Vol 488, No 6 (2019)

The size of a maximum subgraph of the random graph with a given number of edges
Derevyanko N.M., Zhukovskii M.E., Rassias M., Skorkin A.Y.

We have proven that the maximum size k of an induced subgraph of the binomial random graph G(n, p) with a given number of edges e(k) (under certain conditions on this function), with asymptotical probability 1, has at most two values.

Доклады Академии наук. 2019;488(6):587-589
Sharp estimates of the geometric rigidity on the first Heisenberg group
Isangulova D.V.

We prove quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geometry: every (1 + ε)-quasi-isometry of the John domain of the Heisenberg group Η is close to some isometry with order of closeness  in the uniform norm and with the order of closeness ε+ε in the Sobolev norm. An example demonstrating the asymptotic sharpness of the results is given.

Доклады Академии наук. 2019;488(6):590-594
On the existence and uniqueness of the solution of a nonlinear integral equation
Nikolaev M.V., Nikitin A.A.

In this paper we study the nonlinear integral equation that arose in the spatial model of biological communities developed by Austrian scientists Ulf Dieckmann and Richard Law. Sufficient conditions for the existence of the solution of this equation (the fixed point of the integral operator) were found. The question of uniqueness of the solution is also studied.

Доклады Академии наук. 2019;488(6):595-598
Control Processes
Spectral decompositions for the solutions of Lyapunov equations for bilinear dynamical systems
Yadykin I.B., Iskakov A.B.

In this paper, novel spectral decompositions are obtained for the solutions of generalized Lyapunov equations, which are observed in the study of controllability and observability of the state vector in deterministic bilinear systems. The same equations are used in the stability analysis and stabilization of stochastic linear control systems. To calculate these spectral decompositions, an iterative algorithm is proposed that uses the residues of the resolvent of the dynamics matrix. This algorithm converges for any initial guess, for a non-singular and stable dynamical system. The practical significance of the obtained results is that they allow one to characterize the contribution of individual eigen-components or their pairwise combinations to the asymptotic dynamics of the perturbation energy in deterministic bilinear and stochastic linear systems. In particular, the norm of the obtained eigen-components increases when frequencies of the corresponding oscillating modes approximate each other. Thus, the proposed decompositions provide a new fundamental approach for quantifying resonant modal interactions in a large and important class of weakly nonlinear systems.

Доклады Академии наук. 2019;488(6):599-603
Emission spectrum and trajectory of a charged particle in the field of an inhomogeneous electromagnetic wave
Lapshin V.B., Skubachevskiу A.A., Belinsky A.V., Bugaev A.S.

Using the example of a non-uniform electromagnetic wave created by superposition of two plane monochromatic electromagnetic waves that are arbitrarily directed relative to each other, an approach is demonstrated that allows one to simulate a wide spectrum of electromagnetic waves. The complete system of equations describing the motion of an electron in a non-uniform electromagnetic field is solved numerically. The features of the trajectory and emission spectrum of the electron were found and investigated.

Доклады Академии наук. 2019;488(6):604-608
Results of applicability analysis of satellite observations and reanalysis data for autonomous photovoltaic unit simulation
Frid S.E., Lisitskaya N.V., Popel O.S.

The accuracy analysis of energy performance prediction of autonomous photovoltaic units using various climate databases (NASA POWER, SARAH-E, CLARA-A, ERA5, Meteonorm, etc.) for some geographic points in Russia was performed by comparing with calculations using data of World Radiation Data Center. It is shown that the considered databases provide a spread of predictions of the required power of solar battery at the level of 10-20% only when solar fraction is less than 70%. For larger solar fraction, the prediction error of the required power of solar battery can reach hundreds of percent.

Доклады Академии наук. 2019;488(6):609-611
Energy science
An impact of atmospheric and climate changes on the energy potential of Russian forest resources
Klimenko V.V., Tereshin A.G., Mikushina O.V.

Biofuels are an important source of energy, currently providing about 10% of the world energy demand, including 2% of power generation and 2.5% of liquid fuel consumption. Wood fuel in Russia is one of the most affordable and most important source of renewable energy resources. In this paper, the possible changes of energy potential of the forest resources of Russia induced by changes in the atmosphere composition and climate are studied. The estimates of changes of the global carbon dioxide concentrations and mean annual air temperature across the Russian territory for the period up to 2050 are presented, simulated using global carbon cycle model and regional climate model developed in MPEI. It is projected that the change of net primary production of Russian forests due to an increase of CO2 abundance in the atmosphere and raising both air temperature and precipitation will increase available energy resources of wood fuel at the mid-century by up to 30% or more than 9 million tce/year.

Доклады Академии наук. 2019;488(6):612-618
Physical chemistry
Nanotone spatial dissipative structures with rotational curving of the grid around three mutually perpendicular directions
Маlkov V.B., Shveikin G.P., Plaksin S.V., Pushin V.G., Маlkov А.V., Маlkov О.V., Shulgin B.V.

Transmission electron microscopy and microdiffraction have been used to investigate nanothin spatial dissipative structures (SDS) obtained by thermogradient processing of an amorphous selenium film by one-sided heating of its lower surface at T = 413 K. It has been established that the obtained nanothin SDS of hexagonal selenium possess a specific curved habit and a nonlinear fan-shaped system of bending contours in their electron-microscopic image; the lattice of nanothin SDS undergoes an elastic-plastic rotational curvature around three mutually perpendicular directions; the lattice rotation angles of nanothin SDS hexagonal selenium reach: around [001], 25º, around the direction perpendicular to [001] and lying in the plane of the amorphous film 32º, around the direction perpendicular to the first two and not lying in the plane of the amorphous film 35º.

Доклады Академии наук. 2019;488(6):619-623
A find of mollusks Watsonella crosbyi Grabau (Gastropoda: Helcionelliformes) in the Botomian of China
Parkhaev P.Y.

The mollusk species Watsonella crosbyi Grabau, 1900 is found among other mollusks in the Lower Botomian strata of the Xinji Formation on the Northern China Platform (Shaanxi Province). Taxonomically the mollusks assemblage is extremely similar to those from the Mernmerna Formation, Parara Limestone, and Sellick Hill Formation of Southern Australia, Bastion Formation of Laurentia, and the uppermost Emyaksin Formation of the Siberian Platform. All these starta can be aged as Early Botomian. The new find of Watsonella crosbyi confirms the significant time range of the species distribution (Tommotian-Botomian) and raises doubts in newly proposed correlations of the Lower Cambrian of Southern Australia pushing down the previously determined age of the formations for one or even two ages older.

Доклады Академии наук. 2019;488(6):624-629
Thermochronology of cordilleran metamorphic core complexes: example of Song Chay massif in Northern Vietnam
Vladimirov A.G., Travin A.V., Anh P.L., Murzintsev N.G., Mikheev E.I.

Based on the reconstruction of the thermal evolution of the Song-Chai granitoid massif (Northern Vietnam) the long-term existence of granitoid magma at deep levels of the Earth’s crust (H = 15-20 km, Δt ~ 20-50 Ma) is established. Geodynamic analysis and mathematical modeling of thermal history of the granitoid batholith cooling shows that the magmatic chamber should be considered as thermal trap on the lower level of the earth’s crust, preserving residual granite melts for a long time. Activation of the magmatic chamber occurs in post-collisional strike-slip tectonics zones and is associated by tectonic exhumation of large segments of the earth’s crust. Ultimately, this leads to the transformation of the batholith into Cordilleran type metamorphic core complexes, emplacement of residual rare-metal melts and the formation of commercial deposits.

Доклады Академии наук. 2019;488(6):630-639
Phase relations at interaction of phlogopite with carbonate melt at Р = 3.8 GPa
Gorbachev N.S., Kostyuk A.V., Shapovalov Y.B., Gorbachev P.N., Nekrasov A.N., Soultanov D.M.

The phase relations in the phlogopite-carbonate system were studied at P = 3.8 GPa, T = 1200-1300 °C. The interaction of phlogopite with carbonate melt resulted in the formation of a polymineral association of relic and newly formed phases of the phlogopite-carbonate-clinopyroxene-spinel-garnet composition coexisting with carbonate melt. By increasing the temperature from 1200 to 1300 °C in the carbonate melt increases the solubility of phlogopite and the concentrations of its components - Si, Al, Mg, K. The phase composition of the quenching phases of the carbonate melt varies from substantially carbonate with isolated microcrystals of apatite and phlogopite at 1200 °C to phlogopite-carbonate with a variety of texture ratios at 1300 °C, reflecting the spontaneous crystallization of the carbonate melt during quenching. In the studied P-T, close to the mantle adiabate, phlogopite remains stable in the presence of silicate-carbonate melt.

Доклады Академии наук. 2019;488(6):640-644
Sources of Pechenga structure terrigenous layers clastic material according to detrital zircon isotopic analysis data (SIMS SHRIMP-II, LA-ICP MS)
Smolkin V.F., Mezhelovskaya S.V., Mezhelovsky A.D.

The results of Pechenga ore-bearing Paleoproterozoic structure, located on the northern-western part of Kola region, research, are presented in this article. Secondary ions mass-spectrometry (SIMS) was used for U-Th-Pb-zircon age definition, on SRHIMP-II device and mass spectrometry with inductively associated plasm with LA-ICPMS ablation on ThermoQuest Finnigan MAT Neptune device. Televi Formation basalt conglomerates, Luchlompo Formation red colored gravelites and middle part Matert Formation high siliceous turbidites were tested. On U-Pb diagram with Concordia part of analytical points for zircon from conglomerates are approximated by Discordia with the top intersection 2792 ± 7 Ma. All gravelite zircon grains are located on Concordia. The main part of their age values is within interval 2700-2820, the lesser - 2840-3000 Ma (with the maximums 2718, 2779, 2854, 2972). The single grains have the age from 3037 ± 4 up to 3698 ± 8 Ma. Concordant value 207Pb/206Pb age 2640 ± 16 Ma is fixed for turbidite zircon. The sources of zircon for conglomerates and gravelites were the rocks of Northern zone Pechenga structure basement: gneisses of Kirkenes, Varanger and Svanvik Complexes (2715, 2803 and 2825 Ma) and high aluminous gneisses (2798-2830 Ma), for turbidites - Southern slope granitoides. The dominating role of zircon group with 2. 7 billion years proves a global growth of continental crust in this period. Ancient values of zircon age (3.0-3.7 billion years) of red colored gravelites are connected with the deeper erosion of the basement and outcrop of Eoarchaean and Mezoarchaean age rocks on erosive surface in Northern zone within the period of the first global “Oxygen revolution” (2.4-2.3 billion years).

Доклады Академии наук. 2019;488(6):645-650
Specific features of earth’s free oscillations after deep-focus sea of Okhotsk earthquake of May 24, 2013
Kuzin I.P., Lobkovsky L.I., Dozorova K.A.

A description of initial excitation of spheroidal mode 0S2 initiated by the 2013 Sea of Okhotsk earthquake (Mw= 8.3) is presented. It is based on newly revealed fact of standing P-wave origination in the epicenter of the Sea of Okhotsk earthquake and excitation of traveling surface P-waves on the Earth’s surface by this wave. A new interpretation of the nature of free spheroidal Earth’s oscillations in case of strong earthquake (М ≥7,5) is proposed. The spheroidal mode 0S2 is interpreted as combination of standing and traveling P-waves, transferring the Earth’s strain energy.

Доклады Академии наук. 2019;488(6):651-654
Laws for the size distribution of Khasyreis
Victorov A.S., Orlov T.V., Arkhipova M.V.

The paper presents the results of empirical verification of the theoretical law, validated in a mathematical model of the morphological structure of thermokarst plains with fluvial erosion - the exponential distribution of the areas of khasyreis. The empirical testing based on the remote sensing data of high resolution involved 18 key sites at different regions of the cryolithozone in different natural environments. Eighty percent of the testing samples confirmed this theoretical statement. This result validates the suggested model and provides for the conclusion about the khasyrei radii corresponding to the Rayleigh distribution in different natural environments.

Доклады Академии наук. 2019;488(6):655-657
Climatic causes of the current expansion of the Italian locust range in Russia and neighboring countries
Popova E.N., Popov I.O.

Modeling of climatic ranges of a dangerous locust pest - the Italian locust on the territory of Russia and neighboring countries over two periods: 1956-1975 and 1996-2015 was performed. Analysis of the constructed map scheme demonstrates expansion of the climatic range of the Italian locust mainly in the northern direction in the period 1996-2015 compared with the period 1956-1975 resulting from continuing trend of increase in mean global air temperature observed in recent decades. Obtained data can be used in monitoring locust pests in agriculture.

Доклады Академии наук. 2019;488(6):658-660
Holocene deposits of the South-East coast of Gorlo Strait (White Sea): new data of diatom and radiocarbon analyses
Shilova O.S., Zaretskaya N.E., Repkina T.Y.

Diatom analysis and radiocarbon dating of the sedimentary cover of the terraces on the South-East coast of Gorlo Strait (White Sea) from Cape Veprevsky to Cape Intsy were carried out for the first time. The Holocene marine sediments traced to 4 m a.s.l. The rise in relative sea level occurred during Boreal and first half of Atlantic. The sea level reached the present value not earlier than 8500 14C yrs BP and probably stabilized at 3,5-4,0 m a.s.l. about 6300 14C yrs BP. The regression of the sea dates approximately 3000 14C yrs BP when coastal sedimentation changed to sediment formation in land environments. Higher levels were formed earlier 9500-8500 14C yrs BP and were not later flooded by the sea according to the diatom analysis data. During the Early Holocene regression, assumptive paleosoil horizons were formed there. They are covered by lacustrine, peaty, and aeolian sediments.

Доклады Академии наук. 2019;488(6):661-666
About the possibility of registration of waves and sea level fluctuations in coastal areas of the World Ocean based on analysis of video on the Internet
Dolgikh G.I., Fishchenko V.K., Goncharova A.А.

The paper describes a technology of recording surface wave signals and sea level fluctuations in coastal areas of the World Ocean based on real-time analysis of live video from surveillance cameras presented on the Internet. A wave signal obtained with described method in the port of Crotone (Italy) is compared with data from nearby station of the Global Sea Level Observing System (GLOSS). The example demonstrates the high recording quality of the seiche oscillation system of the port with periods from 40 to 2 minutes, which is comparable to GLOSS. At the same time, unlike the GLOSS stations, signals obtained through video contain responses of even shorter-period (up to tens of seconds) seiches, swell waves, wind and ship waves.

Доклады Академии наук. 2019;488(6):667-672
Biochemistry, biophysics, molecular biology
Comparative analysis of the biosynthesis of isoprenoid and aromatic cytokinins
Oslovsky V.E., Savelieva E.M., Drenichev M.S., Romanov G.A., Mikhailov S.N.

To compare the biosynthesis pathways of aromatic and isoprenoid cytokinins, a series of nucleoside derivatives of natural cytokinins was synthesized and their cytokinin activity was determined in a test system based on the model plant Arabidopsis thaliana. Cytokinin nucleosides are known to lack the hormonal activity until cleaving the ribose moiety at the position 9. Our experiments have shown that both ribo- and 5′-deoxyribo derivatives of N 6-isopentenyladenine were able to turn into active cytokinins in planta exhibiting cytokinin activity. By contrast, 5′-deoxy nucleosides of aromatic cytokinins did not show similar activity. Since 5′-deoxy nucleosides cannot phosphorylate in vivo, the direct pathway of active cytokinin formation by cleavage of nucleotides is blocked here. The detected activity in 5′-deoxy nucleosides of isoprenoid cytokinins and the lack of the activity in 5′-deoxy nucleosides of aromatic cytokinins indicates a difference in the biosynthesis of these compounds.

Доклады Академии наук. 2019;488(6):673-676
Effect of salicylic acid on the oxidative and photosynthetic processes in plants tomatoes by invasion with root-knot nematode Meloidogyne Incognita (Kofoid et White, 1919) Chitwood, 1949
Udalova Z.V., Zinovieva S.V.

A study of the processes of lipid peroxidation and the activity of the peroxidase enzyme, as well as photosynthetic pigments in susceptible tomato plants treated with salicylic acid (SA), during infection with the root-knot nematode Meloidogyne incognita. It was shown that in the roots of SA-treated plants, the activity of lipid peroxidation is higher compared to untreated ones, especially in the case of nematode invasion. A significant increase in the activity of lipid peroxidation in SA-treated invasive plants compared with untreated was noted during the transition of larvae to the sedimentary stage and the beginning of the formation of feeding places - giant cells (3-5 days after invasion). This, apparently, contributes to the inhibition of the development of the parasite and the reduction of plant infection, and also indicates the involvement of oxidative processes in the mechanism of the induced resistance of plants to root-knot nematodes. In the SA-treated plants, the qualitative and quantitative composition of photosynthetic pigments, disturbed by invasion, was restored and corresponded to the control level.

Доклады Академии наук. 2019;488(6):677-681
Efficiency of penetration of dopamine and serotonin peptide derivatives through the artificial membranes
Shevchenko V.P., Andreeva L.A., Nagaev I.Y., Shevchenko K.V., Myasoedov N.F.

A mass spectrometric method has been developed for determining the content of dopamine and serotonin derivatives, which allows to evaluate the efficiency of their penetration through artificial membranes depending on the structure of their peptide fragment. In this case, the diffusion of dopamine and serotonin derivatives through the membrane occurred as a result of competitive interactions. It was shown which compounds in this mixture more easily penetrate through artificial membranes. It was found that the most promising in terms of overcoming the BBB are Boc-Pro-Srt and Boc-Pro-DOPA.

Доклады Академии наук. 2019;488(6):682-684
General biology
Jasmonic acid enhances the resistance of potato plants in vitro to salt stress
Efimova M.V., Mukhamatdinova E.A., Kovtun I.S., Kabil F., Medvedeva Y.V., Kuznetsov V.V.

The protective effect of jasmonic acid (JA) was evaluated under stress (100 mM NaCl) condition. The investigations were carried on potato plants (Solanum tuberosum L.) of the mid-season variety Lugovskoy. Plant-regenerants were grafted and cultured in test tubes on modified Murashige-Skoog agar medium in the absence (control) or in the presence of JA at concentrations of 0.001; 0.1 and 10 µM under optimal growing conditions or with the addition of NaCl. After 28 days of cultivation, growth (length of stem and root, number of tiers and leaves, plant mass) and physiological (proline content and photosynthetic pigments, determination of the osmotic potential of cell exudate) of the plants were assessed. For the first time it has been shown that jasmonic acid (0.1 and 10 µM) manifests a pronounced protective effect on potato plants under salt stress condition. The protective effect based on the partial removal of the salt negative effect on the main photosynthetic pigments and the maintenance of the osmotic status of cell contents during salinization.

Доклады Академии наук. 2019;488(6):685-689

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