A method to obtain the domains of the functions of global dependences based on the refined approximations of the set of tiles is developed. The exact presentation of the boundaries of the domains of the functions of global dependences avoids redundant computations in the performance of communication operations and provides more opportunities for granular paralleling algorithms.

The representation of a special class of integrals with respect to spin variables by means of integrals with respect to anticommuting variables is obtained. Evaluation of integrals with respect to anticommuting and spin variables by means of the formulas for Gaussian integrals with respect to anticommuting variables is presented.

The approximation error of the expectation of a class of random functionals of a Gaussian process and the approximation error of solution of the Burgers equation based on Gaussian chaos development are investigated.

The theorem of a general structure of equations in the K₂ hierarchy is proved. The order of movable poles of solutions is determined. The resonant polynomials are constructed in explicit form, and the character of their roots is determined.

The article deals with the construction of extreme third degree polynomial defined on a rectangle in the complex plane. The main theoretical methods prove extreme polynomials in complex domains are those based on the criteria of A. N. Kolmogorov (1948) and V. K. Ivanov E. Y. Remez (1953). Extreme polynomials are used in the construction of optimal high-order iterative processes for linear bounded operators in a Banach space, with the region of spectrum localization in the rectangle.

In the article a relation between the number of square and cubic integer polynomials of bounded degree and discriminant values for these polynomials is established.

In this article the local features for the existence of plane spanning trees in a geometric graph have been obtained. Thereby Rivera-Campo’s conjecture has been confirmed for almost all geometric graphs.

In this article nonlinear programming problemis considered under the relaxed Mangasarian-Fromovitzconstraint qualification. We prove that the relaxed Mangasarian-Fromovitz constraint qualification implies the local error bound property without additional assumptions for constraints.

The distributions and properties of the estimations of the parameters of the multidimensional-matrix linear empirical regression are obtained.

The problem of statistical assignment of arbitrarily distributed multivariate observations to the classes determined by training samples is considered. The decision rule based on the histogrammic estimators of probability densities is proposed and its efficiency is analytically investigated.

The influence of the physical parameters of Cu_xIn_xZn_2—2xSe₂ films on the characteristics of Mo/Cu_xIn_xZn_2—2xSe₂/CdS/ZnO thin-film solar cells were investigated. The model developed is based on one-dimensional drift-diffusion approach using the Poisson’s equation and continuity equations for electrons and holes. It taking into accounts the buffer layer effect, zone bending and recombination at grain boundaries and other defects.

Ge/Si nanostructures with closely spaced and interacting Ge quantum dots were grown by molecular beam epitaxy. It was found that the GeSi quantum rings with closely spaced Ge quantum dots can be formed by choosing suitable deposition rate and temperature of Ge. The unit cell parameters and Ge concentration in Ge/Si nanostructures were determined by the X-ray diffraction method. Intense luminescence bands caused by radiative recombination of excitons from both the Ge wetting layers and Ge quantum dots were found in photoluminescence spectra at 4.2 K.

By means of infrared absorption spectroscopy a clear correlation between the disappearance of the divacancy (V₂ in the temperature range 200-275 °C and the appearance of two absorption bands positioned at 833.4 and 842.4 cm^-1 in irradiated oxygen-rich Si crystals has been found. Both these two emerging bands have previously been assigned to a divacancy-oxygen defect V₂O formed via interaction of mobile V₂ with interstitial oxygen (Ot) atoms. The present study shows, however, that the two bands arise from different defects since the ratio of their intensities depends on the type of irradiation and only the band at 833.4 cm^-1 can be assigned to V₂O. The 842.4 cm^-1 band is much more pronounced in neutron irradiated samples as compared to the samples irradiated with electrons. We argue that it is related to a trivacancy-oxygen defect (V₃O) formed via interaction of mobile V₃ with O_i atoms.

The changes in the elemental composition of two-layer target when affected by the radiation of a G0R-100M ruby laser operating in the free oscillation regime were studied. The radiation flux density was varied from 10⁴ до 5-10⁵ Вт/см^-2. The elemental composition of the target before and after irradiation was investigated by means of an ElvaX X-ray spectrometer. The investigations showed that affecting a thin layer (several ^m) nickel layer covering a titanium sample, the concentration of titanium in the surface stratum considerably (by a factor of 1.5 and more) increased. It is important that the titanium concentration with increasing the flux density of the operating irradiation increased monotonically in the mentioned space. The analogous phenomena on the laser irradiation effect on the back side of the thin cupper plate covered with nickel were observed. This testifies to the active metal diffusion from the target into the surface stratum in the zone of pulse heating of the investigated samples by means of laser radiation. 

We see that taking into account direct solar pressure lagrangian triangular points of libration L4 and L5 do not exist, but for each of the trial body there exist two points of photolibration L4* and L5*which, together with the heavy bodies are the vertices of scalene triangles with constant sides. The existence of trial bodies with different «windage» leads to the existence of photolibration lines.

To the 80th Anniversary of Birthday

To the 80th Anniversary of Birthday

To the 70th Anniversary of Birthday