The definition of exegesis is Bible leaning and thus is not a word many outside of the church are familiar with. And yet people can understand the idea of trying to interpret a text as the author or authors meant it to be understood. This applies to the US Constitution. Is there a familiar word that is used by secular society that means to understand what the authors meant when they wrote a text?


Recently, I've been solving problems involving Burnside's Lemma. The question often says: "Find all different colorings if we identify colorings when they transform into each other under some rotation/symmetry/isometry/isomorphism." I get confused about in which cases I need to consider the figure being "turned inside out" like for example tetrahedron can be. It seems to me that: rotation - no symmetry - yes isometry - yes isomorphism - yes Assuming it is possible for a given shape. Is this true? Or it depends?


@JonathanZ Thanks for going all the way to help me out. An oil-pipe has to connect the oil-well O and the factory F, between which there is a river whose banks are parallel. The pipe must cross the river perpendicular to the banks. Find the position and nature of the shortest such pipe and justify your answer. I tried out this problem with some numbers and got the idea of path of minimum pipe length. How can I do it more rigorously? This is what I got through my intuition. I think blue one is the minimal path.


Example: a close friend died of cancer, so you feel very bad. Yet they were old and no longer suffering, so you also feel glad. Both feelings are strong and truthful, yet the emotions about the same object or situation equally oppose each other. Ambivalent comes close, but I was looking for another word to more exactly describe the situation. Ambivalent would describe a struggle where you might not like something about someone, yet still like other characteristics, hence you are uncertain how to balance the situation (be their friend or walk away). What word describes when you are not struggling to balance two truths, but accept both opposing feelings? I ask because we are helping someone who is grieving.


In the literature and comments, I have met two pieces of jargon: Low energy SUSY, High energy SUSY I'm confused about the technical and well-defined conceptual differences between the two type of Supersymmetry? Of course one such difference should be the scale at which SUSY is broken, but I have no idea how high and low are distingushed formally and how they differ fundamentally from each other? For example, I read a comment due to Peter West: that LHC can only rule out low energy SUSY which is different matter from high energy SUSY.


I pasted the whole fragment from the book "Teaching Physics by Laurance Viennot". I generally understand this fragment. However, I am not sure if I understand what author means by the phase at each of those points then has to be readjusted in order for a geometrical optical treatment to be applied to that "object". I circled that fragment with blue. Can you give me more guidance how to understand that?


So during our numerics course we learned a few interpolation methods Aitken/Neville, divided differences,Lagrange and the Vandermonde matrix. How these work is clear to me for the most part, I'm just wondering what are the advantages and disadvantages of the respective methods compared to each other? I know about a few things here and there like some methods being easier to expand when gaining new points but our script seems a bit sparse on that info and I'd like a more holistic picture.


Do two mechanical transverse waves traveling in the same medium have the same speed whatever the source might be? If the answer to this question is yes, can I generalize and say "all waves of the same EXACT category traveling in same medium have the same wave speed" and by the same exact category I meant to specify the exact type of the wave, that is to state its both kinds; mechanical and traverse, or mechanical and longitudinal. That being said, I can't say that two mechanical waves one is transverse while the other is longitudinal have the same speed in the same medium, they could have the same speed though, but its not a general statement, is that right?


I was looking At a couple different replies to some questions on here and I kept seeing people saying that larger mass black holes have a lower gravitaional strength on their surface than lower mass black holes. I am no expert by any stretch of the imagination but I would of assumed that the larger the mass the more powerful the gravity. Does anyone know why this is


I've been playing with this problem for a long time, but I don't see a solution yet. Consider the sides of a trapezoid of lengths a and b, a > b (not heights) ( see edition (and the bases major "a" and minor "b"). Determine the height of this trapezoid using two different methods. Don't use trigonometry Can you help me EDIT Typing error: a and b sides, a and b are not heights, a>b, the bases greatest "p" and least "q" There is also the image that refers to the data


I must learn tons of identities for vector calculus for Electromagnetism, but they were taught as a list of items to memorize. Some of them are reasonable to follow (such as gradient or curl acting on sum or product of vectors), but I'm lost with curl and vector product. I lack any formal math background, so I'd like a book/ page where these expressions are justified/ derived in an understandable way. Thanks in advance!


In the photo I added,there is a question as you can see and its given solution. When the switch S was open, charge on each capacitor was calculated and the voltage was taken as the net voltage of the two connected batteries. But for calculating charges on the two capacitors when the switch S is closed, only the voltage of one battery was taken for the corresponding capacitor. Why is it so. Why the effect/voltage of other battery is ignored.Either I am lacking some concept clarity or the charge must have flown through other sides( A and C) as well. What will be the new charge on the two capacitors after closing the switch S if the charge flowing through each section (A,B and C) is considered?


As we try to refine our spectrometer better and better each day, like first we observed doublets in Hydrogen atom, then we observed fine structure's in hydrogen like and in many heavy elements. Then we saw hyper fine splitting too where atomic nucleus takes part too. My question is what will happen in the case where we have a spectrometer and we are observing one single line of a particular spectrum which is so sharp that (till my knowledge I know splitting till hyper-fine level) will we observe a single a infinite sharp line or what. Or there will be some error like Doppler broadening etc. kind of situation.


I wonder if there is a tex library that can create an equation like this (found in this paper and the authors actually create a figure for this, not in tex) With some research, I see that the arrows can be made using witharrows but I am not sure about the colored part, specifically the I_i(D) part where the two colors (dark green & light green) overlap. Any pointer will be highly appreciated! Thanks!


I was looking through some old documents and pitching them from my time at uni. In there, I found some materials handling notes, and one regarding the handling Uranium metal bars. Basically, it said that they didn't require any special handling. As a thought experiment, this makes sense as the bars are just purified ore and thereby very dense and the radiation would be just surface emission. Is this true?


I read this sentence earlier, and it struck me as incorrect: A number of parameters is associated with an open connection. My first thought was the is should be an are, but talked myself out of that because number is singular. Then I asked my wife (family grammarian), and she says that the sentence is incorrect; it should read as follows: A number of parameters are associated with an open connection. We checked out some examples using an online dictionary, and it seems she may be correct. What's the answer - which is correct?


I was reading a USACO Guide Page on data types and I came across two formulas for the absolute and relative difference in the desired answer and the actual answer that is outputted. This is meant to be calculate the absolute and relative errors but what really is the difference between them? I tried to read this question but could not understand it. From a mathematical standpoint what is this exactly and what are its true applications in programming? Where would I need each type? Here is an image of the text I was reading: Image of text from USACO


I am trying to learn contour integration, for the purpose of learning another technique I can apply to computing definite (real) integrals. Although I can apply the process well enough, ( with some issues in contour selection, but that's a different question). The problem i am dealing with, is how can a person tell if a particular real integrand is a good candidate for contour integration? I've read something about "five cases" where it can be used but it felt weird for such an arcane technique to be limited to precisely five situations so I came here to ask instead.


In many contexts we have the concept of mapping one element to another. Is the mapping itself an object which has a lifecycle? What makes the mapping come into existence? I may not be asking this very articulately but when it is stated that there is a mapping, what causes this? Where is the information that says the mapping exists stored? Is this related perhaps to Axiom of Choice?


I have been trying to solve this question from twitter for like two days could anyone help me with this? All the credits go to the name mentioned in the image My attempt to solve: I think it's harder to understand my messy diagram. But all I have done here is drawing a parallel line from a vertice to the opposite side of the square and with that I have find the lengths of the mentioned segments in terms of x Thank u in advance for looking into this problem


First, I know it "worked", in physics sense. My question is what happened in the math sense. When promoting something, such as a field, to an operator, am I essentially mapping the field to (infinitely dimension) operator that depends on spacetime? And the canonical commutator just somehow followed from this map (my guess is that the map somehow preserve the Poisson bracket and somehow map the bracket to commutator.. or maybe we can just get it somehow from operator's dependence on spacetime?)? Alternatively, could it be that I am mapping the field to a more intricate mathematical object that encompasses canonical commutator (as well as other symmetry and their generator? as the operator version of the charge just somehow works quite well as a generator)?


I am in the process of writing a research paper that compares my Methods A and B against a commonly accepted gold standard (reference) method. All methods produce objects that are identical in the ideal case. I am now in the search for a noun to refer to the objects which are not the reference objects, i.e. objects produced by A and B, in the context of the comparison. Example sentence: The ______ are smaller compared to the reference objects. So far I have tried working with test objects and input objects and sample, but they appear wrong to my intuition. Ideally it would be a term familiar to other academics.


Huygens and Maxwell have wave theories about light. On the other hand Planck and Einstein have theories about particle nature of light and could explain blackbody radiation and photoelectric effect which theories of Huygens and Maxwell unable to explain. What about Newton's particle theory of light? Does it have advantage of explaining a phenomenon that all wave theories unable to explain? Is Newton theory of light could be considered as root for "essential need" for particle imagination of light or it is merely a non-essential theory when we could have wave theories?


I'm not a mathematician, but I've read alot about QFT theory. The way it is visualized are different levels of energy and the fields interacting with one another. Am I correct that these fields overlap each other in the same point in space? What if each point in space has exactly the same amount of energy, and in order to create higher levels of energy, that energy has to be drawn from the points around it which would pull and twist space as it absorbs the surrounding energy to produce the known subparticles. Do we consider QFT fields as more energy in a single space? Or do we consider each field as just a description of a higher energy state?


So here's something I was wondering about. Let's say I have to have boundary conditions in flrw metric which does not leave the universe isotropic and homogeneous. This would go against observations. Thus the boundary condition too must respect this. But I know how to apply killing vectors on tensors not boundary conditions. How does one then proceed to find all possible boundary conditions which leave preserve isotropy and homogeneity?


Today, someone asked me if the pronunciation of the "c" in "exacerbate" is an /s/ or a /z/. In fast speech, it seems indistinguishable if I substitute /z/ for the /s/ , which is the standard dictionary pronunciation). Are both pronunciations acceptable? I did some digging and discovered that between two vowel sounds, the phoneme is voiced (reason, cousin, teasing) , but I'm not sure if this is a hard and fast rule.


According to the special theory of relativity, in moving body all physical processes are slower than they should be for a stationary body according to the time counts of a fixed (laboratory) frame of reference. In the case of moving mechanical clock we have changes in rate of the clock (according to mentioned above mechanical clock ticks slowly). In other case (for other types of clocks) we have the same changes too. But what changes do we have in the case of moving light clock if speed of light is constant? Thanks.


Another weird question, I know, and may sound simple but I'm now trying to see why a lot of the things that we usually do without thinking, have some sense in physics, like this one. Let's say you are in a deep pool, and you are covered with water entirely but, you raise your hand above the water, what happens in the water is that your body actually goes down and sinks. Why is that? Like why by putting some parts of our body outside of the water level makes us to go down in the water? I know it may be simple but I want to know, is it because we are like "lifting" in some sense, our own arm, so it makes us to go down?


When it comes to the reciprocal space of twist bilayer graphene, there is a very typical picture: In this picutre it shows the hoppings bewteen the nearest Dirac point between two layers. And there are six hoppings since there are six Dirac points. And these two Dirac points then form the new moire first brillouin zone of the twisted bilayer graphene, as the picture show: But I don't understand how the brillouin zone of the twisted bilayer graphene is derived. Because the reciprocal space is not even derived since the moire sublattice is not clear in the arbitrary angle. So how to derive the first brillion in formal for arbitrary angles for twisted bilayer graphene and what the reasonibility of the above picture with respect to TBG?


Is it right to say diffraction is a geometrical optics phenomena and scattering a wave physical effect? I am considering a finite-length conducting plane and supposing a wave hitting the surface and reflected upon. In my opinion in addition incident wave should excite current sources on the plane resulting in a traveling surface wave. Upon reaching the edge wave they should scatter; if I assume very thin edge, but in many literature its said diffraction of waves is occurring at the edges. What will be correct from a physics point of view? Thanks


When we try to form a real image on a screen by a convex lens, we place the screen at a distance where the image is focused. But if we try to place the screen at a distance less than the distance where the image is focused(refracted rays still fall on the screen) so will the image appear on the screen or will screen be blank? If image does appear how will we calculate its magnification and position?


I am interested to see if anyone can direct me to a text on using limits and integration in the "Error-Accumulating Real Numbers" field structure. This field consists of the real numbers, but the accuracy of a value diminishes as the reported precision increases, so the error associated with a particular value increases as the precision of reporting on that value becomes greater. How would one go about taking limits and performing integration on such a field? Is it possible?


The classic plate experiment highlights how omitted wavelengths of light create an energy differential and pressure. This pressure is dependent on the distance between the plates, including how this distance determines the omitted wavelengths of light. Could the equation be generalized for any case where wavelengths differ and an energy differential exists? E.g., redshifted cosmological objects being acted on by light sources from our local frame of reference?


When we see an object in a spherical mirror, the different parts of the object has different pictures which are also at different locations compared to each other. The lights that go from the tip of the object reflect and intersect at a point. But the lights that go from the middle of the object reflect and intersect at a different point. We can emit lights from each part of the object, and all of them reflect and intersect at different points. So how do we see the picture of an object as a whole thing in a spherical mirror while the different parts of the object have different pictures?


among the elementary function sets: Polynomial Trigonometric function Exponential Function Hyperbolic Function I don't see the development of algebraic identities, and then the detailed construction of various problems of solving equations, proving identities and simplification for any of their inverse algebras except for the exponentials, in the case of logarithms. What makes logarithms more deserving of this treatment than say, the inverse hyperbolics? I read on wikipedia and actually found some obscure, but few inverse hyperbolic algebraic identities, same for trig. But I've never seen an algebra problem on them, especially in standardised tests, whereas everybody is familiar with logarithmic algebra. Why is it that out of the set of elementary functions, logarithmic algebra occupies a special place out of all the elementary inverse algebras?


If visible photons don't interact with the valence electrons in glass due to large band gap, then how do you explain the slower speed of light in glass the way classical em wave explanation does? Does the interaction (non-orbit shifting) take finite time to complete and thus slowing down the photons? Or is it just phase speed that's retarded, not the individual photons? We can test these two theories with for example a laser pulse through glass rod.


if we have two electrons with their spins entangled like this: And if we measure the spin on the left electron, then right electron spin also change like this: So, my question is, do this spin change on the right electron can cause a chain reaction in other particles near to it?. And what forces will be involved in that chain?. I'm curious on why stimulus in the brain are localized when we aren't aware and propagated when we are.


I have been provided with question in Functional analysis which is stated as below: I also have been provided with a solution which is given by the below picture. Now what they have essentially proved is that all the p norms are equivalent to each other by trying to make it bounded by some constants. My question is that how does it prove that convergence with respect to p-norm is equivalent to the convergence of individual components. Note I have posted image as I am new to math stackexchange. I know we are supposed to write latex. Please ignore for this time and provide me with proper argument instaed of downvoting the question


Can we join two sentences with a comma if written in a conservational tone? Is this sentence grammatically correct? We also need to remember that donations need not be strictly only in cash, they can also be in kind such as making aircraft or helicopters booked in the name of some company or individual, being provided to a political party for its use. Source: Is There Life After Electoral Bonds?


I wanted to know if there is a general formula to figure out the amplitude of an image formed if the object performing SHM about the principal axis or perpendicular to it at some position of a simple, Concave, Convex and all lenses (biconcave & convex,plano concave & convex, concavo-convex and convexo-concave). One numerical I have solved only involved axial SHM (about the principal axis) and involves a simple multiplication of the image's magnification and the objects oscillate along the principal axis with some amplitude. Why would we use its magnification, why wouldn't the image just have the same amplitude?


I'm interested in how people just generate a question from scratch,(i'm preparing for indian highschool level competitive exam "iitjee"), i think people don't just start writing random stuff and label that as a question but, there are only four things i can think of they are using geometry some sort of inequalities complex numbers somehow algebra But i don't know how to generate trig questions from it, if anyone could help in giving some examples and thought processes it would be much appreciated. (Seen my teacher creating questions from Jensens inequality, mth power theorem,am-gm-hm-qm inequality,complex number) (It was my first time asking questions please ignore if any mistakes are made) Thank you!


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


I am learning the theory of large deviations. In so many results in the theory and from the very beginning in each book about this subject one starts by introducing a family of probability measures satisfying some properties and defined on some (Polish) space. I do not understand why one needs in some important context and any context of the theory of large deviations to introduce a sequence or family of probability measures. Can somebody explain and provide some example of why one needs many, i.e. a sequence, measures ? Many thanks.


In the ideal quantum information version of metrology, a maximally entangled state is viewed as the best resource for quantum metrology. The optimal phase uncertainty of the NOON state reaches to the Heisenberg limit. Later we have seen that for same average particle number, an entangled coherent state (ECS) outperforms the phase enhancement achieved by NOON states for small number of photons. Can we say that ECS violates the standard Heisenberg limit? If Heisenberg limit is standard then hoe coherent states give better phase measurement?


I can get a bit overwhelmed trying to find which frac or h symbol corresponds to the output of a complex expression. An easy way is to copy paste into lyx and edit there as you can edit the output directly by clicking on the right symbol but that can cause context switches and might lead to using the mouse which might break the flow and slow down the writing process.


Imagine that a person is walking with a constant velocity along the horizontal plane and turns the fan on the filing into a circular motion. Then, after sometime the fan will achieve a constant velocity, Then derive a relation to know the relative velocity of the fan with respect to that person! Say the radius of the fan is r, the acceleration is a, and the constant velocity achieved by the fan is v in time t.


I know partial derivatives should be used to solve this, but I'm wondering is there any to find the plane using the vector method of getting the Normal vector and a point on the plane. In this case, we already have a point, we just need to somehow find the Normal vector. Also, is there any connection between Normal vectors and partial derivatives in this case of finding equations for tangent planes?


In the communication network given below, link failures are independent, and each link has a probability of failure p. (consider the physical situation). A can communicate with B as long as they are connected by at least one path which contains only in-service links. Given that exactly five links have failed, determine the probability that A can still communicate with B. Given that exactly five links have failed, determine the probability that either g or h (but not both) is still operating properly. Given that a, d, and h have failed (and no other information), determine the probability that A can communicate with B.


Title says it all really. As is commonly known, the trace of the density matrix must be one and the trace over the density matrix times an operator is the expectation value of that operator. If you instead add up ALL the entries of the matrix (perhaps times some function related to the row/column indices) does this represent something OR does it equal some numerical value? Does it have some numerical relationship to the trace (strictly greater, or smaller, etc.?)


I would like to know the structure of the sentence and also meaning. Is the vision subject? What in the sentence is what? The vision to do today what is needed for tomorrow. Can I understand.. like this? the vision we do today is what we need for tomorrow. The sentence was part of a speech as follow. Reject pessimism and fatalism. Refuse limits on our spirations. To do that, we need to have the imagination and confidence to do things differently and better. The vision to do today what is needed for tomorrow.


Correct me if i am wrong but all circuits must follow the law of conservation of energy. And the energy is supplied by the action of source to create a potential difference by moving charges against electric field In a battery the energy of chemical reactions that create potential difference is equal to the energy used so the spin of an electric generator must have enough energy to equal it's usage in multiple homes. So all of heat energy that get's used in multiple homes and rotating fans they all get singled out by a spinning conductor in a magnetic field? Ik this might be stupid but to me it seems sorta impossible


Since the only thing a computer can do is modify its machine state, and you can always change from one state into another state (there exists such a program) and so each program is invertible; and if all the programs are deterministic, then associativity also makes sense. Two programs are considered equivalent iff they do the same thing to the machine's state, given any starting state. So do I have the title right or not?


I found one passage that I really cannot understand the grammar structure. The below is the problematic sentence. The crates feature voids, allowing large volumes of water sufficient surface area to seep back into the ground. - Source I think this sentence should be; The crates feature voids with sufficient surface are, allowing large volumes of water to seep back into the ground. I want ask why you can bring the words "sufficient surface area" suddenly between "water" and "to". Could someone explain this grammar structure ?


I was going through the energy/mass equation and it is said that both of the said quantities are interconvertible. That made me think that if we try putting actual values into the equation, the interconversion is actually very large; speed of light itself is a large constant, and the product of its square and mass of a said object would be large. Putting our energy consumption into consideration then, why do we have energy problems in the world? Relative to our world's energy consumption, we should have infinite amount of energy for the world. Why is it that we still struggle with energy problems all over the world?


A high voltage wire can either have an large excess of electrons (net negative charge density), or a large defect of electrons (net positive charge density). The voltage difference between the wire and the human can be positive or negative. Are both cases equally dangerous? Is there a difference between electric shock from a positive wire and from a negative wire? (In one case electrons will rush into my body, in the other electrons will rush out of my body)


Suppose I have an equipotential surface S. Thus the electric field at each point on said surface is direction normal to the surface. Will the magnitude of this electric field be constant for all points on this surface? (This reasoning comes from the feeling that if the electric field strength were to differ, a closed loop path along such field lines may have work done by electric force as non zero) I may be wrong, so this is just a small thought. Thank you.


Was is generally accepted as singular - 'a dog was in the garden', were, plural - 'some dogs were in the garden. So why is 'You was in the garden' so wrong, (you were in the garden) but have to be 'you were in the garden, singular and plural? It seems to be restricted to only the noun 'you', which could be singular or plural - and in a lot of cases, that fact remains hidden.


In Quantum Mechanics conservation laws are fundamental, I was thinking about spin altering models of interaction such as the Ising Model and realized that it isn't at all clear how angular momentum conservation occurs in such a situation. If there is spin flipping occurring where does the contrary compensating angular momentum go as to have global angular momentum conservation? The interaction fields absorb this angular momentum?


During JJ thomson experiment and similiar other experiments,they found that cathode rays were deflecting from its direction under magnetic fields and electric field,also the gold leaf attached to co-axial cylinders led to conclusion that the cathode rays are negatively charged,but later,By Putting a paddle wheel or fan in path of cathode,the wheel turned and moved,the fan also moved,This led them to conclusion that they must have mass,but is this the only criteria required for an unknown object to have mass,that they can perform mechanical work?The scientists at that time concluded that they have mass,and then went on to calcultate charge to mass ratio of it,assuming rays has mass?Can't any other particle now known do work as well as have no mass?


Are there any experiments done to verify the absence of forces caused by complex structural organisations in systems? Afaik, experiments in QM and Standard model QFT talk about the validity of the interactions in individual particles that are not in any complex sturctures. Experiments in Condensed matter physics involve configurations with some structure. In these cases, there is no requirement of downward causation. Are there any experiments in more complex organizations which rule out downward causation? Is it even practically possible at our current experimental strength?


When the size of the observable universe was small as a proton what was the physical content of it? Was there a limit of particles in such a tiny volume with enormous high density and energy? Can we find more than one proton inside such a volume, can we assume that because an electron, a quark, or a photon are point particles there was no maximum limit for the number of say electrons instide a volume the size of a proton?


For example does a virtual electron have the same characteristic intrinsic values like mass, charge, magnetic moment etc. as a normal stable electron? Or can these range wildly and not having specific values for the case of the virtual particles and if yes don't you think that the term for example "virtual electron" is kinda of misleading? How can for example a virtual particle ten times the mass of its normal stable counterpart be the same particle? Wouldn't it be a less specific but nevertheless more correct description of these particles be the term virtual fermions in general or virtual bosons or virtual pairs without labeling them with a specific normal particle's name of the Standard Model of particles?


While calculating electric flux through an uncharged ring kept near a charge, we tend to draw a spherical Gaussian surface that covers the ring by edges but while using the gauss law, we tend to take the entire circular region of ring as area bounded by it(just like we do for circular disk). However, the ring has electric field passing through it only in the ridges.So why are we taking the entire circular region in case of ring where in the middle there is actually no area?


I decided to use the Maple software to help me solve dynamic optimization problems, and I found this final solution for T. (example in the picture). example What does the LambertW mean for the solution T? Can I get rid of this expression to express T in simple terms? Does theLambertW (including the expression inside it) have a solution or an equivalent expression? If this is the final form, I assume I can no longer proceed with symbolic/analytical solution, and I must move to computation?


i just started my study in organic semiconductor. I realized to increase conductivity, polarons are formed in the polymer backbone. From what i read due to localised energy state level by polaron that can exist in the band gap, the band gap is narrowed. My question is if why is can polaron exist in band gap while electron can't though they are both almost identical. Also, do the formation polaron exist as somewhat of a 'bridge' to narrow the gap between conduction band and valence band? Helps or guides are really appreciated.


The soundness of FOL is proved in meta-language(natural language) by proving every deduce rule is correct, so we feel peaceful using those rules to deduce. But the process of proving every deduce rule is correct also uses deduce rules in natural language. For example, proving the correctness of PC(Proof by Case) also uses PC in natural language, so we assume the PC rule exists and assume PC is correct in natural language. Do we need to construct another meta-language for the natural language to prove those assumptions like we are doing for FOL? Otherwise, how can we feel peaceful using those rules when deducing in FOL? Furthermore, is it possible to construct such a meta-language for an unrestricted language such as the natural language?


At one time or another, you've probably inquired about something (perhaps online) and been met with the curt or critical response. It's meant to showcase their cleverness. It's more of a concealed boast than it is a help. Is there a word or phrase which calls out is the disingenuousness of the help, since it's not that at all? This word or phrase characterizes the response and not the person or the behavior.


recently I was solving questions on uncertainty principle but never came across questions involving system of particles like combination of electron and alpha particle. I wanted to understand how to deal system of particles while solving uncertainty principle questions. My initial thought was to calculate total uncertainty in momentum of the system and then using the conservation of momentum, divide this uncertainty in momentum by the respective masses of electron and alpha particle to obtain their respective uncertainty in velocity. Is this approach right?


Hi there my question is pretty much in the title. I have to create tables which are longer than one page. The caption needs to be above the table, it would also be a great extra option if i could rotate the text inside the cell and i would need an automatically adjustable cell width just like tabularX does. Do you have any recommendations? Thank you


I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution probability for the possible values of the observable, which is better than only expectation values. So why do we claim that 'all we can get is expectation values'? Also, why cannot we model these uncertainties in the a priori knowledge of a measurement using random variables and probability language? Is it really necessary to go through this whole formalism?


How the word livid came (according to Merriam-Webster) to have three different meanings (in addition to the default, 'furious', one)? As I see, it could mean blue-and-black pallid reddish. I mean, I know that all meanings are accepted, but is that so? If I say to someone My car is livid. won't they have any predisposition to favour one of the meanings? At least based on your experience, which option is the first you think of?


I know that the search for Higgs would be quite pointless if there was no estimation of its mass. Namely the perturbative violation of unitatity, gave us an upper bound on its mass.Unitarity Constraints on Heavy Higgs Bosons I wonder if there are enough parameters in the Standard Model of particle physics, such that it introduces sharp bounds on SUSY parameters that cannot escape experiments? Is there in general any model independent prediction made by SUSY or it can always be rescued by means of introducing new fields and couplings phenomenologically?


He brought some food to eat on the road. He found some beer to drink in the fridge. Is it only reality and sanity that keep us from taking the beer example to mean he would be squashed in the fridge like a contortionist, sipping a beer? Or do the verbs license, or if that is too strong, erect interpretive guide-rails for, adjunct phrases? Is meaning accruing as we parse, eliminating certain possibilities and bringing others to the fore? What is the real-time elimination of improbable meanings called in the linguistic literature?


People say my idols are Messi and Ronaldo(no hate) but I dont know why I am attracted to Physics and Math.It always amazes me, this is just a dumb question which i suppose is gonna be closed by midnight today but can someone teach me physics? I would love to and also do questions he/she gives me, it will be like a free trial for me as a student and you as a teacher. Once again, even though this is closed, just know that I love you guys and you are what I aspire to be one day.


Latex IEEE format color problem As you can see the text after the figure until the end of the paper became light blue. But, it supposed to be black. I don't know what happened! I utilized both 'color' and 'xcolor' package in my paper. When I remove the highlighted text inside the paper, the problem is solved. But, I think it is the figure problem in ieee latex format that cause the change of the text after it


In accelerated pure rolling ,as we know velocity of the bottom most point is zero with respect to ground but what makes it to have zero tangential acceleration. If tangential acceleration is to be zero at that point ,it must have net force zero in horizontal direction.The ground applies friction on bottom most point, which in turn applies some internal force on oher points in the body(due to rigidity of body) causing the whole body to get angular acceleration ,the other points applies the same reaction force on the bottom most point .We don't know the magnitude of internal forces. So on what basis we say that these forces cancel each other to make the tangential acceleration or horizontal acceleration of the point zero?


I want to write the i and j as one "ij", as can be seen in the Dutch language, in my LaTeX document, but can't figure out how to do it, even with ChatGPT! If someone knows more, please hit me up! It could be the case that this is just not possible as it is not that frequently used, especially not when actually typing it. If so, please let me know too. Thank you.


I'm using xindy to create indeces. However, the default sort order is not sensible for uppercase and lowercase. Is there a way to create a .xdy file so that the uppercases are sorted in front of lowercases. Here is an example: A Abel....... Alex....... aboutism... account.... axis....... B Bible...... basics..... bigger..... I think the issue is, by default, uppercase letters are mapped to lowercase letters, thus cannot be distinguished former and sorted according to that. I wonder if anyone can help me create a .xdy that sorts alphabet case-sensitively.


I read this thread of articles by Casher(quite marginal in terms of citation) where they show in certain realistic models SUSY is broken by non-perturbative effects. Explicit breaking of supersymmetry by non-perturbative effects The SUSY currents turn out anomalous. Now I want to add a twist: Does the anomaly survive even by addition of extra dimensions? If so, is the number of such dimensions the same as critical superstring theory? Or Super gravity?


Construct a triangle ABC when angle A, length of angle bisector from A and circumradius are given. Since angle A and circumradius are given, we can find out the length of BC. I can elaborate on the same further if you're interested... This seems like a simple problem but I can't get it. Thank you! In a circle with a radius equal to circumradius, an angle equal to angle A constructed from any point will intersect the circle at two points, the distance between which will remain constant and equal, in fact, to side BC. This is how we can get length of side BC given angle opposite it and the circumradius.


Hopefully my question is not out of order in this site. I am trying to weigh an object that is too wide/long for my weight scale. If just put it on top of it it tips over. So my solution is to place my hand on the 'short side' to prevent it from tipping over. Assuming I am not pushing (just holding my hand as an 'stopper'), does that change the weight the weight scale measures? why/why not?. I guess if I push the measured weight would increase (not sure either). details: I am trying to weigh a planter to know if it is safe to put in the balcony.


The statement of class existence theorem includes "F be a formula that quantifies only over sets" then there exists a class A such that it contains only sets and a set x is in A iff F(x) is true. I am curious to see an example which breakz this requirement and have a quantifier over classes, and what kind of paradox it causes. I mean the requirement for the class A to contain only sets pretty much covers Russell's paradox of not belonging to itself. But why for quantifiers should be over sets only? What formula F will cause problems?


If the circulation is negative and flux is clearly not zero then will the flux also be negative? If a curve C and its vector field are going in opposite directions (meaning C is going clockwise and the vector field is going counterclockwise), then circulation will be negative. If the vector field is pointing outwards from the curve meaning it is leaving the curve then will the flux remain positive?


If I penetrate water's surface with needle (using hand) then Cohesive forces> Adhesive forces and water molecules climb up the needle (exactly like capillary action) and needle behaves hydrophilically and when I make it rest like mosquito's legs on water, it floats (mosquitos actually float on water due to surface tension and hydrophobic nature of legs), the needle behaves hydrophobically and Cohesive forces> Adhesive forces in this case. So, my questions is, Is hydrophobic and hydrophilic nature orientation and position dependent (like whether needle is in bulk after penetrating "skin" of water or at surface like mosquito's leg)?


In PWT, the wave function depends on the positions of all the particles. Therefore the velocity of a given particle depends of the positions of the other, it's why the theory is non local. In the model why there is a single wave for all the particle and not a wave for each particle? So that the velocity of a given particle does not depend on the other.


I want to know like for continuity of a function at a given point we can check the limit of the function at that point and the value of the function at that point but how to verify if a function is uniformly continuous or not over a given interval and all kind of interval that is for open , closed and semi open or closed interval


This figure is taken from Wolfram MathWorld. The site classified the third region as not simply connected, and I get it, but it isn't also multiply connected, since multiply connected means that I can connect any two points in the region with a curve that lies entirely in the region. However, it is clear that I cant connect one point in the upper subregion with another one in the down subregion with a curve that lies totally in the region, correct? Note A multiply connected region is a connected region but not simply.


the decision partition problem is Np-complete.Now I would like to proof that if a polynomial Algorithm exists for the decision Problem than another polynomial algorithm would exist too, that would give two sets A and B that fulfill the decision Problem.Clearly this problem is Np hard .I would like a hint or something to help me to approach this problem because I am lost.How can I use the decision partition problem to output the sets A and B


Air can hold water in proportion to partial pressure of water vapor. This is affected by temperature. But is the water capacity of air also affected by ambient pressure? I did find some answers that water holding capacity of air decreases with increasing pressure. Quora link, UCAR link But I was unable to find any equations that would tell me exactly how much it changes. In this case we talk only about change in pressure. So temperature and volume would stay the same. I will be glad for any sources that can answer me this relationship.


I have a man-in-the-street question that was probably "predetermined". If everything around us is co-interacting particles whose source is some infinite small point that started their expansion into nothing due to the Big Bang, how come those particles have any interactions? They should become further with every second, just as grenade fragments that can only meet each other after the explosion only if there are some external preexisting obstacles on their way that cause their bounce.


Wikipedia asserts that The rays represent luminous intensity, which varies according to Lambert's cosine law for an ideal diffuse reflector. Describing this figure: I understand this is a perceptual phenomenon, and we are observing the light coming from an object that is diffusely - and isotropically - reflecting light. and that the Lambert Cosine has to do with how stretching a circle on one axis increase its area. However, I do not understand how or why this stretch happens, since (in my mental representation) we are always looking at small cylinders of light that come straight (normal) to the eye surface. Can you explain, or maybe include a simple draw of how you image this?


I understand that our main supporting evidence for dark matter is the anomalous speed of objects orbiting around the edges of distant galaxies. Is there a reason why dark matter solves this problem better than say, the strength of gravity simply being stronger in the region? My idea is that maybe these galaxies don't seem to be large scale attractors, but it also seems to me that they could be attracted themselves to areas of space where gravity is EVEN stronger.


With Compton scattering the total momentum and the total energy of the photon electron system is conserved, so it has to be ELASTIC Collision/Scattering. But an argument is that just because the kinetic energy of the incoming photon is different than the outgoing photon, it is INELASTIC Collision/Scattering. However, I thought we had to look at the system, which is the photon and electron interaction; not just the scattered photon itself. So, what is the real issue here?


If one plate of an isolated charged parallel plate capacitor is earthed, then that plate must have a potential zero after being earthed as that is what earthing an isolated conductor does, but potential on each plate is only due to the charges on the other plate. Since the other plate(the one which is not earthed) is isolated and non-neutral, potential due to it on the earthed plate should not change. As surface charge density on the unearthed plate cannot be zero... how on earth will I manage to get the potential of the earthed plate to be zero without changing the charge on the other plate?


In the dimensional analysis, relationship of dimensionless parameter is? Above is the previous question I asked. I kinda understand that relationship of dimensionless group can be more complex. However, I was taught using the above method to determine dimensionless groups. Then how should I interpret the last equation? It seems to me that the groups are related by multiplication. Is the method wrong or does the above equation doesn't actually mean equity but shows the fact that they are somewhat related?


So I've heard that all finite abelian groups are isomorphic to direct sums of the integers or of integers modulo a power of a prime, then you get that all extensions of reals are basically the real numbers or the p-adic number. Is there any such theorem for the rationals? Any other way of creating numbers that is not some vector space or an algebra over the reals? The way the complex numbers are just two dimensional real numbers and the grassman algebra is just an algebra of the complex numbers. I gues what I am saying is, is there any other way to do multiplication that is really new? Not having a copy of the natural numbers embedded inside?


Zenithal perspective projections are generated from a point P and carried through the sphere to the plane of projection as illustrated in the figure below. By a simple geometric relationship, we can show that the radius satisfies the following: with . The inverse equation is given by: where I could reproduce the first equation but not the second one. I think the derivation is purely based on algebraic operation of the first one but I have no idea how. Does anyone have any idea how to derive the second equation?


Okay so by the definition of a wave i.e The osciallatory disturbance in a medium which propogates energy is called as wave..the stationary wave contradicts both the crieteria as it doesnt propogate nor does it transmit any energy. Now one may say that a stationary wave is made by two progressive waves with same phase, frequency and amplitude superimposing in opposite direction..and we know that compsition of two waves is also a new wave..by that conclusion the stationary wave must be a wave..but it contradicts the definition of a wave So what do we call the Stationary Wave as? this was asked to me by a physics proffessor and i am pondering since. wave


In my physics high school lecture my teacher taught the concept of electromagnetic induction under diamagnetic materials (though not completely disregarded it in ferromagnetic substance but as a characteristic property of diamagnetic substance) but the typical high school numericals that are in my textbook consist of conducting ring (as resistance will be low so due to induced emf an induced current is easy to imagine). So is electromagnetic induction possible in ferromagnetic ,antiferromagnetic substances etc (ie it is a universal phenomenon, independent of magnetic properties of material) or is it dominant (or observable) only in diamagnetic substances (ie depending on the magnetic properties of material)??


We know that volume is cubicly proportional to radius of a sphere. But if the radius is become half due to relativistic Length contraction, it's being reduced from only one dimension, not three. And the object is not a sphere any more . Does it mean that the volume in that case is directly proportional to radius? And is density inversely proportional to the square of radius? (Since the mass is increasing by same multiple as the radius decreasing?


Usually, when we study algebraic topology, we learn a lot of theory with just a few examples, like compact surfaces (orientable or not), wedge product of many circles, and a combination of those. Are these any slightly more complicated but special examples which shows important facts about the truth/falsity of some interesting statements? I find that I need to know more examples, but I do not know where to start. Some reference would be helpful. To be more focused, I am mostly interested in just singular homology and spaces with "low dimensions". To give an example of something which is more specific, for instance, examples of spaces with homology different from the examples above would be interesting.


Arrow orbit around point C like graph show. Is motion of arrow, rotation or curvelinear translation according to physics definition? What is definition and types of translation and rotation? I find this: "When the paths of motion for any two points on the body are parallel lines, the motion is called rectilinear translation. If the paths of motion are along curved lines which are equidistant, the motion is called curvilinear translation"


Can anyone suggest a reasonably generalisable way to generate these marginal drop caps? The key features are that the drop cap may be more than one glyph long its width is scaled to fill the margin (minus a bit of white space for legibility) its height is scaled to a user-specified whole number of lines (nb. the first example spans five lines and the second four).


Our pre calculus teacher told us to start our mathematical investigation and he gave us three topics to explore to formulate a problem, a title and a our own formula that is novel or cannot be found in the google. Our group decided to focus on the third topic that was given which is algebra. So I would like to ask for help if you could give me ideas on what to research and come up with a problem/situation involving algebra. Thankyou


I made a guess two years ago. I have a strong feeling that there is a proof using the fixed point theorem with geometric visualization, but I couldn't do the proof. If you have a simple closed convex curve, thr line Perpendicular to the tangent on the curve at both ends must be present If this feature is already known, please point to a reference that mentions it If you can prove it would be appreciated, thanks


Bases for vector spaces are non-unique. Also, new bases can be generated from other bases very easily and formulaically. Is there some "prototype" basis, which we could find for every vector space, that defines a specific relationship between the elements in and across the different vectors for every possible basis for the vector space? In the same vein, how generally can we specify what a basis looks like for some vector space?


My sense is that it never means an actual physical defect as in, "The quarterback's knees were shot -- he could still throw, but he knew that to management he was damaged goods." Or can it be used in the case of concrete damage to a person's body as the above example? It seems like for a simple medical issue, the term is too nebulous and indeed would be used when the extent or classification of the problem is not so clearcut, like some psychiatric problem that most people do not fully understand.


I cannot simply know where to use "port" and "interface", because these two words translate into one same word in my native language. So, I wanna figure out the difference between "port" and "interface", and when and where to use which. In my understanding (please correct me if I were wrong), the physical things, such as the holes on the side of laptop into which you plug the power cable are called "ports", whereas the visual holes inside the laptop, such as the signals transmission connection are called "interface"?


I'm Finding it hard to visualize how higher pressure makes the boiling point higher. I understand how pressure increases then temperature increases such that say air molecules compressed gives it energy and then the molecules move fast and average kinetic energy increases hence temperature increases. But When we can say pressure increasing the bonds between molecules can easily be broken with the external force , but it somehow takes more temperature to disassociate bonds such that it transfers into a gas?


Let assume a metal tube open on one side having alpha emitter material on the other blocked side. Since alpha particles are blocked by the metal they will be emitted only through the open side and make thrust by the momentum of the alpha particles. Very small one, but continually accelerate the satellite. Partially depends on other question - how alpha particles are emitted from in depth of a chunk of material, aren't they blocked by the outer layer of this chunk?


It seems like 'my sister and her' are both subjects so it should be 'my sister and she'... And it would be if they worked on something specific together (the obvious object). Eg: My sister and she work on this project. But the "together" at the end changes everything right? Unbundling the sentence it is clear that it is actually saying "my sister works with her", making 'her' the object. In this case should it be my sister and her work together? Does the together really change the object?


I am given: Five points on the ellipse, The sharing center of the ellipse and the circle, And the circle. One of those five points is one of the intersections of a circle and an ellipse. Can we construct the three intersections of an ellipse and a circle that is not given? Blue ones are given, and greens are the points I want to find.


For a conductor in an external field, I would like to know whether the electron clouds of each atom, just shift slightly (resulting in positive charges just on one edge, and negative charges just on the other with all internal area remaining neutral). Or, whether the electrons fully dissociate, leaving positive ions throughout the conductor volume but with all electrons on one side. If this second case, then how would the electric field work out as zero inside?


Question: When we only listen to the sound of that machine (TV), not watching its screen, which is appropriate to say "listen to the TV" or "listen to TV"? Background: When we watch that machine, we say "watch TV"; and when we put it work, we say "turn on the TV." I think these usage indicate that we use "the" when the object is material thing not function. But we say "listen to the radio" or "listen to the music", so I wonder about the question stated above.


I had the following problem with the index: The alphabet order of the words in English: I have the order of capital letters come first then the order of small letters come next. I need the order to come according to the letters regardless of being capital or small. For example: Abed Dep Ced amid bned I need those words to be like: Abed amid bned Dep Ced The next issue is: I have one gap in the index as shown in the below picture


I only recently thought about this, and I can't come to any conclusion. An explanation for ferromagnets is perhaps explainable, and my teacher said Quantum Mechanics complicates things since the magnetic behavior is distorted, given for ferromagnets their origin is the spin of the electrons. But what about materials that are magnets but are not ferromagnets, for whom the origin of magnetism is not spin? Any of my reasonings is too vague for any explanation. If anyone can lead me to a source where I can read about this, I would be very grateful.


In my notes the axiom of extensionality is that 'two equal sets contain the same elements', this language suggests to me that there are two different sets that happen to be equal, which suggests there is an infinite number of sets with the same elements. I see this definition given many places and it causes me some confusion. This seems to defeat the point of equality, which usually defines the 'same value', the above seems incorrect then, is it just a choice of language and clearly there exists only one set with a certain group of elements, or can we have two seperate sets with the same elements?


From school we know examples of energy conversions: from electromagnetic to electric, from electric to heat, from heat to electromagnetic, etc. However, obviously this almost has nothing to do with conversion, because as heat, as electricity, as friction, and so on are electromagnetic field energy. But what if there is some electrically charged and massive particle moving at constant velocity and being accelerated by gravitational field, and not electrical. Will it emit (scatter) gravitational wave (quants) instead of electromagnetic, or both? Also in opposite situation, same particle, accelerated by em field radiates photon, only because of electromagnetic interaction, or it emits photon (and gravitational waves) independently on the type of interaction?


I recently learned that we always break components of force along and perp to direction of net acceleration (for simplification) So in problems involving circular motion.... We resolve forces along centripetal acc So in problems involving vertical circular motion...we break mg along centrifugal force(ofc working from non inertial frame) But in problems involving banking of road w friction....we break centrifugal force along and perp to mg ...Why so?? We should have broken Normal and friction along centrifugal force


Huygens principle. can we accordingly define refraction to be diffraction from an infinitesimal length slit? According to Huygens principle, sticking to classical physics terms. as long as slit length is at most a wavelength, spherical form of waves is maintained. If we look at propagation inside a homogeneous medium the shape of waveforms is maintained and we can claim "mono-refraction". So is diffraction actually a mono-refraction through an infinitesimal length of slit? As a thought experiment...


In PowerPoint, there are often nice three key point diagrams like (source: https://www.slideteam.net/performance-mapping-ppt-powerpoint-presentation-portfolio-graphics-pictures-cpb.html) or (source: https://www.slidegeeks.com/business/product/three-levels-relationship-marketing-examples-ppt-powerpoint-presentation-ideas-display) My question is, how do I best generate such diagrams in LaTeX for usage in beamer? I assume this will likely involve TikZ? Ideally, some guidance, if possible even a MWE could be given to create a similar nice diagram. That way, also LaTeX users can make use of such styles. One central node on the left, like in the first example Three (or even better, a flexible amount) of child nodes arranged around the central node (to the right of it) Text entries next to child nodes like in the second example Color style like in the second example


From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we choose some point, around it in all directions, properties are the same throughout the end of the material from that point, but image taken from here, still says material is isotropic.


I know about the conditional sentences that go as following: "If I were he, I would have forgotten the whole lesson." In the sentence above, "he" is preferable to "him," but can it also be preferred in the following case? Whom can I trust, if not ___. a) he b) him I pardon, if this is related to conditional sentences. Quora has similar question but with very short answers, as in: Edit: I don't think my example sentence is concerned with relative clause, rather the first part of the sentence looks independent: "Whom can I trust, if not he" contains comma between them. And how does following sentence is related to the above sentence: If I can't rebuke him, whom should I rebuke. (Does 'him' makes sense here?)


the xelatex compile output will automatic write some output in content folder, when compile in the root of project, there contains a content folder and it works fine. Now I tweak my command and add the -output-directory parameter like this: xelatex -output-directory=/Users/xiaoqiangjiang/Downloads/cquthesis/out/ main.tex the out folder did not contains the sub-folder content make the compile failed. the error looks like: ! I can't write on file `content/introduction.aux'. Is it possible to make the xelatex compile command auto create the content folder in the output new out folder? because all the compile process was automatcially running by robot. I can not created the content folder by hand one by one.


Is this grammatically defective? The rides were fast and long, as well as exciting, despite my apathy. Context: I often find myself writing sentences that I don't want to reorder but may contain an error, and am ignorant of grammar, if not absolutely naive; I have confused chat-gpt, asking it this. Background: I understand, I think, that it would be: You can either do "The mayor, as well as his brothers, is going to prison" or "The mayor as well as his brothers are going to prison." but am reluctant to admit defeat yet.


I am a student in robotic assocciation and I designed working spectrometer for UV-Vis emission spectrum. The issue is evoking emission spectrum. The spectrometer is designed to be working on board of martian rover. Can I evoke the emission by shining the rock samples with UV lamp or X-ray lamp? We can't use laser beams or burn the sample due to onboard safety. Are there any other methods of obtaining one?


I had a sentence like this in my manuscript: [describing some limitation] .... Some studies worked it around by combining the results of two models ... in the sense that those studies made a workaround for the limitation. The native speaker changed the bold term to "worked around it", but I am almost sure I know the original form (from the IT world, where workarounds are a very common topic :)), and also can find it on the Internet. But I can find his version too, I just like the original one better. Are both acceptable? The result is supposed to be in US English, if it makes a difference. (Note that this paper is not in the IT area, but the statistical modelling methods in ecology).


Suppose a straight current carring wire of finite length if kept in a external magnetic field (perpendicular to its length say dot). I know initially it would experience a magnetic force of magnitude ILB due to drift velocity of charges inside wire but now the wire would gain velocity , but if I use lorentz law to find magnetic force again what way the wire be doing motion.


It is often recommended to the particular symbol from MnSymbol that you require instead of importing the package entirely such as the answer by @egreg. What is the general process of doing this? What if I need several symbols? Is there a difference, say, if I need an arrow vs. delimiters? Not really a question, just a complaint: seems crazy to me that I need to do this just to get a few symbols from a package that offers them.


Wikipedia claims for the proof of Arrow's Impossibility Theorem that when Every voter in segment one ranks B above C and C above A. Pivotal voter ranks B above A and A above C. Every voter in segment two ranks A above B and B above C. (B and C may switch for segments one and two but not pivot) by IIA the societal outcome must rank A above C, as in the previous case Why is this true?


In the light clocks, time ticks via the motion of light and since speed of light is constant therefore when the clock is in motion ,the photon has to cover a greater distance by the perspective of an object at rest . So in the perspective of object in rest time ticks at slow rate but in other clocks such as mechanical clocks .time ticks via the motion of different objects not light. and the speed of the objects are not constant.so from the perspective of an object at rest time ticks at the same rate. How can be this possible as time dilation affects all clocks?


So this was a test question, I answered that both cars have the same acceleration. Since the graphs for A and B both are straight lines, therefore, the acceleration of both must be zero. But the answer given to us was that both are moving with same velocity. These graphs are not always to scale, so I thought that the d option would be more appropriate than c. The beginning of the test says to mark the most appropriate answer.


In the solution to this question, they have first taken the component of downwards-acting gravity(g) along the incline which is the sin component then again they have taken the component of the gsin along the x-axis and y-axis. Now my question is how are we supposed to take the component of a component and why not just g in the downwards direction used for calculation of centre of mass?


Say we have a plate full of soup, why to cool it down we move the spoon around in the plate? Is it to facilitate the thermal interchange between the air and the soup? Also why is the edge of the plate always cooler than the center of the plate? It may be because of how close it is to the plate so it exchanges heat with the plate?


are modus ponens and tollens axioms if not how can they be derived or proved? if I am good at math then I am good at logic, I am good at math, therofe I am good at logic this seems evident but is there any proof for them? looking at the truth table for implication we see p->q is true when P is true and Q is true


I'm trying to name categories on my online shop, I have a category for whimsical items, kids, etc. I'm trying to name a category for items that have actual day to day functionalities. For example, a suction cup used to fix car dents. Thus: Manual lint remover Manual fruit juicers Car back seat bag with pockets Scratch removal device for cars... These products, _____s, are mainly cool looking items, all with special functionalities.


This question about how to choose a singular or plural verb for sentences with number as the subject has been asked a few times here. Nonetheless, will ask again for the following sentence: The number of each type of fruit (apples, oranges, and bananas) is chosen based on the published price. This answer The number of students is larger and this answer A number of questions have been asked describe that the definite article "the" indicates that a single number is chosen. In this case, three numbers are being chosen: one number for each type of fruit.


For college, we are supposed to hand in uncompiled .tex files for the teacher to make the .pdf themselves. However, college computers have very few packages installed ; but I have heard somewhere that one can include the package along with the .tex source. I cannot find a guide on how to do this, can someone explain how or provide a link for me ? I am not asking how to normally use packages, rather how to include them for compilation on a system where installing packages directly is not possible.


Good day, I am a lay person in this field So i am very sorry if my question Is dumb. I am wondering whether the Hypothesis H formulated by Schreiber and Sati stating that C-field is charge quantized in J-twisted Cohomotopy theory doesnt assume already existing spacetime manifold And a C-field which would together constitute the ontology of this theory? Doesnt this go against ideas of Nima Hamed And others who would like to create a deeper mathematical structure from which both spacetime And Quantum fields emerge?


Premise: Verb 'want' is normally (?) stative We use adverbs when we have an action verb and adjectives when the verb is stative In sentence "I want it bad(ly)" we would use the adverb 'badly' and not adjective 'bad' --> "I want it badly" (correct) From that we can infer that the verb 'want' is then an action one. But is this really true? And what action does it describe here? Furthermore, where/when can we use 'want' as a stative verb then?


By Definition Electric field vectors point in the same direction as the electric force that a (hypothetical) positive test charge would experience, if placed in the field. Electric Field Lines are generated by connecting all of electric field vectors together, forming continuous lines and curves. What does electric field line actually represent My search tells me it represents the path any charge would take but then force vector direction is tangent? but it is not a path taken? Fact ref what is paradox here. How is magnitude of the field, indicated by the field line density? ref seems that the this representation is the cause of my lack of understanding? What am i missing here?


I am currently doing some writing, and constantly try to create smooth transition and ease of readability and linkage between sentences. This sentence feels like it kind of halts the reader a bit. Albeit although assemblers are not commonly discussed as much as the two language processors, they are, however, equally important in the pipeline. Replace 'are not commonly discussed as much as' with something that virtually means the exact same but, might be a single word.


I have a bulleted list which describes how to write an effective bulleted list, and is itself an example of all the tips in the list. Terms in this area that I have found so far are: autological / homological self-referential recursive Is one of these best, or is there another term (single word or phrase) that I can use to describe this list? e.g. The ____ list above is...


I know this question has been asked before, but I can't find an old reference on this subject, so feel free to point to my duplicate post if you have a link to an older post. Working with LaTeX, PDF and git is a real headache because at each compilation, the binary PDF file changes but not the visual PDF if no changes are made inside the associated LaTeX file. How do you produce the same PDF after compiling the same LaTeX file several times? Is this type of solution bad? (I have a worse solution for hiding the PDF in git, but I'd like to omit it).


I just got a higher algebra book written by Barnard for a couple bucks. But as I was scrolling through, I found two things that did not make sense. Can anybody tell me the meaning of them (the pic is given below) ? What is that 'L' shaped symbol under the numbers and variables and why is there a limit with "nothing approaching nothing" ?


Knowing the strength of concrete you can get the mass of an object put on a concrete block is able to withstand on given area. As for a falling object, kinetic energy itself doesn't translate to force, so the force decelerating the object while collision occurs is somehow defined by material properties of the block (for simplicity, the object does not deform). Is it possible to calculate fall height of the object at which the concrete block will not undergo permanent deformation? And what the coefficient of restitution would be?