The problem of constructing a transition process with minimal energy costs for a linear singularly perturbed system containing three groups of variables with significantly different rates of change is considered. Asymptotic approximations to solving this problem are constructed in the form of an open-loop and feedback controls. The main advantage of the proposed computational procedures is that the original problem is split into three unperturbed optimal control problems of lower dimension.

According to Massera’s theorem, an ordinary differential linear nonhomogeneous periodic system has a periodic solution with a period coinciding with that of the system if and only if this system has a bounded solution. We introduce the class L of vector functions called growing slower than a linear function. This class contains the class B of bounded vector functions in as its own subclass. It has been proved that Massera’s above-mentioned theorem will remain true if in its formulation a bounded solution is replaced by a slower growing solution than a linear function. It is shown that the set B in the metric space (L, dist_c ), where dist_c is the uniform convergence metric vector functions on intervals, has Baer’s first category, i. e. almost everything in the sense of the category of space vector functions (L, dist_c ) are not bounded. This fact shows the significance of the obtained strengthening of Massera’s theorem.

De novo design and virtual screening of small-molecule compounds with a high potential inhibitory activity against the Bcr-Abl tyrosine kinase playing a key role in the pathogenesis of chronic myeloid leukemia (CML) were carried out by an integrated computational approach including technologies of deep learning and molecular modeling. As a result, according to the calculation data we identified 5 compounds exhibiting low values of binding free energy to the enzyme comparable with those predicted for imatinib, nilotinib and ponatinib, anticancer drugs widely used in the clinic to treat patients with CML. It was shown that these compounds are able to form stable complexes with the ATP-binding sites of the Bcr-Abl tyrosine kinase and its mutant form T315I, which is confirmed by the analysis of the profiles of binding affinity and intermolecular interactions responsible for their energy stabilization. Based on the obtained data, these compounds, which have been generated by the deep learning neural network, are assumed to form promising basic structures for development of new effective drugs for treatment of patients with CML.

The mechanochemical method yielding a composite photocatalyst TiO₂/V₂O₅ of tubular morphology under localized mechanic impact on a mixture of dispersed oxides has been proposed. It has been shown that under contact loading amounting to 25–39 MPa, tubular TiO₂ is growing due to bonding of hydrated oxide particles via polycondensation. In the case of a mixture of titania and vanadium oxides, the tubular structure growth is accompanied with dispersing V₂O₅ particles resulting in the release of free standing lamellae. The mechanochemical activation produces nanоheterojunctions TiO₂/V₂O₅ able to ensure an effective separation of photo-induced charges and their accumulation in redox active V₂O₅. Employing mechanochemical activation for synthesis of a TiO₂/V₂O₅ composite photocatalyst results in 2.5-fold enhancement of the oxidation activity induced by preliminary photocatalyst exposure.

The article presents some information on two new families of Ptychodictyidae fam. nov. and Nostolepidae fam. nov. that were established on the basis of the author’s personal research and the available literature data. Their main diagnostic features, generic composition, number of species, comparison, stratigraphic and geographical distribution are given. The obtained data supplement the taxonomy of the Palaeozoic acanthodian fishes.

Currently, much attention is paid to studying the vascular endothelial growth factor (VEGF) that stimulates angiogenesis, as a potential target for antiangiogenic therapy. The purpose of this work was to study the effect of polymorphic variants rs2010963 (G-634C), rs699947 (A-2578C), and rs3025039 (C+936T) of the VEGF gene, encoding a vascular endothelial growth factor, on the overall (OS) and adjusted survival (AS) of patients with non-small cell lung cancer (NSCLC) at stages I–III. The effect of VEGF rs699947 polymorphic variants on the extent of tumor spread was shown. A connection between AS and polymorphic variants rs2010963 (G-634C) and rs699947 (A-2578C) was established. The one-year adjusted survival (AS) in the -634G/C genotype carriers was 81.9 ± 3.9 %; in the -634G/G genotype carriers – 92.8 ± 2.5 %; and p = 0.016 was the significance level. Two-year AS was as follows: in the carriers of the -634G/C genotype was 70.4 ± 4.6 %; in the carriers of the -634G/G genotype – 84.3 ± 3.5 %; and p = 0.015. Three-year AS: in the carriers of the -634G/ genotype C was 63.0 ± 4.9 %; in the carriers of the -634G/G genotype – 76.7 ± 4.1 %; and p = 0.029. One-year and two-year AS in the carriers of the -2578A/A genotype was significantly higher than in the carriers of the -2578C/C genotype (p = 0.015 and p = 0.042 respectively). The identified influence of the polymorphic variants rs2010963 and rs699947 on the survival of NSCLC patients during the first three years after the established diagnosis shows a need to use knowledge about the genetic characteristics of a tumor during therapy.

Thyroid-binding proteins play an important role in regulating thyroid status. However, the question of the radiation effect on the functional state of thyroid blood transport systems remains insufficiently studied. The aim of the work was to assess the indicators of thyroid status and thyroid blood transport in persons exposed to radiation as a result of the Chernobyl accident. The task of the work was also to analyze the results of an oral test for thyroxine pharmacokinetics in patients with thyroid carcinoma who received radioiodine therapy. Screening studies conducted 5−6 years after the Chernobyl accident indicate the radiation effect on the free thyroxine content in the blood and the functional activity of thyroid protein transport in children and adolescents living in the territories of the Khoiniki district of the Gomel region. The dose-dependent effect of an absorbed dose of ¹³¹I was also detected in children and adolescents displaced from the 30 km zone of the Chernobyl accident. The results of an oral test for thyroxine pharmacokinetics demonstrate an increase in the free T4 content against the background of a stable total T4 fraction in patients with thyroid carcinoma who received high dose loads as a result of radioiodine therapy. The conducted studies confirm the possibility of the influence of a high dose of ¹³¹I on thyroid blood transport systems and on the ratio of free and bound fractions of thyroid hormones in the blood.

Based on the mesoscale hydrodynamic model WRF (Weather Research and Forecasting), the balance model of atmospheric moisture and the remote sensing data, we obtained the estimates of microclimate changes as a result of reswamping of lands in Belarusian Polesie. The calculations were performed on the example of the Khoiniki district of the Gomel region of Belarus. Numerical experiments considered the driest summer periods of the last two decades. Based on the modeling results, the maps of changes in mean daily temperature, amplitude of daily temperature variations, evapotranspiration and precipitation were constructed, which can be used to predict the consequences of land reclamation in different scenarios of adaptation to climate changes.

Pollution of the environment, in particular water sources, with heavy metals is a serious environmental problem. In this regard, it is relevant to develop new sensor systems that allow rapid tests and are not inferior in analytical parameters to classical methods for detecting heavy metals. Promising materials for creating such sensor systems are composite coatings based on polymer compounds with inorganic nanoparticles. The article presents the results of using poly(methyl methacrylate) (PMMA) coatings and PMMA nanocomposites with silicon dioxide nanoparticles (SiO₂ NPs) to develop capacitive sensors for analyzing the content of Ni²⁺ ions in water. The structural and morphological characteristics of a conductive nickel layer and nanostructured films based on poly(methyl methacrylate) were studied using atomic force microscopy. Based on the experimental data on the dependence of the capacitance characteristics of sensors on the concentration of Ni²⁺ in solutions, the operating characteristics of sensors were established: response time is 5 min; working range of concentrations of Ni²⁺ ions: 1 ‧ 10^–3 – 50 mM; lower detection limit ≈ 0.06 mg/l (maximum nickel concentration limit in water is 0.1 mg/l). It has been shown that the formation of a coating of the composition PMMA + NPs-SiO₂ (1 : 41.7 mol) on a conductive nickel layer using the spin-coating method leads to increasing the sensitivity of a sensor and its service life (up to seven cycles).

To meet the population’s demand for meat pork, breeding programs aimed at breeding and selection of pigs with high reproductive, fattening and meat traits were carried out for several decades. Over the years, a number of new types, lines and breeds of pigs were created and tested in the world. It should be noted that the gene pool of foreign super-meat breeds (Pietrain; Duroc; Danish, French, German, Canadian Landrace and Yorkshire) was used to some extent in the development of new domestic meat genotypes of pigs. A rational use of the genetic potential of farm animals allows accelerating the selection to improve their reproductive, fattening and meat traits. The Republic of Belarus arranged its own production of high-value animals represented by intrabreed type-pigs in the Landrace breed with the following productivity indicators: prolificacy – 12.5 animal units, milk yield – 65.5 kg, number of piglets at weaning – 11.6 animal units, litter weight at weaning at the age of 30 days – 91.6 kg, meat content in carcass – 65–67 %, well adapted to the technological conditions of breeding and industrial complexes, providing the overall need of pig breeding in obtaining high-quality pork; saving foreign currency for import; the possibility of exporting finished products to CIS countries.