Compact Ovoids in Quadrangles II: the Classical Quadrangles

In this second part we consider ovoids in the classical compact connected quadrangles. We solve the problem whether closed ovoids or spreads exist in these quadrangles. In fact we prove a slightly more general result: we determine whether the normal sphere bundles of the point- or line space admit sections, or whether they are topologically trivial. We also give explicit geometric constructions for spreads and ovoids. Some of these spreads are apparently new.     

Compact Ovoids in Quadrangles III: Clifford Algebras and Isoparametric Hypersurfaces

In this third part, we consider those compact quadrangles which arise from isoparametric hypersurfaces of Clifford type and their focal manifolds. Sections 9–11 give a comprehensive introduction to these quadrangles from the incidence-geometric point of view. Section 10 contains also a new (algebraic) proof that these geometries are quadrangles.We determine which of these quadrangles have ovoids or spreads and also whether the normal sphere bundles of the focal manifolds admit sections, or whether they are topologically trivial. We give explicit geometric constructions for spreads, ovoids, and sections.     

Intramolecular cycloaddition reactions of exocyclic nitrones: Application in the total synthesis of terpenes

Exocyclic nitrones smoothly participate in intramolecular cycloaddition reactions to provide bridged and fused polycarbocycles. The exploitation of this methodology in the total syntheses of the sesquiterpenes (±)-7,12-secoishwaran-12-ol (44), (±)-hirsutene (56), (±)-coriolin (68) is also presented.     

Compact Ovoids in Quadrangles I: Geometric Constructions

This paper is about ovoids in infinite generalized quadrangles. Using the axiom of choice, Cameron showed that infinite quadrangles contain many ovoids. Therefore, we consider mainly closed ovoids in compact quadrangles. After deriving some basic properties of compact ovoids, we consider ovoids which arise from full imbeddings. This leads to restrictions for the topological parameters (m,m). For example, if there is a regular pair of lines or a full closed subquadrangle, then mm. The existence of full subquadrangles implies the nonexistence of ideal subquadrangles, so finite-dimensional quadrangles are either point-minimal or line-minimal. Another result is that (up to duality) such a quadrangle is spanned by the set of points on an ordinary quadrangle. This is useful for studying orbits of automorphism groups. Finally we prove general nonexistence results for ovoids in quadrangles with low-dimensional line pencils. As one consequence we show that the symplectic quadrangle over an algebraically closed field of characteristic 0 has no Zariski-closed ovoids or spreads.     

Asymmetric Syntheses with the Aid of Homogeneous Transition Metal Catalysts

The progress made in the field of homogeneous catalysis during the last five to six years has led, inter alia, to the development of highly selective catalysts for asymmetric syntheses. Homogeneous asymmetric hydrogenation, using well defined transition metal catalysts, may be achieved with optical yields of 85 to 90% or more. Catalytic reactions, in which the chiral centers are generated by C? C bond formation, can result in optical yields of 70 to 80%. The hydrogenation catalysts consist primarily of rhodium(I) complexes containing “Homer phosphanes”, phosphanes with chiral C atoms, or optically active amides. Catalysts which induce optical activity through the formation of C? C bonds have been developed from π-allylnickel halides, Lewis acids, and phosphanes containing chiral C atoms. The results obtained signify a breakthrough in an area of catalysis previously restricted to syntheses involving enzymes.     

Die stereospezifische Reduktion von (1R)-3-endo-Aminocampher zu (1R)-3-endo-Aminoborneol

The highly stereospecific reduction of (1R)-3-endo-aminobornan-2-one ( 2 ) to [1R]-3-endo-amino-2-endom-bornanol ( 1 ) is described. This reaction is achieved by using alkylaluminumdichlorides, a new group of reducing agents for the reduction of the ketone 2 to the secondary alcohol 1

1 Diesc Reduktion ist Gegenstand van Patcntanmeldungen, z. B. [l].