Bulletin 2 (43) 2022

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I. Tatyana M. Bannikova, Olga M. Nemtsova Geometrical and analytical characteristics of the constructing the polynomial of а circle division

https://doi.org/10.34130/1992-2752_2022_2_4

Tatyana M. Bannikova – Udmurt State University.

Olga M. Nemtsova – Udmurt State University.

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Abstract. The problem of finding circle division polynomials with the condition of specifying some of their coefficients is discussed. The problem of the existence of polynomials of this type is solved, but the problem of the ambiguity of finding circle division polynomials with a given simple or composite coefficient, as well as features of its number (such as decomposition into prime factors and a significant order with respect to a given coefficient) can be used in setting an open key in cryptographic systems. So it is known to use the roots of circle division polynomials as a cyclic group generator in the Berlekamp-Massey algorithm.

Keywords: circle division polynomials, cryptosystem, key’s generation, ciphertext.

References

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For citation: Bannikova T. M., Nemtsova O. M. Geometrical and analytical characteristics of the constructing the polynomial of а circle division. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 2 (43), pp. 4−20. https://doi.org/10.34130/1992-2752_2022_2_4

II. Nadezhda A. Belyaeva, Ilya O. Mashin, Anastasia V. Nadutkina Phase transition of a viscous fluid in a nonisothermal flow

https://doi.org/10.34130/1992-2752_2022_2_21

Nadezhda A. Belyaeva – Pitirim Sorokin Syktyvkar State University.

Ilya O. Mashin – Institute of Physics and Mathematics of the Federal Research Center Komi
Scientific Center of the Ural Branch of the Russian Academy of Sciences.

Anastasia V. Nadutkina – Pitirim Sorokin Syktyvkar State University.

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Annotation. A mathematical model is constructed for a nonisothermal pressure flow of an incompressible viscous fluid between two parallel planes. The basic relations of the model are the Navier-Stokes equation of motion, the heat conduction equation, the corresponding initial and
boundary conditions. In the flow process the possible phase transition ¨liquid – solid¨is taken into account.The condition for matching the temperatures of the solid and liquid phases is specified at the interface.The corresponding dimensionless flow model is constructed. A numerical analysis of the flow is carried out with varying the dimensionless parameters of the problem.The graphical results of numerical experiments are presented and analyzed. Graphical results of numerical experiments are presented and analyzed.

Keywords: viscous fluid, non-uniform temperature field, phase transition, numerical analysis.

References

  1. Belyaeva N. A., Nadutkina A. V. Non-isothermal flow of a viscous fluid. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, V. 3 (32). Pp. 20–30. (In
    Russ.)
  2. Belyaeva N. A. Heterogeneous flow of the structured liquid. Matematicheskoye modelirovaniye [Mathematical modeling], 2006, V. 18. Pp. 3–14. (In Russ.)
  3. Belyaeva N. A., Yakovleva A. F. Frontal wave of pressure flow. [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2017, V. 2 (23). Pp. 3–12. (In Russ.)
  4. Belyaeva N. A., Stolin A. M., Stelmakh L. S. Dynamics of Solid-State Extrusion of Viscoelastic Cross-Linked polymeric Materials. Theoretical Foundations of Chemical Engineering, 2008, V. 42. Pp. 549– 556.
  5. Pryanishnikova E. A., Belyaeva N. A., Stolin A. M. Compressible material flow in cylindrical channel with variable cross section. MATEC Web of Conferences 129, 06011 (2017), ICMTMTE 2017.
  6. Khudyaev S. I. Porogovye yavleniya v nelinejnyh uravneniyah [Threshold phenomena in nonlinear equations]. Moscow: Fizmatlit,272 p. (In Russ.)
  7. Belyaeva N. A. Matematicheskoye modelirovaniye: uchebnoye posobiye [Mathematical modeling: a training manual]. Syktyvkar: Publishing House of the Syktyvkar State University, 2014. 116 p. (In Russ.)
  8. Belyaeva N. A. Osnovy gidrodinamiki v modelyakh: uchebnoye posobiye [Fundamentals of hydrodynamics in models: a training manual]. Syktyvkar: Publishing House of the Syktyvkar State University, 2011. 147 p. (In Russ.)

For citation: Belyaeva N. A., Mashin I. O., Nadutkina A. V. Phase transition of a viscous fluid in a nonisothermal flow. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022,
No. 2 (43), pp. 21−31. https://doi.org/10.34130/1992-2752_2022_2_21

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III. Andrey S. Penin, Nikita O. Tursukov Development of components of a model for assessing the state of a cyberphysical system operator

https://doi.org/10.34130/1992-2752_2022_2_15

Andrey S. Penin – ITMO University.

Nikita O. Tursukov – ETU.

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Abstract. During the research work, the main biological markers of the human body were studied and those of them that met the requirements were selected for further research. A system for
evaluating employee performance based on a bidirectional LSTM network was developed, the accuracy of activity recognition was 88%, the value of the loss function was 0.504. In the future, the employee activity assessment system and biological markers will be combined into a model for assessing the state of the cyberphysical system operator.

Keywords: neural networks, LSTM-networks, biomarkers, models, systems, state.

References

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  2. Teplovaya inerciya temperaturnyx datchikov [Thermal inertia of temperature sensors] [Online]. Available at: https://isup.ru/articles/16/15436/ (accessed: 28.03.2022).
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  6. Filtry vysokix i nizkix chastot [High-pass and low-pass filters] [Online]. Available at: https://elar.urfu.ru/bitstream/10995/36102/1/978-5- 7996-1577-2_2015.pdf (accessed: 28.03.2022).
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For citation: Penin A. S., Tursukov N. O. Development of components of a model for assessing the state of a cyberphysical system operator. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 2 (43), pp. 32−54.
https://doi.org/10.34130/1992-2752_2022_2_32

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IV. Nikolay I. Popov, Evgeniya A. Kaneva Forming schoolchildren’s cognitive interest in mathematics using computer educational games

https://doi.org/10.34130/1992-2752_2022_2_55

Nikolay I. Popov – Pitirim Sorokin Syktyvkar State University.

Evgeniya A. Kaneva – Pitirim Sorokin Syktyvkar State University.

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Annotation. At present, due to the effective development of information and communication technologies, global changes affect all spheres of human life, including the educational process at school. Teachers face the problem of combining traditional methods and teaching aids with innovative ones to improve the efficiency and quality of the educational process. Since it is difficult for students to keep their attention on one object of study in the conditions of a large flow of information, teachers need to use modern technologies in their work to increase the motivation and interest of students in the subject. One of such educational technologies is educational computer
games.

Keywords: computer learning games, teaching mathematics, game technologies.

References

  1. Popov N. I. Fundamentalizaciya universitetskogo matematicheskogo obrazovaniya : monografiya [The fundamentalization of university mathematics education: monograph] / Yelets: EGU im. I.A. Bunina,174 p. (In Russ.)
  2. Popov N. I., Kaneva E. A. The use of computer games in mathematics in the educational process of secondary school. Matematicheskoe modelirovanie i informacionnye technologii
    [Electronic resource]: V Vserossijskaya nauchnaya konferenciya s mezhdunarodnym ychastiem [Mathematical modeling and information technologies [Electronic resource]: V All-Russian scientific conference with international participation] (December 9–11, 2021, Syktyvkar):
    collection of materials: text scientific electronic edition on CD. Syktyvkar: Publishing House of SSU im. Pitirim Sorokina, 2021, pp. 57–58. (In Russ.)
  3. Bocharov M. I., Mozharova T. N., Soboleva E. V., Suvorova T. N.Development of a personalized model of teaching mathematics by means of interactive short stories to improve the
    quality of educational results for schoolchildren. Perspektivy nauki i obrazovaniya [Prospects of Science and Education]. 2021. No. 5 (53). Pp. 306–322. (In Russ.)
  4. Zinoveva L .V., Zinovev S.A. Role-playing video games in the space of psychocorrection and psychotherapy. Smalta. 2017. No. 4. Pp. 17–19.
  5. Paiva J. C., Leal J. P., Queiros R. Fostering programming practice through games. Information (Switzerland). 2020. No. 11 (11). Pp. 1– 20.
  6. Kaneva E. A.Computer game in mathematics for schoolchildren. Materialy VII nauchno-obrazovatelnoj studencheskoj konferencii, posvyashchennoj dnyu rozhdeniya Nikolaya Ivanovicha Lobachevskogo [Proceedings of the VII scientific and educational student conferencededicated to the birthday of Nikolai Ivanovich Lobachevsky]. Kazan.S. 126–131. (In Russ.)

For citation: Popov N. I., Kaneva E. A. Forming schoolchildren’s cognitive interest in mathematics using computer educational games. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika.
Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 2 (43), pp. 55−66. https://doi.org/10.34130/1992-2752_2022_2_55

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V. Andrey V. Yermolenko, Viktoria R. Makarova Generalized reaction method for a plate with an inclined base

https://doi.org/10.34130/1992-2752_2022_2_67

Andrey V. Yermolenko – Pitirim Sorokin Syktyvkar State University.

Viktoria R. Makarova – Pitirim Sorokin Syktyvkar State University.

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Annotation. An effective way to solve problems on the interaction of plates and bases is the generalized reaction method. The presented article shows the application of the generalized reaction method to a cantilevered and rigidly fixed plate. The solution using the generalized reaction method is a system of iterated functions, the finding of which in a certain number of iterations will be reduced to solving the problem, which makes it possible to accurately and quickly determine the answer.

Keywords: plate, generalized reaction method, the Sophie Germain–Lagrange equation, contact reaction.

References

  1. Mikhailovskii E.I. Shkola mekhaniki akademika Novozhilova [The Novozhilov School of Mechanics]. Syktyvkar: Publishing House of the Syktyvkar University, 2005. 172 p.
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    of Novozhilov (Novozhilov – Chernykh – Mikhailovsky – Nikitenkov)]. Syktyvkar: Publishing House of the Syktyvkar University, 2002.147 p.
  3. Yermolenko A.V. Fundamentalizaciya universitetskogo matematicheskogo obrazovaniya : monografiya [Contact problems with free boundary: textbook]. Syktyvkar: Izd. Pitirim Sorokin, 2020. 1 opt. compact disc (CD-ROM). 105 p.
  4. Mikhailovsky E.I., Tarasov V.N. O sxodimosti metoda obobshhennoj reakcii v kontaktnyx zadachax so svobodnoj granicej [Convergence of the generalized reaction method in contact problems with a free boundary]. RAS. PMM. 1993. V. 57. Issue. 1. Pp. 128–136.
  5. Yermolenko A. V., Ladanova S. V. Kontaktnaya zadacha dlya dvux plastin s raznym zakrepleniem [Contact problem for two plates with different restraints]. Bulletin of the Syktyvkar University. Ser. 1: Mathematics. Mechanics. Informatics. 2020. Issue. 3 (36). Pp. 87-92.
  6. Yermolenko A. V., Osipov K. S. On using Python libraries to calculate plates. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics]. 2019, 4 (33), pp. 86–95.
    (In Russ.)

For citation: Andrey V. Yermolenko., Makarova V. R. Generalized reaction method for a plate with an inclined base. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022,
No. 2 (43), pp. 67−74. https://doi.org/10.34130/1992-2752_2022_2_67

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