ar X iv : 0 80 2 . 40 18 v 1 [ cs . P L ] 2 7 Fe b 20 08 ALGEBRAIC PATTERN MATCHING IN JOIN CALCULUS

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 . 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 2 . 25 80 v 1 [ m at h . G T ] 1 9 Fe b 20 08 3 - Dimensional Schlaefli Formula and Its Generalization

Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.

ar X iv : 0 80 2 . 38 43 v 2 [ m at h . N T ] 2 7 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 . 30 10 v 1 [ m at h . Q A ] 2 1 Fe b 20 08 THE OPERAD LIE IS FREE

We show that the operad Lie is free as a non-symmetric operad. Then we study the generating series counting the operadic generators, finding a recursive formula for its coefficients, and showing that the asymptotic density of the operadic generators is 1/e.