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Multivariable Goodness Tests and Approximation of the Residues of Quadratic Forms
Automation and Remote Control. 2010. Vol. 71. No. 7. P. 1346–1357.
Martynov G.
Consideration was given to the omega square Cramer–von Mises tests intended to verify the goodness hypothesis about the distribution of the observed multivariable random vector with the distribution in the unit cube. The limit distribution of the statistics of these tests was defined by the distribution of an infinite quadratic form in the normal random variables. For convenience of computing its distribution, the residue of the quadratic form was approximated by a finite linear combination of the χ2-distributed random variables. Formulas for determination of the residue parameters were established.
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
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
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
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
Шагай М. А., Флегонтов А. В., Иофе М. Д., Springer 2021
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. ...
Added: February 6, 2023
М.: Национальный исследовательский университет "Высшая школа экономики", 2022.
Added: January 12, 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
Zhmud V., Dimitrov L., Sablina G. et al., , in: 2021 XV International Scientific-Technical Conference on Actual Problems Of Electronic Instrument Engineering (APEIE).: Newark: IEEE, 2021. P. 465–470.
Added: August 27, 2022
Shchemeleva I., Journal of English as a Lingua Franca 2022 Vol. 11 No. 1 P. 1–23
In the last decade numerous studies have been published in the field of English as an academic lingua franca (academic ELF). The majority of them, however, are devoted to the speaking mode. The present paper investigates written academic ELF texts – research articles in the social sciences and humanities. It explores the ways in which ...
Added: August 13, 2022
Высоцкий Л. И., Журнал вычислительной математики и математической физики 2021 Т. 61 № 5 С. 776–786
Tensorizations of functions are studied, that is, tensors with elements 𝐴(𝑖1,…,𝑖𝑑)=𝑓(𝑥(𝑖1,…,𝑖𝑑)) 𝐴(𝑖1,…,𝑖𝑑)=𝑓(𝑥(𝑖1,…,𝑖𝑑)), where 𝑓(𝑥) is some function defined on an interval and {𝑥(𝑖1,…,𝑖𝑑)} is a grid on this interval. For tensors of this type, the problem of approximation by tensors admitting a tensor train (ТТ) decomposition with low ТТ ranks is posed. For the class ...
Added: October 31, 2021
Yashunsky A., Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 1 P. 217–221
We consider transformations of random variables on finite sets by algebraic operations. A system of operations is said to be approximation complete if any random variable may be approximated with arbitrary precision by applying the given operations to mutually independent identically distributed random variables whose distributions have no zero components. We establish some necessary conditions ...
Added: July 6, 2021
Yashunsky A., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2020 Vol. 14 No. 3 P. 581–591
We consider the transformations of independent random variables over a linearly ordered finite set (a chain) by the join and meet operations. We investigate the possibility of approximating an arbitrary probability distribution on a chain by means of a (possibly iterated) application of the join and meet operations to independent random variables with distributions from ...
Added: July 6, 2021
Igor Kheifets, Velasco C., , in: Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis, Essays in Honor of Halbert L. White Jr.: NY: Springer, 2012. P. 363–382.
This chapter proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct specification of parametric conditional distributions in dynamic discrete choice models, not only of some particular conditional characteristics such as moments or ...
Added: February 23, 2021