Quasi-hexagonal self-organization of nanoparticles upon the laser-controlled deposition of Ga atoms

A cooperative defect-deformation (DD) mechanism is developed for the nucleation of the quasi-monodisperse ensemble of nanoparticles in the low-temperature deposition of Ga atoms in the presence of laser radiation. A comparison with experiment is carried out, and a good agreement between the theoretical and experimental results has been obtained. In particular, in accordance with the DD model, it has been found that the arrangement of nanoparticles is characterized by a latent hexagonal order, and their shape is quasi-hexagonal. It has been shown that the characteristics of the deposited ensemble of nanoparticles can be controlled with the use of an anisotropic deformation.     

Functional approach to the theory of two-dimensional quantum Fermi systems in an external periodic field

The behavior of an adsorbed layer of Fermi particles in a weak external field with symmetry of the centered quadratic lattice is investigated. Instability of the weakly inhomogeneous state of the system with respect to small fluctuations in the vicinity ofa ^*=2k _F is established; herea ^* is the magnitude of the vectors of the neighbors closest to the point in the inverse lattice; k_F is the Fermi momentum.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 29–43, 1988.It remains to thank V. N. Popov for constant interest in the work.     

UniversalR-matrix for quantized (super)algebras

For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A. N. Kirillov, and N. Reshetikhin, Ya. S. Soibelman, and S. Z. Levendorskii. Our approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties ofq-exponential functions. We don't use quantum Weyl group.     

A microeconomic simulation model of reproduction

Translated from Programmnoe Oborudovanie i Voprosy Prinyatiya Reshenii, pp. 152–184, 1989.     

On estimates of the bispectral density of certain models of random processes

Estimates are given for the bispectral densities of stationary random processes. Two models of stationary random processes with discrete time are considered. It is shown that for both models conditions hold under which one can construct a consistent estimate of the bispectral density.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 3–7, 1986.     

Integration of the nonlinear Schroedinger equation with a self-consistent source

It is shown that the nonlinear Schroedinger equation with a self-consistent source admits investigation by the inverse scattering method for the Dirac operator. The conditions are found under which the solutions of the nonlinear Schroedinger equation with a self-consistent source describe the creation and annihilation of solitons.     

Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.