BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quantum state density and critical temperature in M-theory

We discuss the asymptotic properties of quantum states density for fundamental p-branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of the BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory, the critical behavior coincides with the first-order phase transition in the standard string theory at temperature less than the Hagedorn's temperature T-H. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology R-9 circle times T-2. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.

Differential orthogonality: Laguerre and Hermite cases with applications

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamical scaling properties of nanoporous undoped and Sb-doped SnO2 supported thin films during tri- and bidimensional structure coarsening

The coarsening of the nanoporous structure developed in undoped and 3% Sb-doped SnO2 sol-gel dip-coated films deposited on a mica substrate was studied by time-resolved small-angle x-ray scattering (SAXS) during in situ isothermal treatments at 450 and 650 degrees C. The time dependence of the structure function derived from the experimental SAXS data is in reasonable agreement with the predictions of the statistical theory of dynamical scaling, thus suggesting that the coarsening process in the studied nanoporous structures exhibits dynamical self-similar properties. The kinetic exponents of the power time dependence of the characteristic scaling length of undoped SnO2 and 3% Sb-doped SnO2 films are similar (alpha approximate to 0.09), this value being invariant with respect to the firing temperature. In the case of undoped SnO2 films, another kinetic exponent, alpha('), corresponding to the maximum of the structure function was determined to be approximately equal to three times the value of the exponent alpha, as expected for the random tridimensional coarsening process in the dynamical scaling regime. Instead, for 3% Sb-doped SnO2 films fired at 650 degrees C, we have determined that alpha(')approximate to 2 alpha, thus suggesting a bidimensional coarsening of the porous structure. The analyses of the dynamical scaling functions and their asymptotic behavior at high q (q being the modulus of the scattering vector) provided additional evidence for the two-dimensional features of the pore structure of 3% Sb-doped SnO2 films. The presented experimental results support the hypotheses of the validity of the dynamic scaling concept to describe the coarsening process in anisotropic nanoporous systems.

Lap number properties for p-Laplacian problems investigated by Lyapunov methods

In this work we consider a one-dimensional quasilinear parabolic equation and we prove that the lap number of any solution cannot increase through orbits as the time passes if the initial data is a continuous function. We deal with the lap number functional as a Lyapunov function, and apply lap number properties to reach an understanding on the asymptotic behavior of a particular problem. (c) 2006 Published by Elsevier Ltd.

Contact properties of surfaces in r-3 with corank 1 singularities

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)