Finite Definition and 1000 Threads

..though I figure it's sort of an analysis type problem. ∫wvdx=0 (int from 0 to 1) for all v in V. w is continuous on [0,1]. What it means to be in V: v in V satisfies being continuous on [0,1], v(0)=v(1)=0, and derivatives of v are piecewise continuous . Problem is: Show that w(x)=0 for x in...

Homework Statement Let f:[0,1]→ℝ be non-negative and integrable. Prove that \int_{[0,1]}\frac{f(y)}{|x-y|^{1/2}}dy is finite for ae x in [0,1] Homework Equations This looks like a Fubini/Tonelli's Theorem problem from the problem givens. The Attempt at a Solution I honestly don't know...

I use transfer matrix method. I try to plot the phase Φ(ω) versus frequency ω graph in the vicinity of a band gap. The transmission coefficient t(ω) is t(ω) = |t(ω)|*exp(i*Φ(ω)) from which I get the transmission phase Φ(ω) = atan(t_imaginary(ω)/t_real(ω)). Since I assume that -pi/2 ≦ Φ ≦...

Dear Sir, If we consider the Big Bang Hypotesis , the age of the universe and the rate of expansion ogf space, the Universe could be very large , but finite. But Prof Sean Carrol said , in a lecture , that there's a possibility of Infinite Universe. Please elaborate.

Morning everyone, I apologize for bringing up a topic that has probably been discussed to death here in the past. I've been reading the FAQ, and a few old threads about finite vs infinite universe, but I'm still struggling to grasp both of these ideas. I'd be really grateful if someone could...

Let $K=\mathbb{Q}[\omega]$ where $\omega^2+\omega+1=0$ and let $R$ be the polynomial ring $K[x]$. Let $L$ be the field $K(x)[y]$ where $y$ satisfies $y^3=1+x^2$.Which is the integral closure of $R$ in $L$, why?

Hi everyone, I've been looking for the finite sum formulae of trig functions. I've found the easiest ones (sine and cosine). But the one for the tangent seems to be very hard. No mathematical tricks work. Plus I've looked it up on the internet. Nothing. I will greatly appreciate your help...

Hello! If anybody has a minute, I'd appreciate a quick look-through of my proof that a finite abelian group can be decomposed into a direct product of cyclic subgroups. I'm new to formal writing (as well as Latex) and all feedback is greatly appreciated! Thanks in advance for your time...

Hey, it is clear for me that \sum_{i=1}^{n} i = \frac{n(n+1)}{2} how to find a formula for \sum_{i=1}^{n} i^2 \sum_{i=1}^{n} i^3 Thanks

I wish it wasn't out of desperation that I'm making this first post! I have a neural network that is making predictions, the next 5 time points per training. Back testing consists of appending these 5 point sets together to produce a data set that spans time over a much longer period...

Homework Statement Let G be a finite group in which every element has a square root. That is, for each x in G, there exists a y in G such that y^2=x. Prove every element in G has a unique square root. Homework Equations G being a group means it is a set with operation * satisfying...

Here is the question: Here is a link to the question: Finite math problem involving venn diagrams? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement So I am trying to understand this proof and at one point they state that an arbitrary compact subset of a Banach space, or a completely metrizable space is the subset of a finite set and an arbitrary convex neighborhood of 0. I've been looking around and can't find anything...

Homework Statement Hi all, I am struggling with getting an intuitive understanding of linear normed spaces, particularly of the infinite variety. In turn, I then am having trouble with compactness. To try and get specific I have two questions. Question 1 In a linear normed vector space, is...

Homework Statement Prove the collection of all finite order elements in an abelian group, G, is a subgroup of G. The Attempt at a Solution Let H={x\inG : x is finite} with a,b \inH. Then a^{n}=e and b^{m}=e for some n,m. And b^{-1}\inH. (Can I just say this?) Hence...

Homework Statement A particle of mass m is in the potential V(x) = \left\{ \begin{array}{rl} \infty & \text{if } x < 0\\ -32 \hbar / ma^2 & \text{if } 0 \leq x \leq a \\ 0 & \text{if } x > a. \end{array} \right. (a) How many bound states are there? (b) In the highest energy...

Homework Statement Let E have finite outer measure. Show that if E is not measurable, then there is an open set O containing E that has finite measure and for which m*(O~E) > m*(O) - m*(E) Homework Equations The Attempt at a Solution This is what I did... m^*(O) = m^*((O \cap E^c) \cup...

Homework Statement A car is moving with a constant speed of 40 km/h along a straight road which heads towards a large vertical wall and makes a sharp 90° turn by side of the wall . A fly flying at a constant speed of 100 km/h , start from the wall towards the car at an instant when the car...

Homework Statement if f is integrable, then the set N(f) = {x : f(x)≠ 0} is \sigma-finite Homework Equations i am stucked in this proof , somebody help me pleaseThe Attempt at a Solution if f is simple the it seems the set is finite since otherwise the the integral won't exist but how can it...

Hi there, I am reading an article, but I faced the following problem, and I am wondering if it is well known fact. If the integral of a function on some interval is infinity, can we partition this interval into countable disjoint (in their interiors) subintervals such that the integral...

Homework Statement http://puu.sh/1QFsA Homework Equations The Attempt at a Solution I'm actually not sure how to do this question. How do i find Δx^2. I kind of understand the question but I don't know how to prove it. I know that Δy becomes dy when the width becomes...

If the universe is finite in size, what is at the very edge of it?

Hi all, I have been asked the question by a friend of mine who was working on a computer algorithm where he needed pairs of primes to uniquely identify items in a set. What I would like to know is there a way to proof that the set of prime pairs (p, p+2) is finite or infinite. I have been...

I recently got (re)interested in C* algebras. Poking around, I gathered that there is some way of constructing a C* algebra corresponding to a finite graph. I'll put some links here in case anyone knows anything about this. At the moment I'm ignorant but hope to find out more. No idea in...

Hi everyone I 'm having difficulty in proving the following theorem theorem: If L/K ( L is a field extension of K) is a finite extension then it is algebraic. Show, by an example, that the converse of this theorem is not true, in general. Can you help me to find an example in this case? Thanks...

Homework Statement I have the following practice problem which is presented as follows: What is the size of the global stiffness matrix K (i.e., Kuu) for the 2-D problem? http://imgur.com/KZec3 (Unsolved) http://imgur.com/piv1J (Solved) Homework Equations The Attempt at a...

I think I am not understanding the concept of compactness. Can anyone give me an example of a cover that contains finite sub-covers? for example:- G = {S1,S2, ... }, Sn={(1/n,2/n): n ≥ 2} is an example of cover of set (0,1) but it is an infinite collection.

Hi. I'm trying to determine the CFL condition for the fourth-order leapfrog scheme. I'm finding 2 as what's published, which does not match what I'm getting. Does anyone know where I can find a von Neumann (or Fourier) stability analysis of the leapfrog (2,4) scheme (so I can compare my work)...

Homework Statement Given some ElGamal private key, and an encrypted message, decrypt it. Homework Equations Public key (F_q, g, b) Private key a such that b=g^a Message m encrypted so that r=g^k, t=mb^k Decrypt: tr^-a = m The Attempt at a Solution My problem is finding r^-a...

I need help with this theorum, please. How is this (the attachment) true? It's for my cryptology class. The rest of the day's notes are here: http://crypto.linuxism.com/thursday_december_13_2012

The set of all possible streams of brain activity arising from all possible configurations of all possible neurons with all possible connections is finite, so if you accept that natural numbers are a creation of the human mind (brain), then don't you have to accept that the set of number is...

The set of all possible streams of brain activity arising from all possible configurations of all possible neurons with all possible connections is finite, so if you accept that natural numbers are a creation of the human mind (brain), then don't you have to accept that the set of number is...

Homework Statement I have my quantum mechanics final creeping up on me and I just have a question about something that doesn't appear to be covered in the text. Let's say you have a wave function of the following form for a linear harmonic oscillator: \Psi = c_1 | E_1 \rangle + c_2 | E_2...

hi; I have 3 hyperbolic electrodes ,one as a ring and 2 others as endcap electrodes which have potential v and 0 respectively.(quadrupole ion trap) I want to solve potential inside the trap by finite difference method. I don't know how general equations for unshaped materials will change...

Use finite difference method to solve for eigenvalue E from the following second order ODE: - y'' + (x2/4) y = E y I discretize the equation so that it becomes yi-1 - [2 + h2(x2i/4)] yi + yi+1 = - E h2 yi where xi = i*h, and h is the distance between any two adjacent mesh points. This...

Homework Statement A uniform charge Q of length L is placed on the x-axis with one end at the origin as shown a) Find the contribution dE (vector) to the electric field at P on the y-axis a distance y from the origin, from the charge at x in dx, in terms of Q, L, dx, ke, x and y b)...

Homework Statement Let (G,*) be a finite group of even order. Prove that there exists some g in G such that g≠e and g*g=e. [where e is the identity for (G,*)] Homework Equations Group properties The Attempt at a Solution Let S = G - {e}. Then S is of odd order, and let T={g,g^-1...

Let $G$ be a finite group of order $4n+2$ for some integer $n$. Let $g_1, g_2 \in G$ be such that $o(g_1)\equiv o(g_2) \equiv 1 \, (\mbox{mod} 2)$. Show that $o(g_1g_2)$ is also odd. I found a solution to this recently but I think that solution uses a very indirect approach. Not saying that that...

Dear all I am working with a Gamma-Poisson mixture distribution where (and this is not usual) the support of the Gamma distribution (in fact, I am able to restrict to the neg exponential instead of the Gamma...) is finite, e.g. [0,1]. I would like to derive the mean and a Likelihood...

Ok I understand the concept of infinite countability and that say the set of all rational #s is infinitely countable, but if I needed to represent the set how do I do that? S={xε rat. # : x= k , k ε a rational #}? that doesn't seem right. Also say I wanted to show a set of finite countable...

Homework Statement The problem picture is attached(file 1),its a beam subjected to horizonatal ditributed load 2. Relevant examples the MATLAB solution for rectangular shape with vertical load on the upper right corner is like follow, i try to modify it according to the new picture...

Show that every finite field with p+1 elements, where p is a prime number, is commutative. I know this has something to do with composite numbers, but I'm not quite sure how to show this.

Hi, Recently started with FEA - loving it, at least the modelling / load application part. Interpreting the results is tricky - particularly around where loads are applied. Got a project (no pics sorry) which has a drilled hole in a plate, and have applied the load as a a pressure...

Homework Statement I am trying to prove the following: Let G be a finite group and let \{p,q\} be the set of primes dividing the order of G. Show that PQ=QP for any P Sylow p-subgroup of G and Q Sylow q-subgroup of G. Deduce that G=PQ. Homework Equations The set PQ=\{xy: x \in P \text{ and }...

Homework Statement I'm implementing the transfer matrix method (manually) for an EM wave through a 1D layered structure. Basically I'm just considering a plane wave in the positive-x direction, conserving E and H across each material interface, and constructing interface matrices, the...

This post in influenced by 3 new threads in our cosmology forum. Recent observational data favors positive curvature of our Universe. The question I have, however, is why positive curvature implies spatially finite Universe? Yes, it might look quite obvious if we embed curved space into higher...

As I know, the method to solve neutron problem is divided into two steps now, neutron transport calculation for fuel assemblies and neutron diffusion calculation for whole reactor core, both using specified code such as CASMO and SIMULATE from STUSVIK. I want to know whether the commercial...

Homework Statement Let A be a finite subset of R. For each n in N, let x_n be in A. Show that if the sequence x_n is convergent then it must become a constant sequence after a while. Homework Equations The definition of limit. The Attempt at a Solution As A is finite, at least...

Homework Statement Already defined that for a 1D well with one finite wall the eigenvalue solutions are given by k cot(kl) = -α Show the eigenvalue solutions to well with both walls finite is given by tan(kl) = 2αk / (k^2 - α^2) Well is width L (goes from 0 to L) with height V_0...

Folks, I am having difficulty understanding how this global matrix is assembled with the naming convention used as shown in attached. The numbers in the corners such as 1(1,2) etc in figure 4.6.3 (b) denote the global and element numbers respectively. Can anyone shed light on how this...