q] (p) with a pole q [member of] [SIGMA] is a

real-valued function satisfying the following conditions:

Let f be a differentiable

real-valued function defined on Rn.

where [omega] [member of] R and u is

real-valued function.

He proposed that the homogeneous Dirichlet conditions may be satisfied exactly by representing the solution as the product of two functions: (1) an

real-valued function that takes on zero values on the boundary points; and (2) an unknown function that allows to satisfy (exactly or approximately) the differential equation of the problem.

It can be used to perform the validation, compilation, and evaluation of any

real-valued function.

Let A be a Holder continuous complex-valued function on [GAMMA] with A [not equal to] 0 and [gamma] be a Holder continuous

real-valued function on [GAMMA].

A

real-valued function f (t) (t > 0) is said to be in the space [C.

A radial basis function (RBF) is a

real-valued function whose value depends only on the distance from the origin, so that; [empty set] (a) = [empty set] ([parallel]a[parallel] or alternatively on the distance from some other point c, called a center, so that [empty set] (a, c) = [empty set] ([parallel]x - c[parallel].

United extensions are functions that are created by taking a

real-valued function f and computing the range of values f (x) takes as x is varied through an interval X [12].

5] : Let F be a twice-differentiable,

real-valued function of an m x n matrix X.

n], and let h be a differentiable

real-valued function defined on X.

Suppose that [PHI] is a positive multimeasure and f is a

real-valued function on [OMEGA].