Vol 489, No 3 (2019)

According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We prove an analogue of this theorem for linear forms of two independent random variables taking values in an α-adic solenoid containing no elements of order 2. Coefficients of the linear forms are topological automorphisms of the α-adic solenoid.

A new method for constructing exact solutions of nonlinear equations of mathematical physics, which is based on nonlinear integral type transformations in combination with the splitting principle, is proposed. The effectiveness of the method is illustrated on nonlinear equations of the reaction-diffusion type, which depend on two or three arbitrary functions. New exact functional separable solutions and generalized traveling wave solutions are described.

An analogue of optical waveguide consisting of metallic nanoparticles chain was investigated using modified cylindrical dielectric resonators (DR) in the microwave range. The two lowest resonances of the DR correspond to the dipole and quadrupole modes of oscillations similar to plasma oscillations in spherical nanoparticles. It is shown that a waveguide consisting of seven resonators has high frequency selective properties and relatively low losses, if the resonances of quadrupole modes are used to form its bandwidth. The characteristics of the studied waveguide remain almost unchanged at its bending by 90°. Cross-section of the main part of energy localization in waveguide is 5 times less than the length of the electromagnetic wave, which roughly corresponds to the optical waveguides based on plasmon oscillations in nanoparticles.

The connection matrix of the Ising model on a d-dimensional hypercube is investigated. In addition to the interactions between the nearest neighbors, the interactions between the next-nearest neighbors are taken into account. For such a matrix, the exact relations for the eigenvalues and eigenvectors, which are reasonably simply expressed through the corresponding characteristics of the one-dimensional Ising model, are obtained. Both periodic and free boundary conditions are considered.

A technique has been proposed and the possibility of its realization for the initiation of kerosene combustion in supersonic air flow in part of the combustion chamber (CC) of a constant cross section has been confirmed. The intense combustion regime is realized with the use of a package of pulses of variable energy and is preserved at a switch-off of the action after the combustion arrangement in the CC diverging part.

An original method for the synthesis of copper-containing nanosystems for biomedical applications using hydrazine hydrate as a reducing agent, intermediate stage of formation of complex ion [Cu(NH₃)₄]2⁺, which allows to obtain Cu0 nanoparticles without impurities of oxides has been developed. As a macromolecular hydrophilic stabilizer copolymer of 2-deoxy‑2-methacrylamido-D‑glucose with 2-dimethylaminoethylmethaacrylate or bovine serum albumin were used. It has been shown that such stabilization allows to achieve almost unimodal distribution of copper nanoparticles in aqueous solutions due to their rather good shielding by macromolecules.

β ↔ α transformations in a thin ~4 µm foil of PdCu solid solution were investigated by x-ray diffractometry and measurement of electrical resistance in heating-cooling cycles during thermal or rapid photon treatment by radiation of high-power pulsed xenon lamps. It has been found that a single rapid photon treatment for 0,3 s (the energy dose of the radiation entering the sample is 10 j · cm^‑2) leads to a complete disordering of the solid solution at a rate 400 times greater than in the heat treatment mode used (heating at a rate of 15 K · min^‑1).

The methods of molecular hydrodynamics (translational diffusion, velocity sedimentation, viscometry) have been used to study copolymers of N‑methyl-N‑vinylacetamide and N‑methyl-N‑vinylamine hydrochloride with an average content of charged groups (4,4 ± 0,2) mol.% in aqueous 0,2 M NaCl solution. Kuhn-Mark-Houwink-Sakurada scaling relations were obtained. Viscous flow was studied in the widest possible range of ionic strengths of aqueous solutions, from salt-free to 6 M NaCl. The data got were compared with those previously obtained for neutral poly-N‑methyl-N‑vinylacetamide. It was firstly shown experimentally that the character of the dependence of the intrinsic viscosity on the molecular weight of a copolymer of such composition in solutions of minimal ionic strength is typical for the chains exhibiting intrachain volume effects, i.e. electrostatic long-range interactions.

An Ediacaran complex of dyke rocks has been identified for the first time in the Yenisei Ridge orogen. These igneous rocks are represented by basic, intermediate and acid variants and formed in the conditions of the transform active continental margin at the stages of its development before and during the interruption of subduction and slab breakoff: from dykes of the picrodolerite - ​dolerite-quartz diorite - leucogranite association with age in the range of 626-623 Ma (U-Th-U isotope data for zircons, SHRIMP-II method, this work) up to adakite - gabbro-anorthosite magmatism at the end of the Ediacaran.

The article considers the Kansko-Achinsky brown coal basin. Huge reserves of solid organic matter (OM) are concentrated in еру Jurassic age sandy-clay sediments. For example, the average thickness of the Borodino field Itatsky layer is 51 m. Attention is drawn to the paleo-centers of heat generation where the coal layers lost (in a whole or partly) their OM. They were destroyed by the underground fires of the past eras. The loss of large masses of the OM in local areas was accompanied by deformations of the coal layers (as well as overlapping ones), appearance of burned and caved ground, failure topographic form (subsidence, funnels, bolsons), and most importantly, the formation of epigenetic cavernosity and pyrogenic reservoir rocks. It is emphasized that the increased fluid conductivity of burned rocks has survived up to the present days. The areas with the burnt rocks are separated into independent fluid dynamic structures with their own parameters (filtration coefficient, water transmissibility, etc.). It has been suggested that pyrogenic reservoir rocks could occur in oil-and-gas basins with coal shale deposits at certain stages of geological development, and at the oil-and-gas generating depths they are able to become reservoirs of catagenic hydrocarbons.

Olivine (high-Fe forsterite; Fo# 69-76) and associated minerals have been studied in a coesite-bearing diamon-diferous eclogite from the Udachnaya-East kimberlite pipe. Olivine was identified in the rock interstices together with K‑feldspar, sodalite, phlogopite and djerfisherite. The composition of individual olivine grains varies within the xenolith and is characterized by a consistent presence of P2O5, MnO, CaO и Al2O3. The coexistence of olivine and coesite is uncommon for mantle xenoliths. The occurrence of olivine and K, Na, Сl-bearing minerals in the studied sample is suggested to have been caused by the interaction of the eclogite with a protokimberlitic melt enriched in alkali components and chlorine.

Stability of stratified elastic geosystems in a gravity field is studied analytically with regard for the shear stiffness of geomaterial. A sufficient condition for stability of a geomass clamped at the lateral boundaries, is obtained: for any ratios of dimensions of the geomass it is sufficient for stability that the rate of density increase with depth (in the loaded equilibrium state) exceed a certain positive value which depends on shear stiffness so that the greater the stiffness, the less the value, and vice versa (the stabilizing effect of shear stiffness). At zero shear stiffness the value mentioned is maximal and characterizes the necessary and sufficient condition for stability of a bulk-elastic geomass. Geophysical consequences of obtained stability condition are analyzed.

The results of measurements of the area of surging glaciers in 1974 and 2018 are compared to the data on their areas in 1913. A large decadal (middle-term) variability in the area of basin glaciation is revealed, and it is comparable to the respective secular (long-term) changes. It is shown that in, the southern meridional circulation epoch, despite high summer temperatures, the surging glaciers in the Sugran River basin grew in area due to increased precipitation, supporting the idea about their flood-runoff nature.

This work is dedicated to prove our hypothesis that catecholamines and their metabolites play crucial role in development of retinopathy of prematurity, severe disabling fibrovasoproliferative vitreoretinal pathology of premature infants. Research was done on experimental model of retinopathy achieved by hyperohygenation in rats on 7th, 14th, 21st and 30th day of life. Amount of catecholamines and their metabolites in retina of rats was measured by HPLC with electrochemical detection. It was shown that L-DOPA on 21st and 30th day of life were lowered in model animals than in control and noradrenaline on 14 th day increased in model animals than in control. However we did not observed dopamine changes between experimental model and control. Given the literature data on cathecholamines and their role in regulation of vasculogenesis in retina, our data shows that changes in cathecholamine metabolism play crucial role in pathology of this severe illness.

We confirmed the hypothesis that algal mats provoke additional accumulation of heavy metals in the bottom sediments and release of labile metals. This process, in turn, enforce a pollution of the coastal zone. Our results give a new direction to the studies of the “green tides” worldwide problem.