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Неподвижные точки модулярно сжимающих отображений
Доклады Академии наук. 2012. Т. 445. № 3. С. 274-277.
In the framework of modular metric spaces, introduced by the author in 2006, we define a new notion of modular convergence, which is more weak than the metric convergence, and establish the necessary and sufficient condition on the modular under consideration, under which the modular convergence is equivalent to the metric one. We introduce the notion of modular contractive maps, study their relationship with Lipschitz continuous maps with respect to the corresponding metrics and present the main result of the paper concerning the existence of fixed points of modular contractive maps. As an application of the fixed point theorem, we prove the existence of solutions to a Carath´eodorytype differential equation with the right hand side from the Orlicz space.
Research target:
Mathematics
Language:
Russian
Chistyakov V., Доклады Академии наук 2012 Vol. 86 No. 1 P. 515-518
In the framework of modular metric spaces, introduced by the author in 2006, we define a new notion of modular convergence, which is more weak than the metric convergence, and establish the necessary and sufficient condition on the modular under consideration, under which the modular convergence is equivalent to the metric one. We introduce the ...
Added: September 7, 2012
Chistyakov Vyacheslav V., / Cornell University. Series math "arxiv.org". 2011. No. 1112.5561v1.
The notion of a (metric) modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by the author [V.V. Chistyakov, Metric modulars and their application, Dokl. Math. 73 (1) (2006) 32–35, and Modular metric spaces, I: Basic concepts, Nonlinear Anal. 72 (1) (2010) 1–14]. ...
Added: February 6, 2013
Vyacheslav V. Chistyakov, , in : Models, Algorithms, and Technologies for Network Analysis. Issue 32.: NY : Springer, 2013. P. 65-92.
The notion of a metric modular on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces and Orlicz spaces, were recently introduced and studied by the author [Chistyakov: Dokl. Math. 73(1):32–35, 2006 and Nonlinear Anal. 72(1):1–30, 2010]. In this chapter we present yet one more application of the metric modulars ...
Added: August 29, 2013
Vyacheslav V. Chistyakov, Switzerland : Springer, 2015
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a ...
Added: December 31, 2015
Chistyakov V., Труды Математического центра им. Н.И. Лобачевского 2013 Т. 46 С. 56-62
In the context of modular metric spaces we prove a generalization of the Banach fixed point theorem for modular contractive mappings. ...
Added: August 29, 2013
Popkov Y., Popkov A., Dubnov Y. A., Автоматика и телемеханика 2020 № 7 С. 148-172
A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. ...
Added: October 31, 2020
D. V. Gribanov, D.S. Malyshev, P. M. Pardalos et al., Journal of Combinatorial Optimization 2018 Vol. 35 No. 4 P. 1128-1146
In this paper, we present fixed-parameter tractable algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems’ formulations are near square. The parameter is the maximum absolute value of the rank minors in the corresponding matrices. Additionally, we present fixed-parameter tractable algorithms ...
Added: February 19, 2018
Kryuchkov M., Rusakov S. V., Вестник Ижевского государственного технического университета 2015 № 2(66) С. 110-112
This paper describes the results of testing the neuronal technical trend indicator according to the exchange rate of Brent oil in 2014. Testing of the model was carried out on three time series, which characterized by their features. ...
Added: August 31, 2015
Malyshev D., Дискретный анализ и исследование операций 2012 Т. 19 № 4 С. 66-72
Рассматривается конструктивный подход к формированию новых случаев эффективной разрешимости задачи о независимом множестве в семействе наследственных частей множества графов Free({P5,C5}). Именно, доказывается, что если эта задача полиномиально разрешима в классе Free({P5,C5,G}), то для любого графа H, который может быть индуктивно получен из G применением к текущему графу сложения с K1 или умножения на K1, эта ...
Added: August 31, 2012
Barcelona : IEEE, 2017
International Conference on Control, Decision and Information Technologies. ...
Added: January 17, 2018
Beklemishev L. D., Оноприенко А. А., 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
Malyshev D., Вестник Нижегородского университета им. Н.И. Лобачевского 2008 № 6 С. 141-146
Рассматривается понятие граничного класса, которое является полезным инструментом для анализа вычислительной сложности задач на графах. Исследуются два конкретных класса графов, и приводятся задачи, для которых эти классы являются граничными. ...
Added: August 31, 2012
Belomestny D., Iosipoi L., Mathematics and Computers in Simulation 2021 No. 181 P. 351-363
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy-tailed distributions and distributions with analytically intractable densities turns out to be rather problematic. In this paper, we propose a novel approach towards the use ...
Added: October 31, 2020
Revenko A., Kuznetsov S., Fundamenta Informaticae 2012 Vol. 4 No. 115 P. 377-394
An approach for studying relations between properties of functions on sets is proposed. The approach is based on Attribute Exploration. 16 properties of functions are considered, among them monotonicity, idempotency, path independence, exchange properties, convexity, etc. Example functions are partially computer generated on the powersets of sets with 2, 3 and 4 elements. Attribute Exploration ...
Added: December 31, 2012
МГУ, 2014
Тезисы докладов научной конференции «Ломоносовские чтения» 2013 ...
Added: December 11, 2016
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
Kotelnikova M. V., Aistov A., 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
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
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
Sirotkin D., Malyshev D., Дискретная математика 2017 Т. 29 № 3 С. 114-125
Задача о независимом множестве для заданного обыкновенного графа состоит в вычислении размера наибольшего множества его попарно несмежных вершин. Предлагается новый способ редукции графов. С его помощью получено новое доказательство NP-полноты задачи о независимом множестве в классе планарных графов и доказана NP-полнота данной задачи в классе плоских графов, имеющих только треугольные внутренние грани, с максимальной степенью ...
Added: September 7, 2017
Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 3 P. 573-607
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We construct the action of the Yangian of sln in the cohomology of Laumon spaces by certain natural correspondences. We construct the action of the affine Yangian (two-parametric deformation of the universal ...
Added: October 9, 2012
Babash A. V., М. : ИНФРА-М, РИОР, 2013
Пособие предназначено для студентов высших учебных заведений, обучающихся по специальности «Прикладная информатика (в экономике)». Оно также содержит методический материал для ряда инновационных курсов лекций по профилю «Информационная безопасность» и может быть использовано и для блока дисциплин этого профиля. Ряд представленных результатов полезен специалистам и аспирантам, специализирующихся в указанной области. ...
Added: January 14, 2014
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Malyshev D., 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