ar X iv : 0 90 6 . 54 52 v 1 [ m at h . PR ] 3 0 Ju n 20 09 LONGEST CONVEX CHAINS

ar X iv : 0 90 6 . 45 41 v 1 [ m at h . PR ] 2 4 Ju n 20 09 Covariance function of vector self - similar process ∗

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices.

ar X iv : 0 90 6 . 32 38 v 1 [ m at h . N T ] 1 7 Ju n 20 09 GEOMETRIC AND p - ADIC MODULAR FORMS OF HALF - INTEGRAL WEIGHT by Nick

ar X iv : 0 90 6 . 48 35 v 1 [ m at h . O C ] 2 6 Ju n 20 09 The Complex Gradient Operator and the CR - Calculus

ar X iv : 0 90 6 . 55 83 v 1 [ he p - th ] 3 0 Ju n 20 09 Skyrmion – Anti - Skyrmion Chains

Static axially symmetric sphaleron-type solutions describing chains of interpolating Skyrmion– anti-Skyrmions have been constructed numerically. The configurations are characterized by two integers n and m, where ±n are the winding numbers of the constituent Skyrmion and antiSkyrmion and the second integer m defines type of the solution, it has zero topological charge for even m and for odd val...

ar X iv : 0 90 6 . 18 57 v 1 [ m at h . C O ] 1 0 Ju n 20 09 On the circumference , connectivity and dominating cycles

Every 4-connected graph with minimum degree δ and connectivity κ either has a cycle of length at least 4δ − 2κ or has a dominating cycle.