• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Asymptotic estimates for singular integrals of fractions with divisors, given by products of quadratic block-forms
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
June 4, 2026
Machine Learning Models Can Help Reduce Volatility and Boost Stock Market Returns
The use of machine learning models makes it possible to achieve greater accuracy in predicting risks in the Russian stock market compared to classical econometric approaches. The predictive power of these models increases by 23%, while the average investor’s return can reach up to 13% per annum. These conclusions were drawn by Nikita Lysenok from the Department of Financial Market Infrastructure at the HSE Faculty of Economic Sciences. The paper has been published in Fundamental and Applied Mathematics.
June 3, 2026
Pocket Money, Personal Interest, and Family Practices: What Shapes Students Economic Literacy?
University students' economic literacy depends not only on their field of study but also on their interest in economics, the learning environment, and family financial practices. For example, students who received pocket money irregularly tend to perform better on economic literacy tests than their peers who received financial support on a regular basis. These findings come from a study conducted by HSE University involving more than 1,100 students from five Russian universities. The findings have been published in Cakrawala Pendidikan.
June 3, 2026
Creative Work as a Remedy for Burnout
The creative, supportive atmosphere and innovative methods at the Centre for Sociocultural Research make it appealing to early-career scholars. Over years of working at HSE University, they grow into researchers and lecturers recognised both in Russia and abroad. Chief Research Fellow Zarina Lepshokova and Leading Research Fellow Ekaterina Bushina spoke about their journey at the centre and at HSE, their research, and the role of mentors in their academic success.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Asymptotic estimates for singular integrals of fractions with divisors, given by products of quadratic block-forms

Proceedings of the Steklov Institute of Mathematics. 2020. Vol. 310. P. 161–175.
Dymov A. V.
Language: English
Keywords: Singular integralsquadratic formsstationary phase methodwave turbulence
Similar publications
On the Zakharov-L’vov stochastic model for wave turbulence
Kuksin S., Dymov A. V., Doklady Mathematics 2020 No. 101 P. 102–109
In this paper we discuss a number of rigorous results in the stochastic model for wave turbulence due to Zakharov–L'vov. Namely, we consider the damped/driven (modified) cubic nonlinear Schrödinger equation on a large torus and decompose its solutions to formal series in the amplitude. We show that when the amplitude goes to zero and the ...
Added: April 2, 2025
Формы Пфистера и гипотеза Кольё-Телена для случая смешанной характеристики
Панин И. А., Tyurin D., Известия РАН. Серия математическая 2024 Т. 88 № 5 С. 174–186
Let R be a regular local ring of mixed characteristic (0,p), where p≠2 is a prime number. Suppose that the quotient ring R/pR is also regular. We fix a non-degenerate Pfister form Q over R and an invertible element c in R. Then the equation Q=c has a solution over R if and only if it has a solution over the fraction field K. ...
Added: February 11, 2025
Асимптотические разложения для одного класса сингулярных интегралов, возникающих в нелинейных волновых системах
Dymov A. V., Теоретическая и математическая физика 2023 Т. 214 № 2 С. 179–197
We find asymptotical expansions as $\nu \to 0$ for integrals of the form   $\int_{\mathbb{R}^d} F(x) / \big(\omega(x)^2 + \nu^2\big)\, dx$,      where sufficiently smooth functions $F$ and  $\omega$ satisfy natural assumptions for their behaviour at infinity and all critical points of the function $\omega$ from the set $\{\omega(x) = 0\}$ are non-degenerate. ...
Added: November 29, 2023
The Large-Period Limit for Equations of Discrete Turbulence
Kuksin S., Maiocchi A., Vladuts S. et al., Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics 2023 Vol. 24 P. 3685–3739
We consider the damped/driven cubic NLS equation on the torus of a large period $L$ with a small nonlinearity of size $\lambda$,   a properly scaled random forcing and dissipation. We examine its solutions under the subsequent limit when first $\lambda\to 0$ and then $L\to \infty$. The first limit, called the limit of discrete turbulence, is ...
Added: November 28, 2023
Approximate Methods for Solving Hypersingular Integral Equations on Fractals
Boykov I., Boykova A., Potapov A. et al., , in: 14th Chaotic Modeling and Simulation International Conference.: Springer, 2022. Ch. 7 P. 81–95.
The paper consists of three parts. The first one is devoted to approximate methods for evaluating Riemann integrals, singular and hypersingular integrals on closed non-rectifiable curves and fractals in the complex plane. An integral on non-rectifiable curves or fractals is defined as a double integral over a region that bounded by a non-rectifiable curve or ...
Added: January 15, 2023
Formal Expansions in Stochastic Model for Wave Turbulence 2: Method of Diagram Decomposition
Dymov A. V., Kuksin S., Journal of Statistical Physics 2023 Vol. 190 No. 1 Article 3
In this paper we continue to study small amplitude solutions of the damped cubic NLS equation, driven by a random force [the study was initiated in our previous work Dymov and Kuksin (Commun Math Phys 382:951–1014, 2021) and continued in Dymov et al. (The large-period limit for equations of discrete turbulence 2021, arXiv:2104.11967)]. We write solutions ...
Added: October 31, 2022
Шашки Фейнмана: к алгоритмической квантовой теории
М. Б. Скопенков, А. В. Устинов, Успехи математических наук 2022 Т. 77 № 3(465) С. 73–160
We survey and develop the most elementary model of electron motion introduced by R.Feynman. In this game, a checker moves on a checkerboard by simple rules, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk or an Ising model at imaginary temperature. We solve mathematically a problem by R.Feynman ...
Added: August 12, 2022
Formal Expansions in Stochastic Model for Wave Turbulence 1: Kinetic Limit
Dymov A. V., Kuksin S., Communications in Mathematical Physics 2021 Vol. 382 P. 951–1014
We consider the damped/driven (modified) cubic NLS equation on a large torus with a properly scaled forcing and dissipation, and decompose its solutions to formal series in the amplitude. We study the second order truncation of this series and prove that when the amplitude goes to zero and the torus’ size goes to infinity the energy spectrum of the ...
Added: June 29, 2021
Observation of a local maximum in the stationary turbulent spectrum of capillary waves on the surface of liquid hydrogen
Remizov I. A., Musaeva M. R., A. V. Orlov et al., Low Temperature Physics 2019 Vol. 45 No. 4 P. 363–366
The results of experimental studies of wave turbulence in a system of capillary waves formed on the surface of liquid hydrogen at a tempera-ture of 15 K in a cylindrical cell with monochromatic radially symmetric pumping are presented. The local maximum formation with adecrease in the pumping amplitude was observed for thefirst time in the ...
Added: April 14, 2019
Injectivity theorem for homotopy invariant presheaves with Witt-transfers
Чепуркин К. М., St Petersburg Mathematical Journal 2017 Vol. 28 No. 2 P. 291–297
A definition of the category of Witt-correspondences over a field of characteristic different from 2 is given, the presheafs with Witt-transfers are introduced, and a series of general properties of these objects are established. In Theorem 1, the injectivity theorem is shown to be true for a homotopy invariant presheaf with Witt-transfers and for the local ...
Added: February 3, 2019
Низкочастотные субгармоники в турбулентном спектре на поверхности жидкого водорода
Brazhnikov M., Левченко А. А., Межов-Деглин Л. П. et al., Письма в Журнал экспериментальной и теоретической физики 2015 Т. 100 № 10 С. 753–759
Formation of low frequency harmonics on turbulent distribution in the system of waves on the surface of liquid hydrogen has been studied in the frequency range 1-100 Hz (capillary-gravity waves). It is shown that the geometry of the experimental cell has a significant influence on the direct cascade of capillary waves generated by monochromatic force ...
Added: January 20, 2019
Wave turbulence on the surface of liquid hydrogen in restricted geometry: The influence of the boundary conditions
Brazhnikov M., Левченко А. А., Межов-Деглин Л. П. et al., Low Temperature Physics 2015 Vol. 41 No. 6 P. 484–487
Formation of low frequency harmonics on turbulent distribution in the system of waves on the surface of liquid hydrogen has been studied in the frequency range 1-100 Hz (capillary-gravity waves). It is shown that the geometry of the experimental cell has a significant influence on the direct cascade of capillary waves generated by monochromatic force ...
Added: January 20, 2019
Observation of dynamic maximum in a turbulent cascade on the surface of liquid hydrogen
Ремизов И. А., Brazhnikov M., Левченко А. А., Low Temperature Physics 2016 Vol. 42 No. 12 P. 1067–1070
We report on the experimental observation of energy accumulation near the high frequency boundary of the inertial range in the spectrum of turbulence in a system of capillary waves on the surface of liquid hydrogen driven by a harmonic force. The effect is manifested as a local maximum in the spectrum of pair correlation function ...
Added: January 20, 2019
SERIES OF OPERATORS IN L2(ℂ) THAT ARE PROPORTIONAL TO UNITARY ONES
N. A. Shirokov, Journal of Mathematical Sciences 2014 Vol. 202 No. 4 P. 613–622
We prove that singular integral operators in L2(ℂ) defined by the formula w(z)=bz¯¯¯ ...
Added: June 26, 2017
On the scaling limit of a singular integral operator
Krichever I., Phong D. H., Geometriae Dedicata 2008 Vol. 132 No. 1 P. 121–134
The scaling limit and Schauder bounds are derived for a singular integral operator arising from a difference equation approach to monodromy problems. ...
Added: April 17, 2014
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit