For polynomials possessing multiple roots we deduce explicit formulas for higher derivatives of resultants R(f, f ^(k)) (f ^(k) is a derivative of order k). On this basis a number of results linking higher derivatives of resultants and multiple roots of polynomials that differ in ideas from the well-known ones are obtained.

The study aims to analyze the application of the random forest algorithm in addressing the loan classification issue. Furthermore, it intends to perform a comparative analysis by juxtaposing the outcomes with those derived from logistic regression, feedforward neural network, and deep feedforward neural network models. The research determined the ideal maximum number of input indicators and the ideal number of trees in the ensemble when utilizing the random forest algorithm. Additionally, it explored the impact of alternative data partitioning into training and test sets on the accuracy of model forecasting with the random forest algorithm. In conclusion, a strategy for addressing the loan classification issue using the classifiers studied has been proposed.

The change in the diffuse reflectance spectra of nanostructured TiAlN/Cu coatings after thermal cycling under conditions equivalent to 16 hours in near-earth space orbit has been studied. Thin-film TiAlN coatings with the addition of 7–8 % copper and with various Ti / Al ratios in the metallic component as well as between the metallic and non-metallic components of the solid solution were formed by reactive magnetron sputtering. It has been shown that the reflection in the spectral range of 500–2500 nm for samples with a higher titanium concentration is noticeably higher and increases after thermal loading, while for a sample with a lower titanium content, the reflection does not change. The solar absorption coefficient α_s and the thermal emittance ε, as well as the α_s / ε ratio, were calculated from the reflectance spectra. For samples with a predominant metallic component ((Ti + Al) / (N + C) = 1.3) and the Ti / Al ratio of 0.95, this ratio did not change after thermal cycling and amounted to 1.44. For samples with an increased titanium content (Ti / Al = 2.34) and an equimolar ratio of metallic and non-metallic components, the α_s / ε value before thermal cycling was 3.82 and decreased to 3.65 after thermal loading. The band gap width and its change after thermal cycling were also calculated for both types of coatings. The physical processes occurring in TiAlN/Cu composites during thermal cycling are discussed based on optical spectroscopy data.

The article describes the development of a robust pharmacophore model and pharmacophore screening of poten tial inhibitors of the 17,20-lyase activity of the human CYP17A1 enzyme – an important target in the treatment of prostate cancer. To choose the compounds with the best pharmacokinetics parameters ADMET analysis was performed. According to the calculated data of flexible molecular docking, there were found five compounds with low free energies of binding to the catalytic center of the enzyme, which are comparable to the experimental value of the CYP17A1 inhibitor abiraterone used in clinical practice for treatment castration-resistant prostate cancer. It was established that the connection of the identified compounds with the enzyme is due to van der Waals, lipophilic, electrostatic and intermolecular hydrogen bonds with amino acid residues of the active center and π-stacking with the heme group of the enzyme. The results obtained will be used to develop new drugs with minor side effects for the treatment of prostate cancer due to inhibition of the 17,20-lyase activity of CYP17A1.

For the first time in the Republic of Belarus, a large-scale bioinformatic analysis of the genomes of Sus scrofa domesticus species, as well as our own molecular genetic studies, was conducted in order to differentiate Duroc, Landrace, Yorkshire, Belarusian Large White, and Belarusian Meat pig breeds. As a result, a list of polymorphic variants with high differentiating potential was formed. The most informative SNPs for differentiating pig breeds are rs332196135, rs81322965, rs322056535, rs80967182, rs81333725, rs80789418, rs319844693, rs80859281, rs80855833. Based on the statistical analysis of genotypes obtained in silico and using competitive allele-specific PCR technology, high values of accuracy and specificity of the proposed models were determined. Methodological recommendations have been developed for the rapid and accurate differentiation of pig breeds.

The results of a comparative study of the composition of the P-vitamin complex of tall blueberry fruits are presented depending on the treatments of the experimental crop with biological growth regulators Oxidate torpha with trace elements and Rostmoment (each in a concentration of 0.4 %), as well as various concentrations (1, 2 and 5 %) of a new bacterial preparation of fungicidal action Ecoberit. Oxidate torpha had the most pronounced stimulating effect on the biosynthesis of anthocyanins, catechins and the total yield of bioflavonoids. Ecoberit at a concentration of 5 % mainly stimulated the formation of catechins, at a concentration of 2 % – flavonols, and at a concentration of 1 % it inhibited the synthesis of leukoanthocyanins, anthocyanins proper, but at the same time had a stimulating effect on the formation of catechins and flavonols. The use of Rostmoment reduced the synthesis of leukoanthocyanins, anthocyanin pigments and catechins, which generally led to fruit depletion with bioflavonoids. The maximum efficiency of enriching blueberry berry products with P-vitamins is achieved by treating plants with Oxidate torpha in concentration 0,4 % and Ecoberit in concentrations of 2 and 5 %.

Using physiological, biochemical and pharmacological methods in experiments on rats and rabbits, it was shown that the direction and nature of body temperature changes, taking into account the action of bacterial lipopolysaccharide – endotoxin E. coli, depend on the severity of endotoxinemia, the state of the liver detoxification function. It was revealed that when bacterial endotoxin is introduced into the body in trace concentrations, body temperature and the activity of detoxification processes increase, and in the case of severe endotoxinemia, they decrease. It has been established that the ambiguous direction and nature of changes in body temperature in the conditions of endotoxinemia development depend on its severity, the state of the liver’s detoxification function and the thyroid status of the body.

A technique for the forming of thin-film nanostructured coatings based on poly(vinyl carbazole) (PVCz) with silicon dioxide and zinc oxide nanoparticles using the Langmuir−Blodgett (LB) method has been developed. Based on the analysis of the PVCz monolayer compression isotherm and atomic force microscopy data on the structural and morphological characteristics of LB films formed by horizontal deposition on the surface of hydrophilized silicon substrates at different values of surface pressure (π), it has been established that the densest PVCz-based coatings are formed at π = 15 mN/m. The optimal content of nanoparticles (per 1 mol of polymer) in suspensions for obtaining uniform nanostructured coatings is up to 24.44 ‧ 10³ mol (for SiO₂) and up to 4.53 ‧ 10³ mol (for ZnO). The effect of the introduction of nanoparticles on the structure, wettability and local mechanical characteristics of the formed composite coatings is described. Based on the calculated values of the compression modulus of PVCz, PVCz–SiO₂, PVCz–ZnO monolayers and a set of experimental data obtained during the work, it is shown that the compression modulus of polymer and nanocomposite LB monolayers can be used as a quantitative criterion for assessing the density of the formed coatings.

The place is determined and the method of substantiating the principle of resonance in the composition of modern scientific discourse is explicated. This principle will enter it, being included in the philosophical foundations of science, where, along with a group of philosophical categories, as a matrix of thinking, a group of philosophical principles and norms of scientific knowledge is distinguished, expressing the fundamental prerequisites and general orientation of cognitive processes (principles of interaction, reproducibility, reflexivity, consistency, determinism, observability, simplicity, etc.).

In this group, the principle of resonance should also be fixed, expressing the orientation of scientific knowledge towards the search for resonant processes and mechanisms of their action in the reality under study and their significance for its adequate intellectual and practical development. It is shown that the principle of resonance (like any regulatory means of cognitive activity that justifies its productivity) in turn must be substantiated. The article explicated two types of its substantiation: cognitive, as a generalization and distribution of any position (idea) in a certain area of cognitive activity (in this case, about the creative significance of resonant processes) to the entire area; practical as a successful practical activity in accordance with the requirements of the substantiated principle in the technical and technological field (construction, radio engineering, instrument making, practical medicine, development of socio-humanitarian technologies, etc.), where the principle of resonance ensures that the scientific discourse is oriented not only to the search for essentially significant resonant processes in the studied reality, but also on the creation of mechanisms for their conscious cultivation, as well as, if necessary, their neutralization. The direct operational inclusion of the resonance principle in cognitive processes is carried out in the context of a rational basis of research, which correlates with historically conditioned types of rationality.

A method for identifying and separating substandard potato tubers from a common pile based on machine vision and automatic inspection systems is proposed and described. A method based on calculating the color threshold is used for segmenting external defects of potato tubers against the background of a transport conveyor in real time. A centroid tracking algorithm is used to track moving potato tubers. A proprietary dataset consisting of images of commercial and defective potato tubers is created to train the artificial neural network. The results of experimental studies of determining internal defects of potato tubers using nuclear magnetic resonance (NMR) and computed tomography (CT) are presented.

A method of controlled impact on a hard surface is used to create hidden defects in the form of darkening of the tuber pulp. The methodology for conducting experimental studies and the operating parameters of NMR and CT are described. A comparative analysis of images obtained using NMR and CT with natural images of tubers in section was carried out, which made it possible to determine with high accuracy the coincidence of the location of defects detected by a non-invasive method with their real location in the tuber. The work demonstrated the value of NMR and CT for a detailed non-invasive method for determining hidden defects of potato tubers on automatic sorting machines.