Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2011
Volume
Vol. 31
Number
No. 4
Description
Journal Volume
Opuscula Mathematica
Vol. 31 (2011)
Projects
Pages
Articles
A mixed integer nonlinear programming formulation for the problem of fitting positive exponential sums to empirical data
(2011) Alvarez, Adalys; Lara, Hugo
In this work we deal with exponential sum models coming from data acquisition in the empirical sciences. We present a two step approach based on Tikhonov regularization and combinatorial optimization, to obtain stable parameter estimations, which fit the data. We develop properties of the solutions, based on their optimality conditions. Some numerical experiments are shown to illustrate our approach.
Operators in divergence form and their Friedrichs and Kreĭn extensions
(2011) Arlinskij, Ûrij Moiseevič; Kovalev, Ûrij
For a densely defined nonnegative symmetric operator $\mathcal{A} = L_2^*L_1$ in a Hilbert space, constructed from a pair $L_1 \subset L_2$ of closed operators, we give expressions for the Friedrichs and Kreĭn nonnegative selfadjoint extensions. Some conditions for the equality $(L_2^* L_1)^* = L_1^* L_2$ are obtained. Applications to 1D nonnegative Hamiltonians, corresponding to point interactions, are given
Neighbourhood total domination in graphs
(2011) Arumugam, S.; Sivagnanam, C.
Let $G = (V,E)$ be a graph without isolated vertices. A dominating set $S$ of $G$ is called a neighbourhood total dominating set (ntd-set) if the induced subgraph $N(S)$ has no isolated vertices. The minimum cardinality of a ntd-set of $G$ is called the neighbourhood total domination number of $G$ and is denoted by $\gamma _{nt}(G)$. The maximum order of a partition of $V$ into ntd-sets is called the neighbourhood total domatic number of $G$ and is denoted by $d_{nt}(G)$. In this paper we initiate a study of these parameters.
Recursively arbitrarily vertex-decomposable suns
(2011) Baudon, Olivier; Gilbert, Frédéric; Woźniak, Mariusz
A graph $G = (V,E)$ is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to $|V|$, there is a sequence of vertex-disjoint subsets of $V$ whose orders are given by $\tau$, and which induce connected graphs. The aim of this paper is to study the recursive version of this problem on a special class of graphs called suns. This paper is a complement of [O. Baudon, F. Gilbert, M. Woźniak, Recursively arbitrarily vertex-decomposable graphs, research report, 2010].
Free probability induced by electric resistance networks on energy Hilbert spaces
(2011) Cho, Ilwoo; Jørgensen, Palle E.T.
We show that a class of countable weighted graphs arising in the study of electric resistance networks (ERNs) are naturally associated with groupoids. Starting with a fixed ERN, it is known that there is a canonical energy form and a derived energy Hilbert space $H_{\mathcal{E}}$. From $H_{\mathcal{E}}$, one then studies resistance metrics and boundaries of the ERNs. But in earlier research, there does not appear to be a natural algebra of bounded operators acting on $H_{\mathcal{E}}$. With the use of our ERN-groupoid, we show that $H_{\mathcal{E}}$ may be derived as a representation Hilbert space of a universal representation of a groupoid algebra $\mathfrak{A}_G$, and we display other representations. Among our applications, we identify a free structure of $\mathfrak{A}_G$ in terms of the energy form.