Nonadiabatic geometric phase in quaternionic Hilbert space

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.     

Fractal porous media III: Transversal Stokes flow through random and Sierpinski carpets

The transversal Stokes flow of a Newtonian fluid through random and Sierpinski carpets is numerically calculated and the transversal permeability derived. In random carpets derived from site percolation, the average macroscopic permeability varies as (- _c)^3/2, close to the critical porosity _c. This exponent is found to be slightly different from the conductivity exponent. Results for Sierpinski carpets are presented up to the fourth generation. The Carman equation is not verified in these two model porous media.     

On the exceptional zeros of cross-products of derivatives of spherical Bessel functions

The lowest zeros of the cross-products of derivatives of spherical Bessel functions are not obtainable from a McMahon-type formula. This paper derives an analytical approximation for these lowest, exceptional, zeros, through to 4th order in a parameter specifying the thinness of the corresponding concentric spherical region.

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Zusammenfassung Die kleinsten Nullstellen der Kreuzprodukte der Ableitungen von spherischen Bessel-funktionen können nicht durch eine Formel von McMahon Typ erhalten werden. Durch eine Entwicklung bis zu vierter Ordnung in einem Parameter proportional zur Dicke des zugeordneten spherischen Gebietes berechnen wir eine analytische Näherung für diese kleinsten, außergewöhnlichen, Nullstellen.

     

A hydrogenation product derived from the diterpenoid barbatusin:A revised structure

The structure of the hydrogenation product of barbatusin, a diterpenoid from Coleus barbatus Bentham has been revised on the basis of NMR and X-ray data. A geminal coupling of unusually high magnitude has been observed and analysed.