Collocation and quadrature methods for Cauchy singular integral equations on an interval with variable coefficients are studied. Convergence rates are proved in weighted uniform and uniform norms.

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].

Boundedness and convergence of the extended Lagrange interpolating operator are investigated in the space L_u,t^p of Sobolev type.

This paper deals with models of living complex systems, chiefly human crowds, by methods of conservation laws and measure theory. We introduce a modeling framework which enables one to address both discrete and continuous dynamical systems in a unified manner using common phenomenological ideas and mathematical tools as well as to couple these two descriptions in a multiscale perspective. Furthermore, we present a basic theory of well-posedness and numerical approximation of initial-value problems and we discuss its implications on mathematical modeling.