Surface deformation. I

This article surveys results on the theory of deformation and infinitesimal deformation of surfaces in three-dimensional Euclidean space that have been obtained in the last 25–30 years and do not appear in previous survey articles.Translated from Itogi Nauki i Tekhniki Seriya Problemy Geometrii, Vol. 23, pp. 131–184, 1991.     

On mesonic interference phenomena in deep inelastic scattering

Possible effects of a π′ contribution to lepton deep-inelastic scattering (DIS) are analyzed. The exchange of the first radial excitation of the pion (π′(0^?)) has been advocated recently to solve the notorious problem of hard vertex form factors innucleon-nucleon scattering. The π′-meson exchange contribution is calculated in addition to the well known pionic (Sullivan) contribution. Interference between π and π′ contributions and their possible influence on the cut-off mass parameter of the πNN form factor extracted from DIS on the nucleon are examined. It is shown that the orthogonality relation between the π and π′ wave functions, in conjunction with number and momentum sum rules, put strong restrictions on the size of the interference effect. The interference effect between π and π′ is found to be negligible for the nucleon quark distributions and to modify only higher moments of the quark distributions. The interference effects of a pionic contribution with other mesons are discussed.     

Formation of propionitrile and acrylonitrile from acetonitrile and methanol

N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117913 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 9, pp. 2195–2196, September, 1992.     

Bipolarons in the intermediate coupling method

The properties of polarons and bipolarons are studied by the intermediate coupling method, which takes electron-lattice coupling into account. A Coulomb correlation in the electron motion is included. When the Fröhlich coupling constant is reduced, at α*=5.7 a bipolaron decays suddenly from a self-trapped state into two delocalized polarons. A phase diagram is constructed for the region where the stable bipolaron exists. These results are compared with those obtained by integration along trajectories.     

On normal matrices with normal principal submatrices

Let A be a normal n×n matrix. This paper discusses in detail under what conditions and in what way A can be dilated to a normal matrix of order n+1 or n+2. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 229, 1995, pp. 63–94. Translated by Kh. D. Ikramov.     

Formation of multilayer strained-layer heterostructures by liquid epitaxy. I. Theoretical aspects of the problem and mathematical model

Problems concerned with the formation of multilayer strained-layer heterostructures by “capillary” liquid-phase epitaxy with forced hydraulic replacement of the solutions in the growth channel are analyzed. It is shown for short contact times between the solutions and the crystallization surface that the character of their flow in the channel plays an important role in the achievement of uniformity in the physical characteristics of the layers grown. Theoretical estimates of the hydrodynamic stability of solutions moving in narrow channels are performed for several III-V systems. A mathematical model, which permits simulation of the conditions under which strained-layer heterostructures are fabricated, is developed. It takes into account diffusive and convective mass transport in the liquid for various flow regimes in the capillary and the displacement of the heterogeneous equilibria in the system under the influence of elastic stresses. Zh. Tekh. Fiz. 67, 42–49 (July 1997)     

Stochastic dynamics of a Josephson fluxon in an inhomogeneous junction

A study is made of fluxon motion in a long Josephson junction with a local inhomogeneity (microresistor) in the presence of an alternating external current. Nonlinear resonances in the fluxon dynamics are considered. The process by which a fluxon trapped at an inhomogeneity is stochastically depinned under the influence of a periodic current is investigated analytically and numerically. Zh. Tekh. Fiz. 67, 57–61 (August 1997)