Decomposition Definition and 386 Threads

Homework Statement What is the Initial Rate of Decomposition for NO2. Where 2NO2-----> 2NO + O2 K=.54 Concentration at t=0 is .008 M This is a second order reaction.Homework Equations Rate=k[C]2The Attempt at a Solution Rate=.54[.008]2=.000035 (directed to give a two sig fig answer) This...

Homework Statement There is a particle in an infinite square well and the normalized wave function is divided into 3 parts. Psi = A between 0< x < L/3, B where L/3< x < 2L/3, and C from 2L/3 < x < L. I have to prove that the decomposition into psin yields a specific cn. Homework Equations...

Homework Statement Dinitrogen monoxide (nitrous oxide) N2O decomposes producing nitrogen and oxygen gases. The atomic masses are N: 14.0 and O: 16.0 The molar volume of an ideal gas at STP is 22.4 dm3/mol Homework Equations Calculate the total volume of produced gases at STP, when 8.8...

The equation i currently have is (-7s+52)/(s^2-8s+16) I need to convert it into a partial fraction decomposition to do a inverse Laplace Transform, but i seem to be stuck with the algebra of the what I am supposed to do. The equation I am supposed to use to set them is A/(s+a) +...

these are my mfiles for Lu decomposition with partial pivoting and substitution 1.LUdecomp.m function [x]=LUdecomp(a,b,n,tol,er,x) for i=1:n o(i)=0; s(i)=0; end er=0; decompose(a,n,tol,o,s,er) if er~=-1 substitute(a,o,n,b,x); end end 2.decompose.m function...

Homework Statement Using (\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} = \epsilon_{\alpha \gamma} \epsilon^{\beta \delta} + \delta^{\delta}_{\alpha} \delta^{\beta}_{\gamma} show that \Psi_{\alpha} X_{\beta} = \frac{1}{2} \epsilon_{\alpha \beta} (\Psi X) +...

Homework Statement Let H(r) = x^{2}yi + y^{2}zj + z^{2}xk. Find an irrotational function F(r) and a solenoidal function G(r) such that H(r) = F(r) + G(r) Homework Equations From Helmholtz's theorem, any vector field H can be expressed as: H = -\nabla\Psi + \nablaxA So then: F...

Hi... Can anyone one give me a good reference for the decomposition of perturbations into independent scalar, vector and tensor parts, with all the gory details?

Hello everybody, this is the first thread of mine. I try to recover the decomposition of the fundamental representation (the 7) of G2 into irreducible representations of A_2. It is given by 7 = 3 + [tex]\bar {3}[\tex] + 1 It maid be that I didn't understand the procedure, founded...

Homework Statement I've been looking at Paul Langacker's "Grand unified theories and proton decay" for a course on GUTs. I'm stuck with the 16 irrep of SO(10), particularly I don't understand how to prove the statement that the 16 decomposes as 5* + 10 + 1. I can see why it's useful physics...

Homework Statement In the heat equation, we have $T(t,x)=sum of a_k(t)b_k(x)$. Now I want to find a formula for computing the initial coefficients $a_k(0)$ given the initial temperature distribution $f(x)$. Homework Equations We know that in a heat equation , $f(0)=0$, $f(1)=0$...

Homework Statement Calculate the empirical formula of each hydrate Homework Equations Mass of MnSO4 x XH2O... -Hydrate = 1.8g -Anhydrous salt = 1.59g -Water = .21g The Attempt at a Solution I thought you would set 1.8g MnSO4*XH2O((Molecular mass of MnSO4)/(Molecular mass of...

Homework Statement Let T be a linear transformation over V, a finite-dimensional complex inner product space (with inner product < , >). Suppose T has the singular value decomposition Tv = \sum_j^n s_j \left\langle v,e_j \right\rangle f_j where s_1, ... s_n are the singular values of T and...

I need to write a program utilizing LU decomposition of a matrix in Java without using any linear algebra libraries so I was wondering if anyone can give me some pseudo-code or a link or something. I know you're supposed to post your attempt, but I literally have no idea what I'm doing. This is...

For the following problem provide the "form" of the partial fraction decomposition for the given fractional expression. You do not have to solve the undetermined coefficients. 4. 2x^2 - 3x + 8 / x^3 + 9x I took an x out and it's no x(x^2+9) My answer is A/X + BX+C/x^2+9 5. x- 7 / x^4 - 16...

http://news.yahoo.com/s/yblog_upshot/20101012/bs_yblog_upshot/mcdonalds-happy-meal-resists-decomposition-for-six-months" . Who else here has observed several (or perhaps many, yech) food items which have "resisted decomposition" in the same way as Davies' Happy Meal Project? I find this...

Homework Statement Show that any linear operator \hat{O} can be decomposed as \hat{O}=\hat{O}'+i\hat{O}'', where \hat{O}' and \hat{O}'' are Hermitian operators. Homework Equations Operator is Hermitian if: T=T^{\dagger}The Attempt at a Solution I don't know where to start :\ Should I try...

Homework Statement Given matrix, A= (-1 0 2;2 -1 0) and B=(-3 4;2 1) Find SVD using matlab. Homework Equations The Attempt at a Solution matlab code for svd; [d,e,f]= svd(c) c= A*B (but i got an error in MATLAB when i tried this) thanks

Homework Statement Find a singular value decomposition of A. A^T= [7 0 5 1 0 5] Homework Equations A = U\SigmaV^T The Attempt at a Solution I started by doing A^T*A = [ 74 32 32 26] Then i went and found the two eigen values lambda1= 90 and lambda2= 10 and the...

Homework Statement y=[4 8 1]^T u_1 = [2/3 1/3 2/3]^T u_2=[-2/3 2/3 1/3]^T Part 1: Write y as the sum of a vector y hat in W and a vector z in W complement Part 2: Describe the geometric relationship between the plane W in R^3 and the vectors y hat and z from the part above...

[PLAIN]http://upload.wikimedia.org/wikipedia/en/7/7a/Friction.png I can decompose W to get Fn and -Fr. Fn = W cos(\theta) -Fr = W sin(\theta) I know I'm allowed to decompose forces like that but I'm a bit confused as to why. Cause |Fn| + |Fr| > |W| (for the angle in this picture). So...

We are a simple robotics group working in Antarctica. We have a small but nimble ROV that we launch through a hole we drill in the ice. We need to lift heavy objects off the sea floor. I want to use the decomposition of H2O2 to initiate a state change that creates the buoyancy to lift these...

Homework Statement Find the partial fraction decomposition 1. \frac{x^4}{(x-1)^3} 2. \frac{1}{a^2-x^2} Homework Equations The Attempt at a Solution 1. \frac{x^4}{(x-1)^3} \frac{x^4}{(x-1)^3}=\frac{a}{(x-1)}+\frac{b}{(x-1)^2}+\frac{c}{(x-1)^3} x^4=(x-1)^2+(x-1)b+c x^4=ax^2+(-2a+b)x+(a-b+c) I...

Homework Statement Write the Partial Fraction decomposition for: \frac{x}{16x^4-1} Homework Equations The Attempt at a Solution \frac{x}{16x^4-1} =\frac{x}{(2x-1)(2x+1)(4x^2+1)} =\frac{x}{(2x-1)(2x+1)(4x^2+1)}=\frac{a}{(2x-1)}+\frac{b}{(2x+1)}+\frac{cx+d}{4x^2+1}...

Homework Statement Find the Partial Fraction Decomposition. \frac{4x^2+2x-1}{x^2(x+1)} Homework Equations The Attempt at a Solution \frac{4x^2+2x-1}{x^2(x+1)}=\frac{a}{x}+\frac{b}{x^2}+\frac{c}{(x+1)} 4x^2+2x-1=x^2(x+1)a+x(x+1)b+x^2(x)c So i can solve for c by plugging in...

Homework Statement \int 1/(x^{2}+4x+5)^{2} Homework Equations I am using partial fraction decomposition The Attempt at a Solution 1/(x^{2}+4x+5)^{2} = Ax+b/(X^2+4x+5) + Cx+D/(x^2+4x+5)^2 1 = (Ax+b)(X^2+4x+5) + Cx+D When i multiply through to find the values for A and b...

Hello all, I have a small problem that I would appreciate some assistance with. I'm working with the Lie group \mathfrak U(N) of unitary matrices and I have an element P \in \mathfrak U(N) . Furthermore, I have a set \left\{ H_1, \ldots, H_d \right\} that generate the Lie algebra...

Does anyone know of a good discussion of the compatibility (or otherwise) of Weinberg's 'cluster decomposition' principle with the fact that entangled states yield distant but correlated measurements?

Homework Statement \frac{2x + 2}{x^2 - 2x + 1}dxHomework Equations The Attempt at a Solution I factorized the denominator and got \frac{2x + 2}{(x - 1)^2} and I took a look at the solutions manual to see how they handled this but then I see this \frac{2x + 2}{(x - 1)^2} = \frac{A}{(x - 1)} +...

Homework Statement Write the partial fraction decomposition of the rational expression. Check your result algebraically. (x2 – 7x + 16)/[(x + 2)(x2 – 4x + 5)] The Attempt at a Solution [A/(x+2)] + [(Bx+C)/(x2-4x+5)] x2-7x+16= A(X2-4x+5)+(Bx+C)(x+2)...

Im attempting a problem in relativistic optics that's asking me to write k_x, k_y and k_z in terms of lambda, c, and theta (theta being the angle between a source and an observer, at rest relative to each other). Lamda is the wavelength in this reference frame. I started off using trigonometry...

Homework Statement Decompose the rational expression into a sum of partial fractions: (x+1)/(3(x-2)2) I am familiar with the method of decomposing fractions into a sum of partials fractions (solving for A, B, C, etc.). What is confusing me is the coefficient 3 in the denominator. Do I...

I have to show that a generic vector can be decomposed into an irrotational and solenoidal component: V(r) = -Grad[phi(r)] + Curl[A(r)] I'm not sure how to start. Do I need to take the curl or div of V and use a vector identity? Any help would be greatly appreciated!

For the reaction at 523K PCl5 (g) <-> PCl3 (g) + Cl2 (g) and Kp = 0.500 What percentage of PCl5(g) will decompose if 0.100 atm of PCl5(g) is placed in a closed vessel at 523K? I am unsure of how to approach this problem, if anyone could give some insight I would greatly appreciate it.

Hi everyone, I have a problem with the following matrix equation: A = B*inv(B+D) where A is a square matrix, B a positive semi-definite matrix, D a positive diagonal matrix and inv() denotes the inverse matrix. All are real-valued. Does anyone know of any simple way to check whether this...

Homework Statement Find the exact values of A, B, and C in the following partial fraction decomposition.Then obtain the integral using those values. 1/(x^3-3x^2) = A/x + B/x^2 + C/(x-3)Homework Equations I'm not sure at this point.The Attempt at a Solution To make the denominator on the right...

I asked a question about Schmidt decomposition in one of the math forums, but haven't gotten any replies yet. Link. The question is about why the state of a bipartite system (a system that consist of two component systems) can be expressed in the form \sum_{n=1}^\infty...

I would be interested in seeing a correct statement and proof of the Schmidt decomposition theorem that (I think) says that if x\otimes y\in H_1\otimes H_2, there exists a choice of bases for these Hilbert spaces, such that x\otimes y=\sum_{n=1}^\infty \sqrt{p_n}\ a_n\otimes b_n with...

Homework Statement Sorry I don't have equation editor working 1/(z+1)(z2 + 2z + 2) Homework Equations The Attempt at a Solution (z2 + 2z + 2) z2 + 1) can be factor as (z - i)(z + i) However, I'm having trouble seeing the pattern on what (z2 + 2z + 2) would become, I...

If a n x n matrix A has an eigenvalue decomposition, so if it has n different eigenvalues, by the way, is it correct that a n x n matrix that doesn't have n different eigenvalues can't be decomposed? Are the more situations in which it can't be decomposed? Why can't I just put the same...

Hi, I am reading through Weinberg's "Quantum Theory of Fields" (vol. 1) and I am somewhat confused about the signs in the cluster decomposition of the S-matrix. Specifically, referring to eq. 4.3.2, let's say the term coming from the partition \alpha \to \alpha_1\alpha_2,\beta \to...

Homework Statement Prove that if A is an nxn positive definite symmetric matrix, then an orthogonal diagonalization A = PDP' is a singular value decomposition. (where P' = transpose(P))2. The attempt at a solution. I really don't know how to start this problem off. I know that the singular...

I was just wondering if it was possible to find the singular value decomposition of an nxn matrix such as 1 1 -1 1 I tried this but then when finding the eigenvectors of A^T*A I found there were none (non-trivial anyhow). So, is this not possible? EDIT: How embarrassing I made an...

Hello, If I've a real signal, and I do a forward Fourier transformation I receive two parts: Real and Imaginary, what's the difference between them? i need to represent the transform in a software program, which part do i represent ?

How would I calculate the determinant of a square matrix using LU Decomposition. Please be plain, I am not good with technical terms. An example would be nice. Thank you!

Hi, if let's say that there's an even function f(z) then how do we know if its Laurent decomposition (i.e. f(z) = f0(z) + f1(z) ) will be even functions and have even powers of z? Any help will be greatly appreciated.

Homework Statement 1/[s*(s^2 + 4)] Homework Equations The Attempt at a Solution 1/[s*(s^2 + 4)] = A/(s) + (Bs + C)/(s^2 + 4) => 1 = A(s^2 + 4) + (Bs + C)s s = 0 1 = A(0 + 4) + (B*0 + C)*0 A = 1/4 s = i 1 = A(i^2 + 4) + (Bi + C)i 1 = A(i^2 + 4) + Bi^2 + Ci 1 =...

Homework Statement I just can't understand it I've read plenty of guides online, I just can't figure it out. How do you do partial fraction decomposition the farthest i can get is below 1/[(s^2 + 1)(s+1)] Homework Equations The Attempt at a Solution 1/[(s^2 + 1)(s+1)] = A/(s+1)...

Homework Statement An nxn matrix C is skew symmetric if C^t = -C. Prove that every square matrix A can be written uniquely as A = B + C where B is symmetric and C is skew symmetric. Homework Equations The Attempt at a Solution No clue.

Is entangle enough to find that given states have Schmidt decomposition?