We consider a class of integral equations of Volterra type with constant coefficients containing a logarithmic difference kernel. This class coincides for a=0 with the Symm's euqtion. We can transform the general integral equation into an equivalent singular equation of Cauchy type which allows us to give the explicit formula for the solution. The numerical method proposed in this paper consists in substituting this in the experrsion of the solution g.

In this paper we review the dry port concept and its outfalls in terms of optimal design and management of freight distribution. Some optimization challenges arising from the presence of dry ports in intermodal freight transport systems are presented and discussed. Then we consider the tactical planning problem of defining the optimal routes and schedules for the fleet of vehicles providing transportation services between the terminals of a dry-port-based intermodal system.

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM.

Following some general ideas on the discrete kinetic and stochastic game theory proposed by one of the authors in a previous work, this paper develops a discrete velocity mathematical model for vehicular traffic along a one-way road. The kinetic scale is chosen because, unlike the macroscopic one, it allows to capture the probabilistic essence of the interactions among the vehicles, and offers at the same time, unlike the microscopic one, the opportunity of a pro. table analytical investigation of the relevant global features of the system.

In this paper, we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon-positive measures generated by a push-forward recursive relation.

While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models. © EDP Sciences, 2009.

The formation of vascular networks in vitro develops along two rather distinct stages: during the early migration-dominated stage the main features of the pattern emerge, later the mechanical interaction of the cells with the substratum stretches the network. Mathematical models in the relevant literature have been focusing just on either of the aspects of this complex system. In this paper, a unified view of the morphogenetic process is provided in terms of physical mechanisms and mathematical modeling.

In this paper we introduce the Mathematical Desk for Italian Industry, a project based on applied and industrial mathematics developed by a team of researchers from the Italian National Research Council in collaboration with two major Italian associations for applied mathematics, SIMAI and AIRO.