Bounds for solutions of a differential inequality

This work compares the solutions of an th order differential inequality plus boundary conditions with the solution of the related differential equation with boundary conditions. The differential operator is assumed to be disconjugate. It is proved that under suitable conditions the ratio of these solutions is monotone. The solution of the inequality can be replaced by the corresponding Green's function.

     

Microwave-assisted synthesis of dihydropyridones from curcumin

Dihydropyridones were prepared by microwave-assisted reaction between curcumin and primary amines or their acetates in the presence of Montmorillonite (K-10) as a catalyst. The reaction was complete within a few minutes and the yield depends on the amine used.     

Track Extensions of Categories and Cohomology

We introduce the notion of n-fold track extensions of a category C by a natural system D and prove that such extensions represent classes in the cohomology of C with coefficients in D introduced by Baues–Wirsching. This generalizes a result of Huebschmann on the cohomology of groups.     

Trace analysis of parabens,triclosan and related chlorophenols in water by headspace solid-phase microextraction with in situ derivatization and gas chromatography–tandem mass spectrometry

An in situ derivatization solid-phase microextraction method has been developed for the determination of parabens, triclosan and related chlorophenols in water. Acetylated derivatives are selectively determined using gas chromatography with tandem mass spectrometry. Parameters affecting both derivatization and SPME procedures, such as fiber coating, extraction mode, temperature, volume of derivatizating reagent and ionic strength, are studied and optimized through a multifactorial experimental design. The performance of the method is studied in terms of accuracy, linearity, precision and limits of detection. Quantitative recoveries (≥82%) and satisfactory precision (RSD ≤ 12%) are obtained. Limits of detection at the low picogram per millilitre level are achieved for all target compounds. Linearity is studied in a wide range of concentrations and an analysis of variance with a lack-of-fit test is run to validate the calibration data. Extraction time profiles are also obtained. Finally, the applicability of the proposed method is demonstrated for several real samples including river water, wastewaters and swimming pool water. Since no matrix effects are observed, quantification can readily be carried out by external calibration with ultrapure water standards.     

Evaluation of toluene LIF thermometry detection strategies applied in an internal combustion engine

In the context of toluene laser-induced fluorescence (LIF) thermometry, the two common LIF detection strategies, namely one-color and two-color detection, have been simultaneously applied to compare each strategy’s ability to accurately resolve thermal gradients during an engine cycle within an optically accessible internal combustion (IC) engine. Temperature images are obtained from high-speed toluene LIF measurements and are combined with high-speed particle image velocimetry. The combination with flow data and Mie scattering images facilitates the interpretation of differences between the toluene LIF detection strategies. Two-color temperature images are limited in their ability to detect thermal gradients near the end of compression due to larger precision uncertainties. Local regions of cold gases in the two-color images are better identified with the guidance of the one-color images when homogeneous toluene mixtures preside. During expansion, large differences exist between one- and two-color temperature images and likely caused by local mixture fraction heterogeneities that bias the one-color detection strategy. Toluene condensation occurs during the expansion and exhaust stroke and causes local mixture fraction heterogeneities in the combustion chamber. Liquid toluene is in contact with solid surfaces and crevices of the combustion chamber and can evaporate during compression or expansion causing both local temperature and mixture stratification. This work demonstrates the advantage of high-speed imaging and use of multiple image diagnostics to reveal the development of natural temperature and mixture stratification in a motored IC engine. This work also suggests that natural temperature stratification typically regarded from gas-wall heat transfer may also be caused by liquid droplet evaporation on solid surfaces. Such phenomenon, however, is expected to be pertinent for all modern-day engine operating systems.     

Sterisch gehinderte Stickstoffbasen zur selektiven Extraktion von Silber

Zusammenfassung Lösungen von sterisch gehinderten Pyridinbasen wie 4-Octadecylthio-2,6-dimethylpyridin (= Lut-S-18 = III) und anderen sterisch gehinderten aliphatischen (und cycloaliphatischen) Stickstoffbasen in Heptanon-3 werden für die radiochemisch verfolgte Extraktion von Silber(I)-Ionen aus wäßriger Lösung eingesetzt. In Gegenwart von 0,5 M NaNO₃ extrahiert die Pyridinbase Lut-S-18 im pH-Bereich 5–10 bis zu 88% des Silbers in einem einzelnen Extraktionsschritt. Das Extraktionsmittel Lut-S-18 ist selektiv für Silber in dem Sinne, daß unter den genannten Bedingungen die Aquokationen Co²⁺, Ni²⁺, Cu²⁺ und Zn²⁺ nur in sehr geringem Ausmaß extrahiert werden. Die Rückextraktion des Silbers aus der organischen Phase kann leicht mit verdünnter Ammoniak-Lösung durchgeführt werden. Die Amine 3-Amino-2,4-dimethylpentan und 2,2,6,6-Tetramethylpiperidin sind auch gute Extraktionsmittel für Silber, aber sie wirken weniger selektiv.

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Sterically hindered nitrogen bases for the selective extraction of silver

Summary Heptanone-3 solutions of sterically hindered pyridine bases such as 4-octadecylthio-2,6-dimethylpyridine (= Lut-S-18=III) and of other sterically hindered aliphatic (and cycloaliphatic) nitrogen bases are used for the radiochemically monitored extraction of silver(I) ions from aqueous solution. In the presence of 0.5 M NaNO₃ the pyridine base Lut-S-18 extracts up to 88% of the silver in a single extraction step in the pH range 5–10. The extraction agent Lut-S-18 is selective for silver in the sense that under the conditions described the aquo cations Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ are extracted to a very minor extent only. Back extraction of the silver from the organic phase is easily achieved with dilute ammonia solution. The amines 3-amino-2, 4-dimethylpentane and 2,2,6,6-tetramethylpiperidine are also good extraction agents for silver, but they are less selective.

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Herrn Prof. Dr. K. H. Lieser zum 65. Geburtstag gewidmet

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Die Autoren danken der Deutschen Forschungsgemeinschaft und dem Verband der Chemischen Industrie e.V. für Unterstützung sowie der Firma E. Merck, Darmstadt, für Zusammenarbeit. Die Durchführung der radiochemischen Messungen wurde durch das Entgegenkommen der Arbeitsgruppe von Herrn Prof. Dr. K. H. Lieser wesentlich erleichtert. Einige der aliphatischen Stickstoffbasen wurden freundlicherweise von der Fa. Hüls zur Verfügung gestellt.     

A kinetic study of the air oxidation of pyrogallol and purpurogallin

Pyrogallol (1,2.3-benzentriol, 1 ) reacts with dioxygen in weakly alkaline solutions to form purpurogallin (2,3,4,6-tetrahydroxy-5H-benzocycloheptene-5-one, 2 ) which then reacts to form purpurogalloquinone ( 3 ) which then decays to a product absorbing at 440 nm. The formation of 3 requires 1.5 mol O₂ per mol 1 , and 1.0 mol per mol 2 . No O₂ is consumed during the decay of 3 , and this reaction, being insensitive to O₂ concentrations and the presence of both superoxide dismutase (SOD) and catalase, does not appear to be an oxidation. The first-order rate of decay of 3 decreases with increasing pH. 1 and 3 react at pH 9.0 with a second-order rate constant of ca. 100 M^?1 s^?1. SOD inhibits the oxidation of 1 and 2 . Slight and variable apparent inhibition of the oxidation of 2 and 3 by SOD may be due to trace impurities in 2 , but not contamination by 1 . The peak concentration of 3 is attained more rapidly during the oxidation of 1 than during the oxidation of 2 . A kinetic scheme based on parallel oxidation of 1 by dioxygen and superoxide, and it which the semiquinone of 1 oxidizes 2 , is partially successful in simulating the observed kinetic behavior.     

Microwave-assisted synthesis of novel 2,3-dihydro-4-pyridinones

Novel 2,3-dihydro-4-pyridinones were synthesized via the reaction of curcumin and primary amines or amine acetates under microwave irradiation. Montmorillonite K-10 was used as a catalyst. Reaction times did not exceed 120 s. The structures of the compounds were established by elemental analysis and from their mass, 1H- and 13C-NMR spectra.