Bulletin 3 (56) 2025

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I. ON THE BILINEAR CONVOLUTION OPERATOR AND YOUNG’S INEQUALITY

https://doi.org/10.34130/1992-2752_2025_3_4

Evgeny A. Pavlov — Crimean Engineering and Pedagogical University named after Fevzi Yakubov.

Evgeny A. Rybalkin — Crimean Engineering and Pedagogical University named after Fevzi Yakubov, rybalkin_e@mail.ru

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Abstract. In this paper, we prove the continuity of a bilinear convolution operator defined on a Cartesian product of symmetric spaces, which, in particular, implies a strengthening of Young’s inequality and, under some additional conditions, a strengthening of the theorem of S. G. Krein, Yu. I. Petunin and E. M. Semenov. The proof is carried out without using the theory of linear operator interpolation.

Keywords: symmetric spaces, convolution operation, operator norm.

References

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  5. Yong R. M. Interpolation in a Classical Hilbert Space of Entire Functions. Trans. Amer. Math. Soc. 1974. Vol. 192. Pp. 97–114.
  6. Edvards R. Ryady Fur’ye v sovremennom izlozhenii : v 2 t. [Fourier series in a modern presentation : in 2 volumes]. Translated from English by T. P. Lukashenko, V. A. Skvortsova. Moscow: Publishing House of the World, 1985. Vol. 2. 399 p. (In Russ.)
  7. Zigmynd А. Trigonometricheskiye ryady : v 2 t. [Trigonometric series : in 2 volumes]. Translated from English by O. S. Ivasheva-Musatova; edited by N. K. Bari. Moscow: Publishing House of the World, 1965. Vol. 2. 537 p. (In Russ.)
  8. Tribel Х. Teoriya i interpolyatsii. Funktsional’nyye neravenstva. Differentsial’nyye operatory : per. s angl. [Theory and interpolation. Functional inequalities and Differential operators : translated from English]. Moscow: Publishing House of the World, 1980. 664 p. (In Russ.)
  9. Bourbaki N. Vektornoye integrirovaniye, mera Khaara, svortka i predstaveniya : per. s fr. [Vector integration, Haar measure, convolution and representation : trans. from French]. Moscow: Science, 1970. 320 p.(In Russ.)
  10. Hardy G. G., Littlewood D. E., Polia G. Neravenstva [Inequalities]. Moscow: Foreign Literature, 1962. 456 p. (In Russ.)
  11. Blozinski A. P. On a Convolution Theorem for L(p, q) Spaces. Trans. Amer. Math. Soc. 1972. Vol. 164. Pp. 255–265.
  12. Benedek A., Calderon A. P., Panzone R. Convolution operators on functions with values in a Banach space. Matematika [Mathematics]. Vol. 7. Issue 5. Pp. 121–132. (In Russ.)
  13. Boyd D. W. Indices of Function Spaces and Their Relationship to Interpolation. Canadian Journal of Mathematics. 1969. Vol. 21 (5). Pp. 1245–1254.
  14. O’Neil R. Convolution operators and L(p,q) spaces. Duke Mathematical Journal. 1963. Vol. 30. Pp. 129–142.

For citation: Pavlov E. A., Rybalkin E. A. On the bilinear convolution operator and Young’s inequality. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2025, no 3 (56), pp. 4−15. (In Russ.) https://doi.org/10.34130/1992-2752_2025_3_4

II. DESCRIPTION OF THE MOVEMENTS OF THE EUCLIDEAN PLANE IN BARYCENTRIC COORDINATES

https://doi.org/10.34130/1992-2752_2025_3_16

Marina A. Stepanova — The Herzen State Pedagogical University of Russia,
ratkebug@yandex.ru

Ksenia S. Malinnikova — The Herzen State Pedagogical University of Russia,
ratkebug@yandex.ru

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Abstract. The affine transformation of a plane in a barycentric coordinate system is given by a system of linear equations with a barycentric matrix of size 3 × 3, so that each affine transformation of the plane can be associated with a matrix from the barycentric group
B˜(3).

Keywords: affine space, Euclidean plane, affine transformation, motion, barycentric coordinates, barycentric matrix, transformation matrix.

References

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    16–18 aprelya 2024 g. [Contemporary Problems of Mathematics and Mathematical Education: Herzen Readings, 77 : collection of Proceedings of the International Scientific Conference, St. Petersburg, April 16–18, 2024]. A. I. Herzen State Pedagogical University. 2024. Pp. 356–360. (In Russ.)
  6. Stepanova M. A. Some subgroups of the barycentric group. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mehanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer Science]. 2025. No 1 (54). Pp. 4–17. (In Russ.)
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For citation: Stepanova M. A., Malinnikova K. S. Description of the movements of the Euclidean plane in barycentric coordinates. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics.
Mechanics. Informatics], 2025, no 3 (56), pp. 16−32. (In Russ.) https://doi.org/10.34130/1992-2752_2025_3_4

III. METHODS FOR EXTRACTING LEADING INDICATORS OF INVESTMENT ACTIVITY FROM UNSTRUCTURED TEXT DATA

https://doi.org/10.34130/1992-2752_2025_3_33

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

Irina V. Polyakova — Bank of Russia.

Petr V. Borkov — Bank of Russia.

Denis S. Grimalyuk — Pitirim Sorokin Syktyvkar State University.

Yulia A. Yushkova — Pitirim Sorokin Syktyvkar State University.

Evgenija N. Startseva — Pitirim Sorokin Syktyvkar State University.

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Abstract. The aim of this study is to construct a leading index of investment activity in Russia, calculated by assessing news dynamics using natural language processing (NLP) and machine learning methods.

Keywords: NLP, LLM, text analysis, machine learning, investment activity, leading indicators, Bayesian analysis.

References

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  19. Barbaglia L., Consoli S., Manzan S. Forecasting with Economic News. Journal of Business & Economic Statistics. 2023. January. 41 (107). 46 p. DOI: 10.1080/07350015.2022.2060988.
  20. Kalamara E., Turrell A., Redl C. et al. Making text count: Economic forecasting using newspaper text. Journal of Applied Econometrics. 2022. 37 (5). Pp. 896–919. DOI: 10.1002/jae.2907.
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  22. Ash E., Hansen S. Text Algorithms in Economics. Annual Review of Economics. 2023. Vol. 15. Pp. 659–688. DOI: 10.1146/annureveconomics-082222-074352.
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For citation: Maltseva O. A., Polyakova I. V., Borkov P. V., Grimalyuk D. S., Yushkova Yu. A., Startseva E. N. Methods for extracting leading indicators of investment activity from unstructured text data. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2025, no 3 (56), pp. 33−60. (In Russ.) https://doi.org/10.34130/1992-2752_2025_3_33

IV. ON THE MODEL OF INFINITE DECIMAL FRACTIONS FROM THE PERSPECTIVE OF THE AXIOMATIC CONSTRUCTION OF THE THEORY OF REAL NUMBERS

https://doi.org/10.34130/1992-2752_2025_3_61

Vladislav V. Sushkov — Pitirim Sorokin Syktyvkar State University, vvsu@mail.ru

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Abstract. This article addresses the justification of the infinite decimal fractions model within the framework of the axiomatic approach to the theory of real numbers. The relevance of the research is determined by the fundamental importance of a rigorous foundation for models of the continuum.

Keywords: real numbers, axiomatic theory, infinite decimal fractions, continuum, nested intervals, arithmetic operations, mathematical foundations

References

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For citation: Sushkov V. V. On the Model of Infinite Decimal Fractions from the Perspective of the Axiomatic Construction of the Real Number Theory. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2025, no 3 (56), pp. 61−73. (In Russ.) https://doi.org/10.34130/1992-2752_2025_3_61

V. EFFICIENT SOLUTION OF THE BIHARMONIC EQUATION BASED ON SPARSE DATA STRUCTURES

https://doi.org/10.34130/1992-2752_2025_3_74

Andrei V. Yermolenko — Pitirim Sorokin Syktyvkar State University, ea74@list.ru

Lev S. Shadrin — Pitirim Sorokin Syktyvkar State University.

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Abstract. This article presents a numerical solution to the biharmonic equation by reducing it to a system of linear algebraic equations. Two approaches are explored: the first is based on
approximating the biharmonic operator using a 13-point stencil, while the second is based on reducing the original problem to a system of two Poisson equations followed by discretization of the Laplace operator using a 5-point stencil.

Keywords: biharmonic equation, numerical methods, sparse matrices.

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For citation: Yermolenko A. V., Shadrin L. S. Efficient solution of the biharmonic equation based on sparse data structures. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2025, no 3 (56), pp. 74−87. (In Russ.) https://doi.org/10.34130/1992-2752_2025_3_74