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Asymmetric variations of multifunctions with application to functional inclusions
Cornell University, NY, USA
,
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 in the main existence result are essential. As an application, we establish the existence of set-valued solutions $X(t)$ of bounded variation to the functional inclusion of the form $X(t)\subset F(t,X(t))$ satisfying the initial condition $X(t_0)=X_0$.
Vyacheslav V. Chistyakov, Journal of Mathematical Analysis and Applications 2019 Vol. 478 No. 2 P. 421-444
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 ...
Added: July 22, 2019
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
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova, / Cornell University, NY, USA. Series arXiv [math.FA] "Functional Analysis". 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 $V_p(g)$ ...
Added: October 23, 2020
Vyacheslav V. Chistyakov, 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
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
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova, 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
V.V.Chistyakov, Rychlewicz A., Studia Mathematica 2002 Vol. 153 No. 3 P. 235-247
We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show ...
Added: November 10, 2009
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova, 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., 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 <img src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X10003574-si5.gif" /> into a metric semigroup M=(M,d,+), we study properties of the total variation<img src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X10003574-si7.gif" /> of f on <img src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X10003574-si8.gif" /> introduced by the first author in [V.V. Chistyakov, A selection principle for mappings of ...
Added: November 22, 2012
Vyacheslav V. Chistyakov, / Cornell University Library, NY, USA. Series arXiv [math.FA] "Functional Analysis". 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
V. V. Chistyakov, A. Nowak, Journal of Functional Analysis 2005 Vol. 225 No. 2 P. 247-262
We prove the existence of Carathéodory-type selectors (that is, measurable in the first variable
and having certain regularity properties like Lipschitz continuity, absolute continuity or bounded
variation in the second variable) for multifunctions mapping the product of a measurable space
and an interval into compact subsets of a metric space or metric semigroup. ...
Added: November 9, 2009
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova, / 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
Tretyachenko Y., Известия высших учебных заведений. Математика 2010 № 5 С. 41-54
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 ...
Added: September 28, 2012
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
Vyacheslav V. Chistyakov, 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
V. V. Chistyakov, S. A. Chistyakova, Lobachevskii Journal of Mathematics 2022 Vol. 43 No. 3 P. 550-563
Given a Hausdorff uniform space X with the countable gage of pseudometrics of the
uniformity of X, we introduce a concept of the approximate variation of a function f mapping a
subset T of the reals intoX: this is the infimum of the family of Jordan-type variations of all functions
g : T → X which differ from ...
Added: April 30, 2022
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
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019