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I want to confirm if I understand something correctly. We call the "high potential terminal" the positive side (cathode). Though, electrons move from negative to positive. Logically, electrons' potential energy is decreasing so the high potential terminal should be the negative side. In my opinion, from the electrons' ...
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I want to minimize the amount of unused space in a binpacking problem. I keep seeing binpacking being described as using the least amount of bins possible. Example (emphasis mine): assign each item to a bin such that number of total used bins is minimized https://www.geeksforgeeks.org/bin-packing-problem-minimize-numbe...
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I am building a database of sorts and came across this question. I am looking for a word that includes every region that is declared and made up by humans. So no natural regions like forests or continents, but regions that are generally associated with the people residing within its borders and other human-related stuf...
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In the sentence below, Greenland may not be as "green" as the name suggests. The verb "suggest" should preceed an object as it is a transitive verb, but in the sentence, there is none. In this case, should the second "as" be understood as some sort of relative pronoun though there is no noun? Or should it be understood...
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What would be the best books covering topics like Algebra, Geometry (Euclidean geometry) and Calculus? Which classics can be recommended (classics in the sense of historical works that have been widely disseminated throughout the history of mathematics, for example: Euclid's Elements)? I would like to have an overview ...
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A sphere with a radius of one is put inside a cubical box with circular holes cut out such that the ball fits perfectly. The box and the sphere share the same volume; find the surface area of the box. I tried cutting the cube down the middle to get a square and a circle. I then tried to find the distance between the tw...
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I was watching this video. It Showed that light ( green ) changes its color to red after incidence of light. I couldn't think of how this happens because light's color is dependent on frequency rather than wavelength and only the wavelength changes when light enters a new medium , according to these answers on whether ...
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A student asked how to integrate tan x and he was trying while using integration by parts. I taught him the substitution method but he then asked why we can't use integration by parts. My immediate thought was it is possible just much more complicated but in trying it out, I can't seem to do so. Is it simply not possib...
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I am doing some work on the topic "Adjunction" and my current interest is to give some examples. I've wanted to provide some examples connected to some basic concepts from analysis on manifolds if such exists. What I thought maybe would work is the following: Tangent space functor and cotangent space functor Tensor pro...
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If you take an axiomatic view of Classical Mechanics and the concept mass as primitive in this context, you could derive from Newton's laws an operational way of determining masses simply by arbitrarily assigning a mass to an object and demanding momentum conservation in its interactions with other objects. But if ther...
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I'm trying to connect the calculations for the determinant I'm seeing and the idea that the determinant is a signed measure of the factor by which the volume bounded by the basis vectors of a vector space changes when those basis basis vectors are acted on by a linear transformation. Does anyone have a good way of conn...
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In a PhD thesis we have to write a preface wherein some significant theorems from the main body of the thesis are needed to be restated. The amstools or thm-restate package does not help me in this regard. In this package the restated theorem must appear after the original theorem is stated. Till date I am doing it man...
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In quantum field theory, it seems that when we consider a massive particle's spin degree of freedom, we usually do in the particle's rest frame. And I know the little group will only change spin DOF and leave the momentum unchanged. My question is: If there is a Lorentz transformation that only change the momentum of t...
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I'm trying to calculate body trajectory that launched by some impulse. I have two points: start position and finish position which can be located on different heights (points is not symmetric). I know the height that body will reach, so parabola's vertex located that height higher of first point. Vertex located between...
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If time measured by one observer moving at a greater velocity than another observer is observed to be passing more slowly, does this imply that there's such a thing as "absolute time" or "base time" which would be the passage of time as measured by a completely static observer of the universe? Basically time as measure...
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The pressure at a point inside a static fluid is same in all directions because the the collisions of particles take place isotropically. However, at the same time pressure increases with depth. So downward pressure must not be equal to upward pressure at that point. This two statements are contradictory and I am reall...
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I am finding very hard to understand how convexity works and why a correlated strategy if a convex linear combination of Nashes is a correlated equilibrium. (Both concepts of Correlated strat. and correlated equilibrium are clear) The following is the problem I can't grasp: problem Please feel free to modify my post I ...
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tried to submit my thesis to my school. However they told me that my fonts were not embedded, which they need for archival purposes. I thought I took the necessary steps to make sure they were. I think my .pdf figures in the document are likely the culprit.... But they're telling me that it's because in adobe document ...
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Consider the single-hole diffraction of an electron. We can make the hole as small as we like and determine the electron's position with arbitrary accuracy. When it is in the hole, we can hit it with a low-energy photon, and measure its momentum. There is no guarantee that the photon will strike the electron. But it "c...
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I know that the derivative exists when the two sided limit at one point exists and at most of the discontinuities the two sided limit doesn't exist. But at point discontinuities, the two sided limit does exist, right? So it should have a derivative, i.e. it should be differentiable. But I read some of the answers for s...
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As I understand it, sound needs a medium to travel and more often than not, the medium is the atmosphere, however sound can also travel through solid objects. And even we can hear our own voice talking (though less loud) even if we cover our ears since sound travels through our body. So, in case we are on the moon wher...
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Description Hi, I'm looking for an adjective that can be used to describe someone who is skilled at easily identifying the thoughts, abilities, and perspectives of another. The first sample sentence provided effectively captures the effect that I'm trying to convey. Sample Sentences e.g. Chloe is a _____ manager, she a...
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This question is very related with software development. I would like to know if there is a word to refer the way that a word is written. For example somebody has written "HasChildren" for a variable name while the correct way should be "hasChildren". I could tell this person: "you should write hasChildren instead of H...
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How can I start from a Hamiltonian with electron-phonon coupling and show that a kink should show up in the energy dispersion relationship? In a brief communication called "Universal Nodal Fermi Velocity" there is a graph showing a kink in data collected from Angle Resolved Photo-Emission Spectrometry. After looking ar...
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I do not know if this is physics or engineering, but it is complex engineering I think at least. (In the implosion fission bomb first tested at Trinity and used in Nagasaki. Not the gun type.) A big problem with the implosion design was uneven compression and a member of the British team named Tuck suggested explosive ...
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I am seeing many reels on Instagram where they ask a person "Can you spell Y, E, S". The person says "Yes". Then they ask him "Can you spell E, Y, E, S". The person says "E-Yes" instead of "Eyes". Until today I thought that they should be using "pronounce" instead of "spell". Isn't spell the opposite? You ask a person ...
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I want to know whether alternating current will hold you to stick to the socket or throw you away and why? In my textbook it is written that alternating current is attractive in nature but when i researched a bit i found that it will contract your muscles and make you stick to the socket. So i want to know which of the...
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The question says it all. Simply stated: Can one prove grand unification from string theory? What is the argument chain of such a proof? The textbooks I read so far only appear to give hand-waving arguments. The question is not about deducing the standard model. The question is about deducing grand unification. This me...
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Are there good reasons to use, e.g., "customer relationship management solution" over "solution for customer relationship management"? I understand that in certain contexts clusters of nouns, such as in the first example, can increase ambiguity if the adjectives aren't compounded accordingly. The preposition in the lat...
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XeLaTeX and LuaLaTeX support Unicode, and are perhaps also in some other ways better than pdfLaTeX. However, are mathematical and logical journals prepared for submissions prepared with XeLaTeX or LuaLaTeX? Perhaps it is more prudent to prepare one's work with standard pdfLaTeX? I am a bit wary about these things, as I...
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I've been investigating this problem: Given some straight line planar embedding of a simple connected graph with a simple dual graph, does there exist a straight line planar embedding of that dual graph with each vertex lying in its corresponding face in the original embedding? What if we ignore the infinite face? I be...
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I believe I have heard the expression when someone did an analogy about nuclear war, comparing the danger to a game where the opposite player's objective is not to win but to make you lose. This was apparently called, in game theory, "a scorpion player". I thought they were called the "scorpion player" but I can not fi...
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Suppose we have a hollow conducting sphere having a charge Q residing on it's surface. Then we take another such sphere which is bigger than the one mentioned before and surround the smaller one with it, would this cause the charge on the inner sphere to appear on the outer surface of the bigger sphere? If yes, then ho...
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In Halmos'book on naive set theory, Halmos introduced the idea of a "family of sets". He explicitly defined a family to be a function from some indexing set to an indexed set. However, whenever he talks about a family, what he seems to always be refering to is actually the range of the family. I get so confused wheneve...
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Is there an adjective/expression that conveys the meaning that this something fills a role/place that should have been filled long ago because of its high added value? For example: "The ____ exhibition on female figures in the development of modern design..." Perhaps "long-awaited" is something similar but I was hoping...
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Google says just that "toothless wonder" is an individual in the public who is lacking a single front tooth. Well, that's logical. But what's the purpose of word "wonder" then? If this is a slang form I can't get it, please, explain it to me. And I really want to know where it came from. All I could find out is that th...
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In linear algebra, to convert the linear transformation or operator into matrix form, it's not hard, get the standard basis of domain and substitute in the transformation and write the image of the standard basis as a linear combination of standard basis of codomain and finally get the constants (c i's) and write that ...
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I use latex workshop on VS code combined with okular, but I would not mind using the internal viewer. I use forward search and backward search. My question is, whether there is a way to make the editor follow the viewer and the other way round: If i scroll in the editor, that the viewer shows the according segment and ...
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I want to know what the zero electrical resistance of a superconductor means. Does it mean when we connect the terminals of a battery with a superconducting wire, the electrons move within specific tunnels inside the superconductor for which the net Coulomb's force due to the nearby nuclei and the electron clouds are z...
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As far as I understand it, dark energy can affect bound systems at cosmological scales (How does dark energy affect the dynamics of galaxy clusters?) effectively modifying their orbits. This phenomenon and this thesis dissertation made me wonder... Could dark energy make a bound system (like a large galaxy or a satelli...
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What is the basis of the believe that there should be a unified theory which simultaneously gives quantum physics (the regime small things moving very fast) and gravity (the regime of big things moving very slowly)? Is this just wishful thinking? Are there any people who make a strong case of the possibility that no su...
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I was studying Newton's Laws of Motion and my book gives a diagram in order to explain what components together can or cannot be considered a system in the figure given below. Now it says we cannot consider D and E together as a system as they don't travel the same distance because the disc D slides over a string but I...
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We are aware that Microsoft Word has a feature called ink Equation that allows the user to write a formula with a light pen, even if the formula is complex, and then convert it into a real equation with an acceptable font. Obviously, this is an excellent option, since it is not necessary to use multiple commands to wri...
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When we put a circular hole of radius R on an infinite sheet of uniformly disturbed charge we do have an electrical field on a distance z (perpendicular to the sheet) from the center of the circular hole. But if we were to pick a gaussian surface such as a cylinder of radius R there would be no flux according to the ga...
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I am trying to compile the most basic file of the Kaobook template as provided here and it does not work. Now, on my TeXLive, it doesn't because it gives me in the report that it is missing an options.sty file (an issue that I do not really know how to fix). What is more peculiar is that this is not compiling on Overle...
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Background: Masters in CS/Math. I'm brushing up on statistics I see mean squared error everywhere. As a student I took it for granted, but now when I tried to find the reasons for why it's so prevalent I am told: simplicity, emphasis on outliers and mathematical properties like differentiability. So what? It's not the ...
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I understand that every function is equal to some graph, while not every graph corresponds to a function; so that sets aside the difference between functions and graphs. However, I understand that any relation can be represented with a graph, and every graph coresponds to some relation. Therefore, are the set-theoretic...
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Once a body "crosses" the limit where dark energy wins over gravitational forces (Is there a distance from a gravitational source where the influence of gravity and dark energy are balanced out?) would there be any way to make it return to the zone where gravity overwhelms the influence from dark energy? For example, i...
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It seems like homotopy pullback is pullback for the case of D(CW) (derived category of CW-complexes). Is this true? In general, I want to say that homotopy pullback satisfies the universal property of pullback in a derived category. What I know for sure is that the pullback of fibrations is homotopy pullback. In a deri...
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Why not explain the apparent attraction of masses by a repulsion coming from all directions in space (perhaps the dark force)? I.e. there is no gravitational force, just a repulsive force. A point in midspace would be receiving repulsive forces equally from all directions and appear to not accelerate. Mass near the out...
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This question was inspired by the very first exercise in Thurston's Three Dimensional Geometry and Topology, where he gives a picture of a very tangled up loop and asks what manifold it depicts. I understand there are several knot invariants and algorithms that can be used to detect the unknot. But where are the practi...
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I have noticed when I view a hose pouring water the color of water slightly changes when looking from above compared to when looking from the front. Also, the same thing applies when you pour water from your mouth. If you look at it from above there's a color I can't describe very good (but I think there's a yellowish ...
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What is the proof for this (assuming that we draw infinite field lines). I understand why flux through some area is proportional to the number of field lines through that area only in the case of an isolated singular point charge. However, I dont understand why this would be true in other cases, like two unequal charge...
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I want to strap down a big heavy cylinder on a flatbed truck. The strap is attached to the truck bed as shown in the picture and also behind. Will the strap slip off as in the next picture? PS. This is a purely geometrical question about the length of the strap and the shape of the cylinder. Please consider that the bl...
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I've read that the equatorial radius of the ergosphere of a rotating black hole is the Schwarzschild radius. But in this animation made in natural units by Yukterez it doesn't apply. I then used Yukterez equations in Geogebra and I observed the same thing. No surface scales accordingly. In the extremal case, the event ...
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An FTIR spectrum was measured for me (device from Alignment and MCT Detector) and since I'm not very familiar with FTIR I'm looking for some advice. The absorbance spectrum was obtained by measuring the reflectance of a reference sample and the actual sample. The reference sample was stainless steel and the actual samp...
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I have a question. I have a problem that when I learn science, I like to think 'how do they know this is right?'. When we learn physics or science from a textbook, we read and understand it, and then we have exam. But how do you know what is given in a textbook or said in research is correct? Because we didn't do this ...
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Suppose a body is kept in space and is not fixed about any point (i.e, not hinged). If an external force is applied, the body rotates about the centre of mass. I saw one answer pointing out that moment of inertia is minimum about the centre of mass, and thus motion around any other axis is unstable. Is this view correc...
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Both nematic transition and Jahn-Teller distortion distorts the lattice and reduces the symmetry of a crystal; both of the structure transition can take place at higher temperature than the magnetic transition. Why in iron-based superconductors it is called nematic transition, while in molecular system it is called Jah...
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I'm writing a report. In the report we refer to program participants as either dedicated or auxiliary. Each has a unique situation in which they enter the program. Since they are a particular type of participant, I have been capitalizing them to avoid confusion, but I'm not sure if this is correct. For example: When De...
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What is the synonym/counterpart for the word "Default" in NON-IT WORLD? We use the word in computer programs/apps, meaning that there is a pre-specified/pre-defined setting or situation. The word has also different meanings in Law and Banking. But I want an alternative to use in our daily life: for instance, a physicia...
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Could the gravitational effects of exotic matter be replicated by using something like a torus of mass around a point? Because spacetime is relative (I'm pretty sure), for observers on the torus, or just any celestial object i guess, would they not see the other points in spacetime around them having a negative energy,...
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This is a snap of a textbook while describing Uniform Circular Motion. For all the diagrams, and by the vector law, the directions of the del(v) vector is perfectly fine. But I am confused why this del(v) vector will always be pointing towards the center. As it is stated here, just because v is perpendicular to r and v...
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Just wanted to question how Hilbert space dimensions work. From what I've seen, they're used to generalize the mathematics of finite-dimensional Euclidean spaces into infinite-dimensional vectors. I've seen them used in quantum mechanics, and in some cases stated to "inherit finite dimensional space-time" despite the H...
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I'm not sure if this is the right community I could ask to, but I'm looking for a reference in business calculus that has challenging problems. The ones that I found so far have easy problems and can be solved within a day. I'm looking for problems that will probably take time to solve and will use a lot of thinking (a...
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I'm trying to modelise the ping pong and water cup experiment. They were already questions on stackexchange about this: Why does a ping pong ball bounce higher when it is dropped together with a cup of water? but I would try an approach with Archimede Force and superficial tension. I want to apply Newton's law on the p...
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I have some powder in a container with one side open. If I then compress it from that open side, does the powder evenly compress, or will the side closer to the opening (or furthest from the opening) compress more, and end up with a gradient of compression? For example, when tamping ground coffee in an espresso portafi...
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I recently delved into the topic about the reality of the Dirac string. Although several authors show how this object should not be real, this article "Field momentum and the reality of the Dirac String" proves they're wrong. I think the thesis of the article is very strong and I would like your opinion. I am writing m...
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I read about the 'Method of undetermined' in the wikipedia and it said as following: In order to find the particular integral, we need to 'guess' its form, with some coefficients left as variables to be solved for. This takes the form of the first derivative of the complementary function. Below is a table of some typic...
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I see the statement that: Similar to how a car needs fuel to run, a computer needs electricity to power it. In this case, I comprehend its meaning. However, I don't really get why "similar" is used at the top of the sentence here. If "similar to how" is an adveribial clause, my searches don't find any results or any en...
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I have read that if helicopter's engine fails, you set the pitch to minimum but not reverse pitch. The rotor would have to be tilted back to provide an angle of attack on the blades so it glides like a fixed wing aircraft but with the rotor spinning to keep the blades from buckling under the weight of the craft. I thin...
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I know that we have to use 'the' when it comes to groups of people, for example: The French are good at cooking. When nouns and adjectives are the same, we can omit 'the' Americans are good at sport. However, I do not know what to do with a word "Brit". I'd like to know Brits more OR I'd like to know THE Brits more? Ca...
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In an electric circuit, electron flows from the negative terminal of a voltage source to the positive terminal, which in turn, gives us the the conventional direction of electric current. So, the first question that arise in my mind is: On moving to the positive terminal, does the electron gain stability? If it does, t...
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Suppose I have a rhombus based penrose tiling like the following: Is there some coordinate system that allows me to easily uniquely refer to a specific tile, and also from the coordinates efficiently calculate the coordinates of the tiles that border it? I also need to be able to easily tell what tile is on the "opposi...
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I am attempting to apply the Grubler formula (which can be found here: https://learnmech.com/how-to-calculate-degree-of-freedom-of/) to determine the number of degree of freedom, but it does not seem to yield the expected in some cases. Is it correct that there are some cases where the Grubler formula should be avoided...
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Interference is explained by showing a diagram of two parallel waves of light that are in phase or out of phase and showing the result of the fields constructively or destructively interfering. Implicitly it seems to be the case that they are polarised in the same plane as well. What I wanted to know is what this pictu...
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The wavelength or frequency of light determines its color. Photons seen as particles are said to have a frequency, determined by its energy, so I assume that 'is' the same color. But being quantum particles, photons also have a probability wave, determining how likely it is to detect it in a certain state (like, a posi...
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How strong of a gravitational field do you need for a projectile to make a full loop? By full loop I mean it curves once around the by dot, and then it ends up on the same trajectory as it was one before it approached. How many times the Schwarzwald radius would the projectile have to get for this to be possible? I kno...
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I had the feeling that physics has moved on from the idea that spacially bounded objects located in spacetime (such as particles) can be fundamental. Instead, QFT describes everything by quantum fields which are better considered as an everywhere present property of spacetime rather than embedded in it. From this persp...
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I want to know the mean first passage time (MFPT) on a unit interval for two boundary conditions (please see attached figures a and b for your reference). This is in the context of the hydrodynamic dispersion of a particle. In case a) the b.c switch from reflection to absorbing whereas in case b) the b.c is reflective....
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I am currently looking for a cyrillic font (for russian typewritting). It must be an opentype font usable with lualatex and fontspec, and must be complete : roman, italic, bold, small caps, superiors letters and figures, in serif and sans serif. For all I know, Libertinus is very close, but it lacks cyrillic small caps...
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I have a knot about the "secondary" colours and its spectra. So If I look the spectra of white light, I can see that yellow, which is between R and G, has some wavelength. If I do an addition of light of Red and Green, I get yellow. Ok. Now If I do an addition of light of Red and Blue, I get Magenta. But how come that ...
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According to Stephen Boyd's textbook on ADMM, the global variable consensus ADMM updates are given as the following, which is pretty straightforward to understand: However, I've recently seen another variation of the consensus-ADMM updates from this work I tried very hard to derive the primal updates shown above but I ...
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So, I'm trying to make a basic shooter game in desmos, and I have a list of points that act as bullets. The (current) enemies right now are only some triangular jets that fly in a linear manner. My current goal is: Make it so when the point hits the triangle, it deletes itself from the list, and thus itself from the sc...
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My wife mentioned today that she would love to know more about 'how the world is made up'. She stopped learning science at a young age and finds most stuff meaningless or incomprehensible. She is not a child - so the challenge is, how to introduce the history and development of atomic physics with minimal specialist vo...
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I remembered this really corny phrase today when I was on a walk but I forgot later before I could write it down. It's kind of like "You are what you eat" but with different words. It's not: You reap what you sow. You're the sum of your actions. Easier said than done. (It is a different one but they're both about conti...
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Why does she try and pull the stunt? This is probably an elliptic sentence - Why does she try the stunt and why does she pull the stunt (off)? - but it still seems like very bad style to me. Why does she (even) try to pull the stunt (off)? I am aware that it is not clear that the attempt was successful, however the to-...
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I am trying to determine a statistical test to run. My dependent variables is employee retention. The independent variables are exam score and interview score. Unfortunately because employees who failed the the exam did not moved onto the interview, I do not have interview scores for all cases. Do I run a logistic regr...
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To my understanding, the curvature of spacetime is determined by the stress-energy tensor. I was wondering if we could calculate some of those components using radiation. Is it possible that objects that possess immense electromagnetic radiation, for example, will follow with a strong gravitational pull? Does radiation...
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So in my course of quantum computation i came across this question that "What guarantees a quantum gate to be unitary?" i was specially curious about photonic quantum gate. At first i thought that maybe unitary is not something that is guaranteed by any special phenomena but its inherited by the math behind quantum phy...
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We need to solve this problem without using trigonometry. KLMN square is inside ABCD square. Prove that midpoints of the segments AK, BL, CM, and DN are vertices of a square. KLMN can be situated anywhere inside ABCD. I think that we are going to use congruent triangles. I tried to draw so that the intersection point o...
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I wonder if above some energies (or diagram level?) the virtual particles would rather behave (or become) like a micro black hole. Does that make sense? Could this somehow introduce a cut off above which Feynman diagrams would be unnecessary (the micro black holes would always evaporate in perhaps a few different ways)...
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An oxymoron is a figure of speech in which contradictory terms appear in conjunction with one another. Can there be a figure of speech in which similar compatible terms appear in conjunction with one another? For example, how would I describe the following sentence? Nice should be great. Nice being the location, but al...
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As my title says, is a "change in scenery" as correct as a "change of scenery"? I am self-conscious of how a "change in" might sound odd or off or be even absolutely incorrect. Are both forms of this sort of expression truly correct? I know the latter one is (a "change of scenery" makes full sense), but what about the ...
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So there's this debate ongoing on one post that this phrase is incorrect. People are getting confused and wondering how can Adele take a divorce from her own son. The sentence is: Adele says new album will explain her divorce to her young son. Is the above sentence correct? I always thought a divorce was taken from som...
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If all bodies emit thermal radiation, does it mean that it's impossible to build something that can retain all of its energy - and last indefinitely? i.e. is everything in our world, including a dynamic, living system that can self-repair, eventually gonna collapse? OR - there is something in Thermodynamics similar to ...
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I'm looking at an example system which has a very large number of microstates (effectively infinite - not possible to enumerate exhaustively, but possible to sample from). The energies of the microstates however are drawn from a normal distribution with some average energy and standard deviation of the energy. What is ...
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If the vacuum energy of the universe is not at its minimum, that is, the universe is at a false/metastable vacuum state, then it could decay into the true vacuum state. However, if our universe is already at the true vacuum state, then, this decay would not take place. However, in the far future, if we would wait enoug...
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I was thinking of converting a disused chimney into a static periscope, using long focal length lenses at top end of the chimney. A static design would be easier, so I was wondering how one would design the mirror shape such that it converted a cylindrical view onto the lens, which could then be processed at the other ...
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Assuming right to be positive, in this question, is the work done by the boy positive or negative? I would think it is negative because the force that the boy exerts is towards the left while the movement of the boy is towards the right. I would think that work done ON the boy is postive because the force that the stri...
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