On commutativity in point-reflection geometries

To any spatial point-reflection geometry there corresponds a determined commutative kinematic space.Dedicated to Professor Raphael Artzy on his 80^th birthday.Research supported by the NATO Scientific Affairs Division grant CRG 900103.     

1.2 Anorganische analyse

Ohne Zusammenfassung     

Curve design with rational Pythagorean-hodograph curves

The dual Bézier representation offers a simple and efficient constructive approach to rational curves with rational offsets (rational PH curves). Based on the dual form, we develop geometric algorithms for approximating a given curve with aG ² piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation andG ² Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail.     

Structural studies on ruthenium(II) complexes used in interphase catalysis for the hydrogenation of ketones

Structural studies were performed on catalytically active ruthenium(II) complexes used in interphases, by means of XAFS spectroscopy. The EXAFS investigations indicate that the complexes retain their structural integrity when they are embedded on polysiloxane matrices to form stationary phase materials. The AXAFS studies reveal that the variations in the catalytic activity of the complexes with different ligands can be correlated to the differences in the electronic structure around the active ruthenium center. The EXAFS investigations show that, in asymmetric transfer hydrogenation reactions catalysed by ruthenium(II) complexes, the co‐catalyst plays a crucial role not only in enhancing the catalytic activity, but also in determining the structure of the intermediate species. Copyright © 2007 John Wiley & Sons, Ltd.     

On the differentiability of maps into Lie transformation groups

Let G be a Lie transformation group on a manifold M. Then a map f: NG is differentiable, iff for every point pM the map q f(q)·p is differentiable.