darklight03/StackMIAsub huggingface dataset:
Consider a free body, not hinged about any point. If a force is applied to one end of the body, the body has a net nonzero torque about many points in space. About which will it rotate? Am I wrong in thinking that it will rotate at all? Note that I am not asking about a couple, but a single force. I asked a similar question a few days before, but it got closed, with links not at all answering my question.
Jordan rolls eight fair dice, computing the sum of the numbers on the top of the dice after the first three rolls. What is the probability that Jordan is able to find at least one way to pick exactly three of the latter five dice in such a way that the sum of these three dice is the same sum as that of the first three dice?
I would like to know if there is a relation between bounded variation of functions and bounded variation in sequences. I know one can not directly correlate the concepts but if we consider the Fourier series of the function of bounded variation, what can be said about Fourier coefficients, would they be of bounded variation (sequence definition) and what about the vice versa case? Are there any articles or books related to interlinking these concepts?
A frame of reference is the perspective you have on a happenstance. But isn't it a viewpoint or point of view? As in, a literal point, from which something is observed? If so, why is it called a frame and not a point? Does frame of reference literally crops a section of existence as the perspective of observation? Why is it one phrasing over another?
If a photon has a wavelength and a frequency and we depict a graph with multiple hills and valleys like done in basically every explanation regarding photons and their wave/particle behavior, like in this one. is it correct to say that one photon (as simplified as it is) is stretched from one hill to the next? And multiple of those sections are either multiple photons behind each other (when the sun emits them) or the trail of one photon as a record in space or time(depending on what one wants to depict). Or is one photon the entirety of those many hills and valleys? My understanding is, that one photon is one part from hill to hill or valley to valley, depending on how you look at it.
For a set A, we are incrementally building a basis for A. Suppose some oracle keeps giving us new vectors from A that are not spanned by our partially-built basis. There must be some theorem that tells us this constructive procedure of adding new linearly independent vectors will always terminate after the same number of vectors are added (no matter what vectors that oracle gives us), and all sets constructed this way must form a basis for A. What is the theorem? Is it in Axler?
I am no scientist, but I do love science as well as the unknown. Are there laws of creation for biological life? Would it be safe to assume that our bodies are made up from things that came directly out of the big bang and over time made connections through atoms and adjustments through evolution to achieve consciousness? I have much more but I'll keep it as simple as I can for now.
A small circle is tangent to the lower right quarter of a larger ellipse. The ellipse is straight (not rotated), and its lowest point is centered at origo. The following is given: "a", the axis of the ellipse along the x axis. "b", the axis of the ellipse along the y axis. "r", the radius of the circle. "h", the top y coordinate of the circle. I am seeking the x coordinate of the tangent point between the ellipse and the circle as a function of a, b, r and h.
Dirac's initial interpretation of antimatter is the existence of Dirac Sea. However, it doesn't work for bosons since we can't invoke Fermi's exclusion principle. Goldstone boson can be emergent but it's neutral. Xiaogang Wen's work also revealed the possibility of an emergent QED structure from string-net condensation which shows fermi statistics and gauge interactions can be emergent. We also see emergent Lorentz Invariance in the low energy area of condensed matter system. W bosons are charged bosons. It seems impossible to me for charged boson to fit into Xiaogang Wen's "it from qubit" fantasy. Does anyone know the approach to this or related literature?
So if our eye is considered a lens, a parallel beam (sort of like collimated light from a flash light) should converge to a single point, the focal point. So does that mean our eye will see a finite parallel beam as a single dot? That seems contradict real life experience, where I still see the parallel beam as a beam with finite width. What gives?
After reading the paper On the Expressive Power of Homomorphism Count, I was wondering if there were some nice material I could read trying to study graphs from a categorical point of view. Stuff like trying to make it in an abelian category, looking at exact sequences of graphs (maybe you'd need to consider some kind of pointed graphs category), maybe defining stuff like Ext groups and studying them. I hope my question makes sens. Thanks in advance for any answer.
Whether it is Orion or Sagittarius, the speed relative to me is clearly faster than the speed of light. These are not inertial systems, so they are not subject to the constraints of special relativity, but does the fact that their apparent velocity is a circular motion exceeding the speed of light cause any kind of apparent change in time for celestial objects if the argument is based on a celestial coordinate system? They at least don't seem to be unable to follow, unlike the laser beams I shot at the moon or something.
When I was reading the calculus of Variations chapter in Classical Mechanics by John R. Taylor, he mentioned that cart rolling back and forth on cycloid-shaped track are exactly isochronous (period perfectly independent of amplitude). As I was trying to solve this by the original integral, I find it hard to compute and the normal Casio type calculator cannot solve it as well, also I sought help from websites like Integral Calculator, the result function is not independent of the starting angle I set. Can someone help me, great great thanks!
I'm trying to make a comprehensive decision tree for finding integral/improper integral convergence. The goal would be a comprehensive "guide" or list to follow in order to determine the convergence without having these automatisms already learned. Here is what I have made currently: Decision tree Are they any better ways of doing this? More optimized ? How can I make this tree more complete, more accurate ? Apologies if language is off in the image, I'm not great at this.
Aero is not my speciality at all so apologies if missed anything. But when looking at potential flows, i thought the whole point is for there to be no rotation at any point and its that reason the velocity can be described by a scalar fuction at any point, yet the vortex flow has a point of curl in the center and hence circulation. I noticed in J.D Andersons aero book that it is this particular flow that allows for lift in invicid flow which greatly confuses me further. Is there some hidden explination behing the vortex element? Appreciate the comments.
I am not getting the following sattements related to contact force and normal force which are: If the direction of contact force cannot be determined, it should be shown as two components. If perpendicular to the surface of contact cannot be drawn, the normal force will act perpendicular to the surface of the body. If neither can be done, normal force has to be drawn as two components- one in the X- direction and one in the Y-direction. The forces acting along the X and Y directions are independent of each other. What does these following satements are trying to explain?
So I think I understand what binomial coefficients are, "K number of combinations that can be made from set N". However, I keep seeing examples demonstrating K being the number of successes against the number of outcomes. However, my thinking is by the logic of the first example I gave, when finding the number of combinations Tails Tails would be included as it is a combination that can be made from set N. However, this does not feature a heads and is not a success.
I would like to reference addresses throughout a document and as an appendix generate a list with all the address entries used and the link to the places in the document where they were used. Just like it is done with a bibliography. I'm actually thinking it'd be the easiest to use a special kind of entry and store them in a bib file, and then use it as a list of citations. How would you do it? Many thanks!
Suppose We have a charged rotating cylinder such that the magnetic field inside it is the same as a solenoid of the exact same dimensions. Obviously, the current per-unit length for both will be the same. Now, what can we say about the magnetic flux in the cylinder since there is no n (turns per unit length)? What can we comment about inductance? It depends on n and not current.
I want to know if the verb seem can be used only for observable things? For example, if I guess the computer hard disk is failed doing some action and has some logical issues can I say: "It seems the hard disk has logical errors."? In this case, no physical failure is not observed on the disk but I know something is wrong with it. In case the "seem" is not suitable, what alternative verb do you suggest?
I am about to compile a number of different published articles into a single thesis. While each document on its own can compile and produce a PDF, there are several macros files (shorthands for various formulas) that are inconsistent between them. Is there any way to do this with the least amount of change to each latex document? In particular, is there a way to include the macros "locally" for each article so that they don't conflict?
As the name suggests, I am trying tio draw in TikZ the following figure for a surface current distribution (I am used to drawing with hand, so I find the switch to the digital a bit tough): The striped region is a urface that is covered with current densities J, and the second image is a representation that gives an idea on the relation of all the vectors involved. The dashed line between A and B is an "cross-section" that helps to calculate a line integral with the element being dl, and the vector n is a normal vector to the surface with u a vector orthogonal to it. Thanks immensly, and have a wonderful day.
Is there an easy way to list all appearances of all words in the text of a LaTeX document that occur before a makeindex entry for that word arises in that document? When we move text around in a document, we can find that we have moved the definition of a technical term later in the document than one of the instances of that term being invoked. We cannot completely automate the task of eliminating these errors, because the same term might have a technical meaning defined somewhere, but also a common meaning, and the common meaning might be the meaning intended in an instance occurring before the definition. Still, TeX could help by making a list of these, so we could check.
In a theory that predicts gravitons, shouldn't the background be flat and gravitational interaction then be modeled as a scattering event? Answer included below. Credit to /u/broguetrain on Reddit for providing the answer when I asked on there some time ago. I wanted to post this Q&A here (with some edits for clarity) due to recent drama on Reddit so as to assure my ability to reference it in the future. I do encourage additional answers on this that might provide further useful details. For example: elucidating on how specific metrics can be described as the coherent state of strings in the graviton state.
their reasoning was that when the bike lean towards horizontal the reaction acting on the bike by surface will act in an angle through the center of gravity of the slanted bike(not perpendicular to the surface). therefore the horizontal component of that angled reaction will provide the centripetal force even though friction is not present. they also said that if the friction is present this component will be added to the friction and their resultant will act as centripetal force. i find this hard to believe.i think it is impossible to turn on a frictionless horizontal surface. can someone please help me find the correct answer?
Or at least I think it was Pratchett taking a potshot at religion (exact wording unknown either): "When you got them by the balls, you, uhm, got them by the balls." Note that both parts of the sentence are metaphorical, meaning about "When you control their sexuality, you control them totally". Which rhetoric figures are involved here (is the one metapher more, uhm, metaphorous than the other since the first part involves actual balls, at least pars pro toto or so)? Seems to be quite a lot...
There is a misconception that electrons push each other from their mutual repulsion within a circuit. Rather they are pushed by the electric field. I also understand that the electric has the energy rather than the electrons being charged carriers. However, I can't seem to understand why we need wires at all when energy is in the fields rather than the electrons. What is flawed with my logic?
Basically I know how "a" and "an" are used: a member an adult member but how is the same handled when the middle word is inserted parenthetically or even in brackets: I met a member of the club. I met a/an - adult - member of the club. I met a/an (adult) member of the club. Should there be "a" used, because the main phrase is "a member" or should "an" be used because the adjective starts with a vowel? And is there a rule to quote?
I want to drop a cup of water with a ping pong ball within it so that it falls straight (as much as possible) and that I can reiterate the experiment rigorously... I've seen someone using magnet and a specific system that sadly I cannot build at home. My idea is to hold the cup and trigger something that let fall the cup with the ping pong ball but nothing good comes in my mind. Do you have any ideas? Thanks for reading
I was reading an article about high density housing and/or constantly being online and came across a single word I had to check the dictionary for and it was used to mean "the absence of a community spirit". e.g. "The x caused by the complex housing situation." I have had no luck with antonyms for community or synonyms for diaspora. I can no longer remember the word or the article. It may mean the degradation of community or the circumstances preventing it. What word is used to define this asocial vacuum?
I look how to implement the algorithm (program) for solving so called Zebra(Einstein) Puzzle. For that, i look for some formal or mathematical representation of conditions in this puzzle. Can you suggest possible ways to represent it, while this representation should makes easier to solve that? Of course, do not suggest the trivial forms, like list of all possible variants, this is not efficient if there are too many variants.
I've been attempting to get a row of dots from the end of the equation right to the equation label, that allows the reader to easily trace along from, say, an equation on the right of the page, muuch like the format commonly used for contents pages; headings with a row of dots leading to the page number(s) so that the reader doesn't get lost, trying to trace along the "line" with no guide per se. Thanks
The ant on rubber rope paradox says that an ant moving along a rubber rope that can infinitely expand will reach the other end of the rope regardless of how fast the rope expands and how slow the ant moves. Why then multiple sources say that there is cosmic event horizon, and two persons at some distance exceedidng Hubble limit would not be able to meet?
Is there a way to calculate equivalent parameters of a few RL links for direct current circuit (like on the generalized example on the image below)? So far I've studied that known formulas for series/parallel connections of R and L elements cannot be used because it's not R and L elements, which are connected in parallel and series, but RL elements (as a single entity), which can connected in parallel or series.
My former college is starting a departmental journal which I am editing and typesetting. I have edited and typeset every contributed article individually using the article class and initially tried to bring them all together using the combine class then individually tried the subfiles and standalone packages but none of it worked. So finally I decided to use pdfpages package and include all the articles as pdfs in my main document. Now, each included pdf article has a separate title and author BOTH of which I want to add to the main toc. How do I do this?
A large part of the computational physics literature relies on solving Newtons equations for deriving phase diagrams and related properties of the LJ system. In many cases this approach does not require justification since one could be interested only in the dynamics of the system during a short time. But this is not the case if one is interested in caculating partition functions. So I have not found any established result to ensure that this approach is sufficient for sampling the phase space and calculating partition functions.
The universal law of gravitation of Newton calculate the intensity of gravitational force by the radius and mass of an body.. so in a black hole there is very much small radius and a large amount of mass... So I think newtonian gravity would predict large amount of force.... That is similar to the great pull of black holes due to gigantic space time curvature...
I now have a point located at x, and the value at that point is q(x). I want to discretize the point to the surrounding grid points and maintain a Gaussian distribution. A one-dimensional grid is fine. Is there any generally recognized good discrete method? Thank you. As far as I know, B-spline does not satisfy Gaussian distribution, so B-spline is excluded. One method I found is D.E.Shaw's Midtown-splins, but it can only reach the third order, which cannot meet my needs. What is a better discrete interpolation method?
Can anyone suggest existing technologies that must account for electromagnetic momentum? I believe one example to be confinement in nuclear fusion; but momentum there appears in an averaged form, as pressure. Just to give an idea of what I mean with "existing technologies": general-relativistic time dilation has to be concretely taken into account in any phone's GPS. (Edit: many excellent answers have been given, it's really difficult and partly meaningless to choose one as "the" answer! I chose JEB's one mostly because it is about a macroscopic effect and about a directed form of electromagnetic momentum, rather than more "averaged" forms closer to electromagnetic pressure.)
For many (!) years I have written papers in MS Word with numerous embedded equations generated by MathType software. MathType prior to its recent acquisition by Wiris was able to function as a standalone equation editor and save equations as pdf files that could be embedded in Word, and edited either within Word on independently in the saved pdf format. The new version of MathType is an absolute disaster: the interface is pathetic with many controls of sizing and fonts lost, the generated equations are bit-mapped (not vector graphics), etc, etc. I hope to switch to producing all equations in manuscripts with LaTeX, but wonder whether some version of LaTeX can generate Word-embeddable pdf files, and if so what version(s) of LaTeX are suitable. Thank you!
I want to know the temperature of electron plasma whose data has been generated via particle in cell simulation. My professor said if I have histogram of electron density by kinetic energy, then I can get temperature of the electron plasma when I apply the log on density. He also mentioned slope of log applied histogram for calculation. I have tried to find out what is that method, but I couldn't find any reference from it. Does anybody know about this? I need to change my lab and advisor before the september ends so I need to organize what I have done as soon as possible for contancting other labs. And thank you for your helps.
This question Sum of Countable Increasing Absolutely Continuous Functions is Absolutely Continuous says if the functions are all AC, then the sum is also AC. Then if the answer is not true for my question, we only need to consider the case of continuous singular functions. However, I have no clue how to deal with them since I only know the Contor function as an example of continuous singular function, and the summation of the varients of it seems cannot lead to a contradiction.
The wave function collapses anyways whether I wanted to know which slit the electron passed through or not, the only difference there is that in the former case the wave function collapse for any electron at either of the two positions directly behind the slits, i mean the electron still in superposition of all possible locations on the screen, but upon watching the electron passing though which slit, the collapse magically favors only one of two possible location, i.e., the ones directly behind the slits, Is that right?
Recently i have been reading "A radical approach to real analysis" by David Bressoud and this thing got stuck in my mind Here you might lose convergence at the end point is written in last paragraph what is this meant for an infinite trigonometric series .It has also some relation with derivatives somehow. This was written for the explanation of fourier series and crisis in mathematics but what means by phrase losing convergence and how it is related to trigonometric infinite series
Let's say I put a neutral conducting sheet in front of a charge. What will happen to the sheet? If I place a plate with some thickness in front of the charge, charges will develop on the face of the plate to maintain the electric field inside the plate zero. There is no such thing inside the sheet, so how will it react to the charge in front of it?
I'm using the article documentclass to write a simple document, but when i compile the code the tableofcontents look like this: From section "Progetti" there is no space between the number and the name. The code of the section is the following: I already tried to take out the subsubsection thinking it maybe was the cause, but the problem persist. I also tried this method but it add more space between number of section and name but it increase the space between all the sections, correct ones included. Can someone give me a solution? Thank you.
In P Halmos measure theory book it written A Sigma ring S generated by C, the class of compact subsets of X where X is locally compact Hausdorff Space. Then S has open set and sets of S is called Borel Sets. I am very confused. How a sigma ring generated by the class of compact set has open set. P Halmos Measure theory book:
For a new paper I am writing to IEEE journals (double-column formats), many important paragraphs suffer from the default hyphenation in LaTeX. Especially, I don't like the hyphenations given in the Funding Statement at the end of the paper. If I don't want hyphenations in some words such as "under", "Programme", "Excellence", "Operational" etc., how do I instruct LaTeX not to hyphenate these words in the IEEE LaTeX document? Thank you..
I was given this problem in physics class. My teacher said that they reached the ground at the same time, but when I tested it out (video), I got drastically different results. I showed the professor and asked him why real life and theory did not match up, and he said to just accept it and would not explain what is going on in real life. Why is the experimental result so different from the theoretical answer?
Pretty straight forward question. Which of the following sentences is/are "correct"? They are simping on Korean players They are simping in Korean players They are simping for Korean players What I want to express is that a group of people feeling extreme sympathy for Korean players in a online international game. I've always used for but I see a lot of people writing almost the same sentence using mostly on and rarely in