Finite Definition and 1000 Threads

I am not a physicist or a cosmologist, just a science layman who has been doing a lot of reading and thinking. I have been reading a lot in popular literature that if Omega =1, then the universe must also be infinite. Do you think this is just an over-generalization intended for the general...

Hi everybody, I am looking for some help with a problem that has been nagging me for some time now. I'm going to give you the gist of it, but I can provide more details if needed. So, after some calculations I am left with a function of the following form $$ F_L(y) = f(y) -S_L(y)...

Show that $$\sum_{j=1}^{j=n}\binom{n}{j} \frac{(-1)^{j+1}}{j} = 1 +\frac{1}{2} +\frac{1}{3} + \cdots +\frac{1}{n}$$

What are you thoughts about Laura Mersini Haughton´s theory of the multiverse? She predicted a CMB cold spot, power suppression at low multipoles, preferred direction associated with the quadrupole octupole alignment, dark flow, and the deviation of the CMB amplitude. While dark flow remains...

i was given that Z8 to Z4 is given by f= 0 1 2 3 4 5 6 7 0 1 2 3 0 1 2 3 where f is homomorphism. how can i find the kernal K

G is a group and H is a normal subgroup of G. where G=Z6 and H=(0,3) i was told to list the elements of G/H I had: H= H+0={0,3} H+1={14} H+2={2,5} now they are saying H+3 is the same as H+0, how so?

Homework Statement Find the magnetic field generated at the center of a coil of wire with N turns, a radius of r, and a current I running through it Relevant equations B=μ0nI, where n=N/L (L is the total length of the coil) The attempt at a solution B=μ0nI B=μ0I(N/L) L=2πrN B=(μ0NI)/(2πrN)...

Hello, here is the problem that I have: Can you please tell me how to determine what is the sequence of the output. I can see it misses 101 and 010 and it repeats 000 and 100. I think both 101 and 010 are initial states. The answer I have for repeated sequence is 011, 111, 110, 100...

If f be a measurable function. Assume that lim λm({x|f(x)>λ}) exists and is finite as λ tends to infinite Does this imply that ∫|f|dm is finite? Here m is the Lebesgue measure in R If not can anyone give me an example??

let us assume G is not cyclic. Let a be an element of G of maximal order. Since G is not cyclic we have <a>≠G. Let b be an element in G, but not in the cyclic subgroup generated by a. O(a) = m and O(b) = n where O() refers tothe orders. . then how can we use this to construct a subgroup of G...

Homework Statement Let p: E \rightarrow B be a covering map. If B is compact andp^{-1}(b) is finite for each b in B, then E compact. Note: This is a problem from Munkres pg 341, question 6b in section 54. The Attempt at a Solution I begin with a cover of E denote it \{U_\alpha\}. I...

So in the infinite well Energy is proportional to 1/L^2, so I'm assuming in the finite well there is some sort of similar relation. So as the L decreases, the energy increases, so the wavelength decreases. Decreasing the wavelength means more energy, so it should penetrate further, but also if...

In the Wiki article on the FLRW metric, http://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric it says "the universe is nearly an isotropic and homogeneous FLRW spacetime". OK, so spacetime is globally flat, which implies that space is too. This...

Homework Statement Prove that the union of a collection of indexed sets has finite diameter if the intersection of the collection is non-empty, and every set in the collection is bounded by a constant A. The Attempt at a Solution The picture I have is if they all intersect (and assuming...

What are the advantages and disadvantages of both AEM and FEM and which on is easier. I am doing a project and I should use one of these two methods to solve for a truss system. P.S. computer programming shall be used. In the end which method is better for this case?

The problem statement Let ##\mu## be a measure defined on the Borel sets of ##\mathbb R^n## such that ##\mu## is finite on the compact sets. Let ##\mathcal H## be the class of Borel sets ##E## such that: a)##\mu(E)=inf\{\mu(G), E \subset G\}##, where ##G## is open...

A simple question about elasticity theory/finite element method: Suppose I have a tetragonal 2D piece of a linear isotropic elastic material, that has Young's modulus ##E## and Poisson's ratio ##\nu##. The vertices of the tetragon are at positions ##\textbf{x}_{1}##, ##\textbf{x}_{2}##...

if I have a transcendental equation such as this one: tan(l a) = -l / sqrt (64/a^2 - l^2 ) Where l=sqrt(2m(E+V) /hbar^2 ) and 'a' is the width of a finite square well, how can I solve this equation in terms of both l and a. I have successfully graphed the two sides of the equation...

Homework Statement Let A = A(p)\times A' where A(p) is a finite commutative p-group (i.e the group has order p^a for p prime and a>0) and A' is a finite commutative group whose order is not divisible by p. Prove that all elements of A of orders p^k, k\geq0 belong to A(p) The Attempt...

Hi, Are there any open source C or Fortran libraries for solving 3D Poisson'sequation on an irrefular domain? I'm having difficulty finding them. If not, is there any papers or recipes that would be useful so I could write my own? Speed is not a priority, I just need anything that works...

Homework Statement Derive expressions for electric field produced along the axis of radial symmetry for an H km thick cylindrical slab of radius R with charge distributed around the volume. Then, give the electric field on the vertical axis for four of these cylindrical slabs.Homework Equations...

Homework Statement A Carnot engine operates between two finite heat reservoirs of total heat capacity CtH and CtC. a) Develop an expression relating TH to TC at any time. b) Determine an expression for the work obtained as a function of CtH ,CtC , TH and initial temperatures TH0 and TC0...

In K&K's Intro to Mechanics, they kick off the topic of rotation by trying to turn rotations into vector quantities in analogy with position vectors. It's quickly shown, however, that rotations do not commute, making them rather poor vectors. They then show, however, that infinitesimal rotations...

I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

Hello all, I hope this is the write sub-forum for this question. I have been looking at the Laplacian of a 2-D vector field. It is explained nicely by this Wikipedia article here. My question is more regarding how these operators work together. So, in the case of the Laplacian, it tells me...

I think that it is relatively easy to simply count the number of physics that are aware for us as of February 2014. Probably there is statistics that deals with it and can tell us how many laws of physics exist now; maybe this number is equal to 1000, maybe more, I am not aware of it. But...

This isn't a homework problem - I'm just confused by something in a textbook that I'm reading (not for a class, either). I'd appreciate an intuitive clarification, or a link to a good explanation (can't seem to find anything useful on Google or in my textbook). My book states that one of the...

Hey! :o I have a implicit finite difference method for the wave equation. At step 0, we set: $W_j^0=v(x_j), j=0,...,J$ At the step 1, we set: $W_j^1=v(x_j)+Dtu(x_j)+\frac{Dt^2}{2}(\frac{v(x_{j-1})-2v(x_j)+v(x_{j+1})}{h^2}+f(x_j,0)), j=0,...,J$ Can that be that at the step 1 $j$ begins from...

Hey! :o Given the following two-point problem: $$-y''(x)+(by)'(x)=f(x), \forall x \in [0,1]$$ $$y(0)=0, y'(1)=my(1)$$ where $ b \in C^1([0,1];R), f \in C([0,1];R)$ and $ m \in R$ a constant. Give a finite element method for the construction of the approximation of the solution $y$ of the...

Hi, I have to use a wide 5 point stencil to solve a problem to fourth order accuracy. In particular, the one I'm using is: u'' = -f(x + 2h) + 16f(x + h) - 30f(x) + 16f(x - h) - f(x - 2h) / 12h2 or when discretized u'' = -Uj-2 + 16Uj-1 -30Uj + 16Uj+1 -Uj+2 / 12h2 In addition to...

The problem is as follows: A Carnot engine operates between two finite size reservoirs, one a body of water of mass MH at 100°C and the other a body of water of mass ML at 0°C. Find the maximum work obtainable from the two reservoirs. The Attempt at a Solution I haven't done...

Hey! :o I am implementing in a program the finite difference method for the heat equation. The problem is the following: $$u_t(x,t)=(g(x,t)u_x(x,t))_x+f(x,t), \forall (x,t) \in [0,1]x[0,1]$$ $$u(0,t)=u(1,t)=0, \forall t \in [0,1]$$ $$u(x,0)=0, \forall x \in [0,1]$$ where $f(x,t)=\pi x...

Hey guys. It's been awhile I don't posting in this thread. How could space which is nothing, is finite yet unbounded? Aren't beyond the so-called finite yet unbounded universe is just nothing that we called as space?

Hi! I've encountered the series below: \sum_{l=0}^{k-1} (r+l)^j (r+l-k)^i where r, k, i, j are positive integers and i \leq j . I am interested in expressing this series as a polynomial in k - or rather - finding the coefficients of that polynomial as i,j changes. I have reasons to...

If a Hamiltonian is unbounded from below, say the hydrogen atom where the Hamiltonian is -∞ at r=0, is there a way to tell if the ground state is bounded (e.g. hydrogen is -13.6 eV and not -∞ eV)? It seems if the potential is 1/r^2 or less, then the energy will be finite as: \int d^3 r (1/r^2)...

I am considering the gravitational time dilation at the centre of a spherical, non-rotating body (such as the Earth). The usual formula for gravitational time dilation is √(1-r_s/r) where r_s is the Schwarzschild Radius and r is the radius of the clock compared to one at infinity, however, this...

Homework Statement I'm not even attempting the graph yet, but I'm having trouble figuring out how to do this problem for a finite cylinder. All I've found in my notes is finite spheres and infinite cylinders. Homework Equations E=∫[ρdv]/4∏εR2] \hat{R} The Attempt at a Solution...

Homework Statement Let G be a finite complex matrix group: G \subset M_{n\times n}. Show that, for g \in G, |\text{tr}(g)| \le n and |\text{tr}(g)| = n only for g = e^{i\theta}I. 2. The attempt at a solution Since G is finite, then every element g \in G has a finite order: g^r = I for some...

Consider \frac{d^{2}y}{dx^{2}}+\frac{k}{x^{2}}y = 0. Show that every nontrivial solution has an infinite number of positive zeroes if k > 1/4 and a finite number if k ≤ 1/4. Solving gives: y = Asin(\sqrt{k}ln(x)) + Bcos(\sqrt{k}ln(x)) And setting y = 0 gives: tan(\sqrt{k}ln(x)) =...

Hello, I have a question about the character of the universe today and its early state. As I understand it there is no consensus as to whether the universe today (the whole universe, not the observable) is infinite, finite, or finite but looped in on itself. It seems to me to follow that if...

Hey everyone, I have three problems that I'm working on that are review questions for my Math Final. Homework Statement First Question: Determine if R is an equivalence relation: R = {(x,y) \in Z x Z | x - y =5} and find the equivalence classes. Is Z | R a partition? Homework...

Hi, I have been stuck on a problem for a while now (3.24 part c). My attempt is as follows: Internal virtual work = external virtual work T/2 ∫0->L (∂u/dx)(∂v/dx)dx + ∫0->L (∂^2u/∂t^2)vdx = ∫0->L (Pv)dx Stationarity is already invoked on this functional as it's the principle of...

I developed finite element program (MFEM) in java for BVP &IVP to compute partial differential equation. I am facing one problem and description is as follows my problem is on generalized eigenvalue problem generated in wave propagation through rectangular wave guide in TE mode. (Differential...

Just for fun, eh...? (Heidy)For $$z \in \mathbb{R}$$, and $$m \in 2\mathbb{N}+1$$, show that:$$\frac{\tan mz}{\tan z}=\prod_{j=1}^{ \lfloor m/2 \rfloor } \tan\left(\frac{j\pi}{m}+z\right) \tan\left(\frac{j\pi}{m}-z\right) $$

Homework Statement This isn't homework or coursework as such, but i thought it may be the best place to ask this question. The last time i posted in the other section it was deleted! Im considering the case of an electrode of finite width L in the x direction. The y direction is...

Hello! :) I am implementing the finite difference method in a program in C and I got stuck at the rate of convergence.. The formula is \frac{log(\frac{e_{1}}{e_{2}})}{log(\frac{J_{2}}{J_{1}})} , right? where e_{i}=max|y_{j}^{J_{i}}-y(x_{j}^{J_{i}})| , 0<=j<=J_{i} . How can I find the J_{1}...

Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node150.html Again we have assumed a beam of definite momentum incident from the left and no wave incident from the right. Why is the above statement made? What does the reflected wave mean? There is now all why reflected...

I'm going through the text "Linear Algebra Done Right" 2nd edition by Axler. Made it to chapter 4 with one problem I'm unable to understand fully. The theory that two vector spaces are isomorphic if and only if they have the same dimension. I can see this easily in one direction, that is...

Homework Statement How to prove the following: Let p be a prime p=3,5 (mod8). Show that the sequence n!+n^p-n+2 contains at most finitely many squares. Should I build a contardiction or prove it directly? I really need some help 2. The attempt at a solution Use Fermats...

I am thinking about taking a finite element method course. I know what FEM is and how it solves boundary value problems and stuff but I'm wondering how widespread it is used... Is it a useful numerical technique? What industries/research use it? I am interested in research in continuum...