Vestnik Permskogo universiteta. Matematika, mehanika, informatika

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):5-5

5-5

Mathematics

An Analogue of the Euler Equation and Necessary Conditions for Second-order Optimality in an Optimal Control Problem Described by Nonlinear Volterra Integral Equation

Abdullayev A.A.

Abstract

The optimal control problem of the minimum of a multipoint functional defined on solutions of a nonlinear integral equation is considered, and implicit necessary conditions for optimality of the first and second orders are obtained. Also using them, an analogue of the Euler equation was established and constructively verifiable necessary conditions for second-order optimality were obtained. Singular optimality controls in the classical sense have been studied.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):6-17

6-17

Mechanics

Formation of Inspection Motion for Spacecraft in Lunar Orbits

Avariaskin D.P., Velasquez D.P.

Abstract

In this work, the problem of selecting the initial parameters for the relative motion of spacecraft (SC) to ensure and maintain the inspection trajectory is addressed. The study includes modeling the relative motion of two SCs (reference and inspector) in low lunar circular orbits. The orbits for the reference SC considered are known stable and "frozen" orbits, which allowed for the analysis of their applicability in the implementation of inspection tasks. The results of the study demonstrated the presence of three main types of motion of the relative trajectory in the orbital coordinate system: movement along the Ox axis, rotation around the Oy and Ox axes. The use of 15 harmonics of the lunar gravitational potential for the analysis of relative motion of SCs around the Moon was justified. Each relative trajectory was analyzed taking into account deviations along the axes. It was shown that not all stable orbits are suitable for performing inspection tasks. Polar orbits demonstrated their advantages due to greater adaptability and reduced instability of the relative trajectory. It was shown that in non-polar orbits, the effect of increasing the eccentricity of the relative trajectory over time has a significant impact on the inspection movement

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):18-27

18-27

Study of Plane Angular Motion of a CubeSat Nanosattellite Using Phase Portraits

Barinova E.V., Timbai I.A., Mironov E.

Abstract

This paper considers the plane motion relative to the center of mass of CubeSat nanosatellites under the action of aerodynamic and gravitational moments in low Earth orbits. The phase plane method is used for qualitative assessment of motion parameters. Conditions under which the type of phase portrait changes have been obtained. Analytical expressions have been found to determine the equilibrium positions of a nanosatellite relative to the center of mass in the orbital coordinate system with a displacement of the center of pressure relative to the center of mass along two coordinates. Two models of angular motion are compared: the original model, which takes into account the shape of the nanosatellite and its position relative to the oncoming flow, and a simplified one, in which the dependence of the aerodynamic moment on the angle of attack is approximated by a sinusoid.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):28-40

28-40

Investigation of the Influence of Inertial Mass Suspension Structure of Glass Micromechanical Accelerometer on its Properties

Barulina M.A., Golikov A.V., Pankratova E.V., Markelova O.V.

Abstract

The paper deals with a promising MEMS accelerometer made of radiation-resistant glass using the technology of pulling from glass rods and tubes. An alternative structural scheme of a pendulum accelerometer with an inertial mass suspension formed from glass structures of two shapes - hexagonal and tubular - is developed. By using the finite-element modeling methods, a comparative analysis of mechanical characteristics of MEMS models with different inertial mass suspensions has been performed, namely, for both models stresses and deformations at accelerations in the range up to 50g have been calculated. The calculation of natural frequencies was also performed. The analysis of the obtained results demonstrated that both schemes have close values of these characteristics, but a detailed consideration of the stress distribution in the suspension structures allows us to conclude that the hexagonal structure is more resistant to failure. The possible sensitivity of the sensor for two variants of the inertial mass suspension is also evaluated. It is proved that in both cases at accelerations up to 50g the capacitive sensor has a sufficient range of capacitance variation for acceleration registration.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):41-51

41-51

Gyrostat Motion in the Light Flow of Semi-Euclidean Space

Makeev N.N.

Abstract

The motion of a gyrostat in a stationary field of light pressure forces in semi-Euclidean space is investigated. A gyrostat with kinetic axial symmetry and a constant gyrostatic moment moves so that its carrier rotates around the center of inertia. The field of light pressure forces is generated by a stationary light flux of constant intensity, formed by parallel rays of light, and is assumed to be conservative. Based on an improved thermomechanical model of the dynamic interaction of light radiation with a solid surface, a dynamic system is constructed and the limited problem of studying motion of a special type is considered. As a result of applying an affine transformation of the variables determining the motion of the gyrostat, exact solutions to the problem of integrating a dynamic gyrostat system in a conservative field of light pressure forces were obtained. Two modes of gyrostat motion and their analog interpretation are considered.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):52-66

52-66

Production Peculiarities of Hot-Curing Resin Samples for Potential Use in Open Space Conditions

Mokhireva K.A., Kuznetsov K.Y., Osorgina I.V.

Abstract

Deployable structures ensure a new round in manufacturing spacecraft components (compartments and modules, communication and power supply systems). Although there is a great number of engineering approaches and solutions in this field of research, we favor the idea of unfolding in space multi-layer inflatable structures based on a composite material (prepreg). Prepreg consists of reinforcing fibers impregnated with resin (binder) cured under open space conditions. This approach makes it possible to create light and strong structures of various shapes in space. The purpose of this study is to find a domestic material that can serve as a binder and is able to meet the requirements for binders: high curing temperature, low outgassing during curing and long storage life in an uncured state. The paper proposes to use a special resin VST-1208, which meets these requirements, for the production of prepregs. The differential scanning calorimetry method (DSC) was used to analyse the reactions occurring during resin curing. Due to the impossibility of conducting experiments in real conditions, the main step of our study is identifying an optimal strategy for production of resin samples. To this end, it is necessary to model and analyze the process of heating the samples in a vacuum thermo-cabinet. We considered the situations when the sample is in experimental conditions - in a vacuum thermo cabinet on a thermally conductive substrate, and in conditions close to outer space - in a vacuum thermo cabinet without a thermally conductive substrate (for example, on a thermally insulating substrate). Analysis of the data obtained confirmed that the considered material can be used at specified temperatures.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):67-78

67-78

Application of the Method of Multiple Scales to the Problem of Occurrence of Solute Convection in Rectangular Region of Porous Medium

Khabin M.R., Maryshev B.S.

Abstract

Concentration convection has a significant effect on the transport of impurity in porous media. Such transport processes can occur in a variety of geophysical systems. Concentration convection is often considered by analogy with thermogravitational convection in porous media without taking into account the fact that the impurity can be adsorbed on the skeleton of the porous medium. One of the approaches allowing to take this fact into account is the MIM (mobile-immobile media) approach. The paper studies the occurrence of concentration convection in an elongated rectangular region filled with porous medium in the field of gravity at a constant pressure and concentration drop. The Darcy-Boussinesq law is used as a filtration model. The problem is solved analytically by the method of many scales in the approximation of weak buoyancy force. Analytical expressions of concentration and pressure fields for the ground state (the case of no gravity) and the first order of smallness are obtained. The results of numerical calculation are compared with the analytical solution. It is shown that the convective-free case is unstable at any small concentration drop, and the resulting flow is a solitary convective cell. The position of the region of the largest concentration inhomogeneity depends on the ratio of the Peclet and Rayleigh-Darcy numbers.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):79-90

79-90

Computer science

Basic Algorithm for Automatic Spelling Correction of Russian Texts: Development, Evaluation and Prospects

Isaeva E.V., Safarbekov B.Z.

Abstract

Automatic spelling check and correction of texts in Russian is an urgent task in the field of natural language processing. Our research is aimed at developing, evaluating, and describing a computer programme for correcting spelling errors with high accuracy. The proposed method is based on line-by-line text processing using rules for spelling and capitalisation accuracy and a probabilistic model for proposing candidate words for error correction. Our algorithm operates at the level of individual words, which limits its ability to take context into account. The metrics used to test the quality of the model are Precision, Recall, and F1 Score. For ease of use and program refinement, we integrated automated error analysis and detailed report generation to identify the strengths and weaknesses of the algorithm. The detailed development description ensures the reproducibility of the algorithm and is in line with the Open-source ideology. The results showed that the algorithm has high Precision = 1.00, i.e., it corrects only those spelling errors that were specified in the reference text. However, the Recall = 0.84 emphasises the need for further refinement, including handling context-dependent errors and processing stable expressions. The F1 Score = 0.91 confirms the balanced performance of the algorithm and justifies its use as a basic model of text correction in Russian. The conclusions of the study emphasise the potential of the algorithm in the tasks of automatic correction of Russian-language text, and suggest prospective areas for improving the source code, such as the use of n-grams and language models. This work lays the foundation for further research in the field of automatic correction of Russian-language texts.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):91-108

91-108

Development of a Servo Control System With Parametric Adaptation for Rotary Test Stands

Lazarev V.A., Ivanov P.A.

Abstract

A solution to the problem of parametric adaptation of the servo control system of a rotary test stand to the current moment of inertia of the payload (test object) is proposed. The determination of the current moment of inertia of the payload is based on the implementation of feedback from the current sensor of the servo motor windings when reproducing motion with constant angular acceleration. The dynamic change in the moments of inertia of the payload is compensated by adaptive reconfiguration algorithms of this system, which leads to the preservation and maintenance of the set motion control quality parameters. The paper investigates the frequency characteristics of the control circuit for the rotation speed of the faceplate of a rotary test bench at various values of the moments of inertia of the payload mounted on the faceplate of the stand in order to determine the dependence of the contour characteristics on the value of the current moment of inertia of the payload.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):109-117

109-117

Artificial Intelligence Implementation for Customer Engagement in Social Networks: an Overview of Russian and Foreign Experience

Sokolov A.V., Shutkin A.S., Epifanova E.M., Popkova A.A., Beklaryan A.L., Barulina M.A.

Abstract

In modern realities, artificial intelligence plays a key role in marketing, in general, and certainly in engaging new users in social networks, in particular. Neural networks and other machine learning methods are widely used in various recommendation systems, but their application for attracting new customers is underdeveloped. As we know, upscaling of any business is directly related to increasing the number of new consumers, which determines the significance of studying the issue of neuromarketing. The purpose of this study is to conduct a comparative analysis of existing Russian and foreign services for the engagement of new clients and to identify effective methods used for these purposes.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):118-144

118-144

Methods and Tools for Virtual Semantic Integration of Data from Distributed Heterogeneous Sources

Chuprina S.I., Gimasheva K.V.

Abstract

The article is devoted to the natural language processing from distributed heterogeneous sources based on the principles of their virtual semantic integration. The main purpose of data integration is to provide the user with unified access to distributed data as a single virtual storage for performing natural language queries, regardless of the data storage format and location. The article discusses the main approaches focused on virtual semantic data integration, and describes the proposed concept of building an ontology driven instrumental environment based on Data Fabric technology, which allows to automate data processing via intermediate layer of ontologies in a unified form. The article describes NuCoBoShell that is the instrumental environment implementing the proposed approach. NuCoBoShell uses ontology-driven semantic integration mechanism to provide the answering, which, unlike traditional Internet answering services, provides the opportunity to obtain more pertinent answers automatically extracting the necessary information from not only heterogeneous web resources, but also text documents stored in accessible data warehouses and user's local computer without the need to copy data to a single repository.

Vestnik Permskogo universiteta. Matematika, mehanika, informatika. 2025;(1 (68)):145-159

145-159