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I'm trying to reconcile two seemingly conflicting sources of information about Lorenz force. Let's consider a solenoid in proximity to a permanent magnet with the field pointing in the same direction as the axis of the solenoid. From the right hand rule I conclude that the wire should either be pushed towards the center of the solenoid or outside. However, the solenoid also acts as a magnet with poles on each sides and will attract/repel other magnets. How does one reconcile the two explanations ? Is the solenoid both contracting on itself and moving towards the other magnet at the same time ? If yes which force/equations describe the movement of the electromagnet towards a permanent magnet. Thank you! | 0 |
I am aware there are similar questions already asked, however, I find none of the answers satisfactory, they either do not contain any mathematics at all, or mathematics of a level I am not capable of comprehending. My doubt is that, if the change in kinetic energy is dependent on frame, then how is the law of conservation of energy valid in all frames? One possible explanation I have thought of is that the change of potential energy is also frame dependent, but I cannot think of a suitable example to justify the same. Please answer only using newtonian mechanics I do not know statistical or lagrangian mechanics. | 0 |
I have recently started to study integrals and faced some difficulties of understanding why we need antiderivatives to calculate area under curve. I am trying to visualize it using graphs but it just doesn't make sense to me. If anyone can explain me if it's even possible to understand them the way I try. here is the image: enter image description here Thank you :) | 0 |
I was curious if anyone knows the font used by the Desmos graphing calculator. All the formulas are formatted as LaTeX, so I wanted to know if there was a way to use this font in my own documents. It seems at first glance like standard Computer Modern, but upon closer inspection as you can see the "w" and "v" characters are rendered in a style that makes them pointier so that they are much easier to distinguish from omega and u respectively (and imo they just look a bit more pleasant). Here is a side-by-side comparison for context. Computer Modern: Desmos Font: (This is my first time making a post on the site, so apologies if I have made any mistakes!) | 0 |
What is the interpretation of temperature in the Ising model? Can one describe a theoretical thermometer for the Ising model? As far as I know, in the theory of gases, temperature is interpreted as a quantity proportional to the mean kinetic energy. A thermometer is a device capable of converting the average collisions of particles into the movement of a dial. The higher the mean kinetic energy, the more movement the device registers, and the dial goes up. I can't grasp a similar idea for the Ising model. | 0 |
I already know the term anaphora exists for repeating the same word for emphasis. I'm specifically interested in a term for repeating a word twice without additional clarification to express that something is especially strong or genuine. Examples "Do you like her, or do you like like her?" "Are you making quick bread, or are you making bread bread? "I'm so excited, I got a promotion promotion, with a pay raise and everything!" I don't know that I've ever seen this in formal prose; it seems unique to spoken English, but if anyone knows of any written examples please add them. If no term already exists, I'd like to coin the term "duplication duplication," to distinguish it from ordinary duplication. | 0 |
Imagine that Alice is the President of Arstotzka. Alice has a lot of enemies but she's generally an upstanding President so her critics have a hard time building a campaign against her. Instead, the critics are patiently waiting in the shadows until Alice makes a minor mistake - perhaps she misspeaks at a conference or her car driver skips a stop sign. The critics then blow this incident out of proportion and use it to smear Alice before the next election. What's a word or expression specifically describing the act/strategy of waiting for a small transgression to happen? | 0 |
Can you compute geodesics by treating it as a problem where you want to minimize the length of a curve through two points on a specified surface while having the constraint that the curve must reside on the specified surface? If so, can you explain how one could do so for a cylinder? Or is the calculus of variations the only method by which to do so? I tried setting up the constrained optimization problem for a cylinder but was unable to make any progress, leading me to think that maybe it's impossible to solve the problem without the calculus of variations. | 0 |
I am working on my thesis and need to convert my paper to a different format. I'm new to using latex, only having started using it for this project, and am struggling to get the base version of this template working. No error occurs, but compilation appears to halt, judging by the fact that main.log log ceases to update after a certain point. The repository hasn't been updated in a while, so I am guessing that the setup may be outdated. I've tried removing some of the references to other sections, but that doesn't appear to make a difference. If someone could help me get this working, or point me in the right direction, I would greatly appreciate it. https://github.com/davidanastasiu/thesis_template-SJSU_CMPE | 0 |
Show that, given four coplanar points, we can always draw two intersecting circles coplanar with the points, such that two of the given points are diameter endpoints of one circle, and the other two given points are diameter endpoints of the other circle. In this question, "intersecting" means that the circles share at least one common point. Example: I will post my answer. Alternative solutions are welcome. This question and answer serve to provide ideas that might help answer a harder question about five points and two non-intersecting circles. | 0 |
Ive recently been introducing myself to Gaussian Processes. In Bayesian linear regression, one would expect that when adding new features, the likelihood on the training set would weakly increase due to the larger degree of freedom, of course leading to overfitting most likely. I was wondering if this is true in general for marginal likelihood for GPs, regardless of the choice of kernel/specific hyperparameters? If so, what is formal explanation for this? Can we prove it mathematically? Thanks :) | 0 |
I heard that natives use Present Cont. to describe things in the future. As I understood, we use Present Cont. when we have arranged an action or there is at least one person with whom we agreed to have plans. But I saw this: I am teaching English tomorrow. I will be teaching English tomorrow. What is the difference and when I should use Present Cont. to describe action in the future? | 0 |
I work in an office where the airconditioning is not working, so I brought a small mobile airconditioning device: it's a small machine, emitting cooled air. It looks like this: However, according to the laws of thermodynamics, the total amount of heat should always increase in a closed system. Therefore, regular airconditioning systems vent their waste heat to the outside, but this little mobile machine does not have any connection to the outside, so it has no means to discard its waste heat. So my question is: how can such a machine even exist? | 0 |
Two congruent circles that touch at point H are given. Let the line p be their common tangent that doesn't pass through the point H. Construct a circle that touches both given circles and the line p. The most intuitive thing was to construct an equilateral triangle NOL (such that L is on p, and N and O are on the given circles) and find its circumscribed circle. However, the obtained circle intersects given circles at N and O, instead of just touching them. What am I doing wrong? | 0 |
If a set is equipped with total order (reflexive, transitive, antisymmetric, strongly connected), does this necessarily mean there exists an injective mapping from that set to the reals? Alternatively, if a set has larger cardinality than the reals can it not be well-ordered? I'm struggling to think of a counter example. Most of the canonical examples of sets with larger cardinality than the reals (all functions, power set of reals) cannot be equipped with total order. | 0 |
This question is bugging me from a very long time and I don't know whether it can be answered or not but still I am posting to get other's opinions. Is there any inherent property among all the uncountable sets which make them uncountable ? Or more precisely:- If I ever wanted to "make" an uncountable set, what ingredient should I put in so that I am guaranteed of the set being uncountable ? Edit :- My apologies for the wrong terminology used. By "ingredient" , I was just trying to refer to some property which is common to all the well known uncountable sets (e.g. the irrational set, set if real numbers) that I should keep in mind while forming a new set of numbers. | 0 |
Imagine a uniform thin layer of a viscous gel sticking on a vertical wall. A small sphere is submerged in this gel. The gel has a yield stress (Bingham model). How can I calculate the yield stress that will cause the sphere to start sliding with the fluid on the wall? This yield stress will obviously depend on the weight and dimensions of the sphere. | 0 |
I'm having a problem with the second part of the question, which shows that the sum of the vectors equals zero. I came up with a geometric proof, but I wondered how to prove it by using complex numbers and maybe links to the first part of the question. I was thinking about the equally distributed roots of unity, but don't know how to move on. | 0 |
I understand how we can have three coin tosses (or three events if you prefer) such that all three tosses are pairwise independent, but not mutually independent. One trivial example of this would be to just have the third coin be the xor of the first two coins. My question is whether it's possible to have four or more coin tosses such that any two coin tosses are pairwise independent, but any three coin tosses are not independent. If this is not possible, what would a proof be like showing that it isn't? | 0 |
I am a PhD student working on observational cosmology. My research is based on the experimental side of it (receiver design, etc.) but I would like to get deep into the CMB and CMB statistics. I have found several resources and have read some of the papers but I feel like they are a bit "unconnected". Does anyone know where I could start? I thought of just studying Ruth Durrer's (The Cosmic Microwave Background) book, but I am not sure if it will be complete enough. | 0 |
I am studying blackbody radiation and modelling a cavity as a blackbody. However, I am encountering a number of confusions in this description: Many textbooks mention that the cavity consists of metallic walls that act as perfect reflectors. Light entering through the hole, after multiple reflections, get absorbed. However, if the cavity walls are perfectly reflecting, how is the radiation getting absorbed by the walls? For studying the radiation emitted by the blackbody, the textbooks model the radiation inside (emitted by walls due to heating) as standing waves. But how are standing waves being emitted by the cavity? Because standing waves are supposed to be confined inside. Can anyone please explain in simple terms? | 0 |
For example, a carpenter works in carpentry and a plumber works in plumbing. So what trade does an electrician work in? Electrical? I searched the definition for "electrical" and found that it gives the part of speech as an adjective and not a noun like the dictionary does with carpentry or plumbing. This is confusing to me. I would like to understand and know how to talk about the trade for an electrician. I would appreciate it if someone could help clarify and explain this to me. | 0 |
Imagine a mass hanging from a string attached to the ceiling of a lift and the lift descends with a certain acceleration. From the reference frame of the ground the tension in the string would be smaller than when the lift remained stationery. However, let's say your friend was inside the lift and when asked about the tension would say that the tension was same, regardless of the list ascending, descending or stationery. Isn't that really counterintuitive? Isn't the force not relative and the same, regardless of the reference frame? | 0 |
For example: It is a thing that works producing stuff. This feels wrong to me, but I can't quite put my finger on what exactly is wrong about it. It seems like it's trying to be a participle phrase, but it's not necessarily modifying the current state of "it", and is, instead, describing what "it" is -- i.e. by working, "it" produces stuff. If it is, indeed, a participle phrase, then it should be able to be written as Producing stuff, it is a thing that works. But, to me, this doesn't seem correct either, so it leads me to believe that the very structure of the sentence is incorrect. | 0 |
I have been taught that path difference and phase difference are essentially the same thing, except phase difference is measured in an angle unit while path difference is measured in multiples of wavelength. This seems incorrect. I think they are rather different concepts, with path difference representing the difference in distance a wave needs to travel in order to reach a point. Are they really the same thing like I have been taught? | 0 |
For example, when referencing a webpage: Visit the "The Performers" page to learn about our musical lineup. In this case, I want to tell someone to visit a webpage entitled "The Performers" to find more information, but the repetition is throwing me off. If I were to remove the first "the" before "The Performers," though, then it would essentially read as "Visit page" without an article. So, is it okay to use the article of the webpage title as the article for the sentence, or must I include the first "the" before the webpage title? The two iterations: Visit the "The Performers" page to learn about our musical lineup. Visit "The Performers" page to learn about our musical lineup. | 0 |
I think something is missing in the definition of homeomorphism I saw. It just said it maps the collection of open sets to the collection of open sets in a bijective way. What exactly makes this preserve topology? I can think of weird situations where each individual open set is mapped to totally disjoint open sets in a bijective way, throwing the topological structure out the window. | 0 |
The definition of optical path length is the distance that light could have travelled in the same time, in vacuum. So, can we define something analogous for sound waves, like an "acoustical path length", with respect to a specific medium, say air? And if we were to define something similar, how far would it's applications reach? For example, can we use it in doppler effect in cases when the observer and source are in a different media? Or interference, when there is a change of medium in between? If so, kindly guide me on how to do it. | 0 |
I know foliations as a particular topic in differential geometry. I understand the definition and basic properties of a foliation from the DG point of view, including the Frobenius theorem. While trying to understand why this concept is important I came across this Wikipedia page on integrability conditions for differential systems, but couldn't understand much of it. I do not want to too diverge from my other studies now, yet want to understand this association quickly and completely. Can you suggest me a source that is solely focused on the relation between foliations and systems of PDEs? | 0 |
I was going through this paper in which the authors state that : In Landau theory, a continuous phase transition is associated with a broken symmetry. The phase transition in a black hole system can also be characterized by the symmetry and order degrees as in a conventional thermodynamic system. The authors don't explicitly state which symmetry is broken for the black hole phase transition. Also, would such symmetry breaking lead to any chaotic effects? Any explanation in this regard would be truly beneficial. | 0 |
I am attaching the solution of a school question asking to calculate the inverse of a matrix. However, the solution proposed does not fit in anything I ever seen about calculating inverse matrices. I did not found any property that fits the final part of the solution (the one I highlighted in the image below) although the solution is correct, I would like to know which property or reasoning supports the final solution of such a problem. Thanks. | 0 |
I read an article that referred to the idea that a double slit experiment near the event horizon of a black hole observed by someone inside the black hole creates a paradox because the inside observer can break the interference pattern, thereby bringing information of their presence out of the black hole. This seems odd to me. The significant part of "observation" here, as far as I understand, is that it requires interaction. The inside observer can't interact with the particle to measure it's position. He can only detect it's position if something outside the black hole interacted with the particle, which means the superposition would have collapsed whether or not he was there. Am I missing something? Edit: Link: https://www.sciencenews.org/article/black-hole-paradoxes-quantum-states | 0 |
I have often heard that two physically distinguishable mixed quantum states produce different density matrices. However, how would I prove it? I know that they have to differ on the main diagonal, because these elements correspond to measurement probabilities in the standard basis. Moreover, I have seen someone using density matrices to show that two mixed states are physically indistinguishable. Does this process always work? In other words, is it true that for any two physically indistinguishable quantum mixed states, the density matrix is the same? And how to prove it? | 0 |
I'm learning some math by myself and I thought of this question that has to do with how useful complex numbers are: I'm looking for a specific example of an equation that has the following properties: The equation is true, i.e., its LHS and RHS are always equal, no matter the values of its variables, if any. The LHS and the RHS are algebraic expressions (no limits, derivatives, integrals, sin, cos, etc...) The equation only involves real numbers. Its shortest equality proof involves complex numbers. The proof ends with no complex numbers. It has a longer equality proof that doesn't involve complex numbers. It's a short equation (this property is subjective). Please, let me know if my question is wrong or if no such equation can exist. | 0 |
I want to understand in some detail why superconducting qubits need periodic calibration. The usual, hand wavy explanation is environmental effects that tend to vary from time to time. However, I suspect that the actual picture is more complex than that. I want to understand in particular which effects are purely external, like the earth magnetic field (in lack of a better example) and which are internal to the superconducting device. I am especially interested in those factors that are internal to the qubit itself, like manufacturing defects and physical characteristics that may change in time. A good reference on this subject would be appreciated. | 0 |
A spanning tree of a graph is a subgraph obtained by deleting only edges of the graph and which is also a tree. Why does one study "spanning tree" in graph theory? What are "spanning trees" real life application? We know the number of spanning trees of a graph is equal to any cofactor of the Laplacian matrix of the graph. Why is one interested in knowing number of spanning trees of a given graph? I would like to know enough in order to motivate a undergraduate or graduate student. | 0 |
Hi I was trying to determine the basis of the topology on the following collection in R {[a,b), a <b}. Here is what I tried : Knowing that the basis for a subspace topology is equal to the set of all intersections of {[a,b), a <b} with the basis of the topology it is a subspace to. Now I also know that the basis for the euclidean topology on R is {(a,b), a <b}. Can I just take the intersection of {[a,b), a <b} and {(a,b), a <b} to get the basis? If so what does this equal? Or am I totally wrong? Thanks in advance. | 0 |
I understand that Berry curvature sinks and sources correspond to Weyl points. However, I'm curious about the identity of points exhibiting a Berry curvature spiral, highlighted by red circles in the figure below. Could these be Dirac points? Is it possible to differentiate between Dirac and Weyl points based on the direction of the Berry curvature rotation? It's worth noting that these two spirals exhibit opposite rotation directions. | 0 |
I read that a sound wave (a scalar wave) produces monopole radiation, an eletromagnetic wave (a vector wave) produces dipole radiation, and a gravitational wave (a second order tensor wave) produces quadrupole radiation. How do I make sense of multipole radiation physically? The Wikipedia article on multipole radiation is informative on the mathematics, but I can't seem to get a physical picture. Note: my question is different from this post, which asks about the pattern of lowest order multipole radiation produced. | 0 |
first post here. I've been looking into acoustics a bit recently and I'm wondering if for a compressed solid, acoustic impedance should change along different axis in certain cases. Consider a cubic lattice of atoms with pressure being applied to the top and bottom, compressing the lattice. Atoms would be spaced further apart in planes parallel to the applied pressure. I'm hypothesizing that acoustic impedance would be higher for a sound wave travelling through the lattice perpendicular to the plane of applied pressure and lower for a sound wave travelling through the lattice parallel to the plane of applied pressure. Could we consider density as a vector to solve our impedance equation if the above holds true? | 0 |
We know that Maxwell's electromagnetic theory was originally an ether theory. Later, the ether was denied. But Maxwell's electromagnetic theory can be transformed into a theory of "field". The theory opposite to Maxwell's theory is the theory of action and reaction. Or it could be the theory of action-at-a-distance (Wheeler-Feynman absorber theory). According to Maxwell's electromagnetic theory, electromagnetic waves can exist independently of their source or have their own degrees of freedom. According to the theory of action-at-a-distance, electromagnetic waves cannot exist independently of their source. Electromagnetic waves do not have their own degrees of freedom. These two theories have been debated for hundreds of years. Is there a formula that can distinguish which of these two theories is right or wrong. Just like Bell's formula? | 0 |
Consider a few sentences: I read a lot. ?I read much. I don't read a lot. I don't read much. Do you read much? This seems to suggest "much" is a negative polarity item, but then we can say things like "Much of it has to do with you not being here." So how much of a negative polarity item is "much"? I am particularly interested in existing literature on this. | 0 |
While reading the CMU FLAC overview, I stumbled upon the above image. While I have seen Greek numerals before, I had no idea that there was an entire algebraic symbology developed in Greek (though this isn't too surprising). To try and find more about this particular notation, I reverse Google Image searched it and found nothing (well, I was greeted to snippets written in the Tengwar, but that's besides the point). What is this notation? Can you direct me to an overview of the system? | 0 |
As a thought experiment, say, for the sake of simplicity, we have a meson. This meson, which is traveling near light speed, is traveling towards a black hole. And skirts the event horizon in such a way where the anti-quark ends up inside it's event horizon, but the quark does not. What would happen? Would this create a free quark? That seems like the only logical thing to happen, but I know that would also break color confinement. | 0 |
The operational principle of frequency combs is that you generate very short pulses (in time domain), and that in the frequency domain (due to Fourier's transform) the spectrum of such pulses is a comb. But this is just maths. And how it works from the physics perspective? Let's say I have a monochromatic continuous laser pointer that outputs only ONE wavelength. In front of the pointer I place a shutter that chops the beam into short pulses. How can those pulses have multiple optical frequencies (with many different wavelengths)? Or is my idea too simplistic and I'm forgetting something? | 0 |
If so, then why? We know that a current carrying closed loop in a uniform magnetic field experiences no force but when it's suddenly pulled by an external force, according to Lenz law a magnetic force will start acting on it to oppose the external force and eventually reach steady state at infinity. How can this be? Edit: Iam sorry for not specifying the doubt clearly, here is the question in which I was confused as to how there can be a magnetic force acting on the ring | 0 |
What does the Stark-Lo Surdo effect consist of in the interaction of the electromagnetic field and the active medium in a laser? I thank those who want to give a clear and concise answer. In my student notes from the seventies, I found the topic I was looking for, the calculation for which I attach. But what happens in practice (since I don't have an optics laboratory available)? | 0 |
Am getting the following error when I try to do tlmgr install package: tlmgr.pl: package repository http://mirrors.rit.edu/CTAN/systems/texlive/tlnet (not verified: pubkey missing) It appears I need to get the keys somewhere, but I haven't been able to find them on CTAN. Where else can I find them? If it's any use, I just updated my system on Arch, so maybe some other fellow Arch users had a similar problem? | 0 |
Any regular curve may be parametrized by the arc length (the natural parametrization or the unit speed parametrization). But I haven't seen an analogous development for regular parametric surfaces. I hope we can do this at least for orientable surfaces with no umbilical points. For such a surface, there will be two orthogonal lines of curvature through each point, and I suspect that there is a parametrization whose parametric curves coincide with lines of curvature. But I'm not sure how I should approach showing the existence of such a re-parametrization. Is there a such parametrization? If not, what are the conditions that we should impose to have such a parametrization? | 0 |
When talking about black holes and singularities, most books say that combining relativity and quantum mechanics gives the answer of infinity in some equations. They also say that: Infinity is the answer you get when the universe is trying to tell you that you have made a mistake. Why can't equations have answers of infinity? For example, a singularity is infinitely dense, so why can't other things about it be infinite? | 0 |
In the original version of Sequent Calculus by Gentzen for classical and intuitionistic propositional logic there is a structural difference: the classical version admits succedents with multiple formulas but the intuitionistic version admits only succedents with one formula. I'm searching for another formulation of Sequent Calculus in with succedents are restricted to one formula both for classical and intuitionistic logic. In particular I'm searching for a formulation in which Sequent Calculus for classical logic is obtained by Sequent Calculus for intuitionistic logic by adding some rule (i.e. excluded middle). Can someone suggest me some reference? | 0 |
It is often said that the achievability proof for Shannon's coding theorem relies on the channel being discrete and memoryless. At the same time, following the classical proof (using random coding and AEP), I can't find any part of the proof that explicitly uses the fact that the channel is memoryless (except arguably perhaps the guaranteed existence of a supremum of the mutual information?), as AEP has been shown to work for any stationary and ergodic channel. Further, Shannon's original paper does not seem to make any mention of memory in the proof as far as I can tell. Is it true that the classical achievability proof relies explicitly on the channel being memoryless? If so, where in the proof is the memoryless assumption used? | 0 |
Quick question with probably a simple answer. For context, I am currently in undergraduate classical mechanics studying potential energy. My question is, if a conservative force is one in which is only a function of position, can radioactivity be a conservative force? The example I thought of was if we take two identical particles which are undergoing radioactive decay, and we put one in the upper bound regions of the atmosphere, and the other at sea level, can we say that radiation is a function of position? I guess this also poses the question, can atmospheric pressure/temperature affect radioactivity? Feel free to slaughter my logic/understanding. Thanks :) | 0 |
I know work done is equal to product of force, displacement and cosine of angle between them. But that formula works only when we assume that the force is constant during displacement and it acts so long the body moves and also when the direction of force and displacement is constant. But how should I calculate work done if the direction of force or displacement is changing. So in this case there would be no constant angle between them and so dot product won't work as I don't know the cosine value and at this point I have got stuck. | 0 |
I have an object that takes a shape similar to a catenoid, which is known for its zero mean curvature. According to Laplace's law, the pressure difference is proportional to the mean curvature. This implies that if the mean curvature is zero, then the pressure difference is also zero. However, I am aware that when there is a non-zero pressure difference between the inside and outside of the object, which has left me puzzled. Is it possible to have a shape resembling a catenoid but with a constant pressure difference? Furthermore, how can I relate the curvature to the distance, r(z), from the z-axis to any point z on the boundary of this shape? | 0 |
Reading through Einstein's Brownian motion paper "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat", it seems the final argument is that he can calculate the Avogadro's constant by using data on the diffusion rates, particle size and fluid viscosity. But its hard to see the connection that ultimately atoms must exist. Can someone lay out a flowchart of step-by-step reasoning leading to that conclusion? I see all the math steps, but need a more philosophical type of breakdown. Also can't the random movement and diffusion law movement of the particles be just as well explained by fluctuations of pressure and density of continuous matter? | 0 |
Is it correct to say: for any family of bounded operators (proper subset of B(H)) acting on a non-separable Hilbert space there is a non-trivial subspace of the Hilbert space that reduces the family? I know that this is true for any operator on the space so, I assume that it holds also for the von Neumann algebra generated by this operator. Can we generalize to non-commutative families? If the answers is positive (or positive with certain restriction imposed on the family) how can we show it? Is there any reference? | 0 |
If you were to measure a regular hexagon, is there a way to rotate the hexagon so that if there were two lines bisecting the center of the hexagon, both lines would be the same length? Can we then use the lengths of those lines to determine the area of the hexagon? Edit: To clarify, I mean that I intend for the lines to be perpendicular. | 0 |
There are four concepts which are studied in Calculus and Analysis: Convergence, Continuity, Differentiability and Integrability. In Calculus, you can define the latter three in terms of the first, but also you can define integrability without convergence using Darboux approach. In topology, you can define convergence and continuity in terms of neighborhoods, and in measure theory you can define integrability in terms of measurable functions. I wonder if there is a definition of differentiability without making any reference to the concept of limit or convergence, thank you so much by your help. | 0 |
Consider the following diagram Here, the diode is in forward bias, and allows current to flow. However, I am slightly confused why this is the case. A diode is defined to only allow current to flow from the anode ( Positive ) to the cathode ( Negative ). When drawing a diode, the cathode is the line and the anode the base of the triangle. Conventional current flows from the positive terminal to negative terminal, but in reality the electrons flow vice versa. Hence, considering the above diagram, shouldn't the electrons not be able to flow through the diode? The only way I can see around this, is that diodes are also drawn, considering conventional current. Is this correct? | 0 |
In the derivation of Torriceli's law it is assumed that the pressure at the tank hole is equal to atmospheric pressure. I believe this is true when the water starts flowing through the hole but I do not understand why this should hold during the whole purge procedure. Do you have ideas about the explanation? CFD calculations showing this behavior would be great. Many thanks. | 0 |
The second law of thermodynamics states, that entropy (of the universe) always increases. Entropy can, however, be (locally) reduced when energy is provided. At the phase transition from a relatively unordered to a more ordered state (e.g. condensation of vapor to a liquid), the entropy is lowered. At the same time, energy is released from the system (thanks to the enthalpy of condensation). Naively, I would expect that I need to provide energy (instead of gaining some) to the system to lower the entropy. Why does this not contradict the second law of thermodynamics? | 0 |
I know that the Heisenberg Uncertainty principle states that the position of an electron is uncertain, however, if an electron is created due to beta decay, then at what location is it more likely to begin its movement? Is it right inside the proton? Is it the outer edge of the proton? Is it adjacent to the proton? Is it near the proton? I mean is there a possibility of a beta particle from a nuclear decay to come into existence at the far end of the galaxy for example? What is the limiting condition for its position? | 0 |
According to Fermat's principle, light should take the least time between two points. Therefore, is it correct to say that the angle of refraction is solely dependent on the difference between speed of light in two mediums? Surely the the position of the observer is a key factor too, given the findings of the double-slit experiment that show a photon is only actualised on measurement/observation. Does this not imply the necessity of an observer for the existence of an angle of refraction? | 0 |
I've been reading more category theory as a prerequisite to understanding some more complicated theorems, and for the first time I'm running into arrows that are distinctly colored. Examples include these diagrams from Wikipedia for natural transformations and universal morphisms: The Wikipedia articles do not readily show me a link to where the coloring for these diagrams is explained, and I have not seen these colored diagrams in the textbook I have been reading for Category theory. Why are these arrows (and objects) colored blue and red? Better yet, (if possible) can someone give me a link/source/textbook that explains this coloring procedure? Thanks in advance. | 0 |
I understand that the word spook is a racial slur that rose in usage during WWII; I also know Germans called black gunners Spookwaffe. What I don't understand is why. Spook seems to also mean 'ghost' in German. Did the Americans call them spooks because the Germans did? If so, why did the Germans call them that? Or, if the Germans called them that because Americans called them spooks, then why did the Americans call them that? And how did Americans know the Germans had a nickname for black gunners? | 0 |
When researching the reflexive, symmetric, transitive, addition, subtraction, multiplication, division, and substitution properties of equality, the sources I found said they were true "for all real numbers". Are any or all of them not true for complex numbers? i.e., is the "for all real numbers" a necessary caveat, or should it say "for all numbers"? Also, I know the reflexive property applies to mathematical objects as well (any mathematical object is congruent to itself). Do the other properties of equality apply to all mathematical objects as well? | 0 |
I am trying to calculate the determinant of the following matrix. I literally have no idea if there's a general approach for solving such strange looking determinants, but I decided to subtract the first row from each row after the second. I don't know what to do next... May you show me what we're supposed to do and how do we find the determinant? Thanks! | 0 |
Assume a Gaussian surface in a non-uniform electric field that is directed along X-axis. Say the field is getting weaker as we go along positive X direction and it's constant along Y and Z directions. Then, if the Gaussian surface is a cube and charge enclosed is zero, the electric flux coming into the surface is more than that flowing out. So, shouldn't the net electric flux be non-zero contradicting Gauss's law? Does it mean such an electric field is impossible without a charge being distributed along the path? | 0 |
The usual semantics of first-order theories involves models who have a structure-set. Hence it is required to use some sort of set theory as the metatheory. However it is also widely known that one can do logic with a minimal metatheory, say a fragment of Peano. If we are using such a metatheory, what will the semantics become ? What will replace the notion of "set-model" ? | 0 |
Here is the problem, I thought it the I've been thinking for a long time, but I still don't have any ideas. Problem: Let A(S) be the group of all bijective functions on S with composition as its binary operation. then A(S) is finitely generated if and only if S is finite set. I know that proving from the right to the left is relatively easier, but when it comes to proving from the left to the right, I really don't have any ideas. I hope someone can help. | 0 |
I am typesetting my thesis in latex overleaf. I am struggling with one issue. I want to highlight my section with blue rectangular background with white color for heading as can be seen in picture. For subsection I don't want a background rectangle I simply want subsection of a blue color as can be seen in attached picture. I will really appreciate it if someone help me regarding this. Thanks. | 0 |
I was given an honors project to solve for the equations of motions of a pendulum with an oscillating fulcrum. I (somewhat) understand the procedure on how to solve it with lagrangian mechanics and the Euler-Lagrange equation, but I am stuck at a question. How do we know this cannot be solved with Newtonian mechanics? I tried to look up the answer on Google and even tried to solve for it myself but I obtained an equation with theta, acceleration in the x and y direction so Im not sure what to make of it. Does anyone know? Or are there any resources to understand the precise limitations of Newtonian mechanics? I am a physics undergrad who just finished electromagnetism and linear algebra, thank you! | 0 |
I am having trouble understanding why is temperature coefficient for avalanche breakdown is positive? The explanation I found online says as the temperature increase the mean free path decreases making collision and generation of carrier pair easier. But the electric field require to accelerate charge carriers to point of collision remains constant . So why does avalanche breakdown voltage increases with temperature if the electric field remains same? Doesn't increase in voltage indicate it is slightly harder to obtain avalanche breakdown? If the mean free path is decreasing and charge carrier generation is getting easier shouldn't occur at same voltage and not increase further | 0 |
The Coriolis force predicts that winds in the northern hemisphere should be deflected in a clockwise pattern and winds in the southern hemisphere should be deflected in an anti-clockwise pattern. Why is it that in the case of cyclones however, the cyclones spin anti-clockwise in the northern hemisphere and clockwise in the southern hemisphere? If it's indeed true then what is clockwise and anti-clockwise direction?! | 0 |
What is it called when someone says no, but actually doesn't mean that? Imagine this situation: when two lovers have had an argument then one of them is trying to apologise but the other one (usually the girl) says "no, I don't forgive you." but she isn't really angry. She just want him to insist more. She says no in a some kind of seductive or cute way. What is this behavior called? | 0 |
I understand why all non-degenerate energy states can be chosen to be real up to an overall phase (as is highlighted here Is a non-degenerate wavefunction real or complex?). However I've been told the argument holds in the opposite direction -- (that all energy eigenstates that can be represented as purely real are non-degenerate). Is this true? I'm having trouble finding a proof of this. | 0 |
I know that as the kernel parameter for the RBF kernel increases, the Gaussian function becomes less peaked and broader. The reach of the points become larger meaning that farther datapoints have more weight. Intuitively, it makes sense that a larger reach means a smoother decision boundary. However, since I don't have an extensive background in mathematics, I find it difficult to come up with a more mathematical explanation. I was wondering whether anyone could help me with that? | 0 |
I came across this question while studying for the SAT. What the humanities teach are valuable skills. These include the ability to think critically; to construct, analyze, and respond to arguments; to see both sides of an issue; and to understand the processes that have brought us to where we are today. (A) NO CHANGE (B) skills: these The answer sheet says that (A) is correct, but it does not specify why. I thought the answer is (B) as what follows correctly elaborates on the previous information. | 0 |
This stems out of my personal curiosity and it's not related to any homework of sort. Suppose I have a table made of some uniform substance (like plastic), and then I strike some point of the table with a hammer. Will the disturbance/wave I produce travel always the speed of sound in that medium, or will there be cases in which the wave travels at a different speeds? | 0 |
I have a weighted directed graph representing the intensity of movements of individuals between locations, with weights representing the mobility flow. I have another dataset consisting of particular paths that are taken by specific individuals. For example, for a person named Alice, I know how she moved from node A to node B, potentially via some intermediate stops through other nodes. What I want to evaluate is how likely this is given the mobility network (the weighted directed graph). Essentially, can I compute some kind of distance/statistical measure that tells me how "deviant" or how "consistent" these observed paths are, given the mobility network (taking into account the edge weights)? | 0 |
I just discovered Lean and using computers for stating and proving theorems. The first question that came to my mind, can we write any proof with Lean? Or are there limitations (something that you can write a proof for on paper but not in Lean)? I'm not talking about practicality or feasibility. But does the Lean system have the capability? Edit: I posted the same question on proofassistants.stackexchange. | 0 |
So I'm confused with The Second Law of Thermodynamics. It says that heat flows from the high temperature to low temperature. For example, if we put a glass of cold water on the dining room, the cold water will eventually have the same temperature as the dining room, because heat will flow from the air in the dining room into the cold water. The cold water "gains" heat and the air in the dining room "looses" heat. But, why does the temperature in the dining room remain the same? Shouldn't it become colder? The same goes for a thermometer when someone that has a fever uses it. Will their body temperature loose heat because the heat will flow from their body to the thermometer? | 0 |
Geometrically, what is the difference between a diagonizable matrix and an orthogonally diagonizable matrix? I understand the difference algebraically, as explained here and many other places. But I'm struggling to see the difference geometrically: both will not rotate (assuming the field is the reals), but will stretch by different amounts along different axes (Wikipedia calls this a inhomogenous dilation). Graphically, I can't see the difference between, say, a circle or ellipse dilated inhomogenously along orthogonal axes versus non-orthogonal axes: in either case, it will remain an ellipse. | 0 |
I'm a physics graduate that is joining the master degree program of my University. One of the areas of research that i'm very interested is Quantum Field Theory over curved surfaces, but the point is that i don't know how to begin to start studying these subjects. I imagine that i should star from classical field theory and go all through until reach in the quantum field theory over curved spaces. So, do you have suggestions of literature to start those subjects? | 0 |
There is a word for animals like horses and cows that defecate wherever they happen to be when the need strikes them, versus animals like dogs and cats that seek out one place or another to do their business. It may be that all such animals are herbivores but "herbivore" is not the word I'm looking for as it relates to eating habits rather than pooping habits. | 0 |
I am getting confused as I study the AdS/CFT correspondence, so I ask this question. CFT is given on the conformal boundary of AdS, which can be derived from Poincare coordinate patch to AdS. Would this mean that CFT has its AdS dual only on the subspace covered by this Poincare coordinate patch? Or does CFT has its AdS dual on the entire AdS space? | 0 |
This Wikipedia's page says that: David Hume's problem of induction demonstrates that one must appeal to the principle of the uniformity of nature if they seek to justify their implicit assumption that laws which held true in the past will also hold true in the future. For which I'm confused about how to interpret the meaning of appeal in this sentence. Most of the dictionaries I consulted suggest that the phrase appeal to can only be followed by one or more people or organizations but here it is followed by to some law. So how should I interpret that sentence? | 0 |
I just came across this sentence while studying for the SAT and wonder if it makes sense. The women soon disperse, SOME entering the shallow waters at the beach, OTHERS venturing out onto the rocks to access deeper waters. My first question is, it sounds a little awkward to add some additional fragments beginning with SOME and OTHERS here. Are they participial phrases? Can they be added like this beginning with SOME and OTHERS? My second question is, can they be added with just a comma? SOME ... , OTHERS ... I feel there should be some conjunctions to make it more natural. This makes me so confused. I'd really appreciate it if you could enlighten me. Thank you. | 0 |
I am taking a graduate-level mechanics course right now, and we are working with the continuous limit of coupled harmonic oscillators. My professor mentioned that he prefers the "bloch wave method" to the determinant method for finding the wave equation, but I do not know what this is. There is no mention of it in Goldstein, to my knowledge. Does anyone know how this works? | 0 |
For measuring the electric potential difference between two oppositely charged plates A and B, a test charge q is moved from plate A to plate B. My textbook says that the charge is kept in electrostatic equilibrium such that an equal and opposite force to the electrostatic force is applied on the charge to move it opposite to the electric field. However, I don't understand how it is possible for a charge to move if it is acted upon by two equal and opposite forces. My teacher said that the charge moves due to inertia, but I did not understand how, since the charge was initally moving towards the negative plate A. | 0 |
One of the postulates of Copenhagen interpretation of quantum mechanics is that every observable has a Hermitian operator A. With these operators we can then find eigenvalues of observables, make a time-evolution of a wave function and, in general, calculate the properties of the system. However we also introduce anti-Hermitian operators. My question is: What is the use for anti-Hermitian operators, if observables are described with Hermitian operators? NOTE: I am just diving into the subject of Quantum mechanics, so I hope this question makes sense and is not "too basic". | 0 |
I've used both Polish and Reverse Polish (RPN) notation. I get that using them one doesn't have to deal with varying evaluation order. While the benefits to automatic computation (as in software) is clear, it's unclear how this aided human reasoning. Can anyone explain how Polish Notation (or even RPN) simplified reasoning by people over infix notation? I'll be happy with any examples or even references to additional reading. | 0 |
I have a Hotwheels track set. It has a looped structure such that at some point in the car's trajectory, it becomes upside down. But in such a situation, it doesn't fall to the ground. I understand this has something to do with its fast speed. Can someone please explain as to why exactly this happens? Why it doesn't fall down? Something like this. (arrow indicates the position I was talking about) I was wondering what kind of forces were acting on the car at that point. A theory based (and not mathematical) explanation would be helpful since I am not accustomed with mathematical explanations | 0 |
A decimal representation of a rational number is necessarily either terminating or non-terminating and repetitive. This comes from the fact that when you are dividing there are only a finite set of possible remainders (remainder is always less than the divisor). As you go on dividing for decimal representation, the remainder has to repeat. Similarly, in finite fields, as you go on raising the power of an element, the product has to repeat because there are finite number of possible answers. This leads to Fermat's little theorem. In both cases, the finiteness of the possible set of answers is leading to these important and beautiful results. Can you suggest some more examples of this kind - understandable by school and junior college students? | 0 |
(Disclaimer: I'm not all that familiar with any of the two topics) Consider the Ising model on some graph with, lets say, two heavily inter-connected components that are sparsely connected between each other. This "bottleneck" would imply (or would be implied by?) that the Cheeger constant of the graph (and thus the first eigenvalue of the Laplacian matrix) is small and also that it would be very difficult for the spins in one component to interact with the spins in the other component. My question then is: is there any result linking the Cheeger constant with the "magnetization" properties of the graph? Something like a bound on the temperature at which the phase transition occurs that depends on the Cheeger constant or vice versa? Thanks in advance! | 0 |
I'm trying to compile a document which needs the package minted, but it throws the same error over and over: ! Package minted Error: You must have `pygmentize' installed to use this package I can't seem to make it work. Other forums say to install the package "Pygments," which is a Python package, but MikTeX doesn't seem to have that package in its repositories. Am I missing something? Do I have to install another LaTeX motor or something? Edit: Before anybody asks, yes I'm using the "-shell-escape" flag to compile the document which minted requieres. | 0 |
So, when we solve the optimization problem using Lagrange Multiplier method, I know that lambda can be positive or negative. Lambda is simply the rate of change in the optimal value when the constraint changes. So, I understand that lambda can be positive or negative. Now, my question is when we have inequality constraints. In that case, why do we have the requirement that lambda should be non-negative? I could understand the math behind it. But I am not able to follow up the intuition. Simply put, if Lambda is still the rate of change with respect to the change in the constraint, then why THEORETICALLY SPEAKING can't it be negative? | 0 |
I have the following list of points : I'm trying to find the best regression model to fit these points. The logistic regression is not close enough to the points : I guess I need something closer to a spline, but I don't know how to compute a regression model based on a spline, all I can find are interpolation models. Also, I would like to be able to compute the derivative of the regression. With a spline interpolation, I don't know how to compute the derivative over x so that it appears as a function of one-variable. For context, this is in order to build a tool for acid-base titration for chemistry. Thanks ! | 0 |
How to punctuate a quotation which is an exclamation, at the end of a sentence which is a question? The quotation is "Fire!" The sentence is: Did he really shout "Fire!"? OK, this is simply the shortest example I can think of to illustrate the question, the actual quotation of concern is longer, and so is the question sentence. But if it is improper to use both the exclamation point and the question mark, I'd like to know why. Searching has only resulted in lots of hits regarding whether to put a single mark inside or outside the quotation. | 0 |
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