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...

The effectiveness of an orthogonal to backward mean transformation is investigated in the context a non-stationary panel data model. It shown that corresponding estimator as efficient Transformed Maximum Likelihood when autoregressive parameter equal unity. Furthermore, recently introduced bias-corrected version almost Pooled Least Squares estimator.

Model-based development relies on the use of explicit models to describe development activities and products. Explicit process and product models allow the definition and use of complex development steps that are correct by design, the generation of proof obligations for a given transformation, requirements tracing, and documentation of the process. We argue that the concept of model-based deve...

It is known [L. Boelen, W. Van Assche, Proc. Amer. Math. Soc. 138 (2010), 1317–1331] that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semiclassical extension of the Laguerre weight satisfy a discrete Painlevé equation. By using the Toda system for the recurrence coefficients we show that this discrete equation can be obtained from a Bäcklu...