Global in Time Solutions to Kolmogorov–Feller Pseudodifferential Equations with Small Parameter
Russian Journal of Mathematical Physics. 2011. Vol. 18. No. 1. P. 10-25.
Danilov V., Albeverio S.
The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any integral representation. For completeness, we also briefly describe the well-known scheme developed by V. P. Maslov for constructing global-in-time solutions.
Priority areas: IT and mathematics mathematics
, Mathematics of Computation 2017 Vol. 86 No. 305 P. 1499-1524
For an arbitrary set of nonnegative integers, we consider the Euler binary partition function which equals the total number of binary expansions of an integer with ``digits'' from . By applying the theory of subdivision schemes and refinement equations, the asymptotic behaviour of as is characterized. For all finite , we compute the lower and upper exponents of growth of , find when ...
Added: May 11, 2017
, , Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 334-343
The problem of viscous compressible fluid flow in an axially symmetric pipe with small periodic irregularities on the wall is considered for large Reynolds numbers. An asymptotic solution with double-deck structure of the boundary layer and unperturbed core flow is obtained. Numerical investigations of the influence of the density of the core flow on the flow behavior in ...
Added: September 2, 2019
, , Вестник Московского государственного строительного университета 2014 № 7 С. 34-40
A classic pursuit problem is studied in which two material points - a Pursuer and a Pursued - move in a plane at constant speeds. The velocity vector of the Pursued does not change its direction and the velocity vector of the Pursuer turns and always aims at the Pursued. If the Pursuer moves at ...
Added: August 3, 2014
, Математические заметки 2017 Т. 102 № 6 С. 816-827
Asymptotic formulas are obtained for a class of integrals that are Fourier transforms of rapidly oscillating functions. These formulas contain special functions and generalize the well-known method of stationary phase. ...
Added: January 13, 2018
Асимптотическое поведение собственных значений оператора Шредингера в тонких бесконечных и тонких замкнутых трубках
, Наноструктуры. Математическая физика и моделирование 2012 Т. 7 № 2 С. 17-44
В работе получено асимптотическое разложение собственных значений оператора Лапласа с нулевыми данными Дирихле в бесконечных трубках, т. е. в бесконечных изогнутых цилиндрах с внутренним кручением при равномерном сжатии поперечных сечений, по малому параметру, характеризующему поперечные размеры трубки. Аналогичное разложение получено для оператора Шредингера с учетом магнитного поля для конечных изогнутых трубок. Предложен метод сведения задачи ...
Added: December 24, 2012
М. : ИКИ РАН, 2011
Added: March 26, 2013
Added: November 26, 2019
On the asymptotics of the element counting function in an additive arithmetic semigroup with exponential counting function of prime generators
, , , Functional Analysis and Its Applications 2016 Vol. 50 No. 4 P. 291-307
We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators. ...
Added: October 18, 2015
, , , Bernoulli: a journal of mathematical statistics and probability 2015 P. 740-759
In this paper, we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an estimation of the mean distribution. Moreover, when the distributions are a common measure warped by a ...
Added: October 13, 2018
, , Дискретный анализ и исследование операций 2008 Т. 15 № 1 С. 3-10
Доказывается полиномиальная разрешимость задачи о независимом множестве для бесконечного семейства подмножеств класса планарных графов. ...
Added: August 31, 2012
Lanham : University Press of America, 2012
The history of logic and analytic philosophy in Central and Eastern Europe is still known to very few people. As an exception to the rule, only two scientific schools became internationally popular: the Vienna Circle and the Lvov-Warsaw School. Nevertheless, the countries included in this region have not only joint history, but also joint cultural ...
Added: February 13, 2013
, , et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014
, European Journal of Operational Research 2009 Vol. 198 No. 1 P. 102-112
Added: July 31, 2012
Интегрированные модели и мягкие вычисления в искусственном интеллекте. Сб. научных трудов VII-й Международной научно-практической конференции (Коломна, 20-22 мая 2013)
М. : Физматлит, 2013
Conference is devoted to application of the integrated models and soft computing in artificial intelligence. ...
Added: May 26, 2013
, , Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 179-187
In this paper, we show how to construct an asymptotic representation of the fundamental solution to the Cauchy problem for degenerate linear parabolic equations. ...
Added: June 6, 2021
The complexity of the 3-colorability problem in the absence of a pair of small forbidden induced subgraphs
, Discrete Mathematics 2015 Vol. 338 No. 11 P. 1860-1865
We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. ...
Added: April 7, 2014
Nonstationary double-deck structure of boundary layers in compressible flow problem inside a channel with small irregularities on the walls
, , Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 224-243
A subsonic flow of a viscous compressible fluid in a two-dimensional channel with small periodic or localized irregularities on the walls for large Reynolds numbers is considered. A formal asymptotic solution with double-deck structure of the boundary layer is constructed. A nontrivial time hierarchy is discovered in the decks. An analysis of the scales of irregularities at ...
Added: March 22, 2021
, , Сибирский журнал индустриальной математики 2013 Т. XVI № 4 С. 111-120
The paper considers the problem of determining the rate of cooling of metal during solidification at the intersection of the liquidus temperature under intense heat sink from the surface. The solution to this problem it is necessary to determine the process conditions, the boundary and initial conditions for which it is possible to get new ...
Added: November 17, 2013
Increasing the performance of a Mobile Ad-hoc Network using a game-theoretic approach to drone positioning
, , et al., Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya 2019 Vol. 15 No. 1 P. 22-38
We describe a novel game-theoretic formulation of the optimal mobile agents’ placement problem which arises in the context of Mobile Ad-hoc Networks (MANETs). This problem is modelled as a sequential multistage game. The definitions of both the Nash equilibrium and cooperative solution are given. A modification was proposed to ensure the existence of a Nash ...
Added: March 13, 2020
Agent-based modelling of interactions between air pollutants and greenery using a case study of Yerevan, Armenia
, , , Environmental Modelling and Software 2019 Vol. 116 P. 7-25
Urban greenery such as trees can effectively reduce air pollution in a natural and eco-friendly way. However, how to spatially locate and arrange greenery in an optimal way remains as a challenging task. We developed an agent-based model of air pollution dynamics to support the optimal allocation and configuration of tree clusters in a city. The Pareto ...
Added: February 24, 2019
, Journal of Applied and Industrial Mathematics 2020 Vol. 14 No. 4 P. 706-721
The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...
Added: January 30, 2021
, Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Совершенствование преподавания дисциплин математического цикла на основе инвариантов, необходимых для преподавания курса «Эконометрика» экономистам-бакалаврам
, , Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
, , Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016