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If an airplane's altitude at time t is a(t), and the air pressure at altitude x is p(x), then (p ∘ a)(t) is the pressure around the plane at time t. Function defined on finite sets which change the order of their elements such as permutations can be composed on the same set, this being composition of permutations.
The eigenvalue equation of the composition operator is Schröder's equation, and the principal eigenfunction is often called Schröder's function or Koenigs function. The composition operator has been used in data-driven techniques for dynamical systems in the context of dynamic mode decomposition algorithms, which approximate the modes and ...
The arrows or morphisms between sets A and B are the functions from A to B, and the composition of morphisms is the composition of functions. Many other categories (such as the category of groups, with group homomorphisms as arrows) add structure to the objects of the category of sets or restrict the arrows to functions of a particular kind (or ...
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In computer science, function composition is an act or mechanism to combine simple functions to build more complicated ones. Like the usual composition of functions in mathematics , the result of each function is passed as the argument of the next, and the result of the last one is the result of the whole.
Composite function: is formed by the composition of two functions f and g, by mapping x to f (g(x)). Inverse function: is declared by "doing the reverse" of a given function (e.g. arcsine is the inverse of sine). Implicit function: defined implicitly by a relation between the argument(s) and the value.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
[2]: 40 Function composition is the special case of composition of relations where all relations involved are functions. The word uncle indicates a compound relation: for a person to be an uncle, he must be the brother of a parent. In algebraic logic it is said that the relation of Uncle is the composition of relations "is a brother of" and "is ...