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  5. VOL 40, NO 2 (2018)
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  7. 2025 год
  8. 47-4

Electronic modeling

Vol 47, No 4 (2025)

CONTENTS

Mathematical modeling and Computation Methods

 

S.D. Vynnychuk
Organization of the Structure of Heterogeneous Input Data in Modeling Hydraulic Processes in Compressible and Incompressible Fluid Networks
3-20
 

A.I. Krasilnikov
Class of Two-component Mixtures of Non-gaussian Symmetric Distributions with Zero Cumulant Coefficients
21-38
 

G. Dubynskyi, V. Zubok
Topological Approach to Supply Chain Resilience Analysis
39-48

Informational Technologics

 

N. Zayka, O. Verkhovets, M. Komarov, O. Saveliev
Development and Application of an Obfuscator for Cybersecurity of Critical Infrastructure Objects
49-56

Computational Processes and Systems

 

M.S. Yaroshynsky, I.V. Puchko
Ways to Solve the Problem of Asynchronous Changes of the Application Programming Interface in Microservice Architecture
57-72

Parallel Computing

 

S.Ye. Saukh, T.V. Puchko
A Parallel Method for Optimizing the Structure of Generating Capacities Using Metaheuristic Algorithms and the Scip Solver
73-89
  M. Sorokin, M. Zheleznyak, L. Anishchenko, B. Sverdlov
Gpu-Based Parallel Computations of the Hydrological Regime in the Kiliya Delta of the Danube River
90-112

Application of Modeling Methods and Facilities

 

V.V. Shkarupylo, M.V. Lakhno
A Model for Analyzing Digital Traces in Secure Information and Educational Systems
113-125

Organization of the Structure of Heterogeneous Input Data in Modeling Hydraulic Processes in Compressible and Incompressible Fluid Networks

S.D. Vynnychuk

Èlektron. model. 2025, 47(4):03-20

https://doi.org/10.15407/emodel.47.04.003

ABSTRACT

Ensuring high accuracy of modeling hydraulic processes in compressible and incompressible fluid networks is assumed to be possible if process models are used in the structural elements that form the network. A wide variety of such elements characterizes hydraulic networks and, accordingly, process models within them, where each model is characterized by its parameters. Therefore, model-oriented input data may be different in meaning and volume, i.e., heterogeneous. For such heterogeneous information, it is proposed to structure it based on arrays of data on elements of branches and nodes based on the use of a fixed number of numbers equal to three, where, in the case of several parameters exceeding 3, references are made to the corresponding data sets presented in separate files or tables. It has been determined that this method allows for the modeling of hydraulic processes in the class of hydraulic networks, for which the program code implements the capabilities of modeling hydraulic processes in elements of branches, nodes, and processing of structural and operational information. In this context, it is universal, where, when using elements for which additional data is required to be obtained in the corresponding arrays (tables), they can be supplemented without changing the code of the software application, and the capabilities of the software can be expanded by adding new types of elements, which requires the inclusion of mathematical models of processes in them in the program code.

KEYWORDS

hydraulic network, heterogeneous data, structural, structural experimental, mode input data.

REFERENCES

  1. Yevdokimov A.G., Tevyashev A.D. & Dubrovskiy V.V. (1990), Modelling and optimization of load flow in engineering networks, 2nd ed., revised. and ext., Stroyizdat, Moscow, Russia. 368 р.
  2. Merenkov A.P. and Khasilev V.Ya. (1985). Theory of hydraulic circuits. Nauka, Moscow, Russia. 280 p.
  3. Nekrasov B.B. (1967), Hydraulics and its application on aircraft. Mashinostroenie, Moscow, Russia. 352 p.
  4. Abramovich G.N. (1969). Applied gas dynamics. 3rd ed., revised. Nauka, Moscow, Russia. 824 р.
  5. Idelchik I.E. (1975) Hydraulic resistances. Mashinostroenie, Moscow, Russia. 559 p.
  6. Krumina N.N., Ulyanov I.E. et al. (1979). Design of air ducts for aircraft power plants. Mashinostroenie, Moscow, Russia. 96 p.
  7. Vynnychuk S.D. Modeling of hydraulic network tees. / Collection of Scientific Works of the IPME NAS of Ukraine. 2001, issue 14. Kyiv: IPME NAS of Ukraine. P.73-80
  8. Vynnychuk S.D., Kozyuk O.I. All-mode model of hydraulic processes in ejectors // Modeling and information technologies/ Collection of Scientific Works of the IPME NAS of Ukraine. 2019, issue 89. Pp.40-44 http://doi.org/10.5281/zenodo.3860728
  9. Handbook of heat exchangers: in 2 volumes. T.1 / Trans. with English, edited by B.S. Pe­tukhova, V.K. Shykova. (1987) Energoatomizdat, Moscow, Russia. 560 p. with ill.
  10. Handbook of heat exchangers: in 2 volumes. Vol. 2 / Translated from English, edited by O.G.Martynenko et al. (1987). Energoatomizdat, Moscow, Russia. 352 p. with ill.
  11. Vynnychuk S.D. Modeling of processes in a heat exchanger with a small amount of expe­rimental data. /Collection of scientific works of IPME NAS of Ukraine. 2001, issue 13. pp. 86-91

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Class of Two-component Mixtures of Non-gaussian Symmetric Distributions with Zero Cumulant Coefficients

A.I. Krasilnikov

Èlektron. model. 2025, 47(4):21-38

https://doi.org/10.15407/emodel.47.04.021

ABSTRACT

Based on a family of two-component mixtures of distributions, a class К of symmetric non-Gaussian distributions with zero cumulant coefficients s of order is defined. Formulas for finding the values of the mixture’s weight coefficient, at which the coefficients 4, 6 are equal to zero, are obtained. The dependence of the cumulant coefficient on the mixture’s weight coefficient 8 is researched, as a result of which the conditions, under which the mixtu­re’s coefficient 8 is equal to zero, is determined. Formulas for finding of the mixture’s weight coefficient values, at which the coefficient 8 = 0, are obtained. Examples of symmetric non-Gaussian distributions with zero cumulant coefficients 4, 6, 8 are considered. A methodology for computer modeling of non-Gaussian random variables of the class К is given.

KEYWORDS

non-Gaussian symmetric distributions, two-component mixtures of distributions, cumulant coefficients, kurtosis coefficient.

REFERENCES

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    https://doi.org/10.1027/1614-2241/a000057
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  8. Müller, R.A.J., von Benda-Beckmann, A.M., Halvorsen, M.B. & Ainslie, M.A. (2020). Application of kurtosis to underwater sound. J. Acoust. Soc. Am., 148(2). 780-792. 
    https://doi.org/10.1121/10.0001631
  9. Zapevalov, A.S. & Garmashov, A.V. (2021). Skewness and Kurtosis of the Surface Wave in the Coastal Zone of the Black Sea. Morskoi gidrofizicheskii zhurnal, 37(4). 447-459. 10.22449/0233-7584-2021-4-447-459 (in Russian).
    https://doi.org/10.22449/0233-7584-2021-4-447-459
  10. Wang,H. & Chen, P. (2009). Fault Diagnosis Method Based on Kurtosis Wave and Information Divergence for Rolling Element Bearings. WSEAS Transactions on Systems, 8(10). 1155-1165.
  11. Mohammed, T.S., Rasheed, M., Al-Ani, M., Al-Shayea, Q. & Alnaimi, F. (2020). Fault Diagnosis of Rotating Machine Based on Audio Signal Recognition System: An Efficient Approach. International Journal of Simulation: Systems, Science & Technology, 21(1). 8.1-8.8. 10.5013/IJSSST.a.21.01.08
    https://doi.org/10.5013/IJSSST.a.21.01.08
  12. Krasilnikov, A.I., Beregun, V.S. & Polobyuk, T.A. (2019). Kumuliantnyie metody v zadachakh shumovoi diagnostiki teploenergeticheskogo oborudovaniia [Cumulant methods in the problems of noise diagnostics of heat-and-power equipment]. A.I. Krasilnikov [Ed.]. Kyiv: Osvita Ukrainy. (in Russian).
  13. Kunchenko, Yu.P. (2001).Polinomialnyie otsenki parametrov blizkikh k gaussovskim sluchainykh velichin. Ch. 1. Stokhasticheskiie polinomy, ikh svoistva i primeneniia dlia nakhozhdeniia otsenok parametrov [Polynomial Parameter Estimations of Close to Gaussian Random variables. Part 1. Stochastic Polynomials, Their Properties and Applications for Finding Parameter Estimations]. Cherkassy: ChITI. (in Russian).
  14. Hildebrand, D.K. (1971). Kurtosis measures bimodality? Amer. statist., 25(1). 42-43.
    https://doi.org/10.1080/00031305.1971.10477241
  15. Joiner, B.L. & Rosenblatt, J.R. (1971). Some properties of the range in samples from Tu­key’s symmetric lambda distributions. Jour. Amer. Statist. Assoc., 66(334). 394-399.
    https://doi.org/10.1080/01621459.1971.10482275
  16. Kale, B.K. & Sebastian, G. (1996). On a Class of Symmetric Nonnormal Distributions with a Kurtosis of Three. In H.N. Nagaraja et al. (eds.) Statistical Theory and Applications (P. 55-63). Springer-Verlag New York, Inc.
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    https://doi.org/10.1080/01621459.1980.10477464
  18. Krasil’nikov, A.I. (2013). Class non-Gaussian distributions with zero skewness and kurtosis. Radioelectronics and Communications Systems, 56(6), 312-320. 
    https://doi.org/10.3103/S0735272713060071
  19. Krasilnikov, A.I. (2017). Class of Non-Gaussian Symmetric Distributions with Zero Coefficient of Kurtosis. Elektronnoie modelirovaniie, 39(1), 3-17. https://doi.org/10.15407/emodel.39.01.003 (in Russian).
  20. Barakat, H.M. (2015). A new method for adding two parameters to a family of distributions with application to the normal and exponential families. Statistical Methods & Applications, 24(3), 359-372. 
    https://doi.org/10.1007/s10260-014-0265-8
  21. Barakat,H.M., Aboutahoun, A.W. & El-kadar, N.N. (2019). A New Extended Mixture Skew Normal Distribution, With Applications. Revista Colombiana de Estadstica, 42(2), 167-183. 
    https://doi.org/10.15446/rce.v42n2.70087
  22. Sulewski, P. (2021). Two-piece power normal distribution. Communications in Statistics — Theory and Methods, 50(11), 2619-2639. 
    https://doi.org/10.1080/03610926.2019.1674871
  23. Krasylnikov, O.I. (2023). Classification of models of two-component mixtures of symmetrical distributions with zero kurtosis coefficient. Elektronne modeliuvannia, 45(5). 20-38. https://doi.org/10.15407/emodel.45.05.020 (in Ukrainian).
  24. Krasylnikov, O.I. (2024). Analysis of the Excess Kurtosis of Two-Component Mixtures of Shifted Non-Gaussian Distributions. Elektronne modeliuvannia, 46(2), 15-34. https://doi.org/10.15407/emodel.46.02.015 (in Ukrainian).
  25. Krasilnikov, A.I. (2018). The Application of Two-Component Mixtures of Shifted Distributions for Modeling Perforated Random Variables. Elektronnoie modelirovaniie, 40(6), 83-98. https://doi.org/10.15407/emodel.40.06.083 (in Russian).
  26. Krasilnikov, A.I. (2020). Analysis of Cumulant Coefficients of Two-component Mixtures of Shifted Gaussian Distributions with Equal Variances. Elektronnoie modelirovanie, 42(3), 71-88. https://doi.org/10.15407/emodel.42.03.071 (in Russian).
  27. Krasylnikov, O.I. (2021). Analysis of Cumulant Coefficients of Two-Component Mixtures of Shifted Non-Gaussian Distributions. Elektronne modeliuvannia, 43(5), 73-92. https://doi.org/10.15407/emodel.43.05.073 (in Ukrainian).
  28. Krasylnikov, O.I. (2024). Modeling of Two-component Mixtures of Shifted Distributions with Zero Cumulant Coefficients. Elektronne modeliuvannia, 46(4), 19-38. https://doi.org/10.15407/emodel.46.04.019 (in Ukrainian).
  29. Stuart A. & Ord J. (2010). Kendall’s Advanced Theory of Statistics, Vol. 1: Distribution Theory. New Jersey: Wiley.Krasilnikov, A.I. (2019). Family of Subbotin distributions and its classification, Elektronnoie modelirovanie, 41(3), 15-31. https://doi.org/10.15407/emodel.41.03.015 (in Russian).
  30. Krasilnikov, A.I. (2019). Family of Subbotin distributions and its classification, Elektronnoie modelirovanie, 41(3), 15-31. https://doi.org/10.15407/emodel.41.03.015 (in Russian).

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Topological Approach to Supply Chain Resilience Analysis

G. Dubynskyi, V. Zubok

Èlektron. model. 2025, 47(4):39-48

https://doi.org/10.15407/emodel.47.04.039

ABSTRACT

The features of the study of the resilience of digital service supply chains as a complex interaction between cloud providers, telecommunication networks, edge delivery systems, authentication services and user devices are presented. The relevance of the problem is substantiated by a number of int ernational standards (ISO/TS 22318, ISO 28002), US federal recommendations (NIST IR 7622, SP 800-160) and European regulations (NIS2 Directive, DORA). The methods of formally representing supply chains for research using graph methods, methods of queuing theory, stochastic methods, as well as representing supply chains in the form of dynamic equations are considered. It is shown that structural analysis can be effectively carried out using the theory of topological spaces.

KEYWORDS

digital supply chain, resilience modeling, graph theory, flow optimization, cascading failures, digital infrastructure.

REFERENCES

  1. European Commission. (2022). Corporate Sustainability Due Diligence Directive (CSDDD). https://commission.europa.eu/
  2. NIST IR 7622. Notional Supply Chain Risk Management Practices. https://csrc.nist.gov/
  3. ISO/TS 22318:2021 / ДСТУ ISO/TS 22318:2023. Supply Chain Continuity Management.
  4. Supply Chain Resilience: Foundations, Best Practices, and Competitive Advantage. (2025). Internal whitepaper.
  5. Linkov, I., Eisenberg, D.A., Plourde, K., Seager, T.P., Allen, J., & Kott, A. (2013). Resilience metrics for cyber systems. Environment Systems and Decisions, 33(4), 471-476. 
    https://doi.org/10.1007/s10669-013-9485-y
  6. Supply Chain Resilience: Foundations, Best Practices, and Competitive Advantage. (2025). Internal whitepaper.ISO/IEC TS 22237-31:2023(en), Information technology — Data centre facilities and infrastructures — Part 31: Key performance indicators for resilience
  7. ISO/IEC TS 22237-31:2023(en), Information technology — Data centre facilities and infrastructures — Part 31: Key performance indicators for resilience
  8. Hammond, S.P., Polizzi, G., & Bartholomew, K.J. (2022). Using a socio-ecological framework to understand how 8–12-year-olds build and show digital resilience: A multi-perspective and multimethod qualitative study. In Education and Information Technologies. Springer Science and Business Media LLC. 
    https://doi.org/10.1007/s10639-022-11240-z
  9. World Bank Sector Taxonomy and definitions (Revised July 1, 2016). https://pubdocs. worldbank.org/en/538321490128452070/Sector-Taxonomy-and-definitions.pdf
  10. Zubok V., Mokhor V. Cyber security of the Internet Topology : book. Kyiv : PIMEE, 2022. 191 p. : ISBN 978-966-02-9929-0 : DOI:10.5281/zenodo.6795229

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Development and Application of an Obfuscator for Cybersecurity of Critical Infrastructure Objects

N. Zayka, O. Verkhovets, M. Komarov, O. Saveliev

Èlektron. model. 2025, 47(4):49-56

https://doi.org/10.15407/emodel.47.04.049

ABSTRACT

The development of an obfuscator for cybersecurity of critical infrastructure software is considered. The main attention is paid to the analysis of modern threats that may arise from malicious code analysis and the development of obfuscation algorithms to complicate reverse engineering. The impact of obfuscation methods on the performance and compatibility of software with other OCI subsystems is evaluated, and recommendations for the implementation of such methods in the development and operation processes are developed.

KEYWORDS

critical infrastructure objects, information technologies, obfuscator, software protection, cyber protection, personnel, recommendations.

REFERENCES

  1. Brunton F., Nissenbaum H. (2015). Obfuscation: A User’s Guide for Privacy and Protest. 5-6.
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