The article is devoted to the stability properties of the essentially semi-regular operators and essentially regular operators in Banach space under compact commuting perturbations.

In this article, the main results on the behavior of various iterations for approximate solution of ill-posed equations with self-adjoint operators in a Hilbert space are presented: sufficient conditions for iteration convergence are obtained, the behavior of residuals and corrections is studied on subspaces of sourcewise representable functions, the convergence of the approximations in the Hilbert space norm weaker than the original one is established.

It is proved that the dual of Hardy space H¹(G) over compact and connected Abelian groups G with totally dual is topologically isomorphic to the space ВМОА(G) of functions of bounded mean oscillation of analytic type on G.

The Riemann boundary-value problem (linear conjugation problem) is studied in the case when the coefficient of the problem admits a finite number of zeros and/or polar singularities on the contour. The solvability conditions and the explicit formula of the solution are obtained. All studies are performed in the weighted Hölder classes with complex weight.

The radiation resistance of the nanostructured TiN, TiAlN, TiAlYN coatings irradiated with He⁺ ions with an energy of 500 keV over the range of fluences from 5 · 10¹⁶ ions/sm² up to 3 · 10¹⁷ ions/см² was studied. Changes of phase composition, structure, lattice parameters, morphology, and mechanical properties of coatings under helium ion irradiation were investigated. Any blistering was not detected and a nonlinear influence of irradiation fluence on the properties of thin film coatings was revealed. It is found that the nanostructured TiN, TiAlN, TiAlYN coatings are radiation- resistant and are not susceptible to the degradation under high-fluence ion irradiation.

In the present article, the momentum transfer from the field of a plane electromagnetic wave to the plate, which is normal incident on the parallel dielectric plate, and the total force caused by this momentum transfer are calculated.

Within the framework of perturbation theory the energy levels and wave functions are found for an electron in twodimensional semiconductor circular quantum dots in the presence of the Rashba and Dresselhaus spin-orbit interactions with realistic axially symmetric confining square potential of finite depth.

It is shown that arbitrary nonlinear Lorentz-covariant generalizations of Maxwell electrodynamics are dual invariant if, along with the fields, the model parameters are transformed, which in QED are proportional to the electron charge. The transformation properties of the Born–Infeld Lagrangians with respect to two types of dual transformations are found explicitly.

Reactions of nucleophilic substitution of nitro group in N-alkyl-3-nitro-1,2,4-triazoles have been studied both experimentally and theoretically using DFT method. The standard enthalphy and Gibbs free energy of alkoxylation reactions of N-alkyl-3-nitro-1,2,4-triazoles in gas phase and aqueous solution have been calculated. The calculation results show that nucleophilic substitution reactions of N-alkyl-3-nitro-1,2,4-triazoles with alcohols and alcoholate anions are thermodynamically possible both in gas phase and in aqueous solution. Computed activation energies for reactions of N-alkyl-3-nitro-1,2,4-triazoles with methanol decrease in the series of ΔG^≠_S(for 1-isomer) >> ΔG^≠_S(for 4-isomer) > ΔG^≠_S(for 2-isomer). The calculation results are in good agreement with experimental data.

The in vitro study of the antiviral activity of the dextrin-24-epibrassinolide complex in chicken embryos was carried out. The complex was shown to have an inhibitory effect against the infectious laryngotracheitis virus.

Nitrile oxide approach to the synthesis of tetrahydrobenzisoxazole and tetrahydroindazole derivatives with additional isoxazole (isoxazoline) pharmacophoric moiety is developed. Bis heterocyclic derivatives obtained and related compounds are of interest as new compounds possessing potent anticancer, anti-inflammatory, analgesic and antimicrobial activity.

Solubilizing capacity of aqueous micellar solutions of fluorinated and hydrocarbon surfactants in relation to nonpolar fluorocarbon and hydrocarbon substances has been investigated. It has been shown that fluoroorganic nonpolar liquid are solubilized in solutions of fluotinated and hydrocarbon surfactants. Absolute incompatibility of hydrocarbon solubilizate and ionic ftortenside has been found. Detected features of systems containing fluorocarbon component are explained according to affinity of fluorocarbons and hydrocarbons molecules to water molecules.

In work it is shown that microparticles of water dispersions of copolymers (synthetic latex) which was entered in small quantities, they have the strong stabilizing effect on emulsions of the epoxy oligomer. Factors of stability of such mixed disperse systems was detected by methods of the dzetaforometriya, the rheology and the optical microscopy.

The essential oils of Thuja species introduced in Central botanical gfrden of NAS of Belarus have been analysed by GC-technique. A β-cyclodextrin capillary column has been used for the separation of enantiomers. The dominant monoterpene enantiomers of essential oils of Thuja are R-(+)-forms of α-pinene, camphene, limonene. Sabinene and β-pinene are presented only in R-(+)-isomers.

The fiber flax Ariane and linseed Endress Olajlen were used as a subject of investigation in the present work. These flax cultivars form various types of fiber with contrast quality properties. Cellulose synthase genes, which are expressed in different breeds of flax, were identified by the RFLP-analysis. The expression of LusCesA4, LusCesA7, as well as LusCesA9 and/ or LusCesA1 genes was determined in the stems of the both breeds. The functioning of additional genes (probably, CesA6, CesA8, CslD) was found in the stems of fiber flax, but they were not expressed in the stems of linseed.

Two hundred and ten lichen specimens of Cetrelia collected in Belarus during 1954–2012 were examined based on morphological and chemical characters. Three species of Cetrelia (C. cetrarioides, C. monachorum, and C. olivetorum) have been identified in this study. The occurrence of detected species in Belarus is reviewed and distribution maps are provided.

Morphological, biochemical indices of the 20–22 weeks-old WKY and SHR rats were studied to get the model of heart hypertrophy in genetically determinate arterial hypertension. In the research we got the model of heart hypertrophy in genetically determinate arterial hypertension. It was found that heart mass index, oxidative phosphorylation enzymes, DNA injury increased and hematological changes were found in SHR rats as compared with WKY rats.

The aim of this study was to determine the antiischemic and antiarrhythmic effects of remote ischemic pre- and postconditioning in rats with diabetes. It was found that remote ischemic pre- and post-conditioning equally protects myocardium against irreversible ischemia-reperfusion injury. Remote ischemic pre-conditioning protected myocardium against arrhythmias in rats with diabetes.

The mathematical model of the fast pyrolysis of wood particles is presented. The implicit finite difference algorithm for solving the obtained heat and mass transfer equations is constructed. Based on the computational experiments it was found that the fast pyrolysis of pine sawdust entering a heated reactor is possible when the size of their particles does not exceed 0.45 mm, humidity – 10–15 wt. % and at a pyrolysis temperature of above 490 °C.

Results of experimental verification of a new concept of the development of thermal and mechanical processes in viscous compressible flow medium are presented.

The translations of the novel "Minsk direction" by the classic author of the Belarusian literature Ivan Melezh into the Russian language are comprehended theoretically and analyzed. The analysis is made by comparing the texts of translations made by L. Shapiro and L. Rakovsky together with the authors’ editorial boards of the novel organized by I. Melezh during twenty five years.

The comparative analysis of meat productivity of young purebred and crossbred rabbits at fattening of different origin bred in the Republic of Belarus was carried out. The best breeds and their combinations by slaughter traits, morphological carcass content and chemical composition of meat were determined.