Spectral expansions of some representations of Lie groups

We investigate representations of classical noncompact Lie groups induced by representations of the maximal parabolic subgroup. Formulas are obtained for 5O₀(2p, 2q)/U(p, q) and U(2p, 2q) Sp(p, q).Translated from Ukrainskii Mathematicheskii Zhurnal, Vol. 42, No. 1, pp. 128–131, January, 1990.     

Phytoecdysteroids of Rhaponticum carthamoides III. Rhapisterone C

A new ecdysteroid, rhapisterone C, has been isolated from seeds of the plantRhaponticum carthamoides (Willd) Iljin (family Compositae). It has been shown that rhapisterone C is 23-ethylecdysterone.Institute of Chemistry of Plant Substances, Uzbekistan Academy of Sciences, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 231–233, March–April, 1992.     

Synthesis and conversions of metallocycles. 7. A novel approach to the synthesis of 3,4-dialkyl-substituted aluminacyclopentanes in the presence of Cp2ZrCl2

A novel approach was developed for the stereoselective synthesis of trans-3,4-dialkyl-substituted aluminacyclopentanes from -olefins, metallic magnesium, and EtAlCl₂ in the presence of catalytic amounts of Cp₂ZrCl₂. The hydrolysis and deuterolysis products of the 3,4-dialkyl-substituted aluminacyclopentanes obtained are only in the trans configuration.For previous communication, see [1].Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1607–1609, July, 1991.     

Chemical instabilities during oxidation of 1,4-naphthalenediol in a homogeneous medium: II. Thermodynamic analysis and mathematical modeling

A possible mechanism of 1,4-naphthalenediol oxidation in the oscillatory regime has been considered, and a mathematical model describing the kinetics has been developed. Based on a thermodynamic Lyapunov function, it has been shown that the source of chemical instabilities is in the existence of autocatalytic steps and dynamic feedbacks. Qualitative analysis and numerical solution of the set of differential equations that model the reaction kinetics have been performed. The character of the stationary state and the possibility of bifurcations have been determined. The mathematical model satisfactorily describes the processes occurring in the system.     

Many-cluster-systems: models of inhomogeneous matter

First, some general remarks concerning macroscopic “cluster matter” are given. In the second part, three recent, mainly optically and electron-microscopically performed investigations are discussed which deal with special properties of noble metal cluster systems forming the building units of this kind of matter:(1) dressed Au-55 clusters,(2) electromagnetic coupling effects among coagulated clusters,(3) the transition towards compact inhomogeneous matter caused by coalescence of clusters.     

Acetic anhydride as a synthetic reagent

Acetic anhydride has been used widely in synthetic organic chemistry, especially in syntheses and transformations of heterocyclic compounds. These utilities are reviewed under the following classification.     

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