Kinetics of first-order phase transitions in the asymptotic stage

We construct an asymptotic theory that describes the kinetics of first-order phase transitions. The theory is a considerable refinement of the well-known Lifshits-Slezov theory. The main difference between the two is that the Lifshits—Slezov theory uses for the first integral of the kinetic equation an approximate solution of the characteristic equation, which is valid in the entire range of sizes except for the blocking point, i.e., it uses a nonuniformly applicable approximation. At the same time, the behavior of the characteristic solution near the blocking point determines the asymptotic behavior of the size distribution function of the nuclei for the new phase. Our theory uses a uniformly applicable solution of the characteristic equation, a solution valid at long times over the entire range of sizes. This solution is used to find the asymptotic behavior of all basic properties of first-order phase transitions: the size distribution function, the average nucleus size, and the nucleus density. Zh. éksp. Teor. Fiz. 113, 2193–2208 (June 1998)     

Cycloaddition reactions of methyl 2-N-trifluoroacetyliminotrifluoropropionate

Conclusions The methyl ester of 2-(N-trifluoroacetylimino)trifluoropropionic acid reacts with diazo-alkanes at the isolated C=N bond similarly to azomethines, forming [1+2]- and/or [3+2]-cycloadducts, and with unsaturated donating type compounds as a 1,3-dipolar conjugated system to give products of [2+4]-cycloaddition regio- and stereo-selectively.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 132–136, January, 1988.     

On the theory of differential games in systems with aftereffect : PMM vol. 42, no. 6, 1978 pp.969–977

An encounter-evasion differential game is studied for control systems with aftereffect [1–4]. A feature of the system being analyzed is that it has a time-lag effect with respect to the controls which provides the system with important new peculiarities. Using the investigations in [1–4], conditions for the solvability of the problem are indicated and the required control procedures are constructed.