Two-step Newton–Kantorovich method for approximate solution of nonlinear equations with operators satisfying a modified condition of regular smoothness is considered. Using majorants, the convergence of this method is proved and estimates for the convergence rate are obtained.

The interpolation formulas for operators of one, two and many functional matrix variables containing arbitrary matrices are constructed. The classes of matrix polynomials, for which interpolation formulas are exact, are defined. The method of construction based on a given fixed degree interpolation matrix polynomial of other interpolation polynomials of the same degree, but with more number of nodes is proposed.

The linear system with triangular periodic coefficient is considered. Necessary and sufficient conditions for existence of irregular solutions of the linear system with triangular periodic coefficient are obtained.

In this article median eigenvalues of a subcubic outerplanar graph are investigated. Mohar’s conjecture has been confirmed for this class of graphs.

We prove that the Hausdorff dimension of any subset of Moran’s fractal is equal to that of the set of sequences encoding this subset under a suitable choice of metrics on the encoding set.

In case of parallel grained affine algorithm a method of obtaining dependences is developed. Propositions to formalize the dependences in parallel grained algorithms are stated and proved.

Samples of polyurethane with different concentration of carbon nanomaterial loadings were fabricated. Structural, optical and electrophysical properties of these samples were studied. Characteristics of interaction of electromagnetic radiation with samples in the frequency range of 8.15–78.33 GHz were measured. Apparent radiation attenuation was observed in the frequency range of 8.15–37.5 GHz, and more intense attenuation – in the frequency range of 37.5–78.33 GHz.

A study was conducted on the effect of multiwalled carbon nanotubes (MWNT) on the course of free-radical grafting of trans-ethylene-1,2-dicarboxylic acid (TEDA) onto linear low-density polyethylene (LLDPE) and ethylene-propylene copolymer (cPP), containing ethylene units ≈ 7 wt%, using the reactive extrusion process. The extrusion reactor was the material cylinder of the twin-screw extruder TSSK-35/40 (screw diameter = 35 mm; L/D = 40; 10 independent heating zones).

It was found that small amounts of MWNT (0.01–0.3 wt%) influence noticeably the monomer grafting onto macromolecules of LLDPE and cPP, as well as the structure, functionalized products’ mechanical properties, strength and high elasticity properties of their melts. The extent of MWNT influence depends on their concentration and PO-structure. It is shown that the monomer’s grafting efficiency can be raised with MWNT ≥ 0.1 wt% inhibit the secondary process of macromolecular cross-linking; in the case of cPP which mostly undergoes degradation during functionalization, the secondary reactions accelerate catalytically.

It is shown that myeloperoxidase (MPO) initiates an increase in the concentration of intracellular free calcium ions in neutrophils caused both by the release of calcium ions from intracellular stores, and extracellular Ca²⁺ entry across the plasma membrane channels. It is found that MPO modified by hypohalous acids retains its ability to induce Ca²⁺-signaling in neutrophils. It is established that MPO-induced entry of Ca²⁺ into cytosol of neutrophils is not associated with its catalytic activity, but caused by direct binding of MPO to α-subunit of β₂-integrin of neutrophils and tyrosine kinase activation.

A number of new methods for modification of carboxyl, carbonyl, amino groups of 5-aminolevulinic acid using β-di-and β-tricarbonil cyclohexane compounds, aimed to increase their lipophilicity, have been proposed. The obtained compounds are perspective as substanses for research in the field of photodynamic diagnostics and therapy of cancer.

The treatment of millet seedlings with 24-epibrassinolide (24-EBL) was shown to cause a transient increase in their hydrogen peroxide content, the subsequent activation of antioxidant enzymes (superoxide dismutase, catalase, guaiacol peroxidase) and the development of their resistance to salt stress. Antioxidant dimethylthiourea and NADPH oxidase inhibitor imidazole leveled these processes. It was concluded that the induction of millet salt tolerance by exogenous 24-EBL was mediated by the enhancement of reactive oxygen species level associated with the increased activity of NADPH oxidase.

Two-stage screening enabled one to define the composition of enzyme complexes produced by bacteria of genus Arthrobacter in media with specific substrates and activity of individual constituents involved in the t ransformation of milk proteins, lipids and carbohydrates. It was found that enzyme complexes of Arthrobacter strains BIM B-2239, BIM B-2240, BIM B-2241 and BIM B-2242 showed the most balanced activity of lipase, protease, β-galactosidase and glucose(xylose)isomerase components. Following the nucleotide sequence analysis of 16S rRNA gene the examined cultures were identified as Arthrobacter sulfonivorans. 16S rRNA gene sequences over 1400 bp in size were deposited in GenBank database.

Detailed investigation of conditions favoring the efficient hydrolysis of proteins and lipids by proteases and lipases produced by Arthrobacter sulfonivorans strains BIM B-2239, BIM B-2240, BIM B-2241, BIM B-2242 and the transformation of milk lactose and derived hydrolysis products mediated by β-galactosidases and glucose(xylose)isomerases will allow one to select microbial strain to develop the biotechnology of manufacturing hypoallergenic feed additive with prebiotic activity from dairy substrates.

We studied the antioxidant defense enzyme activity in amyloid- modified human erythrocytes in vitro, and the influence of antioxidants on the amyloid-induced modification of erythrocyte membranes. It was shown that a combined action of amyloid structures of lysozyme and tocopherol or quercetin on human erythrocytes in vitro enhances membrane lipids microviscosity changes, but the activation of peroxidation process wasn’t detected. Most likely it happens because a total antioxidant activity of all antioxidant defense enzymes in human erythrocytes in vitro does not change under the influence of amyloidoligomers. The activity of glutathione peroxidase decreases while the catalase activity increases and the superoxide dismutase activity doesn’t change as compared to control.

Molecular modeling complexes of bis-(3′, 5′)-cyclic dimeric guanosine monophosphate (c-di-GMP) with human oxyhemoglobin HbA1 and the analysis of the cyclic diguanylic acid inhibitory effect on the binding of 1,8-ANS to HbA1 carried out by the steady-state fluorescence spectroscopy showed that the most specific binding site of c-di-GMP in hemoglobin oligomers is the central regulatory region of this protein (competitive inhibition constant is 2.91 ± 0.54·10⁻⁵ М). At high concentrations of 1,8-ANS c-di-GMP inhibitory effect on the probe binding is non-competitive (non-competitive inhibition constant is 0.79 ± 0.11·10⁻⁴ М), indicating the ability of c-di-GMP interact with less specific surface areas of human oxyhemoglobin.

A high application efficiency of microbial preparation Ecobel for remediation of soil polluted with hydrocarbons resulting from emergency oil spills was demonstrated.

Expense of liquid biopreparation calculated at 1: 0.025 oil-Ecobel ratio equaled 1.25 liters of the product encharged with microbial titer 1 · 10⁹a CFU/ml and containing 3.125 g biomass of petroleum-degrading species per 1 m² of contaminated soil.

The DNA typing for the estrogen receptor gene (ESR1) in pigs is proposed to carry out with the aid of the technology of the HRM-analysis (High Resolution Melting) and continue to use it as an express method for mass screening of breeding animals in order to increase the fertility and to improve the breeding animals process in the pig. Assessed polymorphism ESR1-PvuII of the estrogen receptor gene in the Belarusian large white pigs (n = 51) with the use of the HRM-analysis, which is highly sensitive and cost-effective as compared to the traditional PCR-RFLP method. The conditions for real-time PCR are worked out, the accuracy of identification of genotypes AA, BB, AB is confirmed, and the effectiveness of the HRM-method is also analyzed.

Results of the first studied peculiarities of the nitrogen dioxide distribution in the atmospheric air in Minsk based on measurements in special conditions in ‘street canyons’ are described. It is shown that the ratio between ‘street canyons’ and background mean air concentrations of nitrogen dioxide is 2.2–5.8. In accordance to measurements, the nitrogen dioxide concentration on the windward side of street canyons is 1.2–1.4 times greater than its content on the leeward when the wind direction is close to the perpendicular direction of the street. A relation between emissions of nitrogen dioxide from vehicles based on the structure of traffic flows and nitrogen dioxide concentrations in street canyons in Minsk is evaluated.

The composite structure, mechanisms and nature of strengthening of tool steels subjected to strengthening thermo-cycling treatment are presented (STCT). The influence of the STCT process on the structure and mechanical properties of tool steels are examined. The developed technology permits increasing the wear resistance of steel tools by a factor of 1.4–12 in comparison with traditionally heat-treated ones.

The organization of an experiment on the verification of the concept of viscous fluid flow theory is substantiated theoretically. The concept is based on specific features of the development of thermohydrodynamic processes in a shear flow between two parallel walls with account for heat dissipation, which are typical of two different theoretical models.

The high heterosis effect was revealed in BLW×BM sows using boars of Yorkshire and Landrace breeds of Danish selection. The value of multiple farrowing was 6.48–5.50 % (P ≤ 0.05), of milkiness – 7.46–7.70 % (P ≤ 0.01), of the number of piglets at weaning – 9.2–8.2 % (P ≤ 0.05) and litter weight – 2.8 % (P ≤ 0.05). When combining BLW×BM sows with Yorkshire and Landrace breeds of pigs of Canadian selection the heterosis effect on multiple pregnancy, milkiness, number of piglets at weaning made 4.6 %, (P ≤ 0.05), 6.3–3.3 % (P ≤ 0.01) and 7.1–5.1 % (P ≤ 0,05), respectively.

In present time Belarusian multy party system in a global crisis. It has some constituent elements. Political parties are not able to work out popular and clear ideas, and to persuade people in accuracy, importance and necessity to put these ideas into effect, to convey to the masses, a clear shortage of people, who can provide these factors.