Is a complex space X which is the union of an increasing sequence X1 ⊂ X2 ⊂ X3 ⊂ · · · of open Stein subspaces itself a Stein space ? From the begining this question has held great interest in Stein theory. The special case when {Xj}j≥1 is a sequence of Stein domains in I C n had been proved long time ago by Behnke and Stein [2]. In 1956, Stein [13] answered positively the question under the ad...

The Pommiez operator (∆ f )(z) = ( f (z)− f (0))/z is considered in the space (G) of the holomorphic functions in an arbitrary finite Runge domain G. A new proof of a representation formula of Linchuk of the commutant of ∆ in (G) is given. The main result is a representation formula of the commutant of the Pommiez operator in an arbitrary invariant hyperplane of (G). It uses an explicit convolu...

This paper presents a novel way of identifying and illustrating the accuracy in the particle tracing method for ow visualization. We make use of explicit Runge-Kutta methods for particle tracing in steady velocity elds, and describe three approaches to estimate the accuracy of the calculated path. These approaches are: reintegration (with smaller tolerance or in a backward direction), global er...