in this note by considering a complete lattice l, we define thenotion of an l-fuzzy hyperrelation on a given non-empty set x. then wedefine the concepts of (pom)l-fuzzy graph, hypergraph and subhypergroupand obtain some related results. in particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (pom)l-fuzzy subhypergroups ...

‎ in the present article‎, ‎we study some categorical properties of the category {$bf‎ cpo_{sep}$-$s$} of all {separately strict $s$-cpo's}; cpo's equipped with‎ a compatible right action of a separately strict cpo-monoid $s$ which is‎ strict continuous in each component‎. ‎in particular‎, we show that this category is reflective and coreflective in the‎ category of $s$-cpo's‎, ‎find the free a...

| This paper presents a new timing analysis algorithm for eecient state space exploration during the synthesis of timed circuits or the veriication of timed systems. The source of the computational complexity in the synthesis or veriication of a timed system is in nding the reachable timed state space. We introduce a new algorithm which utilizes geometric regions to represent the timed state sp...

Riesz potentials of fractal measures μ in metric spaces and their inverses are introduced . They define self–adjoint operators in the Hilbert space L2(μ) and the former are shown to be compact. In the Euclidean case the corresponding spectral asymptotics are derived with Besov space methods. The inverses of the Riesz potentials are fractal pseudodifferential operators. For the order two operato...

An ordered pair X (R) = (X, R ) consisting of a nonvoid set X and a nonvoid family R of binary relations on X is called a relator space. Relator spaces are straightforward generalizations not only of uniform spaces, but also of ordered sets. Therefore, in a relator space we can naturally define not only some topological notions, but also some order theoretic ones. It turns out that these two, a...

where the pk are complex-valued functions of class C k on an interval a < x < b, and pn(x) / 0 there. In the Hilbert space § = 2 {a, b) let S0 be the closure in § 2 of the set of all {ƒ, Lf} for ƒ e C$(a, b), the functions in C°°(a,b) vanishing outside compact subintervals of a < x < b. This S0 in a closed densely defined symmetric operator whose adjoint has the domain 3>(S$), the set of all ƒ ...

We generalise the Riesz representation theorems for positive linear functionals on $$\text {C}_{\text {c}}(X)$$ and {0}}(X)$$ , where X is a locally compact Hausdorff space, to operators from these spaces into partially ordered vector space E. The representing measures are defined Borel $$\sigma $$ -algebra of take their values in extended cone corresponding integrals order integrals. give expl...

Today, in order to confront the growing complexity of products and organisations, Aeronautic, Space and Defence (ASD) manufacturing enterprises are using more and more System Engineering, Product Lifecycle Management and Computer Aided Solutions for various engineering and management activities. Combined with a more and more important outsourcing, such trends led to the emergence of what is cal...

Abstract. Off-stoichiometric alloys exhibit partial disorder, in the sense that only some of the sublattices of the stoichiometric ordered alloy become disordered. This paper puts forward a generalization of the augmented space recursion (ASR) introduced earlier by one of us (Mookerjee et al 1997(*)) for systems with many atoms per unit cell. In order to justify the convergence properties of AS...