by virtue of a complete set of two displacement potentials, an analytical derivation of the elastostatic green’s functions of an exponentially graded transversely isotropic bi-material full-space was presented. three-dimensional point-load green’s functions for stresses and displacements were given in line-integral representations. the formulation included a complete set of transformed stress-p...

An issue in extending databases is to increase the expressiveness of query languages. Based on fuzzy set theory, flexible querying enables users to express preferences inside requirements. Quantifications and preferences on data have led us to define the notion of gradual integers (Nf). This framework has been extended to Zf and Qf, in order to dealing with queries based on difference or divisi...

We prove two results with a common theme: the tension between compactness and incompactness phenomena in combinatorial set theory. Theorem 1 uses PCF theory to prove a sort of “compactness” for a version of Dzamonja and Shelah’s strong non-reflection principle. Theorem 2 investigates Jensen’s subcompact cardinals and their relationship with stationary set reflection and the failure of the squar...

Let % be a preference relation on a convex set F . Necessary and sufficient conditions are given that guarantee the existence of a set {ul} of affine utility functions on F such that % is represented by U ( f ) = ul ( f ) if f ∈ Fl; where each Fl is a convex subset of F . The interpretation is simple: facing a “non-homogeneous” set F of alternatives, a decision maker splits it into “homogeneous...

We study some cardinal invariants of an order-theoretic fashion on products and box products of topological spaces. In particular, we concentrate on the Noetherian type (Nt), defined by Peregudov in the 1990s. Some highlights of our results include: (1) There are spaces X and Y such that Nt(X×Y ) < min{Nt(X), Nt(Y )}. (2) In several classes of compact spaces, the Noetherian type is preserved by...

A sufficient condition for the existence of HNN-extensions in the class of groups of odd exponent n ≫ 1 is given in the following form. Let Q be a group of odd exponent n > 2 and G be an HNN-extension of Q. If A ∈ G then let F(A) denote the maximal subgroup of Q which is normalized by A. By τA denote the automorphism of F(A) which is induced by conjugation by A. Suppose that for every A ∈ G, wh...

For an integer k ≥ 1 and a graph G = (V,E), a set S of V is k-independent if ∆(S) < k and k-dominating if every vertex in V \S has at least k neighbors in S. The k-independence number βk(G) is the maximum cardinality of a k-independent set and the k-dominating number is the minimum cardinality of a k-dominating set of G. Since every kindependent set is (k + 1)-independent and every (k + 1)-domi...

Real world applications often require dealing with the situations in which the exact numerical values of the (sub)measure of a set may not be provided, but at least some probabilistic assignment still could be done. Also, several concepts in uncertainty processing are linked to the processing of distribution functions. In the framework of generalized measure theory we introduce the probabilisti...