ar X iv : 0 90 5 . 27 40 v 1 [ m at h . C O ] 1 7 M ay 2 00 9 Graphs with many ± 1 or ± √ 2 eigenvalues

ar X iv : 0 90 5 . 25 85 v 1 [ m at h . C O ] 1 5 M ay 2 00 9 CHARACTERISTIC POINTS OF RECURSIVE SYSTEMS

Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems.

ar X iv : 0 90 5 . 31 11 v 1 [ m at h . D S ] 1 9 M ay 2 00 9 Relatively finite measure - preserving extensions and lifting multipliers by Rokhlin cocycles

We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.

ar X iv : 0 70 5 . 31 41 v 1 [ as tr o - ph ] 2 2 M ay 2 00 7 The SARG Planet Search

ar X iv : 0 90 5 . 31 11 v 2 [ m at h . D S ] 3 1 M ay 2 00 9 Relatively finite measure - preserving extensions and lifting multipliers by Rokhlin cocycles

We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.

ar X iv : 0 90 5 . 16 85 v 1 [ m at h . A P ] 1 1 M ay 2 00 9 C 1 , α REGULARITY OF SOLUTIONS TO PARABOLIC MONGE - AMPÉRE EQUATIONS

We study interior C regularity of viscosity solutions of the parabolic Monge-Ampére equation ut = b(x, t) (detD u), with exponent p > 0 and with coefficients b which are bounded and measurable. We show that when p is less than the critical power 1 n−2 then solutions become instantly C in the interior. Also, we prove the same result for any power p > 0 at those points where either the solution s...