Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2016
Volume
Vol. 36
Number
No. 3
Description
Journal Volume
Opuscula Mathematica
Vol. 36 (2016)
Projects
Pages
Articles
Multiplicative Zagreb indices and coindices of some derived graphs
(2016) Basavanagoud, Bommanahal; Patil, Shreekant
In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.
Higher order Nevanlinna functions and the inverse three spectra problem
(2016) Boyko, Olga; Martinûk, Ol'ga Mikolaïvna; Pivovarčik, Vâčeslav
The three spectra problem of recovering the Sturm-Liouville equation by the spectrum of the Dirichlet-Dirichlet boundary value problem on $[0,a]$, the Dirichlet-Dirichlet problem on $[0,a/2]$ and the Neumann-Dirichlet problem on $[a/2,a]$ is considered. Sufficient conditions of solvability and of uniqueness of the solution to such a problem are found.
Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain
(2016) Chaieb, Majda; Dhifli, Abdelwaheb; Zermani, Samia
Let $\Omega$ be a bounded domain in $\mathbb{R}^{n}$ $n\geq 2$ with a smooth boundary $\partial \Omega$. We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system $\begin{aligned} -\Delta u&=a_{1}(x)u^{\alpha}v^{r}\quad\text{in}\;\Omega ,\;\;\,u|_{\partial\Omega}=0,\\ -\Delta v&=a_{2}(x)v^{\beta}u^{s}\quad\text{in}\;\Omega ,\;\;\,v|_{\partial\Omega }=0.\end{aligned}$
Here $r,s\in \mathbb{R}$, $\alpha,\beta \lt 1$ such that $\gamma :=(1-\alpha)(1-\beta)-rs\gt 0$ and the functions $a_{i}$ ($i=1,2$) are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory.
Certain group dynamical systems induced by Hecke algebras
(2016) Cho, Ilwoo
In this paper, we study dynamical systems induced by a certain group $\mathfrak{T}_{N}^{K}$ embedded in the Hecke algebra $\mathcal{H}(G_{p})$ induced by the generalized linear group $G_{p} = GL_{2}(\mathbb{Q}_{p})$ over the p-adic number fields $\mathbb{Q}_{p}$ for a fixed prime $p$. We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms of free probability on the Hecke algebra $\mathcal{H}(G_{p})$.
The hardness of the independence and matching clutter of a graph
(2016) Ambarcumân, Sasun; Mkrtčân, Vahan V.; Musoân, Vahe L.; Sargsân, Hovhannes
A clutter (or antichain or Sperner family) $L$ is a pair $(V,E)$, where $V$ is a finite set and $E$ is a family of subsets of $V$ none of which is a subset of another. Usually, the elements of $V$ are called vertices of $L$, and the elements of $E$ are called edges of $L$. A subset se of an edge e of a clutter is called recognizing for e, if $s_e$ is not a subset of another edge. The hardness of an edge $e$ of a clutter is the ratio of the size of $e$'s smallest recognizing subset to the size of $e$. The hardness of a clutter is the maximum hardness of its edges. We study the hardness of clutters arising from independent sets and matchings of graphs.