For sufficiently large Q there exist the intervals I ⊂ [0,1) of length c₁(n)Q⁻¹ that do not contain algebraic numbers of any degree n and of height H(P) ≤ Q. In this article we have found an condition for intervals I in terms of the Diophatine approximations when the intervals of length c₂(n)Q^−γ, γ >1, contain not less than c₃(n)Q^n−2γ+1 algebraic numbers α of height H(α) ≤ Q and degree deg α = n > 2γ -1.

A special case of the singular integral equation with the Cauchy kernel in the case of the complex order of zeros is studied. The solvability conditions and the explicit formula of the solution are obtained. All studies are performed within the weighted Hölder classes with complex weight.

In this article we research the classical solutions of the boudary problems for the third-order unstrict hyperbolic equation. The equation is defined in the half-strip of two independent variables. There are Cauchy’s conditions on the bottom of the area and Dirichlet’s conditions on the side boundary. Using the method of characteristics, the analytic solutions of the considered problem are written out. The uniqueness of the solutions is proved.

For unipotent elements of prime order, the Jordan block structure of their images in the infinitesimally irreducible representations of the classical algebraic groups in odd characteristic, whose dimensions are at most 100, is determined. The approach proposed can be applied for solving a similar problem for representations of larger dimensions. Detailed information on small cases is important for stating reasonable conjectures on the behavior of unipotent elements in irreducible representations of the classical algebraic groups.

The necessary and sufficient conditions for linear time-varying observation systems with scalar output to be transformed to the Schwarz form under the action of a linear continuously differentiable group are obtained.

The control problem for a linear singularly perturbed system with minimum energy is under consideration. The final state of the system and the transition time are assumed to be given. Asymptotic approximations to the optimal open-loop and optimal feedback controls for this problem are constructed. The main advantage of the proposed algorithms is that the original optimal control problem is split into two unperturbed problem of smaller dimension.

The aim of the given paper is to obtain a scheme of computation of reduced Whitehead groups of special unitary groups of anisotropic hermitian forms, related to henselian division algebras with global residue algebras.

We have measured the spectral-luminescent characteristics of tetraphenyltetraazaporphin and a substituted tetraphenyltetraazachlorin, a new potential absorber and emitter for the near IR region, in solutions at 293 and 77 K as well as the quantum yields of fluorescence and singlet oxygen generation. It has been shown that the changes in the excited electronic states energy in passing from tetraphenyl substituted to octaphenyl substituted compounds are not minor. Based on performed quantum-chemical calculation, an explanation of this property is given. It has been found that, for tetraazaporphin, the tetraphenyl substitution results in decreasing the quantum yields of fluorescence and singlet oxygen generation whereas, for tetraazachlorin, on the contrary, tetraphenyl substitution results in the rise of their values.

A mathematical model for the nonlinear absolute decay parametric instability of inhomogeneous plasma is developed. Decay of the Langmuir pump wave on the Langmuir and ion-acoustic waves is considered in detail. The numerical solutions describing the eigen modes of the instability are obtained. It is shown that at the nonlinear stage of the instability, a depletion of a pump wave and a broadening of an ion-acoustic wave spectrum are observed. The simulation results are in agreement with the experimental ones.

A new original method has been proposed for effective use of multi- core systems to simulate liquid properties by the transition matrix Monte Carlo technique. The calculation real time has been reduced substantially. The technique proposed has extended a simulation range of “liquid–vapor” equilibrium to low temperatures, at which simulations by a standard approach are impossible.

It is shown that nanostructured TiO₂ : MoO₃ films are capable to accumulate the charges induced under UV irradiation due to the generation of reduced forms of molybdenum oxide (hydrogen bronzes). Oxidation of these reduced forms in the air condition is accompanied by the generation of reactive oxygen species, due to which TiO₂ : MoO₃ films retain the oxidation ability and the pathophysiological activity for a long time after irradiation completion.

Thermal protective compositions based on polyetherimide and inorganic fillers are proposed, and their thermal characteristics are investigated. The most effective inorganic filler in thermal protective composition was established to be silicon carbide at a content of 45–50 wt. %.

A polyvinyl alcohol (PVA) coating decreases the non-specific binding of magnetic microspheres (MMS) composed of glutaraldehyde-cross-linked chitosan to blood mononuclear cells (BMC) more efficiently than a carboxymethyldextran (carboxylation degree <10 %) coating. PVA-composed MMS coated with an additional PVA layer after glutaraldehyde cross-linking, including ones functionalized with carboxyl groups due to the H2O2 treatment, demonstrate low non-specific binding to BMC. In the pellets resulting from magnetic separation, there were 4670 ± 760 PVA MMS and 2040 ± 400 MagnosphereTM MS300/Carboxyl commercial MMS per one BMC.

In this paper, the effect of brassinosteroids – 24-epibrassinolide and 28-homocastasterone, as well as their stereoisomers – (22S,23S)-24-homobrassinolide and (22S,23S)-28-homocastasterone on the level of reactive oxygen species in cancer cell line A549 (lung adenocarcinoma) has been characterized for the first time, and the results obtained have been compared with the data on their antiproliferative activity.
The effect depended on the structure of the side chain and was more pronounced in the case of the SS-orientation of hydroxyl groups at the C22 and C23 positions ((22S,23S)-28-homocastasterone). This compound also had greater antiproliferative activity, which suggested a possible relationship between the induction of activated oxygen species and cytotoxicity of the substances.
The results of this work allow one to assume that one of the ways of the effect of brassinosteroids on cancer cells may lie in the initiation of oxidative stress, which leads to the death of cancer cells through ROS-dependent mechanisms.

This is the first extensive study of the X-chromosome polymorphism of ethnic Belarusians in a set of 360 male and 423 female samples (783 samples, 1206 chromosomes in total) from 11 regions of Belarus. The study involved 19 STR-loci: DXS10135, DXS8378, DXS10148, DXS7132, DXS10074, DXS10079, DXS10075, HPRTB, DXS10101, DXS10103, DXS10134, DXS7423, DXS10146, DXS8377, DXS10147, DXS9895, DXS7424, DXS7133, and GATA172D05. The frequencies of the alleles have been determined, and the tables of allele frequencies for the pooled Belarusian population sample have been composed.

Validation of 8 allele-specific markers associated with potato tuber quality traits (starch content and chip quality) was performed in tetraploid breeding populations of the Belarusian selection. The possibility of the DNA-based marker application for selection of genotypes with better tuber quality traits is shown.

In the paper new results of investigation of formaldehyde in the air at the sources of release and in the ambient air at the impact zones of wood-processing facilities of Belarus producing laminated wood materials and formaldehyde resins are given. It is shown that highest average concentrations of formaldehyde at sources of release are typical for particleboard and resins production at out of date equipment. It is revealed that levels of formaldehyde content in atmospheric air near particleboard and resins production facilities are higher compared to plywood, fiberboard and MDF production. Stable relation of formaldehyde content in atmospheric air with release rate was established. Relation of content of formaldehyde in atmospheric air with the distance from the source of release and dispersion conditions was estimated.

The article deals with the study of the influence of the location depth of development and main workings on the behavior and deformation intensity of their edge in the conditions of the second and third horizons of the Starobin deposit of potash salts. It is shown that while forecasting the stability of workings, it is necessary to consider not only the location depth, but also the aggregate rock strength, the cross-section size of workings and the availability of compensation slots as the ways of protection. Formulas have been developed to calculate the time of the steady state of workings taking into account the above-mentioned factors.

The results of investigation of elemental and phase composition, structure, microhardness, and friction coefficient of the Ti-6Al-4V alloy surface layer treated by compression plasma flows are presented. The findings showed that the plasma impact resulted in forming a modified layer with the thickness of up to 24 μm containing δ-TiN_x, α′-Ti(N), α-Ti and β-Ti phases. The treatment of the Ti-6Al-4V alloy by compression plasma flows led to a more uniform alloying element distribution in the modified layer and to a decrease of the aluminium concentration. The plasma surface modification allows the surface layer microhardness to be increased by a factor of 1.5 and the friction coefficient to be decreased by a factor of 2 in comparison with the initial sample.

The effect of diisocyanate chain extender (CE) on the rheological, and relaxation properties, as well as on the molecular weight and crystallizability, of poly(butylene terephthalate) (PBT) and thermoplastic polyester elastomer (TPEE) blends with the different-phase structure has been studied. It has been showed that CE in the amount of 0.2 up to 1.25 % leads to an increase in polyesters melt and solutions viscosity because of chain extending and cross-linking reactions. Values of high and low flow limits increase with increasing the CE concentration regardless of the phase structure of blends. It is revealed that СЕ decreases the polyesters melt-crystallization temperature; the crystallinity reduces simultaneously, which is indicative of the crystallization deceleration owing to a growth of the molecular weight.

On the basis of the concepts of Western scientists Anton Popovich, Katarina Rice, Hans Fermeer, Edmund Husserl, Roman Ingarden et al., hard-to solve problems of literary translation from related languages are comprehended theoretically. The translation is a result of an original work of a translator who reproduces the original in the language of another nationality and for different social and cultural environment and is an indication of certain translation outlook and aesthetic position.

The researches are devoted to the study and a comprehensive analysis of use of the index selection in pig breeding, allowing significantly (1.3–1.5 times) the increase in the selection efficiency to be increased significantly (1.3–1.5 times) when improving reproductive, fattening, and meat traits.