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.     

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.     

Substituenteneffekte auf die C–C-Bindungsstärke, 8. Standardbildungsenthalpien und Spannungsenthalpien von 1,1,2,2-Tetraethylethylenglykol-dimethylether und D,L-1,2-Dimethyl-1,2-diphenylethylenglykol-dimethylether

Effects of Substituents on the Strength of C - C Bonds, 8¹. - Heats of Formation and Strain of 1,1,2,2-Tetraethylethylene Glycol Dimethyl Ether and D,L .-1,2-Dimethyl-l,2-diphenylethylene Glycol Dimethyl Ether The heats of combustion of the title compounds 1 and 2 were measured calorimetrically with the result (kcal mol ^-1, s. d. in parentheses) ΔH°_c = − 1880.1 (± 0.6) and − 2373.3 (± 1.4). The heat of vaporisation of 1 ΔH^v = 14.3 (± 0.3) and the heat of sublimation of 2 ΔH^sub = 27.2 (± 0.5) were derived from their temperature dependance of the vapor pressure. The latter were determined between 30 and 80°C using a flow method. The resulting standard heats of formation ΔH°_t(g) = −122.4 (± 0.7) and −43.8 (±1.5) for 1 and 2 correspond to a strain enthalpy (_s) of 15.9 and 8.0 kcal mol^-1, respectively. The steric strain of the dimethoxyethanes 1 and 2 is about one fourth lower than the strain of the corresponding dimethylethanes 3 and 4 bearing the same substituents. Thus, a methoxy group causes less steric stress than a methyl group.     

Dendrimeric Gd(III) complex of a monophosphinated DOTA analogue: optimizing relaxivity by reducing internal motion

A marked increase of relaxivity has been observed upon rigidifying the internal frame of Gd-containing PAMAM dendrimers: the effect has been attained by either protonation of the dendrimer or by forming supramolecular adducts with cationic polyaminoacids.