In this note, we generalize a result of [4] (see also [9]) and set the isomorphism between the iterated cross product algebra H∨#(H#A) and braided analog of an A-valued matrix algebra H∨⊗A⊗H for a Hopf algebra H in the braided category C and for an H-module algebra A. As a preliminary step, we prove the equivalence between categories of modules over both algebras and category whose objects are ...

The Gene Ontology (GO) consists of nearly 30,000 classes for describing the activities and locations of gene products. Manual maintenance of ontology of this size is a considerable effort, and errors and inconsistencies inevitably arise. Reasoners can be used to assist with ontology development, automatically placing classes in a subsumption hierarchy based on their properties. However, the his...

In many papers, the relation between the domination number of a product of graphs and the product of domination numbers of factors is studied. Here we investigate this problem for domination and total domination numbers in the cross product of digraphs. We give analogues of known results for graphs, and we also present new results for digraphs with sources. Using these results we find dominatio...

We study the cross product as a method for generating and analyzing interconnection network topologies for multiprocessor systems. Consider two interconnection graphs G1 and G2 each with some established properties such as symmetry, low degree and diameter, scalability, simple optimal routing, recursive structure (partitionability), fault tolerance, existence of nodedisjoint paths, low cost emb...

Many industry sectors face the challenge of how to satisfy the increasing demand for individualized software systems and software-intensive systems. The software product line (PL) engineering paradigm (SPLE, see [5]) has proven to empower organizations to develop a diversity of similar systems at lower cost, in shorter time, and with higher quality compared to single system development [5]. Key...

In today’s lending environment, cross-sell has become a way of life for most consumer lenders. Moving from a silo-product mentality to a consultative selling approach to help the customer with a variety of needs has resulted in a proliferation of cross-sell initiatives. While crosssell efforts appear widespread, many bankers and lenders are not effectively executing, which results in low cross-...

In a finite partially ordered set, Prob(x > y) denotes the proportion of linear extensions in which element x appears above element y. In 1969, S. S. Kislitsyn conjectured that in every finite poset which is not a chain, there exists a pair (x, y) for which 1/3 ≤ Prob(x > y) ≤ 2/3. In 1984, J. Kahn and M. Saks showed that there exists a pair (x, y) with 3/11 < Prob(x > y) < 8/11, but the full 1...