The appropriate general completeness notion for topological vector spaces is quasi-completeness. There is a stronger general notion of completeness, which proves to be too strong in general. For example, the appendix shows that weak-star duals of infinite-dimensional Hilbert spaces are quasi-complete, but never complete in the stronger sense. Quasi-completeness for Fréchet spaces is ordinary me...

BACKGROUND AND AIM Cold snare techniques are widely used for the removal of small and diminutive polyps. The influence of snare type on the effectiveness of cold snare polypectomy is unknown. METHODS Cold snare polypectomy of 3-7-mm polyps was undertaken using either a thin wire mini-snare (0.30 mm) or a thick wire mini-snare (0.47 mm). Primary outcome was endoscopic completeness of excision....

We propose three different notions of completeness for term rewrite specifications supporting order-sorted signatures, deduction modulo axioms, and context-sensitive rewriting relative to a replacement map μ. Our three notions are: (1) an appropriate definition of μ-sufficient completeness with respect to a set of constructor symbols; (2) a definition of μ-canonical completeness under which μ-c...

in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

We present a sequent calculus for proving that processes in a process algebra satisfy assertions in Hennessy-Milner logic. The main novelty lies in the use of the operational semantics to derive introduction rules (on the left and right of sequents) for the diierent operators of the process calculus. This gives a generic proof system applicable to any process algebra with an operational semanti...

In this paper we consider the expansions of logics of a left-continuous tnorm with truth-constants from a subalgebra of the rational unit interval. From known results on standard semantics, we study completeness for these propositional logics with respect to chains de?ned over the rational unit interval with a special attention to the completeness with respect to the canonical chain, i.e. the a...

This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms (mainly continuous and weak nilpotent minimum t-norms). We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finit...