Finite Definition and 1000 Threads

-In the first few fractions of a second after the big bang, was the universe finite and closed during early inflation, before it smoothed out and became flat and infinite? I am wondering because I would like to know if the theory implies that the universe initially inflated with a finite...

I want to compute the flux surfaces using FEM but i haven't found any good source to read. any help will be appreciated. Thank you

Air typically has a very high but non zero resistance. Given that air is just a medium, and that space is also just a medium, does the vacuum of space have a fundamental constant of electrical resistance, or is the electrical resistance of space truly infinite? How is this proven one way or the...

For possion equation $$u_{xx}+u_{yy}=f$$ I know the general five point scheme is in the form $$a_{1}U_{i,j-1}+a_{2}U_{i-1,j}+a_{3}U_{i,j}+a_{4}U_{i+1,j}+a_{5}U_{i,j+1}=f_{i,j}$$ But , is there have the form...

Hello everyone and thanks for reading my post. I have a problem with an electron, which actually is confined into a region 0 ≤ x≤ L with infinite potential around it, and its energy in the ground state is 0.38eV. Then on the x > L region the potential is 5eV and the energy of the lowest...

Homework Statement Find the determinant of: |1 1| |2 1| The field is Z3. Homework Equations The field is Z3, that is, to multiply two numbers, you first multiply then take the remainder of the division by 3. The Attempt at a Solution I tried: ( 1 x 1 ) - ( 1 x 2 ) 1 x 1 will...

Consider the following solution to the steady state heat diffusion problem on an infinite y domain. \[ T(x, y) = \sum_{n = 1}^{\infty}c_n\exp\left(-\frac{\pi n}{\ell} y\right) \sin\left(\frac{\pi...

Hi, I am hoping someone here could help me understand the finite slope of the counting plateau in Geiger Muller Tubes. Master Knoll says this, "In real cases, the counting plateau always shows some finite slope, as shown in Fig. 7.5b. Any effect that adds a low-amplitude tail to the...

Finite Fourier Transform on a 2d wave How does the finite Fourier transform work exactly? The transform of f(x) is \widetilde{f}(\lambda_{n}) =\int^{L}_{0} f(x) X_{n} dx If I had a 3d wave equation pde and I applied Finite Fourier transform on the pde for z(x,y,t)=X(x)Y(y)T(t)...

I have the differential equation \frac{dM}{dt}=4\pi \rho(r,t)r(t)^2\frac{dr}{dt} which is the first term from M(t)=4\pi\int_0^{r(t)}C(r,t)r(t)^2dr This describes the change in mass (M) of a sphere from a change in radius (r) given a density (rho) that depends on radius and time (t). My...

Someone published a simple computation of the relativistic shift in Mercury's perihelion (over and above classical, ie. the small correction over the classical-mechanical shift) by more or less using the principle of relativity. I believe it was a she and she computed how far mercury travels...

In Dummit and Foote Chapter 15 on page 657 we find the following definition of a k-algebra: Let k be a field. A ring R is a k-algebra if k is contained in the centre of R and the identity of k is the identity of R. This defintion is followed by the definition of a finitely generated k-algebra...

Hi Say I have a finite data set (frequency, absorption) and I would like to find the corresponding dispersion. For this I could use the Kramers-Kronig (KK) relation on the absorption data. What I would do is to make a qubic spline and then perform the KK-transformation. However, the absorption...

so calculating FC on an infinite bus is easy but how do you calculate it by hand for a finite bus? here is the concept i am having an issue understanding: let say i have a transformer that is 225KVA with 5%z and 3 phase 480 to 208. with infinite bus i have 12491A available on the...

Homework Statement Homework Equations I know that energy mentioned in the statement is kinetic energy so keep in mind when reading that ##E\equiv E_k##. In our case the kinetic energy is larger than the potential energy ##\boxed{E>E_p}## and this is why stationary states for the regions 1...

The axiom of choice on a finite family of sets. I just been doing some casual reading on the Axiom of CHoice and my understanding of the is that it assert the existence of a choice function when one is not constructable. So if we have a finite family of nonempty sets is it fair to say we can...

Homework Statement A finite uniform linear charge ρ_L = 4 nC/m lies on the xy plane; start point and end point are (7,0,0) and (0,7,0) .While point charges of 8 nC each are located at (0, 1, 1) and (0, -1, 1). Find E at (0, 0 ,0) Homework Equations dE=ρ_L *dz'/4∏ε *...

Hi, This is a sample problem from logan finite element method. I have attached the problem and solution given in the book. As per the problem i first derived the stiffness matrix and den putting the boundary conditions started solving for the forces. I am stuck as three forces are unknown but...

Is any given finite semigroup isomorphic to some finite semigroup S that consists of some subsets of some finite group G under the operation of set multiplication defined in the usual way? (i.e. the product of two subsets A,B of G is the set consisting of all (and only) those elements of G that...

Dear all, Please tell me the steps are used to find Modal loss factor of composite constrained layer damped beam by using Finite Element software such as ANSYS etc.

In this video (from 27.00 - 50.00, which you don't need to watch!) a guy shows how you can solve the general second order ode y'' + P(x)y = 0 using perturbation theory. However he points out that the domain must be finite in order for this to work, I'm wondering how you would phrase a question...

Hello :blushing: How to do expand this: (\sum_{j=1}^{n}(X(t_j)-X(t_{j-1}))^2 - t)^2 where X(t_j)-X(t_{j-1}) = \Delta X_j to this: (\sum_{j=1}^{n}(\Delta X_j)^4 + 2*\sum_{i=1}^{n}\sum_{j<i}^{ }(\Delta X_i)^2(\Delta X_j)^2 -2*t*\sum_{j=1}^{n}(\Delta X_j)^2+t^2I get near the North Pole... but...

Homework Statement Let w be a primitive n-th root of unity in some finite field. Let 0 < k < n. My question is how to rationalize [\tex]\dfrac{1}{1 + w^k}[\tex]. That is, can we get rid of the denominator somehow? I know what to do in the case of complex numbers but here I'm at a loss...

Homework Statement Hello. Imagine a particle bound in a square well potential of potential energy V0 if |x| > a 0 if |x| < a The wave function of the particle is: (ignoring the time dependency) -A*exp(kx) if x<-a B*sin(3*pi*x/4a) if |x|<a A*exp(-kx) if x>a where k =...

Hi, I have been trying to find analytical solutions for a finite rectangular sheet, say, in the xy plane, with dimensions a and b. Assume it is uniformly charged. An excellent (and short) description of the problem is here. The three integrals for Ex(x,y,z), Ey(x,y,z) and Ez(x,y,z) given on...

Class of all finite sets In a higher algebra book that I'm working through, the natural numbers are constructed in the following manner:- Consider the class S of all finite sets. Now, S is partitioned into equivalence classes based on the equivalence relation that two finite sets are...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my complete response.

Yeah, all of those things, multipled by five thousand, and there we have the current cosmic predicament for human beings. Is there any way in which we can do something about this? Or will Schopenhauer have the last laugh?

Homework Statement A finite line of charge (L=L1+L2) with a linear density of d(x)=k.x, in which k>0. This finite line goes from -L2 to +L1 in the x axis. Calculate the electric field and the electric potential in the point P=(0,H). Homework Equations dV=(1/(4*pi*ε0))*dq/r The...

I believe I understand the definitition of the l^p space, its set of infinite sequences that converge when the sequence is put to the power of p, term by term. However I came across "Let T be a real linear operator from a finite dimensional real l^p space to a real finite dimensional banach...

I keep on reading that cosmologists contemplate two possibilities: either the universe is closed, unbounded and therefore finite, or else it is open (possibly flat) and infinite. I hear that a flat, finite universe "introduces many problems" and is discarded. My question would be "what...

Was wondering if the only required definition for finite groups is closure (maybe associativity as well). It seems that is all that is necessary. The inverse and identity necessarily seem to follow based on the fact that if I multiply any element by itself enough times, I have to repeat back to...

Hi all, I have a question about the concept of complete set when I apply the perturbation theory in two situations -Finite Hilbert Space and Infinite Hilbert Space. Consider a Hamiltonian H=H0+H', where H0 is the unperturbed Hamiltonian and H' is the perturbed Hamiltonian. Let ψ_n be the...

Hello MHB, I got stuck on an old exam determine the area of the finite region bounded by the curves $$y^2=1-x$$ and $$y=x+1$$ the integration becomes more easy if we change it to x so let's do it $$x=1-y^2$$ and $$x=y-1$$ to calculate the limits we equal them $$y-1=1-y^2 <=> x_1=-2 \ x_2=1$$ so...

Homework Statement Consider the problem $$-u''\left(x\right) = 1, \;\; 0 < x < 3, \;\; u \left(0\right) = 0, \; -u' \left(3\right) = u\left(3\right)+1.$$ Formulate a MATLAB code to produce the solution and plot the solution from 0 to 3. Homework Equations The Attempt at a Solution Multiply by...

Howdy, I am trying to formulate a proof to show that the shape function [N(x,y)] = [Ni(x,y) Nj(x,y) Nk(x,y)] and the the basis functions Ni(x,y) = (1/2A)(ai + bix + ciz) Nj(x,y) = (1/2A)(aj + bjx + cjy) Nk(x,y) = (1/2A)(ak + bkx + cky) are valid for triangular, 2 dimensional...

Here is the question: Here is a link to the question: Abstract math question: bijectivity on finite and infinite sets? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Use the boundary conditions to show that \frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}=\frac{k^2_1}{k^2_2} Homework Equations A+B=C+D and k_{1}A- k_{1}B = k_{2}C- k_{2}D C e^{i k_{2}L}+D e^{- ik_{2}L} = F e^{i k_{1}L} and k_{2}C e^{ ik_{2}L}- k_{2}D e^{-i...

Homework Statement http://img842.imageshack.us/img842/4917/physp6.jpg I am trying to solve the above problem. However, I am supposed to solve it with the following values: U=54.7eV L=0.2nm Particle is an electron, so: m=9.109E-13kg=0.511eV/c^2 Essentially I am supposed to...

Homework Statement I am to first write a differential equation that describes a hanging mass influenced by gravity and then write the finite differences equation. Then, the problem asks me to graph this numerical solution and make sure that maximum extension of the spring that I derive matches...

Anyone know of some good, free finite element analysis software? I used NASTRAN in college, but from what I can tell that costs at least several thousand.

Homework Statement Consider the triangular-shaped wire in the picture. The base is of length 2a and is along the y-axis, and the two sides are of length 3a each. The wire is uniformly charged with charge density (per line) \lambda. Find the electrostatic field at all points \vec{x} = x\hat{i}...

Hello I understand how to approach finite potential well. However i am disturbed by equation which describes number of states ##N## for a finite potential well (##d## is a width of a well and ##W_p## is potential): $$ N \approx \dfrac{\sqrt{2m W_p}d}{\hbar \pi} $$ I am sure it has something to...

Lets say we have a finite square potential well like below: This well has a ##\psi## which we can combine with ##\psi_I##, ##\psi_{II}## and ##\psi_{III}##. I have been playing around and got expressions for them, but they are not the same for ODD and EVEN solutions but let's do this only...

Hi, For my Bachelor's thesis I've been working on a finite time Carnot cycle. I've finished my numerical analysis using the differential equations governing the time evolution. My next step should be a simulation. First I should stick to a 1 dimensional system. This system consists of a...

Hey, just trying to get my head around the logic of this. I can see that if composition factors are cyclic then clearly the group is soluble, since there exists a subnormal series with abelian factors, but I am struggling to see how the converse holds. If a group is soluble, then it has a...

Homework Statement "as long as the volume charge density is finite (which is not true of surface charge distributions or point charges), the electric field is continuous. Homework Equations The Attempt at a Solution I know that for surface charges distributions and point charges...

Lets say we have a finite square well symetric around ##y## axis (picture below). I know how and why general solutions to the second order ODE (stationary Schrödinger equation) are as follows for the regions I, II and III. \begin{align} \text{I:}& & \psi_{\text{I}}&= Ae^{\kappa x} \\...

I need to read about finite abelian groups. I searched 'finite abelian group' on amazon and the closest search result was 'finite group theory'. Googling didn't help either. Does there exist a book dedicated to finite abelian groups? If yes, and if you know of a good one then please reply...

Suppose an electron was kept with an alpha particle at a finite separation x. Why does it have a negative potential ENERGY ... In other words, what does a negative electric potential energy mean? I want an answer relating it with potential energy at infinity which is zero. Secondly, if the...