QR code

Abstract. The case of mass distribution across two coplanar concentric rings, with and without a central body, is considered. Expressions are derived for estimating the magnitude of the gravitational field at the points located on the rings themselves. Possible orbital velocities within the rings are estimated.

Keywords: gravitational field strength, ring radius, ring mass.

For citation: Akhramenko, N. A. Gravitational interaction of two coplanar concentric rings / N. A. Akhramenko // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 7–10. – DOI: https://doi.org/10.54341/20778708_2026_3_68_7. – EDN: ZZNUEE

Information about the authors:

QR code

Abstract. Periodontitis is the core cause of periodontal defects. However, the performance of traditional periodontal defect repair materials is single, which is difficult to cope with the complex microenvironment of periodontitis, leading to the persistence or recurrence of inflammation, and easy to form a vicious cycle of repair-infection-redestruction. In order to solve the problem of single material performance, chitosan (CS) and nano- hydroxyapatite (nHAp) were used as raw materials, and glutaraldehyde (GA) was crosslinked with CS to obtain a chitosan/nano-hydroxyapatite (CS/nHAp) aerogel scaffold material. Curcumin (Cur) film was uniformly deposited on the surface of aerogel by low-power electron beam deposition (EBD) as an antibacterial functional layer to prepare a curcumin-chitosan/nano-hydroxyapatite (Cur-CS/nHAp) composite aerogel scaffold material. FTIR, XRD, XPS, SEM and other characterization methods were used to analyze the composition, structure and morphology of the composite aerogel, as well as the antibacterial, coagulation and osteogenic properties. The results show that it has excellent biocompatibility and antibacterial properties. In addition, in vitro experiments showed that Cur-CS/nHAp aerogel scaffolds could induce osteogenic differentiation of rBMSCs. The Cur-CS/nHAp aerogel scaffold prepared in this study has certain application potential in the repair of periodontal bone defects.

Keywords: chitosan, hydroxyapatite, aerogel, structure, antibacterial activity.

For citation: Curcumin-film-coated chitosan/hydroxyapatite composite aerogels for periodontal bone defect repair properties / Jiping Wang, Jiahao Mu, Mengyang Pang, Xiaoxue Tan, Shanbin Zheng, Xin Liu, A. A. Rogachev, Xiaohong Jiang // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 11–17. – DOI: https://doi.org/10.54341/ 20778708_2026_3_68_11. – EDN: VQVPRN

Information about the authors:

QR code

Abstract. A new solution to the parabolic equation describing Cartesian paraxial 2D light beams is proposed. Such beams are described by Hermite functions of complex argument with two free parameters, without Gaussian apodization. The constraints on the parameters under which Hermite beams carry finite power and are physically realizable are established. The formalism for describing 2D Hermite beams is generalized to Cartesian 3D Hermite beams of finite power. Expressions for the energy density and energy fluxes for vector Hermite beams with uniform polarization are presented. The graphical modeling of the intensity and transverse energy fluxes of such Hermite beams confirms the analytical calculations.

Keywords: paraxial beams, Hermite beams, quadratic integrability.

For citation: Girgel, S. S. Hermite beams of a continuous complex index with transferable finite power / S. S. Girgel // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 18–22. – DOI: https://doi.org/10.54341/ 20778708_2026_3_68_18 (in Russian). – EDN: UIYJVT

Information about the authors:

QR code

Abstract. The partial quasipotential Logunov – Tavkhelidze and Kadyshevsky integral equations are solved analytically and numerically for the bound states of a two-particle system with zero energy: the eigenvalues of the coupling constant and eigenfunctions are found. Similar results for the states of a two-particle system with nonzero energy are obtained using numerical methods.

Keywords: quasipotential approach, momentum representation, Green’s function, bound states, s-state.

For citation: Kapshai, V. N. Analytical and numerical solution of integral quasipotential partial equations for s-states of a two-particle system / V. N. Kapshai, A. A. Grishechkina // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 23–29. – DOI: https://doi.org/10.54341/20778708_2026_3_68_23 (in Russian). – EDN: TSCRYC

Information about the authors:

QR code

Abstract. The reflection properties of ultrasonically diffracted light waves in a coating-modulated layer-substrate structure under conditions of total internal reflection from the substrate were studied. For the YIG-GaAs-As₂Se₃ structure, the reflectivity of diffracted waves was calculated for a light wavelength of 1.15 μm. A significant decrease in the reflectivity of zero- and first-order diffracted waves in the presence of layer absorption was demonstrated with changes in the ultrasonic wave intensity and the modulated layer thickness. It was established that the acousto-optic interaction regime under consideration can be used for amplitude modulation of near-infrared light waves.

Keywords: acousto-optic interaction, infrared radiation, ultrasonic wave, reflectivity, three-layer structure, light absorption, total internal reflection.

For citation: Kulak, G. V. Acousto-optic interaction in photoelastic superlattices under total internal reflection / G. V. Kulak, T. V. Nikolaenko, L. A. Tozik // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 30–34. – DOI: https://doi.org/10.54341/20778708_2026_3_68_30 (in Russian). – EDN: NJNYFK

Information about the authors:

QR code

Abstract. The object of the study was the molecular structure and mechanical properties of nanosized three-layer coatings based on organosilicon compounds K-42 and PMS-400 with an outer zinc layer, formed by electron beam dispersion (evaporation) in a vacuum, their changes during annealing up to 600° C. It is shown that the molecular structure of the PMS-400 coatings corresponds to the structure and chemical composition of the original organosilicon liquid and its noticeable changes, unlike K-42 coatings, are recorded at annealing temperatures above 200° C, and when heated to 600° C, the coating is a cross-linked SiO₂ layer. Annealing the K-42 + PMS-400 + Zn coating at this temperature does not result in the formation of the quartz-like structure characteristic of K-42 + PMS-400, K-42, and PMS-400 coatings. This is explained by the chemical interaction of zinc with oxygen-containing fragments of organosilicon macromolecules. Nanoindenitation was used to determine the mechanical properties of the coatings and their values at various distances from the surface, depending on the annealing temperature. It was shown that when heating the K-42 + PMS-400 + Zn coating to 600° C, in contrast to single-component coatings, a significant decrease in hardness and elastic modulus is recorded, which is consistent with the results of molecular structure studies.

Keywords: organosilicon coatings, electron beam dispersion, heat treatment, molecular structure, mechanical properties.

For citation: Molecular structure and mechanical properties of composite coatings based on organosilicon compounds deposited by electron-beam dispersion / M. A. Yarmolenko, A. V. Rogachev, D. G. Piliptsou, A. A. Rogachev, A. S. Rudenkov // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 35–40. – DOI: https://doi.org/10.54341/ 20778708_2026_3_68_35 (in Russian). – EDN: NPJTOH

Information about the authors:

QR code

Abstract. Let t be a chosen positive integer. A subgroup H of G is said to be K-P_t-subnormal in G if there exists a chain of subgroups H=H₀≤H₁≤...≤H_n-1≤H_n=G such that either or |H_i:H_i-1| is some prime p and p – 1 is not divisible by (t + 1)st powers of primes for each i=1,...,n. By and we denote the class of supersoluble groups, respectively, the class of all groups in which every Sylow subgroup is K-P_t-subnormal. In this paper, we prove criteria for a group to belong to these classes and find applications of to groups that are products of K-P_t-subnormal subgroups.

Keywords: saturated formation, supersoluble group, K-P_t-subnormal subgroup.

For citation: Vasil'ev, A. F. On saturated formations of supersoluble groups, their w-extensions and some applications / A. F. Vasil'ev, T. I. Vasil'eva // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 41–45. – DOI: https://doi.org/10.54341/20778708_2026_3_68_41 (in Russian). – EDN: OGDMXN

Information about the authors:

QR code

Abstract. It is proved that in the generalizing polyadic groupoids all elements are zero divisors.

Keywords: groupoid, l-ary operation, l-ary groupoid, zero divisor.

For citation: Gal'mak, A. M. Zero divisors in generalizing polyadic groupoids / A. M. Gal'mak // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 46–50. – DOI: https://doi.org/10.54341/20778708_2026_3_68_46 (in Russian). – EDN: PRVDBM

Information about the authors:

QR code

Abstract. This paper considers the Banach algebra SD[0;1] consisting of functions on the interval that admit only simple discontinuities, and the algebras of multiplication operators by functions SD[0;1] acting on the spaces L_p([0;1],μ) where μ is a given continuous measure. It is shown that all these algebras are isomorphic to the subalgebra T[0;1]⊂SD[0;1], consisting of functions continuous at 0 and left-continuous at all other points, and that the maximal ideal spaces of the operator algebras under consideration are homeomorphic to the Aleksandrov – Urysohn non-metrizable "two arrows" space.

Keywords: discontinuous function, simple discontinuity, operator algebra, function algebra, continuous measure, quotient algebra.

For citation: Luxemburg, I. L. Algebras of operators of multiplication by discontinuous functions / I. L. Luxemburg // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 51–55. – DOI: https://doi.org/10.54341/ 20778708_2026_3_68_51 (in Russian). – EDN: QIDNBE

Information about the authors:

QR code

Abstract. We study a mixed problem in the first quadrant of the plane for the wave equation with the Cauchy conditions and the Dirichlet boundary condition. The Cauchy condition for the time-derivative has a discontinuity of the first kind at a single point. Various approaches to defining a solution are proposed. Explicit analytical representations of solutions to the problem under consideration are constructed. Necessary and sufficient smoothness conditions for the existence of solutions are derived. The uniqueness of solutions is proved. The matching conditions satisfied by the constructed solutions are established.

Keywords: wave equation, mixed problem, nonsmooth initial conditions, compatibility conditions, matching conditions.

For citation: Rudzko, J. V. Existence and uniqueness of solutions to a mixed problem for the wave equation with a discontinuous velocity function at interior and boundary points / J. V. Rudzko // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 56–64. – DOI: https://doi.org/10.54341/20778708_2026_3_68_56 (in Russian). – EDN: QNPSSD

Information about the authors:

QR code

Abstract. The results of a study of the parameters of a hybrid solar module utilizing thermoelectric generators and silicon solar cells are presented. It was experimentally determined that when the experimental solar module sample is heated to 70° C and the ambient temperature is 23° C, the specific voltage generated by the thermoelectric generators relative to the effective area of the solar module sample is 2.2 mV/cm². The development of such a hybrid solar module will increase photovoltaic conversion efficiency to 1.5%.

Keywords: solar module, thermoelectric batteries, Seebeck effect, efficiency.

For citation: Possibility of increasing the efficiency of solar modules in combination with thermal electric generators / V. V. Malyutina-Bronskaya, A. V. Nesterenok, V. M. Kravchenko, A. V. Yakushev // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 65–71. – DOI: https://doi.org/10.54341/20778708_2026_3_68_65 (in Russian). – EDN: KNNDZY

Information about the authors:

QR code

Abstract. The high nonlinearity of pulsed laser cladding processes poses significant challenges for predicting coating quality, particularly when dealing with small experimental datasets. This paper proposes a fuzzy logic-based modeling approach for pulsed laser cladding of high-strength 30ÕÃÑÍ2À steel with nichrome. Using the experimental data, a Mamdani-type fuzzy inference expert system was constructed, linking the laser radiation parameters (pulse energy, duration, and repetition rate) with the geometry of the deposited bead, microhardness, and defectiveness (presence of cracks and pores. The predictive performance of the model was assessed on an independent test dataset, demonstrating satisfactory accuracy. Furthermore, the application of fuzzy interpolation algorithms with integer-valued outputs enabled the development of a physically consistent defect prediction system. The resulting model can serve as an intelligent decision-making core for optimizing process parameters in pulsed laser cladding.

Keywords: laser cladding, steel, fuzzy logic.

For citation: Fuzzy logic-based modeling of coating quality under pulsed laser radiation on 30ÕÃÑÍ2À steel / Yu. V. Nikityuk, L. N. Marchenko, G. A. Bayevich, V. A. Prokhorenko, A. V. Maximenko // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 72–78. – DOI: https://doi.org/10.54341/20778708_2026_3_68_72. – EDN: LAGKPK

Information about the authors:

QR code

Abstract. A method and software tools have been developed for neural-network modeling of adaptive control of the technological operation of laser thermal splitting of silicate glass under external control actions, limited observability of the processing-zone state, and random disturbances. Physical experiments were carried out on an AEON Mira 7 CNC laser machine using single-mode polariscopic video monitoring of the processing zone with a CMOS camera. The observed process-state classes included failure of crack initiation, advancement of the crack tip ahead of the laser spot, crack branching, and stable thermal splitting. To synthesize corrective control actions, a stochastic simulation environment was developed in which a Transformer-based controller was constructed using reinforcement learning methods. Feedback was implemented as a process-parameter correction loop based on current video observations. The algorithmic framework was based on Proximal Policy Optimization in an actor-critic formulation with Generalized Advantage Estimation, which made it possible to obtain an effective neural-network controller.

Keywords: laser thermal cleaving, silicate glass, polariscopic monitoring, simulation modeling, feedback, reinforcement learning, PPO, neural-network regulator.

For citation: Development of a method and tools for modeling the control problem of the technological operation of laser thermal cleaving of silicate glass under real-time polariscopic monitoring / V. A. Prokhorenko, V. S. Smorodin, Yu. V. Nikityuk, S. I. Sokolov // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 79–85. – DOI: https://doi.org/10.54341/20778708_2026_3_68_79 (in Russian). – EDN: LKVDSY

Information about the authors:

QR code

Abstract. This article proposes a study of an anatomically accurate mathematical model of the stress-strain state of the human lumbar spine under various loads. The proposed mathematical model, based on CT image analysis, and the methodology for its study can be used in medical practice to analyze the condition of the spinal segment under normal conditions, abnormal loads, and pathological changes.

Keywords: lumbar spine, CT images, stress-strain state, pathology.

For citation: Kurochka, K. S. Investigation of a mathematical model of the stress-strain state of the human lumbar spine under vertical loading / K. S. Kurochka, T. S. Semenchenia // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 86–90. – DOI: https://doi.org/10.54341/20778708_2026_3_68_86 (in Russian). – EDN: KCMEAI

Information about the authors:

QR code

Abstract. The paper solves the problem of choosing the optimal mathematical model for information flow control in machine-to-machine (M2M) networks of the Internet of Things (IoT). The relevance of the study is due to the lack of a methodological apparatus for comparative analysis of existing network flow control models under constrained resources of IoT devices. The aim of the study is to develop and test a criteria-based apparatus for selecting the optimal model and its subsequent software verification. The methodology includes formalization of three main classes of mathematical models – graph-based, queueing theory-based and SDN-oriented; development of a five-criteria vector for comparative analysis; implementation of the selected optimal model in Java; experimental verification on synthetic and realistic scenarios. As a result, the SDN-oriented model showed the highest comprehensive score, significantly outperforming the alternatives. Its implementation confirmed high accuracy of delay prediction and the ability to reduce delay for critical traffic under high network load. The developed criteria apparatus and verification methodology are of practical value for IoT system designers.

Keywords: Internet of Things, M2M communications, mathematical modeling, software-defined networking (SDN), quality of service (QoS), comparative analysis, algorithmic implementation, model verification.

For citation: Rafalova, E. V. Comparative analysis and verification of mathematical models for flow control in M2M networks of IoT / E. V. Rafalova // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 91–96. – DOI: https://doi.org/10.54341/20778708_2026_3_68_91 (in Russian). – EDN: DZZTSK

Information about the authors:

QR code

Abstract. A method for obtaining a probabilistic assessment of the reliability of an electric power system based on the probabilistic characteristics of the reliability of its structural elements are considered. It is proposed to calculate the probabilistic reliability characteristics of the structural elements of the objects under study using a software package for intelligent spatial and temporal data analysis, which allows automatically aggregating requests for accidents from the public via messenger and conducting situational analysis of incoming data in real time. An example of probabilistic-algebraic modeling of a fragment of an electric power system formalized as a three-pole system is considered.

Keywords: electric power systems, network structures, probabilistic-algebraic modeling, reliability, energy supply, automation, big data, situational analysis, geoinformation systems, telegram bot, data clusterization, containerization.

For citation: Sukach, E. I. Probabilistic-algebraic modeling of reliability of electric power systems using spatial and temporal data analysis / E. I. Sukach, V. A. Kalinichenko // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 97–105. – DOI: https://doi.org/10.54341/20778708_2026_3_68_97 (in Russian). – EDN: DKGWKM

Information about the authors:

QR code

Abstract. The article is dedicated to the 80th anniversary of the birth of the prominent Belarusian mathematician, Doctor of Physics and Mathematics, Professor Viktor Stepanovich Monakhov. It presents his detailed scientific biography, reflects the main stages of his research and pedagogical activities, and highlights his contribution to the development of group theory.

Keywords: mathematics, group theory, Gomel algebraic school, Viñtor Stepanovich Monakhov, scientific biography, anniversary, Belarusian mathematicians, finite groups.

For citation: Viñtor Stepanovich Monakhov // Problems of Physics, Mathematics and Technics. – 2026. – № 3 (68). – P. 106. – DOI: https://doi.org/10.54341/20778708_2026_3_68_106 (in Russian). – EDN: EYQHST