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.     

Hg2(OH)[BF4], the First Basic Mercurous Tetrafluoroborate

The first basic mercurous tetrafluoroborate, Hg₂(OH)[BF₄], was obtained through a synproportionation reaction of red mercuric oxide, HgO, and elemental mercury in a 35% solution of HBF₄ in water as colourless single crystals. The crystal structure (orthorhombic, Pbca, Z = 8, a = 985.0(1), b = 991.0(1), c = 1141.0(2) pm) contains [(HO)_1/2—Hg—Hg—(OH)_1/2]⁺ zig‐zag chains that are further connected via weak Hg—OH interchain interactions to layers between which the [BF₄]^— are located in an up and down fashion.     

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).     

Zum thermischen Verhalten von Li3MnO4. II [1, 2]. Über α- und β- Li2MnO3

Thermal Behaviour of Li₃MnO₄. II. α- and β-Li₂MnO₃ By thermal decomposition of Li₃MnO₄ we obtained two new forms of Li₂MnO₃: α-Li₂MnO₃ crystallizes due to Guinier-Simon photographs cubic face-centered with a = 4.09₂ Å, β-Li₂MnO₃ hexagonal with a = 4,93, c = 14.24 Å, c/a = 2.89. α-Li₂MnO₃ is paramagnetic with μ = 3,82 B.M. Below the Neel temperature (≈? 50 K) β-Li₂MnO₃ is antiferromagnetic. Effective Coordination Numbers, ECoN, are calculated and discussed.     

Anwendung der Streustrahl-Methode zur Bestimmung der Elemente in Mineral?lprodukten mit Hilfe der R?ntgenfluorescenz-Spektral-Analyse am Beispiel der Bleibestimmung in Ottokraftstoffen

Zusammenfassung In einem relativ einfach durchzuführenden Verbundverfahren wird Selen im Sauerstoff-strom innerhalb 15 min bei 1100–1150°C quantitativ aus den Metall- bzw. Metalloxidschmelzen verdampft und in einer mit flüssigem Stickstoff gekühlten Vorlage aufgefangen. Das aus der Vorlage mit einer definierten Menge verdünnter HNO₃ in Gegenwart von Ni-Nitrat gelöste Selen läßt sich direkt durch AAS mit dem Graphitofen (FAAS) äußerst nachweisstark und zuverlässig bestimmen. Die Nachweisgrenze (elektrodenlose Entladungslampe) liegt bei 3×10^–11 g Se. Der Verfahrensverbund erlaubt mit Probenmengen 10 g in Ag und Au Se-Gehalte 0,05 ppb,inCu 0,1 ppb,in Bi 0,2 ppb und in Pb 10 ppb zu erfassen. Für draht-, stab- und spanförmige Proben erhält man für Se-Gehalte von 2–0,002 ppm Variationskoeffizienten zwischen 3 und 6%. Die Vollständigkeit der Se-Verdampfung aus den Matrices Cu, Ag, Au und Bi wurde ebenso wie die Richtigkeit des Gesamtverfahrens durch systematische Untersuchungen belegt.

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Determination of se by furnace atomic absorption spectrometry (FAAS) in the ppb-range in Cu, Cu alloys, Ag, Au, Pb and Bi after volatilization in an oxygen stream

Summary Selenium is evaporated in a multi-stage procedure within 15 min from metals or metal oxides fused at temperatures of 1100–1150°C under a stream of oxygen and is trapped in a receiver cooled with liquid nitrogen. The condensed SeO₂ is dissolved with a definite volume of diluted HNO₃ in the presence of Ni-nitrate and determined with high sensitivity and reliability by FAAS (electrodeless discharge lamp). The detection limit of the FAAS was found to be 3 · 10^–11 g of Se. The multi-stage procedure allows to detect Se levels 0.05 ppb in Ag and Au, 0.1 ppb in Cu, 0.2 ppb in Bi, and 10 ppb in Pb, respectively, with sample weights 10 g. For wire, rod, and chip samples the coefficients of variation are found to be between 3 and 6% for Se contents of 2 to 0.002 ppm. The quantitative evaporation of Se from Cu, Ag, Au, and Bi as well as the accuracy of the whole procedure have been checked systematically.

Die Arbeit wurde durch Mittel der DFG in dankenswerter Weise unterstützt.