Acta Crystallographica Section A: Foundations of Crystallography covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic d...

Proof of Claim 1.1: Of course, we assume that {nj}j=1 are all distinct. Let n1 = 1. Then there must exist An2 such that An2 ∩An1 6= ∅. If not, then An1 ∩Aj = ∅ for all j 6= n1. Thus, An1 ⊆ Aj for all j 6= n1. Now, fix some j0 6= n1 such thatAj0 6= An1 . Then, sinceF is a σ-algebra, we have thatAk0 = A c j0 for some k0 6= n1. Thus, setting j = k0 6= n1, An1 ⊆ Ack0 = ( Acj0 )c = Aj0 . The only wa...

This paper presents FrameNet’s approach to the representation of Support Verbs, as but one type of multiword expression (MWE) included in the database. In addition to motivating and illustrating FrameNet’s newly consistent annotation practice for Support Verb constructions, the present work advocates adopting a broad view of what constitutes a multiword expression.

Starting from an GMRES error estimate proposed by Elman in terms of the ratio of the smallest eigenvalue of the hermitian part and the norm of some non-symmetric matrix, we propose some asymptotically tighter bound in terms of the same ratio. Here we make use of a recent deep result of Crouzeix et al. on the norm of functions of matrices.

In this paper, we demonstrate the impact of Multiword Expression (MWE) resources in the task of MWE recognition in text. We present results based on the Wiki50 corpus for MWE resources, generated using unsupervised methods from raw text and resources that are extracted using manual text markup and lexical resources. We show that resources acquired from manual annotation yield the best MWE taggi...