Search Results for ""

Weak convergence is usually either denoted x_nw; ->x or x_n->x. A sequence {x_n} of vectors in an inner product space E is called weakly convergent to a vector in E if ...

A closed subspace of a Banach space X is called weakly complemented if the dual i^* of the natural embedding i:M↪X has a right inverse as a bounded operator. For example, the ...

A sequence of numbers V={nu_n} is said to be weakly complete if every positive integer n beyond a certain point N is the sum of some subsequence of V (Honsberger 1985). ...

A weakly connected component of a simple directed graph (i.e., a digraph without loops) is a maximal subdigraph such that for every pair of distinct vertices u, v in the ...

An infinite sequence {a_i} of positive integers is called weakly independent if any relation sumepsilon_ia_i with epsilon_i=0 or +/-1 and epsilon_i=0, except finitely often, ...

For R[mu+nu]>0, |argp|<pi/4, and a>0, where J_nu(z) is a Bessel function of the first kind, Gamma(z) is the gamma function, and _1F_1(a;b;z) is a confluent hypergeometric ...

int_0^inftyJ_0(ax)cos(cx)dx={0 a<c; 1/(sqrt(a^2-c^2)) a>c (1) int_0^inftyJ_0(ax)sin(cx)dx={1/(sqrt(c^2-a^2)) a<c; 0 a>c, (2) where J_0(z) is a zeroth order Bessel function of ...

where R[nu]>-1, |argp|<pi/4, and a, b>0, J_nu(z) is a Bessel function of the first kind, and I_nu(z) is a modified Bessel function of the first kind.

If two curves of the same curve genus >1 are in rational correspondence, then that correspondence is birational.

If f is a continuous real-valued function on [a,b] and if any epsilon>0 is given, then there exists a polynomial p on [a,b] such that |f(x)-P(x)|<epsilon for all x in [a,b]. ...