An extended version of the applicative caching technique from functional programming is adapted to OLD resolution as an alternative to OLDT resolution for predicates that are actually functions. An inference system, OLDTF resolution, is given with a proof procedure. It is argued why this special case is interesting in its own right also outside the area of deductive databases. It is outlined ho...

The domain of deenite Boolean functions, Def , can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, previously unexploited computational properties of Def are utilised to develop an eecient and succinct groundness analyser that can be coded in Prolog. In particular, entailment checking is used to pre...

in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

In 1942 I.J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a positive linear combination of the Gegenbauer polynomials. In this paper we extend Schoenberg’s theorem for multivariate Gegenbauer polynomials. This extension derives new positive semidefinite constraints for the distance distribution which can be applied for spherical codes.

Consider a standard probability space (X,μ), i.e., a space isomorphic to the unit interval with Lebesgue measure. We denote by Aut(X,μ) the automorphism group of (X,μ), i.e., the group of all Borel automorphisms of X which preserve μ (where two such automorphisms are identified if they are equal μ-a.e.). A Borel equivalence relation E ⊆ X is called countable if every E-class [x]E is countable a...

I. J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a nonnegative linear combination of Gegenbauer polynomials. This fact play a crucial role in Delsarte’s method for finding bounds for the density of sphere packings on spheres and Euclidean spaces. One of the most excited applications of Delsarte’s method is a solution of the kissing ...