Using the method of reflections, the solutions of the first and second mixed problem for the homogenous Klein–Gordon equation in a quarter plane and of the first mixed problem for the homogenous Klein–Gordon equation in a halfstrip are written out in an explicit analytical form. The Cauchy conditions of these problems are inhomogeneous, but the Dirichlet boundary condition (or the Neumann boundary condition) is homogeneous. Conditions are formulated, under which the solutions to these problems are classical.

The minimal polynomials of the images of the unipotent elements of non-prime order in the irreducible representations of an algebraic group of type F₄ in characteristics 3 and 7 are found. This completes the solution of the minimal polynomial problem for unipotent elements in the irreducible representations of such a group in an odd characteristic.

The mathematical model based on a system of ordinary differential equations is proposed to describe the effect of the vaccination rate on the spread of the COVID-19 epidemic. The results of numerical modeling are presented for the case when vaccination begins after the beginning of the epidemic. A dimensionless vaccination parameter V was obtained, which allows one to characterize the effect of the vaccination rate on the reduction of the incidence of viral diseases with different virulence levels in a large closed population of people. Introducing this parameter allows the simulation results to be generalized to the populations of different size, different epidemic spread rate, different vaccination rate, and different vaccine efficiency. It has been shown that increasing the parameter V decreases the proportion of the sick population. It follows from our model that the vaccination influence on the spread of a respiratory viral disease such as COVID-19 decreases for a later initiation of vaccination. The simulation results should contribute to the development of optimal vaccination scenarios for the population.

The results of study of the developed IR system based on the Fabry–Perot microresonator, functioning on the basis of the thermal-optical effect, are presented for its possible application in thermal imaging technology. The tuning factor of the Fabry–Perot microresonator calculated from the experimental data was k_T = 0.44 nm/°С. An array of Fabry–Perot microresonators with pixel resonators in the form of 8 × 8 µm² squares with a 2 µm gap in the amount of 640 × 480 pieces was made. It is shown that the characteristics of the developed thermal imaging system are not inferior to thermal imaging systems of a comparable class.

The container structures consisting of the core made of layered molybdenum oxide intercalated with 3-amono-1,2,4-triazole (it behaves as the corrosion inhibitor) capped with the shell made of polymerized tungsten oxide were synthesized employing the polycondensation of oxocompounds. It is shown that in the acid (pH < 5.5) and alkali (pH > 8.5) media, the coating continuity appears to be broken reversibly, which facilitates the emission of the encapsulated compounds from the containers. The intrinsic redox activity inherent into the oligooxometalate shell permits one to immobilize the synthesized containers by co-precipitation with galvanic nickel, whereas the possibility to open the container as a result of local pH value variations accompanying the corrosion process ensures the autonomic corrosion protection of the resultant metal-matrix coatings.

The genes of the neurotransmitter systems of the brain play a significant role in the formation of the psychological properties of a person. The dopaminergic system is one of the leading systems influencing the manifestation of individual psychological characteristics and the development of anxiety and depressive disorders. The association of polymorphic variants of the dopaminergic system genes with the psycho-emotional status of a person was analyzed using the molecular genetic analysis. The study involved 1454 representatives of the Belarusian population. The genotypes of 167 employees of the special forces of the Ministry of Internal Affairs of the Republic of Belarus and 235 highly skilled athletes were studied as the groups that were supposedly more stress-resistant. The opposite group consisted of 534 patients of the Republican Scientific and Practical Center for Mental Health with personality disorders and deviant behavior. The population control group included 518 volunteers representing the population of Belarus without known pathologies. As a result of the psychological testing, the groups with low and high emotional stability were identified by the quartile method. Genetic testing of groups with 11 polymorphic variants of 5 genes of the dopaminergic system made it possible to identify informative genetic markers of a person’s psycho-emotional status. The most significant polymorphisms were rs4680 and rs165599 of the COMT catechol-O-methyltransferase gene, rs1611115 of the dopamine-metabolizing enzyme dopamine-β-hydroxylase gene DBH, and rs6275 of the type 2 dopamine receptor gene DRD2. The results obtained can be used for preventive diagnostics of disorders in the psycho-emotional sphere, as well as for the development of programs for correction of borderline states, deviant and delinquent behavior, as well as mental illness.

Using the methods of bioinformatics, the analysis of data on sequencing of the genomes of individuals of the species Sus scrofa domesticus, which are located in the Sequence Read Archive (NCBI-SRA) database, was carried out. Genotypes were determined in silico for five breeds of domestic pigs – Duroc, Landrace, Pietrain, Large White and Yorkshire using an algorithm developed in the Python programming language. Based on a two-stage bioinformatics analysis, a wide range of SNPs with a high potential for differentiation was identified. The results obtained will be used to create express methods for determining the purity of pigs of these breeds. Extended bioinformatics analysis, which included genotyping by 7451 SNPs for 248 Sus scrofa domesticus genomes, revealed a total of 393 SNPs for all breeds for which there is a significant difference in the frequency of alternative alleles in Duroc, Landrace, Pietrain, Large White and Yorkshire pig breeds. Clusters within chromosomes are indicated, in which the density of SNPs with a high differentiating potential is the highest. For Duroc pigs, we identified 184 SNPs with differentiating potential, 24 of which showed a high differentiating potential, for Landrace pigs – 52 SNPs and 7, for Pietrain pigs – 39 and 9, for Large White pigs – 104 and 22, for Yorkshire pigs – 14 and 5, respectively.

The dynamics of the content of various groups of cell wall polysaccharides in the cells of tomato stems during the development of the plant’s response to gravitational stimulation and phytohormonal treatment was studied. It has been shown that gravitational stimulation causes changes in the relative content of stem cell wall polysaccharides in the zone of gravitropic bending over a period of 3–6 hours. At the same time, predominantly multidirectional changes occur in the upper and lower halves of the stem, which ultimately leads to noticeable biochemical differences between the two parts of the stem, which allows it, in all likelihood, to bend due to an uneven growth of cells in different parts of the stem. Under the action of gravitational stimulation and epibrassinosteroid epine, changes in the polysaccharide composition appear earlier (already 1 hour after exposure) in time than with a single gravitational stimulation, and under the influence of ethephon and gravitational stimulation later (only from 6 hours of exposure).

Antimicrobial metabolites of bacterial strain B. amyloliquefaciens BIM B-1125, the basis of Bacto-health preparation, demonstrating antagonism against the representatives of the opportunistic microbiota of valuable fish species, were isolated and characterized. Extracellular localization of antimicrobial compounds was established; their stability is shown in the temperature range of 50–100 °С and in the pH range of 2–10. The lipopeptide nature of antimicrobial metabolites was shown using thin layer chromatography. The mass spectrometric analysis of the active fraction confirmed the production of lipopeptide metabolites belonging to the iturin and surfactin families (iturin A, iturin A4, iturin A6-A7 isomers, surfactin A, surfactin C, and surfactin B isomers).

Sepsis still represents one of the leading causes of death in hospitalized patients worldwide, and its incidence is increasing. Changes in the relative and absolute blood levels of monocytes, dendritic cells, myeloid suppressor cells, and regulatory T-lymphocytes in the blood of patients with sepsis and septic shock were studied on the 3rd–4th day after diagnosis in order to identify the stage of immunosuppression. 33 patients with sepsis (19 men and 14 women, age 57.1 ± 19.9 years) and 6 patients with septic shock (2 men and 4 women, age 49.3 ± 19.6 years) were examined. The control group included 30 healthy donors. Subpopulations of monocytes, dendritic cells, myeloid suppressor cells, and T_reg cells were determined by flow cytometry. A significant decrease in HLA-DR expression on monocytes, a decrease in the relative content of classical monocytes, myeloid and plasmacytoid dendritic cells, an increase in the percentage of intermediate monocytes and G-MLSC CD15⁺, an increase in the absolute content of T_reg cells in patients with sepsis and septic shock were revealed. The revealed functional defects and shifts in the composition of the leukocyte population indicate the development of the stage of immunosuppression in patients with sepsis.

 The article presents an assessment of current changes in air temperature, precipitation, snow and river runoff in the Baltic and Arctic Seas basins in the territories of Belarus and Russia. It is shown that the observed positive air temperature trends during the winter season are associated with the sea level pressure distribution in the North Atlantic and NAO indices. In summer, the temperature growth is correlated strongly with the Atlantic multi-decadal oscillation. Changes in the precipitation regime are synchronized with an increase in the sea level pressure in the baroclinic active zones of the Atlantic Ocean, which led to the precipitation increase in Europe since the second half of the 20th century. Interdecadal precipitation fluctuations in the study region are associated with the dynamics of the circumpolar vortex and Arctic oscillation (AO) indices. In winter, a precipitation increase is observed in the negative AO phase and is caused by an increase in the frequency of southern cyclones. In summer, when the AO phase is negative, the cyclonic activity decreases, and the precipitation growth is associated with convective processes in the atmosphere. Snow precipitation and snow water equivalent are decreasing during recent decades due the air temperature significant growth. That led to the spring floods height decreasing in the region. In the next 30 years, a decrease in the winter air temperature in the Baltic Sea basin and its increase in the Arctic Sea are expected. In summer, the air temperature increase will slow down on the descending AMO branch in the coming decades. In the precipitation regime, the growth of seasonal and daily total precipitation is expected.

An original device for production of nanostructured materials by the method of severe plastic deformation with the imposition of ultrasonic vibrations is described, which provides the grinding of the structure of the material of the workpiece and eliminates the occurrence of defects on its surface and in the end areas. This effect is achieved through the use of an annular spacer made in the form of a hollow waveguide of resonant length, fixed on a fixed support in the displacement unit, connected to a concentrator and an ultrasonic transducer. The physical-mechanical properties of nanostructured samples of nickel and copper after ultrasonic treatment (UST) have been studied. It is shown that UST of nanostructured samples leads to an increase in their plastic properties and a slight decrease in the tensile strength. At small amplitudes of mechanical stresses within 17.5 MPa, a noticeable microhardness increase is observed in copper and nickel samples. A further increase in the mechanical stress amplitude up to 100 MPa during ultrasonic treatment leads to a microhardness decrease.

The processes of mechanochemical reduction of oxides of iron, nickel, and copper with aluminum with a stoichio metric ratio of components and in mixtures with a two-, three-, and four-fold excess of the aluminum content over the stoichiometric, as well as in the presence of an excess of oxide-forming metal and solid solutions of aluminum in iron and copper, were studied by the Mössbauer and IR spectroscopy, X-ray diffraction analysis, including the use of synchrotron radiation, and electron microscopy. The conditions for formation of metals modified with aluminum oxide (iron, nickel, copper) and their monoaluminides are determined. High aluminum content aluminides are formed at a three-fold excess of aluminum, and at a four-fold excess, a mechanochemical reduction of oxides does not occur. The preferred method for modifying metals with alumina is the mechanochemical reduction of oxides with a solid solution of aluminum in the oxideforming metal. Mechanochemical interaction in the high-energy Hf–C system in the presence of 20, 30, and 50 wt. % copper leads to the formation of hafnium carbide; and with an increase in the copper content, the crystallite size decreases.

Studies of the structure formation features of composite inorganic materials formed on the basis of silicon dioxide, namely, pyrogenic silica of the A-380 brand (technical name – aerosil). The main purpose of the research was to study the possibility of improving the uniformity of the distribution of injected dopants on the surface of SiO₂ globules forming the xerogel framework. This goal was achieved due to the uniformity of the distribution of alloying salts (for example, copper nitrate) at the stage of sol formation, which was converted to the state of xerogel as a result of sequential heat treatment in a controlled gas environment (air or dried hydrogen). The final shape of the samples was either micro-powders or tabletshaped blanks obtained on their basis – with a diameter of about 12.5; 2.50; 30; 40 and 80 mm and a phase composition of SiO₂ : CuO and SiO₂ : Cu°.

A change in the external conditions leads to restructuring the adaptive behavior of animals, their motor activity, which makes it possible to use ethological properties to assess the body state in different production modes. In this regard, there is an urgent need for total monitoring of the health status and activity of pigs. The article contains the results on the effect of different-type stress on the pig stock during the rearing period under on-farm conditions. The studies were carried out at the pig farm of the State Enterprise “ZhodinoAgroPlemElita” in the groups of lactating sows kept under identical conditions, based on monitoring by year seasons in the following algorithm: complying with comfort criteria, reducing the stress impact, improving the health status, increasing the productivity. The predominant activity types of sows under on-farm conditions have been studied. It has been found that the predominance of the comfort activity among other types contributes to the offspring viability. Types of the activity of sows are inextricably linked to motivations, that is, the desire of animals to satisfy the priority needs of the body. Examples of high and low food motivation have been identified. Extra space, physical and visual barriers to protect more submissive sows have been found to have a positive effect on reducing overall aggression.