Technical Procedures for the Syntheses of Carotenoids and Related Compounds from 6-Oxo-isophorone: Syntheses of (3R,3′R)-Zeaxanthin. Part I

Starting from the readily available, optically active (4R)-4-hydroxy-2,2,6-trimethylcyclohexanone ( 1 ), a new technical synthesis of (3R,3′R)-zeaxanthin is described. According to a 2(C₉ + C₆) + C₁₀ = C₄₀ construction scheme, the ketone 1 was first transformed with (E)-3-methylpent-2-en-4-yn-1-ol ( 5 ) into a C₁₅-intermediate which, by a three-step sequence, could be converted into the known olefinic C₁₅-Wittig salt 4 . Optimized conditions for the final Wittig reaction of 4 with the C₁₀-dialdehyde 3 are discussed. Based on 1 , the overall yield of the entire technical process is ca. 40%.     

Versatile high-performance liquid chromatographic computer system for solvent delivery, gradient control and data acquisition using the Commodore 64 personal computer

An interface for a high-performance liquid chromatographic system based on the Commodore 64 personal computer has been designed as an alternative to the expensive and somewhat inflexible solvent programmers and data acquisition systems offered by commercial manufacturers. The system consists of the Commodore 64 with a single disk drive and monitor, and an interface that directly controls the flow-rates of two Waters pumps for solvent delivery in either isocratic or gradient mode, as well as analog-to-digital conversion of chromatographic data and either graphic data output to a dot-matrix printer or digital-to-analog conversion for output to a chart recorder. The interface permits computer-controlled flow-rates of up to 10.0 ml/min, with an accuracy of 0.0047 ml/min at flow-rates of 4.1 ml/min and an accuracy of 0.03 ml/min at flow-rates of 10 ml/min. The software for data analysis permits tabulation of elution times and areas for the peaks in a chromatogram with an option for baseline correction. The data are stored on floppy disks together with information pertinent to the chromatogram (flow-rate, solvent composition, etc.).     

Area-preserving diffeomorphisms and supermembrane Lorentz invariance

The Lie algebra of area-preserving diffeomorphisms on closed membranes of arbitrary topology is investigated. On the basis of a harmonic decomposition we define the structure constants as well as two other tensors which appear in the supermembrane Lorentz generators. We derive certain identities between these tensors and analyze their validity when the areapreserving diffeomorphisms are approximated bySU(N). One of the additional tensors can then be identified with the invariant symmetric three-index tensor ofSU(N), while the second has no obvious analog. We prove that the Lorentz generators are classically conserved in the light-cone gauge for arbitrary membrane topology, as a consequence of these tensor identities. This formulation allows a systematic study of the violations of Lorentz invariance in theSU(N) approximation.     

Zur Berechnung von Brückenschwingungen unter rollenden Lasten

Zusammenfassung Das Problem der Brückenschwingungen unter rollenden Lasten läßt in vielen Fällen Lösungen zu, die bei praktisch ausreichender Genauigkeit sowohl im gedanklichen Aufbau als auch in der numerischen Durchführung einfacher sind als die bisher bekannten. Der Stokes-Zimmermannsche Ansatz und — unter Beschränkung auf die Grundfrequenz des Trägers — auch der Timoshenkosche Ansatz lassen sich formal auf die Differential-gleichungen eines einfachen Feder-Masse-Systems zurückführen, wenn man die darin auftretenden Elastizitätswerte als zeitabhängige Variable auffaßt. Die entstehenden Gleichungen sind nach bekannten Methoden schrittweise integrierbar. Die große Anpassungsfähigkeit solcher Integrationsverfahren gestattet eine erhebliche Erweiterung der Betrachtung; sie erweisen sich besonders dann als fruchtbar, wenn analytisch schwer faßbare Funktionen auftreten. Verschiedene Anwendungen sind in Beispielen dargestellt; sie betreffen die Untersuchung einer Folge von wandernden Lasten, das Verhalten des einerseits eingespannten Trägers, und vor allem die Einbeziehung des — selbst als schwingungsfähiges System anzusehenden — Fahrzeugs in die rechnerische Untersuchung. Die bisher allein auf das Verhalten des Trägers gerichtete Betrachtungsweise wird dadurch auf die Gesamtaufgabe der Überfahrt schwingungsfähiger Fahrzeuge über eine schwingende Fahrbahn erweitert.     

Low- and high-energy expansion of heavy-quark correlators at next-to-next-to-leading order

We calculate three-loop corrections to correlation functions of heavy-quark currents in the low- and high-energy regions. We present 30 coefficients both in the low-energy and the high-energy expansion of the scalar and the vector correlator with non-diagonal flavour structure. In addition we compute 30 coefficients in the high-energy expansion of the diagonal vector, axial-vector, scalar and pseudo-scalar correlators. Possible applications of our new results are improvements of lattice-based quark-mass determinations and the approximate reconstruction of the full momentum dependence of the correlators.     

Precise charm- and bottom-quark masses: Theoretical and experimental uncertainties

We consider recent theoretical and experimental improvements in determining charm- and bottom-quark masses. We present a new, improved evaluation of the contribution of the gluon condensate 〈α _s G ² /π〉 to the charm mass determination and a detailed study of potential uncertainties in the continuum cross section for b[`(b)]b\bar b production, together with a study of the parametric uncertainty from the α _s -dependence of our results. The final results, m_c(3 GeV) = 986(13) MeV and m_b(m_b) = 4163(16) MeV, together with the closely related lattice determination m_c(3 GeV) = 986(6) MeV, currently represent the most precise determinations of these two fundamental standard-model parameters. We critically analyze the theoretical and experimental uncertainties.     

Completely automated computation of the heavy-fermion corrections to the three-loop matching coefficient of the vector current

We evaluate the corrections to the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order containing a closed heavy-fermion loop. The result constitutes a building block both for the bottom- and top-quark system at threshold. Strong emphasis is put on our completely automated approach of the calculation including the generation of the Feynman diagrams, the identification of the topologies, the reduction to master integrals and the automated numerical computation of the latter.