In the article we consider the spatial distribution of points, whose coordinates are conjugate algebraic numbers of fixed degree. The distribution is introduced using a height function. We have obtained universal upper and lower bounds of the distribution density of such points using an arbitrary height function. We have shown how from a given joint density function of coefficients of a random polynomial of degree n, one can construct such a height function H that the polynomials q of degree n uniformly chosen under H[q] ≤1 have the same distribution of zeros as the former random polynomial.

This article is devoted to constructing neural network-based models for discrete-valued time series and their use in computer data analysis. A new family of binomial time series based on neural networks is presented, which makes it possible to approximate the arbitrary-type stochastic dependence in time series. Ergodicity conditions and an equivalence relation for these models are determined. Consistent statistical estimators for model parameters and algorithms for computer data analysis (including forecasting and pattern recognition) are developed.

A concept of a middle- and far-infrared detector has been proposed. The detector is built as a planar collection of parallel graphene strips of different length and width. The feature of the detector scheme is the concurrent utilization of two different detection mechanisms: excitation in the given frequency range of low-frequency interband transitions inherent in armchair graphene strips and antenna resonances of strongly slowed-down surface waves (plasmon polaritons). It has been shown that matching these two resonances results in the essential detector signal amplification, thus providing an alternative way how to solve the problem of the low efficiency of resonant graphene antennas. An approach is proposed to analyze the design of such detectors, as well as to discuss the ways of tuning the both mechanisms.

Relativistic system for a vector-bispinior describing a massless spin 3/2 field is studied in the spherical coordinates of Minkowski space. Presentation of the equation with the use of the covariant Levi-Civita tensor exhibits existence of the gauge solutions in the form of the covariant 4-gradient of an arbitrary bispinor. Substitution for 16-component field function is based on the use of Wigner functions, it assumes diagonalization of the operators of energy, square and third projection of the total angular momentum, and space reflection. We derive radial system for eight independent functions. General structure of the spherical gauge solutions is specified, and it is demonstrated that the gauge radial functions satisfy the derived system. It is proved that the general system reduces to two couples of independent 2-nd order and nonhomogeneous differential equations, their particular solutions may be found with the use of the gauge solutions. The corresponding homogeneous equations have one the same form, they have three regular singularities and one irregular of the rank 2. Frobenius types solutions for this equation have been constructed, and the structure of the involved power series with 4-term recurrent relations sre studied. Six remaining radial functions may be straightforwardly found by means of the simple algebraic relations. Thus, we have constructed two types of solutions with opposite parities which do not contain gauge constituents.

An integrated approach including the click chemistry methodology, molecular docking, quantum mechanics, and molecular dynamics was used to perform the computer-aided design of potential HIV-1 inhibitors able to block the membrane- proximal external region (MPER) of HIV-1 gp41 that plays an important role in the fusion of the viral and host cell membranes. Evaluation of the binding efficiency of the designed compounds to the HIV-1 MPER peptide was performed using the methods of molecular modeling, resulting in nine chemical compounds that exhibit the high-affinity binding to this functionally important site of the trimeric “spike” of the viral envelope. The data obtained indicate that the identified compounds are promising for the development of novel antiviral drugs, HIV fusion inhibitors blocking the early stages of HIV infection.

Based on the data of ab initio calculation of the structure of (RSO3)2Mg (H2O)18 and (RSO3Rb)2(H2O)16 clusters, which simulate the structure of swollen sulfostyrene ion exchangers in the corresponding ionic forms and a water cluster of comparable size, the numbers of water molecules directly bound to cations and their coordination numbers, including the oxygen atoms of the sulfonic groups linked to the cation, were calculated. It is shown that the first molecular layer around the magnesium ion is formed from water molecules with the highest binding energy with the cluster, and around the rubidium ion – from the molecules of the nearest environment with the lowest binding energies. This is explained by the fact that the transfer of water molecules from its volume to magnesium hydrate is energetically favorable, but not to rubidium hydrate. Therefore, the magnesium ion builds its hydrate mainly from water molecules with the highest binding energy in order to obtain the greatest energy gain, and the rubidium ion – from molecules with the lowest energy, which provides the smallest energy loss.

It has been shown that the formyl precursors of 3,7-interphenylene 11-deoxyprostanoids, formed during acidic hydrolysis of the corresponding acetals, can undergo isomerization (disproportionation) in the acidic medium to give 2-(arylalkyl)-3-(hydroxymethyl)cyclopent-2-ene-1-ones – the synthons for prostanoids and phytoprostanes of the series B. Acetal precursors of 3,7-interphenylene 11-deoxyprostaglandin analogues with electron-donating alkoxy substituent in position 3′ of the aromatic fragment in the α-chain under similar conditions hydrolyze with the formation of formyl derivatives that spontaneously cyclize to produce 2,3,4,9-tetrahydro-1H-cyclopenta[b]naphthalene-1-ones.

The influence of various concentrations of chemical mutagens on the seed germination, the growth and manifestation of decorative traits in the seed offspring of mountain pine (Pinus mugo Turra), Scots pine (Pinus sylvesrtis L.), and Scots pine “witch’s broom” (“WB”) is assessed. A 0.1 % aqueous solution of colchicine, as well as 0.1, 0.5, and 1.0 % aqueous solutions of dimethyl sulfate (DMS) was used as mutagens. The species-specificity of the influence of chemical mutagens on the seed germination was established. Thus, the treatment of mountain pine seeds with aqueous solutions of colchicine and DMS had some stimulating influence on their germination. On the contrary, the germination of the Scots pine seeds and the seeds collected from the Scots pine “WB” decreased with increasing the DMS concentration in the solution. Among the offspring obtained using chemical mutagens, specimens were identified with changes in the growth strength towards dwarfism, the branching features of which manifested themselves in the form of apical dominance violation and shoot formation growth, with changes in the color of needles, including winter color changes of different-intensity color from green to yellow, bronze or bronze yellow. As a result of the research, 363 specimens with atypical traits were selected for further breeding work.

The cell composition of native transplant autosmes (NTA) used for bone plastics was studied. The histological examination showed the fragments of bone beams with preserved osteoblasts, the foci of myeloid and lymphoid hematopoiesis and the fibrin deposits, which suggested the presence of MMSCs. Immunophenotyping of the NTA cell population revealed a high level of expression of the surface markers CD105, CD73, and CD90 characteristic for MMSC. DNA-flow cytometry of the bone dust confirmed almost complete preservation of graft viability on the 3rd day of culturing (97.7 % of live cells). The data of this study confirm the presence of the osteogenic, osteoinductive, and osteoconductive properties of the bone dust and emphasize the importance of a further study of this-type bone graft for use in surgical interventions.

The trends in changing the content of sulfur and nitrogen in atmospheric precipitation in the territory of Minsk over an 18-year period are characterized on the basis of the analysis of the monitoring results of the chemical composition of atmospheric precipitation at the experimental site. A downtrend in the sulfur and nitrogen content combined with an uptrend in the precipitation acidity was identified. An average decrease (trend) in the content of sulfur in atmospheric precipitation for 2002–2019 was 0.019 mg S/dm3/year, of oxidized nitrogen – 0.008 mg/dm3, of reduced nitrogen – 0.019 mg/dm3. Over an 18-year period, the changes in the content of sulfur and nitrogen in atmospheric precipitation decreased the deposition of sulfur on average by 31.3 kg/km2/year, of oxidized nitrogen – by 15.4 kg/km2/year, of reduced nitrogen – by 25.6 kg/km2/year. It is shown that for the period from 2005 to 2012, the acidification potential of the natural environment decreased parallel to the reduction of the sulfur and nitrogen deposition; in the subsequent period, the trend of the acidification potential basically follows the trend of the precipitation of the main cations. It is revealed that the rates of average reduction in the content of oxidized sulfur and oxidized nitrogen in atmospheric precipitation in Minsk for the period from 2002 to 2017 are comparable to the rates of reduction of these compounds at the stations of the EMEP Program in Europe, and exceed those for reduced nitrogen.

A relationship between aerosol air pollutions and summer air temperatures in Europe was studied. High correlation coefficients between the latitudinal distributions of the zone-averaged trends of the mentioned parameters were found. The potential effects of decrease in the aerosol emission on the cloud optical depth, in the air temperature, and the amount of precipitation in the territory of Europe were estimated on the basis of the obtained regression equations. It was shown that due to the aerosol emission decrease, the average summer temperature in Europe in 2000–2020 could increase by 0.53 °С, which is ~73 % of total summer warming in the region. The empirical estimates obtained in the work were confirmed by the satellite observation data and the numerical calculations of changes in radiation balance components at the top of the atmosphere. It was shown that the radiation emission decrease in the territory of Europe could increase the average radiation balance in Europe in summer months by 2.27 W/m², which is ~65 % of its total change. The increase in the carbon dioxide content in the atmosphere during the same period contributed much less to the observed change in the radiation balance (17.5 %), which supports the hypothesis about the dominant role of aerosols in summer warming in Europe.

Carried out simulation of oscillations of a spring-loaded roll in a roll compactor when interacting the powder being compacted with the rolls. Considering the separation of the feed and compaction areas in the contact area of the roll with the material being compacted, we obtain the dependence of the force acting on the roll on the gap size between the rolls. It is shown that this dependence is non-linear, and it can be described with a sufficiently high accuracy degree by an exponential function with a negative exponent in the working range. The given numerical solution of the equation of free nonlinear oscillations of the spring-loaded roll has shown that considering the deformation of the material being compacted leads to a reduction of the natural frequency of the system by 20–25 % compared to the case, where the pressure force of the powder on the roll is assumed to be independent of the gap size. The nonlinearity of the dependence of the pressure force on the gap also leads to the increase by 10 % in the calculated values of the maximum displacements. The developed approach to the calculation of oscillations of the spring-loaded roll in the roll compactor enables to take into account the peculiarities of deformation of the powder being compacted during its interaction with the rolls. In addition, it allows estimating the frequencies and oscillation amplitudes and setting the optimum range of spring rate values, at which the occurrence of resonance in the machine is not possible.

Anodic alumina membranes with an ordered microstructure have been synthesized and investigated. It was found that Knudsen diffusion is the predominant mechanism for gas penetration through the obtained membranes. The technology made it possible to obtain porous membranes with specified structural characteristics for the separation of gas mixtures. Designs of a diffusion element and a gas separation module based on membranes made of anodic aluminum oxide have been developed, and the features of mass transfer under various operating conditions have been studied. The membrane module without recirculation made it possible to concentrate the heavy component from the model helium-methane mixture (99 % / 1 %) up to 18 %. The membrane module with recirculation made it possible to concentrate a light component from a model helium-methane mixture (1 % / 99 %) up to 40 %.

A fluid withdrawn by a moving inclined surface with account for the near-wall slip effect is analyzed theoretically. A non-Newtonian fluid task is stated in general form. The solving of this task enables revealing the basic physical principles and mechanisms of the process over the entire withdrawal velocity range realized in practice. The case of withdrawing a finite yield stress viscoplastic fluid is considered.

Single crystals of solid solutions (In₂S₃)_x⋅ (AgIn₅S₈)_1–x were grown by the method of directional crystallization of the melt (Bridgman method). Studies of the elemental composition and crystal structure of these single crystals have been carried out. On the basis of solid solutions (In₂S₃)_x⋅ (AgIn₅S₈)_1–x, photosensitive structures have been created for the first time and the photoelectric properties of these structures have been determined. The possibility of using the created structures as broadband photoconverters of optical radiation is shown.