Generalized Drinfel'd-Sokolov hierarchies

A general approach is adopted to the construction of integrable hierarchies of partial differential equations. A series of hierarchies associated to untwisted Kac-Moody algebras, and conjugacy classes of the Weyl group of the underlying finite Lie algebra, is obtained. The generalized KdV hierarchies of V.G. Drinfel'd and V.V. Sokolov are obtained as the special case for the Coxeter element. Various examples of the general formalism are treated in some detail; including the fractional KdV hierarchies.     

Polynomial decay and control of a 1−d hyperbolic-parabolic coupled system

In this paper we consider a linearized model for fluid-structure interaction in one space dimension. The domain where the system evolves consists in two parts in which the wave and heat equations evolve, respectively, with transmission conditions at the interface. First of all we develop a careful spectral asymptotic analysis on high frequencies for the underlying semigroup. It is shown that the semigroup governed by the system can be split into a parabolic and a hyperbolic projection. The dissipative mechanism of the system in the domain where the heat equation holds produces a slow decay of the hyperbolic component of solutions. According to this analysis we obtain sharp polynomial decay rates for the whole energy of smooth solutions. Next, we discuss the problem of null-controllability of the system when the control acts on the boundary of the domain where the heat equation holds. The key observability inequality of the dual system with observation on the heat component is derived though a new Ingham-type inequality, which in turn, thanks to our spectral analysis, is a consequence of a known observability inequality of the same system but with observation on the wave component.     

Mesogenic behaviour in some pyrazole and isoxazole derivatives

Several aromatic β-diketones with a different number of alkyloxy groups in the aromatic rings and their derived pyrazoles, isoxazoles and thallium (I) complexes have been synthesized. The potential mesomorphic properties of these compounds have been investigated by optical microscopy, DSC and X-ray diffraction. The pyrazoles and isoxazoles with one chain in each aromatic ring are mesogenic, showing smectic A and smectic C mesophases, whereas the pyrazoles and isoxazoles with two chains per ring and the β-diketones and thallium complexes are not. The mesogenic potentiality is shown to be related to the molecular linearity and to the number of alkyloxy groups. To the best of our knowledge, this is the first time liquid crystal properties have been described for pyrazole and isoxazole derivatives.     

Structure of CdS/SiO2 Nanocomposites: Influence of the Precursor and Cd Concentration

The influence of using TMOS or TEOS in the formation of CdS quantum dots in a silica matrix have been studied by X-ray absorption spectroscopy (XAS). The amount of Cd-S bonds have been monitored as a function of the nominal Cd concentration. The relative amount of CdS crystals depends on the precursor. The use of TEOS is not recommended because it gives a poor yield, especially for high Cd concentration. A discussion of the influence of CdS concentration in matrices from TMOS is carried out from structural models created from their pore volume distribution. The mean pore size becomes smaller and the size distribution more uniform when CdS concentration increases but the nanocrystals of low CdS nominal content present a more efficient quantum confinement.     

Systematic study of horizontal gauge theories

We analyze all the possible continuous horizontal gauge groups G _H in relation with their possibility to explain m _b ? m _t. We assume that the only effective fermionic degrees of freedom correspond to the known fermions but allow the possibility of adding a right handed neutrino to each family. We assume that the Higgs fields which generate masses for these fermions, trough renormalizable Yukawa couplings, transform as an irreducible representation of SU(3)_c ? SU(2)_L ? U(1)_Y ? G_H. Under these assumptions we find two U(1)_H or U(1) _H1 ? U(1) _H2 models free of anomalies and able to guarantee that only the top has a renormalizable mass-generating Yukawa coupling.     

Sine-Gordon solitons in the presence of a noisy potential

We study the interaction of sine-Gordon solitons with two kinds of impurity potentials localized in space and varying randomly in time. the production of modified kink-antikink pairs is observed with different features depending respectively on the additive or multiplicative nature of the noise.     

Grand unification with local supersymmetry

We study general conditions for obtaining spontaneous breaking of local supersymmetry in N = 1 supergravity coupled to supersymmetric matter. We consider in particular the coupling of N = 1 supergravity to grand unified theories like SU(5) and study the conditions which must be met in order to obtain a realistic model. Specific models are built in which local supersymmetry is broken at a scale √M_Wm_p ～ 10¹⁰ GeV. This breaking of supersymmetry is only detected at low energies through soft terms breaking explicitly the global supersymmetry. These soft terms (scalar masses, gaugino masses and trilinear scalar couplings) are renormalized at low energies according to the renormalization group. The (mass)² of the Higgs doublet evolve towards negative values at low energies giving rise to SU(2) × U(1) breaking as a radiative effect of local supersymmetry breaking. We finally point out the possible relevance of non-renormalizable superpotentials for the problem of fermion masses.