Finite Definition and 1000 Threads

Homework Statement Let X be a topological space, and A a locally finite family of sets in X (i.e. such a family of sets that every point in X has a neighborhood which intersects a finite number of sets in A). One needs to show that Cl(U A) = U (Cl(A)) (i.e. the closure of the union of sets in...

Hi, This is not a homework question. I am a trying to prove a result for myself, and the question is can I always find, in a nonabelian finite group G, and some fixed proper subgroup S < G, two distinct elements, which we shall call x and y, outside of S, such that the cosets Sx = Sx^{-1}, and...

If the universe is flat and finite which is where the evidence points today (WMAP) then wouldn't there be an end to space (like an edge). I don't think the universe is curved back onto itself like a sphere because its flat. I mean what would happen if you were to reach the edge of space itself...

I'm at university, majoring in Economics. After university I'd like to get a job either on the international side of things or working doing something like bond rating, all on the macro level. I have plans to take actual calculus, but am currently forced to take one of the two, and am just...

Homework Statement Show that a finite field of p^n elements has exactly one subfield of p^m elements for each m that divides n. Homework Equations If F \subset E \subset K are field extensions of F , then [K:F] = [E:F][K:F] . Also, a field extension over a finite field of p elements...

Hello all, I am trying to create a simple finite element program in C++ and have been able to build and assemble the GLOBAL stiffness matrix as well as the load vector. I want to apply the boundary conditions using the elimination approach, can anyone tell me how to do this? I am sorry for...

I heard on a recent podcast that most astronomers and physicists of the early 20 th century, if they thought about it at all, believed that the universe always existed, i. e. it had no beginning. Even Einstein accepted the Steady State Theory, along with many others. How did these astonomers...

Homework Statement A uniform line charge of linear charge density \lambda = 5.00 nC/m extends from x = 0 to x = 10m. The magnitude of the electric field at the point y = 12m on the perpendicular bisector of the finite line charge is? Homework Equations E = \intdE = \intk(dq) / r2 Ex =...

Yet another proof I'd like to check. Statement. Let X be a finite set. One has to show that every two metric functions d1, d2 on X are uniformly equivalent. Proof. If X is finite, then X = {x1, ..., xn}. We have to find constants A and B such that for every x, y in X, we have d1(x, y) <= A...

Hi everyone, I'm currently working on coding a finite element heat problem in Matlab that is as follows: I have a cross section of a beam made of an isotropic material (concrete) that is placed in a furnace, and the outside temperature is raised at a constant rate. I am interested in...

Is it true that cyclic groups with x^n = 1 the only finite groups (with order n)? I've been experimenting with a few groups and I think this is true but I'm not sure.thanks

I'm having a little trouble distinguishing the line between what the f.i.p implies and what it does not. **EDIT2** Hopefully this will make things more clear What I'm really interested in is a formal definition of the f.i.p regardless of the set in question or the field. Given the sequence...

Hi Please explain Flux Motion Resistance in Superconductors which causes a superconductor to lose energy after a finite period of time. (Theoretically it shouldn't)

The general problem I'm trying to solve is the probability of rolling a total t on n s-sided dice. A good chunk of the problem is easy enough, but where I run into difficulty is this: How many combinations of dice will yield a sum total of t? Because the number set is limited, {a \choose n-1}...

I know the results for infinite, but how about finite? And where is the cutoff with the aproximation of infinite? I've heard the value 10% tossed around is that right?

Hey folks I'm totally knew to this forums but i assure you I'm a science junky (especially Physics) I figured i post my first question here as it seemed pretty general so I'll give it a go I've heard many statements about the universe being finite, in fact, it seems to be regarded as truth...

Homework Statement Show that each subset of R is not compact by describing an open cover for it that has no finite subcover. b.) N (natural numbers) The correct solution for this is A_n = (n-1/3, n+1/3) for all n in N. But the answer I came up with is [1,n) for all n in N. Is my answer...

just trying to get my head around heat capacity here for an experiment; if conducting a reaction in an adiabatic vessel, of which its material has a finite heat capacity, does this mean that if sufficient heat is produced within the vessel (through a chemical reaction), that the adiabatic...

I'm just having a little trouble getting my head around how representation theory works. Say for example we are working with the dihedral group D8. Then the degrees of irreducible representations over C are 1,1,1,1,2. So there are 4 (non-equivalent) irreduible representations of degree 1...

So this has bugged me for a long time. I'm a physicist in training, and have very little knowledge of the cosmos, but: I've heard for a long time the notion that the universe is infinite. For a long time, this troubled me, because I really couldn't conceptualize how something could be...

Let's have a kind of step potential, V=infinity, where x\leq0, V=constant, where 0\leqx\leqa, V=zero , where x\geqa. Then, my question is that when the energy of the particle is lesser than zero, which means that the particle is in the bound state, is there a probability of getting...

My abstract algebra book is talking about reducing the calculations involved in determining whether a subgroup is normal. It says: If N is a subgroup of a group G, then N is normal iff for all g in G, gN(g^-1) [the conjugate of N by g] = N. If one has a set of generators for N, it suffices...

Homework Statement \left\{ e^{n r \pi i}: n \in \textbf{Z} \right\} , r \in \textbf{Q} I'm trying to show that this set is finite. Homework Equations The Attempt at a Solution Other than the fact that these points lie on the unit circle in the complex plane, I'm not sure...

Let S be a set on which a linear order <= (less or equal) , is defined. Show that a non-empty finite subset has a max.

1-D Conduction+Convection::Deriving a Finite Difference Scheme ***For those of you who would like to skip the derivation of the energy balance, skip ahead to the bold subheading below where the actual Finite Difference Scheme begins*** I am trying to derive a finite difference scheme for...

Trying to do i) and iii) on this past exam paper For part i) I'm pretty stumped I've said that the possible roots of the polynomial are +- all the factors of T In particular rt(T) needs to be a factor of T but this can't be possible? Doesn't sound too good but its the best I've got. Part...

Homework Statement Hi. Find the sum of the first 10 terms in the series: 1, (ln2)/1!, (ln2)^2/2!, (ln^3)/3!... Homework Equations I guess the Maclaurin series, which is e^k = 1, k/1!, (k^2)/2!, (k^3)/3!... In my case, k = ln2. The Attempt at a Solution I tried to use the sum of the first...

Hello all, I came across what I think is a very interesting question the other day; How would you treat a particle trapped in a square well that had one finite wall and one infinite wall? Say for E[SUB]n[SUB]~(n*pi*(h-bar))2/(2m(L+2d)2) would you replace the 2d by 1d? As you can only find the...

Homework Statement How could I prove that the subset of a finite dimensional space is also finite dimensional? Homework Equations N/A The Attempt at a Solution I think it's more intuitive in the sense that since the vector space is finite dimensional the subset is forcibly finite...

Homework Statement Homework Equations There aren't really any relevant equations. The Attempt at a Solution Ok so I just want to see if my idea for the state diagram seems ok, I'm going to give it in table form here but its the same info. F | Bk | A | B | C | D...

Let R be a ring with multiplicative identity 1R. Suppose that R is finite. The elemets xy1, xy2,...xyn are all different. So x y_i=1R for some i. A lemma that is not proven is given. If xyi=1R & yjx=1R, then yi=yj I need to show that yjx=1R. Right now I haven't got much. I took...

Homework Statement A particle with energy greater than the potential is defined as below: V(x) = Vo (x<0) V(x) = 0 (0<x<a) V(x) = Vo (x>a) a) Write the complete solutions (time and space) to the S. Eqn for the 3 regions b) What condition must the width of the potential satisfy for the...

Consider a finite square-well potential well of width 2.8 multiplied by 10-15 m that contains a particle of mass 1.9 GeV/c2. How deep does this potential well need to be to contain three energy levels? (Except for the energy levels, this situation approximates a deuteron. Use the infinite square...

------Question------ a) Research the three finite difference approximations mentioned above (forward, backward and central). Use a spreadsheet to demonstrate each of these numerical methods for the function below. y=x3 −x2 +0.5x Investigate the derivative over the range x = [0,1], using...

Hi everyone, As part of a project, I am required to numerically compute the expression b_{i}^{e} &=& \frac{E_{0}^{i}k_0^2(\epsilon_r-1/\mu_r)}{2\Delta^e}\left[\iint\limits_{\Omega^e}(a_i^e + b_i^e x + c_i^e y)e^{-jk_0 x} dx dy\right] \nonumber\\&&- \frac{jk_0 E_0^i r'}{2\Delta^e...

Hi everybody... I have a simple question for you.. Where can i found the expression of the magnetic field around at the conductor which it has finite lenght? because i always found the megnetic filed in a conductor infinite length .. Sorry for the stupid question... tanks and best regard

Homework Statement Let V be a finite dimensional normed vector space and let U= L(V)*, the set of invertible elements in L(V). Show, f:U-->U defined by f(T)= T-1 is differentiable at each T in U and moreover, Df(T)H = -T-1HT-1 where Df(T)= f'(T). Homework Equations Apparently...

Hi,all Q1: Why take FINITE time for an electron to observe a photon? (Q2: Why not much people answer my questions? Am I put them in a wrong place? what's the definition of General Physics? Classical only?) Thanks in advance? Quuote from Jeff Reid...

I am trying to run a finite element analysis for a collision impact. The program I am using is MD Patran/Nastran. My model consists of moving object colliding with a stationary object. I have created the mesh, applied the appropriate material, applied the boundary conditions (fixed for the...

I do not have physics education pass A-levels, yet. So what I've been thinking of should be very simple to follow. It's just so fascinating that I'm wondering if any experts could either point a logic flaw, or direct me to material that has already mused over this for me. I understand that...

Hi,all, why electron absorb photon costs FINITE time? Not only for electron, when phonon interact with photon(absorbs it) also costs finite time. As I think, it should be instant, can not find any reason for finite time. Helps! Thanks In advance!

Hi, i need help in solving a Fick's Law [ (∂c_k)/∂t = D_k (∂^2 c_k)/(∂x^2 ) ] by Finite Difference Method. Previously, I tried solving the Fick's Law by using the Separation of Variable method but that was not the correct way as told by my Prof as the correct way is to use Finite Difference...

If the approximate time since the big band is correct at about 14 billions years, then the universe should have a limit as to how far it has expanded/inflated. Why then do people still postulate an infinite universe ?

Howdy, all. I am not sure if this is the right forum for this question. It isn't exactly an homework question, but it does stem very closely from a homework assignment in a first year graduate course in Abstract Algebra. The assignment has come and gone with limited success on my part, but...

I am having trouble finding the method to figure out if a shaft has finite or infinite life if it is subjected to a fluctuating load. I know how to solve for n(factor of safety) in these types of problems. Is there a value that if n is above it has infinite life.

Homework Statement An electron is trapped in a finite well of width 0.5 nm and depth of 50 eV. The wavefunction is symmetric about the center of the well (x = 0.25 nm). If the electron has energy 29.66 eV and ψ(0) = 1.42 (nm)-1/2, then what is the probability for finding the particle in the...

If the universe is finite and unbounded why can not we think of the frame that sits with it's origin at the center of the 4-D sphere as a preferred frame? The preferred frame?

Hello to all, I am looking at a scattering example in my book. A particle is incident from the left with energy E > Vo. The barrier is of width L, and located between x = 0 and x = L. The solutions to the time-independent Schrodinger equation in eacch of the regions comprising the left...

Homework Statement I'm trying to find the final temperature of a carnot engine with two finite thermal reservoirs. We're told that the heat capacities for both reservoirs are constant (and equal) and to regard the change in each reservoir's temperature during any 1 cycle as negligible...

Prove that the number of monomials of degree d in finite field F[x] is \binom{n+d}{n} This is not so much a homework question as something I have read and asked my professor about. He said it was too easy and that I should be able to do it and wouldn't help me. I know I'm probably being a...