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Algorithmization of Receiving Orbits of Weierstrass and Orbits of Tangences
Springer. 2021.
Шагай М. А., Флегонтов А. В., Иофе М. Д.
In our paper we seek to find of constructive describe functional classes defined on subsets of the period's parallelogram of doubly periodic Weierstrass functions using the integral norm.
Anton Karamyshev, Artem Krasilov, Evgeny Khorov, IEEE Transactions on Network Science and Engineering 2026 P. 1–18
Modern communication networks shall support mission-critical and real-time applications that demand high data rates, low latency, and ultra-high reliability, which is known as Ultra-reliable Low-latency Communications (URLLC). In URLLC systems, the effective capacity, i.e., the maximum traffic rate at which latency and reliability constraints are satisfied, is a key metric for resource management. Its estimations ...
Added: April 17, 2026
Alexeeva T., Shirokov N. A., St Petersburg Mathematical Journal 2025 Vol. 36 No. 1 P. 25–39
Let L be a chord-arc curve in R3. We introduce a functional class Hr+ω(L) where a modulus of continuity ω satisfies the Dini condition and r≥1. We define neighborhoods of L Ωδ(L)=⋃M∈LBδ(M), Bδ(M)={X∈R3:∥XM∥<δ} and set HarmΩδ(L) for harmonic functions in Ωδ(L). The Theorem 1 states that if f∈Hω+r(L) then there exist functions vδ∈HarmΩδ(L) such that ∣∣f(X)−vδ(M)∣∣≤cfδrω(δ), M∈L, and ∣∣∂αvδ(M)∣∣≤cfω(δ)δ, M∈Ωδ(L), |α|=r+1. The Theorem 2 states that if a function f defined on L satisfies claim of Theorem 1 then f∈Hω+r(L). ...
Added: March 16, 2026
Сильванович О. В., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 Т. 545 С. 179–205
Let ak < bk < ak+1, k ∈ Z, Ik = (ak, bk), Jk = [bk, ak+1]. We assume that |Ik| |Jk|, ak −−−−−→ k→+∞ ∞, ak −−−−−→ k→−∞ −∞ and |Jk| 1 |ak|α , |k| → ∞, α > 0. The distribution of {Jk} satisfies some regularity conditions, E = S k∈Z ...
Added: March 16, 2026
Медведев А. Н., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 № 545 С. 157–167
Let D be a bounded domain on the complex plain C with sufficiently smooth boundary. We denote by Λ αpDq, 0 α 1, the class of analytic functions in D satisfying the α-H¨older condition in D . Each function f P Λ αpDq can be factored as f F I with F ...
Added: March 16, 2026
Popov V., Труды Математического института им. В.А. Стеклова РАН 2025 Т. 329 С. 209–226
Let X be the variety of flexes of plane cubics. The following statements are proved in this paper: (1) X is an irreducible rational algebraic variety equipped with an effective algebraic action of the group PSL(3); (2) X is PSL(3)-equivariantly birationally isomorphic to a homogeneous fiber bundle over PSL(3)/K with fiber being a projective line, ...
Added: December 16, 2025
Kuninets A., Malygina E., Раточка В. Л. et al., Прикладная дискретная математика 2023 № 62 С. 83–105
Рассматриваются теоретические основы алгебраических кривых и их функциональных полей, необходимые для построения алгеброгеометрических (АГ) кодов, а также пар, исправляющих ошибки, с целью их дальнейшего применения для декодирования кодов. Приведены теория, необходимая для обоснования корректности работы алгоритма декодирования АГ-кодов на основе пар, исправляющих ошибки, и сам алгоритм декодирования. Рассмотрены примеры построения АГ-кодов, ассоциированных с эллиптической кривой, ...
Added: December 12, 2025
Popov V., Успехи математических наук 2024 Т. 79 № 6 С. 169–170
Let X be the variety of flexes of plane cubics. The following properties of the algebraic variety X are proven: (1) X is irreducible and endowed with a faithful algebraic action of the group G=PSL(3). (2) X is rational. (3) There is a subgroup K of G isomorphic to the binary tetrahedral group such that ...
Added: December 2, 2024
Nikita Markarian, Polishchuk A., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2024 Vol. 20 Article 037
We prove that a pair of Feigin–Odesskii Poisson brackets on P4 associated with elliptic curves given as linear sections of the Grassmannian G(2,5) are compatible if and only if this pair of elliptic curves is contained in a del Pezzo surface obtained as a linear section of G(2, 5). ...
Added: December 2, 2024
Buchweitz R., Pavlov A., L'Enseignement Mathématique 2024 Vol. 70 No. 1/2 P. 1–24
We give normal forms of determinantal representations of a smooth projective plane cubic in terms of Moore matrices. Building on this, we exhibit matrix factorizations for all indecomposable vector bundles of rank 2 and degree 0 without nonzero sections, also called Ulrich bundles, on such curves. ...
Added: May 24, 2024
Alexander Lazarev, Nikolay Pravdivets, Barashov E., Mathematics 2024 Vol. 12 No. 5 Article 699
The problem of the approximation of the coefficients of the objective function of a scheduling problem for a single machine is considered. It is necessary to minimize the total weighted completion times of jobs with unknown weight coefficients when a set of problem instances with known optimal schedules is given. It is shown that the ...
Added: May 16, 2024
Malygina E., Кунинец А. А., Раточка В. Л. et al., Прикладная дискретная математика 2023 № 62 С. 83–105
We consider the basic theory of algebraic curves and their function fields necessary for constructing algebraic geometry codes and a pair of codes constituting error-correction pair which is used in a precomputation step of the decoding algorithm for the algebraic geometry codes. Also, we consider the decoding algorithm and give the necessary theory to prove ...
Added: March 19, 2024
Шагай М. А., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2023 Т. 527 С. 242–255
Let sk, 1 6 k 6 m, m > 2, be disjoint segments lying in a parallelogram Q. We denote by ℘(z) a doubly periodic Weierstrass function with the fundamental parallelogram Q. Let fk : sk → C be functions, and let f 0 k ∈ L pk (sk), 1 6 k 6 m, 1 ...
Added: February 10, 2024
Sintsova K. A., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2023 Vol. 56 No. 1 P. 46–56
The approximation-theory problem to describe classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, and splines arose over 100 years ago; it still remains topical. Among many problems related to approximation, we consider the two-variable polynomial approximation problem for a function defined on the continuum of an ...
Added: February 10, 2024
Alexeeva T., Shirokov N. A., Алгебра и анализ 2024 Т. 36 № 1 С. 40–59
On the chord-arc curve in R^3 classes of functions similar to Hölder functions with smoothness greater than unity are defined. A constructive description of these classes is obtained in terms of the rate of approximation of functions from them by functions that are harmonic in neighborhoods contracting to the curve. The choice of defining these classes ...
Added: January 10, 2024
Buryak A., Moscow Mathematical Journal 2023 Vol. 23 No. 3 P. 309–317
An algorithm to determine all the Gromov–Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro type constraints that allow to determine all the other Gromov–Witten invariants in terms of the stationary ones. In the case of an ...
Added: November 20, 2023
A. O. Radomskii, Izvestiya: Mathematics 2023 Vol. 87 No. 1 P. 113–153
We obtain some results related to Romanoff’s theorem. ...
Added: September 8, 2023
Kulagin N. E., L.M. Lerman, Physica D: Nonlinear Phenomena 2023 Vol. 454 Article 133845
We study in this pap er the existence of periodically modulated in one variable and localized in another variable solutions to the cubic Swift-Hohenberg equation on the plane R2. In the first part we try to apply the method by Kirschgassner-Mielke to reduce the problem to the search of finite-dimensional submanifolds with periodic orbits on
them in some formal ...
Added: July 27, 2023
Shirokov N. A., Синцова К. А., Вестник Санкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия 2023 Т. 10 № 1 С. 61–72
The problem of describing classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, splines entered in the theory of approximation more than 100 years ago and still retains its relevance. Among a large number of problems related to approximation, we considered the problem of polynomial approximation in ...
Added: May 24, 2023
Lazarev A. A., Lemtyuzhnikova D. V., Tyunyatkin A. A. et al., IFAC-PapersOnLine 2022 Vol. 55 No. 10 P. 2881–2886
This research extends the interpolation approach to approximating the objective function value for the minimization maximum lateness problem. The interpolation approach is defined using a special objective function Lmax(α), which is proven to be continuous and depends only on α transform coefficient. Such a function is proven to be monotonically increasing, and this property is ...
Added: December 5, 2022
Salnikov A., Stepanova I., Gudkova T. et al., , in: 2021 14th International Conference Management of large-scale system development (MLSD).: IEEE, 2021. P. 1–3.
We have constructed an analytical model of the magnetic field over a region of the Martian surface using satellite raw data and S-approximations within the modified structural-parametric approach. The method mentioned above implies considering the environment features as a function included in an integral. We approximated the anomalous field by the sum of simple and ...
Added: October 30, 2022
Burkov A. A., Shneer S., Turlikov A. M., , in: WAVE ELECTRONICS AND ITS APPLICATION IN INFORMATION AND TELECOMMUNICATION SYSTEMS. 2021. (WECONF 2021) St. Petersburg, Russia, 31 May - 4 June 2021.: IEEE, 2021. Ch. 9470700 P. 1–8.
The development of the Internet of Things technology in cellular networks is considered within the framework of massive machine-type communications with the use of random multiple access algorithms such as ALOHA and its modifications. Despite the fact that this class of algorithms has been studied for a long time, there are no numerical methods for ...
Added: October 28, 2022
Begishev V., Moltchanov D., Gaidamaka A. et al., Sensors 2022 Vol. 22 No. 3 Article 977
Unmanned aerial vehicles (UAV) are envisioned to become one of the new types of fifth/sixth generation (5G/6G) network users. To support advanced services for UAVs such as video monitoring, one of the prospective options is to utilize recently standardized New Radio (NR) technology operating in the millimeter-wave (mmWave) frequency band. However, blockage of propagation paths ...
Added: September 15, 2022