Zur Darstellung Miquelscher Möbiusräume

In this paper we prove the following theorem (shown by J.TITS [7] in the case of finite dimension): LetO be a set of at least 2 points of a projective space of dimension 2 and suppose that the intersections ofO and the planes of are either empty or one point sets or Pascalian ovals. ThenO is an ellipsoid (nondegenerate quadric of index 1). As a corollary we obtain that every Miquelian Möbius-space is the geometry of the plane sections of an ellipsoid.     

Über zahlentheoretische Funktionen II

Ohne Zusammenfassung     

Design of pi-conjugated organic materials for one-dimensional energy transport in nanochannels

Various end-substituted distyrylbenzenes have been synthesized to serve as guest molecules in inclusion compounds to promote efficient energy transport along one-dimensional channels. Their optical and photophysical properties have been characterized at both experimental and theoretical levels. All molecules display a large transition dipole moment between the ground state and lowest excited state and hence a short radiative lifetime (on the order of 1-2 ns). They also exhibit a large spectral overlap between the emission and absorption spectra, which enables efficient energy transport between molecules arranged in a head-to-tail configuration in nanochannels. Hopping rates on the order of 10(12) s(-1) are calculated at a full quantum-chemical level; this is much larger than the radiative lifetimes and opens the way for energy migration over large distances. Changes in the nature of the terminal substituents are found to modulate the optical properties weakly but to impact significantly the energy transfer rates.