The connection between the solution of Shemetkov’s problem on Z-saturated formations and the study of classes of groups defined by systems of formation subnormal subgroups was established. A criterion for a superradical formation to be solvably saturated was found. The superradicality of hereditary S -formations was proved. All hereditary formations F of solvable groups that contain every group representable as a product of its subgroups, all H-subgroups of which are F-subnormal (or K-F-subnormal), where H is a saturated homomorph, were described.

We consider a mixed problem for the one-dimensional wave equation in the first quarter of the plane with discontinuous initial and boundary conditions arising from the theory of longitudinal impact on an elastic semi-infinite rod with elastic fastening at the left end. We propose a new approach to solve the problem, which constructs the solution as a limit of classical solutions. The proposed method does not use any additional conditions that were required in previous methods providing a more direct and rigorous construction. We find the solution in an explicit analytical form as a piecewise continuous function. For the problem under consideration, the uniqueness of the solution is proved and the necessary and sufficient matching conditions are established under which the solution exists. 

This paper is devoted to statistical analysis of a binary heterogeneous Markov chain with a single change point (time point of the change in the one-step transition probability matrix). To address this problem, two cases are studied: one where the transition probability matrices are known, and another where they are unknown a priori. Consistent statistical estimators for the parameters are constructed, their asymptotic properties are proved, and an algorithm for estimating the change point is developed. The results of computer experiments are presented.

An urgent task of modern optoelectronics is to extend the spectral sensitivity of silicon into the infrared region for the development of efficient photodetectors and solar cells. A promising approach is the formation of nanocrystals of narrow-gap A³B⁵ semiconductors, in particular indium arsenide (InAs), in the near-surface layer of silicon by ion implantation followed by thermal annealing. The effect of various annealing regimes (furnace annealing, pulsed ion, pulsed laser and rapid thermal annealing) on the depth distribution of implanted indium and arsenic ions in monocrystalline silicon, the structural perfection of doped layers and their optical properties has been investigated. Using Rutherford backscattering spectrometry, transmission electron microscopy and optical spectrophotometry, it was found that rapid thermal annealing at 1400 °C with a hold time of 3 s provides the maximum degree of crystallinity of the silicon matrix (92.2 %) and promotes the formation of nanocrystalline layer. Furnace annealing at 1000 °C for 30 min results in the highest fraction of impurity atoms in substitutional lattice sites (44.8 %), indicating efficient electrical and optical activation of the impurity. It is shown that all studied annealing regimes significantly increase the absorption of silicon in the near-infrared range compared to undoped material, with the maximum absorption coefficients (up to 68 % in the IR region) recorded after pulsed ion annealing. The obtained results demonstrate the possibility of controlling the optical properties of silicon by choosing the post-implantation annealing regime and can be used for the development of silicon-based infrared photodetectors.

This paper presents a specialized method for the experimental modeling of radiation-induced swelling in structural materials, utilizing the technique of high-energy ion implantation. The primary objective of the research is to evaluate the applicability and effectiveness of this approach for the accelerated reproduction of radiation damage and volumetric changes that are characteristic of the harsh operating conditions found in nuclear reactor environments. Irradiation experiments were performed on a wide range of materials, including 12X18N10T, St37-3, and EI-847 steels, D16 and VT-6 alloys, as well as zirconium (Zr) and silicon carbide (SiC). The implantation process was carried out within energy range of 400–1500 keV, with fluences varying from (1 · 10¹⁴)–(2 · 10¹⁸) ions/cm². The evolution of surface layer morphology and the formation of radiation-induced steps were investigated using stylus profilometry. Samples were subjected to annealing within a temperature range of 250–550 °C. Based on the profilometric analysis, clear regularities were established regarding the variation of the swelling coefficient as a function of the total radiation dose and the subsequent annealing temperature. The results indicate that the proposed method of ion implantation can be effectively utilized as a reliable tool for the rapid assessment of the radiation resistance of promising structural materials, significantly reducing the testing time required for reactor-grade material validation.

The paper addresses the problem of improving the accuracy of the course and horizontal speed magnitude estimates produced by coordinate filtering in a multifunction radar operating in continuous-tracking mode with a high data-output rate, where the per-update object displacement is comparable to the single-measurement coordinate error. Under these conditions, the course and speed estimates obtained by differentiating noisy coordinates fluctuate from scan to scan, whereas the radial velocity (range rate), measured directly by the Doppler method, remains stable. A method is proposed for correcting the filtered full velocity vector estimate using an independently filtered radial-velocity estimate: the velocity vector is projected onto the constraint imposed by the radial velocity, with weights given by the variances of the coordinate filter; the course is reconciled with an independent geometric estimate from the track; the result is smoothed with inertia. The method does not change the coordinate estimate. Monte Carlo simulation (2000 runs per scenario) on three typical scenarios – helicopter, airplane, ballistic object – shows that the method reduces the course RMSE by a factor of 2.1 and the horizontal-speed-magnitude RMSE by a factor of 1.8–2.9 for the maneuvering objects; for the ballistic object it gives no benefit in course, which is already accurate, but reduces the speed-magnitude RMSE by a factor of 1.6 owing to a residual mismatch between the constant-acceleration coordinate filter and the true, non-constant deceleration. The method’s applicability condition and the gain’s sensitivity to update period, observation geometry, measurement accuracy, and maneuver intensity are examined separately.