On Unconditional and Absolute Convergence of the Haar Series in the Metric of $ L^{p}[0,1] $ with $ 0

Grigoryan  M. G. 《Siberian Mathematical Journal》2021,62(4):607-615

Synthesis and X-ray diffraction study of complex oxides of the Zn2 ? x(ZraSnb)1 ? xFe2xO4 composition

A multicomponent system of complex refractory oxides of the composition Zn_{2 − x} (Zr _a Sn _b )_{1 − x} Fe_2x O₄ (a + b = 1; a: b = 1: 5, 1: 4, 1: 3, 1: 2, 1: 1, 2: 1, 3: 1, 4: 1; x = 0−1.0; Δx = 0.05) was studied by X-ray diffraction. The samples were prepared from oxides of appropriate metals by low-temperature plasma synthesis (hydrogen-oxygen flame). Two phases with wide homogeneity ranges were identified: α phase crystallized in the crystal system of inverse cubic spinel and β phase with the structure of tetragonal spinel. The phase boundaries were found. Structural data are presented for about 100 solid solutions.     

Asymptotic analysis of collision-induced timing shifts in return-to-zero quasi-linear systems with predispersion and postdispersion compensation

An asymptotic method for calculating the collision-induced frequency and timing shifts for quasi-linear pulses in return-to-zero, wavelength-division multiplexed systems with predispersion and postdispersion compensation is developed. Predictions of the asymptotic theory agree well with quadrature and direct numerical simulations. Using this theory, computational savings of many orders of magnitude can be realized over direct numerical simulations.     

The evolution of the mass of a “preserved” chemical spill as it moves with the river current

A quantitative model describing the process of turbulent diffusion of the liquid mass of a chemical spill as it moves with the river current is constructed. The model contains a representation of the tensor components of the turbulent diffusion coefficients in terms of the initial parameters of the problem – the breadth and depth of the water flow in the river and the average flow velocity. According to the model proposed, the process consists of three stages: the initial, rapid stage, in which, owing to turbulent diffusion along the vertical coordinate, the pollutant concentration distribution evens out along this coordinate; the intermediate stage, in which, because of turbulent diffusion along the horizontal coordinates, the concentrations are likewise evened out along the horizontal coordinate transverse to the river channel; and the third, longest and slowest stage, in which quasi-one-dimensional turbulent diffusion occurs along the longitudinal (channel) coordinate, describing the “spreading” of the chemical slick (volume) carried downstream. Simple explicit formulae are obtained for a quantitative estimation of the characteristic pollutant concentrations at the end of the first and second stages and their “attenuation” with increasing distance as the chemical slick drifts with the current, and also the increasing longitudinal dimension of the slick with distance downstream.     

Structural imperfections of crystals as a result of ion implantation

The diffraction of X-rays has been studied in two-crystal interferometers, the crystals of which had equal interplanar distances and between the blocks of which a non-diffracting zone was formed as a result of ion implantation. Also the X-ray diffraction was studied in two-crystal interferometers, the interplanar distances of which were different and the non-diffracting zone between the crystals had zero width. It was shown in plane wave approximation that the Moiré patterns should not be formed in case of former interferometers and necessarily arose with the latter type interferometers.