ar X iv : 0 90 2 . 17 29 v 1 [ m at h . N T ] 1 0 Fe b 20 09 ON THE DIMENSION OF AG TRACE CODES

ar X iv : 0 90 2 . 19 17 v 1 [ m at h . D S ] 1 1 Fe b 20 09 AVERAGES ON ANNULI OF EULIDEAN SPACE

We study the range of validity of differentiation theorems and ergodic theorems for R actions, for averages on “thick spheres” of Euclidean space.

ar X iv : 0 90 2 . 29 25 v 1 [ m at h . G T ] 1 7 Fe b 20 09 COVERINGS AND ACTIONS OF STRUCTURED LIE GROUPOIDS

In this work we deal with coverings and actions of Lie groupgroupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids. Later, we show the equivalence of the category of smooth actions of Lie group-groupoids on Lie groups and the category of smooth coverings of Lie group-groupoids.

ar X iv : 0 90 2 . 32 39 v 1 [ m at h . D G ] 1 8 Fe b 20 09 Gauge theory in higher dimensions , II

ar X iv : 0 90 2 . 39 12 v 1 [ m at h . G R ] 2 3 Fe b 20 09 Brent Everitt The Combinatorial Topology

ar X iv : 0 90 9 . 29 83 v 1 [ m at h . N T ] 1 6 Se p 20 09 COMBINATORIAL IDENTITIES INVOLVING THE MÖBIUS FUNCTION

In this paper we derive some identities and inequalities on the Möbius mu function. Our main tool is phi functions for intervals of positive integers and their unions.