Vol 484, No 2 (2019)

A direction d is called a tangent direction to the unit sphere S of a normed linear space s  S and lin(s + d) is a tangent line to the sphere S at s imply that lin(s + d) is a one-sided tangent to the sphere S, i. e., it is the limit of secant lines at s. A set M is called convex with respect to a direction d if [x, y]  M whenever x, y in M, (y − x) || d. We show that in a normed linear space an arbitrary sun (in particular, a boundedly compact Chebyshev set) is convex with respect to any tangent direction of the unit sphere.

Left invariant l-infinity sub-Finsler problem on Cartan group is considered as time-optimal control problem. We describe abnormal and singular normal trajectories, then prove that all such trajectories are optimal. We construct the bang-bang flow and obtain upper bounds on the number of switchings on bang-bang and mixed minimizers.

We study the problem of the absence of global solutions of the first mixed problem for one nonlinear evolution equation of Ginzburg–Landau type.We prove that global solutions of the studied problem are absent for “sufficiently large” values of the initial data.

Using numerical models, we have studied what depth of the outer layer the comet nuclei are degassed to when they are in orbits whose perihelion is close to the Sun for tens of years. The problem is topical, because it helps to understand how much the experimentally obtained results on the composition of comet comas depend on how long the comet is in its present-day orbit and how adequately the data obtained reflect the composition of comet nuclei as a whole. The proposed approach, which is demonstrated using comet 67P/Churyumov–Gerasimenko as an example, is based on a 3D comet nucleus surface relief model and takes into account not only its orbital motion, but also its diurnal rotation. The propagation of heat in the nucleus subsurface layers is described by a 1D heat conduction equation for a porous rock-ice composition of matter. Based on this approach, we have derived the temperature distributions in the subsurface layers for several surface patches located in the Ma’at region in 20 revolutions around the Sun, ~130 years.

The influence of the climate change in Russia on the operation of hydroelectric power plants during the 21st century is considered. For obtaining quantitative assessments, the results yielded by global climatic models for river runoff were subjected to ensemble averaging. In addition to the standard RCP climatic scenarios, the MPEI scenario is considered, the fundamental distinctive feature of which is that the most likely development trajectories are selected. It is found that the choice of a scenario has an essential effect on both the qualitative pattern of river runoff changes over the territory and on the quantitative characteristics of this process.An integral assessment for the change in the hydroelectric power plant outputs due to climate change is made.

The trajectories of a mission to an asteroid with the presence of a spacecraft (SC) near the asteroid for some time and including a return to the Earth have been studied. A two-stage method of constructing optimum (with respect to the maximum of the useful SC mass) interplanetary trajectories of an Earth–asteroid–Earth mission with high thrust engines has been developed: in the central Newtonian field of the Sun’s attraction at the first stage and with allowance for disturbances at the second stage. An algorithm of constructing conjugate functions for the case of maximizing the useful mass has been designed. The optimum trajectories for the Earth-Apophis-Earth mission have been constructed and analyzed. The possibility in principle of organizing the Earth-Apophis-Earth space mission based on the "Soyuz" and "Zenit" launch vehicles and "Fregat" upper stage for a flight has been demonstrated.

The interaction of tri-n-butylmethylphosphonium dimethylphosphate and 1,3-dimethylimidazolium dimethylphosphate with elemental sulfur in a benzene medium has been described. According to13C and17O NMR and high resolution mass spectrometry, the chemical reaction involves only the dimethyl phosphate anion. The reaction mechanism and the reaction product composition have been proposed.

In the work, thermal modes of passivation of pyrophoric nanopowders at lower initial temperatures of the layer of the nanopowder are studied with analytical and numerical methods in the context of a macrokinetic approach. It is shown that the decrease in the initial temperature of the layer leads to a transition from a layer-by-layer mode of passivation to the volume one. That allows controlling the acceptable level of a warming up at passivation even at the high concentration of oxidizer in gas. Analytical expressions for delimitation of the layer-by-layer and volume passivation modes are obtained; these are confirmed by the results of numerical calculations.

The stability range of TmFe2O4 has been studied under conditions of low oxygen pressure in the gas phase at the temperature of 1090 °C. The thermodynamic characteristics of thulium ferrite are calculated from experimental data obtained during dissociation of the compound in the temperature range of 750–900 °C. Structural transformations are determined in the temperature range from –140 to 140 °C. They are associated with charge ordering in this compound.

Dromaeosaurid ungual from the Blagoveschensk locality studied for the first time. Dromaeosaurid presence amongst other taxa points on high biodiversity in Amur region, on the eve of K-T event.

Carbonatite are of a great economic importance because this rocks contain valuable rare metals. At present tree models of geodynamic regime of carbonatites formation are actively develop. 1- the generation of carbonatite melts within the lithospheric mantle, 2- the close connection of carbonatites with the zones of orogenesis, 3- a large group of carbonatites links to deepseated mantle plumes. For the first time using the modern model of “absolute” paleotectonic reconstructions and large database was showed the general connection of Phanerozoic carbonatites to the large areas of low velocities of S‑waves located in the lower mantle — zones of the generation of deep mantle plumes.

This paper reports on lithium metallogeny in geological time. The geochronological analysis was conducted on the basis of data on 71 lithium deposits distributed globally. These deposits contain almost all Li resources, which are industrially significant and of potential interest in terms of the economy. It was established that these deposits were formed in different geological epochs, from the Late Mesoarchean to the Holocene. The distribution of their resources on the scale of geological time is distinctly discrete. In the Kenoran, Columbian, and Rodinian supercontinent cycles, only pegmatite deposits of lithium were formed. In the Pangean cycle, the main resources are also attributed to pegmatite deposits, but some of them are concentrated in lithium–fluorine rare-metal granites. In the incomplete Amasian cycle, salars of geodynamically active areas play a main role in the resource base; the epithermal stratiform deposits, pegmatites, and lithium fluorine-granites are of much less significance.

The concentrations of seven heavy metals (HMs) in tissues of bivalve mollusks of the families Unionidae (genera Ensidens, Scabies, Kunashiria) and Cyrenidae (genus Corbicula) and from four natural lakes located on the eastern slope of Sikhote Alin (Primorskii krai, Russian Far East) and the Mekong River delta (Vietnam) were determined. It was established that the HM concentrations in the bivalve mollusks studied, inhabiting unpolluted water reservoirs, are specific for every family and do not depend on the geographical positions of the lakes. They decrease in the following order: Mn > Fe > Zn > Cu > Ni > Cd > Pb for Unionidae, and Fe > Zn > Cu > Mn > Ni ≥ Cd > Pb for Cyrenidae (Corbicula). It is likely that deviations from the revealed sequence are due to anthropogenic pollution of lakes with some metals or the occurrence of a natural geological anomaly.

Kyanite gneiss from the "New Barchinsky" locality (Kokchetav Massif) was studied in detail. This rock is characterized by zonal distribution of the C and SiO2 polymorphs in kyanite porphyroblasts: (1) porphyroblast cores with graphite and quartz inclusions; (2) clean overgrowth zone with inclusions of cuboctahedral diamond crystals. The Raman mapping of SiO2 polymorphs originally showed the presence of an association of disordered graphite + coesite “prohibited” in HT diamond-bearing rocks. Graphitization of diamond is the only likely mechanism of the disordered graphite formation in HT diamond-bearing rocks. However, the absence of disordered graphite in association with diamond in kyanite porphyroblasts from kyanite gneiss from the "New Barchinsky" locality eliminates the process of diamond graphitization at the retrograde stage. Most likely, crystallization of disordered graphite occurred at the retrograde stage from the UHP C-O-H fluid.

We investigated the role of epiphyseal hormone melatonin in the differentiation of naive CD4+T cells into regulatory T cells (Treg). The hormone at physiological and pharmacological concentrations inhibited Treg differentiation, decreasing both the proportion of CD4+FOXP3+ cells in the culture and the level of TGF‑β, the key cytokine for this T cell subpopulation. The inhibitory effect of exogenous melatonin was due to its interaction with the membrane receptors MT1 and MT2. At the same time, the signals realized through RORa — the nuclear receptor for melatonin — stimulated Treg formation; however, they were considerably weaker than the signals from the membrane receptors and were overlapped by the latter. Since the Treg subpopulation plays an important role in physiological and pathological processes in the body, the revealed effects of melatonin should be taken into account in its therapeutic use.

The temperature dependence of the efficiency of energy migration from the CdSe/CdS/ZnS quantum dots (QDs, a fluorescence maximum at 580 nm) to the reaction centers (RCs) of the bacteria Rb.sphaeroides is practically constant over the temperature range from 100 to ~230–240 K but then decreases 2,5–3 times as temperature further increases to 310 K. The analysis of this dependence on the basis of Forster’s theory showed that the major changes in the energy transfer efficiency are associated with the temperature change in the quantum yield of QD fluorescence, which is due to the activation of intramolecular mobility in the RC structure.

Locomotor activity was investigated in smolts of the European river lamprey at alternation of light and darkness (12/12 h) and in the dark. Two groups of smolts were discerned differing in the level of locomotor activity. The presence of the circadian rhythm in smolts has been revealed, and its role in downstream migration has been shown. The locomotor activity leading smolts to channel flow increases with decreasing illumination at evening twilight. The period of high nocturnal activity is completed a short time before morning twilight, under the action of the individual circadian rhythm. This decreases the probability of impact of predators on migrating smolts.