darklight03/StackMIAsub huggingface dataset:
When we work with rational numbers, our continued fraction will have a finite number of elements. Are there ways to estimate the number of elements of a continued fraction when expanding a rational number? For example, in the following form: "For the chosen rational number N, continued fraction will contain at least/at most/strictly M elements" The obvious way is to implement the continued fraction decomposition algorithm and simply count the number of elements each time the loop passes. But this method can be quite time-consuming if there are a large number of elements of the continued fraction. I tried to find the answer and the only thing I found was this thread: Nth number of continued fraction But it ultimately came down to what I said above.
Like how Taylor Swift fans say that she needs to take private jets because fans would make her taking public transport untenable. So it's the fans themselves that are the reason for her behaviour, which they are making excuses for. Is there a term for such people, or for what they are doing? An example of how it could be used: Fans are (creating the exceptional need for an excuse they are making) Taylor Swift's use of private jets' or something like that.
I need to write an equation to determine how rotating a digital balls path with the ball as the center of rotation effects the amount it moves on the x&y axis each frame. I made a table of points on the equation to help me write it, but I'm unable to convert the equation into points. I linked an image of the table here. Does anyone know the answer? I think it's a helix. It's fine if you need to switch which axis each column corresponds to in the equation, as long as you mention which ones you switched. Click here to see the table
I'm looking for an interesting application of Sequences and Series (theory from mathematical analysis) in the field of Operational Research, in particular involving combinatorics or linear optimization problems. I have tried only chat GPT for now and all I could get is an application of Dynamic programming to solve the knapsack problem where series and sequences are defined for recurrence. I was wondering if there is another one or maybe an interesting application not from the Operation Research fields. Thanks in advance.
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!