In this article, an improved lower bound for the spectral radius of a balanced bipartite graph of quite a large order giving the condition of existence of a Hamiltonian cycle in it and depending on the lower bound of the minimum degree of the graph has been obtained.

In this article, for the linearized difference scheme that approximates the Dirichlet problem for the homogeneous multidimensional quasi-linear parabolic equation with unbounded nonlinearity, two-sided point-wise estimates of the solution are established which are fully consistent with the same estimates for the differential problem. It is interesting to note that the proved two-sided estimates do not depend on diffusion coefficient. The direct application of such estimates is the proof of the convergence of the considered difference scheme in the grid norm L₂ . An example of the calculation by the Crank–Nicolson difference scheme is given, showing that the violation of the consistency conditions of differential and difference estimates leads to non-monotonic numerical solutions.

The quasi-crystal model of the radial distribution function for hard disks in the plane is suggested. It is shown that the coincidence with the distribution function, obtained by solving Percus–Yevick’s equation, is found by smoothing a square lattice and injecting vacancy-type defects into it. A better approximation is reached when the lattice is a result of a mixture of smoothened square and hexagonal lattices. Impurity of a hexagonal lattice is considerable at short distances. Dependences of lattice constants, smoothing widths and impurity on the filling parameter are found. In conclusion, it is stated that a basis of such a chaotic system apparently as a gas of hard disks in the plane at rather small filling parameters is a square lattice with some impurity of the hexagonal lattice at small distances. It is of importance to carry out investigations in a range of higher concentration and to compare with the modeling by the Monte-Carlo method.

The La_1–x Sr_x Ni_0.5Mn_0.5O₃ (0 ≤ x ≤ 0.2) perovskites have been studied by the methods of neutron powder diffraction and magnetization and by magnetoresistance measurement. It was shown that Ni and Mn ions are partially ordered in spite of the presence of Ni3+ ions arising from La³⁺ with Sr²⁺ substitution. The magnetic structure changes from ferromagnetic (x = 0) to antiferromagnetic (x ≥ 0.1); however, the transition temperature into the paramagnetic state is constant. Magnetoresistance in the ferromagnetic phase is large and gradually decreases with increasing temperature and Sr²⁺ content. The results are discussed in terms of close in value ferromagnetic and antiferromagnetic parts of Ni²⁺–O–Mn⁴⁺ magnetic interactions and the enforcement of 3d-O2p orbital hybridization in the magnetic field.

With the application of the methods of viscometry, fotosenditometry and optical microscopy, the areas of existence of steady concentrated and high-concentrated emulsions of an epoxy oligomer depending on its concentration, sizes and localization of disperse phase drops are defined.

In the present work, using the cell-free expression system, we prepared the proteins CD79A/CD79B labeled by stable isotopes of carbon-13 and nitrogen-15. It is shown that target proteins are mostly localized in the pellet of the cell-free expression system, which is consistent with their membrane nature and the presence of a transmembrane domain in their structure. Physicochemical parameters of the CD79A/CD79B samples were defined to obtain the multidimensional correlation NMR spectra of high resolution. The analysis of the obtained correlation spectra shows that under experimental conditions, CD79B exists in the disordered state. The splitting of the signal from the NH-group of the side chain of single tryptophan residue indicates the presence of slow conformational transitions in this region of the polypeptide chain. The addition of the trifluoroacetic acid to the solution of CD79B in DMSO leads to the destruction of the intermolecular bonds of “protein micelles” and the formation of its monomeric form that is well detectable by NMR.

The presence of transuranic elements in the Chernobyl fallout determines the longevity of radioecological consequences, especially with their possible involvement in the biological cycle. Without knowledge of transfer and distribution patterns of transuranic elements in plants we cannot make a correct assessment of the radiological situation in the areas affected by radioactive contamination from the Chernobyl accident. The article presents the accumulation factors for the aboveground and underground organs of herbaceous and shrub plants of different ecological groups. It is shown that the accumulation factors of transuranic elements in the underground organs of vascular plants are much higher than their accumulation factors in aboveground biomass.

A systemic administration of human recombinant lactoferrin to male rats caused an increase in a total testosterone level by 200 % in blood serum, the estradiol concentration decreased significantly by 16.7 %. Upon completion of administration, testosterone was still increased (p < 0.05) for 7 weeks, gradually returning to the control group values without inhibition of endogenous testosterone synthesis. In contrast, the level of estradiol returned to control values. Our study of the rat model of age-related hypogonadism revealed that a systemic per os administration of human recombinant lactoferrin to experimental animals had a significant stimulatory effect on testosterone biosynthesis in 2-yearolds, restoring it to the level of physiological values in young rats.

An approximate integral method based on constructing integral identical equalities for the weighted temperature function is proposed for solution of unsteady-state heat conduction boundary-value problems. This method is simple in use and allows one to obtain much more exact solutions as compared to the known approximate methods.

The effect of additives of short basalt fibers (BF) and organoclay – a montmorillonite modified with surfactant (quaternary ammonium salt of hydrochloric acid, in which the nitrogen cation is associated with methyl, tallilnym and two hydroxyethyl hydrocarbon radicals) – on the structure and mechanical properties of polyamide 6 (PA6) has been studied. The component compounding was carried out in the PA6 melt by reactive extrusion (RE) using a twin-screw extruder (screw diameter D = 35 mm and L / D = 40). It was shown that at hybrid filling of PA6 with BF and organoclay, the synergistic enhancement of mechanical characteristics of the composites is observed. This effect is most pronounced at low concentration (15 wt %) of BF in the composite.

Surface layers were prepared by ion beam-assisted deposition (IBAD) of platinum and rare earth metals (Ce, Yb) on the carbon-based Toray Carbon Fiber Paper TGP-H-060 T catalyst support in effort to produce electrocatalysts for direct methanol and ethanol oxidation fuel cells (DMFC, DEFC) with polymer electrolyte membrane. The layer formation in the IBAD mode, by means of the metal deposition and the mixing of a precipitating layer with the substrate by accelerated (U = 10 kV) ions of the same metal, was carried out. In this process, a neutral fraction of metal vapor and ionized plasma of vacuum pulsed electric arc was used. The study of morphology and composition of the layers was performed by scanning electron microscopy and electron probe microanalysis, X-ray fluorescence analysis and Rutherford backscattering spectrometry. Properties of the prepared electrocatalysts were investigated by cyclic voltammetry. It was established that the prepared electrocatalysts show their activity in the processes of electrochemical methanol and ethanol oxidation.

The author has come to a conclusion that the agrarian policy in the USSR and the BSSR was directed to a steep growth of agricultural industry, satisfaction of the consumer’s food product requirements in 1953–1964 years. The modernization project of September 1953 was prepared for an extensive way of development of agricultural industry. A failed competition between the USSR and the USA in production of livestock production per capita in 1957–1961 years relied on this idea. During the period after the adoption of the third CPSU program, the Soviet agrarian policy has been focused on a powerful rise of agriculture, a solution of an agrarian question, a full satisfaction of the peasantry’s needs. This required the state economic priority status for agriculture which was not done. At the same time, the activities and efforts of the Central Committee of the Communist Party of Byelorussia (CC CPB), the BSSR Council of Ministers, and the Belarusian agricultural science allowed the BSSR agricultural industry to carry out the plan targets of the Seven-Year Plan, which facilitated its further development. The author of the article notes that the reorganization of a control system of the Soviet planned economy, which has been carried out in the USSR in 1962–1964 years, has been aimed at strengthening the efficiency and responsibility of the power for the decision of the tasks determined by the third CPSU program.

Algorithms for estimation of the breeding (genetic) value of roadster breeds of horses by variable traits of own performance (development, expert assessment of selected traits) and the progeny quality are developed. The scientific significance of the research results presented in this article lies in the development of the breeding (genetic) value assessment system that does not exist in the country, for the bred roadster horses based on phenotypic and genotypic characteristics. The practical significance of the developed system is to improve the reliability and the earlier assessment of horses by 2–3 years.

The article describes the features and theoretical fundamentals of the mechanical method for potato peeling as most frequently used for manufacturing potato products, its advantages and disadvantages are considered, rational technological parameters of mechanical peeling are determined. The relationship between the amount of waste formed in the process of mechanical potato peeling and tuber sizes is established. Based on the results of the influence of parameters of tubers, the trajectory and speed of their movement in drum and roll peeling machines and action upon tuber forces, the dependence of the amount of waste is found. The amount of waste forming during the peeling of different-size potato tubers in the drum peeling machine МOК-350 is analyzed, and the recommendations to improve the peeling effectiveness are developed.

There are the research results, whose purpose is to justify the regime parameters of the vacuum operating circuit of milking units with high pressure stability, providing stress-free lactation. The “stress-free milking mode” is one of the necessary conditions for the physiologically sparing process of cow machine milking, allowing one to increase the productive longevity of animals and their milk productivity and to reduce unit costs in the milk production. As a result of research, a working vacuum circuit with an increased pressure stability of pressure has been developed, which is characterized by a new functional and spatial structure. Justified is the effective pressure range in the vacuum operating circuit, as well as pressure stability parameters, including a pressure gradient along the pipeline length, a temporary instability, an amplitude of pressure pulsations, and relaxation coefficient of these pulsations.