Evgeniy Konstantinovich Leinartas (1954–2024) A. P. Lyapin, M. S. Apanovich, T. I. Yakovleva, O. A. Shishkina, S. Chandragiri Bulletin of Irkutsk State University Series Mathematics, 2026 The article is devoted to the scientific and pedagogical activity of Doctor of Physical and Mathematical Sciences, Professor of the Department of Function Theory at Siberian Federal University Evgeniy Konstantinovich Leinartas (1954–2024).
D-Finite Discrete Generating Series and Their Sections Svetlana S. Akhtamova, Vitaly S. Alekseev, Alexander P. Lyapin Mathematics, 2025 This paper investigates D-finite discrete generating series and their sections. The concept of D-finiteness is extended to multidimensional discrete generating series and its equivalence to p-recursive sequences is rigorously established. It is further shown that sections of the D-finite series preserve D-finiteness, and that their generating functions satisfy systems of linear difference equations with polynomial coefficients. In the two-dimensional case, explicit difference relations are derived that connect section values with boundary data, while in higher dimensions general constructive methods are developed for obtaining such relations, including cases with variable coefficients. Several worked examples illustrate how the theory applies to solving difference equations and analyzing multidimensional recurrent sequences. The results provide a unified framework linking generating functions and recurrence relations, with applications in combinatorics, number theory, symbolic summation, and the theory of discrete recursive filters in signal processing.
A Combined Method for Localizing Two Overlapping Acoustic Sources Based on Deep Learning Alexander Lyapin, Ghiath Shahoud, Evgeny Agafonov Applied Sciences Switzerland, 2025 Deep learning approaches for multi-source sound localization face significant challenges, particularly the need for extensive training datasets encompassing diverse spatial configurations to achieve robust generalization. This requirement leads to substantial computational demands, which are further exacerbated when localizing overlapping sources in complex acoustic environments with reverberation and noise. In this paper, a new methodology is proposed for simultaneous localization of two overlapping sound sources in the time–frequency domain in a closed, reverberant environment with a spatial resolution of 10° using a small-sized microphone array. The proposed methodology is based on the integration of the sound source separation method with a single-source sound localization model. A hybrid model was proposed to separate the sound source signals received by each microphone in the array. The model was built using a bidirectional long short-term memory (BLSTM) network and trained on a dataset using the ideal binary mask (IBM) as the training target. The modeling results show that the proposed localization methodology is efficient in determining the directions for two overlapping sources simultaneously, with an average localization accuracy of 86.1% for the test dataset containing short-term signals of 500 ms duration with different signal-to-signal ratio values.
Selection of Support System to Provide Vibration Frequency and Stability of Beam Structure Alexander P. Lyapin, Ilya V. Kudryavtsev, Sergey G. Dokshanin, Andrey V. Kolotov, Alexander E. Mityaev Modelling, 2024 The current engineering theories on bending vibrations and the stability of beam structures are based on solving eigenvalue problems through similarly formulated differential equations. Solving the eigenvalue problem for engineering calculations is particularly laborious, especially for non-classical supports, where factors like the stiffness of supports, axial forces, or temperature must be considered. In this case, the solution can be obtained only by numerical methods using specially created programs, which makes it difficult to select supports for a given planar beam structure in engineering practice. This work utilizes established solutions from eigenvalue problems in the theory of vibrations and stability of beams, incorporating factors such as axial forces, temperature, and support stiffness. This combined solution is applicable to beam structures of any type and cross-section, as it is determined solely by the selected support conditions (stiffness) and loading (axial force, temperature). Approximation of eigenvalue problem solutions through continuous functions allows the readers to use them for the analytical solution of the design problem of choosing a support system to ensure the frequency of vibrations and stability of the planar beam structure. At the same time, the known solutions given in the reference books on bending vibrations and stability become their particular solutions. This approach is applicable to solving problems of vibrations and loss of stability of various types (torsional, longitudinal, etc.), and is also applicable in other disciplines where solving problems for eigenvalues is required.
An Approach to Multidimensional Discrete Generating Series Svetlana S. Akhtamova, Tom Cuchta, Alexander P. Lyapin Mathematics, 2024 We extend existing functional relationships for the discrete generating series associated with a single-variable linear polynomial coefficient difference equation to the multivariable case.
Summation of Functions and Polynomial Solutions to a Multidimensional Difference Equation Journal of Siberian Federal University Mathematics and Physics, 2023
Евгений Константинович Лейнартас (1954–2024) АП Ляпин, МС Апанович, ТИ Яковлева, ОА Шишкина, Ш Чандрагири Известия Иркутского государственного университета. Серия «Математика» 55 (0 … , 2026 2026
Boundary value problem for a two-dimensional linear difference equation on the integer lattice A Leinartene, A Lyapin 2025
D -Finite Discrete Generating Series and Their Sections SS Akhtamova, VS Alekseev, AP Lyapin Mathematics 13 (20), 3259 , 2025 2025
A Combined Method for Localizing Two Overlapping Acoustic Sources Based on Deep Learning A Lyapin, G Shahoud, E Agafonov Applied Sciences 15 (12), 6768 , 2025 2025 Citations: 4
Discrete generating series and linear difference equations V Alekseev, T Cuchta, A Lyapin arXiv preprint arXiv:2504.21722 , 2025 2025 Citations: 1
Algorithm for Finding Singular Points of a General Algebraic Hypersurface AP Lyapin, EN Mikhalkin Programming and Computer Software 51 (2), 88-92 , 2025 2025
Selection of Support System to Provide Vibration Frequency and Stability of Beam Structure AP Lyapin, IV Kudryavtsev, SG Dokshanin, AV Kolotov, AE Mityaev Modelling 5 (4), 1687-1708 , 2024 2024
Applying computer algebra systems to study Chaundy-Bullard identities for the vector partition function with weight AB Leinartene, AP Lyapin Programming and Computer Software 50 (2), 176-179 , 2024 2024 Citations: 2
МАТЕМАТИЧЕСКИЙ АНАЛИЗ. ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ АП ЛЯПИН, СС АХТАМОВА, СГ МЫСЛИВЕЦ, ТН ШИПИНА Сибирский фудеральный университет , 2024 2024
Multidimensional discrete generating series of solutions to difference equations A Lyapin 29th International Conference on Difference Equations and Applications , 2024 2024
Полиномиальные решения многомерных разностных уравнений A Grigoriev, E Leinartas, A Lyapin Cовременные проблемы теории функций и их приложения 22, 75-78 , 2024 2024
An Approach to Multidimensional Discrete Generating Series SS Akhtamova, T Cuchta, AP Lyapin Mathematics 12 (1), 143 , 2024 2024 Citations: 7
Solving the Cauchy problem for a three-dimensional difference equation in a parallelepiped MS Apanovich, AP Lyapin, KV Shadrin Programming and Computer Software 49 (2), 61-68 , 2023 2023 Citations: 2
Summation of functions and polynomial solutions to a multidimensional difference equation A Grigoriev, E Leinartas, A Lyapin Journal of Siberian Federal University. Mathematics & Physics 16 (2), 153–161 , 2023 2023 Citations: 16
Algorithm for Computing the Truncation of the Discriminant of a Polynomial AP Lyapin, EN Mikhalkin Programming and Computer Software 49 (1), 49-53 , 2023 2023 Citations: 2
Discrete Generating Functions SS Akhtamova, VS Alekseev, AP Lyapin Математические заметки 114 (6), 1087-1093 , 2023 2023 Citations: 4
Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone A Lyapin, T Cuchta The Bulletin of Irkutsk State University. Series Mathematics 42, 75-89 , 2022 2022 Citations: 20
Algorithm for solving the Cauchy problem for a two-dimensional difference equation with initial data defined in a “strip” MS Apanovich, AP Lyapin, KV Shadrin Programming and Computer Software 48 (4), 286-292 , 2022 2022 Citations: 3
Теория функций комплексного переменного Е Лейнартас, С Ахтамова, А Ляпин ЛитРес , 2022 2022
Информатика. Информационно-правовые системы и базы данных А Ляпин, Е Гохвайс, М Клунникова, Т Осетрова ЛитРес , 2022 2022 Citations: 2
MOST CITED SCHOLAR PUBLICATIONS
On the rationality of multidimentional recusive series EK Leinartas, AP Lyapin Journal of Siberian Federal University. Mathematics & Physics 2 (4), 449-455 , 2009 2009 Citations: 55
Generating functions for vector partition functions and a basic recurrence relation AP Lyapin, S Chandragiri Journal of Difference Equations and Applications 25 (7), 1052-1061 , 2019 2019 Citations: 41
Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation AP Lyapin, SS Akhtamova Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki … , 2021 2021 Citations: 25
Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone A Lyapin, T Cuchta The Bulletin of Irkutsk State University. Series Mathematics 42, 75-89 , 2022 2022 Citations: 20
Evaluating the rational generating function for the solution of the Cauchy problem for a two-dimensional difference equation with constant coefficients AA Kytmanov, AP Lyapin, TM Sadykov Programming and computer software 43 (2), 105-111 , 2017 2017 Citations: 20
Riordan's arrays and two-dimensional difference equations AP Lyapin Journal of Siberian Federal University. Mathematics & Physics 2 (2), 210-220 , 2009 2009 Citations: 19
Summation of functions and polynomial solutions to a multidimensional difference equation A Grigoriev, E Leinartas, A Lyapin Journal of Siberian Federal University. Mathematics & Physics 16 (2), 153–161 , 2023 2023 Citations: 16
Solving the Cauchy problem for a two-dimensional difference equation at a point using computer algebra methods MS Apanovich, AP Lyapin, KV Shadrin Programming and Computer Software 47 (1), 1-5 , 2021 2021 Citations: 12
О многообразиях модулей m p3 (2; 0, 10) и m p3 (2; 0, 11) стабильных 2-расслоений с классами Черна c₁= 0, c₂= 10 и c₂= 11 на комплексном проективном пространстве СА Тихомиров, АП Ляпин, ЕА Рузанов Ярославский педагогический вестник 3 (4), 13-18 , 2012 2012 Citations: 10
On sections of generating series in lattice path problems SS Akhtamova, VY Grishunov, AP Lyapin, SA Tikhomirov Applied Mathematics & Physics 52 (2), 146-151 , 2020 2020 Citations: 8
An Approach to Multidimensional Discrete Generating Series SS Akhtamova, T Cuchta, AP Lyapin Mathematics 12 (1), 143 , 2024 2024 Citations: 7
A Combined Method for Localizing Two Overlapping Acoustic Sources Based on Deep Learning A Lyapin, G Shahoud, E Agafonov Applied Sciences 15 (12), 6768 , 2025 2025 Citations: 4
Discrete Generating Functions SS Akhtamova, VS Alekseev, AP Lyapin Математические заметки 114 (6), 1087-1093 , 2023 2023 Citations: 4
Calculating the sequence of main minors of the Toeplitz band matrix MS Apanovich, AP Lyapin, KV Shadrin Applied Mathematics & Physics 52 (1), 5-10 , 2020 2020 Citations: 4
Algorithm for solving the Cauchy problem for a two-dimensional difference equation with initial data defined in a “strip” MS Apanovich, AP Lyapin, KV Shadrin Programming and Computer Software 48 (4), 286-292 , 2022 2022 Citations: 3
Спектры стабильных 2-расслоений с нечетным первым классом Черна на трехмерном проективном пространстве СА Тихомиров, АП Ляпин, ЕВ Казанцева Ярославский педагогический вестник 3 (4), 21-23 , 2013 2013 Citations: 3
Инварианты стабильных 2-расслоений на комплексном проективном пространстве и адаптация вычислительной технологии Барта СА Тихомиров, АП Ляпин, ОА Войлокова Ярославский педагогический вестник 3 (2), 33-38 , 2013 2013 Citations: 3
Applying computer algebra systems to study Chaundy-Bullard identities for the vector partition function with weight AB Leinartene, AP Lyapin Programming and Computer Software 50 (2), 176-179 , 2024 2024 Citations: 2
Solving the Cauchy problem for a three-dimensional difference equation in a parallelepiped MS Apanovich, AP Lyapin, KV Shadrin Programming and Computer Software 49 (2), 61-68 , 2023 2023 Citations: 2
Algorithm for Computing the Truncation of the Discriminant of a Polynomial AP Lyapin, EN Mikhalkin Programming and Computer Software 49 (1), 49-53 , 2023 2023 Citations: 2
