Tatiana Samrowski: Matherätsel (nicht nur) für Begabte der Klassen 4 bis 6

Mathematische Semesterberichte -     

An implicit function theorem for Banach spaces and some applications

We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie subgroup problem for Banach–Lie groups, as well as Weil’s local rigidity for homomorphisms from finitely generated groups to Banach–Lie groups.      

Die selektive invers-voltammetrische Bestimmung des Antimons in salzsauren L?sungen nach L?sungswechsel in einer einfachen Durchflu?zelle

Summary The selective invers-voltammetric determination of antimony in a simple flow-through cell in hydrochloric acid solutions is described. After double medium exchange for post-electrolysis and inverse-voltammetric determination, the determination of antimony is possible in the presence of a large excess of copper, bismuth and other elements. The limit of determination is 0.2–0.3 ppb Sb, the reproducibility 1.5% (10 ppb Sb).     

Inversvoltammetrische Bestimmung des Bismuts in Biomatrices mit computerunterstützter Me?signalauswertung Teil 3. Bismut-Bestimmung in Wein, Weintrauben und Weinbergsb?den

Summary The ultra trace element bismuth is regulary found in wine on an average of about 0.1 ppb. Very low bismuth contents were also determined in soil and different biomaterials. In spite of those very low quantities even speciation experiments show results, so far that about 90% of the bismuth in the grapes is water-soluble, resumably as saccharic acids. For detecting such low quantities a very sensitive method of differential pulse anodic stripping voltammetry was developped. The speciation experiments were carried out by fractional extraction.

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Herrn Prof. Dr. G. Tölg zum 60. Geburtstag gewidmet     

2.1 Anorganische industrielle Produkte

Summary Digestion-free determination of trace-metals (Zn, Cd, Pb, Cu) in beverages by inverse voltammetry in a flow-through cell equipped with a mercury film-electrode is described. Optimal enrichment potentials are obtained by inspection of the pseudopolarograms of the elements in the original diluted sample solution. After the deposition step in the untreated sample solution stripping is effected in a proper supporting electrolyte after medium exchange. Values obtained by this techniques with various samples compare well with those obtained by usual procedures including wet digestion of the samples.     

Bestimmung des Urangehaltes und der UO2-Stöchiometrie in ThO2-UO2-Kernbrennstoffen

Analysis for uranium and UO₂ stoichiometry in 2.5–5% UO₂ containing ThO₂-UO₂ fuels is made in a single procedure by controlled-potential coulometry. Samples are dissolved in phosphoric acid-hydrofluoric acid with the addition of Al₂(SO₄)₃. With sample weights from 0.2 to 2 g the uranium content is determined with a relative standard deviation of 1%. The minimum detectable hyperstoichiometry of UO₂ amounts to 2.004 with a standard deviation of 0.002.     

Vergleichende Untersuchungen an polarographischen Analysenverfahren

The universal voltammetric instrument, described in part I of this series, is used for comparative studies on the most important polarographic methods, direct current, derivative pulse, simple and phase-sensitive alternating current, double-tone, and harmonic-wave polarography. In general the peak-heights of these methods are influenced in the same measure by the composition of base electrolyte. In single cases characteristic differences are observed.     

Verwendung eines Ge(Li)-Detektors in der radiochemischen Analyse

Zusammenfassung Zur Bestimmung der U- und Th-Gehalte in 0,5–1,5mg wiegenden Mikroproben von ThO₂-UO₂-Kernbrennstoffen wurde die Neutronenaktivierungsanalyse mit zerstörungsfreier-Spektrometrie eingesetzt. Bei Gehalten über 0,1% beträgt die relative Standardabweichung 6%. Der Th-Gehalt der Mikroproben wird durch-spektrometrische Messung des²³³Pa ermittelt; bei Natur-Uran enthaltenden Proben wird der U-Gehalt über²³⁹Np bestimmt, bei hochangereichertes UO₂ enthaltenden Proben über¹³¹J. Mit der beschriebenen Methode können sowohl unbestrahlte als auch bestrahlte ThO₂-UO₂-Kernbrennstoffe untersucht werden.

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Use of a Ge(Li) detector in radiochemical analysisII. determination of U and Th contents in microsamples of ThO²-UO² nuclear fuels

Neutron activation analysis with non-destructive-spectrometry has been used to determine U and Th in microsamples (0.5–1.5 mg) from ThO₂-UO₂ nuclear fuels. With U contents of more than 0.1% the relative standard deviation amounts to 6%. Th in the microsamples is estimated by measuring²³³Pa; in natural UO₂ containing samples²³⁹Np ist measured for U determination, in highly enriched UO₂ samples¹³¹J. Fresh und spent ThO₂-UO₂ nuclear fuels can be investigated by the method described.

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Teil I siehe [3].

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Herrn G. Hofmann danken wir für die Entnahme der Mikro-Bohrproben aus den bestrahlten und unbestrahlten Brennstoffschliffen.