LOCALIZED FAMILIES OF BENDING WAVES IN A THIN MEDIUM-LENGTH CYLINDRICAL SHELL UNDER PRESSURE

The initial-boundary-value problem for the equations describing motion of a thin, medium-length, non-circular cylindrical shell is examined. The shell edges are not necessarily plane curves, with the conditions of a joint support, a rigid clamp or a free edge being considered as the boundary conditions. The shell is supposed to experience normal internal (or external) dynamic pressure which may be non-uniform in the circumferential direction. It is assumed that the initial displacements and velocities of the points at the shell middle surface are functions decreasing rapidly away from some generatrix. Using the complex WKB method the asymptotic solution of the governing equations is constructed by superimposing localized families (wave packets) of bending waves running in the circumferential direction. The dependence of frequencies, group velocities, amplitudes and other dynamic characteristics upon variable pressure and geometrical parameters of the shell are studied. As an example, the wave forms of motion of a circular cylindrical shell with sloping edges under growing dynamic pressure are considered. The effect of localization of bending vibrations near the longest generator as well as the effects of reflection, focusing and increasing amplitude in the running wave packets are revealed.     

The dependence of electron capture rate constants on some molecular parameters

We have analyzed the dependence of the thermal electron capture rate constant on molecular parameters as dipole moment, electronic and orientational polarizabilities. We have found that there is a linear dependence between the logarithm of the rate constant and the electronic polarizability on the electron-accepting center.     

Asymptotic expansions of solutions to singularly perturbed systems

Under the condition that a degenerate system has an exponentially stable integral manifold, an asymptotic expansion of the Cauchy problem that generalizes the well known Vasil'eva expansion is constructed for a perturbed system.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 552–560, April, 1993.     

On complementability of certain generalized hypercenters in Artinian modules

We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.     

Photoionization of impurities in heterojunctions

The spectral dependence of the photoionization cross-section is calculated for shallow donors in GaAs/GaAlAs heterojunctions. The resulting spectra is found to be different for light polarized along and perpendicular to the growth direction. The calculations are repeated for both infinite- and finite-barrier models.     

High-frequency asymptotic behavior of the electromagnetic field on the surface of a stratified medium

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 174–180, Izd. Moskovskogo Universiteta, Moscow, 1990.     

On the localization of topological invariants

The approach of formal differential geometry to the topological invariants which can be localized is developed. The universal space and universal characteristic forms are constructed. They give rise to primary and secondary characteristic forms.     

Metabelian groups with a single defining relation and the Magnus embedding

Translated from Matematicheskie Zametki, Vol. 47, No. 4, pp. 597–605, April, 1995.