P. M. Cohn showed in 1971 that given a ring R, to describe, up to isomorphism, a division ring D generated by a homomorphic image of R is equivalent to specifying the set of square matrices over R which map to singular matrices over D, and he determined the conditions that such a set of matrices must satisfy. The present author later developed another version of this data, in terms of closure o...

As well-known, the concept "hypercyclic" in operator theory is the same as the concept "transitive" in dynamical system. Now the class of hypercyclic operators is well studied. Following the idea of research in hypercyclic operators, we consider classes of operators with some kinds of chaotic properties in this article. First of all, the closures of the sets of all Li-Yorke chaotic operators or...

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...

We consider linear time temporal logic enriched with semiextended regular expressions through various operators that have been proposed in the literature, in particular in Accelera’s Property Specification Language. We obtain results about the expressive power of fragments of this logic when restricted to certain operators only: basically, all operators alone suffice for expressive completeness...

We consider elliptic operators in divergence form L = div (Φ · grad ) either on a closed Riemannian manifold or in a domain with compact closure and piecewise smooth boundary M where Φ : M → End(TM) is a positive definite symmetric smooth section of the bundle of all endomorphisms of TM . We show that the first nonzero L-eigenvalues in the closed or Dirichlet eigenvalue problems can be bounded ...

We establish two global subellipticity properties of positive symmetric second-order partial differential operators on L2(R ). First, if m ∈ N then we consider operators H0 with coefficients in W (R) and domain D(H0) =W (R) satisfying the subellipticity property c (φ, (I +H0)φ) ≥ ‖∆ φ‖2 for some c > 0 and γ ∈ 〈0, 1], uniformly for all φ ∈ W(R), where ∆ denotes the usual Laplacian. Then we prove...