Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Novel silica membrane material for molecular sieve applications

Development of new silica membranes properties, e.g., molecular sieving properties, has been increasingly gaining importance in the last few years. A novel unsupported silica membrane, referred to as hydrophobic metal-doped silica, was developed by cobalt-doping within the organic templated silica matrix. The novel material was prepared by the acid-catalyzed hydrolysis and condensation process of tetraethylorthosilicate (TEOS) and methyltriethoxysilane (MTES), which is the precursor for methyl ligand covalently bounded to the silica matrix. The synthesis and surface properties of the novel unsupported silica membrane as well as the unsupported blank silica and modified silica membranes were revealed by surface and microstructural techniques, such as water contact angle measurement, FTIR, X-ray, Solid-state 29Si MAS NMR, TGA and N2 and CO2 adsorption measurements. The results showed that the thermal stability of the organic templated silica matrix was enhanced by cobalt-doping process. A hydrophobic microporous silica membrane material with high thermal stability up to ∼560 °C in oxidizing atmosphere and a narrow pore size distribution centered at 1.1 nm was obtained. Therefore, a novel precursor material for molecular sieve silica membranes applications has been achieved and developed.

Photogeneration of Hydrogen from Water by Hybrid Molybdenum Sulfide Clusters Immobilized on Titania

Two new hybrid molybdenum(IV) Mo3S7 cluster complexes derivatized with diimino ligands have been prepared by replacement of the two bromine atoms of [Mo3S7Br6]2− by a substituted bipyridine ligand to afford heteroleptic molybdenum(IV) Mo3S7Br4(diimino) complexes. Adsorption of the Mo3S7 cores from sample solutions on TiO2 was only achieved from the diimino functionalized clusters. The adsorbed Mo3S7 units were reduced on the TiO2 surface to generate an electrocatalyst that reduces the overpotential for the H2 evolution reaction by approximately 0.3 V (for 1 mA cm−2) with a turnover frequency as high as 1.4 s−1. The nature of the actual active molybdenum sulfide species has been investigated by X-ray photoelectron spectroscopy. In agreement with the electrochemical results, the modified TiO2 nanoparticles show a high photocatalytic activity for H2 production in the presence of Na2S/Na2SO3 as a sacrificial electron donor system.