darklight03/StackMIAsub huggingface dataset:
Let R be a Commutative ring with unity, such that R[x] is UFD. If R[x] is a PID then it is a Eucledian Domain? Is the last statement about being eucledian domain correct?
There is no other harsher critic than yourself. I'm really stumped on this one. The more I read it the less correct it sounds. I think the word harsher is making the sentence sound fairly off putting. Other variations include: There is no harsher critic other than yourself. Any help would be greatly appreciated!
I'm looking for a word that could describe a person who is very gullible and easily trusts people. My specific example is Fortunato from Edgar Allen Poe's story: The Cask of Amontillado Edit: the character's name is Fortunato.
I'm making several assumptions, not sure if any are correct: there is a black hole at the center of a galaxy the black hole is eating the galaxy Eventually the galaxy will be gone, right? Has this been observed? Do we know what happens afterwards? Posting here since astronomy got merged into physics
https://en.wikipedia.org/wiki/File:Hopf-bif.gif Does anyone know how this animation was produced? I could make it by stitching together snapshots (what I'm doing) but this seems primitive, especially for how nice this animation looks. Any ideas?
I haven't been able to find a proof of this result online. Is there any proof that is relatively simple to understand? In particular, I want to also show that the upper triangle matrix that is similar to the complex one has diagonal values that are the eigenvalues of the complex one.
I was looking to apply a color gradient to some text (i.e. Chapter / section headings) and I searched through the Internet but was unable to find a minimum working example. Is it something that can be done in XeLaTeX? I decided to ask here, thinking someone in the community might have already done similar to that.
Suppose I have a sphere. Inside the sphere I have an inscribed cube. What I am interested in is finding out what is the latitude and longitude (or coordinates) of a point on the sphere which will be projected on a cube's face given the coodinate of a point on one of the cube's faces. Does anyone have any equations for this?
I understand that rectifying antenna (rectenna) is supposed to convert electromagnetic energy to electric current however I do not understand how it's really working. I do get that it's kind of like how transformer works, but beyond that I am clueless. Could someone explain this to me?
What does "characteristic wave" mean in the context of plasma waves? For example, when propagating parallel to the plasma magnetic field, the characteristic wave is circularly polarized. Does this mean that only a circularly polarized wave can propagate in this direction? Could an elliptically polarized wave travel in this direction instead?
Is there a word for days you don't work? In portuguese you have the term "dias de folga" that means the days that you would normally work but will not because the company gave you those days to rest. One is said in portugues to be in "folga". Is there a correspondent word or term in english?
Is there an overview available for Arabic fonts in LaTeX / XeTeX? Ideally with output examples, so that it becomes clear how they compare. So far, I'm aware of Geeza Pro, Amiri (and its variants), Sheherazade and, Al Nile. But I assume there is much more out there.
Well, since the electron is going around the nucleus, it must have an angular momentum (plus its spin). And since it is charged it must create an electric field. If I have understood it correctly it is the interaction with this field that is causing the so-called Anomalous Zeeman effect? Is this correct? And does does this have any other consequences?
According to Wikipedia, an open formula is a WFF without quantifiers. I have read that a propositional function is the same as open formula. Are both of these statements correct? Is it true that one can't have a propositional function with quantifiers?
Of course we can always say "the sun is up", but is it acceptable to say "the sun is risen" just as we use verb "to be" before other past participles like "she is gone"? Or should we say "the sun has risen"? Does it make any difference?
Why the current is the same at all of the positions in a series circuit? although there are different voltages at different positions of the circuit. What i know is that as the electron passes one resistor, the force of attraction from the negative terminal is less. Doesn't this affect the current?
What's the difference in spirit between "gallimaufry" and "farrago"? Are there any sentences where using one or the other would lead to a subtly different meaning? Both are defined in dictionaries as "a confused mixture", or a synonym of "hotchpotch". I'm afraid they're too close to just be able to compare their dictionary definitions.
I am interested in applications problems of Linear Algebra. If somebody can recommend me an interesting book, or papers about, I will appreciate this. Thanks. (I need this for a course of Linear Algebra for Engineering where I am the lecturer).
Does anyone know the font style used in Kato's Perturbation Theory for Linear Operators? Better yet, does anyone know of a TeX package or style file that replicates the layout and style used throughout Kato's book?
One of Twitter's error messages reads: Something is technically wrong. Of course I understand what they mean, but am I wrong to interpret this as "strictly speaking, there is something wrong" instead of the intended "there is a technical issue"? What would be the ideal, succinct way to phrase this, maintaining simplicity and clarity?
This is a very simple question but I wasn't able to find a question like it and I wasn't a math major. Did tangent originate in trigonometry, geometry, or calculus? I remember using tangent lines in geometry, trig, and calculus but I'm curious which came first. http://www.mathopenref.com/tangentline.html
G is a planar graph. E is an arbitrary edge of G. "There exists a planar drawing of G where E is on the unbounded face of the drawing." Why is the above statement true? Any help is appreciated.
I am reading Wilkie Collins' The Moonstone, and a prominent character in the story has the name of Betteredge. My question is (since I like to imagine the dialogue in a British-English book as if spoken with a British accent), would "Betteredge" sound more like "Better edge", more like "Bedderitch", or is it pronounced completely differently?
Does "so that" and "for ... to" have the same usage? For example: I bought this sweater so (that) you can wear it. and: I bought this sweater for you to wear it. Is there any difference between the two expressions or do they have the same meaning?
Can anyone give a specific example of a diffeomorphism and also of composing a function with a diffeomorphism and how this helps mathematics as a whole? In other words, how does this fit into the grand scheme of mathematics? Thanks
In the context of "Which station should I get off?" (asked when you're on the train), what would be another way to say this, without using "get off" (which has other connotations) and still colloquial (either American or British English)? I thought about "exit" or "alight". Are there other, better ways to say this? Thank you.
I'm familiar with the concepts of group isomorphism, ring isomorphism, and graph isomorphism, but it's never been presented to me what an isomorphism is in general: given any X, what is an X isomorphism? Informally, I understand isomorphism as "preservation of structure", where "preservation" is domain specific. Is there a formal definition?
I'm using the align package for multiple-row equations. Some rows the equations are just a bit longer than the textwidth (I'm using double column). I only want to reduce the fontsize of those particular rows, not the whole align environment. How do I do that?
I don't need to list all the proper divisors; I just want to compute their sum. While checking and summing up all proper divisors isn't an issue for small numbers, it becomes significantly slower for larger numbers. Any suggestions? Thanks!
While trying to locate the etymology of the Tamil slang, OB, I ran across the following claim: This entirely Tamilian term, strangely enough, has its origins in the term "off-beat" used in the British Army to refer to retired officers or soldiers. I'd like to know if there's any truth to the claim that "off-beat" was a British Army term for retired officers.
In graph theory what is the difference between isomerism and isomorphism? I found a post somewhat similar to it but couldn't understand my problem from that. So I asked again specifically asking my question.
The following is an excerpt from Chern's Lectures on Differential Geometry: I don't see how the proof shows the other direction of the set inclusion. Would anybody explain the logic in the "furthermore" part of the proof? The following are definitions of the notations:
I use it all the time since I work with databases, but every time I write it somewhere with spell check I get the squiggly line below it. I've seen other people spell it with an "s" instead of a "z" but neither have an entry in the Merriam Webster dictionary. http://www.merriam-webster.com/dictionary/denormalized http://www.merriam-webster.com/dictionary/denormalised Is this just technical jargon or am I misspelling it?
I think the both answer is "yes". How can I prove that Schwartz space is closed under multiplication ? Because if I know that, it is easy to see that being closed under convolution is satisfied. Help me please. Thanks
I am creating a poster using beamerposter, and I would like to include Feynman diagrams generated using feynmp. However, the native scaling of feynmp is indented for letter-size documents, and is far too small for a poster. Is there a way to scale the diagram to poster-size while keeping its features properly proportioned?
I am starting a chapter on divisibility in commutative rings, and I was wondering if there was a way to translate theorems about gcd to lcm and vice versa. I know the concepts are considered "dual" in some sense, so perhaps the theorems relating to them are also dual.
I am unable to see the correctness of this statement. It seems the author has considered this statement trivial and hence has not given any proof of this statement. But I am unable to prove it.
I've seen a lot of work on homomorphisms of modules, but is it possible to construct a homomorphism as a module itself? For example, how would you define a specific module structure on a set of homomorphisms, for example, a dual space.
Which of the three articles (a/an/the) would the blanks in the following sentence take? It is not unusual for ____ editor to tamper with _____ writer's manuscript. I think it should be 'an' and 'the' in the first and second blank respectively, but my colleagues think otherwise. Please suggest.
I would like to know whether it is correct or not to use the word "scope" to refer to a book's section, subsection or paragraph. For instance We will address these matters in the next scope.
A very common type of convergence in probability theory is 'almost sure convergence'. I don't understand why this type is used at all. In principle, we should always be able to substitute it by a uniform convergence almost sure due to Egorov's theorem. So why do people in probability theory refer to this weaker concept? If anything is unclear, please let me know.
I'm kind of confused as to how I should punctuate the following sentence: A land as old as time and whose history defies any simple description. The author added a comma before "and", but i'm not convinced. Can "whose history defies any simple description." stand on its own as a sentence?
I've seen the following (e.g. here): I've learned a bit about groups and I could give examples of groups, but when reading the given table, I couldn't imagine of what a magma would be. It has no associativity, no identity, no divisibility and no commutativity. I can't imagine what such a thing would be. Can you give a concrete example of a magma?
I saw a passage "this doesn't mean to get riches and honors." 'rich' is an adjective but 'riches' is a plural noun according to the dictionary. Are there any other examples where an adjective becomes a noun by adding suffix '-s' or '-es'? or 'riches' is the only case?
I wrote a text about our company's services and added that we also can offer products tailored to the needs of our clients. One of my colleagues insisted that the expression was wrong and I should say that we offered tailor-made products. Is there actually a difference between the two expressions generally or in the context I described?
I have found many places that list the various rules on using hyphens in math, but nothing to explain why we have the rule. I have some students who are asking and I would like to be able to give them an answer instead of saying it is just the rule.
I'm teaching a class with a very gentle introduction to Markov chains (the class is an alternative to taking calculus). I'm not a probabilist, so I haven't spent any time thinking about these objects. Does anyone know of any very compelling non-mathematical examples of Markov chains, or, at least, of non-mathematical things that can be well approximated by Markov chains?
Adherent ("a person who follows or upholds a leader, cause, etc.; supporter; follower") is the word I am considering. For example, would a group of people who support and fight for freedom be called adherents (ignoring the obvious "freedom fighter")?
Assume a scenario in which you talk with someone and then he puts your integrity/reliability "in doubt". Meaning: He doubts that you are truly reliable/innocent/trustworthy. So you want to say to him a phrase that means "Do you really put my integrity in doubt?" or something similar. I'm quite certain that this kind of phrase exists, but I don't remember what it is.
For example if a student wishes for a storm because he wants his classes to be suspended. His main intention is to have no school but not necessarily to have a storm. Not sure if this makes any sense. I'm pretty sure there's no word for it but I don't know because English is not my first language.
A student in my class mentioned his approach to proving isomorphism via the rank-nullity theorem rather than showing an inverse's existence. I didn't quite understand how, but perhaps someone here might be able to explain...
When creating an unconstrained optimization problem from an equality constrained one, the usual way to build the Lagrangian, is by adding a term consisting of a multiplier, multiplied by the equality constraint. Are there problem instances, where it makes better sense to square the equality constraint and then use that in the unconstrained problem?
I use LaTeX and want to create a bookmark which opens a file but I want to specify the page no. I have looked at texdoc bookmark but cannot get it to work. Anyone any ideas?
It seems, to me at least, that most Statistics textbooks focus on the Statistical methods and techniques, or on the mathematics behind them. Would you recommend me some textbooks (or any online source) that discuss the "logical" reasoning behind the techniques? Thanks in advance!
I have been introduced to algorithms, computability and computational complexity (as part of my minor in CS). What are some mathematical topics that I can tackle with the new perspectives I acquired from these ideas of computer science? Could you suggest some reference books (preferably self-contained and accessible to an undergraduate)?
Fourier says that any periodic function can be represented like a infinite sum of sine functions with their appropriate periods,amplitudes and phases. My question is: is it possible to represent the periodic function like a sum of other periodic functions like a square wave function or some other shape, or they must be the sine functions?
What experiments prove that heat can be "trapped" by a layer of material with suitable optical properties, such as carbon dioxide? I've read a little on Wikipedia but I've got only some names, not the experiments.
What is the difference between ago and before when they are both used as adverbs in the following sentences: I saw him seven days ago. and I had seen him seven days before.
Could somebody please provide a sketch of a proof of the fact that the Tor functor commutes with direct limits? I have been trying to show that the Tor of a module with the direct limit of a family of modules satisfies the required universal property, but it seems too complex.
Sometimes when I speak with my fellows at work, I start my sentences with "so" or "um". I don't know if this a bad behavior in business speak or not? If so, how can I get rid of those filler words?
From what I can glean, it'll and I've exist as standard contractions, but I am unsure of whether it'll've either exists or is acceptable. "It will have" should be able to be reduced to "it'll've", shouldn't it?
We say that if any particles from outside fall into the black hole, they eventually hit singularity. Then why not particles already inside the black hole are at singularity? Or are they? If yes, then why does a black hole have a finite size?
What is the meaning of the phrase "new strands of research" in the following sentence: The last two decades have also seen the emergence of new strands of research on multilingualism which have incorporated critical and poststructuralist perspective from social theory and embraced new epistemologies and research methods. Is there any synonym for this phrase or for the word strand in this context?
Given any figure with four vertices and four straight edges, prove that one can construct a perfect parallelogram by connecting the midpoints of such figure. This to me is a very fundamental and interesting geometry problem. How would I begin to prove this?
What actually causes a rocket to move? Is it the pressure in the rocket engine or the amount and velocity of mass that is being ejected out. The reason I am asking is, I found these two explanations for a rocket motion. Are they same or different. If same, is there any correlation between them?
I have a long definition for Picard groups, but it is too abstract for me to really understand and apply. Could someone give an example or two on how to calculate the Picard group for a quadratic integer ring? Also the relevance of the exact sequence?
I am comfortable with the way physicists use differentials as elements of area/volume. I know the (algebraic) formal definition of differential forms, but it makes no intuitive sense, especially since it is not immediately compatible (to me) with the physicist POV. How do the two fit in?
I know what anti-matter is and how when it collides with matter both are annihilated. However, what about anti-photons? Are there such things as anti-photons? I initially thought the idea preposterous. However I am curious because, if anti-photons don't exist, then anti-matter could theoretically transfer its energy to normal matter - through the mechanism of light. Is it right?
I am taking a course in Mathematical Physics Junior Level (Undergraduate). We are working from Arfken's "Mathematical Methods for physicists", but i am finding trouble with it specially in the determinants and matrices chapter, since it is not detailed enough. any suggestions for a more detailed book?
Which one should I use: Are you going somewhere nice on holiday this year? or Are you going anywhere nice on holiday this year? The presence of the word "nice" bothers me a bit and deters me from using "anywhere".
I'm trying to calculate an integral with respect to a complex value. I just want to know if I can estimate the integral using the residue theorem separately for the real and imaginary parts of the mentioned value or I cannot at all use this method here.
By Cantor's intersection theorem I know that a sequence of nonempty compact sets which are nested has nonempty intersection. But how can I use that to prove that arbitrary intersection of compact sets is compact?
Let's say I am having a telephone conference with rest of the team, and somebody asks me "Dude, are you there?" How should I reply? Yes, dude, I am there. or Yes, I am here? It is difficult for me to see the difference.
To what branch of mathematics does the Hodge conjecture belong? I'm aware that it's very advanced, but what kind of prerequisites would one need to understand those problems? Can you suggest some good texts for a senior undergraduate/beginning graduate?
I'd like to write a program that uses the exact (down to the second) amount of time from one new moon (or full moon) to the next. Yet, I am told that this period is irregular. Yet, it seems to be predicted in a number of places (ie, by the navy). How do they do this? http://aa.usno.navy.mil/data/docs/MoonPhase.php
For example a situation where you are on the phone with a friend and he is with a person that you know. You would ask him to say hi for you. The french equivalent would be "Passer le bonjour" I am looking for formal and informal ways to say that.
I'd like to label my nodes with text that has a 'halo' around it of a different colour. Is this possible? The reason is that my label text covers different parts of my diagram with different background colours, so no single colour will make the label legible. I'd ideally like the text to be black, with a white halo.
Each (finite-dimensional) Lie algebra has exactly one simply connected Lie group associated to it (up to isomorphism). What can we say about all other connected groups with the same Lie algebra ? Thank you in advance
When a car is traveling round a banked track as fast as possible, it has a tendency to slip up the slope. Opposite in the case when the car travels slowly and has a tendency to slip down. Can someone please give me an intuitive reason as to why this "tendency to slip up or down" occurs.
Possible Duplicate: What word means what many people think 'ironic' means? While irony actually means 'the opposite of what is expected', it is often misused in a context to make it mean 'an unexpected and amusing coincidence or similarity'. Is there any word that does actually mean this?
Given a parallelogram with congruent diagonals, you are asked to prove that the parallelogram is a rectangle. Would saying: A parallelogram must be a rectangle if the diagonals are congruent. be a valid proof for this question?
I'm developing a web based application that allows people to send email to many customers, for advertisement purposes. What's the correct name for that? newsletter or mailshot? EDIT: to avoid unnecessary answers like "spam" please note that customers subscribe to the service first.
We know that if the infinite sum of a multiplicative function is absolute convergent, then the sum can be expressed as infinite product and the infinite product is absolutely convergent. Does there exists a multiplicative function such that the infinite sum is divergent, yet its Euler product is still absolute convergent? Thanks a lot
I know that a smooth manifold is a topological manifold whose transition maps are smooth. Must the coordinate maps also be smooth? Must they be diffeomorphisms? MathWorld seems to think so, but I do not understand why it follows from the definition that this must be the case.
Since strings are extended objects, is all angular momentum in string theory essentially "orbital" angular momentum? Or is there still a kind of intrinsic angular momentum assigned to a string? Either way, is there anything that prevents the "intrinsic spin" of a particle represented by a string from being arbitrarily large?
Say I had a parameterization of a surface and I wanted to determine if the surface was closed, to determine the applicability of divergence theorem. My math professor said a surface is closed if it does not have a "boundary", such as the sphere or the torus. How would I determine this mathematically? Is there a specific property that is satisfied?
I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus. I was thinking of trying abstract algebra. I would appreciate any book recommendations. Thanks in advance. Andrew