Finite Definition and 1000 Threads

Q7. Name an extension of \(\mathbb{Q}\) over which \(\pi\) is algebraic of degree 3. I have a very simple answer to this (below) but is it correct? Is it likely to be what the text is after? \(\mathbb{Q}(\pi^3)\) is an extension of \(\mathbb{Q}\), it is not an algebraic extension but I am not...

Homework Statement A string of length L =8 is fixed at both ends. It is given a small triangular displacement and released from rest at t=0. Find out Fourier coefficient Bn. Homework Equations what should i use for U0(x) ? The Attempt at a Solution

Homework Statement An electron in a finite square well has 6 distinct energy levels. If the finite square well is 10nm long determine: a) Approximate the possible values for the depth of the finite square well ##V_0##. b) Using a well depth value in the middle of the results obtained from part...

At the time of Big Bang the size of Universe equal the size of an atom.The Universe has expanded and the time from the Big Bang to the present is finite.Then at the present time the size of the Universe is finite or infinite?

Hi I've been trying to get a simple solution to the 2D Navier-Lame equations using finite difference on a rectangular grid. I want to see the displacements, u and v, when a simple deformation is imposed - e.g. top boundary is displaced by 10%. The equations are as follows: \begin{eqnarray*}...

Homework Statement Given an initial value problem: ##x'(t)=f(t,x)\,,x(t_0)=x_0## Use centered finite differences to approximate the derivative, and deduce a scheme that allows to solve the (ivp) problem. Homework Equations For centered finite differences ##\displaystyle\frac{dx}{dt} \approx...

I just noticed in reading Griffiths that he places the base of the infinite square well at a zero potential while he places the base of the finite square well at a negative potential -V_0, where V_0 is a positive, real number; is there any reason for this? I just started learning about them/am...

Hello everyone, my question is about Euclidean correlators (say a 2-pt function to be specific) in presence of non-zero chemical potential. The question in particular is: is it still true that the Minkowski time ordered 2-pt function can be simply obtained from the Euclidean one by analytic...

A number of scientists subscribe to this theory. I read up on it, but none of the explanations I found really answered my questions. How should one attempt to envision a universe that is finite and bounded?

This question is in context of the recent gravitational wave detection by aLigo. Apparently aLigo has detected the entire process, including the before merger, during merger, and aftermath of the completed merger. My understanding is that two black holes should not be seen to be merging in...

I am solving some 2nd order differential equations using the finite element method. Doing so I represent the second order derivative at a given point as: ∂2ψi/∂x2 = 1/(Δx)2 (ψi-1+ψi+1-2ψi) And solve the differential equation by setting up a matrix of N entries and solving for the eigenvectors...

Hello! (Wave) I want to show that a group with finite number of subgroups has to be finite. I thought to suppose that the group is not finite and then get a contradiction.So, suppose that the group is not finite. Then the group has infinite elements. Since the group has a finite number of...

Homework Statement Show that finite dimensional normed vector spaces are complete. Homework Equations ##E## is a finite dimensional vector space and ##N## a norm on ##E## The Attempt at a Solution If ##\{x_n\}_n## is a Cauchy sequence in ##(E,N)##, then it is bounded and each term of the...

what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure

Homework Statement A finite line of uniform charge is on the line joining (4,0,0) (0,8,0) and has λ= 2μC/m find E at (0,0,0) Homework Equations E = Q / (4 π ε0 r^2) dQ = λ dl = λ dx The Attempt at a Solution I first notice that r will depend on 2 changing values x and y. I write an...

If $G$ is a finite group, show that there exists a positive integer $N$ such that $a^N = e$ for all $a \in G$. All I understand is that G being finite means $G = \left\{g_1, g_2, g_3, \cdots, g_n\right\}$ for some positive integer $n.$

Please,I am working on the criticality calculation of an homogeneous finite cylindrical reactor core using four-group diffusion equations. I have been able to discretize the multigroup diffusion equations using the finite difference method(FED). But I am stocked on the iterative method to...

Homework Statement Say x is an infinitesimal number on the hyperreal line, is this expression finite, infinite or infinitesimal Homework Equations (sqrt(4+x)-2)/x The Attempt at a Solution [/B] My approach so far has been that sqrt(4+x) is (2+y) where y is another infinitesimal and y<x...

Let F=Z2 and let f(x) = X^3 +x+1 belong to F[x]. Suppose that a is a zero of f(x) in some extension of F. Using the field created above F(a) Show that a^2 and a^2+a are zeros of x^3+x+1?

I would like to know how to implement internal hinges in a program I'm developing. A hinge is created by changing the stiffness matrix of the beam. The problem is when two interconnected beams have a hinge at the same location, so basically we have a hinged joint, in this scenario I will obtain...

Ok my question: what is the difference between the binding energies of these 2 types of atoms, conceptual wise, which one is greater? I am assuming based on the easy calculations of the potential energy of the finite size atom ( inside and outside) There is a difference between the potential...

I've seen various, wildly different, estimates of the size of the Universe. Do we have evidence demanding that the Universe is finite in size? If so, what are the clues that lead us to estimate that size beyond absolute speculation?

Homework Statement Laser light with a wavelength 633 nm is used to illuminate two slits separated by 0.125 mm. The width of each slit is 0.0150 mm. Assuming that only fringes between the first minima in the pattern are counted, how many bright fringes are visible? lambda = 633nm d = 0.125mm w=...

I have a particle in a spherical well with the conditions that V(r) = 0 is r < a, and V(r) = V0 if r ≥ a. In this problem we are only considering the l=0 in the radial equation. After solving this I found that in the region 0<r<a, u(r)=Bsin(kr) (k=√2mE/hbar), and in the other region...

Homework Statement A finite solenoid with "N" turns of wire, "L" length , "R" is the radius of the solenoid and passes through it a current "I". The objective is to calculate "L" of a finite solenoid. Not the basic formula ##L=\frac{\mu_0·N^2·S}{Length}## which is for a infinite solenoid. See...

I think I am in a misconception concerning laser beams: Even the best lasers have a small line width. The spectral line is gauss-shaped. therefore the wave in position-pace is also a gauss-shaped wave packet, that travels with a certain group velocity. But this gauss shaped wave packet has a...

Homework Statement Find a recursive relation on the number of partitions ##P_n## for a set ##S_n## of cardinal ##n##. ##P_0 = 1## is given. Homework EquationsThe Attempt at a Solution A partition of ##S_{n+1}## is given by the choice of a non-empty ##k##-block ##A_k## of ##S_{n+1}## and a...

Homework Statement Find \sum\limits_{k=0}^{n}k^2{n\choose k}(\frac{1}{3})^k(\frac{2}{3})^{n-k} Homework Equations -Binomial theorem The Attempt at a Solution I am using the binomial coefficient identity {n\choose k}=\frac{n}{k}{{n-1}\choose {k-1}}: \sum\limits_{k=0}^{n}k^2{n\choose...

I've often wondered about what happens when you try to add up the potential due to everything in the universe in a Newtonian way, especially in the context of the "Sum for Inertia" which seems to suggest a connection between Mach's Principle and GR in the context of rotation. Today I noticed an...

Hi, one thing always bothered me about the argument on the size of the Universe. If it started about 13.7 bn years ago then how could it possibly be infinite in extent? Once the time was finite its not possible to attain infinite extent - no matter how fast it expands. Also if there was...

problem statement, all variables and given/known data A finite sheet of charge, of density ρ=2x(x2+y2+4)^3/2, lies in the z=0 plane for 0≤x≤2m and 0≤y≤2m.Determine E at (0,0,2)m Ans:(18x10^9)(-16/3ax-4ay+8az) Homework Equations E=kQ/R2 The Attempt at a Solution dE=ρdA / R^2 aR...

So, according to physicsoftheuniverse.com, "In the centre of a black hole is a gravitational singularity, a one-dimensional point which contains infinite mass in an infinitely small space, where gravity become (sic) infinite and space-time curves infinitely, and where the laws of physics as we...

Light, amount other things, have no mass, and therefore is able to attain the highest speed possible in this universe. Yet for some reason this speed is not infinite, as would what intuition dictate, but has a finite value. Would it be fair to say that the fact light, something that "should" be...

A 2-dimensional creature living on the surface of a 3-dimensional sphere could conclude he lives in a finite, unbounded universe. Is it necessary for a 3-dimensional creature to assume there is a 4th spatial dimension in order to conclude the universe is finite and unbounded? I have seen a...

How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?

\sum^{\infty}_{n=1}\frac{1}{n^{\alpha}}=\zeta(\alpha) For ##\alpha=-1## ##\zeta(-1)=-\frac{1}{12}## I do not see any difference between sum ##1+2+3+4+5+...## and ##\zeta(-1)##. How the second one is finite and how we get negative result when all numbers which we add are positive. Thanks for...

Hi, Recently I had to find a derivative on a uniform grid. Being naive I tried the following scheme: f'(x_{n})=Af(x_{n+2})+Bf(x_{n+1})+Cf(x_{n})+Df(x_{n-1})+Ef(x_{n-2}) Then write the f(x_{n\pm i}) in terms of f^{(n)}(x_{n}) by use of Taylor's theorem. This lead to a system of linear...

I'm trying to replicate the model presented in this [paper](http://www.sciencedirect.com/science/article/pii/S1359431103000474), which is basically to model heat and mass transfer along a one-dimensional duct. There are four characteristic equations for this problem : Momentum conservation...

I am interested in the solutions of the Klein Gordon equation. Plane waves solutions are well known in physics. they look like ## e^ { i (kx - \sqrt{k^2 + m^2} t)}## or superpositions of them. They are finite when t or x go to infinity. I am looking for the general solution of the problem. In...

Hello, Heat transfer through finite temperature difference is known a irreversible process because heat cannot be transferred from cold to hot temperature without doing any additional work. But, how this transfer affect the efficiency of the system? How this heat transfer decrease the amount of...

where i can found an example A FORTRAN control volume finite element method code FOR FLUID FLOW PROBLEMS thanks for help

I am simulating electrons inside a cylindrical well like the one shown on the first figure. My current work has been on solving the Schrodinger equation numerically for the above potential and then finding corrections to the solution such that it is consistent with Poissons equation. To do so...

hi PF! I've attached pictures to help you all see what is happening. Basically, I am running a forward time-centered space finite difference scheme, which is $${h_i^{j+1} \approx \left[ h_i^j \left( \frac{h_{i+1}^j-2h_i^j+h_{i-1}^j}{\Delta z^2} \right) + \frac{1}{2}\left(...

Hi, I have written some codes for the finite difference solution of diffusion equation (\frac{\partial c}{\partial t}= D {\nabla^2 c}, where c is the species concentration and D is the diffusion coefficient) as follows: DO k= 1, tsteps+1 DO i = 2, zsteps DO j = 2, rsteps...

I am trying to solve the following eigenvalue differential equation numerically: ∇2ψ = Eψ , where the coordinate system is polar coordinates and the boundary condition is ψ(R,Φ)=0, where R is the radius of the disk i am working on. To solve it I am using a finite difference scheme, but there...

Take a prime order cyclic group. I want to take that as the additive group of a finite field. Since every finite field of the same order is isomorphic to one another, does the isomorphism define a multiplicative group structure on my cyclic group elements?

If there a finite field where both group structures have hard discrete logs? Discrete log in the additive group means multiplicative inverse.

If someone can check this, it would be appreciated. (Maybe it can submitted for a POTW afterwards.) Thank-you. PROBLEM Prove that if $H$ and $K$ are torsion-free groups of finite rank $m$ and $n$ respectively, then $G = H \oplus K$ is of rank $m + n$. SOLUTION Let $h_1, ..., h_m$ and $k_1...

Hi PF! I was wondering if anyone could help me with a finite difference question? The problem I am doing is a 1-D space and time problem, so ##z## (space variable, from left to right) and ##t## (time) are my independent variables and my dependent variable is ##h##, the height, governed by a PDE...

I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...