Journal of the Belarusian State University. Mathematics and Informatics
type: channel
publisher: Belarusian State University
language: en
publication name: Journal of the Belarusian State University. Mathematics and Informatics
issn: 2520-6508
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items: Current trends in computer data analysis
items: Limit theorem on convergence to the local time of a Brownian excursion
items: Local information geometry for statistical analysis of high-order binary Markov chains
items: On well ve-covered and well ev‑covered graphs
items: Sequential statistical hypotheses testing for discrete random data with block structure
items: Reliability of two-level testing approach in the NIST SP 800-22 test suite
items: Complete convergence for partial weighted sums of negatively orthant dependent random variables
items: Mild solution of a mixed problem for a third-order semilinear hyperbolic equation with the wave operator
items: Generalised Newton ‒ Kantorovich method under the modified regular smoothness condition
items: Multi-model approach with vector search in operational management critical IT service
items: Estimation of the parameters of a second order Markov modulated Poisson process using change-point detection procedure
items: Detection of image objects for autonomous localisation of unmanned aerial vehicles and map formation of the surrounding space
items: Real-time gait recognition system based on lightweight dual-modal pose estimation
items: Asymptotic non-negative correlation of some statistics used in testing the quality of random number generators
items: Managerial decision analysis using small language models
items: Smoke and camera tampering detection system based on single-board computer for real-time fire monitoring
items: On Shemetkov’s problem of describing critical formations in the class of τ-closed σ-local formations
items: A finite-difference interpretation of a nonlocalproblem with a parameterised first-order differential equation
items: About isochrons of strong focus
items: RLD -YOLO: new method for object detection in unmanned aerial vehicle images using YOLOv11 neural network
items: Asymptotic analysis of the statistical estimators of Shannon entropy of binary s-tuples
items: Incorporating fast charging stations accessibility into an urban traffic assignment model based on the Frank – Wolfe algorithm
items: Distribution of finances taking into account statisticalinformation on the reliability of the items produced
items: About the Ricci flow on three-dimensional non-unimodular Lie groups with semisymmetric equiaffine connection
items: A generalisation of the Steiner – Lehmus theorem and critical values transcendence of its parameters
items: Solution of the hypersingular integro-differential equation on a curve located in the angular domain
items: Chebyshev spectral method for solving complete generalised Prandtl equation
items: Conformal Killing equation on a 2-symmetric six-dimensional indecomposable Lorentzian manifold with trivial Weyl tensor
items: Heterogeneous blocked all-pairs shortest paths algorithm for clustered weighted graphs
items: Methodology for information security threat analysis using digital twins

Current trends in computer data analysis
type: item
description: The current trends in computer data analysis presented at the conference «Computer data analysis and modelling: stochastics and data science» and the congress «Information systems and technologies» are described.
subject: Computer Data Analysis
  topic: section
subject: statistical data analysis
  topic: keywords
subject: robustness
  topic: keywords
subject: stochastics
  topic: keywords
subject: count data
  topic: keywords
subject: neural networks
  topic: keywords
subject: computer vision
  topic: keywords
creator: Yuriy S. Kharin
creator: Sergey V. Ablameyko
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-05-06
publication date: 2026-05-06
starting page: 6
ending page: 15

Limit theorem on convergence to the local time of a Brownian excursion
type: item
description: An integer random walk {Si, i ≥ 0} with zero drift and finite variance σ2 is investigated. For a random pro-cess that assigns, to a variable u > 0, the number of hits of the specified random walk into the state \[\left\lfloor {u\sigma \sqrt n } \right\rfloor \] up to time n and is considered under the condition that S1 > 0, …, Sn – 1 > 0, Sn ≤ 0, a functional limit theorem concerning convergence in distribution of the process to the local time of a Brownian excursion is proved.
subject: Probability Theory and Mathematical Statistics
  topic: section
subject: random walk
  topic: keywords
subject: conditional Brownian motion
  topic: keywords
subject: local time of conditional Brownian motions
  topic: keywords
subject: functional limit theorem
  topic: keywords
creator: Valeriy I. Afanasyev
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-05-21
publication date: 2026-05-21
starting page: 36
ending page: 52

Local information geometry for statistical analysis of high-order binary Markov chains
type: item
description: At the 14th International conference «Computer data analysis and modelling: stochastics and data analysis» the author presented some new results on asymptotic properties of statistics derived from purely random (uniformly distributed) binary sequence of increasing length. These results are obtained by methods of information geometry applied to manifolds of Markov probability distributions on the set of infinite binary sequences. In this paper the underlying information-geometric theory and the technics of proofs are describe in more detail. By few examples, it is shown how finding probabilistic and statistical properties comes down to geometric and combinatorial computations.
subject: Probability Theory and Mathematical Statistics
  topic: section
subject: information geometry
  topic: keywords
subject: tangent space
  topic: keywords
subject: asymptotic distribution
  topic: keywords
subject: binary sequence
  topic: keywords
subject: Markov manifold
  topic: keywords
creator: Valeriy A. Voloshko
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-06-04
publication date: 2026-06-04
starting page: 61
ending page: 74

On well ve-covered and well ev‑covered graphs
type: item
description: In this paper, the classes of well vе-covered graphs and well ev-covered graphs are investigated. A graph is called well vе-covered (well ev-covered, respectively) if all its minimal independent vе-dominating (minimal independent ev-dominating, respectively) sets have the same cardinality. It is shown that the problems of recognising the graph classes under consideration are co-NP-complete even for some restrictions of these classes. Characterisations, in terms of forbidden induced subgraphs, for the maximal hereditary subclasses of well vе-covered graphs and well ev-covered graphs are found. The computational complexity of problems related to minimum independent vе-dominating and minimum independent ev-dominating sets is established.
subject: Discrete Mathematics and Mathematical Cybernetics
  topic: section
subject: graph
  topic: keywords
subject: independent vе‑dominating set
  topic: keywords
subject: independent ev‑dominating set
  topic: keywords
subject: well vе‑covered graph
  topic: keywords
subject: well ev‑covered graph
  topic: keywords
subject: hereditary graph class
  topic: keywords
subject: NP-completeness
  topic: keywords
creator: Yury L. Orlovich
creator: Mikita A. Shutro
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-05-22
publication date: 2026-05-22
starting page: 94
ending page: 107

Sequential statistical hypotheses testing for discrete random data with block structure
type: item
description: An important mathematical problem of computer data analysis – the problem of sequential statistical testing of simple hypotheses on probability distributions of discrete random data with a block structure – is considered. Explicit expressions of the sequential tests statistics, transparent for interpretation and convenient for computer realisation, are derived. An approach to calculate the performance characteristics – error probabilities of the decisions and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules – is developed. Asymptotic expansions for the mentioned performance characteristics under distortion of the hypothetical probability model are constructed.
subject: Probability Theory and Mathematical Statistics
  topic: section
subject: discrete random data
  topic: keywords
subject: block structure
  topic: keywords
subject: simple hypotheses
  topic: keywords
subject: sequential statistical test
  topic: keywords
subject: error probability
  topic: keywords
subject: mathematical expectation of the random number of observations
  topic: keywords
subject: asymptotic expansions
  topic: keywords
creator: Alexey Yu. Kharin
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-04-30
publication date: 2026-04-30
starting page: 75
ending page: 80

Reliability of two-level testing approach in the NIST SP 800-22 test suite
type: item
description: The two-level approach for testing random number generators involving the well-known NIST SP 800-22 test suite, i. e. counting the sequences passing a basic test and checking the p-values distribution with a chi-square test, was considered. Such an approach may increase the reliability of the test. However, it is sensitive to the approximation error introduced by the computing of p-values. In this paper it is shown that for AES-based sequences two-level testing approach is not reliable too. Systematic error in the computing of the p-values is dependent only on the accuracy of approximation of the exact distribution of statistic by its theoretical counterpart and the number of bits in the analysed sequences n. For a reliable second-level test, this error should be smaller, or at least, approximately equal to $\frac{\sigma}{N} = \frac{1}{k}\sqrt {\frac{{k\; - \;1}}{N}}$, where $\sigma = \sqrt {\frac{1}{k}\left( {1\; - \;\frac{1}{k}} \right)N}$ is the standard deviation from the mean number of particles in a bin for equiprobable scheme of allocation N particles in k bins. Such heuristic assumptions and carried out experiments suggest that for example in the second-level test of the Frequency test of NIST SP 800-22 test suite with n = 220 the number of tested sequences N should not exceed 26 000. To completely eliminate the systematic error appearing in the Frequency test when determining the number of bin from k bins (disjoint subintervals of the interval [0, 1]), to which the p-value belongs the two-sided estimates of the quantiles of the binomial law are proposed.
subject: Computer Data Analysis
  topic: section
subject: random sequence
  topic: keywords
subject: pseudorandom sequence
  topic: keywords
subject: statistical testing
  topic: keywords
subject: reliability of statistical test
  topic: keywords
subject: binomial distribution
  topic: keywords
subject: two-sided estimate
  topic: keywords
creator: Aleksandr A. Serov
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-06-01
publication date: 2026-06-01
starting page: 22
ending page: 35

Complete convergence for partial weighted sums of negatively orthant dependent random variables
type: item
description: Negatively orthant dependence is regarded as a generalisation of independence for random variables, introduced by K. Joag-Dev and F. Proschan. Numerous researchers have investigated inequalities and laws of large numbers for such sequences of random variables. In particular, the concept of complete convergence, defined by P. L. Hsu and H. Robbins, has attracted significant attention. Complete convergence for partial weighted sums of negatively orthant dependent random variables dominated by a random variable X is established. Sufficient conditions for this type of convergence are provided under mild assumptions on the weights and the moments of random variable X.
subject: Probability Theory and Mathematical Statistics
  topic: section
subject: complete convergence
  topic: keywords
subject: negatively orthant dependence
  topic: keywords
subject: weighted sums
  topic: keywords
subject: limit theorems
  topic: keywords
subject: dependent random variables
  topic: keywords
creator: Tu Ton That
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-01-04
publication date: 2026-01-04
starting page: 38
ending page: 50

Mild solution of a mixed problem for a third-order semilinear hyperbolic equation with the wave operator
type: item
description: For a semilinear hyperbolic equation of the third-order given in the first quadrant we study a mild solution of a mixed problem in which the initial conditions are specified on the spatial half-line and the mixed conditions are specified on the time half-line. The operator in the equation is a composition of the wave operator and the transport operator. Mild solution is defined as a solution to coupled integral equations that are satisfied by a classical solution. It is shown that under some smoothness conditions on the initial and boundary data the problem under consideration admits the existence and uniqueness of the mild solution. It is established that the twice continuously differentiable mild solution is the limit of classical solutions to the problem under study.
subject: Differential Equations and Optimal Control
  topic: section
subject: non-linear hyperbolic equation of the third-order
  topic: keywords
subject: mixed problem
  topic: keywords
subject: generalised solution
  topic: keywords
subject: mild solution
  topic: keywords
creator: Viktor I. Korzyuk
creator: Jan V. Rudzko
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-01-04
publication date: 2026-01-04
starting page: 15
ending page: 28

Generalised Newton ‒ Kantorovich method under the modified regular smoothness condition
type: item
description: The article deals with the generalised Newton – Kantorovich method for solving non-linear operator equations of the form f(x) + g(x) = 0 in Banach spaces, where f is the operator satisfying the regular smoothness condition; g is the non-differentiable operator satisfying Lipschitz condition. The main convergence theorem is proved under the modified regular smoothness condition in which increments of the operator f derivative are majorised by the increments of a scalar function.
subject: Real, Complex and Functional Analysis
  topic: section
subject: generalised Newton – Kantorovich method
  topic: keywords
subject: regular smoothness condition
  topic: keywords
subject: non-linear operator equation
  topic: keywords
creator: Anastasija N. Tanyhina
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-01-04
publication date: 2026-01-04
starting page: 6
ending page: 14

Multi-model approach with vector search in operational management critical IT service
type: item
description: In the work are investigated current problems related to the task of operational management of critical IT services. To improve the quality of management, a new method is proposed, extending the dynamic local approximation approach. It implements linking vector representations of load patterns with trainable neural network models, which allows promptly constructing a predictor for a new pattern based on vector search for semantically close models in the library. Original principles of designing a control system are outlined, which for adaptation to new, uncertainty-related load patterns uses approximation of data obtained in real-time mode. The results of experiments confirmed the effectiveness of the proposed approach and showed that when processing irregular and complex loads, hybrid proactive algorithms in a number of indicators are more effective than reactive ones.
subject: Data Science
  topic: section
subject: decision making
  topic: keywords
subject: proactive control
  topic: keywords
subject: external load uncertainty
  topic: keywords
subject: neural network
  topic: keywords
subject: multi-model system
  topic: keywords
subject: model library
  topic: keywords
subject: vector search
  topic: keywords
creator: Viktor V. Krasnoproshin
creator: Aleksandr A. Starovoitov
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-04-27
publication date: 2026-04-27
starting page: 140
ending page: 155

Estimation of the parameters of a second order Markov modulated Poisson process using change-point detection procedure
type: item
description: The problem of estimating the parameters of a second order Markov modulated Poisson process is considered. A new two-staged algorithm for their estimation is developed. In the first stage initial estimates of the intensity parameters are constructed using the method of moments and maximum likelihood method. In the second stage these estimates are used in the cumulative sums change-point detection algorithm to determine time intervals, during which the process intensity is constant; after that estimates of all parameters are constructed. The developed algorithm is compared with a well-known algorithm for finding maximum likelihood estimates (the EM algorithm). The proposed method is non-iterative, ensuring relatively low computational complexity.
subject: Probability Theory and Mathematical Statistics
  topic: section
subject: Markov modulated Poisson process
  topic: keywords
subject: MMPP
  topic: keywords
subject: cumulative sums
  topic: keywords
subject: method of moments
  topic: keywords
subject: maximum likelihood method
  topic: keywords
creator: Sergey E. Vorobeychikov
creator: Yulia B. Burkatovskaya
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-05-11
publication date: 2026-05-11
starting page: 53
ending page: 60

Detection of image objects for autonomous localisation of unmanned aerial vehicles and map formation of the surrounding space
type: item
description: The problem of autonomous localisation of an unmanned aerial vehicle and construction of a map of its environment is considered. The low stability of keypoint detectors to changing weather and time conditions of image formation in the surrounding space is demonstrated compared to the stability of line detectors. To improve the stability of unmanned aerial vehicles localisation it is proposed to use image regions (segments) with uniform brightness as key identification objects. An algorithm for segmentation based on local minima of the brightness gradient of halftone images obtained from the original colour images of the unmanned aerial vehicle’s surrounding space has been developed. To equalise the growth rates of local minima a wave segmentation algorithm with automatic stopping is proposed. This algorithm is based on identifying new initial and additional growth points of regions using a monotonically varying threshold and taking into account the rate of change of the brightness gradient along the region growth trajectory in the stopping criterion. It is shown that the proposed algorithms provide more stable localisation of areas, when changing weather and time conditions for image formation in comparison with known algorithms for extracting lines and key points.
subject: Data Science
  topic: section
subject: simultaneous localisation and mapping
  topic: keywords
subject: SLAM
  topic: keywords
subject: wave segmentation of images
  topic: keywords
subject: region growing
  topic: keywords
subject: image object identification
  topic: keywords
subject: point detectors
  topic: keywords
subject: line detectors
  topic: keywords
creator: Viktor Yu. Tsviatkou
creator: Viyaleta V. Rabtsevich
creator: Ma Jun
creator: Mikhail I. Zorko
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-05-08
publication date: 2026-05-08
starting page: 156
ending page: 162

Real-time gait recognition system based on lightweight dual-modal pose estimation
type: item
description: A lightweight approach for joint 2D and 3D gait analysis is proposed. A dual-modal gait recognition system is adopted, achieving high-precision real-time analysis through a 2D and 3D collaborative estimation architecture. The system employs MediaPipe for real-time 2D keypoint detection and gait metric extraction. An improved lightweight architecture MTSA-former with 2.5 mln parameters is used for 3D pose estimation. This model utilises cascaded processing incorporating temporal and spatial modules, along with an adjacency matrix based on skeletal topological structure to model physical constraints between joints. A local-global hybrid spatial modelling strategy fusing graph convolutional networks is implemented to achieve efficient 3D pose estimation, attaining high performance while maintaining lightweight characteristics. This approach ensures accurate and efficient 3D pose reconstruction in real time.
subject: Data Science
  topic: section
subject: gait analysis
  topic: keywords
subject: 3D pose estimation
  topic: keywords
subject: lightweight model
  topic: keywords
subject: dual-modal recognition
  topic: keywords
creator: Din Aodi
creator: Ye Shiping
creator: Alexander M. Nedzved
creator: Victor S. Anosov
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-05-19
publication date: 2026-05-19
starting page: 130
ending page: 139

Asymptotic non-negative correlation of some statistics used in testing the quality of random number generators
type: item
description: The problem of testing the hypothesis, stating that the tested sequence consists of independent random variables with a given polynomial distribution, is considered. To solve this problem four types of statistics that are generalisations of statistics of tests of the NIST STS, TestU01 and other packages are used. It is proved that many of these statistics, including 10 statistics of the NIST STS, are asymptotically non-negatively correlated, and some of them, in particular some of the 10 statistics of the NIST STS, are asymptotically uncorrelated.
subject: Computer Data Analysis
  topic: section
subject: NIST STS
  topic: keywords
subject: asymptotically non-negatively correlated statistics
  topic: keywords
subject: asymptotically uncorrelated statistics
  topic: keywords
subject: joint distribution of statistics
  topic: keywords
subject: limit distributions
  topic: keywords
subject: TestU01 package
  topic: keywords
subject: random number generators
  topic: keywords
creator: Maxim P. Savelov
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-05-19
publication date: 2026-05-19
starting page: 16
ending page: 21

Managerial decision analysis using small language models
type: item
description: This paper proposes a method for the automatic assessment of managerial decision quality based on free-form textual responses to Russian-language business cases using a fine-tuned DistilBERT model. The novelty of the study lies in a context-dependent classification algorithm with concatenated input (case description + response) and a post-processing technique that explicitly links predictions to specific managerial competencies or red flags. For the first time, high-accuracy evaluation of managerial decisions in Russian (accuracy = 0.986 8, F1-score = 0.987 0) with interpretable competency-based feedback has been achieved, unlike prior work focused on general text or sentiment analysis. The approach enables the development of automated systems for managerial assessment, personnel selection and personalised leadership development in human resources and corporate training.
subject: Data Science
  topic: section
subject: small language model
  topic: keywords
subject: DistilBERT
  topic: keywords
subject: management decision analysis
  topic: keywords
subject: neural network
  topic: keywords
subject: knowledge distillation
  topic: keywords
creator: Ksenia V. Andrenko
creator: Aliaksandr A. Kroshchanka
creator: Vladimir A. Golovko
creator: Yury B. Krapivin
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-05-21
publication date: 2026-05-21
starting page: 121
ending page: 129

Smoke and camera tampering detection system based on single-board computer for real-time fire monitoring
type: item
description: An edge-based architecture for a video surveillance system with integrated smoke and camera tampering detection is presented. The system consists of parallel-executing modules responsible for configuration management and video data processing, including receive, analysis, and transmission. Smoke detection is performed using computer vision algorithms based on the sequential extraction of discriminative visual features: motion direction, colour characteristics, and impact on background visibility. Camera tampering is detected by evaluating scene sharpness through an edge-detection filter. High-resolution video processing is performed on a single-board computer, with computational tasks distributed across the cores of a multi-core central processor to optimise performance. The proposed approach significantly reduces the load on the central node of the surveillance infrastructure, which is a critical advantage for scalable deployments involving numerous cameras. Experimental results demonstrate high detection accuracy for smoke and tampering, as well as stable real-time operation of the implemented architecture.
subject: Data Science
  topic: section
subject: smoke detection
  topic: keywords
subject: computer vision
  topic: keywords
subject: video surveillance systems
  topic: keywords
subject: single-board computer
  topic: keywords
creator: Yahor R. Adamovskiy
creator: Rykhard P. Bohush
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-06-04
publication date: 2026-06-04
starting page: 108
ending page: 120

On Shemetkov’s problem of describing critical formations in the class of τ-closed σ-local formations
type: item
description: The critical τ-closed σ-local formations of finite groups are studied, where σ is some partition of the set of all primes <span lang="RU" style="font-size: 12.0pt; font-family: 'Euclid Math Two'; mso-ascii-font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-ansi-language: RU; mso-fareast-language: RU; mso-bidi-language: AR-SA; mso-char-type: symbol; mso-symbol-font-family: 'Euclid Math Two'; mso-no-proof: yes;">P, τ is an arbitrary subgroup functor. A description of minimal τ-closed σ-local non-H-formations is obtained for an arbitrary σ-local formation of classical type, i. e. a σ-local formation that has a σ-local definition all of whose non-Abelian values are σ-local formations. Thus, the problem of describing critical formations in the class of τ-closed σ-local formations proposed by L. A. Shemetkov (1980) is solved.
subject: Mathematical Logic, Algebra and Number Theory
  topic: section
subject: finite group
  topic: keywords
subject: subgroup functor
  topic: keywords
subject: τ-closed formation
  topic: keywords
subject: formation σ-function
  topic: keywords
subject: σ-local formation
  topic: keywords
subject: critical σ-local formation
  topic: keywords
subject: formation of classical type
  topic: keywords
creator: Valentina V. Skrundz
creator: Inna N. Safonova
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-06-01
publication date: 2026-06-01
starting page: 163
ending page: 178

A finite-difference interpretation of a nonlocalproblem with a parameterised first-order differential equation
type: item
description: In this work the nonlocal initial value problem and corresponding finite-difference interpretation for the first-order linear ordinary differential equation with a parameter at the derivative is studied. The nonlocal initial value condition is given by terms of multipoint linear combination. The difference scheme with exponential fit is proposed on a uniform mesh. The article identifies the requirements on the location of nonlocal data carriers in the multipoint condition, on the values of corresponding coefficients and on the parameter variation interval, under which a uniform on parameter stability of classical and difference solutions, as well as a uniform on parameter convergence of difference solution to classical solution are proved. The identification and proof of such conditions, which provide a uniform on parameter approximation of the nonlocal initial value problem classical solution by the solution of exponentially fitted difference scheme, define the novelty of the current work.
subject: Computational Mathematics
  topic: section
subject: nonlocal initial value problem
  topic: keywords
subject: uniform stability
  topic: keywords
subject: uniform convergence
  topic: keywords
subject: multipoint condition
  topic: keywords
subject: exponentially fitted parameter
  topic: keywords
creator: Dovlet M. Dovletov
rights: Copyright (c) 2025 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-13
publication date: 2025-10-13
starting page: 89
ending page: 104
doi: 10.33581/2520-6508-2025-2-89-104

About isochrons of strong focus
type: item
description: The article analyses the methods for studying the isochronism of autonomous systems on a plane for different types of singular points: centre, weak focus and strong focus. The difficulty of determining a weak isochronous focus is explained. Examples of systems in the Poincaré – Dulac normal form, which show that the requirement to be isochronous imposes weak restrictions on a system with a weak focus, are given. A theorem on the form of a normalising change of a strongly isochronous strong focus is proved. Isochrones of a strongly isochronous strong focus of a system with quadratic nonlinearities are found. Phase portraits of the obtained isochronous foci and their isochrones are constructed.
subject: Differential Equations and Optimal Control
  topic: section
subject: centre
  topic: keywords
subject: weak focus
  topic: keywords
subject: strong focus
  topic: keywords
subject: isochronism
  topic: keywords
subject: isochrones
  topic: keywords
subject: Poincaré – Dulac normal form
  topic: keywords
subject: system with quadratic nonlinearities
  topic: keywords
creator: Alexander E. Rudenok
creator: Mikhail N. Vasilevich
rights: Copyright (c) 2025 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-13
publication date: 2025-10-13
starting page: 16
ending page: 29
doi: 10.33581/2520-6508-2025-2-16-29

RLD -YOLO: new method for object detection in unmanned aerial vehicle images using YOLOv11 neural network
type: item
description: Unmanned aerial vehicle images are widely used now in many applications. However, these images face many challenges such as dense distribution of small objects, variable object scales, and inconspicuous edge features, leading to missed and false object detection. To address these issues, this paper proposes a lightweight enhanced solution based on the improved YOLOv11n model RLD-YOLO. The algorithm combines RepConv structural reparameterisation technology, retaining multi-branch feature expression capabilities during training and automatically converting to an efficient single-branch structure during inference. It designs the LKAConv large kernel attention module to enhance the feature capture ability of small targets through 7 × 7 depthwise separable convolution and spatial attention mechanism. It introduces the DASI dynamic adaptive fusion module to optimise multi-scale feature interaction through learnable weight allocation. Experimental results show that the improved RLD-YOLO object detection algorithm, which integrates LKAConv, RepConv, and DASI, increases mAP50 and mAP50-95 by 2.02 and 1.17 % respectively on the VisDrone2019-DET dataset. The post-processing speed is optimised by 9.09 %. Although the pre-processing time increases due to feature enhancement operations, the critical inference stage still maintains a real-time performance of 1.7 ms/frame. The RLD-YOLO model, fused with LKAConv, RepConv, and DASI, is very suitable for the task of small object target detection in unmanned aerial vehicle images.
subject: Theoretical Foundations of Computer Science
  topic: section
subject: small object detection
  topic: keywords
subject: YOLOv11
  topic: keywords
subject: UAV images
  topic: keywords
subject: LKAConv
  topic: keywords
creator: Xianyi Wu
creator: Sergey V. Ablameyko
rights: Copyright (c) 2025 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2025-11-11
publication date: 2025-11-11
starting page: 105
ending page: 117
doi: 10.33581/2520-6508-2025-2-105-117

Asymptotic analysis of the statistical estimators of Shannon entropy of binary s-tuples
type: item
description: The asymptotic probability distribution of the statistical estimate of Shannon entropy of s-tuples H(s) and the asymptotic joint probability distribution of the statistical estimates of Shannon entropy of s- and (s+1)-tuples H(s), H(s+1) for a uniformly distributed random binary sequence with increasing length are found. It is proved that as the value of s increase, the correlation coefficient of the statistical estimates of Shannon entropy of s- and (s+1)-tuples H(s), H(s+1) tends to zero. The theoretical results are illustrated by computer experiments.
subject: Probability Theory and Mathematical Statistics
  topic: section
subject: энтропия Шеннона
  topic: keywords
subject: двоичная последовательность
  topic: keywords
subject: статистическая оценка
  topic: keywords
subject: ковариация
  topic: keywords
subject: коэффициент корреляции
  topic: keywords
creator: Uladzimir Yu. Palukha
creator: Yuriy S. Kharin
rights: Copyright (c) 2025 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-13
publication date: 2025-10-13
starting page: 62
ending page: 74
doi: 10.33581/2520-6508-2025-2-62-74

Incorporating fast charging stations accessibility into an urban traffic assignment model based on the Frank – Wolfe algorithm
type: item
description: The growing use of electric vehicles necessitates the adaptation of transport models to account for the specifics of their operation. The aim of this work is to modify the classic traffic assignment model based on the Frank – Wolfe algorithm, widely used in transportation planning, to accurately reflect electric vehicle charging processes in urban environments. The novelty of the research lies in the development of an approach that, unlike existing approaches, comprehensively addresses three key features: the requirement for an electric vehicle needing to charge to route through exactly one charging station; the possibility of routing along paths with cycles to access charging stations and subsequently reach the destination, considering urban road network constraints; the behavioural aspect of a user’s decision to forgo charging if the total time costs (including travel to the station and queuing) exceed a certain threshold. The paper also proposes a time-cost function that accounts for the specifics of the charging process, including queues and the number of charging spots. The results demonstrate that the classic traffic assignment model based on the Frank – Wolfe algorithm can indeed be modified to incorporate these features. It is noted that the proposed model may exhibit multiple equilibrium flow distributions, dependent on initial conditions. The practical significance of the work lies in its potential for more accurate modelling of traffic flows and the load on urban charging infrastructure.
subject: Discrete Mathematics and Mathematical Cybernetics
  topic: section
subject: electric vehicle
  topic: keywords
subject: fast charging station
  topic: keywords
subject: traffic assignment
  topic: keywords
subject: Wardrop equilibrium
  topic: keywords
subject: Frank – Wolfe algorithm
  topic: keywords
creator: Du Sizhuo
creator: Denis S. Sarazhinsky
creator: Denis V. Kapski
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-06-03
publication date: 2026-06-03
starting page: 81
ending page: 93

Distribution of finances taking into account statisticalinformation on the reliability of the items produced
type: item
description: This paper examines the problem of distribution of finances among project contractors taking into account statistical information on the reliability of the items produced. Mathematical programming formulations necessary for constructing an optimal strategy of distribution are presented. To account for the influence of the spent amount of money on the number of component failures, it is proposed to build a linear or generalised linear regression, the coefficients of which are used in mathematical programming formulations.
subject: Short Communications
  topic: section
subject: distribution of finances
  topic: keywords
subject: mathematical programming
  topic: keywords
subject: standard error of a random variable
  topic: keywords
subject: mathematical statistics
  topic: keywords
creator: Maksim S. Barketau
rights: Copyright (c) 2025 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-10
publication date: 2025-10-10
starting page: 118
ending page: 125
doi: 10.33581/2520-6508-2025-2-118-125

About the Ricci flow on three-dimensional non-unimodular Lie groups with semisymmetric equiaffine connection
type: item
description: The Ricci flow on three-dimensional non-unimodular Lie groups with semisymmetric equiaffine connection is studied. The Ricci flow equation in the coordinate system proposed by J. Milnor is reduced to systems of algebraic and differential equations. A solution to the Ricci flow equation in the class of left-invariant Milnor metrics is found. The results of works by K. Onda, D. Knopf and K. McLeod concerning the Ricci flow on three-dimensional Lie groups in the case of Levi-Civita connectivity are generalised.
subject: Geometry and Topology
  topic: section
subject: Ricci flow
  topic: keywords
subject: three-dimensional non-unimodular Lie groups
  topic: keywords
subject: semisymmetric equiaffine connections
  topic: keywords
creator: Danila S. Grigoryev
creator: Dmitrii N. Oskorbin
creator: Eugene D. Rodionov
rights: Copyright (c) 2025 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-10
publication date: 2025-10-10
starting page: 30
ending page: 41
doi: 10.33581/2520-6508-2025-2-30-41

A generalisation of the Steiner – Lehmus theorem and critical values transcendence of its parameters
type: item
description: The internal n-line of a triangle is a segment from the vertex to the opposite side dividing this side into segments proportionally to the nth powers of the adjacent sides. An analogue of the Steiner – Lehmus theorem for the internal n-lines of a triangle is considered. All values n ∈ R for which the mentioned analogue of the Steiner – Lehmus theorem holds are found. Also all values n ∈ R for which there exists a non-equilateral triangle with three equal internal n-lines are determined. The transcendence of positive critical values of n of the generalised Steiner – Lehmus theorem is proved.
subject: Mathematical Logic, Algebra and Number Theory
  topic: section
subject: internal n-line of a triangle
  topic: keywords
subject: transcendental number
  topic: keywords
subject: algebraic number field
  topic: keywords
subject: surface
  topic: keywords
creator: Maksim M. Vaskouski
creator: Maksim A. Firsau
creator: Palina D. Babayeva
rights: Copyright (c) 2025 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2025-11-11
publication date: 2025-11-11
starting page: 42
ending page: 61
doi: 10.33581/2520-6508-2025-2-42-61

Solution of the hypersingular integro-differential equation on a curve located in the angular domain
type: item
description: We solve a new linear integro-differential equation on a closed curve on the complex plane. Some restrictions are placed on the curve location and on coefficients of the equation. The equation contains hypersingular and regular integrals. Initially, it is reduced to the Riemann – Carleman boundary value problem for analytic functions, which has a partial form and an unconventional formulation. Next, two linear differential equations with constant coefficients in domains of the complex plane with additional conditions on the solution are solved. All solvability conditions of the original equation are stated explicitly. When they are performed, the solution to the original equation is given explicitly.
subject: Real, Complex and Functional Analysis
  topic: section
subject: integro-differential equation
  topic: keywords
subject: hypersingular integral
  topic: keywords
subject: generalised Sokhotsky formulas
  topic: keywords
subject: Riemann – Carleman boundary value problem
  topic: keywords
subject: linear differential equation
  topic: keywords
creator: Andrei P. Shilin
rights: Copyright (c) 2025 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2025-11-19
publication date: 2025-11-19
starting page: 6
ending page: 15
doi: 10.33581/2520-6508-2025-2-6-15

Chebyshev spectral method for solving complete generalised Prandtl equation
type: item
description: This article is devoted to the problem of constructing computational schemes for solving Prandtl integro-differential equations that arise in many problems in mechanics. An approximate numerical method for solving singular integro-differential equations of the generalised Prandtl equation type has been developed. The proposed approximate computational schemes are based on representing the solution of the equation as an expansion over an orthogonal basis of Chebyshev polynomials. The use of known spectral relations has made it possible to obtain an analytical expression for the singular component of the equation. As a consequence, the developed method demonstrates excellent accuracy and exponential rate of convergence of the approximate solution in relation to the degree of interpolation polynomials. The computational qualities of this method are demonstrated using a test example. In particular, it is shown that a discrete model based on the representation of the solution as a decomposition by Chebyshev polynomials leads to a well-conditioned system of linear algebraic equations for the decomposition coefficients, and the convergence rate of the approximate solution error can reach a linear speed in relation to the degree of the interpolation polynomial.
subject: Computational Mathematics
  topic: section
subject: approximate numerical algorithm
  topic: keywords
subject: singular equation
  topic: keywords
subject: integro-differential equation
  topic: keywords
subject: orthogonal basis of Chebyshev polynomials
  topic: keywords
subject: Chebyshev spectral method
  topic: keywords
subject: generalised Prandtl equation
  topic: keywords
creator: Galina A. Rasolko
creator: Vasily M. Volkov
creator: Marina V. Ignatenko
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-01-04
publication date: 2026-01-04
starting page: 51
ending page: 61

Conformal Killing equation on a 2-symmetric six-dimensional indecomposable Lorentzian manifold with trivial Weyl tensor
type: item
description: In this paper, we study the conformal analogue of the Killing equation on 2-symmetric six-dimensional indecomposable Lorentzian manifolds, and also study the properties of the conformal factor of this equation. For the case of conformally flat metrics, new non-trivial examples of conformal Killing vector fields with a variable conformal factor are constructed.
subject: Geometry and Topology
  topic: section
subject: conformal Killing vector field
  topic: keywords
subject: k-symmetric space
  topic: keywords
subject: Lorentzian manifold
  topic: keywords
subject: Weyl tensor
  topic: keywords
creator: Maxim E. Gnedko
creator: Olesya P. Khromova
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-01-04
publication date: 2026-01-04
starting page: 29
ending page: 37

Heterogeneous blocked all-pairs shortest paths algorithm for clustered weighted graphs
type: item
description: New heterogeneous blocked algorithm of finding all-pairs shortest paths in a large directed weighted simple graph consisting of weakly connected dense clusters (subgraphs) of different sizes is proposed. The algorithm considers and actively exploits the input and output bridge-vertices and edges of each cluster to speed up computation and localise memory accesses. It divides all blocks of the cost adjacent matrix into four types (square diagonal, rectangular vertical cross, rectangular horizontal cross and rectangular peripheral) and uses a separate computation procedure for each type, considering the design features of the block itself and the way it is computed through other blocks. A theoretical justification of the advantages of the proposed algorithms, which reduce the execution time when searching for the shortest paths, is given. The validity of the formulated statements is also confirmed by the results of computational experiments. We have developed single-threaded implementations and multi-threaded OpenMP implementations of the proposed heterogeneous algorithm and two known homogeneous blocked algorithms of finding shortest paths. Computational experiments on multicore processors were performed on directed weighted random sparse graphs decomposed into weakly connected dense clusters of different sizes. The results are described for four clustered graphs, two of which have 4800 vertices (20 and 41 clusters, respectively) and two of which have 9600 vertices (40 and 80 clusters, respectively). On the MacBook M1 Max computer in the case of single-threaded implementations proposed heterogeneous blocked algorithm for clustered graph with bridge-vertices outperformed the known homogeneous blocked algorithm for the same graphs by a factor of 1.62–1.94; in the case of multi-threaded OpenMP implementations the speedup was 1.87–1.97. On a server with Intel Xeon E5-2620v4 processors heterogeneous algorithm outperformed the known homogeneous algorithm by a factor of 1.5…
subject: Theoretical Foundations of Computer Science
  topic: section
subject: clustered weighted large graph
  topic: keywords
subject: all-pairs shortest paths
  topic: keywords
subject: blocked algorithm
  topic: keywords
subject: heterogeneous computations
  topic: keywords
subject: speedup
  topic: keywords
creator: Anatoly A. Prihozhy
creator: Oleg N. Karasik
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-01-04
publication date: 2026-01-04
starting page: 62
ending page: 75

Methodology for information security threat analysis using digital twins
type: item
description: This paper presents a methodology for analysing information security threats in cyber-physical systems based on digital twins. The proposed approach involves formalising the system and threat space through a multi-layered structure, including technical, process, functional, organisational and sectoral layers. Next, dynamic threat modelling is conducted in a secure virtual environment of the digital twin, enabling the reproduction of attack scenarios and generation of synthetic data to train threat indicator detection algorithms. To identify anomalies, frequency analysis, machine learning and clustering methods are applied, ensuring adaptive and accurate detection of both known and previously unknown attacks. The methodology is verified using a smart grid example, demonstrating the effectiveness of training and testing algorithms on synthetic data that reflect normal and emergency operating modes. The results show the potential for creating self-adjusting information security systems with a high degree of adaptability and threat detection accuracy. The presented methodology provides iterative feedback between stages, enhancing the quality of threat modelling and detection.
subject: Theoretical Foundations of Computer Science
  topic: section
subject: cyber-physical system
  topic: keywords
subject: digital twin
  topic: keywords
subject: information security
  topic: keywords
subject: threat modelling
  topic: keywords
subject: anomaly detection
  topic: keywords
subject: machine learning
  topic: keywords
subject: synthetic data
  topic: keywords
subject: adaptive system
  topic: keywords
subject: smart grid
  topic: keywords
subject: threat analysis
  topic: keywords
creator: Igor V. Kotenko
creator: Igor B. Saenko
creator: Evgenii S. Mityakov
creator: Victar P. Kochyn
rights: Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics https://creativecommons.org/licenses/by-nc/4.0
date: 2026-01-04
publication date: 2026-01-04
starting page: 76
ending page: 91