Here we give mathematical support to the choice of the Helmholtz versus the Laplace equation for the formulation of an inverse problem in infrared thermography. Such a choice accounts for the values of physical parameters like the thermal conductivity and the Biot number. We check the effectiveness of the corresponding boundary value problems and compare the condition numbers. The Helmholtz choice is confirmed to be usually better, but there are cases in which Laplace (less expensive) works well.

The turning circle manoeuvre of a self-propelled tanker like ship model is numerically simulated through the integration of the unsteady Reynolds Averaged Navier-Stokes (URANS) equations coupled with the equations of the motion of a rigid body. The solution is achieved by means of the unsteady RANS solver developed at CNR-INSEAN. The model is considered with two different stern appendages configurations (each one providing a different dynamic behaviour): twin screw with a single rudder and twin screw, twin rudder with a central skeg.

The problem of ship manoeuvrability has reached nowadays a significant consideration, both for merchant ships, with the adoption of IMO standards, and naval ships, with the production of various documents by NATO Specialist Teams. In literature many works regarding manoeuvrability of single screw slow/medium speed ships are present, while a lack of information about twin screw ships (cruise ships, RoRo ferries, megayachts, naval vessels) exists.

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].