extremal of functional
1State (functional analysis) — In functional analysis, a state on a C* algebra is a positive linear functional of norm 1. The set of states of a C* algebra A , sometimes denoted by S ( A ), is always a convex set. The extremal points of S ( A ) are called pure states. If A has …
2Calculus of variations — is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite …
3Hölder's inequality — In mathematical analysis Hölder s inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of Lp spaces. Let (S, Σ, μ) be a measure space and let 1 ≤ p, q ≤ ∞ with… …
4combinatorics — /keuhm buy neuh tawr iks, tor , kom beuh /, n. (used with singular v.) See combinatorial analysis. * * * Branch of mathematics concerned with the selection, arrangement, and combination of objects chosen from a finite set. The number of possible… …
5Gelfand-Naimark-Segal construction — In functional analysis, given a C* algebra A , the Gelfand Naimark Segal construction establishes a correspondence between cyclic * representations of A and certain linear functionals on A (called states ). The correspondence is shown by an… …
6Combinatorics — is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met,… …
7mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …
8Reflective subcategory — In mathematics, a subcategory A of a category B is said to be reflective in B when the inclusion functor from A to B has a left adjoint. This adjoint is sometimes called a reflector. Dually, A is said to be coreflective in B when the inclusion… …
9History of variational principles in physics — A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an extremum (minimum, maximum or saddle point) of a function or functional. This article describes the… …
10Euler–Lagrange equation — In calculus of variations, the Euler–Lagrange equation, or Lagrange s equation is a differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss mathematician Leonhard Euler and… …
