Fully adaptive multiresolution finite volume schemes for conservation laws

The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation. In this approach the solution is still represented at each time step on the finest grid, resulting in an inherent limitation of the potential gain in memory space and computational time. The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid. A crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages. Several solutions to this problem are proposed, analyzed, and compared in terms of accuracy and complexity.

     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

Morphological modifications of Ag/Cu(111) probed by photoemission spectroscopy of quantum well states and the Shockley surface state

Epitaxial ultra-thin Ag films grown on Cu(111) have been investigated by angle-resolved photoemission spectroscopy. The thickness dependence of the binding energy for the Shockley surface state at 300 K could be determined accurately in films up to 5 ML thick. Furthermore, we observe drastic changes in the film morphology after annealing to 450 K. Spectral modifications in the shape of the quantum-well states (QWS), characteristic for these ultra-thin silver films, prove that the surface morphology is homogeneous. The photoemission spectra also indicate that the silver film bifurcates to form a film exhibiting two distinct film thicknesses. For all levels of silver coverage, we identify surface regions that are 2 ML thick, while the thickness of the remaining surface depends on the amount of deposited silver. The almost purely Lorentzian line-shape of the spectral features corresponding to the two different surface regions show that both surface areas are atomically flat. PACS 68.55.Jk; 73.20.At; 73.21.Fg; 79.60.Dp     

Deuterium exchange of 4-pyrimidones and 4-pyrimidthiones

The hydrogen-deuterium exchange of H-2 in 4-pyrimidone, a number of 1- and 3-alkyl-4-pyrimidones and several of their thione analogs in deuterium oxide at moderate temperatures is reported. This reaction is apparently not susceptible to acid or base catalysis. Cations of the 4-pyrimidones were found not to exchange H-2 at all in acid media. Catalytic amounts of bases do not alter the exchange rates whereas more concentrated alkali decompose the pyrimidone. However, 1,4(3,4)-dihydro-1,3-dimethyl-4-oxopyrimidinium iodide (and its 6-methyl analog) exchange H-2 quite rapidly in neutral deuterium oxide, almost instantly when triethylamine is added as a catalyst, and very slowly in dilute solutions of deuterium chloride in deuterium oxide. Mechanisms are proposed to account for these phenomena.     

Als Beitrag zur Analytik von Organozinn-Stabilisatoren

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