darklight03/StackMIAsub huggingface dataset:
This question actually has two parts: a. Prove that every subspace of a topological space with the discrete topology has the discrete topology. b. Prove that every subspace of a topological space with the trivial topology has the trivial topology. If I can do part a, part b will be easy. What do I need to demonstrate, exactly, to show that a is true?
I am looking for a book that explains Linear Algebra, where it is build from axioms to higher level of Linear Algebra. It does not have to be a book on elementary level. As example from other fields, Tao's Analysis would be perfect example. Do you know if there is a book which is in similar manner as Tao's Analysis? Thanks
We all know that the universe is governed by four Fundamental Forces which are The strong force , The weak force , The electromagnetic force and The gravitational force . Now, is there any relationship between Electromagnetism and gravity?
I am trying to figure out which bibliography style this is: I am using the natbib package with the apalike bibliography style, which is what I want for the right column, but I am missing the left column (author year). I think this is a nice addition for easier reference.
I have been asked to construct this plot in maple for an analysis assignment. I have been given no other instructions on how to do this. I am not familiar at all with defining or plotting these kinds of functions in maple. Any help would be greatly appreciated as I have been struggling with this for a few days now. Thank you!
In the bible, "he" and "his" are capitalized when they are used to refer to God. Is this grammatically correct? If so, what rule do we have that allows these words to be capitalized?
From what I understand, superposition is when two states exist in all of their possible forms simultaneously until the moment of wave function collapse, when they essentially reduce into a single state. I'm having trouble demonstrating what a superposition state is using bra-ket notation (a simple example), and I don't really understand where the probabilities for collapse come from?
In the following sentence, what is the function of "not, as one might assume, in English"? For example, is it some type of clause that modifies "wrote"? The Irish author Samuel Beckett originally wrote his most famous play, Waiting for Godot, in French, not, as one might assume, in English.
A metal ring is placed in a magnetic field. The ring has a gap in it though. As it falls through the magnetic field, is it true that it still experiences an induced emf and eddy currents but not a proper current?
Recently a program gave me this text in a dialog box: "All purchases have been downloaded for this account." While I understand its meaning, splitting the subject (the noun and its attributive phrase) makes it awkward in my mind. "All purchases for this account have been downloaded" seems clearer to me. Is there a grammar rule to cover this?
One can easily prove that every covariance matrix is positive semi-definite. I come across many claims that the converse is also true; that is, Every symmetric positive semi-definite matrix is a covariance marix of some multivariate distribution. Is it true? If it is, how can we prove it?
Is it correct to end adjacent words in 's to show possession? For example "My neighbour's dog's ball is always in my yard", or should it be "My neighbour dogs ball is always in my yard" or "My neighbour dog's ball is always in my yard"?
I am trying to craft the following sentence in a way that sounds a lot less cliche. Any ideas? "The ability to write has been a gift that has gotten me through the hills and the valleys of my life"
I'm planning to do an internship and I usually address my supervisor as Mr. X, however, he signs his emails with his first name is that means I can address him with his first name ? Note: I haven't met him yet.(if that's makes a difference)
recently I sat for an exam where I was asked this question - Concurrence means all of the following except: A. Agreement B. Accord C. Consensus D. Coincidence E. Harmony What could be the correct answer ? I opted for D. Coincidence. Was I right ?
Does anyone know anything about how the meaning of "just about" came to have opposite meanings in the UK and North America. For example, in the UK, The team just about won. means that the team won, but it was close (ie The team barely won.). However, in North America, it means that the team almost won.
I have found some information on Wikipedia concerned with XeTeX and the unicode-math package. My question is, if I include the unicode-math package in my document, is it enough to have LaTeX installed and run the Unix latex command on my file, or do I need to have XeLaTeX installed as well in order to transform my source file into a .dvi/.ps/.pdf file? Thanks.
I am relatively new to TeX/LaTeX and so far learnt all about it using online documentation or question-and-answer websites like this one. Should I consider buying a LaTeX guide book though? What would be your advices for doing so?
I'm trying to prove the Arrow's Theorem is not true when there are two candidates, however I'm having trouble trying to prove that there is no dictator. I have suggested that in a majority rules voting system, unanimity and IIA are satisfied but I have no idea how to prove that it isn't a dictatorship.
The phrase "Fire Away", meaning "Ask me questions", appears to be a metaphor stemming from an old military term involving discharging firearms (source). However, "Away" is generally a directional term, yet in the phrase "Fire away" it seems to mean "at will" or "with abandon". How did it get such an unusual meaning? Was this a sarcastic instruction perhaps?
I have MathML that I need to render in my LaTeX document. Is there a recommended way of doing so? So far, from googling, I've found MathParser - a Java converter. But I was hoping there might be a better way to do it.
It is well known that the running time of the simplex algorithm depends on the diameter of the polytope induced by the constraints. Is there any non-linear optimization technique that also has this property ?
I used TeXstudio last year and I had a lot of trouble with referencing and producing a bibliography. Reading around online, this is a widespread problem. Which Latex editor is best to use to make it easier to produce a bibliography?
So far, I've come across several examples of frieze groups, but I've not yet come across an understandable definition of what they are. I've also been asked questions that ask me to state the isometries preserving said frieze groups and I don't really understand how I should know what these are either. Could someone please explain this to me? Many thanks.
I am looking for a generic word for a person who is being visited. The opposite of visitor according to thesaurus.com is host. That's not what I'm looking for. A couple examples: an employee being visited by a guest; a student being visited by their parent at school. I can't think of anything except "visitee" and I couldn't find it officially used anywhere.
I'm having trouble finding typical quantities in fiber optic communication. In particular, what kind of powers are generally used (or what is the minimum that fiber optics receivers can detect effectively)? What frequencies of light are generally used, and what are typical sampling rates?
Recently a colleague of mine said to me that the "Guys who are switched on really annoy me?". Since I am not a native speaker, I do not know what he meant by "switched on". Can you fine folks shed some light on this? Thanks!
The quantum fields are operator valued distributions. In some sloppy books like Peskin and Schroeder the Euler-Lagrange equation are used to get the equations of motion. What does it mean to take a derivative with respect to some operator?
Which is correct? I would like to request you to refrain from shouting. I would like to request of you to refrain from shouting. I would like to request from you to refrain from shouting. Something else?
Somewhere on the internet I've read about a guy ordering a coffee in the name of "Bueller". Apparently, the cashier called out that name repeatedly. I've looked up the term but it gave me no clue as to why it's so hilarious. Is that a cultural reference or a linguistic one?!
Almost all of the orbits of planets and other celestial bodies are elliptical, not circular. Is this due to gravitational pull by other nearby massive bodies? If this was the case a two body system should always have a circular orbit. Is that true?
I heard that, at the Quantum level, events can happen out of order making causality invalid. Thus the future can happen in the present and the present in the future. Is this true?
I know the Schwarzschild event horizon is a null surface generated by null geodesics. But what does that actually mean in terms of the path of a light ray that reaches it? Does that mean the geodesic trajectory of light on the surface will be along the surface? Which way will the light ray go? And what equation shows this?
So I'm guessing it has to do with temperature of surface water, temperature of surrounding, surface area, humidity,... I always wondered if there was an equation to describe evaporation, never learned one in high school.
From: Moduli space we see that moduli of curves is a very algebro-geometric topic. It is easy to understand its relevance and importance in algebraic geometry. But the mind boggles when we try to imagine how on earth such a topic from pure and abstruse mathematics is relevant in physics. I will be thankful if somebody can give some explanation.
I'd like to ask about parity of baryon. When I search a parity section of textbook, it only explain about parity of meson, not baryon. And I can't find experimental method for parity determination of baryons. Am I missing something? Or is there special reason for baryon?
Why is the inner product of a character with an irreducible character a non-negative integer? I can see that by properties of the inner product it will be non-negative but I cannot see why it would be an integer?
I have to find the curvature and torsion of a curve (parametrised by arc length), given only the Binormal vector. Whilst I understand how to find these if I have the curve, I cannot for the life of me work out how to go in this direction. Any help would be appreciated
Hi there I was wondering if someone could please help me? I understand the solution of this until it gets to the Polynomial Estimation Lemma part. What is the Polynomial Estimation Lemma and how can it be applied? Many thanks in advance.
Does anyone know what the chromatic number of a graph chosen randomly on n vertices is, as n tends to infinity? I mean, almost all graphs have chromatic number greater than any fixed k. But in terms of estimates, is O(n), O(log n), O(sqrt(n)) a good estimate for the chromatic number of large random graphs?
Possible Duplicate: How to superimpose LaTeX on a picture? Take this image for example: How can I add labels to an image as done above without manually drawing a line and adding text at the end of the line?
I am looking for a nice compact book in abstract algebra (especially group theory) which develops the material by asking questions the reader must answer. An example of what I'm looking for is Combinatorics through guided discovery.
I am trying to understand the following sentence from a legal document. Can anyone explain me what 'commutation' means? Immovable property presently sold is free and clear of all seigniorial dues having commuted and the price of commutation has been paid.
The two-slit experiment is a classic example of how measurements can affect the behavior of particles. This seems reasonable because, to my knowledge, the measurement is "active" in that it adds energy to the system. But how is this reconciled with macroscopic observations (such as looking at Schroedinger's cat) that are "passive" in that they are collecting information already there without affecting the system?
I have heard that the verb go used to be wend in olden days. I am curious if there is any historical or other explanation why the past form of wend, i.e. went, is still in use while the simple present and past participle forms are gone. Any idea or link to some resources which deal with this fact?
Are there specific rules / conventions at play when creating demonyms? Or are they merely formed organically over time - the most popular winning out? There are many suffixes to choose from, but I cannot find concrete guidelines as to which is proper to use in which instance.
Ok, so I got the answer to part i), but however, I'm not so sure how to get the answer to part ii). The answers say its an ellipse and they specified the equation, but I can't understand how they came to that conclusion. Can anyone help me out, please :)
The Oxford Dictionary of Difficult Words defines vindictive as follows: having or showing a strong or unreasoning desire for revenge. What is a word for a having desire to be destructive or to break something?
I want to turn off printing of DOIs in my BibTex bibliography in Lyx. When I try to add the option doi=false under Document settings -> Bibliography -> Bibliography generation -> Options the bibliography is not generated anymore (i.e. question mark for citation and empty bibliography). How can I set this option via Lyx ?
How can we know that North Korea and Iran (to name a few) are exploding nuclear weapons if no inspectors have ever been granted access to suspected nuclear sites in these countries? How can we passively detect a secret detonation of a nuclear warhead? What are the telltale signs of a nuclear detonation?
I know that Edmond's Blossom algorithm can be used to find a minimum weight perfect matching for a given graph. However, is there an efficient algorithm known that can find all the minimum weight matchings. Or one that can sample uniformly from them all?
I've been reading Lee Smolin's Life of the Cosmos. Great book and it makes a lot of sense that the conditions in black holes are the same as conditions at the big bang. Question is, has his theory about Cosmological Natural Selection been disproved as the wikipedia article states?
Loosely defined, sabermetrics is the study/usage/development of baseball statistics. I get the "metrics" part of the word, and I know what a saber is. But, what do sabers have to do with baseball? My only idea is that the baseball bat is kind of like a saber, but that seems to be a stretch.
I just finished reading the Wikipedia article on the Cauchy condensation test. I understand the trapezoidal view, but apparently "the 'condensation' of terms is analogous to a substitution of an exponential function". Can anyone explain what is meant by this?
How would you describe someone who fritters away money on inexpensive, trivial things, like coffee, but refuses to spend money on expensive, necessary things, like a decent new laptop (buying a lousy one instead)? Is there an expression? I want to say "penny foolish and pound wise", except that "pound wise" is inappropriate here, as skimping on the large outlay is a false economy.
I have heard of the "Big Rip" as one theory for the eventual end of the universe. If the speed at which the universe is expanding, and all the matter inside it is moving away from all other matter at an increasing rate, would the matter eventually have to move at the speed of light? Or would it have to slow down?
People often refer to the country US as America and to the people from the US as Americans. As far as I know, that's the only case in the world where a continent's name is used for a country's name (let me know if I'm wrong). Why does that happen?
I'm looking for the proof of that: d(x,y) = d (y,x). I know that I have to use the "non-negativity" and "triangle inequality" but I don't know how to combine them to get the result.
In discussing Doppler effect, we use the word "apparent frequency". Does it mean that the frequency of the sound is still that of the source and it is some physiological phenomenon in the listener's ears that give rise to the Doppler effect?
Could you please let me know if the following excerpt of a sentence is grammatically correct (specifically the preposition after "effort"): "Should there be anything that you feel we are missing, your insight would be invaluable to our effort in improving our products(...)" An explanation on why it is/isn't correct would also be highly appreciated. Prepositions are tough. :(
I am having trouble reducing the footer space. I have a list of contents that is printing below the page number appearing in the footer. How do I solve this issue? I tried setting the footskip length but it didn't work.
Is there an English equivalent to this familiar saying used in India: Don't speak unless you can improve silence. The saying loosely means it is better to be silent than prattle on about something.
I read that the canonical commutation relation between momentum and position can be seen as the Lie Algebra of the Heisenberg group. While I get why the commutation relations of momentum and momentum, momentum and angular momentum and so on arise from the Lorentz group, I don't quite get where the physical symmetry of the Heisenberg group stems from. Any suggestions?
This question may be redundant and I apologize in advance but I am really having a hard time to digest the notion of proportional to in mathematics. Kindly, can someone simplify the idea of it and when we can say proportional to something. Thank you for your help.
I am currently studying Multivariate Calculus (Larson and Edwards book). I want to do a project in computer science to see some nice applications of things I am learning. Any specific source of papers/journals/books? thanks
Since I am reading some stuff about weak convergence of probability measures, I started to wonder what is the dual space of the space consisting of all the finite (signed) measures (which is well known to be a Banach space with the norm being total variation). Is there any characterization of it? We may impose extra assumptions on the underlying space if necessary.
I see many people using "Dear" while addressing people in email. But, I feel "Dear" is more intimate word in English and should be used with only relations. How does the word "Dear" is used at all places irrespective of relationships?
I'd like to customize verbose biblatex citations to exclude URLs (and DOIs) while keeping them in the bibliography. Is there a simple way to accomplish this? While I'm at it, I'd like to get rid of the "In: " that the verbose styles use (in both the bibliography and citations), and put the URLs and DOIs on separate lines in the bibliography.
According to Feynman in this youtube video the photons that are released when a tree burns are sort of those that were trapped during photosynthesis. Are these the exact same photons produced by the Sun or do photons get destroyed / created somehow?
If I drag an object across a surface and a force due to friction acts on the object which is equal and opposite to the force I apply, the net work done on the object is zero. So where does the energy come from to heat up the object and it's surface?
Given the standard topology, is there any relationship between dense, uncountable sets and isolated points? For example, the set of irrationals is both dense and uncountable and contains no isolated points. Just something I've been wondering working my way through real analysis.
I am trying to build something like the two following pictures, using TikZ (I am still learning): The pictures are just an illustration and there is no need of the shading. Anybody can help me?
I'm British. I am editing a document, and I was going to correct a use of "all together" where the author clearly meant "altogether" (as in "entirely"). But then I realised this might just be a British distinction... is it? Do Americans accept "all together" as a valid alternative to "altogether", i.e. "entirely"? (The document is for an international audience.)
Possible Duplicate: A word for two very different things juxtaposed? What is the word to describe when two ideas (often contrasting) are placed next to each other to enhance the situation or idea being presented? I believe it could describe the placement of two words or ideas in a poem, or two melodies in a song, or two objects in a piece of art.
Since baryons (e.g. protons, neutrons) are composite particles it should be possible to split them apart. If so, is it then possible to extract useable energy out of the splitting of baryons in analogy to nuclear fission?
I've been having an argument with a colleague about this sentence, could you please let me know which one of us is correct: There are no shortage of applications for our product in this space. She is convinced that are should be replaced by is, and I think it should stand as it is. Thanks for your help!
A pendulum clock ticks slower on top of a mountain and ticks faster at ground level, but an atomic clock ticks faster on top of a mountain and ticks slower at ground level. Gravity affects pendulum clocks in the exact opposite way to atomic clocks. Which clock is giving us the correct time? Are they both wrong?
It's the wall that a suspect stands in front of when a mug shot is taken. I don't know what to call it so it's hard for me to find information about the wall itself.
Most references that I have come across refer to the Schottky Barrier in the setting of Metal and Semiconductor Interface. Would it be correct to use the term Schottky Barrier to refer to the mismatch in energy levels in other settings (e.g. semiconductor-seminconductor)?
I'm studying for an exam and came across this problem in the book. Any ideas how one would go about solving this problem? Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and final demand vector d. Round production levels to the nearest whole number.
By Godel's second incompleteness theorem, a consistent theory (to which the theorem applies) cannot prove itself consistent. I learned that it's also impossible to have a pair of consistent theories each proving the consistency of the other. But I can't see how this follows from the second theorem. Or is there something more involved?
If you have a set of points on a hemisphere, how do you find a point on that hemisphere that has the minimum total great circle distance to the points in the set.
I was boiling penne and rigatoni pasta in the same pot (both are hollow cylindrical pasta of approximately the same length, but rigatoni has a noticeably larger diameter) and almost all of the penne pasta managed to find its way inside one of the pieces of rigatoni. Why does this happen? Below is a picture of my dinner showing an example of this.
I don't understand the concept of asymptotic variance. Given the mle of a probability function, the likelihood function and the random variables how do I find asymptotic variance? What exactly is asymptotic variance? I'm finding this concept very confusing.
I had thought that Jew was gender-neutral, until I heard somebody who was asked if their mother was a Jew and responded, "of course not; she's a Jewess". Is Jew a gender-neutral form, or does one need to distinguish between Jew and Jewess?
I noticed that the Kelly Criterion resembles a ratio between the mean and variance in a continuous probability distribution. Now the mean and variance are important values in portfolio optimization (Modern Portfolio Theory). Is there some relationship between the two since both seek to maximize returns and minimize risk?
The wild flowers looked like a soft orange blanket ______________ the desert. A. covering B. covered C. cover D. to cover I chose C. I thought that 'looked' is a past participle and 'cover' would be the predicate. Why is 'looked like' the main verb and not a past participle?
When asking how someone wants their tea, they reply: "lots of milk and sugar". Is that to be interpreted as "Lots of milk and sugar" or "lots of milk and (lots) of sugar" according to the rules of English?
I want to prove this in the infinite dimensional Hilbert space case. What is the easiest way to go about this (What do I need to know, what theorems do I need,etc). My aim is to show every normal operator admits invariant subspaces.