ar X iv : 0 70 7 . 03 35 v 1 [ m at h . O C ] 3 J ul 2 00 7 Label - setting methods for Multimode Stochastic Shortest Path problems on graphs

ar X iv : 0 70 7 . 03 35 v 2 [ m at h . O C ] 2 9 Fe b 20 08 Label - setting methods for Multimode Stochastic Shortest Path problems on graphs

Stochastic shortest path (SSP) problems arise in a variety of discrete stochastic control contexts. An optimal solution to such a problem is typically computed using the value function, which can be found by solving the corresponding dynamic programming equations. In the deterministic case, these equations can be often solved by the highly efficient label-setting methods (such as Dijkstra’s and...

ar X iv : 0 70 7 . 03 46 v 1 [ m at h - ph ] 3 J ul 2 00 7 THE ONE - DIMENSIONAL SCHRÖDINGER - NEWTON EQUATIONS

We prove an existence and uniqueness result for ground states of one-dimensional Schrödinger-Newton equations.

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : 0 70 7 . 04 47 v 1 [ m at h . R A ] 3 J ul 2 00 7 Subrings which are closed with respect to taking the inverse

Let S be a subring of the ring R. We investigate the question of whether S ∩ U(R) = U(S) holds for the units. In many situations our answer is positive. There is a special emphasis on the case when R is a full matrix ring and S is a structural subring of R defined by a reflexive and transitive relation.

ar X iv : m at h - ph / 0 30 70 15 v 1 8 J ul 2 00 3 Integrable geodesic flows on Riemannian manifolds : Construction and Obstructions ∗ Alexey

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.