darklight03/StackMIAsub huggingface dataset:
I was wondering if there is a non-geometric interpretation of the dot product (or the inner product more generally). That is, an interpretation that has no concept of length and angle. My motivation for asking this lies in how, in quantum mechanics, the inner product between the bra and ket vectors are often taken. However, these vectors do not represent spatial concepts, but are rather, a vector containing probabilities (which isn't a spatial concept). Thanks for any help!
What is the way to say that something "should be done" in the past? I know there is a "should have" structure, but it is used for situations, when something was to be done in the past, but it wasn't. E.g. "You should have called me yesterday. Why didn't you?" So, would it be correct to say "It should have been done" in a situation when something was to be done and in fact it WAS DONE?
I was explaining it's vs. its to someone the other day, and I said "None of the pronouns (his, hers, theirs, yours, its, whose, ...) has an apostrophe." Later I got to wondering whether that was really true, and sure enough fairly quickly found one that does: one's, as in "One's memory isn't what it used to be." Are there other pronouns that use an apostrophe?
It seems to me that "optical" relates more to the mechanics of light and vision, whereas "visual" is a much broader term. For example, hallucinations are classed as "visual" or "auditory", rather than "optical" or "acoustic". Other examples are visual puns, visual cliches, visual metaphors, etc. I notice on the Wikipedia page on optical illusions uses the terms interchangeably. Is there a semantic reason why the term "optical illusion" is used instead of visual?
The sentence I wrote is as follows: The idea behind this technique was that the human eye could not differentiate between the individual colors of each point, thereby causing the eye to blend the colors together to form a more complete image. My professor said that the "thereby" in that sentence should have a semicolon behind it and a comma in front, but as far as I know, a semicolon separates two independent clauses. I don't think "causing the eye to blend colors together ..." is a complete sentence, but she said it should be written as ";thereby,". Is she correct?
I'm having trouble putting the pieces together. In SM, neutral kaon oscillation is heavily constrained. This means, roughly, that the squark mass matrices have to be diagonal. And this is called universality of soft parameters. What exactly is universality and why do we have universality in this situation? Furthermore, is having diagonal squark mass matrices sufficient? In a lot of SUSY theories, they go one step further and assume the scalar masses are the same for the first and second generations (pMSSM for instance). Why is this additional step necessary?
Since it's Friday and others are playing games, here's another one to take us into the weekend. Everyone knows about those Russian nesting dolls (called matryoshka dolls, I believe). A small doll nests inside a larger, which itself is inside a larger doll, and so on. This game does the same with words. You start with a three-letter word, add a letter to make another word, and so on. Longest word wins. The catch? Each additional letter has to form a legitimate word. Here's one to start you off: bur burr burro burrow burrows Good luck.
Is there a word that describes a person who tries to get as much information as possible when making a decision for fear of committing a mistake that might affect both him and others in a negative fashion? The only word I could think of was indecisive, but it has a connotation that suggests hesitation and irresolution when making decisions, which is not what I'm going for, since I want a sense of absolute commitment when making the decision.
Which of the following books is better to prepare for a mathematical competition at the undergraduate level? The art and craft of problem solving (ACoPS) or Problem solving through problems (PSTP). I think that ACoPS doesn't have an abstract algebra chapter and PSTP doesn't have a combinatorics chapter, so, which one would you recommend me to use and why (I can't use both right now)? Thanks in advance!
I'm not sure how to phrase this question. I'm sure I could write it in terms of operators between Frechet spaces, or something like that. Let me apologies to any analysts in advance for my lack of rigor. I'm basically interested in "how many" elementary functions have elementary anti-derivatives. I realize that I ought to impose some conditions on the functions, e.g. differentiable, and on the domains of definition. It would be great if someone could give an answer which puts this question in to the correct language, provide sufficient restrictions and then state any known results. Sorry to be so wishy-washy!
Occasionally, I write letters that I actually print out and send by snail mail :). I'd like them to look as formal as possible. Archaic (pre-typewriter) Dutch customs require the sender's address to be in the top left corner and the recipient's in the top right. The place and date should be aligned with the recipient's address. The sign off ("Yours truly") should also be aligned with that. Of course there are also specific rules for the amount of vertical whitespace. Does anyone know of a good package that lets me customize all this stuff, preferably in a .sty file or something that I can include, so I don't have to do it again for every letter?
Are the following two statements written in correct grammar? What do they mean? Can they be written in more easily understandable manner? If yes, how should they be re-written? The student's pass will be issued no earlier than one month from the course commencement date. This letter will be valid for two months or till the course commencement date as indicated above, whichever is later.
In a formal letter addressed to one or more unknown recipients, "Dear Sir or Madam" is the customary salutation. As a German native speaker, who is used to "Sehr geehrte Damen und Herren", writing "Sir" before "Madam" sounds impolite to my ear and I feel the urge to change the order. I know that I must never directly carry over conventional expressions from one language to another, but it makes me wonder: Are there any differences between "Dear Sir or Madam" and "Dear Madam or Sir"? In particular, would the latter sound more polite or rather come across as outlandish?
Ok, so here is an example sentence. "I hoped to lose the race so I wouldn't have to run against him." Here's my dilemma. I was questioning whether a comma was necessary after "race" to separate the two independent clauses connected by "so," the coordinating conjunction, but then it occurred to me: Is "I wouldn't have to run against him" an independent clause, or is it dependent? If it were standing on its own, would it be considered a fragment? Can someone please explain?
I have been googling around, searching for the origins of the phrasal verb "to fall asleep" but so far I have found no references. I was wondering specifically why we use the verb "to fall" to characterize the process of going to sleep and my conjecture is that it somehow links in with the connotations of tiredness and fatigue that the verb "to fall" bears.
The Feynman Lectures on Physics probably constitute the most famous introductory physics textbook ever written. The level of intuition it provides is hard to beat; I first started reading it in middle school, and a decade later I'm still finding new insights in it. Yet when I recommend it to others, they often have sticker-shock. It is a three-volume book, after all. So is there any legal way to read the Feynman Lectures for free, on the Internet?
When passing someone in the hall, you might say "How are you?" as a greeting, but not meaning it literally, as you don't really require an answer. Is "How are you?" (or "How's it going?", etc.) an idiom when used this way? "Idiom" doesn't seem appropriate because that combination of words generally has the literal meaning. Is there another word for this? Sorry if I am not making this clear. If I can clarify in some way, please ask. Edit: Could someone explain why this question might have been voted down? Not complaining, just trying to learn.
I want to know which of the following would be the correct way to phrase my sentence, pasted below. I've come across this problem several times in my writing and want to settle this for good so that I don't always second guess myself: "When he learned of the sins he had committed, Oedipus blinded himself as punishment" or "When Oedipus learned of the sins he had committed, he blinded himself as punishment" Is one of these more grammatically correct than the other, or are they essentially the same? Is there a general rule for phrasing such sentences?
In Australian English there has always been a distinction between "pissed" (intoxicated) and "pissed off" (angry, irritated). I've noticed a trend towards the American usage where "he was really pissed" is now much more likely to mean the latter. I'm aware of the futility of resisting the natural evolution of language, particulary the juggernaut of American language imperialism via films and TV, but it seems a shame that "I did it because I was pissed" is now ambiguous. Is this a trend in other English speaking countries where the Australian usage was common?
I often try to distinguish between immediate-feedback communication, such as talking in person, on the phone, or by instant message, and delayed-feedback communication, such as email. (Or at least, delayed in the sense that it's socially acceptable to not respond right away.) I usually would say something like, "I'd prefer to discuss this in real-time," which usually gets the point across, but I'm wondering if there is a better way to describe this concept. ("Can we talk about this using an immediate-feedback medium?" sounds a little awkward.)
"What does {holding nose} P.U. mean?" my son asked me tonight. I told him I didn't know, and he laughed and said "It means stinky, Mommy!" Very funny and well said, but it left me wondering. A search of Wikipedia and Etymology Online came up wanting and my etymological dictionaries are packed in boxes. What does this abbreviation stand for and why does it mean stinky?
There is a term orbit insertion which means a maneuver performed by a spacecraft flying by a celestial body in order to become an artificial satellite. What word or phrase would you use to describe the result of this process? And from the following sentences, which are correct? The probe entered the orbit of Mars. The probe inserted into the orbit of Mars. The probe was inserted into the orbit of Mars.
What are some simple proofs that the points on an elliptic curve form an abelian group under addition? I am mostly looking for proofs of closure and associativity, since the other three requirements follow immediately from the definitions. Note that I am specifically looking for simpler proofs, since I am only still in high-school, so I have not learned about homomorphisms and isomorphisms and matrices yet. An intuitive 'proof' will also suffice (since again, it's only high-school level). Also, are elliptic curve points always an abelian group under addition? Or only over the rational numbers or over some finite prime field (and not over the reals)? I'm trying to write a paper/essay on elliptic curve cryptography, but I can't get these proofs to work.
Possible Duplicate: An idiom for deriving pleasure from another's suffering We often experience the following: We feel happy when our fellow classmates get a bad grade and not necessarily when we ourselves get a good grade. We feel excited when our opposing team plays really awful and not necessarily when we our team plays well. We feel pleased when one person we hate experiences some kind of misfortune and not necessarily when we ourselves get good luck. What is a word or phrase to describe the phenomenon above?
My highschool textbook states that Zener diodes are a special type of diode which is made of highly doped p and n junctions, and which can survive reverse bias - unlike normal diodes, which get damaged due to the excess heat produced in that mode. How can heavy doping help Zener diodes avoid damage in reverse bias? Is it that it somehow gets rid of the excess heat produced in the diode? How does it do it?
My textbook doesn't explain this very well, so what I want to know is: What is the purpose of parametric equations? What is a parameter? What is the advantage of these equations over a function y=f(x)? What do they essentially enable you to do? I find this topic to be impenetrable so a thorough explanation in simple terms would be very much appreciated. Thank you.
This question may sound dumb, (it will to me, hopefully, in a day or two!), but does the term phase difference apply only for sinusoidal waves? Wikipedia defines 'phase' as the following: Phase in sinusoidal functions or in waves has two different, but closely related, meanings. One is the initial angle of a sinusoidal function at its origin and is sometimes called phase offset or phase difference. Another usage is the fraction of the wave cycle that has elapsed relative to the origin. I'm confused about this specific part: Another usage is the fraction of the wave cycle that has elapsed relative to the origin Can this definition apply for any wave function, or just sinusoidal ones?
Is there a single word that denotes the belief that women are or should be inferior to men? For example, That ideology advocates murder, rape, slavery, homophobia, xenophobia and [insert the requested word here]. The word patriarchy comes to mind but I am not sure if it fits in the sentence above. I am also thinking of sexism, but it denotes prejudice based on sex, which, although in practice usually against women, can work both ways. Any suggestions?
I am reading about the going-up and going-down theorems in Atiyah & Macdonald's commutative algebra book. I'm wondering if anyone could give me some basic facts/examples to help me understand why these two theorems are so important. Neither of these theorems are actually used in Atiyah & Macdonald, and yet I don't find the statements to be so obviously remarkable that they should deserve a special name.
While I was writing a status update today on social media I decided to do some grammar-learning. The status update was "Happy Labor Day everyone!" and I am now wondering if I should place a comma between "Day" and "everyone?" My grammar skills aren't great, and this may be staring me right in the face as I'm thinking about it, but researching on the web and Stack Exchange hasn't brought up the case yet. Help would be much appreciated.
I noticed the following sentence, taken from Mark Twain's "The Awful German Language:" Fifthly, I would do away with those long compounded words; or require the speaker to deliver them in sections, with intermissions for refreshments. What is the grammatical function of the semicolon here? I would have expected a comma to be appropriate here, as to me it coordinates a dependent clause, and that would be solely under the jurisdiction of a comma, as I understood. I thought semicolons were for replacing conjunctions between independent clauses or avoiding confusion with commas when writing a list that requires commas for one of the points within. Thank you!
Find the volume of the solid that remains after a circular hole of radius a is bored through the center of a solid sphere of radius r > a. So in the picture it looks like a circle with a cylinder cut out of the middle. I am not even sure where to start with this. I know this has to do with integrals but I am not sure how to set this up to even get an integral. Any help would be greatly appreciated.
I was reading about different variations of nim game and I'm trying to find the winning strategy in one of them: there are n empty places on the circle. Two players are placing their coins on empty places. They can put their coin only on empty places which aren't next to a coin of the opponent. In one turn each player can place only one coin. The player who can't move loses. Who's got the winning strategy for each n? I think that for even n the second player will win, because he can always place his coins symmetrically to the first player's. But what about for odd n?
I would like to have a definition for non-modular lattices which clearly sets them appart from their modular counterparts, thereby focusing on their main distinctive feature. Besides, I would be very grateful to you if you could provide me with an explanation about orto-modularity, which Birkhoff and von Neumann allegedly considered to be the basis of quantum logic, as opposed to modular logics. Is there any correlation between the two types of lattices and this issue of orto-modularity? Thanks in advance.
Is a Topological Space an Algebraic Structure? I am referring to the Wikipedia definition: algebraic structure generally refers to a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms. Examples of algebraic structures include groups, rings, fields, and lattices. More complex structures can be defined by introducing multiple operations, different underlying sets, or by altering the defining axioms. Examples of more complex algebraic structures include vector spaces, modules, and algebras.
This is an exercise from Alhfors Complex Analysis book- to show that an analytic function with a nonessential singularity at infinity must be a polynomial. It seems like it should probably be pretty straight forward, but I must be missing something. If it has a removable singularity at infinity then it extends to an analytic function on the Riemann sphere, and so must be constant by Liouville's theorem. What if there is a pole at infinity though? This was homework some time ago, and I never finished it :/ but have been thinking about it again recently. Thanks :)
What is the word for "stealing things during natural disasters"? For example, two guys are listening to the news and hear that there will be a huge typhoon tomorrow, and that there will also be no electricity. So, these two guys decide to steal things from a shop on the day of the disaster. Is there any single word for "stealing things during natural disasters"?
I'm looking for a reference for something I thought was easy and well known. There are (at least) two definitions of expander graphs. There is a combinatorial definition via edge expansion, and an algebraic definition using the spectral gap. Neither of these definitions require the graph to be regular. Now, I always thought that the Cheeger inequalities implied that these definitions were equivalent up to the constants. However, when I looked up the Cheeger inequalities it seems that they only talk about regular graphs. Is there a version of Cheeger's inequalities for nonregular graphs as well? In general, is it true that a family of (not necessarily regular) graphs is a family of expanders in the first sense iff they are expanders in the second sense?
I am using graphicx to typeset the figures for my PhD thesis. I have large files in .eps format. However, whenever I try to typeset the file (using pdfTeX), the console says "LaTeX error: File 'Figure' not found" It is in the same directory as my .tex file, and the file will typeset if I create it as a .dvi and then convert it to .pdf. I would rather not do this though, because I want to use hyperref.
Light as an electromagnetic wave can be polarized in different ways, e.g. linear or circular. As far as I understand it currently this can be compared to the spin direction of a propagation electron (spin angular momentum of light). Now I have learned that an electromagnetic wave can also have an orbital angular momentum, which is described for example in Wikipedia as a kind of shifted wavefront. While trying to get my head around these phenomena I was thinking about other wave-like objects in physics besides photons. Do all particles and/or excitations (e.g. a spin wave) exhibit orbital angular momentum and what are the physical consequences?
I'm writing an essay right now and I'm deliberating whether or not I should use Pagan gods instead of Greek gods (to provide variation in the essay). I've looked up the word pagan in the dictionary and it mentioned it was a derogatory term. Would it be acceptable to use it though in an essay or would it be inconsiderate for me to use that term?
I'm trying to phrase a sentence in which I'm wishing that something goes easily for someone, but can't get the wording to sound right, and not awkward. For example, someone may be studying for a test and I wish that their studying goes easy. These are the phrases I could come up with. I hope it goes easy for you. I hope the studying goes easy for you. I wish you the best in studying. I'm hoping the studying goes easily for you. Good luck studying. (I don't really like this one since it's a bit vague) Any other suggestions?
Does anybody know the source of this idiom or have an explanation of how it originated? I know it means that the speaker does not trust the person in question, but I want to know the etymology of the idiom. How did it mutate from something literal into this? Obviously trust is not measured in the same way as distance, so I want to understand the correlation in this context.
Is there any good reference for Poisson geometry/Poisson manifolds out there? I would like to give a deep look to the subject, but all I seem to be able to find are short chapters or interludes in text about symplectic geometry. Looking a bit around on the web, the only thing I found is this book. Has anybody read it? And if so, is it good or is there something better? For those left wondering: the book in the link above seems a good introduction. A more advanced text is given by the book Poisson Geometry, Deformation Quantisation and Group Representations (Cambridge University Press).
I'm not a mathematician, but I'm teaching a bit of algebra to some budding logicians, and introducing them to/reminding them of the notions of isomorphism, homomorphism, etc. I'd like to give them an example of an endomorphism which isn't an automorphism, so that they can see the point of there being a name for these separate concepts. I'd also like the example to be as simple as possible, ideally just with some infinite group. But it's proving to be harder than I expected to do this. Every candidate I've come up with turns out to be either an automorphism or not really a homomorphism in the first place. Suggestions, please? EDIT: Should have said explicitly from the beginning, I'm hoping for an example where the homomorphism is surjective.
Is the probability space associated with a compact group with Haar probability always a standard probability space? I recall seeing somewhere the fact that if the topology generating the Borel sigma algebra is not metrizable then the probability space is not standard, or something along these lines. If so then any non-metrizable compact group would show the answer to the above question to be negative, but I am unable to find any firm reference for the above fact. Any help with answering the above question would be much appreciated.
Please help me determine whether or not to include a comma at the end of the third sentence: "I won't be talking to my ex at the party tonight." -"But what if she talks to you?" "I won't be listening to her either." -or- "I won't be talking to my ex at the party tonight." -"But what if she talks to you?" "I won't be listening to her, either." Thanks!
Can anyone provide a word which describes a person who shows a lot of enthusiasm in the beginning but gets bored gradually and eventually leaves the task uncompleted? I looked at jaded, but it doesn't fulfill the criteria. Jaded seems to describe more of an overworked fellow, whereas the word I'm looking for would describe the nature of person. The word I'm looking for would describe a person who always exhibits this behavior.