The restrictions of irreducible modules of special linear and symplectic groups in an odd characteristic p with p-large highest weights to a subsystem subgroup H of maximal rank with two simple components H1 and H2 are considered. The lower estimate for the number of composition factors for such restrictions, which are p-large for the subgroup H1 and are not too small for H2, is found. The lower estimates of the number of Jordan blocks of maximal size for the images of certain unipotent elements in the corresponding representations of such groups are determined. 

TiAlCuN coatings were deposited by reactive magnetron sputtering on substrates of single-crystal silicon, and Titanium Grade2 wafers. To control and manage the coating deposition process by reactive magnetron sputtering, a previously developed modular gas flow control complex (MGFCC) was used. The elemental composition was studied by energy-dispersive X-ray spectroscopy (EDX). The structural-phase state of coatings was examined by X-ray diffraction (XRD) and scanning electron microscopy (SEM). Mechanical properties, such as hardness and Young’s modulus, were investigated by the nanoindentation using a CSM Instruments Nanohardness Tester NHT2 (Switzerland). The influence of deposition parameters such as: Ti and Al content, reactivity degree α, and nitride concentration on structure and mechanical properties was considered. It was found that a decrease in the reactivity degree α from 0.605 to 0.474 leads to a 23 % increase in the deposition rate of TiAlCuN coating. It was detected that adding Cu to the coating content decreases the mean sizes of crystallites and growth columns in comparison with the TiAlN analogues due to its segregation along crystalline boundaries and thus advances better mechanical characteristics. The hardness of TiAlCuN coatings varies in the range of H = 29.3–35.4 GPa, Young’s modulus E = 235.9–267.6 GPa. The impact strength index as the H / E∗ ratio and the plastic deformation resistance index H3 / E∗2 were calculated. The formed nitride coatings are suitable for use in space technologies.

The influence of the molecular structure of carboxyl-containing polymers on their inhibitory and stabilizing effect in the precipitation processes was studied using a number of polymeric acids with different contents of carboxyl groups (X): polyacrylic acid (Mn = 5100 g-mol–1, X = 61.11 %), polymethacrylic acid (Mn = 5500 g-mol–1, X = 48.79 %), copolymer of methacrylic acid with turpentine terpene (α-pinene) (Mn = 350 g-mol–1, X = 14.54 %). It has been established that polyacid molecules slow down the process of crystal growth and recrystallization of the amorphous phase into more stable crystalline forms, which leads to a change in the morphology and structure of a carbonate precipitate. It has also been shown that polycarboxylic acids increase the colloidal stability of a mixed dispersion of carbonates and kaolin. The synergism of the stabilizing effect of mixtures of different hydrophobicity-polyacids was noted: in the presence of a mixture of polyacrylic acid with a copolymer of methacrylic acid with turpentine terpene, the stabilization effect increases 2 times compared to dispersion without additives and 1.4–1.8 times compared with individual components of the mixture. 

Genotyping of individuals of 7 commercial breeds of domestic pigs was carried out: Duroc, Landrace, Belarusian Large White, Belarusian Black-and-White, Belarusian meat, Pietrain and Yorkshire for the KDM3A and DBX2 genes. The high breed-specific potential of polymorphic loci g.58335217A>G (KDM3A gene) and g.75953650G>T (DBX2 gene) for differentiation of Duroc pigs of the species Sus scrofa domesticus was confirmed. A test model for differentiation of Duroc individuals by bioinformatic assessment of a total contribution of two SNPs of the KDM3A and DBX2 genes was proposed. This test model has no analogues in the world, and its estimation accuracy and specificity are 98.76 and 99.68 %, respectively. Using PCR-RFLP, a fast and simple approach has been developed to differentiate the Duroc breed based on the proposed test model. 

The study was made to evaluate the effect of interleukin-2 (IL-2) as part of the R-CHOP regimen on the rate of a complete metabolic response (CMR) using the data of interim positron emission tomography (PET/CT) and progression-free survival compared to the standard regimen in patients with diffuse B-cell lymphoma (DCLC). The data of 152 patients with biopsy-proven DCLC who were treated in the period 2015–2020 were included. Among them, 59 patients were included in the prospective group (R-CHOP + IL-2 in a total course dose of 5,000,000 IU). The control group consisting of 93 patients received standard R-CHOP therapy. PET/CT was performed after 4 courses of therapy, metabolic response was assessed using the Deauville scale, and Deauville 1-2 was classified as CMR. The rate of CMR in the R-CHOP+IL-2 group was 67.8 %, while in the control group it was 50.5 % (pχ² = 0.044). The 5-year progression-free survival (PFS) in the R-CHOP+IL-2 and R-CHOP groups was 80.7 and 64.5 %, respectively (p = 0.04). In the favorable and intermediate prognosis groups (IPI 0–3), PFS was not statistically significantly different depending on treatment. At high risk (IPI 4–5), the 5-year PFS in the R-CHOP + IL-2 and R-CHOP groups was 71.4 and 25.0 %, respectively (p = 0.02). Including IL-2 in the R-CHOP regimen in the first-line treatment of patients with DCLC increases the incidence of CMR according to 18-FDG PET/CT after 4 courses of chemoimmunotherapy and PFS in the high-risk group.

The article presents a quantitative estimation of intensity of urban “heat islands” in Belarus and their changes as a result of global warming. The potential opportunities for improving the urban microclimate by increasing the area of forest park zones in the city have been evaluated using mesoscale numerical simulation of meteorological conditions in cities. It is shown that in summer, Belarusian regional centers are warmer than suburban areas within 2–3 °С during the day and within 1.2–2.3 °С at night. Over the period that has passed since the beginning of this century, the regional cities have warmed by an average of 1.1–2.2 °C during the day and 1.3–1.9 °C at night. The maximum increase in daytime and nighttime temperatures in Belarusian cities has amounted within 3.1–6.0 and 2.4–4.4 °С, respectively. It is shown that replacing industrial clusters with forest park zones decreases the air temperature in the city within 2 °C and more than 2 times in evapotranspiration in the city of Homel. In the daytime, the northwest wind increases in the city and its suburb and this improves urban ventilation. At night, the afforestation of the city makes the surface layer of the atmosphere less stable, which is accompanied by the activation of local circulation cells, through which the temperature and specific humidity in the city and the suburb are smoothed. 

Several efficient computational schemes, providing the attainment of minimum errors in determining the main parameters of a boundary layer, are presented. The new trinomial polynomial obtained for definition of the velocity profile in the boundary layer much exceeds in accuracy all the known analogous solutions. A scheme of finding a fairly exact solution in the form of the half-sum of the classical Pohlhausen polynomials of the third and fourth degrees is proposed. This solution possesses better approximation properties compared to those of the initial profiles. A high-accuracy solution has been obtained for the velocity profile in the form the velocity profile curve being almost coincident with the exact solution. The friction stress error is . This solution yields an almost exact value of friction stress with very small calculation errors of the displacement thickness (0.12 %) and the form parameter (0.12 %).

The features of the formation of Cu–Ni alloy films by electron beam evaporation are considered. The position of the isobars of the total pressure of copper and nickel on the state diagram of the Cu–Ni during evaporation in vacuum is determined. Calculations of the elemental compositions of films have been carried out. It is shown that the nickel content in films deposited during boiling of Cu50Ni50 alloy in vacuum is 50 times less than in the alloy. The structure and elemental composition of the surface layer of alloys after their evaporation and sublimation, as well as the elemental composition of the deposited films, are investigated. It is shown that the most acceptable way to obtain films of stable composition in the Cu–Ni system is simultaneous electron beam evaporation of copper and nickel from two crucibles. 

The article presents the study results of functioning of the Belarusian legal system on the legal map of the world and its interaction with the legal systems of the continental law family. The main national legal reality components most actively communicating with foreign systemic formations – sources and law system, normative component and national type of legal consciousness – are analyzed. Proposals on the reception of foreign legal experience of French and Scandinavian legal models are made. It is proposed to improve the national law system by updating the administrative law branch according to the French model and judicial practice by the reception of the relevant components of the Scandinavian justice model. The Belarusian-type character of legal consciousness is analyzed separately from the viewpoint of its historical integration by different-type elements of legal cultures, which determines the ability of the Belarusian legal system to qualitatively interact with the legal systems of various law families. The “legal diplomacy” concept is introduced. It implies a new approach in the methodology of legal reception instead of implementation of “legal expansion” of foreign norms and institutions of law into other legal cultures. Proposals are made to include the provisions on the principles and mechanism of legal reception, as well as the rules determining a new quality of national legal consciousness by activating legal propaganda forms into the draft Concept of Legal Policy of the Republic of Belarus and in the draft Law of the Republic of Belarus “On Civil Society”.

For modern domestic breeding programs to be implemented, population genetic techniques and methods must be applied in order to create new types of lines with superior performance characteristics, the use of which will contribute to the efficient pedigree livestock farming. Genomic selection use in domestic breeding programs accelerates genetic progress in herds by determining the breeding value of animals at an early age, and thereby contributes to the development of local animal husbandry and to the reduction of dependence on imports of foreign pedigree material. The article contains the data of the studies that were aimed at forming breeding herds of a new competitive factory type of Yorkshire pigs with the use of genetic techniques and methods. The study included the analysis of productivity marker genes and DNA testing by microsatellite markers of the initial genotypes. It was found that in the populations, young animals with preferred genotypes outperformed their peers in productive traits by 1.95–42.3 % (p ≤ 0.05). The use of the DNA-MS analysis of the animals tested at basic breeding enterprises allowed determining their genetic affiliation with the Belarusian population of the Yorkshire breed on the basis of the genetic distance and allele frequency in the loci under study that were in the range 5.665–11.084.