The notion of a k-automatic set of integers is well-studied. We develop a new notion — the k-automatic set of rational numbers — and prove basic properties of these sets, including closure properties and decidability.

In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean cite{dn} studied compact representations of BL-algebras, L. C. Ciungu cite{ciu} investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim cite{jun} studied relationships between closure operators and BL-algebras,...

For a mixed integer linear program where all integer variables are bounded, we study a reformulation introduced by Roy that maps general integer variables to a collection of binary variables. We study theoretical properties and empirical strength of rank-2 simple split cuts of the reformulation. We show that for a pure integer problem with two integer variables, these cuts are sufficient to obt...

Departing from a suitable categorical description of closure operators, this paper dualizes this notion and introduces some basic properties of dual closure operators. Usually these operators act on quotients rather than subobjects, and much attention is being paid here to their key examples in algebra and topology, which include the formation of monotone quotients (Eilenberg-Whyburn) and conco...

Concurrent games as event structures form a partial order model of concurrency where concurrent behaviour is captured by nondeterministic concurrent strategies—a class of maps of event structures. Extended with winning conditions, the model is also able to give semantics to logics of various kinds. An interesting subclass of this game model is the one considering deterministic strategies only, ...

1. Epistemic closure The general principle of epistemic closure stipulates that epistemic properties are transmissible through logical means. The principle of epistemic closure under known entailment (ECKE), a particular instance of epistemic closure (EC), has received a good deal of attention since the last thirty years or so. ECKE states that: if one knows that p, and she knows that p entails...

The notion of dependencies between ”attributes” arises in many areas such as relational databases, data analysis, data-mining, formal concept analysis, knowledge structures . . .. Formalization of dependencies leads to the notion of so-called full implicational systems (or full family of functional dependencies) which is in oneto-one correspondence with the other significant notions of closure ...

Particle transport in radiation therapy can be modelled by a kinetic equation which must be solved numerically. Unfortunately, the numerical solution of such equations is generally too expensive for applications in medical centers. Moment methods provide a hierarchy of models used to reduce the numerical cost of these simulations while preserving basic properties of the solutions. Moment models...

background: there is some evidence indicating improvement in myocardial performance after atrial septal defect closure, either device closure or surgical, but ventricular dyssynchrony has not been evaluated before and after surgical closure. the aim of this study was to evaluate ventricular mechanical dyssynchrony in patients with atrial septal defect before and after surgical closure. methods:...