ar X iv : m at h / 06 05 58 1 v 2 [ m at h . N A ] 2 8 N ov 2 00 6 EVALUATING THE EVANS FUNCTION : ORDER REDUCTION IN NUMERICAL METHODS

ar X iv : m at h / 06 05 58 1 v 1 [ m at h . N A ] 2 2 M ay 2 00 6 EVALUATING THE EVANS FUNCTION : ORDER REDUCTION IN NUMERICAL METHODS

We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary differential equation depending on the spectral parameter. The problem becomes stiff as the spectral parameter grows. Consequently, the Gauss–Legendre method ha...

ar X iv : m at h / 05 11 37 2 v 1 [ m at h . D S ] 1 5 N ov 2 00 5 EVANS FUNCTIONS , JOST FUNCTIONS , AND FREDHOLM DETERMINANTS

The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first-order matrix-valued differential equations on the real line, and a proof of the fact that the Evans function, a finite-dimensional determinant by construction, coincides with a modified Fredholm determinant associate...

ar X iv : m at h / 06 11 45 2 v 1 [ m at h . A G ] 1 5 N ov 2 00 6 UNIRATIONALITY OF CERTAIN SUPERSINGULAR K 3 SURFACES IN CHARACTERISTIC

We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h / 03 06 23 5 v 2 [ m at h . D G ] 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].