Discriminants of polynomials characterize the distribution of roots of polynomials in the complex plane. In recent years, for integer polynomials, exact lower-bound estimates have been obtained for the number of polynomials of a given degree and height. The method of obtaining these estimates is based on Minkowski’s theorems in the geometry of numbers and the metric theory of Diophantine approximation. A new method is proposed and allows one to obtain upperbound estimates for the number of polynomials with bounded discriminants in Archimedean and non-Archimedean metrics. The method generalizes the ideas of H. Davenport, B. Volkman, and V. Sprindzuk that allowed them to obtain significant advances in solving Mahler’s problem.

The correlation between the multiphase state of the system and its magnetic properties was studied on Bi1–xEuxFeO₃ ceramic samples in the range 0.12 ≤ x ≤ 0.18. The X-ray diffraction results indicate that, with an increase in the concentration of Eu ions, a structural transition from the rhombohedral (R3c) to nonpolar orthorhombic (Pnma) phase is observed through the partial formation of an antipolar orthorhombic structure (Pbam). The mixed phase state in the obtained compounds is observed in the range 0.12 ≤ x ≤ 0.16. Magnetic measurements in a strong magnetic field indicate a weak ferromagnetic interaction. The magnetic response in a strong field is explained by the location of the spins at the phase boundary, as well as by the presence of intrinsic antiferromagnetic spins.

A significant increase in the elasticity of the femoropopliteal artery segments in vitro was found as a result of the action of cavitation generated by powerful low-frequency (24–26 kHz) ultrasound introduced into the vessel by a flexible waveguide. The vessel elasticity was evaluated both by the deflection under the action of an external force and by the degree of its expansion vasodilatation by the internal pressure created by the expanding balloon. The possibility of achieving a more than two-fold decrease in the vascular wall elasticity modulus after 30-s exposure to an ultrasound intensity of 31 W/cm² was shown. It has been established that at the 10 μm amplitude of ultrasonic vibrations, vascular wall damage occurs in the form of small foci of detachment and rupture of the intima accompanied by delamination in the media layer, when polymorphic slit-like cavities are formed with an increase in the amplitude of oscillations above 23 μm.

Antiviral properties of natural brassinosteroids of the campestane, ergostane, and stigmastane series (6-ketones and B-lactones) and their (22S,23S)-analogs were studied using the seasonal human respiratory alpha-coronavirus 229E (HCoV-229E) as an example. The presence of anticoronavirus properties was shown for a number of studied compounds. In general, 6-ketones were more active than B-lactones. The maximum inhibitory effect (EC₅₀ 21.1 µM) in relation to the reproduction of HCoV-229E was noted for (22S,23S)-epicastasterone.

The aim of this study was to determine the methylation status of the promoter regions of MARCH11, HOXA9, PTGDR, and UNCX genes in the tumor and non-tumor lung tissue in patients with non-small cell lung cancer (NSCLC). A relative level of methylation of the promoter regions of MARCH11, HOXA9, PTGDR, and UNCX genes was determined by the quantitative methylation-specific PCR in 73 patients with NSCLC. The quantitative methylation-specific reaction was performed both for tumor tissue samples and non-tumor tissue samples of the same patient. For each of the samples, a reaction was set both by the investigated genes (MARCH11, UNCX, HOXA9, and PTGDR) and by the reference beta-actin gene (β-actin). Positive levels of methylation of the HOXA9 gene were established for 83.5 % patients; the MARCH11 gene – for 80.8 % patients; the PTGDR gene – for 68.4 % patients; the UNCX gene – for 84.9 % patients. In the study group of patients with NSCLC, significant differences were found in the relative levels of methylation of the promoter regions of MARCH11, HOXA9, PTGDR, and UNCX genes in the tumor and non-tumor lung tissue. The data suggest that hypermethylation of MARCH11, HOXA9, PTGDR, and UNCX genes may play a role in NSCLC tumor progression.

The levels of double-strand DNA breaks as a severe disruption of genome integrity were studied using the neutral version of the comet assay in the sperm samples of the men of the Belarusian population with normozoospermia and pathozoospermia, including asthenozoospermia, oligozoospermia, oligoasthenozoospermia, and other combined forms of pathozoospermia. It was demonstrated that double-strand DNA breaks have a large proportion (about 44–50 % on average) of the total number of DNA damage (singleand double-strand breaks, alkaline-labile sites, etc.) analyzed with the alkaline version of the comet assay recommended by the World Health Organization. Higher levels of sperm double-strand DNA breaks were established in the pathozoospermia group and in asthenozoospermia subgroup compared to the normozoospermia group. It was also shown that the levels of double-strand breaks observed at pathozoospermia correspond to the mutagenic effect in vitro of high concentrations (10–30 μg/ml) of bleomycin sulfate that acts as a strong radiomimetic, which points to a significant disruption of the DNA integrity at pathozoospermia. In general, the data obtained demonstrate the usefulness of the sperm double-strand DNA break analysis for male infertility diagnostics.

The article presents a method for analyzing images of cultured cortical cells for a quantitative analysis of the parameters of development of biological neural networks using machine learning approaches. We have developed software modules for segmentation of images into cells, clusters, and neurites using the neural network model and the deep learning method; a training set of images of cultivated neurons and corresponding segmentation masks have been generated. The results were validated by analyzing the development of cultivated neurons in vitro based on the length count of neutrites at different growth stages of the culture. The developed methods for monitoring the processes of formation of biological neuronal networks based on the analysis of the neuronal growth under different conditions and on different substrates provide an opportunity to monitor the processes of stem cell differentiation in the neurogenic direction. The results can be used in monitoring the formation of organoids in bioengineering applications, as well as in modeling the processes of nerve tissue regeneration.

The article presents the computer simulation results for the stress-strain state of the lining sections of the shaft No. 1 of mine 3 of JSC Belaruskali that were obtained using visual and instrumental investigation of the mine lining state. The loading parameters of the shaft take into account the specific feature of the lateral pressure calculation in the considered location. This means that the shaft intersects vertically rocks different in their physical and mechanical properties. Computer simulation of loading of the most problematic vertical mine shaft sections observed by the lining examination results was performed using the Static Structural component of the ANSYS Workbench engineering software package. Distribution diagrams of longitudinal normal, shear and von Mises equivalent stresses in the vertical mine shaft lining are obtained for the design and residual values of the cast-iron tubing thickness. A comparative analysis of the mine shaft residual bearing capacity for various parameters of the lining elements was carried out. Based on the computer simulation results, the conclusions were made on the bearing capacity of the shaft No. 1 of mine 3 of JSC Belaruskali and the recommendations for a further safe operation of the mine shaft were suggested.

The article considers the process of obtaining nanostructured diamond materials due to phase transformation of thin films based on carbon non-diamond forms on the nanodiamond surface into diamond. For the synthesis of nanostructured diamond polycrystalline superhard material, various variants of the initial mixture based on nanodiamond with non-diamond carbon on the surface are proposed (surface-graphitized nanodiamond, surface-graphitized nanodiamond with addition of purified nanodiamond, detonation diamond-containing charge with a surface layer of “amorphous” carbon, including purified nanodiamond additives). The influence of the structure of a thin non-diamond layer on the parameters of graphite to diamond transition is revealed. For a carbon film with a disordered structure (the so-called “amorphous” carbon), the transition pressure to diamond will be about 10–15 GPa, which is significantly higher than the phase transformation pressure for thin graphite films in this temperature range. It is shown that the increase in the pressure of transformation of a thin layer of “amorphous” carbon is caused by its lower surface energy compared to the surface energy of graphite. It has been established that the region of transformation of a thin graphite-like film with a thickness of about 1 nm, formed on the 2–10 nm nanodiamond surface into diamond will be below the graphite-diamond equilibrium line in the temperature range of 1000– 2500 °C. Additional introduction of purified nanodiamond particles leads to a decrease in the pressure of transformation of thin layers of non-diamond carbon into a diamond structure from 10–15 to 2–7 GPa, which is due to the effect of the surface of catalytically active diamond nanoparticles on the thermodynamic stimulus of phase transformation.

The working hypothesis is confirmed that the required fracture toughness of structural concrete can be provided by multi-level reinforcement: at the level of the crystalline joint of cement stone – carbon nanotubes, and at the level of fine-grained concrete – various macro-sized fiber fibers (steel, polymer). Reinforcement of a crystalline splice with carbon nanotubes leads to an increase in tensile strength by 20 %, an increase in Young’s modulus. With dispersed reinforcement of concrete modified with nanoparticles at the level of fine-grained concrete, the tensile strength increases by 109 %, the critical stress intensity coefficient (crack resistance index) increases by 280 % at normal separation, and by 48 % at transverse shear.

Nowadays, due to the current economic situation in the Republic, the sheep breeding of Belarus is developing intensively, since there is a need for mutton in the global market. In some regions, work is already underway to create a promising herd of sheep with high meat productivity. An obligatory element of breeding activities is the evaluation of stud rams for the quality of the progeny, the accuracy of which determines the effectiveness of the selection process. The article contains the results on the development of zootechnical rules for evaluation of selection traits of the Romanov breed sheep that was conducted at the RUE “Vitebsk breeding enterprise”. The object of research was purebred Romanov breed animals that had been used in pedigree breeding since 2017. As a result of research, parameters for sheep ranking by a set of selection traits, algorithms for determining individual and complex estimated breeding values of rams, ewes, and young animals were developed. This will allow the most rational zootechnical measures and evaluation of fur coat and meat type breeding sheep.