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A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Friedrichs ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

A quantitative measure of the simplicity of a geometric construction which reduces geometric constructions to five steps. It was devised by È. Lemoine. S_1 Place a ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

The process of computing or obtaining an integral. A more archaic term for integration is quadrature.

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...