A general methodology, which consists in deriving two-dimensional finite-difference schemes which involve numerical fluxes based on Dirichlet-to-Neumann maps (or Steklov-Poincare operators), is first recalled. Then, it is applied to several types of diffusion equations, some being weakly anisotropic, endowed with an external source. Standard finite-difference discretizations are systematically recovered, showing that in absence of any other mechanism, like e.g.

A genuinely two-dimensional discretization of general drift-diffusion (including incompressible Navier--Stokes) equations is proposed. Its numerical fluxes are derived by computing the radial derivatives of "bubbles" which are deduced from available discrete data by exploiting the stationary Dirichlet--Green function of the convection-diffusion operator. These fluxes are reminiscent of Scharfetter and Gummel's in the sense that they contain modified Bessel functions which allow one to pass smoothly from diffusive to drift-dominating regimes.

Longitudinal defects of the internal coated surface of a metal pipe can be evaluated in a fast, precise and cheap way from thermal measurements on the external surface. In this paper, we study two classes of real situations in which the thickness of the coating is much smaller than the thickness of the metal tube: the transportation of potable water and crude oil. A very precise and stable reconstruction of damages is obtained by means of perturbation methods. To do this, first we translate a composite (coating-plus-tube) boundary value problem in a virtual one on the metallic part only.

We deal with the mathematical model of the incremental degradation of the internal coating (e.g. a polymeric material) of a metallic pipe in which a fluid flows relatively fast. The fluid drags solid impurities so that longitudinal scratches, inaccessible to any direct inspection procedure, are produced on the coating. Time evolution of this kind of defects can be reconstructed from the knowledge of a sequence of temperature maps of the external surface.

The knowledge production provided by universities is essential to sustaining a country's long-term economic growth and international competitiveness. Many nations are thus driving to create sustainable and effective funding environments. The evaluation of university knowledge, productivity and research quality becomes critical, with ever increasing share of public funding allocated on the basis of research assessment exercises.

The rapid development of cyber insurance market brings forward the question about the effect of cyber insurance on cyber security. Some researchers believe that the effect should be positive as organisations will be forced to maintain a high level of security in order to pay lower premiums. On the other hand, other researchers conduct a theoretical analysis and demonstrate that availability of cyber insurance may result in lower investments in security. In this paper we propose a mathematical analysis of a cyber-insurance model in a non-competitive market.