darklight03/StackMIAsub huggingface dataset:
I know multiple singular subjects have been addressed here and singular compound subjects here. However, I came across a sentence with multiple subjects, one single paired with one plural. I could not find this question addressed. For example Does a table and four chairs sound like sufficient furniture for a breakfast room? That doesn't quite sound right to me, but then Do a table and four chairs sound like sufficient furniture for a breakfast room? also sounds a bit off. Which would be correct? Or are both incorrect? Purdue uni subject-verb agreement is confusing.
An intuition that I thought of about a year ago, but my level does not allow me to prove it. I think it needs advanced tools to prove it, or just a counterexample to refute it. Who can help, please, thank you. The locus of the point of intersection of the perpendicular tangents of a convex curve is the convex curve Of course, the intuition is only in this direction and does not constitute an obligation, as the cardioid is a concave curve. Despite this, tracing the perpendicular tangents to it gives a circle
Using Hugyen's principle and wave nature of light, refraction, diffraction are relatively simple to explain but I have been visualing a mental model for a couple of days where the photons on reach the boundary of two media, experience a difference in the structure of the medium of propagation and hence some sort of collision or change in the overall velocity vector of each photon occurs which leads to refraction. Can someone help me understand these phenomenon using particle nature?
how one would know that the given frame of reference will be inertial or non inertial, without the use of 'accelerometers'. earlier physicst has defined this concept and I am sure that they define it without the help of accelerometers. I just want to know about the logic behind the whole concept. And I will be not getting any accelerometers in my exam and not able to conduct any experiment in the frame. i want to know how teachers just say that this frame will be inertial or not without any accelerometer.
How come there is no loss due to coupling between the superconducting channel and the single particle channel? I imaging the two channels being two parallel wires, so the magnetic field from the current running in the superconducting state, should fully inclose the single particle channel generating a electric field, that at least would create a displacement current and introduce a loss. Why is that not so? Also is there no current fluctuation due to the current being carried by discrete charge quanta? I would assume that, that would also create a electric field fluctuation in the single particle channel causing a loss?
I posted about monoid coproduct to try to understand the correct way for constructing them. In the process and from the answer I got, I am further confused whether the product and coproduct of plain monoids compare free monoids, what are the subtle differences in terms of what they look like. I understand in both coproduct of monoids and free monoids, the process of word reduction to strings are applied. I don't know anything beyond that. I am hoping someone can explain to me their subtle differences. Thank you in advance.
If we add a constant to both sides of an equation, we will get a new equation with identical solutions. This is mostly true for multiplication and square roots, but there are some minor complications/exceptions. Taking the derivative of both sides will result in entirely different solutions. Is there a formal way to show how performing some operation/action on both sides of an equation will affect the solutions of the resulting equation?
This is a question about grammar, in particular about a specific language syntax. In the german langage it's legit to write negative prefixes in braces like "Die JSON (De-)Serialisation wurde implementiert." Is this valid in english? "The JSON (de-)serialization has been implemented." As a software developer I need to document the work I've done and the software functionality itself. I often have a lot of language constructs similar to the one above. And if it's legit to use this syntax of negative prefixes it would save me a lot of time.
I wonder whether there is a space filling curve that looks like the following if the width of the domain has an odd number of cells and looks like the following if the width of the domain has an even number of cells. I would like to fill a three dimensional grid none of whose sides (lengths) are guaranteed to be a power of two or even.
How is it paradoxal that a set of all sets exists in set theory? Russel's paradox is about the set of all sets that do not contain themselves cannot exist, that I understand. But what about the set of all sets, in a unrestricted manner? Is it the fact that it contains itself (which may be what allows to define the paradoxal set of Russel's paradox) that is problematic?
Is the result of a contour integral around a closed loop path unique? I'd think it'd be similar to a definite integral, which is unique. This came up regarding the proof of uniqueness of a Laurent Series - if the contour integral is unique, then the definition of the Laurent Series can be used to prove its uniqueness. Edit - as pointed out below, the Laurent Series aspect may be a limiting case, as it's within a specified annulus, so for any of the Cauchy coefficients, the same analytic annulus is used, so the same number of poles will always be within the inner radius.
Is it true that if a curve is increasing, Euler's method will always underestimate an actual solution? So if a curve is either increasing and concave down, or increasing and concave up, we can simply ignore concavity and justify the answer based on the fact that it's increasing? Euler's method will therefore underestimate whenever the function is concave down and increasing, or concave up and increasing?
There are two machine learning models, A and B. Model A classifies samples into 'O' and 'G'. Model B classifies the samples determined to be 'O' into 'S' and 'C'. Each model shows the probabilties of classification. Input samples pass through model A first, and if the result is O, then they enter model B. (If not they don't) In this case, how could I get the probabilities of classifications, G, S or C?
What is a good, up-to-date, well-regarded text on writing physics solvers for (e.g.) game engines or realtime simulations? In particular, treatment of numerical stability, convergence, asymptotic complexity and performance, contact forces, and the handling of constraints are relevant to me. I have solid familiarity of university level physics, calculus, PDEs and ODEs, and linear algebra; and these can be assumed as prerequisites. (An ideal book would be the analogue of Pharr and Humphreys, but for simulation) What text(s) should I consult?
In a Euronews headline I saw the following: Frontex: What would happen if the EU border agency quit Greece?. Shouldn't it be "quits Greece"? As far as I understood EU border agency is singular. Reopen note: Although the original close vote as a duplicate was accepted, Stuart F has since pointed out that the real issue here is that quit is probably past tense. I agree. The 'duplicate'tag here might wrongly lead readers to assume that the issue here is simply about singular/plural subjects.
When I'm not writing a math paper, I write way faster by typing directly into a word processor. I form and revise sentences faster on the screen then I can on paper. But typesetting math is slower than handwriting, and I think better with a pen. I already know it's best to handwrite symbol-heavy text before typing, but what about text that's symbol-light, like an abstract or introduction? Should I write almost the entire paper by hand, or only the math dense portions?
For no reason other than my own curiosity, I have been trying to figure out the solution to the following question: Given a bag of x marbles, what is the probability of having seen every different marble at least once after y draws with replacement? I am interested in making different graphs for specific values of x just to know what it would look like but I can only figure it out when x=y. The moment y>x, I do not know how to approach it. I have scribbled on more pages than is reasonable, so I hope I can find an answer here. Thanks!
We could say it was painted beautifully to convey that the way it was painted was beautiful. "beautifully" being the adverbal form of beautiful (an adjective). What if the adjective is "lovely": How would you convey that the way it was painted was lovely? Is it: it was painted lovelyly This sounds/feels weird and I have never heard/seen it used. Furtherm "it was painted lovely" seems an error of grammar. Is there a rule/guideline that adjectives ending in "ly" have no adverbal form and can't be used as adverbs? Or should we just use the adjectival form for the adverb even if it is grammatically incorrect?
I'm studying instability in Stellar Dynamics (in particular globular clusters instabilities). I have not understood clearly the definition of these concept. Dynamical instability is the study of the instability considering an adiabatic process: we perturb the system and see what happens. Thermal instability happens at much larger timescale than the dynamical one and is due to the exchange of energy between single stars (and since the thermal capacity of the system is negative, this process brings phenomena like the gravothermal catastrophe). Am I missing something?
I want to make a robot that solves a hand-made maze, so that I want to provide it a LIDAR component to measure the distance to read the environment. Before buying a component I want to know if it's capable of measuring distance to a rotated surface. Under rotated surface I mean a wall that is not perfectly aligned with the LIDAR emitter, see the image Is it even possible that the light beam ever reach the LIDAR's receiver and how accurate the measurement can be?
I have read everywhere that the gold foil experiment performed by Rutherford was done hoping that the alpha particles face only a little deflection/no deflection however this doesn't sit right with me, the old model of Thomson clearly shows that atom is a positive sphere with electrons embedded in it, what made him think that positively charged alpha particles moving through this atom wont face a repulsive force from the positively charged cloud?
What exactly would happen if we sent a frequency that was not one of the harmonics into a closed and open pipe? What would happen if we gradually increased this frequency? From my understanding, I think if we were to send down this frequency, a standing wave could not form, so when we gradually increase this frequency, as soon as it matches the harmonic a standing wave is produced and max amplitude creates a loud sound. Would this be correct?
In principle, the comparative form of polysyllabic adjectives has "more" before the word, rather than taking a suffix "-er". But why do adjectives ending in "-y" often take the suffix "-er"? For example, "luckier". (and the same for superlative) Regardless of which from "more lucky" and "luckier" is considered correct, many people use the latter anyway, and it also applies to other words that end with "-y". So why are polysyllabic words ending in "-y" an exception?
In first-order logic, one has a way of constructing all sentences out of some logical symbols, as well as function and relation symbols pertaining to a special kind of signature one is in. Now in the book of Mac Lane on category theory, there is a similar construction, where the atomic statements (instead of only being things like equality over a single structure) involve also things like the domain of an arrow, where there are both objects and arrows, for instance. I would like to ask whether there is some widely used general construction that generalises both.
What do you call it when someone is being back-handed in a way that looks and sounds nice outrightly but is intended to be mean? Passive-aggressive is too obvious. The equivalent to Bless her heart. The rudeness would be hard to tell to anyone who wasn't there to see or wasn't aware of the person's dislike for someone. Typically the person believes it goes unnoticed by the "victim."
A large regular hexagon is cut out of a triangular grid and tiled with diamonds (pairs of triangles glued together along an edge). Diamonds come in three varieties, depending on orientation; prove that precisely the same number of each variety must appear in the tiling. This puzzle is from Gurmeet.net's Tiling with Calissons puzzle page. The "Proof without Words" solution is accompanied by this image: My approach: I tried reading through the solution but it simply blows my mind. The proof without words, how did they even come up with that? Any clue how to start/proceed will help.
I have come across them in a thrift shop and completely fell in love with the method employed by her. Almost nothing is taken for granted and everything from the definition of subtraction to the addition propert of equality is first demonstrated (or proved) before being employed. I have picked up Serge Lang's Basic Mathematics with the hope of reviewing Dolciani's exposition of high school algebra through someone else's words but the book failed me as it doesn't go deeper than your usual half-baked modern algebra book. I don't want to move on to reading the first chapters of some abstract algebra books as I don't know the notation much. Do you guys know of any other book similar to Dolciani's in method of exposition?
On high slopes and rugged terrains, riding a bicycle while standing on the pedals is easier. Even though I cannot physically define what is "easy"; since it is a feeling that my body generates based on the ratio of work output to the energy expenditure and degree of tiredness of my muscles, I am pretty sure a humanoid robot moving exactly like us would also spend much less energy standing and cycling. Why is it so?
Is there a word for people you like but are a pain in the ass? Nothing too vulgar. I am not looking to call someone it, but affectionately think about them "that person is a complete [word]". It's for a friend (of the opposite sex, though I don't necessarily want to signal that here). oh God Debbie, can you stop being a [word] I was thinking of 'frienemy' but that may be the opposite. I was also thinking of 'difficult' but it's potentially offensive and patronizing.
I am studying trigonometry and have wondered if there are generalized power-reduction formulae for sin^n(x) and cos^n(x) yet the best that I found was formulae for odd and even powers on Wikipedia without any proof. Could you write a formula for sin^n(x) or cos^n(x)(if there are any) and a proof if it is possible? I will be thankful! (Also sorry for the wrong tags ) : . I just could not find five accurate tags for the question, my excuses.)
Does spacial coherence mean that if I took a cross section of the laser beam beam, then I can find a relation between the phase of the electric field between any two points across the cross section even after the elapse of a very long time? Whereas the highly temporal coherence means that I can predict the phase of the electric field at any point across the cross section even after let's say a big amount of time?
I have three scenarios: The following setup will experience an induced EMF since the area covered increases with time. (Shaded in orange) If instead of a wire/rod,we had a coil moving within the field, there would be no induced EMF for a constant magnetic flux density since area covered by coil is fixed and does not vary with time. The question is if I have something similar to the first scenario (in that a rod is used) but without borders, such that entire rod lies within the field (like the second scenario), would I get an induced EMF? If yes, what would be the change in area?
Essentially what the title asks-- are matrix models, such as BFSS, believed to capture in any way the large possible space of false string vacua, for instance as saddles in the action with nonminimal energy, in such a way that the dynamics of settling into a false vacuum/metastable state could in principle be probed with such models? This would be from the perspective of answering questions about the "cosmological prior" that people sometimes gesture to in the context of anthropic arguments for the values of certain couplings.
Let's take a hypothetical an experimental scenario where a stream of high-energy photons from a powerful source is directed via a system of mirrors and lenses in a two coherent rays to a vacuum camera. The photons collide in the vacuum camera, producing positron-electron pairs. The pairs are promptly separated before the annihilation by two coils, which lead into two vacuum tubes, that serve as entrances to electromagnetic toroidal containment units that "speed up" the particles, and prevent them from touching the walls of the units. What kind of problems would prevent such a setup from working as intended?
I'm studying method of undetermined coefficients and i can understant what is its idea. But i'm ambiguous when we can use it. Of course, it is obvious that the differential equation is nonhomogeneous. And wikipidia says as following: Undetermined coefficients is not as general a method as variation of parameters, since it only works for differential equations that follow certain forms. But my book or wikipidia don't say the equation need to be linear or non linear To apply the method of undetermined coefficients, the differential equation have to be linear? or non-linear or both?
So, I happened to be reading a grammar book in which I came across this weird looking sentence. This is the car of which parts are not available now. I think it should have been something like this: This is the car, parts of which are not available now. If the improvised version is correct, I do not know why. Can you guys help me with such constructions?
I need some advice on the use of these two words - update and refresh. I am currently working on the desktop app and I need to give a button a correct name. There is a big number of objects that an app stores in the database and multiple users can work with them simultaneously. If one user changes an object, it gets changed for all the other users. And this button can disable or enable this function. I consider two names. Data Auto Refresh and Data Auto Update. Which sounds more native? And is there any significant difference between these words?
I have a theorem in the form : if A is verified and B is verified and C is verified then D is verified. I'd like to show that we can't do without hypothesis C. How can I do this? Do I need to find an example where I have A, B and non(C) which are verified such that D is unverified? If I do this, what will I have shown?
I am not well-versed in the research on topological solitons but am interested to make a good sense of its implication. The highly interesting point in this new talk by Nick Manton was where he is noting that multiple vacua can be modeled using solitons. But are these multiple vacua simply degenerate in energy? Or we can consider non-degenerate multiple vacua in different regions of space?
I am reading Hiroshi Kunita's lecture Stochastic Differential Equations Based on Levy Processes and Stochastic Flows of Diffeomorphisms.It proves Ito's formula for cadlag semimartingale. Kunita's proof The proof is concise, but I doubt that it is not correct. Right in this picture, it constructs a function r(x,y)(in the first highlight), and claims that it suffices the identity(in the second highlight), but I just found the identidy is not valid since we can not get F by the integraton of the second order derivative F'' (this will only get F' instead of F). So I think this is proof is incorrect. Did I make some mistake?
In modern day PV cells you usually have a silver-based grid on the upper end of the cell where it's exposed to the sun creating the optimization game of how thin/thick you can make your busbars and fingers so that maximum current can be passed without covering too much of the silicone surface blocking the sun's exposure to the n-type surface. In the early silicon cells they used to design the cells in the following way: Source: https://www.pveducation.org/pvcdrom/manufacturing-si-cells/early-silicon-cells Why did they stop with this approach? Was it just fabrication costs? This seems more intuitive as you're maximizing the surface area of the layer exposed to the sun?
Following this post, I did this: [Options] --> [Adv. Editor] --> [Special options] panel --> [Go to error when displaying log] which however doesn't resolve my issue; after compiling, the cursor is always stuck at the same place. I'm suspecting some part of my code is colliding with this functionality, but cannot figure which. Edit: I tried unmarking the checkbox for "Go to error when displaying log" and it is now working! I thought it should be marked, but it seems not.
A recent paper "Gravitational Pair Production and Black Hole Evaporation" (discussed in short here) says that any spacetime curvature would produce Hawking radiation, no need for event horizon. If this is correct then a question arises - how negative energy would take energy from observable object? Fermion cannot be partially annihilated and full annihilation is way more energetic then Hawking photon. So the only source of energy would be object's heat. But would that mean that object with temperature near absolute zero would stop radiating? There is nothing about temperature in equation. Does it mean that the paper is wrong? Or is there any mechanism to provide Hawking energy from object's mass? P.S. "Black holes are white hot" Hawkins:
Here are two sentences that sort of mean the same thing, but need your help in identifying which one would be more appropriate. I do already have an idea as to which phrase would be more appropriate but I still chose to go with the other one. His mind pushed back, but he kept willing it to do all that it still could. His mind pushed back, but he kept wanting it to do all that it still could. Does using 'wanting' instead of 'willing' drastically change the meaning here? Since will is more of a statement of commitment, 'willing' might seem more appropriate here. But in some cases using want in its place doesn't change the meaning.
Inspired by Are the visible matter and dark matter separately segregated? I wonder if the constituents (I don't say particles, as we don't know) have actions and forces among themselves, that we cannot detect directly from our observable matter. Might it be that there is a mirror world with the same forces as in our observable world, but just within themselves? Maybe even more than one, given that the dark matter has more mass than the observable one. As of now, we can "observe" the dark matter only by interpreting gravitational effects. If there should be any internal forces in dark matter, there should be a difference in clustering. Unfortunately, this is hard to detect. Is there any theory about that, or experimentation going on, or even results?
Imagine there is no EM or Nuclear Force, and Gravity is the only force. Can gravity alone produce an atomic structure similar to a basic atom? In this scenario, the nucleus is just a single particle. The electron is another particle with only mass and angular momentum, like a planet orbiting a star. How feasible is it for Gravity alone to produce such a structure and hold it together, with energy and mass equivelent to those of simple hydrogen nuclei, electrons and matching speed/energy of orbits and angular momentum
Let's assume we have two charged free particles with the same energy coming toward each other. What will be the time-dependent perturbation in this case? More precisely, I am asking what will be the change in Hamiltonian due to which perturbation is happening? Is it the Columbian potential only which will change? If yes, then how will it change as a function of time? Am I missing something very basic here? To provide more context to this question, I am trying to figure out how the Hamiltonian changes in a muon production process through electron-positron scattering. That is The form of scattering amplitude M .