The article shows the achievements of the Department of Humanitarian Sciences and Arts of the National Academy of Sciences of Belarus at the beginning of the 21^st century.

In this paper, we construct and study unconditionally monotone and globally stable difference schemes for the Fisher equation. It has been shown that constructed schemes inherit the stability property of the exact solution: 0 ≤ u(x, t) ≤ 1, (x, t) ∈ Q_T = {(x, t) : 0 ≤ x ≤ l, 0 ≤ t < +∞} for a given input data of the problem. The unconditional monotonicity of the difference schemes is proved and the a priori estimate is obtained in the uniform norm for the difference solution. The stable behavior of the difference solution in the nonlinear case takes place under slightly more stringent constraints on the input data: 0,5 ≤ u₀ (x), µ₁(t), µ₂(t) ≤ 1.

Let X be a class of groups. Suppose that with each group G ∈ X we associate some system of its subgroups τ(G). Then τ is said to be a subgroup functor on X if the following conditions are hold: (1) G ∈  τ(G) for each group G ∈ X; (2) for any epimorphism φ: A → B, where A, B ∈ X, and for any groups H ∈ τ(A) and T ∈ τ(B) we have H^φ ∈ τ(B) and T^φ-1 ∈ τ( A). In this paper, were considered some applications of such subgroup functors in the theory of finite groups in which generalized normality for subgroups is transitive.

A fibrous carboxylic ion exchanger, obtained by post-radiation grafting of polyacrylic acid to polypropylene fiber, in the ammonium form has an abnormally low swelling in water, corresponding to 10 moles of water per equivalent, and in the form of tetraethylammonium ion (NEt₄⁺) – abnormally high 25 moles of water/eq. Considering that NH₄⁺ is a hydrophilic particle and NEt₄⁺ is hydrophobic, this fact seems paradoxical. The article attempts to explain this phenomenon using molecular modeling (ab initio calculations of the structure of hydrate complexes in the HF MO LCAO approximation with the 6-31G basis set) in combination with the Predominant Hydrates Model, which made it possible to calculate the theoretical water sorption isotherms of the ion exchanger and compare them with experimental data. The abnormally low swelling of the ion exchanger in the NH4+-form is caused by the formation of a strong bond between the carboxylate anion and ammonium with a significant degree of covalence due to the superposition of the Coulomb interaction of the ions and the formation of a hydrogen bond between them. The abnormally high swelling of NEt₄⁺-forms is caused by the absence of a strong interaction between cations and carboxylate groups due to the impossibility of their convergence due to steric reasons. The high swelling of the ion exchanger is caused by the absence of blocking of the hydrophilic carboxylate groups of the ion exchanger by hydrogen bonds with the cation. The ion exchanger matrix does not contain a cross agent and does not create a spatial restriction for the high swelling of the ion exchanger.

The effect of sodium polyacrylate, polyethylene glycol of various molecular weights, and their mixtures on the dispersion stability of calcium and magnesium carbonates was studied. It was shown that in the presence of a binary system, the light transmission of the dispersion decreases 1.2–1.5 times, the content of fine fraction particles increases by 1.1–1.3 times compared to the individual components. The stability of the dispersion of carbonates depends on the components ratio in the binary system and their molecular weight. The formation of adsorption solvated layers of polyacrylate and polyethylene glycol molecules at the interphase boundary contributes to an increase in the stability of the carbonate dispersion.

An Alzheimer-like pathological process was induced in mature female Wistar CRL: (WI) WUBR rats using aluminum chloride (200 mg/kg, intragastrically, 6 weeks) in order to model redox imbalance and oxidative stress (OS) in the hippocampus and study the possibilities of their correction 2 weekly administration of coenzyme A biosynthesis modulators (panthenol – PL, pantethine – PT, homopantothenate – HP) at a dose of 200 mg/kg intragastrically for 2 weeks). Against the background of activation of peroxidation processes and a decrease in acetylcholinesterase activity, a decrease in the reduction potential of glutathione and the level of the acid-soluble fraction of CoA was observed with a simultaneous increase in the activity of glutathione-metabolizing enzymes (GR, GPx, GST), the process of S-glutathionylation of proteins and the level of protein thiols. The consumption of the precursors of CoA biosynthesis in full (PL, PT) or in part (HP) had an antioxidant effect, restored the activity of AChE, the level and reduction potential of glutathione and glutathione-metabolizing enzymes, the process of S-glutathionylation, and stimulated the activity of enzymes generating NADPH+. Taking into account the low modulating effect of coenzyme precursors on the level of CoA in the hippocampus and their high redox pharmacological activity, their non-coenzymatic effect on redox mechanisms leading to an increase in the bioavailability of reducing equivalents and energy status is assumed.

A platelet gel (PG) derived from platelet concentrate (PC) is considered as a perspective therapeutic agent with hemostatic and regenerative properties. PG was obtained from PC separated from human peripheral blood by automatic apheresis by adding human thrombin (30 U/ml). We compared the proliferation of human mesenchymal stromal cells (MSCs) in vitro in the presence of PG and the dependence of gel density on excess of fibrinogen, the presence of calcium chloride, calcium gluconate, and aprotinin. PG was formed from CT in the presence of thrombin during 5–10 minutes. PG as gel-like fibrin membrane contained platelets and an admixture of leukocytes, and was capable to enhance the proliferation of MSCs in vitro. The presence of calcium gluconate (10 mg/ml) increased in the presence of PG the rate of MSCs proliferation in vitro. The presence of aprotinin in PG at a concentration of 10–1000 KIU/ml caused a dose-dependent decrease in the rate of gel biodegradation and did not affect the ability of PG to stimulate the proliferation of human MSCs in vitro.

A new method of teleconnections studding is proposed which is based on the identification of conjugate regions in the global meteorological fields of temperature and pressure by their characteristic coherent quasi-periodic oscillation. This method was implemented in order to select predictors of winter air temperature in Belarus with an advance of 2 months. The degree of coherence of sea level pressure and winter temperature in Belarus on a quasi-8-year cycle was considered as a criterion for the selection of predictors. The forecast was implemented using the advanced deep machine learning model TimesNet and showed rather high metrics of quality for seasonal meteorological forecasting: the correlation coefficient between actual and predicted temperature values was 0.66, and the weighted macro-average values of precision and recall of the forecast in the gradations “normal”, “above normal” and “below normal” were 0.61 and 0.56, respectively.

A multi-stage technique for applying insulating coatings to metal powder particles has been developed in order to create a new class of Fe-based soft magnetic materials with improved characteristics. The density value calculated from the data of X-ray diffraction analysis is approximately 3 % higher than the experimentally measured values, which are 7.4–7.45 g/cm³. The low porosity of the composites is confirmed by the SEM and EDX results. The proposed method of encapsulation of iron powder with an oxide layer is a highly economical method for applying coatings of various chemical compositions to metal powders, and can be widely used in practice to obtain electrical materials. Comprehensive studies of the properties of the obtained samples of powder composite materials based on ABC100.30 iron, the particles of which are encapsulated with phosphorus oxide, have been carried out. It has been established that in a field of 1.5 T, the losses at a frequency of 1 kHz decrease 10 times with an increase in the thickness to 30 nm. The synthesized materials are recommended for use in the development of various types of high-frequency electric motors, generators, chokes, magnetic circuits and electrodes for high-frequency welding and other applications.

The article presents the results of research, according to an energy assessment, of the most common options for combining spatial planning and technological solutions of buildings and structures, the set of technological equipment used on the most typical operating farms and milk production complexes. The most significant elements of technology and technological equipment, its operating modes, energy consumption by cost elements for the processes of preparation and distribution of feed, manure removal and provision of the required microclimate parameters, determining the intensity level of the production process in various variants of building layout and livestock, have been studied. The results obtained allow us to determine the most effective options for mechanization and automation of the production process and improve the technological methods of their implementation.