Finite Definition and 1000 Threads

Hello, I have been following this forum for some time now, but this is the first time I participate. I would appreciate if you could give me a hand in understanding the results of a finite element analysis of an automotive component we have designed. The analysis results indicate that the...

G finite abelian group WTS: There exist sequence of subgroups {e} = Hr c ... c H1 c G such that Hi/Hi+1 is cyclic of prime order for all i. My original thought was to create Hi+1 by reducing the power of one of the generators of Hi by a prime p. Then the order of Hi/Hi+1 would be p, but...

Hello, I need help writing a MATLAB program to solve a heat transfer problem implicitly. For some reason this is very confusing to me. The problem is stated below. Any help is greatly appriciated. Let me know if you need a little more info. I need to write a program to solve this...

Homework Statement Consider two long coaxial metal cylindrical tubes, with radii a and b and length L. (You may assume a,b<<L. Also a<b.) Suppose the inner cylinder is given a charge +Q and the outer cylinder a charge -Q. Using Gauss' Law, compute the electric field for all r between a and...

Homework Statement The deuterium nucleus (a bound state of a proton and a neutron) has one bound state. The force acting between a proton and a neutron has a strong repulsive component of range 0.4 fm and an attractive component of range ~2.4 fm. The energy needed to separate the neutron from...

Hi All; I attach a pdf file on something I have been working on for some time. Any feedback would be appreciated. Regards Garbagebin

For a finite one-dimensional square potential well if a proton is bound, how many bound energy states are there? If m = 1.67*10^(-27) kg a = 2.0fm and the depth of the well is 40MeV. Now I know the energy levels are En = (n^2 * h^2) /(8ma^2) = (n^2*pi*2)/4 * (2hbar^2)/(ma^2) but I am...

Homework Statement Prove: If H is a subgroup with finite index in G Then there is a normal subgroup K of G such that K is a subgroup of H and K has index less than n! in G. Homework Equations Note: |G:H| represents the index of H in G |G:H| is the number of left cosets of H in G, ie...

If f is meromorphic on U with only a finite number of poles, then f=\frac{g}{h} where g and h are analytic on U. We say f is meromorphic, then f is defined on U except at discrete set of points S which are poles. If z_0 is such a point, then there exist m in integers such that (z-z_0)^mf(z)...

I would like to find a nice formula for \sum_{k=0}^{n - 1}ar^{4k}. I know that \sum_{k=0}^{n - 1}ar^{k} = a\frac{1 - r^n}{1 - r} and was wondering if there was some sort of analogue.

When explicitly given a set of polynomial equations, I am interested in describing its singular locus. I read this from several sources that a point is singular if the rank of a Jacobian at a singular point must be any number less than its maximal possible number. Or is it the locus where all...

Homework Statement Factor x^16-x over the fields F4 and F8 Homework Equations factored over Z (or Q), x^16-x = (x*(x - 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)*(x^8 - x^7 + x^5 - x^4 + x^3 - x + 1) The Attempt at a Solution I know the that quadratic and higher terms I have left...

Hello everybody, Yesterday I've read that there exist a real number r which cannot be defined by a finite number of words. This result, although quite awesome, is so strange that it lead Poincaré to doubt Cantor's work and state "never consider objects that can't be defined in finite number...

1. Homework Statement (a) Calculate the electric field at an axial point z of a thin, uniformly charged cylinder of charge density ρ , radius R, and length 2L. z is the distance measured from the center of the cylinder. (b) What becomes of your result in the event z >> L ? 2. Homework...

Hi guys! This is my first post on Physics Forums even, and I have a question regarding potential wells with finite potential. I understand the infinite potential well but what if the well is finite? For example, if we a potential well with infinite potential to the left of 0, but with increasing...

Homework Statement I have a solid cylinder of uniform charge density whose axis is centered along the z-axis. I am trying to calculate the electric field at a point on the z-axis. What I'm trying to do is to start by first calculating the field of a disk centered on the z-axis at a point on...

Homework Statement Consider a finite square-well potential well of width 3.00x10-15 m that contains a particle of mass 1.88 GeV/c2. How deep does the well need to be to contain three energy levels? Homework Equations The Attempt at a Solution I think I have to use the formula for penetration...

My textbook never mentioned what happens when you multiply something by infinity. I would think 4 * ∞ would be ∞. So to me that whole equation should simplify to 1 - ∞ which is ∞. I don't see how they get 2/3

Why is that amperes circuital law gives the same magnetic field around a finite legnth of wrie as if it is an infintie legnth of wire? By biot-savarts law we know that for a finite length of wire magnetic field is μ i ( cos θ1 - cos θ2)/ 2∏r I searched this question in google and one of...

Hi Could anyone point me in the right direction? I'm employed at a small firm, only three employees at the time being. Our competencies spans from architecture to programming. We're in need of somebody who can help us create a finite element solution which we can implement in the cad...

HI, I was reading an article and it says that a finite group of order p^aq^b, where p, q are primes, is solvable and therefore not simple. But I can't quite understand why this is so. I do recall a theorem called Burnside's theorem which says that a group of such order is solvable. But then I...

Hi I am trying to prove that P=\{X\in\mathcal{P}(\mathbb{Z^+})\;|\;X\mbox{ is finite }\} is denumerable. Now here is the strategy I am using. Let A_n=\{X\in\mathcal{P}(\mathbb{Z^+})\;|\; |X|=n\;\} So A_n are basically sets of subsets of \mathbb{Z^+} with cardinality n. So...

I have problem like attached.

Suppose we have non-empty A_{1} and non-empty A_{2} which are both open. By "open" I mean all points of A_{1} and A_{2} are internal points. There is an argument -- which I have seen online and in textbooks -- that A_{1} \cap A_{2} = A is open (assuming A is non-empty) since: 1. For some x...

So this is a very simple question that I am having some trouble figuring out: Let s(t) be a finite energy signal with Fourier Transform S(w). Show that \lim_{w \to \infty } S(w) = 0 We know by defintion that the FT of this signal is \ints(t)e^{-jwt}dt and also that ∫|s(t)|2dt < ∞. I'm a...

Hello I want to resolve a nonlinear partial differential equation of second order with finite difference method in matlab. the equation is in the pdf file attached. Thanks

Hello, I was wondering this, what is the cardinality of the set of all finite subsets of the real interval [0,1] It somehow confuses me because the interval is nonnumerable (cardinality of the continuos \mathfrak{c}), while the subsets are less than numerable (finite). It is clear that it has...

Homework Statement I'm having a hard time understanding when we approximate higher order powers by order notation, especially when it comes to working out the Truncation Error for Finite Differences. My notes say "We use the order notation O(h^{n}) and write X(h) = O(h^{n}) if there exists a...

Hello, I am trying to solve the shallow water equations using finite element method. Can anyone explain me how to treat nonlinear term in the Galerkin equation? so for example in the equation for the velocity we will have the term u\nabla v where u and v are the velocity components. For...

Clarification: I have seen in quantum mechanics many examples of wavefunctions and their Fourier transforms. I understand that a square pulse has a Fourier transform which is nonzero on an infinite interval. I am curious to know whether there exists any function which is nonzero on only a...

Hello all, I am in the process of solving a finite elements problem involving obtaining deflection of a simple mass-spring-damper 2nd order ODE system with a defined forcing function. While going through my class notes, I came across the idea of the central difference method, which is...

WTS, is that such set is a subgroup. I need to show closure under group operation and inverse. I can do the inverse which is usually the hardest part, but I'm stuck on the grp op. So let a in K and b in K, both have finite distinct conjugates. Their conjugates are in the group too. WTS...

I have a system of non-linear coupled PDEs, taken from a paper from the 1980s which I would like to numerically solve. I would prefer not to use a numerical Package like MatLab or Mathematica, though I will if I need to. I would like to know if anyone knows how to solve non-linear coupled...

Homework Statement An electron enters in a finite rectangular potential well of length 4 angstroms. When the entering electrons have a kinetic energy of 0.7 eV they can travel through the region without having any reflection. Use this information to calculate the depth of the potential well...

I am solving the heat equation in a non comercial C++ finite elements code with explicit euler stepping, and adaptive meshes (coarse in the boundaries and finer in the center). I am aware the CFL condition for the heat equation depends on dt/h**2 for the 1D, 2D, 3D case. When I solve the...

Homework Statement Find a simple DFA (i.e. deterministic finite automaton) that accepts all natural numbers n for which n mod 3 = 0. Hint: A natural number is divisible by 3 if its checksum (or sum of digits) is divisible by 3. Homework Equations The Attempt at a Solution...

Hello Guys I could not simplify the finite product bellow to another expression I hope I get an answer from you guys Thank you

I made a small program to simulate the time development of a 1D wavepacket obeying the Schrodinger equation, mostly in order to learn a new programming language - so in order to not have to invoke big numerical methods packages, I opted for the simplest solution: The standard three-point...

Hi everyone. My first post on this great forum, keep up all the good ideas. Apologies if this is in the wrong section and for any lack of appropriate jargon in my post. I am not a mathematician. I have a theory / lemma which I would like your feedback on:- Take a finite set S of integers which...

Hi, I am trying to show that timelike geodesics reach the Rindler horizon (X=0) in a finite proper time. The spacetime line element is ds^{2} = -\frac{g^{2}}{c^{2}}X^{2}dT^{2}+dX^{2}+dY^{2}+dZ^{2} Ive found something helpful here...

I'm attempting to perform interpolation in 3 dimensions and have a question that hopefully someone can answer. The derivative approximation is simple in a single direction: df/dx(i,j,k)= [f(i+1,j,k) - f(i-1,j,k)] / 2 And I know that in the second order: d2f/dxdy(i,j,k)= [f(i+1,j+1,k)...

Homework Statement I have a sequence of functions converging pointwise a.e. on a finite measure space, \int_X |f_n|^p \leq M (1 < p \leq \infty for all n. I need to conclude that f \in L^p and f_n \rightarrow f in L^t for all 1 \leq t < p. Homework Equations The Attempt at a Solution...

Hello all: For modeling flow (or whatever) in a non-rectangular geometry, can anyone comment on whether the finite element method would be better or worse or the same as the integrated finite difference method? I'm reading some papers by competing groups (so I can decide which code to...

Homework Statement Given is \sum_{n=-N}^{N}e^{-j \omega n} = e^{-j\omega N} \frac{1-e^{-j \omega (2N+1)}}{1 - e^{-j\omega}}. I do not see how you can rewrite it like that. Homework Equations Sum of a finite geometric series: \sum_{n=0}^{N}r^n=\frac{1-r^{N+1}}{1-r} The Attempt at a...

Problem - Find backward finite difference approximations to first, second and third order derivatives to error of order h^3 Attempt By Tailor’s series expansion f(x-h) = f(x) - h f’(x) + h^2/2! f’’(x) - h^3/3! f’’’(x) + … Therefore, f’(x) with error of order h^3 is given by f(x-h) = f(x)...

Two idential, finite sized bodies of constant volume and constant heat capacity are used to drive a heat engine- heat is taken from the hot (Th) body, work is done, and heat is ejected to the cold (Tc) body. Both bodies wind up at Tf (a) What is the change in the entropy of the system? (b)...

I found a torrent online of Apostol's "Mathematical Analysis" 1st edition and I think I found a typo, or whoever scanned the book cut off the edge a bit... Apostol writes that the extended real number system R* is denoted by [-∞, +∞] while the regular real number system R is denoted by (-∞...

Homework Statement Let G be a nonempty finite set with an associative binary operation such that: for all a,b,c in G ab = ac => b = c ba = ca => b = c (left and right cancellation) Prove that G is a group. 2. The attempt at a solution Let a \in G, the set <a> = {a^k : k \in N} is a finite...

Homework Statement 1. Mixed Spectrum The finite square well has a mixed spectrum or a mixed set of basis functions. The set of eigenfunctions that corresponds to the bound states are discrete (call this set {ψ_i(x)}) and the set that corresponds to the scattering states are continuous...

Would you please find the McLaurin expansion of the following series to help me: M Ʃ Binomial(m + q - 1,q) [(a x)^q /((a x + b)^(m + q)] q=0 where M , m ℂ N^+; a, b > 0; MANY THANKS FOR YOUR HELP.