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Anatolii Gordeevich Kostyuchenko (obituary)
Russian Mathematical Surveys. 2010. Vol. 65. No. 4. P. 767-780.
Agranovich M. S., Buchstaber V. M., Ismagilov R. S., Kashin B. S., Mityagin B. S., Novikov S. P., Sadovnichii V. A., Sergeev A. G., Sinai Y. G., Shkalikov A. A.
Analysis of mathematical works of A.G. Kostyuchenko.
Keywords: уравнение в частных производныхзадача Кошиполнота собственных функцийсамосопряженный операторнепрерывный спектрcпектральная асимптотиканесамосопряженный оператороператорный пучокпроблема моментовpartial differential equationthe Cauchy problemcompleteness of eigenfunctionsselfadjoint operatorcontinuous spectrumspectral asymptoticnon-selfadjoint operatoroperator pencilmoment problem
Agranovich M. S., Buchstaber V. M., Ismagilov R. S. et al., Успехи математических наук 2010 Т. 65 № 4 С. 179-190
Математический некролог.
Анализ математического творчества А.Г. Костюченко. ...
Added: April 12, 2012
Вишик М. И., Зелик С. В., Chepyzhov V. V., Математический сборник 2013 Т. 204 № 1 С. 3-46
We study regular global attractors of dissipative dynamical semigroups with discrete and continuous time and we
investigate attractors for non-autonomous perturbations of such semigroups. The main theorem states that regularity of global
attractors preserves under small non-autonomous perturbations. Besides, non-autonomous regular global attractors remain
exponential and robust. We apply these general results to model non-autonomous reaction-diffu\-sion systems in ...
Added: February 17, 2013
Бордюков М. М., Галактинов В. С., Знак В. А. et al., Двойные технологии 2009 № 4 С. 34-38
Necessary and sufficient conditions for controlled system final phase state guaranteed estimation is determined based on properties of attainability sets for problem solution of prediction possible system phase state on fixed points of time. Required sets of attainability approximation conditions by convex polyhedrons are obtained. System final phase state vector belongs to required set estimation ...
Added: March 3, 2013
Zlotnik Alexander, Zlotnik Ilya, Computational Methods in Applied Mathematics 2015 Vol. 15 No. 2 P. 233-245
We consider the Cauchy problem for the 1D generalized Schrὅdinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method with the discrete transpa\-rent boundary conditions (TBCs) has recently been constructed. Now we engage the global Richardson extrapolation in time to derive the high order ...
Added: March 3, 2015
Gorshkov O., Колпаков И. Ю., Афанасенко К. А., Академия педагогических идей «Новация» 2017 № 11 С. 146-153
Conditions of solvability of the Cauchy problem for one differential equation of the first order which hasn't been resolved by rather derivative are found in work. Conditions of solvability of the Cauchy problem were received with application theorem of the Leray–Schauder's type. ...
Added: October 15, 2020
Chepyzhov V. V., Conti M., Pata V., Discrete and Continuous Dynamical Systems 2012 Vol. 32 No. 6 P. 2079-2088
For a semigroup $S(t):X\to X$ acting on a metric space $(X,\dist)$, we give a notion of global attractor
based only on the minimality with respect to the attraction property. Such an attractor is shown to be invariant whenever $S(t)$ is
asymptotically closed. As a byproduct, we generalize earlier results on the existence of global attractors in the ...
Added: February 22, 2013
Zlotnik A., Lomonosov T., Doklady Mathematics 2018 Vol. 98 No. 2 P. 458-463
An explicit two-time-level and spatially symmetric finite-difference scheme approximating the 1D quasi-gasdynamic system of equations is studied. The scheme is linearized about a constant solution, and new necessary and sufficient conditions for the L2 -dissipativity of solutions of the Cauchy problem are derived, including, for the first time, the case of a nonzero background velocity ...
Added: September 12, 2018
Brauer Gomez O., Buryak A., Journal of High Energy Physics 2021 Vol. 2021 P. 1-15
The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution analogous to the Dijkgraaf-Witten formula for a descendent Gromov-Witten potential in genus 1. We then prove that at the approximation ...
Added: February 1, 2021
Roeckner M., Shaposhnikov S., Bogachev V., Journal of Evolution Equations 2013 Vol. 13 No. 3 P. 577-593
We prove a new uniqueness result for highly degenerate second-order parabolic equations on the whole space. A novelty is also our class of solutions in which uniqueness holds. ...
Added: October 15, 2014
Baranov A., Yakubovich D., Journal of Mathematical Analysis and Applications 2015 Vol. 424 No. 2 P. 1404-1424
We study spectral properties of one-dimensional singular nonselfadjoint perturbations of an unbounded selfadjoint operator and give criteria for the possibility to remove the whole spectrum by a perturbation of this type. A counterpart of our results for
the case of bounded operators provides a complete description of compact selfadjoint operators whose rank one perturbation is a
Volterra ...
Added: March 6, 2016
Buryak A., Rossi P., Bulletin of the London Mathematical Society 2021 Vol. 53 No. 3 P. 843-854
In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of stable curves of any genus. These quadratic DR integrals are the main ingredients for the computation of the DR hierarchy associated to the ...
Added: February 1, 2021
Matveenko V. D., Korolev A. V., Zhdanova M. O., Прикладная математика и вопросы управления 2017 № 2 С. 55-64
Мы изучаем игровое равновесие в модели с производством в сети с двумя типами агентов, обладающих разной продуктивностью. Каждый агент может инвестировать часть своего начального запаса в первом из двух временных периодов; потребление во втором периоде зависит от его инвестиций и продуктивности, так же как и от инвестиций его соседей в сети. Мы вводим формализацию понятия ...
Added: August 8, 2017
Buryak A., Rossi P., Shadrin S., Letters in Mathematical Physics 2021 Vol. 111 Article 13
We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomological field theory. Various checks are presented to support the conjecture. ...
Added: October 29, 2021
Andreev N. A., Smirnov S. N., Computational Mathematics and Modeling 2021 Vol. 32 P. 22-44
We consider a guaranteed deterministic approach to discrete-time super-replication for guaranteed coverage of contingent claims on options for all possible asset-price scenarios. Price increases during a period are assumed to be contained in a priori specified compacta dependent on price history. A game problem is stated and reduced to the solution of the corresponding Bellman–Isaacs ...
Added: September 30, 2021
Chebotarev A., Долгопрудный : Физтех-полиграф, 2010
Предисловие.
Теория вероятностей возникла в XVI--XVII веках как раздел математики, объясняющий причины выигрыша или проигрыша в азартных играх. Участие знаменитых ученых потребовалось для анализа игровых стратегий и объяснения ряда фактов отнюдь не очевидных с точки зрения здравого смысла. Вероятностные методы описания окружающей реальности остаются актуальными и сейчас, более того, сложность рассматриваемых систем достигла планетарного масштаба. Стохастические ...
Added: December 28, 2013
Vedenin A., Воеводкин В. С., Galkin V. et al., Математические заметки 2020 Т. 108 № 3 С. 463-468
This communication is devoted to establishing the very first steps in study of the speed at which the error decreases while dealing with the based on the Chernoff theorem approximations to one-parameter semigroups that provide solutions to evolution equations. ...
Added: October 21, 2019
Zlotnik Alexander, Zlotnik Ilya, / Cornell University. Series math "arxiv.org". 2014. No. arXiv:1405.3147.
We consider the Cauchy problem for the 1D generalized Schrödinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method with the discrete transpa\-rent boundary conditions (TBCs) has recently been constructed. Now we engage the Richardson extrapolation to improve significantly the accuracy in time step. ...
Added: May 14, 2014
Korolev A. V., М. : Юрайт, 2017
Данный учебник дает читателю необходимые знания по теории обыкновенных дифференциальных уравнений, теории разностных уравнений и теории стохастических дифференциальных уравнений. Все три названные раздела одинаково необходимы для полноценного экономического образования. Учебник состоит из теоретической и практической частей. В практической части курса подробно и обстоятельно демонстрируются на конкретных примерах методы решения различных задач. В результате изучения данного ...
Added: August 9, 2017
Agranovich M. S., Современная математика. Фундаментальные направления 2011 Т. 39 С. 11-45
Статья посвящена спектральным задачам для сильно эллиптических систем 2-го порядка в ограниченных липшицевых областях. Рассматриваются спектральные задачи Дирихле и Неймана, а также три задачи со спектральным параметром в условиях на границе: задача Пуанкаре-Стеклова
и две задачи сопряжения. В порядке обзора обсуждаются основные свойства этих задач, самосопряженных и несамосопряженных. Предварительно объясняется ряд фактов общей теории основных задач ...
Added: April 12, 2012
Arsie A., Buryak A., Lorenzoni P. et al., Communications in Mathematical Physics 2021 Vol. 388 P. 291-328
We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogeneous) flat F-manifold possesses a (homogeneous) integrable dispersive deformation at all orders in the dispersion parameter. The proof is based on the reconstruction of an F-CohFT starting from a semisimple ...
Added: October 29, 2021
Брауэр О., Buryak A., Функциональный анализ и его приложения 2021 Т. 55 № 4 С. 22-39
In a recent paper, given an arbitrary homogeneous cohomological field theory (CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space of local functionals, which conjecturally gives a second Hamiltonian structure for the double ramification hierarchy associated to the CohFT. In this paper we prove this conjecture in ...
Added: September 14, 2022
Baranov A., Yakubovich D., Advances in Mathematics 2016 Vol. 302 P. 740-798
We study spectral properties of nonselfadjoint rank one perturbations of compact selfadjoint operators. The problems under consideration include completeness of eigenvectors, relations between completeness of the perturbed operator and its adjoint, and the spectral synthesis problem. We obtain new criteria for completeness and spectral synthesis in this class as well as a series of counterexamples ...
Added: February 25, 2018
Nikitin A. A., Доклады Академии наук 2007 Т. 417 № 6 С. 743-745
Added: September 24, 2013
Solvability Problems for a Linear Homogeneous Functional-Differential Equation of the Pointwise Type
Beklaryan A., Beklaryan L. A., Differential Equations 2017 Vol. 53 No. 2 P. 145-156
The Cauchy problem for a linear homogeneous functional-differential equation of the pointwise type defined on a straight line is considered. Theorems on the existence and uniqueness of the solution in the class of functions with a given growth are formulated for the case of the one-dimensional equation. The study is performed using the group peculiarities ...
Added: March 6, 2017