Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence.

We present an algorithm to solve Netwon methods for nonlinear hypersingular integral equation of Prandtl's type with the help of GMRES .

In this paper we propose a LWR-like model for traffic flow on networks which allows to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the destination is not assigned a priori, and can be chosen by the drivers during the journey, taking decisions at junctions. The model is then used to describe three possible behaviors of drivers, as- sociated to three different ways to solve the route choice problem: 1. Drivers ignore the presence of the other vehicles; 2.

Double integrals with algebraic and/or logarithmic singularities are of interest in the application of boundary element method, e.g. linear theory of the aerodynamics of slender bodies of revolution and in many other fields, for example computational electromagnetics. Therefore, the numerical evaluation of such type of integrals deserves attention.

First asymptotic relations of Voronovskaya-type for rational operators of Shepard-type are shown. A positive answer in some senses to a problem on the pointwise approximation power of linear operators on equidistant nodes posed by Gavrea, Gonska and Kacs is given. Direct and converse results, computational aspects and Gruss-type inequalities are also proved. Finally an application to images compression is discussed, showing the outperformance of such operators in some senses.

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.

Boundedness and convergence of the extended Lagrange interpolating operator are investigated in the space L_u,t^p of Sobolev type.