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In the mathematical area of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima.Most of these apply to partially ordered sets that are at least lattices, but the concept can in fact reasonably be generalized to semilattices as well.
For example, in elementary arithmetic, one has (+) = + (). Therefore, one would say that multiplication distributes over addition . This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers , polynomials , matrices , rings , and fields .
Example of a biological network between genes and proteins that controls entry into S phase. However, with knowledge of network interactions and a set of parameters for the proteins and protein interactions (usually obtained through empirical research), it is often possible to construct a model of the network as a dynamical system .
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
For example, the position and the linear momentum in the -direction of a particle are represented by the operators and , respectively (where is the reduced Planck constant). This is the same example except for the constant − i ℏ {\displaystyle -i\hbar } , so again the operators do not commute and the physical meaning is that the position ...
For example, hypoxia-induced factor 1α mRNA and β-secretase mRNA are transcribed bidirectionally, ... Complementarity (molecular biology) 23 languages ...
To investigate the left distributivity of set subtraction over unions or intersections, consider how the sets involved in (both of) De Morgan's laws are all related: () = = () always holds (the equalities on the left and right are De Morgan's laws) but equality is not guaranteed in general (that is, the containment might be strict).
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).