A purely flexural mechanical analysis has been carried out for a thin, solid, circular plate deflected by a static transverse central force and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. Monegato and Strozzi [6,7] have considered two particular contact reactions: the case where only a distributed force takes place, and the situation in which a distributed force is jointed to a distributed couple of properly selected profile. Both of these problems can been formulated in terms of an integral equation of the Prandtl type with Hilbert and Volterra operators, associated with two constraints conditions. Capobianco, Criscuolo and Junghanns [2] have studied an integro--differential equation of Prandtl type and a collocation method as well as a quadrature method for its approximate solution in weighted Sobolev spaces. Furthermore, collocation and collocation--quadrature methods for the same integral equation have been studied in weighted spaces of continuous functions \cite{CCJL}. The aim of the present paper is to present an algorithm related to the cited numerical model based on the collocation methods with quadrature methods on orthogonal polynomials as in \cite{CCJ,CCJL}. The optimal convergence rates presented here generalize the results shown in [7].

Oggetto della presente ricerca è stato lo studio, la progettazione e la realizzazione di un sistema, basato sulla tecnologia delle reti neurali, per il monitoraggio non invasivo di grandezze, prevalentemente di tipo fisico sulla facciata del teatro romano d’Aosta. Inoltre, la ricerca ha messo a punto due metodologie per la determinazione dei punti ottimi di prelievo di tipo chimico utilizzando strumenti di elaborazione di immagini e segmentazione basata sul colore e per la definizione di griglie ottime di sensori per la misura di parametri ambientali, utilizzando strumenti di elaborazione delle immagini come l’analisi wavelet. La ricerca si è sviluppata secondo le seguenti tematiche: 1.Sensoristica virtuale non invasiva per il monitoraggio di parametri ambientali; 2.Metodologie per la determinazione ottimale di posizioni di prelievo di dati di composizione chimica relative a regioni di interesse (ROI) evidenziate sul monumento da strumenti di elaborazione delle immagini e segmentazione basata sul colore delle stesse; 3.Metodologie per la determinazione di griglie ottime di sensori di misura di dati ambientali (quali temperatura ed umidità) sulla base di dati acquisiti da un numero iniziale sottodimensionato di sensori.

We study the Perspective Shape from Shading problem from the numerical point of view pre- senting a simple algorithm to compute its solution. The scheme is based on a semi-Lagrangian approximation of the first order Hamilton-Jacobi equation related to the problem. The scheme is converging to the weak solution (in the viscosity sense) of the equation and allows to compute accurately regular as well as non regular solutions. Since the partial differential equation must be complemented with boundary conditions on the silhouette, we analyse the effect of various types of boundary conditions on the numerical solution. Some tests on synthetic and real images are presented.

We propose a mathematical model for the dynamics of spread of a viral infection in the organism which incorporates a continuously distributed intracellular delay. The model, consisting of a set of second type Volterra integral equations, can account for viruses having different mechanisms of propagation. We perform the analysis of the qualitative behavior of the solution by proving its positivity and boundedness and by explicitely giving its limiting values.

We consider a system of ordinary differential equations representing a large class of mathematical models concerning the dynamics of an infection in an organism or in a population and we show that the study of the linearized stability leads to some conditions on the basic reproduction number which are sufficient, not only for the local asymptotic stability of a stationary point, but also for its global asymptotic stability. For a more restricted class of problems also the necessity is proved and the limiting behaviour of the model is described.

Agent-based modeling allows the description of very complex systems. To run large scale simulations of agent-based models in a reasonable time, it is crucial to carefully design data structures and algorithms. We describe the main computational features of agent-based models and report about the solutions we adopted in two applications: The simulation of the immune system response and the simulation of the stock market dynamics.

We present a systematic approach to search for an effective vaccination schedule using mathematical computerized models. Our study is based on our previous model that simulates the cancer vs immune system competition activated by tumor vaccine. This model accurately reproduces in-vivo experiments results on HER-2/neu mice treated with the immuno-prevention cancer vaccine (Triplex) for mammary carcinoma. In vivo experiments have shown the effectiveness of Triplex vaccine in protection of mice from mammary carcinoma. The full protection was conferred using chronic (prophylactic) vaccination protocol while therapeutic vaccination was less effcient. In the present paper we use the computer simulations to systematically search for a vaccination schedule which prevents solid tumor formation. The strategy we used for defining a successful vaccination schedule is to control the number of cancer cells with vaccination cycles. We found that, applying the vaccination scheme used in in-vivo experiments, the number of vaccine injections can be reduced roughly by 30%.