The first mixed problem for the wave equation in the four-dimensional area (three dimensions of space and one dimension of time) is considered. The theorem of existence of the unique classical solution of the given problem is proved with the help of averaging operators. The method of averaging operators was used for obtaining kirchhoff’s and Poisson’s formulas for solving the Cauchy problem for the wave equation in the case of four and three independent variables respectively. Here it is shown that this approach can be used to solve a more complex problem. When using averaging operators, the initial problem is reduced to the first mixed problem for string oscillations, for which the correct solvability criterion has already been proved. However, the smoothness of the functions in the solvability criterion should be enhanced. The enhanced criterion can be proved by the method of characteristics.

Computer prediction of the migration of radioactive contaminants in soil is a promising scientific direction due to the fact that prediction of the radiation situation on the basis of experimental measurements of radionuclides activity requires the use of mathematical and computer methods of data processing. At the same time, most of the specialized software packages for predicting the spread of radioactive contaminants in soil are based on one- and two-dimensional idealizations of this process, while solving the problem of comprehensive assessment of the biosphere’s state requires the data of the contaminant’s spatial distribution. To obtain such data, the author has developed a software module as a part of SPS (Simulation of Processes in Soil) v2.0 software package, which allows predicting the parameters of the spatial migration of radionuclides in natural dispersed media. To assess the possibility of using the developed software in practice, the prediction results were verified by the experimental data. For this purpose, the spatial distribution of the Cs-137 concentration in the experimental area in the Luninets district of the Brest region was predicted using the measurement data of the Cs-137 activities and the soil characteristics. The comparison of the results obtained on the basis of experimental measurements and the predicted values of the spatial distribution of the Cs-137 concentration showed that the predicted values are within the confidence intervals of the measured values. Consequently, the developed software can be used to solve practical problems in the field of forecasting the migration of radionuclides with obtaining a reliable picture of their distribution over the volume of the modeling area and to comprehensively assess their impact on the environment.

The known systems of the radial equations describing the hydrogen atom on the basis of the Dirac equation in the Lobachevsky–Riemann spaces of constant curvature are investigated. In the both geometrical models, the differential equations of second order with six regular singular points are found, and their exact solutions of Frobenius type are constructed. To produce the quantization rule for energy values we use the known condition which separates the transcendental Frobenius solutions. This provides us with the energy spectra that are physically interpretable and are similar to those for the Klein–Fock–Gordon particle in these space models. These spectra are similar to those that previously have appeared in studying the same systems of the equations with the use of the semi-classical approximation.

SiO2 /Si, SiN1.2/SiO2 /Si and SiO2 /SiN0.9/SiO2 /Si structures have been fabricated by chemical vapor deposition and thermal oxidation of silicon. The elemental composition and thicknesses of dielectric layers have been studied using Rutherford backscattering spectroscopy, scanning electron microscopy, and spectral ellipsometry. The electroluminescence (EL) of the samples has been investigated in the “electrolyte–dielectric–semiconductor” system at a positive bias voltage applied to the silicon substrate. An intense band with maxima at 1.9 eV appears on the EL spectra of the SiO2 /Si sample, while the EL spectra of the SiN1.2/SiO2 /Si and SiO2 /SiN0.9/SiO2 /Si samples are characterized by the presence of bands with the maximum values of 1.9, 2.3 and 2.7 eV. The nature of these bands is discussed. Passing a charge in the range of 100–500 mC/ cm2 through the SiO2 /SiN0.9/SiO2 /Si sample, an increase in the EL intensity was recorded in the entire visible range. Passing a charge of 1 C/cm2 through a sample with a three-layer dielectric film resulted in the EL intensity decrease. It can be explained by the upper oxide layer degradation. It has been shown that silicon nitride deposited on top of the SiO2 layer protects the oxide layer from field degradation and premature breakdown. The most stable electroluminescence when exposed to a strong electric field is observed for the structure SiN1.2/SiO2 /Si.

The influence of water-soluble organic compounds (adipic, polyaspartic and phosphonic acids) and their compositions on the crystallization of calcium and magnesium salts in dynamic conditions has been studied. It is found that the induction period of phase formation increases in the presence of polyaspartic and phosphonic acids 2.3–5.2 times in the range of their content from 0.05 to 0.2 ppm. The results of XRD and electron microscopic studies confirm the change in the phase composition and morphology of the crystalline precipitate that is formed. The dibasic carboxylic acid influence on the induction period, composition and structure of the precipitate is much less. It is established that the composition of organic acids also increases the induction period of phase formation. The complex inhibitor provides an increase in the critical supersaturation level in the system. The phosphonic and carboxyl groups of the inhibitor interact with calcium and magnesium ions and block the crystallization nuclei. When interacting with the dicarboxylic acid and polyacid adsorption on the surface of the formed crystals, the microcrystals dissolve.

The composites based on magnesium ferrite and carbon nitride were synthesized by the sol-gel method in combination with thermochemical condensation. The effect of the synthesis method on the crystalline structure, the phase and chemical composition, and the morphology of composites was studied by the X-ray diffraction, IR spectroscopy, scanning electron microscopy, and energy-dispersive X-ray spectroscopy techniques. It was found that, depending on the conditions of the sol-gel stages, the initiation of self-combustion high-temperature synthesis and melanin thermochemical condensation, composites with different crystalline structure and morphology were prepared. The obtained results are important for the development of the heterogeneous Fenton- and photo-Fenton catalysts based on magnesium ferrite and carbon nitride composites.

Colibacteriosis is an acute zoonotic disease manifested by septicaemia, toxemia, enteritis, body dehydration, and central nervous system damage. Depending on the presence of virulence factors and the nature of interaction with the intestinal mucosa, enterotoxigenic, enteroinvasive, enteropathogenic, and enterohemorrhagic E. coli are isolated. Enterotoxigenic strains of E. coli occupy one of the leading places in the etiological structure of calf colibacteriosis in many livestock farms of the Republic of Belarus. The main reason why this disease develops is the presence of thermolabile and thermostable toxins in the causative strain. The thermolabile toxin subunit B is a potent antigen that allows pet immunity to be acquired against E. coli-induced cattle diarrhea. Many foreign vaccines used against intestinal infections of cattle contain either a native or recombinant variant of the subunit B. As a result of the work, we have created a new strain of E. coli 42eLTB – the producer of the recombinant subunit B of the thermolabile toxin E. coli. The producing capacity of the obtained strain is 480 mg with 1 culture liquid liter, which exceeds the already known strains 1.37 times.

The pharmacological regulation of high-frequency rhythms of the behavioral activity (with a period of up to 1/2 hour) is an actual direction of modern medical science. The aim of the study was to assess the influence of oligopeptides structurally related to oxytocin on the parameters of ultradian rhythms of locomotor activity (LA) in outbred ICR laboratory mice. LA was recorded automatically in a multichannel actometer (Ugo Basile, Italy) in the conditions of individual detection. Amplitude, acrophase, and mesor of biorhythms’ were determined by the Cosinor analysis. Oligopeptides structurally related to oxytocin fragments, as well as memantine under systemic (intraperitoneal) administration, had a pronounced influence on the ultradian LA biorhythms of mice. Memantine (10.0 mg/kg), Cyclo-(Leu-Gly) (0.025 mg/kg), Pro-Leu (0.5 mg/kg), and Leu-Gly (0.1 mg/kg) triggered the migration to the right of the acrophase of statistically significant 24-minute LA rhythms versus control. A further study of the peptidergic mechanisms of regulation of fluctuations in ultradian biorhythms can contribute to the development of the theoretical foundations of chronobiology, as well as to the search for the means correcting the desynchronoses.

During archaeological excavation in the territory of the Corpus Christi Church in Nesvizh, the regular burials dated to the 17th–18th centuries were discovered. The genetic material extracted from the bones of seven unidentified individuals was analyzed using the forensic genetics approaches, including STR profiling and DNA phenotyping. The genetic examination revealed that the remains of three samples (#1, #2, #6) belonged to women, and the four others (#3, #4, #5, and #7) belonged to men. Autosomal STR-data and Y-chromosomal profiles were obtained for five samples. The kinship analysis excluded that woman #1 and men #3, #4, #5, #7 were first-degree relatives. According to the Y-STR profiles, men #3, #4, #7 referred to the haplogroup R1a, the haplotype of individual #5 corresponded to I2. The both haplogroups are widely represented in Eastern Europe, which, with a high degree of probability, suggests the Slavic origin of the individuals under investigation. To predict eye and hair color, we used the HIrisPlex DNA phenotyping system. The analysis gave the satisfactory results for woman #1 and man #7. In correspondence to the allelic variants of the 24 SNP system, woman #1 had an intermediate type of iris pigmentation and dark blond hair (p = 0.635) with dark shade (0.639), light skin tone, low tendency to sunburn, and a high probability of freckles and pigmented spots of the skin. For male #7, the HIrisPlex model predicted blue eye color with a high probability (p = 0.915), as well as blond hair color (p = 0.915) and light hair color shade (p = 0.962). Our data allow us to conclude that the unknown individuals under investigation have significant genetical and phenotypical similarity with the modern Belarusian population.

Not only the prevalence, but also the death rate from the coronary heart disease, including myocardial infarction, is higher in older people than among young people. A demographic shift towards an aging population will lead to a further increase in the prevalence of cardiovascular diseases among the elderly population. Therefore, one of the urgent aims of modern experimental and clinical medicine is to develop methods aimed at limiting reversible and irreversible damage to the myocardium, including in elderly patients. There are a lot of the data supporting the cardioprotective efficiency of such phenomena as ischemic and pharmacological pre- and postconditioning that reduce ischemic and reperfusion damage in young hearts. However, the information on the effectiveness of these phenomena in experiments on old animals is very scarce, contradictory, and not fully understood. The aim of the study was to experimentally evaluate the influence of old age on the reproducibility of the cardioprotective efficiency of pharmacological postconditioning using lactic acid in ischemia-reperfusion of the myocardium. In the course of the study, it was found that neutral lactate, after being administered into the blood flow of animals at a dose of 10 mg/kg 25 minutes after the onset of reperfusion, leads to a decrease in the infarct size of the left ventricle of the myocardium in old rats. Pharmacological postconditioning using lactate is not effective in reducing the duration of cardiac arrhythmias in ischemia-reperfusion of the myocardium in old rats; however, there is a tendency to reduce the incidence of reperfusion arrhythmias and the total duration of cardiac arrhythmias. The obtained data suggest that the presence of such a risk factor for cardiovascular diseases as old age is not a criterion to exclude the use of pharmacological postconditioning with lactate as a way to reduce ischemia and reperfusion injury of myocardium.

The objective of the study was to improve the treatment results of patients with total knee arthroplasty (TKA) by substantiating and developing differentiated surgical tactics. The study included 151 patients (212 cases) who underwent TKA without patella replacement. The patients were divided into two groups: the main group is 74 patients (110 cases) and the comparison group is 77 patients (112 cases). In the main group, surgery was performed by using the developed installing tactics. The comparison group included the patients after the traditional surgical technique described in the manuals. There was no statistically significant difference between the groups (p = 0.52). The treatment results were assessed in 3, 6, 12, 24 months and more after surgery. KSS (Knee Society Score) and Kujala scales were used. The tactics of surgical intervention was developed, consisting of the correct installation of femoral and tibial components and capsular-ligamentous balancing of the patellofemoral joint. After the components implantation, the capsular-ligamentous balancing of the patellofemoral joint was performed depending on the patella position relative to the block of the femoral component (tilt, subluxation or dislocation of the patella). 5 types of patellar tendon extension were used: release of the lateral patellofemoral ligament, mobilization of the lateral skin flap from the capsule, “grid” type release, iliotibial tract release. The developed surgical tactics for TKA allowed us to obtain the better immediate and long-term treatment results than the traditional surgical technique. During the femoral and tibial component implantation, it is especially important to take into account the points that are directly related to the biomechanics of the patellofemoral part of the knee joint.

The problem of management of waste plastic of electronic and electrical equipment (EEE) is associated, on the one hand, with the increase in the volume of their formation and the “green” circulation economy requirements for recycling, and, on the other hand, with the hazardous substances contained in them, including persistent organic pollutants (POPs) and heavy metals. The article presents the measurement results of the content of pollutants in EEE plastic samples taken at the enterprises for their collection and processing in Minsk. The content of heavy metals and bromine was determined in 40 plastic samples using X-ray fluorescence spectrometry, polybrominated biphenyls (PBBs) and of polybrominated diphenyl ethers (PBDEs) – in 19 samples using gas chromatography with mass spectrometric detection. It was shown that the content of lead was recorded in 40 % of samples (the maximum value is 259 mg/kg of plastic), of cadmium – 28 % (22 mg/kg), of chromium – 20 % (98 mg/kg); the content of mercury and PBB was found to be below the detection limit. PBDEs are contained in 7.5 % of samples in the range 246–6615 mg/kg. Decabromodiphenyl ether, a persistent organic pollutant, accounted for 89 to 96 % of the total PBDE. A high proportion of bromine-containing plastic (48 %) was revealed, which is consistent with the data of other countries. The need to carry out research in Belarus with the expansion of a list of analyzed pollutants in waste plastic and to develop the regulatory and technical base in relation to the management of waste plastic in accordance with the obligations of the Stockholm Convention on POPs is discussed.

Heat pipes with mesh wicks were designed (working liquid – water, envelope – copper tube). Wicks from the mesh of various weaves (plain, twill, leno and looped) with improved hydrophilic properties and secondary capillary structure were developed. Heat pipes are gravity-independent, adapted to work in various conditions of orientation and localization, and provide the transfer of high heat flux powers (up to 25 W/cm2 ). The peculiar properties of the developed heat pipes in contrast to the traditional heat pipes (with powder wicks) are: high performance characteristics, resistance to deep freezing; vibrostability.

The article presents the results of analysis of new data on the elemental composition of non-ferrous metal products on the territory of certain archaeological sites in Northern and Central Belarus. The author distinguishes two main stages in the non-ferrous metalworking of the region: the X–XIII centuries and XIV–XVIII centuries. It is noted that the period of the X–XIII centuries is characterized by a significant predominance of copper-zinc alloys with average and high concentrations of zinc in metal. Meanwhile, bronze alloys also play an important role, accounting for 35 % of the total number of the items studied. Samples made of copper-zinc and bronze alloys are also characterized by a significant amount of lead. As a result of the analysis of the data on the elemental composition of non-ferrous metal products of the XIV–XVIII centuries, it is concluded that non-ferrous metalworking of this period is characterized by the continuity of traditions with handicraft production of the previous period, which manifested itself in the widespread use of copper-zinc alloys, as well as of tin-lead and multicomponent bronzes. At the same time, a significant difference is the increase in the proportion of alloys with high concentrations of alloying components.

Based on the scientific systematic multi-temporal data and the large-scale soil mapping studies, for the first time we developed a methodological approach to estimating the transformation of the composition and properties of the arable land of the Republic for a 40-year period since the publication of the scientific work “The Soil of the Byelorussian SSR” (1974). At the present stage of the soil development, the transformation of the soil properties of the arable land, involved in the agricultural usage over the 40-year period, is influenced by the cultural process of soil formation and is characterized by the “strong” transformation of the properties in relation to their natural potential: in soils on loamy soil-forming rocks, the CTS value is varied in the range of 20–28 units, on sandy loam soil-forming rocks, СTS is 18–27, and on connected sandy loam soil-forming rocks it is 18–28. According to the research results on the soils of the arable land formed on light soil-forming rocks (sandy, loose-sandy), in contrast to loamy and heavier soil-forming rocks, the transformation degree of the properties is determined as “strong” and “very strong”. The results of the studies point to a clear dependence of the transformation degree of the properties of the gum-accumulative horizons of the studied soil varieties of the granulometric composition, which reflects the specific features of the soil cover of the Republic.