An orthogonal double cover (ODC) of the complete graph Kn by some graph G is a collection of n spanning subgraphs of Kn, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kn is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n− 1 edges. We show that for any given positive integer d, al...

This paper describes the application of a combined orthogonal array design and overlapping resolution mapping to the optimization of miceller electrokinetic chromatography for the separation of 10 substituted benzenes. The most important factors were first determined according to an OA16(2(15)) through 16 pre-designed experiments; a second set of experiments was carried out according to a trian...

An orthogonal double cover (ODC) of the complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we consider the case where the graph to be covered twice is the complete bipartite graph Kmn,mn (for any values ofm,n) and all graphs in the collection are isomorphic to certa...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

When an orthogonal array is projected on a small number of factors, as is done in screening experiments, the question of interest is the structure of the projected design, by which we mean its decomposition in terms of smaller arrays of the same strength. In this paper we investigate the decomposition of arrays of strength t having t + 1 factors. The decomposition problem is well-understood for...