Vol 489, No 4 (2019)

In the paper, we consider a problem of clustering a finite set of N points in d-dimensional Euclidean space into two clusters minimizing the sum over all clusters of the intracluster sums of the distances between clusters elements and their centers. The center of one cluster is defined as centroid (geometric center). The center of the other one is a sought point in the input set. We analyze the variant of the problem with the given clusters sizes. We have proved the strong NP-hardness of this problem.

We study the Dirichlet problem for a functional differential equation containing shifted and contracted argument under the Laplacian sign. We establish conditions for the unique solvability and demonstrate also that the problem may have an infinite dimensional solution manifold.

Today the Arctic region exploration is one of the most important courses for research in our country because large amounts of unexplored oil and gas deposits are located there. Large deposits of hydrocarbons are situated in water areas of the North seas. Gas explosions complicate the development of hydrocarbon deposits in these water areas. They occur as a result of an accidant opening and further spread of gas. It is impossible to carry out the frequent exploration of the area with gas layers, then the numerical modelling of the area with already detected gas deposits is conducted. In this work, we present the results of numerical modelling of seismic waves spread in multilayered geological models with gas-containing inclusions during the four-year period with the use of the grid-characteristic method. Then, the wave patterns of seismic reflections and seismograms for the described problem were obtained. We conducted the comparison of wave patterns and seismograms for the 2-dimensional and 3-dimensional cases. The results demonstrated a good coincidence.

To achieve a thermonuclear ignition threshold in the scheme of indirect irradiation of Z‑pinch by X‑radiation, it is necessary to implode the liner by the current with the amplitude ≈ 65 МА for the time ≈ 100 ns. The currents with such parameters can be achieved with the use of super-power disk explosive magnetic generators and a two-stage current pulse sharpening system based on foil electrically exploded current opening switches in a form of a “serpentine”. The implementation of the explosive current source with a rise time of ≈ 100 ns is advisable to be carried out in stages by increasing the magnitude of current. The results of the first-stage experiments, in which the current with the amplitude of 5 MA was produced on the basis of the helical explosive magnetic generator in the load of ≈ 10 nH for the time of ≈ 110 ns, are presented.

Starting from conservation laws and basic thermodynamic principles, we derive equations for a two-phase granular fluid. The first phase is the granular viscoplastic Bingham fluid and the second phase is the viscous Newtonian fluid. We perform an asymptotic analysis of the equations for the flows in the Hele-Show cell when the channel width is well much below its length. While calculating the fluid fluxes-pressure gradient relationship, we derive laws of flow of the two-phase granular viscoplastic fluid through porous media. A criterium is formulated for the start up of the granular phase flow through a porous medium. Given a yield stress, we prove that such a phase does not flow if either or both pressure gradient and channel width are small. We calculated phase flows varying phase viscosities, phase resistivities and yield stress. We reveal reasons which slow down particle intrusion into a porous medium.

N‑heterocyclic phospholes based on N,N¢-disubstituted 9,10-phenanthrenediimines were synthesized. Dimeric 1,3,2-diazaphospholes were obtained by reduction of 2-bromo diazaphospholes. In case phenanthrediimine with the most sterically hindrance, diphosphole can dissociate into phosphorus-centered radicals at record low temperatures (220 K) for this class. This behavior will allow the synthesis of new metal complexes and phosphorus-organic compounds under mild conditions.

The paper presents new paleomagnetic data on dated Ordovician-Silurian volcanics from four sections in the western frame of the Taratash massif in the Southern Urals. Geological data indicate that the region under study has been part of the paleocontinent Baltica since the beginning of Mesoproterozoic. Paleomagnetic data from studies of the rocks of the most western part of the Ural fold belt did not reveal local and regional rotations with respect to the Baltica. Consequently, the pole obtained can be extrapolated to the entire platform. The presented result has a fairly high degree of reliability and can clarify the part of apparent polar wander path (APWP) for the paleocontinent Baltica on the Late Ordovician - Early Silurian segment, where reliable paleomagnetic data are not available, and can be used for paleoreconstructions.

This article describes the nature of including of Verkhoyansk-Chukotka area Verkhoyansk-Kolyma. Chukotka and South Anyui folded belts. It is shown, that formation these belts is not connected with the impulse of collision of Siberian and Arctic plates. The crumpling rocks of first of them into giant horizontal fold (Kolyma loop) is explained as a drift of Omolonsky massif along the border of Siberian craton. Sigma-form of Chukotka belt is cutting the structures Koluma loop is allow to interpret it as a lateral tectonic flow, which deforms Sigma as a result lock up its “heads” Anui-Novosibirsk part volcanic covers of Ohotsk-Chukotka belt. These data allow uncovering Verkhoyansk-Chukotka region as region of skirmish of structures of two lateral tectonic flowes of Polar province of Earth, composing on South Anyui-Pekulney transform fault.

The phase relationships have been experimentally studied at eclogitization of basalts and the melting of H2O‑containing eclogite in the basalt-H2O system at P = 3,7-4,0 GPa, T = 1000-1300 °C. It is established that the phase relationships depend on temperature. The formation of a supercritical fluid-melt occurs at T = 1000 °C, P =  3,7 GPa, conversion eclogite-granatite occurs at T = 1000-1100 °C, P = 3,9 GPa, partial melting of eclogite with the formation of Na-alkali silicate melt and clinopyroxenite restite at 1150 °C and 1300 °C. The supercritical fluid-melt has a high reactivity, resulting in the formation of megacrists of garnet, its enrichment with Ti, the replacement of garnet with clinopyroxene, the formation of ilmenite, K‑containing amphibole, the conversion of eclogite into garnetite as a result of mass crystallization of garnet.

The analysis of the location of the epicenters of earthquakes that occurred in the central and northern part of the East European platform in 2009-2016, recorded by the seismic stations of the GS RAS and the small aperture seismic array of IGD RAS “Mikhnevo” was performed. The results obtained indirectly indicate the seismic activity of the Riphean structures of the region, disturbing the surface of the basement, and their possible activation at the present time. Available data on historical earthquakes also confirm their relevance to paleorifts. It seems important to take into account the position of the ancient aulacogens in assessing the seismic hazard of the East European platform.

We consider a relaxation equation for turbulence wavenumber for use in semi-empirical turbulence closures. It is shown that the well-known phenomenological equation for the dissipation rate of turbulent kinetic energy can be related to this relaxation equation as a close approximation of the latter for stably stratified quasi-stationary flows. The proposed approach allows for more physically found definition of the empirical constants and improvement of atmospheric and oceanic boundary layer turbulence closures by using direct numerical and large eddy simulation data to define equilibrium states and relaxation mechanisms.

The overview maps of tsunami hazard for the Far East coast of Russian Federation are created. The methodological basis of the PTHA (Probabilistic Tsunami Hazard Assessment) approach are discussed, as well as the problems of constructing seismotectonic models of the main tsunamigenic zones, mathematical models and algorithms for calculating probability estimates of tsunami hazard, and some problems of applying the RTHA methodology both related to the lack of observation data and with the complexity of performing a large amount of scenario calculations. Examples of overview tsunami hazard maps for various recurrence intervals, constructed using the PTHA methodology and presented using the “WTMap” application, are given.

In present work, the APX gene encoding ascorbate peroxidase in the moss Dicranum scoparium was for the first time cloned and sequenced, high homology of APX with ascorbate peroxidase genes of the mosses Grimmia pilifera and Physcomitrella patens was shown. The structure of the protein was characterized using bioinfomatics approach and the activity of the enzyme under abiotic stresses was studied. An increase in the activity of ascorbate peroxidase was detected during desiccation of D. scoparium shoots. When exposed to heat shock, a decrease in the acti-vity of ascorbate peroxidase correlated with a decrease in the expression of APX. Conserved elements, which were found in the structure of ascorbate peroxidase gene and protein, indicate that these sequences are preserved in the plant genome during evolution, in support of the importance of this enzyme in maintaining cellular redox status.

Results obtained showed that infection with HCMV prevented the death of THP‑1 cells treated with DOX in both active and latent forms of infection. In the presence of mTOR inhibitors (rapamycin and Torin2), the sensitivity of the infected cells to DOX was restored. Rapamycin inhibited the expression of HCMV protein IE1-p72 and increased sensitivity to DOX. Molecular targets for the creation of new drugs for the treatment of leukemia in patients infected with HCMV have been determined.