darklight03/StackMIAsub huggingface dataset:
I am an undergraduated student from a non-native English speaking country. In my country, when doing math, which in many contexts that we will be proving something like a theorem, a proposition. What matter is I feel like we don't have a variety of words while doing math. Everything we used in our assignment are just around "we have, we get, hence, thus, therefore, we have this, we have that, we have and we have ...", which is kind of boring to me. I love math and I love solving math problems, but I would love to bring my product with an abundant style of words, just like it's not simply a proof of math, but more like a nice essay of math, to make my products more lively, agile, elegant, refined. So I really appreciate if you guys could enlight me with your knowledge. My very thank you.
We are extracting transformation matrices for different joints from ARKit. These are relative to the parent joint. Since the positions are not very accurate, we have developed a machine learning model that corrects the positions based on ground truth (Vicon data). We only use position data in the model, so now the rotation part of the transformation matrix is no longer valid. My question is: Given that we have the initial transformation matrix (I can have the rotation, scaling, translation separately) is it possible to get an updated transformation matrix that uses the positions of the model? My end goal is if possible to calculate the Euler angles of the updated position for the initial coordinate system. I have checked the Rodrigues' rotation formula but I am not sure if I can use it somehow.
Have an excel financial model, that pretty much is a time series of assets and liabilities. I would like to know what the optimal liability structure / mix is, subject to multiple balance sheet constraints. My objective function is to minimise funding cost. I tried to optimise using Excel Data Solver, but encountered the following issues: Excel may not arrive at a solution (can't converge at times even though there is a solution) Solution is not consistent, eg same starting point (ie initial guess) but different end points (not all are optimum) Solution may not be global minimum Am open to using other softwares like Matlab or Mathematica, with my own "constraints" I won't be able to simplify this down to an analytical equation so will need to be in the format of a financial time series model Ideally arriving at global minimum Scalable Are there any guide you can point me to? Open to software suggestions, algorithms, approach, etc... Thanks
In Meissner effect we say that below critical temperature there is an expulsion of external field lines or field lines do not penetrate inside the specimen. But here is what I am not able to understand, if the sample creates a mystical force which do not allow field line to pass then it can be imagined as if there is an field due to specimen which cancels its effect. I know experimentally field lines are expelled, but why they are expelled I want to know the reason like who are the one that causes no fields to penetrate inside it. Somewhere I have read that a persistent current rises in such a way that it creates a field which cancels the external field. Now how is that possible that a superconductor inside in it already has a field?
I've been told numerous times in high school that "first and second person pronouns in academic writing" should be avoided. This supposed wisdom is echoed in various style manuals as well. However, if you look at any authoritative text, like The Stanford Encyclopedia of Philosophy A simple search of "we" will yield countless articles using the first pronoun all throughout. Given this situation, is it realistic to teach anything stylistically related to using first pronouns? Also, based on experience, trying to stick to this kind of rule damages the entire paper in many ways It takes time to conjure up passive tense sentences which usually is all but required to avoid you/we completely Some concepts more effectively expressed through these words may fall between the cracks and never see it to fruition, which is truly a shame Grades may even suffer trying to stick to the rule -- an irony given that adherence to rules are always motivated by desiring praise and getting good grades, etc. ad nauseum...
Background: ZFC in classical first-order logic. To make a definition, we first need to proof something does exist. So, this question is actually about proving something exists based on a recursion. I know that when you want to prove the existence of a certain function with the domain of ordinal numbers, you can use the transfinite recursion theorem. But our things are not always a function of this sort. For example, when we define the truth value function on the set of formulas in predicate logic, we usually define it recursively based on the number of the logical symbols in a formula(or complexity). But for a certain complexity of the formulae, there're many cases to deal with. I can't figure out how to prove such a definition does make sense, aka the function does exist.
Good day, everybody. I program a simple computer game and there is a "dumbbel" inside of it, which should using some kind of rocket engine. The engine is fixed on one side of the dumbbel and creates a constant force F, which is ALWAYS orthogonal to the dumbbel. Since the dumbbel is ideal, the both sides have only mass m and zero size. The junction is absolut hard, has the length l and doesn't have mass. S. also this figure: There are no other forces than F (especially no gravity) and there are no other bodies than the dumbbel. Therefore no collisions or bumping. The motion happens flat. How can I calculate the trajectory of the "dumbbel"? Is there an analytical or numerical approach I can use in my game program? Thank you very much!
For all the words I know, I can't seem to find the right word for this strange emotion. Some words I have tried come up short in one way or another. Confusion lacks the underlying hatred, annoyance ignores the triggering bafflement, skepticism is to forward to properly describe the abhorrent serenity caused by this mixture of emotions. I tried looking on Google and several other sites for some synonyms for each of them, but my results kept coming up short. Even my 'Better-words-for-authors' guides proved insufficient. I'm starting to think there might not even be a single word in the English lexicon for this emotional mixture that is hatred and anger caused by disbelief. Example of how it could be used: He couldn't help but feel [blank], had the youtuber really sunken below rock bottom. - or - [blank] began to well up inside of her. The others had resorted to Orwellian new speak to justify their problematic behavior.
The normal proof goes as follows: if H(f) is a program that takes the source code of any program f and return whether it halts, we define G to be if(H(G)){ loop forever } else { halt } Which is a contradiction if you run H on G. My problem is the unjustified assertion that a program like G even exists, as presumably it is able to print its own source code and run H on it (or something analogous to that) and halt or not halt based on that. My intuition tells me this violates some information theoretic result I am not smart enough to know about. Furthermore, since we have no idea what H even looks like, this proof only works if you can prove that for every program P, there exists a program G which can print its own source code, run P on it, and then do some stuff based on that. Since the mere existence of Quines, which still conserve information, is already a deep and complicated result (from what I can tell), the truth of Gs existance is sketchy to say the least.
Suppose I have some process that I believe to be the result of a differential equation. It would be reasonable to regard this as the path of a point particle in some notional space. Suppose further that I know the exact shape thaat the path follows, and it is one with a simple description, such as a conic section or a polynomial in two dimensions of low order. Is there a determinate series of steps that will give me a differential equation which has my specified shape as a solution for some initial value, or produce increasingly good approximations of that shape on iteration? If there is an exact solution tell me how to find it. If there is a way to find increasingly good approximations to a numerical solution, describe that way. If the answer or answers to the questions above are reasonably clear and straightforward, but hard to describe compactly, I will accept a citation to a work that contains such answers. However if it is a citation to a book-length work, I want a page range or small number of chapters that contains the answer.
In ceveral textbooks it is said that an ideal LC circuit does not lose its energy, it just bounces from the capacitor to the inductor coil back and forth. On the other hand, any system where charges are going to be accelerated radiate energy (that's should always happen when involved charges are going to be proper accelerated, which is a consequence of Maxwell equations). But then due to this, even an ideal LC circuit should lose after any cycle a certain amount of its energy as radiation, since the charges there are accelerated at all? Therefore I'm confused at that point: Does Bremsstrahlung not occur in an ideal LC circuit (why? That does not make any sense, the charges there are going to be accelerated, so this should give by Maxwell theory radiation losses)? But if this accelerations of charges takes place there, then the energy loss cannot be ignored even in this ideal case, or can it? Does anybody see how to resolve my confusion?
Everywhere it is written that electrons flow through through wire of an eletric circuit, and the reason given is that the battery maintains high potential at one end, and low at another. But, if you think about it from first principle electricity& magnetism, then one would realize by intuition that the provided reason only would imply that the electron would move from the high potential region to the low potential region, not that it takes the specific route of the wire. To find a specific route, it would involve solving of the differential equations. In regards to solution, many places I've seen have written that the eletric field caused by the battery only exists inside the wire, but how do we know that/justify this approximation? I have found this related question, but I felt the answers quite unsatisfactory in regards to the above problem. Also, I Understand that to study circuits, we need more than Maxwell's equations, that is a theory of the matter (charges involved and such) as discussed in this question, but my question is, what is the basis for the justifying that the eletric field is confined to the wire?
Central idea of Michelson and Morley experiment was that if single speed of light predicted is speed of light relative to ether, then as the earth moves through the ether, light travelling along the direction of motion must travel at a different speed relative to the earth and light moving at right angles to the motion. If I get the argument then something like saying say velocity of ball is fixed in air. Then someone watching the ball from a moving train will see the velocity of ball different in the direction of motion. But in the experiment, the measuring apparatus ( equivalent of person measuring speed of ball in train) and the what is being measured i.e. light are in the same frame (frame of earth). Why should the velocity come different in that experiment as they thought? The argument could have worked if someone to look at this experiment outside earth frame? I know I am missing something just not able to pin point.
I don't know if this site is a suitable place to look for examples, but I have a lot of ideas that I would like to find a good example of, and I try to organize these things in a later book. I hope I get to a place where I can discuss my thoughts so that I find people taking these questions seriously, and I think they are thoughts of many people. I am searching for an interesting example/example of a theorem, issue or case in mathematics, in which there is a specific variable that affects the result, while the intuition tells that the result is independent of this variable. In other words, I would like a case where intuition fails to estimate the effect of a factor on a particular problem and one thinks it is ineffective, while reality is otherwise. Are you welcome to find examples of searching for examples on this site?
Urban Dictionary includes one explanation of "play" : Anything to do with sexual relations: fooling around, making out, oral sex or having intercourse. However, most of the formal-language dictionaries don't include this explanation, only interpreting the word as "to tease" which can describe something childlike such as flirtation, except the phrase "play ground" meaning: Having sexual relations with other people who is not your partner. Merriam-Webster Dictionary also suggests "play (n.)" as "flirtation", which can be converted into "flirt" with "play (v.)" Is this a difference between the formal language and slang? This question also leads to an answer which regards "play" as a synonym of "flirt". word for a person that flirts with everyone? Does the slang term have a much broader meanings than the flirty activities implied in the formal language? Does the term imply being unfaithful?
Any introduction of relative simultaneity usually is like this : Alice on a train car shines two beams of light towards both ends where two clock are. She sees both clocks see the light at the same time. Bob on the station looks at the same event and says the trailing clock was hit before the leading clock. I have no doubt about what Bob is measuring, but if speed of the light stays independent of the source, then it should not matter if the frame of reference is moving with the targets -i.e clocks- or not , both Alice and Bob should see clocks are being hit non-simultaneously . Is there any actual experiment that proves Alice is seeing simultaneous clock hit ? I mean has anyone placed clocks on very fast moving objects to prove light hits both leading and trailing sides at the same time ? Or do radio signals arrive at different times to equidistant Eastern and Western stations due to rotation of the Earth?
This question has come up with me in two different Final Fantasy games, where you want or need to collect every memory or skill through random selection where not all memories/skills are available until late in the (main) game (not in the random selection "game"). Collecting a memory/skill does not remove it from the set (you can randomly land on it again) My question is: In terms of getting every entity in the set, does it help (in terms of the expected number of plays to pick every entity) to play this sub-game before all entities have been added to the set (assuming even probability distribution over all entities)? If what I am asking doesn't make sense to you, please ask let me know in a comment and I will try to clarify the question.
I'm trying create a new single-item selection system that has either identical or close to the identical probability of an existing multi-item selection system. The current system has multiple "tables", each containing multiple items. Both a table and each item inside of that table have a selection probability. That is to say we determine if a table is used based off of its probability, and then we go through each item in that table and determine if that item is selected based on the specific items probability. Using the new system, I want there to be only one table containing one item. The one table should have the combined probability of ALL the old systems table probabilities and the one item should have the combined probability of ALL the old systems item probabilities. Would this mean that I would simply find the average of all the tables and the average of all the items and that is the new probability for the table and item? I'm also curious if there is way to shift the old systems table probability on to the item? That is to say, the table would ALWAYS be selected, and the probability of the item in that table would adjust based on the tables previous probability. Is this possible?
In the book To Have or to Be Erich Fromm claims using "have" in English increased due to the rise of the market economy and Protestantism. Where one is alone in the market, with their personal relationship to God, rather than being part of a feudal economy and church where they are taken care of. How well is another conversation, but the point is they didn't talk in terms of how much they personally have so much, unlike in the market economy, where what they have is all they can depend on, with the rise of private property. He wrote that this is the cause of "have" being used in more cases such as "I want to have a party", instead of "I want to make a party", as one may see in other languages. England was ahead of others in the assimilation of a market economy (besides the Dutch). I'm not sure how English compared to others concerning amendability to change though. I did not see similar explanations in the etymology of "have". So the question is, how accurate is his explanation? This question can be answered with examples of people changed lifestyles of people along with changes in language. Things happen for reasons, the answer would give the reason, whether agreeing with the question or not.
When I try to solve a hard problem, I have no idea on what to do before I write anything on the paper: apparently, only after I spent hours on a particular problem I find the key idea by just a coincidence. This makes me feel that training myself by solving tons of hard problems on integration or geometry etc... is a waste of time since for the most of it I randomly run into the solution by coincidence and that is what I mean by randomness when solving a math problem. So my question is: how to overcome that? Should I try to solve each problem on my head without writing down any thing? Or what do you advise me to do? And is this a thing that I can solve or I am just not smart enough?
The main statement is: the EM coupling constant is energy dependent, and the fine structure constant (FSS) is the low energy limit. This means that the flow of the coupling constant vanishes when the energy does not suffice any more to create the lightest charged particles, electrons and positrons (there only remain the classical tree diagrams). Below the electron rest mass energy virtual electrons and positrons are frozen out. Consequently, the FTS is a function of the electron mass, and if the electron mass comes from the Higgs coupling, of the Higgs coupling. All QFT literature is about the scaling limit and high energy (where the electron is effectively massless), and and no clear statements about low energy can be found anywhere. But in statistical mechanics terms the above statement appears to be the only reasonable.
The problem arose of choosing a direction for studying and working within the framework of this topic: neural networks as universal approximators for solutions of partial differential equations. At the moment, as a rule, neural networks are used to obtain more accurate numerical approximations, stable, compared to classical difference schemes. Today, there are many different libraries for training models and predicting solutions. My problem is mainly that I want to try, based on already selected numerical approximations, using neural networks, to obtain a number of analytical solutions. The question is: is it possible in principle to obtain a similar result, and are there any practical problems described in scientific articles in precisely this context (not refining numerical solutions using neural networks, but approximating already obtained solutions and obtaining analytical expression). That is, maybe there is some small problem that has important practical significance, the solution of which can be presented in this form? In fact, my question is quite targeted, since I am not asking for an overview of the available methods for solving partial differential equations using neural networks, but rather solving the inverse problem. In this case, I am more interested in the mathematical formulation of the problem and the mathematical aspect of its solution. If possible, please provide an answer, links to similar topics, and possibly literature. Thank you very much in advance!
I have proven this question but somehow I feel like maybe I have done something wrong or I have been reckless somewhere would you please help me to verify my answer If S is a set with least upper bound and greatest lower bound property assume X and Y are nonempty subset of S such that every element of X <= every element of Y so prove Sup X <= Inf Y I have proven this in the following way from the hypotheses we can conclude everything in Y is an upper bound of X and vice versa. so Sup X and Inf Y exists in s and lets denote them by a and b now lets prove this by contradiction lets suppose a>b since b is infimum of Y everything greater than b is not lower bound and this is in contradiction of a not being a lower bound of Y because a is supremum of X and since everything in Y is an upper bound of X . is my proof true or I am missing something in somewhere?
It is said that if one would attach a load physically to the rotating disc from center to rim no current would flow because both in the load wires and the disc itself currents would be generated in the same directions, everything would cancel out, right? But I don't understand why this is a problem? there is a simple workaround: The wires can lead out of the field or extend far away from the magnetic field range, like so: The blue arrows symbolize induced force vectors when disc with shaft and wires rotates, current should flow from the rim to the center of the disc just like in Faraday brushed version, the upper part of the shaft and the wire does not cut the field lines. However I have build this and no EMF was detected, I don't understand why, the voltage induced in the shaft should not block the current coming from the rim to the center of the disc?
Like 'pretty ugly'. The most used meaning of 'pretty' is contradictory to 'ugly', and it could feasibly be used to mean something like (if it were an oxymoron), 'someone who may be considered ugly, but is actually kinda pretty'. But of course it actually means, considerably ugly. Is there a term to describe such pairings? Edit: I'll add more examples as I think of them: Don't trust casinos, they're fairly rigged. I'm an f'ing celibate. The doctor gave me a sick healthy report. I'm a bad good kid. -- Like they are morally good, but are bad (not morally bad) at actually making much out of it, as some role-models may do. Like they are comparing themselves to others. As opposed to a kid who is generally a good kid, but does still get into trouble some, so they may be teetering on the edge of not being considered a good kid. Which would actually be an oxymoron.