For nonlinear operator equations with non-differentiable operators allowing the separation of a regular smooth component the stability conditions for the generalized Newton Kantorovich method are established. In essence, these conditions mean that successive approximations in the method do not accumulate systematic errors.

Sufficient conditions for existence of the unique solution in class C² for the domains of definition for the first mixed problem for homogeneous and non-homogeneous Klein–Gordon–Fock equation in the curvilinear half-strip are deduced using the characteristics method.Solution of the problem is reduced to solution of Voltaire’s second-type equivalent equation.

A spatial-frequency covariance method of search for low-sized targets on video frames is proposed. It is based on Haar undecimated lifting wavelet transform. The method allows one to reduce computation time and to increase the probability of correct detection of target by using Haar undecimated lifting wavelet transform for calculation of a covariance descriptor.

An ion excitation characteristic X-ray spectrometer was created on the basis of an ion electrostatic accelerator AN-2500. The energy resolution of the spectrometer measured on the 5.9 keV line of the ⁵⁵Fe spectrometric source is about of 151 eV. The characteristic X-ray spectra of the bony tissue section, which were affected to coxarthrosis, were measured. It is shown that the intensity of P and Ca spectral lines in the sick tissue is reduced by 20 and 30 %, respectively. Meanwhile, the amount of chlorine increases almost five times, which indicates the accumulation of salts in the sick tissue.

The results of simulation and experimental study of the one-dimensional electromagnetic band gap structure formed solely by plasma columns in the waveguide of X frequency band (3 cm wavelength range) are presented. The simulations show that the plasma structure is formed at a value of the electron density more than 10¹⁴ cm^–3 and of the plasma column diameter of 3–4 mm. Computations are in good agreement with experimental data. The possibility of variation of the microwave pulse duration from 10 microseconds to tens of nanoseconds is demonstrated. The plasma electromagnetic band gap structure was tested at high microwave power (~50 kW).

Ln_1–ySr_yMn_1–xСo_xO₃ compositions have been studied using neutron diffraction and magnetization measurements. The valence of cobalt ions increases from two to three as the cobalt content is growing. Trivalent cobalt is dominant in the low spin state; however there is a small fraction of cobalt in the high spin state. Exchange interactions between Co³⁺ (high spin state) and Mn⁴⁺ ions are ferromagnetic and are similar in magnitude to positive exchange interactions between Co²⁺ and Mn⁴⁺ ions.

In the drift-diffusion approximation, we considered the migration of both single electrons and pairs of electrons (bipolarons) due to their hops via immobile point defects of one kind in three charge states (–1, 0, +1) when an external electric field is applied to a semiconductor. We found the analytical expressions for the screening length of the stationary electric field and for the diffusion length of electrons hopping via such defects of the crystalline lattice.

General conditions for vanishing the third projection of the current J^z for the Dirac field on two boundaries of the domain between two parallel planes are formulated in a covariant form which is valid for any basis of Dirac matrices. Produced relations contain four arbitrary phase parameters. Solutions of the Dirac equation with such properties of their current are of special interest in connection with investigation of the Casimir effect for Dirac field in the domain restricted by two planes.

The symmetric double-well potential is constructed by means of a smooth combination of three parabolic potentials. The exact analytical solution of the Schrödinger equation is obtained. The comparison is made with the results of application of the modified WKB-approximation.

Theory of nonradiative transitions based on the model of the orientation broadening of electronic levels has been used to interpret the known data for the medium polarity effect on the lifetime of the S₁(Ag⁻) state of peridinin. The findings allow assuming that the molecules of pigment heavily interact with the internal electric field produced by environment. In consequence of this, peridinin at the excited S₁(Ag⁻) state exists in the form of different conformers I and II with permanent dipole moments of 40.7 and 42.8 D, respectively. Their structure is distinguished by turning the epoxycyclohexane ring relative to the polyene chain through about 180°. Conformer I is dominant in nonpolar and low polar media and is at the intramolecular charge transfer state S₁(Ag⁻/ICT), − whereas conformer II exists in polar media and, as suggested, belongs to the charge separated state S₁(Ag⁻/ICT).

The potentiometric response characteristics of film selective electrodes based on trianoniloctadecylammonium tetrachlorocadmium and tetraiodоcadmium in a wide concentration range of ligand ions (from 1 · 10^–2 to 3 M) have been investigated. The influence of the plasticizer nature on functioning cadmium halide electrodes has been studied. It has been established that the membranes of electrodes plasticized of α-brome naphthalene have the most suitable response characteristics.

The structure and properties of the dispersions of multi-walled carbon nanotubes in N,N dimethylacetamide with different polymer dispersive agents: polyvinylpyrrolidone, poly(ethylene glycol), triblock copolymers poly(ethylene glycol)–poly(propylene glycol)–poly(ethylene glycol), ethylenediamine tetrakis(ethoxylate–block–propoxylate) tetrol of different molecular weights were studied. Polyvinylpyrrolidone was found to have the best dispersive capacity. It was shown that the dispersion degree and the particle size of the multi-walled carbon nanotubes in N,N–dimethylacetamide depend on the chemical nature and molecular weight of the dispersive agent and the thermodynamic solvent quality in relation to the dispersive agent.

Effective methods for preparation of tetrazole-containing biscaroxylate complexes of platinum (II) were developed and novel oxalate, malonate and succinate platinum (II) complexes with 1-R- and 2-R-5-aminotetrazoles (R = 1-CH₃, 2-CH₃, 1-C₆H₅, 2-t-C₄H₉), analogues of third-generation antitumor platinum drugs were prepared. Studies of the obtained complexes showed their stability in solution, which is sufficient for biological studies. Cell proliferation tests and bioanalytical studies showed that increasing the hydrophobicity of substituents at the tetrazole heteroring leads to an increase in the intracellular concentration of complexes followed by a growth of their cytotoxic activity. Two platinum oxalate complexes with 5-amino-1-phenyl- and 5-amino-2-tert-butyltetrazoles having cis-configuration were chosen as leader compounds featuring the best combination of the antiproliferative activity, lipophilicity, and solubility.

Approaches to a synthesis of new conjugates of betulonic and betulinic acids with 6,7-dihydro-1H-indazol-4(5H)-one derivatives had been developed and realized. Conjugate of betulonic acid was obtained via the acylation of 1-aryl-3-perfluoroalkyl-6,7-dihydro-1H indazol-4(5H)-one oxime with betulonic chloride. The synthesis of conjugate of betulinic acid was accomplished via the acylation of 7-amino-1-aryl-3-perfluoroalkyl-6,7-dihydro-1H indazol-4(5H)-one with 3-O-(2-chloro-2-oxoacetyl)betulinic chloride.

Belarusian Tatars are an ethnic group with an interesting population history: being descendants of the Golden Horde inhabitants, Belarusian Tatars have been living in the territory of present-day Belarus, Lithuania and Poland for 6 centuries. To figure out their phylogenetic relationships with other peoples, as well as the intensity of gene flow with the host population we have studied the mitochondrial DNA gene pool of Belarusian Tatars. Our data suggest an admixed nature of their matrilineal gene pool with some lineages being phylogenetically close to lineages from Siberia and Central Asia, while others having a Western-Eurasian origin. There is also evidence of women-driven gene flow from the Belarusians to the Belarusian Tatars.

The classification of the indices of local elastic properties of arteries depending on the estimate of the vascular wall (dispensability or elasticity) and also depending on the extent of the arterial pressure influence on them is suggested.

The local energy heterogeneity of the flat surfaces of alumina and titanium oxide is studied using the density functional theory. The periodic total energy calculations have shown that the positions of the adsorption sites corresponding to potential energy minima of the oxide surface interaction with a trial particle (hydrogen atom) depend on its distance to the surface. The active sites of (0001) Al₂O₃ and (001) TiO₂ surfaces at distances of more than 2 Å are characterized by one global minimum of potential energy that localizes upon the surface metal atom. At distances of the order of 1–2 Å the global minimum degenerates in several energy states and number of which is defined by the initial surface symmetry. There are three active sites with hexagonal symmetry within an elementary cell of (0001) Al₂O₃ surface and two sites with the mirror symmetry on a (001) TiO₂ surface, displaced to the metal atom relatively of electronic density maxima positions of oxygen surface atoms. The results obtained are explained by perturbation introduced by the electron of a trial particle into surface electronic density distribution that leads to the degeneration of the active site. New sites positions do not coincide with the space geometry of metal and oxygen atoms at oxide surface.

The effect of dielectric and isothermal heating on the properties of the sodium silicate aqueous solution and the resultant xerogels has been studied in the comparative investigations. It was proved that the viscosity of the solution undergoes changes in two stages. The type of interactions predetermines the structural energy of activation of the viscous flow and the kinetics of structure formation processes in the sodium silicate aqueous solution, phase composition and morphology of the formed xerogels.

A comparative analysis of structures self-organizing under intense complex technological and operational impacts by separating in time the order parameters with cooling surfaces of materials or unloading goods from the definition of sustainable modes of state of a thermodynamic system has been performed. The ways of structure formation intensification in the processing of metals and alloys that implements a combination of the control parameters of thermal and deformation effects have been developed.

On the basis of the interdisciplinary sociological and law approach and systematic methodology the features of the genesis and determination of juvenile delinquency are discussed. The author develops his own theoretical and practical model of prevention of juvenile delinquency in the juvenile justice system of Belarus as an effective measure to improve the national legislation and sustainable reduction in crime among young people.

The main theoretical and methodological aspects of leadership have been worked out, the attitude of people of Belarus to principal political processes and sovereign Belarusian state leaders have been analyzed on the basis of long standing sociological monitoring results.