What is Decomposition: Definition and 411 Discussions

Decomposition is the process by which dead organic substances are broken down into simpler organic or inorganic matter such as carbon dioxide, water, simple sugars and mineral salts. The process is a part of the nutrient cycle and is essential for recycling the finite matter that occupies physical space in the biosphere. Bodies of living organisms begin to decompose shortly after death. Animals, such as worms, also help decompose the organic materials. Organisms that do this are known as decomposers. Although no two organisms decompose in the same way, they all undergo the same sequential stages of decomposition. The science which studies decomposition is generally referred to as taphonomy from the Greek word taphos, meaning tomb. Decomposition can also be a gradual process for organisms that have extended periods of dormancy.One can differentiate abiotic from biotic substance (biodegradation). The former means "degradation of a substance by chemical or physical processes, e.g., hydrolysis. The latter means "the metabolic breakdown of materials into simpler components by living organisms", typically by microorganisms.

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  1. I

    Partial fraction decomposition for .

    Partial fraction decomposition for... [b]1. 3x-1 / x(x^2 +4) Homework Equations [b]3. A/x + Bx + C/ x^2 +4 after multiplying through by the denominator and my attempt at finding A,B,C i get this: 3x-1/x(x^2+4) = - one fourth / x + one fourth + 3/ x^2 +4. I don't feel...
  2. J

    Understanding Markov Chains and Different Types of Approximation

    Homework Statement Quick question, bros. Homework Equations Tell me if I'm right. The Attempt at a Solution A = U∑VT where ∑ contains on its diagonal the singular values of ATA U contains the corresponding eigenvectors for those singular values V...
  3. S

    Decomposition of spinor products

    I am currently trying to find how to derive the decomposition for two particles via the tensor notation, for instance for the product of two particles of spin 1/2 : \frac{1}{2} \otimes \frac{1}{2} = 1 \oplus 0 Giving the components of spin 1 and 0. So to do it, I write down the product...
  4. X

    Partial Fraction Decomposition

    Homework Statement [PLAIN]http://webwork2.math.utah.edu/webwork2_files/tmp/equations/60/0cff8a5107e21ae393dee5038fb6b31.png Homework Equations The Attempt at a Solution I've been attempting to use the general method of solving found at this website...
  5. L

    Scalar Vector Tensor Decomposition

    My notes are talking about this scalar vector tensor decopmosition business. Unfortunately, they are not online but they seem to follow this wikipedia article fairly closely: http://en.wikipedia.org/wiki/Scalar-vector-tensor_decomposition So our perturbed metric is of the form...
  6. W

    Find the partial fraction decomposition of the rational function.

    5x^2 + 8/x3 + x2 I got a 5x^2 + 8 = A/x^2 + B/x + 1 A(x+1) + B(x^2) (Ax+A) + (Bx^2) (Ax + Bx^2) + A 5x^2 + 8 = (A + B) x + (A)x^2 5x^2+x+8=(A+B) + (A) This is about as far as I can get but I think I made a mistake somewhere but I don't know where? Can someone help me?
  7. W

    Partial fraction decomposition question

    Determine A and B in terms of a and b. ax + b divided by x^2− 9=A/x-3 + B=x+3 When i calculate it i get a+b/2 and a-b/2 but that's wrong. I need help with this one.
  8. N

    Is the Plane Wave Decomposition of a Vector Field Accurate?

    Hi When we decompose e.g. the vector potential A into a sum of plane waves, then is it correct to say that we are describing an arbitrary vector field A, since we have decomposed it into its Fourier (= plane wave) components?Niles.
  9. S

    Using SVD for Least Squares Problems in MATLAB

    Homework Statement The link http://www.york.ac.uk/depts/maths/data/ts/welcome.htm gives the average monthly temperature T in Fahrenheits for Dubuque, Iowa from 1964 to 1975. Let T = a0 + sum from i = 1 to k of ai cos(2*pi*i*m/12) + sum from i = 1 to k of bi sin(2*pi*i*m/12) where m is the...
  10. D

    How can I Bel-decompose the Riemann tensor over SO(3,3)?

    Hello, I need to Bel-decompose the Riemann tensor built over SO(3,3). Does anyone have a decent reference? Funny how this topic is elusive. Is this in Wald? Thanks in advance. -drl
  11. C

    Initial Rate of Decomposition

    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...
  12. S

    Particle in a Box/Wave function decomposition.

    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...
  13. C

    Dinitrogen monoxide decomposition

    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...
  14. P

    Partial Fraction Decomposition

    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) +...
  15. J

    Matlab debugging for LU decomposition

    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...
  16. S

    Decomposition of SL(2,C) Weyl Spinors

    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) +...
  17. Z

    What is the Helmholtz Decomposition of a Vector Field?

    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...
  18. Z

    Can Helmholtz Decomposition Simplify Complex Vector Fields?

    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 =...
  19. K

    Reference for scalar-vector-tensor decomposition of perturbations

    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?
  20. T

    Decomposition of irrep. of G_2 into irreps. of A_2

    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...
  21. P

    SO(10) 16 representation, decomposition & young tableau

    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...
  22. chwala

    Asymptotic Analysis & Adomian Decomposition: Explained

    Asymptotic analysis Hi, can someone please give me a highlight of asymptotic analysis and singular cauchy problems...how is asymptotic compared to convergence...to my understanding when you have a polynomial divided by a polynomial= solution + remainder...the solution is the asymptotic and the...
  23. W

    Fourier decomposition and heat equation

    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 , $f(0)=0$, $f(1)=0$...
  24. U

    Thermal Decomposition of Hydrates

    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...
  25. F

    Singular value decomposition of adjoint

    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...
  26. R

    Comp Sci Learn LU Decomposition in Java: No Linear Algebra Libraries Required

    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...
  27. R

    The form of a partial fraction decomposition

    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...
  28. mugaliens

    Happy Meal Resists Decomposition?

    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...
  29. D

    Decomposition of linear operator

    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...
  30. Z

    Singular value decomposition using matlab

    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
  31. S

    Stuck on singular value decomposition problem

    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...
  32. S

    Linear algebra geometry of orthogonal decomposition

    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...
  33. E

    Force Decomposition: Exploring the Physics

    [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...
  34. Z

    How much pressure can be created by the decomposition of Hydrogen peroxide?

    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...
  35. T

    Partial Fraction Decomposition #3

    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...
  36. T

    Partial Fraction Decomposition #2

    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}...
  37. T

    Partial Fraction Decomposition

    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...
  38. A

    Help with Partial Fraction Decomposition

    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...
  39. K

    Lie algebraic decomposition

    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...
  40. M

    Cluster decomposition and EPR correlations

    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?
  41. L

    Linear Algebra - Cyclic Decomposition

    Linear Algebra - Cyclic Decomposition, Rational Canonical Form Homework Statement I am given a 5x5 real matrix A, and I am looking for an invertible matrix P so that P^{-1}AP is in rational form. Homework Equations The Attempt at a Solution I calculated the characteristic...
  42. H

    Partial fraction decomposition

    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)} +...
  43. M

    Partial fraction decomposition of the rational expression

    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)...
  44. M

    Linear Algebra - Polar decomposition

    First i calculated the eigenvalues: I got (i-\lambda)(-i-\lambda)+1, so \lambda_{1,2}=+-\sqrt{2}i Is it correct to go on on like this: \lambda_{1}a+b=\sqrt{\lambda_{1}} \lambda_{2}a+b=\sqrt{\lambda_{2}} After calculating a and b, we plug it into f(x) = ax+b --> f(A^{*}A)=a(A^{*}A)+bI Then...
  45. W

    Decomposition of the wave-vector in terms of wavelength

    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...
  46. P

    Physical Chemistry Question (work done during decomposition)

    Homework Statement A sample consisting of 1.0 mol of calcium carbonate CaCO3(s) was heated to 800°C, when it decomposed (CaCO3 → CaO + CO2). The heating was carried out in a container fitted with a piston which was initially resting on the solid. Calculate the work done during complete...
  47. J

    Decomposition of a rational expression

    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...
  48. L

    Vector decomposition (Helmholtz)

    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!
  49. R

    Kp and Decomposition (Chemistry)

    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.
  50. T

    Matrix Decomposition: Solving for B and D in A = B*inv(B+D)?

    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...
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