ar X iv : 0 81 0 . 06 33 v 1 [ m at h . R A ] 3 O ct 2 00 8 ROUGH SETS DETERMINED BY QUASIORDERS

ar X iv : 0 81 0 . 06 33 v 2 [ m at h . R A ] 1 6 Ju n 20 09 ROUGH SETS DETERMINED BY QUASIORDERS

In this paper, the ordered set of rough sets determined by a quasiorder relation R is investigated. We prove that this ordered set is a complete, completely distributive lattice. We show that on this lattice can be defined three different kinds of complementation operations, and we describe its completely join-irreducible elements. We also characterize the case in which this lattice is a Stone ...

ar X iv : 0 81 0 . 26 81 v 1 [ m at h . PR ] 1 5 O ct 2 00 8 FROM RANDOM WALKS TO ROUGH PATHS

Donsker's invariance principle is shown to hold for random walks in rough path topology. As application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.

ar X iv : 0 81 0 . 05 79 v 1 [ m at h . ST ] 3 O ct 2 00 8 Almost Sure Convergence of Extreme Order Statistics

Let M

ar X iv : h ep - l at / 0 11 00 06 v 2 3 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : 0 81 0 . 17 89 v 1 [ m at h . SP ] 1 0 O ct 2 00 8 SPECTRAL THEORY OF ELLIPTIC OPERATORS IN EXTERIOR DOMAINS

We consider various closed (and self-adjoint) extensions of elliptic differential expressions of the type A = P 06|α|,|β|6m(−1) Daα,β(x)D β , aα,β(·) ∈ C ∞(Ω), on smooth (bounded or unbounded) domains Ω in R with compact boundary ∂Ω. Using the concept of boundary triples and operator-valued Weyl–Titchmarsh functions, we prove various trace ideal properties of powers of resolvent differences of ...