General classes of two variables Appell polynomials are introduced by exploiting properties of an iterated isomorphism, related to the so-called Laguerre-type exponentials. Further extensions to the multi-index and multivariable cases are mentioned. (C) 2004 Elsevier Ltd. All rights reserved.

Multidimensional extensions of the Bernoulli and Appell polynomials are defined generalizing the corresponding generating functions, and using the Hermite-Kampe de Feriet (or Gould-Hopper) polynomials. Furthermore the differential equations satisfied by the corresponding 2D polynomials are derived exploiting the factorization method, introduced in [15].

A mathematical model of blood flow through an arterial vessel is presented and the wave propagation in it is studied numerically. Based on the assumption of long wavelength and small amplitude of the pressure waves, a quasi-one-dimensional (1D) differential model is adopted. It describes the non-linear fluid-wall interaction and includes wall deformation in both radial and axial directions. The 1D model is coupled with a six compartment lumped parameter model, which accounts for the global circulatory features and provides boundary conditions. The differential equations are first linearized to investigate the nature of the propagation phenomena. The full non-linear equations are then approximated with a numerical finite difference method on a staggered grid. Some numerical simulations show the characteristics of the wave propagation. The dependence of the flow, of the wall deformation and of the wave velocity on the elasticity parameter has been highlighted. The importance of the axial deformation is evidenced by its variation in correspondence of the pressure peaks. The wave disturbances consequent to a local stiffening of the vessel and to a compliance jump due to prosthetic implantations are finally studied.

We describe a model for the optimization of the issuances of Public Debt securities developed together with the Italian Ministry of Economy and Finance. The goal is to find the composition of the portfolio issued every month which minimizes a specific “cost function”. Mathematically speaking, this is a stochastic optimal control problem with strong constraints imposed by national regulations and the Maastricht treaty. The stochastic component of the problem is represented by the evolution of interest rates. At this time the optimizer employs classic Linear Programming techniques. However more sophisticated techniques based on Model Predictive Control strategies are under development.

In this paper we propose a simple and effective way to improve the classical Shape from Shading (SFS) problem exploiting light projection information contained in the image data. Edges of concave regions can be split in projecting and the projected points. The geometrical relation between these points allows us to introduce a constraint on the SFS solution. To show the potentialities of our model, we present an application to a Cultural Heritage problem such as the extraction of the boundaries of the degradation zones. (C) 2004 IMACS. Published by Elsevier B.V. All rights reserved.

We prove some properties of the first eigenvalue of the problem \begin{array}{ll} -{\cal A}_p u \colon = - \hbox{\rm div\ } \Big( (A\D u, \D u)^{(p-2)/2}A\D u\Big)= \lambda V(x) |u|^{p-2} u & \hbox{\rm in\ } \O \\ \quad u=0 & \hbox{\rm on\ } \partial \O . \end{array} In particular, the first eigenvalue is shown to be isolated. Moreover, existence and non existence results of solutions in W^{1, p}_0(\Omega) for nonlinear weighted equations with exponential growth are obtained.

A comparison between A(1) and A(2) processes, when used for describing the evolution in time of the global rate of return on investments made by an insurance company, is proposed. In particular, we compare the two processes analysing the parameter sensibility to the size of the sampling interval. An application shows the results. Finally the impact on the global riskiness of a whole life annuity portfolio is evaluated for both the two models.

Il lavoro presenta dei lower bound sul numero cromatico di un grafo con pesi sui nodi.

We consider an empirical Bayes approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, which is usually the case in the existing literature, we elicit the epsilon-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis. The type II maximum likelihood approach to prior selection is used by maximizing the predictive distribution for the data in the wavelet domain over a suitable subclass of the epsilon-contamination class of prior distributions. For the prior selected, the posterior mean yields a thresholding procedure which depends on one free prior parameter and it is level- and amplitude-dependent, thus allowing better adaptation in function estimation. We consider an automatic choice of the free prior parameter, guided by considerations on an exact risk analysis and on the shape of the thresholding rule, enabling the resulting estimator to be fully automated in practice. We also compute pointwise Bayesian credible intervals for the resulting function estimate using a simulation-based approach. We use several simulated examples to illustrate the performance of the proposed empirical Bayes term-by-term wavelet scheme, and we make comparisons with other classical and empirical Bayes term-by-term wavelet schemes. As a practical illustration, we present an application to a real-life data set that was collected in an atomic force microscopy study.

Particular solutions of a class of higher order ordinary differential equations, with non-constant coefficients, are determined by using the properties of the Laguerre exponentials functions introduced by G. Dattoli and P. E. Ricci in [4]. © 2004, Heldermann Verlag. All rights reserved.

Clustering has been one of the most popular methods to discover useful biological insights from DNA microarray. An interesting paradigm is simultaneous clustering of both genes and experiments. This "biclustering "paradigm aims at discovering clusters that consist of a subset of the genes showing a coherent expression pattern over a subset of conditions. The pClustering approach is a technique that belongs to this paradigm. Despite many theoretical advantages, this technique has been rarely applied to actual gene expression data analysis. Possible reasons include the worst-case complexity of the clustering algorithm and the difficulty in interpreting clustering results. In this paper, we propose an enhanced framework for performing pClustering on actual gene expression analysis. Our new framework includes an effective data preparation method, highly scalable clustering strategies, and an intuitive result interpretation scheme. The experimental result confirms the effectiveness of our approach.