Beweis der Invarianz der Dimensionenzahl

Ohne Zusammenfassung     

Stopping Power of Charged Particles I

The stopping power of charged particles is determined in the random phase approximation using Lenard Balescu type collision integrals. The stopping power is closely related to other single particle properties such as self energy and quasi particle life time. In this part I, numerical evaluations are given for equal masses (of test and target particles).     

Beweis des ebenen Translationssatzes

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Über die periodischen Transformationen der Kugel

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How to statistically analyze nano exposure measurement results: using an ARIMA time series approach

Measurement strategies for exposure to nano-sized particles differ from traditional integrated sampling methods for exposure assessment by the use of real-time instruments. The resulting measurement series is a time series, where typically the sequential measurements are not independent from each other but show a pattern of autocorrelation. This article addresses the statistical difficulties when analyzing real-time measurements for exposure assessment to manufactured nano objects. To account for autocorrelation patterns, Autoregressive Integrated Moving Average (ARIMA) models are proposed. A simulation study shows the pitfalls of using a standard t-test and the application of ARIMA models is illustrated with three real-data examples. Some practical suggestions for the data analysis of real-time exposure measurements conclude this article.     

Zur Analysis Situs

Ohne ZusammenfassungMit 2 Tafeln     

On q-analogues and stability theorems

In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.     

Solvatochromic rotaxane molecular shuttles

A strongly fluorescent bistable rotaxane is described in which the relative position of the macrocyclic ring with respect to a solvatochromic fluorophore gives a strong response in the spectral domain.     

SL2-modules of small homological dimension

Let V _n be the SL₂-module of binary forms of degree n and let V = V_n1 ???V_np V = {V_{{n_1}}} \oplus \cdots \oplus {V_{{n_p}}} . We consider the algebra R = O(V)^{\textS\textL₂} R = \mathcal{O}{(V)^{{\text{S}}{{\text{L}}_2}}} of polynomial functions on V invariant under the action of SL₂. The measure of the intricacy of these algebras is the length of their chains of syzygies, called homological dimension hd R. Popov gave in 1983 a classification of the cases in which hd R ≤ 10 for a single binary form (p = 1) or hd R ≤ 3 for a system of two or more binary forms (p > 1). We extend Popov’s result and determine for p = 1 the cases with hd R ≤ 100, and for p > 1 those with hd R ≤ 15. In these cases we give a set of homogeneous parameters and a set of generators for the algebra R.