Linearly implicit time discretization of non-linear parabolic equations

We give a stability and error analysis of linearly implicitone-step methods for time discretization of non-linear parabolicequations. We derive precise error bounds for Rosenbrock andW-methods, and we explain the error reduction by Richardsonextrapolation of the linearly implicit Euler method which occursin spite of the breakdown of asymptotic expansions. The parabolicequations are studied in a Hilbert space framework that includessemilinear and quasilinear parabolic equations, and also stiffreaction-diffusion equations with reactions at different timescales.     

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Book reviews

     

Systematic study of impact parameter dependent K-vacancy probabilities in near symmetric gas- and solid-target collision systems

K-vacancy production probabilitiesP _K (b) were measured with gas and solid targets byK-x-ray particle coincidences (impact parameterb is determined by the particle detection angle) in the region of light (Z _P ?Z _T ?10) up to intermediate heavy (Z _P ?Z _T ?36) collision systems. The measuredP _K (b) reveal a very strong difference in shape between solid and gas targets independent ofZ. Only theP _K (b) measured with gas targets and those measured with solid targets at very small impact parameters show reasonable good agreement with the 2pπ _x-2pσ rotational coupling model. At largeb theP _K (b) from solid targets are strongly influenced by a multiple collision effect, where projectileL-vacancies seem to be produced in collisions beforeK-vacancy production. However, this effect cannot be understood just by a two collision process whereL-vacancy production and 2pπ _x-2pσ rotational coupling occurs in consecutive collisions.     

Development of a high-pressure ion-exchange system for rapid preparative separations of trans-uranium elements

In the course of ion-exchange separations of highly active solutions, the radiolysis gives rise to considerable disturbances and deteriorated separation results. On the example of²⁴¹Am/²⁴²Cm separations some results of radiolysis investigations for Dowex 50X8 are briefly shown, and experiences with the choice of parameters of a high-pressure column system are described for several examples.     

Quality assurance in pesticide residue analysis

Summary During the last few years, the Working Group Pesticide Residues of the Food Chemistry and Forensic Chemistry Division of the Gesellschaft Deutscher Chemiker (German Chemical Society) has organised six laboratory performance tests on the analysis of pesticide residues in which numerous laboratories were involved. In these tests the choice of the analytical methods for the examination of fats or vegetable substrates was free. Organochlorine pesticides in concentrations of over 0.01 mg/kg were mostly readily identified, whereas in the analysis of organophosphorus residues often only the classic compounds (parathion, diazinon, etc.) were reported. Many a false positive result could have been avoided by using more adequate methods for confirmatory analysis. The quantitative results, however, were generally quite reliable and were mostly within the official acceptable dispersion range. It can be concluded that the performance of a residue laboratory is by no means constant, and that it is necessary to assess regularly the quality of the analytical results by participating in such interlaboratory tests.

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Qualitätssicherung bei Rückstandsanalysen von PflanzenschutzmittelnErfahrungen aus Ringversuchen

     

Zur konstruktion bewerteter dicksonscher fastkörper

Zusammenfassung  After a short introduction to the valuation theory of nearfields, we give criteria for when a valuation of a skewfield F is also a valuation of the Dickson nearfield F^K which is derived from F by the coupling K on F. For the construction of examples, a rational function field F =K(t) is given. The set of all prolongations of a valuation v on K to F is well known. Sufficient conditions are given which guarantee that couplings K on F and elements are in this sense compatible so that w is a valuation of the Dickson nearfield F^K. Examples demonstrate the results.

     

Die Konstitution der Michael-1,3-Addukte von Cyanessigsäureäthylester an konjugierte Systeme

Zusammenfassung Es wird gezeigt, daß bei der Einwirkung von Cyanessigester auf p-Benzochinon bzw. auf 2,4-Dimethyl-o-chinolacetat Verbindungen entstehen, denen auf Grund der IR-Spektren die Konstitution von Amino-benzofurancarbonsäure-estern zugeschrieben werden muß. Sowohl bei alkalischer als auch bei saurer Verseifung erfolgt Sprengung des Furanringes, intermediär entsteht ein Nitril, das sehr leicht weiter zur Säure bzw. einem Lacton verseift wird. Die Aminogruppe der genannten Aminobenzofuranderivate ist unter energischen Bedingungen zu einer Diacetylaminogruppe acetylierbar. Die Monoacetylverbindung tritt nur als schwer isolierbares Zwischenprodukt auf und ist besser unter milden Verseifungsbedingungen aus der Diacetylverbindung zugänglich. Die Aminogruppe ist unter üblichen Bedingungen nicht titrierbar; sie verhält sich in diesem Belang chemisch völlig anders als die des Anthranilsäureäthylesters, der titrierbar ist. Im IR-Spektrum zeigen hingegen Anthranilsäureäthylester und Aminobenzofuransäureäthylester sehr große Ähnlichkeiten. Eine Erklärung dieser Diskrepanzen hinsichtlich des chemischen Verhaltens und der spektralen Eigenschaften kann derzeit nicht gegeben werden.Mit 1 Abbildung