Suppose V is a finite set and C a collection of subsets of V that contains ∅ and V and is closed under taking intersections. Then the ordered pair (V, C) is called a convexity and the elements of C are referred to as convex sets. For a set S ⊆ V , the convex hull of S relative to C, denoted by CHC(S), is the smallest convex set containing S. The Caratheodory number, relative to a given convexit...

Convexity invariants like Caratheodory, Helly and Radon numbers are computed for triangle path convexity in graphs. Unlike minimal path convexities, the Helly and Radon numbers behave almost uniformly for triangle path convexity. c © 1999 Elsevier Science B.V. All rights reserved

In this paper continuing our work started in [Br1]-[Br3] we prove the corona theorem for the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of finite type.

This paper characterizes the asymptotic convergence properties of the primal-dual dynamics to the solutions of a constrained concave optimization problem using classical notions from stability analysis. We motivate our study by providing an example which rules out the possibility of employing the invariance principle for hybrid automata to analyze the asymptotic convergence. We understand the s...

this study was conducted to assess the in vitro organic matter digestibility (omd) of pistachio hull using rumen fluid of taleshi sheep. animals were fed diets composed of 34% pistachio hull, 29% grape pomace, 32% alfalfa, and 5% grain barley. the chemical composition and phenolics' levels of pistachio hull, either industrially dried pistachio hull (idph) or sun dried pistachio hull (sdph)...

This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the ...