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Let N be a nilpotent, connected, simply connected Lie group, and let D be a discrete subgroup of N with compact right quotient space. Then N/D is called a nilmanifold.

A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X. The order ...

The oriented matroid of a finite configuration of points extracts relative position and orientation information from the configuration. An oriented matroid can be described ...

Let G be a locally compact Abelian group. Let G^* be the group of all continuous homeomorphisms G->R/Z, in the compact open topology. Then G^* is also a locally compact ...

Evans et al. (2000, p. 6) use the unfortunate term "probability domain" to refer to the range of the distribution function of a probability density function. For a continuous ...

A type of error-correcting code that is related to Hadamard matrices.

sum_(k=0)^dr_k^B(d-k)!x^k=sum_(k=0)^d(-1)^kr_k^(B^_)(d-k)!x^k(x+1)^(d-k).

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube I=[0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

Summation by parts for discrete variables is the equivalent of integration by parts for continuous variables Delta^(-1)[v(x)Deltau(x)]=u(x)v(x)-Delta^(-1)[Eu(x)Deltav(x)], ...