The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.
In this paper, we study the monotone meta-Lindelöf property. Relationships between monotone meta-Lindelöf spaces and other spaces are investigated. Behaviors of monotone meta-Lindelöf $GO$-spaces in their linearly ordered extensions are revealed.
Bounded integral residuated lattices form a large class of algebras containing some classes of commutative and noncommutative algebras behind many-valued and fuzzy logics. In the paper, monotone modal operators (special cases of closure operators) are introduced and studied.
In this paper there are considered Markov decision processes (MDPs) that have the discounted cost as the objective function, state and decision spaces that are subsets of the real line but are not necessarily finite or denumerable. The considered MDPs have a cost function that is possibly unbounded, and dynamic independent of the current state. The considered decision sets are possibly non-compact. In the context described, conditions to obtain either an increasing or decreasing optimal stationary policy are provided; these conditions do not require assumptions of convexity. Versions of the policy iteration algorithm (PIA) to approximate increasing or decreasing optimal stationary policies are detailed. An illustrative example is presented. Finally, comments on the monotonicity conditions and the monotone versions of the PIA that are applied to discounted MDPs with rewards are given.
This second Part II, which follows a first Part I for the discrete-time case (see \cite{DijkSl1}), deals with monotonicity and comparison results, as generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete-time case the generalization is no longer straightforward. A discrete-time transformation will therefore be developed first. Next, results from Part I can be adopted. The conditions, the technicalities and the results will be studied in detail for a reliability application that initiated the research. This concerns a reliability network with dependent components that can breakdown. A secure analytic performance bound is obtained.
Firstly, in this paper there is considered a certain class of possibly unbounded optimization problems on Euclidean spaces, for which conditions that permit to obtain monotone minimizers are given. Secondly, the theory developed in the first part of the paper is applied to Markov control processes (MCPs) on real spaces with possibly unbounded cost function, and with possibly noncompact control sets, considering both the discounted and the average cost as optimality criterion. In the context described, conditions to obtain monotone optimal policies are provided. For the conditions of MCPs presented in the article, several controlled models including, in particular, two inventory/production systems and the linear regulator problem are supplied.
In this paper we describe all algebras A with one unary operation such that by a direct limit construction exactly two nonisomorphic algebras can be obtained from A.
The article presents a brief summary of newly discovered wooden structures in the well-known polycultural site Mohelnice – štěrkovna (also “U cukrovaru” or Za cukrovarem) in the Mohelnice cadastre and its vicinity. Earlier discoveries at this site include Neolithic timbered wells and a sensational find of an oak monoxylon from the La Tène period of the 4th/3rd century BC (dendro 281 or 301 BC). It was found trapped in its home port on the banks of the meandering river Morava and dating has revealed the same age as the absolutely dated simple wooden pole construction. It is the northernmost found monoxylon known in the Czech Republic and also presents the oldest evidence for such use of ships on Czech rivers. The manufacture and use of such ships has been known since the Mesolithic period continuing until modern times. The subsequent exploration of the shores of the Moravičany Lakes banks revealed a number of smaller wooden structures below the water surface, either made up of pointed stakes themselves, or a combination of smaller stakes and branches built into a tapered corridor resembling a structure used for fishing. The latest discovery is a massive oak-fir structure manufactured from stakes, longitudinal and transverse planks and stones, interpretable as a timber trackway, or a bridge. It has been dendrochronologically dated to 1547–1560 and archival sources indicate the structure was repaired in 1645. The structure spans the former meander between Třeština and Mohelnice near one of the mills. The existence of this route is documented on 18th-century maps. Significant discoveries from various times of mainly wooden buildings underscore at least the European significance of the Mohelnice site. It may yield many valuable finds in the future.