Vol 485, No 1 (2019)

Peano-type curves in multidimensional Euclidean space are considered in terms of number theory. In contrast to curves constructed by D. Hilbert, H. Lebesgue, V. Sierpinski, and others, this paper presents results showing that each such curve is a continuous image of universal (shared by all curves) nowhere dense perfect subsets of the interval [0, 1] with a zero s-dimensional Hausdorff measure that consist of only Liouville numbers. An example of a problem in which a pair of continuous functions controlling the behavior of an oscillating system generates a Peano-type curve in the plane is given.

In this paper a new variant of accelerated gradient descent is proposed. The proposed method does not require any information about the objective function, uses exact line search for the practical accelerations of convergence, converges according to the well-known lower bounds for both convex and non-convex objective functions and possesses primal-dual properties. We also provide a universal version of said method, which converges according to the known lower bounds for both smooth and non-smooth problems.

We annonce the results generalizing the Vinberg's Complexity Theorem for the action of reductive group on an algebraic variety over algebraically non-closed field. Also we give new results on the strong k-stability for the actions on flag varieties.

A new construction of a lowpass filter was developed based on a two-dimensional microstrip electromagnetic crystal, which had a steeper slope of the frequency response as compared to a filter consisting of a one-dimensional microstrip electromagnetic crystal. The investigated lowpass filter construction is characterized by a high workability and ease of manufacturing. Electrodynamic numerical simulation of the 3D model of the considered microstrip structure agrees well with the experiment, which allows conducting parametric synthesis of devices with the required properties using a personal computer.

The results of multiyear investigations of cosmogenic radionuclide production rates along the orbits of 42 chondrites, fallen successively to the Earth in 1959-2016 are presented. They constitute a long set of homogeneous data, statistical smoothing of which demonstrates some main regularities of distribution and variation of the galactic cosmic rays (GCR) with energy > 100 MeV in the internal (< 5 AU) heliosphere. This set is exclusive, and it has timeless importance for all the future investigations of magneto-hydrodynamic peculiarities of the GCR solar modulation mechanism. Analysis of ²⁶Al contents in 10 chondrites of known orbits allowed us to educe a spatial profile of the GCR intensity (E > 100 MeV), averaged over a 1 My in the internal heliosphere, testifying to permanent development and dissipation of a layer of the solar wind magnetic irregularities, which efficiently modulates cosmic radiation. It suggests a constancy of magneto-hydrodynamic environment in the Solar system at least for the last million years.

A comparative analysis of experimental results obtained by different researchers using two different experimental approaches is presented: phenomenological (registration of conditions, characteristics and modes of interaction between a drop of a shell and a target drop) and statistical (analysis of collisions of tens and even hundreds of drops of liquids as part of an aerosol). The ranges of Weber criterion values (the basic parameter used for analyzing the effects of collisions of droplets in a gaseous medium) are established, corresponding to bounce, coalescence, reflexive and stretching separation, disruption, according to the results of all considered experimental research. The bounce of droplets upon collision can be observed under the conditions We = 0.35–0.5; the probability of droplet coalescence is maximum in the range We = 1–7.5; it is possible to reliably predict spreading at We = 15–50; splitting of droplets most often occurs at values We > 50. The probability of occurrence of other scenarios in the selected We ranges is not zero. The conclusion about the need to combine experimental techniques to obtain the most reliable data and their further use in the development of prognostic models is formulated.

Two new polyheteroarylenes (polydiimidazopyridines) based on 2,3,5,6-tetraaminopyridine and aromatic dicarboxylic acids were synthesized and characterized. The polymers show high viscosity properties and exceptional thermooxidative stability. Polydiimidazopyridine containing a phosphoric acid group possesses excellent filmforming properties and can be processed to proton conducting membranes that have record high proton conductivity in the temperature range of 20-200 °C after doping with orthophosphoric acid.

New materials based on calcium sulphate with the replacement of calcium cations to magnesium cations – 10, 20 and 40 mol.% were obtained. The synthesis of substituted forms of calcium sulphate, the study of the phase composition, and the strength of the obtained materials were carried out in the work. It is shown that the solubility of the synthesized materials increases with increasing of the degree of substitution. The obtained materials are acceptable for the preparation of composite biomaterials on their basis for the regeneration of bone tissue and carriers of drugs.

A concept of fabrication of well-organized conductive pathways in CP/NP blends in photovoltaic devices. It is assumed that to succeed in this task, one can use the property of AB diblock copolymers that, depending on the chemical structure of A and B blocks and the ratio between their lengths, these copolymers undergo microphase separation in bulk to form thermodynamically stable domains of cubic symmetry with 3D periodicity. Using a mesoscale simulation technique, we demonstrated that the morphology of the photoactive layer of photovoltaic devices can be controlled by selecting the surface NP modifier (responsible for the compatibility of NPs with the polymeric matrix), the chemical structure of the blocks of a conjugated copolymer, and their length.

Results of the study of Sr–Nd–Pb–Hf isotopic composition of Late Paleozoic granitoids of Central Chukotka are represented on the example of Kibera and Kuekvun plutons. The age of granitoids of these plutons and granites from pebbles in conglomerates in the base of overlying Lower Carboniferous deposits is 351–363 Ma (U–Pb zircon, TIMS, SIMS, LA–ICP–MS). Thus, granitoid magmatism corresponds in time to tectonic events of Elsmerian orogeny in Arctic region. Sr–Nd–Pb–Hf isotopic composition of granitoids indicate participation of mantle and crustal components in the source of granite melts. Granitoids formation probably occurred in geodynamic setting of Andean type continental margin during the interaction between mantle melts, forming at the mantle wedge melting in suprasubduction conditions, and continental crust.

The statistical relationships characterizing the concentrations of minor elements in the organic part and mineral impurities in fossil coals are allocated. The confidence ranges for these concentrations are calculated. The concentrations of minor elements within the confidence ranges relate to the clarke distributions; those exceeding the upper boundary of the confidence level, to extremely high values.

The isotopic characteristics ((Nd, ²⁰⁷Pb/²⁰⁶Pb, and ⁸⁷Sr/⁸⁶Sr) of the modern bottom sediments sampled in the Barents Sea during the 67th voyage of the R/V “Akademik Mstislav Keldysh” are considered. It is shown that the major contribution to the formation of the sediments in the central Barents Sea is made by rocks of the North European continental margin, which are found in the zone of influence of the North Cape Current. The values of (Nd, and ⁸⁷Sr/⁸⁶Sr are lower in the bottom sediments of this part of the sea than the corresponding characteristics of sedimentary material incorporated into ices and carried by the Transpolar Drift Stream. This allows one to conclude that such material has not contributed much to the sedimentation in the Barents Sea.

A modification of the commonly used Price-Rind scheme for lightning flashes frequency (LFF), which can be used for calculations with large spatial and time steps, is developed. With such steps, the exponent in the relationship of LFF on convective cloud heights appears to be smaller by a factor of two over land and by one fourth over ocean in comparison to that in the original Price-Rind scheme. The modified version is implemented into the IAP RAS climate model (CM). The results of the lightning flash frequency simulations with the modified scheme agree better with the satellite data than those with the original one. In the IAP RAS CM, global warming (cooling) leads to LFF increase (decrease) in all seasons. The sensitivity of lightning flashes frequency to the surface air temperature change at the global level is estimated equal to 10%/K.

The results of studies of the regularities of evolution of soils and the environment in the steppe zone of the East European Plain are presented. Different culture-based chronological stages for the Bronze Age, Iron Age, and Middle Ages (3rd millennium BC-2nd millennium AD) are considered on the basis of buried soils at archeological monuments (burial mounds).

The contemporary radiation situation in the Arctic Basin and Russian Arctic seas is assessed on the basis of data from 2013 to 2017. Statistically significant differences are revealed in the mean volumetric activity of ¹³⁷Cs in the surface water layer. The tendency toward a west-to-east decrease in seawater pollution is noted. The maximum ¹³⁷Cs concentrations are characteristic of the Barents and Kara seas. The least polluted waters are reported in the Laptev and East Siberian seas, which are the most remote from the sources of technogenic radionuclides in Europe.

The patterns of the seasonal and inter annual variability in the development of phytoplankton, including coc- colithophores, were studied in the northeastern part of the Black Sea in various seasons. The research was carried out on the base of remote sensed data provided by the Modis Aqua ocean color scanner and long-term ship observations. The results indicate that, in the coastal and open waters of the Black Sea, the development of phytoplankton reaches the highest level in the fall-winter and winter-spring seasons, i.e., in the periods of active winter convection. It was noted that there is a relationship between the level of coccolithophore development in the summer period and the minimal temperature of the sea surface layer in the preceding winter. The most active coccolithophore blooms, were observed after the coldest winters. Unusual winter and early spring coccolithophore blooms taking place in mild hydro meteorological conditions were registered in the Black Sea, on the base of satellite data and were confirmed by in situ measurements.

This is the first study to investigate the molecular-genetic organization of polytene chromosome interbands located on both molecular and cytological maps of Drosophila genome. The majority of the studied interbands contained one gene with a single transcription initiation site; the remaining interbands contained one gene with several alternative promoters, two or more unidirectional genes, and “head-to-head” arranged genes. In addition, intricately arranged interbands containing three or more genes in both unidirectional and bidirectional orientation were found. Insulator proteins, ORC, P-insertions, DNase I hypersensitive sites, and other open chromatin structures were situated in the promoter region of the genes located in the interbands. This area is critical for the formation of the interband, an open chromatin region in which gene transcription and replication are combined.

Changes of the blood flow in the shin skin in the case of 12 healthy subjects by laser doppler flowmetry were observed under transcutaneous electrical spinal cord stimulation (TSCS) by subthreshold bipolar pulses with a frequency of 30 Hz were detected. It was found that the TSCS in the area of the vertebrae T₁₁ and L₁ leads to a significant increase in skin blood flow. With a stimulus intensity of 90% of the motor threshold, the microcirculation rate increased by more than 85% relative to baseline.The results of the study show that the stimulation of blood flow in the skin by TSCS is realized mainly due to the antidromic stimulation of sensory nerve fibers. An important mediator that contributes to vasodilation and increase of cutaneous blood flow in PSCS is nitric oxide (NO), which is predominantly endothelial in origin.

The endogenous brassinosteroids content in the roots and shoots of early- and mid-season potato microclones was determined. Among the analyzed plant steroid hormones were representatives of brassinolide group, 24-epi- brassinolide group, 28-homobrassinolide group, B-lactones and B-ketons. The level of all brassinosteroids in plant roots exceeded significantly that in shoots, irrespective of the potato term of ripening. Of interest is the fact that in plant shoots there were no BS groups of 24-epibrassinolide. We have first found a relationship between the terms of potato ripening and endogenous content of different BS groups in the aerial and underground plant parts; we have also assessed the age-related changes in the content of BSs, as well as their ratio in the potato plants of the Red Scarlett variety.