Let M = (L , ∗) be a GL-monoid. An M-valued preordered set is an L-subset endowed with a reflexive and M-transitive L-relation, it is essentially a category enriched in a quantaloid generated by M. This paper presents a study of M-valued preordered sets with emphasis on symmetrization and the Cauchy completion. The main result states that symmetrization and the Cauchy completion of M-valued pre...

Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. It is shown that these conditions can be expressed in terms of each viscoelastic response function ranging over a cone. The elements of each cone are completely characterized by an integral representation. The 1:1 correspond...

As an application of the dual equivalence between the category of L-spatialC-objects and the category of L-sober C-M-L-spaces, it is shown in this paper that for a fixed augmented partially ordered set A, there exists a dual equivalence between the category of A-spatial augmented partially ordered sets and the category of A-sober A-valued spaces. Then, with regard to this duality, for a fixed (...

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

Introduction. Classical logics are based on the bivalence principle, that is, the set of truth-values V has cardinality |V | = 2, usually with V = {T,F} where T and F stand for truthhood and falsity, respectively. Many-valued logics generalize this requirement to more or less arbitrary sets of truth-values, rather referred to as truth-degrees in that context. Popular examples of many-valued log...

Passivity and dissipativity, in Jan Willems’s sense, are known to be powerful tools for stability analysis feedback control design. For instance, passive systems negative interconnection with slope-restricted, static, single-valued, smooth nonlinearities, as Lur’e systems, have been thoroughly studied automatic control, yielding the so-called absolute problem (with famous Popov circle criteria)...

Landmark heuristics are perhaps the most accurate current known admissible heuristics for optimal planning. A disjunctive action landmark can be seen a form of at-least-one constraint on the actions it contains. In many domains, some critical propositions have to be established for a number of times. Propositional landmarks are too weak to express this kind of constraints. In this paper, we pro...