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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. | 0 |
(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? | 0 |
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? | 0 |
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. | 0 |
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. | 0 |
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. | 0 |
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? | 0 |
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 | 0 |
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? | 0 |
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. | 0 |
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: | 0 |
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? | 0 |
Can you recommend me some papers or lectures on finding the solution of elliptic PDE which is the saddle point of its energy functional. I glance over some methods including mountain pass theorem and min-max scheme, but it's hard to select one paper or lecture to do some intensive readings, so I wonder if you can recommend me some classical papers or lectures on this topic? | 0 |
I am currently working through the book Mathematical Logic by Mileti (online version) and just finished the second chapter (induction and recursion). I have to admit that it is quite challenging and whereas I think I can follow through, it really takes a lot of effort and time to thoroughly understand the ideas since they are so abstract for me. Has anyone worked through it and could let me know if the density and difficulty will continue in that rate or if one quickly gets used to it? Thanks | 0 |
I was always fascinated with pure math, but lately I've been increasingly more interested on applications of math (preferably algebra/topology but other fields would be interesting too) in the real world. I am wondering if there are any books that discuss such applications, as I wasn't able to find any. To be clear, I'm not looking for detailed books at the research level. I'm looking for books that I can read in my leisure time just out of curiosity to see how concepts from algebra/toplogy/etc are related to the real world. | 0 |
I am working on a user manual, compiling it from .rst source files with the pdflatex engine. My user manual has two versions: in English and in Russian. The issue that I have is connected with tables that take more than one page. I have 'continues on next page' and 'continued from the previous page' captions added automatically. These captions are not a problem in English. However, they are partially translated to Russian (the 'continues on next page' caption is left unchanged, see the images). Is it possible to edit them or to remove them finally? I guess it might be defined in the preamble but I have no idea how to do this. | 0 |
This is a question I came across on Instagram today, and here's the diagram: (Note: The image is NOT to scale) I attempted to solve it first by amending the quadrilateral in various ways, but each of those methods lead to a strange contradiction, likely because the diagram is not to scale. I'm going to post my successful approach as an answer below, please let me know if my answer is correct or if there's something wrong with the method (the correct answer wasn't revealed, and if there are any other ways to approach this that I missed!) | 0 |
Blum proved that any mathematical theorem can be converted into a graph such that the proof of that theorem is equivalent to proving a Hamiltonian cycle in the graph from Applied Cryptography by Bruce Schneier I'm struggling to understand what the statement means, and I was unable to find anything on it after a few quick google searches. Can someone point me in the right direction, to what this statement is even talking about? | 0 |
Antennas work by accelerating electrons to emit EM radiation. In fact, my understanding is that any accelerating electron will emit EM radiation. But in relativity, no frame of reference is preferred. Therefore, an electron in an antenna can claim that every other electron in the universe is moving around it. So does that mean that when an antenna creates a signal, every other electron in the universe sends the same signal back to it? | 0 |
I am trying to recreate this diagram in a standalone PDF using TikZ or PSTricks. Two extra requirements: I have to be able to alter the viewing angle arbitrarily I want to use relative coordinates rather than hard-coding the absolute coordinates of every cube. I'd like to be able to define cubes relative to nearby cubes using nodes since it will be easy to generalise this code to other shapes. I'm fairly experienced with TikZ, but just looking for a more elegant solution. | 0 |
I will use an example to explain my question... Transphobia is an irrational fear of, aversion to, or discrimination against transgender people. In the above sentence, is the true definition that only the fear is irrational, or is the aversion and discrimination also irrational? Is the true meaning: Transphobia is an irrational fear of transgender people. Transphobia is an irrational aversion to transgender people. Transphobia is an irrational discrimination against transgender people. Or: Transphobia is an irrational fear of transgender people. Transphobia is an aversion to transgender people. Transphobia is discrimination against transgender people. | 0 |
I've been shown an Out of Office template, and one of the sentences in it asks the sender to contact someone else within the company "in case of need", as the email will not be forwarded. I've never come across that phrasing before. Is it British English? Usually, personally, I'd go with "if/as required", although that might be a tad too strong in this context... | 0 |
I have one cylindrical coordinate system attached with a laboratory device and another cylindrical coordinate system that is attached with an object in it. The object is symmetric about the z-axis in its own coordinate system, which is both displaced and tilted with respect to the laboratory system. How do I express the unit vectors in the object coordinate system in terms of unit vectors in the laboratory coordinate system? I can write the coordinate transformation in Cartesian coordinates and then convert the Cartesian coordinates into cylindrical coordinates but do not see how to do that with unit vectors. | 0 |
hello, hello. I am reading the book "Geometry" by Tatiana Alekseyevskaya (Gelfand) and found myself having the question below. An external angle is defined in Wikipedia as an angle formed by one side of a simple polygon and a line extended from an adjacent side. How does that definition applies to the following polygon (delimited by the green line)? If I extend one side of it, the angle will end inside the polygon. I also have found similar questions have been asked over this forum, but I suppose mine is more related to the definition itself being applied, unless this polygon doesn't qualify as "simple" polygon as the Wikipedia definition states. Thanks! -- Caleb | 0 |
Is it possible to have one master .cls file in Overleaf that works across different projects? For example, if I make a change in the .cls file while working in one project, it will be updated in all of the other projects that use that .cls file? I know that I could import the .cls file from another project, but I cannot update it within the project that has imported it. | 0 |
I have a particular model with two couplings, let's call it model A, for which I have the set of beta functions and fixed points. Now I am interested in a model where I have two copies of model A, each with a different fundamental field, let's call that model B. So, model B has two couplings for each field plus a fifth interaction that couples the two fields. I know this might highly depend on the specific scenario, but is there a general strategy as to how one would obtain the beta functions of model B from the beta functions of model A? | 0 |
I am wondering that whether Kolmogorov spectrum, which describes the energy distribution in turbulence be used to describe the plasma fluctuation in the atmosphere of neutron star. As I know, Kolmogorov spectrum has been used in solar physics to model the small scale fluctuations, and there is also research on the turbulence in the core of neutron star and used Kolmogorov spectrum. However, I haven't found references concerning describing the fluctuation in the atomosphere of neutron star, can it use Kolmogorov spectrum or other methods? | 0 |
I know the evolution of a main sequence star to a giant is a process that takes millions and millions of years, but how fast is the VISIBLE change? Basically, will our sun, for example, slowly grow to envelope the orbits of the inner planets, or will there be a sudden inflation of that star to a new much greater volume on a timescale of seconds or minutes or hours etc.? | 0 |
All the sources I have read from say that radial component of acceleration of a body in circular motion only accounts for the change in direction . I do not understand how this is possible. Another thing I do not understand is what provides the torque for such a body to rotate. Could you please explain to me the forces and accelerations involved using the classic ball-and-rope example? | 0 |
Calculus invention happened only few hundred years ago. So I assume that differential equations are being discovered and solved since that time. When I was in school I learnt that most differential equations cannot be solved analytically and are thus solved using numerical methods. The question in my mind is, what difference does it make if we can't solve a differential equation analytically? Is that bad? Are people doing research to find analytical solutions to old differential equations? Also, before computers existed, were people still able to use numerical methods to solve differential equations numerically? That would be quite a lot of work. | 0 |
We have a compactness result, where the "flat limit" of an integral current is itself an integral current. (with some conditions) Now I am curious about submanifolds. I am expecting that an equivalent result does not hold for submanifolds in general. However I am having trouble finding a resource to verify this. Does anyone know of an example, book or article I could check out? | 0 |
so I recently came across the term 'virtual mass' and when I looked up more about it, it just gave me some stuff about fluid mechanics that I dont understand properly. My understanding of virtual mass is that when a body is pushed through a fluid (let's say water) it moves slower than usual and behaves like hoe a big object with more mass would behave on land but then I realized that what I was thinking of is just upthrust/buoyancy so can somebody please explain virtual mass in simple (layman terms) words. (I just cant wrap my head around it) | 0 |
The harmonics of a theoretically infinitely small diameter string are pure integer multiples of the fundamental frequency. However, a real string has a thickness, and when vibrating in a harmonic, the additional node or nodes should be taken into account when considering the string's length. This should mean that higher harmonics would have frequencies higher than the corresponding integer multiple of the fundamental frequency. What is the formula that allows for this calculation, and what effect might it have on the quality of the sound an instrument might produce? | 0 |
In documentation for electrical vehicles there is a common acronym for "state of charge" that is written as "SoC" or "SOC". Are both versions equally ok, or are there rules guiding when to mix case, and when not to mix case? I hope this question doesn't fall under the category "Questions that are primarily opinion-based", which I learned are not be asked here (I just signed up). | 0 |
I am a self learner and I just finished calculus books (Thomas calculus , Larson book ) and I want to learn further topics in integration so I searched for good books on integrals and I heard that the book A Treatise on the Integral Calculus by Joseph Edwards is very good but this book seems very old , so my question is this book still worth reading today or there are modern better books this ? | 0 |
I have been trying to understand how to calculate the kinetic energy of a rotating rod that also has translational movement. I have written my question down on paper because I think it is more clear this way. In case B, I think I have miscalculated the kinetic energy when dividing it as the sum of the rotational and translational energy. I have been days trying to understand this high school level problem. I would be very thankful if someone can point out my error. | 0 |
Let's say the original source says: "They were at the loud, busy, fair. They played many games there." My adaptation is: "They played many games [at the loud, busy, fair]. Since "at the loud, busy, fair" is taken verbatim from the original source, do I need to write my adaptation as: "They played many games ['at the loud busy fair']." to indicate that I have taken it verbatim? | 0 |
Specifically in relation to meteorology. I was wondering if the angular momentum an object, lets say a parcel of air has due to the roation about the earths axis. Is it conserved if moved to a different lattitude. According to my understanding the conservation of angular momentum applies as long as there is no torque on it. Is moving an object in latitudinal direction a torque in this case? | 0 |
Hi been trying to solve this question : Show that the following classes are not closed under ultraproducts: (a) the class of torsion groups; (b) the class of simple groups; Thought about showing that they are closed under isomorphism and to show that they are not axiomatizable hence they are not closed under ultraproducts, couldn't really proof that tho, so I would like some help! Thanks! | 0 |
I am looking for resources treating the problem of simultaneous DC Stark and Zeeman Effects for arbitrary directions of the magnetic and electric fields (not necessarily orthogonal or parallel). I am in particular interested in the effect of such simultaneous fields on atoms with hyperfine structure such as alkali. Of course feel free to write an answer if you yourself know how to treat this problem. | 0 |
You pull cards out of a shuffled deck until you get a jack and a queen. Given see the jack first, what is the expected number of cards between the jack and the queen? I believe this is a conditional expectation problem. Our goal is to subtract the expected position of the jack from the expected position of the queen. However, I am lost on how to find this other than writing out all possible combinations which isn't feasible. I know how to find the expected position of either card without the condition. Do I use this and compute variance in some way? Kind of lost, any guidance is appreciated. | 0 |
Abbot et al. "Experimentally probing the algorithmic randomness and incomputability of quantum randomness" remark that "incomputability is a weaker property than Kolmogorov randomness". I understand that a Kolmogorov random infinite sequence is incomputable. The statement implies that there are incomputable sequences that are not Kolmogorov random. Why? (It's difficult for me to imagine what such a sequence would be like. If the answer is complicated, pointers to textbooks or literature at a similar level would be welcome.) | 0 |
On a fire extinguisher's cover, "In case of fire, break glass" may be written. As you see, in short, instructional contexts, one often finds articles being omitted. Is this grammatically correct? Is there a name for this kind of writing? Must it instead be written as "In case of a fire, break the glass"? This omission of articles is very common in instruction manuals and tutorials. | 0 |
This is a less concrete question I was just curious about. We always talk about straight lines of symmetry and reflections but can non-straight lines of symmetry exist when reflecting something, and if so what would they look like? Logically, I'm not sure if it makes too much sense to ask something like this since I guess for some reflections, the reflection of an object could overlap with its own reflection but I'm asking just for the sake of maybe discovering something new. I guess it's also difficult to visualise what that would look like for example, what would the following circle look like when reflected across the red curve? Any insight into this would be greatly appreciated! | 0 |
I've been playing a game and after completing a mission, one character ask to another the following: How you doing on the feddy? From the context, I assume that it's somehow related to money, but I'm not sure-it's an odd word! The only site I found it was on Urban Dictionary. My question is, what does feddy really mean here, and how did it come to take on that meaning? (Here's the video that shows some more context.) | 0 |
Would a high-pitched unhearable frequency be heard whilst the doppler effect is in play? For example, when a car uses its horn whilst travelling by, the pitch shifts as it passes - which is the Doppler effect. What would happen if someone were to play a frequency so high that humans couldn't hear it and went past a bystander? Would the bystander be able to hear the frequency as the pitch shifts? or would it not affect it? Just a random shower thought that was playing on my mind... | 0 |
Does there exist a continuous function defined on an open interval and being differentiable in a unique point? I have found examples of real-valued functions which are differentiable in a unique point of their sources, but all of them are not continuous at the points where they are not differentiable. I would like to know if there are examples of these kind of functions in the continuous case. | 0 |
Why are pressure hulls machined to be nearly spherical? According to Wikipedia, https://en.wikipedia.org/wiki/DSV_Limiting_Factor has a hull that is machined to be nearly spherical "for enhanced buckling stability". Is this really superior to an unmachined hull in terms of pressure resistance? I can see why it might be useful to trim any excess weight from a diving vehicle, but I don't see how removing material can ever improve pressure resistance. Does anyone have any insights? | 0 |
So I'm learning data science concepts for analysis of stock price data and I've gone into a rabbit hole. I first came across numpy.triu() in the Numpy library which calculates the Triangle Matrix for a dataset to find large movements in stock price points over a range of time. Then I learned more about the concept and how values in the set are calculated. But now I'm wondering what the practical uses for this concept? I'm especially interested in uses in analyzing stock price data. | 0 |
I was reading the paper on the Hall Effect and found that the initial experiment was performed on a metal strip. The experiment on the metal failed to provide any useful results, and then it was stated that Owing probably to the fact that the metal disk used had considerable thickness, the experiment at that time failed to give any positive result. Later when the same experiment was performed with a gold leaf, the experiment gave satisfactory results. So, I wanted to know how thickness impacted the results of the Hall Effect Experiment. | 0 |
Spatial gradients in the refractive index of a medium have an impact on the wavelength, frequency, and direction of waves propagating through them. What about media whose refractive index changes (spatially uniformly) with time? Is it correct to say that there will be no changes to wavelength or direction of propagating waves? What equations should be used to model wave propagation in a medium with time-varying refractive index? As a bonus, how would we model propagation if the index is changing non-uniformly in both time and space? | 0 |
I was invited to review an article by one of the IOP journals (Journal of Physics Communications) a few months ago in which the author claimed that the EM fields, similar to photons, bend in a gravitational field. The calculations were slightly hard and I had not enough time to follow the calculations, and thus I had to decline to review the article. However, the article inspired me to consider that every single electric (or magnetic) field may have a photon-like behavior and it bends inside a gravitational field. Is this a rational deduction? | 0 |
I want to design new characters (mainly ornaments but also mathematical symbols) for the CM modern font family using METAFONT. What is the best way to achieve consistency with the rest of the family? The first idea that came to my mind was to copy paste the cmbase.mf file from https://ctan.org/tex-archive/fonts/cm/mf but that's a lot of duplication and I am not sure I am legally allowed to do so. | 0 |
I'm aware that in sentences using neither-nor constructions, the verb must agree with the subject closest to it. E.g.: Neither the dog nor the cats have been fed. Neither the cats nor the dog has been fed. However, when it comes to question forms, what should the verb agree with? Does the rule still apply? Has/have neither the dog nor cats been fed yet? To make it grammatically sound, should has or have be used in that sentence? Edit: The question should be "Has/have neither the dog nor THE cats been fed yet?", with the definite article "the" before "cats", which preserves the structure of the example I provided. | 0 |
For a phonon mode to be able to emit electromagnetic radiation, it must have a dipole moment. However, it is not intuitive to me why the LA phonon does not have a dipole moment: suppose all atoms in a unit cell are oscillating in phase back and forth relative to the electronic background, isn't this itself a dipole moment? The radiation should came out perpendicular to the oscillatrion direction. Mathematically, when we determine whether a mode "has a dipole moment", what quantity are we actually talking about? Thanks. | 0 |
I am confused about how to understand the sheaf on empty set (as an open subset) of the Zariski Topology over the Spec(Z), which is generated by the additive identity zero in Z. The sheaf I have in mind is the structure sheaf sending open sets to local rings. I read related pages and I cannot understand how sheaf over empty set is a terminal object. Is this terminal object an additive/multiplicative identity of the ring? Is terminal object an element of the local ring? | 0 |
I've seen these words both used but not interchangeably. My guess is that fascistic refers to 'fascist in nature', e.g if a building is fascistic it is reflective of fascist ideology but not necessarily a product of a fascist regime while fascist means relating to actual instances of fascisism e.g, saying a building is fascist means it was a Nazi building or otherwise. I'm not sure though... | 0 |
I have read that the Einstein-Cartan theory introduces torsion into general relativity in a way that produces coupling between gravity and the spin of particles. Then, the gravitational field is able cause the precession of this spin axis. But what about spinless particles? Wouldn't there be a difference between the way gravity acts on particles with spin vs no spin? I guess that even for particles with nonequal nonzero spin there would be a difference If gravity acts differently on the varied kinds of particles, the equivalence principle goes out the window. Plus, I don't know how to make the spin coupling disappear with a simple coordinate change | 0 |
Strictly speaking, a stochastic process can characterize a collection of random variables whose index is not time-related. Please, are there examples in the literature where this has been considered? Otherwise, should we refer to those processes as random fields as opposed to stochastic processes, reserving the term "stochastic process" for the case wherein time is involved? I'm particularly curious about the case wherein there is a process over space as opposed to process over time. | 0 |
I watched a video lecture that talked a bit about when proof by contradiction is and isn't a useful approach. This was useful, but it was from a heuristic approach which caused me to wonder is it the case that "P is provable" implies "there is a proof by contradiction of P"? I suspect this may vary by logic system. If that is the case I would still be interested in know what major systems do/don't have this property. | 0 |
I am helping a friend edit a manuscript for an informal reference book about music. There are several instances where I am perceiving a mixture of tense but I'm not sure how or whether to correct it. Here is an example sentence: If we begin on the first note of the C major scale and skip every other note, the following chords get created: I suggested changing "get created" to "are created." The verbs begin and skip are clearly present tense, and I believe get created and are created are present perfect tense, so my analysis of mixed tense seems incorrect. Why does "get" seem like incorrect usage in this example? | 0 |
I read the following text on This Page: Does every polynomial have at least one imaginary zero? No. Real numbers are a subset of complex numbers, but not the other way around. A complex number is not necessarily imaginary. Real numbers are also complex numbers. Now, FTA states that: every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero. my understanding is that, unless "Complex Root" means something different than "Imaginary Zero", the former page statement is wrong. Please clarify the situation. Thanks. Edit: After reading the good comments below, I came across this diagram which helps: Diagram-Classifying Numbers | 0 |
Recently I saw two interviews, one with Victoria Beckham, the other one with Elton John. They were talking about their past experiences and that's the phrasing they used: But it wouldn't have happened if we HADN'T HAVE GONE to the Ukraine. (Elton) And I probably would still be that way if I HADN'T HAVE MET the girls. (Victoria) Is there any explanation behind the grammar written in capital letters? | 0 |
This is a silly question, but can it be done safely? My friend wanted to have a soup with electrolysis causing it to taste differently on each side of the bowl. I think this is dangerous, because there is table salt in the soup and I suspect that during electrolysis chlorine gas is made. Maybe someone can clarify the soup example or provide an alternative? | 0 |
I am studying some results about existence and uniqueness of solutions to some PDEs and many times Banach fixed point Theorem is used. I saw that the ideia is to consider the integral formulation and use the Theorem to prove existence and uniqueness in a ball but I can't understant how the uniquess extends to all the space. Any one can explain how to get uniquess in all the space and how existence and uniquess of solution to the integral formulation garantees the same for the PDE? Any help is appreciated. | 0 |
I have seen that there exists an intimate relationship between electric and magnetic properties. From what I know is that electric field creates electric potential around the source's space which can allow a charged particle to gain some PE and makes it possible for that particle to have translational and rotational motion. I have searched quite a bit and could see that magnetic potential energy can only cause rotational motion, why not translational motion? | 0 |
I've recently found a really old "Philosophy of Math" book in my University library, and in the book it says that the it has been proven that : if non-euclidean geometry is inconsistent, then so is euclidean geometry, and the reverse is also valid. But the book wasn't as helpful as it doesn't prove, or give some reference or name to this result. Does anyone have a proof for this or for something similar? Even a definition of what exactly "inconsistency" means in this geometric context would be welcome. | 0 |
I am competing in the American Computer Science League (ACSL), and I get problems similar to the following. Look at this directed graph. Now tell me the number of cycles in said graph. These questions need to be completed quickly and by hand. Unfortunately, the ACSL wiki (which provides help and study resources for the test) says to find all cycles by inspection. This obviously is slow and possible erroneous. I want to be able to complete these questions with the utmost accuracy. Is there a method to, given a graph, calculate the number of cycles by hand? | 0 |
The energy of photons is reduced by the expansion of space. Since the photons have been decoupled from matter their wavelengths have decreased from the visible range to the radio range. The same should hold for the neutrinos that emerged from the big bang. They still travel at a speed that's close to the speed of light. Almost all their energy is kinetic. Will their speed be reduced to, say, half the speed of light in the far future? If so, how long will that take? | 0 |
Every number theory book seems to start with divisibility, congruency, the division algorithm, etc., while completely ignoring the rigorous construction of the natural numbers. It seems like a wasted opportunity to explain to the reader what's actually happening. I feel the same about combinatorics. Permutations, combinations, and the rule of product are derived heuristically rather than through rigorous arguments from set theory. Is there a particular reason why number theory books take this approach rather than a rigorous from first principles approach? | 0 |
I am writing a an essay comparing The Great Gatsby and Pride and Prejudice in English (Australian English style), and to save on word count I wondered if it would be appropriate to refer to them, after the first few uses of the names, as Pride and Gatsby respectively. Is this acceptable to do in a relatively formal context, and if so, is there any procedure for first introducing the contracted names? | 0 |
I just built Lyx on Manjaro linux from pamac (there is an entry from the AUR, see https://aur.archlinux.org/packages/lyx). When I try to view a document in pdf using pdflatex an window pops up saying an error has occured in the external program "pdflatex" and that I should see the logs. Unfortunately I can't find the logs for pdflatex... If I type pdflatex in a terminal, it is up and running. Also all of the document classes and modules required by the Help - Introduction, Tutorial, ... are missing. I wonder if I missed a package to install. Thank you for your answers ! | 0 |
I need to quote and excerpt a lot of the same passages from a diverse library in my work. I'd like to find an app that's basically a purpose-built database for this kind of thing -- where I can store the excerpted text, the BibTeX source, the page number, a brief description, maybe some keywords/tags/categories. Basically something like Jabref, but where elements are passages not sources. I found an app called TextCite, but it looks like it's no longer being updated and I had some trouble installing it. Any help is most appreciated. | 0 |
In a nuclear fission reaction the total energy and thus the mass of the products are lower than the total energy of the reactants. I understand the the difference in this energy can be used in a nuclear reactor/atomic bomb. But in the physical sense how does this energy manifest, is the kinetic energy of the reactants or some EM wave emission or combination of both. Also if it is the kinetic energy of reactants, wouldn't that energy be already included in the total energy of reactants? | 0 |
When observed from the ground frame (assuming no friction is present), the only forces that act on the rotating bead are weight and the normal force exerted by the loop towards the center of the loop. I suppose there is no component of the normal force in the direction of the bead's movement, so it shouldn't move upwards. I am unable to comprehend why the bead does move upward. | 0 |
In Tao's Fourier Transform preprint, https://www.math.ucla.edu/~tao/preprints/fourier.pdf, they show explicitly that the Laplacian can be viewed as a Fourier multiplier. In the same paragraph, they write ...This identity shows that the Fourier transform diagonalizes the Laplacian Why is the word "diagonalizes" used in this context? I know it from a Linear Algebra context, in which we diagonalize some matrix, but in this context it seems out of place. Am I missing something? | 0 |
Just a naive question about univalent foundations. As far as I understand, we want to define our mathematical types like sets, groups, categories, etc. such that structurally identical objects are equal in the sense of internal equality. But are we free to choose what kind of isomorphisms we are interested in? For example, can we define both, the type of categories with ismorphisms as equality, and the type of categories with equivalences as equality? Or the type of topological spaces with homotopy equivalences as equality, and the type of topological spaces with homeomorphisms as equality? How would these differences actually look like in the definition? | 0 |
I was just thinking about this studying for a biology test as for cells a greater surface area to volume ratio is desirable, so I wondered if there was a theoretically optimal shape that would maximize this ratio. I thought it might be that there is no such shape as you could just add folds to the surface indefinitely but I don't know if that is truly the case. | 0 |
This question is similar to this post, but in my case the actual numbers do not matter, I'm interested in the equations. I have an arbitrary triangle, of which only angle BAC and side AB are known. The sum of sides BC and AC (therefore the perimeter) is known and fixed. I am looking for an equation that gives me the value of angle ABC. Here's a screenshot, please remember that the exact dimensions are arbitrary, and are only there to show which parts are known. Triangle drawn in CAD This is really driving me crazy, I would appreciate any help! Thank you! | 0 |
I've mostly used and seen "utilitarian" in a negative sense: something that only exists for its function, and specifically for those functions. In other words, something that is single-purpose. utilitarian designed to be useful rather than decorative: But what if I wanted to describe something positively, could utilitarian be an apt adjective? I often see phrases like "utility focused" or "utility oriented" as positive, but utilitarian as negative. Aren't they the same? For example: "I worked at Big Tech Company where I designed and developed utility focused modules" sounds positive or neutral. "I worked at Big Tech Company where I designed and developed utilitarian modules" sounds pretty bad. | 0 |
I am looking into uses of Fourier series. I learned that it can be used to approximate functions (link). However, I think there are ways to approximate functions with polynomials (not limited to Taylor series). What advantage does the Fourier series have over polynomials in approximation? I think there is a disadvantage to the Fourier series. While the way to compute the values of polynomials is obvious, computing the values of Fourier series needs approximate values of the trigonometric functions. | 0 |
I was thinking of the trading of kinetic energy during a gravitational slingshot maneuver and wondered if the kinetic energy lost during that process makes any noticeable impact on the orbit of the planet. Since the planet we are performing this maneuver on loses kinetic energy, it is realistically possible to do enough slingshots that we noticeably change the orbit of the planet? And what would be the consequences of changing the orbit? | 0 |
Taka a standard spinning bicycle wheel with its spokes and place it in a magnetic field that is parallel with the axle. I know that if the spokes were not made of metal but some insulating rods there would be an emf and a corresponding current induced in the rim. My question is what happens when the spokes are made of some conducting metal, will there be an emf induced across the spokes and what will the current be in the rim and spokes? | 0 |
Do Boltzmann brain thought experiments suggest literally anything can form randomly? What are the limitations to what random fluctuations can form? Literally any physical, material object? Lastly, I am curious as to how this compares to an object with a high degree of complexity always existing. For example, is a bike more likely to always exist for no reason than it being created by random fluctuations? Or is it less likely? | 0 |
In a scientific abstract, I have a sentence like this: Yet, numerous capture-mark-recapture data sets, across wide taxonomic range, feature transient individuals. I want to emphasize that there are numerous capture-mark-recapture data sets, and that they all together cover a wide taxonomic range. Not each one of them; each of those data sets is covering only few very specific taxa; but all together they cover the wide taxonomic range. I don't want the expression to be too ambiguous in this direction. Is this sentence correct and unambiguous, or could it be written better? It shouldn't be much longer since I am very close to the word limit. EDIT: would this one be better? Yet, numerous capture-mark-recapture data sets, from a wide taxonomic range, feature transient individuals. | 0 |
I am very new to semiconductors and I'm trying to understand how photodiodes work for imaging sensors. If I am not wrong, a PN junction is required to detect electron/hole pairs that are photo-generated. The electric field in the depletion zone will move the charge carriers and create a current that can be exploited. Why not only use a semiconductor without doping? And then apply an electric field to the semiconductor: when light is emitted, it slightly improves the material's conductivity, and a current is detected. Why is it not that simple? Thanks | 0 |
The statement reads as follows "If is invertible, there are no special solutions in the null space." According to me, its actually true because if the matrix is invertible, it means that it has full rank, and its null space contains only the zero vector. However, the questions asks you to explain why the statement is false. Is there a way for this to be false? Or, is the question wrong and the statement is true? | 0 |
Not that I work in this field, but I have heard the discourse from several people that string field theory is useless. So I would like to ask two simple questions? What makes SFT so difficult? Especially, it seems to me that one can construct an action that satisfies general coordinate transformation invariance and gauge symmetry (more precisely BRST symmetry) by using the BV formalism, as shown by Witten, but why is this useless? When moving from QM to QFT has several practical benefits, for example, one can easily construct relativistic scattering problems in Lorentz-covariant form, but in what way is SFT superior to string theory? | 0 |
A devout Christian, she plays tennis every weekend. The most beautiful of villages, Ullapool has hosted a food festival for the last twenty years. I see this kind of thing a lot in non-fiction writing, particularly things like short bios/blurbs and tourist writing, where people are trying to convey information but also make it attractive/enjoyable to read. The part before the comma feels like it's introducing the part after the comma, but actually the two things have no relation. Like One of the most infamous mass murderers of his generation, his favourite colour is red. Is it a recognised 'thing' and does it have a name? | 0 |
I'm aware that a semantically complete theory can be undecidable. (I believe it's because only logically valid sentences need be provable for a theory to be semantically complete.) But is it possible for a syntactically/negation complete theory to be undecidable? And do "syntactically complete" and "negation complete" mean the same thing? I've heard that: Any consistent, negation-complete, effectively axiomatized formal theory T is decidable. So for a negation complete theory to be undecidable, it'd have to be either inconsistent or not effectively axiomatized. But I have no idea how a theory could be negation-complete without those two other criteria in the first place. | 0 |
I am having a hard time understanding what eigenvectors and values intuitively represent in an adjacency matrix in a graph problem. I understand in a linear transformation, eigenvectors are vectors that are only scaled after the transform is applied and that the eigenvalues are those scale factors. Is it strictly for computational efficiency that we are so interested in the eigenvalues in graph theory, so we can utilize the eigenbasis for computations? | 0 |
I have these two graphs here: I wish to determine if they are Isomorphic. I know that I need to find a one to one and onto function, however I can't find a way to do it. My questions are: I know that these two are isomorphic. What is the function f ? In general, is there a way to find these functions ? Maybe using matrices ? | 0 |
I've seen diagrams for projectors where condenser lenses focus light directly onto the pupil of the projector lens, after going through the image source. Am I misunderstanding the diagram? If not, why does it focus directly onto the projector lens? I was under the impression that you'd want the condenser lens to form a real image somewhere before the projector lens - that way, the projector lens can image it, like this: | 0 |
Being impressed by Barr and Diaconescu paper entitled "Atomic Toposes" (https://www.math.mcgill.ca/barr/papers/atom.top.pdf), I would like to ask whether it makes sense to investigate "Atomistic Categories", namely categories such that for any object the corresponding poset of subobject is atomistic (namely every element is arbitrary join of atoms). Have these categories been studied, are there non-trivial exaples (the category of sets is an example, but I'm searching for other examples!) | 0 |
I am rather rusty and am reading Topology by Graham and Greene. One of the problems refers to a countable complete metric space. The rationals don't seem to be such a space, because the irrationals are adherent to them and one can form a Cauchy sequence of rationals that converges to an irrational. Thus, the rationals are not complete. Could someone please offer an example or two of countable complete metric spaces? | 0 |
I want to say something along the lines of "We must protect everyone, especially children". But this doesn't exactly work for what I want to say. Because I do not mean that children are MORE deserving of protection in this instance. How can I exemplify a group without raising them up to an elevated status? I thought of "in particular" but this has the same problem. | 0 |
In most material I can find on the cosmic distance ladder for a lay-level reader like myself, it never seems to explicitly say what distance its talking about. There is the proper distance when the light was emitted, and the comoving distance, where the light source is now. The light we are receiving however has traveled a different distance, the light travel time distance, which is less than the comoving distance and greater than the proper distance at emission time. What does the distance ladder actually measure? How could it be less than or greater than the distance light actually traveled? | 0 |
Lenz's law was explained to my class using an example wherein there is a bar magnet passing through a current carrying loop in a gravity free space. Our professor told us that the induced magnetic force is repulsive in nature in order to perform negative work on the bar magnet. The kinetic energy lost by the bar magnet as a result of the repulsive force would be lost in the form of heat in the wires of some internal resistance. If the induced repulsion is because of the heating effect of current, won't Lenz's Law be invalid for resistance free wires, where resistance is zero ? If it is valid, why ? | 0 |
In Landau's book of fluid mechanics, the most general formula for stress looks like this: let's call the eta in picture the first viscosity coefficient, call the zeta in the picture the second viscosity coefficient. I would like to know what are the typical values for these two coefficients for air. I am not sure if my memory is correct, but it seems that the second viscosity coefficient is often neglected. By the way, I am not sure if questions regarding fluid mechanics and CFD are appropriate to ask here, or if there is a more suitable place to ask these questions, if you know, please recommend some to me, thanks. | 0 |
As an Electrical Engineer, I have been studying convex optimization for a while. During my study, I see that most textbook claim that both second order cone programming and geometric programming can be solved effectively with modern solver. However, I cannot find any document that compare them together. So my question is does second order cone programming harder to solve than geometric programming ? Futhermore, is there anyway to come up with a Big O complexity to measure the difficulty of solving them in terms of the number of variables and constraints ? Thank you for your enthusiam ! | 0 |
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