Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2022
Volume
Vol. 42
Number
No. 1
Description
Journal Volume
Opuscula Mathematica
Vol. 42 (2022)
Projects
Pages
Articles
Uniqueness of solution of a nonlinear evolution dam problem in a heterogeneous porous medium
(Wydawnictwa AGH, 2022) Attia, Messaouda Ben; Zaouche, Elmehdi; Bousselsal, Mahmoud
By choosing convenient test functions and using the method of doubling variables, we prove the uniqueness of the solution to a nonlinear evolution dam problem in an arbitrary heterogeneous porous medium of $\mathbb{R}^{n}$ ($n \in \{2,3\}$) with an impermeable horizontal bottom.
γ-paired dominating graphs of cycles
(Wydawnictwa AGH, 2022) Eakawinrujee, Pannawat; Trakultraipruk, Nantapath
A paired dominating set of a graph $G$ is a dominating set whose induced subgraph contains a perfect matching. The paired domination number, denoted by $\gamma_{pr}(G)$, is the minimum cardinality of a paired dominating set of $G$. A $\gamma_{pr}(G)$-set is a paired dominating set of cardinality $\gamma_{pr}(G)$. The $\gamma$-paired dominating graph of $G$, denoted by $PD_{\gamma}(G)$, as the graph whose vertices are $\gamma_{pr}(G)$-sets. Two $\gamma_{pr}(G)$-sets $D_1$ and $D_2$ are adjacent in $PD_{\gamma}(G)$ if there exists a vertex $u \in D_{1}$ and a vertex $v \notin D_{1}$ such that $D_2=(D_1\setminus \{u\})\cup \{v\}$. In this paper, we present the $\gamma$-paired dominating graphs of cycles.
Kneser-type oscillation criteria for second-order half-linear advanced difference equations
(Wydawnictwa AGH, 2022) Indrajith, N.; Graef, John R.; Thandapani, Ethiraju
The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.
Edge homogeneous colorings
(Wydawnictwa AGH, 2022) Madaras, Tomáš; Onderko, Alfréd; Schweser, Thomas
We explore four kinds of edge colorings defined by the requirement of equal number of colors appearing, in particular ways, around each vertex or each edge. We obtain the characterization of graphs colorable in such a way that the ends of each edge see (not regarding the edge color itself) $q$ colors (resp. one end sees $q$ colors and the color sets for both ends are the same), and a sufficient condition for 2-coloring a graph in a way that the ends of each edge see (with the omission of that edge color) altogether $q$ colors. The relations of these colorings to $M_q$-colorings and role colorings are also discussed; we prove an interpolation theorem for the numbers of colors in edge coloring where all edges around each vertex have $q$ colors.
Solution of the boundary value problem of heat conduction in a cone
(Wydawnictwa AGH, 2022) Ramazanov, Murat; Dženaliev, Muvašarhan Tanabievič; Gulmanov, Nurtay
In the paper we consider the boundary value problem of heat conduction in a non-cylindrical domain, which is an inverted cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary conditions contain a derivative with respect to the time variable. In practice, problems of this kind arise in the presence of the condition of the concentrated heat capacity. We prove a theorem on the solvability of a boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We use the Carleman-Vekua method of equivalent regularization to solve the obtained singular Volterra integral equation.