Antimicorbial effects of newly synthesized organotin(IV) and organolead(IV) derivatives

Triorganotin(IV) and triorganolead(IV) derivatives of the types Me₃Sn(SCZ) and Ph₃Pb(SCZ) (where SCZ^? is the anion of a semicarbanzone ligand) have been synthesized by substitution reactions of trimethyltin chloride and triphenyl-lead chloride with semicarbazones derived from heterocyclic ketones. The resulting complexes have been characterized by elemental analyses, molecualr weight determinations and conductivity measurements. The mode of bonding has been established on the basis of infrared and ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopic studies. Some respresentative complexes have also been evaluated for their antimicrobial effects on different species of pathogenic fungi and bacteria; the results of these investigations have been reported in the present paper.     

Relativity of the spectrum and discrete groups on hyperbolic spaces

We give a simple proof of the analytic continuation of the resolvent kernel for a convex cocompact Kleinian group.

     

Orbital stratification of the variety of divisors of a polynomial operator bundle

We study the variety of divisors of a polynomial operator bundle and the action of the natural symmetry group on it—the group of invertible operators that commute with the linearizer of the bundle. It is established that the orbits can be parametrized by standard Young tableaux whose form and weight depend on the spectral parameters of the bundle and its divisors. We consider the question of existence of factorizations with prescribed spectral characteristics. The correspondence is given in terms of the Littlewood-Richardson combinatorial rule.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 8–12.     

Nonstationary generalized Duru-Kleinert transformation of path integrals for systems of differential equations in one-dimensional space

We obtain new formulas for the transformations of Wiener path integrals corresponding to the parabolic systems of two differential equations with time-dependent coefficients in one-dimensional space. These formulas determine the transformation of the path integrals under a rheonomous-homogeneous-pointwise transformation of integration variables and the path reparameterization transformation. These formulas allow us to obtain an integral relation between the Green's functions of related systems of differential equations. We show how to obtain the generalized Shepp formula from this relation for the path integral under consideration. We derive these new formulas using the properties of random processes under phase transitions and a random change in time.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 1, pp. 17–27, October, 1996.     

Light transmission by polymer-dispersed liquid crystals

Light transmission of nematic liquid crystals dispersed in a polymeric matrix is investigated. The paper gives a theoretical analysis of light transmission by the liquid crystal-polymer and liquid crystaldye-polymer systems based on determination of the total cross section of extinction. The mathematical model is considered in the anomalous diffraction approximation. The theoretical calculations are in good agreement with experimental data obtained for films based on cyanodiphenyl dispersed into a polyvinyl acetate matrix.Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 6, pp. 118–122, November–December, 1993.Translated by L. Chernomorskaya     

Determination of residual stresses in glass shells by a computational-experimental method

A method is proposed for determining the technological residual stresses in glass shells of revolution based on the solution of inverse problems of shell theory with proper stresses and the use of experimental data obtained by the photoelastic method. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 100–105.     

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.