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. E

    Solve LU Decomposition for Matrix 0 0 1, 1 0 0, 0 1 0

    Homework Statement 0 0 1 1 0 0 0 1 0 decompose this matrix using LU decomposition. Homework Equations The Attempt at a Solution I took this matrix and augmented it with a zero (3 by 3) matrix. Then I performed the same row operations on both...the row operations with the...
  2. J

    Decomposition of direct product into symmetric/antisymmetric parts

    Can anyone explain to me why the 3-rep of SU(3) gives 3\otimes 3 = \overline{3}\oplus 6 whereas for the 5 of SU(5) 5\otimes 5 = 10\oplus 15? I thought the general pattern was N \otimes N = \overline{\frac{1}{2}N(N-1)}\oplus \frac{1}{2}N(N+1) but this second example seems to...
  3. E

    Multivariable factor decomposition

    (Keep in mind, I made this off the top of my head, so if something cancels easy, ignore it) Let's say I had this expression: f(x,y)=\frac{y^2-xy+1}{(x+y)(x-y)} I want to decompose this to: \frac{A}{x+y} + \frac{B}{x-y} So i begin the process: y^2-xy+1=A(x-y) + B(x+y) y^2-xy+1=x(A+B) +...
  4. M

    Complex Cholesky Decomposition

    I am having trouble finding information about decomposing a complex symmetric positive definite matrix. I was wondering if the cholesky decomposition would change to accommodate complex numbers. I understand that multiplying, dividing, and taking the square root of complex numbers is not the...
  5. M

    Complex Cholesky Decomposition

    I am having trouble finding information about decomposing a complex symmetric positive definite matrix. I was wondering if the cholesky decomposition would change to accommodate complex numbers. I understand that multiplying, dividing, and taking the square root of complex numbers is not the...
  6. R

    Partial fraction decomposition

    Problem: Find the integral of 2dx/(2x-3) using partial fraction decomposition Attempt: A/(2x-3) Compare coefficients A = 2 2 \int (1/(2x-3)) = 2ln(2x-3) This is wrong. Can someone please tell me what I'm doing wrong?
  7. A

    Negative Value Matrix: Finding the Singular Value Decomposition

    I did some problems from the example and the questions at end of chapter. I got all of them right except this one. Problem Statement: Consider the matrix [3 0; 0 -2]. Find its singular value decompositions Problem Solution Goal is to find A = U*S*V as below Step1: Find AA', A'A...
  8. N

    Partial Fraction Decomposition

    Homework Statement I am just trying to do partial fraction decomposition on an equation. I'm not too good with it, as far as knowing if I need just A or Ax+B, etc. [e^(-2s) / (s^2+1)(s-1)(s+1)^2] Homework Equations The Attempt at a Solution I'm not quite sure how to work with the...
  9. B

    Navier Stokes Equations - Helmholtz-Hodge decomposition and pressure

    Hi, I've been doing some work with the NS equations. I've read a few papers by fellow undergrads that imply a relationship between the helmholtz-hodge decomposition and the pressure equation. As far as I can see, they're both separate ways of resolving the problem of keeping the flow...
  10. A

    An eigen decomposition problem in programming

    Hi all: I have a covariance matrix which is like: 0.00166713 -0.00060678 4.60534e-05 -0.00060678 0.00178576 -0.000244526 4.60534e-05 -0.000244526 0.000772057 And then I want to eigen decompose the matrix to obtain the eigenvector matrix. I tried several methods, one is to use the...
  11. J

    Singular Value Decomposition question

    Hi everybody and congrats for this forums! I'm studying first course of Industrial Engineering, and last week we were asked in Algebra about the following question: SVD: A=U*Σ*V(hermitic). If A is a matrix which we divide by an horizontal imagine line, so that we have two blocks: one in...
  12. G

    Partial fraction decomposition of the cosine

    Homework Statement Calculate \sum_{n=2}^{\infty}\frac{1}{n^{2}-1} with the "standard" method and with the method of the partial fraction decomposition of the cosine. Homework Equations \pi\cot\pi z=\frac{1}{z}+\sum_{k=1}^{\infty}\frac{2z}{z^{2}-k^{2}} The Attempt at a...
  13. F

    Spherical Harmonic Decomposition of an image

    Hey guys, Homework Statement Basically the question is to explain the meaning of a SHD of an image, specifically the image of the WMAP data of the CMB. Now i understand decomposition when it comes to functions but I am not sure how to extend that to images. Is it simply that you are...
  14. N

    Vector Decomposition: Finding Components w/ Vector Math

    I'm doing some work with vectors, and essentially, I have two vectors: a large vector and a unit vector pointing in a different direction. I would like to decompose the large vector into the components that are in the direction of and perpendicular to the unit vector. This is in three...
  15. R

    Proving Unique Decomposition of a Galilean Transformation

    hi... I´m attending a course of advanced classical mechanics. I´m working on statistical mechanics, so I´m not so familiar with some things on the course. I must solve the follwing problem for homework: show that every galilean transformation g on the (galilean space, using natural...
  16. R

    Exploring the Double Sum Decomposition in Scientific Research

    Hey folks, I'm trying to show that \sum_{m,n=-\infty}^\infty '(n^2+a^2m^2)^{-s}=\sum_{n=-\infty}^\infty 'n^{-2s}+\sum_{m=-\infty}^\infty'\sum_{n=-\infty}^\infty(n^2+a^2m^2)^{-s}. The prime means that we don't include the m=n=0 term. Has anyone seen this relation? Is it standard? Thanks!
  17. K

    Partial Fraction Decomposition Problem

    \frac{7}{3s^{2}(3s+1)} Can this be decomposed, and how?
  18. Z

    Decomposition of cooper II carbonate hydroxide hydrate.

    Homework Statement Lab Experiment: I added 5g of Cu2CO3(OH)2 in a bunsen burner and the resultant was a black product weighing 3.327g, representing a mass ratio of 0.67/1.0 Homework Equations The question is whether the remaining black compound is anhydrous copper carbonate...
  19. E

    Partial fraction decomposition

    Homework Statement Go here: http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1999s.pdf You do not need to read the problem. In solution two for 1999 A3, I can do the partial fraction decomposition but I get something different from that... I am wondering whether that comes from...
  20. F

    Understanding an Unnamed Theorem and the Primary Decomposition Theorem

    Hey guys, Couple of questions here id like some help with. Firstly an unnamed theorem in my textbook that says: suppose s and t are distinct eigenvalues for a 2x2 matrix A, then (A-sI)(A-tI) = 0 The proof goes something like this. We know there is an eigenvector u for the value s such that...
  21. J

    LU Decomposition of A: Find Solution

    Homework Statement A = \left| \begin{array}{ccc} 2 & 0 & 4 \\ 0 & 4 & -8 \\ 3 & -1 & 2 \end{array} \right|.\] Find the LU decomposition. The Attempt at a Solution My question is why do you need to interchange rows 3 & 1 at the start of the problem? My initial attempt was to find...
  22. S

    Determining Moles: H2O2 Decomposition

    2H2O2---> 2H2O+O2 In the decomposition equation above, how many grams of oxygen is made when 15.0 grams of H2O2 decomposes?
  23. J

    Spherical harmonic decomposition

    If you have a function f(x), you can decompose it as an infinite sum of sine waves of the form sin(nx) and cos(nx) for increasing n. If you have a function g(theta,phi), you can decompose it into spherical harmonics; for each order l you have 2l+1 spherical harmonics. Is there anything special...
  24. O

    Gordon decomposition an right current

    Gordon decomposition an "right" current I've got a question about the Dirac equation and the Gordon decomposition of the dirac current. The Gordon decomposition is \bar \psi \gamma^\mu \psi = - \frac{1}{m}\Im (\bar \psi \partial^\mu \psi) - \frac{1}{2m}\partial_\mu ( \bar \psi...
  25. 4

    What is the Orthogonal Decomposition of x from b in terms of RowA and NulA?

    Let A= [ 1 -2 -1 2] [-1 0 3 -2 ] [ 3 -4 -5 6] (sorry, can't line up the columns) I think I've done a) and b) correctly, I don't really understand c), d) and e) a) Find RowA and Nul A RowA={( 1, -2, -1, 2), (0, 1, -1, 0)} Nul A= {(3, 1, 1, 0), (-2, 0, 0, 1)} b) If...
  26. C

    LU Matix decomposition problem with U.

    Homework Statement i'm trying to put the 3x3 matrix: [4 2 6] [ 2 8 2] [-1 3 1] into row echelow from. but i don't know where I'm goin wrong in my row operations. could some1 please tell...
  27. M

    Singular Value Decomposition

    I have a couple questions about the singular value decomposition theorem, which states that any mxn matrix A of rank r > 0 can be factored into A = U \Sigma V into the product of an mxm matrix U with orthonormal columns, the mxn matrix ∑ with ∑ = diag(\sqrt{\lambda_i}), and the nxn matrix V...
  28. P

    Fraction Decomposition: A/a+B/b?

    Just wondering - is there anything you can do with 1/(a + b) to get something like A/a + B/b?
  29. T

    Hess Law: Molar Enthelpy Change for Decomposition

    Homework Statement This is for a chemistry report. This is the task: "Determine the molar enthalpy change for the decomposition of sodium hydrogen carbonate into sodium carbonate, CO(2) and water. 2NaHCO(3) -> Na(2)CO(3) + CO(2) + H(2)O This enthalpy change cannot be measured directly"...
  30. I

    Irreducible Components in a Primary Decomposition

    Let R be a Noetherian Ring and I an ideal in R. Let I = Q_1 n ... n Q_r = J_1 n ... n J_r be two primary decompositions of I. How can I show the number of irreducible components in each decomposition is the same?
  31. B

    Partial Pressure from decomposition

    Homework Statement An atmospheric chemist fills a gas-reaction container with gaseous dinitrogen pentaoxide to a pressure of 130. kPa, and the gas decomposes to nitrogen dioxide and oxygen. What is the partial pressure of nitrogen dioxide, PNO2, (in kPa) when the total pressure is 166 kPa...
  32. S

    Endothermic Decomposition Experiment

    I am doing an assignment and I'm not sure if the answer is endothermic decomposition someone please help me! During an experiment, a metal and an excess of fluorine gas were placed into a combustion chamber at a temperature of 1800°C. The temperature in the sealed chamber continued to rise to...
  33. S

    Decomposition of a nonconvex polygon

    Is there any algorithm to decompose a nonconvex polygon in a set of convex ones?
  34. MathematicalPhysicist

    An LDV decomposition of a matrix.

    i need to prove that if A is symmetric and invertible (i.e A^-1 exists), and A=LDV, when L is lower triangular matrix with ones on it's diagonal and V is an upper triangualr matrix also with ones on the diagonal and D is a diagonal matrix then V=L^t. what i did is: i know that V^t is an LTM...
  35. M

    Chemistry Help - Magnesium Carbonate decomposition

    Hey everyone, I have a homework question that I would appreciate some clarification on. Question: A 3.96g sample of magnesium carbonate decomposed to produce 1.89g of magnesium oxide. What mass of magnesium was in the sample of magnesium carbonate? Calculate the mass percent of of...
  36. T

    Can Any Function Be Decomposed into Odd and Even Subfunctions?

    Hello, the question here says: Show that any given function can be decomposed into the sum of manifestly odd and even subfunctions. What i have done is just assumed a continuous, differentiable function, with a number a in the domain of the function, then shown that a taylor series for a...
  37. R

    Catalytic decomposition of nitrous oxide?

    Does anyone know what types of materials may be used to decrease the activation energy of 2N_2O->2N_2 +O_2. I think perhaps silver may work, but I need to find a material which will withstand the high temperature of decomposition thanks
  38. M

    Proving partial fraction decomposition? integral maybe?

    hello everyone. I'm confused on what he wants here. here are the directions: http://img206.imageshack.us/img206/9692/lastscan2ju.jpg How do you prove such a thing? do i take the integral of the decompoisition and add them together or what? The homework and webworks never asked this...
  39. D

    Partial fraction decomposition

    can someone help me set up this problem. it asks for the partial fraction decomposition of: (7x^3 - 2)/[(x^2)(x+1)^3] i thought you put A/x^2 + B/(x+1)^3 and solve but it doesn't work that way.
  40. T

    Primary Decomposition Theorem

    "Let m(x) be the minimal polynomial of T:V\rightarrow V, \dim V<\infty such that m(x)=m_1(x)m_2(x) where gcd(m_1,m_2)=1, then there exists T-invariant subspaces V_1, V_2 such that V=V_1\oplus V_2." What other names is this thoerem called? It was given to me as the "primary decomposition...
  41. U

    SU(3) Decomposition of Antiquark - Antiquark

    Hello, I have a question with respect to the decomposition in irreducible representations of antiquark - antiquark ( SU(3) color ). In the case of quark - quark what you have is a triplet with an antitriplet and what you obtain is an antitriplet and a sextet, and from the Young tables...
  42. K

    What is the general formula for the decomposition of a hydrate?

    What is the general formula for the decomposition of a hydrate?
  43. kakarukeys

    Eager to learn 3+1 decomposition

    Eager to learn "3+1 decomposition" Is there any post, notes, books that gives complete introduction to "3+1 decomposition" in ADM fashion, as well as in tetrad formalism?
  44. A

    Is it possible to show that so(4) is equal to su(2) direct sum su(2)?

    Hi guys - long time reader first time poster! I'm currently getting to grips with the topic of Lie Algebras, and I've come across something that's baffled me somewhat. I've been asked to show: so(4) = su(2) \oplus su(2) Where the lower so(n) denotes the Lie Algebra of SO(n) etc. Now, in a...
  45. R

    Ricci Decomposition: Questions & Answers

    Hey folks, I am trying to piece together what the point of the Ricci Decomposition is. Wikipedia explains what it is but not really why. I understand that we can break down the Ricci Tensor into: 1) Scalar part 2) Semi-traceless 3) Traceless (Weyl Tensor) I have the following...
  46. D

    Partial Fraction Decomposition

    Hey eveyone, trying to determine the partial fraction decomposition of: (22x^2+60x+58) (s+1)(x^2+4x+5)^2 I got values for my unknowns A, B, C, D,E are: A=5 B=-1777/29 C=-6143/29 D=-570/29 E=840/29 If anyone out there can double check these for me.
  47. Pengwuino

    What Went Wrong in Calculating the Volume of Gas from Decomposition?

    So here's the problem I am faced with... dum dum dummmm So first I figured that there will be 30.6g of hydrogen peroxide. Then I figured that there are 0.4498 moles of O2. Then using the ideal gas law... V=nRT/P I got ((0.4498)(0.08206)(27+273.15))/(746/760) = 11.3 Liters of O2 But...
  48. T

    Partial fraction decomposition

    Having trouble with one more problem: find the parial fraction decomposition for th erational expression: -8x^3-2 x^2(x-1)^3
  49. C

    How Can I Decompose a 3x3 Rotation Matrix into a Product of 3 Rotations?

    Hi, How can I decompose a 3x3 rotation matrix R, into a form: R = rot(v3,c) X rot(v2,b) X rot(v1,a) where v1,v2,v3 are known unit length axes (with angles a,b,c unknowns)? Thank you, Cristian
  50. J

    Decomposition temperature of ZnSe:Cl crystal

    Any one knows what the decomposition temperature of ZnSe semiconductor doped with Cl is? I am doing some annealing with a simple equipment but worring about the volatilization of Cl, which would be dangerous. Thanks a lot!
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