integrable mapping
51Statistical ensemble (mathematical physics) — In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1878, an ensemble (also statistical ensemble or thermodynamic ensemble)cite book |last=Kittel |first=Charles… …
52Winding number — The term winding number may also refer to the rotation number of an iterated map. This curve has winding number two around the point p. In mathematics, the winding number of a closed curve in the plane around a given point is an integer… …
53Anti-aliasing — In digital signal processing, anti aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high resolution signal at a lower resolution. Anti aliasing is used in digital photography, computer… …
54Maximum likelihood — In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum likelihood estimation provides estimates for the model s… …
55Path integral formulation — This article is about a formulation of quantum mechanics. For integrals along a path, also known as line or contour integrals, see line integral. The path integral formulation of quantum mechanics is a description of quantum theory which… …
56Sturm-Liouville theory — In mathematics and its applications, a classical Sturm Liouville equation, named after Jacques Charles François Sturm (1803 1855) and Joseph Liouville (1809 1882), is a real second order linear differential equation of the formwhere y is a… …
57Sobolev space — In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp norms of the function itself as well as its derivatives up to a given order. The derivatives are understood in a suitable weak sense… …
58Harmonic conjugate — For geometric conjugate points, see Projective harmonic conjugates. In mathematics, a function defined on some open domain is said to have as a conjugate a function if and only if they are respectively real and imaginary part of a holomorphic… …
59Toda field theory — In the study of field theory and partial differential equations, a Toda field theory is derived from the following Lagrangian::mathcal{L}=frac{1}{2}left [left({partial phi over partial t},{partial phi over partial t} ight) left({partial phi over… …
60Hilbert's twenty-first problem — For Riemann Hilbert factorization problems on the complex plane see Riemann Hilbert. The twenty first problem of the 23 Hilbert problems, from the celebrated list put forth in 1900 by David Hilbert, was phrased like this (English translation from …
