Reflectionless potentials and soliton series of the KDV equation

Potentials of the Schrödinger equation, slowly decreasing at infinity, generate an infinite discrete spectrum converging to zero. The inverse scattering problem in the class of such potentials is solved in a constructive way similarly to the classical soliton theory. An infinite-dimensional system arising from Backlund transformations over soliton solutions plays the role of a determinant representation of the potential. The asymptotics at infinity is derived by use of the Poisson summation formula. An application to the long-time asymptotics of the solution of the Korteweg-de Vries equation is considered.In Memory of Prof. M. C. PolivanovInstitute of Mathematics, Urals Branch, Russian Academy of Sciences, 450000, Chernyshevsky str. 112, Ufa, Russia. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 93, No. 2, pp. 286–301, November, 1992.     

Essential self-adjointness of operators associated with the Cauchy problem for the wave equation

A sufficient Hartman-Ismagilov type condition for the essential self-adjointness of a one-parameter family of unbounded operators that arise in the solution of a Cauchy problem for the wave equation is established. An analog of this result is stated for unbounded integral operators.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 940–948, July, 1992.     

Properties of neodymium-doped aluminophosphate laser glasses

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 1, pp. 90–95, January, 1992.     

Reaction of D2 with palladium fulleride C60Pd4.9

Fullerene deuteride was obtained by the reaction of deuterium with solid palladium fulleride C₆₀Pd_4.9 under fairly mild conditions. The compound was identified by FD-MS, UV-Vis and IR spectroscopies, and TLC.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 483–484, February, 1996     

Olefin terpolymerizations. II. 4-vinylcyclohexene and cyclooctadiene

4-Vinylcyclohexene (VCH) and cyclooctadiene (COD) were investigated as termonomers in EPDM (ethylene/propylene/diene) synthesis by using rac-ethylenebis (1-η⁵-indenyl) zir-conium dichloride ( 1 ) as a catalyst precursor. Homopolymerizations of VCH, vinylcycloh-exane and cyclohexene were compared. The parameter K_πκ_p, which is the apparent rate constant for Ziegler-Natta polymerization, is about the same for VCH and vinylcyclohexanebut is 10 times smaller for cyclohexene. Therefore, the linear olefinic double bond is more active than the cyclic internal double bond. VCH reduces ethylene polymerization rate but not propylene polymerization rate in copolymerizations. In terpolymerizations, VCH tends to suppress ethylene incorporation especially at elevated polymerization temperature and Lowers the polymer MW by about two-fold. COD has very low activity as a termonomer. © 1995 John Wiley & Sons, Inc.     

The boundary equation method in the third initial boundary value problem of the theory of elasticity. Part 2: Methods for approximate solutions

This work considers the methods for solving approximately the four types of boundary equations arising when the third initial boundary value problem of the theory of elasticity is solved with the help of retarded elastic potentials. The convergence of these methods is proved.