• Decomposition
  Decomposition
  Decomposition is the process by which organic material is broken down into simpler forms of matter. The process is essential for recycling the finite matter that occupies physical space in the biome. Bodies of living organisms begin to decompose shortly after death...
  
  , biological process through which organic material is reduced
• Chemical decomposition
  Chemical decomposition
  Chemical decomposition, analysis or breakdown is the separation of a chemical compound into elements or simpler compounds. It is sometimes defined as the exact opposite of a chemical synthesis. Chemical decomposition is often an undesired chemical reaction...
  
   or analysis, in chemistry, is the fragmentation of a chemical compound into elements or smaller compounds
  • Thermal decomposition
    Thermal decomposition
    Thermal decomposition, or thermolysis, is a chemical decomposition caused by heat. The decomposition temperature of a substance is the temperature at which the substance chemically decomposes....
    
    
• Decomposition, spoilage of votes, see electoral fraud
  Electoral fraud
  Electoral fraud is illegal interference with the process of an election. Acts of fraud affect vote counts to bring about an election result, whether by increasing the vote share of the favored candidate, depressing the vote share of the rival candidates or both...
  
  

Mathematics

• Manifold decomposition
  Manifold decomposition
  In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. When doing so, one must specify both what those pieces are and how they are put together to form M....
  
  , decomposition of manifolds
  • JSJ decomposition
    JSJ decomposition
    In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem:The acronym JSJ is for William Jaco, Peter Shalen, and Klaus Johannson...
    
    , or toral decomposition, a decomposition of 3-manifolds
• Prime decomposition of integer
  Integer
  The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
  
  s, see fundamental theorem of arithmetic
  Fundamental theorem of arithmetic
  In number theory, the fundamental theorem of arithmetic states that any integer greater than 1 can be written as a unique product of prime numbers...
  
   (for the mathematics) or integer factorization
  Integer factorization
  In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer....
  
   (for applications)
• Prime decomposition in a commutative ring, see unique factorization domain
  Unique factorization domain
  In mathematics, a unique factorization domain is, roughly speaking, a commutative ring in which every element, with special exceptions, can be uniquely written as a product of prime elements , analogous to the fundamental theorem of arithmetic for the integers...
  
  
• Matrix decomposition
  Matrix decomposition
  In the mathematical discipline of linear algebra, a matrix decomposition is a factorization of a matrix into some canonical form. There are many different matrix decompositions; each finds use among a particular class of problems.- Example :...
  
  , decomposition of matrices
• Vector decomposition
  Vector decomposition
  Vector decomposition refers to decomposing a vector of Rn into several vectors, each linearly independent .-Vector decomposition in two dimensions:...
  
  , decomposition of vectors
• Helmholtz decomposition
  Helmholtz decomposition
  In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational vector field and a...
  
  , decomposition of a vector field
• Lebesgue's decomposition theorem
  Lebesgue's decomposition theorem
  In mathematics, more precisely in measure theory, Lebesgue's decomposition theorem is a theorem which states that given \mu and \nu two σ-finite signed measures on a measurable space , there exist two σ-finite signed measures \nu_0 and \nu_1 such that:* \nu=\nu_0+\nu_1\, * \nu_0\ll\mu *...
  
  , decomposition of a measure
• Hahn decomposition of a measure space
• Hahn–Jordan decomposition of a signed measure
• Doob decomposition
  Doob decomposition theorem
  In the theory of discrete time stochastic processes, a part of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of any submartingale as the sum of a martingale and an increasing predictable process. The theorem was proved by and is named for J. L....
  
   of a discrete-time sub- or supermartingale
• Doob–Meyer decomposition of a continuous-time sub- or supermartingale
• Decomposition of a semimartingale
  Semimartingale
  In probability theory, a real valued process X is called a semimartingale if it can be decomposed as the sum of a local martingale and an adapted finite-variation process....
  
   in a local martingale and a finite-variation process
• Kunita–Watanabe or Galtchouk–Kunita–Watanabe decomposition in stochastic analysis
• Föllmer–Schweizer decomposition in mathematical finance
• decomposition of group representation
  Group representation
  In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication...
  
  s into irreducible representations
• Lie group decompositions
  Lie group decompositions
  In mathematics, Lie group decompositions, named after Sophus Lie, are used to analyse the structure of Lie groups and associated objects, by showing how they are built up out of subgroups. They are essential technical tools in the representation theory of Lie groups and Lie algebras; they can also...
  
  

Computer science

• Decomposition (computer science)
  Decomposition (computer science)
  Decomposition in computer science, also known as factoring, refers to the process by which a complex problem or system is broken down into parts that are easier to conceive, understand, program, and maintain.- Overview :...
  
  , or factoring, in computer science, refers to the process of breaking a complex problem down into easily-understood and achievable parts
• Decomposition, in computer graphics
  Computer graphics
  Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
  
  , means spatial decomposition