Palladium-catalyzed and organozinc-promoted synthesis of dienes from allylic esters possessing an acyloxy or alkoxy group

Organozinc and a Pd catalyst promoted formation of dienes from allylic esters possessing a leaving group such as acyloxy and alkoxy groups next to the allyl moiety. The reaction proceeded with high regio- and stereoselectivity when applied to secondary allylic substrates.     

Total synthesis of cis-solamin

[structure: see text] A convergent total synthesis of cis-solamin and its diastereomer was accomplished using VO(acac)2-catalyzed diastereoselective epoxidation followed by cyclization of bis-homoallylic alcohol as the key step. By comparison of the optical rotation of two possible diastereomers, it is suggested that the absolute configuration of natural cis-solamin is 1a.     

The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket

The authors rigorously prove that the exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket is