STRIATED SOLUTIONS OF QUASILINEAR HYPERBOLIC TWO SPEED SYSTEMS

It is proved that solutions of quasilinear hyperbolic 2*2 systems in general space dimension are striated if they are so at the initial time or in the past. Results about the propagation of singularities along characteristic curves for both striated and stratified solutions are given.     

Micron-image transfer system with brightness amplifier in gold-vapor laser

A gas-discharge gold-vapor laser on self-terminating transitions with operating wavelength λ=312.2 nm has been used to develop a highly efficient system for image transfer. An optical scheme and all its parameters have been chosen optimal for image quality. It has been found both theoretically and experimentally that the best results on micron-structure image transfer are obtained with 2–5-times image reduction. Various types of masks have been used. A 1-µm structure has been resolved due to the choice of optimal exposure time of 10 ms under a period of pulse repetition (0.6 – 0.8) ms; in this case, the minimal fringe dimension was ≈2 µm with an image dimension of 2 mm for a laser tube 1.8 cm in diameter.     

Temperature dependence of the efficiency at which electrons are captured into axial channeling

A procedure for calculating the efficiency at which electrons are captured into axial channeling with a realistic axis potential is discussed. That region in the space of the electron's total transverse energy E and angular momentum L (integrals of motion) which corresponds to stable bound states of the electron with an atomic row is found. The temperature dependence of the capture coefficient is analyzed. As the crystal temperature is increased, the capture coefficient decreases, to a particularly noticeable extent for beams making a small angle with the crystallographic axis and for crystals having a high atomic number z.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 69–74, May, 1988.     

Infrared reflection spectra in contactless nondestructive measurements of the electron density and mobility in indium phosphide

On the basis of numerical calculations and experimental studies we analyze the possibilities of measuring the electrophysical parameters of indium phosphide by means of infrared reflection spectra at wavelengths ranging from 5 to 200 m. We demonstrate that contactless nondestructive measurements of the electron density in the range 10¹⁶–10²⁰ cm^–3 can be made with a relative error not exceeding 15%, and of mobility with a relative error not exceeding 25%. A nomogram method is presented for rapid conversion of data from infrared reflection spectra into the parameters being measured.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 22–27, January, 1988.     

An example in connection with the Jacobian conjecture

Translated from Matematicheskie Zametki, Vol. 47, No. 1, pp. 127–136, January, 1990.     

On immersions ofn-dimensional Lobachevskií space in 2n-dimensional Euclidean space withn principal direction fields

In this article we prove that the principal direction fields are holonomic and use them to introduce curvilinear coordinates on an immersed region in terms of which the linear element of Lobachevskií space is written in the form where The fundamental system of equations is established for an immersion ofn-dimensional Lobachevskií space into 2n-dimensional Euclidean space withn principal direction fields for the functions _i and, and a way of constructing an arbitrary local analytic immersion is shown.Translated from Ukrainskií Geometricheskií Sbornik, No. 28, pp. 3–8, 1985.     

Determinants of Laplacians in real line bundles over hyperbolic manifolds connected with quantum geometry of membranes

The possibility is discussed of generalizing the Polyakov approach to strings on membranes and the connection of such a generalization with Thurston's classification of three-dimensional geometries. The important ingredients for computing a membrane path integral are the determinants of scalar Laplacians acting in real line bundles over three-dimensional closed manifolds. In the closed bosonic membrane case, such determinants are evaluated for a class of closed 3-manifolds of the H ³/ form with a discrete subgroup of isometries of the three-dimensional Lobachevsky space H ³ and they are expressed in terms of the Selberg zeta function. Some further possible implications of the results obtained are also discussed.     

Deformations of positive linear operators of type B

The concept of the deformation of positive linear operators of type B is introduced, in particular, that of a linear deformation of operators. These concepts are applied to the solving of operator equations of type B. One solves completely the problems of the determination of all positive linear operators of type B for which the covariance of the operators is 1) a polynomial of degrees 3; 2) any power function; 3) an exponential function. In addition, one finds; two families of positive linear operators of type B for which the covariance is a polynomial of degree four.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 888–900, July, 1990.     

Excitation spectrum of anisotropic non-dissipative elastic-plastic medium

The simplest gauge theory of an elastic-plastic medium is considered in this paper that takes account of just translational plasticity. The equations of motion for such a model turn out to be linear and permit the normal modes spectrum of a medium to be obtained. Taking account of plasticity results in a cardinal transformation of the elastic branches of the spectrum and the appearance of a group of plasma oscillations of a dislocation gas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 64–68, June, 1990.     

Elliptic bundle and generating operators

A hierarchy of Poisson Hamiltonian structures connected with an elliptic spectral problem is constructed. Generating operators connected with the Landau-Lifshits equations and asymmetric chiral 0(3)-field are found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 161, pp. 76–87, 1987.The author is profoundly grateful to P. P. Kulish, A. G. Reiman, and M. A. Semenov-Tyan-Shanskii for interest in the present paper and helpful comments.