A refinable set is a compact set with positive Lebesgue measure whose characteristic function satisfies a refinement equation. Refinable sets are a generalization of self-affine tiles. But unlike the latter, the refinement equations defining refinable sets may have negative coefficients, and a refinable set may not tile. In this paper, we establish some fundamental properties of these sets.

The purpose of our work is to improve the performance business processes. Our contribution consists proposing anapproach defining key indicators for a set well-defined objectives. To test approach, we defined aset

A block design D = (V, B) is a set V of v elements together with a set B of b subsets of V called blocks, each containing exactly k elements, such that each element of V occurs in precisely r blocks, for some positive integers rand k. D is called a t-design if every t-subset of V occurs in exactly At blocks, for some positive integer At. Such a design D is described as a t-( v, k, At) design. A...

In two-level logic synthesis, the typical input specification is a set of minterms defining the on set and a set of minterms defining the don’t care set of a Boolean function. The problem is to synthesize an optimal set of product terms, or cubes, that covers all the minterms in the on set and some of the minterms in the don’t care set. In this paper, we consider a different specification: inst...

We compute the arithmetic ranks of the defining ideals of homogeneous coordinate rings of certain Segre products arising from elliptic curves. The cohomological dimension of these ideals varies with the characteristic of the field, though the arithmetic rank does not. We also study the related set-theoretic Cohen-Macaulay property for these ideals. In [12] Lyubeznik writes: Part of what makes t...

Solutions of a variational inequality problemdefined by a closed and convex set and a mapping are found by imposing conditions for the monotone convergence with respect to a cone of the Picard iteration corresponding to the composition of the projection onto the defining closed and convex set and the difference in the identity mapping and the defining mapping. One of these conditions is the iso...

Let IM and IN be defining ideals of toric varieties such that IM is a projection of IN , i.e. IN ⊆ IM . We give necessary and sufficient conditions for the equality IM = rad(IN + (f1, . . . , fs)), where f1, . . . , fs belong to IM . Also a method for finding toric varieties which are set-theoretic complete intersection is given. Finally we apply our method in the computation of the arithmetica...

Greedy algorithm sometimes uses more than χ(G) colors while coloring a graph G. A greedy defining set is an object to eliminate these extra colors so that the greedy coloring results in a minimum coloring of an order graph G. In this note we report some of the previous results as well as new results on greedy defining sets of graphs and Latin squares.

In this paper, we present procedures to obtain facet-defining inequalities for the independence system polytope. These procedures are defined for inequalities which are not necessarily rank inequalities. We illustrate the use of these procedures by deriving strong valid inequalities for the acyclic induced subgraph, triangle free induced subgraph, bipartite induced subgraph, and knapsack polyto...