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Принцип Лере-Шаудера в применении к исследованию одного нелинейного интегрального уравнения
Дифференциальные уравнения. 2019. Т. 55. № 9. С. 1209-1217.
Николаев М. В., Nikitin A. A.
Гаджиев С. Р., Nikitin A. A., Современные информационные технологии и ИТ-образование 2019 Т. 15 № 2 С. 298-305
This article is devoted to the nonlinear integral equation arising in the biological model of Ulf Dieckmann and Richard Low. A brief review of the model of foreign authors Individual-based model is made, the meaning and necessity of introducing spatial moments is described. The following is the derivation of the nonlinear equation (for the equilibrium ...
Added: November 7, 2019
Nikitin A. A., Nikolaev M. V., Differential Equations 2019 Vol. 55 No. 9 P. 1164-1173
We study a nonlinear integral equation arising from the parametric closure for the third spatial moment in the Dieckmann-Law model of stationary biological communities. The existence of a fixed point of the integral operator defined by this equation is analyzed. The noncompactness of the resulting operator is proved. Conditions are stated under which the equation ...
Added: November 7, 2019
Николаев М. В., Nikitin A. A., Доклады Академии наук 2019 Т. 488 № 6 С. 595-598
В данной работе изучается нелинейное интегральное уравнение, возникшее в пространственной модели
биологических сообществ, разработанной австрийскими учёными Ульфом Дикманом и Ричардом Лоу.
Были найдены достаточные условия существования решения данного уравнения (неподвижной точки
интегрального оператора). Также изучен вопрос о единственности решения. ...
Added: November 7, 2019
Nikitin A. A., International Journal of Open Information Technologies 2018 Т. 6 № 10 С. 1-8
This article is devoted to the mathematical formulation and numerical study of the spatial model of stationary biological communities by U. Dickman and R. Low. The main idea of this model is to find a "projection" of the simulated biological process on certain characteristics, the dynamics of which can be written analytically. Such "characteristics" in ...
Added: October 25, 2018
Гаджиев С. Р., Галкин Е. Г., Nikitin A. A., Вестник Московского университета. Серия 15: Вычислительная математика и кибернетика 2021 № 2 С. 11-18
This article explores nonlinear integral equation system that appears in the biological model of spatial stochastic population dynamics by U. Dieckmann and R. Law. We introduce the model and explain the reasoning behind using spatial moments within this model. We show derivation of nonlinear integral equation for equilibrium state after performing third degree closure on ...
Added: December 15, 2020
Nikolaev M. V., Nikitin A. A., Doklady Mathematics 2019 Vol. 100 No. 2 P. 485-487
A nonlinear integral equation arising in the spatial model of biological communities developed by Austrian
scientists Ulf Dieckmann and Richard Law is studied. Sufficient conditions for the existence of a solution of
this equation (a fixed point of the integral operator) are found. The uniqueness of the solution is also analyzed. ...
Added: November 7, 2019
Данченко В. И., Давыдов А. А., Nikitin A. A., М. : Издательский отдел факультета ВМК МГУ им. М.В. Ломоносова, 2009
Added: September 24, 2013
Nikitin A. A., Nikolaev M. V., Moscow University Computational Mathematics and Cybernetics 2018 Vol. 42 No. 3 P. 105-113
Integral equations emerging in a model of stationary biological communities such that their kernels have variable coefficients of excess (kurtosian kernels)are investigated. The dependence of the first and second spatial moment on the dimension of the environment is considered. A fastcomputation algorithm for the multi-dimensional nonlinear convolution is considered. The existence of a radial solution ...
Added: October 25, 2018
Nikitin A. A., Савостьянов А. С., Вестник Московского университета. Серия 15: Вычислительная математика и кибернетика 2017 № 3 С. 18-25
В настоящей статье рассматривается двухвидовая модель самоструктурирующихся стационарных биологических сообществ, предложенная Ульфом Дикманом и Ричардом Лоу. Разработан метод изучения системы интегро-дифференциальных уравнений, описывающей динамику данной модели. ...
Added: December 15, 2016
Nikitin A. A., Бодров А. Г., Вестник Московского университета. Серия 15: Вычислительная математика и кибернетика 2015 № 4 С. 7-13
multidimensional integral equation ...
Added: September 30, 2015
Nikitin A. A., Savost’yanov Anton Sergeevich, Moscow University Computational Mathematics and Cybernetics 2017 Vol. 41 No. 3 P. 122-129
The two-species model of self-structured stationary biological communities proposed by U. Dieckmann and R. Law is considered. A way of investigating the system of integro-differential equations describing the model equilibrium is developed, nontrivial stationary points are found, and constraints on the model parameter space resulting in similar stationary points are studied. The results are applied ...
Added: September 3, 2018
Nikitin A.A., Savost’yanov A. S., Moscow University Computational Mathematics and Cybernetics 2017 Vol. 41 No. 3 P. 122-129
The two-species model of self-structured stationary biological communities proposed by U. Dieckmann and R. Law is considered. A way of investigating the system of integro-differential equations describing the model equilibrium is developed, nontrivial stationary points are found, and constraints on the model parameter space resulting in similar stationary points are studied. The results are applied ...
Added: September 3, 2017
Bodrov A.G., Nikitin A. A., Moscow University Computational Mathematics and Cybernetics 2015 Vol. 39 No. 4 P. 157-162
A computational solution to the integral equation in the biological spatial model is found. The numerical techniques that are used (the Nystr{\"o}m and Neumann series methods, the latter being one of successive approximations) yield a reasonably accurate solution. An approach of moving from multidimensional equations to a one-dimensional equation for high-dimensional spaces is proposed. Explicit ...
Added: September 28, 2017
Gadzhiev S., Галкин Е. Г., Nikitin A. A., Moscow University Computational Mathematics and Cybernetics 2021 Vol. 45 No. 2 P. 53-59
A study is performed of the nonlinear integral equation that arises in the biological
model of Dieckmann and Law. A brief outline of the model is given, and the meaning and need
to introduce spatial moments are described. The nonlinear equation (for the state of equilibrium)
is derived from the system of dynamics of spatial moments after power-3 ...
Added: October 1, 2021
Kalistratova A., Nikitin A. A., Doklady Mathematics 2016 Vol. 94 No. 2 P. 574-577
In this paper, we study the integral equation that has arisen in the spatial model of stationary communities developed by Austrian scientists Ulf Dickman and Richard Low. A special case of this equation is considered with integral kernels, which are the Student’s distribution. The existence of a solution in this case is proved, and the ...
Added: December 8, 2016
Nikitin A. A., Николаев М. В., Вестник Московского университета. Серия 15: Вычислительная математика и кибернетика 2018 № 3 С. 11-19
Integral equations emerging in a model of stationary biological communities such that their kernels have variable coefficients of excess (kurtosian kernels)are investigated. The dependence of the first and second spatial moment on the dimension of the environment is considered. A fastcomputation algorithm for the multi-dimensional nonlinear convolution is considered. The existence of a radial solution ...
Added: October 25, 2018
Николаев М. В., Дикман У., Nikitin A. A., Доклады Российской академии наук. Математика, информатика, процессы управления (Российская Федерация) 2021 Т. 499 № 1 С. 35-39
In this paper, we study a nonlinear integral equation that arises in a model of spatial logistic dynamics. The problem of this equation solution existence is investigated by introducing special spaces of functions that are integrable up to a constant. Sufficient conditions are established for the biological characteristics and the parameters of the third spatial ...
Added: October 1, 2021
Nikolaev M. V., Nikitin A. A., Dieckmann U., Doklady Mathematics 2021 Vol. 104 No. 4 P. 188-192
In this paper, we study a nonlinear integral equation that arises in a model of spatial logistic
dynamics. The solvability of this equation is investigated by introducing special spaces of functions that are
integrable up to a constant. Sufficient conditions for the biological characteristics and the parameters of the
third spatial moment closure are established that guarantee the ...
Added: October 1, 2021
Nikitin A. A., Бодров А. Г., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2014 Т. 455 № 5 С. 507-511
Integral equation ...
Added: September 30, 2015
Калистратова А. В., Никитин А.А., Доклады Академии наук 2016 Т. 470 № 6 С. 628-631
В работе изучается интегральное уравнение, возникшее в пространственной модели стационарных сообществ, разработанной австрийскими учеными Ульфом Дикманом и Ричардом Лоу. Рассматривается частный случай данного уравнения с интегральными ядрами, представляющими из себя распределение Стьюдента. Доказывается существование решения в этом случае, а также описывается применение метода понижения размерности многомерного интегрального уравнения, предложенного авторами ранее. ...
Added: December 15, 2016
Bodrov A.G., Nikitin A. A., Doklady Mathematics 2014 Vol. 89 No. 2 P. 210-213
Added: September 28, 2017
Danilov V., Rakhel M., 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
Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 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
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