Fluorine containing phosphazene polymers

In this paper we highlighted the synthesis, characterization, and practical exploitation of different types of polyphosphazenes substituted with fluorinated groups. There are several ways in which fluorine atoms can be inserted into polyphosphazenes, all of which leading to different polymers showing a wide range of characteristics. In general it is true that the insertion of fluorine atoms into phosphazene macromolecules leads to an enhancement of the thermal stability, flame resistance, low-temperature elastomericity, and chemical inertness of the phosphazenes obtained. The contribution of Italian research groups to the preparation and exploitation of organic commercial macromolecules grafted onto fluorinated polyphosphazenes is also reviewed.     

A landscape of time asymmetry

This is a conceptual overview on a polemical subject: the problem of time asymmetry. It is proved that time asymmetry can be considered as a global generalized symmetry breaking, produced by a choice of a physically admissible state space, in a global Gel'fand triplet. The well-known physics of irreversible process can be studied using this mathematical structure and all the arrows of time can be explained and coordinated. But the deeper problems of time definition and time arrow in quantum gravity remain outside of this landscape.     

Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

Higher order bad loci

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.     

Laser nanosources based on planar photonic crystals as new platforms for nanophotonic devices

Two-dimensional photonic crystal lasers have been fabricated on III–V semiconductor slabs. Tuning of the spontaneous emission in micro and nanocavities has been achieved by accurate control of the slab thickness. Different structures, some of them of new application to photonic crystal lasers, have been fabricated like the Suzuki-phase or the coupled-cavity ring-like resonators. Laser emission has been obtained by pulsed optical pumping. Optical characterization of the lasing modes have been performed showing one or more laser peaks centred around 1.55 μm. Far field characterization of the emission pattern has been realized showing different patterns depending on the geometrical shape of the structures. These kinds of devices may be used as efficient nanolaser sources for optical communications or optical sensors.     

Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method

In this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains. Numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies.

     

A fractal analysis of skin pigmented lesions using the novel tool of the variogram technique

The incidence of the cutaneous malignant melanoma is increasing rapidly in the world [Ferlay J, Bray F, Pisani P, et al. GLOBOCAN 2000: Cancer incidence, mortality and prevalence worldwide, Version 1.0 IARC Cancer Base no. 5. Lyon: IARC Press, 2001]. The therapeutic address requires a method having high sensitivity and capability to diagnose such disease at an early stage. We introduce a new diagnostic method based on non-linear methodologies. In detail we suggest that fractal as well as noise and chaos dynamics are the most important components responsible for genetic instability of melanocytes. As consequence we introduce the new technique of the variogram and of fractal analysis extended to the whole regions of interest of skin in order to obtain parameters able to identify the malignant lesion. In a preliminary analysis, satisfactory results are reached.     

Ab initio X-ray powder diffraction characterisation of molecule-based magnetic materials

Use of ab initio X-ray powder diffraction (XRPD) methods in the study of magnetically active species of covalent nature is presented. Selected cases are chosen in order to underline the power of XRPD methodologies, highlighting the importance of independent physico-chemical information from ancillary techniques.