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. T

    Singular Value Decomposition trouble

    Suppose I want to decompose A = \left(\begin{array}{cc}4&4\\-3&3\end{array}\right). A = U \Sigma V^T => A^T A = V \Sigma^2 V^T and A A^T = U \Sigma^2 U^T So 2 independent eigenvectors of A^T A are a basis for the row space of A and 2 independent eigenvectors of A A^T are a basis for the...
  2. C

    Local decomposition of unitary matrices

    I know that, given an arbitrary unitary matrix A, it can be written as the product of several "local" unitary matrices Ai -- local in the sense that they only act on a small constant number of vector components, in fact it is sufficient to take 2 as that constant, which is best possible. For...
  3. RadiationX

    Partial fraction decomposition

    Use partial fraction decompostion to find: \int_{a}^{b} \frac{2x-1}{x^2(3x+1)(x^2 + 1)} is this partial fraction set up correct? \frac{A}{3x +1} + \frac{Bx + C}{x^2 +1} + \frac{Dx + E}{x^2} = 2x - 1 If this is correct i can solve the integral.
  4. C

    Decomposition of hydrogen peroxide

    For the decomposition of hydrogen peroxide in the presence of manganese(IV) oxide, what is the chemical method to determine the concentration of hydrogen peroxide, at different times? The solution is: To add the reaction mixture in dilute sulphuric acid, and then titrate the reaction mixture...
  5. N

    Spinor Decomposition of a tensor

    Hi, I have heard, that a second rank tensor can always be decompose into a spin-2, a spin-1 and spin-0 part, being reducible. I want to pursue this further. Can anyone suggest me a nice reference for it? TIA Nikhil
  6. O

    Can Ferric Sulfide Decompose into S8 Molecules and Ferric Ions?

    Hi! I was just wondering if the decomposition of ferric sulfide can break down into S8 molecules and ferric ions? Thanks in advance!
  7. A

    Helicity and Clebsch decomposition

    It is well-known that using the Clebsch decomposition of a velocity field, the helicity contained in an any closed vortex tube is zero. Does the converse hold? That is, given zero helicity in any closed vortex tube, does this imply that the velocity field has a Clebsch decomposition?
  8. S

    Matrix Decomposition: Finding A & B for C & D

    Hello, I have a question about what I would call, for want of a better name, matrix decomposition. However, my question does not concern standard decompositions like eigenvalue or Cholesky decomposition. The problem: Assume given two real and square matrices C and D. C is symmetric...
  9. C

    Decomposition of a Divergenceless Vector Field

    Viva! I usually come upon this statement: " Since B is solenoidal, it can be split into Toroidal and Poloidal parts, i.e, B=Bt+Bp, where Bt=curl(Tr) and Bp=curlcurl(Pr)" How can I prove this?? I think it is somehow related with the stokes theorem... Looking forward for...
  10. G

    Helmholtz Theorem on Decomposition of Vectors

    Does anyone know anything about this? I got a look at wolfram.com and I didnt get much. I would like to prove that in fact, any divergenceless vector field can be decompose in a toroidal part and a poloidal part. And I think the proof of this is somehow related with this theorem...
  11. D

    How to go about Synthesis and Decomposition of compounds

    Can anyone explain to me really quick how to go about Synthesis and Decomposition of compounds, can you show me an example with Aluminum Flouride and Potassium Chloride ? Thank you for your help
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