Topology design of distributed local area networks can be classified as a hard combinatorial optimization problem. The problem has several conflicting objectives, such as cost, reliability, network delay, and number of hops between source and destination. These desirable features of a network topology can best be expressed in linguistic terms, which is the basis of fuzzy logic. This paper prese...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

Let T be a completely nonunitary contraction on a Hilbert space H with r(T ) = 1. Let an > 0, an → 0. Then there exists x ∈ H with |〈Tnx, x〉| ≥ an for all n. We construct a unitary operator without this property. This gives a negative answer to a problem of van Neerven. Let X be a complex Banach space. Then each operator T ∈ B(X) has orbits that are ”large” in the following sense [M1], [B]: Let...

We study the computational difficulty of the problem of finding fixed points of nonexpansive mappings in uniformly convex Banach spaces. We show that the fixed point sets of computable nonexpansive self-maps of a nonempty, computably weakly closed, convex and bounded subset of a computable real Hilbert space are precisely the nonempty, co-r.e. weakly closed, convex subsets of the domain. A unif...

In article, I present a study on upper and lower statistical convergence, strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations discrete operator Cesàro, was operators, which are linear too. Given modulus function f, established that sequence is f-upper or convergent, in some supplementary conditions, also f-lower statistically convergent. The re...