In many branches of mathematics, the term map is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a "continuous function" in topology, a "linear transformation" in linear algebra, etc. Some authors, such as Serge Lang, use "function" only to refer to maps in which the codomain is a set of numbers (i.e. a …

In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition, i.e., which is idempotent.The restriction to a subspace of a projection is also called a projection, even if the idempotence property is lost.An everyday example of a projection is the casting of shadows …

Critical point is a wide term used in many branches of mathematics.. When dealing with functions of a real variable, a critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero. When dealing with complex variables, a critical point is, similarly, a point in the function's domain where it is either not holomorphic ...

Definition. Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that () = () well defines a linear map from V to V; here, as usual, the subtraction of two points denotes the free vector from the second one to the first one, and "well-defined" means that = ′ ′ implies ...

The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation …

Someone on mathoverflow writes: aren't there a whole bunch of neat results in combinatorics on discrete analogs of PDE? I'm thinking, for example, of Stone's theorem for the discrete Schrodinger equation; the characterization of graph spectra; and how some solutions of the discrete Laplacian/discrete Helmholtz/discrete modified Helmholtz lead to special instances of …

A computer network is a set of computers sharing resources located on or provided by network nodes.The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections are made up of telecommunication network technologies, based on physically wired, optical, and wireless radio-frequency methods that …

In physics and mathematics, the Ikeda map is a discrete-time dynamical system given by the complex map + = + (| | +) The original map was proposed first by Kensuke Ikeda as a model of light going around across a nonlinear optical resonator (ring cavity containing a nonlinear dielectric medium) in a more general form. It is reduced to the above simplified "normal" form …

Arts, entertainment, and media Fictional entities. Index (A Certain Magical Index), a character in the light novel series A Certain Magical IndexThe Index, an item on a Halo megastructure in the Halo series of video games; Periodicals and news portals. Index Magazine, a publication for art and culture; Index.hr, a Croatian online newspaper; index.hu, a Hungarian-language news …

In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL's use of SELECT) is a unary operation written as or () where: . and are attribute names,; is a binary operation in the set {<,, =,,, >},; is a value constant, is a relation.; The selection () selects all those tuples in for which holds between the and the attribute.. The selection () selects all ...