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Qualitative and numerical analysis of an integral equation arising in a model of stationary communities
Doklady Mathematics. 2014. Vol. 89. No. 2. P. 210-213.
Bodrov A.G., Nikitin A. A.
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
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
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
Николаев М. В., Nikitin A. A., Дифференциальные уравнения 2019 Т. 55 № 9 С. 1209-1217
В работе изучается нелинейное интегральное уравнение, возникающее в результате параметрического замыкания третьего пространственного момента в модели У. Дикмана и Р. Лоу. Исследуется вопрос о существовании неподвижной точки интегрального оператора, задаваемого данным уравнением. Доказывается некомпактность полученного оператора. Формулируются условия, при которых уравнение имеет нетривиальное решение. ...
Added: November 7, 2019
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
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
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
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
Springer, 2020
This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019.
First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. ...
Added: November 1, 2020
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
Switzerland : Springer, 2020
This book constitutes the refereed post-conference proceedings of the 6th Russian Supercomputing Days, RuSCDays 2020, held in Moscow, Russia, in September 2020.*
The 51 revised full and 4 revised short papers presented were carefully reviewed and selected from 106 submissions. The papers are organized in the following topical sections: parallel algorithms; supercomputer simulation; HPC, BigData, AI: ...
Added: December 10, 2020
М. : Издательство АСВ, 2015
The volume contains articles of scientific staff and faculty of the Department of Computer Science and Applied Mathematics and Scientific-Educational Center of computer modeling of unique buildings and complexes of Moscow State University of Civil Engineering (National Research University), devoted to actual problems of applied mathematics and computational mechanics. ...
Added: September 4, 2014
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
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
Malyshev D., Alekseev V., 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
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
P. : Université Paris 13 - Paris Sorbonne Cité, 2013
In this workshop we will bring together participants who have solutions for one or more of the following problems: How can mutual understanding be optimized with the help of technology in hospitals where both patients and professionals have varying language skills, cultural backgrounds and cognitive capacities? Can domain ontologies, natural language processing tools, multilingual knowledge-based ...
Added: December 18, 2014
Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293
Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...
Added: September 29, 2014
Akopov A. S., Beklaryan L. A., Saghatelyan A. K., 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
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
Chernyshev S. V., Cherepanov E. A., Pankratiev E. V. et al., Journal of Mathematical Sciences 2005 Vol. 128 No. 6 P. 3487-3495
Added: January 27, 2014
Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291
The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...
Added: December 7, 2013
Decrouez G. G., Robinson A., Risk Analysis: An International Journal 2013 Vol. 33 No. 12 P. 2142-2153
We propose a new modeling approach for inspection data that provides a more useful interpretation of the patterns of detections of invasive pests, using cargo inspection as a motivating example. Methods that are currently in use generally classify shipments according to their likelihood of carrying biosecurity risk material, given available historical and contextual data. Ideally, ...
Added: September 29, 2014