invariant differential

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• Invariant differential operators — appear often in mathematics and theoretical physics. There is no universal definition for them and the meaning of invariance may depend on the context. Usually, an invariant differential operator D is a map from some mathematical objects… …   Wikipedia

• Differential invariant — In mathematics, a differential invariant is an invariant for the action of a Lie group on a space that involves the derivatives of graphs of functions in the space. Differential invariants are fundamental in projective differential geometry, and… …   Wikipedia

• Invariant (mathematics) — In mathematics, an invariant is a property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually… …   Wikipedia

• Differential operator — In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning… …   Wikipedia

• Differential entropy — (also referred to as continuous entropy) is a concept in information theory that extends the idea of (Shannon) entropy, a measure of average surprisal of a random variable, to continuous probability distributions. Contents 1 Definition 2… …   Wikipedia

• Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

• Differential geometry — A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as… …   Wikipedia

• Differential geometry of curves — This article considers only curves in Euclidean space. Most of the notions presented here have analogues for curves in Riemannian and pseudo Riemannian manifolds. For a discussion of curves in an arbitrary topological space, see the main article… …   Wikipedia

• Invariant factorization of LPDOs — IntroductionFactorization of linear ordinary differential operators (LODOs) is known to be unique and in general, it finally reduces to the solution of a Riccati equation [http://en.wikipedia.org/wiki/Riccati equation] , i.e. factorization of… …   Wikipedia

• Differential topology — In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.… …   Wikipedia

• Invariant measure — In mathematics, an invariant measure is a measure that is preserved by some function. Invariant measures are of great interest in the study of dynamical systems. The Krylov Bogolyubov theorem proves the existence of invariant measures under… …   Wikipedia