T-Periodic solutions of time dependent Hamiltonian systems with a potential vanishing at infinity

We are discussing existence and multiplicity of T-periodic solutions of the time dependent Hamiltonian system = U(x, t) under the assumption that U(x, t) approaches 0 for large |x| meaning that the force U is concentrated in a finite region. Our method is variational and it is shown how the difficulties with the Palais-Smale condition can be overcome in this case.     

über eine Klasse Riemannscher Mannigfaltigkeiten mit raumartigen pkf-ZusammenhÄngen

One considers m-dimensional Riemannian manifoldsM with tangent spaces T_p(M), p M that are a direct sum of a spacelike m-2 planeR _p and a 2-planeH _p. It is supposed that onM there exists a connection whose space-like components are parallel conformal flat (pkf). These components are generated by a vector field X. Assuming that X belongs to a pair X,Y of reciprocal quasi-cocircular vector fields and that the Pfaffian of this pair is the 1-form associated with the connection, the following results are derived: 1. X and Y are of equal constant length (This is true for all Riemannian manifolds). 2. The immersion of the integral manifold ofH _p intoM is cylindrical and the normal connection is flat. 3. The immersion of any space-like submanifold intoM is cylindrical with respect to the sections inH _p and umbilical with respect to all spacelike sections. 4. If m 4, the integral manifoldP _p is flat.

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Herrn Prof. Dr. WERNER BURAU zum 70.Geburtstag Klaus Buchner und Radu Rosca     

A simple tree lemma and its application to a counterexample of philips

We prove a tree lemma on perfect trees to obtain an ultrafilter of definable subsets of , which is Ramsey but not conservative (see [Phi 2]).     

Gas-Phase cationization and protonation of neutrals generated by matrix-assisted laser desorption

The ionization mechanisms involved in matrix-assisted ultraviolet laser desorption/ionization (MALDI) were studied with a time-of-flight mass spectrometer. When protonated or cationized quasimolecular ions generated by MALDI are not extracted promptly, their abundance is a function of the delay time between laser irradiation and ion extraction, maximizing at an optimum delay time (DTM) of a few hundred nanoseconds. The ion abundance at DTM exceeds that of prompt extraction by a factor of 2 or more. Increasing the cation density near the sample surface reduces the DTM, whereas increasing the desorption laser irradiance has the opposite effect. The enhancement suggests extensive gas-phase ion-molecule reactions after irradiation by the desorption laser has ceased.     

First metallamacrocyclic complexes of Pt(iv) with 3,3,3',3'-tetraalkyl-1,1'-phenylenedicarbonylbis(thioureas): synthesis by direct or electrolytic oxidative addition of I(2), Br(2) and Cl(2)

Elemental I(2) and Br(2) cleanly react with the 3:3 Pt(ii) metallamacrocycle of 3,3,3',3'-tetra(n-butyl)-1,1'-terephthaloylbis(thiourea)(cis-[Pt(II)(3)(L(p)(1)-S,O)(3)]3), in chloroform at room temperature, to yield oxidative addition products; (195)Pt NMR studies reveal that a stepwise oxidative addition readily occurs to each of the Pt(ii) centres in the metallamacrocycle to yield the mixed valence species cis-[Pt(II)(2)Pt(IV)I(2)(L(p)(1)-S,O)(3)] and cis-[Pt(II)Pt(IV)(2)I(4)(L(p)(1)-S,O)(3)], and the fully oxidised cis-[Pt(IV)(3)I(6)(L(p)(1)-S,O)(3)] in solution, depending on the mole ratio I(2):3. Similar results are obtained on treatment of solutions of 3 with elemental Br(2). Treatment of the corresponding 2:2 Pt(ii) complex of 3,3,3',3'-tetraethyl-1,1'-isophthaloylbis(thiourea)(cis-[Pt(II)(2)(L(m)(1)-S,O)(2)]4) with iodine, results in facile oxidative addition to yield cis-[Pt(IV)(2)(L(m)(1)-S,O)(2)I(4)], with a trans-Pt(iv)-iodo arrangement. Molecules in the crystal structure of 5 have their trans-Pt(iv)-iodo axes essentially aligned, with very close intermolecular iodide contacts (3.775(1)A), resulting in chains of weakly bound metallamacrocycles in the solid. An alternative electrolytic synthesis method, using a simple two-compartment glass cell containing 4 and a chosen halide salt in dichloromethane, led to the formation of cis-[Pt(IV)(2)(L(m)(1)-S,O)(2)Br(4)] 6 and cis-[Pt(IV)(2)(L(m)(1)-S,O)(2)Cl(4)] 7, completing characterization of a series of first-reported trans-Pt(iv)-X (X=I, Br, Cl) metallamacrocyclic complexes.     

Spektroskopische und theoretische Untersuchungen am Borazolmolekül und seinen Bortrihalogenoderivaten

Zusammenfassung Es werden Hückel-MO-Rechnungen am Borazol und den B-Trihalogenoborazolen durchgeführt und die entsprechenden Parameter an den teils bekannten und teils gemessenen UV-Spektren geeicht. Die für diese Verbindungen bestimmten chemischen Verschiebungen der ¹¹B- und ¹⁴N-Kernresonanz lassen sich mit den berechneten -Elektronendichten erklären.

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Hückel-MO calculations are performed for Borazine and the B-Trihalogenoborazines; the parameters used are calibrated with the UV-spectra, which had either been measured here or obtained from the literature. The calculated -electron densities compare favorably well with the ¹¹B- and ¹⁴N-nuclear magnetic resonances determined for the above mentioned compounds.

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Résumé Le borazole et les B-trihalogenoborazoles sont calculés par la méthode de Hückel en utilisant des paramètres calibrés sur les spectres U.V. mesurés ou obtenus dans la littérature. Les densités électroniques sont en bon accord avec le déplacement chimique de N.M.R. de ¹¹B et ¹⁴N déterminé pour les composés cidessus.

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Herrn Professor Dr. H. Hartmann danken wir für sein stetes Interesse und die wohlwollende Förderung dieser Arbeit. Für die Hilfe bei der Aufnahme des Vakuum-UV-Spektrums von Fluoroborazol danken wir Herrn Diplom-Physiker E. Mohler.     

Der Stoffwechsel von Verbindungen mit Dreifachbindung. VI. Stoffwechselverhalten von Alkincarbonsäuren und Alkindicarbonsäuren

Metabolism of Acetylenic Monocarboxylic and Dicarboxylic Acids Feeding of acetylenic monoacids with chain length of 11 to 18 C-atoms to rats led to excretion of dicarboxylic acids with retained triple bonds. 10-Octadecynoic acid led to the formation of metabolites with even and odd number of C-atoms, suggesting in addition to established ω- and β-oxidation an α-oxidative pathway.     

Splitless on-line coupling of capillary high-performance liquid chromatography,capillary electrochromatography and pressurized capillary electrochromatography with nuclear magnetic resonance spectroscopy

A mixture of unsaturated fatty acid methyl esters was separated with a new splitless capillary set-up. With the employed apparatus configuration different capillary separation techniques such as capillary high-performance liquid chromatography (cHPLC), capillary electrochromatography (CEC) and pressurized capillary electrochromatography (pCEC) could be applied. The detection and identification of the sample compounds were accomplished by hyphenating these capillary separation techniques with nuclear magnetic resonance (NMR) spectroscopy using a novel configuration of the detection capillary set-up. Using modified electrokinetically driven separation techniques, the electric field was applied solely across the separation column. With this improved interface for capillary liquid chromatography-NMR on-line coupling, the stereochemical assignment of the cis and trans configuration of unsaturated fatty acids could be easily accomplished. Finally, the results of cHPLC-NMR, CEC-NMR and pCEC-NMR coupling experiments were compared.Dedicated to Professor Günter Häfelinger on the occasion of his 65th birthday     

A novel MCR of isocyanates, aldehydes, and dienophiles

[reaction: see text] A novel one-pot procedure for the three-component coupling reaction of isocyanates, aldehydes, and dienophiles (IAD reaction) has been developed. Condensation of isocyanates and aldehydes and subsequent Diels-Alder reactions with electron-deficient dienophiles furnishes endo-selective amino-substituted cyclohexenes in good yield.