I. SOME SUBGROUPS OF THE BARYCENTRIC GROUP
https://doi.org/10.34130/1992-2752_2025_1_4
Marina A. Stepanova – The Herzen State Pedagogical University of Russia, ratkebug@yandex.ru
Abstract. By fixing the basic simplex in an affine space, one can introduce a barycentric coordinate system that assigns to each point an ordered set of numbers whose sum is equal to one. The transition matrices from one barycentric coordinate system to another barycentric coordinate system are called barycentric and form the barycentric group (a barycentric matrix is a nondegenerate square matrix, the sum of the elements in each column of which is equal to one).
Keywords: affine space, affine transformation, barycentric coordinate system, basic simplex, barycentric matrix.
References
- M¨obius A. F. Der barycentrishe Calc¨ul: ein neues H¨ulfsmittel zur analytischen Behandlung der Geometrie. Leipzig: J. A. Barth, 1827. XXIV. 454 p.
- Berg´e M. Geometriya : per. s francz. [Geometry : translation from French]. Moscow: Mir, 1984. Vol. 1. 560 p. (In Russ.)
- Kostrikin A. I., Manin A. I. Linejnaya algebra i geometriya. 2-e izd. [Linear Algebra and Geometry. 2 ed.]. Moscow: Nauka. Main editorial office of Phys.-Math. Lit. 1986. 304 p. (In Russ.)
- Stepanova M. A. Application of Barycentric Point Combinations in the Theory of Convex Polyhedra. Metodika prepodavaniya v sovremennoy shkole: aktual’nyye problemy i innovatsionnyye resheniya : materialy II Rossiysko-uzbekskoy nauchno-prakticheskoy konferentsii, Tashkent, 15–16 noyabrya 2024 goda [Teaching methods in a modern school: current problems and innovative solutions : materials of the II Russian-Uzbek scientific and practical conference, Tashkent, November 15–16, 2024]. Herzen State Pedagogical University. 2024. Pp. 263–268. (In Russ.)
- Balk M. B., Boltyansky V. G. Geometriya mass [Geometry of masses]. Moscow: Nauka. Main editorial office of Phys.-Math. Lit. 1987. 160 p. (Library “Kvant”. Issue 61). (In Russ.)
- Ponarin Y. P. E‘lementarnaya geometriya. Stereometriya. 3-e izd. [Elementary geometry. Stereometry. 3 ed.]. Moscow: MCNMO, 2015. Vol. 2. 256 p. (In Russ.)
- Ponarin Y. P. E‘lementarnaya geometriya: Treugol‘niki i tetrae‘dry‘ [Elementary Geometry: Triangles and tetrahedrons]. Moscow: MCNMO, 2009. Vol. 3. 191 p. (In Russ.)
- Stepanova M. A. Barycentric coordinates on a plane. Matematika dlya shkol‘nikov [Mathematics for Schoolchildren]. 2024. No 4. Pp. 8–(In Russ.)
- Ponarin Y. P. Basic metric problems of planimetry in barycentric coordinates. Matematicheskij vestnik pedvuzov Volgo-Vyatskogo regiona [Mathematical Bulletin of Pedagogical Universities of the Volga-Vyatka Region]. 2002. Vol. 4. Pp. 114–132. (In Russ.)
- Ponarin Y. P. The method of barycentric coordinates in metric problems of stereometry. Matematicheskij vestnik pedvuzov VolgoVyatskogo regiona [Mathematical Bulletin of Pedagogical Universities of the Volga-Vyatka Region]. 2004. Vol. 6. Pp. 189–200. (In Russ.)
- Stepanova M. A. Barycentric coordinate system. Barycentric group. Sovremennyye problemy matematiki i matematicheskogo obrazovaniya: Gertsenovskiye chteniya, 77 : sbornik nauchnykh trudov Mezhdunarodnoy nauchnoy konferentsii, Sankt-Peterburg, 16–18 aprelya 2024 g. [Modern problems of mathematics and mathematical education: Herzen readings, 77: collection of scientific papers of the International scientific conference, St. Petersburg, April 16–18, 2024]. A. I. Herzen State Pedagogical University. 2024. Pp. 356–360. (In Russ.)
- Dubrovin B. A., Novikov S. P., Fomenko A. T. Sovremennaya geometriya. Metody‘ i prilozheniya. Geometriya poverxnostej, grupp preobrazovanij i polej. 6-e izd. [Modern Geometry. Methods and Applications. Geometry of surfaces, groups of transformations, and fields. 6 ed.]. Мoscow: URSS, 2013. Vol. 1. 335 p. (In Russ.)
For citation: Stepanova M. A. Some subgroups of the barycentric group. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2025, no 1 (54), pp. 4−17. (In Russ.) https://doi.org/10.34130/1992-2752_2025_1_4

II. CAPTURING COORDINATED EVADERS IN A NONSTATIONARY SIMPLE PURSUIT PROBLEM WITH PHASE RESTRICTIONS
https://doi.org/10.34130/1992-2752_2025_1_18
Nikolai N. Petrov – Udmurt State University, kma3@list.ru
Ekaterina Yu. Ponomareva – Udmurt State University, kma3@list.ru
Abstract. A non-stationary problem of simple pursuit by a group of pursuers of a group of evaders, provided that all evaders use the same control and do not leave the boundaries of a convex polyhedral set, is considered. Sufficient conditions for capturing at least one evader have been obtained.
Keywords: simple pursuit, pursuer, evader, capture.
References
- Chikrii A. A. Conflict-controlled processes. Boston; London; Dordrecht: Kluwer Acad. Publ., 1997. 380 p.
- Grigorenko N. L. Matematicheskie metody upravleniya neskol’kimi processami [Mathematical methods for controlling several dynamic processes]. Moscow: Moscow State University. 1990. 197 p. (In Russ.)
- Blagodatskikh A. I., Petrov N. N. Konfliktnoe vzaimodeistvie grupp upravlyaemyh obiektov [Conflict interaction of groups of controlled objects]. Izhevsk: Udmurt State Unive rsity, 2009. 266 p. (In Russ.)
- Satimov N. Yu. Metody resheniya zadachi presledovaniya v teorii differentsial’nykh igr [Methods for solving the pursuit problem in the theory of differential games]. Tashkent: Publishing House of the National Library of Uzbekistan, 2019. 230 p. (In Russ.)
- Petrov N. N., Petrov N. Nikandr. On the differential game ”Cossacks and Robbers”. Differentsial’nyye uravneniya [Differential equations]. 1983. Vol. 19. No 8. Pp. 1366–1374. (In Russ.)
- Grigorenko N. L. Pursuit of two evaders by several controlled objects. Sov. Math. Dokl. [Report of the USSR Academy of Sciences]. 1985. Vol. 31. Pp. 550–553. (In Russ.)
- Kumkov S. S., Menec S. L., Patsko V. S. Zero-sum pursuit-evasion differential games with many objects: Survey of Publications. Dynamic Games and Applications. 2017. Vol. 7. No 4. Pp. 609–633.
- Garcia E., Casbeer D. W., Von Moll A., Pachter M. Multiple pursuer multiple evader differential games. IEEE Transactions on Automatic Control. 2021. Vol. 66. No 5. Pp. 2345–2350.
- Satimov N., Mamatov M. S. On problems of pursuit and evasion away from meeting in differential games between the group of pursuers and evaders. Doklady Akademii Nauk Uzbekskoj SSR [Reports of the Academy of Sciences of the Uzbek SSR]. 1983. Vol. 4. Pp. 3–6. (In Russ.)
- Vagin D. A., Petrov N. N. A problem of the pursuit of a group rigidly connected evaders. Journal of Computer and Systems Sciences International. 2001. Vol. 40. No 5. Pp. 749–753.
- Petrov N. N. On a Group Pursuit Problem. Avtomatika i telemekhanika [Automation and Remote Control]. 1996. Vol. 56. No 6. Pp. 808–813.
- Petrov N. N., Vagin D. A. A problem of group pursuit with phase constraints.Journal of Applied Mathematics and Mechanics. 2002. Vol. 66. No 2. Pp. 225–232.
- Blagodatskikh A. I., Petrov N. N. Simultaneous multiple capture of rigidly coordinated evaders. Dynamic Games and Applications. 2019. Vol. 9. No 3. Pp. 594–613.
- Petrov N. N. About controllability of autonomous systems. Differentsial’nyye uravneniya [Differential Equations]. 1968. Vol. 4. No 4. Pp. 606–617. (In Russ.)
For citation: Petrov N. N., Ponomareva E. Yu. Capturing coordinated evaders in a nonstationary simple pursuit problem with phase restrictions. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2025, no 1 (54), pp. 18−32. (In Russ.) https://doi.org/10.34130/1992-2752_2025_1_18

III. CONTEXT TASKS: MATHEMATICS, COMPUTER SCIENCE, CONLANGES
https://doi.org/10.34130/1992-2752_2025_1_33
Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University, valmasha@mail.ru
Marija A. Valueva – Petersburg State University of Culture
Nadezhda O. Kotelina – Pitirim Sorokin Syktyvkar State University, nkotelina@kirill
Abstract. In scientific and pedagogical literature, the inclusion of contextual tasks in mathematics education is regarded as a way to enhance students’ interest, develop critical thinking, and foster professional competencies, and the ability to apply mathematical
knowledge in future careers. The article offers for discussion the author’s tasks, compiled based on artificial languages–conlangs. These tasks were tested in courses such as ”Discrete Mathematics”, ”Mathematical Foundations of Programming”, ”Applications of Discrete Mathematics in Computer Science”, and ”Computer Graphics”. The study involved students majoring in ”Applied Computer Science”, ”Applied Mathematics and Computer Science”
and ”Mathematics and Computer Science” at Syktyvkar State University (named after Pitirim Sorokin).
Keywords: contextual tasks, conlangs, mathematics, Python
References
- Shutrova I. V. Development of cross-cutting tasks for the formation of mathematical literacy. Mir nauki, kul’tury, obrazovaniya [The world of science, culture and education]. 2024. No 6 (109). Pp. 353–357. DOI: 10.24412/1991-5497-2024-6109-353-357. (In Russ.)
- Yanushchik O. V., Dalinger V. A. Context mathematical problems in the formation of core competences of engineering students. Vysshee obrazovanie v Rossii [Higher Education in Russia]. 2017. No 3. Pp. 151–(In Russ.)
- Mongush A. S., Tanova O. M. Mathematical problems with a regional context as a tool of motivation in learning mathematics in the republic of Tuva. Vestnik KGPU im. V. P. Astaf’eva [Bulletin of Krasnoyarsk state pedagogical university named after V. P. Astafiev]. No 2 (36). Pp. 22–27. (In Russ.)
- Malalina, Putri R. I. I., Zulkardi Z., Hartono Y. Developing mathematics teaching materials using maritime context for higher-order thinking in junior high school. Journal on Mathematics Education. 2024. Vol. 15. No 1. Pp. 173–190. DOI: 10.22342/jme.v15i1.
- Tyumeneva Yu. A., Shklyaeva I. V. Two Approaches to the Concept of Knowledge Application: Transfer and Modeling. Overview and Criticism. Voprosy obrazovaniya [Educational Studies Moscow]. No 3. Pp. 8–33. DOI: 10.17323/1814-9545-2016-3-8-33. (In Russ.)
- Tyumeneva Y. A., Goncharova M. V. Following the Template: Transferring Modeling Skills to Nonstandard Problems. Russian Education & Society. 2017. No 59 (5–6). Pp. 298–318. DOI:10.1080/10609393.2017.1408370.
- Evelina L. N., Sedova K. P. Creating contextual tasks in the process of teaching students mathematics. Problemy teorii i praktiki innovacionnogo razvitiya i integracii sovremennoj nauki i obrazovaniya : materialy III Mezhdunarodnoj mezhdisciplinarnoj konferencii, Moskva, 16 fevralya 2022 goda [Problems of theory and practice of innovative development and integration of modern science and education : materials III international interdisciplinary conference, Moscow, February 16, 2022]. Editor-in-Chief and compiler V. G. Kostyakova. Moscow: Moscow State Regional University. 2022. Pp. 15–20. (In Russ.)
- Larina G. Analysis of Real-World Math Problems: Theoretical Model and Classroom Application. Educational Studies. Moscow, 2016. No 3. Pp. 151–168. DOI: 10.17323/1814-9545-2016-3-151-168.
- Babikova N. N., Kotelina N. O., Valueva M. A., Startsev N. A. Computer games and combinatorial problems. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mehanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics]. No 1 (50). Pp. 55–72. DOI: 10.34130/1992-2752_2024_1_55.
(In Russ.) - Piperski A. Ch. Konstruirovanie yazykov: ot esperanto do dotrakijskogo [Language construction: from Esperanto to Dothraki]. Moscow: Al’pina non-fikshn, 2017. 224 p. (In Russ.)
- Tolkin Dzh. R. R. Pis’ma [Letters]. Moscow: Eksmo, 2004. 576 p. (In Russ.)
- Reformatskij A. A. Vvedenie v yazykoznanie [Introduction to Linguistics]. Moscow: Aspekt Press, 2000. 536 p. (In Russ.)
- Havel V. The memorandum. New-York: Grave Weidenfeld, 1980. 88 p.
- Gilbert E. N. A comparison of signalling alphabets. Bell System Technical Journal. 1952. Vol. 31. No 3. Pp. 504–522. DOI: 10.1002/j.1538-7305.1952.tb01393.x.
- Keedwell A. Donald, D´enes J´ozsef. Latin Squares: New Developments in the Theory and Applications. Amsterdam: Elsevier, 270 p.
For citation: Babikova N. N., Valueva M. A., Kotelina N. O. Context Babikova N. N., Valueva M. A., Kotelina N. O. Context tasks: mathematics, computer science, conlanges. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2025, no 1 (54), pp. 33−51. (In Russ.) https://doi.org/10.34130/1992-2752_2025_1_33

IV. DEVELOPMENT AND POPULATION OF THE «LATE PALEOZOIC MIOSPORES» DATABASE USING ARTIFICIAL INTELLIGENCE TECHNOLOGIES
https://doi.org/10.34130/1992-2752_2025_1_52
Maria A. Shestakova – Pitirim Sorokin Syktyvkar State University, mariasheska@yandex.ru
Abstract. This article presents an approach to developing and automatically populating a database containing information on Late Paleozoic miospores. A number of scientific publications on palynology have been used as data sources, including structured descriptions of genera of Late Paleozoic miospores. Text was extracted from the printed source using optical character recognition (OCR) technology based on the Python library Pytesseract. Data processing and structuring were implemented using the DeepSeek large language model. A relational database was implemented using the SQLAlchemy library and the SQLite database management system to store the structured information.
Keywords: large language models, OCR, Pytesseract, databases, Late Paleozoic miospores.
References
- Schilling-Wilhelmi M., R´ıos-Garc´ıa M., Shabih S. et al. From text to insight: large language models for materials science data extraction. arXiv preprint arXiv: 2407.16867. 2024. Available at: https://arxiv.org/abs/2407.16867 (accessed: 20.03.2025).
- Goncharov D. S., Grigoryev S. V. Large language models on the example of GPT-3 chatbots: current realities, problems of truth, advantages, and dangers. Vyzovy sovremennosti i strategii razvitiya obshchestva v usloviyakh novoy real’nosti : sbornik materialovm XV Mezhdunarodnoi nauchno-prakticheskoi konferentsii [Challenges of modernity and strategies for the development of society in the new reality : Proceedings of the XV International Scientific and Practical Conference]. Moscow: ALEF Publishing, 2023. Pp. 283–290. (In Russ.)
- Telnova O. P., Babikova N. N., Kotelina N. O. The relevance and possibilities of digital transformation of the diagnostic process of Devonian spores. Geologiya i mineral’nyye resursy Yevropeyskogo Severo-Vostoka Rossii : materialy XVIII Geologicheskogo s”yezda Respubliki Komi, Syktyvkar, 10–12 aprelia 2024 goda [Geology and mineral resources of the European Northeast of Russia : Proceedings of the XVIII Geological Congress of the Komi Republic, Syktyvkar, April 10–12, 2024]. Syktyvkar: Komi Science Centre, Ural Branch of RAS. 2024. Pp. 199–201. (In Russ.)
- Babenko V. V., Kotelina N. O., Telnova O. P. Software and information support for paleopalynological tasks. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mehanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer Science]. 2021. No 1 (38). Pp. 27–42. (In Russ.)
- Telnova O. P. Miospory iz sredne-verkhnedevonskikh otlozheniy Timano-Pechorskoy provintsii [Miospores from the Middle-Upper Devonian deposits of the Timan-Pechora Province]. Yekaterinburg: Ural Branch of the Russian Academy of Sciences, 2007. 136 p. (In Russ.)
- Babenko V. V., Telnova O. P. Problems and Prospects of Digital Identification of Devonian Spores for the Stratigraphy. Paleontological Journal. 2022. Vol. 56. No 9. Pp. 93–99.
- Oshurkova M. V. Morfologiya, klassifikatsiya i opisaniya forma-rodov miospor pozdnego paleozoya [Morphology, classification, and description of form-genera of Late Paleozoic miospores]. St. Petersburg: Publishing VSEGEI, 2003. 377 p. (In Russ.)
- GitHub – Python Tesseract [Electronic resource]. Available at: https://github.com/madmaze/pytesseract (accessed: 20.03.2025).
- GitHub – tesseract-ocr/tesseract: Tesseract Open Source OCR Engine (main repository) [Electronic resource]. Available at: https://github.com/tesseract-ocr/tesseract (accessed: 20.03.2025).
- Saoji S., Singh R., Eqbal A., Vidyapeeth B. Text recognition and detection from images using Pytesseract. Journal of Interdisciplinary Cycle Research. 2021. Vol. XIII. Pp. 1674–1679.
- Bhosale S., Patil M., Patil P. SQLite: Light database system. International Journal of Computer Science and Mobile Computing. Vol. 4. Issue 4. Pp. 882–885.
- SQLAlchemy 2.0 Documentation [Electronic resource]. Available at: https://docs.sqlalchemy.org (accessed: 22.03.2025).
- Together AI – The AI Acceleration Cloud [Electronic resource]. Available at: https://www.together.ai (accessed: 25.03.2025).
- DeepSeek [Electronic resource]. Available at: https://www.deepseek.com/en (accessed: 25.03.2025).
For citation: Shestakova M. A. Development and population of the «Late Paleozoic miospores» database using artificial intelligence technologies. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2025, no 1 (54), pp. 52−68. (In Russ.) https://doi.org/10.34130/1992-2752_2025_1_52

V. ODYNIEC VLADIMIR PETROVICH (TO THE 80TH ANNIVERSARY OF BIRTHDAY)
https://doi.org/10.34130/1992-2752_2025_1_69
Valerian N. Isakov – Pitirim Sorokin Syktyvkar State University
Vyacheslav A. Popov – Pitirim Sorokin Syktyvkar State University
Olga A. Sotnikova – Pitirim Sorokin Syktyvkar State University, sotnikovaoa@syktsu.ru
Abstract. The article tells about professor V. P. Odyniec, a known mathematician and educator. It highlights the periods of his professional activity in St. Petersburg and Syktyvkar.
Keywords: Odyniec Vladimir Petrovich, review of publications over the last ten years.
References
- Vershik A. M., Viro O. Ya., Isakov V. N.et al. Odyniec Vladimir Petrovich (to the sixty-fifth anniversary of his birth).Vladikavkazskiy matematicheskiy zhurnal [Vladikavkaz Mathematical Journal]. 2010. Vol. 12. Issue 4. Pp. 79–81. (In Russ.)
- Popov V. A. Odyniec Vladimir Petrovich. Kafedra matematiki Komi pedinstituta: istoriya stanovleniya i razvitiya [Department of Mathematics of Komi Pedagogical Institute: history of formation and development]. V. A. Popov. Syktyvkar: Komi Pedagogical Institute. Pp. 167–168. (In Russ.)
- Isakov V. N., Nikitenkov V. L., Popov V. A. To the seventieth anniversary of Professor One Vladimir Petrovich. Vestnik Syktyvkarskogo universiteta. Ser. 1. [Bulletin of the Syktyvkar University. Ser. 1] 2015. Issue 1 (20). Pp. 97–102. (In Russ.)
- Isakov V. N., Nikitenkov V. L., Popov V. A. Odinets Vladimir Petrovich (on the 70th anniversary of his birth). Matematicheskiy vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona : periodicheskiy mezhvuzovskiy sbornik nauchno-metodicheskikh
rabot [Mathematical Bulletin of Pedagogical Universities and Universities of the Volga-Vyatka Region : periodic interuniversity collection of scientific and methodological works]. Kirov: Scientific Publishing House of Vyatka State University, 2016. Issue 18. Pp. 24–29. (In Russ.) - Komi pedinstitut: vremya innovatsionnogo razvitiya. 1973–2014 : sbornik materialov i vospominanij [Komi Pedagogical Institute: time of innovative development. 1973–2014 : collection materials and memoirs]. Editorial board (compilers): V. N. Isakov (ch. ed.), Z. I. Nemshilova (corresponding ed.), O. E. Bondarenko, N. V. Zakharova, T. P. Koroleva, V. A. Popov. Syktyvkar: Publishing house of SSU named after Pitirim Sorokina, 2022. 774 p.: ill.
For citation: Isakov V. N., Popov V. A., Sotnikova O. A. Odyniec Vladimir Petrovich (to the 80th anniversary of birthday). Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2025, no 1 (54), pp. 69−79. (In Russ.) https://doi.org/10.34130/1992-2752_2025_1_69
