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## Обобщение теоремы Хелли для функций со значениями в равномерном пространстве

Russian Mathematics. 2010. № 5. С. 41-54.

Tretyachenko Y.

In this paper we consider sequences of functions that are defined on a subset of the real line with values in a uniform Hausdorff space. For such sequences we obtain a sufficient condition for the existence of pointwise convergent subsequences. We prove that this generalization of the Helly theorem includes many results of the recent research. In addition, we prove that the sufficient condition is also necessary for uniformly convergent sequences of functions. We also obtain a representation for regular functions whose values belong to the uniform space.

Tretyachenko Y., Russian Mathematics 2010 Vol. 54 No. 5 P. 35-46

In this paper we consider sequences of functions that are defined on a subset of the real line and take on values in a uniform Hausdorff space. For such sequences we obtain a sufficient condition for the existence of pointwise convergent subsequences. We prove that this generalization of the Helly theorem includes many results of ...

Added: November 14, 2012

Chistyakov V., Chistyakova S. A., The approximate variation of univariate uniform space valued functions and pointwise selection principles / . 2020. No. 2010.11410.

Let $T\subset\mathbb{R}$ and $(X,\mathcal{U})$ be a uniform
space with an at most countable gage of pseudometrics
$\{d_p:p\in\mathcal{P}\}$ of the uniformity $\mathcal{U}$.
Given $f\in X^T$ (=\,the family of all functions from $T$ into $X$),
the {\em approximate variation\/} of $f$ is the two-parameter
family $\{V_{\varepsilon,p}(f):\varepsilon>0,p\in\mathcal{P}\}$,
where $V_{\varepsilon,p}(f)$ is the greatest lower bound of
Jordan's variations $V_p(g)$ on $T$ with respect to $d_p$ of ...

Added: October 23, 2020

Chistyakov V., Tretyachenko Y. V., Journal of Mathematical Analysis and Applications 2013 Vol. 402 No. 2 P. 648-659

Given a rectangle in the real Euclidean n-dimensional space and two maps f and g defined on it and taking values in a metric semigroup, we introduce the notion of the total joint variation TV(f , g) of these maps. This extends similar notions considered by Hildebrandt (1963) [17], Leonov (1998) [18], Chistyakov (2003, 2005) ...

Added: August 29, 2013

Chistyakov V., Chistyakova S. A., The joint modulus of variation of metric space valued functions and pointwise selection principles / Cornell University. Series math "arxiv.org". 2016. No. 1601.07298.

Given a subset T of real numbers and a metric space M, we introduce a nondecreasing sequence {v_n} of pseudometrics on the set M^T of all functions from T into M, called the joint modulus of variation. We prove that if two sequences of functions {f_j} and {g_j} from M^T are such that {f_j} is ...

Added: February 12, 2016

Chistyakov V., The approximate variation to pointwise selection principles / . 2019. No. arXiv: 1910.08490.

Let $T\subset\mathbb{R}$, $M$ be a metric space with metric $d$, and $M^T$ be the set of all functions mapping $T$ into $M$. Given $f\in M^T$, we study the properties of the approximate variation $\{V_\varepsilon(f)\}_{\varepsilon>0}$, where $V_\varepsilon(f)$ is the greatest lower bound of Jordan variations $V(g)$ of functions $g\in M^T$ such that $d(f(t),g(t))\le\varepsilon$ for all $t\in T$. The notion of $\varepsilon$-variation ...

Added: October 21, 2019

Chistyakov V., Chistyakova S. A., Studia Mathematica 2017 Vol. 238 No. 1 P. 37-57

Given a subset $T$ of the reals $R$ and a metric space $M$, we introduce a nondecreasing sequence $\{\nu_n\}$ of pseudometrics on $M^T$ (the set of all functions from $T$ into $M$), called the joint modulus of variation. We prove that if two sequences $\{f_j\}$ and $\{g_j\}$ of functions from $M^T$ are such that $\{f_j\}$ ...

Added: May 11, 2017

Chistyakov V., Chistyakova S. A., Journal of Mathematical Analysis and Applications 2017 Vol. 452 No. 2 P. 970-989

We introduce a pseudometric TV on the set M^X of all functions mapping a rectangle X on the plane R^2 into a metric space M, called the total joint variation. We prove that if two sequences {fj} and {gj} of functions from M^X are such that {fj} is pointwise precompact on X, {gj} is pointwise ...

Added: April 13, 2017

Chistyakov V., Tretyachenko Y., Journal of Mathematical Analysis and Applications 2010 Vol. 370 No. 2 P. 672-686

Given two points a=(a1,…,an) and b=(b1,…,bn) from Rn with a<b componentwise and a map f from the rectangle into a metric semigroup M=(M,d,+), we study properties of the total variation of f on introduced by the first author in [V.V. Chistyakov, A selection principle for mappings of bounded variation of several variables, in: ...

Added: November 22, 2012

Chistyakova S. A., Chistyakov V., В кн.: Труды Математического центра имени Н.И.Лобачевского. Т. 54: Теория функций, ее приложения и смежные вопросы.: Каз.: Издательство Казанского математического общества и Академии наук РТ, 2017.. С. 399-402.

Given a closed interval $I=[a,b]$ and a metric space $(M,d)$, we introduce a
nondecreasing sequence $\{\nu_n\}$ of pseudometrics on $M^I$ (the set of all
functions from $I$ into $M$), called the {\it joint modulus of variation}. We show that
if two sequences of functions $\{f_j\}$ and $\{g_j\}$ from $M^I$ are such that
$\{f_j\}$ is pointwise relatively compact on $I$, ...

Added: August 29, 2017

Chistyakov V., Springer, 2021

This book addresses the minimization of special lower semicontinuous functionals
over (closed) balls in metric spaces, called the approximate variation. The new
notion of approximate variation contains more information about the bounded
variation functional and has the following features: the infimum in the definition
of approximate variation is not attained in general and the total Jordan variation
of a function ...

Added: October 29, 2021

Chistyakov V., Tretyachenko Y., Journal of Mathematical Analysis and Applications 2010 Vol. 369 No. 1 P. 82-93

Given a=(a1,…,an), b=(b1,…,bn)∈Rn with ab componentwise and a map f from the rectangle Iab=[a1,b1]×⋯×[an,bn] into a metric semigroup M=(M,d,+), denote by TV(f,Iab) the Hildebrandt–Leonov total variation of f on Iab, which has been recently studied in [V.V. Chistyakov, Yu.V. Tretyachenko, Maps of several variables of finite total variation. I, J. Math. Anal. Appl. (2010), submitted ...

Added: January 9, 2013

Chistyakov V., Asymmetric variations of multifunctions with application to functional inclusions / . 2019. No. 1901.09722.

Under certain initial conditions, we prove the existence of set-valued selectors of univariate compact-valued multifunctions of bounded (Jordan) variation when the notion of variation is defined taking into account only the Pompeiu asymmetric excess between compact sets from the target metric space. For this, we study subtle properties of the directional variations. We show by examples that all assumptions ...

Added: January 29, 2019

Klimenko A. V., Bufetov A. I., Series C., Convergence of spherical averages for actions of Fuchsian Groups / Cornell University. Series math "arxiv.org". 2018. No. 1805.11743.

Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving ...

Added: September 18, 2018

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

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

Barcelona: IEEE, 2017

International Conference on Control, Decision and Information Technologies. ...

Added: January 17, 2018

М.: Физматлит, 2013

Conference is devoted to application of the integrated models and soft computing in artificial intelligence. ...

Added: May 26, 2013

ООО Фирма "Элист", 2014

В книге представлены тезисы докладов I тура XV Всероссийской научно-технической конференции и школы молодых ученых, аспирантов и студентов. ...

Added: October 17, 2014

М.: ИКИ РАН, 2011

Added: March 26, 2013

Shmid A., Novopashin M., Berezin A., IOSR Journal of Computer Engineering (IOSR-JCE) 2017 Vol. 19 No. 3 P. 113-121

The paper deals with the Forrester’s approach to analysis of heart electrical dynamics based on the hypothesis that heart belongs to the class of Complex Systems and its dynamics can be described by coupled Van der Pol differential equations with a time lag. The chain of such equations suggested by Ginzburg and Landau was used ...

Added: June 13, 2018

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014

Springer, 2020

This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2019 International Symposium, which was held at the University of Szeged, Bolyai Institute and the Hungarian Academy of Sciences, Hungary, October 21st-25th, 2019. The topics covered in this volume include tumor and infection modeling; dynamics of co-infections; epidemic models on networks; ...

Added: March 11, 2021

Kalyagin V. A., Koldanov A. P., Koldanov P. 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

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