Cu(I)-catalyzed stereospecific coupling reactions of enantioenriched α-stannylated benzyl carbamates and their application

Enantioenriched α-stannylated benzyl carbamates were used in highly stereospecific coupling reactions employing Cu(I) as catalyzing transition metal. Acid chlorides and allyl bromide derivatives were used as electrophilic coupling partners. The reaction was applied in the synthesis of two highly enantioenriched indanoles and one enantioenriched tetraline via intramolecular cyclization reactions.     

SINDO1 study of the photoreaction of tetramethylene sulfone

The mechanism of the photoreaction of tetramethylene sulfone (TMSO₂) was investigated by the semiempirical molecular orbital (MO) method SINDO1. The relevant low-lying potential energy surfaces, which were calculated with limited configuration interaction (CI), were studied by optimizing intermediates and transition structures and by introducing linear interpolations between these stationary points. The main initial reaction step for all important products is an α cleavage of one C? S bond. This leads to an intermediate that can be classified as an excited singlet diradical. Its electronic structure is described with a two-electron, three-orbital model. Starting from this initially generated intermediate, the reaction branches into several pathways leading to various products. Feasible reaction pathways were established for all important products consistent with experiments. © 1995 by John Wiley & Sons, Inc.     

Ein Primzahlkriterium nach Mann und Shanks

Ohne ZusammenfassungHerrn Professor Dr.Theodor Schneider zum 65. Geburtstag     

Classification of some 3-subgroups of the finite groups of Lie type E6

We consider the finite exceptional group of Lie type $G=E_6^{\epsilon }(q)$ (universal version) with $3|q?\epsilon$, where $E_6^{+1}(q)=E_6(q)$ and $E_6^{?1}(q){=}^2{E}_6(q)$. We classify, up to conjugacy, all maximal-proper 3-local subgroups of G, that is, all 3-local $M<G$ which are maximal with respect to inclusion among all proper subgroups of G which are 3-local. To this end, we also determine, up to conjugacy, all elementary-abelian 3-subgroups containing $Z(G)$, all extraspecial subgroups containing $Z(G)$, and all cyclic groups of order 9 containing $Z(G)$. These classifications are an important first step towards a classification of the 3-radical subgroups of G, which play a crucial role in many open conjectures in modular representation theory.     

Tangent-Point Repulsive Potentials for a Class of Non-smooth m-dimensional Sets in ℝ n . Part I: Smoothing and Self-avoidance Effects

We consider repulsive potential energies $\mathcal {E}_{q}(\Sigma)$ , whose integrand measures tangent-point interactions, on a large class of non-smooth m-dimensional sets Σ in ? ⁿ . Finiteness of the energy $\mathcal {E}_{q}(\Sigma)$ has three sorts of effects for the set Σ: topological effects excluding all kinds of (a priori admissible) self-intersections, geometric and measure-theoretic effects, providing large projections of Σ onto suitable m-planes and therefore large m-dimensional Hausdorff measure of Σ within small balls up to a uniformly controlled scale, and finally, regularizing effects culminating in a geometric variant of the Morrey–Sobolev embedding theorem: Any admissible set Σ with finite $\mathcal {E}_{q}$ -energy, for any exponent q>2m, is, in fact, a C ¹-manifold whose tangent planes vary in a Hölder continuous manner with the optimal Hölder exponent μ=1?(2m)/q. Moreover, the patch size of the local C ^1,μ -graph representations is uniformly controlled from below only in terms of the energy value $\mathcal {E}_{q}(\Sigma)$ .