darklight03/StackMIAsub huggingface dataset:
Please see here to see question & my solution Here are question & solutions I tried. How should one approach problems where both s-shifting and t-shifting are required? Is there a specific method or sequence that is recommended? I have attempted to solve these problems by applying the first shifting theorem (s-shifting) followed by the second shifting theorem (t-shifting). However, this method seems to lead to incorrect results. Answer said that t-shifting first, s-shifting later. Could you explain why this approach fails? What is the significance of the sequence in which the first and second shifting theorems are applied? When both shifting theorems are necessary, which should be applied first, and how does the order affect the final result? Thank you for your time and assistance.
I have read about wave propagation and dipole antennas here. I do not understand how a single electromagnetic wave (i.e. the electric field in particular - I can come up with the magnetic field later) propagates when its electric field of a dipole antenna is shown below. For example, the iconic picture of an electric field of an electromagnetic wave looks like the figure in the bottom left corner in red below. How does it look in the bottom right diagram? I tried to plot it below again in red, but it doesn't make sense to me. For example, the amplitude of the wave would get bigger. So, I would like to know how a single electromagnetic wave propagates in this field.
In the following sentence is "painted" being used transitively or intransitively? The sunset painted the sky with a tapestry of fiery colors. I asked ChatGPT about this and it gives reasons for both... For intransitive that it's being used metaphorically or poetically; the focus is on the action of sunset creating a visual effect, not the application of paint. When I reminded it that "the sky" certainly seemed to be the direct object it agreed at first that it was actually transitive. Yet when asked to confirm, it stated it was intransitive. Then it finally stated it's a matter of interpretation. Personally, I think it's transitive. Am I right?
I want to make a program that will solve polynomials, but I don't want to just look at another program that already works as I think that would defeat the purpose of the exercise. And that's why I'm asking the question here instead of on Stack Overflow. I think it would be very difficult to implement Alpha-Beta Theory/Veita's Formula, and guessing using Factoring doesn't seem like a neat solution to me, so I'm wondering if there is in fact an easier implementation. I would also like this to be scalable for higher degree polynomials if possible. Thanks.
I'm reading the famous paper by Haah: Local stabilizer codes in three dimensions without string logical operators. In the last sentence of the introduction, he wrote: A logical operator is a Pauli operator possibly with infinite support that commutes with every generator. Since each generator is local, the commutation relation between the generator and an arbitrary Pauli operator is well-defined. Why the locality guarantees the commutation relation is well-defined? Are there examples where removing the locality condition yields a not well-defined commutation relation between the logical operators and the generators of the Hamiltonian?
I'm studying nonlinear control systems and I have some questions about the nature of this optimal control given by PMP: Traditionally, control methods based on Pontryagin's Minimum Principle (PMP) and Euler's method (or Runge Kutta) have been extensively used to address nonlinear system control problems. Is there a potential to get trapped in local minima resulting in suboptimal control outcomes? If there is one, why do we call it "optimal"?
Solving Fresnel integral for vortex beam diffraction is necessary and difficult. Without the necessary integral formula, this isn't easy to derive. Therefore, I need some means to calculate it numerically quickly. I have learned some methods, such as angular spectrum method, fast Fourier algorithm. But I still can't understand its principle and implement it through matlab programs. I think I may need some correct codes or related books to learn, and I also hope to get a good explanation so that I can understand them better.
Just a quick informal Question. I was wondering if the boundary of an LCF Manifold is also LCF ? By definition a LCF manifold is one in which, for each point, there exists a neighborhood around that point that can be conformally transformed to a flat Euclidean space. Since the boundary is a submanifold the answer to the above question should be, yes ! Do I have to be careful to which EUclidean Space i send the conformal transformation? i.e should boundary points only be conformally mapped to an euclidean half space? Thanks for clarification!
Most articles show the plural form of equivalence as equivalences. The wikipedia on logical equivalence uses this form. However, I feel like I have seen equivalencies used in contexts like mathematics as well, like in this paper Equivalencies in Mathematical Structures: An Exploration through Model Theory and Groups Is the choice region specific (American vs European), domain specific (mathematics versus general conversation or other technical fields), or just whatever the writers preferred?
Let's consider a glass slab ABCD. Now a light ray is incident on the near end of the air-glass interface AB and is emerging from the glass-air interface BD. In such a manner: Is there something wrong how I have made my figure. Can light emerge in such a manner from a glass slab. This is my first question and English is not my first language I hope you understood my doubt. I feel like the figure I have drawn does not look like the conventional ray diagram of light entering a glass slab. Also I am not an expert I am just a student who wants to know the answer to my question.
I have a huge .bib file that contains all my references. Very few of them currently have a doi field. Given access to an online database that includes many of the same references, is capable of generating .bib entries, and includes dois, is there any more or less automatic way of using the database to add dois to as many of the references in the .bib file as possible? Note that the citation keys in my .bib file and those generated by the database are not identical, so matching would have to be done by e.g. title and author. Answers using e.g. Jabref or Zotero are fine. It feels like one of those tools ought to be able to do this. I just don't know how.
A cumulative distribution function (cdf) has a countable set of discontinuity points. They need not be isolated. Let us call non-isolated points 'accumulation points' of this set of discontinuity points. Is it possible that a cdf admits also countably infinite accumulation points in its set of discontinuity points? If so, is this something as pathological as requiring a singular distribution or it can also happen with discrete distributions? Thanks for any clarification, it would be nice to have concrete examples.
A long time ago, I had a teacher who said you could write "lit." to mean "read this as". The typical example is to provide a tongue-in-cheek translation from English to English, such as: The power company charges an administrative (lit. bogus) fee on every bill. The author of the sentence is telling the reader to read past the euphemism ("administrative") and understand the subtext that the power company really just wants to take their money for made-up reasons. I just looked this up now, and couldn't find any reference material saying this was an accepted usage of "lit.". Maybe my memory isn't completely accurate?
Given a table with x and f(x) values, g(x) a non-linear least squares approximation, and p(x) the Lagrange interpolating polynomial that passes through all of the points in the given table. What would be the best approximation on f, for a point x = k by only using p(x) and g(x)? Intuitively I thought about calculating p(k) and g(k), then taking the middle point of both, however I have no idea if this is reasonable to think of, nor if it is the best approximation for f(k). Is there a visual way to think of this problem? Or will I have to use the properties of both p and g to find the optimal approximation?
Suppose there are two seeds kept at equal distance from a light source which emits a photon each on either directions. Seed germinates when a photon falls on it. According to rest frame both the seeds receive photons simultaneously but according to moving frame one of the seeds receive a photon earlier than the other seed. The second seed dies off due to delay, so there is only one plant in the moving frame but two plants in the rest frame. Is my line of reasoning correct? What happens when I bring the moving observer to rest so that he should agree with whatever observations made by the observer who was at rest?
I've been asked by a friend taking a TOEIC exam to get an explanation of why "wipe" should be used in the following sentence, as opposed to "wipes": It was mandatory that each person wipe[s] off equipment after use with provided spray and wiping towel. Is it because there is an implied (should) before "wipe"? Or is it related to the fact that it is "each person" - meaning, of course, multiple people and perhaps substitutable with "they" - i.e. you couldn't say "It was mandatory that they wipes"? Or is it something completely different? This one has got me extremely curious, really looking forward to some of your insightful responses.
Is there a word for a decision that's already been made despite the relevant processes not having been followed / analysis done. Foregone conclusion feels similar to what I'm after; but that implies that the facts are so obvious as to make the decision process moot; whilst I'm after a word for where the conclusion is based on one person's perspective without them having consulted relevant stakeholders / investigated the various options / collected evidence to support or dispute their arguments / etc.
Assume that we have positively charged two solid conducting spheres of the same radius and material. It is evident that the surface charge is uniform on them to eliminate the internal electric field everywhere inside the spheres. However, how does the charge distribution change if we bring them close to each other? Recall that we place them close (not in contact) to each other. Does the exerted Coulomb's force upset the uniformity of the surface charges on both spheres? How can we find the new charge distribution so that the internal electric fields remain zero?
I understand it's not possible to transmit information using entangled particles due to the randomness of the measure results. But what if the act of measuring itself IS the information? Let's say there's a constant flow of entangled particles received either side by Alice and Bob Bob measures every other particle. Is it possible for Alice to know which particle has been measured on the other side, and which didn't? I'm assuming unmeasured particles with superposition can show an interference pattern and measured ones don't Sorry if this is a silly question, I'm not a physicist and I fell in the quantum rabbit hole quite recently :)
I was reading about the Pascal barrel bursting experiment, and it almost makes sense to me, save for one bit. I know that pressure corresponds to the number of collisions in the fluid. So my q is: why does adding water in the tall, narrow pipe in the experiment increase the number of collisions down in the barrel drastically? What is actually going on if we zoom in on a molecule of water in the barrel when we add all the extra water at the top? Thank you!
I am not an expert in languages and this is my first question here... To my understanding, most of the languages were spoken before writing was discovered/evolved. What would cause a language to have same/similar sounding words with different meanings when the language was spoken? Wouldn't it cause more confusion when spelling could not distinguish the different words as there was no writing? I can think of some other examples such prey/pray or ate/eight which sound similar but their meanings aren't related. Did these words evolve/change in pronunciation over time, or were they used with similar meanings even a long time back, since before writing was a thing?
For the operation of the transistor, the base-emitter junction is forward-biased and the Base collector junction is reversed-biased. Due to the concentration gradient, electrons from the N side (Emitter) go towards the P side (Base). Since the base is lightly doped and thin and due to the reverse biasing of the base-collector junction(electric field exits between the base and collector), the electrons coming from the N side (Emitter) go towards the N side (Collector) without much recombining with the hole in the P region (Base). Since we have a concentration gradient for electrons to flow from emitter to base then why do we need the base supply voltage in a transistor circuit?
I would like to know some tips or hints to find a way to recognize whether "as" is using a meaning of "when" or a meaning of "because" when "as" connects two sentences. For example, the sentence below which currently confuses me. The third point, where it is in our interests to engage directly with China in a constructive and positive way to shape China's actions and behaviors as they impact on the wider world. In the above sentence, does "as" mean "because"? addtion: this sentence was from an interview script, so I cannot know if there is komma before "as". But thanks for all comments.It seems this "as" doesn't mean "because".
Trying to work out whether to use 'is' or 'are' in the following sentences (aware they might differ): How many grams of flour is/are on the scale? How many centilitres of cough syrup are/is in the measuring cup? How many kilograms of fruit are/is on the scale? 'Are' seems most natural to me when speaking, but have read that units of measurement are usually counted as singular amongst the scientific community. Looking for UK English rules :)
I was reading a preprint on archives (not yet published), and in the introduction the authors say "Following X in [ref]..." and go on to set up the problem. When I went to [ref], it turns out the authors of the preprint actually take three paragraphs word for word from X and include them in their introduction. Is this appropriate? Just saying "Following X...." makes it okay? To me, it still looks like plagiarism.
Suppose we have a finite group G, and we had a configuration of points, lines etc. and lets say that the group acts faithfully and primitively on the set of points. Will the group be guaranteed to be flag-transitive on the entire figure or can G fix some proper subset of lines, for instance? My intuition says that shouldn't be possible, but I can't figure out how to prove it.
Electromagnetic radiation phenomena exhibit a temporal asymmetry: we observe radiation coherently diverging from a radiating source, such the light emitted by a star, but we do not observe radiation coherently converging into a source, unless we delicately set up such a system. What can explain this asymmetry? And how is the asymmetry related to the causal asymmetry, on the one hand, and the thermodynamic asymmetry, on the other?
Next year I have choose a few optative courses from a big list, but syllabi are not available yet, so I have to make a choice based on names only. I am thinking about taking one titled "Groups and representations". I have really enjoyed my Abstract Algebra courses so far, specially the part that covered Group theory. However, we never got into Representation theory, and I ignore what mathematical interest it might have. I was wondering if someone could provide me with a text explaining what is representation theory about and what is the mathematical interest or motivation behind it. I have found some books on the topic, but they all just start giving definitions and theorems and never give a good introduction.
What makes quantum computers faster in certain problems than normal computers? Does quantum computing means that many solutions are explored simultaneously instead of one at a time due to quantum superposition of qubits? Is the complexity of solutions explored proportional to the number of qubits? That's my impression and my understanding of quantum computing. Any books or articles that exactly pinpoint how superposition or any other quantum phenomenon makes computation faster?
A grammatically correct way to ask someone a question would be: Why are you still here? If I want to make a statement (instead of a true question), such as, You've been here too long or Your comments are annoying, or You're either a troll or a quarrelsome person, would "Why you are still here" (meaning- why do you continue arguing with everyone) be acceptable in a conversational English? Do you know why you're still here? is grammatically correct, but I don't want to know if he knows, I just want to express an annoyance with the person.
Has anyone (in general) experimented with simulating moon lighting? It means the following. A gray ball is illuminated with light with a brightness equal to that of the sun. And at the corresponding angular distance from it, the level of illumination by the light reflected from the ball surface is measured and visually assessed. The goal is to compare the illumination intensity of real moonlight and that simulated in the experiment and to check the reliability of the calculated values.
Cambridge says that the idiom home and dry is British English, which explains why I hear it used around me. It means: to have successfully finished something but I have heard it used also literally. Then I understand it as meaning to return home safe and sound after a travel/adventure of some sort. I wonder if this idiom has originated among sailors. I understand home but why dry? Is dry here a synonym of safe (and sound)?
I'd like to know a word to describe a person who loves celebrities, gossips, trends or anything that is popular and is easily affected by them. She said she had moved to Paris because she loved "Emily in Paris" on Netflix. It seems that she is such a " "! I came up with "sheep"(https://www.urbandictionary.com/define.php?term=sheep), but I'd appreciate it if you could tell me other words to describe such a person better or more accurately.
I'm trying to get a deeper understanding of the classification problem for finite groups and in particular the extension problem. I'm looking for some advanced books on the theory of finite group extensions which extensively and deeply covers the topic. Maybe an all-in-one book doesn't exist, in case I'd like also suggestions on books covering related and more specific topics such as Shur's multiplier and Group cohomology.
Is there any book for a Mathematics student who can learn Machine learning in the aspect of Banach space geometry? Or, one can understand the connection between Geometry of Banach spaces and Machine learning? Any suggestions in terms of article, note, book regarding the development of such study is always welcomed. It will be very much helpful if anyone can suggest a good book which contains the discussion about the topic of Geometry of banach spaces that is required for Machine learning, Neural network such things. Thank you in advance.
The professor asked me to write a small computer program that takes double integrals of rapidly varying functions. He did not mention which functions should be integrated but he said that I must use a numerical method with variable step size. I hope someone can recommend me a method that will do the job. It would be nice to have a link where this method is adequately described.
There are many ways to draw a simple flowchart, using packages like tikz. But recently I read a paper and it seems that their complex flowchart is not a picture, but actually generated by latex. Here is what it looks like: I really would like to know how to make a chart like this, if there is a minimal example. EDIT: From what I can see on this picture, it is a combination of table and flowchart, which I don't know how to. So my actual question is, how could we combine a table with a flowchart? Or maybe is it just a complex Tikz (or other packages) implementation?
If the expansion of the universe happens uniformly, how does this affect small objects? For example, are the distances between protons and neutrons inside a nucleus actually expanding? Is the nucleus constantly pulling itself together so its diameter stays constant? What about say between the carbon atoms in a diamond? If I can observe said diamond forever, will its atoms eventually disassociate with each other or will it stay in one piece due to its covalent bonds counteracting the expansion of space?
I have a problem concerning a cylinder, cut by an arbitrary plane which is perpendicular to an axis, z. I know dz, the distance from centre of the cylinder to the plane. I know all dimensions of the cylinder. I know theta, the angle of rotation from the axis z. My poor drawing How do I calculate the volume of the cylinder above the plane? Is it possible? I've tried some trigonometry to get an integral based on the changing size of a circle segment... but it's getting very convoluted.
Say I have some random variables X,Y that are jointly distributed according to some probability distribution (not necessarily independent). Is it possible to construct a Z = f(X,Y) (i.e. Z is solely dependent on both X and Y with no other source of randomness) such that X is independent of Y given Z? I believe this holds for all Z : Z = g(Y) or Z = g(x) for some deterministic function g, although I struggle to prove this formally. One straight forward example is in the binary case with Z = not Y. However, is there any formulation on how the conditional independence requirement restricts the function f?
As far as I understand, the branes of brane cosmology are lower-dimensional "sub-manifolds" of some space. It was hard to imagine for me how such structure could exist and be physical. But then I learned of topological defects, which are essentially that. So my question is: Question: Are the branes of brane cosmology supposed to be topological defects of some sort? If not, how else could a "sub-manifold" be something physical? I also posed a related question which received little attention. Please note that I have only an undergraduate understanding of physics, but are fine with advanced mathematics.
i'm taking a qft theory class, and we are doing a little bit of group theory, today the professor introduced us to Lie groups, but his definition is a little be weird he said that lie groups are groups whose elements are function of n parameters. This kinda confuses me and i can not see how this definition is equivalent to the one where a Lie Group is defined as smooth manifold with some other proprieties like the operation of the group be differentiable. Anyone can help me to clarify and get how these two definitions are equivalent? Thanks
I am struggling to answer this question, and I was hoping for some assistance and/or help, it would be greatly appreciated. This link is a screenshot of the question because it does include diagrams: https://i.stack.imgur.com/wMVod.png The question includes a definition that is used to answer the question; if anyone knows how to answer or go about this, you would be helping me out a lot.
I have some simulated data from a model of an IMU's gyroscopes. I am trying to use Allan deviation to verify that we have correctly modelled various sources of error in the sensor data. I was able to verify angular random walk, and have now moved on to bias instability. I'm following a tutorial on mathworks which describes finding a critical point in the Allan deviation curve, depicted as such: However, my sensors do not output this single, easily spotted critical point. My simulated data looks like so: Is this normal? If so, are there any techniques to choose the best critical point to get an instability reading? If not, what might cause it?