Half-regular and regular points in compact polygons

We investigate the derived structures of compact polygons at half-regular and at regular points. This enables us to give a geometric characterization of the real or complex split Cayley hexagon.     

Local behavior of an iterative framework for generalized equations with nonisolated solutions

 An iterative framework for solving generalized equations with nonisolated solutions is presented. For generalized equations with the structure , where is a multifunction and F is single-valued, the framework covers methods that, at each step, solve subproblems of the type . The multifunction approximates F around s. Besides a condition on the quality of this approximation, two other basic assumptions are employed to show Q-superlinear or Q-quadratic convergence of the iterates to a solution. A key assumption is the upper Lipschitz-continuity of the solution set map of the perturbed generalized equation . Moreover, the solvability of the subproblems is required. Conditions that ensure these assumptions are discussed in general and by means of several applications. They include monotone mixed complementarity problems, Karush-Kuhn-Tucker systems arising from nonlinear programs, and nonlinear equations. Particular results deal with error bounds and upper Lipschitz-continuity properties for these problems. Received: November 2001 / Accepted: November 2002 Published online: December 9, 2002 Key Words. generalized equation – nonisolated solutions – Newton's method – superlinear convergence – upper Lipschitz-continuity – mixed complementarity problem – error bounds Mathematics Subject Classification (1991): 90C30, 65K05, 90C31, 90C33     

Partial Ovoids in Classical Finite Polar Spaces

Ovoids in finite polar spaces are related to many other objects in finite geometries. In this article, we prove some new upper bounds for the size of partial ovoids in Q ^–(2n+1,q) and W(2n+ 1,q). Further, we give a combinatorial proof for the non-existence of ovoids of H(2n +1,q ²) for n>q ³.     

Poly(dimethylaminoethylmethacrylate) hydrochloride (PDMAEM-HCl) a well behaving polycation for multilayer formation on planar surfaces

The polycation preparation of poly(dimethylaminoethylmethacrylate) hydrochloride and the multilayer formation in combination with poly(sodium 4-styrenesulphonate) as polyanion studies onto different substrates, as followed by streaming potential measurements, in situ surface plasmon resonance spectroscopy, and multi-wavelength ellipsometry, are reported. Furthermore, we studied the resulting multilayer buildup of dry surfaces by UV-Vis spectroscopy, X-ray photoelectron spectroscopy, and atomic force microscopy measurements. Thereby, the layer built up at the solid/liquid-interface could be followed and quantified at the molecular level.This revised version was published online in April 2005 with corrections to the article category.