Без рубрики

Full text

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

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

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

Text

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

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

References

1. Shirokov Y. M., Yudin N. P. Yadernaya fizika [Nuclear physics]. Moscow: Nauka, 1980. 728 p. (In Russ.)
2. Naumov A. I. Fizika atomnogo yadra i elementarnykh chastits [Physics of atomic nucleus and elementary particles]. Moscow: Prosveshenie, 1984. 384 p. (In Russ.)
3. Hofmann S., et al. Proton radioactivity of 151Lu. Z Physik A. 1982. Vol. 305. Pp. 111–123.
4. Giovinazzo J., et al. Two-Proton Radioactivity of 45Fe. Phys. Rev. Lett. 2002. Vol. 89. No 10. Art. N. 102501.
5. Pf¨utzner M., et al. First evidence for the two-proton decay of 45Fe. Eur Phys J A. 2002. Vol. 14. Pp. 279–285.
6. Rose H. J., Jones G. A. A new kind of natural radioactivity. Nature. Vol. 307. Pp. 245–247.
7. Alexandrov D. V. et al.Observation of spontaneous departure of 14C nuclei from 223Ra. Pis’ma v ZHETF [Writings in ZhETF]. 1984. Vol. 40. Pp. 152–154. (In Russ.)
8. Oganesyan Yu. Ts., Penionzhkevich Y. E., Grigoriev V. A. Fizika tyazhelykh ionov i yeye prilozheniya [Physics of heavy ions and its applications]. Dubna: JINR, 2021. 363 p. (In Russ.)
9. Nelipa N. F. Fizika elementarnykh chastits [Physics of elementary particles]. Moscow: Vysshaya shkola, 1977. 608 p. (In Russ.)
10. Particle Data Group. Review of Particle Physics. Progress of Theoretical and Experimental Physics. 2022. Vol. 2022. No 8. Art. N. 083C01.
11. Baldin A. M. et al Kinematika yadernykh reaktsiy [Kinematics of nuclear reactions]. 2nd ed., rev. and supplement. Moscow: Atomizdat, 456 p. (In Russ.)
12. ATLAS Collaboration, Aad G. et al. Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B. 2012. Vol. 716. Pp. 1–29.
13. CMS collaboration, Chatrchyan S. et al. Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B. 2012. Vol. 716. Pp. 30–61.
14. CMS collaboration, Tumasyan A. et al. Search for Higgs boson decays to a Z boson and a photon in proton-proton collisions at √ s = 13 TeV. J. High Energ. Phys. 2023. Issue 5. No 233
15. ATLAS Collaboration, Aad G. et al. Searches for exclusive Higgs and Z boson decays into a vector quarkonium state and a photon using 139 fb−1 of ATLAS √ s = 13 TeV proton-proton collision data. The European Physical Journal C. 2023. Vol. 83. No 9. Art. N. 781.
16. Landau L. D., Lifshits E. M. Teoreticheskaya fizika. T. II. Teoriya polya [Theoretical physics. V. II. Field theory]. Moscow: FIZMATLIT, 536 p. (In Russ.)
17. Landau L. D., Lifshits E. M. Theoretical physics. V. IV. Berestetsky V. B., Lifshits E. M., Pitaevsky L. P. Kvantovaya elektrodinamika [Quantum electrodynamics]. Moscow: FIZMATLIT,720 p. (In Russ.)
18. Landau L. D., Lifshits E. M. Teoreticheskaya fizika. T. I. Mekhanika [Theoretical physics. V. I. Mechanics]. Moscow: FIZMATLIT, 2007. 224 p. (In Russ.)

II. Analysis of data on forest fires in the Komi Republic using Excel and Python

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

Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University

Nadezhda O. Kotelina – Pitirim Sorokin Syktyvkar State University

Fyodor N. Tentyukov – Pitirim Sorokin Syktyvkar State University

Text

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

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

References

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

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

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

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

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

Text

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

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

References

1. Mikhailovskii E. I. Shkola mekhaniki obolochek akademika Novozhilova [Academic Novozhilov’s school of mechanics of shells]. Syktyvkar: Publishing House of Syktyvkar University, 2005. 172 p. (In Russ.)
2. Mikhailovskii E.I., Yermolenko A.V., Mironov V.V., Tulubenskaya E.V. Utochnennye nelinejnye uravneniya v neklassicheskih zadachah mekhaniki obolochek : uchebnoe posobie
   [Refined nonlinear equations in non-classical tasks of mechanics of shells]. Syktyvkar: Publishing House of Syktyvkar University, 2009. 141 p. (In Russ.)
3. Yermolenko A. V. Classical contact problems with free boundary. Problemy matematicheskogo obrazovaniya v vuzah i shkolah Rossii v usloviyah ego modernizacii: IV Vserossijskaya nauchno–metodicheskaya konferenciya : sbornik materialov [Problems of mathematical education in universities and schools of Russia in the context of its modernization:
   IV All-Russian Scientific and Methodological Conference: collection of materials]. Syktyvkar: Publishing house of Syktyvkar University, 2014. Pp. 160–167. (In Russ.)
4. Fokin R. R., Atoyan A. A., Abissova M. A. Studying mathematics, computer science, mathematical and information modeling: ways to increase student motivation. Nauchnyj al’manah [Scientific almanac]. 2022. No 1–1 (87). Pp. 111–114. (In Russ.)
5. Zharkova YU. S. Teaching elements of mathematical modeling at a pedagogical university as a means of developing professional competencies. Vestnik Chelyabinskogo gosudarstvennogo
   pedagogicheskogo universiteta [Bulletin of Chelyabinsk State Pedagogical University]. 2014. No 9–1. Pp. 85–93. (In Russ.)
6. 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. (In Russ.)
7. Studenty SGU im. Pitirima Sorokina – stipendiaty Prezidenta i Pravitel’stva Rossii [Students of SSU named after Pitirim Sorokina – scholarship recipients of the President and Government of Russia] [Electronic resource]. Available at: https://www.syktsu.ru/news/17286/
   (accessed: 21.11.2023). (In Russ.)
8. 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.
   (In Russ.)
9. Yermolenko A. V., Lotockaya S. R. Numerical solution of the problem “Predator – prey”. Aktual’nye voprosy sovremennoj nauki : Sbornik nauchnyh statej po materialam III Mezhdunarodnoj nauchnoprakticheskoj konferencii (21 noyabrya 2023 g., g. Ufa) : v 3 ch. [Current issues of modern science: Collection of scientific articles based on the materials of the III International Scientific and Practical Conference (November 21, 2023, Ufa) : in 3 parts]. Ufa: Publishing house. Scientific Research Center Bulletin of Science, 2023. Part 1. Pp. 11–16. (In Russ.)
10. Fokin R. R., Atoyan A. A., Abissova M. A. On motivation to study disciplines from higher education fields of mathematics, computer science, mathematical and information modeling. Sovremennye naukoemkie tekhnologii [Modern high technology]. 2017. No 2. Pp. 172– (In Russ.)
11. Popov N. I., Adiganova N. A. About one mathematical model of the biological problem “predator – prey”. Vestnik MGPU “Estestvennye nauki” [Bulletin of MSPU “Natural Sciences”]. 2017. No 4 (28). Pp. 119–(In Russ.)

For citation: Yermolenko A. V. Introduction to the theory of mathematical modeling when teaching students. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics],
2023, no 4 (49), pp. 47−58. (In Russ.) https://doi.org/10.34130/1992- 2752_2023_4_47

IV. Semantic aspects in the methods of math teaching

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

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

Text

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

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

References

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

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

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

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

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

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

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

References

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

Full text

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

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

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

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

Text

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

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

References

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

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

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

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

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

Irina V. Polyakova – 1Bank of Russia

Evgenija N. Startseva – Pitirim Sorokin Syktyvkar State University

Text

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

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

References

1. Main directions of the unified state monetary policy for 2023 and the periods 2024 and 2025. Bank of Russia. 2023. Available at: http://www.cbr.ru/about_br/publ/ondkp/ (accessed: 01.09.2023). (In Russ.)
2. Christopher A. Sims Macroeconomics and Reality. Econometrica.Vol. 48. No 1. Jan. Pp. 1–48. https://doi.org/10.2307/1912017.
3. Gertler M., Gilchrist S. . Monetary Policy, Business Cycles and the Behaviour of Small Manufacturing Firms. Quarterly Journal of Economics. 1994. Vol. 109. Issue 2. Pp. 309–340.
4. Bernanke B. S., Gertler M. Inside the Black Box: The Credit Channel of Monetary Policy Transmission. Journal of Economic Perspectives. 1995. Vol. 9. No 4. Pp. 27–48.
5. Holtem¨oller O. Further VAR evidence for the effectiveness of a credit channel in Germany. SFB 373 Discussion Paper (Humboldt Univer-sity of Berlin, Interdisciplinary Research Project 373: Quantification and Simu-lation of Economic Processes). Berlin, 2002. No 2002,66. 21 p.
   Available at: https://www.econstor.eu/handle/10419/65303 (accessed: 01.09.2023).
6. Shchepeleva M. A. Modeling the Balance Sheet Channel of Monetary Transmission in Russia. Finansovyy zhurnal [Financial Journal]. 2020. Vol. 12. No 2. Pp. 39–56. (In Russ.) DOI: 10.31107/2075-1990-2020-2- 39-56
7. Pestova A. A. “Credit view” on monetary policy in Russia. Prikladnaya ekonometrika [Applied Econometrics]. 2020. Vol. 57. Pp. 72–88. (In Russ.)
8. Bougheas S., Mizen P., Yalcin C. Access to external finance: Theory and evidence on the impact of monetary policy and firm-specific characteristics. Journal of Banking and Finance. 2006. Vol. 30. No 1. Pp. 199–227.
9. Aliev R., Hajkova D., Kubicova I. The impact of Monetary Policy on Financing of Czech Firms. Czech National Bank, Working Paper. 2014. No 5. 40 p. Available at:
   http://journal.fsv.cuni.cz/storage/1343_hajkova.pdf (accessed: 01.09.2023).
10. Malinowska A. Liquidity constraints and the balance Sheet channel of monetary policy transmission. Economic studies. 2016. Vol. 1. Pp. 71–88 Available at: https://www.researchgate.net/publication/301527925_Liquidity_constraints_and_the_balance_sheet_channel_of_monetary_policy_transmission (accessed: 01.09.2023).
11. Ratnikova T. A., Furmanov K. K. Analiz panel’nykh dannykh i dannykh o dlitel’nosti sostoyaniy : ucheb. posobiye [Analysis of panel data on the duration of states : Textbook]. Moscow: Publishing house of Higher school of economics. 2014. 373 p. (In Russ.)
12. Cloyne J., Ferreira C., Froemmel M., Surico P. Monetary policy, investment and firm heterogeneity. ECB Working Paper. 2018. No 2390 (25366). 48 p. Available at:
    https://www.ecb.europa.eu/pub/pdf/scpwps/ecb.wp2390~f6688df85d. en.pdf (accessed: 01.09.2023).
13. Jeenas P. Firm Balance Sheet Liquidity, Monetary Policy Shocks, and Investment Dynamics. CREI Working Paper. 2019. 83 p. Available at: https://crei.cat/wp-content/uploads/2020/06/Jeenas_JMP.pdf (accessed: 01.09.2023).
14. Ottonello P., Winberry T. Financial heterogeneity and the investment channel of monetary policy. Econometrica. 2020. Vol. 88. No 6. November. Pp. 2473–2502.
15. Anderson G., Cesa-Bianchi A. Crossing the credit channel: credit spreads and firm heterogenety. Staff Working Paper no 854 / Bank of England. 2020. 65 p. Available at: https://www.bankofengland.co.uk/- /media/boe/files/working-paper/2020/crossing-the-credit-channelcredit-spreads-and-firm-heterogeneity.pdf (accessed: 01.09.2023).
16. Prokopev F. Balance Sheet Channel of Monetary Policy: Evidence from Credit Spreads of Russian Firms. Den’gi i kredit [Russian Journal of Money and Finance]. 2021. 80 (4). Pp. 3–30. 2021. (In Russ.)
17. John B. Taylor, Harald Uhlig Spravochnoye rukovodstvo po makroekonomike : v 5 kn. Kn. 1. Fakty ob ekonomicheskom roste i ekonomicheskikh kolebaniyakh [Reference Guide to Macroeconomics: 5 books. Book 1. Facts about economic growth and economic
    fluctuations]. Moscow: Publishing house “Delo” RANEPA, 2019. 528 p. (Academic textbook). (In Russ.)
18. John B. Taylor, Harald Uhlig Spravochnoye rukovodstvo po makroekonomike : v 5 kn. Kn. 2. Metodologiya v makroekonomike [Reference Guide to Macroeconomics: 5 books. Book 2. Methodology in macroeconomics]. Moscow: Publishing house “Delo” RANEPA, 2020.
    1128 p. (Academic textbook). (In Russ.)
19. Oliner S. D., Rudebusch G. D. Is there a broad credit chanel for monetary policy. Economic Review / Federal Reserve Bank of San Francisco. 1996. No 1. Pp. 3–13. Available at: https://www.frbsf.org/economic-research/wpcontent/uploads/sites/4/3-13-2.pdf (accessed: 01.09.2023).
20. Valderrama M. Credit Channel and Investment Behavior in Austria: A Micro-Econometric Approach. European Central Bank. Working Paper. 2001. No 108. 45 p. Available at:
    https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp108.pdf (accessed: 01.09.2023).
21. Love I., Zicchino L. Financial development and dynamic investment behavior: Evidence from panel VAR. The Quartely Review of Economics and Finance. 2006. Vol. 46. Issue 2. Pp. 190–210.
22. Sigmund M., Ferstl R. Panel vector autoregression in R with the package panelvar. The Quartely Review of Economics and Finance.Elsevier. Vol. 80 (C). 2021. Pp. 693–720.
23. Anderson T. W., Hsiao C. Formulation and Estimation of Dynamic Models Using Panel Data. Journal of Econometrics. 1982. 18. Issue 1. Pp. 47–82.
24. Arellano M., Bond S. Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. The Review of Economic Studies. 1991. Vol. 58. Issue 2. Pp. 277–297.
25. Blundell R., Bond S. Initial Conditions and Moment Restrictions in Dynamic Panel Data Models. Journal of Econometrics. 1998. Vol. 87 (1). Pp. 115–143.

For citation: Maltseva O. A., Polyakova I. V., Startseva E. N. Balance Sheet Channel of Monetary Policy: Review of Empirical Methods. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2023, no 3 (48), pp. 18−48. (In Russ.) https://doi.org/10.34130/1992-2752_2023_3_18

III.Table generating language enhancement

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

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

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

Text

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

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

References

1. Fong J., Shiu H. and Cheung D. A relational-XML data warehouse for data aggregation with SQL and XQuery. Software-Practice & Experience. 38 (11). Pp. 1183–1213. DOI: 10.1002/spe.868.
2. Badam S. K., Liu Z. and Elmqvist N. Elastic Documents: Coupling Text and Tables through Contextual Visualizations for Enhanced Document Reading. IEEE Transactions on Visualization and Computer Graphics. 2019. Vol. 25. No 1. Pp. 661–671, Jan. 2019, DOI: 10.1109/TVCG.2018.2865119.
3. Okada M., Takaba M., Kaihara S., Okada M. Formal Representation of Summary Tables for Health Care Statistical Database Management. Computers and Biomedical Research. 1998. Vol. 31. No 6. Pp. 426–450. DOI: 10.1006/cbmr.1998.1491.
4. Amano A., Asada N. Graph grammar based analysis system of complex table form document. Proceedings of the 7th International Conference on Document Analysis and Recognition (ICDAR 2003). Edinburgh, Scotland, 2003. Pp. 916–920.
5. Belykh E. A., Golchevskiy Yu. V. An approach to designing a substitution language for generating electronic documents containing complex tables. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki [Bulletin of Udmurt University. Mathematics. Mechanics. Computer science]. 2019. Vol. 29. Issue 3. Pp. 422–437. (In Russ.)
6. Brian W. Kernighan, Dennis M. Ritchie. The C Programming Language. 2nd edition. Englewood Cliffs, New Jersey: Prentice Hall,272 p.
7. Mehdi Achour, Friedhelm Betz, Antony Dovgal, Nuno Lopes, Hannes Magnusson, Georg Richter, Damien Seguy, Jakub Vrana And several others, Peter Cowburn (eds), 2021 PHP: PHP Manual. Available at: https://www.php.net/manual/en/index.php (accessed: 01.06.2023).
8. The Open Group Base Specifications Issue 6, awk. Available at: https://pubs.opengroup.org/onlinepubs/000095399/utilities/awk.html (accessed: 01.06.2023).
9. ECMA-262 12th edition, June 2021. Available at: https://262.ecmainternational.org/12.0/ (accessed: 01.06.2023).
10. Alfred V. Aho, Monica S. Lam, Ravi Sthi, Jeffrey D. Ullman Compilers: principles, techniques, and tools – 2nd edition. Boston: Addison-Wesley, 2006. 1010 p.
11. The Open Group Base Specifications Issue 6, scanf. Available at: https://pubs.opengroup.org/onlinepubs/009695399/functions/ fscanf.html (accessed: 01.06.2023).

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

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

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

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

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

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

Text

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

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

References

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

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

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

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

Vyacheslav A. Popov

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

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

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

Full text

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

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

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

Oksana I. Turkova – Pitirim Sorokin Syktyvkar State University

Text

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

Keywords: plate theory, reference surface, stresses.

References

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

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

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

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

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

Text

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

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

References

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

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

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

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

Text

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

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

References

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

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

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

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

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

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

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

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

Text

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

Keywords: digital signal processing, software-defined radio.

References

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

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

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

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

Text

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

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

References

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

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

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

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

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

Text

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

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

References

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

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

Full text

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

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

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

Text

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

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

References

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

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

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

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

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

Text

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

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

References

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

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

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

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

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

Dmitriy A. Ushakov – Pitirim Sorokin Syktyvkar State University

Text

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

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

References

1. Severin P. A., Golchevskiy Yu. V. Comprehensive Approach for Cryptographic Computation Acceleration. Informatsionnyye tekhnologii v upravlenii i ekonomike [Information technologies in management and economics]. 2012, no 2, pp. 36–39. (In Russ.)
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.)
3. Fast Stream Encryption. SecurityLab.ru. Available at:http://www.securitylab.ru/analytics/436620.php (accessed: 03.12.2022).
4. Pavlov V. E., Udaltsov V. A. Optimizing the performance of block encryption algorithms. Prioritetnyye napravleniya razvitiya obrazovaniya i nauki [Priority directions of science and education development]. Cheboksary: SCC “Interaktiv plus LLC, 2017, 2(2), pp. 76–80. DOI: 10.21661/r-129822. (In Russ.)
5. Features of national cryptography. SecurityLab.ru. Available at: http://www.securitylab.ru/analytics/480357.php (accessed: 03.12.2022). (In Russ.)
6. Gashin R. A., Golchevskiy Yu. V. Development of Cryptographic Library Based on Algorithms from eSTREAM Project. Bezopasnost’ informatsionnykh tekhnologiy [Information Technology Security], 2015, no 4 (22), pp. 52–57. (In Russ.)
7. Ischukova E. A., Koshutsky R. A., Babenko L. K. Development and implementation of high-speed data encryption using the Kuznechik algorithm. Auditorium, 2015, no 4 (8). (In Russ.)
8. Code Optimization: CPU. Habrahabr. Available at: https://habrahabr.ru/post/309796/ (accessed: 03.12.2022). (In Russ.)
9. Bryant R., Hallaron D. Computer Systems A Programmer’s Perspective. Printice Hall, 2015. 1120 p.
10. Gerber R., Bik A. J. C., Smith K., Tian X. The Software Optimization Cookbook. St. Petersburg: Piter, 2010. 352 p. (In Russ.)
11. Kunin R. Optimizatsiya Koda: pamyat’ [Code Optimization: Memory]. Available at: https://habrahabr.ru/post/312078/ (accessed: 03.12.2022). (In Russ.)
12. Intel Instruction Set Extensions Technology. Available at: https://www.intel.com/content/www/us/en/support/articles/ 000005779/processors.html (accessed: 07.12.2022).
13. Kireev S. E. Kalgin K. V. Effektivnoye programmirovaniye sovremennykh mikroprotsessorov i
    mul’tiprotsessorov [Efficient programming of modern microprocessors and multiprocessors]. Available at: https://ssd.sscc.ru/sites/default/files/content/attach/317/lecture2016
    _01_intro.pdf (accessed: 03.12.2022). (In Russ.)
14. GOST R 34.12-2015 Informatsionnaya tekhnologiya. Kriptograficheskaya zashchita informatsii. Blochnyye shifry [GOST R 34.12-2015. Information technology. Cryptographic data security.
    Block ciphers]. (In Russ.)
15. Intel 64 and IA-32 Architectures Software Developer Manuals. Available at: https://www.intel.com/content/www/us/en/developer/ articles/technical/intel-sdm.html (accessed: 07.12.2022).
16. Intel 64 and IA-32 Architectures Optimization Reference Manual. Available at: https://cdrdv2-public.intel.com/671488/248966-046Asoftware-optimization-manual.pdf (accessed:07.02.2023).
17. Intel SSE4 Programming Reference. Available at:https://www.intel.com/content/dam/develop/external/us/en/ documents/d9156103-705230.pdf (accessed: 07.02.2023).
18. Intel Architecture Instruction Set Extensions Programming Reference. Available at: https://cdrdv2-public.intel.com/671368/architectureinstruction-set-extensions-programming-reference.pdf (accessed: 07.02.2023).
19. GOST R 34.12 ’15 na SSE2, ili Ne tak uzh i plokh Kuznechik [GOST R 34.12 ’15 on SSE2, or Not So Bad Kuznechik]. Habrahabr. Available at: https://habrahabr.ru/post/312224/ (accessed: 03.12.2022). (In Russ.)
20. Using the GNU Compiler Collection. GCC Online Documentation. Available at: https://gcc.gnu.org/onlinedocs/gcc.pdf (accessed: 03.12.2022).
21. Intel C++ Compiler 19.1 Developer Guide and Reference. Intel Developer Zone. Available at:
    https://www.intel.com/content/www/us/en/develop/documentation/ cpp-compiler-developer-guide-and-reference/top.html (accessed: 07.12.2022).
22. Fog A. Optimizing Subroutines In Assembly Language: An Optimization Guide For x86 Platforms. Available at: http://www.agner.org/optimize/optimizing_assembly.pdf (accessed:
    03.12.2022).
23. Kaspersky K. Tekhnika optimizatsii programm. Effektivnoye ispol’zovaniye pamyati [Program optimization technique. Efficient Memory Usage]. St. Petersburg, BHV-Petersburg, 2003. 464 p. (In Russ.)
24. flat assembler 1.73 Programmer’s Manual | flat assembler. Available at: http://flatassembler.net/docs.php?article=manual (accessed: 03.12.2022).
25. Golchevskiy Yu. V. Automation of Encryption Speed Optimization Research. Informatsionnyye tekhnologii v modelirovanii i upravlenii: podkhody, metody, resheniya : sbornik nauchnykh statey V Vserossiyskoy nauchnoy konferentsii s mezhdunarodnym uchastiyem [Information technologies in modeling and management: approaches, methods, solutions: Collection of scientific articles: V All-Russian scientific conference with international participation]. Tolyatti: Publishing House of TSU, 2022, pp. 208–215. (In Russ.)
26. Severin P. A., Golchevskiy Yu. V. Low-Level Performance Optimization on the Example of the Hash Function GOST R 34.11- Sistemnyy administrator [System Administrator]. 2017, no 1–2, pp. 170–171. (In Russ.)
27. Ahmetzyanova L. R., Alekseev E. K., Oshkin I. B. et al. On the properties of the CTR encryption mode of the Magma and Kuznyechik block ciphers with re-keying method based on CryptoPro Key Meshing. IACR Cryptol. ePrint Arch., 2016, 628 p.
28. Gafurov I. R. High-speed software implementation of encryption algorithms from GOST R 34.12-2015. Uchenyye zapiski UlGU. Seriya: Matematika i informatsionnyye tekhnologii [Scientific notes of UlGU. Series: Mathematics and Information Technology], 2022, no 2, pp. 38–(In Russ.)

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

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

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

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

Text

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

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

References

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

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

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

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

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

Natalija V. Nazemnova – Penza State University

Text

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

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

References

1. Dorofeev S. N., Esetov E. N., Nazemnova N. V. Analogy as a basis for teaching schoolchildren the vector method of solving geometric problems. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 2021, issue 4 (41), pp. 69–79. (In Russ.)
2. Menchinskaya N. A. Problemy obucheniya i psikhicheskogo razvitiya studentov [Problems of teaching and mental development of students]. M.: Pedagogy, 1989, 224 p. (In Russ.)
3. Slepkan Z. I. Psikhologo-pedagogicheskiye osnovy prepodavaniya matematiki : metod.posobiye [Psychological and pedagogical foundations of teaching mathematics: method.stipend]. Kiev, 1983, 192 p. (In Russ.)
4. Dorofeev S. N. Teoriya i praktika formirovaniya tvorcheskoy aktivnosti budushchikh uchiteley matematiki v pedagogicheskom vuze [Theory and practice of formation of creative activity of future teachers of mathematics at a pedagogical university, dissertation for the degree of Doctor of Pedagogical Sciences]. Penza, 2000. 410 p. (In Russ.)
5. Dorofeev S. N., Ivanova T. A., Uteeva R. A. et al. Continuity in the preparation of future bachelors of pedagogical education (profile “Mathematics”) for creative activity. Gumanitarnyye nauki i obrazovaniye [Humanities and Education]. 2018, vol. 9, no 4 (36), pp. 25–30. (In Russ.)
6. Dorofeev S. N. Competence-based approach to mathematical education of students of technical universities. Pedagogicheskoye obrazovaniye i nauka [Pedagogical education and science]. 2009, no 1, pp.88–91. (In Russ.)
7. Dorofeev S. N. UDE as a method of preparing future bachelors of pedagogical education for professional activity. Gumanitarnyye nauki i obrazovaniye [Humanities and Education]. 2013, no 1, pp. 14–17. (In Russ.)
8. Dorofeev S. N., Pavlov I. I., Shichiyakh R. F., Prikhodko A. N.Differentiated Training as a Form of Organization of Education fnd Cognitive Activity of Future Masters of Pedagogical Education. Applied Lingvistics Research Jounal, 2021, 5 (3), pp. 216–222.
9. Dorofeev S. N., Shichiyach R. A., Khasimova L. N. Devoloping creative activity abilities of students in higer educaitional esteblishments. Rеvista оn line de politica e gistao educational. 2021, vol. 25, no S2, pp. 883–900.
10. Friedman L. M. Psikhologo-pedagogicheskiye osnovy prepodavaniya matematiki v shkole: uchitel’ matematiki o pedagogicheskoy psikhologii [Psychological and pedagogical foundations of teaching mathematics at school: a teacher of mathematics about pedagogical psychology]. M.: Enlightenment, 1983, 160 p. (In Russ.)
11. Talyzina N. F. Formation of mathematical concepts. Formirovaniye metodov matematicheskogo myshleniya [Formation of methods of mathematical thinking] / edited by N. F. Talyzina. M.: Lomonosov Moscow State University; Ventana-Graf LLP, 1995, pp. 13–28. (In Russ.)
12. Ball G. A. Teoriya obrazovatel’nykh problem: psikhologopedagogicheskiy aspekt [Theory of educational problems: psychological and pedagogical aspect]. M.: Pedagogy, 1990. 184 p. (In Russ.)
13. Zak A. Z. Kak opredelit’ uroven’ razvitiya myshleniya studenta [How to determine the level of development of a student’s thinking]. M.: Knowledge, 1982. 96 p. (In Russ.)
14. Vygotsky L. S. Sobraniye sochineniy : v 6 t. T. 2. Problemy obshchey psikhologii / pod red. V. V. Davydova [Collected works: in 6 vols.Problems of general psychology / edited by V. V.Davydov]. M.: Pedagogika, 1982. 504 p.: ill. (In Russ.)
15. Dorofeev S. N. Vysshaya matematika [Higher Mathematics]. M.: LLC “Publishing House “Mir i obrazovanie”” , 2011. 592 p.: ill. (In Russ.)
16. Kudryavtsev L. D. Mysli o sovremennoy matematike i yeye izuchenii [Thoughts on modern mathematics and its study]. M.: Science, 1977, 123 p. (In Russ.)
17. Vygotsky L. S. Sobraniye sochineniy : v 6 t. T. 3. Problemy razvitiya psikhiki / pod red. A. M. Matyushkina [Collected works: in 6 vols. 3. problems of the development of the psyche / edited by A. M. Matyushkin]. M.: Pedagogy, 1983. 368 p.: ill. (In Russ.)\

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

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

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

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

Text

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

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

References

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

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

Full text

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

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

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

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

Text

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

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

References

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

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

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

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

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

Text

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

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

References

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

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

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

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

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

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

Text

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

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

References

1. Uchebnik 4CIO [4CIO : Textbook]. Available at: https://4cio.ru/content/uchebnik_all_2.pdf (accessed: 10.15.2022) (InRuss.)
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.

References

1. «Post Bank»: we saved hundreds millions rubles using biometrics.
   Available at: https://bloomchain.ru/newsfeed/k-kontsu-2019-godavseh-klientov-pochta-banka-budut-identifitsirovat-po-biometrii (accessed: 2021/10/05). (in Russ.)
2. Loan scoring and fight against swindlers: AI in Russian banking sector. Available at: https://aiconference.ru/en/article/kreditniy-skoring-iborba-s-moshennikami-ob-ii-v-bankovskoy-sfere-rossii-96820 (accessed: 2021/10/05).
3. Neurohive – Neural Networks. Available at: https://neurohive.io/en/
   (accessed: 2021/10/05).
4. Hannun A. Y., Rajpurkar P., Haghpanahi M. et al. Cardiologistlevel arrhythmia de-tection and classification in ambulatory electrocardiograms using a deep neural net-work. Nat Med 25,Pp. 65–69. DOI: 10.1038/s41591-018-0268-3.
5. Koshy R., Padalkar A., Nikam N., Jain V. Easy verdict: Digital assistant to resolve criminal litigation 10th International Conference on Advances in Computing, Con-trol, and Telecommunication Technologies, 2019. Pp. 17–23.
6. Domingos P. The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World. Basic Books, New York, 2015.
7. Mou S., Du P., Cheng Z. A brain-inspired information processing algorithm and its application in text classification. Expert Systems with Applications, Vol. 177, 2021. DOI: 10.1016/j.eswa.2021.114828.
8. Asim M., Javed K., Rehman A., Babri H. A. A new feature selection metric for text classification: eliminating the need for a separate pruning stage. International Journal of Machine Learning
   and Cybernetics, 12(9), 2021. Pp. 2461–2478. DOI: 10.1007/s13042-021-01324-6.
9. Shimomoto E. K., Portet F., Fukui K. Text classification based on the word subspace representation. Pattern Analysis and Applications, 24 (3), 2021. Pp. 1075-1093. DOI: 10.1007/s10044-021-00960-6.
10. Zhang J., Zi L., Hou Y. et al. A C-BiLSTM approach to classify construction accident reports. Applied Sciences (Switzerland ), 10(17), DOI: 10.3390/APP10175754.
11. Chi N.-W., Lin K.-Y., Hsieh S.-H. Using ontology-based text classification to assist Job Hazard Analysis. Advanced Engineering Informatics, 28(4), 2014. Pp. 381–394. DOI: 10.1016/j.aei.2014.05.001.
12. Zhan, T. Classification Models of Text: A Comparative Study. IEEE 11th Annual Computing and Communication Workshop and Conference, CCWC 2021, 2021. Pp. 1221-1225. DOI:
    10.1109/CCWC51732.2021.9375918.
13. Li Y., Dai G., Li G. Feature selection method of text tendency classification. Proceedings – 5th International Conference on Fuzzy Systems and Knowledge Discovery, FSKD-2008, 2008. Pp. 34–37. DOI:10.1109/FSKD.2008.263.
14. Flach P. Machine Learning: The Art and Science of Algorithms That Make Sense of Data. Cambridge University Press, New York, 2012.
15. Rani M.S., Sumathy S. Analysis on various machine learning based approaches with a perspective on the performance. Innovations in Power and Advanced Computing Technologies, i-PACT 2017, 2017. Pp. 1–7. DOI: 10.1109/IPACT.2017.8244998.
16. Bengfort B., Bilbro R., Ojeda T. Applied Text Analysis with Python: Enabling Lan-guage-Aware Data Products with Machine Learning. 1st edn. O’Reilly Media, Inc., 2018.
17. VanderPlas J. Python Data Science Handbook: Essential Tools for Working with Data. 1st edn. O’Reilly Media, Inc., 2017.
18. Chollet F. Deep Learning with Python. Manning Publications Co,2017.
19. G´eron A. Hands-On Machine Learning with Scikit-Learn and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems. 2nd edn. O’Reilly Media, Inc., 2019.
20. Buitinck L., Louppe G., Blondel M. et al. API design for machine learning software: experiences from the scikit-learn project. ECML PKDD Workshop: Languages for Data Mining and Machine Learning,Pp. 108–122.
21. Rashka S., Mirjalil V. Python Machine Learning: Machine Learning and Deep Learning with Python, scikit-learn, and TensorFlow. 2nd edn. Packt Publishing, 2017.
22. Brink H., Richards J. W., Fetherolf M. Real-World Machine Learning. 1st edn. Manning Publications Co, 2016..
23. fastText. Library for efficient text classification and representation learning. Available at: https://fasttext.cc/ (accessed: 2021/10/05).
24. Opitz D., Maclin R. Popular ensemble methods: An empirical study. Journal of Artifi-cial Intelligence Research, 11, 1999. Pp. 169–198. DOI:10.1613/jair.614.

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

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

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

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

Text

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

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

References

1. Research of the metacognitive awareness of university students / N. N. Babikova, O. A. Maltseva, E. N. Starceva, M. S. Turkina. Vestnik Marijskogo gosudarstvennogo universiteta [Vestnik Marijskogo gosudarstvennogo universiteta]. 2018. T. 12. No 3(31). Pp. 9−16. DOI
   10.30914/2072-6783-2018-12-3-9-16. (In Russ.)
2. Metacognitive awareness and student achievement / N. N. Babikova, O. A. Maltseva, E. N. Starceva, M. S. Turkina. Dvadcat pyataya godichnaya sessiya Uchenogo soveta Syktyvkarskogo gosudarstvennogo universiteta imeni Pitirima Sorokina (Fevralskie chteniya) : sbornik materialov: tekstovoe nauchnoe elektronnoe izdanie na kompakt-diske, Syktyvkar, 01–28 fevralya 2018 goda [Twenty-fifth Annual Session of the Academic Council of Syktyvkar State University named after Pitirim Sorokin (February Readings) : collection of materials: text
   scientific electronic edition on CD-ROM]. Syktyvkar: Syktyvkarskij gosudarstvennyj universitet im. Pitirima Sorokina, 2018. 856 p. ISBN 978-5-87661-569-5. (In Russ.)
3. Ashymova N. Sh., Kazakova N. O. Memory performance of 1st year students of the Faculty of Biology and Chemistry of KSU. I. Arabaeva. Problemy sovremennoj nauki i obrazovaniya [The problems of modern science and education]. 2017. No 7 (89). Pp. 16−19. (In Russ.)
4. Byvsheva M. V., Kobalyan A. A., Hanova T. G. The study of mnemonic abilities of students in the context of educational and professional activities. Vestnik Mininskogo universiteta [Bulletin of
   Minin University]. 2017. No 1 (18). P. 19. (In Russ.)
5. Dubinina M. N. The study of short-term memory of the students and graduate students of higher education. Vestnik Donskogo gosudarstvennogo agrarnogo universiteta [Bulletin of the Don State Agrarian University]. 2019. No 1-2 (31). Pp. 37−42. (In Russ.)
6. Borodina A. N. Comparative analysis of memory indicators of modern students and students of the 70-80th. Vestnik Permskogo universiteta. Filosofiya. Psihologiya. Sociologiya [Bulletin of Perm University. Philosophy. Psychology. Sociology]. 2015. No 4 (24). Pp. 122−131. (In Russ.)
7. Sparrow B., Liu J., Wegner D. M. Google effects on memory: cognitive consequences of having information at our fingertips. Science. 2011. Vol. 333. No. 6043. Pp. 776–778. Available
   at: https://psychology.ua.edu/wp-content/uploads/2016/03/Google-IsChanging-the-Way-we-Think.pdf (accessed: 07.09.2022).
8. Davydovskij A., Pishchova A. Influence of the Internet environment on memory processes. Nauka i innovacii [Science and Innovations].No 12 (190). Pp. 28−33. (In Russ.)
9. Chizhikova E. S. The influence of the Internet on memory. Tendencii i perspektivy razvitiya sociotekhnicheskoj sredy: Materialy IV mezhdunarodnoj nauchno-prakticheskoj konferencii, Moskva, 13 dekabrya 2018 goda / Otvetstvennyj redaktor I.L. Surat [Trends and
   prospects of development of socio-technical environment : materials of the IV International Scientific-Practical Conference, Moscow, December 13, 2018 / ed. by I. L. Surat.]. M.: Sovremennyj gumanitarnyj universitet, 2018. Pp. 474−479. (In Russ.)
10. Kuznecova A. V. Mnemic Ability of the Internet Active Schoolboy of 14–16 years. Yaroslavskij pedagogicheskij vestnik [Yaroslavl Pedagogical Bulletin]. 2010. Vol. 2. No 4. Pp. 231−235. (In Russ.)
11. Cheremoshkina L. V. The influence of Internet activity on the mnemonic abilities of the subject. Psihologiya. Zhurnal Vysshej shkoly ekonomiki [Psychology. Journal of the Higher School of Economics].Vol. 7. No 3. Pp. 57–71. (In Russ.)
12. Vulf M. Proust and the Squid: The Neurobiology of Reading. M.: KoLibri, Azbuka-Attikus, 2020. P. 384. (In Russ.)
13. Pintrich P. R. The Role of Metacognitive Knowledge in Learning, Teaching, and Assessing. Revising Bloom’s Taxonomy. Theory Into Practice. 2002. No. 41 (4). Pp. 219–225. Available at:
    https://www.researchgate.net/publication/242670371_The_Role_of_Metacognitive_Knowledge_in_Learning_Teaching_and_Assessing (accessed: 07.09.2022).
14. Savin E. Yu., Fomin A. E. Generalized and subject-specific metacognitive skills in students learning activities. Psihologicheskie issledovaniya [Psychological research]. 2014. Vol. 7. No 37. P. 8.

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.

References

1. Gindikin S. G. Great Art. Rasskazy o fizikax i matematikax [Stories about physicists and mathematicians. 3rd edition, expanded.] M.: ICNMO, 2001. Pp. 8–42. (In Russ.)
2. Nikiforovsky V. A. Iz istorii algebry XVI—XVII vekov [From the history of algebra of the XVI–XVII centuries]. M.: Science, 1979. Pp. 42–88. (In Russ.)
3. Stillwell D. Matematika i ee istoriya [Mathematics and its history]. Moscow-Izhevsk: Institute of Computer Research, 2004. P. 130. (In Russ.)
4. Anokhina E. Yu. History of the development and formation of the theory of the function of the complex variable (TFKP) as a educational subject. Vestnik TGPI. Estestvennye nauki [Bulletin of TSPI. Natural sciences]. 2008. No 1. Pp. 83–87. (In Russ.)
5. Sinkevich G. I. History of geometric representations of complex numbers. Istoriya nauki i tekhniki [History of science and technology]. No 4. Pp. 15–30. (In Russ.)
6. Euler L. Vvedenie v analiz beskonechno malyh [Introduction to infinitesimal analysis]. Moscow-Leningrad, 1936. Vol. 1. (In Russ.)
7. Wessel C. On the analytical Representation on Direction; an Attempt, applied Chiefl y to the Solution of Plane and Spherical Polygons. Smith D.E. A source book in Mathematics. Vol. 3. 1959. New York: Dover publications. Pp. 55–66.
8. History of mathematics. From ancient times to the beginning of the New Age. Istoriya matematiki [History of Mathematics] / еdited by A.P. Yushkevich, in three volumes. M.: Science, 1970. Vol. I. 352 p. (In Russ.)
9. Riemann B. Sochineniya [Works]. M.: OGIZ; Gostekhizdat, 1948. (In Russ.)
10. Markushevich A. I. Contribution of Yu.V. Sokhotsky to the general theory of analytical functions. Istoriko-matematicheskie issledovaniya : v. 3 t. [Historical and mathematical research].Vol. 3. M.; L., 1950. (In Russ.)
11. Smirnov V. I. Kurs vysshej matematiki dlya tekhnikov i fizikov : v 5 t. [Course of higher mathematics for technicians andphysicists : in 5 vols.]. M.; L., 1930. 467 p. (In Russ.)
12. Shabat B. V. Vvedenie v kompleksnyj analiz : v 2 t. [Introduction to complex analysis : in 2 vol.]. Moscow: Lenand, 2020. 344 p. (In Russ.)

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

1. Kazakova A. O., Petrov A. G. Calculation of the flow of a viscous fluid between two arbitrarily moving cylinders of arbitrary section. Zhurnal vychislitelnoj matematiki i matematicheskoj fiziki [Journal of Computational Mathematics and Mathematical Physics]. 2019. Vol. 59. No 6. Pp. 1063–1082. (In Russ.)
2. Yermolenko A. V., Melnikov V. A. Calculation of the contact interaction of a rectangular plate and a base by the Karman theory. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics]. 2018, 2 (27). Pp. 86–92. (In Russ.)
3. Ben-Artzi М., Chorev I., Croisille J.-P., Fishelov D. A compact difference scheme for the biharmonic equation in planar irregular domains. SIAM J., 2009, No 47, pp. 3087—3108.
4. Linden J. A Multigrid Method for Solving the Biharmonic Equation on Rectangular Domains. Advances in Multi-Grid Methods : proceedings of the conference held in Oberwolfach, December 8 to 13, 1984. Braunschweig; Wiesbaden: Vieweg, 1985. (Notes on numerical fluid
   mechanics; Vol. 11), pp. 64–66.
5. Kobel’kov G. M. On the reduction of a boundary value problem for a biharmonic equation to a Stokes-type problem. Dokl. AN SSSR [Reports of the USSR Academy of Sciences], 1985, Vol. 283, No 3, pp. 539–541. (In Russ.)
6. Demidovich B. P., Maron I. A., SHuvalova E. Z. Chislennye metody analiza [Numerical methods of analysis]. Moskva: Gosudarstvennoe izdatel’stvo fiziko-matematichekoj literatury, 1963.
   400 p. (In Russ.)
7. Mihajlovskii E. I. Lekcii po variacionnym metodam mekhaniki uprugih tel [Lectures on variational methods of mechanics of elastic bodies]. Syktyvkar: Izd-vo Syktyvkarskogo universiteta, 2002. 256 p. (In Russ.)
8. Ryazhskih V. I., Slyusarev M. I., Popov M. I. Numerical integration of the biharmonic equation in the square domain. Vestnik Sankt-Peterburgskogo universiteta. Ser. 10 [Herald of St. Petersburg University. Series 10]. 2013, No. 1, pp. 52–62. (In Russ.)
9. Eremenko S. YU. Metody konechnyh elementov v mekhanike deformiruemyh tel [Finite element methods in mechanics of deformable bodies]. Kharkov: Izd-vo “Osnova” pri Har’k. un-t, 1991. 272 p. (In Russ.)
10. Fedorenko R. P. On the rate of convergence of one iterative process. ZH. vychisl. matem. i matem. fiz. [Journal of Computational and Mathematical Physics], 1964, Vol. 4, No 3, pp. 559—564. (In Russ.)
11. Brenner S. C. An optimal-order nonconforming multigrid method for the biharmonic equation. SIAMJ. Numer. Anal. 26 (1989), pp. 1124- 1138.
12. Jiang Y., Wang B., Xu Y. A fast Fourier–Galerkin method solving a boundary integral equation for the biharmonic equation. SIAM J. NUMER. ANAL. 2014, Vol. 52, No 5, pp. 2530–2554.
13. Greenbaum A., Greengard L. , Mayo A. On the numerical solution of the biharmonic equation in the plane. Phys. D, 60 (1992), pp. 216–225.
14. Romakina O. M., Shevcova YU. V. Spline-collocation method and its modification in problems of static bending of a thin orthotropic rectangular plate. Izvestiya Saratovskogo universiteta. Novaya seriya. Seriya: Matematika. Mekhanika. Informatika [Izvestia of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics], 2010, Vol. 10. No 1, pp. 78–82. (In Russ.)
15. 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: 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.

References

1. Tripathi S. K., Gupta B., Soundra Pandian K. K. An alternative practical publickey cryptosystems based on the Dependent RSA Discrete Logarithm Problems. Expert Systems With Applications, 164 (2021), 114047.
2. Sreedharan S., Eswaran C. A lightweight encryption scheme using Chebyshev polynomial maps. Optik – International Journal for Light and Electron Optics, 240 (2021), 166786.
3. Biletsky A. A. Cryptografy applications of primitive matrices Galois and Fibonacci. Zashhita informacii [Information Security Research Journal], 15:32 (2013), pp. 128–132. (In Russ.)
4. Zelenevsky V. V., Zelenevsky V. Yu., Zelenevsky A. V. et al. Statisticheskiy i korrelyatsionnyy analiz adresnykh posledovatel’nostey v kanalakh peredachi s kodovym mul’tipleksirovaniyem dannykh. Izvestiya Instituta inzhenernoy fiziki [Proceedings of the Institute of Engineering Physics]. 4:58 (2020), pp. 31–34. (In Russ.)
5. Dai Z., Huang M. A criterion for primitivity of integral polynomial Mod 2d. Chinese Science Bulletin, 15 (1990), pp. 1128–1130.
6. Zhu Y., Wang X. A criterion for primitive polynomials over Galois rings. Discrete Mathematics, 303 (2005), pp. 244–256.
7. Fedorov G. V. On the Period Length of a Functional Continued Fraction over a Number Field. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniya [Papers of the Russian Academy of Sciences. Mathematics, computer science, control processes], 102 (2020), pp. 513–517. (In Russ.)
8. Susilo W., Tonien J. A Wiener-type attack on an RSA-like cryptosystem constructed from cubic Pell equation. Theoretical Computer Science, 885 (2021), pp. 125–130.
9. Pousin J. Least squares formulations for some elliptic second order problems, feedforward neural network solutions and convergence results. Journal of Computational Mathematics and Data Science, 2 (2022), 100023.
10. Prasolov V. V. Mnogochleny [Polynomials], Moscow Center For Continuous Mathematical Education, M., 2003 (In Russ.)
11. Van der Waerden B. L. Algebra. M.: Nauka, 1979. (In Russ.)
12. Vyalyi M. N., Gimadeev R. A. Separation of words by positions of subwords. Discretnyy analiz i issledovaniye operatsiy [Discrete Analysis and Operations Research], 21:1(115) (2014), pp. 3–14. (In Russ.)
13. Galieva L. I., Galyautdinov I. G. On a class of equations solvable in radicals. Izvestiya vysshix uchebnyx zavedenij. Matematika [Russian Math. (Iz. VUZ)], 55:2 (2011), pp. 18–25. (In Russ.)
14. Savel’ev I. V. Circular polynomials and singularities of complex hypersurfaces. Uspekhi Mat. Nauk [Advances in Mathematical Sciences], 48:2 (290) (1993), pp. 197–198. (In Russ.)
15. Liopo V. A., Sabut A. V. Point groups and syngonies of noncrystallographic symmetry. Vestnik Grodnenskogo gosudarstvennogo universiteta imeni Yanki Kupaly‘. Seriya 2. Matematika. Fizika. Informatika, vy‘chislitel‘naya texnika i upravlenie [Bulletin of Grodno State University named after Yanka Kupala. Series 2. Mathematics. Physics. Informatics, computer technology and management], 1:148 (2013), pp. 115–126. (In Russ.)
16. Fan S., Wang X. Primitive normal polynomials with the specified last two coefficientss. Discrete Mathematics, 309 (2009), pp. 4502–4513.
17. Fan S. Q., Han W. B., Feng K. Q. Primitive normal polynomials with multiple coefficients prescribed: An asymptotic result. Finite Fields and Their Applications, 13:4 (2007), pp. 1029–1044.
18. Fan S. Q., Han W. B., Feng K. Q., Zhang X. Y. Primitive normal polynomials with the first two coefficients prescribed: A revised p-adic method. Finite Fields and Their Applications, 13 (2007), pp. 577–604.
19. Brochero Martнnez F. E., Reis L., Silva–Jesus L. Factorization of composed polynomials and applications. Discrete Mathematics, 342 (2019), 111603.
20. Bakshi G. K., Raka M. A class of constacyclic codes over a finite field. Finite Fields Appl., 18:6 (2012), pp. 362–377.
21. Brochero Martнnez F. E., Giraldo Vergara C. R., de Oliveira L. Explicit factorization of xn – 1 ∈ Fq[x] . Des. Codes Cryptogr., 77 (2015), pp. 277–286.
22. Brochero Martнnez F. E., Reis L. Factoring polynomials of the form f(xn) ∈ Fq[x] . Finite Fields Appl., 49 (2018), pp. 166–179.
23. Li F., Yue Q. The primitive idempotents and weight distributions of irreducible constacyclic codes. Des. Codes Cryptogr., 86 (2018), pp. 771–784.
24. Liu L., Li L., Wang L., Zhu S. Repeated-root constacyclic codes of length nlps. Discrete Math., 340:9 (2017), pp. 2250–2261.
25. Wu Y., Yue Q., Fan S. Further factorization of xn – 1 over a finite fiel. Finite Fields Appl., 54 (2018), pp. 197–215.
26. WOLFRAM MATHEMATICA ONLINE [Электронный ресурс], WolframAlpha.com (2022), Available at:https://www.wolfram.com/mathematica/online/ (accessed05.06.2022).

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

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

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.

References

1. Biomarkery – indikatory sostoyaniya zdorovya [Biomarkers – healthindicators] [Online]. Available at: https://medinteres.ru/interesnyiefaktyi/biomarkeryi.html (accessed: 28.03.2022).
2. Teplovaya inerciya temperaturnyx datchikov [Thermal inertia of temperature sensors] [Online]. Available at: https://isup.ru/articles/16/15436/ (accessed: 28.03.2022).
3. O saturacii kisloroda v krovi [About blood oxygen saturation] [Online]. Available at: https://aptstore.ru/articles/saturatsiya-kisloroda-vkrovi/ (accessed: 28.03.2022).
4. Pulsovoe davlenie v krovi [Pulse pressure in the blood] [Online]. Available at: https://cyberleninka.ru/article/n/pulsovoe-davleniekrovi-rol-v-gemodinamike-i-prikladnye-vozmozhnosti-v-funktsionalnoydiagnostike (accessed: 28.03.2022).
5. Povyshennoe davlenie: prichiny i osobennosti lecheniya [High blood pressure: causes and peculiarities of treatment] [Online]. Available at: https://aptstore.ru/articles/povyshennoe-davlenie-prichiny-iosobennosti-lecheniya/ (accessed: 28.03.2022).
6. Filtry vysokix i nizkix chastot [High-pass and low-pass filters] [Online]. Available at: https://elar.urfu.ru/bitstream/10995/36102/1/978-5- 7996-1577-2_2015.pdf (accessed: 28.03.2022).
7. Mediannaya filtraciya [Median filtering] [Online]. Available at: https://ru.bmstu.wiki/Медианная_фильтрация (accessed: 28.03.2022).
8. Filtr Kalmana [Kalman filter] [Online]. Available at: https://habr.com/ru/post/166693/ (accessed: 28.03.2022).
9. A Guide to RNN: Understanding Recurrent Neural Networks and LSTM Networks [Электронный ресурс]. URL: https://builtin.com/datascience/recurrent-neural-networks-and-lstm (дата обращения: 28.03.2022).
10. Niall Twomey, Tom Diethe, Xenofon Fafoutis, Atis Elsts, Ryan McConville, Peter Flach and Ian Craddock. A Comprehensive Study of Activity Recognition Using Accelerometers. URL:
    https://www.researchgate.net/publication/323847517_A_Comprehensive_Study_of_Activity_Recognition_Using_Accelerometers – March 2018
11. Ivan Ozhiganov. Using LSTM Neural Network to Process Accelerometer Data. URL: https://dzone.com/articles/using-lstmneural-network-to-process-accelerometer – 08.05.2017
12. Arumugam Thendramil Pavai. Sensor Based Human Activity Recognition Using Bidirectional LSTM for Closely Related Activities. California State University, San-Bernardino, Electronic Theses Projects and Dissertations – 776 – 12.2018
13. Matthew Chin Heng Chua, Youheng Ou Yang, Hui Xing Tan, Nway Nway Aung, Jing Tian. Time Series classification using a modified LSTM approach from accelerometer-based data: A comparative study for gait cycle detection. Gait & Posture 74 – 09.2019 – doi:10.1016/j.gaitpost.2019.09.007
14. Categorical crossentropy loss function [Online]. Available at: https://peltarion.com/knowledge-center/documentation/modelingview/build-an-ai-model/loss-functions/categorical-crossentropy
    (accessed: 28.03.2022).
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.
5. Vovk S. P. The game of two persons with fuzzy strategies and preferences. Al’manah sovremennoj nauki i obrazovaniya [Almanac of Modern Science and Education]. 2014. № 7(85). Pp. 47–49. (In Russ.).
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.
13. Lopatin A. S. Method of annealing. Stohasticheskaya optimizacii v informatike [Stochastic Optimization in Computer Science]. 2005. Vol. 1. Pp. 133–149.
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

1. Grosso C., Trentin A., Forza C. Towards an understanding of how the capabilities deployed by a Web-based sales configurator can increase the benefits of possessing a mass-customized product. 16th International Configuration Workshop, CEUR Workshop Proceedings, 2014, Vol. 1220. Pp. 81–88.
2. Sandrin E. Synergic effects of sales-configurator capabilities on consumerperceived benefits of mass-customized products. International Journal of Industrial Engineering and Management, 2017, Vol. 8, No. 3. Pp. 177–188.
3. Streichsbier C., Blazek P., Faltin F., Fr¨uhwirt W. Are de-facto standards a useful guide for designing human-computer interaction processes? The case of user interface design for web based B2C product configurators. 42nd Hawaii International Conference on System Sciences, 2009. Pp. 1–7. DOI: 10.1109/HICSS.2009.80.
4. Leclercq T., Davril J.-M., Cordy M., Heymans P. Beyond de-facto standards for designing human-computer interactions in configurators. CEUR Workshop Proceedings, 2016, vol. 1705. Pp. 40–43.
5. Abbasi E.K., Hubaux A., Acher M., Boucher Q., Heymans P. The anatomy of a sales configurator: An empirical study of 111 cases. Lecture Notes in Computer Science, 2013, LNCS, vol. 7908, Pp. 162–177. DOI: 10.1007/978- 3-642-38709-8_11.
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).
9. Grosso C., Forza C., Trentin A. Support for the social dimension of shopping through web based sales configurators. 17th International Configuration Workshop, CEUR Workshop Proceedings, 2015, vol. 1453. Pp. 115–122.
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

1. Rago A. S., Stevens W. R. Advanced programming in the UNIX environment. Addison-Wesley Professional, 2013. 1032 p.
2. Camden K. R. Apache Cordova In Action. Shelter Island: Manning, 2016. 230 p.
3. Thornsby J. Android UI design. Birmingham: Packt Publishing, 2016. 356 p.
4. Bennett G., Kaczmarek S., Lees B. Swidt 4 for Absolute Beginners. Phoenix: Apress, 2018. 317 p.
5. Petzold C. Cross-platform C# programming for iOS, Android and Windows. Redmond, Washington: Microsoft Press, 2013. 1161 p.
6. Petzold C. Applications = Code + Markup. A Guide To the Microsoft Windows Presentation Foundation. Redmond: Microsoft Press, 2006. 1002 p.
7. Windmill E. Flutter in Action. Shelter Island: Manning, 2020. 368 p.
8. Melnikov V. A. Development Process of game engine core for 2D games and interfaces Sad Lion Engine. Vestnik Syktyvkarskogo universiteta. Ser.1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, 4 (33), pp. 21–37. (In Russ.)
9. Dogsa T., Meolic R. A C++ App for Demonstration of Sorting Algorithms on Mobile Platforms. International Journal of Interactive Mobile Technologies., 2014. Vol. 8, No 1. Available: https://www.onlinejournals.org/index.php/i-jim/article/view/3464/2940 (accessed: 17.07.2020).
10. Cao J., Cao Y. Application of human computer interaction interface in game design. Communications in Computer and Information Science, 2017, 714, pp. 103–108. DOI: 10.1007/978-3-319-58753-0_16.
11. Zaina L. A. M., Fortes R. P. M., Casadei V., Nozaki L. S., Paiva D. M. B. Preventing accessibility barriers: Guidelines for using user interface design patterns in mobile applications. Journal of Systems and Software, 2022, vol. 186. DOI: 10.1016/j.jss.2021.111213.
12. Quinones, J. R., Fernandez-Leiva, A. J. XML-Based Video Game Description Language. IEEE Access, 2020, vol. 8, pp. 4679–4692. DOI: 10.1109/ACCESS.2019.2962969.
13. Derakhshandi M., Kolahdouz-Rahimi S., Troya J., Lano K. A modeldriven framework for developing android-based classic multiplayer 2D board games. Automated Software Engineering, 2021, 28 (2). DOI: 10.1007/s10515- 021-00282-1.
14. Park, H. C., Baek, N. Design of SelfEngine: A Lightweight Game Engine. Lecture Notes in Electrical Engineering, 2020, vol. 621, pp. 223–227. DOI: 10.1007/978-981-15-1465-4_23.
15. West M. Evolve your hierarchy [Online] Cowboy Programming. Available: http://cowboyprogramming.com/2007/01/05/evolve-your-heirachy/ (accessed: 22.08.2020).
16. Hocking J. Unity in action: Multiplatform game development in C#. Manning, 2018. 400 p.
17. Lisovsky, K.Y. XML Applications Development in Scheme. Programming and Computer Software 28, 197–206 (2002). https://doi.org/10.1023/A:1016319000374

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.)
2. Sevostyanova S. A., Shumakova E. O., Martynova E. V. Rating system for assessing students’ knowledge in the study of the discipline «Introductory course of Mathematics». Vestnik Yuzhno-Uralskogo gosudarstvennogo gumanitarno-pedagogicheskogo universiteta [Bulletin of the
   South Ural State Humanitarian Pedagogical University]. 2018. No. 8. Pp. 116–129.
3. Drobysheva I. V., Drobyshev Yu. A. The design model of the introductory course of mathematics. Matematicheskoe modelirovanie v ekonomike, upravlenii i obrazovanii : sbornik nauchny‘x statej po materialam III Mezhdunarodnoj nauchno-prakticheskoj konferencii [Mathematical modeling in economics, management and education. Collection of scientific articles based on the materials of the III International Scientific and Practical Conference]. 2017. Pp. 150–155. (In Russ.)
4. Panfilova T. L. Some features of teaching elementary mathematics to students of pedagogical directions. Sovremennye problemy i perspektivy obucheniya matematike, fizike, informatike v shkole i vuze : mezhvuzovskij sbornik nauchno-metodicheskix rabot, otv. red. S. F. Miteneva [Modern problems and prospects of teaching mathematics, physics, computer science at school and university. Interuniversity collection of scientific and methodological works. Responsible editor S.F. Miteneva]. Vologda, 2018. Pp. 49–52. (In Russ.)
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.

References

1. Golan J. S. Semirings and their Applications. Dordrecht: Kluwer Academic Publishers, 1999. 38 p.
2. Vandiver H. S. Note on a simple type of algebra in which cancelation law of addition does not hold. Bull. Amer. Math. Soc., 1934, V. 40. Pp. 914–920.
3. Dedekind R. Uber die Theorie der ganzen algebraischen Zahlen ¨ Supplement XI to P.G. Lejeune Dirichlet: Vorlessungen Uber Zahlentheorie, 4 Anfl., Druck und Verlag, Braunschweig, 1894.
4. Hilbert D. Uber den Zahlbegriff. ¨ Jahresber. Deutsch. Math. Verein., 1899, V. 8. Pp. 180–184.
5. Hebisch U., Weinert H. J. Semirings: theory and applications in computer science. Series in Algebra. Vol. V. World Scientific, Singapore, 1998. 361 p.
6. Golan J. S. The theory of semirings with applications in mathemayics and theoretical computer science. Pitman monographs and syrveys in pure and applied mathematics, V. 54, 1992 (1991).
7. Glazek K. A Short Guide Through the Literature on Semirings. Preprint No. 39. University of Wroclaw, Math. Inst., Wroclaw, 1985.
8. Glazek K. A Short Guide to the Literature on Semirings and Their Applications in Mathematics and Computer Science. Technical University Press, 2002.
9. Maslyaev D. A., Chermnykh V. V. Skew Laurent polynomial semiring. Sibirskie elektronnye matematicheskie izvestiya [Siberian Electronic Mathematical News], 2020, V. 17. Pp. 521–533.
10. Vechtomov E. M. Vvedenie v polukoltsa: uchebnoe posobie [Introduction to semirings: A Tutorial], Kirov, Izd. Vyatskogo gospeduniversiteta, 2000. 44 p.
11. Lukin M. A. On universal congruence on semirings. Problemy sovremennogo matematicheskogo obrazovaniya v pedvuzah i shkolah Rossii: interaktivnye formy obucheniya matematike studentov i shkol’nikov. Materialy V Vserossiyskoy nauchno-metodicheskoy
    konferentsyi [Problems of Modern Mathematics Education in Pedagogical Universities and Schools of Russia: Interactive Forms of Teaching Mathematics to Students and Schoolchildren : Proceedings of the V All-Russian Scientific and Methodical Conference], Kirov, Izd. VyatGGU, 2012. Pp. 312–316.
12. Vechtomov E. M., Petrov A. A. Multiplicatively idempotent semirings. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2013, V. 18. No. 4. Pp. 41–70.
13. Vechtomov E. M., Cheraneva A. V. On the theory of semidivision rings). Uspehi matematicheskih nauk [Advances in Mathematical Sciences], 2008, V. 63. No. 2. Pp. 161–162.
14. Vechtomov E. M., Cheraneva A. V. Semifields and their properties. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2008, V. 14. No. 5. Pp. 3–54.
15. Polin S. V. Simple semisfields and semifields. Sibirskiy matematicheskiy zhurnal [Siberian Mathematical Journal], 1974, V. 15. No. 1. Pp. 90–101.
16. Chermnykh V. V. Funktsional’nye predstavleniya polukolets: monografiya [Functional representations of semirings: monography], Kirov, Izd. VyatGGU, 2010. 224 p.
17. Vechtomov E. M., Petrov A. A. Polukoltsa s idempotentnym umnozheniem: monografiya [Semirings with idempotent multiplication: monography], Kirov, OOO «Raduga-PRESS»,144 p.
18. Vechtomov E. M., Lukin M. A. Semirings which are the unions of a ring and a semifield. Uspehi matematicheskih nauk [Advances in Mathematical Sciences], 2008, V. 63. No. 6. Pp. 159–160.
19. Lukin M. A. Semiring joins of a ring and semifield. Izvestiya vuzov. Matematika [Proceedings of Higher Education Institutions. Mathematics], 2008. No. 12. Pp. 76–80.
20. Vechtomov E. M., Lubyagina E. N., Chermnykh V. V. Elementy teorii polukolets [Elements of semiring theory], Kirov, OOO «Raduga-PRESS», 2012. 228 p.
21. Vechtomov E. M., Starostina O. V. Structure of abelian regular positive semirings). Uspehi matematicheskih nauk [Advances in Mathematical Sciences], 2007. V. 62. No. 1. Pp. 199–200.
22. Vechtomov E. M., Starostina O. V. Generalized abelian regular positive semirings). Vestnik Syktyvkarskogo universiteta. Seriya Matematuka. Mehanika. Informatika [Bulletin of the Syktyvkar University. Series 1. Mathematics. Mechanics. Informatics], 2007, Vol.Pp. 3–16.
23. Chermnykh V. V., Mikhalev A. V., Vechtomov E. M. Abelianregular positive semirings. Journal of Mathematical Science [New York], 1999, V. 97. Pp. 4162–4176.
24. Vechtomov E. M. Annihilator characterizations of Boolean rings and Boolean lattices. Matematicheskie zametki [Mathematical Notes], 1993, V. 53. No. 2. Pp. 15–24.
25. Bogdalov I. F. Invertibility of the Hilbert basis theorem in the class of semirings. Problemy sovremennogo matematicheskogo obrazovaniya v pedvuzah i shkolah Rossii: Tezisy dokladov Mezhregional’noy nauchnoy konferentsyi [Problems of Modern Mathematics Education
    in Pedagogical Universities and Schools of Russia : Abstracts of the Interregional Scientific Conference], Kirov, Izd. Vyatskogo gospeduniversiteta, 1998. Pp. 171–172.
26. Il’in S. N. Regularity Criterion for Complete Matrix Semirings. Matematicheskie zametki [Mathematical Notes], 2001, V. 70. No. 3. Pp. 366–374.
27. Il’in S. N. On the applicability to semirings of two theorems from the theory of rings and modules. Matematicheskie zametki [Mathematical Notes], 2008, V. 83. No. 4. Pp. 563–574.
28. Il’in S. N. On the homological classification of semirings. Itogi nauki i tehniki. Sovremennaya matematika i ee prilozheniya. Tematicheskie obzory [Results of Science and Technology. Modern Mathematics and its Applications. Thematic reviews], 2018, V. 158. Pp. 3–22.
29. Dale L. Monic and monic free ideals in polynomial semirings. Proc. Amer. Math. Soc., 1976, V. 56. Pp. 45–50.
30. Babenko M. V., Chermnykh V. V. On skew polynomial semirings on Bezout semiring. Matematicheskie zametki [Mathematical Notes], 2022, V. 111.
31. Rao P. R. Lattice ordered semirings. Math. Sem. Notes, Kobe Univ., 1981, V. 9. Pp. 119–149.
32. Swamy K. L. N. Duallity residuated lattice ordered semigroups. Math. Ann., 1965, V. 159. Pp. 105–114.
33. Chermnykh O. V. On drl-semigroups and drl-semirings) Chebyshevskiy sbornik [Chebyshev collection], 2016, V. 17. No. 4. Pp. 167–179.
34. Burgess W. D., Stephenson W. Pierce sheaves of noncommutative rings. Comm. Algebra, 1976, V. 39. Pp. 512–526.
35. Grothendieck A., Dieudonne J. El´ements de G´eom´etrie ´ Alg´ebrique 1. I.H.E.S., Publ. Math. 4. — Paris, 1960.
36. Pierce R. S. Modules over commutative regular rings. Mem. Amer. Math. Soc., 1967, V. 70. Pp. 1–112.
37. Simmons H. Compact representations — the lattice theory of compact ringed spaces. J. Algebra, 1989, V. 126. Pp. 493–531.
38. Chermnykh V. V. Sheaf representations of semirings. Uspehi matematicheskih nauk [Advances in mathematical sciences], 1993, V. No. 5. Pp. 185–186.
39. Chermnykh V. V. Functional representations of semirings. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2012, V. 17. No. 3. Pp. 111–227.
40. Markov R. V., Chermnykh V. V. On Pierce stalks of semirings. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2014, V. 19. No. 2. Pp. 171–186.
41. Markov R. V., Chermnykh V. V. Semirings close to regular and their Pierce stalks) Trydy IMM UrO RAN [Proceedings of IMM UB RAS], 2015, V. 21. No. 3. Pp. 213–221.
42. Babenko M. V., Chermnykh V. V. Pierce stalks of semirings of skew polynomials. Trydy IMM UrO RAN [Proceedings of IMM UB RAS], 2021, V. 27. No. 4. Pp. 48–60.
43. Chermnykh V. V., Chermnykh O. V. Functional representations of lattice-ordered semirings. Sibirskie elektronnye matematicheskie izvestiya [Siberian Electronic Mathematical News], 2017, V. 145. Pp. 946–971.
44. Chermnykh O. V. Functional representations of lattice-ordered semirings. III. Sibirskie elektronnye matematicheskie izvestiya [Siberian Electronic Mathematical News], 2018, V. 15. Pp. 677–684.
45. Chermnykh V. V., Chermnykh O. V. Functional representations of lattice-ordered semirings. III. Trydy IMM UrO RAN [Proceedings of IMM UB RAS], 2020, V. 26. No. 3. Pp. 235–248.
46. Polin S. V. Minimal varieties of semirings. Matematicheskie zametki [Mathematical Notes], 1980, V. 27. No. 4. Pp. 527–537.
47. Pastijn F. Varieties Generated by Ordered Bands. II. Order., 2005, V. 22. Pp. 129−143.
48. Guterman A. E. Frobeniusovy endomorfizmy prostranstva matrits: dissertatsiya na soiskanie uchenoy stepeni doktora fiziko-matematicheskih nauk [Frobenius endomorphisms of the matrix space: dissertation for the degree of Doctor of Physics and Mathematics], M.: MSU, 2009. 321 p.
49. Shitov Ya. N. Lineynaya algebra nad polukoltsami: dissertatsiya na soiskanie uchenoy stepeni doktora fiziko-matematicheskih nauk [Linear algebra over semirings: dissertation for the degree of Doctor of Physics and Mathematics], M.: MSU, 2015. 302 p.
50. Krivulin N. K. On the solution of generalized linear vector equations in idempotent algebra. Vestnik Sankt-Peterburgskogo universiteta. Seriya 1 [Bulletin of Saint Petersburg University. Series 1], 2006. No.Pp. 23–36.
51. Krivulin N. K., Romanova E. Yu. Approximate factorization of positive matrices using tropical optimization methods. Vestnik SanktPeterburgskogo universiteta. Seriya 10 [Bulletin of Saint Petersburg University. Series 10], 2020, V. 16. No. 4. Pp. 357–374.
52. Vorob’ev N. N. Extreme algebra of positive matrices. Elektronische Informatiosverarbeitung und Kybernetik [Electronic information processing and cybernetics], 1967, V. 3. Pp. 39–71.
53. Joswig M. Essentials of Tropical Combinatorics. Graduate Studies in Mathematics. V. 219, 2021. 398 p.
54. Maslov V. P., Kolokol’tsov V. N. Idempotentnyi analiz i ego primenenie v optimal’nom upravlenii [Idempotent analysis and its application in optimal control], M.: Nauka, 1994.
55. Gondran M., Minoux M. Graphs, Dioids and Semirings. New Models and Algorithms. New York: Springer, 2008. 400 p.
56. Kolokoltsov V. N., Maslov V. P. Idempotent Analysis and its Applications. Mathematics and its Applications, V. 401, Dordrecht: Kluwer Academic Publishers, 1997.
57. Litvinov G. L., Maslov V. P., Shpiz G. B. Idempotent functional analysis: an algebraic approach. Matematicheskie zametki [Mathematical Notes], 2001, V. 69. No. 5. Pp. 758–797.
58. Gillman L., Jerison M. Rings of continuous functions. New York,300 p.
59. Varankina V. I., Vechtomov E. M., Semenova I. A. Semirings of continuous non-negative functions: divisibility, ideals, congruences. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 1998, V. 4. No. 2. Pp. 493–510.
60. Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V. Elementy funktsionalnoy algebry: monografiya. V 2 tomah [Elements of functional algebra: monography. In 2 volumes] [edited by Vechtomov], Kirov, OOO «Raduga-PRESS», 2016, V. 1, 384 p.; V. 2. 316 p.
61. Vechtomov E. M., Mikhalev A. V., Sidorov V. V. Semirings of continuous functions Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2016, V. 21. No. 2. Pp. 53– 131.
62. Vechtomov E. M., Chuprakov D. V. The principal kernels of semifields of continuous positive functions. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics],
    2008, V. 14. No. 4. Pp. 87–107.
63. Vechtomov E. M., Chuprakov D. V. Extension of congruences on semirings of continuous functions. Matematicheskie zametki [Mathematical Notes], 2009, V. 85. No. 6. Pp. 803–816.
64. Bestuzhev A. S., Vechtomov E. M. Cyclic semirings with commutative addition.Vestnik Syktyvkarskogo universiteta. Seriya Matematika. Mehanika. Informatika [Bulletin of the Syktyvkar University. Series 1. Mathematics. Mechanics. Informatics], 2015, V.Pp. 8–39.
65. Vechtomov E. M., Chuprakov D. V. Finite cyclic semirings with semilattice addition given by the two-generated ideal of natural numbers. Chebyshevskiy sbornik [Chebyshev collection], 2020, V. 21. No. 1. Pp. 82–100.
66. Vechtomov E. M., Orlova (Lubyagina) I. V. Cyclic semirings with idempotent noncommutative addition. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics],
    2012, V. 17. No. 1. Pp. 33–52.
67. Vechtomov E. M., Orlova I. V. Cyclic semirings with idempotent commutative addition. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2015, V. 20. No. 6. Pp. 17– 41.
68. Bestuzhev A. S., Vechtomov E. M., Orlova I.V. Structure of cyclic semirings. Sbornik materialov IX nauchnoy konferentsii EKOMOD-2016 “Matematicheskoe modelirovanie razvivayuscheysya
    ekonomiki, ekologii i tehnologii” [Proceedings of the IX Scientific Conference ECOMOD-2016 “Mathematical modeling of developing economy, ecology and technology”], Kirov: Izd. VyatGU, 2016. Pp. 21–30.
69. Vechtomov E. M., Petrov A. A. Multiplicatively idempotent semirings with three elements. Matematicheskiy vestnik Vyatskogo gosudarstvennogo universiteta [Mathematical Bulletin of Vyatka State University], 2021. No. 2. Pp. 13−23.
70. Zhao X., Ren M., Crvenkovic S., Shao Y., Dapic P. The varietygenerated by an ai-semiring of order three. Ural Mathematical Journal,2020, V. 6. No. 2. Pp. 117–132.

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.
2. Nikolai Ye. L. Trudy po mekhanike [Writings on mechanics]. Moscow, Gostekhizdat, 1955. 584 p.
3. Andryukova V., Tarasov V. Nonsmooth problem of stability for elastic rings. Abstracts of the International Conference “Constructive Nonsmooth Analysis and Related Topics” Dedicated to the Memory of Professor V.F. Demyanov. CNSA-2017. 22-27 may 2017, Part I. SaintPetersburg. Publisher: BBM. Pp. 213–218.
4. Birger I. A. Prochnost’. Ustoychivost’. Kolebaniya [Strength. Stability. Oscillations]. M.: Mashinostroenie, 1988. 831 p.

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.

References

1. Bosnic S., Papp I. The development of hybrid mobile applications with Apache Cordova. 24th Telecommunications Forum. 2016. Pp. 1−4.
2. Tomozei C. Assessment of the evolution in quality for XamarinAndroid Multimedia Applications. 19th International Conference on Informatics in Economy. Education, Research and Business
   Technologies. 2020. Pp. 47−52.
3. Melnikov V. A. Development Process of game engine core for 2D games and interfaces Sad Lion Engine. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, 4
   (33). Pp. 21–37.
4. Fisz K., Kopniak P., Galan D. A multi-criteria comparison of mobile applications built with the use of Android and Flutter Software Development Kits. Journal of Computer Sciences Institute. Vol. 19.Pp. 107−113.
5. Dabit N. React Native in action. Shelter Island: Manning Publishing. 320 p.
6. Java Native Interface Specification [Online]. Oracle. Available: https://docs.oracle.com/javase/7/docs/technotes/guides/jni/spec/ jniTOC.html (Accessed: 22.10.2020).
7. Rago S., Stevens W. Advanced programming in the UNIX environment, 3rd ed. Upper Saddle River, NJ, Boston, Indianopolis, San Francisco, New York, Toronto, Montreal, London, Munich, Paris, madrid, Capetown, Sydney, Tokyo, Singapore, Mexico City: AddisonWesley, 2013. 1032 p.
8. Corbet J., Kroah-Hartman G., McKellar J., Rubini A. Linux device drivers, 4th ed. Beijing, Cambridge, Farnham, Koln, Sebastopol, Taipei, Tokyo. 2017. 600 p.
9. Thornsby J. Android UI design. Birmingham: Packt Publishing. 2016. 356 p.
10. Anugerah M. A., Sekar G. S. Designing Android User Interface for University Mobile Library. International Conference on Computing, Engineering, and Design (ICCED). 2021. Pp. 224−229.
11. Neuburg M. Programming iOS 13: Dive Deep into Views, View Controllers, and Frameworks. Sebastopol: O’Reilly. 2020. 1208 p. New York: Oracle.
12. Nystrom R. Game programming patterns. San Bernardino: Genever Benning, 2018. 345 p.
13. Ginsburg D., Purnomo B. OpenGL ES 3.0 Programming Guide 2nd Edition. Upper Saddle River, NJ, Boston, Indianopolis, San Francisco, New York, Toronto, Montreal, London, Munich, Paris,
    madrid, Capetown, Sydney, Tokyo, Singapore, Mexico City: AddisonWesley, 2014. 560 p.
14. Sellers G. Vulkan Programming Guide. The Official Guide to Learning Vulkan. Boston, Columbus, Indianapolis, New York, San Francisco, Amsterdam, Cape Town Dubai, London, Madrid, Milan, Munich, Paris, Montreal, Toronto, Delhi, Mexico City San Paulo, Sydney, Hong
    Kong, Seoul, Singapore, Taipei, Tokyo: Addison-Wesley, 2017. 480 p.
15. Clayton J. Metal programming guide. Addison-Wesley. 2018. 352 p.
16. Stroustrup B. The C++ programming languege 4th edition. Uppder Saddle River, Boston, Indianopolis, San Francisco, New York, Toronto, Montral, London, Munich, Paris, Madrid, Capetown, Sydney, Tokyo, Singapore, Mexico city: Addison-Wesley. 2013. 1345 p.
17. Stroustrup B. Programming: Principles and Practice using C++. 2nd Edition. New Jearsey: Pearson Education. 2015. 1312 p.
18. Shieldt H. Java: The Complete Reference, Eleventh Edition 11th Edition. 2019. 1248 p.
    

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.
2. Preskill J. Kvantovaya informaciya i kvantovye vychisleniya [Quantum Information and Computation]. Izhevsk: RHD, 2008; 2001. Vol 1-2. 464+312 p.
3. Breuer H.-P., Petruccione F. Teoriya otkrytykh kvantovykh sistem [The theory of open quantum systems]. Izhevsk: RHD, 2010. 824 p.
4. In¨on¨u E., Wigner E. P. On the contraction of groups and their representations. Proc. Nat. Acad. Sci. USA. 1953. Vol. 39. Pp. 510–524.
5. Saletan E. J. Contraction of Lie groups. J. Math. Phys. Vol. 2. Pp. 1–21.
6. Gromov N.A. Kontraktsii klassicheskikh i kvantovykh grupp [Contractions of classical and quantum groups]. Moscow: FIZMATLIT, 2012. 318 p.
7. Ibort A., Man’ko V. I., Marmo G. et al. The quantumto-classical transition: contraction of associative products. Physica Scripta. 2016. Vol. 91. 045201. ArXiv:1603.01108 [quant-ph].
8. Alipour S., Chru´sci´nski D., Facchi P. et al. Dynamically algebra of observables in dissipative quantum systems. J. Phys. A: Math. Theor. 2017. Vol. 50. 065301.
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