Let Γ denote the spaces of all double entire sequences. Let Λ denote the spaces of all double analytic sequences. This paper is devoted to a study of the general properties of Nörlund double entire sequence space η ( Γ ) , Γ and also study some of the properties of η ( Γ ) and η ( Λ ) .

We show that any graph that contains k edge-disjoint double rays for any k ∈ N contains also infinitely many edge-disjoint double rays. This was conjectured by Andreae in 1981.

Let G = (X, Y; E) be a balanced bipartite graph of order 2n. The path-cover number pc(H) of a graph H is the minimum number of vertex-disjoint paths that use up all the vertices of H. S ⊆ V(G) is called a balanced set of G if |S ∩ X| = |S ∩ Y|. In this paper, we will give some sufficient conditions for a balanced bipartite graph G satisfying that for every balanced set S, there is a bi-cycle of...

We construct a combined non-perturbative path integral over geometries and topologies for two-dimensional Lorentzian quantum gravity. The Lorentzian structure is used in an essential way to exclude geometries with unacceptably large causality violations. The remaining sum can be performed analytically and possesses a unique and welldefined double-scaling limit, a property which has eluded simil...

DNA computing often makes use of hybridization, whether for vastly generating the initial candidate answers or amplification by using polymerase chain reaction (PCR). The main idea behind DNA computing approaches for solving weighted graph problems is that if the degree of hybridization can be controlled, then it is able to generate more double stranded DNAs (dsDNAs), which represent the answer...

A recurrent 2-dimensional (double) sequence t(m,n) is given by fixing particular sequences t(m, 0), t(0, n) as initial conditions and a rule of recurrence t(m,n) = t(a(m,n − 1), t(m − 1, n − 1), t(m − 1, n)) for m,n ≥ 1. We display such a sequence with values in the set {0, 1} and show that all rows are periodic and that the minimal period of the n-th row has length 2. We conclude that this 2-d...

A closed 2-cell embedding of a graph embedded in some surface is an embedding such that each face is bounded by a cycle in the graph. The strong embedding conjecture says that every 2-connected graph has a closed 2-cell embedding in some surface. In this paper, we prove that any 2-connected graph without V8 (the M obius 4-ladder) as a minor has a closed 2-cell embedding in some surface. As a c...

— Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with generators given by central simple algebras over the function field of X and relations coming from the Néron-Severi group of X. The path to this result nat...

Let G be a simple graph of order n. The path cover number μ(G) is defined to be the minimum number of vertex disjoint paths required to cover the vertices of G. Ore proved that in general μ(G) ≤ max{1, n − σ2(G)}. We conjecture that if G is k-regular, then μ(G) ≤ n k+1 and we prove this for k ≤ 5.

We give a necessary and sufficient condition for the maximum multiplicity of a root of the matching polynomial of a tree to be equal to the minimum number of vertex disjoint paths needed to cover it.