darklight03/StackMIAsub huggingface dataset:
Today i studied about mirror formula, its derivation and sign convention used while deriving it, a question which i have is, why do i have to use sign convention while doing the derivation ? focal length, object and image distance all are distance so what is the point of using sign convention ? and while solving problems based on mirror formula why we use the sign convention again ? I have seen some answers on internet, they say that we use sign convention two times to cancel the effect of sign convention, but if want to cancel the effect of sign convention in the end then why do we use it, can't we solve without it ?
When thinking about a "random" atom in space (say a Hydrogen atom), should I assume that the electron is in a ground state (or any particular excited eigenstate) or is it in a superposition of all energy levels before I measure the energy of the atom? On the one hand, If the latter is the case that would mean that there is a nonzero probability to measure any arbitrarily large energy for the system, which seems weird. On the other hand, should not any quantum system be assumed to be in a superposition of all the eigenstates before making a measurement, then is there any mechanism by which the superposition of such atom is collapsed even before measurement?
I'm not sure where else to ask this since I'm not very familiar with this area. What is the backdrop of a theatre play act called? Like when the actors are behind the curtains and their silhouettes are instead flashed on the white screens or curtains. The play or act is all going on in the background just like a puppet play... What's it called? May I please know if this really is a thing or not?
Baum-Welch is an instantiation of the more general Expectation-Maximization (EM) algorithm. But recently when I learned about it I couldn't figure out where the Maximization step is used. Because the Baum-Welch algorithm give me a sense of just iterating between computing some intermediate variables according to old parameters and updating parameters according to computed intermediate variables. Out of the reason, I searched this problem online, but I only find this article useful to me. My problem is a step in the derivative process troubled me(it's shown in the figure below). Could you please explain it to me? I asked my professor and she couldn't help me. enter image description here
Consider a vessel completely filled with water and a vertically oriented capillary. If the water vessel was open at the top, you would expect capillary action to occur, lowering the water level in the vessel until a force equilibrium is reached. However, if we seal the vessel, the water would have to increase its volume/reduce its density for capillary action to take place, as no air can enter the vessel to fill up the volume. Does the (high) bulk modulus of water also apply here, as this expansion is nothing else than negative compression, i. e. would the hydrogen bridge bonds mostly suppress capillary action?
Order the following functions in terms of little oh notation: where: Im actually confused on how to do it. I think its the functions that confuse me not the method on how to do it. I know that: But either my mathematical skills are failing me or there's a different way to do it, that I don't know. Any help is appreciated. Thanks a lot in advance.
I just wanted to bring up some discussion about an apparently essential concept for some fields in mathematics as so as for some in physics, as already mentioned in the title, I'm referring to the word "symmetry". I'm currently studying about Lie symmetry method to search for first integrals of ODE's, and already saw that the main problem would be, exactly, to compute the symmetries, which involves a PDE. In adition, I constantly hear "symmetry breaking" from some working with QFT. It sounds like a joke but, are we trying to find those symmetries for you guys to "break'em"? Despite the kidding, could these two contexts be related in some degree?
In an infinite universe composed of single point masses which can be simplified as a uniformly distributed mass density, what is the equation for the gravitational field intensity in Newtonian gravity? I assume that: The gravitational field intensity is constant through space since the matter density is constant. The net force on any test particle must be zero, because all forces must cancel out due to symmetry. The gravitational field intensity is infinite since the its the sum the gravitational field intensity of each mass point, and there are endless mass points at infinite distance. But it must converge to a specific value since contributions of far away point masses contribute less and less with the square of distance.
Is there a word that means "lost thing"? Ir perhaps a word for "forgotten thing/ something that has been forgotten"? Similar to how requirement means "that which is required" or necessity is "something necessary"? I'm ideally looking for a noun or other words that are constructed to from an adjective describing something to the noun that stands for it. Here are two sample sentences: This book contains a list of major [lost things] throughout history. The [forgotten things] inspire many mythological stories. I am also okay if there's an archaic or uncommon word for this!
I don't know much about this topic, but I read something saying that gravity is not a force using an example of inertial observation. I started thinking about the topic again when I was researching photon spheres and thought why does gravity (if it is a force) curve light when photons have no mass. The only possible answer would be that gravity is not a force but rather the warp of space around mass. Would this be right?
I don't understand why you can't invert a hessian matrix using gauss jordan method. Can't you integrate or differentiate an entire row (because they are linear operators) and then subtract/add/swap? To clarify, I mean inverting the generic hessian formulation before it is applied to any function. In this way, I can get the hessian inverse so I can apply it to other functions. otherwise, I'd need to calculate hessian of a function and then invert, which takes a larger time complexity.
Can we calculate the total observed time dilation on a spaceship and a planet by combining the planet's relativistic spin velocity and the spaceship's approach or recession velocity from the planet it came from and where it's heading? Would the spaceship see both planets as time-dilated due to their combined relativistic spin and approach/recession velocities? Should we consider both the spin velocity and the apparent recession/approach velocity, or just one of them, in such calculations?
As I understand, it is perfectly possible to explain the standard double slit experiment with a laser beam using only classical physics. On the other hand, this experiment is one of those experiments which is mentioned the most when quantum theory is introduced. So at what point of the experiment -- or through which variation -- does quantum theory come in where classical physics fails ?
In Baby Rudin a subset E of a metric space X is defined to be connected if "E is not a union of two nonempty separated sets." This may be nit picking, but should this not be E is not a union of two or more seperated sets ? Wikipedia agrees. To be super nit picking, by Rudin's definition (and taking it super literally) a set that is the union of three nonempty separated sets would be connected since... two is not equal to three.
According to the argument in this post, a theory of Quantum Gravity should not be compatible with the notion of time evolution. This is also called "The Problem of time". However, the target spacetime formulation of string theory does have a notion of universal background time given by the target spacetime. So it seems like it does not address the problem of time. The CFT part of AdS/CFT is also a QFT with a well-defined universal time. So does String theory not address this problem? If no, then what does it say about it?
I heard this dialog in a Western film: Ruffian: Are you Josey Wales? Josey: That['d] be me. Methinks Josey responded That be me and not That'd be me. Is the former even correct? Is That be me. also a sentence in subjunctive mood, just as That'd be me is. If That be me is correct, what would be the difference in meaning between That'd be me and That be me? Please, take note that this question is not a duplicate.
The intended meaning is that 'it', described simply, is 'everything'. Would I write: It is in short...everything. Or: It is, in short...everthing. Instinctively, I believe that a comma is needed before "in short". But the confusion arises here: Is it a common enough phrase that the comma is not needed? Is it a publisher's preference situation? Author's preference? I've seen the phrase 'in short' both with and without commas. Normally two commas are used, as it's a parenthetical, but the ellipsis makes the second one unnecessary.
In one of our informal math research club sessions we are thinking of hosting a math meme making competition. Our idea is that math memes will trigger curiosity and interest among the participants. This would not only help in questioning and understanding the mathematical ideas behind the meme but the participants will also have fun doing it. Lets say that I go ahead with this idea. What could be a possible way achieve best results?
What is the meaning of the phrase, 'as thus construed'? I was writing an essay and felt that phrase was appropriate, but I looked it up with quotes on google and found only references in some legal documents and academic papers. Is there a similar phrase that I am thinking of, or does this make sense by itself? For example, suppose I just described x a certain way. I then say, "x, as thus construed, is Y." Does this make sense? Or is there a phrase that is more accurate here?
so I am looking for good text books that treat signed measures, integration thereof and total variation etc. In particular also for finitely additive signed measures. I have found Dunford and Schwartz a little bit too general in that they dont necessarily consider (signed) measures but more generally set functions. I would also like the book to be as standard in notation and the used concepts as possible. So can you give me any suggestions for text books?
I am in charge of deciding the name of a skill in a role-playing game that serves as a catch-all for abilities/skills that are otherwise unlisted in our handbook (think skills that will help players flesh-out their character's personality, quirks, and life). Such a skill could be a profession type, a craft (e.g.,whittling), or something more exotic like hyperlexia. Profession and Craft do not capture the spirit well enough. Ability seems too generic, as are its multi-word variants, e.g. Unlisted Ability. Knack seems closer to the mark but open to suggestions.
I am currently studying a paper on Wasserstein Fair Classification. Several places they mention the Wasserstein barycenter, weighted barycenter distribution or the Wasserstein barycenter distribution. What is it? How is it defined? I can only find very deep measure-theoretic explanations, which are both a bit out of my league as a statistician, who never enjoyed analysis very much, but they simply also lack an intuition behind.
I was wondering is it possible to try and do optimisation of an ellipsoid given the formulae for its volume and surface area? I would be trying to keep the volume constant whilst minimising SA. This is for one of my maths investigations, basically trying to minimise packaging of a kinder egg, so if this is somewhat of a dead end, what are some alternative approaches I can take forwards? Any help would be really appreciated! Update: Ive derived the equations for the SA and Volumes of an egg shape Would the Lagrangian Multiplier Method work here
I happened upon this video purportedly showing a coin on a horizontal table receding away from a lens would disappear from bottom up. The explanation via diffraction resolution limit is wrong. However, I would like to find the correct explanation of the phenomenon. When the camera zooms in and focuses on the coin, the coin appears clearly. This can be explain by the fact that part of the light from the coin still enters the aperture of the lens. However, how would one explain the abrupt disappearance of the bottom of the coin below the table upper edge when the focus of the lens is on the table edge?
My question is this: Why can't electric potential energy be defined at one point. Surely a point charge has some inherent electric potential energy cause by force applied by the source field. The applied force would cause the charge to accelerate. The acceleration approaches zero as you get farther from the field, so the velocity could also approach a known limit (depending on the function). That velocity can be used to calculate the maximum kinetic energy, which would equal the original electric potential energy imparted on the charge by the field. I know this is a classical treatment of the situation, but what's wrong with this line of thinking?
I have questions about the inner product and coordinate transformation matrix. For F inner product space V, consider vector a and b in V and its inner product <a,b> then the inner product is invariant about changing the Basis of V? And let B and B' be Basiss of V. Then can I think that the coordinate transformation matrix from B to B', denoted by R is a unitary matrix because it preserves the inner product <a,b>?
Electrons have an e-field, and a moving e-field causes a b-field. These fields are defined in such a way that it makes calculating things like forces much simpler. Is this just a model and there aren't actual 'waves' traversing around us, but rather mere forces caused by a movement of an electron? If the force caused by a charge wasn't viewed as a wave, would electromagnetism only be a model for calculating the effects of the charge, utilizing waves as a tool? If so, is it fine to propose that visible light is simply our brain's reaction to certain forces caused by moving electrons in a certain frequency?
I have always been told that if you press the brake pedal fully and fast it can make the wheels lock themselves, and that you shouldn't do so because it would take longer to stop the car than if you push the brake pedal progressively, why so? I can imagine that when done progressively the car won't start doing jumps due to the wheels block as if you would brake immediately but I can't see why.
The existence of dark energy leads negative pressure. Is the pressure can be anisotropic? What situation can cause anisotropy of pressure? Further, Is the pressure can be negative in some directions and be positive in other directions? Such as in spherical coordinates, the radial pressure is negative and the tangential pressure is positive. Will this happen when matter and Dark energy exist at the same time?
I want to determine the largest area ellipse inscribed in a rectangle, in order to write a code that can determine the lengths c and d given a and b (see image here). I know the obvious answer would be c and d are halves of a and b, but I want the derivation (and also the maximum area) so I can stop thinking about this, saddly I can't seem to figure this one out. I remember doing the opposite in school (rectangle inside ellipse) but can't do it properly now. Hope you can help me.
I'm quite close to release my first game, and I can't decide which is grammatically correct on my first user facing screen. My game will surely have some grammatical mistakes but I would appreciate it if the first screen would be more or less accurate ;P So the title wants to welcome the user into my game but I dunno which way I should go. Welcome to {Game Title} or Welcome in {Game Title} Any feedback is appreciated!
i would like to find a way to study physics online and get academic credentials in it and be able to contribute to the research and publish. I know some topics are experimental and require physical attendance, however there must some subfields in physics that can be studied online. Now there are many online masters in STEM fields like computer science from reputable universities. Is it the same for physics?
The Wikipedia page for locally constant function says that a locally constant function is constant on each connected component, but that the converse only holds if the space is locally connected. What would be an example of a function that is constant on each connected component but not locally constant? I first thought of the topologist's sine curve, which is not locally connected, but since this is a connected space, such a function would be constant on the entire space and therefore automatically locally constant.
I need to prove in graph theory that if L(G)=G then G is a combination if simple cycles. I already did it assuming G is connected, so feel free to use this fact as given. My only issue is that it may be possible that in a non-connected graph not every one of the connected components will satisfy L(G)=G. For example, if the Connected components in G are A,B,C it may be possible that L(A)=B, L(B)=C, L(C)=A.
Suppose there is constant diameter pipe where a liquid flows through it, and if pressure of a liquid is due to external force or its weight when it is constrained or semi constrained (according to the accepted answer on this question), how can someone visualize how does pressure drop occur due to frictional losses? Does the force on the liquid decrease somehow or does it become less constrained so it has lower pressure?
I am studying the spontaneous symmetry breaking in the mean-field Ising model and it's clear to me the necessity of taking first the thermodynamic limit and then the zero-field limit to see the phase transition, otherwise we only see zero magnetisation even under Tc. I was wondering if there was a phase space approach underlying this result and if the spontaneous symmetry breaking implied and ergodicity breaking as well, as I imagine that the ensemble average is anyway zero, but this is not what we observe physically. Can someone give me a hint?
I went through a quite a lot of posts here but did not find the information I wanted. I'm looking for a beginner / introductory (yet mathematically rigorous) book recommendation for differential geometry / topology required for General Relativity. I'm perfectly fine (in-fact I like) the so-called dry mathematics books (theorem-proof-theorem). What I need is - Very clear definition of Mathematical objects used in GR Crisp / rigorous proof in modern notation I need the book at advanced undergraduate or beginner graduate level. Thanks in advance.
Is there any way one can modify a known functional so as to get a solution for another quantity related to it? Because this is too general I would like to make it more clear with an example. Given the classical EM Lagrangian, we acquire the equations of motion for a particle in an EM field. Starting from this, is there anyway one can find a functional that when varied will give the solution for, let us say, the electric potential, for a given charge distribution and known boundary conditions?
To understand the attractive and repulsive force between two currents, I am looking at two electrons moving parallel and antiparallel to each other. How can an attractive (or less repulsive) Lorentz force between two charges and its directional dependence be explained? I would like to understand this in terms of dynamical effects of the electric field and not in terms of a magnetic field which is the common approach for correctly treating and not further looking at such details.
Pramod Achar's book on perverse sheaves has a quick reference in the back that looks like this. How can I achieve something similar? The important things to me are: the general spacing (although maybe I would enjoy less margins on the outside), the two columns, the numbering and labeling, the horizontal line separators. For language, I only care about English. I don't have any font preference.
Consider this fact that we all know from school mathematics: There is a one to one correspondence between real numbers and points of a line. But the problem is I have never seen a rigorous proof of this fact. This is what Apostol writes. And similar is the case with other modern analysis books. So my question is, where can I find the proof of this one to one correspondence. I don't care if geometry is in Hilbert's axioms or Tarski's or anyone else all I care about is correspondence.
I'm bit confused about the current flow in capacitors. My question is, let's assume those two electric circuits: As shown in the picture, the only difference is only the capacitance. I'm wondering about the current flow magnitude. In which of the circuits the current flow will be bigger? or will it be the same? To start, I assume both plates of the capacitor are uncharged. My guess is that right at the moment of closing the switch before the capacitors are charged from the voltage source, the current flow will be even. Once they are fully charged, of course, the current will be bigger in the system with the bigger capacitor. But till this point, what will be the current flow? thanks
it is said that the time period of a simple pendulum in space is infinite. it is because the gravity in space is zero and anything divided by zero is equal to infinity.how can time period be infinite? also, in space, everything just floats around. how can a pendulum in space do oscillations if there is no restoring force to bring the mass back to mean position. how can a simple pendulum exhibit SHM in space? if it cannot exhibit SHM , how is the time period formula for the simple pendulum applicable to the pendulum in space and what is the meaning of infinite time period. why do the time period of pendulum in space even exists?
I was wondering if it is posssible to write my own environment for writing redox equations in form of: O: ... R: ... ___________________________ S: ... O stands for oxidation, R for reduction and S for the summary equation. Also, there is line that should separate O and R from S. I have never written any environment in LaTeX, so could anyone just help me start? I've seen that there are some packages that are about chemistry, but none help me about this problem.
In surface integrals the process is to use the dot product of the vector field with the unit normal vector first and multiply that with the area element. In the line integral the process is to use the dot product of the vector field with the length element. Why isn't the unit tangent vector used in the line integral computations while in the surface integral computations the unit normal vector is used?
While deriving the Planck's radiation formula, why do we use MB statistics when we calculate the average energy of oscillators? Shouldn't we use BE? Is this because temperatures concerned are very high and quantum stat goes to classical at high temperatures? But again, in a similar calculation, while calculating the lattice specific heat of the solid using Einstein's model or the Debye model, I have seen books calculate the average energy of oscillators using MB distribution only, but we use this formula to predict specific heats at very low temperatures also. So I don't understand, what is the reason?
The sentence is as follows: "Isn't it evident who/whom they have in mind for the position?" Depending on how you try to reword it to figure it out, the answer seems different. --Is it not evident that he is the one they have in mind for the position? (This seems to be a case for "who" here.) --Is it not evident that they have him in mind for the new position? (This seems to be a case for "whom" here.) Should it be who or whom? Why?