Advanced in the synthesis of heterocyclic compounds from aliphatic nitro derivatives. A review

The literature on the synthesis of heterocyclic compounds from aliphatic nitro derivatives in the past decade has been summarized.Moscow State Textile Academy, 117918, Moscow. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1299–1336, October, 1994. Original article submitted October 6, 1994.     

Collisions for the quantum Coulomb Hamiltonian

We study the propagation of phase space singularities for the time dependent Schrödinger equation with potential having Coulomb-type singularities in space dimension equal tothree. We prove that the singularities (frequency set) of the solution are reflected by a Coulomb center exactly as in the classical problem, i.e. the frequency set follows theregularized trajectories of Classical Mechanics after a collision.     

Method of fictitious regions for second-order quasilinear elliptical equations

We consider the application of the fictitious region method to solve the first and second boundary-value problems for a second-order quasilinear elliptical equation. Rate of convergence bounds are obtained for two versions of the fictitious region method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 7–14, 1985     

Role of orientation in kinetics of nucleation and growth of crystals in polymers

A theoretical framework is provided for generalizing the inferences drawn from the results of earlier experimental studies of kinetics of crystallization in oriented poly(ethylene terephthalate). The framework is obtained by combining extensions of classical nucleation theories in polymers^3,4 and a theory of crystal growth with anisotropic incorporation of segments into growing crystals.¹⁵ It is shown that, while a very strong dependence of rate of primary nucleation on orientation does exist, there is a only a much weaker dependence of rate of crystal growth on the orientation of the crystallizing polymer. The theoretical formulation provided here would allow qualitative estimates for comparison with experiments.     

Active interferometer as an antenna for gravitational waves

It is demonstrated that a gain medium in the cavity of the Michelson interferometer that serves as a detector of gravitational waves allows a sharp decrease in the output power of the external laser source.