We consider the dynamics of the harmonic crystal in the half-space with zero boundary condition. We assume that the initial data are a random function. We prove the convergence of the distributions of the solutions to a limiting measure for large times. The formula for the limiting energy current density (in mean) is derived. The application to the case of the Gibbs initial measures is given. We find the stationary non-equilibrium states, in which there exists a non-zero heat flow passing through the points of the crystal.

For generalized functions with Laplace transform has nonnegative imaginary part in tube domain over positive actant, we found sufficient conditions for existence of quasiasymptotic, the function with regular behavior with respect to which the quasiasymptotic exists being explicitly found. The obtained results are used to steady of the asymptotic behaviour of solutions of the Cauchy problem of passive operators.

We determined a small parameter that determines the possibility of using the n-vicinity 06_method to calculate the free energy of a spin system, and found the types of spin systems for which this method is applicable. It is shown that this method is applicable for the analysis of spin systems, where the number of nearest neighbors is greater than 16/3.

The paper presents the results of studies of flow behind cylindrical flow bodies in a flat-flow hydrodynamic generator, obtained on the hydrodynamic bench of the experimental base of the National Scientific Center NBMT RAS with the degree of flow blocking by flow bodies S_t/S₀ = 10-80%, Re numbers (0,5-5) · 10⁵, PVH inlet pressure = 0,1-0,8 MPa. It was found that with the same pressure drop two different types of flow can be realized behind the flow bodies: with a developed cavitation zone, within which there is an extensive low pressure area and without it, but with the formation of vortex structures with the presence of centers of cavitation bubbles in them. At a certain value of input to output pressure, which is constant for each value of the degree of overlap of the flow, powerful pressure peaks of the resonant type arise with an amplitude of 2-2,5 times the maximum value of the input pressure. The frequency of occurrence of these pressure peaks increases linearly with increasing pressure drop, and decreases by an order of magnitude with an increase in the degree of overlap of flow up to 80%. The frequency dependence of the number Re for each value of S_t/S₀ is linear. The value of the Strouhal number St with an increase in S_t/S₀ increases linearly with S_t/S₀ = 0,82 and the value St = 1,2.

Direct numerical simulation data of a stably stratified turbulent Couette flow contains two types of organized structures: the rolls that arise at neutral and close to neutral stratification, and the layered structures, which manifest themselves as the static stability increases. It is shown that both types of structures have spatial scales and forms that coincide with the scales and forms of the corresponding optimal disturbances of the simplified linear model of the Couette flow with the same Richardson numbers.

A new strategy of synthesis of thiacalix[4]monothiacrown-ethers in 1,3-alternate stereoisomeric form has been suggested and implemented through macrocylization of the lower rim of 3-bromopropoxy-substituted thiacalixarene by dithiols.

Composites of hydroxyapatite (HA) with polyvinylpyrrolidone (PVP) were synthesized by precipitation in water solutions, mass relations of HA/PVP varied in region 3,6-14,5. The composite materials were investigated using XRD, IR, electron paramagnetic resonance (EPR) spectroscopy and transmission electron microscopy (TEM). Based on the TEM results it was found that during calcination of composites at 400 °C small agglomerates consisting of individual crystalline HA particles were formed, resulting in a particle size (according to TEM) slightly larger than coherent scattering region. Using the method of photoinduced EPR spectroscopy confirmed the presence of interaction between HA and PVP. The resulting composites can be used as materials for reconstructive surgery.

The effect of low-frequency oscillations on a system consisting of two biochemically active components: the dye of methylene blue and ascorbic acid is investigated. Each of these components can be reversibly oxidized and reduced. The system is interesting in that it makes it possible to trace the influence of the low-frequency acoustic field on the mutual redox process and to reveal the features of the effect of such oscillations. It was found that, in this system, with the introduction of low-frequency effects, redox processes are not accelerated, but slowed down. There is an effect inhibition of the sound-chemical process in the field of low-frequency acoustic effects. The effect is quantified.

Based of study of the morphological features of a coal seam in a mine of the Eastern Donbas, the mineral and coal elements of the object studied were identified as a single sedimentary association of a pseudo-washout nature. Specific criteria for attributing coal-bearing structures to epigenetic or syngenetic washouts of a coal seam were elaborated.

The phase formation in the Na₂O-TiO₂-SiO₂-H₂SO₄-H₂O system during hydrothermal has been studied. The obtained data were used for the producing of a new type of sorbents with a frame structure similar to the mineral ivanyukite. Excess amounts of silicon and sodium in relation to titanium (III) and titanium (IV) as well as pH up to 12 provide “supersaturating” of the salt mass and affect the rate of precipitation, phase composition, structure and surface properties. The framework arrangement of SiO₄ tetrahedron and TiO₆ octahedron create channels where Na⁺ and water molecules are located. The structure of ivanyukite along with mesoporosity provides its high ion-exchange properties.

Based on the data of experimental studies of wave disturbances in the Earth’s atmosphere before and after the earthquakes in Uzbekistan (May 26, 2013) and Kyrgyzstan (January 8, 2007), earlier unknown changes in the parameters of internal gravity waves are revealed. These changes were manifested during the period of five days before the earthquake and in certain cases can be used for short-term prediction of the time when seismic events are to occur.

The use of the apparatus of nonadditive statistical mechanics for the evaluation of thermodynamic ecosystem variables based on multispectral measurements of reflected solar radiation is discussed. The parameter q is accepted corresponding to the conditions of the Förster’s maximum of organization. On the basis of remote information (Landsat) the entropy, Kullback information, Förster measure of organization, free energy, exergy, bound and internal energy, energy costs for evapotranspiration and photosynthesis for q-index values measured for each pixel of remote sensing scenes. It is shown that the seasonal dynamics of the q-index and the organization measures fully correspond to consequences that follow from the theory of open nonequilibrium systems, and thermodynamic variables reflect well the current state of ecosystems.

The results of an experiment conducted in September 2017 to substantiate the applicability of the “acoustic mudslide” effect when solving the positioning problems of autonomous underwater vehicles in cases of their operation at depths substantially exceeding the depth of the axis of the underwater sound channel are discussed. The results of the experimental studies and numerical analysis of the effect of an acoustic energy focusing in the near-bottom layer of the shelf and its transition into deep-water (up to 500 m) layers of the Sea of Japan for summer-autumn hydrological conditions are presented. Mathematical modelling of the propagation of acoustic waves in a model waveguide reproducing the experimental conditions using the parabolic equation method has been performed. The observed effective signal propagation speeds are explained using the normal wave method.

We studied the effect of zinc excess (1000 µM) and low temperature (4 °C) on the IRT1 gene expression in barley roots and leaves. Exposure at each of the stress factors separately, induced an increase in the content of the HvIRT1 gene transcripts, more pronounced in the leaves. At the same time, growth of seedlings continued. Under the combined action of factors in the first 3 days, the amount of mRNA also increased, but after 7 days of exposure it significantly declined, which corresponded with a complete inhibition of seedlings growth. It is assumed that the seedlings growth inhibition under the combined effect of the zinc excess and low temperature is associated with a decrease in the transcriptional activity of the HvIRT1 gene, due to the deficiency of a number of trace elements under these conditions.

The effect of soil compared to sand on the germination of wheat seeds and the development of their seedlings, as well as the effect of seed treatment with humic substances on their development in sand and soils was studied. For a number of the Russian Plain soils, it was shown that the soils inhibit seed germination significantly. It was established that pre-sowing treatment of seeds with humic preparations has a noticeable stimulating effect when sowing treated seeds in sod-podzolic soil and has no effect practically when sowing these seeds in sand. On the basis of the known phenomenon of soil allelotoxicity, it was suggested that the stimulating effect of humic substances on seed development is to limit the influence of allelotoxins on their development.