In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are act...

The sentential theory of propositional attitudes is very attractive to AI workers, but it is difficult to use such a theory to assign semantics to English sentences about attitudes. The problem is that a compositional semantics cannot easily build the logical forms that the theory requires. We present a new notation for a sentential theory, and a unification grammar that builds logical forms in...

The aim of this paper is to describe a technique for identifying the sources of several types of syntactic ambiguity in Arabic Sentences with a single parse only. Normally, any sentence with two or more structural representations is said to be syntactically ambiguous. However, Arabic sentences with only one structural representation may be ambiguous. Our technique for identifying Syntactic Ambi...

This paper proposes a generation method for feature-structured)ased unification grammars. As comlx~red with fixed ~rity term notation, feature structure notation is more tlexible for representing knowledge needed to generate idiom~ttic structures as well as genem~l constructions. The method enables feature strncture retrieval via nmltiple indices. The indexing mechanism, when used with a semant...

The paper presents an algorithm, written in PROLOG, for processing English sentences which contain either Gapping, Right Node Raising (RNR) or Reduced Conjunction (RC). The DCG (Definite Clause Grammar) formalism (Pereira & Warren 80) is adopted. The algorithm is highly efficient and capable of processing a full range of coordinate constructions containing any number of coordinate conjunctions ...

In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are act...

Positive definite matrix approximation with a condition number constraint is an optimization problem to find the nearest positive definite matrix whose condition number is smaller than a given constant. We demonstrate that this problem can be converted to a simpler one in this note when we use a unitary similarity invariant norm as a metric. We can especially convert it to a univariate piecewis...

We show in this note how support preconditioners can be applied to a class of linear systems arising from use of the finite element method to solve linear elliptic problems. Our technique reduces the problem, which is symmetric and positive definite, to a symmetric positive definite diagonally dominant problem. Significant theory has already been developed for preconditioners in the diagonally ...