Prognosefehler im Overdispersed Poisson Modell für Abwicklungsdreiecke

Two simple analytic formulas for the prediction error and the variance of the claims development result in the overdispersed poisson model for loss development triangles are derived. The formula for the prediction error is the analog to the well known formula of Mack for the mean squared error of prediction in his chain ladder model. The formula for the variance of the claims development result is the analog to the results of Merz/Wüthrich. The transpose-invariance property, mentioned by Barnett, Zehnwirth, Dubossarsky, for the overdispersed poisson model applies not only to the forecast, but of course also to prediction error and claims development result, as is shown by our symmetric formulas.     

Über den Rang geschlossener Liescher Gruppen

Ohne ZusammenfassungL. E. J. Brouwer zum 60. Geburtstag     

Über die algebraische Anzahl von Fixpunkten

Ohne ZusammenfassungEine Voranzeige dieser Arbeit ist unter dem Titel:A new proof of the Lefschetz formula on invariant points in den Proceedings of the Nat. Acad. of Sciences U.S.A. 14,Nr. 2 (1928) erschienen. Bezüglich der Unterschiede zwischen den Beweisen in dieser Note und der vorliegenden Arbeit s. unten, Fußnote 27).     

Second Joint NSF–ESF Symposium on, ‘Nanoparticles: Technologies and Applications,’ Tacoma,Washington, USA,October 10, 1999

Journal of Nanoparticle Research -     

The spectrum of relativistic atoms according to Bethe and Salpeter and beyond

We review Evans’ contributions to the spectral theory of operators describing relativistic particle systems. We will concentrate on no-pair operators and recent extensions of that work.     

Asymptotic behavior of the one-particle density matrix of atoms at distances $Z^{-1}$ from the nucleus

We prove that the suitably rescaled density matrix of ground states of atomic Schr?dinger operators with nuclear chargeZ converges on the scale 1/Z to the projection of the negative spectral subspace of the Schr?dinger operator of the hydrogen atom (Z=1). Received March 9, 2000 / Published online February 5, 2001