Rational approximations on a segment [–1, 1] of singular integrals of the form , by integral operators, in a sense related to each other are studied. The first of them is Fourier–Chebyshev’s rational integral operator associated with the system of Chebyshev–Markov’s rational functions. It is a natural generalization of partial sums of Fourier–Chebyshev’s polynomial series. The second operator is the image of the first one when transformed by a singular integral under study. An integral representation of approximations is established for each of the operators. Approximations on the segment [–1, 1] of a singular integral with a density having a power-law singularity are studied. For each of the operators, we consider the case of an arbitrary fixed number of geometrically different poles and the case when the poles represent some modifications of the “Newman” parameters. It is established that the classes of the studied singular integrals reflect the rational approximation features by the considered integral operators in the sense that with a special choice of parameters of approximating functions, the orders of their approximations turn out to be higher than the corresponding polynomial analogues. 

An algorithm for tracking an object observed on video frames is presented. The specific feature of the constructed algorithm is the automatic detection and capture of an object of one of predetermined types, its further reliable tracking, the rapid re-capture of the tracked object in the case of a failure of tracking, the capture of another object of desired type if the tracked object disappears. An object of interest on video frames is detected using a neural network detector, whereas tracking is performed by the developed algorithm.

The effect of pulsed laser annealing (PLA) on the structure and optical properties of Mn-, Seand (Mn+Se)implanted silicon layers was studied. 95 keV Mn+ and 200 keV Se+ ions were implanted separately and together into p-type Si wafers up to the fluence 1 · 1016 cm–2 at room temperature. Then, the samples were irradiated in the ambient air with a single 2 J/cm2 ruby laser pulse. The detailed redistribution of Mn and Se atoms in the implanted layers during PLA was examined using Rutherford backscattering spectroscopy in random and channeling configuration. It was found that a notable percentage of implanted manganese atoms diffuses to the silicon surface, while the Se concentration depth profile broadens in both directions after PLA. Mn co-implantation enhances the Se diffusion to the surface, which leads to a Se decrease in crystalline silicon, but it does improve the crystal structure of the implanted silicon layer due to the increase of diffusion velocity. In contrast to the Mn-implanted sample, Se-implanted and (Mn+Se)-co-implanted samples after PLA exhibit strong optical absorption in the infrared range. The observed band at 0.6 eV is associated with electronic transitions from the intermediate band to the lowest energy levels of the conduction band.

Using solid-phase, hydrothermal and sol-gel synthesis methods, adsorbents based on double oxides Li₂TiO₃ and Li₄Ti₅O₁₂ were obtained. The influence of the synthesis conditions of samples on their phase composition, surface morphology, texture and adsorption properties was studied. It has been established that as a result of solid-phase synthesis reactions initiated by heating at 700 and 800 °C, single-phase oxides Li₄Ti₅O₁₂ and Li₂TiO₃ are obtained, the values of the parameter a of the crystal lattice of which are close to the reference data and are 8.289 and 5.026 Å, respectively. The samples have a macromesoporous texture and have a low specific surface area (8 and 9 m²/g) and a mesopore volume (0.01 and 0.02 cm³/g). The adsorption capacity of the obtained oxides Li₄Ti₅O₁₂ and Li₂TiO₃ reaches 7.9 and 6.3 mmol/g, respectively. The obtained oxides are of interest for further research as selective adsorbents of Li⁺ ions.

The experiment examined the effect of temperature on the parameters of reproduction and growth in female marbled crayfish. At temperatures close to 20 °C, females began to reproduce at 10–11 months with a body weight of 0.84–1.20 g, but up to 80 % of their egg clutches were nonviable. The duration of egg embryogenesis with an increase in temperature from 16–17 to 26–27 °C decreased from 66–69 days to 21–24 days with a lower temperature development threshold equal to 13.1 °C. A similar molting value that determined the growth rate of individuals in juveniles weighing up to 0.34 g was 13–14 °C, but in sexually mature females it decreased to 5 °C. In water bodies of the temperate zone with a short growing season, females were able to reach sexual maturity only in the third summer of life and produced no more than two clutches of eggs during their life cycle. Hence, the invasive potential of marbled crayfish in the temperate zone of Europe is very limited.

For the first time, an in vivo experiment has established a positive combined (angiogenic and antinociceptive) effect of using the domestic genetically engineered construction pcDNA_VEGF165 under conditions of simulated limb muscle ischemia. A plasmid with a gene encoding the protein VEGF165 (pcDNA_VEGF165) may be the basis for creating the first gene therapy drugs in the Republic of Belarus.

The frequency of serine carbapenemases in phenotypically multi-drug resistant K. pneumoniae obtained from patients of surgery and intensive care units in Belarus was assessed. Beta-lactamase genes KPC, OXA-48, OXA-23, and OXA-24 were detected by PCR in 115 phenotypically multi-drug resistant K. pneumoniae. The most common carbapenemase gene was blaOXA-48 (70 %). The genes KPC and blaOXA-24 were identified in 43.6 and 39.1 % isolates, respectively. Single serine carbapenemase gene was detected in 23.5 % strains. On other strains, the molecular analysis determined double or triple carbapenemase gene combinations.

The article examines the manifestation features of modern endogenous geological processes in the territory of Central Belarus. A scheme of their distribution has been constructed. A comprehensive methodology has been used to study these processes. It includes the analysis of published and fund materials, multi-age geological, geomorphological, topographic maps of different scales, remote sensing data and the results of field and route observations, measurements at geodynamic testing sites, cartometric and cartographic works. It has been established that despite the location of the region in the western part of the Precambrian East European Platform, the processes of modern endogenous geodynamics develop quite diversely and with varying intensity within its boundaries. They are expressed in the activation of linear faults (faults, cosmoand topolineaments), ring structures, vertical and horizontal displacements of the earth’s crust and its shaking (seismicity).

Hydration of cementitious materials is accompanied by the formation of calcium hydrosilicates (CSH). Accordingly, the hydration process is completed in the early, middle and late periods, leading to the formation of two types of CSH phases: low density (LD) and high density (HD). Using the nanoindentation method, it was explained nanogranular nature of the CSH gel, which is due to the contact forces of the CSH gel particles for these phases.

The compatibility and interactions of polyamide 6 (PA6) and aliphatic polyketone (APK) were studied when they were mixed in a melt by extrusion. Using the relaxation spectrometry (RS) method, it was shown that the studied PA6/ APK blends had one glass transition temperature (Тg) located on the temperature scale between Тg of initial PA6 and APK. It was also found that in these mixtures, the PA6 b-relaxation peak, responsible for the local movement of small-scale structural units of the main chain and side branches, was socialized with the b-peak of APK. On this basis, conclusions were drawn about the compatibility of PA6 and APK at the segmental and small-scale level. The mutual influence of polymer components of PA6/APK blends on the dynamic shear modulus and the zG₃ criterion is shown. The DSC analysis has revealed a slowdown in the crystallization of PA6 and APK in their blends, which is probably due to the formation of extensive interfacial (transitional) layers in the PA6/APK blend, in which crystallization of polymer components is hindered due to intermolecular interactions. The analysis of the IR-spectra in the range of 3000–3800 cm–1 has made it possible to establish the formation of hydrogen bonds between the polyamide –NH-groups and carbonyls –C=O, being part of APK, which contributes to an increase in the compatibility of the polymer components of the blend under study.