Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2000)https://www.openstarts.units.it/handle/10077/41612024-08-13T13:04:22Z2024-08-13T13:04:22Z121An analytical introduction to stochastic differential equations: Part I - the Langevin equationClément, Ph.van Gaans, O. W.https://www.openstarts.units.it/handle/10077/42652019-03-02T05:54:34Z2000-01-01T00:00:00Zdc.title: An analytical introduction to stochastic differential equations: Part I - the Langevin equation
dc.contributor.author: Clément, Ph.; van Gaans, O. W.
dc.description.abstract: We present an introduction to the theory of stochastic differential equations, motivating and explaining ideas from the point of view of analysis. First the notion of white noise is developed, introducing at the same time probabilistic tools. Then the one dimensional Langevin equation is formulated as a deterministic integral equation with a parameter. Its solution leads to stochastic convolution, which is defined as a Riemann-Stieltjes integral. It is shown that the parameter dependence yields a Gaussian system, of which the means and covariances arde computed. We conclude by introducing briefly the notion of invariant measure and the associated Kolmogorov equations.
2000-01-01T00:00:00ZContinuous dependence results for an inverse problem in the theory of combustion of materials with memoryColombo, Fabriziohttps://www.openstarts.units.it/handle/10077/42642019-03-02T06:02:18Z2000-01-01T00:00:00Zdc.title: Continuous dependence results for an inverse problem in the theory of combustion of materials with memory
dc.contributor.author: Colombo, Fabrizio
dc.description.abstract: We prove theorems of continuous dependence on the data for both direct and inverse problems for semilinear integrodifferential equations. Such results are applied to the specific case of the combustion of a material with memory.
2000-01-01T00:00:00ZFilters and pathwise connectificationCostantini, CamilloFedeli, AlessandroLe Donne, Attiliohttps://www.openstarts.units.it/handle/10077/42632019-03-02T05:59:39Z2000-01-01T00:00:00Zdc.title: Filters and pathwise connectification
dc.contributor.author: Costantini, Camillo; Fedeli, Alessandro; Le Donne, Attilio
dc.description.abstract: Let p be a free open-filter on a Hausdorff space X. In this paper we investigate when $X \cup {p}$ can be densely embedded in a pathwise connected $T_2$-space. The main part of the paper is devoted to the cases where X is the rational or the real line.
2000-01-01T00:00:00ZRelaxed parabolic problemsSmolka, Maciejhttps://www.openstarts.units.it/handle/10077/42622019-03-02T06:00:23Z2000-01-01T00:00:00Zdc.title: Relaxed parabolic problems
dc.contributor.author: Smolka, Maciej
dc.description.abstract: Let $G_{n}$ be a sequence of open subsets of a given open and bounded
$\Omega\subset\mathbb{R}^{N}$. We study the asymptotic behaviour
of the solutions of parabolic equations $u_{n}'+Au_{n}=f_{n}\:\textrm{on}\: G_{n}$.
Assuming that the right-hand sides $f_{n}$ and the initial conditions
converge in a proper way we find the form of the limit problem without
any additional hypothesis on $G_{n}$. Our method is based on the
notion of elliptic $\gamma^{A}$-convergence.
2000-01-01T00:00:00ZUniqueness and multiplicity for perturbations of the Yamabe problem on $S^n$Esposito, Pierpaolohttps://www.openstarts.units.it/handle/10077/42612019-03-02T06:02:15Z2000-01-01T00:00:00Zdc.title: Uniqueness and multiplicity for perturbations of the Yamabe problem on $S^n$
dc.contributor.author: Esposito, Pierpaolo
dc.description.abstract: Motivated by an uniqueness result for linear perturbations with constant coefficients of the conformal laplacian on the
sphere, we investigate, via a finite dimensional reduction, more
general perturbations of the conformal laplacian, exibiting cases
in which uniqueness fails
2000-01-01T00:00:00ZExistence and uniqueness of periodic solutions for a quasilinear parabolic problemBadii, Mauriziohttps://www.openstarts.units.it/handle/10077/42602019-03-02T05:57:11Z2000-01-01T00:00:00Zdc.title: Existence and uniqueness of periodic solutions for a quasilinear parabolic problem
dc.contributor.author: Badii, Maurizio
dc.description.abstract: We are concerned with the existence and uniqueness of
the nonnegative periodic weak solution to a quasilinear parabolic
problem of degenerate type, which describes a mathematical model
in petroleum engineering. The existence of periodic solutions is
established by means of the Schauder fixed point Theorem applied
to the Poincaré map. Instead, the uniqueness of the periodic
solution is proved under the assumption that $b(\varphi^-1)$ is Hölder
continuous of order 1/2, adapting a technique utilized in the study
of nonlinear hyperbolic equations.
2000-01-01T00:00:00ZDecomposition of some hypergeometric polynomials with respect to the cyclic group of order $n$Ben Cheikh, Youssèfhttps://www.openstarts.units.it/handle/10077/42592019-03-02T05:55:30Z2000-01-01T00:00:00Zdc.title: Decomposition of some hypergeometric polynomials with respect to the cyclic group of order $n$
dc.contributor.author: Ben Cheikh, Youssèf
dc.description.abstract: Let $\left\{ P_{m}\right\} _{m\geq0}$ be a sequence of polynomials
with complex coefficients and let n be an arbitrary positive integer.
The components with respect to the cyclic group of order n of the
polynomial $P_{m},m=0,1,...,$ are given by:
\[
\left(P_{m}\right)_{\left[n,k\right]}\left(z\right)=\frac{1}{n}\overset{n-1}{\overset{\sum}{l=0}}\;\omega_{n}^{-kl}P_{m}\left(\omega_{n}^{l}z\right)\:,\quad k=0,1,...,n-1\;,
\]
where $\omega_{n}=exp\left(\frac{2i\pi}{n}\right)$. In this paper,
we consider two class of hypergeometric polynomials, the Brafman polynomials
and the Srivastava-Panda polynomials. For the components of these
polynomials, we establish hypergeometric representations, differential
equations and generating functions.
2000-01-01T00:00:00ZPositive solutions of quasilinear elliptic systems with the natural growth in the gradientZubrinic, Darkohttps://www.openstarts.units.it/handle/10077/42582019-03-02T05:59:34Z2000-01-01T00:00:00Zdc.title: Positive solutions of quasilinear elliptic systems with the natural growth in the gradient
dc.contributor.author: Zubrinic, Darko
dc.description.abstract: We study the problem of existence and nonexistence of
positive, spherically symmetric solutions of a quasilinear elliptic
system involving p-Laplacians, with the natural growth in the gradient on the right-hand sfide. The existence proof is constructive,
with solutions possessing explicit integral representation. We also
obtain various qualitative results. The elliptic system is studied
by relating it to the corresponding system of singular ODE's of
the first order.
2000-01-01T00:00:00ZVerlinde-type formulae and twistor transformHerrera, Rafaelhttps://www.openstarts.units.it/handle/10077/42572019-03-02T05:54:18Z2000-01-01T00:00:00Zdc.title: Verlinde-type formulae and twistor transform
dc.contributor.author: Herrera, Rafael
dc.description.abstract: We study certain aspects of the topology of six moduli spaces of orthogonal vector bundles over Riemann surfaces, with genus between 2 and 7, in order to find generalizations of the well-known Verlinde formula and the Newstead conjectures.
2000-01-01T00:00:00ZRemark on subharmonic solutions of periodic planar systemsWójcik, Klaudiuszhttps://www.openstarts.units.it/handle/10077/42562019-03-02T05:55:32Z2000-01-01T00:00:00Zdc.title: Remark on subharmonic solutions of periodic planar systems
dc.contributor.author: Wójcik, Klaudiusz
dc.description.abstract: Let W be a periodic isolating segment for the periodic planar system.
Assume that time O section W$_{0}$ is a topological manifold with
boundary and $H\left(W_{0},W_{0}^{-}\right)\neq0$ where W$^{-}$
is the exit set of W. Then there is a subharmonic solution.
2000-01-01T00:00:00Z