Тула: Тульский государственный педагогический университет им. Л.Н. Толстого, 2025.
Сборник содержит материалы, представленные на XXIV Международной конференции «Алгебра, теория чисел, дискретная геометрия и многомасштабное моделирование: современные проблемы, приложения и проблемы истории», посвящённой 110-летию со дня рождения академика Юрия Владимировича Линника и 110-летию со дня рождения профессора Андрея Борисовича Шидловского и 80-летию со дня рождения профессора Геннадия Ивановича Архипова. Материалы конференции будут полезны научным работникам, ...
Added: August 27, 2026
World Scientific Publishing Co. Pte. Ltd, 2011.
In this paper the analogue of the Hopf–Cole transformation is introduced for manifolds. It has been shown that under certain conditions this transformation connects the Burgers equation and Kolmogorov–Petrovsky–Piskunov equation on pseudo-Riemannian manifolds. ...
Added: October 26, 2025
Flamarion M. V., Pelinovsky E., Makarov D., Physics Letters A 2024 Vol. 527 Article 130000
In this work, we examine the classical Burgers equation and investigate the effects of a random force on the wave
field. Two scenarios are considered: the impact of a random force on different wave fields within the viscous
Burgers equation and the effect of a periodic random force in the inviscid Burgers equation. For the first case,
we ...
Added: October 23, 2024
Idrisova V. A., Tokareva N. N., Gorodilova A. A. et al., Prikladnaya Diskretnaya Matematika 2023 No. 62 P. 29–54
Every year the International Olympiad in Cryptography Non-Stop University CRYPTO (NSUCRYPTO) offers mathematical problems for university and school students and, moreover, for professionals in the area of cryptography and computer science. The main goal of NSUCRYPTO is to draw attention of students and young researchers to modern cryptography and raise awareness about open problems in ...
Added: March 19, 2024
Kalmynin A. B., Konyagin S., / Series math "arxiv.org". 2023. No. 2303.14833.
Added: November 22, 2023
Vedenin A., Журнал Средневолжского математического общества 2022 Т. 24 № 3 С. 280–288
This paper is devoted to a new method for constructing approximations to the solution of a parabolic partial differential equation. The Cauchy problem for the heat equation on a straight line with a variable heat conduction coefficient is considered. In this paper, a sequence of functions is constructed that converges to the solution of the ...
Added: May 18, 2023
Dragunova K., Гаращенкова А. А., Remizov I., / Series arXiv "math". 2021.
Chernoff approximations are a flexible and powerful tool of functional analysis, which can be used, in particular, to find numerically approximate solutions of some differential equations with variable coefficients. For many classes of equations such approximations have already been constructed, however, the speed of their convergence to the exact solution has not been properly studied. ...
Added: December 16, 2021
Maslov V. P., Mathematical notes 2021 Vol. 109 No. 2 P. 241–246
In this article, the notions of tropical mathematics and subtropical mathematics are studied. The main principles of tropical analysis and examples of their application to various problems are considered. ...
Added: February 7, 2021
Maslov V. P., Mathematical notes 2017 Vol. 102 No. 4 P. 583–586
Added: November 17, 2018
Maslov V. P., Russian Journal of Mathematical Physics 2017 Vol. 24 No. 2 P. 249–260
In the paper, the problem of partitioning a natural number into summands is considered in connection with the BKT (Berezinskii–Kosterlitz–Thouless) phase transition and its two critical points. As examples, the passage from superfluid state to normal state and from a cell-like vortical state to turbulent state are considered. ...
Added: November 17, 2018
Maslov V. P., Mathematical notes 2017 Vol. 101 No. 3 P. 488–496
Abstract—Regularization of the Bose–Einstein distribution using a parastatistical correction,
i.e., by means of the Gentile statistics, is carried out. It is shown that the regularization result
asymptotically coincides with the Erdo˝ s formula obtained by using Ramanujan’s formula for the
number of variants of the partition of an integer into summands. TheHartley entropy regarded as the
logarithm of the ...
Added: October 28, 2018
Maslov V., Mathematical notes 2017 Vol. 101 No. 4 P. 660–665
In the paper “The relationship between the Fermi–Dirac distribution and statistical
distributions in languages” (This issue of “Math. Notes”), the Bose–Einstein and Fermi–Dirac
distributions are considered in connectionwith frequency distributions in languages in the context of
the author’s approach to thermodynamics and number theory problems. The present article presents
certain clarifications of certain notions used in that approach, in ...
Added: October 28, 2018
Remizov I., Infinite Dimensional Analysis, Quantum Probability and Related Topics 2018 Vol. 21 No. 4 P. 1850025-1–1850025-35
A parabolic partial differential equation u 0 t (t, x) = Lu(t, x) is considered, where L is a linear second-order differential operator with time-independent (but dependent on x) coefficients. We assume that the spatial coordinate x belongs to a finite- or infinitedimensional real separable Hilbert space H. The aim of the paper is to ...
Added: October 5, 2018
Remizov I., Journal of Functional Analysis 2016 Vol. 270 No. 12 P. 4540–4557
For a densely defined self-adjoint operator $\mathcal{H}$ in Hilbert space $\mathcal{F}$ the operator $\exp(-it\mathcal{H})$ is the evolution operator for the Schr\"odinger equation $i\psi'_t=\mathcal{H}\psi$, i.e. if $\psi(0,x)=\psi_0(x)$ then $\psi(t,x)=(\exp(-it\mathcal{H})\psi_0)(x)$ for $x\in Q.$ The space $\mathcal{F}$ here is the space of wave functions $\psi$ defined on an abstract space $Q$, the configuration space of a quantum system, ...
Added: March 3, 2018
Zybin K., Il'yn A. S., Physics-Uspekhi 2016 Vol. 59 No. 12 P. 1241–1244
This paper reviews the statistical properties and calculates the velocity structure functions of flows produced by a large-scale random scaling force in the Burgers model. ...
Added: September 22, 2017
Tyurin N. A., Успехи математических наук 2017 Т. 72 № 3 С. 131–169
В настоящем обзоре представлено обобщение понятия торической структуры на компактном симплектическом многообразии, получившее название псевдоторической структуры. На языке этих новых структур оказалось удобным и естественным описание многих нестандартных лагранжевых подмногообразий и циклов (а именно, экзотических торов Чеканова, циклов Миронова в некоторых частных случаях и др.), а также построение лагранжевых слоений (например, специальных в смысле Д. ...
Added: June 13, 2017
Kolokolov I., Lebedev V., Falkovich G. et al., International Journal of Modern Physics B 1997 Vol. 11 No. 26/27 P. 3223–3245
We consider
the tails of probability density functions (PDF) for different characteristics
of velocity that satisfies Burgers equation driven by a large-scale force.
The saddle-point approximation is employed in the path integral
so that the calculation of the PDF tails
boils down to finding the special field-force configuration (instanton) that
realizes the extremum of probability. We calculate high moments of the ...
Added: March 6, 2017
Kolokolov I., Lebedev V., Falkovich G. et al., Physical Review Letters 1997 Vol. 78 No. 8 P. 1452–1455
We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For ...
Added: March 6, 2017
Kolokolov I., JETP Letters 2000 Vol. 71 No. 1 P. 12–14
Leading terms of the asymptotic behavior of the pair and higher order correlation functions for finite times and large distances have been calculated for the Burgers equation involving thermal noise. It is shown that an intermittence phenomenon occurs, whereby certain correlation functions are much greater than their reducible parts. ...
Added: March 5, 2017
Kolokolov I., Turitsyn K., Journal of Experimental and Theoretical Physics 2002 Vol. 94 No. 6 P. 1193–1200
For the field u(x, t) governed by the Burgers equation with a thermal noise, short-time asymptotics
of multipoint correlators are obtained. Their exponential parts are independent of the correlator number. This
means that they are determined by a single rare fluctuation and exhibit the intermittency phenomenon ...
Added: February 25, 2017
Maslov V. P., Dobrokhotov S. Y., Nazaikinskii V. E., Mathematical notes 2016 Vol. 100 No. 5 P. 828–834
We develop the recent research [1] and introduce the notions of volume and entropy in abstract analytic number theory. The introduction of negative numbers in the generalized partition problem, together with the meaning of such a generalization in some applications of the theory, is discussed. ...
Added: February 21, 2017
Kolokolov I., Korshunov S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2009 Vol. 80 P. 031107
The free-energy distribution function of an elastic string in a quenched random potential, PLF, is investigated
with the help of the optimal fluctuation approach. The form of the far-right tail of PLF is found by
constructing the exact solution of the nonlinear saddle-point equations describing the asymptotic form of the
optimal fluctuation. The solution of the problem is ...
Added: February 8, 2017