We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent is inspired by the parametrisation introduced Cabr\'e, Fontich de la Llave. By iteratively solving so-called conjugacy equation, our simultaneously computes parametrisations of bundles, as well dynamics on these objects, to arbitrarily high...

In this paper, we study jumps of nonlinear DAEs caused by inconsistent initial values. First, propose a simple normal form called the index-1 Weierstrass (INWF) for DAEs. Then generalize notion consistency projector linear to case. By an example, compare our proposed projectors with two existing consistent initialization methods show that are not coordinate-free, i.e., points calculated invaria...

A general construction for complete embedded minimal surfaces of nite total curvature in Euclidean three space is carried out In particular ex amples with an arbitrary number of ends are given for the rst time The construction amounts to desingularizing the circles of intersection of a col lection of coaxial catenoids and planes The desingularization process uses Scherk s singly periodic surfac...