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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

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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

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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

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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

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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

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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

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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

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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

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

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

References

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

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

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

DOI: 10.34130/1992-2752_2021_3_83

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

Text

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

Keywords: Alexander Nikolaevich Tikhomirov

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

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

DOI: 10.34130/1992-2752_2021_2_04

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

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

Text

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

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

References

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

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

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

DOI: 10.34130/1992-2752_2021_2_13

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

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

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

Text

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

Keywords: competitive programming, teaching, biography.

References

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

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

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

DOI: 10.34130/1992-2752_2021_2_20

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

Text

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

Keywords: Caputo derivative, control system, reachability set.

References

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

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

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

DOI: 10.34130/1992-2752_2021_2_27

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

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

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

Text

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

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

References

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

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

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

DOI: 10.34130/1992-2752_2021_2_44

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

Text

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

Keywords: shock wave, defeat, liquefied gas.

References

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

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

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

DOI: 10.34130/1992-2752_2021_2_58

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

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

Text

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

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

References

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

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

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

DOI: 10.34130/1992-2752_2021_2_78

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

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

Text

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

Keywords: shell, droplet form, reservoir.

References

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

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

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

DOI: 10.34130/1992-2752_2021_2_85

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

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

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

Text

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

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

References

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

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

Full text

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

DOI: 10.34130/1992-2752_2021_1_04

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

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

Text

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

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

References

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

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

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

DOI: 10.34130/1992-2752_2021_1_13

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

Text

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

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

References

1. Gakhov F. D. Krayevyye zadachi (Boundary problems), 3rd ed., Moscow: Nauka, 1977, 640 p.
2. Aksent’ev L. A. Svvaz’ vneshnev obratnov krayevoy zadachi s vnutrennim radiusom oblasti (Connection of the outer inverse boundary value problem with the inner radius of the domain), Izv. universities. Mathematics, 1984, no. 2, pp. 3-11.
3. Tumashev G. G., Nuzhin M. T. Obratnyye krayevyye zadachi i ikh prilozheniya (Inverse boundary value problems and their applications), 2nd ed., Kazan: Kazan, un-t, 1965, 333 p.
   I. Aksent’ev L. A., Kazantsev A. V., Popov N. I. Ekstremal’nyve zadachi diva ploshchadev pri konformnom otobrazhenii i ikh primenenive (Extremal problems for areas under conformal mapping and their application), Izv. universities. Mathematics, 1995, no. 6, pp. 3-15.
4. Popov N.I. Ob odnom uslovii podchinennosti pri lokalizatsii maksimuma konformnogo radiusa (On one condition of subordination in the localization of the maximum of the conformal radius), Trudy Matematicheskogo tsentr im. N. I. Lobachevsky, Kazan: Kazan, unt, 2013, V. 46, Theory of functions, its applications and related issues, pp. 368-369.
5. Goluzin G. M. Geometricheskaya teoriya funktsiy kompleksnogo peremennogo (Geometric theory of functions of a complex variable), 2nd ed., Moscow: Nauka, 1966, 628 p.
6. Hayman W., Kennedy P. Subgarmonicheskiye funktsii (Subharmonic functions), Moscow: Mir, 1980, 304 p.
7. London D. On the zeros of the solutions of w”(z) + p(z)w(z) = 0, Pacif. J. Math., 1962, V. 12, no. 3, pp. 979-991.

For citation: Popov N. I. Using the area estimate for localizing the maximum of the conformal radius, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 13-18.

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

DOI: 10.34130/1992-2752_2021_1_19

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

Text

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

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

References

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

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

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

DOI: 10.34130/1992-2752_2021_1_27

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

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

Text

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

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

References

1. Marca D. A., McGowan С. L. Metodologiya strukturnogo analiza i proyektirovaniya SADT (Structured Analysis and Design Technique), Moscow, 1993, 240 p.
2. Tel’nova О. P., Shumilov I. Kh. Middle-Upper Devonian Terrigenous Rocks of the Tsil’ma River Basin and Their Palynological Characteristics, Stratigraphy and Geological Correlation, 2019, Vol. 27, No. 1, pp. 27-50. DOI: https://doi.org/10.31857/S0869-592X27131- 56.
3. Tel’nova О. P., Marshall J. E. A. Devonian Spores of Krvshtofovichia africani Nikitin (Tracheophvta): Morphology and Ultrastructure, Paleontological Journal, 2018, Vol. 52, No. 3, pp. 342-349. (c) Pleiades Publishing, Ltd., 2018, published in Paleontologicheskii Zhurnal, 2018, No. 3, pp. 119-124. ISSN 0031-0301, DOI: 10.1134/S0031030118030152.
4. Zhang Y., Fountain D. W., Hodgson R. M., Flenley J. R., Gunetileke S. Towards automation of palynology: Pollen recognition using Gabor transforms and digital moments, J. Quat., 2004, Sci. 19, pp. 763-768.
5. Zhang Wang-Xiang, Zhao Ming-Ming, Fan Jun-Jun, Zhou Ting, Chen Yong-Xia, & Cao Fu-Liang. Study on relationship between pollen exine ornamentation pattern and germplasm evolution in flowering crabapple., 2017, Sci. Rep. 7, 39759.
6. Geus A. R. d., Barcelos C. A. Z., Batista M. A. and Silva S. F. d. Large-scale Pollen Recognition with Deep Learning. 27­ th European Signal Processing Conferencen (EUSIPCO), A Coruna, Spain, 2019, pp. 1-5. DOI: 10.23919/EUSIPC0.2019.8902735.
7. C. Romero Ingrid, Kong Shu, C. Fowlkes Charless, Jaramillo Carlos, A. Urban Michael, Oboh Ikuenobe Francisca , D’Apolito Carlos, W. Punyasena Surangi. Improving the taxonomy of fossil pollen using convolutional neural networks and superresolution microscopy. Proceedings of the National Academy of Sciences Nov 2020, 117 (45), 28496-28505. DOI: 10.1073/pnas. 2007324117.
8. Huang G., Liu Z., Van Der Maaten L., Weinberger K. Q. Densely connected convolutional networks. In: Conference on Computer Vision and Pattern Recognition. Vol. 1, pp. 4700-4708 (2017).
9. Do Chuong B., Ng Andrew Y. Transfer learning for text classification. Neural Information Processing Systems Foundation, NIPS. 2005. Available at:https://proceedings.neurips.cc/paper/2005/ file/ bf2fb7dl825aldf3ca308ad0bf48591e-Paper.pdf (accessed:12.10.2020) .
10. Keras: the Python deep learning API [Electronic resource] / Keras official site. Available at: https:// keras.io (accessed: 12.10.2020).
11. Glubokoye obucheniye: raspoznavaniye izobrazheniy s pomoshch’vu svertochnvkh setev (Deep learning: image recongition with convolutional neural networks) [Electronic resource] / Wunder Fund company blog, Algorithms, machine learning. Available at: https://habr.com/ru/company/wunderfund/blog/314872/ (accessed: 12.10.2020).
12. Gal Yarin, Ghahramani Zoubin. Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning Proceedings of the 33-rd International Conference on Machine Learning, New York, NY, USA, 2016. JMLR: W&CP. Vol. 48. http://proceedings.mlr.press/v48/gal16.pdf.
13. The Keras Blog [Electronic resource] / Available at: https://blog.keras.io/building-powerful-image-classification-models-using-verv-littledata.html (accessed: 12.10.2020).
14. Sevillano V., Aznarte J. L. Improving classification of pollen grain images of the POLEN23E dataset through three different applications of deep learning convolutional neural networks. PLoS ONE 13(9): e0201807. DOI: https://doi.org/10.1371/journal.pone.0201807. 2018.

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

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

DOI: 10.34130/1992-2752_2021_1_43

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

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

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

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

Text

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

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

References

1. GOST R 34.10-2012 Information technology. Cryptographic information protection. Processes for generating and verifying electronic digital signature, Available at:http://docs.cntd.ru/document/gost-r34-10-2012 (accessed: 09.01.2021).
2. Raspberry Pi 3 Model A+. Available at: https://www.raspberrypi.org/ products/raspberry-pi-3-model-a-plus/ (accessed: 09.01.2021).
3. Python bindings for the Qt cross platform application toolkit, Available at: https://pypi.org/project/PyQt5/ (accessed: 09.01.2021).
4. Pillow Library Documentation, Available at: https://pillow.readthedocs. io eti stable (accessed: 09.01.2021).
5. A high-performance open source universal RPC framework, Available at: https://grpc.io (accessed: 09.01.2021).
6. Raspberry Pi 4 vs Pi 3 – What are the differences? Available at: https://cnx-software.ru/2019/06/25/raspberrv-pi-4-vs-pi-3-v-chemrazlichiva/ (accessed: 09.01.2021).

For citation: Gertner D. A., Leontiev D. 0., Nosov L. S., Shuchalin D. S. Hardware and software complex for ensuring information security when using electronic signatures, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 43-55.

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

DOI: 10.34130/1992-2752_2021_1_56

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

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

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

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

Text

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

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

References

1. Mitchell R. Web Scraping with Python, Sebastopol: O’Reilly Media, Inc., 2018, 306 p.
2. Openweathermap Service. Available at: https://openweathermap.org/ api (accessed: 11.01.2021).
3. Kotelina N. O., Arsenyev V. V., Solovyev I. A. Poisk korrelvatsiv mezhdu inkrementom i dekrementom prodolzhitel’nosti zhizni i chislo vzaimodevstviv gena v kletke konkretnogo organizma (Search for correlations between the increment and decrement of life span and
   the number of gene interactions in the cell of a particular organism), Mathematical modeling and information technologies: IV all-Russian scientific conference with international participation (12-14 November 2020, Syktyvkar): collection of materials, Executive editor A. V. Yermolenko, Syktyvkar: Publishing house of SSU Pitirima Sorokina, 2020, pp. 42.
4. Babenko V., Golchevskiy Yu., Yermolenko A. The strategy of development of educational programs connected with IT in the regional educational institutions, DEFIN ’20: Proceedings of the III International Scientific and Practical Conference, 2020, No. 38, pp. 1-4.
5. 30+ parserov diva sbora dannvkh s lvubogo savta (30+ parsers to collect data from any site), Available at: https://habr.com/ ru/companv/click/blog/494020/ (accessed: 11.01.2021).
6. Gabor L. H. Website Scraping with Python, Library of Congress Control Number: 2018957273, 235 p.
7. Website of the Central Bank of the Russian Federation (Bank of Russia), Available at: https://cbr.ru/ (accessed: 11.01.2021).
8. Gruzdev A., Heidt M. Izuchayem pandas. Vysokoproizvoditel’naya obrabotka i analiz dannykh v Python (Exploring pandas. High-performance data processing and analysis in Python), Moscow: DMK Press, 2019, 684 p.
9. COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University, Available at: https://github.com/CSSEGISandData/COVID-19 (accessed:11.01.2021).
10. AnvChart. Available at: https://www.anychart.com/ru/ (accessed:11.01.2021).
11. Golchevskiy Yu. V., Vinogradov I. M. Opvt razrabotki Internetservisa raspisaniva uchebnvkh zanyatiy (Schedule Internet-service developing experience), Informatization of education and science, 2016, No. 1, pp. 16-25.
12. Golchevskiy Yu. V., Severin P. A. Analiz dinamiki obnaruzheniva uvazvimostev populvarnykh sistem upravleniva kontentom (Dynamics of common content management systems vulnerability detection analysis), Information security issues, 2013, 4 (102), pp. 58-66.
13. Golchevskiy Yu. V., Kuznetsov D. I. Avtomatizatsiya mekhanizmov poiska informatsii na osnove otkrytykh istochnikov v seti Internet (Information search in open sources on the internet technique automation), Information and security, 2017, Vol. 20, No. 3 (4), pp. 414-417.
14. Ushakov D. A. Razrabotka programmnogo obespecheniva diva proverki ssvlok na elektronnyve izdaniya v rabochikh programmakh distsiplin (Development of software for checking links to electronic publications in the work programs of disciplines), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 2 (35), pp. 49-58.
15. Kotelina N. O., Matviyuchuk B. R., Solovyev I. A. Rekonstruktsiva grafov vzaimodeystviya genov i ikh prioritizatsiya na osnovanii dostupnvkh baz dannvkh (Reconstruction of gene interaction graphs and their prioritization based on available databases), Mathematical modeling and information technologies: IV all-Russian scientific conference with international participation (12-14 November 2020, Syktyvkar): collection of materials, Executive editor A. V. Yermolenko, Syktyvkar: Publishing house of SSU Pitirima Sorokina, 2020, pp. 44.
16. Dokumentatsiva Pandas (Pandas documentation), Date: Feb 09, 2021 Version: 1.2.2. Available at: https://pandas.pydata.org/pandasdocs/stable/index.html (accessed: 11.01.2021).
17. Dokumentatsiva Beautiful Soup (Beautiful Soup 4.9.0 documentation), Available at: https://www.crummy.com/software/BeautifulSoup/bs4/ doc/ (accessed: 11.01.2021).
18. Dokumentatsiva Seaborn (Seaborn 0.11.1 documentation), seaborn. pydata.org. Available at: https://seaborn.pydata.org/generated/ seaborn.heatmap.html (accessed: 11.01.2021).

For citation: Yermolenko А. V., Kotelina N. О., Startseva Е. N., Yurkina M. N. On the demand for data parsing training for web developers, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 56-69.

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

DOI: 10.34130/1992-2752_2021_1_70

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

Text

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

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

References

1. Kniga pamyati Sankt-Peterburgskogo (Leningradskogo) universiteta (The book of Memory of St.-Petersburg (Leningrad) university), St.Petersburg: Izd-vo SPbGU, 1995, V. 1, 352 p.
2. Odyniec W. P. О leningradskih matematikah, pogibshih v 1941-1944 godah (On some Leningrad — based Mathematicians perished in 1941-1944), Syktyvkar: Izd-vo SGU im. Pitirima Sorokina, 2020, 122 p.
3. Nauka i nauchnye rabotniki 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. Hand book / Compiled under the direction of S. T. Oldenburg), Leningrad: Izd-vo AN SSSR, 1934, 723 p.
4. Blokada 1941-1944- Kniga pamyati. Leningrad. K-K (Klopin-Konstantinov) (The blockade 1941-1944. The book of Memory, Leningrad),
   Vol. 14, St.Petersburg: Selesta, 2004, 717 p.
5. Matematika v SSSR za sorok let. Biobibliografiya (The URSS Mathematics for forty years: 1917-1957. Biobibliography), Moscow: Fizmatlit, 1959, Vol. 2, 819 p.
6. Sbornik materialov dlya shkolnyh matematicheskih kruzhkov (temy i zadachi) /Pod Red. G. M. Fichtenholz, 0. K. Zhitomirsky, V. A. Krechmar i V. A. Tartakovsky (The collection of materials for the school mathematical study group / subjects and problems / Under the direction of G. M. Fichtenholz, О. K. Zhitomirsky, V. A. Krechmar and V. A. Tartakovsky), Leningrad: LENGORONO, 1941, 72 p.
7. Trudy 1-go Vsesovuznogo s’ezda matematikov (Kharkov 1930) (Proceedings 1-th All Union Congress of Mathematicians (Kharkov 1930)). Moscow-Leningrad: ONTI NKTP SSSR, Glavn. Red. obschtchetehn. lit-ry i nomograhi, 1936. 372 p.
8. Trudy 2-go Vsesoyuznogo s’ezda matematikov (Leningrad 2f-30 Iyunya 1934), T. 2, Sekcionnye doklady (Proceedings of the 1th. All Union Congress of Mathematicians (Leningrad, 24-30 June 1934), Vol. 2, Section-Reports), Leningrad, Moscow: Izd-vo AN SSSR, 1936, 467 p.
9. Khudekov N. N. Ob odnom formalnom svovstve iterirovannvh funkcvi (On one formal feature of iterated functions), Uchenye zapiski universiteta, Ser. matem, 6, 1939, p. 115-118.
10. Khudekov N. N. О tipah obschtchego raspolozheniva n + 2 tochek v Rn (Upon types of the general placement of n + 2 points in Rn) Matematichesky sbornik, Vol. 9, No. 2, 1941, p. 249-276.
11. Nikolskii S. M. Vospominaniya (Memoirs), Moscow: MIAN, 2003, 160 p.
12. Trudy Vserossiyskogo s’ezda matematikov v Moskve (27 aprelya — 4 maya 1927), Pod red. prof. I. I. Privalova) (Proceedings of the All Russian Congress of Mathematicians in Moscow (27 April — 4 May 1927), Under the direction of prof. I. I. Privalov ), Moscow-Leningrad:
    Glavnauka, 1928, 280 p.
13. Janczewski S. Oscillation theorem for the differential boundary value problem of the fourth order, Ann. of Math., 29, 1927-1928, pp. 521-542.

I Andrykova V. Yu., Tarasov V. N. On the stability of rod with one-sided restrictions on the moving

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

I To the 25th anniversary of the MMIK department

Text

II Belyaeva N. A. Internal stresses symmetric products in their formation based nonzero critical depth conversion

Text

III Belyaeva N. A., Pryanishnikova E. A. Thr averaging method in the problem of mathematical modeling of composite extrusion

Text

IV Belyayev Yu. N. Symmetric polynomias in the calculation of the matrix exponential

Text

V Mikhailovskii E. I. The half century with the mechanics of shells (Part II – the nonlinear theory)

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VI Nikitenkov V. L., Kholopov A. A. Stability of a flexible core in elastic enviroment

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VII Grytczuk A. An effective algoritm to peivate-key in the RSA cryptosystem

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VIII Markov R. V., Chermnykh V. V. Pierce chains for semirings

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IX Mekler A. A. On Marcinkiewicz Modulars on [0, 1] and [0, ∞) – II

Text

X Orlova I. V. About finite cyclic semirings with nonidempotent non-commutative addition

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XI Martynov V. A., Mironov V. V. The problem of the optimization of the standart sorting through technology MPI

Text

I A word about Mikhailovsky Evgeny Ilyich

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II Prof. EI Mikhailovsky from prof. V. F. Demyanova

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III Mikhailovskii E. I. Mechanics of shells

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IV Belyaeva N. A., Pryanishnikova E. A. Mathematical modeling in the extrusion

Text

V Yermolenko A. V. On analitical solution of the contact problem

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VI Maloxemov V. N. On the fortieth anniversary of MDM-method

Text

VII Tarasov V. N., Andryukova V. Yu. On stability behavior of a toroidal shell with a one-sided reinforcement

Text

VIII Vechtomov E. M., Lubiagina E. N. Semirings of sc-functions

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IX Golovneva E. V. A class of matrices with diagonall domination

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X Grytczuk A. Ankeny, Artin and Chowla conjecture for even generators

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XI Mekler A. A. On Marcinkiewicz Modulars on [0, 1] and [0,∞)

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XII Mironov V. V., Mayburov A. S. The method of nonlinear integral equations in the problem of bending of a closed cylindrical shell with rigidly clamped edges

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XIII Nikitenkov V. L., Jidkova O. A., Shekhurdina E. S. The boundaries of finding the critical force in the environment multimoduls

Text

XIV Popova N. K., Ogirchyk T. A. 3D animation and simulation of an object with Autodesk 3ds Max 2009

Text

XV Odynec W. P. Returning to H. Kummer

Text

XVI Poroshkina A.A., Poroshkin A.G. Three counterexamples in analysis

Text

I Luca F., Odyniec W.P. The characterisation of Van Kampmen-Flores complexes by means of system of diopantine equations

Text

II Poroshkin A. G. On the problem of order continuity of Choquet functional

Text

III Andryukova V. Yu., Tarasov V. N. Some problems of stability of elastic system

Text

IV Antonova N. A. Dynamics of two demensional pulse-width modulated control system

Text

V Belyaeva N. A., Gorst D. L., Khudaev S. I. Cuat nonuniform flow of the structured liquid

Text

VI Golovach P. A. L(2,1)-coloring of precolored cacti

Text

VII Mikhailovskii E. I., Ermolenko A. V., Mironov V. V. Elements of the applied tensor analysis in the deformed bodies

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VIII Mikhailovskii E. I., Nilitenkov V. L., Chernykh K. F. On some aspects of the account of transversal deformations in the theory of shells and plates

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IX Pevnyi A. B. Multiresolution analysis in the space of square summable discrete signals

Text

X Poleshikov S. M., Kholopov A. A. The problem of optimal positions for a triple of four-dimensional orts

Text

XI Kholmogorov D. V. Supercritical behavior of a substantianed plate

Text

XII Khudyaev S. I. Symmetrical flaming on phase transform conditions

Text

XIII Chernykh K. F. On anisotropic nonlinear elasticity

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XIV Mikhailovskii E. I., Osipova O. P. About one a form of dynamic equilibrium of compressed part for drill column

Text

XV Mikhailovskii E. I., Tulubenskaya E. V. The influence of transversal deformation on the frequency spectrum of round plate

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XVI Somorodnitski A. A., Kotelina N. O. Systems of generators in measure spaces

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XVII Somorodnitski A. A., Muravjev A. A. Kakutani-Oxtoby theorem in the non-separable

Text

XVIII Tarasov V. N., Loginov I. N. The influence of boundary conditions to lamina’s stability with rigid constraints on displacement

Text

XIX Kholopov A. A., Stenina N. A. A continuous model of equipment replacing problem

Text

XX Zvonilov V. I. Rigid isotopy classificatin of real algebraic curves of bidegree (4,3) on a hyperboloid

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I Bazhenov I. I. Atoms of set families and of vectors measures

Text

II Poroshkin A. A., Poroshkin A. G. On the topology generated by the collection of quasi-norms

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III Poroshkin A. A., Shergin Yu. V. On the Choquet functional and one its application in measure theory

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IV Timofeev A. Y., Cyvunina T. E. The problem of Ricaman-Hilbert for the generalized Cauchy-Riemann system with a singularity

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V Tikhomirov A. N. On the Central Limit Theorem

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VI Kholopova M. A. Generalized Caushy problem for the American Put option cost

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VII Yurchenko V. A. Limit theorems for wavelet-statistics

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VIII Antonova N. A. T-periodic models in linear integral pulse-width modulated control system

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IX Belyaeva N. A., Parshukova N. N. A thermoviscoelastic model of a spherical product hardering

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X Colovach P. A., Fomin F. V. Search and node search number of dual graphs

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XI Zheludev V. A., Pevnyi A. B. Lifting schemes for wavelet transform of discrete signals

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XII Karmanov O. G. Group analysis and invariant solutions of Carman equations

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XIII Mikhailovskii E. I., Ermolenko A. V. On the question of soft-flexible shells bending

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XIV Nikitenov V. L. Rarefied matrixes in problems of shell theory

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XV Khudyaev S. I., Koynova L. V. Approximate solution of the equation of V. A. Ambartsumyan

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XVI Afanasyev A.P., Gaverdovskiy V.S., Kuzivanova N.S.Automated geographic information system of etymologized geographical names of the Komi Republic

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XVII Gaverdovskiy V.S., Gerasimov E.P. Objective-oriented software package for developing applications in the environment of GIS technologies

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XVIII Ermakov A.A., Prokhorov V.N., Stepanenko V.I.Automated system of cadastres of natural resources of the Komi Republic

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XIX Polshvedkin R.V., Serov A.V., Stepanenko V.I., Prokhorov V.N., Gerasimov E.P., Popova O.I.Preparation for the reception and use of space information by means of GIS technologies in the forestry of the Republic Komi

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XX Serov A.V. Object identifier systems and work with them

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XXI Serov A.V. Review of the possibilities of using three-dimensional elevation models for solving various applied problems

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XXII Ezovskih V. E. Fast algorithm for transformation of lattices

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XXIII Sheyin A. A., Milnikov A. V. Optimal parametrs for samples processing

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XXIV Vityazeva V.A.Glare of informatization

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XXV Alexander Grigorievich Poroshkin (on the occasion of his seventieth birthday)

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XXVI Alexander Alekseevich Vasiliev (on the occasion of his fiftieth birthday)

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XXVII Tarasov Vladimir Nikolaevich (on the occasion of his fiftieth birthday)

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I Bazhenov I. I. The property of nonatomicity under some constractions of nonatomic vector measures

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II Bobkov S. G. Remarks on Gromov-Miliman’s inequality

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III Ekisheva S. V. The Bahadir representation of sample quantile for sociatedstochastic sequence

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IV Zhubr A. V. The bordism groups of spin-maps and their application to the problem of classification of 6-manifolds

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V Zvonilov V. I.Rigid isotopy classification of real algebraic curves of bidigree (4,3) on a hyperboloid

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VI Karmanov O. G. Group analysis of Durbreil-Jacotin’s equations

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VII Lovyagin Y. N. About one class of the Boolean algebras

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VIII Lovyagin Y. N., Matveeva O. P. Classification of the Boolean algebras with sufficient number (o)-continuous kwasimeasures

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IX Samorodnitski A. A. Some questions of Lebesgue-Rohlin spaces theory

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X Antonova N. A. Dynamic of one dimentional pulse-width modulated control systems

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XI Golovach P. A. Invariants of graphs defined through optimal numbering of vertexes and the operation of join of graphs

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XII Zheludev V. A., Pevnyi A. B. On the cardinal interpolation by discrete splines

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XIII Kasev D. W., Khudyaev S. I. Analysis of spontaneous ignition conditions for cylinder with thermal insulated hole

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XIV Mikhailovskii E. I., Badolkin K. V., Ermolenko A. V. The plane plate bending theory of Karman’s type without Kirchhoff’s hypothesis

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XV Mikhailovskii E. I., Ermolenko A. V. Refiniment of nonlinear quasi Kirhhoffian K. Chernykh’s theory of shells

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XVI Poleshchikov S. M. The regularization of motion equations of fivedimentional Kepler problem

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XVII Tarasov V. N. Stability of hingle-fixed lamina with one-sided constrains on displacement

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XVIII Ezovskih V. E. Lowering the degree of Bezier curves

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XIX Student scientific conference in memory of F. A. Babushkin

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XX Poet and scientist: he worked both in poetry and in mathematics (for the 90th birthday of Professor N.A.Frolov)

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XXI Report at the plenary session of the scientific conference of graduate students and students dedicated to N.A.Frolov

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XXII Vladimir Dmitrievich Yakovlev (on his fiftieth birthday)

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