Obituary Gilbert Grynberg (1948-2003)

We mourn the death of Professor Dr. Gilbert Grynberg, April 17, 1948 - January 27, 2003. We have lost an excellent and highly esteemed scientist, an outstanding character and a good friend. He has been a very active colleague in the merger of Zeitschrift für Physik and Journal de Physique in the early days. As one of the Co-Editors-in-Chief of The European Physical Journal D, from its start, he has formed the scienti.c standards of EPJ. Untiringly he has served our Journal with greatest dedication. We are grateful that he has been with us. The editorial board and o.ce of EPJ B Siegfried Grossmann, Denis Jérome, Antonio Paoletti     

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.     

Selective metal promoted hydrolysis of nitrile groups in the side chain of tetraazamacrocyclic Cu2+-complexes

The metal promoted hydrolysis of nitrile groups in the side chains of tetraazamacrocyclic Cu2+ complexes has been studied by stopped-flow techniques. It is shown that the reaction proceeds by an intramolecular attack of an axially coordinated OH- onto the nitrile group to give the corresponding amide. In alkaline solution the amide then deprotonates and binds to the axial position of the Cu2+ thus preventing further coordination of an OH-. This explains mechanistically that in the Cu2+ complexes of macrocycles carrying two nitrile functions only one is selectively hydrolysed. The nitrile hydrolysis has also been used on a preparative scale to synthesize tetraazamacrocycles with two different side chains. X-Ray diffractions of several products are presented to confirm the structures and the results from the kinetics and equilibria measurements.     

Eine einfache Theorie des mechanischen Relaxationsverhaltens der amorphen Polymeren

Zusammenfassung In der Arbeit wird eine einfache Theorie der mechanischen Relaxation der amorphen Polymeren entwickelt. Als kinetische Grundeinheit des Relaxationsvorgangs tritt ein ausN Monomereinheiten bestehendes Segment auf. Unter Einwirkung mechanischer Kräfte erfolgt eine Orientierung des Segments. Au\erdem werden durch die mechanischen Kräfte Umlagerungen der Monomereinheiten hervorgerufen, die eine Längenänderung des Segments bedingen. Davon ist die Segmentorientierung im wesentlichen nur vom freien Volumen abhängig, während die Umlagerungen als ein Diffusionsproze\ in einem äu\eren Potentialfeld betrachtet werden, das durch die benachbarten Monomereinheiten der gleichen Kette und der anderen Ketten gebildet wird.Die Theorie liefert für dieYoungsche Nachgiebigkeit; zwei Relaxationsgebiete, wobei im einzelnen Aussagen über die Temperaturabhängigkeit der Relaxations-frequenz, der Intensität und des Breitenparameters der Relaxationsgebiete erfolgen.     

Ein neues statistisches Segmentmodell zur Deutung der dielektrischen Eigenschaften hochpolymerer Lösungen

Zusammenfassung Es wird ein neues statistisches Segmentmodell angegeben, das zur Deutung der dielektrischen Eigenschaften der Lösungen von Kettenmolekülen mit seitständigen Dipolgruppen herangezogen werden soll.Es wird zunächst die exakte Lösung für das Relaxationsspektrum angegeben. Anschlie\end wird eine Näherungslösung abgeleitet, die einen Vergleich mit den Me\ergebnissen vonBrouckère und Mitarb. gestattet. Dabei zeigt sich eine gute übereinstimmung zwischen Experiment und Theorie.     

Accurate calibration of TXRF using microdroplet samples

TXRF has been applied in combination with VPD to the analysis of trace impurities in the native oxide layer of Si wafer surfaces down to the range of 10(8) atoms. cm(-2). Proper quantification of VPD/TXRF data requires calibration with microdroplet standard reference wafers. The precision of calibration function has been evaluated and found to allow quantification at a high level of 3 sigma confidence with microdroplet standard reference.     

New tools: Expert systems for uncertainty budgets

An important part of quality assurance in any analytical laboratory is the production of comprehensive results integrating uncertainty measurements. Many testing laboratories face the problem that the expenditure required to evaluate small uncertainties (high precision and high accuracy) is often uneconomic. In most cases an uncertainty of high reliability has to be calculated from only a few data (one calibration, few replications, etc.). This problem can be solved by an expert system. To achieve this the analytical procedure has to be structured into a dialouge and divided into parts. The uncertainty has to be calculated for each part of the procedure. Addition of the individual uncertainties results in the combined and expanded uncertainty. During the dialouge the system should advise the analyst how to get an efficient and effective calculation of uncertainty. All calculations, mathematical and statistical procedures have to be surveyable but running the system should not be too time consuming for economic reasons. Within the scope of the EURECA-project initiated by the Eidgenössische Materialprüfungs- und Forschungsanstalt (EMPA), St. Gallen, Switzerland, expert system software is being developed in cooperation with other research institutes and manufacturers of analytical instruments. Using this software it will be possible to calculate the uncertainty for analytical procedures such as titration, atomic emission spectrometry (ICP-OES), atomic absorption spectrometry (AAS) and gas- and liquid chromatography (GC, HPLC).