2.1. The Cebotarev density theorem. We have seen in the proof of Theorem 1.3 that for any nontrivial ray class character χ : H → C× we could show nonvanishing L(1, χ) = 0 provided that χ factors through J/NL/KJ L · P for some finite extension L/K. By Theorem 1.2 the subgroup P is the norm subgroup of the ray class field K(m)/K. Hence we get nonvanishing for all nontrivial χ and this allows to p...

These survey lectures are devoted to a new subject of the large scale dimension theory which was initiated by Gromov as a part of asymptotic geometry. We are going to enter the large scale world and consider some new concepts, results and examples which are parallel in many cases to the corresponding elements of the standard (local) dimension theory. We start our presentation with the motivations.

The paper contains an exposition of the basic results on reduction theory in reductive groups over global fields, in the adelic language. The treatment is uniform: number fields and function fields are on an equal footing.

Commenting on a recent editorial in this journal which presented four challenges global health networks will have to tackle to be effective, this essay discusses why this type of analysis is important for global health scholars and practitioners, and why it is worth understanding and critically engaging with the complexities behind these challenges. Focusing on the topics of problem definition ...

In this paper, progressive damage and global failure of composite laminates under quasi-static, monotonic loading are investigated using 3D continuum damage mechanics. For this purpose, a finite element program has been developed using an eight-node 2D layered element including layer-wise plate theory. Damage analysis of a single orthotropic layer under various uniform in-plane and transverse l...

The economic dependency of the Eastern Caribbean on tourism has been welldocumented (Ferguson 1997, Lea 1998, Patullo 1996). A large element of its attractiveness depends on its connotations of paradise in the Minority World, and therefore it is an economic necessity that paradise is continually simulatable. The widespread development of all-inclusive resorts, or what Bauman has termed ‘reserva...

This article provides a tutorial overview of recent progress in numerical methods for the reachability analysis and deterministic global optimization of DAE models. These problems are highly interrelated, and are global problems in the sense that they concern the parametric solutions of a DAE model over a potentially large range of model parameters, rather than locally about a single value. Man...