• unify, and generalize seemingly disparate, classical sufficient conditions: polyhedrality of the cone, and “Slater” type conditions; • are necessary and sufficient, when the dual cone belongs to a class, that we call nice cones. Nice cones subsume all cones amenable to treatment by efficient optimization algorithms: for instance, polyhedral, semidefinite, and p-cones. • provide similarly attr...

In this note, we first define the concept of convex fuzzy processes. Second, we present some basic properties of convex fuzzy processes and important connection between convex fuzzy processes and their graphs. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-convex fuzzy sets, Convex fuzzy cones, Convex fuzzy processes.

In this paper we study a class of convex sets which are called closed pseudo-cones and new duality class. It turns out that the characterizes is essentially only possible abstract them.The characterization corresponding to classification endomorphisms pseudo-cones.

We introduce the notion of a Tits arrangement on a convex open cone as a special case of (infinite) simplicial arrangements. Such an object carries a simplicial structure similar to the geometric representation of Coxeter groups. The standard constructions of subarrangements and restrictions, which are known in the case of finite hyperplane arrangements, work as well in this more general settin...

The parallel X-ray of a convex set K ⊂ R in a direction u is the function which associates to each line l parallel to u the length of K ∩ l. The problem of nding a set of directions such that the corresponding X-rays distinguish any two convex bodies has been widely studied in geometric tomography. In this paper we are interested in the restriction of this problem to convex cones, and we are mo...

Tom Richmond* ([email protected]). Complementation in the Lattice of Locally Convex Topologies. We find all locally convex homogeneous topologies on (R,≤) and determine which of these have locally convex complements. Among the locally convex topologies on a n-point totally ordered set, each has a locally convex complement, and at least n of them have 2n−1 locally convex complements. For any ...