Impossibility of a Certain Cyclotomic Equation with Applicationsto Difference Sets

Under certain conditions, we show the nonexistence ofan element in the p-th cyclotomicfield over , that satisfies . As applications, we establish the nonexistence ofsome difference sets and affine difference sets.     

Locally projective spaces which satisfy the Bundle Theorem

We give a complete and short proof of KAHN's Theorem that every locally projective space (M,M) with dim M3 satisfying the Bundle Theorem is embeddable in a projective space. The central tool of KAHN's proof is the fact that (M,M) is locally projective, while we use mainly the Bundle Theorem.Dedicated to Professor Dr. H. Mäurer on the occasion of his sixtieth birthday     

1H NMR study on the inclusion of bicyclo[3.3.1]nonanes in cyclodextrins

- and -cyclodextrins were found to form 1:1 inclusion complexes with 2,6- and 2,9-substituted bicyclo[3.3.1]nonanes. The binding constants and the structure of the complexes were estimated from titration studies and 2D ROESY experiments.     

An approach to pancratistatins via ring-closing metathesis: efficient synthesis of novel 1-aryl-1-deoxyconduritols F. cv

Structurally novel cyclitols, 1-aryl-1-deoxyconduritols F, were efficiently prepared from d-xylose, utilizing RCM as a key step. Various aromatic residues were incorporated in the cyclitol skeleton with total stereochemical control, utilizing a diastereoselective aryl cuprate addition to a gamma-alkoxy enoate. The synthetic route establishes a firm foundation for a practical synthesis of the antitumor alkaloid pancratistatin and its aryl analogues. [structure: see text]     

Determination of the helicity of oriented photofragments

Equations to enable determination of the helicity (angular momentum orientation) of photofragments resulting from single-photon dissociation of an isotropic sample of molecules are presented. The symmetry of the photofragment distribution is illustrated by three-dimensional vector plots of the expectation values of projections of the fragment total angular momentum. Equations describing circular polarization of light in the spherical tensor basis are presented. Methods for the optical measurement of angular momentum orientation are discussed, including determination of the helicity of circularly polarized light by a quarter-wave plate or single Fresnel rhomb.