Surface ablation by excimer laser irradiation of Ti and Ti6Al4V alloy

This paper presents the surface microstructure of Ti and Ti6Al4V alloy irradiated with a high output energy XeCl ( = 308 nm) excimer laser. The treatments are carried out on both materials at two beam fluences and the effects of single- and multiple-pulse irradiation are compared. The results of the scanning electron microscopy and of the X-ray diffraction techniques suggest the possible influence of both time-behaviour and energy fluence of the laser pulse on the relative weight of the ablation rate and of the reaction product deposition rate at the sample surface.     

The modified bordering method to evaluate eigenvalues and eigenvectors of normal matrices

A bordering procedure is here proposed to evaluate the eigensystem of hermitian matrices, and more in general of normal matrices, when the spectral decomposition is known of then–1×n–1 principal minor. The procedure is also applicable to special real and nonsymmetric matrices here named quasi-symmetric. The computational cost to write the characteristic polynomial isO(n ²), using a new set of recursive formulas. A modified Brent algorithm is used to find the roots of the polynomial. The eigenvectors are evaluated in a direct way with a computational cost ofO(n ²) for each one. Some numerical considerations indicate where numerical difficulties may occur. Numerical results are given comparing this method with the Givens-Householder one.     

Minimum blocking configurations

Some results on configurations realizing minimum blocking sets of a finite projective plane are obtained by introducing a suitable attraction property.Dedicated to Professor M. Scafati Tallini on the occasion of her 65th birthday     

A smooth method for the finite minimax problem

We consider unconstrained minimax problems where the objective function is the maximum of a finite number of smooth functions. We prove that, under usual assumptions, it is possible to construct a continuously differentiable function, whose minimizers yield the minimizers of the max function and the corresponding minimum values. On this basis, we can define implementable algorithms for the solution of the minimax problem, which are globally convergent at a superlinear convergence rate. Preliminary numerical results are reported.This research was partially supported by the National Research Program on Metodi di ottimizzazione per le decisioni, Ministero dell'Università e della Ricerca Scientifica e Tecnologica, Italy.