darklight03/StackMIAsub huggingface dataset:
Consider for example the open sentence, x lives in India where 'x' is a variable, which can be substituted by various constants to make declarative sentences. For instance, Harshit lives in India Carol lives in India Zaid lives in India where 'x' has been replaced by constants 'Harshit', 'Carol' and 'Zaid', respectively. I don't understand how do we exactly come to know which constants can substitute the variables in an open sentence. I mean, if someone says, significant substitutes are names of people, in this example, I would say why not of pets? Why not just of people of a particular City or ethnicity? Since, this question is from logic, which is a prerequisite (AFAIK) of set theory, I would humbly expect no notions from set theory to be used.
In the most known incarnations of string theory, we have to compactify the needed, additional dimensions that are then taken to be a.) periodic and b.) "small" in some sense (most of the time their size/radius is taken to be on the order of the Planck length). Some models do propose so-called large extra dimensions but even in these the extra dimensions are compact. Now my question is, are there any string theory models in which some or all of the extra dimensions are non-compact and if there are, can you recommend me any literature? I am thinking of brane world scenarios such as this, but with six or at least some non-compact dimensions (but I would be glad about any example, even if it is not a brane world scenario).
Find the perspective sequence that maps collinear points A,B,C,D to D,C,B,A. Attempt: If we need to find a sequence of three perspectives that (A,B,C)->(A,C,B), where A, B, C are collinear, then first we mark p is a line through A, B, C, let S be some point that does not lie on p, let q be a line through A and S, let p' be a line through A different from p and q, let B' be an element of the line BS and C' an element of the line CS, and let S' be the intersection of the lines BC' and B'C. Then the first pespectivity maps us from the line p to the line p' and has its center in S: A->A, B->B', C->C', and the second one from p' to p and has its center in S': A ->A, B'->C, C'->B.
I would (like many before me) like to take my lecture notes using LaTeX. As writing pure LaTeX-code is very time consuming and not nearly as fast as handwriting, I can only really consider switching to LaTeX if I can use snippets and anything else that makes notetaking faster. I have discovered this post on how to get faster using vim, but at this point I don't really want to learn vim anymore. I know it is very hyped, and probably worth learning, but I have so much else do learn already that I don't know if I will ever find the time. At the moment I am very happy with VS Code (or really VSCodium) for all developing, scripting and stuff that I do, and as I can perfectly do just about everything within this one editor, I would very much like to keep it. Saying this, has anyone an idea or a hint for me on how to set up something like the blog post describes using VS Code? That would be very appreciated.
I am confused whether I should use "a" or "the" when I refer to an object given/identified by some other object. For example: The package is now in [a / the] deposit box with the number you received by SMS. For me this is the deposit box I previously stored the package in, but it seems to me, that for others (including the listener), it is still just some deposit box in the given vault: if I make a typo in the SMS message, my listener may hear from the front desk of the vault: A box with this number does not exist in our vault. Regardless of any such mistake, my assumption at the moment of speaking is that the listener will be able to find or identify the box unambiguously based on the number. Which is the correct article in such situations?
Take a primordial black hole and measure the Hawking radiation over a large amount of time by gamma-ray detectors, as well as a Large neutrino detector. Using theoretical calculations about the composition of Hawking radiation combined with the detected neutrino flux you can determine the neutrino luminosity. Combine that with the luminosity in the form of gamma rays and whatever particles the Black hole is hot enough to produce, and then compare that with the loss in mass over time. If you detect a discrepancy, it's likely the missing flux is in the form of gravitons. Would this experiment work? I did also consider using a primordial black hole cold enough to not emit neutrinos but the Hawking radiation calculator I used gave a black hole lifetime greater than most estimates of the lifetime of a proton.
Many problems in classical mechanics, classical and quantum field theory among others require the study of systems of partial differential equations where questions like existence and uniqueness cannot be answered with the typical counting-equations/variables arguments - questions which have physical relevance and that need to be addressed before going to numerics. For instance, problems in surface mechanics always involve the Gauss-Codazzi equations which is a non-linear overdetermined system of PDE. The most powerful technology to properly study general systems of PDEs are Exterior Differential Systems, and there are some canonical references in the mathematics literature like Bryant et. al. I found this challenging for a standard theoretical physics graduate because it requires a solid background in non-conventional math topics for physics like commutative algebra and number theory, so I wonder if there is any reference treating EDS for physicist.
I'm looking at a few English sentences, and I've realized that many verbs can be used as nouns in their infinitive form. For example. I am going on a run and in the present tense I am running. There are many more verbs that this can be done to. Are you going to take the jump? Why did you do three pitches? You know he would have hit one of them. (baseball) Can you please do your exercise elsewhere? It is too loud right here. So 'pitches' in the example is not in the true infinitive, but is in the plural infinitive, so this may not be a true example. 'jump' and 'exercise' are however. Normally, I would say that these are gerunds, however, after looking online for a while,. it seems that gerunds always use the present tense, and never the infinitive. What is the name for these verbs that can be nouns when in the infinitive form?
I'm writing longer mathematical texts (lecture notes) regularly, and I don't know where else to ask this question. I regularly find myself enunciating (in the typographical sense) every statement I make. This means that I will put any even vaguely mathematical statement, not only theorems, corollaries, definitions, etc., into an enumerated environment in Latex. As of now, I always use Remark for them, and I feel like I'm overusing it. Question: When do you write mathematical comments in some numbered environment, like Discussion, Observation, Remark, Idea, etc., and when do you write mathematical comments standalone in the running text? What other environments do you use to mark up mathematical comments? Edit: The reason why I enunciate this often is simple: Later on in the text or in the lecture, I might want to refer to this comment. E.g. in a mathematical comment, we combine all results in an informal discussion on how to compute fibres of maps between prime spectra. This result is somewhat important as it will come up every now and then, but its statement in the lecture was more or less like an argument, making it difficult to encase this as a corollary.
I have written a long book in latex memoir. I now want to feed its content to a machine translator into another language (say, German). I will use the automated translation for a first pass for a better human translation. Translators do not understand latex. There are a couple of methods to go about feeding them. I could use some online latex parsers, write a quick parser myself, etc. It occurs to me that I could also ask latex to create a pdf that is better suited to pdftotext (poppler). It should make big spaces between paragraphs, not break paragraphs across pages, etc., probably take out tables and figures, page headings, footings, and sidemargins, footnotes. (Eventually, I will also need to write a parse-match to integrate the translation back into a latex document that uses the original structure, but just replaces the text. Thus, I am thinking of adding a number for each paragraph, so that I can take the translation input and output and reconstruct a latex file.) Has someone written a style file to improve the results of pdf text extraction? or found a better solution?
I am trying to learn about neural networks. I was reading the paper An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem which uses graph neural networks such that given a graph we get a hamiltonian cycle which hopefully is nearly optimal. However, they use as ground truth the concorde algorithm, which when I ask google and chat-GPT seems seem to be an exact algorithm but in section E (solution visualization), there are some cases where the author say : The model predicts a shorter tour than Concorde for this instance by choosing a different contour around the nodes at the top-left of the graph But how can it be better? Doesn't concord compute the optimal solution already? Did I get something wrong about the traveling salesman problem?
i have taken two course in complex analysis, one variable and the other in several variable and the begining of complex manifolds, my understanding in one variable go well but in several variable our prof use two books, one of krantz and the other of Hoermander, i think due to my lack in the theory of integration(multiple and differential forms integration) i don't understand some proofs,in particular some construction for Hartog's extension theorem and the other about separate Holomorphicity And this brings me to my questions: do you think a good understanding of Lebesgue integral and Mesure theory can replace Riemann integration theory. what to study in complex analysis to develop geometric intuition,in particular for abstract algebraic geometry and sheaf theory, and if possible is there an approach that don't depend on functional analysis and PDE. and thanks
I use LaTeX for a lot of my classwork (worksheets, graphics, etc). One thing I have not transitioned is my exam writing. An example page of an exam might look like this. This is just a portion, doesn't have the header and such, I'm comfortable working with those. I've not moved to LaTeX because of my need to be placing the answer boxes and blanks in specific spots on the page, and it's frankly pretty easy to drag little rounded text boxes around MS Word to achieve my layout. But there could be a fair bit of programmatic benefit in being able to make some of those blanks more consistently, layout chemical equations more simply, etc. I also have a page of multiple choice for each exam that I'd love to shuttle off a lot of that layout work to LaTeX. Is achieving looks like this reasonable with enough flexibility to be able to shift around those blanks and such on a question-by-question basis? I've found this page about using a zero-sized box. Seems like it be applicable, but just want to check before I start down this path. Any resources or general code ideas for doing what I'd like would be appreciated. I'm sure in the future I'll come back with some MWE, but for now just gathering info on even executing this. Also if the answer is "Probably more work than it's worth and keep using MS Word", I can accept that too :)
I am posting the specific problem I am dealing with for reference and then explain the part I am confused with. My Understanding and approach to the problem I identified that in the ground frame the disc will have some inertia and thus simply remain stationary as the plank below slides away.When viewing from the plank's reference frame it's acceleration will be added to the COM of the disc in the opposite direction.So initially the instantaneous center of rotation is at the exact center. The Confusion I am unable to visualise how the instantaneous center of rotation will change as the COM gains velocity due to the acceleration. The solution that I found said that the points that have tangential velocity along the acceleration will have some added velocity while those against will have some net velocity in the direction of the acceleration.According to me if that happened then the rotation would completely stop which does not make any intuitive sense. Here's the solution for reference Conceptual Confusion The main concept I am struggling with is the instantaneous centere of rotation of the disc.I tried reading up about it on wikipedia but that doesn't clarify it for me.
This question is born out of the riddle where there are two characters, one that always lies and one that always tells the truth, and you want them to tell you which of two doors is the "good" or "bad" door. You can ask either character, "what would the other character say is the good door?" And the lier will answer with the bad door, and the truther will also answer with the bad door. My question is a variation, given two characters where each character might always tell the truth, or might always lie, but both characters think the other always tells the truth, are there any questions you can ask that allow you to determine more information about the composition? For example it could be that character A and B both always tell the truth (and each thinks the other always tells the truth) or it could be that character A and B both always lie (but again each thinks the other always tells the truth), or it could be that one character always tells the truth and the other always lies (but again they both think the other always tells the truth). Are there any questions that can be asked to determine the composition?
Is there a possible slight difference between protons and electrons behaviour while they are accelerated at speeds that cause relativistic changes to their mass. Why am I asking that? Because for a proton we know that it is made of several components which of them are the three quarks. If they have some speed inside the proton it is logical that this is not the same as they have no any intrinsic speed and that this speed does not matter as a portion that is added to the overall speed of the proton that is accelerated to a relativistic speed. Should that small part of the overall speed make a difference between the theoretical calculation of the particle speed to relativistic mass ratio and the empyrical results as the theoretical calculation threats the proton as an elementary particle because the intrinsic speeds of proton components are neglected in the formula?
An electromagnetic wave is usually illustrated with two sine wave shaped fields, one for the electric field and one for the magnetic field. As in the picture below: But as how I understand magnetism, it consists of two poles, north and south (alternatively described with field lines, with a direction, where north and south connects). So to focus only on the magnetic field (the red, B) in an electromagnetic wave; where are the poles located in such a sine wave (the red part)? Is only one of the poles illustrated, such that another sine wave could be added for the other pole? Update: In this video, Maxwell's second equation is described as the field lines in the magnetic field is always connected (north and south pole) - how these field lines are organized in a wave is what I don't understand. Later in the same video, the fields emitted from an antenna, are illustrated as "bubbles of fields" - quite different from how the "arrows/vectors" are illustrated in my picture above. Field lines from the video:
Lill's method is a visual way to find the real roots of a polynomial equation. It involves drawing a straight line with lengths equal to the coefficients of the polynomial. The solution can be found by using a slope of a right triangle. Lill's method - Wikipedia The values of a polynomial function can be "defined" as a distance between the vertice of the last polynomial coefficient and the path that we draw using right angles. Polynomial function's value Cubic function with defined function's value What I want to do is to find the local maximum and minimum in Lill's path. So, I'm curious if I can "define" a line that represents the first derivative of a cubic function and let it equal to zero, or if it can't be done. What I have done is by using the derivative's definition, and I got that a point (P in the picture) is the derivative of a function which its value is zero. But I think that's not the correct way to do it. My way to do the derivative in cubic function I drew the function and its derivative with the same "first coefficient" Please correct me if I'm wrong, Thanks.
I need to retrieve Roll and Pitch (but not Yaw) rotation values from rotation matrix (or euler angles, or quaternion, input can be different, fortunately, it can be converted from one form to another). [Info table] X points Left. Y points Up. Z points Forward. Rotation around local X axis is Pitch. Rotation around local Y axis is Yaw. Rotation around local Z axis is Roll. If I just use Euler Angles then, in some situations, I get wrong values. As I think, this due to rotation can be represented with multiple variations of Euler Angles, so it breaks when rotation around X axis (Pitch) and Z axis (Roll) is represented also using Y axis (Yaw). gif (How it works | How it should be, but I need rotation without Yaw axis) Also algorithm is running in time, so, solutions, computing some delta rotation, are also accepted.
When fluids are subject to external perturbations or put in certain geometries, they always show arguably the most fascinating structures : Starting from the eddies and vortices in pipe flows at large Reynold numbers, vortices of flows past an obstacle, or the vortices in fluids confined between two rotation cylenders. Yet, a fluid at rest is often thought of just as a completely structureless phase : Apart from very small-scale features such as the arrangement of nearest neighbors or solvation structures in liquids, it is just a random phase and the trajectory of a tagged particle from the fluid simply obeys the Brownian law, without any other features. But what I somehow intuitively expect is that most of the above mentioned "non-equilibrium" structures appearing under well defined conditions are present in the resting "equilibrium" fluid. This means if were to look at the trajectory of some fluid particle I expect to see imprints of the coherent non-equilibrium structures in the equilibrium trajectory, and not just see a Brownian trajectory. Can you somehow relate to this ?
Lets imagine you have a universe where the average matter density is extremely close the the boundary between one that will expand forever and one that will eventually re-collapse. Now lets imagine that there are very large scale fluctuations in density at the Gpc/Tpc scale and above. Could this result in differences in the rate of expansion between some parts and others, causing parts of the universe to collapse and parts to expand forver? If yes what would this look like near the boundary? What if the region was non simply connected. (E.G. a torus, or hollow ball.) How about a universe with bee marginally above the critics density with some very large under dense regions, perhaps ones large enough for the centre to become causally disconnected form the edges.
There is a good discussion here (Referring to past times with "hence") that concludes that hence can't be used like "ago" to refer to a past event, not even to describe how much time has passed "since" that event. However, what if using the past perfect and then referring to time forward from that point, Could "hence" be used there? The specific construction I'm wondering about goes like this: They had left me there to die. Even now, one-and-a-half moons hence, it would be a simple matter to follow their trail. In that case, "hence" is a time forward from a point in the past as made clear by use of the past perfect ("had left me"). Is that appropriate usage, or can "hence" only refer to the actual future, not a future relative to a point in the past?
There is a closed continuous loop, and you have a stick of a random fixed positive length,so that You can slide the stick on the loop. Take the stick's midpoint. It's track will form another closed continuous loop. Take another stick of another random fixed positive length. Slide it on the new loop again. It's midpoint will form another loop. Do this again and again. Will the shape of the loops tend towards a circle(well, the area of the loop may decrease, but you can magnify the area to not let it become a point)? Or could it become another shape? The thing I found was that circles and ellipses will tend towards a circle, and I think the question is intuitive, because this operation of sliding sticks round's spikes and makes concave shapes convex.
Imagine a ball with diameter "a" at rest and another observer at rest at a distance of 'l' w.r.t to the ball in this rest frame.Say the ball suddenly starts moving at velocity v towards the observer .(Assume it accelerates instantaneously).What does the observer measure the distance between them?What does the observer measure the diameter of the ball to be?If the diameter is contracted by gamma factor then why is not 'l' contracted by the same?Because acc to me by time dilation,as the time interval is zero wrt to the observer between the events (ball moving and ball at rest),so the distance moved is zero acc to observer and hence observed distance remains 'l'.I asked my professor,he also said that diameter would contract but distance of ball wrt observer wont , but I didnt understand why this partial treatment of two lengths ?.They are identical in properties with regard to lorentz transformations so if one contracts wrt observer the other should also.
Maybe this belongs on "Linguistics" but since it's about an English word, I suppose they'd only send me here. Over time, some words gather more and more meanings to themselves. Ironically, these words are often small like, "by". Other words seem to shed meanings, or rather, they devolve meanings to new words. In the New Testament, Jesus tells people to "arise" from their bed, elsewhere "the resurrection" appears. But this is actually just the noun form, i.e. "the arising." Now, no one except by poetic license would refer to their "resurrection" from bed; it has become a specialized form of "standing up" (from death.) Is there a pair of words to describe on the one hand the accreation and on the other the fragmentation of words and their meanings?
In my current understanding, I have been told that the spin of quantum particles is simply intrinsic to them. That, particles are simply right-handed or left-handed... just because they are. To me, that seems then that we should then treat handedness like it is just as distinguishing of a property as mass, or charge, or color charge. Almost like the standard model should be doubled, or mirrored. Like, right-handed, blue, up quarks should be considered as a wholly different particle from a left-handed blue up quark. But wouldn't something HAVE to catalyze the spin? Like a ball rolling down a hill hits a rock, and how it first strikes that rock determines whether it continues its rolling spinning to the right or to the left. Could spin be acquired, for instance, during the big bang, by the first interaction of a particle as it "hits" the higgs field? And some characteristic of the particle to that point determines which way it "glances" off of the higgs field?