The concept of the discriminant of a quadratic polynomial allows for easy extraction of information about its real and complex roots. The discriminant of a polynomial of an arbitrary degree is also an important characteristic of the polynomial, which proves useful in many problems in the theory of Diophantine approximation. In 2023, Belarusian mathematician D. Badziahin solved a problem posed by Davenport in the 1960s concerning the range of values of discriminants in the cubic case. The paper provides a complete solution to the problem of divisibility of discriminants by large powers of prime numbers in the case of cubic polynomials.

Replenishing the range of natural and synthetic medicinal substances with different anti-inflammatory activity is an urgent task of modern pharmaceuticals. Studying the anti-inflammatory activity of chemical compounds through bioscreening and in vitro and in vivo studies is a lengthy and labor-intensive procedure. This paper presents the data on the antyinflammatory activity of nitrogenous heterocyclic compounds on a model of acute exudative reaction (peritonitis) and comparison of the obtained data with the results of ab initio quantum chemical calculations using the density functional theory method. Among the 16 studied compounds, 7 representatives were identified with the highest potential antyinflammatory action.

T-cell activation begins upon antigenic recognition by T-cell receptor and is regulated by signals generated by co-stimulating and co-inhibiting molecules. These molecules, known as immune checkpoints, are attractive therapeutic targets for the therapy of cancer and autoimmune diseases. Co-inhibiting signal pathway formed between TNF-receptor HVEM (Herpes- Virus Entry Mediator, TNFRSF14) and BTLA (B and T Lymphocyte Attenuator) limits T-cell activation. However, BTLA can serve also as activating ligand when interacts with HVEM on adjacent cell. Mutagenesis experiments have shown that the same interface is formed between HVEM and BTLA both upon cis and trans interactions thus suggesting significant conformational rearrangement in the HVEM stalk region between ectodomain and transmembrane domains upon transfer from cis to trans binding to BTLA. However, because of technical problems of the crystallization of surface receptor with long stalks, HVEM atomistic 3D-structures including stalk region are absent up to now. In this study, the approaches of structural bioinformatics were used to determine the structures of full-length proteins HVEM and BTLA and their complexes upon cis- and trans-interactions. The results obtained can be used upon developing immunoregulators for the immunotherapy of cancer and autoimmune diseases.

Lentivirus-based vectors encoding two engineered melanoma associated MLANA proteins, named MLANAFLAG^® and MLANA-FLAG^®-LAMP1, were developed and tested. Transcriptional and translational activity of engineered proteins was confirmed in HEK 293T cells and dendritic cells by fluorescence confocal microscopy and flow cytometry. These new vectors can be used for lentiviral transduction of dendritic cells and the creation of new cell therapies for human melanoma.

The significance of the polymorphic variants rs10490924 (A69S) of the age-related maculopathy susceptibility 2 gene (ARMS2) and rs1061170 (Y402H) of the complement factor H gene (CFH) for risk assessment of neovascular agerelated macular degeneration (nAMD) in the Belarusian population was studied. It was established that by minor alleles hetero- and homozygotes are associated with a high risk of nAMD. It was shown that the risk of disease development increases many times with each minor allele copy (the log-additive inheritance model) both for rs10490924 and rs1061170. The ARMS2 rs10490924 polymorphism has the greatest risk significance. At the same time, the analysis of paired genotype combinations by the loci studied is more informative for risk assessment than for individual loci. The results obtained can be used to assess a genetic predisposition to nAMD in the Belarusian population.

Acute-on-chronic liver failure is an acute liver decompensation in cirrhotic patients, which leads to organ failures and high short-term mortality. The treatment is based on the management of complications and, in severe cases, liver transplantation. Liver transplantation is the most effective treatment, but the lack of donor livers and a high cost of transplantation limit its broad application. Human placenta-umbilical cord complex derived mesenchymal stem cells (MSCs) can be considered as an allogeneic source for liver disease. The aim of the study was to assess the safety and potential effectiveness of systemic administration of mesenchymal cells from the human placental-umbilical cord complex for liver failure correction in patients with decompensated cirrhosis of the liver. An open interventional prospective case-control study was conducted, including 40 patients over 18 years of age with decompensated liver cirrhosis who were hospitalized awaiting liver transplantation. Laboratory efficacy of therapy was confirmed by a significant decrease in a total bilirubin level by 39 %, an increase in total protein was noted (by 11 %), as well as stabilization of coagulopathy (decrease in INR by 25 %). Systemic administration of mesenchymal cells of placental origin is a promising therapeutic option for patients with decompensated liver cirrhosis, allowing one to increase the waiting period for emergency liver transplantation and stabilize the clinical course of the disease.

The plastics of electrical and electronic equipment (EEE) contain various chemicals that are introduced during production with flame retardants, stabilizers, dyes and other additives to impart the necessary properties. Among the hazardous substances, polybrominated diphenyl ethers (PBDEs), which are persistent organic pollutants (POPs), are of particular concern. The article discusses the results of chemical and analytical tests of EEE plastic waste and the first estimates for Belarus of the volumes of waste generation subject to environmentally sound management in accordance with the obligations of the Stockholm Convention on POPs. PBDEs were determined using gas chromatography in bromine-containing plastics (281 samples), bromine – using X-ray fluorescence spectrometry (760 samples). It was shown that bromine was detected in 37 % of cases, PBDEs – in 31 % of samples of bromine-containing plastics or in 11.4 % of their total amount. The maximum concentrations of PBDEs reach 12–17 % by weight. In terms of PBDEs occurrence in EEE plastics, they are ranked as follows: monitors and TVs – 15.4 % of cases, large household appliances – 14 %, IT and telecommunications equipment – 11.7 %, copying equipment – 6.9 %, small household appliances – 3 %. As of 2022, the volume of EEE plastic waste containing brominated flame retardants is estimated at 5.5 thousand tons, of which about 65 % is subject to environmentally sound management. More than 70 % of PBDE-containing waste is represented by monitor and TV plastics. Measures to improve the EEE collection system and the need to separate EEE plastic waste during their recycling in order to prevent the recycling of hazardous substances are discussed.

During radar tracking often a situation arises when two targets are unresolved in one or more coordinates. The aim of this work is to develop an analytical technique for analyzing the accuracy of tracking of unresolved targets using methods of statistical linearization and integration of equations of probabilistic moments. Initially, the problem of analyzing the accuracy of tracking a single target is solved, and then the problem of tracking of two targets which are unresolved in one of the coordinates. A technique for analyzing the accuracy of radar tracking of two unresolved targets, the signals of which are within the width of the discriminatory characteristic is proposed. The nonlinear nature of the problem is caused by the need to take into account the form of this discriminatory characteristic. When developing the technique, the method of statistical linearization of nonlinear functions and the method of integrating equations of probabilistic moments were used.

Mathematical simulation of a single target tracking system and a tracking system for two unresolved targets was carried out. The accuracy of the technique was assessed by comparing the results of calculating means and variances of tracking errors using Monte Carlo method with the results of analytical calculations. The obtained results can be used to solve problems such as tracking a paired target, handling crossing trajectories, tracking in conditions of radar jamming, etc.

The work presents the results of mathematical simulation of dynamic atomic force microscopy (AFM). Influences of spring constant, the quality factor of AFM-probe on its vibration amplitude and phase shifts are studied for semi-contact interaction of tip probe and sample surface. The deformation depths of sample by probe are calculated. Also the influence of oscillation amplitude of piezogenerator, which forces probe vibration, on the characteristics of probe oscillation is shown. 

The paper presents the results of studying cytoplasmic male sterility (CMS) of winter rape (Brassica napus ibernalis L.). Using histological, morphobiological, and biochemical methods, 12 sterility fixer lines for Ogura-type CMS as well as 2 lines for Ogura CMS and 1 line for Polima CMS with 100 % restoring ability were isolated. The combining ability of more than 20 maternal parental CMS lines was evaluated and more than 500 experimental simple sterile and restored hybrids based on Ogura CMS were obtained. Using in vitro culture, doubled haploids of parental lines of winter rape were obtained, and the peculiarities of embryoidogenesis, morphogenesis and rhizogenesis were established.