Scanning Kelvin Microscope: a new method for surface investigations

Based on the well known Kelvin probe for work function measurements a new microstructure analysis system - the Scanning Kelvin Microscope - has been developed. It allows to measure simultaneously with high lateral resolution the distribution of the contact potential difference (CPD) between a conductive sample and a reference probe together with the topographical structure of the sample surface. The measurement is contact free and non-destructive and can be carried out in natural environments. At present the lateral resolution of the measurement approaches 5 microm. The results can be displayed on a computer in three dimensional colour pictures.     

Triangulations and moduli spaces of Riemann surfaces with group actions

Summary We study that subset of the moduli space of stable genusg,g>1, Riemann surfaces which consists of such stable Riemann surfaces on which a given finite groupF acts. We show first that this subset is compact. It turns out that, for general finite groupsF, the above subset is not connected. We show, however, that for ℤ₂ actions this subsetis connected. Finally, we show that even in the moduli space ofsmooth genusg Riemann surfaces, the subset of those Riemann surfaces on which ℤ₂ actsis connected. In view of deliberations of Klein ([8]), this was somewhat surprising. These results are based on new coordinates for moduli spaces. These coordinates are obtained by certainregular triangulations of Riemann surfaces. These triangulations play an important role also elsewhere, for instance in approximating eigenfunctions of the Laplace operator numerically. This work has been supported by the European Communities Science Plan Project No SCI^*-CT91 (TSTS) “Computational Methods in the Theory of Riemann Surfaces and Algebraic Curves,” by Academy of Finland and by the Swiss National Science Foundation Grant 20-34099.92. We thank M. C. Petrus for providing excellent motivation for this work. This article was processed by the author using the LATEX style filecljourl from Springer-Verlag.     

Bell-type inequalities in horizontal sums of Boolean algebras

We give a necessary and sufficient condition for a Bell-type inequality to hold in a horizontal sum of finitely many finite Boolean algebras.