ar X iv : 0 80 1 . 02 89 v 1 [ m at h . L O ] 1 J an 2 00 8 Is Randomness “ native ” to Computer Science ?

ar X iv : a st ro - p h / 02 10 42 8 v 1 1 8 O ct 2 00 2 Star Clusters in Interacting Galaxies : The Case of M 51 Nate

ar X iv : 0 80 3 . 44 39 v 1 [ m at h . D S ] 3 1 M ar 2 00 8 PERIODIC UNIQUE BETA - EXPANSIONS : THE SHARKOVSKIĬ ORDERING

Let β ∈ (1, 2). Each x ∈ [0, 1 β−1 ] can be represented in the form

ar X iv : 0 80 7 . 00 58 v 1 [ m at h . D G ] 1 J ul 2 00 8 EQUIVARIANT DIFFERENTIAL CHARACTERS AND SYMPLECTIC REDUCTION

We describe equivariant differential characters (classifying equi-variant circle bundles with connections), their prequantization, and reduction.

ar X iv : 0 80 7 . 00 58 v 2 [ m at h . D G ] 1 6 Ju l 2 00 8 EQUIVARIANT DIFFERENTIAL CHARACTERS AND SYMPLECTIC REDUCTION

We describe equivariant differential characters (classifying equi-variant circle bundles with connections), their prequantization, and reduction.

ar X iv : h ep - p h / 02 10 07 4 v 1 4 O ct 2 00 2 Effective vertex for π 0 γγ §

The π 0 γγ vertex is used as an explicit example of the subtleties connected with the application of equation of motion within Chiral Perturbation Theory at the order O(p 6).