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Decomposition or rot 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 .
Chemical decomposition, or chemical breakdown, is the process or effect of simplifying a single chemical entity (normal molecule, reaction intermediate, etc.) into two or more fragments. [1] Chemical decomposition is usually regarded and defined as the exact opposite of chemical synthesis .
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Decomposition, the process by which organic matter is decomposed, occurs in several phases. Micro- and macro-organisms that feed on it rapidly consume and absorb materials such as proteins , lipids , and sugars that are low in molecular weight , while other compounds such as complex carbohydrates are decomposed more slowly.
Permutation decomposition, decomposition of a permutation into disjoint cycles; Primary decomposition, decomposition of ideals into primary ideals; Vector decomposition, decomposition of vectors into components or coordinates of basis vectors; Wavelet decomposition, re-expressing a given function as the sum of a series of wavelet functions
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
The Helmholtz decomposition in three dimensions was first described in 1849 [9] by George Gabriel Stokes for a theory of diffraction. Hermann von Helmholtz published his paper on some hydrodynamic basic equations in 1858, [10] [11] which was part of his research on the Helmholtz's theorems describing the motion of fluid in the vicinity of vortex lines. [11]
Decomposition: = where C is an m-by-r full column rank matrix and F is an r-by-n full row rank matrix; Comment: The rank factorization can be used to compute the Moore–Penrose pseudoinverse of A, [2] which one can apply to obtain all solutions of the linear system =.