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Cycle decomposition information


In mathematics, the term cycle decomposition can mean:

  • Cycle decomposition (graph theory), a partitioning of the vertices of a graph into subsets, such that the vertices in each subset lie on a cycle
  • Cycle decomposition (group theory), a useful convention for expressing a permutation in terms of its constituent cycles

In commutative algebra and linear algebra, cyclic decomposition refers to writing a finitely generated module over a principal ideal domain as the direct sum of cyclic modules and one free module.

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Cycle decomposition

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In mathematics, the term cycle decomposition can mean: Cycle decomposition (graph theory), a partitioning of the vertices of a graph into subsets, such...

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Permutation

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as a list of cycles; since distinct cycles involve disjoint sets of elements, this is referred to as "decomposition into disjoint cycles". To write down...

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Nitrogen cycle

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or in the intermediate products of organic matter decomposition. The processes in the nitrogen cycle is to transform nitrogen from one form to another...

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Decomposition

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decomposition. The science which studies decomposition is generally referred to as taphonomy from the Greek word taphos, meaning tomb. Decomposition can...

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Thermal decomposition

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Thermal decomposition (or thermolysis) is a chemical decomposition caused by heat. The decomposition temperature of a substance is the temperature at which...

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Potential output

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associated with changes in the output gap and over time and in decomposition of trend and business cycle in the economy relative to the output gap. Mitchell, William...

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Cholesky decomposition

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linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...

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Decomposer

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Decomposers are organisms that break down dead or decaying organisms; they carry out decomposition, a process possible by only certain kingdoms, such as...

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Cyclic permutation

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If X is finite, its cycles are disjoint, and their union is X. That is, they form a partition, called the cycle decomposition of σ . {\displaystyle...

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Cycle index

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distinct cycle length of the cycles that appear in the cycle decomposition of the permutation. In the previous example there were three different cycle lengths...

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Decomposition of time series

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unpredictable components). See Wold's theorem and Wold decomposition. Kendall shows an example of a decomposition into smooth, seasonal and irregular factors for...

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Solar cycle

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The solar cycle, also known as the solar magnetic activity cycle, sunspot cycle, or Schwabe cycle, is a nearly periodic 11-year change in the Sun's activity...

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Hamiltonian decomposition

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Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles. Hamiltonian decompositions have been studied...

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Microbiology of decomposition

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Microbiology of decomposition is the study of all microorganisms involved in decomposition, the chemical and physical processes during which organic matter...

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Detritus

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and the action of decomposers, including grazers, bacteria, and fungi. Decomposition, the process by which organic matter is decomposed, occurs in several...

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Carbon cycle

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sediments. The fast cycle includes annual cycles involving photosynthesis and decadal cycles involving vegetative growth and decomposition. The reactions of...

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Cell cycle

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The cell cycle, or cell-division cycle, is the series of events that take place in a cell that causes it to divide into two daughter cells. These events...

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Biogeochemical cycle

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biogeochemical cycles include the carbon cycle, the nitrogen cycle and the water cycle. In each cycle, the chemical element or molecule is transformed and cycled by...

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Hamiltonian path

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arrows and the edges traced "tail-to-head"). A Hamiltonian decomposition is an edge decomposition of a graph into Hamiltonian circuits. A Hamilton maze is...

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Glossary of graph theory

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property that is held by all cards). decomposition See tree decomposition, path decomposition, or branch-decomposition. degenerate degeneracy A k-degenerate...

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Ecosystem

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microbial decomposition occurs. Temperature also affects soil moisture, which affects decomposition. Freeze-thaw cycles also affect decomposition—freezing...

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Systems development life cycle

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engineering, the systems development life cycle (SDLC), also referred to as the application development life cycle, is a process for planning, creating, testing...

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Putrefying bacteria

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Putrefaction is defined as the final step of decomposition after death. Because these bacteria play a role in decomposition after death, putrefying bacteria also...

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Nutrient cycle

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nutrients is cyclic. Mineral cycles include the carbon cycle, sulfur cycle, nitrogen cycle, water cycle, phosphorus cycle, oxygen cycle, among others that continually...

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