darklight03/StackMIAsub huggingface dataset:
I have a subtle doubt about the physical interpretation of the mathematical definition of vector field as a derivation. In basic physics we understand a vector quantity as a quantity that needs more than magnitude to be fully specified, in other words, quantities with the notion of direction. This goes very well with the also basic mathematical definition that a vector is an equivalence class of oriented line segments. However, when we go to the study of manifolds, we see that a better definition of vector is to say that a vector at a point is a derivation on the algebra of smooth functions on that point. But then, we represent forces for instance with vectors, what's the interpretation of representing one force acting on a point by a derivation on the smooth functions on the point? I imagine that there must be some interpretation for that, but I didn't find what's it. Sorry if this question seems silly. I'm just trying to bring together those concepts. And thanks you all in advance.
I have a question about the appropriate usage the possessive personal pronoun "mine" over the possessive determiner "my". I have done some research and understood the differences between them, but my questions isn't quite about that. One of the main purposes of pronouns is to eliminate repetitions, yet I cannot be sure whether to use it or not if there isn't a possessive determiner such as my, your, her, their etc that establishes the noun being referred to. For example, I thought of the sentence below: Your dog attacked mine! ('Mine' used as a substitute for 'my dog', as 'your dog' established the noun in question) The above is no doubt a better construction than: Your dog attacked my dog! Which sounds somewhat awkward in comparison. However, if there isn't a possessive determiner preceding it in a sentence: A wild dog attack mine! It sounds jarring and not as natural as: A wild dog attack my dog or My dog was attacked by a wild one. I don't know if there is a grammar rule that would explain my question, but fellow memebers, is it still correct to use the possessive personal pronoun (such as mine) in the case above, or can it only be used if a possessive determiner (such as your) is used before it? Many thanks!
When I used to play video games, "all in" meant that you were devoting your army to a "do or die" effort. In other words, you were either going to win or lose in the next battle. The "all in" meant that you typically brought all of your soldiers to fight, holding none back. But years ago I was doing the Daily Jumble, and the hint was something like "After running a marathon he was _ __". This was before the web, so I had nothing to fall back on. It turns out the answer was "ALL IN" meaning "tired". I asked a friend and he said "that's a usage from the eastern U.S." I certainly hadn't heard it before then and I still haven't since. Is this a common meaning? Maybe some easterners can chime in?
In this sentence, would you use "to inform" or "for informing"? These findings are critical ______ future research Likewise, would you use "to understand" or "for understanding" in the following? These results provide a powerful framework _____ existing patterns. This is a question that comes up a lot in science writing: when do you use the "to" vs. the "for" version of a verb? Is there a word for these two different uses? And is there a rule for deciding which one is correct? They often get used interchangeably, but I can't find any hard rules for deciding between the two. People often use the "to" version because it sounds less passive, but I find it more ambiguous and a bit clunky, but I can't find any actual sources to say which is correct.
I don't get this joke: It smells like up dog in here, What's up dog? Nuuthin dog, what's up with you? (source) I understand that the person asking "What's up dog" is tricked into asking a question they didn't intend to ask. I also understand the meaning of the "What's up?" question. I don't understand why this exact question has been chosen. If anything, it sounds demeaning to the person who's making the joke and is referred to as dog by the receiver of the joke. If I were to make a similar joke, I'd replace dog with something like master, so that it'd sound like the receiver of the joke respects the person making the joke more than it might be in reality. Does the word dog in this context have some alternative meaning, perhaps? Or is this joke funny simply because the receiver of the joke asks a funny question, no matter what the question is?
How common is it for native English speakers to actively replace the past tense 'did' with the past participle 'done'? I used to think it was only really done in rather vulgar dialects, but I have increasingly heard this usage now by people who speak otherwise normal Received Pronunciation, or Standard American English: I done the report. You done it yesterday. He done it already. I can't help but interpret this replacement of 'did' as sounding somehow uneducated, but is it becoming a standard in some dialects? Is the word 'did' dying out? And do these speakers use the 'done' replacement when switching the word order around in a question; for example, would they say: Done you do it today? ... or even: Done you it today? ... instead of: Did you do it today?
In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with. First of all, the S-matrix is a scattering matrix which comes from scattering processes. In the context of quantum mechanics and quantum field theory, we often compute the S-matrix, and we use well-known formulas, i.e, the LSZ reduction formula On Wikipedia, they describe a R-matrix, as related with the Yang-Baxter equation (governing equation for integrability), and they add some comments that it is related with resonance. My questions are, then: Can you give me a clear definition and a governing equation for a R-matrix? How are S-matrix and R-matrix related to each other? Why is the R-matrix important in integrability (Yang-Baxter equation)?
I am confused about the usage of the words like and unlike in sentences. Like and unlike make me confused because I see them being used everywhere almost interchangeably, and to make matters worse I even saw commas making difference in meaning. Which of the following sentences is most correct, and least ambiguous? Unlike Xbox, Playstation can't play Halo. Playstation can't play Halo unlike Xbox can. Playstation can't play Halo, unlike Xbox can. Like Xbox, Playstation can't play Halo. Playstation can't play Halo like Xbox can. Playstation can't play Halo, like Xbox can. Playstation can't play Halo unlike Xbox. Playstation can't play Halo, unlike Xbox. Playstation can't play Halo like Xbox. Playstation can't play Halo, like Xbox. In case you don't know what I actually wanted to say in those sentences: I'm trying to say that Playstation can't run the Halo video game and Xbox can run that game. I probably should have tried sentences with no brands but I can't imagine any meaningful sentences at this moment which contains like/unlike.
I'm new to finite fields - I have been watching various lectures and reading about them, but I'm missing a step. I can understand what a group, ring field and prime field is, no problem. But when we have a prime extension field, suddenly the elements are no longer numbers, they are polynomials. I'm sure there is some great mathematical tricks which show that we can (or must?) use polynomials to be able to satisfy the rules of a field within a prime extension field, but I haven't been able to find a coherent explanation of this step. People I have asked in person don't seen to know either, it's just assumed that that is the way it is. So I have two questions: What is a clear explanation of "why polynomials?". Has anyone tried using constructs other than polynomials to satisfy the same field rules? Thanks in advance.
There are many books, written by highly decorated academics, which feature proofs that I can hardly comprehend in an acceptable amount of time. Roughly each week, it happens that I find myself having spent around three hours to convince myself of a single proof - usually, the proofs are from textbooks for undergraduates. Sometimes, I am horribly slow at finding detailed arguments which connect the presented conclusions (and which are necessary to convince myself that the conclusions are beyond question). Then, I feel that the authors take steps that are not small enough for me; and I wonder whether I should digest every proof (or merely use the theorems). I am not particularly gifted. Still, I strive to improve myself. Do you think that one can learn or train to understand proofs faster?
I want to typeset diagrams describing functions which take multiple inputs and return multiple outputs. These should look like boxes with labels in them like "f" or "g" and with some input wires coming in and some output wires going out. The diagrams I'd like to typeset will involve several such boxes with some output wires connected to some input wires. I can draw some examples of what I want if this description is unclear. I would prefer to be able to do this in xy-pic, for example using xy-graph somehow. Is this a good idea, or should I just learn how to do this in TikZ? Or is there an even better way? Edit: To be more specific, here are the diagrams I want (although their orientation is negotiable, e.g. if you show me how to do this with the diagrams going to the right instead of down that's great). I should have mentioned that I also want to label the wires.
Suppose I was standing in the sea, and touched an electric fence; I would receive an electric shock, because both my body and the sea are conductors, and create a path for the electricity to flow. The sea is so big that it has the capacity to draw and dissipate a great quantity of charge. However, if the sea was drained away, and I was standing on some rocks, would I still receive an electric shock, even though rock is not a conductor? And if I did receive a shock, where would this electricity even flow to? Would it just be dissipated amongst the rocks / soil / sand beneath my feet (even though they are insulators)? My question comes from me wondering why we receive electric shocks at all, when there is usually some form of insulator between you and the charged object, such as your shoes, the carpet, several layers of bricks, and indeed the entire composition of soil and rocks beneath the building that make up the "Earth".
I will be writing a report in which I analyse the performance of a piece of software. I would like to show my data using PGFPlot. My plan of attack is to schedule a script to run on the machine I am using, which will run the program a number of time with a variety of parameters (the main one being the number of processors I use) and dump all the data in to a .dat file. Can PGFPlot this? Can I ask it to average all the tests with the same parameters? I will be plotting a line graph with the average time, but I would also like to plot the standard deviation of the results. Is PGFPlot the tool for this? Or should I be using LibreOffice to generate the relevant data, and only use PGFPlot at the end? Thank you
I dont get why a forward gear allows sliding a car backwards. Any ideas? So this is a car with an automatic transmission. The transmission is in the drive mode (move forward). Car is at the slope facing the hill up. I am in the car pushing the gas pedal very gently. The car is supposed to move forward going up the hill. Instead it moves backwards down the hill, because I am not pushing the gas pedal hard enough. I haven't switched it to reverse. This is where I don't get it, because it turns out that the wheels are spinning in the opposite direction of what the transmission gears tell them to spin. How can this be possible? Or, to put it in a different way, how can a car move backwards when it is in "drive" mode (supposed to go forward)?
I am simultaneously taking courses in functional analysis and commutative algebra. In doing so, I found that there is, at least heuristically, some similarity between the notion of an algebraic variety (essentially, the zero locus of a family of polynomials) and the annihilator of a subspace of a Banach space (the collection of continuous functionals that "kill" the subspace). In doing some reading, I came upon the Banach-Stone theorem, which implies that the algebra of scalars is an analogue of the structure sheaf of a ring, and is evidently an essential ingredient in non-commutative geometry (thank you, Wikipedia). One finds a one-to-one correspondence between finitely generated nilpotent free k-algebras and affine varieties by first asking what algebraic structure (finitely generated nilpotent free k-algebra) corresponds to the geometric object (affine variety). Then, inspecting what sort of geometric object gives the correspondence with the more general commutative rings, we find schemes. This analogue of a structure sheaf makes me think that there might be analogous sort of correspondence in the Banach algebra setting. Is this the case? If so, can anybody provide some references, interesting papers, etc?
The following is a GRE sentence completion question. The most striking thing about the politician is how often his politics have been (i)_____rather than ideological, as he adapts his political positions at any particular moment to the political realities that constrain him. He does not, however, piously (ii)_____political principles only to betray them in practice. Rather, he attempts in subtle ways to balance his political self-interest with a (iii)_____, viewing himself as an instrument of some unchanging higher purpose. Options: a. quixotic, brandish, thoroughgoing pragmatism b. strategic, brandish, deeply felt moral code (correct answer) c. self-righteous, flout, deeply felt moral code d. self-righteous, brandish, profound cynicism e. strategic, follow, profound cynicism I am able to get how strategic and deeply felt moral code fits in the first and third blank but confused about the second blank. What is the intention behind choosing brandish? Why not follow or flout?
While studying Faraday rotation (linear magneto-optic rotation) I came across a fact that Faraday rotation can be enhanced. Verdet constant which depends on the wavelength can be enhanced as change in refractive index with change in wavelength is maximum near resonant light. Now if the incident light frequency is resonant with the atomic transition frequency then light will get absorbed in the medium and we'll get very less light at the output for observation. It is my understanding that optical pumping is done to make medium transparent to the resonant light, as when majority of electrons will be trapped in dark state we'll get considerable light at the output to measure change in the plane of polarization. Is my understanding accurate or is there anything that i have missed? Does optical pumping enhance faraday rotation in some other way also?
I had previously asked about how useful everyday solar physics data is to other astronomers ... But about a year from now, we will have another Venus transit, where Venus will pass between the sun and the earth ... I was just in a meeting with some EPO (education and public outreach) folks about trying to prepare something for the event, and we can do the basic 'make a pinhole camera' kids activities, and use it for awareness of our field ... But is there any novel science that we could use the event for? We're especially interested in trying to find something 'Citizen Science', where we could try to organize people to contribute some data from across the world that might help advance our knowledge of something. (it doesn't even have to be astronomy ... We had an idea of trying to get people to take pictures of the transit, and send the images, and we could try to use it to estimate how the quality of seeing varies, but we weren't sure if there were liability issues if someone managed to ruin a camera or their eyes in the process)
(Please note: I've seen some other questions asked like the one I myself am asking, I realize that I am indeed late to the party, but I am genuinely curious and none of the previous answers have satiated me as of yet. Note that this is a highly hypothetical question, asked by somebody who isn't even a college student studying the idea of physics at this point in time, so go easy on me here. Sorry if this isn't worded well, but I still haven't studied much on the subject, nor am I used to typing up thesis papers. Excuse me please.) Theoretically, it is stated that if you were to travel through a Kerr Black Hole- a Black Hole with a rotating ring singularity- it would allow you to go back to an earlier point in time. Another says you can travel through time using a Wormhole and exotic matter. What I'm curious about is whether or not time travel is hypothetically feasible were one of these true, as in whether or not the sheer force would crush a human by attempting to use one of these routes.
A BibTeX question (using BibDesk). I am having trouble working out how to make BibTeX handle the new Digital Library of Mathematical Functions (DLMF) web page. No authors or editors are listed. DLMF itself suggests (http://dlmf.nist.gov/help/cite) When referring to the web site from a print publication, it is recommended to use the following format. Digital Library of Mathematical Functions. Release date. National Institute of Standards and Technology from http://dlmf.nist.gov/. where the Release date can be found at the bottom of all DLMF pages. None of book, webpage, url, ... does it like this. Also, if I put NIST or DLMF in the author field, with or without braces, I get "NIST, " in the refernce list, i.e., it is expecting a first initial. This is going to be a very highly cited web page. It is the replacement for the venerable Abramowitz & Stegun and will be the standard reference for mathematical functions.
Sometimes I see something like "a mapping preserves the structures of its domain and of its codomain". From Wiki about morphisms in category theory: a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory, group homomorphisms; in topology, continuous functions, and so on. I was wondering why the structure-preserving mappings between two topological/measurable spaces are defined by the "inverse" of the mapping, while the structure-preserving mappings between two groups/vector spaces are not? Why are the structure-preserving mappings between two topological spaces chosen to be continuous mappings instead of open mappings? I also see that "a mapping preserves some property of subsets, points or whatever". Such as Continuous linear mappings between topological vector spaces preserve boundedness. According to Brian's reply to my earlier question, this quote should be understood as "under a continuous linear mapping, the image of any bounded domain subset is also a bounded codomain subset", not as "under a continuous linear mapping, the inverse image of any bounded codomain subset is also a bounded domain subset". I wonder why? It seems at first to me like how continuous mappings preserve topologies, but it is actually in the same way as how group homomorphisms preserve group structures. Thanks and regards!
We tried my electrolyzer with a friend today, we filled a small bottle with HHO gas, and set it on fire. It was loud but not a big deal, like a firecracker. Then we added some soapy water and created HHO bubbles instead of filling the bottle with HHO underwater. Then we lit the bubbles and it exploded so loud that for a while all we heard was just ringing. It was way too louder than when before, same gas same bottle, we even tried it twice with same result. Im wondering why is it so unbelievably louder. I thought that maybe the sound just traveled in a different way, because the bottle was turned in the opposite way (towards the ceiling instead of towards the floor), but im not sure.
Sometimes in quantum cosmology, when we are thinking about 'wave functions of the universe' we have in mind some sort of formal path integral, where we include not just the variations in the dynamical fields (metric and so forth), but also possibly some sort of prescription for summing over all possible topologies. At least, that seems to be some sort of heurestic guess often encountered in the literature (Hawking et al). Now, in String theory, admittedly a different context but there is a rather well defined notion of how this works (basically as a generalization of Feynman graphs over Riemann surfaces). However I don't understand exactly how this is supposed to work in quantum cosmology exactly (say in the Wheeler-De Witt context). First of all there seems to be a massive amount of overcounting already at the metric level (where presumably one needs to mod out by all the diffeomorphisms), but how exactly does one deal with the topologies? Do they only include connected topologies? Is there even a mathematical formalism on how to even approach this problem? Any good papers that deal with this in a comprehensive way?
When I'm pushing a tall, cylindrical object stood on its end (like a Pringles can) I can push it near its bottom, and it will slide forwards, or push it near the top, and it will topple over. So, there must obviously be a point somewhere on the side of the cylinder where it stops moving forwards and begins falling forwards. My question is, how can I calculate where this point occurs? It might be something fairly obvious, like: "above the center of mass" or something like that, but I'm guessing that it's something more complicated, taking into account friction, etc. This knowledge will be very useful in my life, as the next time someone asks me to "slide along the beer" I can whip out my pocket calculator, my ruler and measuring instruments, and finally stop being such an embarrassment. I swear, it falls over every single time.
This image from Wikipedia shows how a black hole would look like: A black circle that acts as a gravitational lens for light rays coming from behind. How would a rotating black hole look like? How would it look like when viewed from side and when viewed from the top (along its axis of rotation)? If I understand it correctly, withing the ergosphere photons are dragged in the direction of the rotation, and just outside it photons would be still heavily influenced by the rotation. Also this video descibes in detail how would it be to descend into a black hole. What would be different when descending into a rotating one? In particular, what would we see inside the ergosphere? And how would it be different below the event horizon?
I've began learning LaTeX for the expressive purpose of eventually creating a resume template of my own. A business school friend of mine showed a very professionally-looking resume he created from a workshop, and I would like to turn it into a LaTeX template. I know there are already many existing resume templates, but I would like to create my own. I also know that there are many tutorials and guides for LaTeX, but I would like to know if there are any that can lead me towards creating templates, specifically something in resume/cv form. I know that it will be a long and arduous task to learn how to create templates, much less a template for a stylized resume, but I would like to make that my goal for learning the language. Would it be simpler to just modify or tweak a preexisting template?