A note on maximal progression-free sets

Erd?s et al [Greedy algorithm, arithmetic progressions, subset sums and divisibility, Discrete Math. 200 (1999) 119-135.] asked whether there exists a maximal set of positive integers containing no three-term arithmetic progression and such that the difference of its adjacent elements approaches infinity. This note answers the question affirmatively by presenting such a set in which the difference of adjacent elements is strictly increasing. The construction generalizes to arithmetic progressions of any finite length.     

A portable ultrahigh‐vacuum system for advanced synchrotron radiation studies of thin films and nanostructures: EuSi2 nano‐islands

A portable ultrahigh‐vacuum system optimized for in situ variable‐temperature X‐ray scattering and spectroscopy experiments at synchrotron radiation beamlines was constructed and brought into operation at the synchrotron radiation facility ANKA of the Karlsruhe Institute of Technology, Germany. Here the main features of the new instrument are described and its capabilities demonstrated. The surface morphology, structure and stoichiometry of EuSi₂ nano‐islands are determined by in situ grazing‐incidence small‐angle X‐ray scattering and X‐ray absorption spectroscopy. A size reduction of about a factor of two of the nano‐islands due to silicide decomposition and Eu desorption is observed after sample annealing at 1270 K for 30 min.     

Mechanochemische Mikroreaktionen

Zusammenfassung Für die Ausführung mechanochemischer Mikroreaktionen, die durch Zerkleinern, Verreiben, Ritzen oder Drücken von Feststoffen hervorgerufen werden, genügen häufig außerordentlich kleine Substanzmengen von z. B. 10^–6 bis 10^–9 g, um das Reaktionsprodukt zu erkennen. Einige mechanochemische Mikroreaktionen werden beschrieben, die sich zum Nachweis von Eisen, Kobalt, Nickel, Wolfram, Molybdän bzw. Silber eignen. Beim Verreiben von Natriumsulfit mit Schwefel wird Natriumthiosulfat gebildet, das in gewissen Fällen Kristallkeime enthält, die an der Auslösung der Kristallisation aus übersättigten Thiosulfatlösungen zu erkennen sind.

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Summary Frequently extremely small amounts of material, such as 10^–6 to 10^–9 g, are sufficient for recognition of the product resulting from mechanochemical microreactions brought about by pulverizing, grinding, scratching, or pressing solid materials. Several such reactions are described that are suitable for the detection of iron, cobalt, nickel, tungsten, molybdenum, silver. Sodium thiosulfate is formed by grinding sodium sulfite together with sulfur; the product in some instances contains crystal nuclei that can be identified through their initiation of crystallization when added to supersaturated thiosulfate solutions.

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Résumé Des quantités de substances extraordinairement petites, 10^–6 à 10^–9 g par exemple, suffisent la plupart du temps pour caractériser les produits finaux dans le cas de réactions mécanochimiques à l'échelle micro, provoquées par porphyrisation, par pistage, par rayage ou par pression, sur des substances solides. On en décrit certaines qui conviennent à la recherche du fer, du cobalt, du nickel, du tungstène, du molybdène et de l'argent. En triturant du sulfite de sodium avec du soufre, on obtient du thiosulfate de sodium qui contient dans certains cas des germes cristallins et que l'on reconnaît en amorçant la cristallisation dans des solutions de thiosulfate sursaturées.

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Herrn Professor Dr.A. A. Benedetti-Pichler zum 70. Geburtstag gewidmet.     

Similarity Issues of Kerosene and Methane Confined Flames Stabilized by Swirl in Regard to the Weak Extinction Limit

One of the most promising methods for reducing NO _x emissions of jet engines is the lean combustion process. For realization of this concept the percentage of air flowing through the combustor dome has to be drastically increased, which implies high volume fluxes in the primary zone of the combustion chamber and represents a substantial challenge in regard to the flame stabilization. Swirl motion is thus applied to the air flux by the swirl generator and decisively contributes to the flame stabilization. The current paper reviews an atmospheric investigation of a burner configuration in regard to the weak extinction limit, comprising a confined non-premixed swirl-stabilized flame. The burner can be supplied with either kerosene or after a small adaption with natural gas (methane). Therefore, a comparison of a kerosene-fuelled flame (spray flame) to a natural gas fuelled one (methane flame) can be performed. Both are realized by almost identical burner configuration and at identical conditions. The main idea of this work is to align the stability characteristics of both flames by means of similarity. However, fundamental differences regarding the flame structures of the flames are detected through in-flame measurements. This determines the limits of the current approach and motivates an appropriate choice of flame modeling.     

Towards an Axiomatization of Interval Arithmetic

In this paper intervals are viewed as approximate real numbers. A revised formula for interval multiplication of generalized intervals is given. This formula will be useful for further axiomatization of interval arithmetic and relevant implementations within computer algebra systems. Relations between multiplication of numbers and multiplication of errors are discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Factors Affecting the Adsorption of Bacteriocins to <Emphasis Type="Italic">Lactobacillus sakei</Emphasis> and <Emphasis Type="Italic">Enterococcus</Emphasis> sp.

Bacteriocins bacJW3BZ and bacJW6BZ produced by Lactobacillus plantarum, and bacJW11BZ and bacJW15BZ produced by Lactobacillus fermentum, inhibit Gram-positive and Gram-negative bacteria. Treatment of Enterococcus sp. HKLHS and Lactobacillus sakei DSM 20017 with these bacteriocins deformed the cells and resulted in DNA and β-galactosidase leakage. The bacteriocins adsorbed to sensitive and resistant strains. Optimal adsorption of bacJW3BZ and bacJW6BZ to Enterococcus sp. HKLHS was recorded at pH 10.0, whereas adsorption of bacJW11BZ and bacJW15BZ was favored at pH 4.0–8.0 and 2.0–4.0, respectively. Adsorption to L. sakei DSM 20017 was less influenced by pH. Incubation temperature had a major influence on the adsorption of bacJW6BZ and bacJW11BZ to sensitive cells, with better results recorded below 30°C. Although variable results were recorded for bacJW3BZ and bacJW15BZ, optimal adsorption occurred between 37 and 60°C. Variable levels of adsorption were recorded in the presence of inorganic salts and solvents, and this seems to be species-specific. Maximal adsorption (100%) was recorded for bacJW3BZ and bacJW15BZ to L. sakei DSM 20017 in the presence of most inorganic salts and solvents tested. Maximal adsorption of bacJW6BZ to Enterococcus sp. HKLHS (50%) was recorded in the presence of Triton X-114 and little (17%) or no adsorption in the presence of other reagents.     

Variational calculations on the vibrational level structure of S0 HDCO

We perform converged high precision variational calculations to determine the frequencies of the vibrational levels in S₀ HDCO, extending up to 5000 cm^?1 of vibrational excitation energy. For these calculations we use our specific vibrational method (recently employed for studies on H₂CO and D₂CO), consisting of a combination of a search/selection algorithm and a Lanczos iteration procedure and based on the Martin, Lee, Taylor potential energy surface for formaldehyde. The calculated level structure is compared to the recently measured frequencies by Ellsworth et al. in order to improve their assignments and further clarify the vibrational mixing pattern and vibrational resonances in HDCO that are very different from the other more symmetric formaldehyde species H₂CO and D₂CO studied recently.