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In all textbooks the magnetic field around a wire carrying a current is found from Ampere's Law. However, I would like to know what the expression for the magnetic field is, using the full time-dependent Maxwell's equations (and how to get there): Hopefully this will give me some insight into how the field is set up vi... | 1 |
I am a computer science student that is struggling with a problem of mathematical nature. Thus far I have only studied calculus, discrete mathematics and linear algebra, but cannot figure out how to approach this problem. I tried Stack Exchange, but due to the mathematical nature they suggested me to ask here, so here ... | 1 |
As far as I understand it, quantum mechanics requires that a particle's position to be not specifically determined in space, but rather be 'spread' out through space, in the sense that we can only know the probability a particle is at a particular location. This can be visualised through the wavefunction. When we then ... | 1 |
I am by no means an expert in the realm of physics. I do from time to time, try to understand the concepts of modern physics and their applications. I came across this video that I am currently watching, and in the beginning it explains what would happen to someone if they crossed over the event horizon of a black hole... | 1 |
What determines whether something is a "noun adjunct" or just a garden-variety adjective? Does it matter in any meaningful way? Here is my hypothesis, but I can't find any authoritative source to back it up. I'm hoping someone here can weigh in more definitively. Classification of noun adjuncts is based subjectively on... | 1 |
The past few months I have been studying astronomy and Integral Field Spectroscopy (IFS). What I want to do is to fit a galaxy kinematic model to data (ie: estimate the model parameters that give the best fit result). At the moment I extract the velocity and velocity dispersion maps from an IFS datacube but I am not su... | 1 |
Before getting into the question, here are some remarks: Given a single point charge, the value of electric field at the position of the charge is singular/undefined, which makes sense, since a particle cannot interact with itself. Given a discrete charge distribution, the value of the field at an empty point(i.e. no p... | 1 |
A rather simple question for liquids specialists I guess but I have hard time finding information about this. Here is my problem. I understand the ideal gas theory and the Maxwell's speed distribution. I see an ideal gas as small balls (mostly surrounded by void) moving around very fast and colliding elasticly with eac... | 1 |
We can speak of "microbes" or "micro-organisms," and I used to think that these terms clearly included viruses. And they are used this way by at least some other people; here's a website that refers to viruses as a category of microbe. However, I recently discovered that these terms are usually defined as referring to ... | 1 |
I recently had an argument with a friend around the question "have you ever thought about something?" The question was asked in the context of exploring some life possibilities, such as buying a sports car or moving to a different country. The disagreement was around whether an affirmative answer to the question bears ... | 1 |
Ok so I'm a programmer, I'm not a mathematician, I've got a minor in math but I didn't even do particularly well at it so please bear with some possibly really stupid thoughts. Just please try to explain to me why what I'm asking is stupid so that I don't keep making a fool of myself. I recently found myself thinking a... | 1 |
This question was actually asked by Alan Munn in a comment to How do I create a LCM tree diagram?. I repeat (and self-answer) it here because the answer is too long to fit the margin :-) qtree is a well-known and heavily used package for drawing trees using the so-called bracket notation. (The bracket notation is espec... | 1 |
My good friend is from Pittsburgh and frequently uses the word whenever to mean the word when. I am aware this is a regional dialect and really wish to respect that, but it is causing numerous problems in our spoken communication. (I am also a native English speaker but am not accustomed to this usage of "when" and "wh... | 1 |
I have an object with incident light rays traveling away from this object. Some of these rays are traveling from the left-hand side through a simple lens (say, a double-convex converging lens). As these rays enter the lens, they are partially refracted, reflected, and absorbed. As these rays leave the lens, they are re... | 1 |
Recently I was asked to explain the difference between reflection and total internal reflection from a purely conceptual standpoint (no math). Let me explain what I already know. Reflection and refraction at the quantum level are the same thing. Light is a photon. A photon is a discrete particle that has wave character... | 1 |
A few months ago I was telling high school students about Fermat's principle. You can use it to show that light reflects off a surface at equal angles. To set it up, you put in boundary conditions, like "the light starts at A and ends at B". But these conditions by themselves are insufficient to determine what the path... | 1 |
I have a long-term goal of acquiring graduate-level knowledge in Analysis, Algebra and Geometry/Topology. Once that is achieved, I am interested in applying this knowledge to both pure and applied mathematics. In particular, I am interested in various aspects of smooth manifolds, co/homology and mathematical physics. I... | 1 |
On StackOverflow.com I often find that people ask questions about problems that arise due to poor design choices (typically due to a lack of knowledge about the particular programming language). For example, the OP will make a choice at point A that is wrong, then in order to correct follow-up errors goes on to B, C, D... | 1 |
Related: How would a black hole power plant work? I have put a bit of commentary enumerating my confusions in parentheses I read in Black Holes and Time Warps (Kip Thorne), that quasars can generate their jets from four different processes. These all involved the accretion disk, but there was one which doesn't make qui... | 1 |
I can't seem to find a specific answer to this anywhere. I understand that in a rocket there is a chemical reaction that causes gas particles to leave the rocket at high velocity. By Newton's third law, and the conservation of momentum, this caused the rocket to be propelled. What is missing is a physical explaination ... | 1 |
Here is a traditional derivation of time dilation: There's a train with a lamp in the ceiling, moving at velocity v with respect to an observer. In the frame of the observer, the path taken by the light from the lamp straight down to the ground is actually diagonal because the train has moved forwards by the time the l... | 1 |
Context: I prepare my scientific documents using LaTeX and compile to a PDF. I often need to seek comments on drafts from collaborators who do not use LaTeX. Most of these collaborators use Windows OS. Assume also that the collaborator does not need to edit the document. They only need to be able to add comments to the... | 1 |
I read everywhere the famous, but offhand statement that "the universe began from a single point" and this bugs me because that surely isn't true. My understanding has always been that this was an oversimplification for the sake of explaining it to children when it fact the universe is - and always has been - infinite.... | 1 |
The famous Riemann rearrangement theorem states that for a conditionally convergent real number series, we can rearrange the order of summation to make it converge to any prescribed number in the extended real line. In particular, this result sheds much light on the significance of absolute convergence, without which i... | 1 |
My questions concerns that classic train paradox, wherein there is a train and a tunnel of equal length, and the train is traveling and some fraction of the speed of light towards the tunnel. According to the Special Theory of Relativity, an observer outside the tunnel will see the train length contracted (Lorentz Cont... | 1 |
I was reading on wavelets and it seems that its hard to find a precise mathematical definition of what this concept is. My confusion first arose due to Gilbert Stang's linear algebra book. In particular consider the following extract: It talks about how to change a vector from one basis to another but it never rigorous... | 1 |
I have confused myself about the following variant of Maxwell's demon and I can't seem to find out where the energy went. Consider this: You have a chain (one dimension) of spins (up/down) with a nearest-neighbor coupling. Energy is minimized if spins are aligned. Let us say the energy difference between alignment and ... | 1 |
Consider an American actor who is tasked with mastering British Received Pronunciation for an upcoming role. If he has a talent for vocal mimicry, as many actors do, he should have no trouble picking up the "rules" of RP just from listening to people speak it: the non-rhotacism of the dialect, the aspiration of intervo... | 1 |
Suppose I am conducting the Quantum Eraser experiment. The results of this experiment are easy to understand with the traditional quantum mechanical interpretation of a pair of entangled photons. Specifically, suppose that I am performing the "eraser" part of the experiment in which one photon is diagonally polarized s... | 1 |
In a previous Phys.SE question, Does a spaceship travelling at near lightspeed see the universe aging slow or fast?, the answer (which was followed by a proof involving co-moving reference frames) was given as The short answer is that yes, an astronaut moving relative to the cosmic microwave background would measure a ... | 1 |
I tried to make rain with a bottle and a balloon but it failed. The bottle was small, only a couple inches wide and the threaded part that I had the balloon on was less than an inch. In particular it was the size of this hydrogen peroxide bottle: It was originally a hydrogen peroxide bottle but all the hydrogen peroxid... | 1 |
The principle conservation of energy is often taken as an obvious fact, or law of nature. But it seems to me the definition of energy is far from obvious, or natural: http://en.wikipedia.org/wiki/Energy lists lots of different types of energy. So if I want to apply this principle in some concrete experiment, I have to ... | 1 |
I'm nearing the end of the semester of an introductory-level complex variables class. (Very introductory -- it's the version of the class that's only required for engineering and physics majors, as it doesn't require two semesters of undergrad analysis that are prerequisite to the complex variables class for math major... | 1 |
I'm quite perplexed by the notion of 'observation' in regards to the collapse of a particle's probability wave. Does a particle's wave only collapse when it is involved in a strong interaction (such as a collision with another particle, like bouncing a photon off another particle to determine the other particle's posit... | 1 |
First I will have to explain my question. Look at the image below. This shows doppler shift when an object is moving horizontally to the direction of the wave. Keep the word 'horizontally' in mind. Now this happens because: I will quote Jim from his answer for Redshifting of light from a moving light source We all know... | 1 |
I'm a math student, starting a PhD in the near future. My field of research will be mostly in the field of applied mathematics / numerics. Topics will deal with Kinetic Theory, Moment Equations, Fractional Diffusion, Spetral Methods. I think I have a solid background in numerical computing, especially for PDEs. Now for... | 1 |
Suppose I have plotted the body angles of a flying aeroplane.I have two such plots. One of a normal plane, and the other plot in which a primary sensor of the aeroplane is removed. So with the absence of a sensor you are expected to see an instability in their flight. Below are the two graphs--- The first one is the co... | 1 |
During an episode of Archer, he criticized a journalist's grammar for her misuse of the word 'child-murderer'. She meant one who murders children, and Archer argued in using the hyphenated form, she implied the accused man is a child who murders. Is this correct? I searched "child-murder" and "child-murderer", only to ... | 1 |
I'll try my best to explain my question with examples because I don't have much knowledge on the theory. So say that I had a block of water in air, a cube of water, that is dropping. If the cube wasn't too big, I believe that as it will drop, then the air from underneath it will rush to either side of it, as the water ... | 1 |
Saw a question about faster than light travel... I still have the same question though none of the answers offered any resolution for me. It is so summarily assumed by all physicists and commentaries that exceeding the speed of light would turn back the clock. I can't see the relation. Doubling the amount of any speed ... | 1 |
Everyone does know that the surface of a conductor is at equipotential during equilibrium. I was reading Feynman's lectures where I found this (bold)line: Suppose that we have a situation in which a total charge Q is placed on an arbitrary conductor. Now we will not be able to say exactly where the charges are. They wi... | 1 |
I'm thinking of writing a short story set on a version of Earth that is tidally locked to the Sun. I'm not exactly sure how to research the topic. Here's a number of questions about what would happen: How hot would the light side get? Are we talking ocean-boiling levels? I imagine that life would eventually flourish, g... | 1 |
I was asking the other day how to find certain fonts of a document. Well at last it was easy. I came to the Mathematical Pi LT Std font and ITC New Baskerville Std results and for that part, I was pleased because I finally managed to get those fonts. So far, I have only used LaTeX for my documents and papers for the Un... | 1 |
It's not really clear to me how does QM attacks determinism. It sure attacks computability, which is a component of newtonian, naive determinism, but it's often claimed to destroy determinism itself (which says that we can't compute events, but they are determined anyway). A photon is both a particle and a wave; a part... | 1 |
I have recently been studying continuous dynamical systems whose phase space can be divided into a number of regions. Inside each of these the flow is smooth, but there is a discrete jump in the flow just at the boundaries. In the mathematical description, the right hand side of the differential equation is different f... | 1 |
I posed a closely related question here but it received a tumbleweeds award. So I thought I would post it from a different angle to see if I can illicit at least some thoughtful comments if not answers. The modeling of many physical systems utilize the mathematical tools of calculus, by writing the relationship of phys... | 1 |
Right now I'm writing an essay on Death in Venice, and I'm having trouble finding the right word or phrase to express how Aschenbach is parallel to the old man on the boat to Venice (both dress up to fit in with youth, some repetition of specific phrases in descriptions, youth from Pola vs youth from Poland, etc.). The... | 1 |
I was looking at this question on SE and the answers seemed to say that the reason why matter doesn't expand along with space is because of forces like gravity, electromagnetism, etc. However, i feel like this has to mean the fields themselves don't "expand" along with space. Let me explain... From my understanding, th... | 1 |
I play the flute as a hobby, and I've noticed that when playing middle D or E flat, one can interrupt the air column by releasing a certain key (which is near the middle of the air column), and yet have no effect on the pitch (though the quality changes for the better). I'll be putting a few diagrams here, since it is ... | 1 |
Having been an avid lover of Mathematics, it is my dream to become a mathematician one day. I have been learning some "Advanced Mathematics" (Real Analysis and some Abstract Algebra mostly, and a little bit of Linear Algebra). The first thing that anyone jumping from High School Math to proof based, rigorous math, shou... | 1 |
I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical constructs, operations, entities, and even the basic terminology (which I have come to understand is incredibly elegant, ... | 1 |
There's a poem in bahasa indonesia, titled "Aku Ingin (I want)" by Sapardi Djoko Damono, translated to english by John H. McGlynn. This is the english version: I want I want to love you simply, in words not spoken: tinder to the flame which transforms it to ash I want to love you simply, in signs not expressed: clouds ... | 1 |
I have never understood what measuring process (if any) is supposed to be continuously polling the quantum state of an unstable bound system subjected to decay via quantum tunnelling. The reason I reckon some kind of polling process should exist in the first place is the following: According to the QM postulates, the u... | 1 |
We have statements, and we have questions. A request made in the form of a statement has a question equivalent. But is that question equivalent implicit, or is it simply a rewording of the statement form? Take the following: "Please tell me why I sound like a sissy." This has the question form of: "Why do I sound like ... | 1 |
Recently I became very much intrigued by algebraic topology and am spending quite some time learning it. My reasons are three-fold: it's a beautiful theory; it gives geometric justification to (or perhaps rather an application of) many purely algebraic structures; and it has fascinating applications in quantum field th... | 1 |
I have been inspired by some sci-fi cannons that seem to operate by initially spinning up a projectile inside the cannon, and then suddenly firing the projectile out at high speed. Now, I am wondering whether it is possible for such a cannon to perform practically. So, from an energy point of view, it appears that this... | 1 |
So, to make it abundantly clear what I am asking for, here is an example picture edited (poorly) in a drawing software: At left, you can see my current TexStudio look: the are where real text is indeed entered had its colors properly customized with a .txsprofile object. However, the menu toolbar, the tabs area and so ... | 1 |
So I've recently seen a few people use the word "sufferer" to describe themselves having a certain mental disorder. I know that a person thinking that they are suffering a certain disorder may be quite subjective, but their usage is still questionable. The best exhibit I have for this question is somebody calling thems... | 1 |
This question isn't answered here: Differentiate between past and present just by pronunciation when word is followed by d- or similiar sound That question asks about what happens when the following word begins with a consonant in general. This one is asking about the various possibilities for an intervocalic tap if a ... | 1 |
For the sake of time, is it bad to just accept some fast paced class's theorem's (such as MIT's algebra class) as true even if you don't completely understand the proof or can't remember the proof off top of your head (after a while has passed?). I often find myself wasting too much time trying to memorize proofs when ... | 1 |
We make an important distinction between the topological insulators (which are essentially uncorrelated band insulators, "with a twist") and topological order (which covers a variety of exotic properties in certain quantum many-body ground states). The topological insulators are clearly "topological" in the sense of th... | 1 |
I've been thinking about infrared radiation and noticing more and more how the human skin seems actually pretty sensitive to it. You can easily feel a bonfire from several meters away, far away from where any convection would heat your skin. When you open the hood of your car you can feel the heat from the engine even ... | 1 |
Has anyone actually developed a Program Synthesis system for creating computer programs automatically from a non-procedural specification that is taken from a fairly robust system of specifications? For example, I might say "Check if X is a factor of Y." or "List all prime numbers between X and Y." and out pops a progr... | 1 |
I was recently in an argument with a friend who - equipped with an apparent understanding of the etymology of the words lend and borrow - insisted that to lend an object required not just the temporary exchange of its possession, but also a geographical displacement. He compared the words lend and borrow to take and br... | 1 |
Rational numbers, rational functions, and Gaussian rationals are examples of fields of fractions. In each of those cases, one knows what the quotients are long before one hears of the idea of constructing the field of fractions of an integral domain. One case where one (typically??) does not know of such a thing in adv... | 1 |
Assuming that antimatter is matter with time arrow reversed, would it be right to say that matter beyond black hole event horizon then would become antimatter because of space and time axes exchanged? Would not black hole then appear like a nice universe consisting from antimatter that slowly expands as matter falls in... | 1 |
One only needs to search MMA.SE, math journals, wikipedia, or god-forbid, n-cat lab, for keywords listed in the title, which can be extended with: uniform-, regular-, complete-, local-, partial-, non- (see below) &c&c, to be convinced that modified concepts are replete across maths, proliferating, and their diversity i... | 1 |
I think physicists can deal with this question best. I answered a question about "immortality" when some guy claimed I got it wrong that neurons die (I argued that even if you live a billion years you die slowly many times over because all your cells incl. nervous cells will have to be replaced, meaning you will regula... | 1 |
There's a list of "New York" words and phrases that's been surfacing on the Web periodically for quite a few years. Not all New Yorkers speak like that, I assure you. Only barely-above-the-gutter white New Yorkers with Brooklyn roots, plus lower-middle-class Jews from Borough Park and wanna-be Italian mafiosi from Bens... | 1 |
This question related to Why are magnetic lines of force invisible? and is motivated by a comment of @BlackbodyBlacklight, based on that, the illustrating example may depend on that linked question as context to be clearly understandable. A remote magnetic field, in the sense that it is not at the location of measureme... | 1 |
I have a question about adjoint operator. I have known that bounded linear operator on Hilbert space has a unique adjoint operator, but I am wondering whether there is similar existence result about bounded linear operator on Banach space? Thank you. | 1 |
I am learning measure theory this semester. The definition for sigma-algebra is "a collection of sets that is closed under complements and countable unions and intersections." I wonder what does it mean by "closed under complements and countable unions and intersections." Thank you so much for your help! | 1 |
I know that "callipygian" means "having beautiful buttocks"... so I was wondering if there is an English word that means "having beautiful hair". I tried googling this but couldn't find anything so far. | 1 |
I'm preparing for an exam and I can't seem to figure out the reasoning behind the answer to this question. Why do they use a chi-squared test? Can someone walk me through their explanation? Thanks. | 1 |
I'm looking for a good textbook for an introduction to Stochastic Analysis, preferably one that focuses on rigour. I am familiar with measure theory and basic probability theory. The direction I am mostly interested in is stochastic differential equations. | 1 |
I'm terribly confused on the concept of "rank of a linear transformation". My book keeps using it, but it doesn't clarify what it means (or at least I haven't been able to find it). Is it the same as the rank of the matrix? For example, if A is a mxn matrix, what would be the rank(A)? | 1 |
I've recently been working through a lot of physics problems and a lot of them say to assume that the mass of the string used in a problem involving a pulley, for example, is negligible. Why is this important? What would happen if the mass of the string wasn't negligible? | 1 |
How do I properly punctuate this sentence: "I prepared, packaged, and priced beef, pork, chicken, and seafood." I am trying to say that I did those three actions to those four kinds of meat, but I am unsure of what to do. Should there be a colon or semi-colon between priced and beef? | 1 |
I'm not a native English speaker, and I don't understand the meaning of the phrase "in your general direction." I have found its use in the line from Monty Python and the Holy Grail: I fart in your general direction. | 1 |
This problem is taken from the book Mathematical Circles by Dmitri Fomin, et al., translated by Mark Saul and published by the American Mathematical Society. Can anyone describe what the question actually means? | 1 |
I'm reading a book on probabilistic robotics and it mentions that "this probability density function is quadratic in x." I haven't heard of the phrase "quadratic in x" before. Can someone explain what it means? Does it mean that the graph has a quadratic shape? | 1 |
I don't want subsections to appear in the table of contents of my Lyx document. How do I turn them off? I went to Tools -> Settings -> Numbering & TOC, but it won't let me modify anything. What should I do? | 1 |
I just read this interesting interview with Frank Wilczek and he talks a couple of times about gate symmetry, without ever defining the term. This isn't a term I've come across, and google throws up a blank. What is gate symmetry, and are there any good references? | 1 |
I have a LaTeX document that contains proprietary information. I need to print a version of the document that has a box around the text with a disclaimer (something to the effect of "Proprietary information of company XYZ, do not redistribute without express consent'). How can I do this? If it matters, I'm using MacTex... | 1 |
Density Functional Theory (DFT) is formulated to obtain ground state properties of atoms, molecules and condensed matter. However, why is DFT not able to predict the exact band gaps of semiconductors and insulators? Does it mean that the band gaps of semiconductors and insulators are not the ground states? | 1 |
I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost. Is there a way to explain how the Higgs field works, in a way that people like me might have a hope of understanding? | 1 |
Is it possible to establish that the lines joining the mid points of opposite sides of a quadrilateral bisect each other. I attempted using mid point theorem of triangles but I couldn't prove it | 1 |
I am trying to find an English translation of Camille Jordan's work "Cours D'analyse". Only the French edition is on Amazon, so since this is a somewhat specialized topic, I thought perhaps someone in this forum might know. TIA, Matt | 1 |
I am currently studying Electrical & Electronic Engineering. I wish to pursue Quantum Mechanics or Quantum Computing as my research subject. Is it possible for me to do my M.Tech. and then pursue my research subject? What are the prerequisites for studying these subjects? I would be grateful if you could help me. | 1 |
Prove that if the real part of an entire function is bounded so is the imaginary part, without using Liouville's theorem. In particular, is there a way to prove this using the Cauchy-Riemann equations? | 1 |
I'm sorry if I ask this question at the wrong place, but I don't know a better one. I am a Master's student and I am really interested in analysis, but I also want to get into AI. Does anyone know a natural way to combine these two interests? Thanks in advance. | 1 |
The title basically states the whole question..I was trying to invoke the Mean Value Theorem on it but it hasn't worked..I was wondering if I'm supposed to solve it some other way. I just need hints, please. Thank you. | 1 |
This has been bugging me. Why is the lower case letter "a" used to spell "abelian group" when upper case letters are used to spell the terms, "Gaussian Integral", "Cantor set" or "Cauchy sequence"? Don't know where else to ask. | 1 |
As far as I can tell, if a function is holomorphic on its domain, then it's also meromorphic and vice versa. Can someone tell me what the difference between these two properties are (if any)? A counter-example and an explanation of why it's a counter-example would be nice. | 1 |
I'm reading "The Portrait of a Lady" by Henry James, and I found the following two sentences. "I suppose that after a girl has refused an English lord she may do anything," her aunt rejoined. "After that one needn't stand on trifles." What does "one needn't stand on trifles" mean? | 1 |
I am making a piece of software which has the ability to send out Emails and SMS messages. My boss has asked for both facilities to go under the same heading in a dropdown menu. But I can't think of a suitable work that encapsulates both. Any suggestions? | 1 |
We've all seen that label on our passenger side mirrors that says, "Objects in mirror are closer than they appear." Why is this? Further, why does it only apply to the passenger side mirror, and not the driver-side or rear-view mirrors? | 1 |
Show that Lebesgue measure can be expressed as a countable sum of probability measures. I'm trying to do something with the countable additivity property in order to show this, but so far nothing is working. I don't think this is supposed to be difficult, but I'm not seeing it, so any help you could give would be most ... | 1 |
I'm trying to compile a LaTeX template to a PDF, but it's not working. The template is available in this link (on the right side in Article Templates). I'm using TeXnic Center. Can anyone please try to compile this and let me know if it's working. | 1 |
I am trying to use Egorov's Theorem in a proof. However, I only have convergence in measure of f_k to f and uniform integrability of f_k. How can I combine these two to get convergence point wise so that I can use Egorov? Thank you so much for your help! | 1 |
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