. Does anybody have any suggestions? I'm just a highschool student so the project should be easy and small. Any blueprints or tips will help. Thank you.


so my goal is to detect an odd-cycle in a directed graph. I know for the undirected graph, the graph contains the odd-cycle iff it's non-bipartile. So I can check whether or not the graph is bipartile. If it is then the undirected graph doesn't contain the odd-cycle, otherwise it does. For the directed graph, does the same algorithm apply? Do I need more condition for the directed graph to have odd-length cycle? Thanks


I have always wondered about the similarity of the two words Astronomy and Astrology that describe two very different things but have their beginning in common and are sometimes confused in everyday language. The linguistic difference (if one can say so) between them is only in the endings '-onomy' and '-ology'. Two further examples are Topology and Topography Geology and Geography where now we have the endings '-ology' and '-ography'. What are the meanings of the different endings '-onomy', '-ology' and '-ography' ? I would also be curious about whether it is a coincidence that '-ology' appears in all the examples above? Does it maybe have historical reasons? And furthermore, are there more such pairs to be found? (I can't think of any others)


In the quote in the title, "of" refers both to the material that makes up the cup and to the stuff that the cup holds. I remember reading that there is a literary device that describes this, but I can't remember what it's called. The device, if I remember correctly, refers to the parallel structure of a phrase whereby a thing is described in two aspects or, as in this case, an aspect and a function. Shakespeare commonly used it, though I can't think of a quote. Syliva Plath uses it in the line: I am silver and exact to refer to a mirror--what it's made from and how it does its job. Could someone tell me what this structure is called.


I am looking for a phrase that is in the same spirit such as "single point of failure", or "bottleneck". Example: Being two engineers short is <-term goes here-> in this situation. If we find two engineers, the project will meet the deadline. Another one: Electric cars are improved enough to be on par with internal combustion engine cars. However, the long charging time is <-term goes here-> behind the problem that electric cars are not as widespread as internal combustion engine cars.


What constructions allow a writer to preserve strict logical coherence and reduce redundancy when conjuncting two noun-phrases? Example Many cultures have used gold or silver bullion as a currency. That sentence could imply that many cultures have used gold -in any form- or silver -only when cast as- bullion, but I intended it to mean that many cultures have used gold bullion or silver bullion as a currency. Moreover, a reader could interpret the sentence to mean that many cultures have used gold -in any form, for any purpose- or silver -only when cast as- bullion -and only- as a currency. How can I construct that sentence to ensure it imparts only the meaning I intend it to impart?


When the word that is used in a sentence to introduce some relative clause it is always an essential element which follows. Therefore, no comma is required. Example: I'm sure that you are lying. When I leave out the word that, it is still a correct sentence, right? Do I have to use a comma then? Because, when you read the sentence aloud, it kind of feels like there is a pause. Examples I'm sure you are lying. I have the evidence right here in my pocket (that) you are lying. Especially in the second case, I would prefer a comma at the place of the that. Is there a strict rule?


In the following sentence, what is the function of "You"? You, go to the store. I know the sentence is in the imperative mood, and that generally means there is an implicit second-person subject. If we dropped the initial "You", the subject would be that implicit subject. While "you" matches that second-person subject, that seems just incidental and it seems like it is just an expression of address that happens to match the implicit subject. Is it the subject, or merely a vocative expression? Or in other words, is the subject the "You" in the sentence, or is it the implicit subject from the imperative mood?


I have to show that if a metric space is path connected and countable then it is complete. I'm pretty lost where to start this at all. I have the basic definitions of complete, path-connected, compact and sequentially compact spaces. Any help how to do this would be great (this is a past paper question-non assesed, just for practice so I think it should be reasonable simple) Thanks very much for any help


can anyone help me by using geometric transformations to solve this problem: construct the triangle whose sides bisectors and their intersection point is given; my professor told me that if I assumed the problem to be solved I would notice that we have compositions such as symmetries, reflections, rotations . I can't really understand what he meant, if anyone can help me with a hint or the solution I would be very thankful


I'm sitting here in the metro station, drinking a bottle of water, and watching how the flow of water out of my mouth changes as air rushes into the bottle. My questions is: in space, obviously the effect would be different. How is this effect different as compared to with earth, and can the change in behaviour be solely attributed to the effects of gravity?


I want to randomly distribute some(in thousands) objects over a surface. This I can achieve with a function say x,y = rand(). This will evenly distribute objects over the surface, but is it possible to have some control over the randomness like having some groupings (some objects close together). I can try to achieve this with multiple iterations of distribution, but that might run into objects overlapping. So was looking for some kind of parameterized algorithm that might help in this area. I do not have much knowledge in mathematics so would appreciate some help. Thanks!


I'm looking for an adjective, saying or idiom for an analogy which makes the things even harder to grasp, that was supposed to make things easier to understand. Examples: A guy makes an analogy to express that playing violin and driving a car is similar, when he teaches driving cars. But since very limited people know how to play violin, it does not make things easier. A guy teaches culinary on Youtube. But he rather than he explains the basics of culinary (say boiling water), he says 'oh this process is similar to gamma radiation'. It is not important if the analogy is good or bad. Just it makes things harder to understand.


I am seeking a word, should it indeed exist, that describes a dramatic or literary device found when a new character is introduced into a story which disrupts the natural equilibrium, driving the story. For example, in J. B. Priestley's An Inspector Calls, there is a natural equilibrium at the Birlings' home. This exists, however, until the Inspector arrives - disrupting the natural order, it seems, and goes on to defining the narrative.


We know that a small object moving fast enough can pass by a planet and escape its gravity. Would this be (theoretically) true in reverse? Meaning a planet moving fast enough past a stationary smaller object would not assert its gravitational pull on the small object? Would this mean that gravity is mitigated by velocity regardless of whether the more massive object is moving as opposed to the small object?


Humans see only a narrow band of light wavelengths. Many animals see much deeper into infrared. Maybe one clue to explain why we don't see IR naturally, has to do with the light intensity as a function of wavelength? How would such a function look like on Earth in daylight and at night respectively? I suppose that shorter wavelengths are less intense, because they are harmful. But what about IR, is it more or less intense than visible light in daylight outdoors?


I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to have the sample rate considerably faster than the plant dynamics, but the physics of this system are such that this is inherently impossible. I can get some control of the system by hand-tuning a PID, but it seems considerably sub-optimal. Is there a strategy for developing a controller like this? Edit: I should add that the plant is this situation is a relatively complex LTI plant with reverberations caused by pure time delays. The delay cycles are a bit slower than the Nyquist frequency. The plant is stable.


I've been thinking about the following pattern for some time: Linseed oil... soaks into the (visible and microscopic) pores When I was a kid, this wasn't the way I was taught to use parentheses: they go after an idea, and explain it further. Yet it makes perfect sense--"visible and microscopic" is an aside, explaining details. Is this the right punctuation? Is it informal, or only acceptable in technical writing? My gut says brackets might be more correct, but I can't justify it: Linseed oil... soaks into the [visible and microscopic] pores


I'm using the document class scrartcl and appendix. This currently results in a letter instead of a number for section enumeration in the TOC and section title ("A My Code Listing"). I need to change this to "Appendix A My Code Listing", i.e. add the word "Appendix" to the section title. I have found a manual workaround on http://web.reed.edu/cis/help/latex/thesis#appendices but would like to know if there is a way to change this automatically.


I'm going to teach very elementary combinatorics (limited to basic enumeration) during two weeks to middle school students. At the beginning, I want to demonstrate the importance of counting in real life or technology using concrete examples which students are familiar with, so that they appreciate what they are learning. In this discussion, almost all examples are advanced and are not appropriate for middle school students. I'm looking forward to your suggestions. Thanks.


Is there a character in any established alphabet (I couldn't find anything in the IPA) to denote a sharp intake of breath, as if by surprise? I want to include it in a character's name. Initially I thought "!" would suffice, making the name, for example, "!Davis" (pronounced -breath-Davis) based on its usage in demonyms like "!Kung-San", but it seems I have mis-remembered what the exclamation point here does. Googling just gives me information on "a sharp intake of breath", which I'm sure is wonderful but is of little use to me at the time of writing. Thanks.


I recently encountered this word while reading an article and found that its two basic definitions are "Bewildered" and "Unfazed." How can the word mean both these things as they seem to be direct opposites of each other? Should the sentence in which it's used always explicitly reveal the intended meaning? And while many of us might be a little taken aback if Mom showed up at our offices, Secrist is utterly nonplussed, even happy about it. source In the above sentence, it's obvious that Secrist is "unfazed" without even knowing the definition of nonplussed. Instead of adding clarity to the meaning being conveyed, "nonplussed" seems to just add confusion. Then again, maybe I'm missing something. Thoughts? My first post here so please edit/re-tag as appropriate.


The definition of a topological space is a set with a collection of subsets (the topology) satisfying various conditions. A metric topology is given as the set of open subsets with respect to the metric. But if I take an arbitrary topology for a metric space, will this set coincide with the metric topology? I'm trying to justify why we call the elements of a topology "open". If my above question is true, then at least in a metric space, the set of open sets is equivalent to the topology of the metric space. So am I right in thinking that when we remove the metric, we are generalising this equivalence by defining the open sets as those that satisfy the conditions of a topology?


If i put a pen on a table in its horizontal position and then i try to move it horizontally by giving it a small push, so that it would fall off a table, i expect it to move horizontally but my pen ( and all other pens too! ) moves diagonally when it starts moving down the table!When i remove the notebook , the pen moves like,its shown in the picture ( if i keep it horizontally also, it gives the same result)- Why does this happen? Why does it not move horizontally ?


I'm looking for a word that can describe a long-term inhabitant (inhabitant is the best I've come up with so far) of a hospital. Specifically, a soldier living (retained? - again, word might fit here too) in a War Hospital not long after the First World War, however the answer doesn't have to take into account the time period, as I feel there is a word at the back of my mind I simply cannot find right now which means "inhabitant of hospital." I'd like to be able to use it to complete this sentence: The gravel pathway was bordered by short, waist-height shrubberies behind which were the colourful flowerbeds intended to pacify the hospital's ________.


I've got an undirected weighted graph G with c:E(G)->IR. Now I want to find a spanning tree, such that a node v arbitrary, shall be an internal node, and among all spanning trees, in which v is only an internal node, it has got minimal weight. My Idea: Use Kurskal. If v is an internal node than stop. But if v is not an internal node I'm not sure what to do. Do you know how this could be solvable? Thanks in advance.


I often heard that it is possible to show by using the inverse function theorem that if a function is smooth (i.e. arbitrarily often differentiable), a bijection between open sets, and has a non-singular jacobian, then it is a smooth diffeomorphism. but somehow the inverse function theorem that I know and that wikipedia seems to know, only states that if it is a continuously differentiable bijection with nonzero jacobian, then its inverse function is also continuously differentiable. But how do you get from this, to the statement that I proposed above? I don't see the implication.


I was going through a text about ancient civilization. There, I found a sentence which says, "Some ancient human being recognized even cannibalism." After reading that sentence, I started to think that, as the word 'cannibalism' is disgusting, the writer would had written this sentence in another way e.g. "Eating human flesh too was practiced by some human beings in ancient period." What do you think about which one of them sounds better--- 'cannibalism' or 'eating human flesh'?


I'm trying to speak about the nature of music; I want to say that the very nature of the medium of sound, a kind of universal language, makes it impossible not to interpret what is presented to us. (The laws of physics make music from different cultures ultimately very similar.) How might I express this with some interesting parallelism? I tried using the read-understand pair, but I'm not sure if this makes my meaning obvious enough. I feel like there's some word that I can't think of that would make this analogy (or another) work. It is possible to read and not understand, but impossible to listen and not hear.


Terminal Velocity depends on two things: surface area and speed. These are inversely proportionate. If both these variables affect terminal velocity, why do parachutes slow you down? Initially you had a small surface area but a fast speed- with the parachute you have a larger surface area but lower speed. You have increased one variable but decreased the other. Therefore why do parachutes decrease speed?


I am not sure how to approach this problem. A similar question has gone unanswered before. If the conductor was at rest, then the charge would have distributed evenly. Now all the charges will feel pushed out due to the rotation of the sphere. However the amount of "push" is proportional to the distance from the axis (centripetal force is proportional to the radius if angular velocity is constant). But the electrons would not like to accumulate together, so they must be resisting the urge to group together (near the equator). Have I missed any other electromagnetic effect (other than the Coulombic repulsion)?


Edit note: This question with some good answers does not explain (or ask) why it is an adjective that's used as opposed to an adverb in this type of construction: Is this an objective complement or adjective phrase? My Question: Consider this sentence: "Garlic can be eaten raw or cooked". In the dictionary, "raw" is an adjective only and is not an adverb. "Cooked" is also an adjective. So, why can an adjective be placed after "eat" as in "Garlic can be eaten raw"?


I am looking for an idiom or a phrase to denote the situation where someone is unfairly taken advantage of (Ex: Gets a lot of work dumped on his lap on a Friday evening like Harold in Harold and Kumar series) because that someone is nice and does not say no. In my mother tongue there is a usage for this; when translated verbatim it sounds like this "keep on digging where it is wet" - is there something similar in English?


I'm in doubt about a situation that I've seen sometimes: imagine we have a resistor in parallel with a resistor and a capacitor in series. Since I don't know how to generate figures of circuits to post here, the situation can be described as: a single resistor on the right, and on the left a resistor and a capacitor in series. If there was no capacitor, I know I could replace the resistors by an equivalent one. My doubt is, do this continues to be true in this case? I mean, can I replace this configuration by one capacitor with one resistor in series such that this resistor is equivalent to the other two? If we can, what's the argument beyond this?


I'm developing a website on which photos and videos will be shared. But I couldn't decide on the main menu name to use under which there will be two subcategories Photo Gallery and Videos. Which one do you think makes more sense to visitors: multimedia or media? Once they see it, they should immediately realize this menu is all about photos, videos and things related to graphics.


The question is Suppose that events A and B are that people have diseases a and b, respectively. Suppose that having either disease leads to hospitalization H = A U B. If A and B are believed to be independent events, show that P{A | BH} < P{A | H} I think I understand why this holds but do not know how to explain it. I know that P{A|H} is equivalent to P{A} since it's independent from H and I also (think I) know that P{A|BH} is equal to P{AB} and since they are independent this equals P{A}P{B} but now how do I go about proving P{AB} < P{A}? Assuming all the assumptions I've made are correct.


I saw the word admixture used in a sentence recently and looked it up in the Paperback Oxford English Dictionary only to find that its definition is "a mixture". This is the sentence: The 'Natura' section features a series of sixteen prose poems, redolent in many ways of Hill's Mercian Hymns in their admixtures of natural and urban landscape, dramatised autobiography and historical reference, fomal and colloquial styles. Why is "admixtures" used here rather than "mixture"?


I'm working on definition essays. As I read a couple of sentences, I came up with a question. I'll appreciate your help: "Two years ago, I read a story which revolved around the life of a spoiled family "--> Wouldn't it be more appropiate to use the present tense for "revolve around"?, as the story's plot was and still IS the same Another example: "She said: 'I became a teacher because I want to change the world.' That got me thinking about what being a teacher really meant." -->Shouldn't the writer've said "means"??


Diproton is an isotope of helium without any neutrons. It commonly forms in the Sun, where protons are fused constantly. However, it is extremely unstable, and will revert back to two protons almost immediately after. Now, nucleons are held together by the strong interaction. So if the electromagnetic interaction is weaker than the strong interaction, why won't the protons stay held together instead of repelling one another?


I have to do a project for my high school calculus class. I am interested in figuring out how to create equations for simple outlined shapes like this bird if I were to plot it on a coordinate plane. I have investigated the Fourier Series, but I am not quite sure how to implement it (where to start, I guess). I assume I should start by taking coordinates from the curve once at certain intervals, but I'm not sure where to go from there.


I want to use a word/phrase/idiom etc. to describe someone action by which they try to stop another person talk or sharing their plans. I want specifically to use it in following situation: During conversation with my uncle, he was telling me their future plans to sell house but my Aunt stopped him by secretly putting her finger on lips as a gesture to shut up.


In his book "Origins", Neil deGrasse Tyson says that "if you seek to split iron nuclei apart, you must them with additional energy. On the other hand, if you combine iron atoms they will also absorb energy[...] For all other elements only one or the other half of this dual description applies." According to him, that is the reason why stars can't make iron. Maybe I'm forgetting something important here but to me that reason is not clear. Is it because up until iron all lighter elements when fused released energy, while when it's time to fuse iron the stars actually lose energy? If this is true than the other part of the sentence (fission) is irrelevant. What is the actual explanation?


To my understanding, work is done on object A when object B is applying a force on object A, causing object A to displace. Since energy is the ability to do work, what work does a moving object do, due to its kinetic energy? I mean, if I kick a ball, it has kinetic energy due to its velocity, but what force does it apply? On what object?


The Big Bounce theory says that before the Big Bang there were other Big Bangs over and over. For example, the universe would have a Big Bang within it and then this new mini-universe would expand, then start collapsing, and as it finishes collapsing, it would "bounce" back into a Big Bang, while the greater universe stays constant. Since this is a big explosion, nothing resists it, so we can't find any trace of the other universe ours started in, but would we be able to find evidence for this in the small dimensions that exist in string theory? They're so small they would resist the Big Bang. If the LHC found these dimensions, would it confirm the theory?


What is/are the word(s) for a person who writes/speaks with the attitude of always being right, having the final answer(s), never having their position or interpretation questioned, having the final say on a subject? One who positions him- or herself as the ultimate and final authority on a subject, who entertains no possible alternatives to their interpretation of a subject? "He writes as though he is the ______ on this topic." Not the authority, but a word meaning the presumed authority - seeing this as a negative trait.


"abuse" is often defined as improper usage. When speaking about an illegal drug, it seems impossible to properly use it (I mean here recreational consumption, not specially licensed medical or research use). So then, is any consumption automatically abuse? EDIT: I see that somehow, several users appear to have misinterpreted my question. I would like to clarify: Even substances which are illegal may be used legally by people such as medical doctors and scientists, by special permit. Obviously this is not abuse. It falls within the special exemptions provided by the law. I am asking about using the word "abuse" to describe use of these drugs outside such special permits, when the law considers the use clearly illegal.


Let F be a field, E a finite field extension of F, K the field of separable elements of E over F, C an algebrically closed field containing F. Is it true that every F-homomorphism from K to C extends uniquely to E? If yes, why would it be true? The point should be that the minimum polynomial over K of an inseparable element of E has only a root, but I can't prove this fact. Thank you for help.


What does a subspace say A spanned by another subspace B and a vector x mean ? Does that imply anything about a basis or does it just mean that every vector in subspace A is either present in subspace B or can be expressed as linear combination of vectors from B and x. Or anything else perhaps ? Any help would be much appreciated.


I have exhausted everything I know about solving for the determinant after operations have been done to it following the general principles of matrix determinants. I see that the first row was multiplied by a scalar and the second row was multiplied by a scalar. It was my general assumption that I would take the original determinant and multiply by the first scalar and then add the original times the scalar multiplied by the second row. Obviously got the wrong answer and feel like I am missing something very basic here. Thanks for the assistance.


As is shown in wikipedia: Click [here] (http://en.wikipedia.org/wiki/White_noise#Mathematical_definitions) A random vector (that is, a partially indeterminate process that produces vectors of real numbers) is said to be a white noise vector or white random vector if its components each have a probability distribution with zero mean and finite variance, and are statistically independent. Here comes my question, does the vector is still white noise, if the variances of the components are not the same any more? Thank you very much.


Thin has a meaning of "not well fleshed," but does it also carry a meaning of "being weak or feeble"? In the Merriam-Webster, it does carry a meaning of "lacking substance of strength," but it uses "thin plot/broth" to make the example. Is it okay to say someone is to thin to do anything which needs a lot of strength? I just find it misleading to say, because thin doesn't always means weak. If you google, there is a title such as "Michael Jackson is too thin to play live." Is it OK to say so? Somebody argued that it's a euphemism to say so.


The definition of explicit that I wish to use: stated clearly and in detail, leaving no room for confusion or doubt. E.g. the speaker's intentions were not made explicit. My motivation: I'm analyzing 'Follower' (by Seamus Heaney) right now and I want to comment on the word "exactly" in 'Mapping the furrow exactly'. My comment is something along the lines of "Mapping the furrow" already attributes a high level of skill and precision to his father. The use of the word 'exactly' adds an extra layer to the phrase and makes it explicit.


I wonder about this. If you pour water in a closed tank, it makes a noise. I have noticed that as the container becomes more and more full, the pitch of this noise also increases. Why is that? I do not study, nor have any knowledge of beyond basic concepts, of the physics involved in sound and vibrations. However, my hypothesis is that this happens because the "chamber" where the sound is produced gets progressively smaller, therefore it behaves like a flute - as you change the shape of the chamber, the sound that air makes as it passes also changes.


If I have two sub-areas confined in a larger area, and I have the intersection of these two sub-areas. If I replace one of the sub-areas with a new sub-area, which is the same size. What is the probability of the new intersection being bigger than the old one? (By that I mean how could I solve this?) If the question is too vague or written badly then just comment aand I'll try to explain it a little better. Thanks Keri


Does the uncertainty principle imply the non-deterministic universe, or just the fact that our model of the universe, the one based on observation, can be at most non-deterministic, since we will not be able to measure with perfect accuracy, even if such would exist (and therefore we will have to provide probability distributions rather than an event which should happen with overwhelming probability (term used by Terence Tao))?


As a web developer, this is a question that has bugged me for some time: when providing a way for users to reset their password, which link wording is more suitable or is the "proper" use? "Forget your password?" (as in, "Did you forget your password?") "Forgot your password?" (as in, "Have you forgot(ten) your password?") There is a nicely related post here (Is it correct to use 'Forgot password' or 'Forgotten password'), but that addresses "forgot" vs. "forgotten." Thank you for your insight!


Could anyone tell me the difference between "have wanted to do" and "have been wanting to do"? I often say "I've been wanting to go there!" when someone invite me to the restaurant that I got to know before and has been thinking I want to go since then. But one of my friends said "I've wanted to go there." in the same situation today. Which is correct/common usage?


Inevitability just sounds so depressing to me. The "inevitability of death" is a glaring example. There has to be a word that means "unavoidable but in a good way" right? Edit: The sentence I'm trying to make right now is about "the [inevitability] of technological progress in our society". Technological progress at least in what I'm arguing for is good so I'm looking for a word that would be a positive replacement for [inevitability].


Environmentally induced decoherence makes wave function collapse unnecessary. But the environment, usually taken to be some heat bath, introduces a preferred frame. (That in which the total (spatial) momentum vanishes.) So, doesn't then the decoherence time depend on the motion of the prepared state relative to the environment? And, doesn't the ultimate environment, all particles in the universe, introduce a preferred frame into quantum mechanics in the sense that the decoherence time is relative to this frame? And would this be measureable, at least in principle? I.e. I could go into a frame with high boost relative to the CMB restframe and notice that the decoherence time changes?


I'm near the end of Velleman's How to Prove It, self-studying and learning a lot about proofs. This book teaches you how to express ideas rigorously in logic notation, prove the theorem logically, and then "translate" it back to English for the written proof. I've noticed that because of the way it was taught I have a really hard time even approaching a proof without first expressing everything rigorously in logic statements. Is that a problem? I feel like I should be able to manipulate the concepts correctly enough without having to literally encode everything. Is logic a crutch? Or is it normal to have to do that?


In order to collect all pokemon Tazos, I went to a shop and bought bags of chips. Now I am worried whether I have bought enough bags of chips or not. You need to tell me the probability of getting all the distinct Pokemon Tazos from the N bags of chips. Lets say N is the number of bags i bought and K is the distinct pokemon available. So how do i calculate probability?


I would like to put an address in my document as follows: | | | Name | | Street #| | City | | ZIP | | | where the | mark the left and right page borders. I would like the items of the address (Name, Street etc.) to be left-flushed, but the box right-flushed so that the longest item touches the right page border. Is there a simple way to accomplish this?


I'm writing a short story set in an artificial planet-sized sphere with an ecosystem in its inner surface, whose "gravity" is created through spinning. Energy sources aside, what other interesting physical characteristics should I take into consideration, apart from varying force levels as one moves relative to the direction of the spin (may be minute given the size of the structure), as well as increasing "weightlessness" as one gets closer to the axis? Also, with sufficient mass in its shell, what is the effect of (real) gravity on objects on the inner surface?


When driving on a wet highway at night, any surface emitting or reflecting light will have a reflection right under it that is blurry and seems to stretch to infinity. This is not exactly what I am picturing in my mind, but I couldn't find better images. Anyway, I think it'll do. Does anybody know why it is such a long reflection? I never figured it out myself.


English.SE, Hi, first time being here. I have had this confusion about the pronunciation of "a priori" and "a posteriori" for a long time, normally I just read the last vowel as /i/, however today my office mate asked me about this for he saw the pronunciation on Merriam-Webster online dictionary shows that the last vowel reads as /ai/, this reminded me that the philosophy professors whose lectures I took before didn't agree on this pronunciation either. Since I learned that Immanuel Kant borrowed these words from Latin, I wonder what is the correct way to pronounce these words in Latin or at least in a Latin'ish way.


I have a question on electron and non-polar optical phonon scattering in GaAs. Is it allowed to consider intravalley electron non-polar optical phonon scattering in L-valley of GaAs? I found in the literature, people only consider intervalley (L to L) electron non-polar optical phonon scattering in GaAS. I wonder if anyone can help me why this is the case? Why do not people consider intravalley non-polar optical phonon scattering in L-valleys of GaAs?


Black is the absence of light because it absorbs light, but when we create black paint or black objects, light is always reflected, either in all directions in matte or smoothly in shiny black objects, making it never a true black. Would it be possible to use polarization to create an object that does not reflect any light, creating a truly black substance, without any shadows or reflection of light?


I see all the files in titlesec here at ctan: http://www.ctan.org/tex-archive/macros/latex/contrib/titlesec/ I also see a titlesec folder in my texmf-texlive tree. Apparently what happened is that during a fresh installation of texmaker, the installation process cleared out the titlesec.sty and related files. Why it would do such a thing, I do not know. It seems obvious to me that I should just put all the files on the ctan site into the titlesec folder. Do I have to download all those ctan files individually or is there another way?


I have seen the following line in mail replies from customer care executives - Thanks for your patience They write this when they are not yet ready with a desired solution. They write in the mail that it will be ready after some more time. Writing "Thanks for your patience" in such a mail seems like we are assuming the other person is patient, whereas he actually may not be, and instead, what is probably desired is to ask the person to be patient. What would be a polite way of asking the same, knowing that the person desires the solution ASAP.


As far as I know, a measurable function is Lebesgue integrable if and only it is absolutely integrable. It is simply because the definition of the integrability requires each of the positive part and the negative part has a finite integral. However, some theorems explicitly state that a function need to be "absolutetly integrable". For example, Fubini-Tonelli theorem says that if one of the iterative integrals or the double integral is absolutely integrable they have the same value. What's the point / importance of the absolute value here? Can I just replace the condition of absolute integrability with just integrability?


It's easy enough to show that the theory of algebraically closed fields of characteristic p is decidable (since its complete). But does it follow from this that the theory of algebraically closed fields of any characteristic is? I suspect that the answer is "yes", but I'm not quite sure why. The reason for my suspicion is that we can simply that the greatest lower bound of each of these theories and arrive at the right set. But I'm not sure if decidable sets are closed under countable intersections.


I've used this site to my benefit in the past, and now I have my own question. I have looked through some of the answers (although I admit not every one as I am short on time) and cannot find what I am looking for. Could someone help me regarding punctuation of my sentence? I find an airplane's symbolic freedom appealing: whether it is soaring through the sky; industriously filling and disgorging passengers; or exultantly defying gravity on take-off, it remains independent and far-reaching in all of its manoeuvres. Is this correct British English or do I need to change the colon to a comma? Also how is that last tacked on bit?


I was recently studying Pair Production and Annihilation. The author mentions that a nearby nucleus is required when the photon materialises into a particle and an anti-particle. The explanation given is that the momentum and the energy must be conserved. However, there is no calculation given that shows the violation of energy. The reason is just blankly stated. Is there more to this concept. Please explain? As far as I know that from the knowledge of Particle Physics, virtual photons can violate the conservation laws if the time scales are very small due to the Heisenberg Uncertainty Principle. Then why can't we apply the same idea here? PS: I've read the other answers but none of them include the contribution of Nucleus' energy/momentum to conserve momentum or energy.


I have a document with quite a number of figures, some of which have a longer figure caption (in particular some take multiple lines). The image shows such a case: I would like the second and consecutive lines to be aligned with the 'F' from 'Figure', i.e. get rid of the white space below the figure label. The gecko expample from the wikibook (https://en.wikibooks.org/wiki/LaTeX/Floats,_Figures_and_Captions) shows this. But they seem to do nothing special to achieve this. Maybe a different software version? How can this be done? Thanks Soraltan


We know that space cannot spread a sound wave as there is no "air" or a medium that would support the spread of a sound wave. However if we put ourselves in the vicinity of an exploding star, would it be possible to hear something? The question arises from the idea that within the explosion of a star (first few seconds or less) you may hear a noise due to the explosion of the star...


For me the relevant number of subgroups of a finite group is the number of non-isomorphic subgroups. Mathematicians seems to have an other opinion. There is a related classification called automorphic subgroups, when there is an automorphism on the main group that maps a subgroup on a subgroup, which seems to be a stronger condition. A weaker condition than automorphic subgroups is conjugate subgroups. What is the relation between conjugate subgroups and isomorphic subgroups? Why isn't isomorphic subgroups more interesting in mathematics?


Given the fact that the force stopping me falling through the ground is the electromagnetic repulsion between the electrons in my feet and the ground, would it be possible to increase this repulsive force? Also is friction generated due to this repulsion of angular faces at a very small scale ? if so could a material be made so smooth it had zero friction because the electromagnetic force simply kept the two apart instead of causing friction? Sorry if its a stupid question but im very interested to find out and why not if i am wrong.


I would like to understand the difference between reflection of light and re emission. Indeed in both case an observer far from the object will se an electromagnetic field coming to him. When we take a perfect conductor an a E.M wave going to it, we know that the wave is "reflected" but can we also see it in the way that the material absorbed the light and re emitted it ? Is the difference based on the fact that in re emission the energy is stored for a finite amount of time in the material and the re emitted as a ray whereas in reflection the energy of the incident beam is never stored by the material ? Thank you for your answers.


Experience and hardship come to mind but they seem too general and they don't communicate the end result. They can be used depending on the context of course but there might be a word for a type of experience that conveys this proverb better. (if not a single word, a two-word phrase). Example sentence: I've suffered through a lot of adversity in my life, experiences that didn't kill me, but made me stronger, turned me into a fighter. These ordeals were (my) _______.


This is a newbie question, but I don't quite understand the forces at work when an object is rotating. So I've read that i can use my right hand to determine the direction of the force at the axis which depends on the direction and the magnitude of a spinning wheel. (Fingers pointing in the direction of rotation, thumb is pointing in the direction of the resulting force.) Does that mean that in a car, the wheels on one side constantly want to fall off, while on the other side they want to move to the enter of the axis?


Suppose that in the future a highly resistant spacecraft went to the Sun and collected three samples of the Sun: one from its surface, one from its core, and one midway. The three samples were put into three high-tech jars which could preserve the samples perfectly (so the temperature, pressure, etc, of the three samples are not altered). The three jars were then brought back to Earth, and exposed into a museum. What would we see? Would the three samples look almost identical to each other? Would they look like some kind of fire/flames? Or would they just look like some kind of boring gas? Please provide pictures if you can.


The word visualization is often used to describe an image or interactive piece of media that represents a data set. I am trying to think if there is an equivalent for something that is not only visual, but also tangible. That is, an object that represents data and that people can touch and see. If there is no word for this, can you think of a neologism for it e.g."tangiblelization"? EDIT: By tangible I mean an object that can you can youch with your hands.


Any action of a finite group on a (non-empty) tree has a global fixed point (in the sense that there is a vertex fixed by all group elements or an edge fixed by all group elements). There is a hint which says we can consider the diameter of the corresponding orbit is minimal. However I don't find the definition of diameter in the book. Can someone clarify the diameter? Or give the details of proof? Thank you.


Why does special relativity exist? Via studying the outcome(s) of such relativity, one can end up with all the equations involved in special relativity. Thus one runs into things such as contraction, dilation, transformations, velocity addition, etc. But these are the outcomes. My question is what is the cause of special relativity, and is the knowledge of this cause currently being shared in the world of physics? Or, to put it another way, is it currently accepted despite there being no cause that is known of, thus an acceptance of an effect without a cause? If you give this question a negative vote, please present your reasoning and or evidence to support such a vote.


This question has been asked before under other guises. I am not a scientific profesional however i have some schooling in pyhsics and mathematics and have a keen interest in these subjects. It seems plausible to me and was a thought i had my self many years ago whilst at college, that the universe could possibly be expanding from within itself. Ie matter and space were expanding at the same rate as each other. I observe there is no relative distance increase between the objects i see on a day today basis and as such this type of expansion wouldn't change our perception of this relatively speaking. Everything we observe would remain the same and we would be unaware of the expansion..


I need a word to describe going out and doing something, which is thought through but not necessarily fully planned. Like all of a sudden thinking "I want to go to a club" while sitting on your couch, then going out and just doing it. A contextual example will be: You're doing nothing and want to do something. You're presented with a list of possible chooses that may interest you. You pick one, and just do it.


My brother asked me this question: You can be disruptive, but can you be ruptive? For example, one can be disrespectful and it is also possible to be respectful... I thought ruptive would have to mean the opposite of disruptive (because...pattern?). I have looked up the definition of ruptive and it seems that both ruptive and disruptive have the same meaning. Why is this so and why is there a distinction if they both mean the same thing? Upon further investigation eruptive and irruptive are also in the same boat. Again why? Is this a common pattern? Examples?


I have been seeing phrases "The board of directors resolved on the budget." but have never heard, and in dictionaries have not found, a combination of "resolve" with preposition "on" to refer to the topic that a body must make a decision on. The OED says to resolve in this sense generally takes an object clause, such as "The Committee resolved that it accepts the chairman's proposal." or "The shareholders resolved to go forward with the takeover bid." But when the actual tenor of the decision is not stated, only the topic on which a resolution must be passed, is it correct to use "resolve on"?


How can an image pass through a window if the atoms in the glass randomly emit photons in any direction? I've read that glass is transparent because the atoms don't readily adsorb visible light, so it passes right through. But then how can a glass lens refract anything if it's not even interacting? Yet magnifying glasses burn ants! I've also read that refraction has to do with the difference of velocity of the wave in different mediums, but I thought that had to do with adsorption also. Maybe it's because a small number of photons get adsorbed and that holds the whole wave back some how? Or is this just another one of those places where classical intuition breaks and you have to go mathy/qm?


Does Gravity / curved space cause rotation? Meaning, if a spaceship is heading not directly toward Earth, but slightly off to one side, and when finally being close to the Earth it falls into earth orbit, does the spaceship continue to point in the same directions as it was when approaching the earth, or does it now rotate at a frequency that is equal to its orbital frequency? I would expect the spaceship to be pointing in the opposite direction after completing one half of an earth orbit.


Well, I guess the 'odds' in 'overcome the odds' means kind of 'diffculties'. But I cannot find such kind of explaining in dictionary (oxford dict online) nor in "Practical Everyday English (by Steven Collins)". The closest explaining, seem to me, is 'The chances, probalility of winning, being successful'. But then it doesn't explain well for the following sentence (from "BBC Life Story") Animals have just one goal at the end of this journey, to leave offspring, and everyone begins its life with an irrepressible instinct to survive and overcome the odds. What does 'odds' mean here?


I have following propositions: p:Grizzly bears have been seen in the area. q:Hiking is safe on the trail. r:Berries are ripe along the trail. I need to convert following compound statement to logical expressions by using logical connectives. If berries are ripe along the trail,hiking is safe if and only if grizzly bears have not been seen in the area What I think is true is: ~p <-> (r^q) Note:I have considered comma in above statement as and. But answer given at the end of book is: r -> ( q <-> ~p )


I used to think that things called "parabolic" must have something to do with parabolas or their defining quadratic equations. In fact, terms like parabolic coordinate, parabolic partial differential equation and so on, are indeed related to parabolas and their equations. But, why are parabolic groups in algebraic group theory (correspondingly, parabolic subalgebras in Lie algebra theory) named "parabolic"? Do they have anything to do with parabolas or parabolic equations? Thank you very much.


My guess is that when you throw a ball, which is held by your hand, using you arm, the radius of the circular path being constant, the outermost part of the ball has a bigger radius than the innermost part, therefore greater linear acceleration for the outermost part of the ball. And so when you release it, the outermost part is always ahead in the direction of rotation than the innermost part.


I am currently studying mathematical course at my college, and I cannot seem to grasp the concept of inequalities. What troubles me is that, like it's said, "triangle inequality matters because many other theorems are dependent of it". But I have no idea why triangle inequality matters, why bernoullie's inequality or why sin function inequalities matter? I would be grateful if anyone explained all of this. Practical examples would be much appreciated.


In my current project we are writing a program to convert a newer protocol to an older one. These conversion programs are being referred to as adapters, but the team cannot agree which spelling to use: adapter or adaptor. I personally plump for adapter, as adaptor sounds like its a person (like actor, realtor, etc.) rather than a device. Is there a case for using one rather than the other?


Is there a name for a pair of words or phrase that can have a double meaning? I was thinking homophones, but I thought that homophones are only applied to single words (ie their, there, and they're). The example: The term "werewolf hunter" can have two meanings A hunter who is also a Werewolf A hunter who hunts werewolves The term "English teacher" can have two meanings A teacher who is English in race A teacher who teaches English Is there a specific term for this kind of phrase?


I am making a video game, and when player tries to walk into wall he should slide along it. However I am confused how to resolve the vectors for it. Here is image illustrating problem: I know the v vector, as well as angles A and B (although angle A is wrongly illustrated here, it should be counter clockwise). How do I find b vector?


It might be a silly question, but one of my friends just got asked this question at an oral exam, and he could not answer it, and didn't receive the answer either (Or at least he forgot). And I've been thinking a while, and I'm not sure what would really happen. If I take, lets say a wedding ring, made from a conducting material, placed it on a table, and turned on an external electric field, what would happen ? The inside of the ring is field free, right ? So does anything even happen, and if so, is it only on the surface of the ring ?


If decoherence time of quantum decoherence is zero, or if off-diagonal elements of density matrix of quantum system (without environment considered) vanished immediately after interaction with environment, then one can say that "classical" probability transition occurred, and this is why we get appearance of wavefunction collapse and measurement. However, decoherence time is almost always not zero, and off-diagonal elements of density matrix of system, as far as I know, do not vanish to zero even though they remain very close to zero. If this observation is correct, then I wonder how quantum decoherence explains how/when measurement occurs - with emphasis on "when".


Since the Lagrangian of our quantum field theories is covariant under Lorentz transformations I'm asking myself if there is any link to some symmetries (like that we get from gauge transformations which also let the Lagrangian unchanged)? So is it possible to apply Noether's theorem to this invariance or doesn't this makes any sense? So what is the mathematically difference between this two transformations and their behavior?


Possible Duplicate: Biblatex: remove commas between last and first names in bibliography Is there an easy work-around with the last-first biblatex macro so that the comma after the last name in the bibliography entry can be removed? The goal is to print Kruse, JS as Kruse JS To see some more background to this question, you may refer to my post: biblatex conditional for printing an extradate.


I'm working on package that (among other things) writes an external file during compilation. I'd like to provide an option to the package to not write the external file. I know I can set up a boolean and test for it everywhere in the package the writes take place. But it would be nice to just set the openout command at the beginning to write to /dev/null or its equivalent. Is that possible? I need to keep this package supported on Windows, Mac, and Unix.


The last couple of days i have been thinking about temperature and heat and i thought : What happens to temperature if i continually supply a particle with energy? Then i thought at sometime i would run out of energy (the energy of the whole universe) so that would be the limit of temperature. But temperature is proportional to the jiggling of the particle but the particle cannot move as fast as light so i used an equation from thermodynamics from Kinetic theory of gases which suggests that: So i figured the limit of Temperature would be : Can you follow this possibly crazy train of thought? Please explain to me: Does temperature have a limit? If so what is it?


I am trying to find the correct opposite of a delegate in the context of a person being a representative of someone else that have allowed or chosen them to be their delegate. What would you call that "someone else?" The only word I could find is a delegator (which isn't a real word in English) or assigner, but they are technical words rather than descriptive. Any other word I could use? Think of it in a sentence like this: Here is a list of all the delegates in the company. But that is the list of their _ _ _ _ _ (what can go here?). I am trying to avoid fillers such as: bosses, agents, managers, etc.


How can I visualize Lorentz transformations? I know it's four dimensional, but without a visual picture in my mind I can't understand any of this. For example how do: Time reflection Space reflection Proper Lorentz transformations Improper Lorentz transformations Homogeneous Lorentz transformations Orthochronous Lorentz transformations Antichronous Lorentz transformations look like? I don't have any idea about how they look like. Maybe this can be explained with Minkowski diagrams or in some other form.


Question: If air was significantly compressed, and then the force compressing it suddenly disappeared (no container), what would happen? Side Question: I'm imagining significantly compressed, but what kind of pressure would be necessary for that? Thoughts: It has been a while since I took chemistry and physics, but what I think is that it would rapidly expand and exert similar pressure to whatever the container was exerting on it in all directions? So similar to what an explosion from heating gas or what not would do?


In my dialect of American English, the word "tush" or "tushy" is a dimminuitive of "rear end" (e.g., something you'd say about a baby, not as harsh as "butt" and a word you aren't ashamed to say to your mother). The word derives from Yiddish, and I am from a Jewish family in the New York area, so I'm generally understood when I say it. How broadly is this word understood? What do folks who don't use it say in its stead?


What is the best strategy to survive a free fall naked out of a jetliner at cruising altitude (ignoring temperature)? For instance, my strategy would be to streamline my fall so that my terminal velocity was very high. Then at some critical distance above the ground I would pitch upward and attempt to use my forward velocity to achieve lift. Presumably this would slow my fall to some survivable speed. (This is roughly what the space shuttle does after all.) Would it work? And idea if it would be survivable?


My question is this: suppose we create two different standing waves in a string . So, is the energy of the standing wave dependent on the frequency of the wave ?(assume that the amplitude is unchanged) My guess is this: the energy of the standing wave is equal to the sum of the energy of the individual waves. Since the energy of individual waves remain the same( as the amplitude is constant) , the energy of the standing wave remains constant too. Am I right?


What do you call the practice of using (overly) complex words specific to a subject? I am thinking of scientific or academic fields where the common terminology used in the field is very unapproachable to someone not in the field. The situation I am imagining is when one professor gives a lecture using field specific language and the topic seems very difficult to approach to the lay person. On the other hand, another professor may give a lecture conveying the same information using terminology and phrasing easily understood by outsiders. Is there a word to describe this difference in style practice?


"I would like to talk today about what I think is one of the greatest adventures." In this sentence, is "what I think" is used like this "I would like to talk today about what, I think, is one of the greatest adventures." or like this? "I would like to talk today about what I think is (the thing I think is) one of the greatest adventures." Any explanations please? Which is correct?


I was going through the book HANDBOOK OF PRODUCT GRAPHS by Richard Hammack, Wilfried Imrich, and Sandi Klavzar. In the preface section, application of direct product of graphs is mentioned. I am interested in gaining more information about the real life applications of other graph products. Can anyone suggest me a link or good book as a reference? This will be very helpful to me. Thanks a lot for giving time.


I am interested on drawing (I suspect that using pgf/tikz is one of the easiest ways to accomplish this) a picture like the following one It is supposed to be a grid of the plane (I only care about the points with natural coordinates), where there are some "red bags" which contain some of these points , and there is a region that is coloured on yellow (one of the red bags corresponds exactly to the points in the yellow region). Any idea about how to use pgf/tikz to draw something like this?


The following sentence is from a mathematical lecture note here: It takes a little bit of getting used to the idea of a function that cannot actually be evaluated at any specific point, but with some practice you will find that it will not cause any significant conceptual difficulty. Is there anything wrong with this sentence? I guess it is supposed to be "It takes a little bit of time for getting used to the idea...". Any idea for understanding the sentence?


I would like to know about the larger picture, current state and future prospects of the sequence of papers that were written by Sheldon Katz and Cumrun Vafa on F-theory. (Freddy Cachazo was also a co-author in many of these papers) I guess the same is also known as "geometric engineering". (Kindly explain if that is not the same) There have been recent works on F-theory by Cumrum Vafa, Jonathan Heckman and others. I would like to know of how this recent work fits in with the earlier work by Katz and Vafa and where do people see this pursuit to be going and what does the community think of its future prospects. Are these Katz-Vafa works a prospective field for beginning grad students?


Lots of people have wondered why English seems to be one of very few languages with such irregular spelling, far from its pronunciation. The answers include the Norman invasion, and the Great Vowel Shift. Ok, cool. But why did all those other languages not have the same thing happen to them? German, Spanish, Italian, all Slavic languages, etc. They don't have a silent 'e', they don't have the day/date poke/soak treat/tree vowel dualities, etc. They still ascribe vowels the same sounds they ascribed them many centuries ago. Is it because England had more trade contact and colonies? Or because they're on an isolated island? Or why?


I'm trying to figure out the angle between the direction to an objective point relative to a player looking a certain direction. This will be used in making a direction indicator for a game. Here's a diagram made in Geogebra that shows the scenario Updated diagram to avoid confusion I have X,Y coordinates of the player and objective and I have the rotation of the player to work with.


Say, you buy some new office furniture. You get the furniture parts delivered including the service to put the different parts - for example the desk top and the desk legs - together to complete furniture ready for usage. Is the person who carries out this service called "Assembler", "Installer" or "Fitter" and is his service called "Assembly", "Installation" or "Fitting"? Are the words interchangeable? Do they have different connotations? Are there other contexts where they are not interchangeable?


I am searching for math competitions for college students. Of course I am familiar with Putnam, but I am looking for a lower ranking competition. Either US-national or regional (South/Texas). I tried this list but my first three links were stale. So I thought I ask a live audience. If you have organized such competitions for your students I would like to hear your reviews and rankings. Also, if you have used high school-level competitions for university students I would like to hear your views about that as well.


I've been pondering over a questions from a while. Please forgive me if I am being too naive. We all know that because of Pauli's exclusion principle no two electrons can populate one state. This prevents the electrons from being collapsed into nucleus, as explained here from the anti-symmetric nature of their wave functions, also as explained in a comment by ACuriousMind. Is there any simple man perspective (classical analogue/picture) why there should be any such principle in the first place?


One of my relatives had a probability question that they asked me that was a little puzzling... What do you think? Can anyone explain how to do a problem like this? A container has six yellow marbles and nine black marbles. Ruth and Dave each start taking a marble. They choose these marbles at random and Ruth was the first to draw a marble. If they do not replace any of the marbles, until one of them get's a yellow marble. What is the probability that Dave will be the one to draw the yellow marble. If anyone could explain how to do a problem like this, that would be great. Thanks!


Just like the previous question, Even I have been studying Hawking's A Brief History Of Time and even I was thinking of Einstein's General Relativity. But I was unable to accept his view of GRAVITY. I have been working on a theory which needs that Gravity effects Light. And so my question is that, Is there any kind of mass for Light? as it was being effected by Gravity? Excuse me if any mistakes were done. Plzz answer me.


I am in a serious doubt about it. Consider a battery of emf E and we connect it to an inductor. Initially the switch is open, now we close the switch. My question is: What mechanism happens just after closing the switch? When we close the switch, the electric field produced in the conductor by the battery causes the electron to flow in the inductor. As the electrons flow inside the inductor, the flux changes and an emf is induced, my question is that how is this induced emf Ldi/dt is equal to the external emf e, not simply by saying Kirchoff voltage law but by the mechanism happening that it should be E only?


How do molecules absorb and retain heat, and how is that heat able to still affect nearby molecules? On Venus there is a green-house effect where the large, dense Carbon-Dioxide atmosphere absorbs heat from the sun and traps it- but how does that occur? What is the interaction between light and a molecule which causes heat to transfer and be trapped? Thanks for your time! Sincerely, Sigismund


In AmEng vernacular, is the word tab specific to restaurant and bar checks, or can it also be used for hotel bills? E.g. Guest: We'll be checking out early tomorrow morning, so if it isn't too much trouble, I'd like to close out my account right now. May I get the tab, please? Front Desk: Certainly, Mr. Smith. Just one moment, please. I'll print it out for you. tab: A creditor's statement: bill, check M-W chiefly US and Canadian A bill, esp. one for a meal or drinks Collins English Dictionary informal, chiefly North American A restaurant bill: the waiter brought three drinks and a new tab ODO


I would appreciate any suggestions for book or notes on ANT at a level that I would characterize as advanced beginner. I.e., something assuming familiarity with topics in Dummit & Foote, that is a little less than Samuel or Marcus. I would especially like accessible discussions of topics such as fractional ideals, ramification, and ideal classes. Any suggestions would be appreciated. (I have seen several enthusiastic endorsements of Stewart and Tall.) Thanks.


There are words to modify justifications or reasons given. One means "the real motive", and the other means "a plausible explanation, but not the true motivator". I searched quite a bit, but was unable to find anything. I think one of the words is like "obstinate", but not that, and now that it's in my head, it's all I can bring to mind... Does anyone know the words I am trying to think of?


I wrote this sentence: Living a busy life, full of stress, sweat and sacrifice, can make us think that we are actually doing something worthy with our lives. Which is actually saying is that being busy can give us the illusion of doing something worthy with our lives. Is it clear enough or ambiguous (is it possible for the reader to misunderstand this sentence as "being busy really makes our lives worthy"?)?


This question is a follow-up of Macro: Replace all occurrences of a word, but I would like the same for different colours, that is to have different pre-defined sets of text strings which will be coloured in a predefined way, where the colour depends on the set they are in. Requirement: Each string should be able to include spaces and/or punctuation marks (e.g. a string could be foo's foo doesn't foo). Edit: I was asked to provide a MWE, and while I was making one, suddenly I achieved an answer which I failed in creating before. Trial-and-error-and-trial-and-success.


This answer of mine has been strongly criticized on the ground that it is no more than a philosophical blabbering. Well, it may well be. But people seem to be of the opinion that HUP alone does not ensure randomness and you need Bell's theorem and other features for the randomness in QM. However, I still believe it is the HUP which is all one needs to appreciate the probabilistic feature of QM. Bell's theorem or other such results reinforces this probabilistic view only. I am very much curious to know the right answer.


They most often come as advice on how to solve problems that seem the reverse of what would be expected: In order to think of a solution you must stop thinking about the problem. In order to be a good leader you must know when not to give orders. I'm sure there must be a name in rhetoric at least, they often have the quality of being immediately pleasing or slightly amusing in the same way a joke or a pun does. Sort of like a stronger form of antithesis that goes beyond putting opposites together and suggests the opposite is actually the solution.


I am wondering if someone could provide me with additional information with regard to the so called Yale sparse matrix format, other that what can be already found here: https://en.wikipedia.org/wiki/Sparse_matrix In particular, which specific programms make use of it? Which (research or practical) goals does it achieve as compared with other options? Can it be considered a standard way to make a sparse matrix out of a dense one? Thnaks in advance.


Consider the situation when a cell of an unknown emf is being measured using a potentiometer. We slide the jockey so as to obtain the null point. Now, is there any current in the potentiometer wire at the null point? Since we know that there is no current in the arm containing the unknown cell, its terminals have acquired equal potentials,how is it possible that there is any current in the potentiometer wire when that is in parallel to that cell. Potential difference across AB= Potential difference across CD?


Oxford defines "close" thus: Adj (With reference to a competitive situation) won or likely to be won by only a small amount or distance: "the race will be a close contest" "she finished a close second" My question: Based on the same sense of the word, can I describe the 'difference' or the 'differential' between two numbers or amounts of something as 'close'. For example: The differential between what you owe and the credit you have is close. The difference between their numbers of followers on Twitter is close. Does this sound nearly native? If not, what would be? I know we usually say "small difference" but I wonder if 'close' would be more effective, especially in the second sentence.


I was wondering if Quantum Fluctuations are completely unpredictable, but do our observations tell us if these fluctuations happen evenly through space or are there regions where more quantum fluctuations occur than others? If they are completely unpredictable and are forming at specific places, could this be reasoned why they are being created in these areas MORE than in other areas of our universe? If possible can you present any observations or any evidence, for your answer?


I would like to learn exterior algebra, wedge product and geometric product along with their applications in physics. Is there a good source you can recommend? Should I study differential geometry in order to grasp them? I started studying tensor analysis but even the concept of contravariance and covariance is not explained well enough in most of the textbooks. I would be grateful if you point at a source that guides one well and assumes no prior knowledge of the topics except calculus and linear algebra.


The dot is placed in a position that is relative to the other dots and the timing as to when the item was posted I'm okay with the first half of this sentence (the part before and). I'm wondering if the second half is a legitimate ellipsis here. If so, how does it interact with the first half? In other words, what could be the full form of the entire sentence?


I'm writing a document in which I need to state that my work is unsupervised instead of supervised. I have thought in these two sentences, but don't know whether they are correct, or whether is there a better one to explain this situation. "from an unsupervised decision making point of view" "with an unsupervised decision making approach" also, what's the correct way, "decision making" or "decision-making"?


Should I use a comma before the word who? This sentence is confusing me: I made this blog because I want to help all of the other people who have problems that are similar to mine. If I did use a comma in that sentence, then what would be the benefits & disadvantages? In what cases should a comma be put before the word who?


In granulometry, say I have a tube with an heterogeneous mix of particles of different sizes (sand and stones, by instance). The tube is vertical in the usual gravity field and is placed in the air. If I randomly shake the tube, the smallest particles will eventually be at the bottom, and the largest ones at the top. So the particles are now sorted by size. Why? A friend of mine considers a volume of the bottom part of the tube has a greater density (or mass) than of the top's. And denser things go downward. I consider however, by shaking the particles, small ones can fall through the space left between larger ones. What is the correct explanation?


What is the word that means a 'what if' phrase? In a college course, I vaguely remember, the instructor wrote a word on the board that loosely meant or perhaps described any sentence that was a what-if statement. If I remember correctly it was essentially a word for classes of phrases, like say an appositive phrase. It was a more technical word, not something common like hypothetical, and for the life of me I can't recall it. Any help would be much appreciated.


If a set is closed and open, it may be bounded (e.g., the empty set), or it may be unbounded (e.g., the set of real numbers). But what about a closed set that is not open? Such as: a singleton a set of finite points a closed interval the union of a finite collection of closed intervals the nonempty intersection of an arbitrary (possibly infinite) collection of closed intervals These are all examples of closed, non-open sets, and they are all bounded. Prove that if a set is closed and non-open, then it is bounded; or disprove by providing an example of a closed, non-open set that is unbounded.


I plan on asking my professor what he meant by "average continuous function," but as it is possible that this is a concept as vague as the statement, I was hoping to get some interesting answers/interpretations from stack exchange first. How do you think of the average of some infinite group of things? Or does this just mean that the real line is so dense/big that it is somehow likely that a function would bounce around everywhere except on some countable number of points? I'm sorry this is vague, I will be sure to post his response if I get a good one. I would also appreciate any resources or reading; googling around hasn't been fruitful.


In a global company, I often need to address someone in another country without knowing his/her gender in emails with a third person or with a group of people. It's awkward and inefficient to spell his/her name every time in reference of this person, especially if it's a long name. The only solution seems to find out the person's gender after all. If I have to do so, using emails only, Should I ask someone who knows him/her or should I ask the person directly? Personally I feel awful to approach the person with this kind of questions. How should the question be worded to be appropriate? Examples? Please indicate the culture background of the answer if you don't mind.