Studying the Electrically Driven Switching of the Planar Light Guide

Liquid crystalline materials can be used as an active media for the new generation of planar light guides. The main characteristics which governs light-guiding and switching abilities of such devices are the spatial distributions of the refraction indices (defined via the distribution of nematic director) for the liquid crystal confined within a light-guiding pore. We aim to obtain these distributions from the molecular dynamics simulation of the liquid crystalline cell with the homeotropic boundary conditions being applied. We discuss the reorientation kinetics of the homeotropic-planar transition and obtain the equilibrium director profile upon application of the planar reorienting field.     

Factorisation of Non-negative Fredholm Operators and Inverse Spectral Problems for Bessel Operators

We study the problem of factorisation of non-negative Fredholm operators acting in the Hilbert space L₂(0, 1) and its relation to the inverse spectral problem for Bessel operators. In particular, we derive an algorithm of reconstructing the singular potential of the Bessel operator from its spectrum and the sequence of norming constants.     

On the Similarity of Perturbed Multiplication Operators

Let S be the multiplication operator by an independent variable x in L ₂(0,1), and let V be an integral operator of Volterra type. In this note, we find sufficient conditions for the similarity of the operators T := S + V and S and discuss some generalizations to an abstract setting of the results obtained.     

On the Lax Solution to the Hamilton–Jacobi Equation and Its Generalizations. Part II

This article is a continuation of [J. Math. Sci., 99, No.5, 1541–1547 (2000)] devoted to the validity of the Lax formula (cited in the article of Crandall, Ishii, and Lions [Bull. AMS, 27, No.1, 1–67 (2000)])

Canonical quantization for classical Neumann-type dynamical systems within the framework of the Moser spectral approach

The classical Neumann-type dynamical systems describe the motion of particles constrained to remain on an N-sphere S ^N in (N + 1)-dimensional space ^N+1 and subject to quasi-harmonic forces. Following the Moser spectral approach to the connection of Lax finite-zoned infinite-dimensional dynamical systems with Neumann-type finite-dimensional dynamical systems on a sphere in ^N+1 a regular procedure of appropriate quantization of these systems is proposed. Quantum expressions of commutative laws of conservation for Neumann-type quantum dynamical systems are determined in the general case of a canonical Dirac quantization.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 913–922, July, 1992.     

Nanostructures on the Basis of Porous Alumina with Intercalated with Cholesteric Liquid Crystal

The introduction of liquid crystal materials into the porous material host will help us to get optically active nanocomposites. Nanocomposite based on aluminum oxide host with cholesteric liquid crystal is characterized by a shift of bandwidth wavelength minimum. In case of intercalation of cholesteric liquid crystals into the pores of aluminum oxide host the shift of transmittance minimum into the short wave region are observed. We analyzed the ways, which indicate the deformation of the pitch of the cholesteric helix and showed the role of capillary forces in the deformation of the pitch of cholesteric liquid crystal.     

Singular Perturbations of Self-Adjoint Operators

Singular relatively compact perturbations of self-adjoint operators are studied. The results obtained are applied to the Schrödinger operator with a singular potential.     

Convergence of Partial Sums of Dirichlet Series and Rational Approximation of Functions

A rational approximation on [0,1) of functions that are analytic in the unit disk is investigated.