Konstruktion regulärer Hüllen konstanter Breite

LetM be a compact, convex set of diameter 2 inE ^d. There exists a bodyK of constant width 2 containingM such that every symmetry ofM is one ofK and every singular boundary point ofK is a boundary point ofM, for which the set of antipodes inK is the convex hull of the antipodes, which are already inM.

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Prefix classes of krom formulae with identity

Two small classes of first order formulae without function symbols but with identity, in prenex conjunctive normal form with all disjunctions binary, are shown to have a recursively unsolvable decision problem, whereas for another such class an algorithm is developed which solves the decision problem of that class. This solves the prefix problem for such classes of formulae except for the Gödel-Kalmàr-Schütte case.     

Third-order equation for two-component spinors

We present the properties of a two-component spinor field that obeys a third-order equation. It is separated into a massive part that corresponds closely to a Dirac field, and a massless part that obeys the Weyl equation. We discuss the interaction of such a field with an external electromagnetic field and the (weak) interactions of two such fields. They can be considered both in terms of relativistic quantum mechanics and quantum field theory. We conclude that this formulation has some attractive features, such as a unified treatment of electrons and muons with their neutrinos, a special role of thePC transformation, a more convergent propagator and a new approach to interactions. It also has some serious difficulties, aside from those generally associated with higher-order equations. These are mainly related to inconsistencies in the simultaneous considerations of electromagnetic and weak interactions. The approach also suggests a further unification of the electron and muon fields into a single bispinor field.     

Ein allgemeiner Korovkin-Satz für lokalkonvexe Vektorverbände

Ohne Zusammenfassung     

Experimental study of the synthesis of fused silica by direct combustion hydrolysis

Oxy-fuel flames for direct combustion hydrolysis of fused silica (DQ) are characterized, using non- intrusive optical measurement techniques only. Flow, temperature, concentrations, development of silica nano-particles in the flame, and surface temperature of the glass in the flame are measured. The setup used for characterization of particle distribution via Rayleigh scattering as well as mandatory improvements of the Raman/Rayleigh technique for temperature and concentration measurements in oxy-fuel flames have been developed in the framework of this study and are presented. The measurement techniques herein demonstrated are not only capable of describing these special extremely hot flames, but are broadly applicable in oxy-fuel flames as well as in chemical vapor deposition (CVD) processes. The presented data evidently shows that if the special character of oxy-fuel flames is taken into account, some of the results drawn from earlier investigations into CVD, concerning particle growth, flame stability, and particle deposition efficiency, are transferable into DQ. From the extensive data given, connections between different information are detected and help to reduce required measurements for further investigation and point to simple techniques that might be used for online process monitoring, at least during research and development of similar flames. Received: 18 December 2000 / Accepted: 14 June 2001     

Performances of LES and RANS Models for Simulation of Complex Flows in a Coaxial Jet Mixer

Flow and mixing processes in a classical coaxial jet mixer have been investigated numerically. Calculations have been performed using three Large Eddy Simulation models and three unsteady RANS models. The time averaged mixture fraction and axial velocity, their rms values and energy spectra are compared with LIF and LDA measurements for both j- and r-modes of the jet mixer flow. A special attention is paid to the ability of different models to reproduce unsteady effects. The analysis demonstrates the superiority of the LES method with the dynamic mixed SGS model (DMM) with respect to other RANS and LES models.     

beta-Hydrogen Kinetic Effect

A combined kinetic and DFT study of the uncatalyzed isomerization of cationic solvent complexes of the type cis-[Pt(R')(S)(PR3)2]+ (R' = linear and branched alkyls or aryls and S = solvents) to their trans isomers has shown that the reaction goes through the rate-determining dissociative loss of the weakly bonded molecule of the solvent and the interconversion of two geometrically distinct T-shaped 14-electron three-coordinate intermediates. The Pt-S dissociation energy is strongly dependent on the coordinating properties of S and independent of the nature of R'. The energy barrier for the fluxional motion of [Pt(R')(PR3)2]+ is comparatively much lower ( approximately 8-21 kJ mol-1). The presence of beta-hydrogens on the alkyl chain (R' = Et, Prn, and Bun) produces a great acceleration of the reaction rate. This accelerating effect has been defined as the beta-hydrogen kinetic effect, and it is a consequence of the stabilization of the transition state and of the cis-like three-coordinate [Pt(R')(PR3)2]+ intermediate through an incipient agostic interaction. The DFT optimization of [Pt(R')(PMe3)2]+ (R' = Et, Prn, and Bun) reproduces a classical dihapto Pt....eta2-HC agostic mode between the unsaturated metal and a dangling C-H bond. The value of the agostic stabilization energy (in the range of approximately 21-33 kJ mol-1) was estimated by both kinetic and computational data and resulted in being independent of the length of the hydrocarbon chain of the organic moiety. A better understanding of such interactions in elusive reaction intermediates is of primary importance in the control of reaction pathways, especially for alkane activation by metal complexes.