Joint probability distribution of nonmarkovian SDE

We obtain a time convolutionless partial differential equation for the two events joint probability distribution of nonmarkovian processes defined by stochastic differential equations with colored noise. As an example we discuss nonmarkovian brownian motion.     

Thermogravimetric Analysis for Acidity Determination in Pillared Clays

Thermogravimetric analysis of pyridine adsorption was applied to study the acidity at different temperatures of clays pillared with Al pillars and mixed Al-Ga pillars, in relation to the starting montmorillonite. These results were compared with those obtained by means of a pulse-chromatographic technique. The pillaring process produces a large number of acid centers in the samples. Al-Ga-PILC has a higher acidity than Al-PILC. This revised version was published online in July 2006 with corrections to the Cover Date.     

Polarization and Transverse Mode Behaviour of VCSELs under Optical Injection

A theoretical analysis of the polarization and transverse modes of Vertical-cavity Surface-emitting lasers with external optical injection is performed. We show that, for single-mode operation, weak injection of linearly polarized light can lead to stable output power in the injected polarization. We also show that, for multitransverse mode operation, weak injection of linearly-polarized light can lead to stable emission of the fundamental transverse mode in the injected polarization over wide current ranges. The previous selection can occur when the transverse modes have parallel or orthogonal polarizations.     

Selectivity in the conversion of n-heptane on an Al-PILC modified with Ga

This work compares the catalytic activity for the hydroisomerization and hydrocracking of n-heptane for two pillared clay materials, one with polyoxycations of Al and the other with the same cation modified by the inclusion of Ga. The conversion rate for the clay pillared with mixed cations is lower than that for the material pillared only with aluminum throughout the temperature range, which is attributable to its smaller specific surface area. However, at high temperatures the conversion rate of the material with mixed pillars continues to rise steadily, indicating a greater thermal stability. The incorporation of Ga also increases the selectivity for isomerization.     

Synthesis,characterization and catalytic performance of Al-MCM-41 mesoporous materials

A series of MCM-41 molecular sieves has been synthesized by using different Si/Al molar ratios and appropriate conditions for the synthesis. Silica fumed and sodium aluminate, both of inorganic origin, have been used in the synthesis, avoiding the use of organic sources. Isomorphous substitution of silicon in tetrahedral framework positions of structure by Al in the Al-MCM-41 material was observed by ²⁷Al NMR and ²⁹Si NMR spectra. The nitrogen adsorption isotherms of the samples showed higher specific surface area and more mesopore volume when there was an increase in the aluminium content. Simultaneously, a smaller thickness of the wall and diameter pore by XRD was observed. At higher degrees of incorporation of aluminium, the acidity of the samples increased, as is clearly shown by the results of temperature-programmed desorption of ammonia and pyridine adsorption by IR. As more aluminium was incorporated into the samples, the higher were the catalytic performances. The increase of the conversion, in hydroisomerization of n-heptane, shows that these materials acted as acid catalysts. This increase in the total conversion is related to the higher number of acid sites in the samples.     

Random walk in dynamically disordered chains: Poisson white noise disorder

Exact solutions are given for a variety of models of random walks in a chain with time-dependent disorder. Dynamic disorder is modeled by white Poisson noise. Models with site-independent (global) and site-dependent (local) disorder are considered. Results are described in terms of an affective random walk in a nondisordered medium. In the cases of global disorder the effective random walk contains multistep transitions, so that the continuous limit is not a diffusion process. In the cases of local disorder the effective process is equivalent to usual random walk in the absence of disorder but with slower diffusion. Difficulties associated with the continuous-limit representation of random walk in a disordered chain are discussed. In particular, we consider explicit cases in which taking the continuous limit and averaging over disorder sources do not commute.