R. Häggkvist proved that every 3-regular bipartite graph of order 2n with no component isomorphic to the Heawood graph decomposes the complete bipartite graph K6n,6n. In [1] Cichacz and Froncek established a necessary and sufficient condition for the existence of a factorization of the complete bipartite graph Kn,n into generalized prisms of order 2n. In [2] and [3] Cichacz, Froncek, and Kovar ...

In this paper we study gcd (( n t ) , ( n t+1 ) , ..., ( n n−t )) . By arranging these numbers in a triangle and exploring a local divisiblity property of its elements, we uncover relations among them which lead to an interesting description of their complete prime factorization.

The processes of a light neutral vector meson, V = ρ 0 , ω, φ, electroproduction and a heavy quarkonium, V = J/Ψ, Υ, photoproduction are studied in the framework of QCD factorization. We derive a complete set of hard-scattering amplitudes which describe these processes at next-to-leading order (NLO).

Let Γ(Zm) be the zero divisor graph of the ring Zm. In this paper we explore the p-partite structures of Γ(Zm), as well as determine a complete classification of the chromatic number of Γ(Zm). In particular, we explore how these concepts are related to the prime factorization of m.

This thesis investigates relations over a category C relative to an (E;M)-factorization system of C. In order to establish the 2-categoryRel(C) of relations over C in the rst part we discuss su cient conditions for the associativity of horizontal composition of relations, and we investigate special classes of morphisms in Rel(C). Attention is particularly devoted to the notion of mapping as de ...

So far, the smallest complete bipartite graph which was known to have a cyclic type decomposition into cubes Qd of a given dimension d was Kd2d−2,d2d−2. Using binary Hamming codes we prove in this paper that there exists a cyclic type factorization of K2d−1,2d−1 into Qd if and only if d is a power of 2.

Given a triple T on a complete category C and a factorization system E /M on the category of algebras, we show there is a 1-1 correspondence between full subcategories of the category of algebras that are closed under U -split epimorphisms, products, and M -subobjects and triple morphisms T S for which the induced natural transformation between free functors belongs to E .

So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes Qd of a given dimension d was Kd2d−1,d2d−2 . We improve this result and show that also Kd2d−2,d2d−2 allows a cyclic decomposition into Qd. We also present a cyclic factorization of K8,8 into Q4.

We consider the factorization problem of regular hedge languages. This problem is strongly related to the type checking problem in rule based transformations of valid XML documents. We propose the representation of regular hedge languages by reduced, complete, and deterministic linear hedge automata, and indicate algorithms for the computation of right factors and factor matrix.

Site-specific pK(a) determination of the carboxylate-binding subunit in artificial peptide receptors is achieved by pH-dependent UV resonance Raman scattering with subsequent matrix factorization. This quantitative methodology allows to determine accurately the local acidity of a binding site based on the complete vibrational spectrum and, most importantly, without the need of selecting any par...