The classical solution of the mixed problem with integral conditions for the Klein–Gordon–Fock type equation in the half strip is considered when inhomogeneous matching conditions are fulfilled. An equivalent conjugation problem is formulated where conjugation conditions are set on characteristics. Constructed inhomogeneous conditions uniquely define gaps of the solution or its derivatives on characteristics and given gaps can be either remained or smoothed while the time argument increases depending on the kernel of the integral operator in unlocal conditions. The solution of this problem is reduced to solving the second-type Volterra integral equations and their systems. The unique solution of these equations in the class of the twice continuously differentiable functions exists when the initial functions are smooth enough. While considering the given problem the method of characteristics is used to construct both an analytical solution, when the solution of the integral equation can be found explicitly, and an approximate solution. Moreover, approximate solutions can be constructed in numerical and analytical form. When the numerical solution is constructed, matching conditions are significant and need to be considered while developing numerical methods.

The study is devoted to the analytical theory of ordinary differential equations. In the introduction, it is said that the object of investigation is nonlinear third-order autonomous differential equations with a moving singular line, and whose two-parameter rational solutions are known. The study aims to clarify how to obtain two-parameter rational solutions from the general solutions of these equations. In the analytical theory of differential equations, as a rule, nonlinear differential equations have negative resonances. Among these resonances is the resonance equal to –1 (trivial case). However, it is asserted in some of the researchers’ papers that the nature of these negative resonances has not been found until now. The equations only with non-trivial negative resonance arose the interest of researchers. And it appears that the rational solutions of
the equations can be constructed by their negative resonances. In this paper, a necessary and sufficient condition is indicated, at which the two-parameter rational solution of the equation with a moving singular line can be obtained from its general solution.

Nanostructured titanium dioxide (TiO2) coatings were formed on rigid aluminum and flexible fiberglass substrates using the sol-gel method modified by adding nano- and submicron TiO2 particles to the sol. The use of sols with such particles leads to the formation of a rough coating of agglomerates of nano- and submicron particles bonded with sol-gel synthesized TiO2. The antibacterial activity of the coatings was confirmed under irradiation with visible light from an LED source for 120 minutes. The most activity was demonstrated by all samples in relation to Staphylococcus aureus.

The equilibrium distribution of ammonia, ethylamine, diethylamine and triethylamine between their aqueous solutions and the gas phase at 25 ± 0.1 °C have been investigated under equilibrium conditions. Based on the results obtained (using the equations of Henry’s law and the ionization constant), Henry’s constants for these substances have been calculated with the consideration of their interaction with water. It was established that Henry’s law is valid, at least, in the range
of amine concentrations in the air 0–200 mg/m3.

The features of photoisomerization and photoorientation of azo dye brilliant yellow (BY) in the thin film state are studied. The trans-cis-isomerization of the dye molecules is established to proceed upon irradiation of the films based on BY with a full light of an ultra-high pressure lamp DRT-1000 (UV / VID light), this reaction is described by the first-order reaction equation. Under the action of linearly polarized blue light (λ = 457 nm), an optical anisotropy arises in films of BY. Optically anisotropic films of BY with a high dichroic ratio (>10) are shown to be formed using N-methylpyrrolidone and N, N-dimethylformamide as solvents and cellulose acetate as the polymer matrix.

Based on the DNA-barcoding data, a molecular-genetic identification of the dominant microbiome species composition of the perennial floral plants phytophages was carried out. Various variants of species combinations in the microbiota–phytophagous system, as well as the ways of phytophagous transmission of pathogenic microflora have been identified.

Bacterial variant PS-K-17 was isolated from wheat grain contaminated by polysaccharide-producing microbiota for further characterization. It was found that the isolate grown on agar slants and in submerged culture on media with specific substrates synthesized beta-galactosidase, amylase, protease, pectinase, cellulase, beta-glucanase, lipase (esterase), alginase, extracellular polysaccharides, and pigments, probably carotenoids. Based on cultural-morphological and physiological-biochemical properties and phylogenetic analysis of nucleotide sequences of 16S rRNA gene (access code MF443394 in GenBank) the bacterial culture was identified as Paenibacillus species PS-K-17. The studied isolate forms one phylogenetic branch with type strains Paenibacillus nicotianae (98.3 %), Paenibacillus hordei (98.2 %), Paenibacillus kyungheensis (97.9 %), holding wherein a separate position. Strain Paenibacillus sp. PS-K-17 may find use in biotechnology as a producer of extracellular polysaccharides and enzymes splitting plant polymeric substances as well as a component of microbial consortium-ingredient of a new complex feed additive.

Lactoferrin (Lf) was discovered in the thirties of the twentieth century. Since that time a number of useful properties of Lf (antibacterial, antiviral, pro- and anti-inflammatory, etc.) have been found. That’s why Lf became a promising candidate for pharmaceuticals use. The concentration of Lf strikingly increases in inflammatory focuses due to neutrophil degranulation. At the same time, activated neutrophils starts to generate reactive oxygen and halogen species (ROS and RHS), which leads to the development of oxidative/halogenative stress. In this work, using the fluorescence analysis we found the change of the Lf structure and properties in the inflammation conditions (under oxidatives/halogenative stress). We use two forms of Lf – human Lf, excreted from human milk, and recombinant Lf, excreted from milk of transgenic goats. It was established that the amino acids of Lf (decreasing the number of tryptophanils and primary amines) and protein restructuring undergo modification under the HOCl action, while H2O2 has no influence. These changes in the molecule under the HOCl treatment result in decreasing the iron-binding capacity of Lf.

The experiment established the long-term effects of low-intensity electromagnetic radiation from a mobile phone (EMR MP 1745 MHz, xpd = 7.5 ± 0.3 μW/cm2) in the offspring of male rats from parents, one of which was either subjected to a prolonged exposure of the investigated factor. A change in the sex ratio of the born offspring and a decrease in their body weight have been established. The analysis of the reproductive system of the offspring of males when they reached the age of 2 and 4 months, revealed significant impairments, with the most pronounced changes found in the offspring obtained from both the irradiated parents or when only the male was irradiated. These changes are manifested in the disruption of the normal functioning of the spermatogenic epithelium, namely, an intensification of the initial stage of spermatogenesis is noted, with a significant inhibition at the stage of spermatid transformation. A decrease in the number of mature germ cells – spermatozoa and a pronounced deterioration of their viability, as well as an increase in testosterone secretion is established.
The revealed violations in the morphofunctional state of the reproductive system of the offspring suggest that the trans-generation effect of EMR exposure generated by cellular sources can be considered as a factor affecting the decline in the male fertility.

Thyroid hormones can affect the cardiovascular system directly by binding to nuclear thyroid receptors, as well as indirectly by changing the neuro – humoral status of the body as a whole. The aim of the work was to assess the effect of levothyroxine suppressive therapy on the regulation of the heart rate and activity of the sympathoadrenal system, as well as the level of cortisol in the blood of young patients with thyroid cancer. It is shown that the effect of suppressive therapy with levothyroxine on the state of the cardiovascular system is manifested in an increase in the risk of tachycardia and changes in heart rate variability associated with the body mass index. Patients with thyroid cancer had a sharp decrease in normetanephrine (norepinephrine metabolite) in the urine. The levels of metanephrine (metabolite of adrenaline) and dopamine in the urine was dependent on the tonus of the autonomic nervous system and blood pressure. The revealed shifts indicate that against the background of subclinical hyperthyroidism, the mechanisms aimed at stabilizing the heart rate and preventing the effects of hyperstimulation of thyroid and beta-adrenoreceptors of the myocardium are included.

Data on the earthquakes recorded in the Soligorsk mining area during the years 1983–2017 were used to investigate their distribution features both in the energy, and space-time characteristics. Based on the sketch maps of the epicenters and the graphs of the accumulated numerical values of the earthquakes the periods and areas of the repre sentative earthquakes were determined for each energy class К = 5, 6, 7, 8. A normalized graph of the earthquake recurrence was created.

The paper describes the important aspects of the developed technology for manufacturing silicon-carbide substrates for optical mirrors intended for future use in space applications. It is shown that the material with the best combination of thermophysical and mechanical properties (Maksutov’s criterion) among the known analogs used for making astronomical mirrors is obtained. The characteristics of a mirror made of a lightweight mirror substrate with a diameter of 205 mm are described, compared with the parameters of most known mirrors made of silicon carbide for various space missions and as proto types. It is shown that the produced substrate is characterized by a rather low specific gravity – 16.5 kg/m2, which is comparable with the indicators of the best world analogues.

The results of extended researches of processes of modification of morphology, composition and structure of polydispersed refractory powders and microcomposites based on CrB2, TiB2, TiCrB2, Al2O3 in the flow of low-temperature plasma and its use for the formation of plasma coatings – layered composites are presented.

The necessity to form the integration policy at the subnational level to the existing mechanism of economic integration in the EAEU is shown. The content of the conceptual framework of its elaboration, the features of the object and the subnational level of management as a subject of the policy is disclosed. Taking into account the existing regional restrictions, the directions of the integration policy are justified, including the regional policy aligned at the level of the EAEU member countries, the institutional framework, the measures to deepen interregional and border relations based on the implementation of regional reserves and a closer linkage with the regional development.

As a result of the research conducted, it was determined that the performance indicators of created plant type correspond to the indicators of the target standard. Performance of first litter gilts, as well as sows with two or more farrowings, amounted to 11.8 and 11.9 piglets of multiple pregnancy rate, 54.5–55.2 kg of milk yield, for the number of piglets and litter weight at weaning – 10 animals, 84.3–85.1 kg, respectively. Among the selected boars for reproduction according to a greater part of traits, animals of Zaslon line were the best, with indicators of the age of reaching a live weight of 100 kg and an average daily weight gain from birth to 100 kg of live weight made 170.5 days and 717 g, respectively. During the lifetime assessment of meat traits in young animals of the created type selected for self-repair, the back fat thickness values measured at two points of the back, as well as the height of the longest muscle and the lean meat content in body made 16.0, 18.7 and 44.2 mm and 52.0 %, for gilts, respectively, and 15.7, 17.2 and 45.3 mm and 53.2 % for boars, respectively. Calculation of the complex index of sows showed that in most animals its value made 100 points. Assessment of the genetic structure of animals of the new plant type in the Belarusian meat breed by genes RYR 1, ESR, H-FABP and IGF2 was carried out.