Miniversal deformations of matrices of bilinear forms

Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29-43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence. (C) 2011 Elsevier Inc. All rights reserved.

The r-matrix of the Alday-Arutyunov-Frolov model

We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Mail let for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Mail let's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.

Femtosecond laser processing of glassy and polymeric matrices containing metals and semiconductor nanostructures

Tailoring properties of materials by femtosecond laser processing has been proposed in the last decade as a powerful approach for technological applications, ranging from optics to biology. Although most of the research output in this field is related to femtosecond laser processing of single either organic or inorganic materials, more recently a similar approach has been proposed to develop advanced hybrid nanomaterials. Here, we report results on the use of femtosecond lasers to process hybrid nanomaterials, composed of polymeric and glassy matrices containing metal or semiconductor nanostructures. We present results on the use of femtosecond pulses to induce Cu and Ag nanoparticles in the bulk of borate and borosilicate glasses, which can be applied for a new generation of waveguides. We also report on 3D polymeric structures, fabricated by two-photon polymerization, containing Au and ZnO nanostructures, with intense two-photon fluorescent properties. The approach based on femtosecond laser processing to fabricate hybrid materials containing metal or semiconductor nanostructures is promising to be exploited for optical sensors and photonics devices.