Vol 485, No 6 (2019)

Mathematics
A new approach to the Farkas theorem of the alternative
Evtushenko Y.G., Tret’yakov A.A., Tyrtyshnikov E.E.
Abstract

The classical Farkas theorem of the alternative is considered, which is widely used in various areas of mathematics and has numerous proofs and formulations. An entirely new elementary proof of this theorem is proposed. It is based on the consideration of a functional that, under Farkas’ condition, is bounded below on the whole space and attains a minimum. The assertion of Farkas’ theorem that a vector belongs to a cone is equivalent to the fact that the gradient of this functional is zero at the minimizer.

Доклады Академии наук. 2019;485(6):655-658
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On the bisection method for normal matrices
Ikramov K.D.
Abstract

A technique that can be considered an analog of the bisection method for Hermitian matrices is proposed for general normal matrices.

Доклады Академии наук. 2019;485(6):659-661
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Sufficient maximality conditions for surfaces on two-step sub-lorentzian structures
Karmanova M.B.
Abstract

We deduce sufficient maximality conditions for graph surfaces on two-step Carnot groups with sub-Lorentzian structure.

Доклады Академии наук. 2019;485(6):662-666
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On infinite-dimensional integer Hankel matrices
Platonov V.P., Petrunin M.M.
Abstract

We construct a parametric family of infinite-dimensional integer Hankel matrices, each of matrices of this family has the following property: its principal submatrices are nonsingular, and the set of prime divisors of the determinants of the principal submatrices coincides with the set of all primes.

Доклады Академии наук. 2019;485(6):667-669
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Physics
Bifurcations of Liouville tori in a system of two vortices of positive intensity in a Bose-Einstein condensate
Ryabov P.E.
Abstract

In this paper we consider a completely Liouville integrable Hamiltonian system with two degrees of freedom, which describes the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a harmonic trap. For vortex pairs of positive intensity detected bifurcation of three Liouville tori into one. Such bifurcation was found in the integrable case of Goryachev-Chaplygin-Sretensky in the dynamics of a rigid body. For the integrable perturbation of the physical parameter of the intensity ratio, identified bifurcation proved to be unstable, which led to bifurcations of the type of two tori into one and vice versa.

Доклады Академии наук. 2019;485(6):670-675
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Dynamics of the structural transformation of crystalline hydrogen upon the transition into the conductive state under compression
Norman G.E., Saitov I.M.
Abstract

The structural transformation of solid hydrogen under compression along the isotherm of 100 K in the region of transition into the conductive state was studied within the density functional theory. The pressure, the pair correlation function of protons, the density of electron states, and the electrical conductivity were calculated within a range of hydrogen densities from 1,14 to 2,11 g/cm3. The transition of the monoclinic structure of molecular solid hydrogen into the orthorhombic Cmca structure with 12 hydrogen atoms in a unit cell was revealed. In this case, the electrical conductivity was observed to grow, though hydrogen remained molecular. Hydrogen molecules decomposed under compression to the density of 1,563 g/cm3. A unit cell, the thus-formed quasi-tetrahedron, was built of five protons with a distance of 0,92 Å from the central proton to the four others.

Доклады Академии наук. 2019;485(6):676-681
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The one glass transition criterion for liquids
Sanditov D.S.
Abstract

In this communication, a condition based on the deactivation of the trigger mechanism of creep is proposed for the liquid-glass transition of an amorphous substance. This mechanism is confined to the atom delocalization process, which in silicate glasses represents the ultimate displacement of the bridging oxygen atom in the Si-O-Si bridge due to the local low-activation elastic strain of the silicon-oxygen network.

Доклады Академии наук. 2019;485(6):682-685
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Mechanics
The effect of distributed dislocations on bending of a rectangular beam with a preliminarily stressed layer under superposition of large strains
Levin V.A., Zubov L.M., Zingerman K.M.
Abstract

The formulation of problems on the equilibrium of a nonlinearly elastic solid with continuously distributed dislocations is proposed for the case of superposition of large strains. The numerical results showing the effect of distributed dislocations on the stress-strain state of the beam are presented.

Доклады Академии наук. 2019;485(6):686-690
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The accuracy of finite-difference schemes calculating the interaction of shock waves
Ostapenko V.V., Khandeeva N.A.
Abstract

The accuracy with which the shock-capturing finite-difference schemes calculate the flows with interaction of shock waves is studied. It is shown that, in the domains between the shock waves after their incidence, the calculation accuracy of invariants of the combined schemes is several orders of magnitude higher than the accuracy of the WENO-scheme, which is fifth-order in space and third-order in time.

Доклады Академии наук. 2019;485(6):691-696
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Chemistry
Cationic copolymerisation of cholesterol vinyl ether with N-allenylpyrrolidone; a route to pharmacologically promising oligomers
Markova M.V., Tatarinova I.V., Tarasova O.A., Apatrsin K.A., Kireeva V.V., Trofimov B.A.
Abstract

Cationic copolymerization of cholesterol vinyl ether with N-allenylpyrrolidone yielded co-oligomers with molecular mass of 1200-2100. The polymerization of N-allenylpyrrolidone involves both 1,2- and 2,3-positions of the allenyl substituent to give four types of units as a result of prototropic isomerization of the initially formed structures. In the developed method, the composition of co-oligomers can be controlled and, hence, their hydrophilic/hydrophobic balance, solubility, and membranotropic properties can also be controlled to change the potential biological activity of the products.

Доклады Академии наук. 2019;485(6):697-700
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Chemical Technology
Production of high-flexural-strength corundum ceramics
Panasyuk G.P., Semenov E.A., Kozerozhets I.V., Danchevskaya M.N., Lukin E.S., Belan V.N., Voroshilov I.L., Azarova L.A., Izotov A.D.
Abstract

A new method was proposed to produce high-flexural-strength corundum ceramics from α-Al2O3 samples synthesized by heat treatment of boehmite AlOOH at 1300 °C for 5 h. It was shown that hydrothermal treatment of MDGA-grade hydrargillite at 200 °C in a 0.4 wt % magnesium acetate solution for 3 days gives finely crystalline boehmite, which is a feedstock for synthesizing corundum ceramics with a flexural strength of 400 MPa.

Доклады Академии наук. 2019;485(6):701-703
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Physical chemistry
The strength properties dependence of aluminum materials on the ZrO2 nanoparticles concentration
Mironov V.V., Agureev L.E., Eremeeva Z.V., Kostikov V.I.
Abstract

New data were obtained on the effect of small additions of zirconium oxide nanoparticles on the strength properties of powder matrices based on pure aluminum, including those with the addition of 1.5% copper cold pressed and sintered in forevacuum. It is shown that even with an insignificant concentration of nano-additives, there is a noticeable increase in the mechanical properties of materials: tensile strength, bending, compression, and yield strength.

Доклады Академии наук. 2019;485(6):704-707
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Geology
U-Th-He dating of pyrite from the Uzelga Copper-Zinc massive sulfide deposit (South Urals, Russia): first application of a new geochronometer
Yakubovich O.V., Vikentyev I.V., Zarubina O.V., Bryanskiy N.V., Gorokhovskii B.M., Kotov A.B., Dril S.I., Bortnikov N.S.
Abstract

Based on a study of pyrite from the Uzelga Cu-Zn volcanogenic massive sulfide (VMS) deposit (South Urals) the age of ore mineralization was first determined with the direct age-dating method, based on the fraction of radiogenic helium, incorporated into the pyrite crystal lattice from submicron inclusions of U and Th minerals. Taking into account the measurement errors, the obtained age of 377 ± 8 Ma (MSWD = 1.2) is quite consistent with the independent age dates available for the ore mineralization (Late Eifelian-Early Givetian, 385-390 Ma).

Доклады Академии наук. 2019;485(6):708-712
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Geochemistry
Lubavinskoe Au-bearing ore deposit: petrochemical features of rocks and ores, and the origin conditions (Eastern Transbakalia)
Abramov B.N., Posohov V.P., Kalinin Y.A.
Abstract

Lubavinskoe Au-bearing ore deposit is situated to submeridional deep layered tectonic zone. In these zones the ore veins are associated with small Mesozoic stocks of granodiorite and rocks of the dyke complexes of the sublatitudinal spread. According to geochemical features these intrusions are correspond to adacits. The proportion isotopic ratio of the oxygen and strontium at granodiorites indicates to their origin due to mantle-core interaction. Calculated oxygen isotope composition δ18 in the fluid in equilibrium with quartz in the productive phase 220-280 °С changes from 3,59 to 9.59‰, which corresponds to water of magmatic fluid nature. This is confirmed by the isotopic composition of sulfar for sulphides δ34S, ‰ from +0.7 to +6.7‰, corresponding to hydrothermal orogenic ore deposits.

Доклады Академии наук. 2019;485(6):713-719
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The Se2 (GAS) fugacity in systems with noble metals: chrisstanleyite Ag2Pd3Se4-naumannite Ag2Se-β-PdSe2 and luberoite Pt5Se4-sudovikovite PtSe2
Kristavchuk A.V., Vymazalova A., Osadchii E.G., Vikentyev I.V., Chareev D.A., Bortnikov N.S.
Abstract

The reactions of 6Ag(cr) + 3PdSe2(cr) = 2Ag2Se(cr) + Ag2Pd3Se4(cr) and 12Ag(cr) + 5PtSe2(cr) = 6Ag2Se(cr) + Pt5Se4(cr) were studied with the EMF method in a completely solid-state galvanic cell with an Ag ion-conducting solid electrolyte with overall gas space (Ar under atmospheric pressure). The EMF vs T dependencies were obtained in the temperature ranges of Т = 425-648 K and 501-713 K, respectively. Then, they were recalculated for gaseous Se fugacity in dependence on the temperature for non-variant equilibriums of Ag2Pd3Se4 (chrisstanleyite)-β-PdSe2 (the phase, which transforms into verbeekite under low temperatures)-Ag2Se (naumannite) and Pt5Se4 (luberoite)-PtSe2 (sudovikovite): logfSe2(gas)(Ag2Pd3Se4/Ag2Se/PdSe2) = 7.71 ± 0.05 - 8.524 ± 0.026(1000/T), logfSe2(gas)(Pt5Se4/PtSe2) = 7.135 ± 0.027 - 12.274 ± 0.016(1000/T).

Доклады Академии наук. 2019;485(6):720-725
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The age and evolution of the lithospheric mantle in the East Antarctic Craton: osmium isotope composition and the distribution of the platinum group elements in spinel lherzolite nodules
Krymsky R.S., Antonov A.V., Belyatsky B.V., Sushchevskaya N.M., Sergeev S.A.
Abstract

The mantle xenoliths of lherzolite composition from Mesozoic alkaline-ultrabasic diatremes of the Jetty Oasis were studied. The studied xenoliths represent the mantle section of the East Antarctic Craton down to depths of 60-80 km. The osmium isotope composition of these nodules testifies to the beginning of the formation of the lithospheric mantle in the considered region at about 2400 Ma. The absence of any signs of Early Archean lithosphere points either to partial destruction of the lithosphere at the convergent boundary of the plates in the Late Archean or to thermal erosion of the Archean lithosphere under the deep-seated plume impact at the Mesozoic time during rift propagation.

Доклады Академии наук. 2019;485(6):726-731
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Carbon budgets in the steppe ecosystems of Russia
Kurganova I.N., Lopes de Gerenyu V.O., Zhiengaliyev A.T., Kudeyarov V.N.
Abstract

Abandoned lands formed in the place of former arable lands occupy considerable areas in the steppe zone and are a basic reserve for the restoration of the steppe biome in Russia. Taking into account the secondary steppe ecosystems developed in the place of the abandoned lands, the total carbon dioxide sink in the steppe zone of Russia can reach 92-121 Mt С per year. This is comparable to the СО2 sink in the managed forests of the Russian Federation (96 Mt/yr) and accounts for 10-20% of the total sink of СО2 in the terrestrial ecosystems of Russia. To increase the sink potential on the territory of the Russian Federation, the natural and restored steppe ecosystems should be preserved.

Доклады Академии наук. 2019;485(6):732-735
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Ore-forming fluids of the gold-bearing interval of the Kola Superdeep Borehole
Prokofiev V.Y., Lobanov K.V., Pek A.A., Chicherov M.V., Borovikov A.A.
Abstract

This paper reports on the physical-chemical parameters and vertical distribution of different types of fluid inclusions in quartz from the Au-bearing interval of the Kola Superdeep Borehole. We assume that gold ore mineralization was formed when a deep flux of CO2 interacted with brines at depths of 10 205-9269 m due to tectonic factors. In this paper, we discussed the role of these processes in the formation of the orogenic gold deposits including the gold mineralization of the Southern Pechenga structural zone.

Доклады Академии наук. 2019;485(6):736-740
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Palladogermanide Pd2Ge from sulfidized anorthosite of the Yoko-Dovyren intrusion: first finding in Russia
Spiridonov E.M., Orsoev D.A., Ariskin A.A., Kislov E.V., Korotaeva N.N., Nikolaev G.S., Yapaskurt V.O.
Abstract

The Yoko-Dovyren ultramafic-mafic layered intrusion includes the Baikal deposit of Cu-Ni sulfide ores with Pt-Pd mineralization in the bottom part, and “horizons” and pockets of low-sulfide ores with Pt-Pd mineralization at the upper levels of the section. The highest concentration of Pd, Pt, Au, Ag, Hg, and Cd, as well as the widest variability in the noble-metal minerals, is typical of the vein-like bodies of anorthosite and pegmatoid anorthosite in the upper part of the critical horizon at the boundary between troctolite and the overlying gabbronorite. Most of the noble-metal minerals are the postmagmatic pneumatolytic (fluid-metasomatic) phases. Among them are palladogermanide with 19.8 wt % Ge, paolovite with 8.1% Ge, and zvyagintsevite with 0.55% Ge. The composition of palladogermanide is Pd2.03(Ge0.80As0.15Bi0.02)0.97; Ge is significantly replaced with As in this phase, which is typical of endogenic Ge minerals.

Доклады Академии наук. 2019;485(6):741-744
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Geophysics
Irregular variability of spatiotemporal distributions of wildfires and emissions of harmful trace gases in Europe based on satellite monitoring data
Bondur V.G., Tsidilina M.N., Kladov V.L., Gordo K.A.
Abstract

Based on the results of satellite monitoring, the anomalies of spatiotemporal distributions of wildfire areas, as well as the volumes of caused emissions of carbon-containing trace gases (CO, CO2) and aerosols (PM2.5), for the territory of European Russia and Eastern and Central Europe from 2005 to 2018 are detected. It is found that, for 2005-2013, the annual areas of wildfires shrank for the territory of European Russia by almost a factor of 10, and the volumes of emissions of harmful gas traces into the atmosphere decreased by a factor of 7. However, starting from 2014, they were recorded to increase. The seasonal (spring and summer) maxima occurred in the distributions of the burned areas and the emission volumes in the time period under study. An anomalously large number of fire sources was recorded on the territory of Ukraine in 2014-2018 (70% of all fires in Eastern and Central Europe) where the specific density of fire sources, their relative areas, and the relative volumes of emissions increased by a factor of 3-5.7 compared to 2010-2013 and grew by a factor of 5-7.5 in August 2014-2018 compared to other territories of Eastern, Central Europe, and European Russia.

Доклады Академии наук. 2019;485(6):745-749
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Biochemistry, biophysics, molecular biology
Multiplex PCR test-system development for the genotyping of transgenic mice with pBC1 MILK expression vector-based transgene
Kalmykov V.A., Kusov P.A., Deykin A.V.
Abstract

Developed multiplex PCR test-system for identification of transgenic cis-regulatory elements (promoter, insulator) from genetic constructions based on pBC1 Milk expression vector incorporated into the Mus musculus genome. Test-system was validated by genotyping producent strains generated by linearized vector DNA microinjection into fertilized zygote with occasional transgene genome integration, expressing the following transgenes in mammary gland, in milk: Human lactoferrin protein in different length, heat-shock protein HSP-70, Firefly luciferase protein, lysozyme protein. Reaction conditions selection described in details for better reproducibility.

Доклады Академии наук. 2019;485(6):750-753
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Comparison of earthworms’ bioluminescent systems
Rodionova N.S., Petushkov V.N.
Abstract

The results of a comparative study of the luciferin-luciferase systems of seven species of bioluminescing oligochaetes - Henlea petushkovi, Henlea rodionovae, Fridericia heliota (Enchytraeidae), Microscolex phosphoreus (Acanthodrilidae), Pontodrilus litoralis (Megascolecidae), Eisenia lucens, and Avelona ligra (Lumbricidae) - are presented.

Доклады Академии наук. 2019;485(6):754-759
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Microbiology
Complex method of instrumental microbiоtesting ecological safety of various products, waste and territories
Sibirtsev V.S., Uspenskaya M.V., Garabadgiu A.V., Shvets V.I.
Abstract

A microbiotesting technique is described, which involves recording changes in pH, redox potential, electrical conductivity, optical density, light scattering and luminescence intensities, as well as other parameters of samples with viable test microorganisms, incubated in a liquid nutrient medium in the presence and in the absence of tested factors. The results of the analysis using this system of pro- and antibiotic activity of various oil products, as well as weak electromagnetic fields of the megahertz range are presented. It is shown that the proposed method, in comparison with standard methods, allows to obtain more detailed and objective information, and also requires less time and labor.

Доклады Академии наук. 2019;485(6):760-763
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