Congruences,equational theories and lattice representations

We survey results concerning the representations of lattices as lattices of congruences and as lattices of equational theories. Recent results and open problems will be mentioned.To László Fuchs on the occasion of his 70th birthday     

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.     

A mathematical model of a class of problems for the transport of a mixture in air

An analytic solution of a class of boundary-value problems of mathematical physics describing the transport of a mixture in the atmosphere is considered. To solve these problems we apply the substitution method and the Fourier method. The solution of a boundary problem describing the process of contamination of the atmosphere by various substances is presented in the form of a series. The result obtained is useful for the solution of problems concerning the protection of the atmosphere.Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 87–90, 1989.     

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.     

Calculation of microdosimetric characteristics in electron and gamma-ray irradiated water

The results of a calculation of the characteristics of fluctuations in the absorption of energy of electrons and gamma rays in small sensitive volumes of a material in electronic equilibrium are presented. The calculations were performed by the method developed in [1]. The efficiency and accuracy of the method are demonstrated by comparisons with the experimental results and direct numerical simulation. The experience gained in using the method is analyzed. The main numerical result of this work is a table of coefficients enabling the calculation of the probability of the absorption of energy and the first two moments of the energy absorbed in spherical regions with radii of 1, 2, 4, and 8 m, starting only from the electronic spectrum in these regions, for water absorbers with arbitrary shape and arbitrary electronic or photonic sources with energies up to 1 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 77–82, February, 1988.