Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2010
Volume
Vol. 30
Number
No. 3
Description
Journal Volume
Opuscula Mathematica
Vol. 30 (2010)
Projects
Pages
Articles
Uniformly continuous set-valued composition operators in the space of total φ-bidimensional variation in the sense of Riesz
(2010) Aziz, Wadie; Giménez, José; Merentes Díaz, Nelson José; Sánchez, José Luis
In this paper we prove that if a Nemytskij composition operator, generated by a function of three variables in which the third variable is a function one, maps a suitable large subset of the space of functions of bounded total $\varphi$-bidimensional variation in the sense of Riesz, into another such space, and is uniformly continuous, then its generator is an affine function in the function variable. This extends some previous results in the one-dimensional setting.
Trees with equal global offensive k-alliance and k-domination numbers
(2010) Chellali, Mustapha
Let $k \geq 1$ be an integer. A set $S$ of vertices of a graph $G=(V(G),E(G))$ is called a global offensive $k$-alliance if $|N(v) \cap S| \geq |N(v) - S| + k$ for every $v \in V(G)- S$, where $N(v)$ is the neighborhood of $v$. The subset $S$ is a $k$-dominating set of $G$ if every vertex in $V(G) - S$ has at least $k$ neighbors in $S$. The global offensive $k$-alliance number $\gamma_0^k (G)$ is the minimum cardinality of a global offensive $k$-alliance in $G$ and the $k$-domination number $\gamma _k (G)$ is the minimum cardinality of a $k$-dominating set of $G$. For every integer $k \geq 1$ every graph $G$ satisfies $\gamma_0^k (G) \geq \gamma_k (G)$. In this paper we provide for $k \geq 2$ a characterization of trees $T$ with equal $\gamma_0^k (T)$ and $\gamma_k (T)$.
On the approximation theorem of Wong-Zakai type for the Lasota operator
(2010) Dawidowicz, Antoni Leon; Twardowska, Krystyna
We consider in this paper a stochastic evolution equation with Professor A. Lasota's operator as the infinitesimal generator of a strongly continuous semigroup of transformations and with Hammerstein operator connected with a noise being the Wiener process. We show that such evolution equation satisfies the Wong-Zakai type approximation theorem. The idea of the definition of the Lasota operator has the origin in the mathematical model of the creation and differentiation of cells in biology and medicine.
Graph choosability and double list colorability
(2010) Fanaï, Hamid-Reza
In this paper, we give a sufficient condition for graph choosability, based on Combinatorial Nullstellensatz and a specific property, called »double list colorability«, which means that there is a list assignment for which there are exactly two admissible colorings.
Decomposition of complete graphs into small graphs
(2010) Froncek, Dalibor
In 1967, A. Rosa proved that if a bipartite graph $G$ with $n$ edges has an $\alpha$-labeling, then for any positive integer $p$ the complete graph $K_{2np+1}$ can be cyclically decomposed into copies of $G$. This has become a part of graph theory folklore since then. In this note we prove a generalization of this result. We show that every bipartite graph $H$ which decomposes $K_{k}$ and $K_{m}$ also decomposes $K_{km}$.