Separation of copper and bichromate ions by complex methods

Separation of Cu²⁺ and Cr₂O₇ ^2– has been studied by electrodialysis combined with preliminary adsorption on bentonite. The influence of concentration, pH, and electric current on the degree of desalination has been studied. The optimum conditions for almost complete separation of the ions studied have been found. Real galvanic sewage has been examined by this method.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1191–1193, July, 1994.     

Stereoselectivity of electroreduction of a menthone-isomenthone mixture

Electroreduction of an equilibrium menthone-isomenthone mixture at a controlled potential in a diaphragm cell on various cathodes was studied. The influence exerted by the nature of a solvent and of an electrode, electrode material, and various additives on the reduction stereoselectivity of ketones was examined. Conditions for a predominant formation of the most stable of the four isomeric alcohols being formed, menthol, were found.     

Adsorption properties of Ni-Pd catalysts supported on aluminum oxide

The surface composition of Ni-Pd/Al₂O₃ catalysts has been studied using XPES and adsorption methods. The bimetallic catalysts differ from the single-metal Ni and Pd catalysts in the dispersivity of the metal phase which depends on the method of preparation and the presence of K⁺ promoter. A catalyst produced by the immersion method is strongly enriched in Pd compared with impregnated catalysts.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1746–1751, August, 1991.     

Chemisorption and hydrogen spillover on framework ruthenium catalysts

Conclusions Thermal-desorption and isotope methods were used to investigate the state of hydrogen found on the surface of ruthenium framework catalysts. The possibility of the migration of chemisorbed hydrogen from the ruthenium was demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1712–1715, August, 1988.     

Time averages and Boltzmann extremals for Markov chains,discrete Liouville equations,and the Kac circular model

Time averages are proved to coincide with Boltzmann extremals for Markov chains, discrete Liouville equations, and their generalizations. A variational principle is proposed for finding stationary solutions in these cases.     

Kinetic and quantum chemical studies of the mechanism of formation of 1,2-dialkyldiaziridines

The regularities of AlkNHBr consumption in the reaction of formation of 1,2-dialkyldiaziridines in aqueous media were studied for the first time by UV spectrometry. The rate constants of particular steps of the reaction were estimated starting from the possibility of formation of the precursor of 1,2-dialkyldiaziridine, N-halogenaminal, due to the amination of the intermediate iminium cation along with the parallel halogenation of the intermediate gem-diamine. The quantum chemical calculations (DFT, B3LYP, 6–31++G(d,p) and 3–21G basis sets) were performed for the spatial and electronic structures of the compounds and indices of the local reactivity and global electrophilicity of the key intermediates of the reactions. The results of the calculations allowed us to explain the retardation of the reaction when using EtNHBr instead of MeNHBr.     

Representations of general commutation relations

General commutation relations involving creation, annihilation, and particle number operators are considered. Such commutation relations arise in the context of nonstandard Poisson brackets. All possible types of irreducible representations in which the particle number operator or the product of the creation and annihilation operators has a basis of orthonormal eigenvectors are constructed. The irreducible representations that involve the particle number operator reduce to one of four types and those that do not involve the particle number operator reduce to one of five types. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 3, pp. 369–383, December, 1997.     

On the connection of the formulas for entropy and stationary distribution

As is well known in statistical physics, the stationary distribution can be obtained by maximizing entropy. We show how one can reconstruct the formula for entropy knowing the formula for the stationary distribution. A general case is discussed and some concrete physical examples are considered.