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I. Integration with various payment systems: challenges and solutions

https://doi.org/10.34130/1992-2752_2024_3_4

Timur I. Vasilev – Paybis LTD Scotland, timmi129@yandex.ru

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Abstract. In today’s fast-paced digital world, the ability to integrate with various payment systems is most important for companies of any size. Whether you run a small online store or a
large organization, providing customers with easy and secure payment options should always remain a top priority. However, the process of integrating with multiple payment processors can be complex and present many challenges.

Keywords: payment systems, integration optimization, automation, web application.

References

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For citation: Vasilev T. I. Integration with various payment systems: challenges and solutions. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 3 (52), pp. 4−19.
(In Russ.) https://doi.org/10.34130/1992-2752_2024_3_4

II. Discrete mathematics for computer scientists: three-valued logic

https://doi.org/10.34130/1992-2752_2024_3_20

Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University, valmasha@mail.ru\

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Abstract. The use of three-valued logics in the development of information systems is primarily associated with the problem of incompleteness and uncertainty in data. All commercial database
systems using the structured query language SQL offer a solution for processing incomplete information based on three-valued logic.

Keywords: three-valued logic, Kleene’s logic, discrete mathematics, learning outcomes.

References

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2. Karpenko A. S. Razvitie mnogoznachnoj logiki [Development of multivalued logic]. Moscow: Publisher of the LKI, 2010. 448 p. (In Russ.)
3. Maksimov D. Yu. N. A. Vasiliev’s logic and multivalued logic. Logicheskie issledovaniya [Logical research]. 2016. Vol. 22. No 1. Pp. 82–107. DOI: 10.21146/2074-1472-2016-22-1-82-107. (In Russ.)
4. Kotov Yu. B. Logical decision-making tools in the tasks of medical diagnostics. Upravleniye razvitiyem krupnomasshtabnykh sistem (MLSD’2009) : materialy tret’yey mezhdunarodnoy konferentsii (sektsii 4–6), Moskva, 05–07 oktyabrya 2009 goda. Institut problem
   upravleniya im. V. A. Trapeznikova RAN [Management of LargeScale Systems Development (MLSD’2009) : proceedings of the Third International Conference (sections 4–6), Moscow, October 5–7, 2009. V. A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences]. Moscow: Establishment of the Russian academy institute of management problems named after V. A. Trapesnikova RAS, 2009. Vol 2. Pp. 254–256. (In Russ.)
5. Men‘shix A. V., Men‘shix T. V. The choice of methods for modeling estimates of the criminal situation. Okhrana, bezopasnost’, svyaz’ [Security, safety, communication]. 2024. No 9–3. Pp. 133–137. (In Russ.)
6. Men‘shix A. V., Men‘shix T. V. Using logical and arithmetic methods to model uncertainty. Tekhnika i bezopasnost’ ob”yektov ugolovno-ispolnitel’noy sistemy : sbornik materialov Mezhdunarodnoy nauchno-prakticheskoy konferentsii, Voronezh, 17–18 maya 2023 goda
   [Technology and safety of penal facilities : collection of materials from the International scientific and practical conference, Voronezh, May 17–18, 2023]. Voronezh: FCOU Voronezh Institute of the Federal Penitentiary Service of Russia, Lines, 2023. Pp. 78–80. (In Russ.)
7. Men‘shix A. V., Men‘shix T. V. Modeling of partial uncertainty and incompleteness of data in management decision-making. Vestnik Voronezhskogo instituta MVD Rossii [Bulletin of the Voronezh Institute of the Ministry of Internal Affairs of Russia]. 2023. No 2. Pp. 132–137. (In Russ.)
8. Bessmertny I., Koroleva J., Sukhikh N., Vedernikov J. Ternary Logics in Decision Making. Reliability and Statistics in Transportation and Communication : Selected Papers from the 20th International Conference, Riga, 14–17 october 2020. Riga: Springer Nature, 2021. Pp. 411–419. DOI: 10.1007/978-3-030-68476-1_38.
9. Giniyatullin V. M., Gabitova E‘. A. Clustering of loan application data into a ternary vector. Elektrotekhnicheskiye i informatsionnyye kompleksy i sistemy [Electrical and information complexes and systems]. 2018. Vol. 14. No 1. Pp. 49–54. (In Russ.)
10. Filippov M. N. A method for processing incomplete data based on three-digit logic. Avtometriya [Autometry]. 2009. Vol. 45. No 5. Pp. 124–131. (In Russ.)
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    Sciences]. 2023. Vol. 35. No 2. Pp. 73–100. DOI: 10.15514/ISPRAS2023-35(2)-6. (In Russ.)
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    universiteta imeni V. I. Vernadskogo. Filosofiya. Politologiya. Kul’turologiya [Scientific notes of the Crimean Federal University named after V. I. Vernadsky. Philosophy. Political science. Cultural studies]. 2021. Vol. 7 (73). No 1. Pp. 5–25. (In Russ.)
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15. Yablonskij S. V. Vvedenie v diskretnuyu matematiku : ucheb. posobie dlya vuzov [Introduction to Discrete Mathematics : a textbook for Universities]. Moscow: Higher education, 2008. 384 p. (In Russ.)
16. Gavrilov G. P., Capozhenko A. A. Zadachi i uprazhneniya po diskretnoy matematike : ucheb. posobiye [Problems and exercises in discrete mathematics : textbook]. Moscow: Physical education, 2005. 416 p. (In Russ.)
17. Tarannikov Yu. V. Discrete Mathematics. Problem Book : textbook for Universities. Moscow: Yurayt Publishing House, 2024. 385 p. Obrazovatel‘naya platforma Yurajt [sajt] [Yurayt educational platform [web-site]]. Available at: https://urait.ru/bcode/536541 (accessed:
    15.09.2024). (In Russ.)
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21. Console M., Guagliardo P., Libkin L. Do We Need Manyvalued Logics for Incomplete Information? IJCAI International Joint Conference on Artificial Intelligence. Macao, China, 10/08/19. 2019. Pp. 6141–6145. https://doi.org/10.24963/ijcai.2019/851.

For citation: Babikova N. N. Discrete mathematics for computer scientists: three-valued logic. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 3 (52), pp. 20−35.
(In Russ.) https://doi.org/10.34130/1992-2752_2024_3_20

III. On the formation of critical thinking of students of a technical university in mathematics classes

https://doi.org/10.34130/1992-2752_2024_3_36

Marija S. Parmuzina – Ukhta State Technical University, mparmuzina@ugtu.net

Marina G. Rocheva – Ukhta State Technical University.

Ekaterina A. Terenteva – Ukhta State Technical University.

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Abstract. Developed critical thinking is necessary for every person to improve the quality of life in the conditions of modern realities: a large information field, an increased number of fraudulent
schemes, widespread use of computer technology, a fast pace of life, etc. It is especially important for students to have developed critical thinking, since this category of the population is most susceptible to malevolent manipulation from the outside.

Keywords: students of technical universities, critical thinking, teaching mathematics.

References

1. Plotnikova N. F. Formirovanie kriticheskogo myshleniya studentov vuza v usloviyah komandnoj formy organizacii obucheniya : monografiya [Formation of critical thinking of university students in the conditions of the command form of the organization of education : monograph]. Kazan: Kazan University Press, 2015. 84 p. (In Russ.)
2. Barbashina E. V. Critical thinking in the system of higher education abroad. Idei i idealy [Ideas and ideals]. 2022. No 4–1. Pp. 120–136. (In Russ.)
3. Lisenkova A. D. Clusters of critical thinking skills of modern high school students. Pedagogika. Voprosy teorii i praktiki [Pedagogy. Questions of theory and practice]. 2023. No 5. Pp. 463–469. (In Russ.)
4. Manakova E. O., Manakov A. S., Zvereva T. S., Borodina A. A. Technology of critical thinking. Teoriya i praktika sovremennoy nauki [Theory and practice of modern science]. 2022. No 1 (79). Pp. 232–235. (In Russ.)
5. Maryukov A. M. Problem-based learning and the formation of critical thinking. Obrazovatel’naya politika [Educational policy]. 2022. No 4 (92). Pp. 56–64. (In Russ.)
6. Dewey J. Psihologiya i pedagogika myshleniya [Psychology and pedagogy of thinking] Transl. from English by N. M. Nikolskaya; edited by N. D. Vinogradov. Moscow: Publishing House of the Mir Association,202 p. (In Russ.)
7. Kluster D. Chto takoe kriticheskoe myshlenie? [What is critical thinking?] [Electronic resource]. Available at: http://testolog.narod.ru/Other15.html (accessed: 25.10.2024). (In Russ.)
8. Butenko A. V., Hodos E. A. Kriticheskoe myshlenie: metod, teoriya, praktika : uchebno-metodicheskoe posobie [Critical thinking: method, theory, practice : an educational and methodical manual]. Moscow: MIROS, 2002. 176 p. (In Russ.)
9. Rocheva M. G., Terenteva E. A. To the problem of memorizing educational information by students of a technical university. Kommunikatsii. Obshchestvo. Dukhovnost’ – 2023 : materialy XXIII Mezhdunarodnoy nauchno-prakticheskoy konferentsii [Communications. Society. Spirituality – 2023 : materials of the XXIII International Scientific and Practical Conference]. Ukhta: UGTU. 2023. Pp. 244–249. (In Russ.)
10. Parmuzina M. S., Sokolova N. S. Informatization of teaching mathematics to students of technical fields. Vestnik NTsBZhD [Bulletin of Scientific Center for Life Safety]. 2024. No 1 (59). Pp 57–67. (In Russ.)
11. Derbush M. V., Skarbich S. N. Innovative approaches to the use of information technologies in the process of teaching mathematics. Nepreryvnoye obrazovaniye: XXI vek [Continuing education: XXI century]. 2020. Vol. 2 (30). Pp. 66–80. DOI: 10.15393/j5.art.2020.5689.
    (In Russ.)
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13. Terenteva E. A., Rocheva M. G. Features of the use of digital technologies in teaching mathematics. Upravleniye ustoychivym razvitiyem toplivno-energeticheskogo kompleksa – 2023 : materialy IV Vserossiyskoy nauchno-prakticheskoy konferentsii [Management of sustainable development of the fuel and energy complex – 2023 : materials of the IV All-Russian scientific and practical conference]. Ukhta: UGTU, 2023. Pp. 45–49. (In Russ.)
14. Grambovskaya L. V., Badanina L. A. Problems of teaching mathematical statistics in a technical university using MS Excel. Mezhdunarodnyy nauchno-issledovatel’skiy zhurnal [International
    Scientific Research Journal]. 2022. No 7–3 (121). Pp. 118–122. (In Russ.)

For citation: Parmuzina M. S., Rocheva M. G., Terenteva E. A. On the formation of critical thinking of students of a technical university in mathematics classes. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 3 (52), pp. 36−51. (In Russ.) https://doi.org/10.34130/1992-2752_2024_3_36

IV. Teaching mathematics to foreign students at a pedagogical university

https://doi.org/10.34130/1992-2752_2024_3_52

Marina E. Sangalova – Arzamas branch of the National Research Lobachevsky State University of Nizhni Novgorod, smolyanka77@mail.ru

Svetlana V. Fedorova – Arzamas branch of the National Research Lobachevsky State University of Nizhni Novgorod, smolyanka77@mail.ru

Elvira V. Frolova – Arzamas branch of the National Research Lobachevsky State University of Nizhni Novgorod, smolyanka77@mail.ru

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Abstract. The article considers the problem of organizing the teaching of mathematics to foreign students of a pedagogical university. Approaches to solving the problems of adapting the
content of mathematical disciplines to the level of training of this category of students, as well as the features of the teaching methodology are discussed.

Keywords: higher education, mathematics education, international students, pedagogical university.

References

1. The popularity of educational programs of Russian pedagogical universities among foreign students has increased one and a half times over the past three years. Minprosveshcheniya Rossii: sayt [Ministry of Education of Russia: website]. 2021. May 27 [Electronic
   resource]. Available at: https://edu.gov.ru/press/3770/populyarnostobrazovatelnyh-programm-rossiyskih-pedvuzov-sredi-inostrannyhstudentov-v (accessed: 25.05.2024). (In Russ.)
2. O nacionalnih celyah razvitiya Rossiiskoi Federacii na period do 2030 goda i na perspektivu do 2036 god : ukaz Prezidenta RF ot 07.05.2024 № 309 [On the national development goals
   of the Russian Federation for the period up to 2030 and for the future up to 2036 : decree of the President of the Russian Federation dated 05/07/2024 No 309] [Electronic resource]. Available
   at: http://publication.pravo.gov.ru/document/0001202405070015 (accessed: 25.05.2024). (In Russ.)
3. Yakovleva E. V. Teaching mathematics to foreign students at the university based on a cognitive-visual approach Matematicheskiy vestnik Vyatskogo gosudarstvennogo universiteta [Mathematical Bulletin of Vyatka State University]. 2020. No 1. Pp. 84–93. (In Russ.)
4. Kochetkova I. V., Mumryaeva S. M., Egorchenko I. V. Features of the organization of independent work in teaching mathematics to foreign students at the university Pedagogicheskoe obrazovanie v Rossii [Pedagogical education in Russia]. 2018. No 8. Pp. 189–196. (In Russ.)
5. Fedorova S. V., Frolova E. V. Video content in the structure of the electronic educational course “Mathematics”. Sovremennye obrazovatel’nye web-tekhnologii v realizacii lichnostnogo potenciala obuchayushchikhsya : sbornik statej Mezhdunarodnoj nauchnoprakticheskoj konferencii “Sovremennye obrazovatelnye web-tekhnologii v realizacii lichnostnogo potenciala obuchayushchikhsya” [Modern educational web-technologies in the implementation of the personal potential of students : collection of articles from the International
   scientific and practical conference “Modern educational webtechnologies in the implementation of the personal potential of students”]. Arzamas: Arzamas branch of UNN, 2022. Pp. 288–292. (In Russ.)

For citation: Sangalova M. E., Fedorova S. V., Frolova E. V. Teaching mathematics to foreign students at a pedagogical university. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2024, No. 3 (52), pp. 52−65. https://doi.org/10.34130/1992-2752_2024_3_52

V. On the works of Ivan Alexandrovich Skopin (1900–1942), one of first students of Professor I. M. Vinogradov

https://doi.org/10.34130/1992-2752_2024_3_66

Vladimir P. Odyniec – W.P.Odyniec@mail.ru

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Abstract. The article deals with the works on number theory of Ivan Alexandrovich Skopin (1900–1942) against the background of the situation in the country in 20–30s.

Keywords: distribution of indices, prime module, primitive root, Euler function.

References

1. Nauka i nauchnye rabotniki SSSR. Chast V. Nauchnye rabotniki Leningrada : Spravochnik [Scientists of USSR. Part V. Scientists of Leningrad : handbook]. L.: Publishing House of the USSR Academy of Sciences, 1934. 723 p. (In Russ.)
2. Skopin I. A. About the distribution of indices in a prime module. Zh. Leningradskogo Fiz.-mat. obshchestva [Journal of Leningrad Physics and Mathematics society]. Vol. 2. Issue 1. 1928. Pp. 82–93. (In Russ.)
3. List of reports read at the Meetings of the Leningrad Physics and Mathematics Society from 1922 to 1927 Zh. Phiz.-mat.ob-va [Journal of the Physics and Mathematics society]. 1928. Vol. 1. Issue 2. Pp. 323–(In Russ.)
4. Na Leningradskom matematicheskom fronte. Sb. dokumentov Leningradskogo obshchestva matematikov-materialistov pri LOKa) [On the Leningrad Mathematical Front. Col. of documents of the Leningrad Society of Mathematicians-Materialists at the Leningrad Department of the Communist Academy]. Compiler L. A. Leifert. Leningrad: State social-economic publishing house, 1931. 44 p. (In Russ.)
5. Skopin I. A. On the distribution of fractional parts of a system of integer polynomials. Izvestya AN. Seria matematicheskaya [Proceedings of the USSR Academy of Sciences. Mathematical series].Pp. 547–560. (In Russ.)
6. Skopin I. A. On a System of Diophantine inequalities. Trudy 2- go Vsesouznogo matematicheskogo s’ezda. T. 2. Sekcionnye doklady [Proceedings of the 2nd All-Union Mathematical Congress. Vol. 2. Sectional pre- treasures]. Leningrad: Publishing House of the USSR Academy of Sciences, 1934. Pp. 17–19. (In Russ.)
7. Blokada. 1941–1944. Leningrad. Kniga pamyati. T. 27 (Sednev – Skorodumov) [Blockade. 1941–1944. Leningrad. Book of Memory. Vol. 27 (Sednev – Skorodumov)]. St. Petersburg: Publishing House of the Government of St. Petersburg, 2005. 712 p. (In Russ.)

For citation: Odyniec V. P. On the works of Ivan Alexandrovich Skopin (1900–1942), one of first students of Professor I. M. Vinogradov. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 3 (52), pp. 66−72. (In Russ.) https://doi.org/10.34130/1992-2752_2024_3_66

Full text

I. A coupled model of viscoelastic curing of a cylindrical product

https://doi.org/10.34130/1992-2752_2024_2_4

Nadezhda A. Belyaeva – Pitirim Sorokin Syktyvkar State University.

Ilya O. Mashin – Institute of Physics and Mathematics, Federal Research Centre Komi Science Centre, Ural Branch, RAS.

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Abstract. This work considers the formation of a hollow cylindrical product under the conditions of the coupled theory of thermoviscoelasticity. The study is a continuation of work on an “uncoupled” problem and includes consideration of the influence of an additive viscoelastic term in the thermal conductivity equation on the process of product formation. A mathematical model is constructed
and investigated. The finite difference method is used for numerical analysis. Graphical results of studies reflecting the distribution of temperature, polymerization depth and stress-strain state of the formed product are presented.

Keywords: coupled problem, thermoviscoelasticity, finite difference method, numerical analysis.

References

1. Demidov A. V. Mathematical models for predicting the deformation of polymer materials based on the integral Boltzmann – Volterra relations. Izvestiya vyshikh uchebnih zavedenii. Severo-Kavkazskii region. Tekhnicheskie nauki [News of higher educational institutions. The North Caucasus region. Technical sciences]. 2006. No 4 (136). Pp. 35–37. (In Russ.)
2. Kartashov E. M., Nagaeva I. A., Benevolenskiy S. B. Generalized model of thermoviscoelasticity in the theory of heat stroke. Vestnik MITHT im. M.V. Lomonosova [Moscow State University of
   Fine Chemical Technologies named after M. V. Lomonosov]. 2014. Vol. 9. No 3. Pp. 105–111. (In Russ.)
3. Orlov V. P. Investigation of the mathematical model of thermoviscoelasticity. Doklady Akademii nauk [Reports of the Academy of Sciences]. 1995. Vol. 343. No 3. Pp. 320–322. (In Russ.)
4. Oshmyan V. G., Patlazhan S. A., Remond Y. Principles of structural and mechanical modeling of polymers and composites. Vysokomolekulyarnie soedineniya. Seriya A [High molecular weight compounds. Series A]. 2006. Vol. 48. No 9. Pp. 1691–1702. (In Russ.)
5. Belyaeva N. A. Mathematical modeling of product curing under the conditions of the related theory of thermoviscoelasticity. Teoreticheskaya i prikladnaya mekhanika: mezdhunarodnyi nauchnothenicheskii sbornik [Theoretical and Applied Mechanics: an international scientific and technical collection]. Minsk: The Belarusian National Technical University, 2020. No 35. Pp. 139–145. (In Russ.)
6. Veselovskiy V. B., Syasev A. V. Mathematical modeling and solution of related problems of thermoviscoelasticity for two-phase bodies. Teoreticheskaya i prikladnaya mekhanika [Theoretical and applied mechanics]. 2002. No 35. Pp. 93–100. (In Russ.)
7. Belyaeva N. A., Klychnikov L. V. The method of the integral equation in the problem of volumetric curing. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 1996. No 2. Pp. 125–134. (In Russ.)
8. Lychev S. A. The related dynamic problem of thermoviscoelasticity. Izvestiya Rossiiskoi Akademii Nauk. Mekhanika tverdogo tela [Proceedings of the Russian Academy of Sciences. Solid State Mechanics]. 2008. No 5. Pp. 95–113. (In Russ.)
9. Landau L. D., Lifshitz E. M. Teoreticheskaya fizika : Uchebnoye posobiye : v 10 t. T. VI. Gidrodinamika [Theoretical physics : a textbook : in 10 vols. Vol. VI. Hydrodynamics]. 3rd ed., reprint. Moscow: Nauka, 1986. 736 p. (In Russ.)
10. Rabotnov Yu. N. Elementy nasledstvennoy mekhaniki tvordykh tel [Elements of hereditary mechanics of solids]. Moscow: Nauka, 1977. 384 p. (In Russ.)

For citation: Belyaeva N. A., Mashin I. O. A coupled model of viscoelastic curing of a cylindrical product. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 2 (51), pp. 4−13. (In Russ.) https://doi.org/10.34130/1992-2752_2024_2_4

II. Visualization of Numerical Calculations with Python

https://doi.org/10.34130/1992-2752_2024_2_14

Anatolij A. Durkin – Pitirim Sorokin Syktyvkar State University

Andrey. V. Yermolenko – Pitirim Sorokin Syktyvkar State University, ea74@list.ru

Nadezhda O. Kotelina – Pitirim Sorokin Syktyvkar State University

Oksana. I. Turkova – Pitirim Sorokin Syktyvkar State University

Text

Abstract. The simplicity of the syntax and the large number of Python libraries make it an indispensable tool for conducting laboratory work on a number of subjects, simplifying routine
operations when visualizing numerical calculations. In the article, the authors show examples of using Python libraries for plotting surfaces and interpolation curves, animating numerical methods.

Keywords: Python, visualization, numerical experiment, animation.

References

1. Bakunova O. M., Burkin A. V., Protko D. E. at al. Data visualisation with .NET F#. Web of Scholar. 2018. Vol. 1. No 4 (22). Pp. 19–22. (In Russ.)
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5. Yermolenko A. V., Osipov K. S. On using Python libraries to calculate plates. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 2019. No 4 (33).
   Pp. 86–95. (In Russ.)
6. D’yakonov, V. P. Maple 9.5/10 v matematike, fizike i obrazovanii [Maple 9.5/10 in mathematics, physics and education]. Moscow: SOLON-PRESS, 2006. 720 p. (In Russ.)
7. Golovanov N. N. Geomyetricheskoe modelirovaniye [Geometry modeling]. Moscow: Izdatyelstvo Phisiko-matematicheskoy lityeratury [Publishing House of physical and mathematical literature], 2002. 472 p. (In Russ.)
8. Piegl L., Tiller W. The NURBS Book. Monographs in Visual Communications. New York: Springer, 1995. 646 p.

For citation: Durkin A. A., Yermolenko A. V., Kotelina N. O., Turkova O. I. Visualization of Numerical Calculations with Python. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 2 (51), pp. 14−26. (In Russ.) https://doi.org/10.34130/1992-2752_2024_2_14

III. What is a semimodule

https://doi.org/10.34130/1992-2752_2024_2_27

Evgeny M. Vechtomov – Vyatka State University, vecht@mail.ru

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Abstract. The article deals with the beginnings of the theory of semimodules over a semiring. It considers initial properties and formulates some structure theorems about semimodules. The material is of a mathematical and methodological nature and includes a system of educational exercises.

Keywords: a semimodule over а semiring, study of the theory of semirings and semimodules.

References

1. Vechtomov E. M. What is a semiring. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics],No 1 (50). Pp. 21–42. https://doi.org/10.34130/1992-2752_2024_1_21. (In Russ.)
2. Vechtomov E. M. Vvedeniye v polukol’tsa [Introduction to Semirings]. Kirov: Izd-vo vyatsk. gos. ped. un-ta. 2000. 44 p. (In Russ.)
3. Vechtomov E. M., Lubyagina E. N., Chermnykh V. V. Elementy teorii polukolets : monografiya [Elements of the theory of semirings : monograph]. Kirov: Izdatelstvo OOO «Raduga-PRESS». 2012. 228 p. (In Russ.)
4. Golan J. S. Semirings and their applications. Dordrecht: Kluwer Academic Publishers, 1999. 382 p.
5. Vechtomov E. M. Two general structure theorems about semimodules. Abelevy gruppy i moduli [Abelian groups and modules].Vol. 15. Pp. 17–23. (In Russ.)
6. Vechtomov E. M. On three radicals for semimodules. Vestnik Vyatskogo gosudarstvennogo gumanitarnogo universiteta [Bulletin of Vyatka State University of Humanities]. 2005. No 13. Pp. 148–151. (In Russ.)
7. Vechtomov E. M., Shirokov D. V. Uporyadochennyye mnozhestva i reshetki : uchebnoye posobiye [Ordered sets and lattices : study guide]. Sankt-Peterburg: Lan’. 2024. 248 p. (In Russ.)
8. Vechtomov E. M., Petrov A. A. Funktsionalnaya algebra i polukoltsa. Polukoltsa s idempotentnym umnozheniyem : uchebnoye posobiye [Functional algebra and semirings. Semirings with idempotent multiplication : study guide]. Sankt-Peterburg: Lan’. 2022. 180 p.
   (In Russ.)
9. Vechtomov E. M., Lubyagina E. N. Lineynaya algebra : uchebnoye posobiye dlya vuzov. 2-e izd. [Linear algebra : a study guide for universities. 2nd ed.]. Moscow: Urait. 2019. 150 p. (In Russ.)

For citation: Vechtomov E. M. What is a semimodule. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics.
Mechanics. Informatics], 2024, no 2 (51), pp. 27−43. (In Russ.) https://doi.org/10.34130/1992-2752_2024_2_27

IV. One example of studying abstract algebra methods in mathematic degree programs

https://doi.org/10.34130/1992-2752_2024_2_44

Olga A. Sotnikova – Pitirim Sorokin Syktyvkar State University, sotnikovaoa@syktsu.ru

Vasilij V. Chermnykh – Pitirim Sorokin Syktyvkar State University

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Abstract. The article addresses some techniques which are instrumental for outlining abstract algebra methods when exploring some subject matters within the algebra course. As exemplified
in such chapters as Substitution, Complex Numbers, Matrices and Polynomials, the phenomena considered in these theories are shown to detect connections which offer the possibility to characterize the objectivity of the elements of the sets under consideration, the procedural nature of the interpretation of algebraic operations, and also the formalized nature of the properties of algebraic operations. According to the authors, the conditions mentioned can be used to illustrate the methods of abstract algebra.

Keywords: algebra course, math teacher training, abstract algebra, conceptual connections, formalization.

References

1. Yashina E. Yu. Dokazatel’stvo teoremy Frobeniusa kak zavershenie kursa algebry i chislovyk sistem v pedagogicheskom universitete. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 2023. No 2 (47). Pp. 69–82. (In Russ.)
2. Fried E. Elementarnoe vvedenie v abstraktnuyu algebru [An Elementary Introduction to Abstract Algebra]. Perevod s vengerskogo Yu. A. Danilova. Moscow: Mir, 1979. 260 p. (In Russ.)
3. Sotnikova O. A., Chermnykh V. V. On attracting students to study abstract algebra (using the example of one problem in group theory and its applications). Psihologiya obrazovaniya v polikul’turnom prostranstve [Psychology of education in a multicultural space]. 2024. No 2 (66). Pp. 138–147. (In Russ.)
4. Sotnikova O. A. Tselostnost’ vuzovskogo kursa algebry kak metodologicheskaya osnova ego ponimaniya : monografiya [The integrity of a university algebra course as a methodological basis for its understanding : monograph]. Arhangel’sk: Pomorskiy universitet,356 p. (In Russ.)

For citation: Sotnikova O. A., Chermnykh V. V. One example of studying abstract algebra methods in mathematic degree programs. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika.
Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 2 (51), pp. 44−56. (In Russ.) https://doi.org/10.34130/1992-2752_2024_2_44

V. About the works of three mathematicians graduates of Kazan and St. Petersburg universities who died in the Great Patriotic War

https://doi.org/10.34130/1992-2752_2024_2_57

Vladimir P. Odyniec – W.P.Odyniec@mail.ru

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Abstract. The article describes the works of two deceased graduates of Kazan University Marachkov (Morochkov) Vasyly Petrovich (1914–1942), Shishkanov Vasily Stepanovich (1914–1941) as well as graduate of the Imperial St. Petersburg University Zinserling Dmitry Petrovich (1864–1941) who died of starvation in besieged Leningrad.

Keywords: almost periodic function, characteristic number, stability of integrals, stability of the system of differential equations, prismatic rod bending, solving of plane problem of elasticity theory, elementary algebra, geometry of the ancient Egyptians, arithmetic of the ancient Egyptians.

References

1. Marachkov V. P. Stability of integrals of a system of differential equations with almost periodic coefficients. Izv. Phiz.-mat. o-va [Izv. Phys.-math. society]. Kazan, 1945. (3), 13. Pp. 3–50. (In Russ.)
2. Kniga pamyati Kazanskogo universiteta [Kazan University Memorial Book]. Kazan: Kazan University Publishing House, 2010. 124 p. (In Russ.)
3. Shishkanov V. S. Bending a Prizmatic Rod in Pairs. Uchenye zap. universiteta [University Sci. Notes]. Kazan, 1949. 109:3. Pp. 39–61. (In Russ.)
4. Zvolinsky N. V., Riz P. M. On Some Problems of the Nonlinear Theory of Elastcity. Prikl. mat. mechan. [Appl. Math. Mech.]. 1939. Vol. II. Issue 4. Pp. 417–428. (In Russ.)
5. Matematika v SSSR za sorok let 1917–1957. T. 2. Biobibliografiya [Mathematics in the USSR for forty years 1917–1957. Vol. 2. Biobibliography]. Moscow: Phizmatlit, 1959. 819 p. (In Russ.)
6. Zinserling V. A. Zinzerlings [Zinserlings]. Moscow: Prakticheskaya medicina, 2023. 120 p. (In Russ.)
7. Zinserling D. P. Prakticheskoye rukovodstvo statistiki [A Practical Guide to Statistics]. Leningrad: Gosizdat, 1924 (cover 1925). 167 p. (In Russ.)
8. Vulf N., Zinserling D. Elementarnaya algebra [Elementary Algebra]. St. Petersburg: Tip. A. S. Suvorina, 1912. 344 P. (Reprints in 1916 and 1923). (In Russ.)
9. Zinserling D. P. Geometry in the Ancient Egyptians. Izvestiya Rossiiskoi academii nauk. VI ser. [News of the Russian Academy of Sciences. VI series]. Leningrad: Izd-vo AN, 1925. Vol. 19. Issue 12. Pp. 541–568. (In Russ.)
10. Nauchnyye rabotniki Leningrada [Scientists of Leningrad]. Leningrad: Izd-vo AN USSR, 1934. 721 p. (In Russ.)
11. Zinserling D. P. Mathematics in the Ancient Egyptians. Matematika v shkole [Mathematics at school]. 1939. No 2. Pp. 5–20. (In Russ.)
12. Zinserling D. P. Mathematics in the Ancient Egyptians. Matematika v shkole [Mathematics at school]. 1939. No 3. Pp. 3–15. (In Russ.)
13. Kniga pamyati. Leningrad 1941–1945 [Memorial Book. Leningrad 1941–1945]. St. Petersburg: Pravitelstvo St. Peterburga, 2006. Bd.33. 712 p. (In Russ.)

For citation: Odyniec V. P. About the works of three mathematicians graduates of Kazan and St. Petersburg universities who died in the Great Patriotic War. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 2 (51), pp. 57−72. (In Russ.) https://doi.org/10.34130/1992-2752_2024_2_57

VI. Metaheuristic algorithms for the traveling salesman problem. Python library Scikit-opt

https://doi.org/10.34130/1992-2752_2024_2_73

Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University

Mikhail M. Glukhoy – Pitirim Sorokin Syktyvkar State University

Evgenija N. Startseva – Pitirim Sorokin Syktyvkar State University

Nikita A. Chernyan – Pitirim Sorokin Syktyvkar State University

Text

Abstract. The article discusses metaheuristic methods for solving the traveling salesman problem. The results of testing the ant colony algorithm and the genetic algorithm of the Python Scikit-opt library on two data sets (benchmarks) of the popular and widely used TSPLIB library are presented. Testing showed the possibility of using the library in practice and in the educational process: solutions close to optimal were obtained in an acceptable time.

Keywords: Python, Scikit-opt, TSPLIB, genetic algorithm, ant colony algorithm.

References

1. Zaporozhets D. Yu. Combined algorithm for solving transcomputational problems. Informatika, vychislitel’naya tekhnika i inzhenernoye obrazovaniye [Informatics, computing and engineering
   education]. 2018. No 1 (32). Pp. 10–20. (In Russ.)
2. Kobak V. G., Porksheyan V. M., Zhukovsky A. G., Peshkevich A. A. Solving the traveling salesman problem with a hybrid genetic model using the path approach. Izvestiya vuzov. SeveroKavkazskiy region. Seriya: Tekhnicheskiye nauki [News of universities. North Caucasus region. Series: Technical Sciences]. 2017. No 2 (194). Pp. 5–9. DOI: 10.17213/0321-2653-2017-2-5-9. (In Russ.)
3. Shcherbina O. A. Metaheuristic algorithms for combinatorial optimization problems (review). TVIM [TWIM]. 2014. No 1 (24). Pp. 56–72. (In Russ.)
4. Yashin S. N., Yashina N. I., Koshelev E. V., Ivanov A. A. Metaevristicheskiye algoritmy v upravlenii innovatsiyami : monografiya [Metaheuristic algorithms in innovation management :
   monograph]. Nizhniy Novgorod: LLC “Printing Workshop RADONEZH 2023. 200 p. (In Russ.)
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   optimal program control : textbook]. Moscow: Infra-M, 2020. 396 с. (In Russ.)
6. Using the Bees Algorithm to solve combinatorial optimisation problems for TSPLIB. IOP Conference Series Materials Science and Engineering. May 2020 847:012027 DOI:10.1088/1757-899X/847/1/012027 Available at: https://www.researchgate.net/publication/341711573_Using_the_ Bees_Algorithm_to_solve_combinatorial_optimisation_problems_ for_TSPLIB (accessed: 27.05.2024).
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13. Discrete and Combinatorial Optimization. Available at: http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/tsp/ (accessed: 21.04.2024).
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15. Andreev A. M., Shtutsa I. M. Study of the computational (time) complexity of a genetic algorithm using the example of solving the traveling salesman problem. Vestnik Izhevskogo gosudarstvennogo tekhnicheskogo universiteta [Bulletin of Izhevsk State Technical University]. 2008. No 4 (40). Pp. 144–146. (In Russ.)

For citation: Babikova N. N., Glukhoy M. M., Startseva E. N., Chernyan N. A. Metaheuristic algorithms for the traveling salesman problem. Python library Scikit-opt. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 2 (51), pp. 73−88. (In Russ.) https://doi.org/10.34130/1992-2752_2024_2_73

Full text

I. Development of a web service for automating the process of professional development for employees of government organizations based on the generation of individual educational routes

https://doi.org/10.34130/1992-2752_2024_1_4

Yuriy V. Golchevskiy – Pitirim Sorokin Syktyvkar State University, yurygol@mail.ru

Artem S. Garmatko – LLC “Philosophy IT”, garmatko.art@mail.ru

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Abstract. Thе paper presents a study of the problem of creating a web service for automating control over the professional development of employees process using the example of a state agencies working in the field of art and culture. An approach has been used that implies
individual training routes generation containing sets of courses, as a result of which the employee will receive all the necessary competencies. At the same time, the process becomes completely
controlled by the employer, who also has the opportunity to form and/or confirm an individual employee training route and track the progress.

Keywords: professional development, individual educational route, automation, web resource.

References

1. Golchevskiy Yu., Novokshonova E., Yermolenko A. Digital economy competencies as a vital necessity of a modern successful specialist. Advances in Economics, Business and Management Research.Vol. 156. Pp. 291–296. DOI: 10.2991/aebmr.k.201205.048.
2. Galkin O. A. Professional development in the system of lifelong professional education in the sphere of culture: the role and issues of content. Problemy i perspektivy razvitiya vysshego obrazovaniya v sfere kul’tury i iskusstv [Problems and prospects for the development
   of higher education in the field of culture and the arts]. Proc. of the scientific and methodological conference of the educational institution teaching staff. Minsk: The Belarusian State University of Culture and Arts, 2023. Pp. 103–111. EDN: PCPNDH. (In Russ.)
3. Babikova N. N. Education in the digital age: remember or google. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics]. 2022. No 3 (44). Pp. 33–46. DOI:
   10.34130/1992-2752_2022_3_33. (In Russ.)
4. Normansky N. S. Gamification as a Mechanism of Digital Transformation of Personnel Training in the Field of Culture and Art. Kul’turnaya zhizn’ Yuga Rossii [Cultural Studies of Russian South].No 1 (84). Pp. 101–110. DOI: 10.24412/2070-075X-2022-1-101-(In Russ.)
5. Karavaev N. L., Soboleva E. V. Analysis of software services and platforms that have the potential for educational process gamification.Nauchno-metodicheskiy elektronnyy zhurnal «Kontsept» [Scientific and methodological electronic journal “Concept”]. 2017. No 8. Pp. 14–25.
   EDN: ZEGUJZ.(In Russ.)
6. Golchevskiy Yu. V., Babenko V. V. Problems of gaming technologies introducing into business processes and interfaces of business-oriented software systems. Informatsionnyye tekhnologii v
   modelirovanii i upravlenii: podkhody, metody, resheniya: sbornik nauchnykh statey I Vserossiyskoy nauchnoy konferentsii. 12–14 dekabrya 2017 g.: v 2 ch. [Information technologies in modeling and management: approaches, methods, solutions: collection of scientific articles of the I All-Russian Scientific Conference. December 12–14,
   2017: at 2 a.m.]. Tolyatti: TSU, 2017. Part 2. Pp. 318–324. EDN: YWGOJL. (In Russ.)
7. Zeybek N., Saygı E. Gamification in Education: Why, Where, When, and How? – A Systematic Review. Games and Culture. 2024. Vol. 19. Issue 2. Pp. 237–264. DOI: 10.1177/15554120231158625.
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   10.1007/s10639-022-11122-4.
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   Culture]. 2019. No 3 (11). Pp. 127–133. DOI: 10.31443/2541-8874-2019- 3-11-127-133. (In Russ.)
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    Experimental Education]. 2017. No 1. Pp. 74–78. EDN: XVGSSD. (InRuss.)
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14. Taipalus T. Database management system performance comparisons: A systematic literature review. Journal of Systems and Software. 2024. Vol. 208. 111872. DOI: 10.1016/j.jss.2023.111872.

II. What is a semiring

https://doi.org/10.34130/1992-2752_2024_1_21

Evgeny M. Vechtomov – Vyatka State University, vecht@mail.ru

Text

Abstract. The article discusses the beginnings of the theory of semirings. The author analyzes the definition (axiomatics) of a semiring and introduces the initial concepts of the theory of
semirings. The work provides basic examples, indicates the most important classes of semirings, and also formulates the first structure theorems about semirings. The presented material is educational and mathematical in nature, includes comments, explanations and 25 exercises.

Keywords: algebraic structure, semiring, study of the theory of semirings

References

1. Vechtomov E. M. Vvedeniye v polukol’tsa [Introduction to Semirings]. Kirov: Izd-vo vyatsk. gos. ped. un-ta, 2000. 44 p. (In Russ.)
2. Vechtomov E. M. Student educational and research seminar on algebra. Matematicheskiy vestnik Vyatskogo gosudarstvennogo universiteta [Mathematical Bulletin of Vyatka State University]. 2021. No 3. Pp. 36–45. (In Russ.)
3. Vechtomov E. M. Studying the basics of the theory of semirings. Prime Ideals. Matematicheskiy vestnik Vyatskogo gosudarstvennogo universiteta [Mathematical Bulletin of Vyatka State University]. 2021. No 4. Pp. 4–14. (In Russ.)
4. Vechtomov E. M. Matematika: osnovnyye matematicheskiye struktury: uchebnoye posobiye. 2-e izd. [Mathematics: basic mathematical structures: study guide. 2nd ed.]. Moscow: Urait.296 p. (In Russ.)
5. Vechtomov E. M., Sidorov V. V. Abstraktnaya algebra. Bazovyy kurs : uchebnoye posobiye [Abstract algebra. Basic course : study guide]. Kirov: OOO «Izdatelstvo “Raduga-PRESS”», 2014. 260 p. (In Russ.)
6. Sidorov V. V. Algebra: algebraicheskiye struktury. kompleksnyye chisla. mnogochleny : uchebnoye posobiye [Algebra: algebraic structures, complex numbers, polynomials : study guide]. Kirov: OOO «Izdatelstvo “Raduga-PRESS”», 2013. 232 p. (In Russ.)
7. Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V. Elementy funktsionalnoy algebry: monografiya: v 2 t. [Elements of functional algebra: monograph: in 2 vol.]. Kirov: OOO
   «Izdatelstvo “Raduga-PRESS”», 2016. Vol. 1. 384 p. (In Russ.)
8. Vechtomov E. M., Lubyagina E. N., Chermnykh V. V. Elementy teorii polukolets: monografiya [Elements of the theory of semirings: monograph]. Kirov: OOO «Izdatelstvo “Raduga-PRESS”», 2012. 228 p.(In Russ.)
9. Vechtomov E. M., Petrov A. A. Funktsionalnaya algebra i polukoltsa. Polukoltsa s idempotentnym umnozheniyem : uchebnoye posobiye [Functional algebra and semirings. Semirings with idempotent multiplication : study guide]. Sankt-Peterburg: Lan’, 2022. 180 p.
   (In Russ.)
10. Vechtomov E. M., Cheraneva A. V. Semifields and their properties. Fundamentalnaya i prikladnaya matematika [Fundamental and applied mathematics]. 2008. Vol. 14. No 5. Pp. 3–54. (In Russ.)
11. Vechtomov E. M., Chermnykh V. V. Main directions of development of the theory of semirings. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin
    of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 2021. No 4. Pp. 4–40. (In Russ.)
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    (In Russ.)
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18. Mal’tsev A. I. Algebraicheskiye sistemy [Algebraic systems]. Moscow: Nauka, 1970. 392 p. (In Russ.)

For citation: Vechtomov E. M. What is a semiring. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics.
Mechanics. Informatics], 2024, no 1 (50), pp. 21−42. (In Russ.) https://doi.org/10.34130/1992-2752_2024_1_21

III. About one of the axiomatics for determining trigonometric functions when training future mathematics teachers

https://doi.org/10.34130/1992-2752_2024_1_43

Elena N. Shustova – Pitirim Sorokin Syktyvkar State University, shustovaen@yandex.ru

Text

Abstract. The article outlines the main theoretical principles of the methodology for teaching future mathematics teachers at a university the definition of trigonometric functions using one of the
axiomatics. The sequence of studying the properties of functions and axioms of the proposed system is given, as well as a brief description of the results of applying the described approach in the process of training students in pedagogical areas of university training.

Keywords: axiomatic method, trigonometric functions, university training for future mathematics teachers

References

1. Sadovsky V. N. Axiomatic method of constructing scientific knowledge. Filosofskie voprosy sovremennoy formal’noy logiki. M.: Izdvo Akademii nauk SSSR [Philosophical issues of modern formal logic. M.: Publishing House of the USSR Academy of Sciences]. 1962. Pp. 215–(In Russ.)
2. Masalova S. I. The role of axiomatization in the process of constructing a mathematical theory. Vestnik DGTU [Bulletin of DSTU].
3. No 3. Pp. 71–77. Available: https://cyberleninka.ru/article/n/rolaksiomatizatsii-v-protsesse-postroeniya-matematicheskoy-teorii (accessed: 08.02.2024). (In Russ.)
4. Popov N. I., Shustova E. N. Application of the axiomatic method for introducing the exponential function when training future mathematics teachers. Vestnik Moskovskogo gosudarstvennogo
   oblastnogo universiteta. Seriya: Pedagogika [Bulletin of Moscow State Regional University. Series: Pedagogy]. 2020. No 3. Pp. 86–94. (In Russ.)
5. Lyubetsky V. A. Osnovnye ponyatiya shkol’noy matematiki : uchebnoye posobie dlya studentov ped. in-tov po spec. № 2104 “Matematika” [Basic concepts of school mathematics : Proc. manual for pedagogical students. Institute for specialties No 2104 “Mathematics”]. Moscow: Prosveshchenie, 1987. 400 p. (In Russ.)
6. Lihtarnikov L. M. Elementarnoe vvedenie v funkcional’nye uravneniya: kn. dlya nachinayushchih izuchat’ funkzion. uravneniya i prepodavateley [Elementary introduction to functional equations: book. for beginners to learn functions. equations and teachers]. SPB.: Lan’,158 p. (In Russ.)
7. Ilyin V. A., Sadovnichy V. A., Sendov Bl. X. Matematicheskiy analiz : v 3 t. T. 1: Nachal’nyj kurs: uchebnik dlya studentov vuzo, obuchayushchihsya po special’nosti “Matematika”, “Prikladnaya
   matematika” [Mathematical analysis : in 3 volumes. T. 1: Initial course: textbook for university students studying in the specialty “Mathematics”, “Applied Mathematics”]. Pod red. A. N. Tihonova. 2-e izd., pererab. Moscow: Izd-vo MGU, 1985. 660 p.
8. Korobeinikov A. I. Functional equations and their applications Molodye issledovateli – Respublike Komi: sbornik tezisov Pyatoy respublikanskoy nauchno-prakticheskoy konferencii. Syktyvkar: MO i VSh Respubliki Komi, SGU [Young researchers – the Komi Republic:
   collection of abstracts of the Fifth Republican Scientific and Practical Conference]. Syktyvkar: Moscow Region and Higher School of the Komi Republic, SGU, 2002. Pp. 34–41 (In Russ.)
9. Alexyuk V. N., Shustova E. N. Elementarnye funkcii. 2 [Elementary functions. 2]. Ped. in-t. Syktyvkar, 2010. 12 p. Dep v VINITI 25.10.2010, no 610-B2010 (In Russ.)
10. Alexyuk V. N. Elementarnye funkcii. 1 [Elementary functions. 1]. Ped. in-t. Syktyvkar, 2010. 13 p. Dep v VINITI 11.10.2010, no 577- B2010 (In Russ.)
11. Shustova E. N. Methodology for presenting the course “Theory of elementary functions”. Vestnik KGPI [Bulletin of KSPI]. Syktyvkar: Komi Pedagogical Institute, 2010. Pp. 268–270. (In Russ.)
12. Shustova E. N. Features of using the axiomatic method of introducing elementary functions in teaching future teachers of mathematics at the university. Obrazovatel’nyj vestnik “Soznanie” [Educational Bulletin “Consciousness”]. 2022. Vol. 24. No 4. Pp. 23–30. (In Russ.)
13. Shustova E. N. Formation of components of methodological competence of mathematics teachers when studying the axiomatic method of introducing elementary functions at a university. Mir nauki, kul’tury, obrazovaniya [World of science, culture, education]. 2022.
    No 3 (94). Pp. 78–81. (In Russ.)
14. Popov N. I., Shustova E. N. Elementarnye funkcii v shkol’nom kurse matemayiki : uchebnoe posobie. 2-e izd., ispr. i dop. [Elementary functions in a school mathematics course : a textbook. 2nd ed., rev. and additional]. Syktyvkar: Izd-vo SGU im. Pitirima Sorokina, 2023. 165 p.
    (In Russ.)

For citation: Shustova E. N. About one of the axiomatics for determining trigonometric functions when training future mathematics teachers. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 1 (50), pp. 43−54. (In Russ.) https://doi.org/10.34130/1992-2752_2024_1_43

IV. Computer games and combinatorial problems

Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University, valmasha@mail.ru

Nadezhda O. Kotelina – Pitirim Sorokin Syktyvkar State University, valmasha@mail.ru

Marija A. Valueva – St. Petersburg State University of Culture

Nikolaj A. Startsev – St. Petersburg State Electrotechnical University “LETI” named after V. I. Ulyanov (Lenin)

Text

Abstract. The author’s problems in combinatorics, based on computer games, are offered for discussion in the article. Examples of problems for practical classes and laboratory work are presented on the following topics: sum and product rules, permutations with and without repetitions, placements with and without repetitions, combinations with and without repetitions, partitioning a number into terms and partitioning a number into terms, each of which does
not exceed given value, inclusion and exclusion formula. The problems were tested in the process of teaching the discipline “Discrete Mathematics” to students in the field of study “Applied Informatics”.

Keywords: combinatorics, combinatorial problems, computer games, training, author’s problems

References

1. Tyumeneva Yu. A., Val’dman A. I., Karnoi M. What Does Subject Knowledge Give for Its Applying in New Context. The First Results from Studies TIMSS-2011 and PISA-2012. Voprosy obrazovaniya [Questions of education]. 2014. No 1. Pp. 8–24. DOI 10.17323/1814-9545-2014-1-8-24. (In Russ.)
2. Tyumeneva Yu. A., Shkliaeva I. V. Two Approaches to the Concept of Knowledge Application: Transfer and Modeling. Overview and Criticism. Voprosy obrazovaniya [Questions of education]. 2016. No 3. Pp. 8–33. DOI 10.17323/1814-9545-2016-3-8-33. (In Russ.)
3. Tyumeneva Y. A., Goncharova M. V. Following the Template: Transferring Modeling Skills to Nonstandard Problems. Russian Education & Society. 2017. No 59 (5–6). Pp. 298–318. DOI
   10.1080/10609393.2017.1408370.
4. Vilenkin N. Ya., Vilenkin A. N., Vilenkin P. A. Kombinatorika [Combinatorics]. Moscow: FIMA, MCzNMO, 2006. 400 p. (In Russ.)
5. Knuth D. Iskusstvo programmirovaniya. Tom 4, A. Kombinatornyye algoritmy [The Art of Computer Programming, Vol. 4, A: Combinatorial Algorithms]. Moscow: I.D. Williams LLC, 2013. Part 1. 960 p. (In Russ.)
6. Babikova N. N. Aligning assessment methods with learning outcomes based on taxonomy. Obrazovaniye i pedagogicheskiye nauki v XXI veke: aktual’nyye voprosy, dostizheniya i innovatsii : sbornik statey II Mezhdunarodnoy nauchno-prakticheskoy konferentsii : v 2 chastyah
   [Education and pedagogical science in the XXI century: current issues, achievements and innovations : collection of articles of the international scientific and practical conference : in 2 parts]. Penza, 2017. Part. 1. Pp. 93–100. (In Russ.)
7. Babikova N. N. Education in the digital age: remember or google Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 2022. No 3 (44). Pp. 33–46. DOI
   10.34130/1992-2752_2022_3_33.(In Russ.)
8. Patrashov A. S. Matematicheskoe rukovodstvo po sozdaniyu komp‘yuterny‘x igr: spravochnik [A mathematical guide to creating computer games: guide.] Ekaterinburg: Internet-izdatel‘stvo Ridero, 316 p. (In Russ.)
9. Patrashov A. S. Application of higher mathematics in computer game design. Sistemnyy administrator [System Administrator]. 2020. No 5 (210). Pp. 46–49. (In Russ.)

For citation: Babikova N. N., Kotelina N. O., Valueva M. A., Startsev N. A. Computer games and combinatorial problems. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika.
Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 1 (50), pp. 55−72. (In Russ.) https://doi.org/10.34130/1992-2752_2024_1_55

V. Educational and innovative potential of network interaction between organizations using the example of the development of research and project activities of students

https://doi.org/10.34130/1992-2752_2024_1_73

Irina V. Kleshcheva – Herzen State Pedagogical University of Russia, iv-kl@list.ru

Abstract. The article examines the substantive, organizational, and functional problems of implementing network interaction in the field of education. The timeliness and effectiveness of network interaction as a tool for integrated and effective solution of various problems in education is argued. The pedagogical feasibility of using network interaction to improve the quality of mathematics education has been scientifically substantiated and experimentally confirmed.
The methodological basis of network educational interaction is motivated by a systematic approach that determines the design and functioning of the educational network at the conceptual, structural
and elemental levels. The system-forming factor in this case is most often common goals, for the sake of which pedagogical efforts are consolidated.

Keywords: networking, systems approach, research activities, project activities, quality of mathematical education

References

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2. Atlas novykh professii 3.0 [Atlas of new professions 3.0]. Ed. D. Varlamova, D. Sudakova. Moscow: Intellectual literature, 2020. 456 p. (In Russ.)
3. Korotayeva Ye. V. Teoriya i praktika pedagogicheskikh vzaimodeystviy : uchebnik i praktikum dlya vuzov [Theory and practice of pedagogical interactions : textbook and workshop for
   universities]. Moscow: Yurayt, 2021. 241 p. (In Russ.)
4. Obrazovatel’naya dinamika setevoy lichnosti : sbornik trudov IV nauchno-prakticheskoy konferentsii, Sankt-Peterburg, 28 yanvarya 2021 goda [Educational dynamics of network personality: collection of proceedings of the IV scientific and practical conference, St.
   Petersburg, January 28, 2021]. Editors: A. A. Akhayan, E. V. Piskunova; Letters to The Emissia. Offline Letters. St. Petersburg: Publishing House of the Russian State Pedagogical University named after A. I. Herzen, 2021. Vol. 2: Methodological application. 127 p. (In
   Russ.)
5. Shvetsov M. Yu., Aldar L. D. Network interaction of educational institutions of vocational education in the region. Uchenyye zapiski Zabaykal’skogo gosudarstvennogo universiteta. Seriya: Pedagogika i psikhologiya [Scientific notes of the Transbaikal State University. Ser.:
   Pedagogy and psychology]. 2012. Pp. 33–38. (In Russ.)
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   276/ (accessed: 16.02.2024). (In Russ.)
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   obshchego obrazovaniya: prikaz Minprosveshcheniya Rossii ot 31 avgusta 2023 g. № 650 [On approval of the Procedure for implementing activities for professional guidance of students in
   educational programs of basic general and secondary general education: Order of the Ministry of Education of Russia dated August 31, 2023 No 650] [Electronic resource]. Available at:
   https://docs.edu.gov.ru/document/53d3c69503ab48125815993c07525 6b0/ (accessed: 15.02.2024). (In Russ.)
8. Bugrova N. S. Network models as a trend in the development of advanced training of teaching staff in modern Russia. Izvestiya Rossiyskogo gosudarstvennogo pedagogicheskogo universiteta imeni A. I. Gertsena [News of the Russian State Pedagogical University
   named after A. I. Herzen]. St. Petersburg, 2007. No 17 (43). Part 2: Pedagogy and psychology, theory and teaching methods. Pp. 50–53. (In Russ.)
9. Ob organizatsii i osushchestvlenii obrazovatel’noy deyatel’nosti pri setevoy forme realizatsii obrazovatel’nykh programm: prikaz Ministerstva nauki i vysshego obrazovaniya RF i Ministerstva prosveshcheniya RF ot 5 avgusta 2020 g. № 882/391 [On the
   organization and implementation of educational activities in the network form of implementation of educational programs: Order of the Ministry of Science and Higher Education of the Russian
   Federation and the Ministry of Education of the Russian Federation of August 5, 2020 No 882/391] [Electronic resource]. Available at: https://base.garant.ru/74626602/ (accessed: 15.02.2024). (In Russ.)
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    3156 (accessed: 14.03.2024). (In Russ.)
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For citation: Kleshcheva I. V. Educational and innovative potential of network interaction between organizations using the example of the development of research and project activities of
students. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 1 (50), pp. 73−93. (In Russ.) https://doi.org/10.34130/1992-2752_2024_1_73

Full text

I. Some features of production angles of particles born in decay reactions in relativistic and nonrelativistic cases

https://doi.org/10.34130/1992-2752_2023_4_4

Pavel A. Makarov – Institute of Physics and Mathematics, Federal Research Centre Komi Science Centre, Ural Branch, RAS, makarovpa@ipm.komisc.ru

Text

Abstract. On the basis of kinematic approach some features of production angles of particles born in decay processes are studied. Statement and theorems describing the kinematics of decay reactions in the nonrelativistic and relativistic cases are formulated and proved. Corollaries allowing to determine the maximum of production angles of born particles are obtained and analyzed.

Keywords: decay, kinematics, conservation laws, production angles, Lorentz transformations

References

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5. Pf¨utzner M., et al. First evidence for the two-proton decay of 45Fe. Eur Phys J A. 2002. Vol. 14. Pp. 279–285.
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7. Alexandrov D. V. et al.Observation of spontaneous departure of 14C nuclei from 223Ra. Pis’ma v ZHETF [Writings in ZhETF]. 1984. Vol. 40. Pp. 152–154. (In Russ.)
8. Oganesyan Yu. Ts., Penionzhkevich Y. E., Grigoriev V. A. Fizika tyazhelykh ionov i yeye prilozheniya [Physics of heavy ions and its applications]. Dubna: JINR, 2021. 363 p. (In Russ.)
9. Nelipa N. F. Fizika elementarnykh chastits [Physics of elementary particles]. Moscow: Vysshaya shkola, 1977. 608 p. (In Russ.)
10. Particle Data Group. Review of Particle Physics. Progress of Theoretical and Experimental Physics. 2022. Vol. 2022. No 8. Art. N. 083C01.
11. Baldin A. M. et al Kinematika yadernykh reaktsiy [Kinematics of nuclear reactions]. 2nd ed., rev. and supplement. Moscow: Atomizdat, 456 p. (In Russ.)
12. ATLAS Collaboration, Aad G. et al. Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B. 2012. Vol. 716. Pp. 1–29.
13. CMS collaboration, Chatrchyan S. et al. Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B. 2012. Vol. 716. Pp. 30–61.
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16. Landau L. D., Lifshits E. M. Teoreticheskaya fizika. T. II. Teoriya polya [Theoretical physics. V. II. Field theory]. Moscow: FIZMATLIT, 536 p. (In Russ.)
17. Landau L. D., Lifshits E. M. Theoretical physics. V. IV. Berestetsky V. B., Lifshits E. M., Pitaevsky L. P. Kvantovaya elektrodinamika [Quantum electrodynamics]. Moscow: FIZMATLIT,720 p. (In Russ.)
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II. Analysis of data on forest fires in the Komi Republic using Excel and Python

https://doi.org/10.34130/1992-2752_2023_4_29

Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University

Nadezhda O. Kotelina – Pitirim Sorokin Syktyvkar State University

Fyodor N. Tentyukov – Pitirim Sorokin Syktyvkar State University

Text

Abstract. The article presents the results of data analysis on forest fires in the Komi Republic for 2010–2023. The study was carried out using the Excel spreadsheet processor and Python libraries: Scikit-learn, Pandas, Numpy, Openpyxl, Folium.

Keywords: data analysis, Python, k-means clustering, DBSCAN clustering, forest fires

References

1. Kolerov D. A. Improving methods for monitoring and responding to forest fires in the Komi Republic (using the example of artificial intelligence). OBZH: Osnovy bezopasnosti zhizni [FLS. Fundamentals of Life Safety]. 2022. No 1. Pp. 56–59. (In Russ.)
2. Volokitina A. V., Sofronova T. M., Korec M. A. Regional Scales of Fire Danger Rating in the Forest: Improved Technique. Sibirskij lesnoj zhurnal [Siberian Journal of Forest Science]. 2017. No 2. Pp. 52–61. DOI: 10.15372/SJFS20170206. (In Russ.)
3. Geoinformatsionnyy portal Respubliki Komi [Geoinformation portal of the Komi Republic] [Electronic resource]. Available at: https://gis.rkomi.ru/ (accessed: 11.11.2023). (In Russ.)
4. Kotelina N. O., Matvijchuk B. R. Image clustering by the k-means method. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of the Syktyvkar University. Ser. 1: Math. Mechanics. Informatics]. 2019. No 3 (32). Pp. 101–112. (In Russ.)
5. Scikit-learn documentation [Electronic resource]. Available at: https://scikit-learn.org/stable/modules/clustering.html#hdbscan (accessed: 11.11.2023).
6. Anisimov O. A., Borsch S. V., Georgievsky V. Yu. et al. Metody ocenki posledstvij izmeneniya klimata dlya fizicheskih i biologicheskih sistem [Methods for assessing the effects of climate change on physical and biological systems]. Institute of Global Climate and Ecology of the
   Federal Service for Hydrometeorology and Environmental Monitoring and the Russian Academy of Sciences. Moscow: Scientific Research Center of Space Hydrometeorology «Planet», 2012. 512 p. (In Russ.)

For citation: Babikova N. N., Kotelina N. O., Tentyukov F. N. Analysis of data on forest fires in the Komi Republic using Excel and Python. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 4 (49), pp. 29−46. (In Russ.) https://doi.org/10.34130/1992-2752_2023_4_29

III. Introduction to the theory of mathematical modeling when teaching students

https://doi.org/10.34130/1992-2752_2023_4_47

Andrey V. Yermolenko – Pitirim Sorokin Syktyvkar State University, ea74@list.ru

Text

Abstract. The article discusses the issues of introducing students to mathematical modeling in junior years. Ways of getting to know each other through individual training, instilling interest through historical and philosophical excursions, and familiarization with mathematical modeling in fundamental disciplines are proposed.

Keywords: numerical methods, training of scientific personnel, Lotka-Voltaire model, mathematical modeling

References

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   [Refined nonlinear equations in non-classical tasks of mechanics of shells]. Syktyvkar: Publishing House of Syktyvkar University, 2009. 141 p. (In Russ.)
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   No 3 (44). Pp. 47–63. (In Russ.)
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   (In Russ.)
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For citation: Yermolenko A. V. Introduction to the theory of mathematical modeling when teaching students. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics],
2023, no 4 (49), pp. 47−58. (In Russ.) https://doi.org/10.34130/1992- 2752_2023_4_47

IV. Semantic aspects in the methods of math teaching

https://doi.org/10.34130/1992-2752_2023_4_59

Olga A. Sotnikova – Pitirim Sorokin Syktyvkar State University, sotnikovaoa@syktsu.ru

Text

Abstract. The article features the analysis of methodology of mathematics in relation to the semantics of mathematical matter. The author’s assumptions are based on the need to gain
understanding in learning mathematics. It is justified that semantic aspects of teaching math involve establishing meaningful connections within mathematical matter.

Keywords: understanding mathematics in teaching, meaningful connections, comprehension of mathematical concepts

References

1. Bibler V. S. Ot naukoucheniya – k logike kul’tury: Dva filosofskikh vvedeniya v dvadtsat’ pervyy vek [From science studies to the logic of culture: Two philosophical introductions to the twenty-first century] [Electronic resource]. Available at: https://platona.net/load/ knigi_po_filosofii/kulturologija/bibler_v_s_ot_naukouchenija_k_ logike_kultury_ dva_filosofskikh vvedenija_v_dvadcat_pervyj vek/16-1-0-1042 (accessed: 28.11.2023). (In Russ.)
2. Doblaev V. P. Smyslovaya struktura uchebnogo teksta i problemy ego ponimaniya [The semantic structure of the educational text and the problems of its understanding]. Moscow: Pedagogy, 1982. 176 p. (In Russ.)
3. Ruzavin G. I. Understanding as a complex methodological problem. Problemy ob”yasneniya i ponimaniya v nauchnom poznanii : sb. st. [Problems of explanation and understanding in scientific cognition : digest of articles]. USSR Academy of Sciences, Institute of Philosophy;
   answer ed. G. I. Ruzavin. Moscow: Institute of Philosophy, 1982. Pp. 1– (In Russ.)
4. Zinchenko V. P. Psihologicheskie osnovy pedagogiki [Psychological foundations of pedagogy]. Moscow: Gardariki, 2002. 431 p. (In Russ.)
5. Frege G. Smysl i znacheniye [Meaning and significance] [Electronic resource]. Available at: https://kant.narod.ru/frege1.htm (accessed: 12.11.2023) (In Russ.)
6. Cherch A. Vvedenie v matematicheskuyu logiku [Introduction to Mathematical Logic]. Moscow: Izdvo foreign. lit., 1960. 485 p. (In Russ.)
7. Mader V. V. Vvedeniye v metodologiyu matematiki [Introduction to the methodology of mathematics] [Electronic resource]. Available at: https://fileskachat.com/view/
   42260_f37ce0eec2526c065cec09140f140be3.html (accessed: 03.10.2023) (In Russ.)
8. Shafarevich I. R. Osnovnye ponyatiya algebry [Basic concepts of algebra]. Izhevsk: Izhevsk Republican Printing House, 1999. 348 p. (In Russ.)
9. Vechtomov E. M. Metafizika matematiki [Metaphysics of Mathematics]. Kirov: Izd-v VyatGGU, 2006. 508 p. (In Russ.)
10. Vejl’ G. Matematicheskoe myshlenie [Mathematical thinking]. Moscow: Nauka, 1989. 400 p. (In Russ.)

For citation: Sotnikova O. A. Semantic aspects in the methods of math teaching. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 4 (49), pp. 59−69. (In Russ.) https://doi.org/10.34130/1992-2752_2023_4_59

V. On the works of the mathematician, defender of Moscow, Korean Shin Deng Yun (1912–1942)

https://doi.org/10.34130/1992-2752_2023_4_70

Vladimir P. Odinets – W.P.Odyniec@mail.ru

Abstract. The article discusses the works on quasi-differential equations and quasi-differential operators in the Hilbert space by Korean Shin Deng Yun (1912–1942), post-graduate student at the Faculty of Mechanics and Mathematics of Moscow State University.

Keywords: quasi-differential equations, quasi-differential operators, Hilbert space, linearly independent Solutions, defense of Moscow

References

1. Matematika v SSSR za sorok let 1917–1957. T. 2. Biobibliografiya [Mathematics in the USSR for Forty Years 1917–1957. Bd. 2. Biobibliography]. Moscow: Fizmatlit, 1959. 819 p.
2. Shin Deng Yun. Oscillation theorems of boundary problems of a self-adjoint differential system of the 4th order. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1938. 18. No 6. Pp. 323–324. (In Russ.)
3. Shin Deng Yun. Theorems for the existence of a quasi-differential equation of the nth order. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1938. 18. No 8. Pp. 515–518. (In Russ.)
4. Shin Deng Yun. Solutions of a self-adjoint differential equation u[n] = lu, I(l) 6= 0, belonging to L2(0, ∞). Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1938. 18. No 8. Pp. 519–522. (In Russ.)
5. Odyniec V. P. О Leningradskih matematikah, pogibshih v 1941–1944 godah. II [About Leningrad mathematicians, who died in 1941–1944. II]. Syktyvkar: Izd-vo SGU named after Pitirim Sorokin, 2021. 108 p.
6. Janchevski S. Oscillation theorem for the differential boundary value problem of the fourth order. Ann. of Math. 1927–1928. 29. Pp. 521– 542.
7. Janchevski S. Oscillation theorem for the differential boundary value problem of the fourth order. Ann. of Math. 1930. 31. Pp. 663–680.
8. Shin Deng Yun. Solutions of a linear quasi-differential equation of nth order. Matem. sb. [Mathematical collection]. 1940. 7(49). Pp. 479– (In Russ.)
9. Matematika v SSSR za tridcat’ let 1917–1947 [Mathematics in the USSR for Thirty Years 1917–1947]. Edited by A. G. Kurosh,A. I. Markushevich, P. K. Rashevsky. M.; L.: OGIZ, Izd-vo tekhn.-
   teor. litters, 1948. 1045 p.
10. Shin Deng Yun. Quasi-differential operators in Hilbert space. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. No 8. Pp. 523–526. (In Russ.)
11. Shin Deng Yun. Solutions of the System of Quasi-Differential Equations. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1940. 28. No 5. Pp. 392–395. (In Russ.)
12. Nikolsky S. M. Vospominaniya [Memories]. Moscow: Izd-vo MIAN,160 p.
13. Shin Deng Yun. Quasi-differential operators in Hilbert space. Matem. sb. [Mathematical collection]. 1943. 13 (55). Pp. 39–70. (In Russ.)

Full text

I. On the structure of the ideals of the semiring of natural numbers

https://doi.org/10.34130/1992-2752_2023_3_4

Daniil E. Menyaev – Pitirim Sorokin Syktyvkar State University, dahnny@yandex.ru

Vasily V. Chermnykh – Pitirim Sorokin Syktyvkar State University, vv146@mail.ru

Text

Abstract. The article investigates the ideals of the semiring of natural numbers. A criterion is obtained for a natural number to belong to an ideal in terms of integer solutions of a certain system of linear inequalities. Applications of this criterion are demonstrated.

Keywords: semiring, ideal, Frobenius constant, Sylvester’s theorem.

References

1. Roberts J. B. Note on linear form. Proc. AMS. 1956. Vol. 7. Pp. 465–469.
2. Dulmage A.L., Mendelsohn N.S. Gaps in the exponent set of primitive matrices. Illinois J. Math. 1964. Vol. 8. Pp. 642–656.
3. Hofmeister G.R. Zu einem Problem von Frobenius. Norske Videnskabers Selskabs Skrifter. 1966. Vol. 5. Pp. 1–37.
4. Selmer E. S. On the linear diophantine problem of Frobenius. Journal F¨ur Die Reine Und Angewandte Mathematik (Crelles Journal). 1977. Vol. 293–294. Pp. 1–17. doi:10.1515/crll.1977.293-294.1.
5. Sylvester J. J. Mathematical questions, with their Solutions. Educational Times. 1884. Vol. 41. P. 21.
6. Golan J. S. Semirings and their applications. Dordrecht: Kluwer Acad. Publ., 1999. 365 p.
7. Chermnykh V. V. Funktsional’nye predstavleniya polukolets [Functional representations of semirings]. Kirov: VyatGU, 2010. P. 224. (In Russ.)
8. Allen P. J., Dale L. Ideal theory in the semiring Z +. Publ. Math. Debrecen. 1975. Vol. 22 (3–4). Pp. 219–224.
9. Chermnykh V. V., Nikolaeva O. V. On ideals of semirings of natural numbers. Matematicheskiy vestnik pedvuzov i unirsitetov Volgo-Vyatskogo regiona [Mathematical Bulletin of Pedagogical
   Universities and Universities of the Volga-Vyatka Region]. 2009. Vol. 11. Pp. 118–121. (In Russ.)

For citation: Menyaev D. E., Chermnykh V. V. On the structure of the ideals of the semiring of natural numbers. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics],
2023, no 3 (48), pp. 4−17. (In Russ.) https://doi.org/10.34130/1992-2752_2023_3_4

II.Balance Sheet Channel of Monetary Policy: Review of Empirical Methods\

https://doi.org/10.34130/1992-2752_2023_3_18

Olga A. Maltseva – Bank of Russia, maltseva.rs@yandex.ru

Irina V. Polyakova – 1Bank of Russia

Evgenija N. Startseva – Pitirim Sorokin Syktyvkar State University

Text

Abstract. Research on the balance sheet channel of monetary policy is extensive, especially for developed country economies. The question of the specifics of the operation of the balance sheet (broad credit) channel in Russia remains open.

Keywords: monetary policy, balance sheet channel, vector autoregression, panel data, generalized method of moments, local projections approach.

References

1. Main directions of the unified state monetary policy for 2023 and the periods 2024 and 2025. Bank of Russia. 2023. Available at: http://www.cbr.ru/about_br/publ/ondkp/ (accessed: 01.09.2023). (In Russ.)
2. Christopher A. Sims Macroeconomics and Reality. Econometrica.Vol. 48. No 1. Jan. Pp. 1–48. https://doi.org/10.2307/1912017.
3. Gertler M., Gilchrist S. . Monetary Policy, Business Cycles and the Behaviour of Small Manufacturing Firms. Quarterly Journal of Economics. 1994. Vol. 109. Issue 2. Pp. 309–340.
4. Bernanke B. S., Gertler M. Inside the Black Box: The Credit Channel of Monetary Policy Transmission. Journal of Economic Perspectives. 1995. Vol. 9. No 4. Pp. 27–48.
5. Holtem¨oller O. Further VAR evidence for the effectiveness of a credit channel in Germany. SFB 373 Discussion Paper (Humboldt Univer-sity of Berlin, Interdisciplinary Research Project 373: Quantification and Simu-lation of Economic Processes). Berlin, 2002. No 2002,66. 21 p.
   Available at: https://www.econstor.eu/handle/10419/65303 (accessed: 01.09.2023).
6. Shchepeleva M. A. Modeling the Balance Sheet Channel of Monetary Transmission in Russia. Finansovyy zhurnal [Financial Journal]. 2020. Vol. 12. No 2. Pp. 39–56. (In Russ.) DOI: 10.31107/2075-1990-2020-2- 39-56
7. Pestova A. A. “Credit view” on monetary policy in Russia. Prikladnaya ekonometrika [Applied Econometrics]. 2020. Vol. 57. Pp. 72–88. (In Russ.)
8. Bougheas S., Mizen P., Yalcin C. Access to external finance: Theory and evidence on the impact of monetary policy and firm-specific characteristics. Journal of Banking and Finance. 2006. Vol. 30. No 1. Pp. 199–227.
9. Aliev R., Hajkova D., Kubicova I. The impact of Monetary Policy on Financing of Czech Firms. Czech National Bank, Working Paper. 2014. No 5. 40 p. Available at:
   http://journal.fsv.cuni.cz/storage/1343_hajkova.pdf (accessed: 01.09.2023).
10. Malinowska A. Liquidity constraints and the balance Sheet channel of monetary policy transmission. Economic studies. 2016. Vol. 1. Pp. 71–88 Available at: https://www.researchgate.net/publication/301527925_Liquidity_constraints_and_the_balance_sheet_channel_of_monetary_policy_transmission (accessed: 01.09.2023).
11. Ratnikova T. A., Furmanov K. K. Analiz panel’nykh dannykh i dannykh o dlitel’nosti sostoyaniy : ucheb. posobiye [Analysis of panel data on the duration of states : Textbook]. Moscow: Publishing house of Higher school of economics. 2014. 373 p. (In Russ.)
12. Cloyne J., Ferreira C., Froemmel M., Surico P. Monetary policy, investment and firm heterogeneity. ECB Working Paper. 2018. No 2390 (25366). 48 p. Available at:
    https://www.ecb.europa.eu/pub/pdf/scpwps/ecb.wp2390~f6688df85d. en.pdf (accessed: 01.09.2023).
13. Jeenas P. Firm Balance Sheet Liquidity, Monetary Policy Shocks, and Investment Dynamics. CREI Working Paper. 2019. 83 p. Available at: https://crei.cat/wp-content/uploads/2020/06/Jeenas_JMP.pdf (accessed: 01.09.2023).
14. Ottonello P., Winberry T. Financial heterogeneity and the investment channel of monetary policy. Econometrica. 2020. Vol. 88. No 6. November. Pp. 2473–2502.
15. Anderson G., Cesa-Bianchi A. Crossing the credit channel: credit spreads and firm heterogenety. Staff Working Paper no 854 / Bank of England. 2020. 65 p. Available at: https://www.bankofengland.co.uk/- /media/boe/files/working-paper/2020/crossing-the-credit-channelcredit-spreads-and-firm-heterogeneity.pdf (accessed: 01.09.2023).
16. Prokopev F. Balance Sheet Channel of Monetary Policy: Evidence from Credit Spreads of Russian Firms. Den’gi i kredit [Russian Journal of Money and Finance]. 2021. 80 (4). Pp. 3–30. 2021. (In Russ.)
17. John B. Taylor, Harald Uhlig Spravochnoye rukovodstvo po makroekonomike : v 5 kn. Kn. 1. Fakty ob ekonomicheskom roste i ekonomicheskikh kolebaniyakh [Reference Guide to Macroeconomics: 5 books. Book 1. Facts about economic growth and economic
    fluctuations]. Moscow: Publishing house “Delo” RANEPA, 2019. 528 p. (Academic textbook). (In Russ.)
18. John B. Taylor, Harald Uhlig Spravochnoye rukovodstvo po makroekonomike : v 5 kn. Kn. 2. Metodologiya v makroekonomike [Reference Guide to Macroeconomics: 5 books. Book 2. Methodology in macroeconomics]. Moscow: Publishing house “Delo” RANEPA, 2020.
    1128 p. (Academic textbook). (In Russ.)
19. Oliner S. D., Rudebusch G. D. Is there a broad credit chanel for monetary policy. Economic Review / Federal Reserve Bank of San Francisco. 1996. No 1. Pp. 3–13. Available at: https://www.frbsf.org/economic-research/wpcontent/uploads/sites/4/3-13-2.pdf (accessed: 01.09.2023).
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    https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp108.pdf (accessed: 01.09.2023).
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For citation: Maltseva O. A., Polyakova I. V., Startseva E. N. Balance Sheet Channel of Monetary Policy: Review of Empirical Methods. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 3 (48), pp. 18−48. (In Russ.) https://doi.org/10.34130/1992-2752_2023_3_18

III.Table generating language enhancement

https://doi.org/10.34130/1992-2752_2023_3_49

Evgeniy A. Belykh – Pitirim Sorokin Syktyvkar State University, hunter_x5_95@mail.ru

Yuriy V. Golchevskiy – Pitirim Sorokin Syktyvkar State University, yurygol@mail.ru

Text

Abstract. This paper is about designing a specialized C-like language, made to generate complex tables based on large number of various data sources.

Keywords: electronic documents, document generating, programming languages, electronic tables.

References

1. Fong J., Shiu H. and Cheung D. A relational-XML data warehouse for data aggregation with SQL and XQuery. Software-Practice & Experience. 38 (11). Pp. 1183–1213. DOI: 10.1002/spe.868.
2. Badam S. K., Liu Z. and Elmqvist N. Elastic Documents: Coupling Text and Tables through Contextual Visualizations for Enhanced Document Reading. IEEE Transactions on Visualization and Computer Graphics. 2019. Vol. 25. No 1. Pp. 661–671, Jan. 2019, DOI: 10.1109/TVCG.2018.2865119.
3. Okada M., Takaba M., Kaihara S., Okada M. Formal Representation of Summary Tables for Health Care Statistical Database Management. Computers and Biomedical Research. 1998. Vol. 31. No 6. Pp. 426–450. DOI: 10.1006/cbmr.1998.1491.
4. Amano A., Asada N. Graph grammar based analysis system of complex table form document. Proceedings of the 7th International Conference on Document Analysis and Recognition (ICDAR 2003). Edinburgh, Scotland, 2003. Pp. 916–920.
5. Belykh E. A., Golchevskiy Yu. V. An approach to designing a substitution language for generating electronic documents containing complex tables. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki [Bulletin of Udmurt University. Mathematics. Mechanics. Computer science]. 2019. Vol. 29. Issue 3. Pp. 422–437. (In Russ.)
6. Brian W. Kernighan, Dennis M. Ritchie. The C Programming Language. 2nd edition. Englewood Cliffs, New Jersey: Prentice Hall,272 p.
7. Mehdi Achour, Friedhelm Betz, Antony Dovgal, Nuno Lopes, Hannes Magnusson, Georg Richter, Damien Seguy, Jakub Vrana And several others, Peter Cowburn (eds), 2021 PHP: PHP Manual. Available at: https://www.php.net/manual/en/index.php (accessed: 01.06.2023).
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10. Alfred V. Aho, Monica S. Lam, Ravi Sthi, Jeffrey D. Ullman Compilers: principles, techniques, and tools – 2nd edition. Boston: Addison-Wesley, 2006. 1010 p.
11. The Open Group Base Specifications Issue 6, scanf. Available at: https://pubs.opengroup.org/onlinepubs/009695399/functions/ fscanf.html (accessed: 01.06.2023).

For citation: Belykh E. A., Golchevskiy Yu. V. Table generating language enhancement. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 3 (48), pp. 49−71. (In Russ.) https://doi.org/10.34130/1992-2752_2023_3_49

IV. Development and organization of business processes for preparing frequency dictionaries in order to automate natural language processing when performing tasks of linguistic text analysis

https://doi.org/10.34130/1992-2752_2023_3_72

Mikhail S. Krasheninnikov – SAI of the Komi Republic «Information Technology Center», Pitirim Sorokin Syktyvkar State University, kib@syktsu.ru

Ivan I. Lavresh – Pitirim Sorokin Syktyvkar State University, kib@syktsu.ru

Vladimir A. Ustyugov – Pitirim Sorokin Syktyvkar State University, kib@syktsu.ru

Text

Abstract. This article discusses the processes of processing text data within the framework of information and analytical support for the activities of authorities of the Komi Republic. The interaction of state information systems and authorities of the Komi Republic and their various divisions is shown.

Keywords: natural language processing, frequency analysis of text, linguistic analysis of text, frequency dictionaries, information and analytical support.

References

1. Shirshov E. V. Informatsionno-analiticheskoye obespecheniye menedzhmenta : uchebnoye posobiye po napravleniyu podgotovki bakalavrov 38.03.02. «Menedzhment» [Information and analytical support for management : Textbook for bachelor’s training 03.38.02. “Management”]. Moscow: Publishing House “Academy of Natural Sciences”, 2022. 156 p. (In Russ.)
2. Gaverdovsky V. S. Practical evolution of information and analytical systems for regional management created at the State Autonomous Institution of the Republic of Kazakhstan “Information Technology Center”in 2009–2016. IT Arktika [IT Arctic]. 2017. No 1. Pp. 12–27. (In Russ.)
3. Luchshiye praktiki regional’noy informatizatsii «PROF-IT.2014» : cbornik [Best practices of regional informatization “PROF- IT.2014”: Collection] [Electronic resource]. Available at: https://d-russia.ru/wpcontent/uploads/2015/03/prof-it-2014.pdf (accessed: 01.15.2023) (In Russ.)
4. Epifantsev B. N. Information and analytical security systems: possibilities of using resources of other specialties to form a laboratory base. Informatsionnoye protivodeystviye ugrozam
   terrorizma [Information counteraction to the threats of terrorism].Vol. 1. No 25. Pp. 159–166. (In Russ.)
5. Mukhametov M. R. Frequency analysis of text in Python. Mavlyutovskiye chteniya: Materialy XVI Vserossiyskoy molodezhnoy nauchnoy konferentsii : v 6 t. Ufa, 25–27 oktyabrya 2022 goda
   [Mavlyutov readings: Materials of the XVI All-Russian Youth Scientific Conference. In 6 volumes, Ufa, October 25–27]. Ufa: Ufa State Aviation Technical University, 2022. Vol. 5. Pp. 1054–1056. (In Russ.)
6. Preobrazhensky A. P., Choporova E. I., Menyailov D. V. Thematic analysis of text information based on frequency characteristics. Tsifrovaya obrabotka signalov i yeyo primeneniye
   (DSPA-2022): 24-ya Mezhdunarodnaya konferentsiya, Moskva, 30 marta – 01 aprelya 2022 goda [Digital signal processing and its application (DSPA-2022): 24th International conference, Moscow, March 30 – April 1, 2022]. Moscow: Russian Scientific and Technical Society of Radio Engineering, Electronics and Communications named after A. S. Popova, 2022. Issue XXIV. Pp. 136–140. (In Russ.)

V. Instructional features of the elementary algebra and pre-calculus: practical course teaching guide

https://doi.org/10.34130/1992-2752_2023_3_90

Olga A. Sotnikova – Pitirim Sorokin Syktyvkar State University, sotnikovaoa@syktsu.ru

Vyacheslav A. Popov

Text

Abstract. The article explores instructional aspects of the contents of the teaching guide prepared for publication. The teaching methods applied are based on the focus on obtaining math learning experience.

Keywords: math learning activity, studying the elementary algebra and pre-calculus.

For citation: Sotnikova O. A., Popov V. A. Instructional features of the elementary algebra and pre-calculus: practical course teaching guide. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 3 (48), pp. 90−95. (In Russ.) https://doi.org/10.34130/1992-2752_2023_3_90

Full text

I. Andrey V. Yermolenko, Oksana I. Turkova Determination of stresses on the front surfaces of the plate

https://doi.org/10.34130/1992-2752_2023_2_4

Andrey V. Yermolenko – Pitirim Sorokin Syktyvkar State University, ea74@list.ru

Oksana I. Turkova – Pitirim Sorokin Syktyvkar State University

Text

Abstract. When solving contact problems, it is necessary to set the interaction conditions using the displacements of the front surfaces of the plate.

Keywords: plate theory, reference surface, stresses.

References

1. Mikhailovskii E. I., Toropov A. V. Matematicheskiye modeli teorii uprugosti [Mathematical models of theory of elasticity]. Syktyvkar: Syktyvkarskij un-t [Syktyvkar: Syktyvkar State University], 1995. 251 p. (In Russ.)
2. Mikhailovskii E. I. Shkola mekhaniki obolochek akademika Novozhilova [Academic Novozhilov’s school of mechanics of shells]. Syktyvkar: Izd-vo Syktyvkarskogo un-ta [Syktyvkar: Publishing House of Syktyvkar University], 2005. 172 p. (In Russ.)
3. Mikhailovskii E. I.,Badokin K. V., Ermolenko A. V. Karman type theory of flexure of plates without Kirhgof’s hypotheses. Vestnik Syktyvkarskogo universiteta. Seriya 1 [Bulletin of Syktyvkar University. Series 1], 1999, issue 3, pp. 181–202. (In Russ.)
4. Timoshenko S. P. Kurs teorii uprugosti, ch. II. Sterzhni I plastinki [Course of theory of elasticity, part II. Shafts and plates]. Petrograd: Izd-vo in-ta inzh. putej soobscheniya, 1916. Izd. 2-e. Kiev: Naukova dumka [Petrograd: Publishing House of institute of Railway Engineers,
5. Vol. 2. Kiev: Publishing House of Naukova Dumka], 1972. 507 p. (In Russ.)
6. Naghdi P. M. On the theory of thin elastic shells. Quarterly of Applied Mathematics. 1957, 14, no 4, pp. 369–380.
7. Chernyh K. F. Nelinejnaya teoriya uprugosti v mashinostroitel’nyh raschetah. [Nonlinear theory of elasticity in mechanical engineering calculations] L.: Mashinostroenie [Leningrad: Mechanical engineering], 336 p. (In Russ.)
8. Yermolenko A. V., Mironov V. V. Mechanism of the effect of transverse shifts on the stress state in the problems of plate and shell mechanics. International Journal of Recent Technology and Engineering (IJRTE). 2019, vol. 7, issue 5, January, pp. 318–321.
9. Mikhailovskii E. I., Ermolenko A. V., Mironov V. V., Tulubenskaya E. V. Utochnennye nelinejnye uravneniya v neklassicheskih zadachah mekhaniki obolochek : uchebnoe posobie [Refined nonlinear equations in non classical tasks of mechanics of shells]. Syktyvkar: Izd-vo Syktyvkarskogo un-ta [Syktyvkar: Publishing House of Syktyvkar University], 2009. 141 p. (In Russ.)
10. Kulikov G. M., Plotnikova S. V. Solvation of three dimensional tasks for thick elastic shells based on method of base surfaces. Mekhanika tverdogo tela [Mechanics of solid body], 2014, no 4,
    pp. 54–64. (In Russ.)
11. Hallquist J. O., Benson D. J. A comparison of an implicit and explicit implementation of the Hughes-Liu shell. Finite Element Metdods for Plate and Shell Structures / eds T. J. R. Hughes, E. Hinton. Swansea: Pineridge Press, 1986. Vol. 1. Pp. 394–431.
12. Korobejnikov S. N., Shutov A. V. The choice of basic surface in equations of plates and shells. Vychislitel’nye tekhnologii [Computing technologies], 2003, vol. 8, pp. 38–59. (In Russ.)
13. Schoop H. Oberfl¨achenorientierte Schalentheorien endlicher Verschiebungen. Ing.-Archiv. 1986. B. 56, no 6, s. 427–437.
14. Nikabadze M. U. Parameterization of shells based on two basic surfaces. Dep. V VINITI AN SSSR [Department of All-Union Institute for Scientific and Technical Information of USSR Academy of Sciences], 12.07.1988. № 5588–V88. 29 p. (In Russ.)
15. Kim Y. H., Lee S.W. A solid element formulation for large deflection analysis of composite shell structures. Comp. Struct, 1988, vol. 30. no 1–2, pp. 269–274.
16. Kulikov G. M., Plotnikova S. V. Comparative analysis of two algorithms of numerical solution of nonlinear tasks of static of multilayer anisotropic shells of rotation. 2. Accounting of transverse compression. Mekh. kompozit. materialov [Mechanics of composite materials], 1999,
    vol. 35, no 4, pp. 435–446. (In Russ.)
17. Nikabadze M. U. Some geometry ratios of theory of shells with two basic surfaces. Izv. RAN. MTT [Mechanics of Solids. A Journal of Russian Academy of Sciences], 2000, no 4., pp. 129–139. (In Russ.)
18. Kulikov G. M., Plotnikova S. V. Finite deformation plate theory and large rigid-body motions. Int. J. Non-Linear Mech, 2004, vol. 39, no 7, pp. 1093–1109.
19. Ermolenko A. V. Theory of Karman-Timoshenko-Nagdi type plane plates regarding of arbitrary basic plane. V mire nauchnyh otkrytij [In the World of Scientific Discoveries]. Krasnoyarsk: Science and Innovation Center Publishing House, 2011. No 8.1 (20), pp. 336–347. (In Russ.)
20. Yermolenko A. V. The choice of basic surface in contact tasks with free boundary. Vestnik Syktyvkarskogo universiteta. Seriya 1 [Bulletin of Syktyvkar University. Series 1]. 2013, issue 18, pp. 42–47. (In Russ.)

For citation: Yermolenko A. V., Turkova O. I. Determination of stresses on the front surfaces of the plate. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 2 (47), pp. 4−16. https://doi.org/10.34130/1992-2752_2023_2_4

II. Vadim A. Melnikov About architectural features of collisions filtering in the physics engine for 3D games

https://doi.org/10.34130/1992-2752_2023_2_17

Vadim A. Melnikov – Pitirim Sorokin Syktyvkar State University, muller95@yandex.ru

Text

Abstract. The article discusses parallel and sequential approaches to the implementation of collision filtering based on array sorting and measures the performance of various sorts with different numbers of threads.

Keywords: physics, collisions, filtering, AABB, sorting.

References

1. Melnikov V. A. Development Process of game engine core for 2Dgames and interfaces Sad Lion Engine. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, 4 (33), pp. 21–37. (In Russ.)
2. Melnikov V. A., Yermolenko A. V. Development of XMLbased Markup Language. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2022, 1 (42), pp. 61–73.
3. Gregory J. Game engine architecture, 3rd edition. Boca Raton: CRC Press. 2019, 1200 p.
4. Zubek P. Elementy geymdizayna. Kak sozdavat’ igry, ot kotorykh nevozmozhno otorvat’sya [Elements of game design. How to create games from which it is impossible to break away]. M.: Bombora, 2022. 272 p. (In Russ.)
5. Strashnov E. V., Torgrashev M. A. Collision detection algorithms of bounding cylinders with terrain model. International Journal of Open Information Technologies. 2020, vol. 8, no 7, pp. 40–49. (In Russ.)
6. Ericson C. Real-time collision detection. Amsterdam, Boston, Heidelberg, London, New York, Oxford, Paris, San Diego, San Francisco, Singapore, Sydney, Tokyo: Morgan Kaufman Publishers, 593 p.
7. Huang X., Liu Z., Li J. Array sort: an adaptive sorting algorithm on multi-thread. The Journal of Engineering. 10.1049/joe.2018.5154. 2019, pp. 3455–3459.
8. Millington I. Game physics engine development. Amsterdam, Boston, Heidelberg, London, New York, Oxford, Paris, San Diego, San Francisco, Singapore, Sydney, Tokyo: Morgan Kaufman Publishers, 456 p.
9. Huynh J. Separating axis theorem for oriented bounding boxes [Electronic resource]. Available at: http://www.jkh.me/files/tutorials/Separating%20Axis%20Theorem% 20for%20Oriented%20Bounding%20Boxes.pdf (accessed: 30.05.2023).
10. Bhagrav N. Cache-friendly code [Electronic resource].Baeldung. Available at: https://www.baeldung.com/cs/cache-friendly-code (accessed: 30.05.2023).
11. House D. H., Keyser J. C.Foundations of physically based modelling and animation. Boca Raton: CRC Press, 2017. 382 p.
12. Fundamental types [Electronic resource]. C++ reference. Available at: https://en.cppreference.com/w/cpp/language/types (accessed: 30.05.2023).
13. Godot [Electronic resource]. Godot. Available at: https://godotengine.org/ (accessed: 30.05.2023).
14. std::stable_sort [Electronic resource]. C++ reference. Available at: https://en.cppreference.com/w/cpp/algorithm/stable_sort (accessed: 30.05.2023).
15. Array [Electronic resource]. Godot docs. Available at: https://docs.godotengine.org/en/stable/classes/class_array.html (accessed: 30.05.2023).
16. Ozeritskiy A. V. Computational simulation using particles on GPU and GLSL language. Vych. met. programmirovaniye[Numerical Methods and Programming]. 2023, issue 1 (24), pp. 37–54. (In Russ.)
17. Knuth D. Iskusstvo programmirovaniya. T. 3. Sortirovka i poisk. [The art of computer programming. Vol. 3. Sorting and searching]. M.: Vilyams, 2001. 824 p.

III. Vladimir P. Odinets On the works of five Moscow mathematicians who died during
the Great Patriotic War

https://doi.org/10.34130/1992-2752_2023_2_29

Vladimir P. Odinets – W.P.Odyniec@mail.ru

Text

Abstract. The article describes the works of five Moscow mathematicians: M. Bebutov, N. Vedenisov, M. Gleserman, D. Shklyarsky, D. Junovic’, who died in 1941–1942. In the description of the works the biographies of these mathematicians are also given.

Keywords: dynamical system, stability in sense of Lyapunov, Hausdorff space, first axiom of countability, second axiom of countability.

References

1. Bebutov M. V. On dynamical systems stable according to Lyapunov. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 18, no 3, pp. 155–158. (In Russ.)
2. Bebutov M. V. One theorem on simplicial complexes. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1939. 19, no 5, pp. 347–348. (In Russ.)
3. Bebutov M. V., Shneider V. E. About one countable topological space. Uchenye zap. uni-ta [Academic Notes of the University]. 1939. 30, pp. 157–160. (In Russ.)
4. Bebutov M. V. Mapping the trajectories of a dynamical system to a family of parallel lines. Moscow: Byull.uni-ta (A) [University Bulletin]. 2, no 3, pp. 3–23. (In Russ.)
5. Bebutov M. V., Stepanov V. V. On the change of time in dynamical systems with an invariant measure. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1939. 24, no 3, pp. 217–219. (In Russ.)
6. Bebutov M. V. On invariant measurement in dynamical systems that differ only by times. Matem. sb. [Mathematical collection]. 1940. 7 (49), no 1, pp. 143–166.
7. Bebutov M.V. On dynamical systems in the space of continuous functions. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1940. 29, no 9, pp. 904–906. (In Russ.)
8. Bebutov M. V. O dinamicheskikh sistemakh v prostranstve nepreryvnykh funktsiy [On dynamical systems in the space of continuous functions]. Moscow: Izd-vo MGU, 1940. 52 p. (Byulleten’ Moskovskogo gosudarstvennogo universiteta. Matematika [Bulletin of Moscow State University. Mathematics] / eds B. V. Gnedenko, A. N. Kolmogorov, V. V. Stepanov. Vol. 2, no 5). (In Russ.)
9. Bebutov M. V. Markov chains with compact state space. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1941. 30, no 6, pp. 180–181. (In Russ.)
10. Bebutov M. V. Markov chains with compact state space. Matem. sb. [Mathematical collection]. 1942. 52, no 3, pp. 213–238. (In Russ.)
11. Alekseev V. M., Fomin S. V. Mikhail Valeryevich Bebutov. UMN [Russian Mathematical Surveys]. 1970. 25, no 3, pp. 237–239. (In Russ.)
12. Tychonoff A. N., Vedenissoff N. B. Sur le d´evelopment modern de la th´eorie des espaces abstraits. Вull. sci. math. 1926. 50. Pp. 15–27.
13. Vedenisov N. B. About full metric spaces. J. math. pur. et appl. 9, pp. 377–392.
14. Vedenisov N. B. On continuous functions in topological spaces. Fund. Math., 1936. 27, pp. 234–238.
15. Vedenisov N. B. About one problem of Pavel Alexandrov. Ann. of Math. 1936. 37, pp. 427–428.
16. Vedenisov N. B. On manifolds in the sense of E.Cech. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1937. 16, no 9, pp. 443–445. (In Russ.)
17. Vedenisov N. B. On some topological properties of ordered sets. Uchenye zapiski gos. ped. inst-ta. Ser. fiz.-mat. [Uchen. notes of the State ped. in-ta. Ser. of phys.-math.]. 1938, 2, pp. 15–26. (In Russ.)
18. Vedenisov N. B. Remarks on continuous functions in topological spaces. Uchenye zapiski gos. ped. inst-ta. Ser. fiz.-mat. [Uchen. notes of the State ped. in-ta. Ser. of phys.-math.]. 1938, 2, pp. 47–52. (In Russ.)
19. Vedenisov N. B. Remarks on the dimensionality in topologicalspaces. Uchenye zapiski uni-ta [Academic Notes of the University].1939, 30, pp. 131–140. (In Russ.)
20. Vedenisov N. B. Generalization of one theorem of dimensionality theory. Uchenye zapiski gos. ped. inst-ta. Ser. fiz.-mat. [Uchen. notes of the State ped. in-ta. Ser. of phys.-math.]. 1940, 7, pp. 35–40. (In Russ.)
21. Vedenisov N. B. Generalization of several theorems of dimensionality. Comp. Mathem., 1940, 7, pp. 194–200.
22. Vedenisov N. B. On the dimensionality in the sense of E. Cech. Izv. AN USSR. Ser. matem. [Proceedings of the Academy of Sciences of the USSR. Ser. mathem.]. 1941, 5, pp. 211–216. (In Russ.)
23. Vedenisov N. B. Bicompact spaces. UMN [Russian Mathematical Surveys]. 1943, 3, no 4, pp. 67–79. (In Russ.)
24. Alexandrov P. S. Nicolay Borisovich Vedenisov. UMN [Russian Mathematical Surveys]. 1970. 25, no 3, pp. 239–241. (In Russ.)
25. Kazhdan Ya. M. Mark Efimovich Glezerman. UMN [Russian Mathematical Surveys]. 1970, 25, issue 3, pp. 241–243. (In Russ.)
26. Pontryagin L. S., Glezerman M. E. Intersections of manifolds. UMN [Russian Mathematical Surveys]. 1947, 2, issue 1, pp. 58–155. (In Russ.)
27. Golovina L. I. David Oskarovich Shklyarsky. UMN [Russian Mathematical Surveys], 1970, 25, issue 3, pp. 248–252. (In Russ.)
28. Shklyarsky D. O. Moscow Mathematical Circle. UMN [Russian Mathematical Surveys]. 1945, 1, issue 3, pp. 212–217. (In Russ.)
29. Cherneev S. V., Romanyuk V. Ya., Vdovin A. I. and others. Moskovskiy universitet v Velikoy Otechestvennoy voyne [Moscow University in the Great Patriotic War]. 4-e izd. Moscow: Izd-vo MGU, 632 c. (In Russ.)
30. Shklyarsky D. O. On the partitioning of two-dimensional sphere. Matem. sb. [Mathematical collection]. 1945, 58, no 2, pp. 126–128. (In Russ.)
31. Junovic’ B. M. On the differentiation of absolutely additive functions of sets. Doklady AN USSR [Reports of the Academy of Sciences of the USSR]. 1941, 30, no 1, pp. 112–114. (In Russ.)

For citation: Odinets V. P. On the works of five Moscow mathematicians who died during the Great Patriotic War. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 2 (47), pp. 29−55. https://doi.org/10.34130/1992-2752_2023_2_29

IV. Vladimir A. Ustyugov, Ivan I. Lavresh, Yuriy N. Istomin ,Pavel A. Makarov The use of SDR devices in the educational process for technical specialties of universities

https://doi.org/10.34130/1992-2752_2023_2_56

Vladimir A. Ustyugov – Pitirim Sorokin Syktyvkar State University, kib@syktsu.ru

Ivan I. Lavresh – Pitirim Sorokin Syktyvkar State University, kib@syktsu.ru

Yuriy N. Istomin – Pitirim Sorokin Syktyvkar State University, kib@syktsu.ru

Pavel A. Makarov – Federal Research Centre Komi Science Centre, Ural Branch, RAS, makarovpa@ipm.komisc.ru

Text

Abstract. The article deals with the principles of modern software defined radio (SDR). Interest in such devices is due to the low cost of certain models, as well as a wide range of tasks in the
search and digital processing of electromagnetic signals in the context of technical protection of information, the study of the spread of digital and analog signals in urban environments, construction of new digital communication systems. Specific examples of defined signals and software tools for developing radio receiver configurations are considered.

Keywords: digital signal processing, software-defined radio.

References

1. Bikkenin R. R., Chesnokov M. N. Teoriya elektricheskoj svyazi [The theory of electrical communication]. Мoscow: Akademia, 2010. 336 p. (In Russ.)
2. Gepko I. A. Sovremennye besprovodnye seti: sostoyanie i perspektivy razvitiya [Modern Wireless Networks: Status and Prospects of Development]. Кiev: «EKMO», 2009. 672 p. (In Russ.)
3. Sklyar B. Cifrovaya svyaz. Teoreticheskie osnovy i prakticheskoe primenenie [Digital communication. Theoretical foundations and practical applications]. Мoscow: Wiljams, 2007. 1104 p. (In Russ.)
4. Galkin V. A. Osnovy programmno-konfiguriruemogo radio [Fundamentals of reconfigurable radio]. Мoscow: Goryachaya liniya – Telekom, 2020. 372 p. (In Russ.)
5. Fokin G. A. Texnologii programmno-konfiguriruemogo radio [Software-configurable radio technologies]. Мoscow: Goryachaya liniya – Telekom, 2023. 316 p.(In Russ.)
6. Kheld G. Texnologii peredachi dannyx [Data transmission technologies]. SPb.: BHV, 2003. 720p. (In Russ.)
7. Ratynskij M. V. Osnovy sotovoj svyazi [Cellular basics]. Мoscow: Radio i svyaz, 2000. 248p. (In Russ.)

V. Elena Yu. Yashina Proof of Frobenius’ Theorem as Completion of Algebra and Numerical Systems Course at Pedagogical University

https://doi.org/10.34130/1992-2752_2023_2_69

Elena Yu. Yashina – The Herzen State Pedagogical University of Russia, elyashina@mail.ru

Text

Abstract. The article presents an original proof of Frobenius’ theorem on finite-dimensional division algebras over a field of real numbers. The theorem shows the impossibility of extension of the concept of number, so its proof is useful for the formation of professional competencies of future mathematics teachers.

Keywords: number line, real numbers, finite-dimensional division algebra, Frobenius’ theorem.

References

1. Zhmurova I. Yu. The study of Numerical Systems in a Pedagogical University in the context implementing links. Mezhdunarodnyy nauchno-issledovatel’skiy zhurnal [International Research Journal]. 2020, no 8-3 (98), pp. 28–31. (In Russ.) https://doi.org/10.23670/IRJ.2020.98.8.073
2. Panteleymonova A. V., Belova M. A. Development of the concept of number in the school mathematics course. Continuum. Matematika. Informatika. Obrazovaniye [Continuum. Mathematics. Computer science. Education]. 2019, no 4 (16), pp. 31–37. (In Russ.)
3. Drozd Yu. A., Kirichenko V. V. Konechnomernye algebry [Finitedimensional algebras]. Kiev: Visha shkola, 1980. 192 p. (In Russ.)

For citation: Yashina E. Yu. Proof of Frobenius’ Theorem as Completion of Algebra and Numerical Systems Course at Pedagogical University. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 2 (47), pp. 69−82. https://doi.org/10.34130/1992-2752_2023_2_69

VI. Evgenija A. Kaneva About the work of the scientific and methodological seminar on the problems of education and the methodology of teaching mathematics

https://doi.org/10.34130/1992-2752_2023_2_83

Evgenija A. Kaneva – Pitirim Sorokin Syktyvkar State University, kaneva.zhenya@mail.ru

Text

Abstract. In modern society, specialists of various profiles are required, in particular, to have developed logical thinking, the ability to quickly adapt to changing socio-economic conditions and
search for non-trivial solutions in problem situations, and the ability to work in a team.

Keywords: scientific and methodological seminar, research activity, pedagogical mentoring, student science.

References

1. Popov N. I., Kaneva E. A. The use of correlation analysis in the study of the quality of education of future teachers of mathematics and computer science. Gumanitarnye nauki i obrazovanie [Humanities and Education]. 2022, vol. 13, no 4 (52), pp. 95–99. (In Russ.)
2. Popov N. I., Yakovleva E. V. Methodological aspects of blended teaching of mathematics to students of medical specialties at the university. Perspektivy nauki i obrazovaniya [Prospects for science and education]. 2022, no 3 (57), pp. 232–252. (In Russ.)
3. Yakovleva E. V. Innovative Approaches in Teaching Mathematics to Future Doctors at a Regional University. Mir nauki, kul’tury, obrazovaniya [The world of science, culture, education]. 2022, no 5 (96), pp. 176–181. (In Russ.)
4. Popov N. I., Bolotin E. S. Using the Python IDLE Development and Training Environment for Students to Learn Probability. Vestnik MGPU. Seriya: Informatika i informatizaciya obrazovaniya [Bulletin MGPU. Series: Informatics and informatization of education]. 2023, no 1 (63), pp. 79–85. (In Russ.)
5. Shustova E. N. Obuchenie aksiomaticheskomu metodu vvedeniya elementarnyh funkcij v vuze kak komponent sistemy formirovaniya metodicheskoj kompetentnosti budushchih uchitelej matematiki: dissertaciya . . . kandidata pedagogicheskih nauk: 13.00.02 [Teaching
   the axiomatic method of introducing elementary functions at the university as a component of the system for the formation of methodological competence of future teachers of mathematics:
   dissertation . . . candidate of pedagogical sciences: 13.00.02]. E. N. Shustova; [Mesto zashchity: RGPU im. A. I. Gercena]. SPb, 275 p. (In Russ.)
6. Popov N. I. Fundamentalizaciya universitetskogo matematicheskogo obrazovaniya : monografiya [Fundamentalization of University Mathematical Education : Monograph]. Yelets: EGU im. I. A. Bunina, 174 p. (In Russ.)
7. Popov N. I., Kaneva E. A. Using the electronic course “School Mathematical Practicum”in the preparation of future teachers. Vestnik MGPU. Seriya: Informatika i informatizaciya obrazovaniya [Bulletin MGPU. Series: Informatics and informatization of education]. 2022, no 4 (62), pp. 109–118. (In Russ.)
8. Popov N. I., Kaneva E. A. Formation of cognitive interest of schoolchildren in mathematics using computer learning games. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mehanika.
   Informatika [Bulletin of the Syktyvkar University. Ser. 1: Math. Mechanics. Informatics]. 2022, no 2 (43), pp. 55–66. (In Russ.)
9. Popov N. I., Kaneva E. A., Bolotin E. S. Study of the special abilities of university students in teaching mathematics. Mir nauki, kul’tury, obrazovaniya [The world of science, culture, education]. 2022, no 1 (92), pp. 110–113. (In Russ.)
10. Shustova E. N. Features of using the axiomatic method of introducing elementary functions in teaching future teachers of mathematics at the university. Obrazovatel’nyj vestnik «Soznanie»
    [Educational bulletin “Consciousness”]. 2022, vol. 24, no 4, pp. 23– (In Russ.)
11. Popov N. I., Bobrova G. Yu. Methodological features of teaching the basics of probability theory in high school. Dvadtsat’ devyataya godichnaya sessiya Uchenogo soveta Syktyvkarskogo
    gosudarstvennogo universiteta imeni Pitirima Sorokina [Elektronnyy resurs] : Fevral’skiye chteniya : Natsional’naya konferentsiya : sbornik statey / otv. red.: O. A. Sotnikova, N. N. Novikova [Twenty-ninth annual session of the Academic Council of Syktyvkar State University named Pitirim Sorokin [Electronic resource] : February readings : National conference : collection of articles / ed.: O. A. Sotnikova, N. N. Novikova]. Syktyvkar: Publishing House of the SSU Pitirim Sorokin, 2022, pp. 473–476. (In Russ.)

For citation: Kaneva E. A. About the work of the scientific and methodological seminar on the problems of education and the methodology of teaching mathematics. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 2 (47), pp. 83−92. https://doi.org/10.34130/1992-2752_2023_2_83

Full text

Elena A. Sozontova On new cases of solvability of the Goursat problem in quadratures for one hyperbolic type system

https://doi.org/10.34130/1992-2752_2023_1_4

Elena A. Sozontova – Elabuga Institute KFU, sozontova-elena@rambler.ru

Text

Abstract. The paper investigates the Goursat problem for a hyperbolic type system with two independent variables. With the help of factorization of the equations of the system under consideration, new cases of solvability in the quadratures of the problem are obtained.

Keywords: hyperbolic system, the Goursat problem, solvability in quadratures.

References

1. Bicadze A. V. Nekotorye klassy uravnenij v chastnyh proizvodnyh [Some classes of partial differential equations]. Moscow: Nauka, 1981, 448 p. (In Russ.)
2. Sozontova E. A. On solvability by quadratures conditions of boundary value problems for second order hyperbolic systems. Ufimskij matematicheskij zhurnal [Ufa mathematical journal], 2016, vol. 8, no 3, pp. 135–140. (In Russ.)
3. Sozontova E. A. On new cases of solvability of the Goursat problem in quadratures for a second-order system. Trudy Matematicheskogo centra imeni N. I. Lobachevskogo: materialy XVI molodezhnoj nauchnoj shkoly-konferencii “Lobachevskie chteniya – 2017” [Proceedings of the N. I. Lobachevsky: materials of the XVI Youth Scientific School-Conference “Lobachevsky Readings – 2017”], 2017, pp. 140–141. (In Russ.)
4. Bicadze A. V. Uravneniya matematicheskoj fiziki [Equations of mathematical physics]. Moscow: Nauka, 1982, 336 p. (In Russ.)
5. Zhegalov V. I., Mironov A. N. Differencial’nye uravneniya so starshimi chastnymi proizvodnymi [Differential equations with higher partial derivatives]. Kazan: Kazanskoe matematicheskoe obshchestvo, 2001, 226 p. (In Russ.)
6. Zhegalov V. I. On solvability cases for hyperbolic equations in terms of special functions. Neklassicheskie uravneniya matematicheskoi fiziki [Nonclassical Equations of Mathematical Physics]. Novosibirsk: Mathematical Institute, Russian Academy of Science, Siberian Branch,
   2002, pp. 73–79. (In Russ.)
7. Zhegalov V. I., Sarvarova I. M. Solvability of the Goursat problem in quadratures. Izvestiya vuzov. Matematika [Russian Mathematics], 2013, no 3, pp. 68–73. (In Russ.)
8. Zhegalov V. I., Sozontova E. A. An addition to the cases of solvability of the goursat problem in quadratures. Differencial’nye uravneniya [Differential equations], 2017, vol. 53, no 2, pp. 270–272. (In Russ.)
9. Chekmaryov T. V. Solution of a hyperbolic system of two partial differential equations with two unknown functions. Izvestiya vuzov. Matematika [Russian Mathematics], 1959, no 6, pp. 220–228. (In Russ.)

For citation: Sozontova E. A. On new cases of solvability of the Goursat problem in quadratures for one hyperbolic type system. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 1 (46), pp. 4−13. https://doi.org/10.34130/1992- 2752_2023_1_4

II. Nadezhda N. Babikova Using NumPy to vectorization of Python code

https://doi.org/10.34130/1992-2752_2023_1_14

Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University, valmasha@mail.ru\

Text

Abstrakt. Code vectorization is the process of moving from operations on individual elements of arrays to operations that occur on entire arrays or their parts. The NumPy library tools that allow to vectorize Python code are discussed in the article: vector functions, broadcasting, masking, fancy indexing. The effectiveness of these tools is demonstrated on the example of two machine learning problems.

Keywords: NumPy, Python, vectorization, multidimensional arrays, loops.

References

1. Harris C. R., Millman K. J., van der Walt S. J. et al. Array programming with NumPy. Nature, 2020, no. 585. pp. 357–362. https://doi.org/10.1038/s41586-020-2649-2.
2. NumPy documentation. Version: 1.25.dev0. Available at: https://numpy.org/devdocs/user/basics.copies.html (accessed: 07.02.2023).
3. Ues Makkinli. Python i analiz dannyh / per. s angl. A. A. Slinkin [Python for data analysis] M.: DMK Press, 2015. 482 p.
4. Plas Dzh. Vander. Python dlya slozhnyh zadach: nauka o dannyh i mashinnoe obuchenie [Python for complex tasks. Data Science and Machine Learning]. SPb.: Piter, 2018. 576 p. (In Russ.)
5. Nicolas P. Rougier. From-python-to-numpy. Available at: https://www.labri.fr/perso/nrougier/from-python-to-numpy/#codevectorization (accessed: 07.02.2023).
6. Shenoy A. How Are Convolutions Actually Performed Under the Hood. Available at: https://towardsdatascience.com/howare-convolutions-actually-performed-under-the-hood-226523ce7fbf (accessed: 07.02.2023).

For citation: Babikova N. N. Using NumPy to vectorization of Python code . Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 1 (46), pp. 14−29. https://doi.org/10.34130/1992-2752_2023_1_14

III. Yuriy V. Golchevskiy, Dmitriy A. Ushakov Cryptographic Calculations Acceleration by Low-Level Optimization of Basic Blocks

https://doi.org/10.34130/1992-2752_2023_1_30

Yuriy V. Golchevskiy – Pitirim Sorokin Syktyvkar State University, yurygol@mail.ru

Dmitriy A. Ushakov – Pitirim Sorokin Syktyvkar State University

Text

Abstract. Thе paper presents a study of optimizing the program code problem when implementing encryption algorithms. The basic blocks of the cryptographic algorithm are highlighted on the example of the Kuznechik algorithm. Implemented variants of the algorithm using different versions of vector instructions and their combinations have been tested on processors of various microarchitectures. Some developed algorithm implementation variants show a higher encryption speed than existing software products.

Keywords: cryptographic computing, low-level optimization, basic blocks, algorithm Kuznechik.

References

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2. Golchevskiy Yu. V., Severin P. A. Cryptographic Algorithms Optimization by Means of Assembly Inserts in Integer Division. Izvestiya TulGU. Tekhnicheskiye nauki [News of TulGU. Technical sciences]. 2013, vol. 3, pp. 295–301. (In Russ.)
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6. Gashin R. A., Golchevskiy Yu. V. Development of Cryptographic Library Based on Algorithms from eSTREAM Project. Bezopasnost’ informatsionnykh tekhnologiy [Information Technology Security], 2015, no 4 (22), pp. 52–57. (In Russ.)
7. Ischukova E. A., Koshutsky R. A., Babenko L. K. Development and implementation of high-speed data encryption using the Kuznechik algorithm. Auditorium, 2015, no 4 (8). (In Russ.)
8. Code Optimization: CPU. Habrahabr. Available at: https://habrahabr.ru/post/309796/ (accessed: 03.12.2022). (In Russ.)
9. Bryant R., Hallaron D. Computer Systems A Programmer’s Perspective. Printice Hall, 2015. 1120 p.
10. Gerber R., Bik A. J. C., Smith K., Tian X. The Software Optimization Cookbook. St. Petersburg: Piter, 2010. 352 p. (In Russ.)
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    _01_intro.pdf (accessed: 03.12.2022). (In Russ.)
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26. Severin P. A., Golchevskiy Yu. V. Low-Level Performance Optimization on the Example of the Hash Function GOST R 34.11- Sistemnyy administrator [System Administrator]. 2017, no 1–2, pp. 170–171. (In Russ.)
27. Ahmetzyanova L. R., Alekseev E. K., Oshkin I. B. et al. On the properties of the CTR encryption mode of the Magma and Kuznyechik block ciphers with re-keying method based on CryptoPro Key Meshing. IACR Cryptol. ePrint Arch., 2016, 628 p.
28. Gafurov I. R. High-speed software implementation of encryption algorithms from GOST R 34.12-2015. Uchenyye zapiski UlGU. Seriya: Matematika i informatsionnyye tekhnologii [Scientific notes of UlGU. Series: Mathematics and Information Technology], 2022, no 2, pp. 38–(In Russ.)

For citation: Golchevskiy Yu. V., Ushakov D. A. Cryptographic Calculations Acceleration by Low-Level Optimization of Basic Blocks. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 1 (46), pp. 30−49. https://doi.org/10.34130/1992-2752_2023_1_30

IV. Svetlana A. Deynega Components of Geometric-graphic Competence, Formed in the Study of Descriptive Geometry at a Technical University

https://doi.org/10.34130/1992-2752_2023_1_50

Svetlana A. Deynega – Uсhta State Technical University, deynega07@mail.ru

Text

Abstract. The article considers the generalized components of the professional competencies of students of a technical university. The significance of the formation of a cognitive and creative component at the initial stage of professional training is revealed. The possibilities of forming a cognitive and creative component of geometry and graphic competence in the study of descriptive geometry are shown.

Keywords: studying projective geometry, mathematical and graphic competence, technical education.

References

1. Yakunin V. I., Guznenkov V. N. Geometric and graphic disciplines at the technical University. Teoriya i praktika obshchestvennogo razvitiya [Theory and practice of social development]. 2014, no 17, pp. 191–195. (In Russ.)
2. Guznenkov V. N., Zhurbenko P. A. Model as a key concept of geometric-graphic training. Alma mater (Vestnik vysshei shkoly) [Alma mater (Bulletin of the Higher School)]. 2013, no 4, pp. 82–87. (In Russ.)
3. Vyazankova V. V. Formation of graphic competence of bachelors of technical areas of training in the conditions of information and educational environment. Sovremennyye problemy nauki i obrazovaniya [Modern problems of science and education]. 2021, no 2. Available
   at: https://science-education.ru/ru/article/view?id=30663 (accessed: 03.03.2023). (In Russ.)
4. Guznenkov V. N., Yakunin V.I., Seregin V.I. et al. Computer graphics – the basis of geometric-graphic training. Mezhdunarodnyy nauchno-issledovatel’skiy zhurnal [International Research Journal]. 2016, no 4 (46). Available at: https://research-journal.org/archive/4-
   46-2016-april/kompyuternaya-grafika-osnova-geometro-graficheskojpodgotovki (accessed: 07.03.2023). doi: 10.18454/IRJ.2016.46.298 (In Russ.)
5. Savchenko E. V. Components of the information competence of the future engineer, formed in the study of fundamental disciplines. Sovremennoye obrazovaniye [Modern Education]. 2020, no 4, pp. 37–48. Available at: https://nbpublish.com/library_read_article.php?id=31606 (accessed: 07.03.2023). doi: 10.25136/2409-8736.2020.4.31606 (In Russ.)
6. Kovalenko A. V. Graphic competence as one of the components of the professional competence of a bachelor of vocational training in the direction “051000.62 Vocational training (by industry)”. Vestnik YuUrGGPU [Bulletin of the SUSUGPU]. 2011, no 10, pp. 83– Available at: https://cyberleninka.ru/article/n/graficheskayakompetentsiya-kak-odna-iz-sostavlyayuschih-professionalnoykompetentnosti-bakalavra-professionalnogo-obucheniya-po/viewer (accessed: 09.03.2023). (In Russ.)
7. Volkhin K. A., Leibov A. M. Problems of formation of graphic competence in the system of higher professional education. Filosofiya obrazovaniya [Philosophy of education]. 2012, no 4 (43), pp. 16–22.

For citation: Deynega S. A. Components of Geometric-graphic Competence, Formed in the Study of Descriptive Geometry at a Technical University. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 1 (46), pp. 50−63. https://doi.org/10.34130/1992 2752_2023_1_50

V. Sergej N. Dorofeev, Natalija V. Nazemnova Numerical sequences as a fundamental factor in the formation of creative activity in future bachelors

https://doi.org/10.34130/1992-2752_2023_1_64

Sergej N. Dorofeev – Togliatti State University, komrad.dorofeev2010@yandex.ru

Natalija V. Nazemnova – Penza State University

Text

Abstract. This article examines the problems of training engineering personnel for creative activity in the process of studying the basics of higher mathematics.

Keywords: mathematical education, continuity, fundamentality, quality of mathematical training, numerical sequences, integrals.

References

1. Dorofeev S. N., Esetov E. N., Nazemnova N. V. Analogy as a basis for teaching schoolchildren the vector method of solving geometric problems. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 2021, issue 4 (41), pp. 69–79. (In Russ.)
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3. Slepkan Z. I. Psikhologo-pedagogicheskiye osnovy prepodavaniya matematiki : metod.posobiye [Psychological and pedagogical foundations of teaching mathematics: method.stipend]. Kiev, 1983, 192 p. (In Russ.)
4. Dorofeev S. N. Teoriya i praktika formirovaniya tvorcheskoy aktivnosti budushchikh uchiteley matematiki v pedagogicheskom vuze [Theory and practice of formation of creative activity of future teachers of mathematics at a pedagogical university, dissertation for the degree of Doctor of Pedagogical Sciences]. Penza, 2000. 410 p. (In Russ.)
5. Dorofeev S. N., Ivanova T. A., Uteeva R. A. et al. Continuity in the preparation of future bachelors of pedagogical education (profile “Mathematics”) for creative activity. Gumanitarnyye nauki i obrazovaniye [Humanities and Education]. 2018, vol. 9, no 4 (36), pp. 25–30. (In Russ.)
6. Dorofeev S. N. Competence-based approach to mathematical education of students of technical universities. Pedagogicheskoye obrazovaniye i nauka [Pedagogical education and science]. 2009, no 1, pp.88–91. (In Russ.)
7. Dorofeev S. N. UDE as a method of preparing future bachelors of pedagogical education for professional activity. Gumanitarnyye nauki i obrazovaniye [Humanities and Education]. 2013, no 1, pp. 14–17. (In Russ.)
8. Dorofeev S. N., Pavlov I. I., Shichiyakh R. F., Prikhodko A. N.Differentiated Training as a Form of Organization of Education fnd Cognitive Activity of Future Masters of Pedagogical Education. Applied Lingvistics Research Jounal, 2021, 5 (3), pp. 216–222.
9. Dorofeev S. N., Shichiyach R. A., Khasimova L. N. Devoloping creative activity abilities of students in higer educaitional esteblishments. Rеvista оn line de politica e gistao educational. 2021, vol. 25, no S2, pp. 883–900.
10. Friedman L. M. Psikhologo-pedagogicheskiye osnovy prepodavaniya matematiki v shkole: uchitel’ matematiki o pedagogicheskoy psikhologii [Psychological and pedagogical foundations of teaching mathematics at school: a teacher of mathematics about pedagogical psychology]. M.: Enlightenment, 1983, 160 p. (In Russ.)
11. Talyzina N. F. Formation of mathematical concepts. Formirovaniye metodov matematicheskogo myshleniya [Formation of methods of mathematical thinking] / edited by N. F. Talyzina. M.: Lomonosov Moscow State University; Ventana-Graf LLP, 1995, pp. 13–28. (In Russ.)
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17. Vygotsky L. S. Sobraniye sochineniy : v 6 t. T. 3. Problemy razvitiya psikhiki / pod red. A. M. Matyushkina [Collected works: in 6 vols. 3. problems of the development of the psyche / edited by A. M. Matyushkin]. M.: Pedagogy, 1983. 368 p.: ill. (In Russ.)\

For citation: Deynega S. A. Components of Geometric-graphic Competence, Formed in the Study of Descriptive Geometry at a Technical University. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 1 (46), pp. 50−63. https://doi.org/10.34130/1992-2752_2023_1_50

VI. Vladimir P. Odinets On the works of three prewar mathematicians from Alma-Ata, Moscow, and Leningrad

https://doi.org/10.34130/1992-2752_2023_1_78

Vladimir P. Odinets – W.P.Odyniec@mail.ru

Text

Abstract. The article considers the works of three mathematicians: I. Akbergenov, specialist in Fredholm integral equations, a student of Professor L. Kantorovich, S. Arshon, specialist in combinatorics and function theory and Professor B. Izvekov, in the field of teaching higher mathematics, who lived accordingly, in Alma-Ata, Moscow and Leningrad and perished in 1938–1942.

Keywords: integral equations, Fredholm equation of second kind, Sarrus rule, combinatorial analysis, asymmetric sequence, vector analysis.

References

1. Akbergenov Ibadulla. The National encyclopaedia. Almaty. Kazak encyclopedijasy, 2004. Vol. 1, p. 13. (In Russ.)
2. Ahmetzhanova A. T. The fate of the academic – consequence of imperial policy of Soviet State. Vestnik KazNU [KazNU Bulletin]. Almaty, 2012, pp. 7–21. (In Russ.)
3. Akbergtnov I. A. On the estimation of the mistake of the approximate solution of the Fredholm integral equation of a second kind by E. Nistrom method. Leningrad. Trudy 2-go Vsesouznogo Matematicheskogo s’ezda (1934). T. 2. Sekcionnye doklady [Proceedings of the 2nd All-Union Mathematical Congress. Vol. 2 (Sectional reports)], 1935, pp. 386–387. (In Russ.)
4. Akbergenov I. A. Upon an approximate solution of the Fredholm integral equations and the determination of its eigenvalues. Mat. sb. [Mathematical collection], 1935, vol. 42. no 6, pp. 679–698. (In Russ.)
5. Matematika v SSSR za sorok let 1917–1947. T. 2. Biobibliograph [Mathematics in the U.S.S.R. after forty years 1917–1957. Vol. 2. Biobibliography]. M.: Fizmatlit, 1959, 819 p. (In Russ.)
6. Akbergenov I. A. Upon an approximate solution of the Fredholm Integral equations and the determination of its eigenvalues. Tashkent: Izd-vo Sredne-Aziatskogo universiteta, T.16, 1937, 48 p. (In Russ.)
7. Arshon S. E. Victims of political terror in U.S.S.R. Arhivnoe delo: P- 48248 [Archival file: P-48248]. (In Russ.)
8. Arshon S.E. Upon a method of combinatorial analysis. Trudy 2- go Vsesouznogo Mathematicheskogo s’ezda, 1934. T. 2. Sekcionnye doklady [Proceedings of the 2nd All-Union Mathematical Congress.Vol. 2 (Sectional reports)]. L.: Izd-vo AN U.S.S.R., 1935, pp. 24–(In Russ.)
9. Arshon S. E. A generalization of the Sarrus rule. Mat. sb. [Mathematical collection], 1935, vol. 42, no 1, pp. 121–128. (In Russ.)
10. Arshon S. E. A property of the arithmetic proportion. Mat. prosv. [Mathematical education], 1936, no 5, pp. 24–28. (In Russ.)
11. Arshon S. E. A proof of the existence of n-valued infinite asymmetrical sequence. Mat. sbornik [Mathematical collection], 1937, vol. 44, no 4, pp. 769–779. (In Russ.)
12. Kirsanov V. S. The books Destroyed: an echo by the Stalin’s terror in Soviet historical science. Sem’ iskustv [Seven arts], no 12. 05.01.(2015), pp. 21–34. (In Russ.)
13. Balach-Izvekova T. B. Vospominaniya moyey zhizni [Memories of my life]. SPb.,2008 (Return). 171 p.; 2009 (Continuation). 114 p.; 2010 (Epilogue). 120 p. (In Russ.)
14. Nauka i nauchnyye rabotniki v SSSR. Ch. V. Nauchnyye rabotniki Leningrada [Science and the scientific workers in the USSR. Part V. Scientific workers of Leningrad]. L.: Izd-vo AN U.S.S.R., 1934. 746 p. (In Russ.)
15. Izvekov B. I. Osnovy vektornogo analiza [A basis of vector analysis]. L.: Izd-vo Kubuch, 1934, 176 p. (In Russ.)
16. Izvekov B. I.. Sbornik zadach po prikladnoy matematike dlya studentov, aspirantov i prepodavateley vtuzov [A collection of problems in applied mathematics for students, past-graduate students and the instructors of higher technical education]. M., L.: Gos.technikoteoreticheskoe izd-vo, 1935. Part 1. 218 p. (In Russ.)\

For citation: Odinets V. P. On the works of three prewar mathematicians from Alma-Ata, Moscow, and Leningrad. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 1 (46), pp. 78−90. https://doi.org/10.34130/1992- 2752_2023_1_78

Full text

I. Nikolai N. Petrov, Dilshodbek M. Allashkurov To modeling conflicts in cyberspace using matrix games

https://doi.org/10.34130/1992-2752_2022_4_4

Nikolai N. Petrov – Udmurt State University, e-mail: kma3@list.ru

Dilshodbek M. Allashkurov – Urgench State University, Uzbekistan, e-mail: allashkurovdilshod@gmail.com

Text

Annotation. The problem of a conflict in cyberspace between a group responsible for the operation of servers and a group trying to disrupt the operation of these servers is considered. It is assumed that due to limited resources not all of the servers receive additional protection, and one or two servers are under attack. The aim of the attacking side is to increase the probability of bringing down some of the servers. A model of such a conflict is constructed in the form of a
matrix game. An equilibrium situation is found in mixed strategies.

Keywords: cyberspace, matrix game, mixed strategies,equilibrium situation.

References

1. Guts A.K., Vakhniy T. V. Teoriya igr i zashita informacii [Game theory and information protection]. Omsk: Izd-vo Omskogo un-ta, 2013.160 p. (In Russ.)
2. Grobotun E.E. Teoreticheskie osnovy postroeniya sistem zashhity ot kompyuternyx atak dlya avtomatizirovannyx sistem upravleniya [Theoretical foundations for building protection systems against computer attacks on automated systems management]. SPB.: High technologies, 2017. 120 p. (In Russ.)
3. Manshaei M. H., Zhu Q., Alpcan T., Basar T., Hubaux J.-P. Game theory meets network security and privacy. ACM Comput. Surv.Vol. 45, no. 3, Article 25 (June 2013), 39 p.
4. Corona I., Giacinto G., Roli F. Adversarial attacks against intrusion detection systems: Taxonomy, solutions and open issues. /Information Sciences. 2013. Vol. 239, pp. 201-–225.
5. Bykov A. Yu., Shmatova E. S. The Algorithms of Resource Distribution for Information Security Between Objects of an Information System Based on the Game Model and Principle of Equal Security of Objects. Science and Education of the Bauman MSTU. 2015, no 09, pp. 160–187. (In Russ.)
6. Petrosyan L. A., Zenkevich N.A., Shevkoplyas E. V. Teoriya igr [Game Theory]. SPB.: BHV-Peterburg, 2012. 432 p. (In Russ.)

For citation: Petrov N. N., Allashkurov D. M. To modeling conflicts in cyberspace using matrix games. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 4 (45), pp. 4−16. https://doi.org/10.34130/1992-2752_2022_4_4

II. Kirill A. Fofanov The Hausdorff ‘s measure behaviour under the mappings

https://doi.org/10.34130/1992-2752_2022_4_17

Kirill A. Fofanov – Herzen State Pedagogical University of Russia, e-mail: kirfof@mail.ru

Text

Abstract. Alforse’s «principle of lenght and area» gives the estimation of the fraction of the measures of set and its image under the analytical function. In 1974 this result was generalized by N.A.Shirokov by replacing Lebesgue measures whith Hausdorff‘s measures. In this article it will be shown that considering a broader class of functions in the definition of the Hausdorff‘s measure does not change the previous estimation.

Keywords: Hausdorff’s measure, analytical function, measure integral.

References

1. Shirokov N. A. On one generalization of the Alphors theorem. Zap. nauchnyx seminarov LOMI [Notes of LOMI scientific seminars], 1974. Vol. 44, pp. 179–185. (In Russ.)
2. Vinogradov O. L. Matematicheskij analiz: uchebnik [Mathematical Analysis: Textbook] SPb.: BHV-Peterburg, 2021. 752 p. (In Russ.)

For citation: Fofanov K. A. The Hausdorff‘s measure behaviour under the mappings. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 4 (45), pp. 17−32. https://doi.org/10.34130/1992-2752_2022_4_17

III. Ivan I. Lavresh, Vladislav D. Kuznetsov Simulation modeling of the processes of providing IT-services using the method of gradual formalization

https://doi.org/10.34130/1992-2752_2022_4_33

Ivan I. Lavresh – Pitirim Sorokin Syktyvkar State University, e-mail: ilavresh@mail.ru

Vladislav D. Kuznetsov – Information technology center, e-mail: hirufu96@yandex.ru

Text

Annotation. In the article c using the gradual formalization method described by the ability to build processes for providing IT services using simulation modeling to ensure management decisions are made on the effective and efficient workload of departments and the organization as a whole in order to achieve the organization’s business goals.

Keywords: IT-services, simulation modeling, gradual formalization, service Service-desk.

References

1. Uchebnik 4CIO [4CIO : Textbook]. Available at: https://4cio.ru/content/uchebnik_all_2.pdf (accessed: 10.15.2022) (InRuss.)
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   after Academician D.N. Pryanishnikov”. Perm: CPI Prokrost, 2020. 112 p. (In Russ.)
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7. Margolis N. Y. Imitacionnoe modelirovanie : ucheb. posobie [Simulation modeling : textbook. manual]. Tomsk: Publishing House of Tomsk State University, 2015. 130 p. (In Russ.)
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    https://mysmartservice.com/blog/itil-i-itsm (accessed: 10.15.2022). (In Russ.)
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13. Lavresh I. I., Kuznetsov V. D. Development of technology of simulation modeling of IT services in the processes of digitalization of the Komi Republic / IT-Arktika [IT-Arctic]. 2021. No 4, pp. 3–16. (In Russ.)
14. Anylogic. Available at: https://www.anylogic.ru / (accessed:10.10.2022).

For citation: Lavresh I. I., Kuznetsov V. D. Simulation modeling of the processes of providing IT-services using the method of gradual formalization. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 4 (45), pp. 33−45. https://doi.org/10.34130/1992-2752_2022_4_33

IV. Svetlana A. Deynega, Olga A. Sotnikova Features of building mathematical and graphic competence when studying projective geometry

https://doi.org/10.34130/1992-2752_2022_4_46

Svetlana A. Deynega – Ukhta State Technical University, e-mail: deynega07@mail.ru

Olga A. Sotnikova – Pitirim Sorokin Syktyvkar State University, e-mail: sotnikovaoa@syktsu.ru

Text

Annotation. The article validates the need for the formation of the cognitive and creative component as part of professional competencies among technical university students. The article reveals the essence of this component. Its formation at the initial stage of professional training is recognized to be reasonable. The formation of the cognitive and creative component of mathematical and graphical competence in the study of descriptive geometry is shown to start the mechanism for the development of notions about the ideas and methods of mathematical and graphical modeling.

Keywords: studying projective geometry, mathematical and graphic competence, technical education.

References

1. Kostryukov A.V., Semagina Yu. V. Geometric-graphic language as a basis for the organization of the educational process in the formation of graphic culture of a university student. Nauchno-metodicheskij elektronnyj zhurnal «Koncept» [Scientific and methodological electronic journal “Concept”]. 2018. No. 5 (May), pp. 309–320. Available at: http://econcept.ru/2018/181027.htm (accessed: 23.11.2022). (In Russ.)
2. Guznenkov V. N. Geometric and graphic training at a technical university. Rossijskij nauchnyj zhurnal [Russian Scientific Journal].No. 6, pp. 159–166. (In Russ.)
3. Yakunin V. I., Guznenkov V. N. Geometric and graphic disciplines at the technical University. Teoriya i praktika obshchestvennogo razvitiya [Theory and practice of social development]. 2014. No. 17, pp. 191–195. (In Russ.)
4. Dmitrieva I. M., Ivanov G. S. O professionalnyh kompetenciyah v prepodavanii nachertatelmoj geometrii [About professional competencies in teaching descriptive geometry]. Available at: https://dgng.pstu.ru/conf2017/papers/3/ (accessed: 23.11.2022). (In Russ.)

For citation: Deynega S. A., Sotnikova O. A. Features of building mathematical and graphic competence when studying projective geometry. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 4 (45), pp. 46−51. https://doi.org/10.34130/1992-2752_2022_4_46

V. Natalia A. Zelenina Selection of basic problems in the study of the theme «The equation of a circle in problems with parameters»

https://doi.org/10.34130/1992-2752_2022_4_52

Natalia A. Zelenina – Vyatka State University, e-mail: sezel@mail.ru

Text

Annotation. Ensuring a high quality of teaching mathematics to students is inextricably linked with teaching how to solve creative mathematical problems. These problems traditionally include tasks of high educational, developmental and diagnostic value. The purpose of this research is to develop and describe a teaching methodology for solving problems with parameters based on the allocation of basic (key) problems.

Keywords: teaching methods of mathematics, tasks with parameters, basic (key) tasks, equation of a circle.

References

1. Zdorovenko M. Yu., Zelenina N. A., Krutikhina M. V. The use of various methods for solving problems with a parameter on the Unified State Exam in Mathematics. Nauchno-metodicheskiy elektronniy zhurnal «Kontsept» [Scientific and methodological electronic journal «Concept»]. 2016. No 8, pp. 139–150. Available: http://e-koncept.ru/2016/16176.htm (accessed: 21.11.2022). (In Russ.)
2. Kolyagin Yu. M. Zadachi v obuchenii matematike. Ch. I [Tasks in teaching mathematics. Part I]. M.: Prosveschenie, 1977. 110 p. (In Russ.)
3. Krupich V. I. Teoreticheskiye osnovi obucheniya resheniyu sshkolnikh matematicheskikh zadach [Theoretical foundations of teaching solving school mathematical problems]. M.: Prosveschenie, 1995. 166 p. (In Russ.)
4. Sarantsev G. I. Uprazhneniya v obuchenii mahematike [Exercises in Teaching Manematics]. M.: Prosveschenie, 1995. 240 p. (In Russ.)
5. Zilberberg N. I., Khazankin R. G. Klyucheviye zadachi v obuchenii matematike [Key tasks in teaching mathematics]. M: Mir, 1984. 179 p. (In Russ.)
6. Gornshtein P. I., Polonsky V. B., Yakir M. S. Zadachi s parametrami [Problems with parameters]. Kyiv: RIA «Tekst», MP «Oko», 1992. 326 p. (In Russ.)
7. Kozhukhov S. K., Kozhukhova S. A. Uravneniya i neravenstva s parametrom [Equations and inequalities with a parameter]. Orel: OIUU,76 p. (In Russ.)
8. Kozko A. I., Chirsky V. G. Zadachi s parametrom i drugiye slozhniye zadachi [Problems with a parameter and other complex problems]. M: MTsNMO, 2007. 296 p. (In Russ.)
9. Koryanov A. G., Prokofiev A. A. Using the visual-graphical interpretation method when solving equations and inequalities with parameters. Matematika v shkole [Mathematics in School]. 2011. No 1, pp. 25–32. (In Russ.)
10. Modenov V. P. Zadachi s parametrami. Coordinatnoparametricheskiy metod: uchebnoye posobiye [Problems with parameters. Coordinate-parametric method: study guide]. M.: Examen,285 p. (In Russ.)
11. Yastrebinetskiy G. A. Zadachi s parametrami [Problems with parameters.]. M.: Prosveschenie, 1986. 128 p. (In Russ.)

For citation: Zelenina N. A. Selection of basic problems in the study of the theme «The equation of a circle in problems with parameters». Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 4 (45), pp. 52−66. https://doi.org/10.34130/1992- 2752_2022_4_52

VI. Andrei V. Yermolenko, Anatoliy A. Durkin On the contact problem for a cylindrical panel and a rectangular bar

https://doi.org/10.34130/1992-2752_2022_4_67

Andrei V. Yermolenko – Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Anatoliy A. Durkin – Pitirim Sorokin Syktyvkar State University

Text

Annotation. The contact problem for an infinite cylindrical panel and an infinite rectangular beam is analytically solved using the classical theory, a system for determining the interaction zone is built. According to the parameters found numerically from the system, the deflection and contact reactions are determined. The obtained result agrees with the solution obtained by the generalized reaction method.

Keywords: cylindrical panel, contact problem, generalized reaction method.

References

1. Mikhailovskii E. I. Shkola mekhaniki akademika Novozhilova [The Novozhilov School of Mechanics]. Syktyvkar: Publishing House of the Syktyvkar University, 2005. 172 p.
2. Mikhailovsky E.I., Tarasov V.N. Convergence of the generalized reaction method in contact problems with a free boundary. RAN. PMM. [RAS. PMM]. 1993. Vol. 57. Issue 1, pp. 128–136.
3. Michailovskii E. I., Badokin K. V., Yermolenko A. V. The Karman type theory of flat plates without Kirchhoff’s hypotheses. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika.
   Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics]. 1999. No. 3, pp. 181–202.
4. Yermolenko A. V., Osipov K. S. On using Python libraries to calculate plates. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics]. 2019, 4 (33), pp. 86–95.

For citation: Yermolenko A. V., Durkin A. A. On the contact problem for a cylindrical panel and a rectangular bar. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 4 (45), pp. 67−74. https://doi.org/10.34130/1992-2752_2022_4_67

VII. Maya I. Burlykina Dear Teacher and Grateful Student (in memory of E. I. Mikhailovsky and V. L. Nikitenkov)

https://doi.org/10.34130/1992-2752_2022_4_33

Maya I. Burlykina – Pitirim Sorokin Syktyvkar State University

Text

Abstract. This biographical article is about the work and scientific career of E. I. Mikhailovsky and V. L. Nikitenkov, two distinguished mathematics professors Syktyvkar State University.

Keywords: Syktyvkar State University, anniversary.

For citation: Burlykina M. I. Dear Teacher and Grateful Student (in memory of E. I. Mikhailovsky and V. L. Nikitenkov). Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 4 (45), pp. 75−89. https://doi.org/10.34130/1992- 2752_2022_4_75

Full text

I. Ebgeniy M. Vechtomov About commutative multiplicatively idempotent semirings with the property of maximality of prime ideals

https://doi.org/10.34130/1992-2752_2022_3_4

Ebgeniy M. Vechtomov – Vyatka State University, vecht@mail.ru

Text

Annotation. The article continues investigation of commutative multiplicatively idempotent semirings with the property of maximality of prime ideals. The author gives a detailed proof of a
theorem claiming that any distributive lattice has the property of maximality of prime ideals if and only if it is a lattice with relative complements. For an arbitrary of commutative multiplicatively idempotent semiring with the identity x + 2xy = x the following is proved: the property of maximality for prime ideals there is equivalent the fact that the lattice associated with this semiring is a lattice with relative complements.

Keywords: semiring, commutative multiplicatively idempotent semiring, property of maximality of prime ideals.

References

1. Vechtomov E. M., Petrov A. A. Funkcionalnaya algebra i polukolca. Polukolca s idempotentnym umnozheniem [Functional algebra and semirings. Semirings with idempotent multiplication]. St. Petersburg:Lan, 2022. 180 p. (In Russ.)
2. Vechtomov E. M., Petrov A. A Prime ideals in multiplicatively idempotent semirings. textitMatematicheskie zametki [Mathematical notes]. 2022. Vol. 111. Issue 4. P. 494–505. (In Russ.)
3. Vechtomov E. M., Petrov A. A. Multiplicatively idempotent semirings in which all congruences are ideal. Matematicheskie zametki [Mathematical notes]. 2022. Vol. 112. Issue 3. Pp. 376–383. (In Russ.)
4. Vechtomov E. M., Petrov A. A. Multiplicatively idempotent semirings with the annihilator condition. Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy, prilozheniya i problemy istorii : materialy XXI Mezhdunarodnoj konferencii, posvyashhennoj 85-
   letiyu so dnya rozhdeniya A. A. Karacuby [Algebra, number theory and discrete geometry: modern problems, applications and problems of history: Materials XXI International conference dedicated to the 85th anniversary of the birth of A. A. Karatsuba]. Tula: TSPU im. L.N. Tolstoy, 2022. Pp. 125–128. (In Russ.)
5. Vechtomov E. M., Petrov A. A. Multiplicatively idempotent semirings with additional conditions. Materialy 41-go Mezhdunarodnogo nauchnogo seminara prepodavatelej matematiki i informatiki
   universitetov i pedagogicheskix vuzov «Matematika i problemy obrazovaniya» [Proceedings of the 41st International Scientific Seminar for Teachers of Mathematics and Informatics of Universities and Pedagogical Universities «Mathematics and Problems of Education»]. Kirov: VyatGU, 2022. Pp. 4–8.
6. Vechtomov E. M. Annihilator characterizations of Boolean rings and distributive lattices. Matematicheskie zametki [Mathematical notes].T. 53. Issue 2. Pp. 15–24. (In Russ.)
7. Chermnykh V. V. Funkcionalnye predstavleniya polukolec [Functional representations of semirings]. Kirov: Publishing house of VyatGGU,224 p. (In Russ.)
8. Gretzer G. Obshhaya teoriya reshetok [General theory of lattices]. M.: Mir, 1982. 456 p. (In Russ.)
9. Skornyakov L. A. Elementy teorii struktur. 2-e izd., dop. [Elements of the theory of structures. 2nd ed., add.] Moscow: Nauka, 1982. 160 p. (In Russ.)

For citation: Vechtomov E. M. About commutative multiplicatively idempotent semirings with the property of maximality of prime ideals. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika.
Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 3 (44), pp. 4−20.https://doi.org/10.34130/1992-2752_2022_3_4

II. Yuriy V. Golchevskiy, Lidiya P. Shilova Selecting a Solution Method for the Problem of Automating the Classification of Texts Related to Industrial Safety Audits

https://doi.org/10.34130/1992-2752_2022_3_21

Yuriy V. Golchevskiy – Pitirim Sorokin Syktyvkar State University, e-mail: yurygol@mail.ru

Lidiya P. Shilova – Semantic machines, e-mail: shilovalp@bk.ru

Text

Abstract. The importance of solving problems arising from text classification in to-day’s world is undeniable, due to the fact that a huge amount of textual in-formation of different kinds is generated, which needs some processing and analysis.

Keywords: Machine Learning, Text Classification, Industrial Safety Audits.

References

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For citation: Golchevskiy Yu. V., Shilova L. P. Selecting a Solution Method for the Problem of Automating the Classification of Texts Related to Industrial Safety Audits. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 3 (44), pp. 21−32. https://doi.org/10.34130/1992-2752_2022_3_21

III. Nadezhda N. Babikova Education in the digital age: remember or google

https://doi.org/10.34130/1992-2752_2022_3_33

Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University, e-mail: valmasha@mail.ru

Text

Abstract.We live in an age of rapid changes in all areas of human practice, associated with the development of digital technologies. How do these changes affect the memory performance of modern students, what do students themselves think about these changes, and what cognitive
memory strategies are used in the learning process? How can we help students form the necessary level of memorization of educational material? The article presents the results of a study based on these questions.

Keywords: memory, memory performance, memory strategies, Internet, digital technologies.

References

1. Research of the metacognitive awareness of university students / N. N. Babikova, O. A. Maltseva, E. N. Starceva, M. S. Turkina. Vestnik Marijskogo gosudarstvennogo universiteta [Vestnik Marijskogo gosudarstvennogo universiteta]. 2018. T. 12. No 3(31). Pp. 9−16. DOI
   10.30914/2072-6783-2018-12-3-9-16. (In Russ.)
2. Metacognitive awareness and student achievement / N. N. Babikova, O. A. Maltseva, E. N. Starceva, M. S. Turkina. Dvadcat pyataya godichnaya sessiya Uchenogo soveta Syktyvkarskogo gosudarstvennogo universiteta imeni Pitirima Sorokina (Fevralskie chteniya) : sbornik materialov: tekstovoe nauchnoe elektronnoe izdanie na kompakt-diske, Syktyvkar, 01–28 fevralya 2018 goda [Twenty-fifth Annual Session of the Academic Council of Syktyvkar State University named after Pitirim Sorokin (February Readings) : collection of materials: text
   scientific electronic edition on CD-ROM]. Syktyvkar: Syktyvkarskij gosudarstvennyj universitet im. Pitirima Sorokina, 2018. 856 p. ISBN 978-5-87661-569-5. (In Russ.)
3. Ashymova N. Sh., Kazakova N. O. Memory performance of 1st year students of the Faculty of Biology and Chemistry of KSU. I. Arabaeva. Problemy sovremennoj nauki i obrazovaniya [The problems of modern science and education]. 2017. No 7 (89). Pp. 16−19. (In Russ.)
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IV. Ramiz M. Aslanov, Vladislav V. Sushkov – Historical ways of emergence and development of complex analysis

https://doi.org/10.34130/1992-2752_2022_3_47

Ramiz M. Aslanov – Institute of Mathematics and Mechanics, National Academy of Sciences of
Azerbaijan, e-mail: r_aslanov@list.ru

Vladislav V. Sushkov – Syktyvkar State University named after Pitirim Sorokin, e-mail: vvsu@mail.ru

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Abstract. The work considers the history of the emergence and development of the theory of the function of a complex variable as a branch of science and its influence on the development of the
corresponding educational discipline. In both cases, the main stages of the historical process are highlighted, key figures, dates, facts, publications and results are indicated. It is argued that the traditional logic of the presentation of the educational discipline “Theory of functions of the complex variable”to a greater or lesser extent repeats the historical logic of the development of the scientific industry. The development of either specialized or as universal as possible textbooks adapted to different levels of teaching should take into account the history of the development of the discipline, but should be based on modern educational technologies and the possibilities of electronic
teaching tools and resources.

Keywords: theory of functions of complex variable, complex analysis, history of mathematics, educational discipline, stages of development, educational technologies, methodological component.

References

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For citation: Aslanov R. M., Sushkov V. V. Historical ways of emergence and development of complex analysis. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022,
No 3 (44), pp. 47−63. https://doi.org/10.34130/1992-2752_2022_3_47

V. Andrey V. Yermolenko, Nikita V. Kozhageldiev On the solution of the inhomogeneous biharmonic equation

https://doi.org/10.34130/1992-2752_2022_3_64

Andrey V. Yermolenko – Pitirim Sorokin Syktyvkar State University, ea74@list.ru

Nikita V. Kozhageldiev – Pitirim Sorokin Syktyvkar State University.

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Annotation. When calculating the stress-strain state of plates, it becomes necessary to solve an inhomogeneous biharmonic equation, the complexity of which is due to the presence of fourth derivatives. The article considers a review of methods for solving such equations, while the implementation of three solution methods is given – the Galerkin method and two iterative methods. An algorithm for constructing test cases is given.

Keywords: biharmonic equation, Galerkin method, iterative methods

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For citation: Yermolenko A. V., Kozhageldiev N. V. On the solution of the inhomogeneous biharmonic equation. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2022, No 3 (44), pp. 64−78. https://doi.org/10.34130/1992-2752_2022_3_64