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A sequence {mu_n}_(n=0)^infty is positive definite if the moment of every nonnegative polynomial which is not identically zero is greater than zero (Widder 1941, p. 132). ...

Let f:R->R, then the positive part of f is the function f^+:R->R defined by f^+(x)=max(f(x),0) The positive part satisfies the identity f=f^+-f^-, where f^- is the negative ...

A pseudoanalytic function is a function defined using generalized Cauchy-Riemann equations. Pseudoanalytic functions come as close as possible to having complex derivatives ...

A function f defined on a subset S subset R^n is said to be pseudoconcave if -f is pseudoconvex.

An algebraic structure whose elements consist of selected homeomorphisms between open subsets of a space, with the composition of two transformations defined on the largest ...

A distance g on a set that fulfils the same properties as a metric except relaxes the definition to allow the distance between two different points to be zero. An example of ...

A diagram used in the solution of ordinary differential equations of the form (dw)/(dz)=(g(z,w))/(h(z,q)) which vanish when z=0, where g(0,0)=h(0,0)=0 (Ince 1956, pp. 298 and ...

One of the four regions of the plane defined by the four possible combinations of signs (+,+), (+,-), (-,+), and (-,-) for (x,y).

If N is a submodule of the module M over the ring R, the quotient group M/N has a natural structure of R-module with the product defined by a(x+N)=ax+N for all a in R and all ...

A hypergeometric class of orthogonal polynomials defined by R_n(lambda(x);alpha,beta,gamma,delta) =_4F_3(-n,n+alpha+beta+1,-x,x+gamma+delta+1; alpha+1,beta+delta+1,gamma+1;1) ...