786 research outputs found

    Relation-based Galois connections: towards the residual of a relation

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    Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego, Relation-based Galois connections: towards the residual of a relation, CMMSE 2017: Proceedings of the 17th International Conference on Mathematical Methods in Science and Engineering ( ISBN: 978-84-617-8694-7) , pp. 469--475We explore a suitable generalization of the notion of Galois connection in which their components are binary relations. Many different approaches are possible depending both on the (pre-)order relation between subsets in the underlying powerdomain and the chosen type of relational composition.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

    A decomposition theorem for maxitive measures

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    A maxitive measure is the analogue of a finitely additive measure or charge, in which the usual addition is replaced by the supremum operation. Contrarily to charges, maxitive measures often have a density. We show that maxitive measures can be decomposed as the supremum of a maxitive measure with density, and a residual maxitive measure that is null on compact sets under specific conditions.Comment: 11 page

    Quantale Modules and their Operators, with Applications

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    The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators - that turn out to be precisely the homomorphisms between free objects in those categories - find concrete applications in two different branches of image processing, namely fuzzy image compression and mathematical morphology

    Smearing of Observables and Spectral Measures on Quantum Structures

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    An observable on a quantum structure is any σ\sigma-homomorphism of quantum structures from the Borel σ\sigma-algebra of the real line into the quantum structure which is in our case a monotone σ\sigma-complete effect algebras with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ\sigma-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there is its spectral measure

    A Recipe for State-and-Effect Triangles

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    In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an adjunction between state- and predicate-transformers. The current paper exploits a classical result in category theory, part of Jon Beck's monadicity theorem, to systematically construct such a state-and-effect triangle from an adjunction. The power of this construction is illustrated in many examples, covering many monads occurring in program semantics, including (probabilistic) power domains

    Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

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    Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra EE that is not an orthomodular lattice there exists an (o)(o)-continuous state ω\omega on EE, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras
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