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     

Ion Beam Driven Ion Cyclotron Double Layers

We present here a self consistent theory of small amplitude double layers associated with electrostatic ion cyclotron waves in a plasma containing hot electrons, cold ions and traversed by an ion beam. It has been shown that compressive type of double layers solution exists when θ_b (beam temperature) < α_b (beam concentration) < 1.     

Hybrid integrator backstepping control of robotic manipulators driven by brushless DC motors

In this paper, a hybrid integrator backstepping controller is proposed for robotic manipulators actuated with brushless DC motors in the presence of arbitrary uncertain inertia parameters of the manipulator and the electrical parameters of the actuators. The main features are: 1) the design, requiring at most the joint velocities and stator currents feedback; 2) the semiglobal asymptotic stability of the controller being established in the Lyapunov sense; and 3) suitability of the scheme for multijoint robots. Simulation results are included to demonstrate the tracking performance.     

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.     

Group-theoretic description of external gauge fields

For an arbitrary external gauge field we construct an infinite group which contains all the information about the given field and describes some of its properties. We construct a field representation of the group . We show that covariant derivatives become translation generators in such a representation of the group . This allows us to interpret transformations from the group as motions in an external gauge field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 31–35, December, 1988.     

Experimental study of regions of reversed magnetization in an amorphous layer of Co70Fe5Si10B15

The characteristics of the distribution of magnetization and remagnetization of microsections of the surface in the amorphous alloy Co₇₀Fe₅Si₁₀B₁₅, prepared in the form of thin ribbons, were studied by the magnetooptical method. It was found that the magnetization I on the surface of the amorphous ribbon studied was strongly nonuniform. It was established that heat treatment (HT) of the sample leads to the appearance of regions of reversed magnetization in the surface layer of the ribbon, while thermomagnetic annealing reduces the nonuniformity of I. The conservation of the transverse component in the HT sample in fields where the magnitude of the component of magnetization parallel to the length of the ribbon remains virtually unchanged suggested that a domain structure of the magnetization ripple type, owing to the strong microdispersion of the magnetic anisotropy, is realized in this sample.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 89–94, March, 1988.