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?


Background: In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets. "Measurement" takes place when a screen is placed on one end, blocking one of the states. The final measurement we perform (spin state of particles exiting) is heavily dependent on whether we perform a measurement or not, whether by blocking particles exiting the device or by blocking particles by setting up a screen within a modified SG device The interaction between the particles and magnets should also exert a force on the magnets, causing them to move slightly. The motion of these magnets seems to not affect the outcome of the experiment significantly, yet that would imply that the motion of the magnets could be measured without affecting the outcome of the experiment. This seems at odds with Heisenberg's uncertainty principle, that we are getting information for free. My Professor tells me that the force exerted on the magnets by the particles is so minuscule that it cannot be measured (I assume it is similar to how we can't measure particles' momentum and position simultaneously, because any photons we shoot at the particle will end up imparting change?) What's going on here? I wanted to double check here and see where I went wrong with my assumptions.


How are Superposition and Entanglement related? I don't know much of Quantum Mechanics. I am CSE student and got started with this Quantum Computing. It is interesting! If anybody can help me on this, without digging deep into mathematical details. "The principle of quantum superposition refers to pure states of a quantum system. One considers a primary beam of quantal entities that passes into a primary beam splitter or quantum analyser that has multiple output channels. A beam has a pure state when every one of its quantal entities passes into one and the same output channel. A primary beam with a pure state is passed into another, different, secondary beam splitter or quantum analyser. Then the emerging quanta are probabilistically in its several output channels. These several emergent, intermediate, beams are respectively pure with respect to the secondary analyser. They are then passed to respective copies of the secondary analyser, arranged so as to bring them together into a single reconstituted beam. That beam is then passed to a copy of the primary analyser. In general, it will be probabilistically split into the several output channels." - Wikipedia I did not get that! Any help is appreciated.


There are lots of ways to apply the mean field method to deal with the Ising model whose ground state is a ferromagnetic state. Hence, it is easy to find the order parameter named magnetization to describe the mean behavior of spin-spin interaction. But, in the antiferromagnetic Ising model, the ground state is an antiferromagnetic state, and I realize it is difficult to find a parameter which effectively describes the mean interaction. If I choose magnetization similar to what we did in Ising model, then, I find it is zero, the mean field is always zero. I get nothing from this mean field. I cannot find a direct physical parameter describing the system to replace the spin-spin interaction. Does this imply that the mean behavior of spin-spin interaction is always zero? Is there a mean field method to deal with the antiferromagnetic Ising model? I hope you can help me, thanks!


My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an equation, but that's about it. Similarly, I can follow arguments that pseudovectors behave differently in "mirrors" than vectors. But my response to this is always: Okay, so what? When would I ever "do physics" in a mirror? The usefulness eludes me. I'd like to gain a better understanding of the importance of this difference. When is it useful for an experimental physicist to distinguish between the two? When is it useful for a theoretical physicist to distinguish between the two? I believe symmetry is important to at least one of these, but would appreciate a practical rather than abstract argument of when one has to be careful about the distinction.


We are two partners about to launch a product that is currently called "Coralline". We are inspired from the animal and its habitat in underwater. Since this will be an international product I am having second thoughts about this word because it is hard to pronounce and transcribe for non-native English speakers. Also I believe it is not a commonly used word in English so even native English speakers will not grasp the meaning at first glance. I am looking for a word that resembles Coralline or coral reefs, like "seaweed" etc. My criteria are: Unique Easy to remember Easy to spell Any help would be much appreciated. Additional information: We ended up with Coralline through a research on fractals. That might be a cue for any suggestion. We are going with underwater/reef theme some words related to that can also help.


I can understand the causative form (quite less frequently, we simply say causal verb) with make and get but when used with have/has, it sometimes makes me think differently. Of course, I can understand the construction like the following. I had a barber cut my hair yesterday. In its passive form, it can be written as I had my hair cut yesterday (by a barber). I can also understand that the preceding sentence (passive construction) cannot be rewritten as follows. I had cut my hair yesterday. If it's modified in this way then both the sentences have a significant difference in meaning that I can understand. The thing I don't understand properly when a bare infinitive is replaced with an infinitive in such kind of constructions, such as. He has his wife cook dinner for him. What happens, if the bare infinitive i.e cook is replaced with an infinitive like the following. He has his wife to cook dinner for him. At a glance, you will be able to understand the difference between them but for me, it's not English but it's my native language in which as far as I know there is no difference between these two sentences and even the causative construction is simply made by just using some suffixes to the main verb in a sentence. So please take it easy. Could you please expose the important difference between these preceding two sentences?


Referencing Stephen Hawking's recent paper Information Preservation and Weather Forecasting for Black Holes and this question. I understand concept of holding the information on the apparent horizon of a black hole for later release in the form of garbled radiation, but how is it that this differs ( if at all ) from the Hawking Radiation generated by the Unruh effect near the horizon? My, possibly flawed, train of thought is that the aforementioned black hole sucks in everything in matter in it's immediate surroundings, and due to the Feynman diagram that corresponds to particle-antiparticle pairs spontaneously popping into existence with one particle on the other side of the horizon, the energy from the matter sucked in, is imparted to which ever particle is outside of the event horizon to repay the energy debt to the Universe.


I'd like to know why in a parallel loop, the voltage, along with the current, isn't divided. e.g. in this image from a youtube video the voltage in parallel loop is the same across both resistors, for some reason this seems counter-intuitive to me. Also later on in the video, the resistance was proportional to the voltage. I talked about this in class today, there was some debate on whether the voltage is inversely or directly proportional to the resistance. My argument was that because the resistance is higher, there must be less voltage going through at that point. So as resistance increases, voltage drops, showing an inverse proportion, but then someone in the class brought up the equation V=IR, in the circuits we've looked at, the current is seen to be the same throughout, in series, so it can be simplified to V=(K)R, V(proportion sign)R which would mean as Voltage went up, so would the resistance. Then we were talking about this in parallel, and things got more confusing, he spoke about the current not being the same across both resistors therefore we cant use the above rule, which I understood, but he didn't explain what actually happens. I'm getting confused writing this question.. perhaps I should do a few practice questions. My teacher was worryingly also unsure. I Hope this question doesn't come across too ambiguously.


I have joined a grammar MOOC starting with an introduction to English tenses. One of the practice questions left me confused. The question is as follows: Do these two sentences have similar meaning or different meaning? Julie has studied French for two years. Julie has been studying French for two years. I'm not sure how similar is similar, but having a questionable sense of the language I think I should follow the rules. Grammar books state that Continuous tenses are designed to emphasise duration. If an author finds relevant to emphasise the duration, this semantic or emotional meaning is relevant to the reader. Both of the sentences deliver information about the duration. I'm not sure if there exists any difference in connotation or the second sentence is an example of 'grammatical tautology'.


(Too) Long ago, I had some problems with some equation. I wanted them to look like this (this is how they looked in LyX), but when compiled they looked like this: . What botheres me compared to how it looks in LyX is that way too much spacing between the columns is used in the compiled version. there isn't a space after the "=" the last column is aligned to the right (not to the left, as I wanted it to be). Because only now I found time, to post this question here, I unfortunately don't remember the name of the environment used for this (I only kept the screenshots). But I remember that I tried out all of the AMS environments( align, alignat etc.) as well as the eqnarray environment and not a single one provided me with an output that looks like the one in LyX. Has anyone an idea how I could get LaTeX make these (test)equations look like the LyX screenshot ?


Personally I learned Physics in high-school and found it very interesting, I read up a lot about physics in my free time. Personally I am also a programmer which I think is also good when it comes to Physics. Now I want to start studying in a university and my dilemma right is mainly between Math/Computer Science/Physics. It's possible to do a degree in just one or combine two of them. Currently, the subjects that I find most interesting in Physics are the most advanced ones: Relativity and most of all Quantum Mechanics. I've always been fascinated with materials, what they are formed of at the most elementary level. Now for the real question. From what I usually read it's very hard to get into physics research, of course it's not impossible but still I'd like to ask: Are there careers that are related to quantum mechanics or relativity that are not as a researcher? If so, what are they? can you give examples?


Why does the definition of an irreducible element require us to be in an integral domain? Why can we not define an irreducible element exactly the same in a commutative ring that is not an integral domain? We have that an element is irreducible if it cannot be written as a product of two non-unit elements. Unit elements are well defined and unique in a commutative ring that is not an integral domain, so I cannot see that being the problem. I've proven a proposition of my own design (probably well known and elementary, an definitely trivial). I used irreducible elements, but otherwise nothing that requires me to move from a commutative ring to an integral domain. Do irreducible elements really require me to be in an integral domain?


I am not sure whether the sun originally emits everything in the electromagnetic spectrum, (whatever the relative strengths of each portion might be), but I do read that many waves, including gamma / x-ray, and UVC, are filtered or 'converted' to heat after travelling through solar plasma and atmospheric layers like ozone. But what I am interested in is the lower end of the spectrum (frequency-wise) - like those we ourselves harness for communication. Does the sun emit low frequency radiation (below infrared), in the first place, and if so, how much of it - if any - actually reaches us on Earth within that same range? I am guessing it is either none, or only a very small amount as otherwise I assume it would interrupt severely with our own radio communication here on Earth.


When a nuclear device is detonated at ground level, we see the familiar mushroom cloud, which is undoubtedly caused by the weight of the atmosphere suppressing the upward thrust, causing the debris and dust to be curved down back towards the Earth. The horizontally propelled mass again does not travel very far from the point of detonation. One would expect the nuclear explosion to escape from the atmosphere, after all Gravity is thought to be the weakest force? But in reality, gravity is the only force and both nuclear and magnetic forces would not be present without gravity. So are we in error comparing like for like, when in reality we are comparing what are currently thought to be separate forces? Gravity is responsible for holding all particles, from sub atomic to planets and suns together and the nuclear explosion merely illustrates it perfectly?


While googling about whether "atheist" should be capitalized, and skimming past posts by people blogging about atheism rather than about English grammar, I came across http://uwf.edu/writelab/reviews/capitalization/ It says [Capitalize] Religions and religious terms Examples: Catholicism, Hinduism, Buddha, the Bible, Christian, the Ten Commandments, Baptist church, Mt. Zion Methodist Church NOTE: Do not capitalize the following: Examples: church, communion, atheist, agnostic, spirituality but I don't recall hearing of such a prescription before. Wouldn't most of the examples listed be capitalized because they're proper nouns? Are there good examples of words being capitalized solely because they're religious terms? I'm mainly interested in modern English, rather than days of past where a lot more words were capitalized than they are nowadays. Somewhat related: When should the word "God" be capitalized? - use "God" when referring to the name of the god of Judaism and Christianity (a proper noun), but "god" when referring to the general concept of a deity (common noun).


Say you have an author who has a lot of random personal stories from their life, all interesting, but don't stand on their own to be an interesting, single story. The author decides, "why not combine them all into one story?" Well, that sort of becomes an autobiography, I guess, if you actually tell the story in a more chronological way that follows the timeline of their life. What if the author decides not to do everything chronologically? Basically, taking these non-fictional stories, reordering them a little, and placing them all into a fictional character's life, somewhat shortening the timespan in the process? Basically, the story itself and the character would be fictional, but each separate story within the fictional story is non-fictional. Does the fictional part of the story trump the non-fictional parts of the story and just classify the entire thing as fiction, or a novel? Or is there any special word or perhaps genre that would be used to better identify something like this? Ultimately, is there a word to identify a fictional story made up of non-fictional stories? I've seen this similar question, but it talks about historical settings in a novel, mainly the non-fictional location a book is set in. I can't imagine that's really the same thing, as the situation I'm outlining is kind of the opposite. The stories themselves are non-fictional, but the setting, location, characters, etc are all fictional.


I am looking for a figurative or graphic expression to describe the minimal luggage content, fast to pack, or that you always have with you, without which you would feel less safe when travelling. The expression should be concise too. When I take a plane, and since luggage in the cargo area can get lost, I generally have a toothbrush and underwear. With those, I am not afraid of spending an unplanned night in an hotel in a unknown town. I would say in my language that I have my "pants and brush", as a short for "a second pair of underpants, socks and a toothbrush", but this does not seem colloquial in English. In other words, is there a colloquial figurative expression for what one carries when travelling light?


I'm taking the curl of the deviatoric stress tensor in index notation, and I've ran across something that I can't seem to be able to simplify. The issue is shown in the following portion of the curl operation: The first two terms on the right hand side should be zero because the curl of a scalar and the curl of a gradient of a scalar are zero. The last term will then be given by: Since U has a subscript m on that last term on the RHS, then I can't just define it as the gradient of the vorticity like I did on the first term on the RHS. Is there any further way to simplify it or does that just have to be the curl of the gradient of velocity?


The setting: Imagine the scenario where I am searching for something and once I find it I identify it, then afterwards when I no longer need it I discard it. If at some point I need to identify it again I perform the search again and will succeed since it's still there. The problem: The noun for the process of identifying something would most likely be "identification". I'm pretty sure the word "discardation" is not an actual word, and "discard" or "discardure" just leaves me wanting for something less overlapping and more commonly used. The Question: What would be a nice noun to describe the process of "discarding" something temporarily. Looking at the thesaurus words like: remove, reject, cancel, reject, relinquish and the like come into play but I feel like those words have a more dramatic impact imposed behind them than I would like to portray. Something similar to dislocate perhaps, with an intention to remove. Disconnect seems like a good option yet I feel like I would have to change identify to connect if I choose to do so.


Although I know the clear meaning of commonly used prepositions in English, sometimes, I'm a little confused with them and cannot understand the difference between them. A week or so ago, I asked a question on StackOverflow which was titled by me as follows. Varargs in method overloading in Java. In this simple question title, Java is a programming language as everybody knows, "Varargs" (abbreviated to variable arguments, specifically variable number of arguments) and "method overloading" are two concepts used in the Java programming language. Before I asked the question, I was not sure at all whether the question title should have been as it is mentioned above or it should have been modified as follows. Varargs with method overloading in Java. Which one is grammatically correct, both or none of them?


Many of the books I use are parts of series. biblatex gives you more fields to add bibliographic information to than BibTeX does, but it has no fields appropriate for the editor of a series. If I use the EDITOR field, the bibliography will (by default) print edited by, which doesn't give the right impression of what the role of the series editor is. I'm wondering if there is any easy way to add a new field SERIESEDITOR, which will make biblatex by default print its content preceded by Series edited by or make sure that whatever is in SERIESEDITOR gets printed directly after the name of the series, such that is says something like [Name of series], edited by [series editor]. In other words, is there any way I can do this in the preamble of my document, without having to venture into writing new bibliography styles?


Pardon my ignorance, but I am really interested in understanding the quantum mechanics and it's interesting implications, but clearly I don't, since I keep coming up with violations to many physics theorems. In particular, the delayed choice quantum eraser experiment is of interest. Consider the wikipedia diagram, In this experiment, there is random chance for the path that will be taken in the lower part of the diagram. Hence, one must wait till the end of the experiment and then (using the coincidence counter) filter the information of each photon's path. Hence, the patterns one sees are only known after the experiment. The Quantum entanglement is only verified after the experiment is completed. But instead of allowing random chance, what if you forced all photons to go to a particular path. To my understanding, if PS was modified (see the following diagrams) into a switch that forced either "separate slit" detection or "interference" then would that allow "faster than light" communication?


On this site, people ask questions and then answers and proofs for those answers come from readers. Readers mark the best answer and then people focus on the next interesting topic. Sometimes, a question will have many answers with proofs from different points of view and people commenting on whether the proofs are valid or not. My question is this, "given a statement, how many valid proofs are there for that statement?" For example, if one is interested in the irrationality of root two there are many proofs available, all equally valid, some longer than others, some requiring basic math skills, others requiring in-depth knowledge. We have a proof for Fermat's last theorem, but how many other proofs are there? Is it possible to look at a statement and know that it has a finite number of proofs or an unlimited number?


I would like to make the bubbles in my soda drink last longer. For example, one good thing to do is to keep the bottle shut when you don't drink. But what else I can do? Should I try to minimize the surface between the drink and the air from the bottle? How about the surface of contact with the bottle? The bottle should be made of glass, or plastic? Does the temperature matter? Should I keep the bottle in a vertical position, to ensure more pressure at least for a part of it? Other, less realistic methods, are to keep it under pressure all the time, use a carbonating device, or drink it on the ocean floor. Or never open the bottle :), but assume that I want to open and drink from time to time.


I'm trying to understand where energy is located in a quantum field world. For force fields, there are conserved properties that (in my mind's eye) are always stuck in that field. These arise from symmetries in the fields, by Noether's Theorem. As such, I imagine that properties such as charge can move around in the field but never leave or appear. Noether's Theorem also explains conservation of energy as related to a symmetry, the invariance of the laws of nature at any point in time. It seems fair, then, to say that energy is a property of the field that makes up spacetime itself. When a charge is carried by a particle, that particle can have different masses with equal charge. I am not sure how I should picture the difference in the fields. A muon, for instance, has both mass and charge. My question is then, which fields contain the muon's properties? Is it all in the muon field? And does this mean that both charges and energy can transfer between fields? Or is a muon a sympathetic coupling between the muon field, EM field (charge) and spacetime curvature (energy)?


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.


I have been trying to read about the energetics of observed supernovae for some time. And while the observed core-collapse supernovae have many scientific papers about them trying to estimate the energy released in different evemts like this one, I couldn't find similar reports for Type Ia SNe telling how much energy was actually released. All I could find about energy estimates for Type Ia SNe were different model of detonation and they are very close in the numbers they compute. So, is this lack of Type Ia SNe energetics because they are essentially the same and only one model can be applied to all of them ? I know Type Ia SN is the result of a thermonuclear runaway in a WD with a Chandrasekhar mass limit, so they should actually produce the same amount of kinetic energy for the ejecta. So is it true that all Type Ia supernovae observed share have similar released energy ? PS : I am concerned about kinetic energy more than optical and light curves, so the mass of the Ni produced and the luminosity is not important for me here.


I was wondering if there has been any category theoretic advancements in the study of the Riemann Hypothesis and the theory surrounding it? This question is meant in the same vein as these questions, but specifically for category theory. These other two questions do not have any answers related specifically to category theory. EDIT: Just to be clear, and because Zhen Lin brought up a good point about category theory being mostly a language for mathematics: I understand that category theory is a language like thing, but it can still be useful in mathematics. I had in mind maybe an advancement in one of the fields related to the RH, in which category theory plays an important or central role. Or perhaps a category theoretic equivalent statement or something similar.


One of my friend who stopped studying maths in high school told me once You study maths, can you help me fill my tax forms? In her mind, advancing in maths studies implied manipulating an increasing amount of numbers. The reality I faced was the contrary: I dropped numbers for some more abstract notions (i.e. letters and symbols). I wonder if a (putative) link between abstraction and use of numbers has been investigated. For instance, can we say that one area of mathematics is more abstract than another one just because it uses less numbers in its formulation? Or, is this particular domain of maths became more complex as it uses less numbers? One possible metric I think of would be the number of numbers per "mathematical" line. This question may not be within the scope of math.stackexchange, but I didn't find a more suitable site. Thanks!


I have a ... pdf file, which contains figures of plots such as the following: Now the second plot isn't too hard to draw on TikZ (I assume... I hope? I don't have any experience apart from drawing circuits!), but it's figures like the first picture that I'm more worried about. I want to re-draw them in code (like in TikZ or any package really) so that they appear in higher quality than if I were to just take a screenshot and post that in my LaTeX doc. Are there any tools that can automatically convert images like these into code? It doesn't have to be perfect, I can tweak it as necessary, I would just like at least the basic code done so that I don't have to start new with every single one. Even examples found online don't really match up to something like the first picture, and I'd rather not go through mountains of examples/pdfs/how-tos to draw something relatively simple. So how can I tackle something like the first drawing in code easily, i.e. convert it to compilable code? Any help would be appreciated!


I'm reading a Mathematical Logic book (A course in mathematical logic, Bell.M ) and the author is saying that the symbols of a formal language don't have a well-defined shape, he's claiming that they are abstract entities. I think he is saying that even though symbols are usually defined by its shape, the symbols of a formal language have 'abstract' shapes. He goes on explaining that we couldn't possible be able to define an exact shape in a formal language because that wouldn't be reproduceble in all metalanguages studying the symbols of that objective language ( the formal language ). He proposes them, that when we are studying a formal language ( objective language ) by means of a meta-language, and we want to reference the objects of the formal language ( its symbols ), we use as name, metalinguistic symbols. By doing this, we don't have to worry with the "shape" of the symbols in the objective languaeg when we are changing the meta-language that is studying the formal language, because the shape is not well-defined, they are allowed to vary with the meta-language. All in all, i think he is claiming that the symbols, lexicon or alphabet of a formal language, and hence the syntax is independent of its visual representation. I'm curious if this approach is worth to make and also if people are worried to make such distinction ( or is it only him ) ? Also, i would like to be corrected if i misunderstood the point.


The thought experiment goes like this: Say there is some circuit which turns a lamp on/off with just a flick of a switch. Say its off; you flick it, it turns on; flick it again it turns off, and so on. So say you are conducting the experiment for two minutes. When the remaining time halves, you flick the switch; and when that remaining time halves, you flick again...This process goes on infinitely, until two minutes is reached. Mathematics says that the sum of all those remaining half-times will eventually tend to two minutes. And the outcome i.e. the final state is always unpredictable. We can't really know if its on/off. Lets not concern about the final state. What would we actually observe towards the end, few micro seconds towards the two minute mark? Wouldn't the lamp appear turned on? What would happen if the time between two flicks tend to zero?


Imagine the following gedankenexperiment. Observer Alice is right here on Earth. Observer Bob is at say Alpha Centauri. A pair of maximally entangled qubits is formed with one qubit handed over to Observer Alice and the other sealed in a box on Pluto shielded from decoherence. It takes a few years for any signal to reach Observer Bob. Observer Alice measures her qubit and "collapses" it. To her, the pair of qubits is no longer entangled. However, for a few years, will Observer Bob think there is an entanglement? We have to be careful here. Once the qubit on Earth has been measured by Earthlings, the entanglement is "shared". By the well known monogamy of entanglement theorem, any correlation between both qubits by themselves will have become classical. However, Observer Bob, who has a very good working knowledge of quantum mechanics and relativity, knows that for a few hours, until light signals can reach Pluto, the system consisting of an expanding bubble around Earth and the Pluto qubit are in an entangled state. Alice, who lives inside this bubble, will beg to differ. Is quantum entanglement an objective or subjective property? Closely related to Wigner's friend and intersubjectivity in quantum mechanics and Given entanglement, why is it permissible to consider the quantum state of subsystems?.


Many dictionaries use a semicolon in a meaning for a word. For instance for the word impertinent I have seen: "outside the bounds of proper speech or behaviour; impudent; insolent; saucy" Then there is a synonym explanation of connotations for impertinent, impudent, insolent, and saucy. My question is: Does the semicolon introduce synonyms always? Does it mean that the word following a semicolon SHARES the meaning of the main entry word you are looking up; that is, the sense preceding the first semicolon in the meaning? I know that insolent cannot be substituted for impertinent, but maybe impertinent can be substituted for insolent with a loss of connotation. Just what the heck are these guys who write dictionaries trying to convey with the semicolon in the meaning of a word?


A question that has been bugging me for quite a while was raised by some communication between my employer and a partner organisation based in Dubai. It turned out that more than once, it's been noticed that this other party tend to use a particular tone of address in letters and emails. Whereas they will address male members of staff as 'Mr Bloggs' - which is quite acceptable and polite, even somewhat deferential given that it's quite uncommon and most other third parties tend to address you by first name after it's been quoted at least once in the exchange - they rigorously insist on referring to female colleagues as Miss Helen, and so on. That is, declining to use the individual's (known) surname, and presuming unless corrected that she is unmarried. Is this due to some antiquated perception of propriety in English correspondence, or is it a custom originating from the culture of the people involved? I would lean toward guessing the latter; since in parts of the Middle East having women in the workplace is less common and perhaps one might presume that a female employee is unmarried, unless it is determined otherwise. Is it thought by the demographic that we are talking to that using the maiden name of a woman known in a professional capacity is in some way vulgar?


I'm reading Yelizaveta Bam of Daniil Kharms (tr. Neil Cornwell) and stumbled upon the following dialogue: Ivan I.: But who then lights the lamp? Pyotr N.: No one, it burns by itself. Ivan I.:But that surely cannot be! Pyotr N.: Empty, stupid words! There is an infinite movement, the breathing of the lighter elements, planetary motion, the earth's rotation, the crazed alternation of day and night, the combination of remote nature, the anger and strength of remote nature, anger and strength of untamed beasts and the laws of light and wave. (I emulated the formatting used in the book) What does "the breathing of the lighter elements" mean here (or in general)? Since it is supposed to be an "infinite movement" I cannot relate it to the breathing of a living thing.


First of all: I was not able to compile a MWE, since the error seems to be connected to one of my documents, all of which are classified. I'm experiencing (for the first time) the following error: When opening a file in Acrobat Reader and then trying to print, I receive the errors The document could not be printed There were no pages selected to print My file is structured as follows: A beamer-file created in LuaLatex In the beamer-file, several other PDFs are included. Either created by AutoCAD or - and this seems to be the problem - by Latex (pdflatex). Some of the other PDF-files are included inside a tikz-environment (if that matters). All PDF pages are included as images using the graphics-package. By trying to include different PDFs and varying the amount of PDFs I discovered that the problem seems to be that different pages are included in different tikz-environments (it could be a completely different reason as well, this is just a feeling). I've created several other presentations using beamer all of which included multiple PDFs - but those PDFs were NOT Latex-created files. These other presentations work (and print) like a charm. Using a different PDF viewer solves the problem. However, as the created presentation will be sent off to customers, using a different PDF viewer is no valid solution. Also, the problem seems to be connected to some printers. E.g. using CutePDF causes the error, while (sometimes) using the network HP printer works.


I am looking for a method to save the lecture materials, and examples without hand copying from the boards during the lectures. Unfortunately some courses don't have the material available, and sometimes you want to copy a specific example. EDIT: The reason I would like to avoid copying by hand is that it is sometimes very distracting, especially when the example is complex. I would like to focus on the material itself and devote less time and effort to handwriting it. So far I thought of using a tablet with an application such as Camscanner to take photos of the board during the lectures. However sometimes I would want to add a hand note or an notation on the photo itself using a stylus pen (or similar). UPDATE: Camscanner will auto recognize the board boundaries for you and fix the perspective. Also once you took one photo you automatically add subsequent photos to the same document, i.e. same lecture. Very handful feature is that you can add hand notes on the image right after taking it, making notations easy. Any advice on an effective method or an application designed for that?


I was writing a market research report the other day and listed the challenges my company faced in the market in question, then I created a new section header for the... uhh... easy bits? That's when I realized I could think of no reasonable antonym for challenge in the noun form. I can certainly describe it -- characteristics of the market that will be of benefit to our entry "Advantages" is close to the mark but doesn't quite capture the idea because I feel that is in reference to our company, rather than in reference to the market itself. To give an example: Challenges > customer purchasing power is low > public perception of our manufacturing location is negative (Easy Bits / Cakewalks / Happy Things / etc.) > no competitive product on the market > strong transportation network with low logistical costs "Incentives" also seems close, but not quite there. Any ideas?


When speaking with my mother a couple of days ago, I read to her a message I was sending to my cousin on her behalf ending with: "... the birthday of your youngest." [implying her child] She immediately leapt on this and said that as my cousin only had two children, the use of the superlative was not permitted and the comparative must be used instead: "... the birthday of your younger child." She was adamant that this was a solid grammatical rule that she was taught throughout her education. As a younger Briton, I have relatively little formal grammatical education to older people who were better taught in this regard, so I usually defer to her on grammatical rule knowledge. Is she right? Are superlatives not permitted when the domain of the object is only two? To me it seems bizarre. The minimum or maximum of any set does not only exist when there are different minima and maxima, or indeed something which is neither.


English or any other language could be written or spoken in both the forms, either the user could use simple words or he could use some technical words, my question regarding English is which has more impact on listener, Simplicity in language? or Complexity by using technical words? and is it dependent of whether you are speaking or writing? Simplicity, i.e, using simple words in your language can be effective as it helps the listener understand you better. The brain of listener can easily understand what you meant to say, whereas Complexity brings elegance. A speech or text with some technical words used in it looks more promising and can express much more than the same text written in a simple language. So ultimately, which is better? PS : By Complexity, I didn't meant to say English which could not be understood, I just meant the use of more complicated and technical words in the language.


Unlike the use of "no problem" as an alternative to "you're welcome" or "my pleasure," neither of which bothers me much in common speech, its use as a reply to an instruction or directive to put right what the respondent has done wrong, particularly if at great expense or at substantial loss of available time, tests my patience and my temper. To my Boomer-generation ear, it says the respondent somehow feels that s/he is doing me a favor by setting things right rather than accepting responsibility for them, and somehow cannot see that a problem truly is involved. Is this a generational shift that I should get used to, or is the use of "no problem" in this context an erroneous use of this expression? (For now, at least.)


Here is a sentence from Chapter Seventeen of Huckleberry Finn. The sentence appears in a grammar worksheet: When I got to the three log doorsteps I heard them unlocking and unbarring and unbolting. My English teacher stated that "them" was an indirect object, and unlocking and unbolting was a direct object, as that is what was being directly heard. She states that indirect objects can answer the questions "by whom", referring to the direct object. (The doing could be done by the indirect object.) This doesn't really make sense to me. My first impression was that them was the direct object and the participles unlocking and unbolting were modifying them. So, can an indirect object in a sense do the action of a gerund direct object? Any help is welcome!


I've always been able to manipulate equations found in school homework easily. But when tackling more challenging questions from puzzle books - where I might need three quarters of a page to manipulate the equation into the ideal form - I find myself easily making mistakes. The obvious solution is more practice. But I can't find a suitable landfill of questions where the focus is on manipulating tediously long/complicated algebraic equations instead of practicing some kind of technique or problem. Has anyone had the same problem as me and found a felicitous way to overcome it? (Other than the obvious advice to be more careful, which you have to sacrifice speed for unless you've already had lots of practice) P.S. I'm not sure if this question belongs here; if it does not, I'll be glad to remove it.


I am currently an undergraduate and thinking about applying to graduate school for math. The problem is that I don't know what field I want to go. Taking graduate classes even more confuse me because the more I learn the less I know what specifically I want to do. My question is to where to find an information about different fields of mathematics? Maybe you can recommend me some good journals about math with overview of top areas of math or popular fields. I already spoke with my professors, asked graduate students about their history but I think that my knowledge about math in a broad sense grows slower than I want it. Maybe there is some good website with people chatting about different fields of research? What about conferences: is there a conference available for undergrad about top-trands in mathematics? All sources and all answers are welcome. I am mostly interested in pure math, but I also like applied math.


I have searched for some time for the "insider scoop" on how academics operate when it comes to mathematical research (theoretical physics research would also be interesting, but mostly interested about math research).I read "Letters to a young mathematician" which was a nice book but didn't talk much about the research process. If I google "Research process", or "How is research done", I mainly get recommendations of steps of how to do independent research. These step include brainstorming, choosing a research subject and looking through background information and articles. But how are these done in an academic setting and in a group setting? I understand usually while doing a PhD you would have an advisor which would help you with these things but you would mostly do them independently. But I mean people who are employed as mathematics professors at a university, how do they go about it? Do they do just this independent process? Do they cooperate together on the same research? Mostly what is interesting to me is how a group of people can research something together, and if this is even attempted.


TikZ provides the two keys execute at end picture={<code>} and execute at end scope={<code>} which can be used to execute any code at the end of the picture and of the current scope, respectively. I now like to execute some code at the end of the picture if a TikZ key defined by me is used outside a scope environment, i.e. in the optional argument of tikzpicture or at the end of the scope if it is used inside the scope, i.e. in its optional argument. I also like to access the bounding box of that area, i.e. the complete one or only the one of the scope, respectively. Is there am easy way to do this? Cascaded scopes should also be supported. I don't see a possibility to detect if I'm inside a scope or not. In theory the whole tikzpicture is a scope by itself and execute at end scope seems to work but the manual explicitly states it should only be used in the optional argument of a scope environment. I know about 'local bounding box' but then I would have to use it for every scope with a different name to avoid collisions.


I'm trying to submit a journal paper through ScholarOne Manuscript (an outdated automatic build system some scientific journals use). The issue is that I'm using biblatex. I tried with both backends, biber and bibtex, and I couldn't get it through. Has any of you managed to make a successful submission to ScholarOne with biblatex? Update: They use some build tool which forcefully calls bibtex. After many unsuccessful attempts to make it work with biblatex (also with backend=bibtex), I decided to convert everything to bibtex. The main issue is their referencing style: a mix of author-numeric(superscript) which I was not able to replicate easily without biblatex and I had to hardcode some citations: If you have a better idea regarding the citation style let me know although maybe I should open a new question for that.


Frequently I hear Americans (admittedly mainly in TV/movies) say "personal" and "regular" in the following contexts: "Don't take it personal." "I like that he treats me regular." Both of these are horribly incorrect to my British ear - I have never heard either here, it would be "personally" and "regularly", ignoring the fact that the second sentence is slightly awkward anyway (we would probably say "like a regular person"). My question is, do Americans 'know' this is incorrect, i.e. would John hear Jane speaking in this manner and think "her English isn't great" or whatever, or would it sound perfectly normal - is this an accepted use, that all Americans would use? I could easily believe it would be the latter, since 'momentarily' for example has a totally different meaning in AE. ('in a moment for undisclosed amount of time' vs. 'for a moment at an disclosed time').


I think I kind of understand this process but I would like someone to explain it more completely. For those who aren't aware here is the scenario I'm talking about: As terrain maintenance at my local ski slope we often use salt to firm the snow around jumps on warm slushy days. Throwing down a even layer of salt causes the snow to become firm and icy on its top layer (thus causing jumps to hold up better during heavy use). My best guess to this phenomena is that the latent heat of vaporization in the melting of some of the snow causes the snow below to become colder. As the snow on top melts it sinks down leaving an icy layer on top. Am I on the right track? or is something else going on?


I am a native German speaker and in German it is considered very bad style to use a word more than once in a sentence or even in close proximity. So you usually have a big list of synonyms in your head and you always cycle though these words while writing or even change complete sentences so you will not have to use the same words. I always automatically assumed that this is also the case in English. Now someone told me that this is actually nothing you have to be concerned about. (This sentence is actually a good example for this. I could have written: "Now someone told me that this is actually not the case in English." but I already used "the case in English" in the sentence before that and such repetitions are considered to be extremely clumsy writing in German.) Could someone please comment on this?


I want to tell that something reminds/hint us of another thing. For example, in an application, a sorting method used in it has similarities to bubble sort but not completely the same. In this case, when reading about the sorting method used in the application reminds or hints me of, or brings to mind the idea of bubble sort. So, I tried to put this idea into a sentence this way: The sorting method used in the application reminisces bubble sort. But in this sentence, is the word reminisces used appropriately? So I thought of phrasing it the other way: The sorting method used in the application is a reminiscent of bubble sort. I seldom hear the word reminiscent being used in this context and it sounds weird when I use it this way. Is it correct? Since it also feels like a hint, I thought maybe I could use the word "allude": The sorting method used in the application alludes bubble sort. Here, again, alludes doesn't sound like a right word to use. What word or way of phrasing should I use to get this idea across clearly?


With the following definition: To lower in quality or character. Synonyms found: corrupt, pervert, subvert, demoralize, demoralise, debauch, debase, profane, vitiate, deprave, misdirect However all of those have a very "intentionally evil" connotation. I would say more along the lines of "messed up", but it needs to portray that it's somewhat intentional, just not with the evil slant. Intentionally done, but unintentionally wrong, is what I'm looking for. Perfect Example: My nick name on here is Aequitarum Custos, which is a "bastardized" Latin, it should have been Aequitatis Custos (the correct way to say what I wanted). I intentionally created my nick like that, but had no intention to make it wrong. Reason for desiring a synonym is due to the perceived obscenity of the word bastard by some people.


What is the formal definition of an event? According to Wikipedia, "an event is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it." This definition seems too large because it includes even points where no identifiable process is happening. On the other hand, what about particle-fields interaction: a comet passing through the gravitation field of the Sun a collision between two particles where one particle is entering the field of another particle and then bouncing off in a parabolic worldline (deceleration & acceleration). In both cases a field is continuously acting on an object, thus the event itself seems to be somewhat continuous. Can someone provide a formal definition which is taking into account particle-fields interaction? Do continuous events exist? Edit: The Wikipedia definition (which also might be found in textbooks) is inacceptable for a particular reason: Events (such as a particle collision) have somewhat observer-independent character, i.e.all observers agree on the fact that an event happened, even if they disagree on the time & the simultaneity of the event. In contrast, we cannot say that observers agree on any "point in spacetime". => A sufficient answer would be a good reference for what @By Symmetry wrote.


There's an experiment demonstrating the properties of super-fluid Helium compared to normal fluid Helium, in which the Helium is put in a jar who's bottom is porous. The super-fluid can pass through the small capillaries, while the normal fluid can not. Another experiment uses a fine grained powder (implying the same holds for percolation through porous medium as wall as though the capillaries) The video of this experiment can be seen here My question is: Is the permeability threshold determined only by the viscosity of the fluid? Doesn't surface tension also play a role in determining whether the liquid will percolate? Or do they implicitly assume there's no difference in surface tension between the two phases? Mercury has similar viscosity as water, with a much higher surface tension - and it will not get absorbed in fine sand, while water will - isn't it because water wets the send, while mercury does not?


In some posts in this forum I've read that sign convention in optics is useful for making formula memorizing easier, and that we have to use sign convention again while applying the formulae to neutralize the effect of taking sign convention... I tried to use geometry and saw that indeed without sign convention we get two formulae for lens maker's formula and so on... so in that way sign convention is useful... But i could not derive the formula for linear magnification by geometry - without sign convention the derivation does not match the formula given in the text books (which says m must be negative for convex lens when image is real). Can somebody please explain how to get it, and if not why don't we get it? The Sign Convention used is: The direction of the incident ray is positive. Incident ray is always incident from the left side on the refracting surface. Perpendicular distance of an object is positive when measured upwards from principal axis. Distance is always taken FROM the pole of the refracting surface.


From Planetmath A meager or Baire first category set in a topological space is one which is a countable union of nowhere dense sets. A Baire second category set is one which contains a countable union of open and dense sets. From Wikipedia: A subset of a topological space X is called nowhere dense in X if the interior of its closure is empty of first category or meagre in X if it is a union of countably many nowhere dense subsets of second category or nonmeagre in X if it is not of first category in X I was wondering according to Wikipedia's definition, is any subset of a topological space either of first category or of second category? are the definitions for second category set in Planetmath and Wikipedia consistent with each other? Wikipedia says these definitions are used for "historical definition" of Baire space. I was wondering if they are archaic i.e. no longer in use? Thanks and regards!


This is the law of stable equilibrium, according to Hatsopoulos and Keenan: A system having specified allowed states and an upper bound in volume can reach from any given state one and only one stable state and leave no net effect on its environment. Consider the following system: two sealed containers of gas. Container A contains a weight on a raised platform. Container B contains a flywheel. A string-pulley system connects the flywheel to container A. Let our system be both containers combined. Here are two options to reach stable equilibrium We slide the weight in A off the platform; it crashes to the bottom, raising the temperature of A. Instead, we slide the weight onto the string's hook, such that, as the weight gently falls, the flywheel spins and raises the temperature of B. It seems we have reached two different stable states despite making no effect on the environment, contrary to the law. What am I missing here?


Is it correct to say: Would you like to start a cooperation (with us)? Or should it be: Would you like to cooperate (with us)? I feel like the first sentence is wrong, as it sounds to much like saying would you like to start a corporation (with us)? (with a dutch accent) but the second sentence suggests more aggressive style of asking for someone to cooperate with you. Maybe there is a better way to ask this question? edit I should also state I am referring to a international business venture / collaboration. Where for example we would like to sell electronics on our website from his/her company for a small commission or put your vacation house up for rent on our website for a small commission. You would eventually sign a contact to do this(of course). So what I'm asking is: is it correct to ask the above stated questions? or is there a better way? Note: It should not sound like you would want to 'hook up' with the person your talking to e.g. partnering relationship


Colon or semicolon when because is omitted from a sentence e.g., I am sorry I disturbed you (;) (:) (because) it looked like you were having a lot of fun there. Because explains and clarifies a preceding clause so would it be correct to use a colon preceding the explanatory clause if because is omitted? Alternatively, because can be replaced by for, which is a coordinating conjunction and would correctly be punctuated with a semicolon. I am sorry I disturbed you, for it looked like you were having a lot of fun there. I am sorry I disturbed you; it looked like you were having a lot of fun there. For is of course reasonably archaic but is useful sometimes for grammatical clarity. And if anyone wants to comment on the that omission and comma replacement, I'd be very happy. I am sorry (that)(,) I disturbed you because it looked like you were having a lot of fun there.


Im taking a class in graduate probability. My background is in engineering (very used to math in an applied sense). I am also taking an undergraduate class in real analysis along side (should have taken it before, but I couldn't) I have a couple of questions: We're spending time looking at measurable functions on measurable sets. The definition of a "measurable set" is one who lies in a sigma algebra. My conceptual understanding of a sigma algebra (I know the technical def: countable additivity, etc.) is the resolution with which we understand a certain space - the sets that can be measured - even more simply: the sets we can actually use. We say a sigma algebra is the "domain" of our measure. In other words, a (prob) measure can't measure just any old arbitrary set/sets of set. We define a sigma algebra to handle this, and say our measure operates over this sigma algebra. However, the power set is actually a sigma algebra (the largest one, according to our definition), and yet not every element of the power set is measurable? I'm having a little trouble reconciling my conceptual understanding of a sigma algebra (the behave good-measurable sets) with its actual def (which gives us the power set dilemma). How does the Borel Sigma Algebra fit into this conceptual understanding? How about non measurable sets? Is there a concept of the largest sigma algebra of only measurable sets, which is a subset of the power set?


The hyperreal number system adds infinities and infinitesimals, allowing Calculus to be done using these things instead of limits (sort of like when calculus was originally invented, but with rigor).This got me thinking, could this be done with topology to create hypertopology (an equivalent but perhaps more intuitive way of doing topology)? It should be able to translate, since hyperreals can be represented as ultrafilters of reals. Hypertopology would involve ultrafilters of the points of the topology presumably. To define the topology, I presume you would define when two points of the hypertopology are infinitesimally close. To convert a metric space into a topology, you would simply define two hypertopology points as close whenever their distance is infinitesimal (again, ultrafilters can be applied point wise.) Has this ever been studied? What axioms would hypertopology "closeness" need to follow to be equivalent to regular topology? Is there an axiomatic approach (not requiring the ultrafilters (the hyperreals have an axiomatic basis))?


Imagine a cat jumping off a roof onto a sledge on ice. Model this as simply as possible, e.g. no resistive forces, perfectly rigid cat, sledge and floor. Moreover, the cat and sledge move in a straight line. The cat will have a vertical component to its momentum when it lands, but the sledge will - more or less - move off horizontally. What happens to the vertical component of momentum? Should we consider the Earth as a third body in the collision, and conclude that the Earth moves away with an immersurably small velocity? When performing calculations, can we simply ignore the vertical component post-landing? In reality, roughly what factor of the vertical motion's kinetic energy goes into heat, sound, vibrations, etc? (I don't mean list them one-by-one, just what is "non-Earth moving"?)


I got confirmed from a graduate school starting from next year and I will major algebraic geometry. Until now, I have never thought that I study little things than others with my age. However, I heard that some of my colleagues already studied Hartshorne at least once and quite a few of them have read Rudin's RCA when they were undergaduates. It's kinda unbelievable to me, but it seems like if they really did study and understood, then they will write absolutely a better Ph.D thesis than mine. So I'm now very worrying myself. I want to know whether this situation is general. Is it recommenable to study graduate subjects as early as possible? Or are there people here who experienced the same thing too? Was that beneficial? Between "studying each thing deep and slow" and "skimming many subjects as fast as possible", which one is better?


While researching about lasers (it's my hobby), it suddenly hit me: there are lasers for every color of the visible spectrum, but there are no brown lasers. Brown isn't even on the rainbow. How is it possible that we can see it? Even stranger, brown as a color is produced with red and green, but when you mix red and green light, it makes yellow. Now this is where it gets VERY interesting: There are forbidden colors, colors that cannot be perceived by the human eye though they are a mix of perceivable colors. They are caused because the cones devoted to complimentary colors will cancel each other out. Red-green is one. Blue-yellow another. The highly interesting thing is, brown absorbs all other colors but reflects red and green. I don't think it's a coincidence that while brown is, for some unknown reason, not on the visible spectrum but still perceivable, it reflect out red and green, components of a forbidden color. I also don't think that it's a coincidence that magenta does not lie on the rainbow, is nevertheless perceivable, and that it reflects...blue-yellow?


I am already fluent in portuguese and english, and I can also read spanish well. I have to read a text which is in french, and I'm having some difficulties. Knowing that there are a lot of people out there in the field of mathematics that are able readers of several languages, I would like to get the opinions of more experient professionals about their own experiences with different languages and from which ones they get/got more benefits from. I intent to use these opinions as a guide to choose the next language I will learn how to read, if not everything, at least mathematical texts. My initial belief is that I will get the most beneficial experience by learning french and then german, but I'm not sure; I never had experience to acknowledge mathematical texts in more strange languages (although once I started trying to learn korean - gave up some weeks later for lack of time). Opinions?


In my notes I wrote that Rutherford's model of the atom could not explain spectral lines, because that is what my textbook says. I'm not really sure about the details of spectral lines though. I know that when electrons interact with photons of specific frequency, they transition between energy levels (ie they could increase and become excited). After they become excited, they 'de-excite'. This allows them to release a photon and jump back to a lower orbit after they release a photon. This photon has frequency that corresponds between the difference in transition. This frequency correlates to a particular colour. So how then does this colour produce spectral lines, and therefore balmer series? (is that the right word usage?). How does Bohr's model not explain spectral lines (does it not talk about electron transitions, electron orbits etc and thus cannot deduce further?). What current model explains this?


After working on my oral skills in English for a couple of years, I know more interested in learning written English, specially by reading. I have been reading a couple of books over the last months (Game of Thrones, the whole Sherlock Holmes, Lord of the Rings, some Stephen King...) and articles (the Guardian, the New York Times, the Atlantic, mostly). But although I've felt some improvements in my understanding, and learned lots of words, I'm still not enjoying reading English as much as I do enjoy reading French (which is my natural language), and I'm not even what you could call a literary (checking my other stackexchange affiliations would prove you that...). When reading English I just follow the plot, but I'm really totally insensitive in the style of writing, in the choice of words, ... I hardly realized that when reading a few pages of French the other day, it's even way easier to focus on what I read when it is French than English. Fellow who learned English as a second (or third, or more...) language, have already felt that? Have you been through that? How long did it take? Or is it just a never ending job in progress but I'll never reach the ease I have with French?


I know this might not be an easy question, I've already read the wikipedia page, and there is an interesting view: Therefore, the main difference between chaotic systems and complex systems is their history. Chaotic systems do not rely on their history as complex ones do. Chaotic behaviour pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'. On the other hand, complex systems evolve far from equilibrium at the edge of chaos. However, I want to know a little bit more of their differences and intersections. If I'm not (terribly) mistaken, according to how the development of chaotic systems started, the emphasis was put on deterministic systems (should that part be of dynamic systems?), but now, with complex systems, according to what I understood of what Prigogine said, the emphasis should be put in other types of systems more close to reality. So what can you guys tell me about these two?


Generally speaking, by the well-known BCS theory, the more carrier density( density of state at Fermi surface) leads to higher critical temperature. However, in many researches, people fond that the relation between critical temperature and carrier density is not simple. There is a superconducting dome in phase diagram, no matter what carriers are electrons or holes. There exist a critical carrier density which gives the maximum critical temperature. Why is there a superconducting dome? What reduces the critical temperature when carrier density is higher than the critical carrier density? What is the physical reason? By the way, I don't think it can be simply explained by inducing disorder or impurity when doping. It is usually happen in chemical doping. However, there are many electrostatic doping researching on this topic, and usually it would only induce high carrier density without impurity or disorder, but also show similar nature of superconducting dome.


Consider the sentence: While this assumption, on its own, is relatively innocuous, if implausible, in practice, it is supplemented by assumptions... The 'if' here really means something more like 'but perhaps also'. Another sentence: He appeared very happy, if not exuberant, at her arrival. 'if not' here means something like 'and perhaps even', as if the latter statement should be a more extreme version of the former. But it also feels like an exclusive disjunction. That is, it is one or maybe the other, but not both. On the other hand, 'if' by itself feels like both statements could be true. I can conjure up many examples where both 'if' and 'if not' violate my above descriptions and many more which just seem malformed and awkward but fit them, e.g., 'He seems happy, if not a little confused'. or 'The proof appeared correct, if sloppily constructed,'... Adding further confusion, if I make a small change to the previous example: 'The proof appeared correct, if a little sloppy, .., it feels correctly formed although the semantics or grammar have not changed substantially (although I could be wrong as I am thoroughly confused now). So my questions are: are there any concise descriptions of how to use 'if' and 'if not'? Does this grammar usage have a name? When are they interchangeable and when not? Thanks


I'm facing a difficulty about referring to previously mentioned words. It's something that bothers me a lot about the English language. Please consider Mathematicians can use these theorems to their advantage. versus Mathematicians can, to their advantage, use these theorems. Which is more correct? The first sounds more natural and most people would probably say it's correct. However, I would think that technically the first is wrong and the second is correct, even though the second is a bit more unnatural. Why? Because in the first, their is referring to the last thing mentioned, namely these theorems, which is absurd. In the second, their actually refers to the mathematicians, as it should. What do you think? If the first is (also) correct, my question is simply this: Since when can sentences be counted as being correct just because they happen to make sense from the context?


I was suggested to use the term bullet-proofed by a colleague. Someone else now pointed out that bullet-proofed might not even exist, because we can't build the past tense of an adjective. Part one of the question is: can to bullet-proof be a verb which describes "making something bullet-proof"? And in consequence bullet-proofed then means "having made something bullet-proof"? So far, that's just for me, learning about it. I actually have decided to replace the word by something else. The word is intended to be used like "a bullet-proofed solution", which is close to foolproof or stable or tested. However, I would not use foolproof as a term here, because it might sound offending in the business context it is used. Can you think of the correct term my colleague might have had in mind when suggesting bullet-proofed? Note that we're both non-native English speakers. Update: @skymninge hit the definition. The intended use is like "not subject to correction, alteration, or modification", so I am looking for a synonym of that.