Einführung in die Welt der Mathematik, die sich bemüht, die Idee der mathematischen Konzepte verständlich zu machen. Ziel ist es, den Mathematik-Schein leichter erwerben zu können - und das mit nachhaltigem Nutzen für das weitere Studium. -- I Grundlagen. Logik. Mengen und Abbildungen. --...

In this paper we prove a Faber-Krahn-type inequality for regular trees and give a complete characterization of extremal trees. The main tools are rearrangements and perturbation of regular trees.

The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles and W and shorter cycles. It is shown that each minimum cycle basis contains the same number of...

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the t-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the...