On Barron and Strachey's Cartesian Product Function

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Secret Sharing Based On Cartesian product Of Graphs

The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of graphs. We seek to prove that the information ratio of prism graphs $Y_{n}$ are equal to $frac{7}{4}$ for any $ngeq 5$, and we will gave a partial answer to a question of Csirmaz cite{CL}. We will also study the information ratio of two other families $C_{m}times C_{n}$ a...

On subgraphs of Cartesian product graphs

Graphs which can be represented as nontrivial subgraphs of Cartesian product graphs are characterized. As a corollary it is shown that any bipartite, K2,3-free graph of radius 2 has such a representation. An infinite family of graphs which have no such representation and contain no proper representable subgraph is also constructed. Only a finite number of such graphs have been previously known.

Turing instabilities on Cartesian product networks

The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The...

On Set Coverings in Cartesian Product Spaces