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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

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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

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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\

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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

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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

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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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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

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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

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   46-2016-april/kompyuternaya-grafika-osnova-geometro-graficheskojpodgotovki (accessed: 07.03.2023). doi: 10.18454/IRJ.2016.46.298 (In Russ.)
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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

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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

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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

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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

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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

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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

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.)
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

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.

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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.)
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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

Text

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.

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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.

Text

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

References

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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

Full text

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.

Text

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.

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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.

Text

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.)
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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

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.

Text

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.

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15. Confusion Matrix [Online]. Available at: https://devopedia.org/confusion-matrix (accessed: 28.03.2022).
16. Pereobuchenie [Retraining] [Online]. Available at:http://www.machinelearning.ru/wiki/index.php?title=Переобучение (accessed: 28.03.2022).

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

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.

Text

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

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.

Text

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.
2. Chernykh K.F., Mikhailovskii E.I., Nikitenkov V.L. Ob odnoy vetvi nauchnoy shkoly Novozhilova (Novozhilov – Chernykh – Mikhaylovskiy – Nikitenkov) [About one branch of the scientific school
   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

Full text

I. Chernov V. G. Non-cooperative antagonistic game with fuzzy estimates

https://doi.org/10.34130/1992-2752_2022_1_5

Vladimir G. Chernov – Vladimir State University, e-mail: vladimir.chernov44@mail.ru

Text

Abstract. In the study of operations a significant place is occupied by problems, the formal model of which are antagonistic games. The classical methods of solving such games are based on the principle of “common knowledge”according to which the participants in a game have full information about possible solutions and their consequences. Studies are known in which information reflexivity of the participants of the game is allowed, i.e. their uncertainty in
assessing the situation requiring a decision is allowed. To formalize this uncertainty, it is proposed that the values of the elements of the payment matrix should be presented in the form of fuzzy numbers. The choice of the best solution is based on the conversion of fuzzy estimates of the consequences of possible solutions in the form of equivalent fuzzy sets with triangular membership functions.

Keywords: antagonistic game, payment matrix, fuzzy set, membership function

References

1. Myerson R. B. Game theory: analysis of conflict. London Harvard: Harvard.Un.Press, 1991. 584 p.
2. Geanakoplos J. Common Knowledge. Handbook of Game Theory. V.ed. R. Aumann and S. Hart. Elsiever Science B.V. 1994. Pp. 1438– 1496.
3. Sigal A. V. Game theory model of investment decision making of investment decisions. Uchenye zapiski Tavricheskogo nacional’nogo universiteta imeni. V.I. Vernadskogo, seriya “Ekonomika i upravlenie” [Scientific Notes of the Taurida National University named after. V. I. Vernadsky. Series “Economics and Management”]. 2011. № 1, V. 24(63). Pp. 193–205. (in Ukrainian).
4. Butnariu D. Fuzzy games: a description of the concept. Fuzzy Sets and System. 1978. 1. Pp. 181–192.
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6. Ghosh D., Chakravorty S. On Solving Bimatrix Games with Triangular Fuzzy Payoffs. International Conference on Mathematics and Computing. 2018. Pp. 441–352.
7. Stalin T, Thirucheran M. Solving Fuzzy Matrix Games Defuzzificated by Trapezoidal Parabolic Fuzzy Number. SRDInternational Journal for Scientific Research and Development. 2015.
   V. 3. Issue 10. Pp. 341–345. 14 Чернов В. Г.
8. Verma Tina, Kumar Amit, Kacprzyk Janusz. A Novel Approach to the Solution of Matrix Games with Payoffs Expressed by Trapezoidal Intuitionistic Fuzzy Numbers. Journal of Automation, Mobile Robotics and Intelligent Systems. 2015. No 3. V. 9. Pp. 25–46.
9. Dubois D., Prade H. Theoriedes Possibilites. Applications a la representation des conisisancesen in for antique. Masson, 1980. 288 p.
10. Chernov V. G. Choosing a Solution Based on Fuzzy Game with Nature. Prikladnaya informatika [Journal of Applied Informatics]. V. 16. № 2(92). 2021. Pp. 131–142. (In Russ.)
11. Voroncov Ya. A., Matveev M. G. Methods of parametrized comparison of fuzzy and trapezoidal numbers. Vestnik VGU, Seriya Sistemnyj analiz I informacionnye tekhnologii [Vestnik VSU. Series System analysis and information technologies]. 2014. No 2. Pp. 90–96. (In Russ.)
12. Chernov V. G. Comparison of fuzzy number on the basis of construction linear order relation. Dinamika slozhnyh sistem – XXI vek [Dynamics of Complex Systems – XXI Century.]. 2018. No 2. Pp. 81–87. (In Russ.)

For citation: Chernov V. G. Non-cooperative antagonistic game with fuzzy estimates. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 5−14. https://doi.org/10.34130/1992-2752_2022_1_5

II. Kotelina N. O., Pevnyi A. B. Quadratic problem of mathematical diagnostics

https://doi.org/10.34130/1992-2752_2022_1_15

Nadezhda O. Kotelina – Pitirim Sorokin Syktyvkar State University, nkotelina@gmail.com.

Aleksandr B. Pevnyi – Pitirim Sorokin Syktyvkar State University, pevnyi@syktsu.ru.

Text

Abstract. Let m points be given in n-dimensional space, and G is the convex hull of these points. In the simplest problem of mathematical diagnostics, it is checked whether a point p belongs to the set G. In other words, if the coordinates of the points are signs of some disease, it is necessary to determine whether a new patient has a disease by the similarity of its signs in him and in patients with a confirmed diagnosis. In this paper, we attach its epsilon neighborhood to G and check whether p belongs to an extended set. To do this, we solve a quadratic programming problem in which we need to find the point of the set G closest to the point p in the Euclidean norm. In the article, we write out the necessary minimum conditions, obtaining a problem that can be solved using a modified simplex method with an additional condition for the bases.

Keywords: mathematical diagnostics, machine learning, modified simplex-method, quadratic programming

References

1. Malozemov V. N., Cherneutsanu E. K. The simplest problem of mathematical diagnostics. Seminar «O & ML». Izbrannye doklady [Seminar «O & ML». Selected papers]. 2022-02-09. Available: http://www.apmath.spbu/oml/reps22.shtml#0209 (accessed: 04.04.2022).
2. Pevnyi A. B. Finding the point of polyhedron closest to the origin (in Russian). Optimizaciya [Optimization]. Issue 10 (4). Novosibirsk, 1972.
3. Wolfe P. The simplex method for quadratic programming. Econometrics. 1959. Vol. 27. Pp. 382–398.

For citation: Kotelina N. O., Pevnyi A. B. Quadratic problem of mathematical diagnostics. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 15−22. https://doi.org/10.34130/1992-2752_2022_1_15

III. Maslyaev D. A. Current state of the higher school timetabling problem

https://doi.org/10.34130/1992-2752_2022_1_23

Denis A. Maslyaev – Komi republican academy of public service and administration, e-mail:
dmaslyaev@gmail.com

Text

Abstract. The article contains a review of Russian and foreign literature sources of solving the high school timetabling problem. The distinctive features of the schedule for the university are listed, as well as the peculiarities of scheduling in Russia. The comparison of various software tools for automatic scheduling is given. The existing software is not enough to solve this problem. A feature of the task is the presence of “block”classes that need to be compactly placed in the schedule, a large number of training streams, and a lot of external part-timers. Methods and algorithms for solving similar problems are considered. The existing heuristic methods have their advantages and disadvantages. A conceptual statement of the problem is formulated in a verbal form in relation to a specific educational institution. Hard and soft restrictions are formulated. Violation of soft restrictions will affect the penalty function – the only target function. The author came to the conclusion that it is necessary to develop a set-theoretic mathematical model for the problem under consideration and a hybrid heuristic solution method that would combine the advantages of various heuristic methods and offset their disadvantages. The data for the problem must be presented in an aggregated form.

Keywords: timetabling problem, high school, combinatorial optimization, automatization, methods, heuristic, literature review, algorithm, conceptual model

References

1. Klevanskij N. N. Formation of the schedule of classes of higher educational institutions. Obrazovatel’nye resursy i tekhnologii [Educational resources and technologies]. 2015. No 1(9). Pp. 34–44.
2. Chavez-Bosquez O., Hernandez-Torruco J., Hernandez-Ocana B., Canul-Reich J. Modeling and Solving a Latin American University Course Timetabling Problem Instance. Mathematics. 2020, Vol. 8(10), 1833 p.
3. Gafarov E. R. Software product for drawing up educational schedules of higher education institutions. XII Vserossijskoe soveshchanie po problemam upravleniya VSPU-2014 (16-19 iyulya, g. Moskva) [XII All-Russian Meeting on Management Problems VSPU-2014 (July 16-19, Moscow)]. M.: Institut problem upravleniya im. V. A. Trapeznikov RAN, 2014. Pp. 8804–8809.
4. Abuhaniya Amer Y. A. Modeli, algoritmy i programmnye sredstva obrabotki informacii i prinyatiya reshenij pri sostavlenii raspisaniya zanyatij na osnove evolyucionnyh metodov [Models, algorithms and software tools for information processing and decision-making when drawing up a class schedule based on evolutionary methods] Avtoreferat dissertacii na soiskanie uchenoj
   stepeni kandidata tekhnicheskih nauk. Novocherkassk, 2016. 20 p.
5. Sidorin A. B., Likucheva L. V., Dvoryakin A. M. Methods of automation of scheduling classes Part 1. Classical methods). Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Proceedings of the Volgograd State Technical University]. 2009. No 12 (60). Pp. 116–120.
6. Maslov M. G. Razrabotka modelej i algoritmov sostavleniya raspisanij v sistemah administrativno-organizacionnogo upravleniya [Development of models and algorithms for scheduling in administrative and organizational management systems] Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. M., 2004. 25 p.
7. Sidorin A. B., Likucheva L. V., Dvoryakin A. M. Methods of automation of scheduling classes Part 2. Heuristic methods of optimization. Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Proceedings of the Volgograd State Technical University] 2009. No 12 (60). Pp. 120–123.
8. Asvad Firas M. Modeli sostavleniya raspisaniya zanyatij na osnove geneticheskogo algoritma na primere vuza Iraka [Models of scheduling classes based on a genetic algorithm on the example of a university in Iraq]. Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. Voronezh, 2013. 16 p.
9. Kabal’nov Y. S., SHekhtman L. I., Nizamova G. F., Zemchenkova N.A. Compositional genetic algorithm for scheduling training sessions. Vestnik Ufimskogo Gosudarstvennogo Aviacionnogo Universiteta [Bulletin of the Ufa State Aviation University]. 2006. No 2. Vol. 7. Pp. 99–109.
10. Nizamova G. F. Matematicheskoe i programmnoe obespechenie sostavleniya raspisaniya uchebnyh zanyatij na osnove agregativnyh geneticheskih algoritmov [Mathematical and software for scheduling training sessions based on aggregate genetic algorithms]. Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. Ufa, 2006. 18 p.
11. Skiena S. Algoritmy. Rukovodstvo po razrabotke [Algorithms. Development guide] BHV-Peterburg, 2014. 720 p.
12. Matveev A. I. Algorithm for optimizing resource planning (on the example of the annealing method) Perspektivnye informacionnye tekhnologii (PIT 2018). Trudy mezhdunarodnoj nauchno-prakticheskoj konferencii. Pod redakciej S.A. Prohorova [Perspective Information Technologies (PIT 2018) : Proceedings of the International Scientific and Practical Conference / ed. by S. A. Prokhorov.] 2018. Pp. 1046–1059.
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14. Song T., Liu S., Tang X., Peng X., Chen M. An iterated search algorithm for the University Course Timetabling Problem. Applied Soft Computing, Vol. 68 (2018). Pp. 597–608.
15. Podinovskij V. V. Idei i metody teorii vazhnosti kriteriev v mnogokriterial’nyh zadachah prinyatiya reshenij [Ideas and methods of the theory of criteria importance in multicriterial decision-making problems]. M.: Nauka,103 p.
16. Silva J. D. L., Burke E. K., Petrovic S. An Introduction to Multiobjective Metaheuristics for Scheduling and Timetabling. Metaheuristics for multiobjective optimisation. Lecture notes in economics and mathematical systems, vol. 535, Pp. 91–129.
17. Aziz N. L. A., Aizam N. A. H. A Brief Review on the Features of University Course Timetabling Problem. AIP Conference Proceedings, 2016. 020001 (2018).

For citation: Maslyaev D. A. Current state of the higher school timetabling problem. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 23−40.
https://doi.org/10.34130/1992-2752_2022_1_23

IV. Golchevskiy Y.V., Shchukin N. Yu. Design and Development of a Service Web Configurator for Computer Assembly

https://doi.org/10.34130/1992-2752_2022_1_41

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

Nikolay Yu. Shchukin – Mobile Solution LLC, e-mail: sedfar.08.09@mail.ru

Text

Abstract. Thе paper presents a study of designing and implementing a service web configurator based on a configurator for computer assembly. The analysis of web configurators application and analog products is carried out. The specifics of the subject area are considered and the functional modules of the service with their goals and requirements are highlighted. The diagram of the web service main functional modules, the diagrams of the process of selecting components in the configurator, the database models, the interfaces of the developed product are provided.

Keywords: web configurator, computer assembly

References

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6. Sandrin E., Trentin A., Grosso C., Forza C. Enhancing the consumerperceived benefits of a mass-customized product through its online sales configurator: An empirical examination. Industrial Management and Data System, 2017, vol. 117, no. 6. Pp. 1295–1315. DOI: 10.1108/IMDS-05-2016- 0185.
7. Leclercq T., Cordy M., Dumas B., Heymans P. Representing repairs in configuration interfaces: A look at industrial practices. ACM IUI2018 Workshop on Explainable Smart Systems (ExSS), 2018, Available at:https://explainablesystems.comp.nus.edu.sg/2018/wpcontent/uploads/2018/02/exss_12_leclercq.pdf (accessed 01.03.2022).
8. Leclercq T., Cordy M., Dumas B., Heymans P. On studying bad practices in configuration UIs. ACM IUI2018 Workshop on Web Intelligence and Interaction. Available at: http://ceur-ws.org/Vol-2068/wii1.pdf (accessed: 01.03.2022).
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10. Grosso C., Forza C. Users’ Social-interaction Needs While Shopping via Online Sales Configurators. International Journal of Industrial Engineering and Management, 2019, vol. 10, no. 2. Pp. 139–154. DOI: 10.24867/IJIEM2019-2-235.
11. Mahlam¨aki T., Storbacka K., Pylkk¨onen S., Ojala M. Adoption of digital sales force automation tools in supply chain: Customers’ acceptance of sales configurators. Industrial Marketing Management, 2020, vol. 91. Pp. 162–173. DOI: 10.1016/j.indmarman.2020.08.024.
12. HardPrice – Sravnenie i dinamika cen na komplektuyushhie PK v internet magazinax [HardPrice – Comparison and dynamics of prices for PC components in online stores]. Available at: https://hardprice.ru/ (accessed: 01.03.2022). (In Russ.)
13. Konfigurator PK – sobrat‘ komp‘yuter na zakaz. Sobrat‘ sistemny‘j blok v onlajn konfiguratore [PC configurator – to assemble a computer to order. Assemble the system unit in the online configurator]. Available at: https://www.citilink.ru/configurator/ (accessed 01.03.2022). (in Russ.)
14. Sborka PK – DNS – internet-magazin cifrovoj i by‘tovoj texniki po dostupny‘m cenam [PC assembly – DNS – online store for digital and home appliances at affordable prices]. Available at: https://www.dns-shop.ru/configurator/ (accessed: 01.03.2022). (In Russ.)
15. Sobrat‘ komp‘yuter onlajn s proverkoj sovmestimosti Konfigurator/sborka igrovogo PK [Assemble a computer online with a compatibility check Configurator/build a gaming PC]. Available at: https://www.ironbook.ru/constructor/ (accessed: 01.03.2022). (In Russ.)
16. Shchukin N. Yu., Golchevskiy Yu. V. The logic of the software configurator at the stage of selecting compatible computer components // XXVIII godichnaya sessiya Uchenogo soveta SGU im. Pitirima Sorokina: Nacional‘naya konferenciya : sbornik statej [XXVIII annual session of the Academic Council of the Pitirim Sorokin Sykt. State Univ.: National conference: collection of articles: text. sci. electr. ed. Syktyvkar: Publishing House of Pitirim Sorokin Sykt. State Univ.] 2021, pp. 649–660. (In Russ.)

For citation: Golchevskiy Yu. V., Shchukin N. Yu. Design and Development of a Service Web Configurator for Computer Assembly. Bulletin of Syktyvkar University, Series 1: Mathematics.
Mechanics. Informatics, 2022, No. 1 (42), pp. 41−60. https://doi.org/10.34130/1992-2752_2022_1_41

V. Melnikov V. A., Yermolenko A. V. Development of XML-based Markup Language

https://doi.org/10.34130/1992-2752_2022_1_61

Vadim A. Melnikov – Pitirim Sorokin Syktyvkar State University

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

Text

Abstract. Modern approaches in the field of software development assume not only the functionality of the product being developed, but also the convenience, clarity and familiarity of the interfaces. Today, the developed software can be used on various devices, with different configurations, and users may also need a different language to work with the software. To address the issue of universality in the field of 2D games, the approach used in the development of the user interface for the Sad Lion Engine is proposed. Within the framework of this approach, it is supposed to use the markup language Sad Lion Markup Language, the description and use of which is given in the article.

Keywords: user interfaces, C++, mobile development, markup languages

References

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For citation: Melnikov V. A., Yermolenko A. V. Development of XML-based Markup Language. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 61−73. https://doi.org/10.34130/1992-2752_2022_1_61

VI. Pavlova L. V. Methods of teaching elementary mathematics in preparation a mathematics teacher at a university

https://doi.org/10.34130/1992-2752_2022_1_74

Lydia V. Pavlova – Pskov State University, pavlovalida@mail.ru

Text

Abstract. Today, the education system is rapidly undergoing changes that future teachers should be ready for. Consequently, their training at the university cannot remain the same as 10 or even 5 years ago and requires revision and adaptation to modern requirements and demands of society. The professional training of a future mathematics teacher involves subject and methodological training. At the same time, the quality of subject training at the university depends on the level of proficiency in school mathematics. However, many first-year students are experiencing a number of difficulties, which the researchers note and which were identified by us during the control work on the school mathematics course and the survey of first-year students of the Institute of Mathematical Modeling and Igropractic Pskov State University. The identified problems and difficulties were taken into account when developing the program of the discipline «Introductory Course of Mathematics», which is aimed at repeating and studying the material necessary for the successful study of the university course of mathematics. The article presents the methodology of teaching elementary mathematics (using the example of the section «Trigonometry») to future teachers of mathematics, the feature of which is the inclusion of methodological aspects in the learning process. This allows not only to form subject knowledge on trigonometry, but also to show students how to teach schoolchildren in modern conditions, for example, with distance or mixed learning format. The proposed method has shown positive results.

Keywords: introductory mathematics course, elementary mathematics, school mathematics course, distance learning course, independent study, trigonometry

References

1. The working program of the discipline «Elementary Mathematics» for the direction of training Pedagogical education (with two training profiles «Computer Science and Mathematics»), full-time education. Developer: L. V. Pavlova. Pskov State University, 2020. Available: https://pskgu.ru/eduprogram (accessed: 01.02.2022). (In Russ.)
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5. The work program of the discipline «Introductory course of mathematics» for the direction of training Pedagogical education (with two training profiles «Computer Science and Mathematics»), full-time education. Developer: L. V. Pavlova. Pskov State University, 2020. Available: https://pskgu.ru/eduprogram (accessed 01.02.2022). (In Russ.)
6. Bostanova M. M., Dzhaubaeva Z. K., Uzdenova M. B. Electronic textbook as a means of increasing the effectiveness of independent work of students in the conditions of distance learning in the study of the discipline «Elementary Mathematics». Sovremenny‘e problemy‘ matematicheskogo obrazovaniya : materialy‘ Mezhregional‘noj nauchno-prakticheskoj konferencii [Modern problems of mathematical education. Materials of the Interregional
   scientific and practical conference]. 2020. Pp. 44–48. (In Russ.)
7. Kochegurnaya M. Yu. The use of distance learning in teaching the discipline «Elementarnaya matematika». [Information systems and technologies in modeling and management. Proceedings of the V International Scientific and Practical Conference. Editor-in-chief K. A. Makoveychuk.] 2020. Pp. 411–413.
8. Popov N. I. On the effectiveness of using the model of learning technology in trigonometry in teaching mathematics students. Education and science. No. 9 (108). Pp. 138–153. (In Russ.)
9. Stefanova G. P., Baigusheva I. A., Tovarnichenko L. V., Stepkina M. A. Formation of cognitive independence of first-year students in the study of elementary mathematics at the university. Sovremennye problemy nauki i obrazovaniya [Modern problems of science and education]. 2018. No. 4. Pp.(In Russ.)

For citation: Pavlova L. V. Methods of teaching elementary mathematics in preparation a mathematics teacher at a university. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 74−89. https://doi.org/10.34130/1992-2752_2022_1_74

VII. Sotnikova O. A. ASLANOV RAMIZ MUTALLIM OGLY (ON THE 75TH ANNIVERSARY)

https://doi.org/10.34130/1992-2752_2022_1_90

Sotnikova Olga Alexandrovna – Pitirim Sorokin Syktyvkar State University

Text

Abstract. The article is dedicated to Aslanov Ramiz, PhD in Physics and Mathematics, Doctor of pedagogical sciences, professor, corresponding member of the International Academy of Sciences of Pedagogical Education.

Keywords: Aslanov Ramiz

For citation: Sotnikova O. A. Aslanov Ramiz (on his 75th birthday). Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 90−94.
https://doi.org/10.34130/1992-2752_2022_1_90

Full text

I. Vechtomov E. M., Chermnykh V. V. Main directions of the development of the semiring theory

DOI: 10.34130/1992-2752_2021_4_4

Vechtomov Evgeny Mikhailovich − Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Fundamental and Computer Mathematics, Vyatka State University, e-mail: vecht@mail.ru

Chermnykh Vasily Vladimirovich − Doctor of Physical and Mathematical Sciences, Pitirim Sorokin Syktyvkar State University, chief scientist, e-mail: vv146@mail.ru

Text

The article highlights and analyzes the main directions of formation and development of Semiring Theory. The first ring-module direction summarizes and extends the theory of rings and modules onto semirings and semimodules over them. The next one is a universal algebraic direction that is based on Universal Algebra and Group Theory. The third direction is connected with study of special classes of semirings and is aimed at using semirings within Mathematics, in Computer Sciences and in applications of Mathematics. The first two directions contain investigating of the general theory of semirings, building structural theories for certain important and interesting classes of abstract semirings. The third direction includes describing of finite semirings with certain conditions.

Keywords: semiring, semifield, semimodule, ring, distributive lattice, development of Theory of Semirings.

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For citation: Vechtomov E. M., Chermnykh V. V. Main directions of the development of the semiring theory. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021. No. 4 (41), pp. 4−40. DOI: 10.34130/1992-2752_2021_4_4

II. Andryukova V. Yu. Variational approach to calculating critical loads in the case of spatial deformation of curved rods

DOI: 10.34130/1992-2752_2021_4_41

Andryukova Veronika Yuryevna − Associate Professor, Komi Science Center, Ural RAS Department, e-mail: veran@list.ru

Text

A detailed derivation of the formulas of elastic energy and work of external forces for rings loaded with central forces is given. xpressions for calculating the critical load are presented in the case of plane deformation of the ring, as well as in the case of the spatial form of buckling.

Keywords: curvilinear bar, critical load, stability, Euler equations, work of external forces, elastic energy

References

1. Perel’muter A. V., Slivker V. I. Ustoychivost’ ravnovesiya konstruktsiy i rodstvennyye problemy [Stability of the structures equilibrium and related problems]. Vol. 2. Moscow, Izdatel’stvo SKAD SOFT, 672 p.
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For citation: Andryukova V. Yu. Variational approach to calculating critical loads in the case of spatial deformation of curved rods. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 4 (41), pp. 41−49. DOI: 10.34130/1992-2752_2021_4_41

III. Yermolenko A. V., Melnikov V. A. Solving the problem of abstraction from platform-specific code for iOS and Android applications using the example of SadLion Engine

DOI: 10.34130/1992-2752_2021_4_50

Yermolenko Andrei Vasilievich − PhD in Physics and Mathematics, Associate Professor, Head of Department of Applied Mathematics and Computer Science, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Melnikov Vadim Andreevich − Postgraduate student, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Text

The paper examines existing solutions for cross-platform mobile development, compares their features, advantages and disadvantages. It describes the solution to various problems arising in the development of your own cross-platform engine for development for iOS and Android.
The construction of a system for displaying a visual interface on a user screen using a GPU is considered. The architectural solutions used to write high-performance logic of application behavior in the C ++ programming language are described. The life cycles of applications for the iOS and
Android platforms are considered and a way to abstract from the native life cycle is proposed to generalize the application code on both platforms.The implementation of interlanguage interaction between Java and C ++ using JNI on the Android platform and Objective-C and C ++ is described,
architectural solutions are given for building an abstraction layer that hides such low-level interactions in the engine core.

Keywords: cross-platform development, C ++, Android, iOS.

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    madrid, Capetown, Sydney, Tokyo, Singapore, Mexico City: AddisonWesley, 2014. 560 p.
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For citation: Yermolenko A. V., Melnikov V. A. Solving the problem of abstraction from platform-specific code for iOS and Android applications using the example of SadLion Engine. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 4 (41), pp. 50−69.
DOI: 10.34130/1992-2752_2021_4_50

IV. Dorofeev S. N., Esetov E. N., Nazemnova N. V. Analogy as the basis for teaching students the vector method of geometric problem solving

DOI: 10.34130/1992-2752_2021_4_70

Dorofeev Sergey Nikolaevich – Doctor of Pedagogy, Professor of the Department of Higher Mathematics and Mathematical Education, Togliatti State University (Russia, 445020, Samara Region, Tolyatti, Belorusskaya St., 14)

Esetov Yelzhan Nurlykhanovich – postgraduate student of the department “Higher Mathematics and Mathematical Education” Togliatti State University (Russia, 445020, Samara region, Tolyatti, Belorusskaya st., 14)

Nazemnova Natalia Vladimirovna − Candidate of Pedagogical Sciences, Senior Lecturer, Department of Higher Mathematics, Penza State University (Russia, 440020, Penza region, Penza, Krasnaya st., 40

Text

This article examines the ways and the methods that contribute to improving the quality of teaching students the basics of vector algebra and methods of their application to solving geometric problems. For this purpose, the necessary knowledge of the basics of vector algebra, which students should learn in the process of studying the topic “Fundamentals of
vector algebra”, is highlighted and systematized. The paper substantiates the fact that such a method of cognition as analogy plays an important role in the effectiveness of the process of
teaching high school students to apply the basics of vector algebra to solving geometric problems. Some examples of interrelated tasks that contribute to improving the quality of teaching students the use of the vector method are given.

Keywords: Vector method, training in solving geometric problems, analogy.

References

1. Boltyanskij V. G. Analogy — commonality of axiomatics. Sovetskaya pedagogika [Soviet pedagogy], 1975. No. 1. Pp. 83−93.
2. Dorofeev S. N. Teoriya i praktika formirovaniya tvorcheskoj aktivnosti budushhix uchitelej matematiki v pedagogicheskom vuze, dissertaciya na soiskanie uchenoj stepeni doktora pedagogicheskix nauk [The theory and practice of forming the creative activity of future
   teachers of mathematics in a pedagogical university], Penza, 2000. 410 p.
3. Atanasyan L. S., Butuzov V. F., Kadomcev S. B. et al. Geometriya. 7−9 klassy [Geometry. 7-9th grade]. M.: Prosveshhenie, 384 p.
4. Aleksandrov A. D., Verner A. L., Ry‘zhik V. I. Geometriya. 9 klass [Geometry. 9th grade]. M.: Prosveshhenie, 2015. 175 p.
5. Atanasyan L. S., Butuzov V. F., Kadomcev S. B. et al. Geometriya. 7−9 klassy [Geometry. 7-9th grade]. M.: Prosveshhenie, 255 p.
6. Dorofeev S. N., Zhuravleva O. N., Ry‘bina T. M., Sarvanova Zh. A. Formation of research competencies of students in the mathematics classroom. Sovremenny‘e naukoemkie texnologii
   [Modern knowledge-intensive technologies]. 2018. No. 10. Pp. 181−185.
7. Uteeva R. A. Teoreticheskie osnovy‘ organizacii uchebnoj deyatel‘nosti uchashhixsya pri differencirovannom obuchenii matematike v srednej shkole. Dissertaciya doktora ped. nauk [Theoretical foundations of the organization of students’ learning activities in differentiated learning of mathematics in high school]. Moscow, 1998. 363 p.
8. Kudryavcev L. D. Mysli o sovremennoj matematike i ee izuchenii [Thoughts on Modern Mathematics and its Study]. M.: Nauka, 1977. 123 p.
9. Dorofeev S. N. UDE as a method of preparing future bachelors of teacher education for professional activities. Gumanitarny‘e nauki i obrazovanie. MordGPI im. M. E. Evsev‘eva [Humanities and Education / M. E. Evsevyev Mordovian State Pedagogical University].
   No. 1, 2013. Pp. 14−17.
10. Sarancev G. I. Kak sdelat‘ obuchenie matematike interesny‘m [How to make learning math interesting]. M.: Prosveshhenie. 2011. 160 p.
11. Dorofeev S., Pavlov I., Shichiyakh R., Prikhodko A. Differentiated Training as a Form of Organization of Education and Cognitive Activity of Future Masters of Pedagogical Education.
    Applied Lingvistics Research Jounal, 2021, 5(3), Pp. 216−222.

For citation: Dorofeev S. N., Esetov E. N., Nazemnova N. V. Analogy as the basis for teaching students the vector method of geometric problem solving. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 4 (41), pp. 70−82. DOI: 10.34130/1992-2752_2021_4_70

V. Yermolenko A. V., Belyaev E. A., Turkova O. I. One contact problem for two plates

DOI: 10.34130/1992-2752_2021_4_83

Yermolenko Andrei Vasilievich − PhD in Physics and Mathematics, Associate Professor, Head of Department of Applied Mathematics and Computer Science, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Belyaev Evgeniy Anatolievich − Postgraduate student, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Text

Using the generalized reaction method, a numerical solution of the contact problem for two plates is given. One plate is hinged, the other one is rigidly fixed. It is shown that the distribution of contact reactions significantly depends on the relative position of the plates. In this case, the contact zone is either a segment or a point.

Keywords: plate, contact problem, generalized reaction method, numerical solution.

References

1. Yermolenko А. V., Ladanova S. V. Contact problem for two plates with different fixing. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2020, 3 (36). Pp. 87- 92.
2. Ермоленко А. В. Kontaktnye zadachi so svobodnoj granicej [Free Boundary Contact Problems]. Syktyvkar: Izd-vo SGU im. Pitirima Sorokina, 2020. (CD-ROM). 105 p.
3. 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.
4. Mihajlovskii E. I., Toropov A. V. Matematicheskiye modeli teorii uprugosti [Mathematical models of the theory of elasticity]. Syktyvkar: Sykt Publishing House. University, 1995. 251 p.
5. Mikhailovskii E. I., Tarasov V. N. On the convergence of the generalized reaction method in contact problems with a free boundary. Jurnal prikladnoy matematiki i mekhaniki [Journal of Applied Mathematics and Mechanics], 1993, v. 57, No. 1. Pp. 128–136.

For citation: Yermolenko A. V., Belyaev E. A., Turkova O. I. One contact problem for two plates . Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021. No. 4 (41), pp. 83−89. DOI: 10.34130/1992-2752_2021_4_83

VI. Rogosin S. V. Remark to the paper

DOI: 10.34130/1992-2752_2021_4_90

Rogozin Sergey Vasilyevich − PhD in Physics and Mathematics, Associate Professor at the Department of Analytical Economics and Econometrics, Belarusian State University, Minsk, Belarus, e-mail: rogosin@bsu.by

Text

An assertion on p. 31 “Note that X(z) is a rational matrix which is analytic outside of the unit disc (but not necessary analytic at infinity) since. . . ” is imprecise. This assertion including the expression after it be omitted since on the first stage of factorization the corresponding
transformation is performed only on the unit circle and does not involve any analyticity properties of the matrix X(z).

For citation: Rogosin S. V. Remark to the paper. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021. No. 4 (41), pp. 90−91. DOI: 10.34130/1992-2752_2021_4_90

Full text

I. Babenko M. V. Pierce stalks of semirings with some finiteness conditions

DOI: 10.34130/1992-2752_2021_3_4

Babenko Marina − Associate Professor, Department of Applied Mathematics and Informatics, Vyatka State University, e-mail: usr11391@vyatsu.ru

Text

Let ϕ be an automorphism of the semiring S, the set of central complemented idempotents BS be finite, ϕ(e) = e for any e ∈ BS, and R = S[x, ϕ] be skew polynomial semiring. Then S is Noetherian iff every Pierce stalk of the semiring R satisfies ascending chain condition of monic ideals and the set of all central complemented idempotents of every Pierce stalk is finite. We also obtain a description of regular symmetric semirings and Boolean semirings in terms of Pierce stalks of skew polynomial semirings.

Keywords: skew polynomial semiring, monic ideal, Pierce stalk.

References

1. Ore O. Theory of non-commutative polynomials. Ann. of Math. 1933, 2(34), No. 3. Pp. 480–508.
2. Gooderl K. R., Warfield R. B. An introduction to noncommutative Noetherian rings. Cambridge University Press, 2004. 370 p.
3. McConnell J. C., Robson J. C. Noncommutative Noetherian rings. Graduate studes in mathematics, 2000. Vol. 30, 636 p.
4. Dale L. Monic and monic free ideals in polynomial semirings.Proc. Amer. Math. Soc. 1976. V.56. Pp. 45–50.
5. Dale L. The k-closure of monic and monic free ideals in a polynomial semiring. Proc. Amer. Math. Soc. 1977. vol. No. 2. Pp. 219–226.
6. Tuganbaev A. A. Teoriya kolec. Arifmeticheskie kolca i moduli [Ring Theory. Arithmetic rings and modules]. M.: MCNMO. 2009. 472 p.
7. Pierce R. S. Modules over commutative regular rings. Mem. Amer. Math. Soc. 1967. V.70. Pp. 1–112.
8. Burgess W. D., Stephenson W. Pierce sheaves of noncommutative rings. Comm. Algebra. 1976. V.39. Pp. 512–526.
9. Burgess W. D., Stephenson W. Rings all of whose Pierce stalks are local. Canad. Math. Bull. 1979. V.22, Pp. 159–164.
10. Beidar C. I., Mikhalev A. V. and Salavova C. Generalized identities and semiprime rings with involution. Math. Z. 1981. V.178. Pp. 37–62.
11. Chermnykh V. V. Beam half-ring representations. Uspekhi matematicheskikh nauk [Аdvances in mathematical sciences]. 1993. T. 48, No. 5. Pp. 185–186.
12. Markov R. V., Chermnykh V. V. About the pierce layers of the half-rings. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics].T. 19, No. 2. Pp. 171–186.
13. Markov R. V., Chermnykh V. V. Half-rings close to regular rings and their pierce layer. Trudy IMM UrO RAN [Proceedings of the IMM UB RAS]. 2015. T. 21, No. 3. Pp. 213–221.
14. Dale L. The structure of monic ideals in a noncommutative polynomial semirings. Acta Math. Acad. Sci. Hungar. 1982. V. 39, 1–3. Pp. 163–168.
15. Vechtomov E. M., Mikhalev A. V., Chermnykh V. V. Abelian regular positive semi-rings. Trudy seminara imeni I. G. Petrovskogo [Proceedings of the I. G. Petrovsky Seminar.]. 1997. T. 20. Pp. 282–309.
16. Chermnykh V. V. Functional representations of semi-rings. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics]. 2012. Vol. 17, No. 3. Pp. 111–227.
17. Obshhaya algebra [General Algebra]. Vol. 2. (red. L. A. Skornyakov). M.: Nauka. 1991. 480 p.
18. Golan J. S. Semirings and their applications. Kluwer Acad. Publ., Dordrecht. 1999. 382 p.

For citation: Babenko M. V. Pierce stalks of semirings with some finiteness conditions. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 3 (40), pp. 4−20. DOI: 10.34130/1992-2752_2021_3_4

II. Gromov N. A., Kostyakov I. V., Kuratov V. V. Coherent evolution of qutrit

DOI: 10.34130/1992-2752_2021_3_21

Gromov Nikolai − Doctor of Physics and Mathematics, Professor, Chief Researcher of the Institute of Physics and Mathematics, Komi Science Center, Ural RAS Department, email: gromov@dm.komisc.ru

Kostyakov Igor − Researcher at the Institute of Physics and Mathematics, Komi Science Center, Ural RAS Department, e-mail: kostyakov@dm.komisc.ru

Text

We consider the time variation of the density matrix of a three-level quantum system with the symmetry of the Lie algebra su(3), interacting with an external field in such a way that the coherence property is preserved. The commutatation relations in the algebra of observables in this case also change and in the limit can pass to another algebra.

Keywords: open quantum system, algebra of observables, qutrit, coherence, contraction of Lie algebras.

References

1. Nielsen M. A., Chuang I. L. Kvantovye vychisleniya i kvantovaya informaciya [Quantum Computation and Quantum Information]. Moscow: Mir, 2006. 824 p.
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9. Chru´sci´nski D., Facchi P., Marmo G., Pascazio S. The Observables of a Dissipative Quantum System. Open Systems & Information Dynamics. 2012. V. 19, No. 01, 1250001.
10. Gromov N. A., Kostyakov I. V., Kuratov V. V. Dissipaciya qubita i kontraktsii algebr Lie [Qubit
    dissipation and contractions of Lie algebras]. Proc. of the Komi Sci. Centre, Ural Branch, RAS. 2019. No 4 (40). Pp. 7–14.
11. Gromov N. A., Kostyakov I. V., Kuratov V. V. Kogerentnost v otkrytoy kvantovoy sisteme [Coherence in an open quantum system]. Proc. of the Komi Sci. Centre, Ural Branch, RAS. 2019. No 4(44). Pp. 30–33.
12. Gromov N. A., Kostyakov I. V., Kuratov V. V. Evoluciya kutrita i kontrakciya algebr Li su(3) [Qutrit
    evolution and contraction of Lie algebra su(3)]. Proc. of the Komi Sci. Centre, Ural Branch, RAS. 2021. No 4(50).
13. Aref ’eva I. Y., Volovich I. V., Kozyrev S. V. Metod stokhasticheskogo predela i interferentsiya v kvantovykh mnogochastichnykh sistemakh [Stochastic limit method and interference in quantum multiparticle systems]. TMF.Vol. 183. No. 3. Pp. 388–408.
14. Aref ’eva I. Y., Volovich I. V. Holographic Photosynthesis. ArXiv: 1603.09107 [hep-th]. 40 Громов Н. А., Костяков И. В., Куратов В. В.
15. Ohya M., Volovich I. Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems. Springer. 2011, 759 p.
16. Kozyrev S. V., Mironov A. A., Teretenkov A. E., Volovich I.V. Flows in nonequilibrium quantum systems and quantum photosynthesis, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4. 2017. 1750021. ArXiv: 1612.00213.
17. Chru´sci´nski D., Kimura G., Kossakowski A., Shishido Y. On the universal constraints for relaxation rates for quantum dynamical semigroup. ArXiv:2011.10159 [quant-ph], 9 p.

For citation: Gromov N. A., Kostyakov I. V., Kuratov V. V. Coherent evolution of qutrit.. Bulletin of
Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 3 (40), pp. 21−40. DOI: 10.34130/1992- 2752_2021_3_21

III. Golchevskiy Yu. V., Nepein A. V. Design and development of a chatbot for presenting a schedule in a social network

DOI: 10.34130/1992-2752_2021_3_41

Golchevskiy Yuriy − PhD in Physics and Mathematics, Associate Professor, Head of Information Systems Department, Pitirim Sorokin Syktyvkar State University, e-mail: yurygol@mail.ru

Nepeyin Andrey Vladimirovich − student, Pitirim Sorokin Syktyvkar State University, e-mail: ise@syktsu.ru

Text

The paper presents a study of the problem of delivering schedules to the educational process participants based on the design and development of a chatbot for a social network. The
business process of schedule creating was modeled, the platforms for implementing dialog interfaces (chatbots) were analyzed, the software architecture and database were designed and developed, as well as some aspects of implementing the software interaction interface.

Keywords: chatbot, schedule, educational institution, software architecture, social network.

References

1. The chatbot market in numbers and facts. Infographics. Zhurnal PLAS [Journal PLAS]. Available at: https://plusworld.ru/daily/tehnologii/403076-2/ (access date: 26.05.2021).
2. Chto takoe chat-bot? Oracle Rossiia i SNG [What is a chatbot? Oracle Russia and CIS]. Available at: https://www.oracle.com/ru/chatbots/what-is-a-chatbot/ (access date: 26.05.2021).
3. Maniou T.A., Veglis A. Employing a Chatbot for News Dissemination during Crisis: Design, Implementation and Evaluation. Future Internet, 2020, 12, No. 7, 109 p. DOI: https://doi.org/10.3390/fi12070109.
4. Carisi M., Albarelli A., Luccio F. L. Design and implementation of an airport chatbot. Proceedings of the 5th EAI International Conference on Smart Objects and Technologies for Social Good (GoodTechs ’19). Association for Computing Machinery, New York, Pp. 49–54. DOI: https://doi.org/10.1145/3342428.3342664.
5. Zarouali B., Evert Van den Broeck, Walrave M., Poels K. Predicting Consumer Responses to a Chatbot on Facebook. Cyberpsychology, Behavior, and Social Networking, 2018, Vol. 21, No. 8, Pp. 491–497. DOI: http://doi.org/10.1089/cyber.2017.0518.
6. Aarthi Ganitha N., Vaishnavee V., Oviya K., Jayaseelan J. Salem. Implementation of Chatbot in Trading Application Using SQL and Python. Bioscience Biotechnology Research Communications, 2020, Vol. 13, No. 2, Pp. 111–115.
7. Tsai M-H., Chan H-Y., Liu L-Y. ConversationBased School Building Inspection Support System. Applied Sciences, 2020, Vol. 10, No. 11. 3739. DOI: https://doi.org/10.3390/app10113739.
8. Ho C. Chun, Lee H. L., Lo W. K., Lui K. F. A. Developing a Chatbot for College Student
   Programme Advisement. International Symposium on Educational Technology (ISET), 2018, Pp. 52–56. DOI: https://doi.org/10.1109/ISET.2018.00021.
9. Lee L-K., Fung Y-C., Pun Y-W., Wong KK., Yu M. T-Y., Wu N-I. Using a Multiplatform Chatbot as an Online Tutor in a University Course. International Symposium on Educational Technology (ISET), 2020, Pp. 53–56. DOI: https://doi.org/10.1109/ISET49818.2020.00021.
10. Wang J., Hwang G-H., Chang C-Y. Directions of the 100 most cited chatbot related human behavior research: A review of academic publications. Computers and Education: Artificial Intelligence, 2021, 2, 100023.
11. Golchevskiy Yu. V., Vinogradov I. M. Experience in developing an online class schedule service. Informatizatsiia obrazovaniia i nauki [Informatization of education and science]. 2016. No. 1, Pp. 16–25.
12. Krasilnikov R. B., Golchevskiy Yu. V. Non-periodic approach to organizing and presenting electronic timetable. Dvadtsat shestaia godichnaia sessiia Uchenogo soveta SGU im. Pitirima Sorokina (Fevralskie chteniia) [Twenty-sixth Annual Session of the Academic Council of SyktSU (February Readings)]: sbornik materialov [collection of materials]: tekstovoe nauchnoe elektronnoe izdanie na kompakt-diske. Syktyvkar: Izd-vo SGU im. Pitirima Sorokina, 2019. Pp. 471–476.
13. Skjuve M., Folstad A., Fostervold K. I., Brandtzaeg P. B. My Chatbot Companion – a Study of Human-Chatbot Relationships. International Journal of Human-Computer Studies, 2021, Vol. 149, May, 102601.

For citation: Golchevskiy Yu. V., Nepein A. V. Design and development of a chatbot for presenting a schedule in a social network. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 3 (40), pp. 41−61. DOI: 10.34130/1992-2752_2021_3_41

IV. Aslanov R. M., Ignatushina I. V. To the 685th anniversary of the birth of Regiomontanus

DOI: 10.34130/1992-2752_2021_3_62

Aslanov Ramiz − PhD in Physics and Mathematics, Professor, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, e-mail: r_aslanov@list.ru

Ignatushina Inessa − PhD in Physics and Mathematics, Associate Professor, Orenburg State Pedagogical University, email: streleec@yandex.ru

Text

The article is devoted to the life of the outstanding German mathematician and astronomer Johann M¨uller (Regiomontanus), his scientific heritage and role in the development of modern mathematics and astronomy, as well as the book “Five books about triangles of all kinds”.

Keywords: life, mathematics, astronomy, trigonometry, calendar.

References

1. Belyi Iu. A. Iogann Miuller (Regiomontan). 1436–1476 [Iohann M¨uller (Regiomontanus). 1436–1476]. M.: Nauka,128 p.
2. Matvievskaia G.P. Ocherki istorii trigonometrii: Drevniaia Gretsiia. Srednevekovyi Vostok. Pozdnee Srednevekove [Essays on the History of Trigonometry: Ancient Greece. Medieval East. Late Middle Ages]. M.: Knizhnyi dom “Librokom”, 2012. 160 p.
3. Tsinner E. Three manuscripts of Regiomontanus from the Archive of the Academy of Sciences of the USSR. Istoriko-astronomicheskie issledovaniia [Historical and astronomical research]. M., 1962. Vyp. VIII. Pp. 373-380.
4. Newton R. R. An analysis of the Solar observations of Regiomontanus and Walther. Quarterly Journal of the Royal Astronomical Society. UK, 1982, Vol. 23, No. 1. Pp. 67-93

For citation: Aslanov R. M., Ignatushina I. V. To the 685th anniversary of the birth of Regiomontanus. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 3 (40), pp. 62−70. DOI: 10.34130/1992- 2752_2021_3_62

V. Oditets V. P. About a forgotten Leningrad topologist

DOI: 10.34130/1992-2752_2021_3_71

Odinets Vladimir − PhD in Physics and Mathematics, Professor, Syktyvkar State University named after Pitirim Sorokin, e-mail: W.P.Odyniec@mail.ru

Text

The life and work of Leningrad topologist Lvovsky Vyacheslav Dmitrievich (1899−1937) is described. He, along with B. I. Delone (1890−1980), O. R. Zhytomirsky (1891−1942), V. I. Milinsky (1898−1942), A. A. Markov (1903−1979) and later with A. D. Aleksandrov, stood at the origins of the Leningrad school of geometry and topology

Keywords: one-sided surface, closed double line, Boy surface, closed two-sided space, homeomorphisms of domains, Heegaard diagram.

References

1. Nauka i nauchnye rabotniki v SSSR. CH. V. Nauchnye rabotniki Leningrada, Spravochnik / sost. pod ruk. S. F. Oldenburga [Science and scientific workers in the USSR. Part V. Scientific Workers of Leningrad: Handbook] Leningrad: Izd-vo AN SSSR, 1926. 437 p.
2. Voitsekhovskii M. I. Formula Kronekera. Matematicheskaia entsiklopediia [Kronecker’s formula.
   The Encyclopedia of Mathematics] M.: Izd-vo «Sovetskaia entsiklopediia». 1982. Vol. 3. 1183 p.
3. Lvovskii V. D. Some homeomorphisms of regions of three-dimensional space. Trudy 2-go Vsesoiuznogo matematicheskogo sieezda. T. 2. Sektsionnye doklady [Proceedings of the 2nd All-Union Mathematical Congress. Vol. 2. Section papers]. M.: Izd-vo AN SSSR, 1936. Pp. 129-131.
4. Lvovskii V. D. Heegaard’s diagram and the fundamental group. Trudy 2-go Vsesoiuznogo matematicheskogo sieezda. T. 2. Sektsionnye doklady [Proceedings of the 2nd All-Union Mathematical Congress. Vol. 2. Section papers] M.: Izd-vo AN SSSR, 1936. Pp. 131-135.
5. Odinets V. P. O leningradskikh matematikakh, pogibshikh v 1941-1944 godakh [On the Leningrad mathematicians who died in 1941−1944.]. Syktyvkar: Izd-vo SGU im. Pitirima Sorokina. 2020. 122 p.

For citation: Oditets V. P. About a forgotten Leningrad topologist. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 3 (40), pp. 71−82. DOI: 10.34130/1992-2752_2021_3_71

VI. Zhubr A. V. Alexander Nikolaevich Tikhomirov (on his 70th birthday)

DOI: 10.34130/1992-2752_2021_3_83

Zhubr Alexey − Doctor of Physics and Mathematics, Leading Researcher, Institute of Physics and Mathematics, Komi Scientific Center, Ural RAS Department Ignatushina Inessa − PhD in Physi

Text

The article is dedicated to A. N. Tikhomirov, Doctor of Physical and Mathematical Sciences, Professor, Chief Scientific Associate of the Komi Scientific Center Institute of Physics and Mathematics.

Keywords: Alexander Nikolaevich Tikhomirov

For citation: Zhubr A. V. Alexander Nikolaevich Tikhomirov (on his 70th birthday). Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 3 (40), pp. 83−86. DOI: 10.34130/1992- 2752_2021_3_83

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I. Golenev I. I., Yermolenko A. V. Designing a neural network for recognizing handwritten cyrillic symbols

DOI: 10.34130/1992-2752_2021_2_04

Yermolenko Andrey — Ph.D., Associate Professor, Head of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Golenev Ilya — student, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Text

This paper deals with the modeling of a convolutional neural network (CNN). The model was developed in Python 3.8 using the TensorFlow and Keras.

Keywords: convolutional neural networks, character recognition, deep learning.

References

1. Goodfellow I., Bengio Y., Courville A. Glubokoe obuchenie [Deep learning] / transl. A. A. Slinkina, M.: DMK Press, 2018, 652 p.
2. Keras: the Python deep learning API [Electronic resource] / Keras official site. Available at: https://keras.io (Accessed: 28.04.2021).
3. Deep learning: image recognition with convolutional neural networks [Electronic resource] / Blog kompanii Wunder Fund, algoritmy, mashinnoe obuchenie [Wunder Fund company blog, Algorithms, machine learning]. Available at: https://habr.com/ru/company/wunderfund/ blog/314872/ (Accessed: 05.05.2021).
4. Babenko V. V., Kotelina N. O., Telnova О. P. Software and information support of the paleopalinological problem, Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2021, 1 (38), pp. 26-40.
5. Gradient descent [Electronic resource] / Svobodnaya enciklopediya Vikipediya [Wikipedia The Free Encyclopedia], Available at: https:// en.wikipedia.org/wiki/Gradient_descent (Accessed: 17.05.2021).
6. Neural network optimization methods [Electronic resource] / @Siarshai. Available at: https://habr.com/ru/post/318970/ (Accessed:15.05.2021).
7. Valeev D. I. Development of a system for processing mathematical handwritten formulas with using neural network technologies, VKR. Chelyabinsk, 2018, 43 p.
8. Kulakova О. A., Voronova L. I. Handwritten letters recognition using neural network, Materialy IX Mezhdunarodnoj studencheskoj nauchnoj konferencii «Studencheskij nauchnyj forum» [Materials of the IX International Student Scientific Conference «Student Scientific Forum»]. Available at: https:// scienceforum.ru/2017/article/2017033009 (Accessed: 10.05.2021).

For citation: Golenev I. I., Yermolenko A. V. Designing a neural network for recognizing handwritten cyrillic symbols, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 2 (39), pp. 4-12. DOI: 10.34130/1992-2752_2021_2_04

II. Yermolenko А. V., Korablev A. Yu., Kotelina N. К., Yurkina M. N. N. К. Popova and her contribution to the development of competitive programming

DOI: 10.34130/1992-2752_2021_2_13

Yermolenko Andrey — Ph.D., Associate Professor, Head of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Korablev Anatoly — Lecturer, College of Economics, Law and Informatics, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Kotelina Nadezhda — Ph.D. in Physics and Mathematics, Associate Professor of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: nkotelina@gmail.com

Text

The article is devoted to the biography of the associate professor of the Department of Applied Mathematics N. K. Popova, who has worked at Syktyvkar State University for more than 40 years.

Keywords: competitive programming, teaching, biography.

References

1. Popova N. K. Algoritmy i algoritmicheskiye yazyki [Algorithms and algorithmic languages], Syktyvkar: SSU im. Pitirim Sorokina, 2017, 88 p.
2. Popova N. K. Modelirovaniye prilozheniy [Modeling applications], Syktyvkar: SSU im. Pitirim Sorokin, 2019, 43 p.
3. Kotelina N. О., Popova N. К., Yurkina М. N. About the SSU open programming championship, Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Ser. 1: Mathematics. Mechanics. Computer science], 2018, Issue 3 (28), pp. 3-18.
4. Kotelina N. O., Popova N. K. Organization of programming competitions on the YANDEX.CONTEST platform, Informacionnye tekhnologii v modelirovanii i upravlenii: podhody, metody, resheniya : cbornik nauchnyh statej I Vserossijskoj nauchnoj konferencii [Information technologies in modeling and control: approaches, methods, solutions: Collection ofscientific articles of the I All-Russian Scientific Conference], December 12-14, 2017, Togliatti: Publisher Kachalin Alexander Vasilievich, 2017, pp. 373-377.

For citation: Yermolenko А. V., Korablev A. Yu., Kotelina N. К., Yurkina M. N. N. К. Popova and her contribution to the development of sports programming, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 2 (39), pp. 13-19. DOI: 10.34130/1992­ 2752_2021_2_13

III. Bannikov A. S. To construction of the reachability set for a fractionalorder linear control system

DOI: 10.34130/1992-2752_2021_2_20

Bannikov Alexander — Ph.D., associate professor, Associate Professor of the Department of Differential Equations, Udmurt State University, e-mail: asbannikov@gmail.com

Text

A description of the reachability set in space by a phase change is given. An extremal control is constructed that transfers the initial position to the boundary of the reachability set as a solution to the corresponding optimal speed problem. Numerical examples are given. When conducting the numerical experiment, programs in MATLAB and Wolfram Language were used.

Keywords: Caputo derivative, control system, reachability set.

References

1. Kilbas A. A., Srivastava H. M., Trujillo J. J. Theory and applications offractional differential equations, Amsterdam: Elsevier, 2006, 540 p.
2. Chikrii A. A., Matichin I. I. On linear conflict-controlled processes with fractional derivatives, Trudy Instituta Matematiki i Mekhaniki UrО RAN [Proceedings ofthe Institute ofMathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences], 2011, Vol. 17, no. 2, pp. 256-270.
3. Matychyn I., Onyshchenko V. On time-optimal control offractional-order systems, Journal of Computational and Applied Mathematics, 2018, Vol. 339, pp. 245-257.
4. Polovinkin E. S., Balashov M. V. Elementy vypuklogo i siTno vypuklogo analiza [Elements of convex and strongly convex analysis], Moscow: FIZMATLIT, 2004, 416 p.
5. Garrappa R., Popolizio M. Computing the matrix Mittag-Leffler function with applications to fractional calculus, Journal of Scientific Computing, 2018, Vol. 17, no. 1, pp. 129-153.

For citation: Bannikov A. S. To construction of the reachability set for a fractional-order linear control system, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 2 (39), pp. 20-26. DOI: 10.34130/1992-2752_2021_2_20

IV. Rogosin S. V., Primachuk L. P., Dubatovskaya M. V. On solution to R-linear conjugation problem with rational coefficients

DOI: 10.34130/1992-2752_2021_2_27

Rogozin Sergey — Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Analytical Economics and Econometrics, Belarusian State University, Minsk, Republic of Belarus, e-mail: rogosin@bsu.by

Primachuk Leonid — Candidate of Physical and Mathematical Sciences, Associate Professor, Belarusian State University, Minsk, Republic of Belarus, e-mail: dubatovska@bsu.by

Dubatovskaya Marina — Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Analytical Economics and Econometrics, Belarusian State University, Minsk, Republic of Belarus, e-mail: dubatovska@bsu.by

Text

The paper is devoted to an analysis of an effective method of solution to R-linear conjugation problem recently developed bv the authors. The method uses a generalization of G. N. Chebotarev’s algorithm for factorization of the triangular matrix-functions.

Keywords: R-linear conjugation problem, rational coefficients, factorization of matrix-functions, partial indices.

References

1. Markushevich A. I. On a boundary value problem in the theory of analytic functions, Uch. notes of Moscow University, 1946, I. 100, pp. 20-30.
2. Mikhailov L. G. Novyy klass osobykh integral’nykh uravneniy i уego primeneniya k differentsial’nym uravneniyam s singulyarnymi koeffitsiyentami [A new class of singular integral equations and its application to differential equations with singular coefficients], Dushanbe: Academy of Sciences of the Tajik SSR, 1963, 1836 p.
3. Litvinchuk G. S. Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift, Mathematics and its Applications, 2000, V. 523, Dordrecht: Kluwer Academic Publishers, 205 p.
4. Mityushev V. V. R-linear and Riemann-Hilbert problems for multiply connected domains, Advances in Applied Analysis (Sergei V. Rogosin, Anna A. Koroleva eds.), Springer: Basel, 2012, pp. 147-176.
5. Mityushev V. V., Rogosin S. V. Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions: Theory and Applications [Monographs and surveys in pure and applied mathematics], Vol. 108, Chapman & Hall / CRC PRESS: Boca Raton – London – New York – Washington, 1999, 296 p.
6. Litvinchuk G. S. Two theorems on the stability of the quotient indices of the Riemann boundary value problem and their application, Izv. vuzov. Matem. [Izv. universities. Mat.], No. 12, 1967, pp. 47-57.
7. Litvinchuk G. S., Spitkovsky, I. M. Factorization of measurable matrix functions, Basel-Boston: Birkhauser, 1987, 372 p.
8. Rogosin S., Mishuris G. Constructive methods for factorization of matrix-functions, IMA J. Appl. Math., 2016, Vol. 81 (2), pp. 365-391.
9. Sabitov I. Kh. On the general boundary value problem of linear conjugation on a circle, Sib. mat. zh. [Sib. mat. J.], 1964, T. V (1), pp. 124-129.
10. Primachuk L., Rogosin S., Dubatovskaya M. On R-linear conjugation problem on the unit circle, Eurasian Mathematical Journal, Vol. 11 (3), 2020, p. 79-88.
11. Chebotarev G. N. Partial indices of the Riemann boundary value problem with a triangular matrix second order, Uspekhi mat. nauk [Advances mat. nauk], 1956, T. XI, Iss. 3, pp. 192-202.
12. Gakhov F. D. Krayevyye zadachi [Boundary value problems], 3rd ed, M.: Science, 1977, 544 p.
13. Adukov V. M. Wiener-Hopf factorization of meromorphic matrixfunctions, St. Petersburg Math. J., 1993, V. 4 (1), pp. 51-69.
14. Muskhelishvili N. I. Singulyarnyye integraTnyye uravneniya [Singular integral equations], 3rd ed., M.: Science, 1968, 511 p.
15. Primachuk L., Rogosin S. Factorization of triangular matrixfunctions of an arbitrary order, Lobachevsky J. Math., V. 39 (6), 2018,pp. 809-817.

For citation: Rogosin S. V., Primachuk L. P., Dubatovskaya M. V. On solution to R-linear conjugation problem with rational coefficients, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 2 (39), pp. 27-43. DOI: 10.34130/1992-2752_2021_2_27

V. Shilov S. V. Simulation of explosions of gas-air mixtures taking into account the cloud drift by wind

DOI: 10.34130/1992-2752_2021_2_44

Shilov Sergey — Candidate of Physics and Mathematics, Associate Professor of the Department of Physics and Technology, Pitirim Sorokin Syktyvkar State University, e-mail: shilovsykt@rambler.ru

Text

The paper simulates the damaging effect of a shock wave during an explosion of a liquefied propane-butane mixture. Calculations were performed using two methods. The first one was used to calculate the zones of destruction of buildings and destruction of people. For the second one, the values of the drift of the gas-air mixture cloud by the wind were determined. With this in mind, the possible danger zones were much wider. Thus, the zones of destruction of buildings and damage to people due to the spread of clouds along the earth’s surface increase by about five to six times. These facts must be taken into account when placing objects that use liquefied gases, as well as when transporting such gases. A probabilistic model was used to determine hazardous areas. As zones of possible destruction of buildings, such distances are conventionally accepted at which the probability of destruction is 90 %. Similarly, for people in dangerous areas, the probability of damage to the eardrums was 90 % or higher.

Keywords: shock wave, defeat, liquefied gas.

References

1. Rachevsky B. S. Szhizhennyye uglevodorodnyye gazy [Liquefied petroleum gases], Moscow, Oil and gas Publ, 2009, 164 p.
2. Gazovozy. Avtotsisterny SUG [Gas carrier. Tankers. Liquefied petroleum gas]. Available at: https://rodisgroup.ru (Accessed 14 October 2020).
3. Hramov G. N. Goreniye i vzryv [Burning and explosion], SaintPetersburg, St. Petersburg State Technical University Publ, 2007. 278 p.
4. Vaidogas, ER (Vaidogas, Egidijus Rytas); Kisezauskiene, L (Kisezauskiene, Lina); Girniene, I (Girniene, Ingrida). The risk to structures built near roads and rails used for moving hazardous materials, Journal of civil engineering and management. Volume: 22, Issue: 3, Pages: 442-455. DOL10.3846/13923730.2015.1120773. Published: APR 2 2016. Document Type: Article.
5. Barilla, N (Barilla, Nilambar); Mishra, IM (Mishra, Indra Mani); Srivastava, VC (Srivastava, Vimal Chandra). The risk to structures built near roads and rails used for moving hazardous materials, Journal of civil engineering and management. Volume: 40, Pages: 449-460. DOI: 10.1016/j.jlp.2016.01.020. Published: MARDocument Type: Article.
6. Rukovodstvo po bezopasnosti «Metodika otsenki posledstviy avariynykh vzryvov toplivno-vozdushnykh smesey» [Safety Guide «Methods for assessing the effects of emergency explosions of fuel-air mixtures»]. Series 27. Issue 15. Moscow, Closed Joint Stock Company «Scientific and Technical Center for the Study of Industrial Safety Problems»,44 p.
7. RB G-05-039-96. «Rukovodstvo po analizu opasnosti avariynykh vzryvov i opredeleniyu parametrov ikh mekhanicheskogo deystviya» [RB G-05-039-96. «Guidelines for analyzing the danger of emergency explosions and determining the parameters oftheir mechanical action»]
   (approved. By the resolution of Gosatomnadzor of Russia of 31.12.1996 N 100).
8. Golovataya O. S., Petrakov A. P., Shilov S. V. Modeling of explosion hazards of liquefied gas tankers, Matematicheskoye modelirovaniye i informatsionnyye tekhnologii: NatsionaVnaya (Vserossiyskaya) nauchnaya konferentsiya (6-8 dekabrya 2018 g., g. Syktyvkar) : sbornik materialov [Mathematical modeling and information technologies: national (all-Russian) scientific conference (December 6-8, 2018, Syktyvkar): collection of materials], Syktyvkar: publishing house of SSU. Pitirima Sorokina, 2018, pp. 49-51.

For citation: Shilov S. V. Simulation of explosions of gas-air mixtures taking into account the cloud drift by wind, Bulletin ofSyktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 2 (39), pp. 44-57. DOI: 10.34130/1992-2752_2021_2_44

VI. Gubar L. N., Popov N. I. Implementation of the technology of guaranteed learning when students study the course of probability theory and mathematical statistics

DOI: 10.34130/1992-2752_2021_2_58

Gubar Lyudmila — Senior Lecturer, Department of Physics, Mathematics and Information Education, Pitirim Sorokin Syktyvkar State University, e-mail: lyudmila.336878@yandex.ru

Popov Nikolay — Doctor of Education, Ph.D. in Physics and Mathematics, Professor, Head of the Department of physics, mathematics and information education, Pitirim Sorokin Syktyvkar State University, e-mail: popovnikolay@yandex.ru

Text

The article presents the results of a pedagogical experiment related to the study of the use of guaranteed learning technology in the educational process when students study the section of mathematics “Probability theory and mathematical statistics”. The conducted research has confirmed that the application of this technology can significantly increase the level of mathematical knowledge and the effectiveness of teaching students.

Keywords: guaranteed learning technology, technological map, probability
theory and mathematical statistics, algorithm for solving mathematical
problems, pedagogical experiment.

References

1. Popov N. I., Gubar L. N. Interdisciplinary relations as the basis of formation of students’ professional competences corresponding to the standards of WorldSkills, in study of probability theory and mathematical statistics by students, Vestnik MGPU. Seriya «Informatika i informatizaciya obrazovaniya» [Vestnik MGPU … Series Informatics and informatization of education], 2019, no 4 (50), pp. 73-80.
2. Popov N. I., Gubar L. N. About the interdisciplinary relations of the course of probability theory and mathematical statistics in teaching college students, Vostochno-evropejskij nauchnyj zhurnal [East European Scientific Journal], no 9 (61), Vol. 1, 2020, pp. 42-48.
3. Choshanov M. A. E-Didactics: a new look at learning theory in the digital age, Obrazovatel’nye tekhnologii i obshchestvo [Educational technologies and society], 2013, no 3, pp. 684-696.
4. Monakhov V. M. Vvedenie v teoriyu pedagogicheskih tekhnologij [Introduction to the theory of pedagogical technologies: monografiya]. Volgograd: Peremena, 2006, 319 p.
5. Gefan G. D., Kuz’min О. V. Comparative analysis of the effectiveness of educational methods on the example of teaching the probability theory and mathematical statistics, Vestnik Tomskogo gosudarstvennogo pedagogicheskogo universiteta [Bulletin ofthe Tomsk State Pedagogical University], 2017, no 4 (181), pp. 49-56.
6. Safuanov I. S., Atanasyan S. L. Mathematical education in Singapore: traditions and innovations, Nauka i shkola [Science and school], 2016, no 3, pp. 38-44.
7. Krivshenko L. P., Vajndorf-Sysoeva M. E. Pedagogika [Pedagogy]: Uchebnik. M.: Iz-vo Prospekt, 2010, 432 p.
8. Monakhov V. М., Silchenko А. Р., Tikhomirov S. A. Genesis and Function of Professional Pedagogical Activity in Terms of IEE, Yaroslavskij pedagogicheskij vestnik [Yaroslavl Pedagogical Bulletin], 2017, no 6, pp. 112-122.
9. Monakhov V. M. Pedagogical aspects of the integration of pedagogical technologies and information technologies as a qualitatively new stage of informatization of mathematical education, Informatizaciya obucheniya matematike i informatike: pedagogicheskie aspekty: Materialy mezhdunarodnoj nauchnoj konferencii, posvyashchennoj 85- letiyu Belorusskogo gosudarstvennogo universiteta [Informatization of teaching mathematics and computer science: pedagogical aspects : materials of the international scientific conference dedicated to the 85th anniversary of the Belarusian State University], Minsk, 2006, pp. 287-291.
10. Popov N. I. Rukovodstvo к resheniyu zadach po teorii veroyatnostej i matematicheskoj statistike dlya psihologov [Guide to solving problems in probability theory and mathematical statistics for psychologists], Uchebnoe posobie, Joshkar-Ola: Izd-vo Mar. gos. un-t, 2006, 76 p.
11. Gmurman V. E. Rukovodstvo к resheniyu zadach po teorii veroyatnostej i matematicheskoj statistike [A Guide to problem solving in probability theory and mathematical statistics], Moscow: Higher school, 1979, 400 p.
12. Yilmaz R., Argun Z. Role of visualization in mathematical abstraction: The case of congruence concept, International Journal of Education in Mathematics, Science and Technology (IJEMST), 2018, 6(1), pp. 41-57.

For citation: Gubar L. N., Popov N. I. Implementation of the technology of guaranteed learning when students study the course of probability theory and mathematical statistics, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 2 (39), pp. 58-77. DOI: 10.34130/1992-2752_2021_2_58

VII. Pevnyi А. В., Kozhagel’diev N. V. New equations for a reservoir of equal resistance

DOI: 10.34130/1992-2752_2021_2_78

Pevny Alexander — Doctor of Physical and Mathematical Sciences, Professor, Department of Applied Mathematics and Information Technologies in Education, Syktyvkar State University named after Pitirim Sorokin,University e-mail: pevnyi@syktsu.ru

Kozhageldiev Nikita — student, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Text

New equations for the shape of equal resistance reservoir are obtained. The reservoir has the shape of a drop. The results of computer experiments are given.

Keywords: shell, droplet form, reservoir.

References

1. Yermolenko A. V., Kozhagel’diev N. V. Graphoanalytical method for calculating an equal resistance reservoir, Vestnik Syktyvkarskogo universiteta Ser. 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2020, 2 (35), pp. 85-91.
2. Novozhilov V. V., Chernyh K. F., Mihajlovskij E. I. Linejnaya teoriya tonkih oboochek [Linear theory of thin shells], L: Politekhnika, 1991, 656 p.
3. Gordon J. Konstrukcii, Hi Pochemu ne lomayutsya veshchi [Structure, or why things do not break], M: Mir, 1980, 390 p.
4. Yermolenko A. V., Osipov K. S. On using Python libraries to calculate plates, Vestnik Syktyvkarskogo universiteta Ser. 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, 4 (33), pp. 86-95

For citation: Pevnvi А. В., Kozhagel’diev N. V. New equations for a reservoir of equal resistance, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 2 (39), pp. 78-84. DOI: 10.34130/1992-2752_2021_2_78

VIII. Popov N. I., Arihin E. M., Yermolenko I. A. The use of an electronic course when students study the basics of mathematical analysis

DOI: 10.34130/1992-2752_2021_2_85

Popov Nikolay — Doctor of Education, Ph.D. in Physics and Mathematics, Professor, Head of the Department of physics, mathematics and information education, Pitirim Sorokin Syktyvkar State University, e-mail: popovnikolay@yandex.ru

Arihin Eduard — student, Pitirim Sorokin Syktyvkar State University, e-mail: popovnikolay@yandex.ru

Yermolenko Ilya — student, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Text

The transition to educational standards of a new generation in a higher educational institution involves the renewal of technologies, means and forms of training for future teachers of mathematics, physics and computer science. When designing an electronic course in the educational environment of the university «Short Course in Differential Calculus», the problem of modular training is considered.

Keywords: fundamentals of mathematical analysis, modular training, electronic course.

References

1. Popov N. I., Nikiforova E. N. On the effectiveness of the use of the electronic course «Mathematics» in teaching students in agroengineering areas of training, Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Seriya Informatika i informatizatsiya obrazovaniya [Bulletin of the Moscow City Pedagogical University. Series Informatics and informatization of education], 2017, No (40), pp. 45-50.
2. Suvorova T. N. Analysis of approaches to the typology of electronic educational resources, Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Seriya Informatika i informatizatsiya obrazovaniya [Bulletin of the Moscow City Pedagogical University. Series
   Informatics and informatization of education], 2015, >1 (31), pp. 70-84.
3. Dikov A. V., Rodionov M. A., Chernetskaya T. A. The educational blogosphere as an effective means of organizing the educational process, Informatika i obrazovaniye [Computer science and education], 2018, No 1 (290), pp. 38-46. I. Kedraka K., Rotidi G. University Pedagogy: A New Culture is Emerging in Greek Higher Education, International Journal of Higher Education, 2017, Vol. 6, No 3, pp. 147-153.
4. Popov N. I. Fundamentalizaciya universitetskogo matematiche-skogo obrazovaniya [Fundamentalization of university mathematics education] : monograph, Yoshkar-Ola: MarSU, 2012, 135 p.
5. Popov N. I., Nikiforova E. N. Kratkij kurs differencial’подо ischisleniya : uchebnoe posobie [Differential Calculus Short Course: A Study Guide], Syktyvkar: Publishing house of SSU named after Pitirim Sorokin, 2019, 85 p.

For citation: Popov N. I., Arihin E. M., Yermolenko I. A. The use of an electronic course when students study the basics of mathematical analysis, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 2 (39), pp. 85-89. DOI: 10.34130/1992 2752_2021_2_85

Full text

I. Kalinin S. I., Sokolova D. A. Application of Jensen’s inequality to solving equations and optimization tasks

DOI: 10.34130/1992-2752_2021_1_04

Kalinin Sergey — Doctor of Education, Ph.D. in Physics and Mathematics, Professor, Department of Fundamental Mathematics, Vyatka State University, e-mail: kalinin_gu@mail.ru

Sokolova Darya — 4rd year student of the Faculty of Computer and Physical and Mathematical Sciences, Vyatka State University, e-mail: darya_sokoloval999@mail.ru

Text

In this article, we consider equations and optimization tasks that can be effectively solved by using Jensen’s inequality for convex or concave functions. The main feature of the proposed problems is that when formulating and solving them, the convex (concave) functions, which are compositions or products of convex (concave) functions that are simple according to the analytical description are used. This circumstance makes it possible to determine the character of the convexity of the function used in a specific task without referring to its differentiability or its secondorder derivative. The work is addressed to everyone interested in the issues of convex functions and the themes of inequality. Its content can be useful in organizing the research activities of students and schoolchildren of specialized classes.

Keywords: Jensen’s inequality, product of functions, composition of functions, equation, optimization tasks.

References

1. Kalinin S. I., Sokolova D.A. Konstruirovanive vypuklykh funktsiv bez obrashcheniva k proizvodnvm (Construction of convex functions without reference to derivatives), Mathematical bulletin of pedagogical universities and universities of the Volga- Vyatka region: period, interuniversity. Sat. scientific method, works, 2019, No. 21, pp. 146-153.
2. Sokolova D. A. Ob odnom privome konstruirovaniya slozhnykh vypuklykh funktsiy bez obrashcheniva к proizvodnym (On one method of constructing complex convex functions without referring to derivatives), Mathematical education at school and university: experience,
   problems, prospects (MATHEDU’2019) M-ly IX Intern, scientificpractical conf., Kazan: Kazan Federal University, 2019, pp. 166-171.
3. Kalinin S. I. Sredniye velichiny stepennogo tipa. Neravenstva Koshi i Ki Fana: Ucheb. posobiye po spetskursu (Average values of power type. Cauchy and Ki Fan inequalities: Textbook, special course manual), Kirov: VGGU Publishing House, 2002, 368 p.
4. Fikhtengol’ts G. M. Kurs differentsial’nogo i integral’nogo ischisleniya (A course in differential and integral calculus), Moscow: Nauka, 1966, Vol. 1, 607 p.
5. Vychegzhanin S. V. Dokazatel’stvo neravenstva Yvensenametodom prvamogo i obratnogo induktsii (Proof of Jensen’s inequality by the method of direct and reverse induction), Mathematical bulletin of pedagogical universities and universities of the Volga- Vyatka region.
   Issue 15: periodic interuniversity collection of scientific and methodological works, Kirov: Publishing house of ООО «Raduga-PRESS», 2013, pp. 166-172.
6. Kalinin S. I. Metod neravenstv resheniy uravneniy. Uchebnoye posobiye po elektivnomu kursu dlya klassov fiziko-matematicheskogo profilya (Method of inequalities for solutions of equations. Textbook for an elective course for classes of physical and mathematical profile),
   Moscow: Publishing house «Moscow Lyceum», 2013, 112 p.

For citation: Kalinin S. I., Sokolova D. A. Application of Jensen’s inequality to solving equations and optimization tasks, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 4-12.

II. Popov N. I. Using the area estimate for localizing the maximum of the conformal radius

DOI: 10.34130/1992-2752_2021_1_13

Popov Nikolay — Doctor of Education, Ph.D. in Physics and Mathematics, Professor, Head of the Department of physics, mathematics and information education, Pitirim Sorokin Syktyvkar State University, e-mail: popovnikolay@yandex.ru

Text

A condition for the uniqueness of the critical point of the conformal radius is obtained using an isoperimetric inequality.

Keywords: area estimate, conformal radius, critical point of conformal radius, uniqueness of the solution to the exterior inverse boundary value problem.

References

1. Gakhov F. D. Krayevyye zadachi (Boundary problems), 3rd ed., Moscow: Nauka, 1977, 640 p.
2. Aksent’ev L. A. Svvaz’ vneshnev obratnov krayevoy zadachi s vnutrennim radiusom oblasti (Connection of the outer inverse boundary value problem with the inner radius of the domain), Izv. universities. Mathematics, 1984, no. 2, pp. 3-11.
3. Tumashev G. G., Nuzhin M. T. Obratnyye krayevyye zadachi i ikh prilozheniya (Inverse boundary value problems and their applications), 2nd ed., Kazan: Kazan, un-t, 1965, 333 p.
   I. Aksent’ev L. A., Kazantsev A. V., Popov N. I. Ekstremal’nyve zadachi diva ploshchadev pri konformnom otobrazhenii i ikh primenenive (Extremal problems for areas under conformal mapping and their application), Izv. universities. Mathematics, 1995, no. 6, pp. 3-15.
4. Popov N.I. Ob odnom uslovii podchinennosti pri lokalizatsii maksimuma konformnogo radiusa (On one condition of subordination in the localization of the maximum of the conformal radius), Trudy Matematicheskogo tsentr im. N. I. Lobachevsky, Kazan: Kazan, unt, 2013, V. 46, Theory of functions, its applications and related issues, pp. 368-369.
5. Goluzin G. M. Geometricheskaya teoriya funktsiy kompleksnogo peremennogo (Geometric theory of functions of a complex variable), 2nd ed., Moscow: Nauka, 1966, 628 p.
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For citation: Popov N. I. Using the area estimate for localizing the maximum of the conformal radius, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 13-18.

III. Sushkov V. V. About the discrete spectrum of the characteristic equation in case of the Bhatnagar – Gross – Crook model

DOI: 10.34130/1992-2752_2021_1_19

Sushkov Vladislav — Ph. D. in Physics and Mathematics, Associate professor, head of the educational department, Pitirim Sorokin Syktyvkar State University, e-mail: vvsu@mail.ru

Text

The objective of the publication is to show that the technique used in the particular case of solving the problem for one-, two- and polyatomic gases can be effectively extended to a wider class of problems, in particular, arising when solving boundary problems for the Boltzmann equation with
the collision integral in the form of Bhatnagar-Gross-Crook. The case of a vector-matrix integrodifferential equation with a polynomial kernel is investigated, the structure of the continuous and discrete spectrum of the characteristic equation is determined. Eigenfunctions of the continuous spectrum are found.

Keywords: integrodifferential equations, Bhatnagar, Gross and Crook model, spectrum of characteristic equation, distributions.

References

1. Bhatnagar P. L., Gross E. P., Crook M. Model’ processov stolknovenij v gazah (Gas Collision Process Model), Problems of modern physics, Moscow, 1956, No. 2, pp. 82-107.
2. Bedrikova E. A., Latyshev A. V. Reshenie zadachi о techenii Kuetta diva Fermi-gaza s pochti zerkal’nvmi granichnvmi uslovivami (Solution of the problem of the Couette flow for a fermi gas with almost specular boundary conditions), Russian Physics Journal, 2016, V. 59, No. 2, pp. 217-230.
3. Khachatryan А. К., Khachatryan К. A. Kachestvennoe razlichie reshenij diva stacionarnyh model’nvh uravnenij Bol’cmana v linejnom i nelinejnom sluchavah (Qualitative difference between solutions of stationary model Boltzmann equations in the linear and nonlinear
   cases), Theoretical and Mathematical Physics, 2014, V. 180, No. 2, pp. 272-288.
4. Zhvick V. V. Raskhod razrezhennogo gaza v techenii Puazejlva skvoz’ kruglyj kapillyar (Rarefied gas flow rate in Poiseuille flow through a circular capillary), Fluid Dynamics, 2015, V. 50, No. 5, pp. 711-720.
5. Sushkov V. V., Latyshev A. V. Analiticheskoe reshenie granichnvh zadach diva semejstva BGK-uravnenij metodom kanonicheskoj matricv (Analytical solution of boundary problems for a family of BGK equations obtained by the application ofthe canonical matrix method), Izvestia: Herzen University Journal of Humanities & Sciences, 2002, No. 4, pp. 72-85.
6. Cercignani C. Matematicheskie metody v kineticheskoj teorii gazov (Mathematical methods in the kinetic theory of gases), Moscow: Nauka, 1973, 245 p.

For citation: Sushkov V. V. About the discrete spectrum of the characteristic equation in case of the Bhatnagar – Gross – Crook model, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 19-26.

IV. Babenko V. V., Kotelina N. O., Telnova О. P. Software and information support of the paleopalinological problem

DOI: 10.34130/1992-2752_2021_1_27

Babenko Victor — Ph.D., associate professor, Pitirim Sorokin Syktyvkar State University, e-mail: bvvskt@mail.ru

Kotelina Nadezhda — Ph.D. in Physics and Mathematics, Associate Professor of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: nkotelina@gmail.com

Text

The article proposes promising options for optimizing studies of paleopalinologv (spore-pollen analysis of ancient rocks), which is one of the most important branches of paleontology.

Keywords: machine learning, deep learning, convolutional neural network, databases.

References

1. Marca D. A., McGowan С. L. Metodologiya strukturnogo analiza i proyektirovaniya SADT (Structured Analysis and Design Technique), Moscow, 1993, 240 p.
2. Tel’nova О. P., Shumilov I. Kh. Middle-Upper Devonian Terrigenous Rocks of the Tsil’ma River Basin and Their Palynological Characteristics, Stratigraphy and Geological Correlation, 2019, Vol. 27, No. 1, pp. 27-50. DOI: https://doi.org/10.31857/S0869-592X27131- 56.
3. Tel’nova О. P., Marshall J. E. A. Devonian Spores of Krvshtofovichia africani Nikitin (Tracheophvta): Morphology and Ultrastructure, Paleontological Journal, 2018, Vol. 52, No. 3, pp. 342-349. (c) Pleiades Publishing, Ltd., 2018, published in Paleontologicheskii Zhurnal, 2018, No. 3, pp. 119-124. ISSN 0031-0301, DOI: 10.1134/S0031030118030152.
4. Zhang Y., Fountain D. W., Hodgson R. M., Flenley J. R., Gunetileke S. Towards automation of palynology: Pollen recognition using Gabor transforms and digital moments, J. Quat., 2004, Sci. 19, pp. 763-768.
5. Zhang Wang-Xiang, Zhao Ming-Ming, Fan Jun-Jun, Zhou Ting, Chen Yong-Xia, & Cao Fu-Liang. Study on relationship between pollen exine ornamentation pattern and germplasm evolution in flowering crabapple., 2017, Sci. Rep. 7, 39759.
6. Geus A. R. d., Barcelos C. A. Z., Batista M. A. and Silva S. F. d. Large-scale Pollen Recognition with Deep Learning. 27­ th European Signal Processing Conferencen (EUSIPCO), A Coruna, Spain, 2019, pp. 1-5. DOI: 10.23919/EUSIPC0.2019.8902735.
7. C. Romero Ingrid, Kong Shu, C. Fowlkes Charless, Jaramillo Carlos, A. Urban Michael, Oboh Ikuenobe Francisca , D’Apolito Carlos, W. Punyasena Surangi. Improving the taxonomy of fossil pollen using convolutional neural networks and superresolution microscopy. Proceedings of the National Academy of Sciences Nov 2020, 117 (45), 28496-28505. DOI: 10.1073/pnas. 2007324117.
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14. Sevillano V., Aznarte J. L. Improving classification of pollen grain images of the POLEN23E dataset through three different applications of deep learning convolutional neural networks. PLoS ONE 13(9): e0201807. DOI: https://doi.org/10.1371/journal.pone.0201807. 2018.

For citation: Babenko V. V., Kotelina N. О., Telnova О. P. Software and information support of the paleopalinological problem, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 27-42.

V. Gertner D. A., Leontiev D. О., Nosov L. S., Shuchalin D. S. Hardware and software complex for ensuring information security when using electronic signatures

DOI: 10.34130/1992-2752_2021_1_43

Gertner Dmitry — General Director of ООО «Kreif», e-mail: nosovvv@yandex.ru

Leontiev Denis — student, Pitirim Sorokin Syktyvkar State University, e-mail: nosovvv@yandex.ru

Nosov Leonid — Ph.D., Associate Professor, Head of the Department of Information Security, Pitirim Sorokin Syktyvkar State University, e-mail: nosovvv@yandex.ru

Shuchalin Denis — student, Pitirim Sorokin Syktyvkar State University, e-mail: nosovvv@yandex.ru

Text

This paper presents prototype of a software and hardware complex for secure signing of electronic documents on the basis of a trusted device specialized for these operations.

Keywords: hardware and software system, electronic digital signature, Raspberry Pi, Python

References

1. GOST R 34.10-2012 Information technology. Cryptographic information protection. Processes for generating and verifying electronic digital signature, Available at:http://docs.cntd.ru/document/gost-r34-10-2012 (accessed: 09.01.2021).
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For citation: Gertner D. A., Leontiev D. 0., Nosov L. S., Shuchalin D. S. Hardware and software complex for ensuring information security when using electronic signatures, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 43-55.

VI. Yermolenko A. V., Kotelina N. O., Startseva E. N., Yurkina M. N. On the demand for data parsing training for web developers

DOI: 10.34130/1992-2752_2021_1_56

Yermolenko Andrey — Ph.D., Associate Professor, Head of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Kotelina Nadezhda — Ph.D. in Physics and Mathematics, Associate Professor of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: nkotelina@gmail.com

Startseva Evgeniya — Senior Lecturer, Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University,
e-mail:startseva2011@gmail.com

Yurkina Marina — Senior Lecturer, Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: yurkinamn@gmail.com

Text

In the article, from the point of view of training a modern web developer, the process of acquiring the skill of parsing data is considered. Approximate model problems that should be considered in laboratory classes are given. The practical tasks of data parsing solved in the framework of scientic
research are described. The solution to the problem of obtaining SEO characteristics of sites is described in detail.

Keywords: parser, web scraping, web development, training.

References

1. Mitchell R. Web Scraping with Python, Sebastopol: O’Reilly Media, Inc., 2018, 306 p.
2. Openweathermap Service. Available at: https://openweathermap.org/ api (accessed: 11.01.2021).
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   the number of gene interactions in the cell of a particular organism), Mathematical modeling and information technologies: IV all-Russian scientific conference with international participation (12-14 November 2020, Syktyvkar): collection of materials, Executive editor A. V. Yermolenko, Syktyvkar: Publishing house of SSU Pitirima Sorokina, 2020, pp. 42.
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12. Golchevskiy Yu. V., Severin P. A. Analiz dinamiki obnaruzheniva uvazvimostev populvarnykh sistem upravleniva kontentom (Dynamics of common content management systems vulnerability detection analysis), Information security issues, 2013, 4 (102), pp. 58-66.
13. Golchevskiy Yu. V., Kuznetsov D. I. Avtomatizatsiya mekhanizmov poiska informatsii na osnove otkrytykh istochnikov v seti Internet (Information search in open sources on the internet technique automation), Information and security, 2017, Vol. 20, No. 3 (4), pp. 414-417.
14. Ushakov D. A. Razrabotka programmnogo obespecheniva diva proverki ssvlok na elektronnyve izdaniya v rabochikh programmakh distsiplin (Development of software for checking links to electronic publications in the work programs of disciplines), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 2 (35), pp. 49-58.
15. Kotelina N. O., Matviyuchuk B. R., Solovyev I. A. Rekonstruktsiva grafov vzaimodeystviya genov i ikh prioritizatsiya na osnovanii dostupnvkh baz dannvkh (Reconstruction of gene interaction graphs and their prioritization based on available databases), Mathematical modeling and information technologies: IV all-Russian scientific conference with international participation (12-14 November 2020, Syktyvkar): collection of materials, Executive editor A. V. Yermolenko, Syktyvkar: Publishing house of SSU Pitirima Sorokina, 2020, pp. 44.
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For citation: Yermolenko А. V., Kotelina N. О., Startseva Е. N., Yurkina M. N. On the demand for data parsing training for web developers, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 56-69.

VII. Odyniec W. Р. About four mathematicians – victims of the siege of Leningrad period

DOI: 10.34130/1992-2752_2021_1_70

Odyniec Vladimir — Doctor of Physical and Mathematical Sciences, Professor, Pitirim Sorokin Syktyvkar State University, e-mail: W.P.Odyniec@mail.ru

Text

The life and work of four Leningrad based mathematicians born on the late 19th and early 20-th century is sketched. All of them A. G. Kolpakov (1902-1942), A. A. Herzfeld (1885-1941), N. N. Khudekov (1900-1942), and S. A. Janczewski (Yanchevskv) (1900-1941) perished during the blockade of Leningrad period.

Keywords: A. G. Kolpakov, A. A. Herzfeld, N. N. Khudekov, S. A. Janczewski (Yanchevsky), the double Fourier series, n-dimensional ordered sets, the solution of complex Fredholm equations.

References

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2. Odyniec W. P. О leningradskih matematikah, pogibshih v 1941-1944 godah (On some Leningrad — based Mathematicians perished in 1941-1944), Syktyvkar: Izd-vo SGU im. Pitirima Sorokina, 2020, 122 p.
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I Andrykova V. Yu., Tarasov V. N. On the stability of rod with one-sided restrictions on the moving

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II Kostyakov I. V., Kuratov V. V. Contractions of Lagrangian in calssical mechanics

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III Mikhailovskii E. I., Korablev A. J. The longitudinal stability of a cylindrical cover supported by stringers in a multimoduls elastic surroundings

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IV Pevnyi A. B., Kotelina N. O. Complex spherical semidesigns

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V Vechtomov E. M., Petrov A. A. Multiplicative idempotent semirings with identity x+2xyx=x

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VI Ilchukov A. S. Singular integral with Cauchy kernel in spaces defined by modulus of continuity

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VII Mekler A. A. Multiplicativity of Marcinkiewicz Modulars. Tables of Bases

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VIII Mekler A. A. On semigroup of Marcinkiewicz Modulars.

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IX Moskin G. V., Nikitenkov V. L., Sitkarev G. A. Synthesis of perspective transformation matrix

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X Nikitenkov V.L., Koyushev P.I.Stability of a rod in a medium with linearly varying rigidity (solution using power series)

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XI Nikitenkov V.L., Pobrey A. A. Scanned text binarization and segmentation

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XII Odynec V. P. About Boris Zakharovich Vilikh – hereditary mathematician and typical St. Petersburg born and bred citizen (To centenary anniversary of his birth)

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