Vol 488, No 6 (2019)

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.

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.

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.

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.

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.

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.

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.

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.

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).

A description of initial excitation of spheroidal mode ₀S₂ initiated by the 2013 Sea of Okhotsk earthquake (M_w= 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.

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.

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.

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.

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.

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.

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.