Differential form methods in the theory of variational systems and Lagrangian field theories

This paper will attempt to unify diverse material from physics and engineering in terms of differential forms on manifolds. A variational system will be defined by means of a scalar-valued differential form on a manifold and an ideal in the Grassmann algebra of differential forms on that manifold to serve as constraints. Two types of extremal submanifolds will be defined. The first-called the Euler-Lagrange extremals-will be defined by a method that is the generalization of the classical methods in the calculus of variations. The second—a generalization of a method used by Cartan in his treatise Leçons sur les invariants intégraux-will define extremals as integral submanifolds of an exterior differential system invariently attached to the variational system. As examples, the variational systems attached to string theories in Riemannian manifolds and Yang-Mills fields will be discussed from this differential form point of view. Finally, as application, the differential geometric properties and definition of energy will be presented from the differential form point of view.This work was supported by a grant from the Applied Mathematics program of the National Science Foundation.     

Determination of the plasticizer N-butylbenzenesulfonamide and the pharmaceutical Ibuprofen in wastewater using solid phase microextraction (SPME)

A rapid, inexpensive and solvent-free method for the simultaneous determination of the polyamide plasticizer N-butylbenzenesulfonamide (NBBS) and the widely used pharmaceutical Ibuprofen by solid phase microextraction (SPME) combined with gas chromatography/mass spectrometry (GC/MSD) in wastewater samples was developed. Besides the optimized analytical conditions, results of investigations with varying analytical parameters are reported. Problems, which may occur during the analytical procedure (e.g. salt deposits, adsorption phenomena, carry-over), are discussed. For the determination of Ibuprofen, it is important to carry out the extraction under acidic conditions with sufficiently buffered samples; the GC/MSD system must be very clean and well maintained. SPME allows an extraction of Ibuprofen without derivatization of its carboxylic group. For quantification in complex matrices, the standard addition technique is necessary. Limit of detection and limit of determination are 0.1 μg/L for both analytes. NBBS and Ibuprofen were detected in several raw and treated wastewater samples from municipal wastewater treatment plants in the range from < 0.1 to 3.5 μg/L.     

Der Reaktionsmechanismus der allgemeinen Säure—Basen-Katalyse der Mutarotation der Glucose, 8. Mitt.: Die Aktivierungsenergie der heterogenen Kupfer-Katalyse der Glucose-Mutarotation (Kurze Mitteilung)

Ohne Zusammenfassung7. Mitt.:Hermann Schmid undG. Bauer, Mh. Chem.96, 1508 (1965); dort ältere Mitt. dieser Reihe zitiert.     

Über Verbindungen mit Urotropin-Struktur, 37. Mitt.: Eine neue Methode zur Herstellung von Hydroxy-ketonen und Diketonen sowie ihre Anwendung auf die Synthese des 2,4-Dioxa-adamantan-Ringsystems

Zusammenfassung Es wird eine neue Methode zur Herstellung von Hydroxyketonen und Diketonen beschrieben, die im ersten Schritt der Reaktionsfolge die Umsetzung von Hydroxycarbonsäureestern mit Phenylsulfonalkylmagnesiumbromid zu -Sulfonylketonen erfordert. Diese werden dann im zweiten Schritt mit Al-Amalgam zu den Hydroxyketonen oder den Halbketalen der Diketone entschwefelt. Mit Hilfe dieser Reaktionsfolge gelang auch, ausgehend von 3,5-Dihydroxy-phenylessigsäureester, die Synthese des bisher noch unbekannten Ringsystems des 2,4-Dioxa-adamantans.Herrn Prof. Dr. habil.Friedrich Asinger zum 60. Geburtstag in freundschaftlicher Verbundenheit zugeeignet36. Mitt.:H. Stetter, J. Gärtner undP. Tacke, Chem. Ber.99, 1435 (1966).     

Doppler-free two-photon absorption spectroscopy ofn 2 P J -levels (n=7, 8, 9) in203,205Tl

The hyperfine splittings and isotope shifts of n²P_J-levels in^203,205Tl have been measured by high resolution two-photon spectroscopy with a cw dye-laser and an actively stabilized marker cavity for laser frequency scancalibration.