darklight03/StackMIAsub huggingface dataset:
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.