Preprints (rote Reihe) des Fachbereich Mathematik
Year of publication
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- Vigenere-Verschlüsselung (1999)
- In der folgenden Arbeit wird das klassische Verschlüsselungsverfahren von Vigenere vorgestellt. Die mathematischen Grundlagen werden präzise formuliert und anschliessend wird die Theorie durch ein praktisches Beispiel erläutert.
- Theoretische Alternsmechanismen II (2003)
- Theoretische Alternsmechanismen I (1997)
- The average density of planar Brownian motion (1997)
- We show that the occupation measure on the path of a planar Brownian motion run for an arbitrary finite time intervalhas an average density of order three with respect to thegauge function t^2 log(1/t). This is a surprising resultas it seems to be the first instance where gauge functions other than t^s and average densities of order higher than two appear naturally. We also show that the average densityof order two fails to exist and prove that the density distributions, or lacunarity distributions, of order threeof the occupation measure of a planar Brownian motion are gamma distributions with parameter 2.
- Tangent measure distributions of hyperbolic Cantor sets (1996)
- Tangent measure distributions were introduced by Bandt and Graf as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by contractive mappings, which are not similitudes. We show that the tangent measure distributions of these sets equipped with either Hausdorff or Gibbs measure are unique almost everywhere and give an explicit formula describing them as probability distributions on the set of limit models of Bedford and Fisher.
- Tangent measure distributions of fractal measures (1999)
- Tangent measure distributions are a natural tool to describe the local geometry of arbitrary measures of any dimension. We show that for every measure on a Euclidean space and every s, at almost every point, all s-dimensional tangent measure distributions define statistically self-similar random measures. Consequently, the local geometry of general measures is not different from the local geometry of self-similar sets. We illustrate the strength of this result by showing how it can be used to improve recently proved relations between ordinary and average densities.
- Symmetry properties of average densities and tangent measure distributions of measures on the line (1995)
- Answering a question by Bedford and Fisher we show that for every Radon measure on the line with positive and finite lower and upper densities the one-sided average densities always agree with one half of the circular average densities at almost every point. We infer this result from a more general formula, which involves the notion of a tangent measure distribution introduced by Bandt and Graf. This formula shows that the tangent measure distributions are Palm distributions and define self-similar random measures in the sense of U. Zähle.
- Rank two Cohen-Macaulay modules over singularities of type ..... (2004)
- We describe, by matrix factoizations, all the rank two maximal Cohen-Macauly modules over singularities of type ......