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

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

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

**Abstract.** In the study of operations a significant place is occupied by problems, the formal model of which are antagonistic games. The classical methods of solving such games are based on the principle of “common knowledge”according to which the participants in a game have full information about possible solutions and their consequences. Studies are known in which information reflexivity of the participants of the game is allowed, i.e. their uncertainty in

assessing the situation requiring a decision is allowed. To formalize this uncertainty, it is proposed that the values of the elements of the payment matrix should be presented in the form of fuzzy numbers. The choice of the best solution is based on the conversion of fuzzy estimates of the consequences of possible solutions in the form of equivalent fuzzy sets with triangular membership functions.

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

**References**

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- Butnariu D. Fuzzy games: a description of the concept. Fuzzy Sets and System. 1978. 1. Pp. 181–192.
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V. 3. Issue 10. Pp. 341–345. 14 Чернов В. Г. - Verma Tina, Kumar Amit, Kacprzyk Janusz. A Novel Approach to the Solution of Matrix Games with Payoffs Expressed by Trapezoidal Intuitionistic Fuzzy Numbers. Journal of Automation, Mobile Robotics and Intelligent Systems. 2015. No 3. V. 9. Pp. 25–46.
- Dubois D., Prade H. Theoriedes Possibilites. Applications a la representation des conisisancesen in for antique. Masson, 1980. 288 p.
- Chernov V. G. Choosing a Solution Based on Fuzzy Game with Nature. Prikladnaya informatika [Journal of Applied Informatics]. V. 16. № 2(92). 2021. Pp. 131–142. (In Russ.)
- Voroncov Ya. A., Matveev M. G. Methods of parametrized comparison of fuzzy and trapezoidal numbers. Vestnik VGU, Seriya Sistemnyj analiz I informacionnye tekhnologii [Vestnik VSU. Series System analysis and information technologies]. 2014. No 2. Pp. 90–96. (In Russ.)
- Chernov V. G. Comparison of fuzzy number on the basis of construction linear order relation. Dinamika slozhnyh sistem – XXI vek [Dynamics of Complex Systems – XXI Century.]. 2018. No 2. Pp. 81–87. (In Russ.)

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

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

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

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

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

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

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

**References**

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

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

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

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

**Denis A. Maslyaev** – Komi republican academy of public service and administration, e-mail:

dmaslyaev@gmail.com

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

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

**References**

- Klevanskij N. N. Formation of the schedule of classes of higher educational institutions. Obrazovatel’nye resursy i tekhnologii [Educational resources and technologies]. 2015. No 1(9). Pp. 34–44.
- Chavez-Bosquez O., Hernandez-Torruco J., Hernandez-Ocana B., Canul-Reich J. Modeling and Solving a Latin American University Course Timetabling Problem Instance. Mathematics. 2020, Vol. 8(10), 1833 p.
- Gafarov E. R. Software product for drawing up educational schedules of higher education institutions. XII Vserossijskoe soveshchanie po problemam upravleniya VSPU-2014 (16-19 iyulya, g. Moskva) [XII All-Russian Meeting on Management Problems VSPU-2014 (July 16-19, Moscow)]. M.: Institut problem upravleniya im. V. A. Trapeznikov RAN, 2014. Pp. 8804–8809.
- Abuhaniya Amer Y. A. Modeli, algoritmy i programmnye sredstva obrabotki informacii i prinyatiya reshenij pri sostavlenii raspisaniya zanyatij na osnove evolyucionnyh metodov [Models, algorithms and software tools for information processing and decision-making when drawing up a class schedule based on evolutionary methods] Avtoreferat dissertacii na soiskanie uchenoj

stepeni kandidata tekhnicheskih nauk. Novocherkassk, 2016. 20 p. - Sidorin A. B., Likucheva L. V., Dvoryakin A. M. Methods of automation of scheduling classes Part 1. Classical methods). Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Proceedings of the Volgograd State Technical University]. 2009. No 12 (60). Pp. 116–120.
- Maslov M. G. Razrabotka modelej i algoritmov sostavleniya raspisanij v sistemah administrativno-organizacionnogo upravleniya [Development of models and algorithms for scheduling in administrative and organizational management systems] Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. M., 2004. 25 p.
- Sidorin A. B., Likucheva L. V., Dvoryakin A. M. Methods of automation of scheduling classes Part 2. Heuristic methods of optimization. Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Proceedings of the Volgograd State Technical University] 2009. No 12 (60). Pp. 120–123.
- Asvad Firas M. Modeli sostavleniya raspisaniya zanyatij na osnove geneticheskogo algoritma na primere vuza Iraka [Models of scheduling classes based on a genetic algorithm on the example of a university in Iraq]. Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. Voronezh, 2013. 16 p.
- Kabal’nov Y. S., SHekhtman L. I., Nizamova G. F., Zemchenkova N.A. Compositional genetic algorithm for scheduling training sessions. Vestnik Ufimskogo Gosudarstvennogo Aviacionnogo Universiteta [Bulletin of the Ufa State Aviation University]. 2006. No 2. Vol. 7. Pp. 99–109.
- Nizamova G. F. Matematicheskoe i programmnoe obespechenie sostavleniya raspisaniya uchebnyh zanyatij na osnove agregativnyh geneticheskih algoritmov [Mathematical and software for scheduling training sessions based on aggregate genetic algorithms]. Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. Ufa, 2006. 18 p.
- Skiena S. Algoritmy. Rukovodstvo po razrabotke [Algorithms. Development guide] BHV-Peterburg, 2014. 720 p.
- Matveev A. I. Algorithm for optimizing resource planning (on the example of the annealing method) Perspektivnye informacionnye tekhnologii (PIT 2018). Trudy mezhdunarodnoj nauchno-prakticheskoj konferencii. Pod redakciej S.A. Prohorova [Perspective Information Technologies (PIT 2018) : Proceedings of the International Scientific and Practical Conference / ed. by S. A. Prokhorov.] 2018. Pp. 1046–1059.
- Lopatin A. S. Method of annealing. Stohasticheskaya optimizacii v informatike [Stochastic Optimization in Computer Science]. 2005. Vol. 1. Pp. 133–149.
- Song T., Liu S., Tang X., Peng X., Chen M. An iterated search algorithm for the University Course Timetabling Problem. Applied Soft Computing, Vol. 68 (2018). Pp. 597–608.
- Podinovskij V. V. Idei i metody teorii vazhnosti kriteriev v mnogokriterial’nyh zadachah prinyatiya reshenij [Ideas and methods of the theory of criteria importance in multicriterial decision-making problems]. M.: Nauka,103 p.
- Silva J. D. L., Burke E. K., Petrovic S. An Introduction to Multiobjective Metaheuristics for Scheduling and Timetabling. Metaheuristics for multiobjective optimisation. Lecture notes in economics and mathematical systems, vol. 535, Pp. 91–129.
- Aziz N. L. A., Aizam N. A. H. A Brief Review on the Features of University Course Timetabling Problem. AIP Conference Proceedings, 2016. 020001 (2018).

**For citation: **Maslyaev D. A. Current state of the higher school timetabling problem. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 23−40.

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

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

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

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

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

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

**Keywords**: web configurator, computer assembly

**References**

- Grosso C., Trentin A., Forza C. Towards an understanding of how the capabilities deployed by a Web-based sales configurator can increase the benefits of possessing a mass-customized product. 16th International Configuration Workshop, CEUR Workshop Proceedings, 2014, Vol. 1220. Pp. 81–88.
- Sandrin E. Synergic effects of sales-configurator capabilities on consumerperceived benefits of mass-customized products. International Journal of Industrial Engineering and Management, 2017, Vol. 8, No. 3. Pp. 177–188.
- Streichsbier C., Blazek P., Faltin F., Fr¨uhwirt W. Are de-facto standards a useful guide for designing human-computer interaction processes? The case of user interface design for web based B2C product configurators. 42nd Hawaii International Conference on System Sciences, 2009. Pp. 1–7. DOI: 10.1109/HICSS.2009.80.
- Leclercq T., Davril J.-M., Cordy M., Heymans P. Beyond de-facto standards for designing human-computer interactions in configurators. CEUR Workshop Proceedings, 2016, vol. 1705. Pp. 40–43.
- Abbasi E.K., Hubaux A., Acher M., Boucher Q., Heymans P. The anatomy of a sales configurator: An empirical study of 111 cases. Lecture Notes in Computer Science, 2013, LNCS, vol. 7908, Pp. 162–177. DOI: 10.1007/978- 3-642-38709-8_11.
- Sandrin E., Trentin A., Grosso C., Forza C. Enhancing the consumerperceived benefits of a mass-customized product through its online sales configurator: An empirical examination. Industrial Management and Data System, 2017, vol. 117, no. 6. Pp. 1295–1315. DOI: 10.1108/IMDS-05-2016- 0185.
- Leclercq T., Cordy M., Dumas B., Heymans P. Representing repairs in configuration interfaces: A look at industrial practices. ACM IUI2018 Workshop on Explainable Smart Systems (ExSS), 2018, Available at:https://explainablesystems.comp.nus.edu.sg/2018/wpcontent/uploads/2018/02/exss_12_leclercq.pdf (accessed 01.03.2022).
- Leclercq T., Cordy M., Dumas B., Heymans P. On studying bad practices in configuration UIs. ACM IUI2018 Workshop on Web Intelligence and Interaction. Available at: http://ceur-ws.org/Vol-2068/wii1.pdf (accessed: 01.03.2022).
- Grosso C., Forza C., Trentin A. Support for the social dimension of shopping through web based sales configurators. 17th International Configuration Workshop, CEUR Workshop Proceedings, 2015, vol. 1453. Pp. 115–122.
- Grosso C., Forza C. Users’ Social-interaction Needs While Shopping via Online Sales Configurators. International Journal of Industrial Engineering and Management, 2019, vol. 10, no. 2. Pp. 139–154. DOI: 10.24867/IJIEM2019-2-235.
- Mahlam¨aki T., Storbacka K., Pylkk¨onen S., Ojala M. Adoption of digital sales force automation tools in supply chain: Customers’ acceptance of sales configurators. Industrial Marketing Management, 2020, vol. 91. Pp. 162–173. DOI: 10.1016/j.indmarman.2020.08.024.
- HardPrice – Sravnenie i dinamika cen na komplektuyushhie PK v internet magazinax [HardPrice – Comparison and dynamics of prices for PC components in online stores]. Available at: https://hardprice.ru/ (accessed: 01.03.2022). (In Russ.)
- Konfigurator PK – sobrat‘ komp‘yuter na zakaz. Sobrat‘ sistemny‘j blok v onlajn konfiguratore [PC configurator – to assemble a computer to order. Assemble the system unit in the online configurator]. Available at: https://www.citilink.ru/configurator/ (accessed 01.03.2022). (in Russ.)
- Sborka PK – DNS – internet-magazin cifrovoj i by‘tovoj texniki po dostupny‘m cenam [PC assembly – DNS – online store for digital and home appliances at affordable prices]. Available at: https://www.dns-shop.ru/configurator/ (accessed: 01.03.2022). (In Russ.)
- Sobrat‘ komp‘yuter onlajn s proverkoj sovmestimosti Konfigurator/sborka igrovogo PK [Assemble a computer online with a compatibility check Configurator/build a gaming PC]. Available at: https://www.ironbook.ru/constructor/ (accessed: 01.03.2022). (In Russ.)
- Shchukin N. Yu., Golchevskiy Yu. V. The logic of the software configurator at the stage of selecting compatible computer components // XXVIII godichnaya sessiya Uchenogo soveta SGU im. Pitirima Sorokina: Nacional‘naya konferenciya : sbornik statej [XXVIII annual session of the Academic Council of the Pitirim Sorokin Sykt. State Univ.: National conference: collection of articles: text. sci. electr. ed. Syktyvkar: Publishing House of Pitirim Sorokin Sykt. State Univ.] 2021, pp. 649–660. (In Russ.)

**For citation:** Golchevskiy Yu. V., Shchukin N. Yu. Design and Development of a Service Web Configurator for Computer Assembly. Bulletin of Syktyvkar University, Series 1: Mathematics.

Mechanics. Informatics, 2022, No. 1 (42), pp. 41−60. https://doi.org/10.34130/1992-2752_2022_1_41

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

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

**Vadim A. Melnikov** – Pitirim Sorokin Syktyvkar State University

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

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

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

**References**

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- Windmill E. Flutter in Action. Shelter Island: Manning, 2020. 368 p.
- Melnikov V. A. Development Process of game engine core for 2D games and interfaces Sad Lion Engine. Vestnik Syktyvkarskogo universiteta. Ser.1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, 4 (33), pp. 21–37. (In Russ.)
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- Lisovsky, K.Y. XML Applications Development in Scheme. Programming and Computer Software 28, 197–206 (2002). https://doi.org/10.1023/A:1016319000374

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

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

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

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

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

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

**References**

- The working program of the discipline «Elementary Mathematics» for the direction of training Pedagogical education (with two training profiles «Computer Science and Mathematics»), full-time education. Developer: L. V. Pavlova. Pskov State University, 2020. Available: https://pskgu.ru/eduprogram (accessed: 01.02.2022). (In Russ.)
- Sevostyanova S. A., Shumakova E. O., Martynova E. V. Rating system for assessing students’ knowledge in the study of the discipline «Introductory course of Mathematics». Vestnik Yuzhno-Uralskogo gosudarstvennogo gumanitarno-pedagogicheskogo universiteta [Bulletin of the

South Ural State Humanitarian Pedagogical University]. 2018. No. 8. Pp. 116–129. - Drobysheva I. V., Drobyshev Yu. A. The design model of the introductory course of mathematics. Matematicheskoe modelirovanie v ekonomike, upravlenii i obrazovanii : sbornik nauchny‘x statej po materialam III Mezhdunarodnoj nauchno-prakticheskoj konferencii [Mathematical modeling in economics, management and education. Collection of scientific articles based on the materials of the III International Scientific and Practical Conference]. 2017. Pp. 150–155. (In Russ.)
- Panfilova T. L. Some features of teaching elementary mathematics to students of pedagogical directions. Sovremennye problemy i perspektivy obucheniya matematike, fizike, informatike v shkole i vuze : mezhvuzovskij sbornik nauchno-metodicheskix rabot, otv. red. S. F. Miteneva [Modern problems and prospects of teaching mathematics, physics, computer science at school and university. Interuniversity collection of scientific and methodological works. Responsible editor S.F. Miteneva]. Vologda, 2018. Pp. 49–52. (In Russ.)
- The work program of the discipline «Introductory course of mathematics» for the direction of training Pedagogical education (with two training profiles «Computer Science and Mathematics»), full-time education. Developer: L. V. Pavlova. Pskov State University, 2020. Available: https://pskgu.ru/eduprogram (accessed 01.02.2022). (In Russ.)
- Bostanova M. M., Dzhaubaeva Z. K., Uzdenova M. B. Electronic textbook as a means of increasing the effectiveness of independent work of students in the conditions of distance learning in the study of the discipline «Elementary Mathematics». Sovremenny‘e problemy‘ matematicheskogo obrazovaniya : materialy‘ Mezhregional‘noj nauchno-prakticheskoj konferencii [Modern problems of mathematical education. Materials of the Interregional

scientific and practical conference]. 2020. Pp. 44–48. (In Russ.) - Kochegurnaya M. Yu. The use of distance learning in teaching the discipline «Elementarnaya matematika». [Information systems and technologies in modeling and management. Proceedings of the V International Scientific and Practical Conference. Editor-in-chief K. A. Makoveychuk.] 2020. Pp. 411–413.
- Popov N. I. On the effectiveness of using the model of learning technology in trigonometry in teaching mathematics students. Education and science. No. 9 (108). Pp. 138–153. (In Russ.)
- Stefanova G. P., Baigusheva I. A., Tovarnichenko L. V., Stepkina M. A. Formation of cognitive independence of first-year students in the study of elementary mathematics at the university. Sovremennye problemy nauki i obrazovaniya [Modern problems of science and education]. 2018. No. 4. Pp.(In Russ.)

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

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

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

**Sotnikova Olga Alexandrovna** – Pitirim Sorokin Syktyvkar State University

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

**Keywords**: Aslanov Ramiz

**For citation:** Sotnikova O. A. Aslanov Ramiz (on his 75th birthday). Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 90−94.

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