The stationary problem of thermoelasticity for a plate with a heated slit

We consider the stationary heat conduction and thermoelasticity problem for a plate that whose lateral surfaces are thermally insulated and which has a slit on whose edges a constant temperature is maintained. The heat conduction problem is solved using a modified logarithmic single-layer potential by reducing it to integral equations.Translated fromMatematicheskie Melody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 50–54.     

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.     

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.     

Positron states in KCL crystals before and after radiation exposure

The features of positron annihilation in KCl crystals before and after radiation exposure is investigated. A significant increase in the efficiency of the ortho-vapor process of positronium state conversion is detected. A model is proposed for taking part in the ortho-vapor conversion of conduction electrons drawn into the conduction band by a positron field that affords a qualitative interpretation of the results obtained and permits values of the electron concentration in a spur to be obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 98–102, July, 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.     

Study of perfection of layers of AlGaSb(AS) solid solution

Studies have been carried out on the perfection of then-Al_xGa_1–xSb_1–yAs_y (0.12x0.26) layer grown on GaSb substrates under different conditions of lattice matching. During the relaxation of the mechanical stresses at first a system of tilt dislocations with a density of up to 5 · 10⁵ cm^–2 is formed while in thick layers (h 20 m) a network of misfit dislocations parallel to the heteroboundary is formed. The time required to dissolve a weighed amount of GaAs in the melt is shown to be of major importance for obtaining layers of a solid solution that are isoperiodic with the substrate. The entry of arsenic only in the initial portion of the epitaxial layer can reduce the dislocation density in the layer without decreasing the measured value of Aa. Dissolution of a weighed amount of GaAs in a Ga + Sb melt for two hours at T=730–750°C is sufficient to obtain layers of Al_xGa_1–xSb_1–yAs_y solid solution that are isoperiodic with the substrate.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 84–89, January, 1988.In conclusion, we thank L. V. Druzhinina for useful discussions as well as Z. V. Korotchenko, L. S. Khludkova, and F. S. Kim for assistance in the performance of the experiments.     

Estimates for the fractal dimension and the number of determining modes for invariant sets of dynamical systems

Majorants of the fractal dimension and of the number of determining modes for unbounded sets, invariant with respect to operators of semigroups of classes 1 and 2, are obtained. They are computed for the Navier-Stokes equations (two- and three-dimensional) under the first boundary condition and under periodicity conditions in the spaces and .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 105–129, 1987.     

An inverse scattering problem for the Schrödinger equation with a potential having a periodic asymptotics

A theorem is proved regarding the expansion in the eigenfunctions of the one-dimensional Schrödinger equationL = –d ^z/dx ²+q(x)(–<x<)with a potential q(x), satisfying the condition