Finite Definition and 1000 Threads

Homework Statement Prove that if A: V - >V is a linear map, dim V = n, and h1,...,hk (where 1,...,k are subscripts) are pairwise different eigenvalues of A such that their geometric multiplicities sum to n, then A does not have any other eigenvalues. Homework Equations Note sure if this is...

Hello fellow physicists! Last meeting with my supervisor I had just recovered from disease so all I have left are some equations for the math behind path integrals that don't make to much sense.. I was wondering if, maybe someone can help and clarify what he was trying to get at. It would be...

Homework Statement Prove that the intersection of a number of finite convex sets is also a convex set Homework Equations I have a set is convex if there exists x, y in the convex S then f(ax + (1-a)y< af(x) + (1-a)y where 0<a<1The Attempt at a Solution i can prove that f(ax + (1-a)y) <...

i need to know is there a difference between the method of finding the asymptote of a function and the finite expansion of the same function when x tends to infinite i have the exam very soon and i am hoping for really detailed quick reply

Homework Statement Comment on the electric field lines of a pair of finite parallel plates (a) between the plates and (b) near the edges of the plates. Homework Equations The Attempt at a Solution

This is probably easy. It's really annoying that I don't see how to do this... A finite rank operator (on a Hilbert space) is a bounded (linear) operator such that its range is a finite-dimensional subspace. I want to show that if T has finite rank, than so does T*. I'm thinking that the...

Homework Statement If G is a finite simple group and H is a subgroup of prime index p Then 1. p is the largest prime divisor of \left|G\right| (the order of G) 2. p2 doesn't divide \left|G\right| I think I have this proved, but want to confirm my reasoning is sound. this problem is...

Hi everyone, I'm reading Rudin's Analysis and in the topology section, he implies that the finite intersection of closed sets is not necessarily closed. (pg. 34) Can someone give an example of this? I can't seem to find one.

A simplest example of a chemical bond is that formed by two hydrogen atoms in a H2 molecule. a) Show that in the ground state (both electrons in the bonding orbital), the molecular energy has a minimum at a finite distance r=.074nm, defining the bond length for H2. b) Determine the energy...

Homework Statement Suppose that S is a countably infinite subset of \ell_2 with the property that the linear span of S′ is dense in \ell_2 whenever S\S′ is finite. Show that there is some S′ whose linear span is dense in \ell_2 and for which S\S′ is infinite. The Attempt at a Solution I...

Hi, I am taking a class in Linear Algebra II as a breadth requirement. I have not studied Algebra in a formal class, unlike 95% of the rest of the class (math majors). My LA2 professor mentioned the following fact in class: "The number of elements of a finite field is always a prime power and...

The cross section for scattering by a Coulomb potential 1/r is the same for both classical and quantum mechanics, and the total cross section is infinite. I understand this classically as saying that no matter how large an impact parameter an incoming particle has, it will still be deflected at...

Given a finite volume of space, can a finite amount of matter and energy store an infinite amount of information?1 Given x grams of matter, y joules of energy, and Z ml of volume, does the amount of information that could be stored (states that each bit of matter / energy could exist) diverge?2...

Homework Statement Assume F is a field of size p^r, with p prime, and assume f \in F[x] is an irreducible polynomial with degree n (with both r and n positive). Show that a splitting field for f over F is F[x]/(f). Homework Equations Not sure. The Attempt at a Solution I know from...

Homework Statement The formulation of the problem confused me a little, so just to check. No T1 space has a locally finite space unless it is discrete. The Attempt at a Solution This means that, if X is a discrete T1 space, it has a locally finite basis, right? Btw, for the...

In a noetherian ring, why is it true that there are only a finite number of minimal prime ideals of some ideal? (And is it proven somewhere in the Atiyah-mcdonald book?)

A "countable basis" vs. "countably locally finite" problem Homework Statement Sometimes it's fairly difficult to name a thread for a specific problem. :smile: So, one needs to show that, if X has a countable basis, a collection A of subsets of X is countably locally finite of and only if...

Homework Statement I'm not especially good at creating examples, so I'd like to check this one. One needs to find a point-finite open covering of R which is not locally finite. (A collection is point-finite if each point of R lies in only finitely many elements of that collection) The...

do suggest a good book for finite element method?some books have left me confused over the various methods

Finite Dimensional Inner-Product Space Equals its Dual!? Let V be a finite dimensional inner-product space. Then V is 'essentially' equal to its dual space V'. By the Reisz Representation theorem, V is isomorphic to V'. However, I've been told that V=V', which I am having a hard time...

Homework Statement Construct a finite field of order 16. And find a primative element. Homework Equations The Attempt at a Solution What I did was find an irreducible polynomial in Z/<2> of degree 4. I used f(x)=x^4+x+1. Then I took a to be a root of f(x) and set a^4=a+1...

Homework Statement A is compact and B is an open covering of A. Each a in A is contained in at least 2 subsets of B. Show that B has a finite sub-covering where A is still contained in at least 2 members of this finite sub-covering. Homework Equations I just posted the general idea of my...

Homework Statement A single infinitely conductor with a diameter of 10mm and a height of 3m above ground is charged to a voltage of 20kV above earth a. Find the charge/meter on the conductor. b. Find the capacitance/meter on the conductor. Homework Equations I don't know if these...

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I'm trying to understand the proof given in the last 10 minutes or so of this video lecture, but after some struggle, it occurs to me that I may be misinterpreting what the theorem says. According to this, Cantor's finite intersection principle states the following. Given a metric space (X,d)...

Homework Statement We have a solenoid of radius a, length L, with ends at z = +/- L/2. The problem is to use Ampere's law to show that the longitudinal magnetic induction just outside the coil is approximately B_z (\rho=a^+, z) \approx \left(\frac{2 \mu_0 N I a^2}{L^2} \right) \left(1+...

Homework Statement 1. Let G and H be finite groups and let a: G → H be a group homomorphism. Show that if |G| is a prime, then a is either one-to-one or the trivial homomorphism. 2. Let G and H be finite groups and let a : G → H be a group homomorphism. Show that if |H| is a prime, then a...

please check math in code for em-force on moving particle due to finite straight wire could someone pretty please make sure I'm doing the calculations correctly? this is for a computer simulation of charged particles in an electromagnetic field. it's to calculate the electro-static and...

Find the volume of the finite region enclosed by the surfaces z = 0 and x2 + y2 + z = 1 I know I have to do triple integration on dV to accomplish this but do not know where to start and what limits to use for x, y and z? Cheers guys

Homework Statement Solve 3x + 50 = 11 in F53 Homework Equations Extended Euclidean AlgorithmThe Attempt at a Solution To find 3-1 mod 53 using the euclidean algorithm: gcd(53,3) 1)53/3 = 17 + 2R 53 = 17 * 3 + 2 2 = 53 - 17 * 3 3/2 = 1 + 1R 3 = 1 * 2 + 1 1 = 3 - 1 * 2 = 3 - 2Now...

Homework Statement The problem is basically solving the Klein-Gordon equation for a finite well for a constant potential under the condition V > E + mc^2 Homework Equations V = 0 -a<x<a V = V_o elsewhere KG Equation: [\nabla^2 + \left({{V-E} \over {\hbar c}}\right)^2 - k_c^2]\phi(x) = 0...

Homework Statement Hi guys. Electrical engineering student here trying to get some real physics under his skin. I'm trying to derive the field and ultimately the inductance of a finite solenoid based on the spiral shape of the windings (because I assume - for no good reason - that the exact...

Hello, I'm triying to solve the unidimensional heat transfer equation in transient scheme for an sphere with Crank Nicholson discretization. Because I must to obtain the Heisler Charts, I'm triying to solve the adimensional equation, that is this equation: Where 4.1 is the equation, 4.2...

Homework Statement If E has finite measure and \epsilon>0, then E is the disjoint union of a finite number of measurable sets, each of which has measure at most \epsilon. Homework Equations The Attempt at a Solution I proceeded by showing that by definition of measure, there is a...

Let x>0 be a random variable with some distribution with finite mean and let E denote the expectation with respect to that distribution. By Jensen's inequality we have Elog(x) =< logE(x) < +inf But, does this imply that -inf < Elog(x) too? Or is it possible that Elog(x) = -inf Sorry if my...

I am considering a second order ODE of the form y''(x) + f(x) y(x) = 0, with boundary conditions that y(x) = 0 at plus/minus infinity. Note that f(x) is complex for my case. It seems that the standard techniques for numerically solving this problem are (a.) the finite difference method and...

Homework Statement The random variable X has uniform density on the interval [0,2], so that p(x)=1/2 for x in the interval [0,2] and p(x)=0 otherwise. Give the range of a (between minus/plus infinity) such that E[X^a] < infinity. Homework Equations The Attempt at a Solution I...

Homework Statement Find all the subgroups of Q* (set of all non-zero rational #s) under multiplication. Explain how you know that Q* has no other finite subgroups.Homework Equations The subgroups must satisfy the properties of association, closure, inverse, and identity. The Attempt at a...

Homework Statement A thin rod extends along the z-axis from z=-d to z=d, carrying uniformly distributed charge along it's length with charge density lambda. Calculate the potential at P1 on the z-axis with coordinates (0,0,2d). Then find an equal potential at point P2 somewhere on the x-axis...

I'm reading a book (Numerical Techniques in Electromagnetics by Sadiku) & just finished the section on finite difference methods. As what I thought would be an easy exercise, I tried to apply what I'd learned to the telegraphers equations that describe the voltage, V(x, t), and current, I(x, t)...

Are magnetic field lines around a finite current carrying straight conductor concentric circles in plane perpendicular to length of wire? I have seen texts derive an expression for it : B = μ0.i/4πd [cos Φ1-cosΦ2] where d is perpendicular distance of separation of the point...

Hi, We all know that the finite difference formulae for the derivatives are given by: \frac{dy}{dx}_{i}=\frac{y_{i}-y_{i-1}}{\delta x} and \frac{d^{2}y}{dx^{2}}=\frac{y_{i-1}-2y_{i}+y_{i+1}}{\delta x^{2}} What would be the formulae for the boundary terms? when i=1? I think I can...

Let's say I have this statement. {a^p | p is prime and p < N} a is considered a string so so a^2 = aa, a^3 = aaa and so on... anyway, in this case, since it says that p< N, then is mean that p will be finite right??

Homework Statement I have to program a three component decay chain using finite difference approximation. I understand finite difference and have written my code, but I have an error I can not find which is giving me an erroneous answer. The curve is correct, but the magnitude of the...

Prove that the collection F(N) of all finite subsets of N (natural numbers) is countable.

A field K is called algebraically closed field if any no-zero polynomial has at least one root in K. Given finite field F_q, q=p^m, p is a prime and m is non-negative integer. A famous property of finite field is any element in F_q satisfies: x^q=x. Then I have such an assumption...

Homework Statement An electron is confined to a potential well of finite depth and width, 10^-9 cm. The eigenstate of highest energy of this system corresponds to the value \xi = 3.2. a. How many bound states does this system have? b. Estimate the energy of the ground state with respect...

Homework Statement As the title says Homework Equations Definitions of "open" and "closed" The Attempt at a Solution Suppose a finite set S is not closed. Then Sc is not open, and there exists an element x of Sc, so that for all µ > 0, either x + u, or x - u, is an element of S...

I know this is really stupid and it looks like i haven't tried at all but i am genuinely confused about this so any guidance at all would help big time. so here is the question. A steel bar, 70mm long is struck at one end by a heavy mass moving at 20m/s. The impact causes a compression wave...