darklight03/StackMIAsub huggingface dataset:
The below question was asked in national English exam in Turkey: Choose the best word or expression to fill the spaces in the passage. As Henry Hill, the actor Ray Liotta gives a complex portrayal of an Irish-Italian kid who succeeds in his youthful ambition ....... popularity as a wealthy gangster, only to have his position slowly eroded until it almost destroys him. A) to gain B)gaining C) to have gained D)having gained E) to be gaining My choice was b (gaining). But the correct answer is A (to gain). I thought the phrase "succeed in " takes gerund not infinitive. Why am I wrong for the answer.
I'm studying X-Ray reflectivity at interfaces and the book I'm reading reads: ... The ideally flat, but graded interface, and the ideally sharp, but roughened interface, will be considered... I'm struggling to understand the difference between the two kinds of interfaces mentioned. Please consider that English is not my first language. Exactly speaking, what do they mean with graded and sharp? How do these two surfaces differ from each other?
Imagine a system with a parallel plate capacitor with holes in the middle where the plates are charged before being disconnected and insulated. Neutral atoms are introduced between the plates and are subsequently ionized in some way. The created ions will gain momentum and travel through the hole after which their kinetic energy can be collected. As long as the kinetic energy gained by the ions is higher than the ionization energy we just gained energy. I know that this should not be possible so where am I wrong?
Assuming we can't block neutrinos, and most of them pass through the earth, how do we know that the change in the neutrino detector is not just happened randomly? Is the detection of neutrinos more frequent when earth is closer to the sun, or are we just always seeing the same amount of neutrinos in the detectors because we have no way to block them?
I'm doing mathematical analysis and I'm stuck with the following question: Give an example of a nowhere dense closed set of irrational numbers with no isolated points (that is, a perfect set of irrational numbers) I read this: Is this a perfect set? so apparently we can find such a set through specific enumeration of rational numbers, taking their vicinities union and taking its complement, but I struggle to find such enumeration that would not create isolated points.
I came across this interview question online: Suppose you sit on the road side and observe cars driving by. Assume the distribution of cars driving by is according to an exponential distribution. Now you observe a first car after sitting for x mins, a second car after sitting for y min. Given those observations, can you estimate the parameter in the distribution? I don't see how I am able to solve it without additional information. Thanks
I begin a PhD in coding theory next fall, and it concerns coding over certain types of rings (e.g. finite chain rings) instead of fields, and in consequence submodule codes. I have a fair amount of knowledge in comm. algebra and have had a standard undergraduate coding theory over finite fields course, so I was wondering: Is there a well-respected graduate text, or a good set of notes, covering more advanced tools in algebraic coding theory? Thanks, and let me know if I need to clarify anything.
If I understand correctly, massive objects cause time dilation, and so time seems to pass more slowly for observers closer to a massive object than those who are farther away. Do cosmologists take the local gravitational effects of earth, the sun, and the Milky Way into account when calculating the expected speeds of stars orbiting distant galaxies? Do galaxies that are more distant rotate faster, by our observations, than those closer to us, even if comparing galaxies of similar mass?
I am an undergraduate, studying physics. I have studied maths courses like Groups, Linear Algebra, Real analysis, Differential geometry and probability. I wish to get into mathematical physics, similar to what Arnold's book has to teach. But i find it a really difficult read since it's a graduate text in mathematics. Can anyone suggest me what stuff do i need to study before getting a good intuitive picture of Arnold's book. Or any resources that provide a road map, intuitive picture of the maths used in physics.
Now I am studying elementary number theory, I am interested in arithmetic function, I have studied Burton's Number Theory but I can't find Dirichlet Convolution as a particular topic, I will be highly glad if anyone suggest some good book to study arithmetic function where I can find Dirichlet Convolution in details with some theorem like 'the set of all arithmetic function forms integral domain under pointwise addition and Dirichlet Convolution'. Thank you.
I am trying to understand the concept of regular conditional distribution. I found the definition quit difficult to grasp . This is what i understood . A regular conditional distribution also called a probability kernel is a two variable function (x,A) -> K(x,A) x a scalar and A a set that verifies the following. when we fix x, we have a probability measure, when we fix A we get a measurable function. Can someone confirm this definition ? and give me an example of a non regular conditional distribution .
The uncertainty principle holds for pairs of certain observables, such as position and momentum. All these observables have a relation to spacetime. Other particle properties, by contrast, such as mass or electric charge can be measured at arbitrary precision. Quantum theories do not even model them as observables, but as parameters to the field. So, what is the philosophical argument for why there is a uncertainty principle for some quantities, but not for others?
I am currently using a software called "SCOUT" to thin film interference simulation, and I would like to know if there is a better software to do this type of simulations. My goal is to vary the thickness of a thin film in a multilayer, in order to create interference between the various thin films, and then create a specific color. So I want to freely change the thickness and get a graph of reflectance or transmittance corresponding to that change. The software should allow me to put my own materials with the respective reflectance and transmittance properties. I know some softwares, like "zemax" and "lumerical" but there are no videos doing what I intend. Does anyone have suggestions? Thank you!
I've got a Literate Agda document, which contains a large number of unicode characters. It builds nicely with XeLaTeX and life is good. The problem is that arxiv only supports pdflatex, and I'd like to upload the file to arxiv. Are there any tools/scripts that can process a latex document written for xelatex and add the necessary commands to compile it with pdflatex? Things like declareUnicodeCharacter for each used character. Basically, I'm just looking for a better way than "start compiling with pdflatex, get an error, add the unicode character, repeat". Most of the unicode symbols are math symbols, so it shouldn't be too hard to map from the characters to TeX commands automatically.
Hi, I'm taking a course of Electrical and Computer Engineering in my university. I don't understand why the partial circuit on the right side of the switch is ignored after the switch is closed. As you can see, the book says the network becomes (c) from (a) via the short circuit. What happens to the short circuit and the circuit on the right side? I think the resistor and the voltage source can still affect the network but it seems not..
I have two non-orthonormal basis vectors, and I want to represent a third vector as a pair of coordinates using the aformentioned basis vectors. How would I do that? The dot product, which usually transforms a vector into coordinates in each basis vector, doesn't work for non-orthonormal bases. How would I get coordinates in terms of my non-orthonormal basis vectors? I should also mention that I am coding, and so all my vectors are currently represented as pairs of numbers on an (x, y) plane. Please ask if you need any clarification, I explained it really poorly here. Also, I do not know very much linear algebra, so it would be appreciated if you answer in simpler terms :)
If Alice is located just beyond the event horizon of a black hole, and Bob is at some other point in space with de minimis gravitiational effect, what, if any, effect would it have on the "spooky action at a distance" between these two entangled entities? I'm a wannabe sci-fi writer looking to exploit untested but possibly plausible concepts derived from my own madness and admittedly poor understanding of the universe.
I am struggling with prooving convergence for an optimizer which uses adaptive step-size with heavy ball algorithm for convex and non-convex functions. In some literature, I could find a regret bound analysis/proof for convex functions and proving that the estimated gradient at t -> inf goes to zero. Could anyone please guide me through the process of convergence proof for non-convex functions or give me literature recommendations for the same. Thank you very much in advance.
I need help understanding how particles do what they do and maintain the structures they maintain if so many of them exist for such a short time? In the case of the nucleus and pions, pions only exist for mere nanoseconds. So if they decay, and their properties change, what is holding that nucleus together? Are the nucleons continually exchanging a stream of pions that perpetuates the interaction that holds the nucleus together? Like I said... Explain like I'm five.
I really like the greek letters of the default LaTeX font but I want the rest of the characters to be in Times New Roman using the Mathptmx font. I find the greek letters of the mathptmx package rather ugly since they're disproportionately bolder than the usual text. So may I know how can I change the greek characters only and retain the times new roman text? I have tried many suggestions from countless websites but to no avail. Alternatively, can I ask if there's a way to change the greek letters somewhat more similar to the greek letters in the books like those in University Physics by Young and Freedman?
When observing interference fringes one often uses a lens after the diffraction grating to focus the fringes on a screen like this: At first sight, one might think that after the lens the path difference between the rays is altered. I think this is not the case, but don't see a clear argument why. Maybe one could apply Fermat's principle, but this - as far as I know - is restricted to the situation that we compare the path from a point A to a point B (in this case P). But here we start with parallel rays and not from a single point A. So, is it right, that it doesn't alter the optical path difference and how to explain exactly why?
I had a debate with a buddy about this. He said you could get a chord by drawing the triangle formed by the two points and the center of the sphere and that chord corresponds to a single great circle arc. I can get to the chord but then projecting that chord on to a path on the surface of the sphere seems non obvious. So is it true that two points not colinear with the spheres center on the surface of a sphere have a unique great circle connecting them and if so how does one prove it?
As the diagrams of categories can be represented as graphs of objects and morphisms, I was wondering if (the diagrams of) higher-dimensional categories could be represented as hypergraphs, and if not why? And in the more general sense, what would be the best west to represent higher-dimensional categories (thinking of diagrams, but also data structures to represent them in programming languages)? And if we reverse the question, are there classes of categories whose diagrams would be best encoded as hypergraphs?
We know a way of measuring energy of a electromagnetic wave is the Poynting vector, which is independent of the frequency. But let's say we want to make two different electromagnetic waves, with different wavelengths and so different frequency, but with the same amplitude (so same Poynting vector). In my opinion the guy in the image is spending more energy for the wave with higher frequency. But the Poynting vector, doesn't care. So is there another property of Electromagnetic Waves that accounts for the energy that the guy used to make the wave?
Two people, A and B, starts from two different points and move in a perfectly straight line in an infinite plane. When they move they leave a visible trace after them. Question: What is the probability that their path (of traces) will intersect at some point regardless of where they start? What I've tried so far is to draw two circles and split it in quadrants. That helped a little bit but didn't really solve the problem, just got an overview. Here's some examples of interesecting paths (first row) and non intersecting paths (second row) which gives you an idea of the criterias for when they intersect and don't intersect: How would you approach and solve this problem?
I don't see why or how this could be argued against or if it really matters, but that's why I ask the forum. I am just trying to understand the nature of the fields in the universe. Am I correct in thinking that the entire universe is just a few fundamental fields laid over each other, getting influenced by the different particles that happen to interact with them?
In a nuclear reaction, protons and neutrons are exchanged and the resulting elements have a number of different protons and neutrons that uniquely define the element that we are studying. However, can we say that a hydrogen atom without any electrons (what we would usually call an ionised atom of hydrogen) is really hydrogen? Or do electrons fundamentally indicate the element that results from the reaction? Can we really say that an atom of hydrogen without electrons is actually hydrogen?
My textbook says: Similarly, non-polar (i.e., covalent or organic) compounds like naphthalene, anthracene etc. are soluble in non-polar (i.e., covalent or organic) solvents like benzene, ether, carbon tetrachloride, etc. and are very little soluble in water. My question is that if we have a non polar compound, then it seems as if it should not dissolve to any extent. However, the quote says that non polar molecules are a little soluble in water. Thus I want to know why non polar solutes dissolve in water at all, even if it is only to a very lesser extent?
What is a word to describe how a cat looks when it's groomed? My husband described it as nappy, which I don't think would be the correct word. To give an image of what I am trying to describe, think of a medium-haired cat that licked its fur and looks messy, with wet fur sticking up a bit. It's a weird request and may be too specific, but I hope there's some kind of answer to what I am asking.
I just read a quote in which someone, on behalf of herself and her spouse, wrote "Our heart goes out for ....". I Googled to know if when it comes to speaking about heart not as a body organ, is it possible to use it in the singular form, but I could not find any reliable source for that. So, what is the correct form for such situations and does it apply for other organs, specifically brain?
If I shred a book into numerous pieces, and scatter them, so that the original text is completely unreadable, then for me, as a reader, the book has lost all its information. Its entropy has greatly increased. As a reader, the book's information rested upon a state of minimal entropy. However, my (limited) understanding of Shannon's information theory is that the 'information' in the shredded book has increased along with its entropy. Is there a way of reconciling the conventional/layperson's understanding of information as an ordered presentation of knowledge (like a well-written book) with the Shannon equation of information with entropy/disorder? Apologies if I have failed to grasp something fundamental.
In the image above, we have the principle of induction cooking. An alternating current is run through the coil, which causes a change in flux. This change in flux induces eddy currents in the conductive pan, and by Joule heating/resistive heating (P=VI), this causes the pan to heat up. So the only thing that you need is a pan that can conduct electricity/the eddy currents right? As long as the pan does not have a too low or a too high resistance. However, why is the effect specifically optimal for ferromagnetic materials/conductors? How does the ability to magnetize somehow enhance the effect of induction heating? Does the magnetization of the pan itself somehow enhance the eddy currents or something?
Often charge is defined as a measure of interaction with the electromagnetic field. However, electromagnetic field is often defined as a field produced by moving electrical charges, or relates to charges in some way or the other. Due to this circular definition, I am not able to understand what really is charge and its influence on electromagnetism, or any interaction. So what exactly is charge and what does it have to do with electromagnetism, or any other interaction?
There is a word in German, ausgezeichnet which vaguely sounds like the English phrase "out of sight" but that is usually translated as "excellent". I could see some non-German speaker hearing it and, knowing that it meant "very good" from context, deciding to use it and approximating its sound with "out of sight". Note that I am interested in whether the German word and the phrase are related, not the general history of "Out of Sight" Is there any evidence to support this etymology?
Assume I have a hemispherical container of water and an eyedropper. Is it possible to add water to the container one drop at a time, such that each drop continues to add kinetic energy to the water? When a water drop is added, it creates waves. I am wondering if it is possible to keep adding water drops in time with the waves, so that it acts like constructive interference, and adds more energy into the waves. I think this could be a very interesting sculpture, to have a computer-controlled eyedropper which slowly builds up the amplitude of the waves.
(I'm South Korean, so non-native question here.) I saw the sentence 'that looks about it'. Does it mean that something is seemingly almost done? I searched this expression on google but I couldn't find the exactly same pattern of the expression but I found at the Cambridge dictionary: that's (about) it : there's no more to be said or done So I guess the sentence 'that looks about it' means something like 'I think it's almost done'. Is my interpretation right? How often is this expression used?
In quantum field theory we often hear that particles sometimes behave like waves and sometimes behave like particles. In quantum field theory we say particles are fundamentally fields. Is it correct to say that particles and waves are limits of quantum fields? For example, if we take a quantum field and apply the limits appropriate for a double-slit set-up, would the field come out a wave?
I am no expert in the calculus of variations but I had some lectures about it and attended some talks. I noticed that searching for minima of functionals seems way more popular than searching for saddles. I know about some MiniMax theory or mountain pass theorems that can be used to search for saddles aswell but especially in the context of actual variational problems it seems to me that people are more often looking for minima. From a PDE point of view that seems kind of odd, because saddles could solve corresponding EL-equations aswell. Question: Are people actually more interested in minima? If yes, why? If you got any literature recommendations on saddles or similar topics, I would be very thankful aswell. Thanks in advance.
I am once again asking more software-related questions, but I am happy to learn a general answer as well. I'm curious about how the is_infinite function works in SageMath (or in GAP). Does it simply check whether we input something that is already known to be infinite or not? Or does it print "infinite" after a specific number of elements? Or does it actually check if the group is infinite? I assume it's not a numerical answer to check if the group is infinite or not since the program can't count until infinity. So, I'm wondering what the method is for checking if a group is infinite or not (in SageMath and in general). Thank you for your answer.
Can you refer me to books that are at the same advanced level of real analysis via measure theory as Folland's and Royden's books? I want to have a solid foundation and I've been referred to books like Cohn's and Axler's, but I don't have deep knowledge of real analysis (I'm still going to start studying introduction to analysis) and I don't know if these books combine measure theory and real analysis like the ones I mentioned in the title or whether they are purely measure theory. If possible it was a Dover book because they have affordable prices here in Brazil. Thanks to everyone who can help me.
I've always been taught that vectors that form a closed polygon represent an object being at equilibirium, that is there is no resultant force on the object. However, this has never been intuitive to me. How does one prove, that if the vectors form a closed polygon, the resultant force has to be zero? Furthermore why must the arrows form a closed loop, why is it not enough for the lines themselves to form a closed loop?
When reading about the notion of affine connection, the Levi-Civita connection appears naturally as the unique affine connection that preserve the metric and is torsion free. In this case, it is possible to express the connection coefficients analytically as a function of the metric and its derivatives. What I am curious of are alternative affine connections, possibly admitting explicit formulas for the Christoffel symbols. In other terms, what are other connections that agree with the definition, but are not necessarily compatible with the metric and do rather reflect some other underlying structure? Thanks
I know what a collocation method is and how it can be useful for the direct transcription of optional control problems, using specific collocation points. I also know what a quadrature rule is and how it can be used to solve integrals numerically, using specific quadrature points. But I'm struggling to see the mathematical connections between these two concepts, that are obviously related (for example: the trapezoidal collocation method has to be related to the trapezoidal quadrature rule somehow). So basically I'm wondering: is there a one-to-one correspondence between one collocation method and the related quadrature rule? If so, is it possibile to show how they are reciprocally related, in general, from a mathematical point of view?
I am writing to ask for references. I have been trying for hours to find some paper/ book containing information on cycles in cubic graphs. It is known that to determine whether a given cubic graph contains a Hamiltonian cycle is NP-hard, but since it is not a tree we know that it must contain at least one cycle. But do we know we can find such cycles in cubic graphs in polynomial time? Do we know an upper/ lower bound on the size of the cycles in cubic graphs? I would be grateful if you share any references or any information on this topic.
In some parts of my document math environments, such as "align", are not recognized, e.g. there is no arrow on the left to hide it, there is no automatic indent, and the theme colors are not applied properly. The same happens with "subsection", "section", etc. However, in other parts of the document the environments work. What could be the reason and how do I fix this? I am using pdfLaTeX compiler. Here is an example of how it looks in the editor:
For example, prove that if A AND B and A AND C are logically equivalent. How would I go doing this? I thought of using two truth tables: A | B | A AND B T T T T F F F T T F F T A | C | A AND C T T T T F F F T T F F T Then concluding they are logically equivalent. However, they are from two seperate truth tables. Would that be correct? Or do I have to combine the truth tables?