The Experts below are selected from a list of 219 Experts worldwide ranked by ideXlab platform
Alexander J. Zaslavski - One of the best experts on this subject based on the ideXlab platform.
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Generic Existence of Solutions of Symmetric Optimization Problems
Symmetry, 2020Co-Authors: Alexander J. ZaslavskiAbstract:In this paper we study a class of symmetric optimization problems which is identified with a space of objective functions, equipped with an appropriate complete metric. Using the Baire category approach, we show the existence of a subset of the space of functions, which is a Countable Intersection of open and everywhere dense sets, such that for every objective function from this Intersection the corresponding symmetric optimization problem possesses a solution.
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A random weak ergodic property of infinite products of operators in metric spaces
Optimization, 2018Co-Authors: Simeon Reich, Alexander J. ZaslavskiAbstract:ABSTRACTWe study the random weak ergodic property of infinite products of mappings acting on complete metric spaces. Our results describe an aspect of the asymptotic behaviour of random infinite products of such mappings. More precisely, we show that in appropriate spaces of sequences of operators there exists a subset, which is a Countable Intersection of open and everywhere dense sets, such that each sequence belonging to this subset has the random weak ergodic property. Then we show that several known results in the literature can be deduced from our general result.
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Relatively Nonexpansive Operators with Respect to Bregman Distances
Developments in Mathematics, 2014Co-Authors: Simeon Reich, Alexander J. ZaslavskiAbstract:The following problem often occurs in functional analysis and optimization theory, as well as in other fields of pure and applied mathematics: given a nonempty, closed and convex subset K of a Banach space X and an operator T:K→K, do the sequences iteratively generated in K by the rule x k+1=Tx k converge to a fixed point of T no matter how the initial point x 0∈K is chosen? It is well known that this indeed happens, in some sense, for “standard” classes of operators (e.g., certain nonexpansive operators and operators of contractive type). In this chapter we show that the question asked above has an affirmative answer even if the operator T is not contractive in any standard sense, but is relatively nonexpansive with respect to a Bregman distance induced by a convex function f. More precisely, we prove that in appropriate complete metric spaces of operators which are relatively nonexpansive with respect to Bregman distances there exists a subset which is a Countable Intersection of open and everywhere dense sets such that for any operator belonging to this subset, all its orbits converge strongly.
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Turnpike Properties of Optimal Control Problems
SpringerBriefs in Optimization, 2013Co-Authors: Alexander J. ZaslavskiAbstract:In this chapter we study a class of optimal control problems (with the same system of differential equations, the same functional constraints and the same boundary conditions) which is identified with the corresponding complete metric space of objective functions (integrands). The main results of this chapter establish the turnpike property for any element of a set which is a Countable Intersection of open everywhere dense sets in the space of integrands.
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Generic uniqueness of minimal configurations with rational rotation numbers in Aubry-Mather theory
Abstract and Applied Analysis, 2004Co-Authors: Alexander J. ZaslavskiAbstract:We study (h)-minimal configurations in Aubry-Mather theory, where h belongs to a complete metric space of functions. Such minimal configurations have definite rotation number. We establish the existence of a set of functions, which is a Countable Intersection of open everywhere dense subsets of the space and such that for each element h of this set and each rational number α, the following properties hold: (i) there exist three different (h)-minimal configurations with rotation number α; (ii) any (h)-minimal configuration with rotation number α is a translation of one of these configurations.
Quentin Menet - One of the best experts on this subject based on the ideXlab platform.
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Simple strategies for Banach-Mazur games and sets of probability 1
Information and Computation, 2015Co-Authors: Thomas Brihaye, Axel Haddad, Quentin MenetAbstract:In 2006, Varacca and Volzer proved that on finite graphs, ω-regular large sets coincide with ω-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try to understand relations between sets of probability 1 and various notions of simple strategies (including those introduced in a recent paper of Gradel and Le?senich). Then, we introduce a generalisation of the classical Banach-Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability 1 (as classical Banach-Mazur games characterise large sets). We obtain a determinacy result for these games, when the winning set is a Countable Intersection of open sets.
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Simple strategies for Banach-Mazur games and fairly correct systems
Electronic Proceedings in Theoretical Computer Science, 2013Co-Authors: Thomas Brihaye, Quentin MenetAbstract:In 2006, Varacca and Volzer proved that on finite graphs, omega-regular large sets coincide with omega-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try to understand relations between sets of probability 1 and various notions of simple strategies (including those introduced in a recent paper of Gradel and Lessenich). Then, we introduce a generalisation of the classical Banach-Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability 1 (as classical Banach-Mazur games characterise large sets). We obtain a determinacy result for these games, when the winning set is a Countable Intersection of open sets.
Thomas Brihaye - One of the best experts on this subject based on the ideXlab platform.
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Simple strategies for Banach-Mazur games and sets of probability 1
Information and Computation, 2015Co-Authors: Thomas Brihaye, Axel Haddad, Quentin MenetAbstract:In 2006, Varacca and Volzer proved that on finite graphs, ω-regular large sets coincide with ω-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try to understand relations between sets of probability 1 and various notions of simple strategies (including those introduced in a recent paper of Gradel and Le?senich). Then, we introduce a generalisation of the classical Banach-Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability 1 (as classical Banach-Mazur games characterise large sets). We obtain a determinacy result for these games, when the winning set is a Countable Intersection of open sets.
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Simple strategies for Banach-Mazur games and fairly correct systems
Electronic Proceedings in Theoretical Computer Science, 2013Co-Authors: Thomas Brihaye, Quentin MenetAbstract:In 2006, Varacca and Volzer proved that on finite graphs, omega-regular large sets coincide with omega-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try to understand relations between sets of probability 1 and various notions of simple strategies (including those introduced in a recent paper of Gradel and Lessenich). Then, we introduce a generalisation of the classical Banach-Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability 1 (as classical Banach-Mazur games characterise large sets). We obtain a determinacy result for these games, when the winning set is a Countable Intersection of open sets.
George M. Eid - One of the best experts on this subject based on the ideXlab platform.
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On Wallman Spaces and the Lindelöf Property
Annals of the New York Academy of Sciences, 1992Co-Authors: George M. EidAbstract:It is assumed that X is an abstract set and ℒ is a lattice of subsets of X. The consequences of ℒ being regular, and of ℒ being regular together with other lattice properties such as prime complete or even Lindelof, are discussed first. Next, the important problem of enlarging an ℒ-filter or an ℒ-ultrafilter with the Countable Intersection property is considered. It is much easier to express this in terms of zero–one-valued finitely additive measures on the algebra generated by ℒ. Conditions for the preceding to hold in terms of topological spaces of measures associated with the lattice ℒ are then obtained.
Santi Spadaro - One of the best experts on this subject based on the ideXlab platform.
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P-spaces and the Whyburn property
Houston Journal of Mathematics, 2011Co-Authors: Angelo Bella, Camillo Costantini, Santi SpadaroAbstract:We investigate the Whyburn and weakly Whyburn property in the class of P-spaces, that is spaces where every Countable Intersection of open sets is open. We construct examples of non-weakly Whyburn P-spaces of size continuum, thus giving a negative answer under CH to a question of Pelant, Tkachenko, Tkachuk and Wilson. In addition, we show that the weak Kurepa Hypothesis (an assumption weaker than CH) implies the existence of a non-weakly Whyburn P-space of size aleph2. Finally, we consider the behavior of the above-mentioned properties under products; we show in particular that the product of a Lindelof weakly Whyburn P-space and a Lindelof Whyburn P-space is weakly Whyburn, and we give a consistent example of a non-Whyburn product of two Lindelof Whyburn P-spaces.
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P-spaces and the Whyburn property
arXiv: General Topology, 2009Co-Authors: Angelo Bella, Camillo Costantini, Santi SpadaroAbstract:We investigate the Whyburn and weakly Whyburn property in the class of $P$-spaces, that is spaces where every Countable Intersection of open sets is open. We construct examples of non-weakly Whyburn $P$-spaces of size continuum, thus giving a negative answer under CH to a question of Pelant, Tkachenko, Tkachuk and Wilson. In addition, we show that the weak Kurepa Hypothesis (a set-theoretic assumption weaker than CH) implies the existence of a non-weakly Whyburn $P$-space of size $\aleph_2$. Finally, we consider the behavior of the above-mentioned properties under products; we show in particular that the product of a Lindel\"of weakly Whyburn P-space and a Lindel\"of Whyburn $P$-space is weakly Whyburn, and we give a consistent example of a non-Whyburn product of two Lindel\"of Whyburn $P$-spaces.
