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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 th...
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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 a...
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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 t...
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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 m...
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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...
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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 i...
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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 disjoin...
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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-b...
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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 bla...
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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...
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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...
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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 se...
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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, be...
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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 ra...
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"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 ...
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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...
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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 ...
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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, be...
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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 spec...
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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...
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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 ...
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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...
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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 co...
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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 ag...
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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 speci...
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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 ther...
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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 ...
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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 r...
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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/pe...
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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 igno...
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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'...
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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 t...
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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 po...
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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 wond...
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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 tha...
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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...
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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 coul...
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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 ...
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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 fu...
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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 ...
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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 com...
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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 int...
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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 ...
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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,...
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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, jus...
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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 r...
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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 sole...
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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 t...
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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 ...
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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 exis...
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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 veloci...
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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 shor...
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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 in...
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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 ...
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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 workaroun...
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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 learni...
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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 demonym...
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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 ma...
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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 ...
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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 mov...
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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...
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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...
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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 wikipedi...
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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...
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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 inter...
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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 incr...
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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 (...
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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...
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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 translate...
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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...
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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 me...
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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. ...
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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 natu...
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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...
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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 we...
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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 ...
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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 ...
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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 i...
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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 app...
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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 s...
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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 p...
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"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 misinter...
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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 el...
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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 ...
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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 origin...
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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 w...
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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? ...
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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 ...
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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 h...
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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...
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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 di...
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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 passwor...
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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 ...
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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 le...
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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 env...
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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 ...
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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 po...
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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 the...
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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 dir...
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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...
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