darklight03/StackMIAsub huggingface dataset:
Theoretically, a change in either electric or magnetic field will cause a current to flow , I am already familiar to Faraday's law of electromagnetic induction, so I tried to search about producing a current using a varying electric field, didn't find anything, I found an interesting apparatus though: Tesla's electrostatic induction apparatus. My question here is about Lenz's law, will this law be applicable here? I know the law is in case of magnets , but I tried to imagine what will happen if we tried the coil magnet situation where approaching coil to the coil a resisting force will develop , but if we replaced the magnet with an electret (electrostatic equivalent of permanent magnet), as it approaches the loop the side near the electret will obtain a partial charge opposing to charge of the electret causing it to approach faster (the opposite of what happens with a magnet). In the end of the article Tesla wrote The output of such an apparatus is very small, but some of the effects peculiar to alternating currents of short periods may be observed. The effects, however, cannot be compared with those obtainable with an induction coil which is operated by an alternate current machine of high frequency, some of which were described by me a short while ago. Why was the output of such an apparatus small? Does an electric field have a smaller influence on electrons than a magnetic field?
I just met with a very basic question. (Might even sound silly!) My textbook kinda says(not exactly), 'Whatever flows is a fluid'. That got me wondering because we are creating a whole category of matter just because they flow! So there must be some significance to 'flowing'. That further led me to ask why in the first place should we say liquids and gases "flow" and not "move"?! It seems to tell me that there should be a major difference between the physics of flow and movement. What is it? PS:- I don't want the difference in meaning from a dictionary but a scientific difference. Please don't get too mathematical. I haven't acquired good mathematical skills YET. Edit:- Okay. Since a comment below says "Movement is actually seldom defined very rigorously", I suppose I must refine my question here. Consider someone is saying that a box moves on a table as you applied a force on it. Now why is that person saying it 'moved' rather than it 'flowed', here? What is the difference between flow and movement in this case and how can we generalize the idea?
I have a hard time understand the statement that When you only look at the classical limit or classical physics, string theory exactly agrees with general relativity Because from what I know, String Theory assumes a fixed space time background (ie, all the strings and membranes interact in a fix background, and their interaction gives rise to fundamental particles that we observe), but General Relativity assumes that the space time background is influenced by what is in it and the interaction between them. Given that both have very different assumptions, what do string theorists mean when they say string theory agrees with general relativity in a classical limit? Or more specifically, how does string theory--a fix spacetime background theory-- reconciles with the general relativity on dynamic spacetime background part? I can understand a fix, static spacetime in the context of changing, dynamic spacetime background, but I cannot understand a chanding, dynamic spacetime in the context of a fix, static spacetime background.
What are the rules for typesetting superscript, subscript and fractions (as in a/b but with an horizontal fraction bar)? I am centring the subscript on the baseline, the superscript on the cap height and the fraction bar on the x height. Latex appears to be doing that as well. What I haven't figured out is how to position the numerators and denominators relative to the fraction bar. I know the bounding box of the numerator and denominator, but how much spacing should there be with the fraction bar? I can access all the regular metrics of the font (ascender, descender, leading, cap-height, x-height). Edit: (based on appendix g) As far as I can tell, the distance between the fraction bar and the numerator/denominator box is three times the fraction bar thickness. It seems to me that this would not produce a symmetrical output if the font descent value is different from the ascent value minus the cap height value. I mean the apparent distance between the fraction bar and the bottom of the numerator text, and, the distance between the fraction bar and the top of the denominator text. Visually either the numerator or denominator would appear further away from the fraction bar even if both contain the same text.
The idea is that the difficulty of the game of chess is derived primarily from the asymmetry between the king and queen. all other chess pieces are arranged symmetrically and can move symmetrically, then, if there were two queens (or two kings) instead of a king and queen for each player, the game would be exactly symmetrical. The idea is that, in this case, if the second player repeats symmetrically the moves of the first, the outcome should be a draw. But I'm not able to prove this (and perhaps it is not true) but it seems that the symmetry should introduce a simplification in the game who may moreover allow to define a strategy. My knowledge of game theory is very poor, but I'd like to know if there are any studies on this symmetrical variant of the chess game.
I have gone through a lot of seemingly similar questions/issue but have not find a solution. Since we are working as a group there are some that prefer to write using MS Word-EndNote. I have all references in BibTeX and these are updated from time to time (when something moves from pre-print to actual publication with addition of issue/page etc, minor corrections in citations in the main database, etc). I have no problem importing my automatically generated BibTeX file into EndNote. However, this BibTeX file gets updated from time to time and I would like to keep the EndNote database up to date as well. Re-importing the new BibTeX file into EndNote makes the process unnecessarily difficult, since you would end up doing deduplication of the results. Does anyone have a solution? There is a willingness to change to Zotero, so if you have a solution using Zotero, I'm also quite interested. Simply put: .bib file that is updated from time to time, is there a way to keep my EndNote/Zotero database updated based on this .bib file?
I am writing a technical research article. I have an experiment where precision can be easily determined (bid-ask spreads for the economists). Calculating some formula twice based on the precise observation of the upper bound and the lower bound does change the results (obviously) and is not negligible, but it does not negate the theory that is underlying. That is, the effect of the measurement error is clearly visible, but in general the theory can still be accepted. How do i express this in a concise way? Thanks. edit: Per request, more details. I can observe market values, but with limited precision. I only observe two values, bid and ask, and the true value lies between those. Calculating measurements using bid-values gives me different results than using ask-values. Both results confirm the theory I'm testing. The difference exists, but it does not fundamentally change the conclusion that the theory itself can be confirmed. Is there a concise expression for 'confirms, but not as strongly' or 'doesn't negate, but differences are considerable'? I guess it is obvious why I need a concise expression...
John Rennie's answer to this question got me thinking about the water supply in a house. I know that water supplies are normally operated at an over-pressure with respect to atmospheric pressure to make sure that if you open the tap the water will flow out due to the lower pressure at the exit of the tap (including a correction for pressure losses due to the plumbing and potential height differences). What I am wondering is how adjusting the tap results in an adjustment of the flow rate from that tap if the water pressure in the main supply is a constant (probably by approximation)? Because in that case the pressure upstream is fixed, the pressure downstream (atmosphere) is fixed so pinching or opening a valve should not change the flow rate. Obviously it does change the flow rate so there must be something else going on. The only thing I can think of is that the water supply somehow acts as if there are parallel connected (hydraulic) resistances as illustrated in the schematic below which makes sure that the distribution at the flow split can be adjusted. Is that the right thinking or is there a different argument why the flow is adjustable? (The dashed line indicates some way of rerouting the water back to the mains, although that cannot be a direct connection because that would allow a pressure drop over this section)
Wikipedia mentions that: Some languages flexibly integrate onomatopoeic words into their structure. This may evolve into a new word, up to the point that it is no longer recognized as onomatopoeia. One example is English "bleat" for the sheep noise: in medieval times it was pronounced approximately as "blairt" (but without an R-component), or "blet" with the vowel drawled, which is much more accurate as onomatopoeia than the modern pronunciation. Did bleat really lose its onomatopoeic character? Is "baa" used instead in all situations? Furthermore from the book "A Grammar of Iconism" By Earl R. Anderson: According to the passage above: When onomatopoeic words are used as verbs, do they lose their onomatopoeic character? ( not all of them but some of them in time? or depends on the context?) Can we still say that shiver, growl and bleat are onomatopoeic words? Or did they inherit their onomatopoeic label from their more mimetic versions: brr, grr and baa?
When using the method of action variation to establish GR field equation in one of the steps we use Stock's theorem on an arbitrary manifold to show that one of the terms contributes nothing to the variation wrt the inverse metric. See for example the Wikipedia entry on Einstein-Hilbert action. Most texts that I read, without writing the actual steps of calculations, simply say that variation at infinity vanishes and hence the above mentioned term vanishes. Can someone please do the actual calculation involving the application of Stoke's theorem for an arbitrary manifold here, which I do no see in textbooks, as I am confused, in particular, are we assuming the variation of the inverse metric or its covariant derivative to be zero at infinite timelike or spacelike coordinates?
In this question the issue came up as to whether there's any difference in the level of politeness/correctness involved in I'd rather not say as opposed to I'd prefer not to say. My own gut feeling is the prefer form is a bit more "formal" (and thus arguably more correct/polite). This NGram shows that I'd rather occurs far more often than I'd prefer. Partly that's just because the rather form is more common, but the difference is far less marked with the more formal I would rather/prefer. I take this to mean rather is more suited to casual use/conversation when used with this meaning. It could be lots of verbs besides say, and I don't think the not is necessarily relevant here either. But usages vary for certain alternatives - for example, go blind only seems to work with rather. That's just my opinion. Does anyone have arguments/evidence/sources to either back up or refute the proposition that I'd prefer not to say is more formal than I'd rather not say?
I'm about to dive into LaTeX in preparation for writing a (technical) Master's Thesis. Since I'm kind of disappointed with the disregard to typography that is sometimes shown in such works I want to do it better, and just picked up The Elements of Typographic Style by Robert Bringhurst. Thanks to LaTeX and clever templates there are of course many things I no longer need to worry so much about, but there were interesting notions such as using small caps for acronyms and text figures ("old-style" small numbers), which I'll likely use rather frequently. I've found the syntax for these two, but I fear there are other aspects that I should also know right from the beginning so that I correctly set the markup right away and don't later need to go through the document for all that stuff. So long story short: Does someone know a nice guide on using LaTeX in regards of good typography, rather than all the technical aspects of constructing and structuring a document for which there's plenty of reference?
This is a soft question. It's extremely commonplace for mathematician's to refer to work as "elegant," "beautiful," and I've seen many compare the process of doing mathematics to painting, or playing music. I think that for the most part, I can understand how certain theorems, formula, or general theory can be evocative, surprising, or maybe just confounding. However, what is less clear is how far the analogy of art can be extended. Art, as much as it makes one elated or excited, also has the capacity to elicit feelings of sadness or melancholy (or any further scope.) I was wondering if this is the case for mathematics as well. I know certainly some people have cited the proof for the four-color theorem as "disappointing," (although I don't have a suitable background to have a stake in this) but this doesn't seem to have quite the same flavor as a musical masterpiece that makes one feel negatively. I cannot think of such an experience that I have had, and I'm curious to see if maybe there are some examples that others feel strongly about. Here are some non-examples: Freshman's Dream: I'm not really interested in the feeling of something you'd hope works, but winds up being false because of an error Math that's too difficult for you to understand. edit: I was surprised to see such a decidedly negative response to my question. Maybe I have it all wrong, in which case, I'd also like to be corrected with a convincing argument.
I think this is a genuine math problem. And it's somehow related to knot energy but not directly solved by the latter. Why can't I tie a hard knot on a rope of infinite length? By infinity I mean you never pull back either ends of the rope. And I attentively add a constraint to the rope that the rope is smooth thus no friction. So the problem is only about the topology (not exactly) of that rope. I cannot think of a better word than topology since the topology of the rope should never change. But apparently I don't know a better one. In my preliminary thoughts, there should be a solution that performs a integration involving the direction and twist of the rope along the infinite length. And the sign of the integration determines whether it's a hard knot or not. And the fact that you cannot pull back the end means you cannot change that sign.
I was soldering an LED when accidentally the soldering wire touched the LED's other Pin while the soldering iron was touching the other and the LED lit up, not bright but bright enough to be seen. I did it again to see did it actually light up, and it did. I noticed my bare feet were touching the ground so I raised it to observe, the LED got dim. Another thing I observed was that no matter what pin (cathode or anode) touched what (soldering iron or soldering wire), it lit up. Why did it lit up? I know that heat causes particles (electrons in this case) to move (kinetic molecular theory), but does it move enough to make an LED light up? As a diode it has a voltage value after it allows current to flow, was the heat enough to make it past that limiting voltage? (I don't remember the actual term). Why did the polarity not matter? I have no clue about this. LED like any other diode is biased means allowing current flow in one direction, than why does this happen? Does the electron movement not matter in this case?
Sometimes I hate classes for mathematicians. It is not their precision and formality in building the concepts, but they never give a motivation. So in the course my professor started right with the definition of vector space, assuming I suppose that everybody knows what he is talking about. Well, reading some books for beginners like me I've realized that vector spaces are actually a generalization of working with the properties of Euclidean spaces. Now the topic is about linear transformations. I understand the definition, they are special cases of mappings. Well, the thing is that I don't know why the definition has to be so, what is the real motivation for such a definition?. what is behind the meaning of 'linear'? My first impression is that maybe it has something to do with just preserving the operations of vectors, though I don't know why. What makes linear transformations to be special compared with those that are not linear? Sorry for this question, maybe it is too naive but it's really important to me.
I had an interesting conversation with CuriousOne the other day about the question Experiment that demonstrates the wave-particle duality of electrons. I thought that wave-particle duality existed, CuriousOne thought it didn't (whether CuriousOne thought this wasn't true for both light and matter, or just matter I'm not really sure). Some of the comments were really interesting, and I wanted to know what some of the physicists here thought. The comments on the question are just below the main question, and are just below my answer to the question (now moved to chat). Please don't close this with "not enough research" as the reason, I did look into it, but some of CuriousOne's comments left me kind of confused. In terms of people thinking this is a duplicate: I am asking whether there is experimental evidence for electrons having a wave-particle duality (this duality being like the one light has) and whether the double-slit experiment is an example of experimental evidence for this. Question: Was de Broglie's hypothesis that electrons (and other matter) have wave-particle duality correct? Does the double-slit experiment prove this, or have anything to do with this? What is some experimental evidence for de Broglie's hypothesis? Thanks!
In elementary school, I was taught the rhyme: "i" before "e" except after "c", and in words like "neighbor" and "weigh" Obviously this means that "ei" is used in "deceive" (it comes after "c") and "sleigh" ("gh" follows it). The word "weird" does not follow this rule, and I have always thought that to be weird (please pardon the pun). It has neither a "c" nor "gh", so why does it have this "ei" vowel combination instead of "ie"? While writing this post, I noticed that "neither" also disobeys the rule, just like "weird". At first, I thought that maybe the "English gods" thought it would be a funny meta-joke to let "weird" have a weird spelling (like how "awkward" awkwardly has a "k" surrounded by two "w"s), but apparently there are other words as well!
To start with, I have almost no any experience in the theory of finitely additive (f.a.) measures, but I work a bit with countably additive (c.a.) ones and find the theory in the latter case amazingly beautiful. My concern is that at the moment measures have been introduced as an extension of such notions as area and volume, I can understand that the additivity property came alone naturally. However, I believe, that at that moment the choice f.a. vs. c.a. might not have any strong arguments. Later, it appeared that in many cases the space of c.a. (but not f.a.) measures is the dual of a corresponding space of all bounded continuous functions. Since the latter is a pretty "natural" object, I would say that its dual is "natural" as well. Would it be right to say that c.a. measures are more "natural" than f.a. ones, or that it appeared to be more successful/useful, and if so - why do we need the f.a. measures? I hope, that a bit loose formulation of the question still allows for an answer.
I recently started reading the book Multiple View Geometry by Hartley and Zisserman. In the first chapter, I came across the following concepts. Projective geometry is an extension of Euclidean geometry with two lines always meeting at a point. In perspective, geometry parallelism does not exist. Then he goes on to explain how the points at infinity in the world like the points at the horizon appear as a line in the image of the world taken by a camera. Then he says a line which I cannot relate is the following.. The geometry of the projective plane and a distinguished line is known as Affine Geometry and any projective transformation that maps the distinguished line in one space to the distinguished line of the other space is known as an Affine transform. I have the following questions Is the camera plane the projective space of the real world? Is the line which is the image of the horizon the distinguished line? Whenever we do an Affine transform do we need to look out for a distinguished line? Why does just a distinction of the geometry a line in the perspective plane make the geometry an Affine geometry?
I've landed in a physics debate amongst bike mechanics. In a typical bicycle hub you have a simple bearing; the cups are set in the hub, the race (cone) threads onto the axel and there are just loose ball bearings in between (no ball retainer). When properly adjusted, there is no play in the system, and the axel turns smoothly. I imagine this is an elementary question, but when you put weight on the axel (rider on the bike) is the force concentrated on the bottom of the cone, or is it evenly distributed to all of the balls around the cone? What forces are at work in a bicycle hub? I made this image for the sake of convenience if anyone feels so inclined to be awesome and use it to make a diagram/illustration: Exceptionally illustrated answers will be worthy of additional bounty (more up-votes means more bounty to give :) I will offer a bounty of everything I have for an exemplary answer to this question).
Is it correct, and safe to say, that -- generally speaking -- verbal constructions with "with' are to a certain extent more widely and commonly used in AE than in BE and other varieties of English ? E. g. Speak/talk with (as opposed to the shared speak/talk to); visit with (=chat/converse with); meet (up) with (originally chiefly AE); get back with someone (as opposed to the shared "get back to"); stick with (as opposed to the shared "stick to"); check back with (as opposed to "check back to"); compare with (as opposed to the shared "compare to"); correspond with something (as opposed to the shared "correspond to"); interview with someone (as opposed to the shared "interview someone"); consult with someone (as opposed to the shared "consult someone"); conform with (as opposed to the shared "conform to");(...)
Before starting algebraic geometry, I got some understanding of Compact Riemann Surfaces which is more or less rigorous; and then I attended a couple of lectures on analytic geometry. I did not quite fully grasp the analytic geometry rigorously; but it stuck in my mind and this previous experiences helped me greatly when learning algebraic geometry. However I am not able to imagine what would be the precise analogue of Cartan's Theorem A for algebraic varieties over a field. There is the wikipedia article: http://en.wikipedia.org/wiki/Cartan's_theorems_A_and_B which tells me the precise analogue of Cartan Theorem B in the book of Hartshorne. And indeed it is really analogous. But it does not mention Theorem A. Note that here I am restricting the situation to varieties out of fear of any pathologies schemes might have.