The strong Lefschetz property of the coinvariant ring of the Coxeter group of type H4

We prove that the coinvariant ring of the irreducible Coxeter group of type H₄ has the strong Lefschetz property.     

Ruthenium-catalyzed reaction of alpha,beta-unsaturated imines with carbon monoxide and alkenes leading to beta,gamma-unsaturated gamma-butyrolactams: involvement of direct carbonylation at olefinic C[bond]H Bonds as a key step

The reaction of alpha,beta-unsaturated imines with CO and alkenes in the presence of Ru(3)(CO)(12) as a catalyst results in a three-component coupling reaction that gives alpha,alpha-disubstituted beta,gamma-unsaturated gamma-butyrolactams. The reaction proceeds via a two-step sequence involving the initial formation of ketone derivatives by catalytic carbonylation at the beta-olefinic C-H bonds of alpha,beta-unsaturated imines, followed by the (uncatalyzed) intramolecular nucleophilic attack of the imine nitrogen on the ketonic carbon to generate a tetrahedral intermediate, which then undergoes a 1,2-ethyl migration. The reaction of a cyclic unsaturated imine, derived from the reaction of (1R)-(-)-myrtenal with tert-butylamine, gives a beta-aminocyclopentene derivative, which is formed by an aldol-type condensation of the initially formed ketone, indicating the initial formation of ethyl ketone.     

Rigid-rod polymers with polysiloxane side chains. 2. Synthesis and characterization of aromatic polybenzobisoxazoles with polysiloxane side chains and composite formation with polysiloxane matrices

Aromatic polybenzobisoxazoles, having polydimethylsiloxane side chains (SCPBOs), were prepared using terephthaloyl chloride-terminated polydimethylsiloxane macromonomers and 3,3′-bis(trimethylsiloxy)-4,4′-bis(trimethylsilylamino)biphenyl for the purpose of dispersing rigid-rod molecules in silicone matrices for molecular reinforcement. The degree of polymerization of the side chain was varied from 7.8 to 45.4, and a small amount of (3-butenyloxy)terephthaloyl chloride was copolymerized to give the polymers a functionality that can be linked to the matrices. For all the SCPBOs, the WAXD pattern showed only diffuse reflections, suggesting limited structural regularity, although the polymers were optically anisotropic. No melting transition was observed below the side chain decomposition temperature, 350°C. A polydimethylsiloxane/polybenzobisoxazole composite elastomer was obtained first curing the polysiloxane matrix containing the prepolymer of the SCPBO, followed by in situ thermal ring closure of the prepolymer. Some reinforcement was observed, but the presence of plasticizing effect by the unbound SCPBO was suggested at the same time. © 1995 John Wiley & Sons, Inc.