Effect of the rhenium additive to VOx/TiO2 and MoOx/TiO2 catalysts on their properties in oxidative dehydrogenation of propane

VO_x/TiO₂ and MoO_x/TiO₂ catalysts with the addition of Re (Re/V or Mo = 0.5) were synthetized and tested in oxidative dehydrogenation of propane and in reduction by propane. XPS measurements showed depletion of the surface in Re. The Re additive does not affect the total conversion of propane, but increases the selectivity to propene. The effect is more pronounced for the MoO_x/TiO₂ catalyst. The increase in the selectivity to propene is accompanied with the increase in the reducibility of the catalysts.     

From finitary to infinitary second‐order logic

A back and forth condition on interpretations for those second‐order languages without functional variables whose non‐logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language. When applied to second‐order languages with an infinite non‐logical vocabulary, excluding functional constants, the back and forth condition is sufficient but not necessary. It is shown that there is a class of infinitary second‐order languages whose non‐logical vocabulary is infinite for which the back and forth condition is both necessary and sufficient. It is also shown that some applications of the back and forth construction for second‐order languages can be extended to the infinitary second‐order languages. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inertial Manifolds for von Karman Plate Equations

Inertial manifolds associated with nonlinear plate models governed by dynamical von Karman equations are considered. Three different dissipative mechanisms are discussed: viscous, structural and thermal damping. Though the systems considered are subject to some dissipation, the overall dynamics may not be dissipative. This means that the energy may not be decreasing. The main result of the paper establishes the existence of an inertial manifold subject to the spectral gap condition for linearized problems. The validity of the spectral gap condition depends on the geometry of the domain and the type of damping. It is shown that the spectral gap condition holds for plates of rectangular shape. In the case of viscous damping, which is associated with hyperbolic-like dynamics, it is also required that the damping parameter be sufficiently large. This last requirement is not needed for other types of dissipation considered in the paper.     

Global existence to a three‐dimensional non‐linear thermoelasticity system arising in shape memory materials

This paper is concerned with the unique global solvability of a three‐dimensional (3‐D) non‐linear thermoelasticity system arising from the study of shape memory materials. The system consists of the coupled evolutionary problems of viscoelasticity with non‐convex elastic energy and non‐linear heat conduction with mechanical dissipation. The present paper extends the previous 2‐D existence result of the authors Reference [1] to 3‐D case. This goal is achieved by means of the Leray–Schauder fixed point theorem using technique based on energy arguments and DeGiorgi method. Copyright © 2004 John Wiley & Sons, Ltd.     

Raman spectroscopy studies of structural changes in hydrated titanium and tin dioxide gels under drying

Raman spectroscopy is used in this work to reveal an increase in the size of anatase crystallites in the process of drying of hydrated titanium dioxide gel and ordering of the structure of primary particles of hydrated tin dioxide gel under drying. Raman spectra are interpreted with account of dimensional effects. It is found that mechanical stresses that arise in the materials under drying have a great effect on the structural changes found there. TERMOXIDE Research and Production Company, 624051 Zarechnyi, Sverdlovsk Region, P/O Box 94, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 266–268, March–April, 1997.     

4-Nitrophenyl N-(1-Aryl-2,2,2-trifluoroethylidene)urethanes: Novel 1,3-Electrophilic Components of Reactions Leading to 6- and 7-Membered Heterocycles

We propose an approach to synthesis of N,O,S-containing 6- and 7-membered heterocycles based on using 4-nitrophenyl N-(1-aryl-2,2,2-trifluoroethylidene)urethanes as the electrophilic components in heterocyclizations with bifunctional nucleophilic reagents.     

The minimal free resolution of a Borel ideal

We consider the Eliahou–Kervaire minimal free resolution of a 0-Borel ideal and its applications.     

Characteristics of wave processes in earth under the action of explosions of charges with air sheaths

Given here are the results of experimental investigations of wave processes in earth under the action of explosions of charges surrounded by sheaths of air, and some general laws are established.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 105–110, March–April, 1972.