Monotonic models and cycles

A partitional model of knowledge is monotonic if there exists a linear order on the state space such that, for every player, each element of her partition contains only a sequence of consecutive states. In monotonic models, the absence of alternating cycles is equivalent to the property that, for every pair of players, the join of their partitions contains only singletons. Under these equivalent conditions any set of posteriors for the players is consistent (i.e., there is a common prior). When checking for consistency in a monotonic model, it is not necessary to evaluate all cycle equations; if the cycle equations corresponding to cycles of length two hold, then there is a common prior.     

A finitely convergent “row-action” method for the convex feasibility problem

We present a modification of the Cyclic Subgradient Projection (CSP) method by Censor and Lent, which solves the convex feasibility problem in a finite number of steps when a Slater type condition holds, while preserving its row-action properties. A linear rate of convergence for the CSP method is established assuming the same hypothesis.Research partially supported by CNPq, under Grant No. 301699/81.     

Structural transformation of MoO<Subscript>3</Subscript> nanobelts into MoS<Subscript>2</Subscript> nanotubes

The structural transformation of MoO₃ nanobelts into MoS₂ nanotubes using a simple sulfur source has been reported. This transformation has been extensively investigated using electron microscopic and spectroscopic techniques including scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), electron diffraction (ED), and energy-dispersive X-ray analysis (SEM-EDAX and TEM-EDX). The method described in this report will serve as a generic route for the transformation of other oxide nanostructures into the chalcogenide nanostructures.     

Enhanced photocatalytic activity of zeolite-encapsulated TiO2 clusters by complexation with organic additives and N-doping.

In the literature it was found that titanium oxide clusters of a few metal atoms encapsulated inside the micropores of zeolite Y exhibit large blue shifts in the Ti-O ligand-to-metal charge-transfer band as compared to non-encapsulated bulk titanium dioxide particles. This blue shift of the Ti-O absorption band is believed to have a negative effect on the photocatalytic activity of zeolite-encapsulated TiO2. We report here on circumventing this problem and increasing visible-light absorption by means of a red shift of the absorption band caused by addition of some organic molecular modifiers containing acidic OH groups that can strongly bind with titanol groups TiOH. In the studied series of zeolite-encapsulated TiO2 samples, the red shift of the optical spectrum follows the order: catechol > 4-aminobenzoic acid > benzoic acid. Also N-doping of zeolite-encapsulated TiO2 clusters by thermal treatment with urea leads to a red shift of the TiO2 absorption band that depends on the annealing and hydration conditions. By comparison to the degradation of phenol in aqueous solution, we have demonstrated that these changes in the absorption spectrum on addition of the organic modifier are also reflected in the photocatalytic activity of the samples; a greater increase in photocatalytic activity (about 30%) was observed for the additive catechol.     

Consecutive palladium-catalyzed Hiyama-Heck reactions in aqueous media under ligand-free conditions

Symmetric and asymmetric (E)-1,2-diarylethenes are synthesized from aryl bromides by consecutive one-pot Hiyama-Heck reactions carried out in water and under air; the only additives required are sodium hydroxide, palladium acetate and poly(ethylene glycol), and the products are isolable in many cases by simple filtration of the water solution.