The paper considers the problem of optimizing a long-term transient process in a linear singularly perturbed system, which consists of finding a multidimensional admissible control with the minimal value of an integral quadratic performance index. This problem can be interpreted as a control problem with minimal energy consumption. By passing to “slow time”, the problem is reduced to that of optimizing a singularly perturbed system with two groups of fast variables at different rates in the absence of slow variables. Using an approach based on the maximum principle and the method of boundary functions, an asymptotic approximation to the solution of this problem is constructed as a sum of optimal controls in two unperturbed problems of lower dimension with infinite process duration.

The paper proposes an approach to the study and optimization of optical nanotransceiver parameters based on the “metal nanoparticle – quantum emitter” model using machine learning methods. To speed up multidimensional search, a surrogate model based on Gradient Boosting Machine (GBM) was built, for which 60,000 points were generated using the Latin Hypercube Sampling (LHS) method in a six-dimensional parameter space: excitation and emission wavelengths, nanoparticle radius, particle–emitter distance, refractive index of the medium, and intrinsic quantum yield of the emitter. The coefficient of determination R2 = 0.947 was reached in the test sample. Global optimization based on model predictions was performed, followed by refinement by direct calculation, and it was shown that the surrogate model is effective for multiparametric analysis and narrowing the search area for parameters necessary for optimizing the experiment.

The solution is obtained for determining electric and magnetic field energy densities formed by a twodimensional array of spherical particles located in a light-absorbing medium near their surface, at normal incidence of a plane electromagnetic wave. It is based on the statistical description of spatial distribution of particles in an array using the radial distribution functions, quasi-crystalline approximation of the theory of multiple scattering of waves, and multipole expansion of fields and tensor Green’s function in terms of vector spherical wave functions. The amplification of fields in such a system is considered relative to their values in the medium without introducing an array of particles. The influence of the absorption index of the medium and the type of spatial ordering of the array on this effect was investigated. The calculation results are in excellent agreement with the data from numerical simulation using the finite element method.

A comparative assessment of the resolving power of chloroplast (rbcL, psbA-trnH, matK) and nuclear (ITS1, ITS2) molecular markers for species identification of representatives of the genus Betula was performed. It was shown that chloroplast sequences are characterized by low variability, with the poorest performance obtained for rbcL. In contrast, markers of the ITS region possess significantly higher discriminatory power. ITS2 demonstrated potential for the identification of ten species (ranging from 61.7 to 93.1 %), whereas the best performance was revealed for ITS1: the highest number of reliably identified species (five species with 100 % efficiency and eleven above 65 %), the barcoding index reached its maximum among all markers studied (6.04), and the proportion of overlapping intra- and interspecific variability pairs was the lowest (26.66 %). Taken together, the data support ITS1 as the most reliable molecular marker for identification of species of the genus Betula.

Metagenomic analysis was used to study the structure of prokaryotic communities in soils subjected to long-term technogenic salinization within the impact zone of emissions from JSC Belaruskali. The results demonstrate that bacteria (phyla of the domain Bacteria) constitute the core of the soil microbiome, whereas representatives of the domain Archaea (phyla Thermoproteota and Methanobacteriota) make up a smaller fraction. It was found that bacteria belonging to the classes Actinomycetes, Bacteroidia, Alphaproteobacteria, and Gammaproteobacteria dominate at sites where clay-salt sludge is stockpiled. Photosynthetic prokaryotes of the class Cyanobacteriia were detected directly at the base of the spoil heaps and in the immediate vicinity, while bacteria of the class Bacilli were uniformly present in all samples analyzed. These findings expand our understanding of the functional diversity of soil microbial communities under anthropogenic stress and may serve as a basis for developing biotechnologies for the remediation of saline lands.

The oil-saturated block identified in 2012 in the Rechitsko-Vishansky fault area within the Tishkovsky field is a geological phenomenon attributable to the timing and stage of oil-deposit formation in the Pripyat trough. Based on a comprehensive analysis of geological and geophysical data, materials from seismic, industrial, geodynamic, and fluid dynamics studies, the block is associated with a broader inter-salt oil deposit that existed at the end of the Hercynian stage. In the process of geotectonic development, the separated part moved under the influence of geotectonic and halokinetic processes in an isolated position into the subduction zone with the creation of abnormally high formation pressure in the reservoirs.

A new homotopy-based approach is proposed, embodied in the Limit Homotopy Decomposition Method (LHDM). This method departs from a fundamental property of standard homotopy constructions – namely, the requirement that the original nonlinear differential equation be fully preserved at the parameter value p = 1. In the proposed approach, the original form of the nonlinear differential equation is modified at p = 1 by introducing a coefficient (a matching parameter) multiplying the nonlinear term; this coefficient approaches unity as the order of approximation increases (M → ∞). This approach enables the derivation of approximate analytical solutions for boundary-value problems governed by nonlinear differential equations in a simpler form. Using LHDM, an approximate solution was obtained for the problem of radiative heat transfer in a thin rectangular fin. It is demonstrated that LHDM yields analytical solutions that are more compact and simpler in form than those obtained via the standard version of the Optimal Homotopy Analysis Method (OHAM), while maintaining comparable accuracy. Furthermore, the matching parameter rapidly C M/N approaches its limiting value of unity with each successive approximation. These results suggest that the proposed LHDM is a viable alternative to the standard OHAM.

Using mathematical modeling in the Geant4 software package designed for simulating particle transport through matter via the Monte Carlo method and taking into account the self-absorption effect, the optimal thickness of the 63Ni beta source for a betavoltaic energy converter was determined. The surface activity reaches 90 % relative to the saturation value at a source thickness of 2 µm and is equal to 4.6‧108 Bq/cm2. The electron energy spectra on the source surface were calculated as a function of its thickness. These spectra were used for optimization of the parameters of a p-i-n barrier structure, in which beta-particles are absorbed, electron-hole pairs are generated and separated by a built-in electric field. According to the calculations, the maximum electric power generated by a GaN-based betavoltaic converter is equal to 0.12 μW‧cm–2, which corresponds to a betavoltaic conversion efficiency of 6.7 %. The results will be used in the design of a prototype of a gallium nitride betavoltaic energy converter.

The influence of small additive of aliphatic polyketone (APK) on the structural, mechanical, and rheological characteristics of polyamide 6 (PA6) has been investigated. It was established that the introduction of even minimal APK concentrations (0.3–0.5 wt. %) leads to a significant reduction in the melt flow index of PA6, indicating intensive intermolecular interaction between the components. The impact of small APK additives on the thermophysical properties of PA6 exhibits complex behavior. Within the 0.3–0.5 wt. % range, APK stimulates the crystallization of the polyamide matrix, increasing the phase transition enthalpies and the crystallinity index. Conversely, further increasing the APK content to 1.0– 5.0 wt. % suppresses PA6 crystallization, resulting in a decrease in all studied thermophysical parameters. The study revealed an extremal nature of the effect of small APK additions on the strength properties of PA6. The optimal APK concentration for enhancing the mechanical strength of PA6 is 1.0 wt. %, at which maximum values for the elastic modulus, yield point, and tensile strength are achieved.

Monitoring of the main documents regulating state socioeconomic forecasting and planning made it possible both to identify common directions of human development at the national and regional level, and to establish “bottlenecks” in this mechanism. This circumstance defined the purpose of the study, which is to develop scientifically based and practiceoriented proposals for improving the system of state socio-economic planning. To achieve it, the following tasks were accomplished: the directions for state regulation of formation and development of rural human capital were systemized; scientific justification was provided for proposals to improve the system of state planning for socio-economic development of the Republic of Belarus from the perspective of ensuring the resilience of rural human capital.