darklight03/StackMIAsub huggingface dataset:
I am writing a document which will contain many small (approximately a page) snippets of text, potentially organized in sections or subsections. To each such section, I would like to attach several "tags" from a predefined list. At a different place in the document, I would like to make a list of all tags and the sections which are associated with each. I have an idea how to make a very primitive tagging system if the tags list occurs in the end of the document (e.g. I can successively redefine a command adding text to it; later I can place this command to list the contents). Does anyone know a better solution? Ideally I would like to organize my tags in the beginning of the document, after the table of contents. I feel there might be a package which does this but I haven't been able to find one.
Suppose, sometime in the future I develop an experimental superweapon capable of blowing up the entire Moon. If I used it to break the Moon into multiple pieces of varying sizes, we would then have giant chunks of Moon rocks floating around. We all know the Moon is drifting away from us at a constant rate. But now, rather than there being a single concentrated mass we have multiple masses. If I understand Newtonian Gravitation correctly, the bigger the object the more gravitational pull it has. For example, if I landed on Phobos (if that is possible) and jumped, it would take a longer time for me to fall down than it would, say if I jumped while on Earth's Moon. After being broken up into smaller pieces, which of the following would happen to the Earth's Moon? A) The Moon remnants keep drifting away from us, regardless of the fact that the pieces are now smaller. B) The Moon now does not have the "power" to counter Earth's gravity due to not being the massive object it used to be, so the pieces all fall to the Earth and that ends everything. C) The Moon gets close to Earth but does not fall down on the surface. The pieces form an asteroid belt made of lunar remains much like the Jovian planets, which will never get away or closer to us and remain in a relatively perfect ellipse?
I am always surprised by the subtleties that are embedded in the wave/particle dualism. That is why I read again and again the paragraph in the Dirac's classical text dealing with the single photon interference. Here, it is clearly stated that any measurement of the kick-off of a mirror would cause the photon wave function to collapse, then completely spoiling the quantum interference of the probability distribution. So I wonder if here some ad hoc definiton of measurement is assumed, since in general terms, no matter how I chose to support the mirror, that support will experience a momentum transfer (or radiation pressure) therefore its kick-off will be definitely measured. To be precise, I found no reason to assume that, provided I have a sensitive enough device, I could not measure the single photon radiation pressure (gravitational wave interferometers actually can do that). So the point is that I could, but I don't do it? Subsequent inspections of the Dirac's text unfortunately did not improve my understanding.
First of all, English is my foreign language. I've never thought of this until the release of the film Dr. Strange the supreme sorcerer. My co-worker argued that Dr. means Doctor (as a job), while I translate it to Dr (as a title, like Master, bachelor, doctor). I think Dr is, of course, short for Doctor, which can be both a title or a job. However, I'm not so sure if they have the same meaning (when using as a prefix). The question is: Does Dr. as a prefix could mean both as a job and a title or only one? If it has only one meaning, how do I distinguish those two? How do I know if it's being used as a job or as a title? P/S: Also, does Dr. as a title has anything relate to those in {Master, Doctor, Bachelor}?
The class of words called 'words of comparison' includes words such as 'higher' and 'highest'. The words 'higher' and 'highest' express comparative height. The term for the class of words that includes 'higher' is 'the comparative'. The term for the class of words that includes 'highest' is 'the superlative'. Is there a linguistic term that denotes the class of properties that words of comparison compare? I'd appreciate whatever answers people can offer, but I'd prefer answers that include a completion one of these two similes. The word 'higher' and the word 'highest' are to the word 'height' as the phrase 'the comparative' and the phrase 'the superlative' are to '_____'. The word 'higher' and the word 'highest' are to the property called 'height' as the phrase 'the comparative' and the phrase 'the superlative' are to _____. Thank you, -Hal
Is there an adjective that can express the concept of a law that supersedes other laws? I would prefer a single adjective that has legal connotations, although a present participle will suffice. The phrases supreme law and overruling law approximate this concept, but supreme merely seems to indicate significance, and overruling implies direct contradiction, rather than "displacement in favor of another" as supersedure indicates (the laws do not run completely contrary to one another, but one is more appropriate and takes precedent). Also, the phrases the law which has primacy over other laws and the law which supersedes other laws are too wordy and awkward for my intended usage in a paper about a certain contentious Supreme Court decision. Is there an adjectival form of "primacy" or "supersedure", or another adjective which accurately describes this legal usage? Here is the sort of context in which I intend to use such an adjective: The ruling demonstrated disregard for the ________ constitution/law/legal right.
I want to fill the holes in my knowledge and get to a masterful level at undergraduate material, so I am looking for books to help me with that. I recently took the GRE Math Subject test and I focused on calculus problems. I am not sure how I did and I will be happy getting into just one graduate school, but what I really want to do is get better. I do not have much to do for the next few months, so I want to become expertly proficient in calculus, linear algebra, ODE, abstract algebra, number theory, and any other core subject. I have taken classes on these subjects so I am looking for books that do the following: Cover material in a concise and complete manner Have advanced questions that help me prepare for future learning Have answers to the questions Thanks!
Tchrist's comment here on my answer to an etymology question brought the following to mind: Ox (from Old English oxa) maintains the same vowel in the plural oxen that it has in the singular. But child has a different vowel (an English short vowel) in the plural. Brethren, an archaic or specialized form of the plural of brother, is a similar case; it changes its vowel in the plural as well, through i-mutation. (Yet brothers does not.) I've looked at http://etymonline.com to find these two words, as well as looking briefly in an introduction to Old English published by the Medieval Institute at Western Michigan University, and discovered that child has an older plural, which might be childer in Modern English. But I'm still not entirely clear on its history; and I'm confused about what the text says about brother. Why do these two words with (standard, archaic, or alternative) plurals ending in -en have vowel changes in the plural, when ox does not?
I just had a conversation where the sentence 'The system is broken because it's fixed!' was correctly spoken under the pretense where fixed means that it's rigged. Assuming that context of rigged matches as a weak synonym for broken, the question came up - what's the word for a pair of words that are simultaneously synonyms and antonyms? I am not asking about autoantonyms. I am not even looking for a single word. I am trying to find a term to describe the relationship of two different words, where one is an autoantonym and where one of its definitions is synonymous with the second word, causing the two words to be synonyms and antonyms at the same time. In my example: fixed = rigged: fixed and rigged are synonyms fixed = repaired: fixed and rigged are antonyms What is the label given to the relationship between fixed and rigged?
In the Hindi language there is an equivalent phrase which is widely used when a common man who is trying to suggest an idea to a person in power or some higher authority respectfully without challenging the latter's incompetency to 'not see the flaw' in the system. Example: A head of the police department being addressed by a common man (person of a lower stratum) giving an intellectual suggestion. I have translated a suggestion which was originally in Hindi. Common man: Small mouth big words but Sir, wouldn't it be a better idea to install wireless communication systems in police station too? Is this phrase used in a similar fashion in English too? The only phrase I have seen is 'in my humble opinion' used at the start of sentence in such cases. Another phrase I know is 'Small mouth, big talk' but I haven't seen it used as a prefix in sentences. Any other appropriate suggestions are also welcome.
I am a physics undergrad, wishing to pursue a PhD in Math. I am mostly self taught in the typical math undergrad curriculum. I am looking for more input, in ways I can improve my mathematical thinking. So, my question is once you read a proof of a particular theorem, what should be the important things that you are looking for in the proof. How should you approach it? So, one of the things I have learnt to do is to look at every hypothesis of the theorem, and see its effect on the proof, or how do the subsections of the proof correspond to parts of the hypothesis, and how they fit together. However, what I find difficult is to recognize how the proof fits together in the general scheme of things. What should I ask or explore after the proof? How can I learn to solve problems more quickly and effectively through proof - reading? I am very slow are problem solving and wish to improve that. Lastly, I am terrible at coming up with new examples, and I don't even seem to remember examples beyond very typical ones. How can I improve this ability through reading of proofs? I hope this question is welcome here. Otherwise, please feel free to close it. I understand this is a vague and difficult question, but any kind of input (however small) will be highly appreciated.
I've learned that there is no authoritative dictionary for English. I wonder on what juristic basis students are corrected when making mistakes in an English class. How can someone say that whatever the student did wrong is not considered correct English by other people. In German schools, students may only be "punished" (by getting a bad mark) when they had the chance to know better. For example when they have violated a rule in the official German dictionary. That is impossible when there is no official dictionary. How do schools in Britain or the US handle that issue? Note: There is no official reference of the German language either. However, authorities in Germany are advised to use the German language as specified in a dictionary called "Duden". Pupils in Germany are graded using the "Duden" dictionary. Other German-speaking countries may use other dictionary.
On our sister site a user recently used the term "tags" in relation to taxis in China. I thought it might mean some kind of official authorization to operate a taxi. But upon clarification I was told "tags" actually means "License plates and stickers that show the registration is currently valid". I'm a native speaker of Australian English and I've travelled in almost every English speaking country and didn't know this use of "tags", though I guess this is not a topic that's come up in conversation in my travels often either. In which countries would this sense be known? Just USA? USA and it's neighbours in Canada and Belize? All English speaking countries other than Australia? Even in Australia and I somehow remained ignorant of it despite having classic cars as a hobby for a number of years?
I am working on a Project and one of the major part of it is a GAS Detector, The GAS Detector detects the large number of flammable gases, but in order to test the Detector I am required to release certain gases in a room from the GAS cylinder with different flammable gases. There is no such thing in a room which could cause ignition, still i wonder if the Static electricity produces in a room somehow, can it cause the fire or some harm due to this gases ?? Is there even the slightest possiblity that it could be harmful ? I just want to know if it may cause so that I could tell my Professors why I am testing the GAS sensor with the Hydrogen gas present in air.
Let us assume that we want to describe the full process of photon emission by electron A and absorption by electron B. Therefore electron B must be on the forward lightcone of electron A. In the normal forwards in time description a virtual photon propagates from A to B depositing a certain amount of energy and momentum onto electron B. But does this process alone also describe the recoil of electron A? Should one also include the backwards-in-time virtual photon which propagates from B to A depositing an equal amount of negative energy and momentum back onto electron A? Between measurements no-one is "looking" at a quantum system so in the spirit of "what isn't prohibited is compulsory" maybe it evolves both forwards and backwards in time. One could say that the product of the forward-in-time and backward-in-time propagators give the full probability of photon emission by A and absorption by B. Is this where the Born rule comes from (as in John Cramer's TIQM)?
Let q be a generalized coordinate with a conjugate momentum p and a potential resulting in a periodic motion of q. What is the meaning of the Fourier transform of q(t) over its period? Can this be interpreted as the distribution of momenta? I know this is the case in QM but what happens in the Classical case? For instance for a particle in a box (classical) with an initial velocity of p/m, the motion is a triangle wave. The Fourier transform is a squared sinc function. As the triangle wave gets smaller, the F transform spreads out and vice versa. Very nice but the only two momenta for the particle are p and -p as the particle either moves up with constant speed or moved down at constant speed.
Complex analysis, and in particular contour integrals and the residue theory have proved a very powerful tool in computing a large class of real function integrals which would be quite troublesome to compute if only within the scope of real calculus. There are a great many techniques designed for this purpose, for instance, both the choice of the complex variable function and the choice of an appropriate contour is critical to our success of computation. I want to study these techniques systematically, so I want recommendations for tutorials that cover them in a systematical way, the more inclusive the better. In a word, I want to learn as many those techniques as possible, so I think such a tutorial is a must. Any advice is welcome. Thanks! Ps: the tutorial I currently have at hand is Stein's Complex Analysis, it is good but covers too few exercises about such techniques.
S.E friends, Due to my genuine interest to Goldbach's conjecture, I decided to self-study the subject of additive number theory on this upcoming Fall. Before jumping to such fascinating field of mathematics, I decided to self-study "introductory" number theory as I never took a number-theory course in past. While browsing through websites and libraries, I found books like Ireland/Rosen, Apostol, Nathanson,Hardy/Wright, Sierpinski, and Niven/Zuckerman/Montogomery. I really like them but I am not sure what book would be best for my plan to study additive number theory. Ireland/Rosen looks like it emphasizes algebraic aspect and assumes familiarity with elementary number theory from readers, Hardy/Wright and Apostol looks like an introduction to analytic number theory (which I am doubting if it is better idea to just start with additive number theory), etc. Currently, I fear that choosing wrong book might kill my curiosity to the number theory. What books do you recommend to prepare for analytic number theory?
I hope this is the right word to use. To me, these forces seem kind of fanciful (except for General Relativity and Gravity, which have a geometric interpretation). For example, how do two charged particles know that they are to move apart from each other? Do they communicate with each other somehow through some means? I've heard some people tell me that they bounce together messenger photons. So does one electron receive a messenger photon, go, "Oh hey, I should move in the direction opposite of where this came from, due to the data in it", and then move? Aren't photons also associated with energy, as well? Does this type of mediation imply that electrons give off energy in order to exert force on other electrons? Every electron is repelled by every other electron in the universe, right? How does it know where to send its force mediators? Does it just know what direction to point it in? Does it simply send it in all directions in a continuum? Does that mean it's always giving off photons/energy? I'm just not sure how to view "how" it is that electrons know they are to move away from each other. These questions have always bugged me when studying forces. I'm sure the Standard Model has something to shed some light on it.
Is it possible to let LaTeX manage minipage placement similar to how LaTeX manages figures and tables to be placed? This question comes from my previous question. I could move the minipages around manual for the best use of space but this becomes a hassle as the number of minipages increases. If possible, it would convenient for LaTeX to handle this task. Can this be done? Note: I want management like a float environment but not a float. As I stated in the linked post, I want to place minipages that butt up against each other across three columns. I dont want wasted white space (like a float would induce). I do want the the minipages to be able to rearrange themselves for the best use of the page without me going in and placing them higher or lower in the document.
In case of a charged particle which is travelling at a uniform velocity, the electric field due to it at a given point doesn't change instantaneously . The reason for this delay in change of electric field , physically , can be explained as the time the electric field needs to propagate to that point, or, let's say, the change in electric field takes some time to propagate . I would like to know what exactly does it mean by a propagating electric field, and how exactly does it propagate ? What can we put forth as a reason to explain this propagation at a speed equal to the speed of EM radiations ? (I hope the coming up answers would comprise an important part explaining this physically. ) I guess we can derive the speed of EM radiation from Maxwell's equation ; can we show that this propagation too has the same speed ?
Mass and energy are interchangeable. Does that mean time and space are interchangeable too? Reason for question: The only difference I can comprehend between matter and energy is that energy has no duration; a photon does not age (even if the universe does). Matter has endurance, and travels through time. Close to a black hole (in regions of high gravitational fields), time slows, and the speed of light (as measured externally) would seem slower (would give doppler-like transformations); effectively time is converted into space; a photon may "appear" to take a year to travel a few yards (again, as seen from outside). But from the inside (the photon's-eye view) a light year is still a light year. So, can an area of space a few feet across (externally) be a light-year wide (internally) (TARDIS sort of thing)?
I've asked a question about olfactory's relation to observational and it got me thinking about other senses as well. There are five (or six if you're supernaturally believing), so, what are the exact term to fill out the blanks in the following? It's the bold parts that are interesting and I wonder if the already filled out ones are correct. Visual the beauty is in the eye of the beholder Audial the euphony is in the ear of the listener(?) Olfactious the fragrance is in the nostril of the inhaler Flavorous(?) the taste(?) is in the bud of the eater/taster(?) Touchy/sensefull(?) the feeling is in the hand of the caresser Supernatural the spookiness(?) is in the mind(?) of the medium(?) Kindly, please note that I've no intention to start using these expression outside when interacting with average people. I'm just curious about the linguistic translation between senses and my mathematical mind craves completeness. I know how to express all six sentences in English. I just don't know how to express those while "following the suit", so to speak. It's a purely and strictly academic curiosity.
Take a look at the image below. At the point B a motor is spinning really fast in anticlockwise direction. The motor should be connected to a propeller (I didnt draw it) that will pull the bar upwards but let's suppose the propeller is not connected and the motor is just spinning really fast at X rpm. A person is holding the bar at position A. What torque or force will the person at A feel? The bar has length L. I know if I connect the propeller the bar will be pulled upwards (you dont need to tell me about this) but I am pretty sure it's gonna generate a "reaction torque" in the bar that will be transmited to the person holding at A. I would like to know the formula to understand the force/toque that A will feel.
This part of the book says that, because the two liquids have the same pressure at the same height (that's true), then if a liquid has a higher height, the liquid would have more pressure at a horizontal line, and then the liquid would tend to flow to the weaker side. However, it isn't really pressure that drives the liquid, it is force (or acceleration). So the flow of a liquid shouldn't depend of the pressure, but the force at that line. And the force, depends of the diameter of the tube, because force is dependente of pressure. So in this case, the two tubes have diferente diameters, therefore the acceleration that drives the liquid from one place to another would depend of the diameter. Then we couldn't just say that the liquids tend to equate.
So I have often read that, at least in e.g. northern Europe, in the colder seasons, there is not enough UV (-B) light arriving from the sun, so many people have not enough vitamin-D from that. At first I thought it was simply due to the sun "shining" for only a much shorter period of time in winter compared to summer and hence less possible exposure (not to mention that most of the skin area is covered then). But I just had a thought coming to my mind, thinking about that in the mornings and evenings, we mostly see red light here, the higher end of the visible spectrum not getting through. I am not familiar with the physics behind that phenomenon, but thought that the higher-end of the spectrum like the invisible UV light may not be getting through here for even longer parts of the day towards and away from high noon, and that in winter, the part of the day where UV gets through is maybe very narrow and that's why it's said not to be enough. Is that correct? And how exactly does this work physically?