Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2012
Volume
Vol. 32
Number
No. 4
Description
Journal Volume
Opuscula Mathematica
Vol. 32 (2012)
Projects
Pages
Articles
Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels
(2012) Castro, Luís P.; Saitoh, Saburou; Nguyen, Minh Tuan
This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).
Energy integral of the Stokes flow in a singularly perturbed exterior domain
(2012) Dalla Riva, Matteo
We consider a pair of domains $\Omega^{b}$ and $\Omega^{s}$ in $\mathbb{R}^n$ and we assume that the closure of $\Omega^{b}$ does not intersect the closure of $\epsilon \Omega ^s$ for $\epsilon \in (0,\epsilon _0)$. Then for a fixed $\epsilon \in (0,\epsilon_0)$ we consider a boundary value problem in $\mathbb{R}^n \setminus (\Omega ^b \cup \epsilon \Omega ^s)$ which describes the steady state Stokes flow of an incompressible viscous fluid past a body occupying the domain $\Omega^{b}$ and past a small impurity occupying the $\epsilon \Omega ^s$. The unknown of the problem are the velocity field u and the pressure field $p$, and we impose the value of the velocity field $u$ on the boundary both of the body and of the impurity. We assume that the boundary velocity on the impurity displays an arbitrarily strong singularity when $\epsilon$ tends to $0$. The goal is to understand the behaviour of the strain energy of $(u, p)$ for $\epsilon$ small and positive. The methods developed aim at representing the limiting behaviour in terms of analytic maps and possibly singular but completely known functions of $\epsilon$, such as $\epsilon ^{-1}$, log $\epsilon$.
A note on a one-parameter family of non-symmetric number triangles
(2012) Falcão, Maria Irene Ferrão de Carvalho Ribeiro Almeida; Malonek, Helmuth R.
The recent growing interest in special Clifford algebra valued polynomial solutions of generalized Cauchy-Riemann systems in $(n+1)$-dimensional Euclidean spaces suggested a detailed study of the arithmetical properties of their coefficients, due to their combinatoric relevance. This concerns, in particular, a generalized Appell sequence of homogeneous polynomials whose coefficient set can be treated as a one-parameter family of non-symmetric triangles of fractions. The discussion of its properties, similar to those of the ordinary Pascal triangle (which itself does not belong to the family), is carried out in this paper.
Symbolic approach to the general cubic decomposition of polynomial sequences. Results for several orthogonal and symmetric cases
(2012) Mesquita, Teresa A.; Da Rocha, Z.
We deal with a symbolic approach to the cubic decomposition (CD) of polynomial sequences - presented in a previous article referenced herein - which allows us to compute explicitly the first elements of the nine component sequences of a CD. Properties are investigated and several experimental results are discussed, related to the CD of some widely known orthogonal sequences. Results concerning the symmetric character of the component sequences are established.
Recursively arbitrarily vertex-decomposable graphs
(2012) Baudon, Olivier; Gilbert, Frédéric; Woźniak, Mariusz
A graph $G=(V,E)$ is arbitrarily vertex decomposable if for any sequence $\tau$ 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 main aim of this paper is to study the recursive version of this problem. We present a solution for trees, suns, and partially for a class of 2-connected graphs called balloons.