ar X iv : 0 80 2 . 13 38 v 1 [ cs . D M ] 1 0 Fe b 20 08 Some results on ( a : b ) - choosability

ar X iv : 0 80 2 . 38 39 v 1 [ m at h . G R ] 2 6 Fe b 20 08 Quadratic equations over free groups are NP - complete

We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete

ar X iv : 0 80 2 . 38 43 v 1 [ m at h . N T ] 2 6 Fe b 20 08 COMPUTATIONAL CLASS FIELD THEORY

Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such extensions.

ar X iv : 0 80 2 . 15 86 v 1 [ cs . S E ] 1 2 Fe b 20 08 Program Promises

The framework of promise theory offers an alternative way of understanding programming models, especially in distributed systems. We show that promise theory can express some familiar constructs and resolve some problems in program interface design, using fewer and simpler concepts than the Unified Modelling Language (UML).

ar X iv : 0 80 1 . 48 21 v 2 [ he p - ph ] 2 8 Fe b 20 08 X ( 1835 ) and η ( 1760 ) observed by BES Collaboration

ar X iv : 0 80 2 . 38 70 v 1 [ m at h . A P ] 2 6 Fe b 20 08 GRADIENT NLW ON CURVED BACKGROUND IN 4 + 1 DIMENSIONS

We obtain a sharp local well-posedness result for the Gradient Nonlinear Wave Equation on a nonsmooth curved background. In the process we introduce variable coefficient versions of Bourgain’s X spaces, and use a trilinear multiscale wave packet decomposition in order to prove a key trilinear estimate.