A recent approach to generate a zero divergence velocity field by operating directly on the discretized Navier-Stokes equations is used to obtain the decoupling of the pressure from the velocity field. By following the methodology suggested by Amit, Hall, and Porsching the feasibility of treating three dimensional flows and multiply connected domains is analyzed. The present model keeps the main features of the classical vector potential method in that it generates a divergence-free velocity field through an algebraic manipulation of the discrete equations. At the same time the boundary conditions are still imposed on the discrete values of the primitive variables. The accuracy of the method is tested against the exact solution for a recirculating unsteady flow both in simply and doubly connected domains. Several applications to flow fields in three-dimensional enclosures or in multiply connected domains are presented and discussed in terms of accuracy and efficiency of the method. © 1991.

The non-inertial flow of a shear thinning fluid between intersecting planes is studied using a multi-parameter continuation technique. Unlike the classical linearly viscous fluid, it is found that boundary layers develop even in the case of non-inertial flows in both converging and diverging flow. The boundary layers develop due to the non-linearities in the equation which reflect the fact that the fluid can shear thin. © 1991.

Visual reconstruction problems tend to be mathematically ill-posed. They can be reformulated as well-posed variational problems using regularization theory. A generalization of the standard regularization method to visual reconstruction with discontinuities leads to variational problems which include the discontinuity contours in their unknowns. The minimization of the corresponding functionals is a difficult problem. This paper suggests the use of the ?-convergence theory to approximate the functional to be minimized by elliptic functionals, which are more tractable. A ?-convergence theorem which is of relevance to vision applications is discussed, and the results of computer experiments with both synthetic and real images are shown.

In this paper the author gives a new proof to evaluate the convergence of a collocation method for the Abel integral equations of the first kind.

The problem of the computation of stereo disparity is approaehed as a mathematically ill-posed problem by using regularization theory. A controlled continuity constraint which provides a local spatial control over the smoothness of the solution enables the problem to be regularized while preserving the disparity discontinuities. The discontinuities are localized during the regularization process by examining the size of the disparity gradient at the gray value edges. An iterative algorithm for the computation of stereo disparity is obtained, and a computer experiment with synthetic data is shown.

Some research regarding the quality of the water in the Mar Piccolo of the Gulf of Taranto are presented comprehending statistical and hydrodynamical analysis.

The authors consider some procedure for solving a class of singular integral equations of Cauchy type by the collocation method on the zeros of orthogonal polynomials with respect to a weight function similar to that of Jacobi. Uniform convergence theorems are proved.

The problem of the computation of stereo disparity is approached as a mathematically ill-posed problem by using regularization theory. A controlled continuity constrant which provides a local spatial control over the smoothness of the solution enables the problem to be regularized while preserving the disparity discontinuities. The discontinuities are localized during the regularization process by examining the size of the disparity gradient at the gray value edges. An iterative algorithm for the computation of stereo disparity is obtained, and a computer experiment with synthetic data is shown.

A numerical method to solve Abel-type integral equations of first kind is given. In this paper we suggest the research of a numerical solution for Abel-type integral equations of the first kind, by using a collocation method employing an interpolatory product-quadrature formula with a trigonometric polynomial of the first order. Some results of numerical examples are reported.

In this paper, a semi-implicit finite difference method for the 2-D shallow water equations is derived and applied. A characteristic analysis of the governing equations indicates those terms to be discretised implicitly so that the stability of the method will not depend on the celerity. Such terms are the gradient of the water surface elevation in the momentum equations, and the velocity divergence in the continuity equation. The convective terms are discretised explicitly by using either an upwind or an Eulerian-Lagrangian formula. The resulting algorithm, at each time step, required the solution of a linear give-diagonals system which is diagonally dominant with positive elements on the main diagonal and negative ones elsewhere. Thus, existence and uniqueness of the numerical solution is assured at each time step. An application of this method is finally considered for computing the tidal circulation in the MARE PICCOLO, an embayment in the Gulf of Taranto.

The problem of computing depth from stereo images is approached as a mathematically ill-posed problem by using regularization theory. A variational principle for the reconstruction of surfaces in the presence of depth discontinuities is presented. Discontinuities are preserved using a controlled-continuity stabilizing functional which provides a local control over the smoothness properties of the solution. A discontinuity stabilizing functional imposes a curvilinear smoothness constraint on discontinuities to enable their reconstruction. The location of depth discontinuities is further restricted by using information from intensity edges. An iterative optimization method for the computation of depth is obtained, and a computer experiment with synthetic data is shown.