Search Results for ""

For an integer n>=2, let gpf(x) denote the greatest prime factor of n, i.e., the number p_k in the factorization n=p_1^(a_1)...p_k^(a_k), with p_i<p_j for i<j. For n=2, 3, ...

Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...

Jacobi's imaginary transformations relate elliptic functions to other elliptic functions of the same type but having different arguments. In the case of the Jacobi elliptic ...

A closed two-form omega on a complex manifold M which is also the negative imaginary part of a Hermitian metric h=g-iomega is called a Kähler form. In this case, M is called ...

Zygmund (1988, p. 192) noted that there exists a number alpha_0 in (0,1) such that for each alpha>=alpha_0, the partial sums of the series sum_(n=1)^(infty)n^(-alpha)cos(nx) ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...

The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^(-1) such that AA^(-1)=I, (1) where I is the identity matrix. Courant and Hilbert (1989, ...

The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...