In this article we study the solvability of the analogue of the Cauchy problem for ordinary differential equations with Riemann–Liouville’s fractional derivatives with a nonlinear restriction on the right-hand side of functions in certain spaces. The conditions for solvability of the problem under consideration in given function spaces, as well as the conditions for existence of a unique solution are given. The study uses the method of reducing the problem to the second-kind Volterra equation, the Schauder principle of a fixed point in a Banach space, and the Banach-Cachoppoli principle of a fixed point in a complete metric space.

In this article, n-dimensional stochastic differential equations driven by multivariate fractional Brownian motions with the Hurst indices greater than 1/3 and a drift term are considered. We have obtained an expansion of expectations P_tg (x) = Eg (X^x_t) for small t, where X^x_t denotes the solution of the mentioned equation with an initial value x, and g: Rⁿ → R is a sufficiently smooth function.

The insulating side of the concentration insulator–metal phase transition (Mott’s transition) in p-type silicon crystals doped with acceptor (boron atoms) is considered under the conditions of stationary hopping electrical conduction. The boron atoms substitute silicon atoms in the crystal lattice and can be in one of the three charge states (−1, 0, +1), while the compensating impurity (donors) is in the charge state (+1). The distribution of impurity atoms is supposed to be random (Poisson’s distribution). The A0-band is formed from the energy levels of boron atoms in the charge states (0) and (−1), while the A+-band is formed from the energy levels of boron atoms in the charge states (+1) and (0). The decrease in the activation energy ε2 of thermally assisted tunneling transitions (hops) of holes between electrically neutral boron atoms, i. e. boron atoms that are in the charge state (0), is calculated. The ε2 quantity is approximately equal to an energy gap between A0- and A+-bands, i. e. Hubbard’s gap. In the quasi-classical approximation it is shown that the narrowing of the energy gap between A0- and A+-bands occurs due to: (i) the formation of a quasi-continuous band of allowed energy values for v-band holes from excited quantum states of boron atoms in the charge state (0), thus the value of the v-band shift into the band gap is determined by a maximum radius of the hole orbit in a boron atom, which does not exceed the half of the average distance between the nearest impurity atoms, and (ii) the splitting of the ground (non-excited) energy levels of the “molecular” pairs of boron atoms in the charge states (0) into triplet and singlet states of two holes. Calculations of ε2 without any adjustable parameters are quantitatively agree with the known experimental data on p-Si:B.

Ti–Al–C–N coatings were produced by reactive magnetron deposition at different substrate temperatures Ts (220, 340 and 440 °C) and bias voltages Ubias (–90, –150 and –200 V). Using the energy dispersive X-ray spectroscopy method, it was found that the increase of the bias voltage led to a growth of argon atomic concentration and the (Al + Ti) / (Ti + N) ratio and to a decrease of the trace oxygen concentration in Ti–Al–C–N coatings. The growth of Ts promoted a decrease in the oxygen concentration. By means of scanning electron microscopy, a change in the type of the microstructure (columnar, granular and mixed columnar-granular) of coatings by varying Ts and Ubias was found. Electrophysical measurements showed the change of the film resistivity (1982–3169 μΩ · cm) when the deposition conditions were varied. The solar absorptance αs was varied from 0.24 to 0.54, the emittance ε was varied from 0.33 to 0.52, and the αs / ε ratio was varied from 0.60 to 1.44 by changing Ts and Ubias. The obtained results indicate the opportunity to vary the Ti–Al–C–N films electrophysical and optical characteristics by choosing optimal substrate heating temperature and bias voltage.

To study the influence of the amino acid substitution of Phe470Ile, correlating with the spastic paraplegia of type 5, on the structure of human cytochrome P450 7B1, the spatial full-atomic models of this enzyme and its mutant form were created. It was found that Phe470 does not influence directly the catalytic properties of the enzyme because of its localization far from the active site. It was shown that the residue under investigation belongs to a highly conservative region of the protein structure and can influence the CYP7B1 correct folding. In particular, the amino acid substitution of Phe470Ile increases rigidity and stability of sterol 7α-hydroxylase. This can be a reason of changes in the CYP7B1 hydroxylase activity in relation to neurosteroids.

The hydrogels based on nanocomposite pectin-Ag exhibiting the antibacterial activity (MIСAg = 0.02–0.81 mM) were obtained by ionotropic gelation. It was shown that the synthesized hydrogels had a high capacity for kanamycin (up to 70 wt. %). The obtained hydrogels provided a prolonged release of kanamycin in 0.9 % NaCl and enhanced its antibacterial activity (MIC decreased 10–20 times) due to the synergistic effect.

The article presents the results of research of the chemical composition of easily volatile components in the leaves of nine taxa representing species and varieties of the genus Citrus L. cultivated under the conditions of greenhouses of the Central Botanical Garden of the National Academy of Sciences of Belarus as: C. unshiu (Tanaka ex Swingle) Marcow., C. grandis Osbeck cv. Bogatyr, C. sinensis Osbeck cv. Washington Navel, C. medica L. cv. Sarcodactilis, C. medica cv. Pavlovskiy Shishkan, Lemon Skernevitsky (’Ponderosa lemon’) is a clone of the hybrid C. medica L. × C. limon (L.) Burm. f., Citrofortunella microcarpa, C. limon (L.) Osbeck cv. Pavlovskiy, C.meyeri (Ju. Tanaka). The volatile components were extracted using a Supelco™ solid-phase microextractor placed in the vapour-air space above air-dried, finely ground and heated to 40 °C leaf samples. The component composition of the extracts was analyzed by the GC/MS method using the Agilent Technologies 6850 Series II system (Network GC System/5975B (VL MSD). Total 36 components were identified in the leaves of citrus plants: monoterpenes (14), sesquiterpenes (11), and oxygen-containing compounds: terpene alcohols, aldehydes, ethers (11). The studies have shown that the cyclic hydrocarbons monoterpene (Z)-β-trans-Ocimene and 3 sesquiterpenes (β-caryophyllene, (3E, 6E)-α-farnesene, and α-caryophyllene) were detected in the volatile components in leaves in the whole citrus group. While 2 sesquiterpenes: (3E,6E)-α-farnesene and α-caryophyllene are dominant for the most taxa based on their proportions in the total volume of volatile compounds. Sesquiterpene beta-Elemene is present as a dominant component exclusively in species and varieties representing the so-called “sweet citrus” group as it follows from the results of the studies: C. unshiu, C. grandis cv. Bogatyr, C. sinensis× cv. Washington Navel, C. meyeri, which allows one to consider it as a significant feature in the taxonomy of the genus Citrus L.

For the first time, a detailed study of the qualitative and quantitative composition of ginsenosides in the Panax ginseng roots was carried out with the help of high-performance liquid chromatography combined with mass spectrometry (HPLC-MS). The plants were introduced into the conditions of the Republic of Belarus at the experimental plot of the Central Botanical Garden of the National Academy of Sciences of Belarus. It was found that in the examined roots, all basic neutral glycosides of ginseng (ginsenosides Rb1, Rc, Rb2/Rb3, Rd, Rf, Rg1 and Re), as well as their malonylated derivatives (malonylginsenosides Rb1, Rc, Rb2/Rb3, Rd, Rg1 and Re) and some “minor” ginsenosides (20-gluco-ginsenoside Rf, notoginsenosides R1 and R2, isomers of malonyl-ginsenosides Rb1 and Rd) are present. The research also showed that different parts of the P. ginseng roots differ significantly in a total content of ginsenosides: for the main root, this parameter was 3.3 % of dry mass, and for the lateral roots – 7.8 % of dry mass.

Stress-associated proteins (SAPs) are the transcription factors containing the zinc-finger domains A20 and/or AN1. Genome-wide identification and characterization of an apple variety of Golden Delicious stress-associated proteins was performed, potential SAPs were found. Each of them contains, at least, one zinc-finger domain AN1. A phylogenetic tree was constructed on the basis of the amino acid sequences of apple SAP and homologues from other species (dicotyledonous cotton and monocotyledonous rice) to assess their phylogenetic relationships. The sequences ahead of the translation initiation site of SAPs genes were analyzed to discover cis-elements involved in the gene expression regulation. The analysis shows that apple SAPs are involved in a complex network of regulatory elements that controls the vitality of plant cells. It can be assumed that the expression of SAPs in apple trees occurs constantly, but if conditions of a plant growth are changed, their level increases. Regulation of the SAP expression may depend on a plant ontogenesis stage and it may vary in different tissues.

A promising scope of modern scientific research is the use of autologous and allogeneic mesenchymal stem cells for regeneration of periodontal tissues. The aim of the study was to evaluate the nature of morphological changes in the pathologically altered periodontal tissues after injection of a biotransplant containing mesenchymal stem cells of the adipose tissue immobilized on a collagen carrier in an animal experiment. In the experiment, 60 randobbred females of white rats were used as a model, whose adipose tissue was taken to obtain allogenic mesenchymal stem cells. All animals were divided into 5 groups, depending on the planned method of treatment – 10 rats each. The control group consisted of 10 laboratory animals with healthy gingiva. The experimental gingival recession model was created by the V-shaped excision of periodontal tissues. The bioplastic collagen material “Collost” gel 7 % in isolated form determines the fibrosis intensification and serves as a “matrix” for the formation of a fibrous tissue, ensures the adhesion of stem cells and their transformation into pro- and fibroblasts. Injection of a cell transplant suspension into physiological saline activates the processes of cell proliferation and transformation of fibroblast differentiating cells. Suspension of the cell transplant on a sterile bioplastic collagen material “Collost” gel 7 % enhances the effects of gel and stem cells, promotes the leveling of atrophic and dystrophic changes in the gum, strengthening a mechanical component, reducing the recession of the gum and the depth of the gingival pocket.

Decoding the seismic-velocity structure of the earth crust and the upper mantle on the basis of deep seismic sounding according to the Georift-2013 program along the Pripyat and Dnieper troughs along the Nesvizh-Bragin-ChernigovPoltava profile allows one to develop the ideas about the structure and Hercynian synriftic geodynamics of the contiguous adjacent structures of the Pripyat-Dnieper-Donets aulacogene. The abnormally powerful regional high-speed body, which is interpreted as a rift pillow, established in the lower crust under the Dnieper graben, is one of the indicators of manifestation of active plume tectonics in the process of Hercynian rifting in this segment of the aulacogen PDD. In the Pripyat segment, separated from the Dnieper segment by echeloned deep structures in the zone of the Bragin-Loevsky saddle, the structure of the crust– mantle boundary differs in comparison with the Dnieper segment by a lower level of the Moho surface; it is subhorizontal in the cross sections of the Pripyat paleorift. There were no active plume-tectonic events in scale.

The effect of addition of functionalized polyolefins (fPO) in an amount of 28 wt. % – mixtures of polyethylene and copolymer of ethylene with higher olefin containing 0.43 and 0.77 wt. % grafted monomer having two carboxyl groups in its composition – to aliphatic polyamides PA6 and PA66 on the structural features, the rheological behavior of melts and the mechanical properties of mixed materials was investigated. The materials studied were prepared by reactive mixing of the components in a melt in an extrusion reactor. It is shown that mixtures of PA66/fPO are characterized by more significant changes in the characteristics under analysis compared with those based on PA6 when the concentration of a grafted monomer is varied. An abnormally sharp increase (by more than two decimal orders) of the melt viscosity of a mixture of PA66 with fPO containing 0.77 wt. % of the grafted monomer, compared with the viscosity of initial PA66, is due to the specificity of the interphase interactions in the mixtures.

Economy is a system, including a set of levers and regulatory mechanisms, methods and measures for support and development, evaluation methods, schemes and models of strategic devices and tools, current setting, etc. In this regard, system economics implies a whole set of measures and instruments in the appropriate system to achieve the target effect. Then the economy system can be represented as a scientifically ordered economy, where all structural components have their place and fulfill the role of functioning as a holistic system and allow you to get the programmed result. Such an economy eliminates the spontaneity of development and inconsistency of actions of a set of measures and instruments. However, in Belarus the subject of system of the economy has not yet developed, therefore all sections of the economy are presented separately, does not allow to achieve synergetic efficiency of economic entities in practice.

Research shows that system economics has its well-established infrastructure. It has five main levels: nanoeconomics, microeconomics, mesoеconomics, macroeconomics and megaeconomics. System Economics goes back to the intelligence, persisted in innovation, it not only represents a balanced interaction of measures and levers, but “doing” is based on the latest ideas, innovations and high technologies.

It is established that the first pattern is the system of Economics is based on intelligence. Regardless of the field generator for the reproduction and sustainability is a scientific-innovative potential. Another natural system of the economy should be the emphasis on real material production, although it is assumed the optimum balance of real (material) and intangible industries. The balance of industries in different spheres of employment – is an essential attribute of any modern economic infrastructure, driven by the mechanisms of the system of the economy.

In this regard, the article emphasizes that systematizing ideas and innovations constitute the main value of human capital determines his level of competition, the ability to be proactive. Capital creative individuals, primarily scientists, should be considered as the fundamental base for generating new ideas, the ability to select personnel and to encourage them to develop new competitive solutions for the more significant results of economic activities.

The theocratic models of dialogue between church and state were reconstructed. The central problem of the article is the explication of emergence of the socio-historical situation that once again called for a new formulation of the traditional problem of the church and state interaction as a significant resource for achieving a social consensus and a successful development of society as a whole. The strategy of socio-dynamics of modern society is substantiated, in which the constant and constructive church and state interaction should be considered as a necessary and unique resource for its civilizational capabilities to successfully resolve both global and regional-local problems and contradictions of the modern world. The analysis of the history of Europe and a subsequent secularization of its cultural space justify the fact that just the elaboration of the strategy of the church and state interaction led to the situation that Christian cultural values, remaining in many respects a meaningful constant of the European culture, arrange their clerical nature and successfully integrate into the secular cultural landscape.

The measures taken in the recent years to improve performance traits of farm animals allowed one to ensure the production of more than 7.0 million tons of milk and 1726 thousand tons of meat on all-category farms in 2017. 760 kg of milk and 130 kg of meat were produced per capita in the Republic.

For the period up to 2025, main attention should be paid to the application of resource-saving technologies and the latest scientific developments and improvements of the resource potential of the industry in the livestock breeding of Belarus. Priority should be given to the implementation of innovative technologies and improvement of breeding work.

The perfect number of dairy cows in the country with a total cattle number of 4.3–4.5 millions of farm animals should be at a level of approx. 1.5–1.6 million of farm animals. The pig livestock will slightly increase and will amount to 3.3–3.6 millions of farm animals by 2025. The increase in the number of the poultry livestock is not planned and it will remain at a level of 49.5 billions.

Taking into account that the genetic pool of farm animals is the national wealth of the country and using market mechanisms, it is necessary to create the most favorable conditions for breeding enterprises (especially breeding farms). There are few such enterprises, and the state could realize this to ensure the future of the Belarusian livestock.