Harmonic Calculus on Fractals - A Measure Geometric Approach I

Differentiation of functions w.r.t. finite atomless measures with compact support on the real line is introduced. The related harmonic calculus is similar to that of the classical Lebesgue case. As an application we obtain the Weyl exponent for the spectral asymptotics of the Laplacians w.r.t. linear Cantor-type measures with arbitrary weights.     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Feasibility study for the preparation of certified reference materials part I – mineral oil contaminated soils

The international joint project HYCREF (Contract No. G6RD-CT-2002-00854), funded by the European Commission in the 5th Framework programme, aimed to develop methods to prepare homogeneous and stable reference materials of water, soil, and waste contaminated with mineral oil hydrocarbons and to certify the mineral oil content by gas chromatographic methods. The results of a feasibility study for the preparation of three soil reference materials are discussed in this paper, and for the preparation of three waste reference materials in the second part (Koch et al., Accred Qual Assur submitted for publication). The soil materials were selected to represent different soil types and contamination levels. The project plan set three requirements for these reference materials: uncertainty in the mineral oil content resulting from the certification exercise <5%, a sample inhomogeneity of <3% and a minimum long-term stability of 5 years. For the most part, these requirements were met within this project.     

Impact of photodepletion to amplified spontaneous emission of proton-transfer dyes in polymeric matrices

A six level rate equation system was used to investigate the impact of photodepletion to amplified spontaneous emission (ASE) of intramolecular proton-transfer (IPT) dyes incorporated into polymeric hosts. The model includes the most important transitions for the normal and tautomer form of the molecule as well as intersystem crossing and triplet–triplet transitions. The experimentally observed pulse shape as well as photodepletion phenomena, i.e. a first order exponential decay of the ASE intensity and a shortening in ASE pulse width, have been simulated successfully. Additionally, the model was used to propose an explanation of the unexpected high photodepletion of proton-transfer dyes in solids. The results show that the emission cross section and reabsorption cross section of the tautomer form of the molecule are the most important parameter not only for efficiency but also for photodepletion. The model was tested by comparison with experimental results of 2-(2’-hydroxyphenyl)benzimidazole in polymethylmethacrylate (PMMA), polystyrene (PS) and a 1:1 alternating copolymer matrix PS-co-PMMA. PACS 78.45.th; 42.55.Mv; 42.70.Jk     

Ueber die Bestimmung der Alkalien im Brunnen-, beziehungsweise Trinkwasser

Ohne Zusammenfassung     

Stability of Crystalline Ion Beams

Hyperfine Interactions - In this paper, the conditions for which three-dimensional crystalline ion beams were attained in the rf quadrupole storage ring PALLAS at a velocity of around 2800 m/s are...     

Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems

It is shown that, if a parametrized fämily of extremals F can be stratified in a way compatible with the flow map generated by F, then those trajectories of the family which realize the minimal values of the cost in F are indeed optimal in comparison with all trajectories which lie in the region R covered by the trajectories of F. It is not assumed that F is a field covering the state space injectively. As illustration, an optimal synthesis is constructed for a system where the flow of extremals exhibits a simple cusp singularity.