Linear Independence of q-Analogues of Certain Classical Constants

Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σ_n≥1 a_n/(qⁿ ? 1) ? K for non-zero periodic sequences (a_n) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82     

Strangeness saturation: Dependence on system-size, centrality and energy

The dependence of the strangeness saturation factor on the system size, centrality and energy is studied in relativistic heavy-ion collisions.     

Stress relaxation and viscosity of a bulk Pd<Subscript>40</Subscript>Cu<Subscript>30</Subscript>Ni<Subscript>10</Subscript>P<Subscript>20</Subscript> metallic glass under isochronous heating conditions

Isochronous relaxation of tensile stresses is measured in a bulk Pd₄₀Cu₃₀Ni₁₀P₂₀ metallic glass in the initial state and after certain thermal treatments. The results of measurements are used to find the energy spectrum of irreversible structural relaxation, from which the temperature dependence of shear viscosity is then calculated. This dependence is also found independently from measurements of creep in the same glass. The calculated viscosity is shown to agree well with the experimental data.     

Piecewise Deterministic Markov Control Processes with Feedback Controls and Unbounded Costs

The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover the discount rate may be zero. The value function is shown to be solution to the Bellman equation in a weak sense; however the solution concept is strong enough to generate optimal policies. Continuity and compactness conditions are given for the existence of nonrelaxed optimal feedback controls.     

Aspects of operator theory in hereditarily indecomposable Banach spaces

We examine certain special features exhibited by various classes of linear operators acting in a hereditarily indecomposable Banach space. For instance, we show that the family of all Riesz operators in a H.I. space forms a closed, 2-sided ideal. We also give further characterizations of the class of scalar-type spectral operators (to those already given in [16]). The final section discusses some properties of the spectral maximal spaces of (necessarily decomposable) linear operators in such spaces. Conferenza tenuta il 16 settembre 1997 The support of the German Academic Exchange Scheme (DAAD) is gratefully acknowledged     

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.