The first mixed problem for a nonlinear equation is considered in the quarter plane. The Cauchy conditions are set at the bottom of the boundary. The Dirichlet condition is set on the left part of the boundary. The solution is constructed using the method of characteristics in an implicit analytical form as a solution of the integral equation. The solvability of these integral equations, the smoothness of the solutions, and their dependence on the initial data are investigated. The uniqueness is proved and the conditions are established, under which there exists a piecewise smooth and classical solution of the first mixed problem.

Abstract. In this article, we consider a compact difference approximation of the schemes of order O(| h|⁴  +  τ²), h = (h₁, h₂, ..., h_p) for the Klein–Gordon equations in the multidimensional case. In studying the stability of these difference schemes, the theory of operator-difference schemes by A. A. Samarskii is used, and the strong stability of difference schemes is proved with respect to a small perturbation of the initial conditions, the right-hand side and the coefficients of the equations. The theoretical results are confirmed by test numerical calculations.

The problem of optimizing the transient process in a quasi-linear dynamic system with a performance index, being a linear combination of the energy costs and the process duration, is considered. Asymptotic approximations of a given order to the solution of this problem are constructed.

R(T, B) of the natural black arsenic (b-As) polycrystal was studied. It was shown that the polycrystalline b-As sample contains the b-As phase and also the traces of its oxide, as well as grey arsenic and arsenolite (As₂O₃). The behavior of the relative magnetoresistance of the b-As crystal was described by the relation MR(B) = bBⁿ + cB^m, where the coefficients b and c and the exponents n and m were also affected by the mechanisms of magnetoresistance formation and temperature. At the temperatures below 10 K, MR(B) shows the presence of a competition between negative (with b < 0 and n ≈ 0.5) and positive (with c > 0 and m ≈ 1) contributions. Above 10 K, only the PMR effect was presented. For the PMR effect, at 10 < T < 100 K it is observed that the values of b > 0, n ≈ 1 and c → 0. Above 100 K, it is observed that the values of b, c > 0 and n ≈ 1 and 1.30 < m < 1.47. The observed behavior of the R(T, B) dependences is associated with strong inhomogeneity and/or disorder of the investigated black arsenic crystal.

Experiments on the effect of brassinosteroids and their salicylates on the mycelium biomass during submerged cultivation of oyster mushroom (Pleurotus ostreatus) were carried out. It was shown that their addition to the nutrient medium at a concentration of 0.05 mg/l significantly increases the biomass of the mycelium. It was found that, when exposed to 24- epi- and 28-homocastasterone for 9 days, the mycelium colony developed only in the depths of the culture liquid, and the mycelium was formed into glomeruli with a dense structure. The use of salicylates 24-epicastasterone and 6-deoxo-24-epicastasterone promoted the development of an extensive colony of mycelium both on the surface and in the depth of the culture liquid. Salicylates also influenced the structure of the mycelium – the jellyfish-like loose mycelium was observed in flasks with a medium containing 24-epi and 6-deoxo-24-epicastasterone salicylates. For the first time, the determination of the content of endogenous brassinosteroids in the fruiting body and mycelium of P. ostreatus was carried out.

In this research, the ability of pure recombinant human lactoferrin (rhLF), originated from the milk of transgenic goats, to bind ferric and europium ions has been shown by the methods of spectrophotometry, fluorescent spectroscopy, and inductively coupled plasma mass spectrometry. The apo-form of rhLF and its complexes with Fe³⁺ or Eu³⁺ saturated in 76 or 22 %, respectively, were obtained. A method for detection of total or released (“free”) lanthanide at acidic or neutral pH and high or low concentrations of chelating agents by time-resolved fluorescence was proposed.

Priestia megaterium BIM В‑1314D is a halotolerant strain able to adapt to osmotic stress. The analysis of a full nucleotide sequence of bacterium P. megaterium BIM В‑1314D has revealed that the genome of the studied strain is represented by one circular chromosome and nine plasmids, deposited in the database of GenBank NCBI under the registration number CP058262–CP058271. The size of the bacterial genome constitutes 5 984 922 base pairs with an average GC content of 37.7 %. The genome contains 6 187 genes where 5 978 were annotated as protein-enconding, 92 – as pseudogenes, 154 – as tRNA genes, 8 – as ncRNA, 47 – as rRNA. The genes responsible for synthesis and transport of betaine and proline osmolytes and transport of potassium ions ensuring the adaptation of strain P. megaterium BIM В‑1314D to osmotic stress were local-ized in the genome. Gene loci were defined encoding production of metabolites involved in the synthesis of phytohormones and polyamines accounting for the growth-promoting microbial ability. Gene clusters determining the synthesis of secondary metabolites, cold and heat shock proteins were revealed in the genome. The genome analysis of strain P. megaterium BIM В‑1314D provides the valuable data on the bacterial culture for stimulation of the plant growth in the salinized conditions.

The photomodifying and cytotoxic profile obtained for thirty-five extracts isolated from five species of distributed lichens in the South-East of Belarus was analyzed. According to the research results, the extracts were classified as toxic and non-toxic to human keratinocytes (HACaT). The dependence of the quantitative toxicity indicators of extracts on the lichen species, to a lesser extent, on the extraction conditions was revealed. Extracts that reduce the toxic effect of ultraviolet radiation on skin cells and possess photosensitizing properties were revealed. A group of the extracts that revealed the properties of a radiation modifier was identified. The statistical analysis of the factors associated with the modification of the radiation effects by extracts showed the greatest influence on this indicator of the solvents used for extraction. Most of the extracts show both the photoprotective and photosensitizing effects in the extract concentration range from 2.5 to 5 μg/ml. Increasing the concentration to 10 μg/ml, on average, enhances their photosensitizing properties. The statistical analysis confirmed the significant concentration-dependent changes in the photomodifying properties of a number of extracts.

Modern medicine faces the problem of a steady growth of alcoholic pathology. As you know, morbidity and mortality with a regular consumption of alcoholic beverages is associated with the toxic effects of ethanol on the most important human organs and, first of all, on the liver. To date, a sufficient number of facts are accumulated, indicating the importance of liver arginase and Kupffer cells in vital processes in health and disease. The aim of the study was to elucidate the significance of the activity of liver arginase and Kupffer cells in the detoxification processes and the thyroid status formation in rats with chronic ethanol intoxication of different severity. In rat experiments using modern physiological, biochemical research methods and a pharmacological approach, it was found that liver arginase and Kupffer cells participate in changes in the liver detoxification function and the thyroid status formation induced by chronic ethanol intoxication. The activity of liver arginase and Kupffer cells determines the severity of detoxification processes and the thyroid status formation in chronic alcohol intoxication. The direction and severity of changes in the arginase activity and the liver detoxification function during chronic alcoholism depends on the severity of chronic alcohol intoxication. Under the influence of daily intragastric administration for 60 days, a 30 % aqueous solution of ethanol (3.5 g 92 % ethanol per kg of body weight) in animals inhibited the activity of liver arginase and the detoxification function, but the introduction of a 10 % aqueous solution of ethanol (1.0 g 92 % ethanol per kg of body weight) within 2 months leads to an increase in the activity of liver arginase and detoxification processes. Kupffer cells depression by GdCl₃ as the action in the body of the NO-synthase inhibitor methyl ester NG-nitro-L-arginine weakens and the arginase inhibitor Nω-hydroxy-nor-L-arginine contributes to the development of characteristic changes in the processes of detoxification and triiodothyronine level in plasma during chronic alcohol intoxication caused by intragastric introduction of ethanol at a dose of 3.5 g/kg for 60 days.

An approach has been developed to construct functional expressions for calculating the effective mechanical characteristics of the undermined rock massif during its repeated mining, taking into account the disturbance of the different-type massif continuity and the time passed after the undermining. The approach was developed as applied to the conditions of the Starobin potash salt deposit. It is based on introducing special correction factors into the expressions for mechanical characteristics of the massif. At the same time, the state of the undermined massif area is considered in the continuum model approximation. It is shown that one of the most important factors to be considered when constructing the functional dependence for mechanical characteristics of the undermined layered massif is to take into account the mutual slippage of layers and their lamination related to it, because the strength characteristics such as bonding strength and internal friction coefficient mainly change when the massif is undermined. The algorithm for calculating the mechanical properties of the undermined massif proposes the use of correction factors that take into account the heterogeneity of the rock massif; lamination and slippage of the contacting layers; changes in the properties of the undermined massif with variation of the depth of repeated mining; changes in the properties resulting from the technological disturbance of the massif initial equilibrium state (primary undermining, time passed since the primary undermining).

The article presents the results of the cartographic analysis of the Belarusian Cancer Registry data, including the spatial features of morbidity due to cancer in different sex and age groups of the rural population. The maps, characterizing the features of the spatial heterogeneity of the oncological diseases (OD) in the Gomel and Mogilev regions of Belarus, were built for the first time. The performed mapping revealed the anomalous zones, representing the groups of compactly located rural settlements, for which the OD level (including OD of different localizations observed in both men and women) differs by a factor of 4 or more. The assessed differences in the OD risk are statistically significant. On this basis, we infer that the anomalous zones in the territory of Belarus, in any case, demonstrate both a high spatial contrast of OD manifestation and regular spatial organization. These confirm the hypothesis about a relationship between the OD risk and the environmental parameters and, in turn, allow a reasonable conclusion about the endemic nature of cancer as a provoked “human disease”. We consider that the detected zones of positive and negative anomalies must have significant ecological and geochemical differences. Therefore, they should be recognized as the objects of priority control since the population living in the high-risk areas undoubtedly needs priority screening and applying the corresponding preventive measures.

In the Neoproterozoic and Paleozoic, different-type sedimentary basins, some of which are oil-and-gas bearing, were formed in the western East European Platform (EEP). These basins are confined to two types of regional structures – rift intracontinental and passive-coastal. Their tectonic features determined the geological conditions of oil and gas formation and oil and gas accumulation. The Pripyat paleorift oil and gas bearing basin, which is the closing western segment of the Hercynian Pripyat-Dneprov-Donetsk avalacogenes, has the largest hydrocarbon reserves in the region and a complex structure. High density of block and plicate-block divisions of oil-and-gas bearing complexes is connected with syngenetic faults and salt tectonics. The oil-and-gas content of the sedimentary basins of the Caledonian passive margin of the West WEP – Baltica, Podlaska-Brest, Lublin, Volyn-Podolsk, is caused by the extended areal of the oil-and-gas formation in the sub- and near-thrust deep-submerged sedimentary complexes in the Teisser-Tornquist zone. It was the main source of hydrocarbon-fluid migration eastward into the sedimentary basins of the WEP passive margin.

carbon nanotubes (MWCNTs) in the range of 0.00004–0.000006 wt. % of the mass of cement on the structure and mechanical properties of concrete was demonstrated. A correlation was found between an increase in the mechanical strength of concrete by 56 % with changes in the structure of the cement stone, at which the proportion of crystals of calcium hydroaluminate, calcium hydrosulfoaluminate and type 14A tobermorite increases significantly. The results obtained lay the foundations for the development of a technology for the industrial production of complex additives in concrete with a combination of nanoparticles (MWCNT + SiO₂), which make it possible to improve the mechanical and physical characteristics of concrete and increase its durability.

The results on the impact of additives on the ultra-fine composite powder system, obtained by MASVS on the tribotechnical properties of friction material based on tin bronze with 12 % of tin are presented. It is shown that the powder additive in the range of 0.5–2.5 % increased the dynamic friction coefficient from 0.040 to 0.051. The introduction of a 1.5 % composite powder reduced the surface roughness of the counter body from 2.9 to 0.9 μm. The change in the tribotechnical properties is due to the structural changes in tin bronze, the additive particles, the surface layer of the friction material and the counter body.

In cows of the Belarusian black-motley breed, the polymorphism of genes for lactoferrin and mannose-binding leсtin was established. The genotypes LTF^AA, LTF^AB and MBL1^TT, MBL1^TC, MBL1^CC were identified. The milk productivity (yield, fat content, amount of milk of basic fat content), the number of somatic cells in milk were studied, and the economic efficiency of milk production from cows with different genotypes for the genes of lactoferrin and mannose-binding leсtin was calculated. It was found that the profit in cows with the LTF^AA genotype was 7.91 rubles higher than in cows with the LTF^AB genotype, in individuals with the MBL1^CC and MBL1^TT genotypes, and a higher profit per head was obtained from cows with the LTF^ABMBL1^CC and LTF^AAMBL1^TC genotypes, which amounted to 3249.49 and 2855.40 rubles respectively.