Kähler manifolds of quasi-constant holomorphic sectional curvature

In correspondence with the manifolds of quasi-constant sectional curvature defined (cf [5], [9]) in the Riemannian context, we introduce in the K?hlerian framework the geometric notion of quasi-constant holomorphic sectional curvature. Some characterizations and properties are given. We obtain necessary and sufficient conditions for these manifolds to be locally symmetric, Ricci or Bochner flat, K?hler η-Einstein or K?hler-Einstein, etc. The characteristic classes are studied at the end and some examples are provided throughout.      

On the structural stability of thermoelastic model of porous media

In the present paper we study the structural stability of the mathematical model of the linear thermoelastic materials with voids. We prove that the solutions of problems depend continuously on the constitutive quantities, which may be subjected to error or perturbations in the mathematical modelling process. Thus, we assume to have changes in the various coupling coefficients of the model and then we establish estimates of continuous dependence of solutions. We have to outline that such estimates play a central role in obtaining approximations to these kinds of problems. To derive a priori estimates for a solution we first establish appropriate bounds for the solutions of certain auxiliary problems. These are achieved by means of so‐called Rellich‐like identities. We also investigate how the solution in the coupled model behaves as some coupling coefficients tend to zero. Copyright © 2007 John Wiley & Sons, Ltd.     

Quadrature rule-based bounds for functions of adjacency matrices

Bounds for entries of matrix functions based on Gauss-type quadrature rules are applied to adjacency matrices associated with graphs. This technique allows to develop inexpensive and accurate upper and lower bounds for certain quantities (Estrada index, subgraph centrality, communicability) that describe properties of networks.     

Photocatalytic titania based surfaces: Environmental benefits

The use of photocatalytic titania nanoparticles in the development of self-cleaning and de-polluting paints and microbiological surfaces is demonstrated. In the former case surface erosion and sensitised photooxidation is shown to be controlled by the use of catalytic grades of anatase nanoparticles. For environmental applications in the development of coatings and cementitious materials for destroying atmospheric pollutants such as nitrogen oxides (NOX) stable substrates are also illustrated with photocatalytic nanoparticles. Here porosity of the coatings through calcium carbonate doping is shown to be crucial in the control of the effective destruction of atmospheric NOX gases. Good environmental stability of the coatings is also crucial for long-term durability and this aspect is examined for a variety of material substrates. For the development of microbiological substrates for the destruction of harmful bacteria/fungi effective nanoparticle anatase titania is shown to be important with hydrated high surface area particles giving the greatest activity. Data from commercial pilot studies is used to signify the important practicalities of this type of new technology.     

Rate of Convergence in Trotter’s Approximation Theorem

We give a quantitative estimate of the convergence in Trotter’s approximation theorem on the convergence of iterates of linear operators to an assigned semigroup. An application is given concerning the classical Bernstein operator on the d-dimensional simplex.      

Calibration-quality adiabatic potential energy surfaces for H3(+) and its isotopologues

Calibration-quality ab initio adiabatic potential energy surfaces (PES) have been determined for all isotopologues of the molecular ion H(3)(+). The underlying Born-Oppenheimer electronic structure computations used optimized explicitly correlated shifted Gaussian functions. The surfaces include diagonal Born-Oppenheimer corrections computed from the accurate electronic wave functions. A fit to the 41,655 ab initio points is presented which gives a standard deviation better than 0.1 cm(-1) when restricted to the points up to 6000 cm(-1) above the first dissociation asymptote. Nuclear motion calculations utilizing this PES, called GLH3P, and an exact kinetic energy operator given in orthogonal internal coordinates are presented. The ro-vibrational transition frequencies for H(3)(+), H(2)D(+), and HD(2)(+) are compared with high resolution measurements. The most sophisticated and complete procedure employed to compute ro-vibrational energy levels, which makes explicit allowance for the inclusion of non-adiabatic effects, reproduces all the known ro-vibrational levels of the H(3)(+) isotopologues considered to better than 0.2 cm(-1). This represents a significant (order-of-magnitude) improvement compared to previous studies of transitions in the visible. Careful treatment of linear geometries is important for high frequency transitions and leads to new assignments for some of the previously observed lines. Prospects for further investigations of non-adiabatic effects in the H(3)(+) isotopologues are discussed. In short, the paper presents (a) an extremely accurate global potential energy surface of H(3)(+) resulting from high accuracy ab initio computations and global fit, (b) very accurate nuclear motion calculations of all available experimental line data up to 16,000 cm(-1), and (c) results suggest that we can predict accurately the lines of H(3)(+) towards dissociation and thus facilitate their experimental observation.     

Atropisomers of hindered triarylisocyanurates: structure, conformation, stereodynamics, and absolute configuration

The syn and anti diastereoisomers of some 1,3,5-triarylisocyanurate derivatives were isolated and their configuration assigned by NOE experiments and by X-ray diffraction. The kinetics of the syn/anti interconversion were determined, and the experimental activation energies matched satisfactorily the values predicted by DFT computations. Low-temperature NMR spectra were employed to determine the rotation barrier of N-bonded unhindered aryl substituents: these barriers, too, are satisfactorily reproduced by DFT computations. In the case of racemic diastereoisomers, the two expected enantiomers (atropisomers) were isolated by enantioselective HPLC and the absolute configuration established by DFT simulation of the electronic and vibrational circular dichroism spectra.     

Xylanase and β-Xylosidase Production by <Emphasis Type="BoldItalic">Aspergillus ochraceus</Emphasis>: New Perspectives for the Application of Wheat Straw Autohydrolysis Liquor

The xylanase biosynthesis is induced by its substrate—xylan. The high xylan content in some wastes such as wheat residues (wheat bran and wheat straw) makes them accessible and cheap sources of inducers to be mainly applied in great volumes of fermentation, such as those of industrial bioreactors. Thus, in this work, the main proposal was incorporated in the nutrient medium wheat straw particles decomposed to soluble compounds (liquor) through treatment of lignocellulosic materials in autohydrolysis process, as a strategy to increase and undervalue xylanase production by Aspergillus ochraceus. The wheat straw autohydrolysis liquor produced in several conditions was used as a sole carbon source or with wheat bran. The best conditions for xylanase and β-xylosidase production were observed when A. ochraceus was cultivated with 1% wheat bran added of 10% wheat straw liquor (produced after 15 min of hydrothermal treatment) as carbon source. This substrate was more favorable when compared with xylan, wheat bran, and wheat straw autohydrolysis liquor used separately. The application of this substrate mixture in a stirred tank bioreactor indicated the possibility of scaling up the process to commercial production.     

Update on selective oxidation using gold

This critical review aims to update the recent development in the selective oxidation of organic compounds by gold catalysis, highlighting the progress in the last three years. Following the impressive developments in the last decades, several protocols for catalytic oxidation are today available, which are based on the extraordinary properties of gold in terms of catalytic activity, selectivity, reusability and resistance to poisons. Beside many other applications, gold can be recommended for green processes dedicated to fine chemicals, pharmaceuticals and the food industry owing to its recognized bio-compatibility. The collected literature is focused on experiments concerning the oxidation of different chemical groups and could be of interest, in the wide area of organic chemistry, for improving previous processes or for exploring new catalytic pathways (174 references).