Well-balanced schemes, nowadays mostly developed for both hyperbolic and kinetic equations, are extended in order to handle linear parabolic equations, too. By considering the variational solution of the resulting stationary boundary-value problem, a simple criterion of uniqueness is singled out: the C1 regularity at all knots of the computational grid. Being easy to convert into a finite-difference scheme, a well-balanced discretization is deduced by defining the discrete time-derivative as the defect of C1 regularity at each node.

Given a population of N elements with their geographical positions and the genetic (or lexical) distances between couples of elements (inferred, for example, from lexical differences between dialects which are spoken in different towns or from genetic differences between animal populations living in different faunal areas) a very interesting problem is to reconstruct the geographical positions of individuals using only genetic/lexical distances.

[object Object]Metals, extensively used in technology applications as well as in art metal works, have a chemical affinity for oxygen, water, sulphur and are particularly susceptible to electrochemical processes due to the environment. For this reason the monitoring of the effect of environmental conditions (temperature, humidity, pollutant concentration) on their mechanical and physical properties are considered a primary necessity for metal conservation and preservation.

A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement-invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in our analysis is a new reduction principle for the relevant embeddings, showing their equivalence to a couple of considerably simpler one-dimensional inequalities.

Kinetic BGK numerical schemes for the approximation of incompressible Navier-Stokes equations are derived via classical discrete velocity vector BGK approximations, but applied to an inviscid compressible gas dynamics system with small Mach number parameter, according to the approach of Carfora and Natalini (2008). As the Mach number, the grid size and the timestep tend to zero, the low Mach number limit and the time-space convergence of the scheme are achieved simultaneously, and the numerical viscosity tends to the physical viscosity of the Navier-Stokes system.

We consider homogeneous linear Volterra Discrete Equations and we study the asymptotic behaviour of their solutions under hypothesis on the sign of the coefficients and of the first- and second-order differences. The results are then used to analyse the numerical stability of some classes of Volterra integrodifferential equations.