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 ∗

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 7 . 41 78 v 1 [ m at h . PR ] 2 3 Ju l 2 00 9 An Introduction to Stochastic PDEs

2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...

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.

ar X iv : 0 90 4 . 09 09 v 1 [ m at h . FA ] 6 A pr 2 00 9 On Sobolev extension domains in R

We describe a class of Sobolev W k p -extension domains Ω ⊂ R n determined by a certain inner subhyperbolic metric in Ω. This enables us to characterize finitely connected Sobolev W 1 p -extension domains in R 2 for each p > 2 .

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