We present a multiphase mathematical model for tumor growth which incorporates the remodeling of the extracellular matrix and describes the formation of fibrotic tissue by tumor cells. We also detail a full qualitative analysis of the spatially homogeneous problem, and study the equilibria of the system in order to characterize the conditions under which fibrosis may occur. © 2010 Elsevier Ltd.

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.

The Hilbert transform of a function g, H(g) is an important tool in many mathematical fields. Expecially its numerical evaluation is often useful in some procedures for searcing solutions of the singular integral equations. In this context an approximation of (HV^alpha,beta,f;t), |t|1, where f is a continuous function in [-1,1] and v^alpha,beta, alpha,beta>-1 is a Jacobi weight, is required. In the last decade more then one paper appeared on this subject and among others we recall [1,2,3,4,5,14,15,20]. The procedure used in these papers can be described as follows.

General classes of two variables Appell polynomials are introduced by exploiting properties of an iterated isomorphism, related to the so-called Laguerre-type exponentials. Further extensions to the multi-index and multivariable cases are mentioned. (C) 2004 Elsevier Ltd. All rights reserved.

The work deals the monitoring of a single ancient landslide detected in the Vonace area, southwards of Maierato (Calabria, Italy). A 18-hour-measurement campaign has been carried out using the Ground-based Synthetic Aperture Radar (GBSAR) interferometry technique carried between March, 25th and 26th. Displacement maps have been geolocated and overlaid to a Digital Elevation Model of the scene. It has been observed that the Vonace area is almost stable except two portions located at the foot of the ancient landslide and at the centre of the town, respectively.

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.

A proposal for particles' initialization in PSO is presented and discussed, with focus on costly global unconstrained optimization problems. The standard PSO iteration is reformulated such that the trajectories of the particles are studied in an extended space, combining particles' position and speed. To the aim of exploring effectively and efficiently the optimization search space since the early iterations, the particles are initialized using sets of orthogonal vectors in the extended space (orthogonal initialization, ORTHOinit).