We give an upper bound on the number of vertices of PI, the integer hull of a polyhedron P, in terms of the dimension n of the space, the number m of inequalities required to describe P, and the size ~ of these inequalities. For fixed n the bound is O(mn~n-1). We also describe an algorithm which determines the number of integer points in a polyhedron to within a multiplicative factor of 1 qE in...

The purpose o f this paper i s to introduce and study the concepts of intuitionistic fuzzy π generalized s e m i c o n n e c t e d n e s s in intuitionistic fuzzy topological space. Some of their properties are explored.

Let A be a unital Banach function algebra with character space Φ A. For x ∈ Φ A , let M x and J x be the ideals of functions vanishing at x, and in a neighbourhood of x, respectively. It is shown that the hull of J x is connected, and that if x does not belong to the Shilov boundary of A then the set {y ∈ Φ A : M x ⊇ J y } has an infinite, connected subset. A variety of related results and appl...

in this note first by considering the notion of general fuzzy automata (for simplicity gfa), we define the notions of direct product, restricted direct product and join of two gfa. also, we introduce some operations on (fuzzy) sets and then prove some related theorems. finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given gfa....

Relaxations of the bilinear term, x1x2 = x3, play a central role in constructing relaxations of factorable functions. This is because they can be used directly to relax products of functions with known relaxations. In this paper, we provide a compact, closed-form description of the convex hull of this and other more general bivariate monomial terms (which have similar applications in relaxation...

Let Mφ denote the set of Borel probability measures invariant under a topological action φ on a compact metrizable space X. For a continuous function f : X → R, a measure μ ∈ Mφ is called f -maximizing if ∫ f dμ = sup{ ∫ f dm : m ∈Mφ}. It is shown that if μ is any ergodic measure in Mφ, then there exists a continuous function whose unique maximizing measure is μ. More generally, if E is a non-e...