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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">izvestswsu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1560</issn><issn pub-type="epub">2686-6757</issn><publisher><publisher-name>ЮЗГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1560-2025-29-2-109-129</article-id><article-id custom-type="elpub" pub-id-type="custom">izvestswsu-1459</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Информатика, вычислительная техника и управление</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Computer science, computer engineering and IT managment</subject></subj-group></article-categories><title-group><article-title>Формирование индивидуальной образовательной траектории в онлайн обучении на основе технологий скрытых марковских моделей</article-title><trans-title-group xml:lang="en"><trans-title>Individual educational trajectory in online learning based on hidden Markov model technologies</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0006-1953-2914</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бурукина</surname><given-names>И. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Burukina</surname><given-names>I. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Бурукина Ирина Петровна, кандидат  технических наук, доцент, заведующий  кафедрой "Системы автоматизированного проектирования",  </p><p> ул. Красная, д. 40, г. Пенза 440026.</p></bio><bio xml:lang="en"><p>Irina P. Burukina, Cand. of Sci. (Engineering), Associate Professor, Head of the Computer-Aided Design Systems Department, </p><p>40, Krasnaya str., Penza 440026.</p></bio><email xlink:type="simple">burukinairina@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Горшенин</surname><given-names>Л. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Gorshenin</surname><given-names>L. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Горшенин  Лев Николаевич, аспирант, </p><p>ул. Красная, д. 40, г. Пенза 440026.</p></bio><bio xml:lang="en"><p>Lev N. Gorshenin, Post-Graduate Student,</p><p>40, Krasnaya str., Penza 440026.</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Пензенский  государственный университет</institution></aff><aff xml:lang="en"><institution>Penza State  University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>01</day><month>10</month><year>2025</year></pub-date><volume>29</volume><issue>2</issue><fpage>109</fpage><lpage>129</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Бурукина И.П., Горшенин Л.Н., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Бурукина И.П., Горшенин Л.Н.</copyright-holder><copyright-holder xml:lang="en">Burukina I.P., Gorshenin L.N.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://izvestswsu.elpub.ru/jour/article/view/1459">https://izvestswsu.elpub.ru/jour/article/view/1459</self-uri><abstract><sec><title>Цель исследования</title><p>Цель исследования. Целью настоящего исследования является разработка и обоснование методики формирования индивидуальной образовательной траектории в рамках онлайн курсов посредством анализа учебной активности учащихся и уровня их академической успеваемости.  </p></sec><sec><title>Методы</title><p>Методы. В работе применяются скрытые марковские модели, которые хорошо сочетаются с современными подходами машинного обучения, что усиливает их потенциал в плане аналитики и точного подбора образовательных траекторий. Выделены ключевые характеристики учебной активности учащихся, которые можно использовать в качестве наблюдений, а также выбрано подходящее количество скрытых состояний, соответствующее разным уровням академической успеваемости учащихся.</p></sec><sec><title>Результаты</title><p>Результаты. Для экспериментального построения модели использовалась библиотека scikit-learn, разработанная для языка программирования Python. Обучение модели осуществлялось на двух массивах данных: реальная выборка включала 48942 записей результатов студентов по онлайн курсу «Технологии разработки интернет ресурсов», а дополнительный набор данных содержал 18052 записей из открытого репозитория Kaggle. Проведенное тестирование подтвердило эффективность предлагаемой методики, продемонстрировав улучшение качества образования благодаря точной оценке текущего состояния учащегося (учебной активности, уровня академической успеваемости), гибкому подбору учебных материалов и иной формы взаимодействия.</p></sec><sec><title>Заключение</title><p>Заключение. Полученные результаты доказали перспективность использования предлагаемого подхода, способствующего повышению вовлеченности учащихся за счет особенностей восприятия учебного материала, увеличению скорости освоения новых компетенций путем оптимизации последовательности подачи учебного материала и возможности автоматизации процессов мониторинга прогресса учащихся. Исследование представляет особый интерес для специалистов, работающих над повышением эффективности онлайн обучения, и разработчиков образовательных платформ, желающих интегрировать такие модели в свои сервисы для поддержки педагогов и организаторов образовательного процесса.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Purpose of research</title><p>Purpose of research. The purpose of this study is to develop and substantiate a methodology for the formation of an individual educational trajectory in online courses by analyzing the educational activity of students and their level of academic achievement.</p></sec><sec><title>Methods</title><p>Methods. Hidden Markov models are used in the work, which are well combined with modern machine learning approaches, which enhances their potential in terms of analytics and accurate selection of educational trajectories. The key characteristics of students' learning activity that can be used as observations are highlighted, and a suitable number of hidden states corresponding to different levels of students' academic performance are selected.</p></sec><sec><title>Results</title><p>Results. The scikit-learn library, developed for the Python programming language, was used for experimental model construction. The model was trained on two data arrays: the real sample included 48942 records of students' results in the online course «Internet Resource Development Technologies», and an additional data set contained 18052 records from the Kaggle open repository. The conducted testing confirmed the effectiveness of the proposed methodology, demonstrating an improvement in the quality of education due to an accurate assessment of the student's current state (academic activity, academic achievement), flexible selection of educational materials and other forms of interaction.</p></sec><sec><title>Conclusion</title><p>Conclusion. The obtained results proved the prospects of using the proposed approach, which helps to increase student engagement due to the peculiarities of the perception of educational material, increase the speed of mastering new competencies by optimizing the sequence of presentation of educational material and the possibility of automating the processes of monitoring student progress. The study is of particular interest to specialists working to improve the effectiveness of online learning, and developers of educational platforms who want to integrate such models into their services to support teachers and organizers of the educational process.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>индивидуальная стратегия</kwd><kwd>онлайн обучение</kwd><kwd>скрытая марковская модель</kwd><kwd>академическая успеваемость</kwd><kwd>активность учащихся</kwd><kwd>машинное обучение</kwd></kwd-group><kwd-group xml:lang="en"><kwd>individual strategy</kwd><kwd>online learning</kwd><kwd>hidden Markov model</kwd><kwd>academic performance</kwd><kwd>student activity</kwd><kwd>machine learning</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Li D., Xing W. A comparative study on sustainable development of online education platforms at home and abroad since the twenty-first century based on big data analysis // Education and Information Technologies. 2025. P. 1-22. https://doi.org/10.1007/s10639-02513400-3.</mixed-citation><mixed-citation xml:lang="en">Li D., Xing W. A comparative study on sustainable development of online education platforms at home and abroad since the twenty-first century based on big data analysis. Education and Information Technologies. 2025. P. 1-22. https://doi.org/10.1007/s10639-02513400-3.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Бурукина И.П. LX Design в разработке онлайн курсов: принципы, методы и практика // Педагогическая информатика. 2025. № 1. С. 117-123.</mixed-citation><mixed-citation xml:lang="en">Burukina I.P. LX Design in the development of online courses: principles, methods and practice. Pedagogicheskaya informatika = Pedagogical informatics. 2025; (1): 117-123. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Rajabalee Y.B., Santally M.I. Learner satisfaction, engagement and performances in an online module: Implications for institutional e-learning policy analysis // Education and Information Technologies. 2021. №3. P. 2623-2656. https://doi.org/10.1007/s10639-02010375-1.</mixed-citation><mixed-citation xml:lang="en">Rajabalee Y.B., Santally M.I. Learner satisfaction, engagement and performances in an online module: Implications for institutional e-learning policy analysis. Education and Information Technologies. 2021; (3): 2623-2656. https://doi.org/10.1007/s10639-020-10375-1.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Kedia P., Mishra L. Exploring the factors influencing the effectiveness of online learning: a study on college students // Social Sciences &amp; Humanities Open. 2023. №1. P. 100559. https://doi.org/10.1016/J.SSAHO.2023.100559.</mixed-citation><mixed-citation xml:lang="en">Kedia P., Mishra L. Exploring the factors influencing the effectiveness of online learning: a study on college students. Social Sciences &amp; Humanities Open. 2023; (1): 100559. https://doi.org/10.1016/J.SSAHO.2023.100559.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Lalitha T.B., Sreeja P.S. Personalised self-directed learning recommendation system // Procedia Computer Science. 2020. Vol.171. P. 583-592. https://doi.org/10.1016/j.procs.2020.04.063.</mixed-citation><mixed-citation xml:lang="en">Lalitha T.B., Sreeja P.S. Personalised self-directed learning recommendation system. Procedia Computer Science. 2020; 171: 583-592. https://doi.org/10.1016/j.procs.2020.04.063.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Alper A., Okyay S., Nihat A. Hybrid course recommendation system design for a real-time student automation application // Avrupa Bilim ve Teknoloji Dergisi. 2021. Т.26. P. 85-90. https://doi.org/10.31590/ejosat.944596.</mixed-citation><mixed-citation xml:lang="en">Alper A., Okyay S., Nihat A. Hybrid course recommendation system design for a real-time student automation application. Avrupa Bilim ve Teknoloji Dergisi. 2021; 26: 85-90. https://doi.org/10.31590/ejosat.944596.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Когнитивные технологии в принятии управленческих решений / С.П. Серегин, А.Р. Федорова, Ю.А. Халин, А.И. Катыхин // Известия Юго-Западного государственного университета. 2024; 28(4): 57-66. https://doi.org/10.21869/2223-1560-2024-28-4-57-66.</mixed-citation><mixed-citation xml:lang="en">Seregin S. P., Fedorov A. R., Khalin Y. A., Katykhin A. I. Cognitive technologies in management decision-making. Izvestiya Yugo-Zapadnogo gosudarstvennogo universiteta = Proceedings of the Southwest State University. 2024; 28(4): 57-66 (In Russ.). https://doi.org/10.21869/2223-1560-2024-28-4-57-66.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Thaipisutikul T., Shih T.K., Enkhbat A., Aditya W. Exploiting long- and short-term preferences for deep context-aware recommendations // IEEE Transactions on Computational Social Systems. 2021. Vol. 9, №4. P. 1237-1248.</mixed-citation><mixed-citation xml:lang="en">Thaipisutikul T., Shih T.K., Enkhbat A., Aditya W. Exploiting long- and short-term preferences for deep context-aware recommendations. IEEE Transactions on Computational Social Systems. 2021; 9(4): 1237-1248.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Лапенок М.В., Макеева В.В. Формирование индивидуальной траектории обучения в информационно-образовательной среде школы // Педагогическое образование в России. 2016. №7. C. 37-43.</mixed-citation><mixed-citation xml:lang="en">Lapenok M.V., Makeeva V.V. Formation of an individual learning trajectory in the information and educational environment of the school. Pedagogicheskoe obrazovanie v Rossii = Pedagogical education in Russia. 2016; (7): 37-43. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Троицкая Е.А. Психологическая устойчивость и субъективное благополучие личности как ресурсы для проявления эмпатии // Вестник Московского государственного лингвистического университета. 2014. №. 7. С. 46-59.</mixed-citation><mixed-citation xml:lang="en">Troitskaya E.A. Psychological stability and subjective well-being of an individual as resources for the manifestation of empathy. Vestnik Moskovskogo gosudarstvennogo lingvisticheskogo universiteta = Bulletin of the Moscow State Linguistic University. 2014; (7): 46-59. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Васильченко С. Х. Функциональные особенности формирования персональной образовательной среды как средства индивидуализации обучения на основе информационных технологий // Информатика и образование. 2010. №. 12. С. 104-108.</mixed-citation><mixed-citation xml:lang="en">Vasilchenko S.Kh. Functional features of the formation of a personal educational environment as a means of individualization of learning based on information technology. Informatika i obrazovanie = Computer Science and Education. 2010: (12): 104-108. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Wang S., Wang F., Zhu Z. Artificial intelligence in education: A systematic literature review // Expert Systems with Applications. 2024. P. 124-167. https://doi.org/10.1016/j.eswa.2024.124167.</mixed-citation><mixed-citation xml:lang="en">Wang S., Wang F., Zhu Z. Artificial intelligence in education: A systematic literature review. Expert Systems with Applications. 2024. P. 124-167. https://doi.org/10.1016/j.eswa.2024.124167.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Подколзин М.М. Интеллектуальная система адаптивного обучения на основе нейронных сетей для персонализации образовательных траекторий студентов российских вузов // Информатика и образование. 2024. 39(6). C. 65–81. https://doi.org/10.32517/0234-0453-2024-39-6-65-81.</mixed-citation><mixed-citation xml:lang="en">Podkolzin M.M. Intelligent adaptive learning system based on neural networks for personalization of educational trajectories of students of Russian universities. Informatika i obrazovanie = Computer Science and Education. 2024; (39): 65–81. (In Russ.). https://doi.org/10.32517/0234-0453-2024-39-6-65-81.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Варнухов А.Ю. Скрытая марковская модель: метод построения модели бизнеспроцесса // Бизнес-информатика. 2024. Т. 18, №. 3. С. 41-55. DOI: 10.17323/2587814X.2024.3.41.55.</mixed-citation><mixed-citation xml:lang="en">Varnukhov A.Yu. Hidden Markov Model: Method for Constructing a Business Process Model. Biznes-informatika = Business Informatics. 2024; 18(3): 41–55. (In Russ.). https://10.17323/2587-814X.2024.3.41.55.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Земсков А.В. Аналитический подход к исследованию неоднородных марковских цепей с кусочно-постоянными изменениями переходных вероятностей // Известия высших учебных заведений. Приборостроение. 2024. Т. 67, №. 8. С. 657-669. https://doi.org/10.17586/0021-3454-2024-67-8-657-669</mixed-citation><mixed-citation xml:lang="en">Zemskov A.V. Analytical approach to the study of non-homogeneous Markov chains with piecewise constant changes in transition probabilities. Izvestiya vysshikh uchebnykh zavedenii. Priborostroenie = Bulletin of higher educational institutions. Instrument engineering. 2024; 67(8): 657-669. (In Russ.). https://doi.org/10.17586/0021-3454-2024-67-8-657-669.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Ravari A., Ghoreishi S.F., Imani M. Optimal inference of hidden Markov models through expert-acquired data // IEEE Transactions on Artificial Intelligence. 2024. Vol. 5, № 8. P. 3985-4000. https://doi.org/10.1109/TAI.2024.3358261.</mixed-citation><mixed-citation xml:lang="en">Ravari A., Ghoreishi S.F., Imani M. Optimal inference of hidden Markov models through expert-acquired data. IEEE Transactions on Artificial Intelligence. 2024; 5 (8): 3985-4000. https://doi.org/10.1109/TAI.2024.3358261.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Pan W. Research on pig sound recognition based on deep neural network and hidden Markov models // Sensors. 2024. Vol. 24, № 4. P. 1269. https://doi.org/10.3390/s24041269</mixed-citation><mixed-citation xml:lang="en">Pan W. Research on pig sound recognition based on deep neural network and hidden Markov models. Sensors. 2024; 24(4): 1269. https://doi.org/10.3390/s24041269</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Jithendar T.R., Devi M.T., Saritha G. Determination of viterbi path for 3 hidden and 5 observable states using hidden Markov model // Reliability: Theory &amp; Applications. 2024. Vol. 19, №. 2 (78). P. 509-515.</mixed-citation><mixed-citation xml:lang="en">Jithendar T.R., Devi M.T., Saritha G. Determination of viterbi path for 3 hidden and 5 observable states using hidden Markov model. Reliability: Theory &amp; Applications. 2024; 19(2): 509-515.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Zhu K. Physics-informed hidden markov model for tool wear monitoring // Journal of Manufacturing Systems. 2024. Vol. 72. P. 308-322. https://doi.org/10.1016/j.jmsy.2023.11.003.</mixed-citation><mixed-citation xml:lang="en">Zhu K. Physics-informed hidden markov model for tool wear monitoring. Journal of Manufacturing Systems. 2024; 72: 308-322. https://doi.org/10.1016/j.jmsy.2023.11.003.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Харин Ю.С. Критерий отношения правдоподобия проверки сложных гипотез sмерной равномерности двоичных последовательностей //Вероятностные методы в дискретной математике. 2024. Т. 1. С. 122.</mixed-citation><mixed-citation xml:lang="en">Kharin Yu.S. Likelihood ratio criterion for testing complex hypotheses of sdimensional uniformity of binary sequences. Veroyatnostnye metody v diskretnoi matematike = Probabilistic methods in discrete mathematics. 2024; 1: 122. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Wong Z.Y. et al. Student engagement and its association with academic achievement and subjective well-being: A systematic review and meta-analysis // Journal of Educational Psychology. 2024. №. 1. P. 48–75. https://doi.org/10.1037/edu0000833.</mixed-citation><mixed-citation xml:lang="en">Wong Z.Y., et al. Student engagement and its association with academic achievement and subjective well-being: A systematic review and meta-analysis. Journal of Educational Psychology. 2024; (1): 48–75. https://doi.org/10.1037/edu0000833.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Zhao J. et al. Choosing the number of factors in factor analysis with incomplete data via a novel hierarchical Bayesian information criterion //Advances in Data Analysis and Classification. 2024. Р. 1-27. https://doi.org/10.1007/s11634-024-00582-w.</mixed-citation><mixed-citation xml:lang="en">Zhao J., et al. Choosing the number of factors in factor analysis with incomplete data via a novel hierarchical Bayesian information criterion. Advances in Data Analysis and Classification. 2024: 1-27. https://doi.org/10.1007/s11634-024-00582-w.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Yang F., Balakrishnan S., Wainwright M.J. Statistical and computational guarantees for the Baum-Welch algorithm // Journal of Machine Learning Research. 2017. Vol. 18, № 125. P. 1-53.</mixed-citation><mixed-citation xml:lang="en">Yang F., Balakrishnan S., Wainwright M.J. Statistical and computational guarantees for the Baum-Welch algorithm. Journal of Machine Learning Research. 2017; 18 (125): 1-53.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Wang C., Li K., He X. Network risk assessment based on Baum Welch algorithm and HMM // Mobile Networks and Applications. 2021. Vol. 26, №. 4. P. 1630-1637. https://doi.org/10.1007/s11036-019-01500-7.</mixed-citation><mixed-citation xml:lang="en">Wang C., Li K., He X. Network risk assessment based on Baum Welch algorithm and HMM. Mobile Networks and Applications. 2021; 26 (4): 1630-1637. https://doi.org/10.1007/s11036-019-01500-7.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Anderson K.S. Python: 2023 project update // Journal of Open Source Software. 2023. Vol. 8, №. 92. P. 5994.</mixed-citation><mixed-citation xml:lang="en">Anderson K.S. Python: 2023 project update. Journal of Open Source Software. 2023; 8 (92): 5994 p.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Библиотеки python для начинающих / В.В. Сааков, Л.Х. Кучмезова, А.А. Дзамихова, З.Х. Шаущева // Молодой учёный: сборник статей III Международной научнопрактической конференции. Пенза, 2023. С. 19-21.</mixed-citation><mixed-citation xml:lang="en">Saakov V.V., Kuchmezova L.Kh., Dzamikhova A.A., Shaushcheva Z.Kh. Python libraries for beginners. In: Molodoi uchenyi: sbornik statei III Mezhdunarodnoi nauchnoprakticheskoi konferentsii  = Young scientist: collection of articles of the III International Scientific and Practical Conference. Penza, 2023. P. 19-21. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Сальников А.В. Верификация и валидация компьютерных моделей // Известия высших учебных заведений. Машиностроение. 2022. №. 9 (750). С. 100-115. doi: 10.18698/0536-1044-2022-9-100-115.</mixed-citation><mixed-citation xml:lang="en">Salnikov A.V. Verification and validation of computer models. Izvestiya vysshikh uchebnykh zavedenii. Mashinostroenie = News of higher educational institutions. Mechanical engineering. 2022; (9): 100-115. (In Russ.). https://doi.org/10.18698/0536-1044-2022-9-100-115.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
