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## 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.

Language:
English

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

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

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

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

Grushin V. V., Математические заметки 2016

...

Added: December 13, 2016

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

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

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

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

Krichever I. M., 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

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

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

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

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