The first mixed problem for the Klein-Gordon-Fock type equation in the half strip is considered in the case when inhomogeneous matching conditions are fulfilled. The method of characteristics is used to prove that the fulfillment of the homogeneous matching conditions is not only sufficient but also a necessity for the existence of a unique smooth enough classical solution defined in the whole half strip. The equivalent conjugation problem is formulated when inhomogeneous conditions are fulfilled where conjugation conditions are set on the characteristics. Constructed inhomogeneous conditions uniquely define gaps of the solution or its derivatives on characteristics and given gaps are remained while the time-argument increases.

The solution of the problem is reduced to solving the second-type Volterra-integral equations. Theorems of existence and uniqueness of the solution in the class of the twice continuously differentiable functions were proven for these equations when the initial functions are smooth enough. This approach can be used in constructing as analytical solution, when the solution of the integral equation can be found explicitly, so for the approximate solution. Moreover, approximate solutions can be constructed in numerical and analytical form. When the numerical solution is constructed, the matching conditions are essential and they need to be considered while developing numerical methods.

Based on a comparative analysis of relativistic constitutive equations of the Bokut-Serdyukov-Fedorov (BSF) and Tamm, it was shown that the dual invariance of the latter requires the reversibility of the Tamm material tensor, while the BSF equations are properly dual-invariant. The connection of the mentioned approaches is demonstrated by the example of the equations of axion electrodynamics which were first formulated in the BSF formalism.

Communicated by Corresponding Member Lev M. Tomilchik

The radio absorption properties of polymer composite materials with ferrite and graphene additives in the microwave frequency range (26-38 GHz) were studied. It was shown that graphene-like structures have a significant effect on the ability of composite materials to shield from electromagnetic radiation.

Effective enhancement of the fluorescence signal of chromophores adsorbed directly onto plasmonic films can be observed under conditions of strong spectral resonance between plasmon and chromophore absorptions. This effect seems to contradict the established mechanisms of complete quenching of the fluorescence of chromophores under their adsorbtion directly onto the metal surface. However, under certain conditions, enhancement of the fluorescence signal is observed for both inorganic and organic chromophores. To understand the effect and conditions of its observation, we propose to use the quantum concept of virtual photon exchange in the near optical field - dressed photons. This concept is borrowed from the physics of elementary particles and is already well adapted to the problems of nanophotonics by M. Otsu. In this paper, we discuss exclusively the key factors responsible for enhancement of fluorescence of CdSe/ZnS nanocrystals and the effective dressed photons exchange: the size of nanoparticles, the distance between them, and the presence of spectral overlap indicating the possibility of resonant interactions between plasmons and chromophores.

Communicated by Academician Sergei V. Gaponenko

Tyrosine kinase inhibitors became a common treatment option for chronic myelogenous leukemia (CML). Still secondary resistance of patients connected with disease progression remains a major challenge. More effective kinase inhibitors are of great need. In this study, design and molecular docking of combinatory library of de novo imatinib-like structures was performed using Autodock Vina. The main design approach was to replace a benzene linker in the structure of imatinib with a pyrrole ring. Crystal structures of CML-related C-ABL, Human ABL and T315I mutant ABL were used as receptors. Ligands were prepared in MGL Tools. Chimera 1.10 was used for receptor preparation, binding site parametrization and visualization of results. Vina’s exhaustiveness of search was set to 24. All docked structures were filtered based on the known inhibitors results. Two structures showed the promising predicted binding affinities (Autodock Vina’s score -13.6 and -13.1 respectively) comparable with those of approved kinase inhibitors imatinib and nilotinib.

The efficiency of free radical oxidation of higher fatty acids (palmitic, oleic, linoleic, linolenic acids, complex of unsaturated fatty acids of omega-3 and omega-6 plant origin) under the influence of UV irradiation (λ = 180-400 nm) as a possible marker of lipid peroxidation is studied. Micelles of fatty acids (FA) in ethyl alcohol were used as a model of the lipid phase. The effect of UV irradiation on fatty acids was determined from the spectral changes of myoglobin in the region of the Soret band. The level of peroxide oxidation of the lipid phase at the same time was estimated from the accumulation of malonic dialdehyde as a well-known product of irradiation of phospholipids. The direct proportional dependence of the intensity of the difference spectrum of Mb (ΔD) on the number of double bonds in the molecule of oxidized fatty acids, as well as on the time of their UV irradiation and the accumulation of secondary LPO products is obtained. This shows that the spectral changes of Mb under the action of the pool of oxidized forms of fatty acids correlate well with the level of lipid phase peroxidation and can characterize the antioxidant potential of the blood when combined with the known antioxidant Trolox as a calibrator-inhibitor.

Communicated by Corresponding Member Sergei A. Usanov

A recipe for the nutrient granular substrate for growing plants (the working name is “Zion”) has been developed. The substrate contains all necessary for plant nutrient elements in the chemically bound state in high concentration; it does not contain any organic matter and nitrates, and does not need additional fertilization during the plant vegetation. All nitrogen in the substrate is contained in ammonium form. The substrate has been tested in the laboratory conditions in pot experiments for fertility and nitrates concentration in the biomass of the two cultures accumulating a large amount of nitrates that is leaf salad (Lactuca sativa L.) cultivar Afficion and ryegrass (Lolium perenne L.). The plants were grown on a 100 % substrate as well as on its mixtures (3-10 %) with different fruitless media - quartz sand, peat, and vermiculite. It appeared that in all the cases, when Zion has been used, the maximal content of nitrates in the plant biomass was 209 mg/kg dry, the minimal one was less than 50 mg/kg dry, which is lower by an order of magnitude than the admitted sanitary norm for the plants used in the study.

The dependence of the phospholipase D (PLD) activity, catalyzing the catabolism of glycerophospholipids, on exogenous soluble sugars under the conditions of sugar starvation caused by darkening of plants was studied in oat (Avena sativa L.) seedlings. It was found that the PLD activity in etiolated oat seedlings was suppressed by the treatment of plants with mono- and disaccharides: glucose, sucrose and mannose. These sugars neutralized the activating effect of darkening on the activity of PLD in green oat seedlings. The treatment of oat seedlings with inorganic phosphate also led to the modulation of the PLD activity similar to that with sugars. In this case, the action of the tested sugars mimicked the light modulation of the PLD activity. Sequencing the partial mRNA sequence of oat PLD gene showed more than 80 % homology with the sequences PlDαof other cereal species. Illumination of etiolated oat seedlings with red light and darkening of green seedlings in darkness inhibited or induced the PLD expression, respectively. Thus, the expression of PLD and the enzymatic activity of PLD showed the sensitivity to changes in the light conditions of a plant growth. Consequently, these data indicate that PLD plays an important role in adaptation of oat plants to darkening and sugar starvation.

The study of the physical state of membrane lipids after the exposure of lymphocytes to ZnO NRs revealed a decrease in the lipid microviscosity of the hydrophilic membrane area and its increase in the hydrophobic area (external monolayer). The effects of ZnO NPs on membrane lipid components were not significant. Investigations of the membrane proteins conformation state revealed a rise of the protein NH₂-groups level on the membrane surface only after the lymphocytes exposure to ZnO NRs. The level of SH-groups of the membrane protein after the action of ZnO NPs increased, otherwise the interaction of ZnO NRs with cells leads to the oxidation of thiol groups. According to the results of SEM, the geometric size of ZnO NPs did not exceed 30-100 nm, the diameter of ZnO NRs was 70-150 nm and the length - more than 500 nm. So the obtained results of toxicological tests can be partly explained by the possibility of ZnO NPs to enter into the cell but the most probable mechanisms for the NRs interaction with the cell are an electrostatic interaction or membrane puncturing.

In this study, we evaluated the genetic diversity of silver (Hypophthalmichthys molitrix Val.) and bighead (Hypophthalmichthys nobilis Rich.) carps grown in aquaculture in the territory of the Republic of Belarus. Genotyping was obtained for 11 STR-loci - Hmo11, Hmo13, Hmo15, Hmo25, Hmo26, Hmo31, Hmo33, Hmo 34, Hmo36, Hmo37, and Hmo40. The following parameters were calculated: the average number of alleles per locus, the effective number of alleles, the levels of expected and observed heterozygosity, the value of the Shannon information index and the fixation indexes F_IS and F_ST. The obtained results indicate a moderate (for silver carp) and sufficiently high (for bighead carp) genetic diversity of the studied samples of carps up to the possibility to allocate several groups for subsequent work on obtaining linear material and further reproduction, including commercial fish. However, to achieve these goals, it is necessary to pay special attention to the selection of pairs of producers taking into account the results of molecular genetic analysis. The scheme for the differentiation of hybrid individuals between silver and bighead carps and the use of molecular genetic analysis of STR-loci would be proposed. This approach can be used as a minimally invasive rapid test in breeding and reproductive programs for the studied fish species.

Communicated by Academician A. V. Kilchevsky

The summarized data on indoor radon concentrations and estimated effective radon doses in the Vitebsk, Mogilev and Gomel regions of Belarus are presented. The passive track detector method was used to carry out the indoor radon monitoring. The measurement results are summarized in the geoinformation database. The map of the annual radon equivalent equilibrium concentrations distribution in administrative districts was created. The analysis of the results revealed that in 2.3, 1.3 and 0.4 % of dwelling of the Vitebsk, Mogilev and Gomel region correspondingly, the indoor radon equivalent equilibrium concentration exceeded the regulatory established limit of 200 Bq/m³. For effective planning of further radon monitoring, maps of absolute and relative number of measurements per administrative district were built. The calculated effective radon doses for the population and comparison to those from the “Chernobyl” radionuclides showed that radon is the main contributor to the public exposure.

New results of the analysis of the specific content of lead in dust emissions in Europe and its connection with air pollution by lead are given to explain the odserved differences in trends of lead emission and its content in ambient air. A close correlation has been revealed between trend in lead content in atmospheric air and trend of the specific content of lead in dust emissions. The relative content of lead in dust emissions (specific lead emission) is proposed as an indicator of the impact of various industrial sectors on the air. The calculated ratio of lead emissions to total dust emissions (specific lead content content in dust) in the EU-28 decreased from 3014.2 mg/kg in 1990 to 1096.5 mg/kg in 2000 and 530.5 mg/kg in 2015. It is concluded that lead pollution in the atmosphere decreased mainly due to the reduction in lead content in aerosols. The possible contribution of insufficiently accounted sources to ambient air pollution by lead has been analyzed. It is shown that the most likely among the expected insufficiently accounted sources of lead emissions is the wear of the brakes of motor vehicles.

Communicated by Academician Vladimir F. Loginov

The method of calculating a new structural model of a lens with a variable focal length is presented. The main composition is represented by three components, two of which are movable. The schemes of the lens with mechanical and optical compensation of an image are examined. It was found that the composition with a movable first component provides small sizes. On the basis of the proposed formula the parameters of the composition with a movable first component providing a small size and given the design parameters of a zoom lens of three components and the discrete-type lens with ten-fold magnification. Mathematical models prove that there are two and four potential solutions to the infinite and finite conjugate systems, respectively, and all roots can be obtained by simple algebraic calculations.

In this paper, we present a new conceptual model of the driver-car-road-environment system based on the theory of functional systems and the hierarchical driver model that consists of three levels that are strategic, tactical and physical levels. In this model, the information interactions at the tactical level of the driver are considered as interactions of multimodal images of actual, desired and current road situations. The proposed concept also includes an attention function that plays a significant role in providing safe driving and demonstrates the importance of cross-modal interactions in perception and cognition while driving. This conceptual model can be used to develop appropriate mathematical models of driving with increased cognitive load to study the mechanisms underlying the driving abilities in a person. Additionally, such mathematical models can be used to develop and investigate new methods to improve professionally important qualities of drivers and the resumption of the driver’s control over the vehicle.

Communicated by Corresponding Member Leonid G. Krasnevsky

The influence of the component ratio in the stabilized binary blends of amorphous polycarbonate (PC) and polyethylene terephthalate glycol (PET-G) on the compatibility of components, relaxation, rheological and mechanical properties was studied. The materials were prepared by reactive mixing of the components in the melt in a mixing rectifier based on a twin-screw extruder with unidirectional screw rotation. It is established that the components in the blends are mutually soluble over the entire range of their concentrations. The temperature of the а-process of relaxation (the glass transition temperature, Tg, in the mixtures) is in the interval between the values of Tg_PC = 148.3 °C, Tg_PET-G = 82.0 °C and obeys the Fox equation for single-phase blends. The mechanical characteristics of the mixtures change in a non-additive way when the concentration of the components is varied. In particular, in blends in which the PC content prevails, a significant increase in the upper yield limit is observed in comparison with the additive values, which, according to the relaxation spectrometry, is due to intense intermolecular interactions.