Spin glass theory: Numerical and experimental results in three-dimensional systems

Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental verifications.     

Direct and inverse computation of Jacobi matrices of infinite iterated function systems

We introduce a new set of algorithms to compute the Jacobi matrices associated with invariant measures of infinite iterated function systems, composed of one–dimensional, homogeneous affine maps. We demonstrate their utility in the study of theoretical problems, like the conjectured almost periodicity of such Jacobi matrices, the singularity of the measures, and the logarithmic capacity of their support. Since our technique is based on a reversible transformation between pairs of Jacobi matrices, it can also be applied to solve an inverse/approximation problem. The proposed algorithms are tested in significant, highly sensitive cases: they perform in a stable fashion, and can reliably compute Jacobi matrices of large order.     

New spline spaces with generalized tension properties

The paper describes a new space of variable degree polynomials. This space is isomorphic to ℙ₆, possesses a Bernstein like basis and has generalized tension properties in the sense that, for limit values of the degrees, its functions approximate quadratic polynomials. The corresponding space of C ³, variable degree splines is also studied. This spline space can be profitably used in the construction of shape preserving curves or surfaces. AMS subject classification (2000)  65D07, 65D17, 65D10     

Metal complexes of C2-symmetric chiral bipyridine ligands. X-ray structure of [bis(nitrato)(4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane cobalt(II)]

Chelating properties of C₂-symmetric chiral bipyridine ligands are discussed. In particular we report the syntheses of the cobalt(II), nickel(II), zinc(II) and copper(II) complexes of (4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane. All compounds have been characterized by IR spectroscopy, and an X-ray diffraction analysis has been carried out on one of them: Co(L)(NO₃)₂. The ligand coordinates the cobalt atom by the two nitrogen donors N(1) and N(2). A seven-membered chelation ring is formed, presenting a remarkable non-crystallographic twofold pseudosymmetry around the axis connecting Co and the midpoint of the C(6)–C(7) bond. The metal also binds two monodentate nitrates, thus completing a distorted coordination tetrahedron.     

Langmuir–Blodgett films of pyridinium-dicyanomethanide dyes mixtures with photobleachable absorption bands

We report on Langmuir-Blodgett (LB) films characterization of 4-[5-dicyanomethanido)thien-2-y1]-N-(n-hexadecyl)pyridinium (C₁₆H₃₃-PDCNT), and 1-(N-(n-hexadecy]-4-pyridinio)-2-[5-(dicyanomethanido)thien-2-yl]ethene (C₁₆H₃₃-PDCNTE); LB films of the pure compounds and of the mixtures of the two compounds were prepared at 291 K: UV-vis investigation revealed the presence of photobleachable absorption bands, the ones at about 530 nm and 640 nm were due to charge transfer transitions of the monomer of C16H33-PDCNT and C₁₆H₃₃-PDCNTE, respectively; the sharp, photobleachable ones shifted to shorter wavelengths were due to H-aggregates of the two compounds. By changing the molar ratios of the two compounds in the mixtures and in other cases by annealing the LB films, the absorption maxima of the sharp, photobleachable bands due to H-aggregates could be tuned in the range 415–467 nm. These LB films are thus very promising in view of optical data storage applications.     

Dynamical systems and numerical analysis: the study of measures generated by uncountable I.F.S.

Measures generated by Iterated Function Systems composed of uncountably many one-dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or singular continuous.