Search Results for ""

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 ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

Functional analysis is a branch of mathematics concerned with infinite-dimensional vector spaces (mainly function spaces) and mappings between them. The spaces may be of ...

Let p>3 be a prime number, then 4(x^p-y^p)/(x-y)=R^2(x,y)-(-1)^((p-1)/2)pS^2(x,y), where R(x,y) and S(x,y) are homogeneous polynomials in x and y with integer coefficients. ...

_2F_1(a,b;c;1)=((c-b)_(-a))/((c)_(-a))=(Gamma(c)Gamma(c-a-b))/(Gamma(c-a)Gamma(c-b)) for R[c-a-b]>0, where _2F_1(a,b;c;x) is a (Gauss) hypergeometric function. If a is a ...

The Goddard-Henning enneahedron, a term coined here, is the canonical polyhedron obtained from the Goddard-Henning graph. It has 9 vertices, 16 edges (consisting of 3 ...

Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

A grid usually refers to two or more infinite sets of evenly-spaced parallel lines at particular angles to each other in a plane, or the intersections of such lines. The two ...

The Griewank function is a function widely used to test the convergence of optimization functions. The Griewank function of order n is defined by ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...