Abstract. The present paper is devoted to the construction of monotone difference second-order schemes for local approximation on non-uniform grids in space for 2D quasi-linear parabolic convection–diffusion equation. Two-sided estimates of the difference solution are found and an important a priori estimate in a uniform norm C is proved.

The purpose of the work is a description of three-dimensional non-reductive homogeneous spaces that allow invariant affine connections together with their curvature and torsion tensors, holonomy algebras. We are concerned with the case, when Lie group of transformations is unsolvable and a stabilizer is unsolvable too. An object of investigation is concerned with non-reductive spaces and connections on them. The basic notions, such as an isotropically-faithful pair, a reductive space, an affine connection, curvature and torsion tensors, and holonomy algebra are defined. The local description of three-dimensional non-reductive homogeneous spaces with unsolvable Lie group of transformations and an unsolvable stabilizer, which allow affine connections, is given. The local classification of homogeneous spaces is equivalent to the description of the effective pairs of Lie algebras. All invariant affine connections on those spaces are described, curvature and torsion tensors, holonomy algebras are found. Studies are based on the use of properties of Lie algebras and groups, as well as homogeneous spaces and they are mainly local in character.  The features of the methods presented in the work is the application of a purely algebraic approach to the description of homogeneous spaces and connections on them, as well as the combination of methods of differential geometry, the theory of Lie groups and algebras and the theory of homogeneous spaces. The results can be used in the study of manifolds and can find application in various areas of mathematics and physics, since many fundamental problems in these areas relate to the investigation of invariant objects on homogeneous spaces.

The article is devoted to the problem of constructing an integrated and characteristic base of modular arithmetic. In particular, calculation estimates are obtained for conversion of a modular code (MC) into a code of a generalized positional number system (GPNS) and based on them the sequential and parallel configurations of the appropriate procedure are synthesized. With its modular structure, the developed algorithms are easy to implement. They include subtraction with multiplication by constants used by the modules of the basis. Computational complexity of sequential and parallel implementations of conversion of MC into the GPNS code according to the proposed algorithms is О(k²) and О(k) of modular operations (k is the power of the basis of the number system) respectively.

New technologies of obtaining composite media were studied, which can reveal the properties of metamaterials: porous aluminum oxide films with a system of periodic nanoholes filled with noble metals; multilayer metal-dielectric (including, metal-polymer) nanostructures; polymer films with implemented metal nanoparticles, fish-net polymer structures with metal filling of cells. Dielectric and resonance properties of synthesized structures were investigated; the peculiarities of excitation of new types of quasi-non-diffracting plasmon-polaritons in them were established. The original methods and devices for characterization of optical properties of created composite nanostructures were proposed. The perspectives were shown how to use metamaterials when creating flat superlenses, to manipulate light beam parameters and also resonance-assisted evanescent nanolithography.

Mesons as bound states of quarks with coordinate-dependent mass are modeled. The interaction of quarks is described by the QCD modified Cornell potential with a strong position-dependent coupling αS(r). The equation of motion for the system of two interacting spinless particles in the center-of-mass frame is suggested. Two asymptotic solutions of this equation for large and small distances are obtained. The mass formula is derived for quark-antiquark bound states on this basis. The mass spectra of the ρ and D±* calculated in the framework of the model are in a good agreement with experimental data.

The exact description of tunneling is given for a smooth symmetric double barrier which is constructed with the help of both parabolic and inverted parabolic potentials. The analytical expression for transmission coefficient is found. The resonant tunneling condition is obtained. The dependence of transmission coefficient on incident particle energy is presented for different values of double barrier parameters. It is established that the number of resonances increases with growing the width of barriers and the distance between barriers. The continuous wave functions are expressed in terms of the confluent hypergeometric functions. The real and imaginary components of wave functions are shown at the resonance values of energy. The proposed smooth parabolic potential extends a very limited list of exactly solvable models that describe tunneling through double barriers. The variable shape of the considered double barrier gives the supplementary possibilities to simulate tunneling processes.

For the first time the capacitance of a semiconductor p⁺n⁺-diode is theoretically calculated, in which both the p⁺-region and the n⁺-region are completely compensated with point irradiation-induced defects (rt-defects) of one kind. Each rt-defect introduces two energy levels into a band gap of crystalline host matrix and can be one of three charge states (−1, 0, +1). Such a diode, in which both electrons in the conduction band and holes in the valence band are absent, is called a ζ-diode. The ζ-diode current is performed by electron hopping via rt-defects only. In the drift-diffusion approximation, a system of stationary nonlinear differential equations for hopping migration of electrons via rt-defects is numerically solved. The static capacitance-voltage characteristics of the ζ-diode based on crystalline silicon are calculated for the operating temperature ranging from 78 to 373 K. It is shown that the ζ-diode can be used as radiation-resistant varicaps operating at low (cryogenic) temperatures.

The efficiency of free radical oxidation of phospholipid membranes under exposure to UV radiation (λ = 180– 400 nm) by the phospholipase A₂ PLA₂ IB as a marker of lipid peroxidation was studied. Mixed micelles of phosphatidylcholine and sodium deoxycholate were employed as the model of phospholipid membranes. The PLA₂ activity was determined by spectral changes in hemoglobin upon the interaction with fatty acids, resulting from a phospholipolysis product. At the same time, the level of lipid peroxidation was estimated by accumulation of malondialdehyde as a well-known product of irradiation of phospholipids. The directly proportional dependence of the PLA₂ activity on the UV irradiation time of phospholipids is obtained. It is shown that the level of the PLA₂ activity correlates well with the lipid peroxidation level, pointing to the antioxidant capacity of blood in comparison with the well-known antioxidant Trolox as standard.

Rheological properties and concentration cross-overs of nonionic polyacrylamide and anionic acrylamide copolymers in saline solutions (sodium and potassium chlorides) of different concentration (0.07 and 3.4 mol/l) were investigated using the capillary viscometer method. It is shown that increasing the content of ionic groups of macromolecules reduces crossover concentration. The area of non-overlapping coils between the crossover concentration and the concentration of fluctuation mesh formation was determined for polyelectrolytes; it was shown that with increasing salt concentration this area practically disappears, i.e. the mass transfer mechanism changes near crossover concentration as in the saline solution of nonionic polyacrylamide. An effective volume of polymer macromolecules is higher in the sodium chloride solution than in the potassium chloride solution; for polyelectrolytes, it is higher than for nonionic polymers and grows with increasing the number of ionic groups of polyelectrolyte macromolecules.

3-(4,5-Dichloroisothiazol-3-yl)-1-ferrocenylprop-2-en-1-one was synthesized by condensation of acetyl ferro-cene with 4,5-dichloroisothiazole-3-carbaldehyde. The reaction of isothiazolylferrocenyl ketone obtained with guanidine resulted in amino substituted ferrocenylisothiazolyl pyrimidine. The interaction of isothiazolylferrocenyl ketone with thiourea proceeded by heterocyclization, leading to the formation of ferrocenylisothiazolyl-3,4-dihydropyrimidin-2(1H)-thione. Hybrid derivatives of azaheterocycles and ferrocene are of interest for biotesting as antitumor agents.

The data are presented on kinetic correlations of the growth of parent and lactose-adapted strains of bacteria Arthrobacter sulfonivorans and the production of extracellular beta-galactosidase. It was found that the adapted strain BIM B-499-D was distinguished by a shorter lag phase than the parent strain BIM B-2242 by a reduced period of reaching a maximum specific growth rate (μ_max = 0.316–0.319 h–1) and a stationary phase of culture. Synthesis of extracellular enzyme in both strains occurred during the exponential growth phase and attained a peak specific rate (ε_max = 0.247–0.250 U · mg–1 · h–1) with a 6 h time interval. BIM B-499-D exceeds BIM B-22421.6 times in the level of enzyme biosynthesis and in the duration of the process – 1.3 times. The kinetic parameters of growth (tµ_max = 6–9 h) and beta-galactosidase production (tε_max = 18–24 h) established for the examined strains indicate the disconnection of processes in time at least by 12–15 h.

Malignant tumors possess the mechanisms allowing one to evade the degradation of tumor-carrier by the immune system. One of the mechanisms is the formation of a tumor immunosuppressing microenvironment acted upon by extracellular adenosine. Earlier, we proposed the idea to eliminate a cancer protection barrier from the host cell immunity using adenosine deaminase fused with annexin A5. The conducted study resulted in the first development of the strain Escherichia coli producing the chimeric protein structurally composed of human annexin A5 and homologous adenosine deaminase. The generating capacity of the obtained microbial strain with respect to chimeric protein was 18 mg/l of culture fluid. 13 mg of highly purified chimeric protein showing the adenosine deaminase activity was produced. The adenosine deaminase productivity of the strain equaled 7.1 µmol/min/ml of culture fluid. The obtained chimeric protein is intended for a further investigation as a promising cancerostatic agent.

The present paper considers the deformation of a three-layer elastoplastic bar with a compressible filler in the temperature field. To describe kinematic properties of an asymmetric through thickness pack we have accepted the hypotheses of a broken line as follows: Bernoulli’s hypothesis is true in thin bearing layers; Timoshenko’s hypothesis is true in the compressible through thickness filler with a linear approximation of displacements through the layer thickness. The physical stress-strain relations correspond to the theory of small elastoplastic deformations. Temperature variations were calculated by the formula obtained by averaging the thermophysical properties of layer materials in terms of the bar thickness. A system of differential equilibrium equations has been derived using the variational method. An analytical solution has been derived by the method of elastic solutions for the case of a uniform distribution of a continuous load. Its numerical analysis has been performed.

Abstract. Oxygen exchange in single erythrocytes is studied with the use of magnetophoretic magnetometry based upon the registration of cell trajectories in a microfluidic Hele-Shaw cell under the action of high-gradient magnetic field. It is found that, at atmospheric conditions, the equilibrium oxygenation degree of cellular hemoglobin is four times smaller as against a standard level of blood hemoglobin. Also, an application of shear flow leads to an instantaneous increase of cellular hemoglobin oxygenation up to a standard level, and it takes minutes for a low equilibrium level to be re-established. These findings give a new notion as upon erythrocyte functions and may be of use for the hematocrit diagnosis.

The effect of adding 0.9 wt% of a diisocyanate chain extender (CE) on rheological and mechanical properties of PET/PTEP blends, reinforced with a 30 wt% short glass fiber (GF) is studied. TPEE concentration in the blends was varied from 7 wt% to 50 wt%, which affected changes in their phase structure. Composites were obtained through reactive extrusion using a twin screw mixing reactor with unidirectional screw rotation. Interfacial adhesion in the “polyester binder – GF surface” system was estimated using micromechanical tensile tests of mixed polyester matrices and glass fiber reinforced composites that are based on them, as well as using the relaxation spectrometry data. It was determined that CE has a strong effect on the mechanical properties of composites with a different phase structure, increasing their mechanical tensile and bending capabilities up to 1.5 times, and increasing Charpy impact strength of materials up to 1.6 times. The reasons for these effects are an increase in the average length of GF in composites containing CE, as well as intensified interaction between interfacial adhesive polyester binder and GF surface.

Abstract. A further increase of the technology efficiency for livestock produce cannot be ensured with no complex application of modern genetics methods in the breeding system and technological solutions. A genotype selection (breeding), assuming the determination of genes directly or indirectly related to economic traits (marker selection) has a number of advantages compared to a traditional selection. It makes it possible to evaluate animals of tender age, does not consider traits variability due to environment conditions, and as a result increases the efficiency of selection. The search, research and experimental substantiation of using the molecular and genetic markers of animals’ performance traits are sore issues of the modern animal science.