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Decomposition (mathematics)
Biology and ecology * Decomposition is the process through which organic matter is broken down into simpler molecules. * Biodegradation Decomposition, decompose may also refer to: Chemistry * Chemical decomposition or analysis, in chemistry, is the fragmentation of a chemical compound into elements or smaller compounds ** Thermal decomposition, chemical decomposition caused by heat Econometrics * Blinder–Oaxaca decomposition, a statistical method that explains the difference in the means of a dependent variable between two groups. Mathematics * Decomposition of time series, a statistical task that deconstructs a time series into several components * Doob decomposition theorem of an integrable, discrete-time stochastic process * Doob–Meyer decomposition theorem of a continuous-time sub- or supermartingale * Fourier decomposition, re-expressing a given periodic function as the sum of a series of trigonometric functions * Graph decomposition, partition of the edge set of a g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decomposition
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. Although no two organisms decompose in the same way, they all undergo the same sequential stages of decomposition. Decomposition can be a gradual process for organisms that have extended periods of dormancy. One can differentiate ''abiotic'' decomposition from ''biotic'' decomposition ( biodegradation); the former means "the 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. Animals, such as earthworms, also help decompose the organ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JSJ Decomposition
In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: : Irreducible orientable closed (i.e., compact and without boundary) 3-manifolds have a unique (up to isotopy) minimal collection of disjointly embedded incompressible tori such that each component of the 3-manifold obtained by cutting along the tori is either atoroidal or Seifert-fibered. The acronym JSJ is for William Jaco, Peter Shalen, and Klaus Johannson. The first two worked together, and the third worked independently. The characteristic submanifold An alternative version of the JSJ decomposition states: :A closed irreducible orientable 3-manifold ''M'' has a submanifold Σ that is a Seifert manifold (possibly disconnected and with boundary) whose complement is atoroidal (and possibly disconnected). The submanifold Σ with the smallest number of boundary tori is called the characteristic submanifold of ''M''; it is unique (u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume Number One
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length and height (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume). In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
