Mathematical model of tumour cord growth along the source of nutrient

A mathematical model of the tumour growth along a blood vessel is proposed. The model employs the mixture theory approach to describe a tissue which consists of cells, extracellular matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is paid to consistent description of oxygen consumption and growth processes based on the energy balance. A finite difference numerical method is proposed. The level set method is used to track an interface between the tissues.

Multidimensional extensions of the Bernoulli and Appell polynomials

Multidimensional extensions of the Bernoulli and Appell polynomials are defined generalizing the corresponding generating functions, and using the Hermite-Kampe de Feriet (or Gould-Hopper) polynomials. Furthermore the differential equations satisfied by the corresponding 2D polynomials are derived exploiting the factorization method, introduced in [15].

Flexible services for people transportation: a simulation model in a discrete events environment

The realization of innovative transport services requires greater flexibility and inexpensive service. In many cases the solution is to realize demand responsive transportation system. A Demand Responsive Transport System (DRTS) requires the planning of travel paths (routing) and customer pick-up and drop-off times (scheduling) according to received requests. In particular, the problem has to deal with multiple vehicles, limited capacity of the fleet vehicles and temporal constraints (time windows). A DRTS may operate according to static or dynamic mode.

Mathematical modeling of vehicular traffic: A discrete kinetic theory approach

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.