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.     

Coordination properties of 6-deoxy-6-[1-(2-amino) ethylamino]-β-cyclodextrin and the ability of its copper(II) complex to recognize and separate amino acid enantiomeric pairs

The functionalized cyclodextrin 6-deoxy-6-[1-(2-amino)ethylamino]--cyclodextrin was synthesized, and an NMR, EPR, pH-metric, and calorimetric investigation was carried out in aqueous solution in order to ascertain its behaviour towards protonation and copper(II) complex formation. The thermodynamic parameters of the ternary complex formation with alanine, phenylalanine and tryptophan enantiomeric pairs were also determined (25° C andI=0.1 mol dm^–3). No thermodynamic enantioselectivity was observed in these systems, while a chiral, though poor, discrimination was observed in LEC: c.d. spectra also show enantiomeric stereoselectivity. The results of the present investigation, compared with previously reported results, suggest the occurence of acis-complex trans-complex equilibrium in such systems.     

A θ-stable approximations of abstract Cauchy problems

Summary We study the approximation of linear parabolic Cauchy problems by means of Galerkin methods in space andA -stable multistep schemes of arbitrary order in time. The error is evaluated in the norm ofL _t ² (H _x ¹ ) L _t (L _x ² ).     

Breaking of permutation symmetry and diagonal group action: Nielsen model and the standard model as low-energy limit

We point out that, on the basis of a theorem by L. Michel, every model based on the symmetryG ... G has a generic low-energy limit the breaking to diagonal action, i.e., toG. This applies in particular to the proposal by Nielsen to consider such a model withG the standard model group.     

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.     

Properties of Integers and Finiteness Conditions for Semigroups

Let h and k be integers greater than 1; we prove that the following statements are equivalent: 1) the direct product of h copies of the additive semigroup of non-negative integers is not k-repetitive; 2) if the direct product of h finitely generated semigroups is k-repetitive, then one of them is finite. Using this and some results of Dekking and Pleasants on infinite words, we prove that certain repetitivity properties are finiteness conditions for finitely generated semigroups.