Bulletin 2 (51) 2024

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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

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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.)
  2. Bondarev A., Galaktionov V. Modern development directions of data visualization in computational mechanics of fluid and gase. Nauchnaya vizualizatsiya [Science visualisation]. 2013. Vol. 5. No 4. Pp. 18–30. (In Russ.)
  3. Akberova N. I., Kozlova O. S. Osnovy analiza dannyh i programmirovaniya v R : uchebno-metodicheskoe posobie [Fundamentals of data analysis and programming in R : a textbook]. Kazan’: Al’yans,33 p. (In Russ.)
  4. Egoshin V. L., Ivanov S. V., Savvina N. V. at al. Visualization of biomedical data using the R software environment. Ekologiya cheloveka [Human ecology]. 2018. No 8. Pp. 52–64. (In Russ.)
  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


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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.)
  5. Panteleev A. V., Skavinskaya D. V., Aleshina E. A. Metaevristicheskiye algoritmy poiska optimal’nogo programmnogo upravleniya : uchebnik [Metaheuristic algorithms for searching for
    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).
  7. Aco-routing documentation. Available at: https://pypi.org/project/aco-routing/ (accessed: 21.04.2024).
  8. ACO documentation. Available at: https://pypi.org/project/aco/(accessed: 21.04.2024).
  9. Pygad documentation. Available at: https://pypi.org/project/pygad/(accessed: 21.04.2024).
  10. DEAP documentation. Available at: https://pypi.org/project/deap/(accessed: 21.04.2024).
  11. Scikit-opt documentation. Available at: https://scikitopt.github.io/scikit-opt//en/README (accessed: 21.04.2024).
  12. Reinelt G. TSPLIB95. Available at: http://comopt.ifi.uniheidelberg.de/software/TSPLIB95/tsp95.pdf (accessed: 21.04.2024).
  13. Discrete and Combinatorial Optimization. Available at: http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/tsp/ (accessed: 21.04.2024).
  14. TSPLIB95 documentation. Available at: https://tsplib95.readthedocs.io/en/stable/pages/usage.html (accessed: 21.04.2024).
  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

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