Bulletin 4 (45) 2022

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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

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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

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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

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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.)
  2. Arsenyev Yu. N. Davydova T. Y. Informacionnyj menedzhment: teoriya i praktika : uchebnik [Information management: theory and practice : textbook] / under the general editorship of Yu. N. Arsenyev. Moscow: KNOGUS. 2022. 438 p. (In Russ.)
  3. Petukhov O. A., Morozov A. V., Petukhova E. O. Modelirovanie: sistemnoe, imitacionnoe, analiticheskoe : ucheb. posobie [Modeling: system, simulation, analytical : textbook. manual]. 2nd ed., ispr. and add. St. Petersburg: Publishing House of NWTU, 2008. 288 p. (In Russ.)
  4. Kashtaeva S. V. Matematicheskoe modelirovanie : uchebnoe posobie [Mathematical modeling : textbook] / Ministry of Agriculture of the Russian Federation, Federal State Budgetary Educational Institution of Higher Education “Perm Agrarian and Technological University named
    after Academician D.N. Pryanishnikov”. Perm: CPI Prokrost, 2020. 112 p. (In Russ.)
  5. Zvonarev S. V. Osnovy matematicheskogo modelirovaniya : uchebnoe posobie [Fundamentals of mathematical modeling : a textbook]. Yekaterinburg: Ural Publishing House. un-ta, 2019. 112 p. (In Russ.)
  6. Limanovskaya O. V. Imitacionnoe modelirovanie v AnyLogic 7: 2 Volumes. Ch. 1 : uchebnoe posobie [Simulation modeling in AnyLogic from 7. Part 1 : textbook]. Yekaterinburg: Ural Publishing House. un–ta,152 p. (In Russ.)
  7. Margolis N. Y. Imitacionnoe modelirovanie : ucheb. posobie [Simulation modeling : textbook. manual]. Tomsk: Publishing House of Tomsk State University, 2015. 130 p. (In Russ.)
  8. Akopov A. S. Kompyuternoe modelirovanie : uchebnik i praktikum dlya SPO [Computer modeling: textbook and workshop for SPO]. Moscow: Yurayt Publishing House, 2019. 389 p. (In Russ.)
  9. Zhuravlev R. Illyustrirovanniy ITSM [Illustrated by ITSM]. Moscow: Live Book, 2013. 125 p. (In Russ.)
  10. England R. Vvedenie v realniy ITSM [Introduction to real ITSM]. Moscow: Live Book, 2011. 132 p.
  11. ITIL i ITSM: opredelenie metodologij, sravnenie, preimushhestva i nedostatki [ITIL and ITSM: definition of methodologies, comparison, advantages and disadvantages]. Available at:
    https://mysmartservice.com/blog/itil-i-itsm (accessed: 10.15.2022). (In Russ.)
  12. Biblioteka IT–infrastruktury (ITIL) [IT Infrastructure Library (ITIL).] Available at: https://www.ibm.com/ru-ru/cloud/learn/itinfrastructure-library (accessed: 03.23.2022). (In Russ.)
  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

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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

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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

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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

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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

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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

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