darklight03/StackMIAsub huggingface dataset:
What are the differences between "unto" and "to"? It seems that in many contexts where the word "unto" is used, "to" could be substituted and would be perfectly correct. It reminds me of flammable/inflammable, where "flammable" came into use because the "in" in "inflammable" caused people to think that it meant not inflammable. Is this a similar situation?
Is it possible that the universe is infinitely large and contains an infinite amount of mass that is distributed in such a way that gravitational force is never infinite? If so, is it possible that the infinite amount of mass that is outside of our light cone could affect us with gravitational force?
Which one is correct? I am a new graduate and have been teaching German for a few weeks now. I am a newly graduate and ... I can't decide whether to use "new" or "newly".
I have noticed the appearance of the phrase "not so much" in the language recently. It strikes me as both grammatically incorrect and humorous when used. For example,"Jim is very smart; his brother, not so much." Or,"That girl has a beautiful face; her figure, not so much." Has anyone else noticed this new colloquialism?
I'm having trouble understanding how to find an invariant to check if it's preserved, and generally how induction is used in proving the correctness of algorithms (binary search primarily, but others as well).
I'm doing a science project, and we're wondering if it is possible to compress pure carbon (C) to the point where it becomes diamonds? What would the process have to be and how much energy would this take? Has this been done and is this feasible?
Prove that any graph that can be obtained from the Petersen graph by adding one extra edge has a Hamiltonian cycle. So I've found that removing any vertex yields a Hamiltonian cycle -- I'm not sure if that's relevant or helpful, as I wasn't able to link that to the main question above. I thought I'd include that in case though.
Are both "an hour and a half" and "one and a half hours" correct? If so, is either more appropriate in different contexts? Example context: "The Superbowl starts in less than one and a half hours." "The Superbowl starts in less than an hour and a half."
Does anyone have a link to Hilbert's Original Proof of the Nullstellensatz, or know a book where it's printed? I'd be interested to see what it was like. I only really know the Noether normalisation and Zariski proofs. While these are both good, it would be nice to have it 'from the horse's mouth'! Many thanks in advance.
The term "ginger" is often used as a slang term for someone with bright red hair. But ginger (the spice) is actually a bright yellow in color. Where does this term come from, then?
I have been trying to understand clearly the concept of non locality, hidden variables, quantum measurement etc through research papers. I also read Quantum Theory and measurment by Wheeler and Zurek but I feel I've got nothing into my head. Please recommend some introductory books on above mentioned topics for beginners.
I have been trying to learn some basics of topology on my own, I have learnt the basic definitions. I have not been able to understand the proof provided in the text. Could anyone provide a clearer proof, or kindly explain me the outline of the proof provided here?
In a commutative ring (with unity), is it true that (a) any maximal ideal is a prime ideal? (b) any prime ideal is a maximal ideal? (b) is almost certainly false, because a maximal ideal is a stronger concept than a prime ideal, but I don't know of any example to give. And I'm not sure about (a).
An orthogonal matrix necessarily has orthonormal columns, and orthonormal columns necessarily give an orthogonal matrix. Also, orthonormal columns imply orthonormal rows. But how about the converse of the last statement? Meaning, do orthonormal rows necessarily imply orthonormal columns? Thanks
I wanted to know what is the typical strength of the magnetic field generated by the tip of a magnetic screwdriver, but couldn't find it anywhere on the manufacturers' webpages. So I was wondering, is it possible to estimate it from the sort of objects that a magnetic screwdriver can pick up?
I just want to confirm that I am right about these expressions. The "foot of the stairs" is the bottom of the staircase, and the "head of the stairs" is the top, correct? Are these expressions commonly used? Or is there a better alternative?
The speed of light in a medium is independent of motion of source relative to medium but it depends on the motion of observer relative to the medium. I don't understand why it is so.
I'm working on an app which displays status messages, like: "XY is now available" "XY is now offline" I'm wondering which of the followings is correct: "XY is now idle" "XY is now idling"
Is there a word or phrase to describe someone who is willing to do extra work in the short term to avoid work in the long run? I have seen "lazy" used for this, but I'd like to know if there's a more precise term.
In our daily life a lot of photons of visible light, infrared and radio etc move around us. We know that light is an electromagnetic radiation. So why doesn't that electromagnetic radiation affect a magnetic compass?
Is there a word or expression describing a phone call when the caller doesn't hang up, but also doesn't say anything (or at least nothing can be heard)? I'm specifically looking for a term describing such call made to scare someone (with the caller breath being heard). My initial thought was that it's called silent call, but according to Wikipedia it means something different.
"If matrices B and AB have the same rank, prove that they must have the same null spaces." I have absolutely NO idea how to prove this one, been stuck for hours now. Even if you don't know the answer, any help is greatly appreciated.
I am an absolute newcomer when it comes to quantum physics. So kindly suggest me a book which covers all the fundamental ideas, equations and all such stuff related to qp, so that i can master the basics and then move on to the advanced stuff.Thank you.
I have recently read the proof that the Brownian Motion and Fractional Brownian motion are almost surely Holder Continuous. I was wondering if this can be extended to a higher class of continuous stochastic process, is there a characterisation of such class? Is this class much bigger than the Brownian Motion/ Fractional Brownian motion? Maybe even the whole set of continuous stochastic processes?
I am studying finite element method.While studying i am confuse with numerical integration and interpolation.Is this two methods are same or different?. If they are different then is there any relation between them?.
I need some help understanding Gaussian mixture models. In particular, I am trying to find the relationship between GMMs and K means. What is the basic algorithm for GMM? I am not sure where the "clustering" comes in. Can someone give me a basic example as to how this actually works?
I'm currently prepping for some high school math competitions soon, and I was wondering if anyone knows any resources that are out there with an abundance of contest-math-related geometry problems. Geometry is definitely my weak point in contest math, and any input would be appreciated. Thanks!
How come the following sentences have the same meaning when they have different voices? I can be substituted for John. (Passive) I can substitute for John. (Active) They both mean "I can replace John."
I am studying a function whose Fourier transform is zero on a set of strictly positive Lebesgue measure and I need to know this: If a set has a strictly positive Lebesgue measure can we prove that it contains an interval? Help is much appreciated
Please describe how a vacuum flask/thermos works. How does the vacuum prevent convection/conduction/radiation? How does the lid with the curvy lines prevent either of the aforementioned heat transfers? If there are any other parts that may prevent heat transfer, please also list them.
I'm trying to show that the quotient of the Heisenberg group with it's own center, H/Z(H), is abelian. I'm not entirely sure what makes up this quotient group in the first place though... and I'm a little confused as to what quotients of matrix groups with multiplicative operators look like. Help, thanks
There has been a similar question before: How to convert a hexadecimal number to an octal number? But, in my case I need an Algorithm to directly convert a number from Octal to Hexadecimal and back without converting it to binary/decimal as an intermediate step. Is it possible?
Gentlemen, thought my practice in solving Gauss Jordan elimination questions, I faced this question and I got stuck in it for quite long time, and I couldn't figure out the answer. Could you lend me a hand in solving this question. Thank you!
Someone recently pointed out to me that most English-speakers will say "I saw a big brown spider," rather than "I saw a brown big spider". However, the second sentence has the same literal meaning as the first. Are there instances in which adjectives are non-commutative, so that permuting the order of the adjectives changes the literal meaning of what's being said?
I've read that attraction and repulsion between particles is caused by the exchange of virtual photons, and that virtual photons carry information. I don't understand how a virtual photon actually causes any attraction or repulsion, and how does it carry information anyway if it's "virtual"? Aren't photons an excitation of the electromagnetic field?
Why is the standard for implementations of the AES algorithm called "Rijndael"? Is it simply a name? Or has it some kind of meaning? I tried googling this one, but without any helpful results.
From the linear algebra books that I've encountered, they either discuss exclusively about finite-dimensional vector spaces, or assume that the reader already knows about infinite-dimensional vector space, Hamel basis, etc. What books explain the concept of infinite-dimensional vector space and its structures?
In Dutch we use it to refer to (the airtime of) tv-shows that start around dinner. Is there an equivalent to it? I suppose it's sort of an idiom, but probably too specific to be considered so.
I would like to measure the energies of particles emitted from a variety of ionizing radiation sources (alpha and beta), and then convert these energies to velocities. However, I am not too sure about how I might go about measuring these energies. Would this even be feasible? If so, how could it be done? How are these energies measured by professionals?
Are there any integral domains in which no nonzero prime ideal is finitely generated? (Other than fields, of course, where the condition is vacuously satisfied.) I asked a similar question the other day, but the solution there relied on using zero-divisors and that didn't really help clear up the situation I was considering.
If I have an ordered set X = {a, b, c} and another ordered set Y = {a, b}, I know that that Y is a subset of X but I also want to convey that Y is the prefix of X if that makes sense. Is there a name for that?
The Great Dark Spot is an anti-cyclone in Neptune. But unlike the Great Red Spot of Jupiter which lasts for more than hundred years, the Great Dark Spot exists for only one year or so. Why is it so??
I was attending my college re-union and a speaker just said that "Having an ebook reader is status quo". Apparently, it means that it is in vogue or in fashion. I do not think it is the correct usage. But I am a bit confused. Can someone clarify?
I know from reading about the gravitational waves detected by Ligo, that when an object has angular acceleration, it produces gravitational waves. I'm wondering if an object creates gravitational waves when only accelerating in one direction, however? I'm also curious as to how the nature of the waves would differ in this case.
Possible Duplicate: What is the correct way to pluralize an acronym? How would you make the plural form of an acronym? For example, if you have two of Nintendo's game console, the DS. Would you say, "I have two DSes," "I have two DSs," or something else?
I am going to send a email to a secretary of a CEO thanking her for scheduling a meeting. What would be a good phrase for the opening of email? Should I write: Thank you for scheduling the meeting or would it be more appropriate to write: Thank you for accommodating our request
Recently, I am interested in the Hecke algebras, but I'm not very familiar with it. Who can provide me some meterials about the history and the development of the Hecke algebras? Is there any good books or papers about Hecke algebras? Any help will be appreciated.
When you get an error in LaTeX, the message "Undefined control sequence" is printed. Why is it called "control sequence" and not "command", for example? How does the sequence work? Is this a TeX or LaTeX thing?
I'm an Android programmer and am working on a graphing calculator. I have been looking for a formula for sine and cosine to put in there. I have a decent understanding of mathematics but can not seem to find this formula. Any help would be great, thanks.
I am having difficulty in understanding about weighted linear least squares. Could anybody explain me instead of minimizing the residual sum of squares why we need to minimize the weighted sum of squares? Further, I want to know about the term weighted? Although I have gone through some wiki notes but I am not able to understand. Thank you very much for the help.
I just downloaded and installed MikTex and TexMaker today, and was wondering if you have any advice. I'm starting to read through various wikipedia tutorials, and other guides, but videos would be an immense help!
A and B worked together to complete a certain task in three hours. If A works alone, he can complete the task in five hours. If B works alone, how much longer will it take him to complete the task? I have the answer to this question, but I just don't get how that works. Please help me out.
Most important theorems in measure theory do not assume the completeness of measure spaces. Monotone convergence theorem, Dominated convergence theorem, and Fubini's theorem, to name a few. So I wonder if the completion of a measure space is necessary. In particular do we need to consider Lebesgue measurable sets which are not Borel sets?
When i put a pencil in the middle of a paper and rotate it very fast, whatsoever is written on it, will appear in concentric circles. What is the reason behind this phenomenon and what is it called?
The variational method, as it pertains to quantum mechanics, is used to approximate the energies of a particular system. Is it possible to use the same variational method to approximate the eigenvalues of other observables?
I have been searching in vain for statistics about the runtime of pdfTeX, LuaTeX and XeTeX. My impression is that (ordering by increasing runtime), LuaTeX > XeTeX > pdfTeX, but exactly how big is this difference?
In referring to a particular femme fatale, I described her "femme fataleness." That is "ungrammatical" (I believe) but got the point across. Is there a correct term for this particular attribute? If so, what is it?
I'm struggling to understand how to define multiplication and addition, now that I've been told that multiplication is not just repeated addition. It seems that the axioms for the two are identical, save that multiplication is said to not have an inverse for the additive identity. Doesn't this imply that multiplication cannot be defined without an addition?
I know that any Riemann integrable functions have at most countably many discontinuities, and similarly, any bounded functions with countable number of discontinuities are Lebesgue integrable. But is it necessarily true that any Riemann integrable functions have at most countably many discontinuities? Thanks
I see that you can use a Stern-Gerlach apparatus for massive particles that can be deflected, but that doesn't work for photons. What would you do instead to measure photon spin in a lab?
I would appreciate it if you could explain to me the difference between implementing and executing in the context of the following sentence: The implementing agency(ies) for this project is UNEP and the national executing agency is the Department of Environment.
Can you please clarify for me which is the correct answer to the following question: Do you often have visitors? a. Yes, pretty much every day b. Yes, quite often c. Not very often.
As the title says it, I want to know how people find the work function of a metal without knowing the threshold frequency. Yes I've already searched on Google but I didn't find anything really relevant. I just found how to calculate Work function with threshold frequency.
I was given a piecewise function, which happens to be continuous on some interval. It asks me to prove that it's Riemann integrable. I know that continuous functions are Riemann integrable, but is there a way to prove it for some specific function (without using that theorem that continuous functions are Riemann integrable)?
For any graph G, prove that the line graph L(G) is claw-free. I have a fairly good intuition for this one but it's hard to put into words. I really need help with this one! I feel that I should use the pigeonhole principle...
This integral comes from a physics book when calculating a field of an uniformly charged sphere (without Gauss' Law). It says that it can be done by partial fractions, but I cannot imagine how.
Question: Prove that at any given moment, there exists a pair of diametrically opposed points on the equator of the Earth that have the same temperature. Use the Intermediate Value Theorem. Now I've been kinda struggling with how to deal with the Intermediate Value Theorem and I have no idea where to even start on this one.
You can visualize a first-order Markov chain as a graph with nodes corresponding to states and edges corresponding to transitions. Are there any known strategies to visualize a second-order Markov chain, i.e. where transitions have two past elements and one future element?
In graph theory, what is the difference between a cycle and a simple cycle? My impression is that a simple cycle is the same as a cycle except that you cannot repeat vertices. Is this correct?
I have been searching in the literature, with no results, for the (Zero Field) Magnetic Susceptibility of BiSCCO, but I cannot find any article regarding that. Does someone have a reference that might be useful to me? Thanks a lot.
Consider a recursive Mergesort implementation that calls Insertion Sort on sublists smaller than some threshold. If there are n calls to Mergesort, how many calls will there be to Insertion Sort? Why? Wouldn't this depend on the threshold, or is there another way to look at this?
Does "feel committed to" require an infinitive or gerund complement? For example, which of the following is grammatical? I feel committed to following up on that. I feel committed to follow up on that.
Even if Lebesgue measure and integration can be defined without using the extended reals, it might not be a very helpful formulation. My motivation for asking this question is that I'm curious about in which ways Lebesgue integration is an extension of Riemann integration, which doesn't necessarily use extended reals.
The Cayley table tells us whether a group is abelian. Because the group operation of an abelian group is commutative, a group is abelian if and only if its Cayley table is symmetric along its diagonal axis. Sorry, but why is this true?
What is the difference between pull over and pull away? I am still trying to get used to American English. It seems like if I do not understand the driving vocabulary I am going to fail in the driving test.
What's the difference in the usage of these two adverbs continuously and continually? Here are some examples: a) She was told off for continually being late. b) It rained continuously for three hours this morning. c) The firemen worked continuously through the night. d) I'm afraid you continually make the same mistakes.
Does adding the word "ok" to the end of a statement imply a choice instead of a command or order? Example: "Wash the dishes now". as opposed to "Wash the dishes now, ok?" Does this weaken your statement?
The four major cities in the Netherlands, i.e. Amsterdam, Rotterdam, The Hague and Utrecht belong to the Randstad. What is the English translation for the Dutch word Randstad? I have found downtown but I wonder whether this is the correct translation.
I was wondering about discrete metric space. Is it a proper metric space? I am trying to find some example of non proper metric space. I am not sure whether discrete metric space is proper or not.
Possible Duplicate: Why is matter drawn into a black hole not condensed into a single point within the singularity? When we speak of black holes and their associated singularity, why is matter drawn into a black hole condensed into a single point within the singularity?
I've heard a lot about the CJK package, so I want to give that a try. There is, however, no documentation for that package (see the link), nor do the available documentation files at CJK's website tell me anything about how to use the package. So how do I figure out how to use this package?
In my physics textbook it describes the events at the beginning of the Universe. I'm confused about the order at a certain point. It says that at some point primordial helium is created, then it says that later atoms are formed. Isn't primordial helium made of atoms? Thank you :)
Will we ever come up with non-gender specific pronouns and possessive pronouns for the English language? It seems that there are many new words in the English language every year, so why not gender-neutral pronouns? This would solve many problems, in literature and in everyday life.
Which would be better to say? He reminds me of Dill from To Kill a Mockingbird. He reminds me of Dill in To Kill a Mockingbird. He reminds me of Dill of To Kill a Mockingbird. Also, which is more appropriate in a formal context?
Possible Duplicate: What are your favorite English language tools? I have a question regarding the English language that is too general for this site according to the faq. OTOH, I don't know where to look for the answer. Is there a list of sites, books, etc. that are commonly used to answer questions?
While playing around with cyclotomic fields, I started to wonder about taking the roots of unity in higher dimensional analogues of the complex plane. Are the roots of unity well defined in the quaternions, octonions, and other hypercomplex algebras? Are there higher dimensional cyclotomic fields, and if so do they have any interesting properties like unique factorization or interesting morphisms?
Do the Law of Sines and the Law of Cosines apply to all triangles? Particularly, could you use these laws on right triangles? That is, could you use these laws instead of the Sine=opposite/hypotenuse, Cosine=adjacent/hypotenuse, and Tangent=opposite/adjacent rules to solve right triangles? I can't find this stated in any of my textbooks, nor has my instructor said anything about it, which I find odd.
Is there any difference between the following two statements: I have to pay bills I have bills to pay Could you please tell us the difference between the above two statements and when to use them?
I've always found it irksome when people form sentences such as "I'm done my homework." It is of my understanding that you are never done something, but rather you are done with something. Am I right to be bothered by this?
I'm told at school that the Electromotive Force (e.m.f) of a battery equals the potential difference between the terminals of the battery when there is no current. How is that possible? How can there be a potential difference with no charge flowing?
How do you exactly define what is and isn't a dimension? I heard somewhere that it is "anything you can move through" but if that is right, why wasn't time and space considered a dimension before Einstein?