On the Robustness of Gaussian Elimination with Partial Pivoting

It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.     

Close-loop three-laser scheme for chaos-encrypted message transmission

In this paper, we numerically evaluate private data transmission using a three-laser scheme, consisting of a pair of twin semiconductor lasers, driven to chaos by delayed optical feedback in a short cavity, and optically injected by a third chaotic laser which forces them to synchronize. This laser is selected with different internal parameters with respect to the twin pair, so that the emissions of the synchronized, matched lasers, are highly correlated, whereas their correlation with the driver is low. The digital message modulates the emission of the transmitter, as in a standard Chaos Modulation scheme. Message recovery is then obtained by subtracting, from the transmitted chaos-masked message, the chaos, locally generated by the synchronized receiver laser. Simulations have been performed with the Lang-Kobayashi model, and, in view of application to private transmission, we have investigated the effect of the parameter mismatch, between transmitter and receiver, on message recovery. A preliminary experimental evaluation has been also performed using specially designed InP integrated modules.     

Aziridination of 3-methyl-4-nitro-5-styrylisoxazoles

Herein we describe the preparation of a novel class of isoxazolyl aziridines. The products were obtained exclusively as cis diastereoisomers.     

Bismuth Modified Gold Microelectrode for Pb(II) Determination in Wine Using Alkaline Medium

Electrodeposition of bismuth on gold microelectrodes for determination of Pb(II) by square wave anodic stripping voltammetry (SWASV) was accomplished by an in situ procedure in alkaline solution. A linear calibration plot for Pb(II) in the concentration range 40 to 6700 nmol L^?1 (r=0.998) was obtained, the detection limit was found to be 12.5 nmol L^?1 (S/N=3) and the relative standard deviation in solutions containing 1 μmol L^?1 Pb(II) was 4% (n=12). The analytical performance of the proposed sensor was tested by measuring the Pb(II) concentration in a wine sample. The result was in good agreement with the one obtained by GFAAS.     

Decomposition of formamide assisted by microwaves, a tool for synthesis of nitrogen-containing heterocycles

Generation of ammonia via thermal decomposition of formamide was studied under microwave conditions to provide an efficient tool for the synthesis of nitrogen-containing heterocycles. Quinazolin-4-ones, which are known as building blocks for molecules with pharmaceutical interest, were chosen as examples. Our work confirms that reactants may have different behaviours under microwaves, depending on power input, reached temperature and pressure in the vials. Full control and fine tuning of these parameters are achievable using modern microwave technology.     

A globally convergent descent method for nonsmooth variational inequalities

We propose a descent method via gap functions for solving nonsmooth variational inequalities with a locally Lipschitz operator. Assuming monotone operator (not necessarily strongly monotone) and bounded domain, we show that the method with an Armijo-type line search is globally convergent. Finally, we report some numerical experiments. This work has been supported by the National Research Program PRIN/2005017083 “Innovative Problems and Methods in Nonlinear Optimization”.