We investigate the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with re- spect to the given constraints well approximates a given function. This procedure was, at ¯rst, successfully introduced for the polynomial inter- polation with constraints on bounded intervals [1].

We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow, analyzing the system by varying the extent of compressibility and the reaction rate. We find that the bulk burning rate vf in a shear flow increases with compressibility intensity ?, following the relation ?vf??2. Furthermore, the faster the reaction is, the more important the difference is with respect to the laminar case.

We study the inverse problem of determining the conformational freedom of two protein domains from residual dipolar coupling (RDC) measurements. For each paramagnetic ion attached to one of the domains we obtain a magnetic susceptibility tensor ? from the RDC of couples of atoms of that domain, and a mean paramagnetic susceptibility tensor ?¯ from the RDC of couples of atoms of the other domain. The latter is an integral average of rotations of ? which depends on the conformational freedom of the two domains.