On compactly-supported approximation of closed differential forms on Riemannian manifolds of special type

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 3, pp. 102–117, May–June, 1993.     

Monoarylhydrazones of di- and tricarbonyl compounds in the knorr synthesis of pyrroles

A method was developed for the preparation of various pyrrole, tetrahydroindole, and octahydrocarbazole derivatives from the monophenylhydrazones of di- and tricarbonyl compounds. As a rule, the yields of the substituted pyrroles obtained were higher than those obtained via the Knorr method using isonitroso ketones.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 342–344, March, 1972.     

Macrokinetics of decomposition of loose packed RDX in shock and detonation waves

The boundary retardation method was used to study the decomposition of loose packed density RDX behind the front of shock waves with amplitudes ranges from values critical for reaction initiation to those typical of detonation. The threshold pressure P* and temperature T* at which the transition from a relatively slow decomposition in hotspots to fast bulk conversion occurs. It was demonstrated that this transition is associated with a change in the macrokinetics of the conversion of HE material behind the shock front. At pressures below P*, an analogy with the kinetic regularities of the thermal decomposition of RDX at normal pressure is observed. At P > P*, the conversion occurs in the regime of an adiabatic thermal explosion at a very high rate and has no analogues in chemical kinetics. The normal detonation regime is realized at P > P*. It was shown that the macrokinetic characteristics of normal detonation cannot be described within the framework of traditional approaches, with the help of the Arrhenius law or the concept of deflagration propagating from hotspots.     

Maslov's complex germ and the asymptotic formula for the Gibbs canonical distribution

The Gibbs canonical distribution for a system of N classical particles is studied under the following conditions: the external potential isO(1), the potential of pairwise interaction isO(1/N), the potential of triple interaction isO(1/N ²), etc. The asymptotics of free energy and of the partition function asN is found. An asymptotic formula approximating the normalized canonical distribution in theL ¹ norm asN is also constructed. It is proved that the chaos property is satisfied fork-particle distributions,k = const, and is not satisfied for theN-particle distribution.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 622–636, October, 1998.The author wishes to thank Professor V. P. Maslov, member of the Russian Academy of Sciences, for setting the problem, permanent attention to the work, useful discussion on a number if issues, and valuable remarks.This research was supported by the Royal Society of Great Britain.