Vol 486, No 3 (2019)

For classes of graph mappings constructed from $C_H^1$ -mappings of nilpotent graded groups, we prove area formula on sub-Lorentzian structures of arbitrary depth with multi-dimensional time.

The study describes a new modification of the method of functional separation of variables for nonlinear equations of mathematical physics. Solutions are sought in an implicit form that involves several free functions; the specific expressions of these functions are determined in the subsequent analysis of the arising functional differential equations. The effectiveness of the method is illustrated by examples of nonlinear reaction-diffusion equations and Klein-Gordon type equations with variable coefficients that depend on one or more arbitrary functions. A number of new exact functional separable solutions and generalized traveling-wave solutions are obtained.

A two-dimensional time-optimal control problem with a state constraint is studied for a closed mechanical system consisting of a mass point and a solid body that interact via internal forces. It is assumed that the mass point is not allowed to move further away from the body's center of mass than a prescribed distance. A control function is found allowing the body to be turned through a given angle in a minimum time by choosing the velocity of the mass point. In the case of reaching the state constraint, the solution is constructed in explicit form via quadratures representing elliptic integrals. A numerical example of using the derived formulas is given.

A plasma method for producing pure solutions of hydrogen peroxide during activation of water by plasma of electrodeless microwave discharge has been developed. It is shown that the activated water has a pronounced effect on agricultural plants, being non-toxic and chemically pure regulator of biological activity. In particular, the treatment of seeds of agricultural plants with activated water solutions can improve their drought resistance.

The effect of the replacement of the exact yield condition by that averaged over the distribution of residual stresses in a thin hollow disk subjected to external pressure and subsequent unloading is investigated. The formulation of the boundary-value problem is specially simplified so that it is possible to obtain a mathematically exact semi-analytical solution, with the help of which it is easy to investigate the effect of averaging the yield condition on the stressed state including the distribution of residual stresses. The accepted exact yield condition is averaged using several generally accepted approaches. The comparative analysis of the distribution of residual stresses shows a significant deviation of the distribution resulting from solutions for the averaged yield conditions from the exact distribution of residual stresses.

In this work, the possibility of combining the methods of chemical functionalization of a mixture of polychlorinated biphenyls before the formation of a mixture of hydroxy- and methoxy-chlorinated biphenyls and the bacterial transformation of the compounds obtained with the aim of their utilization was investigated. As a result of a 100% conversion, a mixture of compounds identified as methoxy- (30 compounds), hydroxy- (44 compounds) and methoxy (hydroxy) derivatives (47 compounds) was obtained by reacting a mixture of Sovol with MeONa in MeOH and DMSO. PCB congeners. The total content of all hydroxy derivatives was 77.2%. It was established that the strain Rhodococcus wratislaviensis KT112-7 carries out the destruction of 73-93% of this mixture at the initial concentration of 0.25-1.50 g/l. The best result was obtained with a decomposition of 0.1 g/l of a mixture of methoxy- and hydroxy-polychlorobiphenyls (on the 10th day the total absence of the starting compounds). The specific rate of destruction was in direct correlation with the initial concentration of the mixture. It has been shown that during bacterial transformation there is no accumulation of toxic intermediate compounds.

A rapid heuristic computational algorithm for optimizing the energy and resource efficiency of a local process of multistage drying of a moving mass of phosphorite pellets was developed. The algorithm is distinguished by the use of heuristic computational procedures and heuristic rules of the iterative construction of a vector criterion of the efficiency of the chemical and energy engineering system. The criterion takes into account the energy consumption cost and the pellet quality indicators using both special barrier functions for deterministic constraints on control process variables (feed velocity and temperature of the carrier gas), and penalty functions for state variables of a local drying process (temperature gradient, heating rate, moisture content, moisture-transfer rate in pellets, temperature of the carrier gas at the outlet of the vertical multilayer pellet packing). Using the developed algorithm and software package, the scientifically grounded, optimal in energy consumption and dried pellet quality, operating conditions in local zones of drying of a travelling grate machine were determined.

For a heterogeneous liquid - liquid system in which an exothermal reaction takes place, the topology and stability of the steady states of CSTR are investigated. It is shown that the thermal effect of the reaction, the magnitude of the energy barrier and the intensity of mass transfer strongly influence the type of steady state that arises. In this case, a change in the topological picture occurs through degenerate steady states.

On the basis of U-Pb dating of zircon and baddeleyite from gabbro-dolerite of the Goloustnaya dyke swarm (southern margin of the Siberian Craton), the age of basites was established as 1338.0 ± 2.9 Ma. It is shown that the basite intrusions of close ages from the Goloustnaya and Listvyanka areas (southern Siberian Craton) and Victoria Island (northern Laurentia, Barking Dog complex) could have been formed under the influence of the same mantle plume and belong to the same Large Igneous Province of Ectasian (Middle Mesoproterozoic) age.

This article presents first tephrochronological data on the volcanic activity in the valley of the Jom-Bolok River (East Sayan Mountains, Siberia), which is the largest manifestation of the Holocene eruptions in Central Asia. The data results from our study of the proglacial Kaskadnoe-1 Lake situated near the Jom-Bolok basalt field. The lake sediments include a series of tephra-rich layers. Radiocarbon dating of the lake sediments provided a robust age model which allowed us to build timing of eruptions formed the Jom-Bolok volcanic field. We recognize two large phases of volcanism separated by almost 5 thousand years dormant phase. The first phase is traced back to ca. 14.3 cal ka BP and lasted until 6.3 cal  ka BP. Ten clusters of microtephra layers in the sediments of the first phase show 300-800 years recurrence of the volcanic events weakening upward. The event of 14.3-13.3 cal ka BP probably represents the strongest eruptions of the Jom-Bolok. The second phase started ca. 1.6 cal ka BP and highly likely continues in our days. Its strongest eruptions occurred between 1.6 and 0.8 cal ka BP with periodicity of 200 years. This tephrostratigraphy shows a multiplicity of the Jom-Bolok volcanic events and amplifies the earlier built scheme resulted from investigations of the stratified basalts, pyroclasts and lake damming events.

The first determine organic complex nature-modification montmorillonite of Sakhalin Island bentonite. In result, obtained data allowed identify volume chain of polyethylene, alkylammonium and other parts of humic molecule, which included in the surrounded bentonite humus.

The results of mineralogical-geochemical studies of the oligotrophic pine-fruticulose-sphagnum segment of the Vasyugan Swamp (West Siberia) in the winter of 2017 are presented. A mathematical model is developed for the depth distribution of chemical elements in water and acid extracts of peats, organo-mineral sediments, and inorganic soil. It is shown that two complex geochemical barriers related to the changes in filtration properties of soils and contributing to the formation and/or accumulation of Fe compounds and other chemical elements function in the peat deposit. The first (oxidizing, reduction, sulfide, and adsorption hydroxide) barrier is found approximately at a depth of 0.40-1.25 m; the second (alkaline carbonate and hydrolytic, adsorption hydroxide, clayey, and carbonate) barrier lies in the lower layer of the peat deposit (a depth of 2.25-2.50 m). The result obtained is important for understanding the production-destruction methane cycle.

The paper presents data obtained during the 69th and 72nd expeditions of the research vessel Akademik Mstislav Keldysh (2017, 2018). A mechanism of methane discharge that explains the localization of the seep fields in a limited area of the outer shelf and suggesting a system of deep and surface faults is proposed. Along the deep faults, gas fluid is transferred to the upper strata of the sedimentary cover, where it is accumulated below the gas hydrate stability zone and the permafrost horizon. The surface faults of the outer shelf break this caprock, creating conduits for the gas to migrate to the surface and to jet-release into the water column.

The aim of the study was to obtain the data of stable oxygen isotope composition of Late Pleistocene and Holocene ice wedges of Mamontova Gora and Syrdakh exposures and their chronology, and reconstruction of winter air temperature during the time of ice wedge formation. Direct dating of organic microinclusions from the ice wedges of Mamontova Gora outcrops allowed to establish that the ice wedges are younger than 20 ka, but older than 10 ka BP. δ¹⁸O values of the Late Pleistocene ice wedges of Mamontova Gora vary from -24.7 to -30.9 ‰, δ¹⁸O values of the Holocene ice wedges of this exposures range from -23.2 to -25.9 ‰. δ¹⁸O values in the Late Pleistocene ice wedges near Syrdakh Lake vary from -29.2 to -32.5 ‰. Reconstructed mean winter air temperature during the most part of the ice wedge growth period in Mamontova Gora site within Late Pleistocene varied from -28 to - 31°C, mean January temperature reached -42, -46°C, for the Syrdakh Lake site Late Pleistocene winter conditions were more severe: mean winter air temperature varied from -30 to -32°C, mean January air temperature reached -44, -48°C. Holocene mean winter air temperature were higher and varied from -24 to - 28°C, mean January temperature varied from -36 to -42°C.

Numerical modeling of a 28'th September Tsunami on the  Sulawesi Island (Indonesia) is executed. It is shown that observed distribution of a Tsunami heights in the extensive territory can be explained direct action of a strong earthquake, and in a center zone (the district of Palu) - submarine landslide.

The oxidative modification of human hemoglobin Hb treated with ydrogen peroxide was investigated. The method of mass spectrometry were detected oxidized amino acid residues of the hemoglobin molecule: αTrp14, αTyr24, αArg31, αMet32, αTyr42, αHis45, αHis72, αMet76, αPro77, αLys90, αCys104, αTyr140, βHis2, βTrp15, βTrp37, βMet55, βCys93, βCys112, βTyr130, βLys144, βHis146. The antioxidant potential of the Hb molecule in the intracellular space and when it enters the blood plasma is discussed.

Infection of mice with influenza A viruses led to the formation of clones of lymphocytes that specifically recognizes viral domains in the central zone of the NSP protein (amino acid positions 83-119). Computer analysis of the primary structure of the NSP protein showed the presence of T-cell epitopes in the central part of the NSP molecule. The findings indicate that the viral NSP gene is expressed in the infected animals and support the concept of the bipolar strategy (ambisense strategy) of the influenza A virus genome.

This paper presents the preliminary results of the Chaetopterus variopedatus bioluminescent system separation into luciferin and luciferase and a brief description of some their properties.