Characteristics of propagation of light beams in gyrotropic crystals

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 5, pp. 815–819, May, 1991.     

Temperature dependence of corundum roentgenoluminescence and thermoluminescence

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 3, pp. 438–444, March, 1991.     

Compact spreads and compact translation planes over locally compact fields

We prove that a spread S over a locally compact nondlscrete field F defines a topological translation plane if and only if the spread is compact. For F=R, this is implicit in Breuning's thesis [Bre], cf. [B 2]. For the proof, we describe the point set of the projective translation plane as a quotient space of some projective space, with identifications taking place in one hyperplane. This is new even for F=R.     

Geometrical method for determining the surface damage threshold for femtosecond laser pulses

A new geometrical method to determine the surface damage threshold for ultrashort pulses is presented. It consists in the formation of a surface damage profile by a movement of the sample across the laser beam focus. A single measurement of the maximum transversal dimension of this damage profile, which depends solely on the laser beam power, is used to calculate the local damage threshold intensity. It is also theoretically shown that the damage in the transverse dimension can be controlled under the diffraction-limited spot.     

Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

The excitation of eigen surface waves by tubular electron beams in cylindrical discharge devices is studied. The influence of the wave‐field azimuthal structure on the excitation efficiency and nonlinear stage of the plasmabeam instability is investigated both numerically and analytically. Analytical expressions for the saturation amplitude and excitation efficiency of the wave under study are derived. They are found to agree well with results obtained by numerical modelling of the plasma‐beam interaction presented in this paper. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parametric resonance in the problem of a heavy rigid body rolling along a straight line on a plane

The problem of the stability of a heavy rigid body, bounded by the surface of an ellipsoid and with a cavity in the form of a coaxial ellipsoid, rolling along a straight line on a horizontal rough plane is investigated. It is shown that in the case of a body that is close to being dynamically symmetrical, parametric resonance always occurs leading to instability of the rolling. Each ellipsoid has its own “individual” resonance angular velocity. In the general case, regions in which the necessary stability conditions are satisfied can be distinguished in parameter space. The problem of calculating the resonance coefficient corresponding to instability for parametric resonance in a reversible third-order system is solved.     

Kalman filtering of a space-time Markov random field

In this paper, finite-dimensional recursive filters for space-time Markov random fields are derived. These filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the parameters of the model.     

The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.