We investigate a number of factorisation conditions in the framework of sets of probability measures, or coherent lower previsions, with finite referential spaces. We show that the so-called strong product constitutes one way to combine a number of marginal coherent lower previsions into an independent joint lower prevision, and we prove that under some conditions it is the only independent pro...

Propositional Product Logic is known to be standard finite-strong complete but not a strong complete, that is, it is complete for deductions only from finite sets of premises with respect to evaluations on the standard product chain over the real unit interval. On the other hand, Montagna has defined a logical system, an axiomatic extension of the Hájek’s Basic Fuzzy Logic BL with an storage op...

Let G and H be graphs. The strong product G⊠H of graphs G and H is the graph with vertex set V (G) × V (H) and u = (u1, v1) is adjacent with v = (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we study some properties of this operation. Also, we obtain lower and upper bounds for...

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by δ(X) the sharp hyperbolicity const...

We prove that the class of nontrivial connected strong product graphs is weakly reconstructible. We also show that any nontrivial connected thin strong product graph can be uniquely reconstructed from each of its one-vertex-deleted deleted subgraphs. © 2006 Elsevier B.V. All rights reserved. MSC: 05C