We introduce and present results about a class of quantales, the topological relational quantales, that can be associated with tuples (X,R) such that X is a topological space and R is a lower-semicontinuous equivalence relation on X (see Definition 1 below). Our motivating case studies and examples of topological relational quantales include concrete quantales such as the relational quantales o...

in this paper‎, ‎we study convergence behavior of the global fom (gl-fom) and global gmres (gl-gmres) methods for solving the matrix equation $axb=c$ where $a$ and $b$ are symmetric positive definite (spd)‎. ‎we present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual‎. ‎in particular‎, ‎the obtained upper...

For a completely distributive quantale L, L-fuzzy strongest postcondition predicate transformers are introduced, and it is shown that, under reasonable assumptions, they are linear or affine continuous mappings between continuous L-idempotent semimodules of L-fuzzy monotonic predicates. © 2012 Elsevier B.V. All rights reserved.

A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

background and objectives: preparation and evaluation of nanocomposite films have become prevalent in recent years. depending on the purpose of using the film, and considering the effects and interaction effects of nanomaterial and other modifiers on the film properties, the amounts of nanomaterials and modifiers should be optimized. the effects of montmorillonite (mmt), glycerol (gl), and thei...

In this paper, we study the category of quantale-valued preordered spaces. We show that it is a normalized topological and give characterization zero-dimensionality D-connectedness in Moreover, characterize explicitly each T0, T1, pre-T2, T2 NT2 Finally, examine how these are related to other full subcategory Ti(pre-T2(L-Prord)) (i=0,1,2) pre-T2(L-Prord), Ti (L-Prord) (i=1,2) L-Prord isomorphic.

The paper provides a quantitative algebraic analysis of a BB’84-type quantum key distribution protocol. The analysis is done in an algebraic setting, where classical and quantum variables form a module for the quantale formed from the communication and quantum actions. The module-quantale pair is endowed with sup-maps that encode uncertainties of agents involved in the protocol, about the varia...