We consider a model for supply chains governed by partial di®eren- tial equations. The mathematical properties of a continuous model are discussed and existence and uniqueness is proven. Moreover, Lipschitz continuous dependence on the initial data is proven. We make use of the front tracking method to construct approximate solutions.

A mathematical model for the diffusion-transport of a substance between two porous homogeneous media of different properties and dimensions is presented. A strong analogy with the one-dimensional transient heat conduction process across two-layered slabs is shown and a similar methodology of solution is proposed. Separation of variables leads to a Sturm-Liouville problem with discontinuous coefficients and an exact analytical solution is given in the form of an infinite series expansion. The model points out the role of four non-dimensional parameters which control the diffusion mechanism across the two porous layers. The drug-eluting stent constitutes the main application of the present model. Drug concentration profiles at various times are given and analyzed. Also, qualitative considerations and a quantitative description to evaluate feasibility of new drug delivery strategies are provided, and some indicators, such as the emptying time, useful to optimize the drug-eluting stent design are discussed.

We consider a hyperbolic conservation law with discontinuous flux. Such a partial differential equation arises in different applications, in particu- lar we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak en- tropic solutions.

This paper is focused on continuum-discrete models for supply chains. In particular, we consider the model introduced in [ ], where a system of conservation laws describe the evolution of the supply chain status on sub-chains, while at some nodes solutions are determined by Riemann solvers. Fixing the rule of flux maximization, two new Riemann Solvers are defined. We study the equilibria of the resulting dynamics, moreover some numerical experiments on sample supply chains are reported. We provide also a comparison, both of equilibria and experiments, with the model of [ ].

We are concerned with the numerical study of a simple one-dimensional Schr\"odinger operator $-\frac 1 2 \Dxx + \alpha q(x)$ with $\alpha \in \Re$, $q(x)=\cos(x)+\eps \cos(kx)$, $\eps >0$ and $k$ being irrational. This governs the quantum wave function of an independent electron within a crystalline lattice perturbed by some impurities whose dissemination induces long-range order only, which is rendered by means of the quasi-periodic potential $q$. We study numerically what happens for various values of $k$ and $\eps$; it turns out that for $k > 1$ and $\eps\ll 1$, that is to say, in case more than one impurity shows up inside an elementary cell of the original lattice, ``impurity bands" appear and seem to be $k$-periodic. When $\eps$ grows bigger than one, the opposite case occurs.

We consider the approximation of a microelectronic device corresponding to a $n^+-n-n^+$ diode consisting in a channel flanked on both sides by two highly doped regions. This is modelled through a system of equations: ballistic for the channel and drift-diffusion elsewhere. The overall coupling stems from the Poisson equation for the self-consistent potential. We propose an original numerical method for its processing, being realizable, explicit in time and nonnegativity preserving on the density. In particular, the boundary conditions at the junctions express the continuity of the current and don't destabilize the general scheme. At last, efficiency is shown by presenting results on test-cases of some practical interest.

The aim of this text is to develop on the asymptotics of some 1-D nonlinear Schr\"odinger equations from both the theoretical and the numerical perspectives, when a caustic is formed. We review rigorous results in the field and give some heuristics in cases where justification is still needed. The scattering operator theory is recalled. Numerical experiments are carried out on the focus point singularity for which several results have been proven rigorously. Furthermore, the scattering operator is numerically studied. Finally, experiments on the cusp caustic are displayed, and similarities with the focus point are discussed. Several shortcomings of spectral time-splitting schemes are investigated.

Colorization refers to an image processing task which recovers color in grayscale images when only small regions with color are given. We propose a couple of variational models using chromaticity color components to colorize black and white images. We first consider total variation minimizing (TV) colorization which is an extension from TV inpainting to color using chromaticity model. Second, we further modify our model to weighted harmonic maps for colorization. This model adds edge information from the brightness data, while it reconstructs smooth color values for each homogeneous region. We introduce penalized versions of the variational models, we analyze their convergence properties, and we present numerical results including extension to texture colorization.

We analyze a variational problem for the recovery of vector valued functions and compute its numerical solution. The data of the problem are a small set of complete samples of the vector valued function and some significant incomplete information where the former are missing. The incomplete information is assumed as the result of a distortion, with values in a lower dimensional manifold. For the recovery of the function we minimize a functional which is formed by the discrepancy with respect to the data and total variation regularization constraints. We show the existence of minimizers in the space of vector valued bounded variation functions. For the computation of minimizers we provide a stable and efficient method. First, we approximate the functional by coercive functionals on W-1,W-2 in terms of Gamma- convergence. Then we realize approximations of minimizers of the latter functionals by an iterative procedure to solve the PDE system of the corresponding Euler-Lagrange equations. The numerical implementation comes naturally by finite element discretization. We apply the algorithm to the restoration of color images from limited color information and gray levels where the colors are missing. The numerical experiments show that this scheme is very fast and robust. The reconstruction capabilities of the model are shown, also from very limited ( randomly distributed) color data. Several examples are included from the real restoration problem of A. Mantegna's art frescoes in Italy.

We describe the methods employed for the generation of possible scenarios for term structure evolution. The problem originated as a request from the Italian Ministry of Economy and Finance to find an optimal strategy for the issuance of Public Debt securities. The basic idea is to split the evolution of each rate into two parts. The first component is driven by the evolution of the official rate (the European Central Bank official rate in the present case). The second component of each rate is represented by the fluctuations having null correlation with the ECB rate.

Motivation: Highly Active AntiRetroviral Therapies (HAART) can pro- long life significantly to people infected by HIV since, although unable to eradicate the virus, they are quite effective in maintaining control of the infection. However, since HAART have several undesirable side effects, it is considered useful to suspend the therapy according to a suitable schedule of Structured Therapeutic Interruptions (STI). In the present paper we describe an application of genetic algo- rithms (GA) aimed at finding the optimal schedule for a HAART simulated with an agent-based model (ABM) of the immune system that reproduces the most significant features of the response of an organism to the HIV-1 infection. Results: The genetic algorithm helps in finding an optimal therapeu- tic schedule that maximizes immune restoration, minimizes the viral count and, through appropriate interruptions of the therapy, minimizes the dose of drug administered to the simulated patient. To validate the efficacy of the therapy that the genetic algorithm indicates as optimal, we ran simulations of oppor tunistic diseases and found that the selected therapy shows the best survival curve among the different simulated control groups.

We show that the condition is not necessary, though sufficient, for the asymptotic stability of . We prove the existence of a class of Volterra difference equations (VDEs) that violate this condition but whose zero solutions are asymptotically stable.

We consider the heat equation for director fields, with values in the unit sphere. A variational approach is used to construct axially symmetric traveling wave solutions defined in an infinitely long cylinder. The traveling waves have a point singularity of topological degree 0 or 1. The construction of solutions with degree 0 is based on minimization of a relaxed energy.

: In this article we present the implementation of an environment supporting Levy's optimal reduction for the X-calculus on parallel (or distributed) computing systems. In a similar approach to Lamping's, we base our work on a graph reduction technique, known as directed virtual reduction, which is actually a restriction of Danos-Regnier virtual reduction. The environment, which we refer to as PELCR (parallel environment for optimal lambdacalculus reduction), relies on a strategy for directed virtual reduction, namely half combustion. While developing PELCR we adopted both a message aggregation technique, allowing reduction of the communication overhead, and a fair policy for distributing dynamically originated load among processors. We also present an experimental study demonstrating the ability of PELCR to definitely exploit the parallelism intrinsic to lambda-terms while performing the reduction. We show how PELCR allows achieving up to 70-80% of the ideal speedup on last generation multiprocessor computing systems. As a last note, the software modules have been developed with. the C language and using a standard interface for message passing, that is, MPI, thus making PELCR itself a highly portable software package.