For a one-dimensional semilinear wave equation with a free term that is a solution value at one given point (a Dirac potential), we consider the Cauchy problem in the upper half-plane. We construct the solution using the method of characteristics in implicit analytical form as a solution of some integral equations. The solvability of these equations, as well the smoothness of their solutions, is studied. For the problem in question, we prove the uniqueness of the solution, and establish the conditions under which its classical solution exists. 

A generative semi-supervised adversarial neural network trained on graph embeddings was developed for de novo design of potential inhibitors against beta-ketoacyl-[acyl-carrier protein] synthase I (KasA), an enzyme critically important for biosynthesis of mycolic acids of the Mycobacterium tuberculosis cell wall. The designed model was trained and tested on a set of compounds from a virtual library of small molecules containing structural elements capable of selective interactions with the therapeutic target. Using the developed neural network, 3,637 compounds were de novo designed, followed by assessment of their inhibitory activity against the KasA protein using molecular docking methods. Based on the analysis of the obtained data, six compounds exhibiting high affinity to the malonyl-binding site of the enzyme were selected. The identified compounds are assumed to form promising basic structures for further theoretical and experimental studies on the development of new effective inhibitors of drug-resistant tuberculosis.

The electrophysical properties and the resistive switching effect of the Ni/SiN_x/p⁺Si/Ni memristor structure are investigated. Silicon nitride films with a thickness of ~40–60 nm were deposited in inductively coupled plasma from a SiH₄– N₂–Ar mixture at [SiH₄]/[N₂] ratios of 2.19 and 2.55, which ensured the formation of SiN_x with an excess of Si compared to stoichiometry. To investigate the effect of thermal annealing on the resistive properties of SiN_x, one of the wafers with a nitride film was annealed using rapid thermal annealing (RTA, 1200 °C, 3 minutes in Ar). The resistive switching effect was observed when applying a voltage from −4 to +10 V for test structures based on nitride films with refractive indices of 2.34 and 2.5. It is shown that the conductivity and charge transport mechanism in SiN_x films with resistive properties depend on the deposition conditions and subsequent heat treatment. Possible mechanisms of resistive switching are discussed.

A simple and convenient method for the synthesis of 2-alkyl-substituted analogues of isoflavonoids with nonaromatic ring A is proposed. The method consists of acylation of 2-[2-(aryl)acetyl]cyclohexane-1,3-diones with carboxylic acid anhydrides followed by intramolecular aldol-crotonic condensation of the resulting enolacylates in the presence of basic agents (triethylamine, sodium acetate, potassium carbonate). 2-[2-(Aryl)acetyl]cyclohexane-1,3-diones were obtained by condensation of 5-substituted cyclohexane-1,3-diones with arylacetic acids under the action of dicyclohexylcarbodiimide and 4-(dimethylamino)pyridine-catalyzed O-C isomerization of the resulting O-acylates.

The European buckthorn (Rhamnus cathartica L.) – a shrub native to most parts of Europe and Western Asia – has been successfully naturalized in the Midwest and Northeast of the USA, dominating various habitats and displacing native species. It is known that Rhamnus cathartica L. plants contain a wide range of secondary metabolites with pharmacological effects. Permanent sample plots with R. cathartica – the species native for Belarus (two sites) and invasive in the USA (two sites) – were selected. This study investigated the level of anthraquinones, catechins, and leucoanthocyanins, and identified anthraquinones using HPLC with mass spectrometry and UV detection, showing a significant variation in these indicators depending on the conditions and the geographical area of growth. Rhamnus cathartica chemorases were identified, which will allow further isolation of samples with a required set of phenolic compounds and a directed selection for obtaining artificially introduced populations with an increased content of one or another valuable compound.

It has been shown that in order to identify patients with high risk for developing immunological complications after allogeneic hematopoietic stem cell transplantation (alloHSCT), it is advisable to measure quantitatively the proliferative activity of lymphocytes in alloHSCT recipients on the day of transplantation. A high donor and recipient lymphocyte stimulation index (>11.55) is an unfavorable factor in terms of development of a graft-versus-host disease (GVHD) in the early posttransplant period. In the course of the work, it was found that the study of the cytokine profile of blood plasma of alloHSC recipients in the early posttransplant period can be used as an additional method for diagnosing GVHD. The levels of IL-8 and IL-21 in the blood plasma of alloHSC recipients can act as potential biomarkers of acute GVHD.

A zoning scheme (in points) of the Central Belarus area by the degree of comfortability of the geological environment for the people’s life was constructed. It was based on the analysis of maps and diagrams of modern geological processes, literature, field work materials and stationary observations. The following types of territories were identified: comfortable (less than 30 points), moderately comfortable (30–50 points), low comfort (50–70 points), uncomfortable (more than 70 points) and uncomfortable in active fault zones (more than 70 points). It was established that the degree of comfort correlates with the features of the earth’s surface relief, the probability and intensity of modern geological processes.

The structure and functioning algorithms of the simulator of radar signals reflected from small-sized unmanned aerial vehicles (UAVs) have been developed. A specific feature of the simulator is the ability to generate arbitrarily correlated signal implementations of the radar input influence for the cases where the random amplitude of the reflected signal (RS) has a Rayleigh, Nakagami, Weibull or lognormal distribution. Analytical expressions are presented for calculating the parameters of the probability density function, as well as generating samples of the random amplitude of the RS with a given distribution law from the samples of the initial implementations of the Gaussian process. Provision is made for normalizing the RS average power to the average value of the modeled target RCS and a specified correlation time for fluctuations of RS complex amplitudes is ensured. The parameters of the generated RS implementations correspond to the values of real radar characteristics of small-sized UAVs obtained experimentally. The application of the proposed simulator is to analyze the effectiveness of newly developed and known UAV detection algorithms using the mathematical modeling method.

The analysis of the experience of space exploration allows us to note a stable tendency of filling spatial objects and phenomena with meanings and their subsequent perception as signs of human spirituality and culture. As a result of the semantics study of the space images in the works of Belarusian literature, their spiritual and aesthetic essence and symbolic content are revealed. For the first time in Belorussian literary criticism at studying the polyvalent phenomenon of spatiality in literary works, aesthetic vision of the authors, philosophical depth of their reflections, and the desire to understand civilizational and cultural logic of the society development are problematically combined. Such methods of artistic space modeling provide us an opportunity to demonstrate its image resources in the geopoeticization of the people and the country, the embodiment of national axiology, moral and ethical ideals and existential meanings. The identification of ideological and semantic content of spacial images in the works of Ya. Kupala, Ya. Kolas, M. Tank, I. Shamyakin, V. Gnilomedov allows us to reveal the techniques and methods of creative development of the surrounding world by writers, the embodiment of the fundamental principles of the national lifestyle and the reflection of evolutionary processes in society, revealing the spirituality of the Belarusian, the specifics of his thinking and worldview. New approaches to understanding the essence of man through the ontology of space and its figurative and symbolic embodiment in Belarusian classics are demonstrated in the study.

Rhizosphere bacteria Azospirillum brasilense, saving in the collection of the Institute for Soil Science and Agrochemistry, were characterized as perspective plant inoculants in conditions of intensive application of herbicide glyphosate. Bacteria strains A. brasilense 2(в)3, A. brasilense Дп1 and A. brasilense 1’ were found to metabolized glyphosate without formating aminomethylphosphonic acid. Bacteria strains A. brasilense 2(в)3, A. brasilense Дп1 and A. brasilense 1’ are capable of glyphosate decomposition with the formation of safe chemical products – sarcosin (methylglycine) and inorganic phosphate (Pi). Destruction activities of A. brasilense strains were calculated on the base of accumulation of inorganic phosphate in culture liquids. Under a glyphosate concentration of 300 mg/l the destruction activities of А. brasilense 2(в)3, А. brasilense Дп1 and Azospirillum brasilense 1’ were equal to 80.9; 62.5 and 61.1 %; under a glyphosate content of 500 mg/l the destruction activities were equal to: 82.2; 48.5 and 47.9 % respectively. Application of glyphosate-utilizing bacteria as inoculants resulted in the polyfunctional anti-stress effect on plants at high diapason of glyphosate content in soil (0–50 l/ha). Anti-stress effect is manifested in a plant growth (steams and roots), an increase of assimilation square and chlorophylls content.