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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.

Netay I. V., Savvateev A. V., Bulletin of the Korean Mathematical Society 2017 Vol. 54 No. 5 P. 1597-1617

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely ...

Added: April 11, 2018

Kamenev I., Каменев Г. К., Труды Института системного анализа Российской академии наук 2018 Т. 68 № 2 С. 30-33

The article describes mathematical analysis methods of distributions in multidimensional space of subject’s characteristics in social sciences. The necessity is motivated to take into account measure (frequency) and metric. Methods of metric reliability analysis for the general population are considered using (e, d)-sets (Shannon). As an example UN Human Development Data are analyzed. ...

Added: August 2, 2018

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

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

Pavlov A., Journal of Algebra 2019 Vol. 526 P. 211-242

We apply Orlov's equivalence to derive formulas for the Betti numbers of maximal Cohen-Macaulay modules over the cone an elliptic curve $(E,x)$ embedded into $\mathbb{P}^{n-1}$, by the full linear system $|\mathcal{O}(nx)|$, for $n>3$. The answers are given in terms of recursive sequences. These results are applied to give a criterion of (Co-)Koszulity.
In the last two ...

Added: May 24, 2019

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

Bliznets Ivan, Cygan M., Komosa P. et al., , in : Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Vol. 60.: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2016. Ch. 3. P. 1-17.

The H-free Edge Deletion problem asks, for a given graph G and integer k, whether it is possible to delete at most k edges from G to make it H-free, that is, not containing H as an induced subgraph. The H-free Edge Completion problem is defined similarly, but we add edges instead of deleting them. ...

Added: October 31, 2018

Martynov G., Automation and Remote Control 2010 Vol. 71 No. 7 P. 1346-1357

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 ...

Added: March 23, 2014

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

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

Silvanovich O. V., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2018 Vol. 51 No. 3 P. 267-275

For more than a century, the constructive description of functional classes in terms of the possible rate of approximation of its functions by means of functions chosen from a certain set remains among the most important problems of approximation theory. It turns out that the nonuniformity of the approximation rate due between the points of ...

Added: November 26, 2018

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

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

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

Чирухин В. А., Записки Горного института 2014 Т. 208 С. 197-202

In the article the methods of processing of statistical data about periodic process by the least squares method with usage of Bessel functions and Fourie numbers are analyzed. The simple method for approximation with a choice of the fluctuation period, proceeding from a minimum of the estimated error is offered. ...

Added: October 31, 2017

Синцова К. А., Записки научных семинаров ПОМИ РАН 2023

Added: September 5, 2023

Yashunsky A., Algebra Universalis 2019 Vol. 80 No. 1 (5) P. 1-16

We consider the problem of approximating distributions of Bernoulli random variables by applying Boolean functions to independent random variables with distributions from a given set. For a set B of Boolean functions, the set of approximable distributions forms an algebra, named the approximation algebra of Bernoulli distributions induced by B. We provide a complete description ...

Added: September 9, 2020

Poberezhny V. A., Matveeva A., Journal of Geometry and Physics 2017 Vol. 114 P. 384-393

We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along a−cycle is ...

Added: October 26, 2016

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

Serge Lvovski, Springer, 2020

This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they ...

Added: October 27, 2020

Puzino Y. A., Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния 2014 № 22 С. 46-52

The increasing of the efficiency of technological modes of steel products manufacturing requires simulation of metal forming during hot deformation. To obtain correct results, one should set the correct initial and boundary conditions, including the mechanical properties of materials, which represent the dependence of the stress-strain and strain rate at maintained temperature.
In the experiments one ...

Added: January 19, 2015

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

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

Gorchakov A., Ignatov A., Малышев Д. И. et al., International Journal of Open Information Technologies 2019 Т. 7 № 1 С. 1-7

Рабочей областью робота называется множество положений, которые может принимать его рабочий инструмент. Знание рабочей области необходимо при проектировании роботов, их размещении, оценке их функциональных возможностей, прокладке траектории движения робота. К настоящему времени разработано много методов для определения рабочей области. Следует заметить, что наибольшим потенциалом обладают детерминированные методы, позволяющие в автоматическом режиме получать аппроксимации с заданной ...

Added: October 23, 2019