In this article, monotone difference schemes for linear inhomogeneous parabolic equations, the Fisher or Kolmogorov-Petrovsky-Piskunov equations are constructed and investigated. The stability and convergence of the proposed methods in the uniform norm L_∞  or С is proved. The results obtained are generalized to arbitrary semi-linear parabolic equations with an arbitrary nonlinear sink, as well as to quasi-linear equations.

In the linear approximation of general relativity, an exact spherically symmetric non-static solution of Einstein's equations is obtained. It describes a gravitational wave depending on a retarded argument. The non-zero expressions for the momentum density of the wave and the forces acting on a test particle are obtained.

The electrophysical properties and the resistive switching effect of the ITO/SiN_x/Si memristor structure were studied. A silicon nitride film with a thickness of ~200 nm with an inhomogeneous element depth distribution was deposited by low-pressure chemical vapor deposition. Based on the Rutherford backscattering data, it was shown that the concentration of excess silicon atoms in the SiN_x film increases from 9 to 44 % when approaching the Si substrate. The analysis of the current-voltage characteristics of ITO/SiN_x/Si structures revealed that the conduction mechanism in the high-resistance state is determined by the nitride film properties and is described by the Poole-Frenkel model taking into account the hopping model of electron transport between traps. Switching to the low-resistance state is probably caused by the migration of indium or tin ions from the ITO contact to the SiN_x layer. The conduction of the ITO/SiN_x/Si structure in the low-resistance state is determined by both the mechanisms of charge-carrier injection from the contact and charge-carrier transport through the dielectric layer. Reverse polarity results in destructing the conductive channel and switching the structure to the high-resistance state. The photo-switching effect was found for the ITO/SiN_x/Si structure, which opens up new possibilities of using memristors in silicon optoelectronic systems.

The phase state, viscosity and optical properties of polysulfone (PSF) solutions in N,N-dimethylacetamide (DMAc) with the addition of block copolymer Pluronic F127 and polyethylene glycol (PEG-4000, M_n = 4000 g-mol^-1) were studied. Additives are both pore-forming and hydrophilizing agents. It was found that 18-22 % PSF solutions in DMAc with the Pluronic F127 content t ≥5 wt. % feature a lower critical solution temperature (LCST). Mixed matrix PSF/Pluronic F127 and PSF/PEG membranes were obtained by the phase inversion technique and the comparative studies of their structure and performance were carried out. It was found that the average surface roughness parameters of PSF/Pluronic F127 membranes significantly exceed those of PSF/PEG membranes. The presence of the both additives in the casting solution leads to the effective hydrophilization of the membrane selective layer. It was shown that the increase in the membrane flux and the decrease in the polyvinylpyrrolidone (K-30, M_n = 40000 g-mol^-1) rejection coefficient are a result of adding both Pluronic F127 and PEG-4000 to the casting solution. It was shown that PSF/Pluronic F127 membranes are characterized by higher shrinkage resistance and a lower total flux decrease during ultrafiltration of bovine serum albumin solutions. It was found that the antifouling performance of PSF/Pluronic F127 membranes significantly exceeds that of PSF/PEG membranes.

The structural parameters of the molecular model of a swollen sulfostyrene ion exchanger in lithium form were calculated. The calculations were performed using the non-empirical method (HF/basis using the Mini Huzinaga basis) and the Firefly software for the (RSO₃Li)₂- (H₂O)₂₀ cluster. The distances between the Li⁺ ions and the oxygen atoms in the cluster, which belong to the water molecules and sulfonic groups, were found and sorted in ascending order. The obtained data allowed one to establish that in the first molecular layer, strictly four oxygen atoms of water molecules are present around the Li⁺ ion, and the ion itself does not form a direct bond with the sulfonic group. A sharp jump in the Li⁺-O distances takes place between the first and second molecular layers around the cation.

The reaction of a 2-carene containing mixture, obtained by 3-carene isomerization, with 4-methoxybenzalde-hyde in the presence of halloysite nanotubes treated with 5.0 % HCl was studied. The main reaction products are the chiral derivatives of isobenzofuran. Selectivity to these compounds (71.4 %) is comparable to that when only 2-carene is used as a reactant. Thus, the possibility is shown how to use halloysite nanocatalysts for selective production of isobenzofuran compounds based on 3-carene isomerization products (major component of turpentine) without preliminary mixture separation.

The trajectories of molecular dynamics simulation of phosphorylated S258 (CYP17A1), T162 and Y361 (CYP19A1) were analyzed to understand a possible mechanism of influence of post-translational modification (PTM) on the structure and functions of human sterol-hydroxylases CYP17A1 and CYP19A1. It was found that PTM has no dramatic influence on the structures of the enzymes but stabilizes them. According to our data, the phosphorylation of S258, T162 and Y361 influences the interface of interaction between human sterol-hydroxylases and the corresponding electron donors by decreasing the mobility of amino acids that take part in forming molecular complexes of the enzymes and the corresponding redox-partners. The phosphorylation of T162 (CYP19A1) decreases the mobility of amino acids forming access channel. The obtained results can shed light on the mechanism of fast regulation of human CYP17A1 and CYP19A1 activity by PTM.

Alien amphipods were found in Belarus in the early 2000s. During long-term observations of the macrozoobenthic community in the rivers, a decrease of native amphipods was revealed in the southern part of Belarus. Several laboratory experiments were conducted to reveal the predatory effects of four alien species (Dikerogammarus haemobaphes (Eichwald, 1841), Echinogammarus ischnus (Stebbing, 1898), Obesogammarus crassus (Sars, 1894), Obesogammarus obesus (Sars, 1896) on some macrozoobenthic groups. D. haemobaphes has a maximum predation rate and a broad food spectrum in comparison with other studied species. The above-mentioned data can be one of the reasons of wide spreading and very abandoned populations of D. haemobaphes in various rivers in Belarus.

A comparative analysis of the molecular process of nanostructured zinc oxide of different shape (rod and spherical particle) and zinc chloride as a source of free ions on human lymphocytes was carried out. Our data indicated that ZnO nanostructures induced a decrease in the lymphocyte viability and an increase in the intracellular labile Zn²⁺ pool in a concentration-dependent manner after 20 and 40 h incubation with cells. It was found that ZnO NRs have the lowest cytotoxicity, but ZnCl₂ - the highest. The Zn-mediated activation of free radical processes - ROS accumulation in the cells -is a possible mechanism of the cytotoxic action of these agents. Thus, the shape of ZnO nanomaterial and its ability “to shed” zinc ions make the main contribution to the detected molecular and membrane process on human lymphocytes in vitro.

Some disadvantages of the extracorporeal blood purification (EBP) methods as reducing plasma levels of different important metabolites are described. Disorders of amino acid metabolism in sepsis are manifested into microcirculation interruptions, a decreased immune response and an increased mortality. The aim of the study is to investigate the EBP influence on the levels of nonessential amino acids in the blood plasma of patients with sepsis. 28 patients diagnosed with “sepsis” were selected. Standard treatment protocols of plasma filtration, hemofiltration and hemadsorption with various sorbents were used. A significant decrease in the levels of asparagine, phosphoethanolamine, proline; α-aminobutyric acid showed a significant increase in these levels in patients who underwent “Proteasosorb” sorbent hemadsorption. A significant decrease in the levels of ornithine, aspartic acid, 3-methylhistidine, 1-methylhistidine in patients treated with hemofiltration was found. The EBP methods significantly influence the amino acid metabolism.

А replicate designed open-label, randomized, crossover single-dose bioequivalence study using three periods and three sequences was conducted to assess the comparative bioavailability of the sorafenib-containing medicinal products Flutrixan (200 mg tablet, Institute of Bioorganic Chemistry of NAS of Belarus, Belarus) and Nexavar (200 mg tablet, Bayer Pharma AG, Germany), in healthy volunteers under fasting conditions. It was shown that all criteria used to assess the bioequivalence of compared medicinal products were fulfilled. The Test/Reference geometric mean ratios obtained for the pharmacokinetic parameters C_max and AUC_0-72 and the corresponding 90 % confidence intervals were within the acceptance range of 80.0-125.0 %. Both sorafenib products were well tolerated and had a favorable safety profile. Therefore, it can be concluded that the generic medicinal product Flutrixan is bioequivalent to the reference medicinal product Nexavar.

A study was made of the features of rock pressure manifestation and the deformation nature of development and assembly workings depending on the binding of the roof and its location relative to the longwalls mined by the chamber system for layers 2, 2-3, 3, as well as of the panels mined by the chamber system in the extraction conditions of the worked out fourth sylvinite layer of the Third potash horizon at a depth of more than 600 m. It was established that the service life of newly designed workings depends on their location on the panel, the roof binding and fastening parameters. The longest service life of workings will be noted when they are located in the mined space above the mined longwalls along the lower layers, and the shortest service life will be marked when they are carried out in the central part of the safety intercolumn pillars. Based on the studies performed, the recommendations were made on the selection of locations, roof bindings and on the protection and maintenance of development workings for the sites of the mine fields of the JSC “Belaruskali” mines extracting the worked out fourth sylvinite layer at depths over 600 m. The developed recommendations are aimed at improving the work safety and efficiency when extracting abandoned mineral reserves. Using the study results, the project was developed to conduct development workings of a new panel of the longwall 11-5 that provides the necessary stability of workings for the entire period of winning operations and, ultimately, safe extraction of potash ore in the amount of at least 2 million tons.

The research results of the influence of graphite content, type and dispersion on the structure, mechanical and physical properties of copper—graphite composite material are presented. It is shown that in the sintering process, when the content of grade GL graphite is 1, 5, 7 %, shrinkage is 5.7; 2.4 and 0.6 %, respectively, with 20 and 30 % — no volumetric changes. In copper—graphite material, when the content of grade MG graphite is less than 10 %, a growth of samples of 1—1.6 % is observed; when the graphite content is higher, the volume practically does not change. With a graphite content of more than 20 %, regardless of its grade and dispersion, the strength of copper—graphite material sharply decreases due to both a reduction of the metal contact area and a transition of the material structure from frame-metal to matrix. In a material with grade MG graphite with the dispersion of 140 and 65 µm, multiple microcracks are formed in the deformation process. When the content of grade MG graphite is 10 %, the electrical resistivity of copper-graphite material is equal to 11—13•10⁸ Ohm•m, when it is 30 %, the electrical resistivity is equal to 136—140•10⁸ Ohmrm; when the content of grade GL graphite — 8 and 18•10⁸ Ohm•m, respectively.

Two new variants of approximate analytical solution of the one-phase Stefan problem with a convective boundary condition at a fixed boundary are proposed. These approaches are based on the use of new integral relations forming infinite sequences. It is shown that the most exact variant of solving the Stefan problem with a convective boundary condition is to refuse from the classical Stefan condition at the free boundary and to replace it with its integral relation. By the example of solving the test Stefan problem with a Robin boundary condition, having an exact analytical solution, it is shown that the proposed approach is much more exact and efficient compared to the known variants of the integral computational scheme, including the heat-balance integral method allowing the Stefan condition at the free boundary to be satisfied. The solutions obtained with the use of the square-law and cubic polynomials are presented. As for the test problem using the cubic polynomial, the relative error in determining the free boundary comprises hundredths and thousandths of percent. In this case, at the time instant t = 1, the relative error in determining the temperature profile is ε_T = 0.075 %.

During rapid economic development and emergence of new technologies, as well as the expansion of intercultural communications, improving the knowledge of foreign languages is one of the conditions for a successful adaptation of new generations in the social space and for the mastery of global scientific, technical, spiritual and cultural competencies. According to the latest data, about 70% of the world population speaks more than one language, while the bilingual people communicate to the best of their education. Nevertheless, the bilingualism problem is not removed from the agenda and is quite relevant for Belarus, which requires further scientific study.