Rhenium

Ohne Zusammenfassung     

Trigonometric polynomials with many real zeros

This is a contribution to the theory of “incomplete trigonometric polynomials”T _n , but mainly for the case when their zeros are not concentrated at just one point, but are distributed in some intervalI whose length is not too large. We begin with the simple theorem that if ∥T _n ∥ ≤ 1 and ifT _n has ≥θn, 0<θ< 2, zeros at 0, thenT _n (t) must be small on the interval |t|<2 arcsin (θ/2). There are similar but more complicated and more difficult to prove results whenT _n has ≥θn zeros onI. These results have the following application: IfT _n →f a.e., and if ∥T _n >∥_∞<-1, thenf vanishes on a set of the circleT whose measure is controlled by lim sup (N _n /n), whereN _n is the number of zeros ofT _n onT. In turn, this has further applications to series of polynomials, to norms of Lagrange operators, and to Hardy classes.     

Die Grundlagen der Polarographie

Ohne Zusammenfassung     

Chemiluminescent determination of reactive hydrocarbons

Summary Chemiluminescent reactions of ozone with several classes of compounds at different temperatures are described. In a reaction chamber in front of a photomultiplier ozone is mixed with the compounds studied such as alkanes, olefins, alcohols, aromatics, C₂H₂, NO, vinyl chloride or H₂S. The chemiluminescent emission is proportional to the concentration of the compound involved. At room temperature only olefinic hydrocarbons respond but at temperatures above 150°C also a response for alkanes, alcohols, CO etc. is obtained. It is suggested that next to the ozonide-excited formaldehyde mechanism the CO-CO ₂ ^* mechanism is responsible for the chemiluminescent emission at high temperature. A detection limit of a few ppb is achieved. Possible applications are a selective gas-chromatographic detector, an air pollution monitor for instance for CO, and a photochemical reactivity monitor.

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Bestimmung reaktiver Kohlenwasserstoffe durch Chemiluminescenz

Zusammenfassung Chemiluminescenzreaktionen von Ozon mit verschiedenen Verbindungsgruppen (hauptsächlich Kohlenwasserstoffe) bei unterschiedlichen Temperaturen werden beschrieben. In einer Reaktionskammer werden die Verbindungen vor einem Photomultiplier mit Ozon vermischt. Es handelt sich u. a. um folgende Verbindungstypen: Alkane, Olefine, Alkohole, Aromaten, C₂H₂, NO, Vinylchlorid, H₂S. Die Emissionsintensität ist proportional der Konzentration. Bei Raumtemperatur sprechen nur Olefine an, die übrigen Verbindungen erst über 150°C. Die Emission bei höherer Temperatur wird neben der Bildung von Formaldehyd auf die Reaktion CO-CO ₂ ^* zurückgeführt. Die Nachweisgrenze beträgt wenige ppb. Als mögliche Anwendungsgebiete werden ein selektiver GC-Detektor, ein Monitor für Luftverunreinigungen (z.B. für CO) sowie ein Monitor zur Messung photochemischer Reaktivität der Luft genannt.

Presented at the 6th Annual Symposium on Recent Advances in the Analytical Chemistry of Pollutants, April 21–23, 1976; Vienna, Austria.     

The determination of molybdenum and tungsten in sea and surface water

A simple method for the determination of molybdenum and tungsten in sea and surface water is presented. Molybdenum and tungsten are concentrated on activated charcoal by adsorption as the ammonium pyrrolidine dithiocarbamate complex; the optimal pH for adsorption is 1.3. Mo and W are then determined by thermal neutron activation, forming ⁹⁹Mo (T_{$\text{1}\text{2}$} = 66.7 h) and ¹³⁷W (T_{$\text{1}\text{2}$} = 23.8 h), respectively. The ^99mTc daughter of ⁹⁹Mo is measured as soon as the equilibrium between ^99mTc(T_{$\text{1}\text{2}$}= 6 h) and ⁹⁹Mo is established. The detection limits are 0.05 μg Mo l^-1 and 0.05 μg W l^-1 (or 0.001 μg W l^-1 after a simple chemical separation).     

Die Deprotonierung von Metallaquoionen II: Aquochrom(III)-ion. Zur Struktur aktiver Chromhydroxide

On alkalinization of solutions of the chromiun(III)-aquo ion simple deprotonation takes place first. The degree of hydroxylation n _OH however can be brought up to only about 1 (the exact value depending on the total concentration [Cr]_t), before the uncharged complex Cr(OH)₃(OH₂)₃ is precipitated. The structure of the very sparingly soluble complex (solubility ～10^?7M ) is held together by hydrogen bonds of type I between the molecules, so that its formula may be written as Cr(OH)₂H_6/2-lattice. The formation of the well ordered structure is extremely fast. On aging, the metallic centers become connected by μ-hydroxo-bridges (type II) and the substances become amorphous and very insoluble. The dinuclear (H₂O)₄Cr(OH)₂Cr(OH₂)₄⁴⁺ behaves similar on deprotonation. Concerning the various equilibria constants see Table 1.