On the existence of harmonic morphisms from symmetric spaces of rank one

Summary In this paper we give a unified framework for constructing harmonic morphisms from the irreducible Riemannian symmetric spaces ℍH ⁿ, ℂH ⁿ, ℝH ² _t+1, ℍP ⁿ, ℂP ⁿ and ℝP ²ⁿ⁺¹ of rank one. Using this we give a positive answer to the global existence problem for the non-compact hyperbolic cases. This work was supported by The Swedish Natural Science Research Council. This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.     

Synthesis of Cyclic Alkenylsiloxanes by Semihydrogenation: A Stereospecific Route to (Z)‐Alkenyl Polyenes

Cyclic alkenylsiloxanes were synthesized by semihydrogenation of alkynylsilanes—a reaction previously plagued by poor stereoselectivity. The silanes, which can be synthesized on multigram scale, undergo Hiyama–Denmark coupling to give (Z)‐alkenyl polyene motifs found in bioactive natural products. The ring size of the silane is crucial: five‐membered cyclic siloxanes also couple under fluoride‐free conditions, whilst their six‐membered homologues do not, enabling orthogonality within this structural motif.     

Analysis of t-butylphenol acetylene condensed resin with methyl-methine linkages in vulcanized rubber by pyrolysis-gas chromatography/mass spectrometry

Methyl-methine linkages of Novolac, a commercially available t-butylphenol acetylene condensed (TBPA) resin, have been identified by recognition of pyrolysis pathways using pyrolysis-gas chromatography/mass spectrometry (Py-GC/mS) in vulcanized rubber. The diagnostic mass spectrum of t-butylphenol with methyl-methine linkages between phenolic rings was observed at m/z 192, corresponding to 4-t-butyl-2-ethyl-6-methylphenol. Other molecular ions were observed at m/z 178, 164, and 150 in the characteristic pyrolyzates. The ion at m/z 192 in the TBPA resin was observed to be characteristic for methyl-methine linkages between the phenolic groups, and the analytical pyrolysis-GC/mS method was thus able to identify the resin at low levels in vulcanized rubber. Copyright 1999 John Wiley & Sons, Ltd.     

Far-infrared spectroscopy of quantum wires and dots, breaking Kohn’s theorem

We review far-infrared experiments on quantum wires and dots. In particular, we show that with tailored deviations from a parabolic external lateral confinement potential one can break Kohn’s theorem. This allows a detailed investigation of the internal relative motion in quantum dots and wires and the study of electron–electron interaction effects, for example, the formation of compressible and incompressible states in quantum dots and antidots.     

Transverse plasmon in two-dimensional electrons

We calculated the retarded transverse current-current response function of an ideal two-dimensional electron gas and obtained a dispersion relation for the transverse plasmon in the system.     

Harmonic morphisms from the classical non-compact semisimple Lie groups

We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups SLn(R), SU^∗(2n) and Sp(n,R) equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO^∗(2n), SO(p,q), SU(p,q) and Sp(p,q). Applying a duality principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.     

Non-holomorphic harmonic morphisms from Kähler manifolds

We give a method for constructing non-holomorphic harmonic morphisms from Kähler manifolds. The method is then used to obtain many such examples defined locally on the complex Grassmannians.