Photochemical carbosilylation of Lu₃N@Ih-C80 was performed using siliranes (silacyclopropanes) to afford the corresponding [5,6]- and [6,6]-adducts. Electrochemical studies indicated that the redox potentials of the carbosilylated derivatives were shifted cathodically in comparison with those of the [5,6]-pyrrolidino adducts. The electronic effect of the silirane addends on Lu₃N@Ih-C80 was veri...

Reduction of scandium nitride clusterfullerene, Sc3N@Ih-C80, by sodium fluorenone ketyl in the presence of cryptand[2,2,2] allows the crystallization of the {cryptand[2,2,2](Na(+))}2(Sc3N@Ih-C80(-))2·2.5C6H4Cl2 (1) salt. The Sc3N@Ih-C80˙(-) radical anions are dimerized to form single-bonded (Sc3N@Ih-C80(-))2 dimers.

We consider the problem of enumerating permutations with exactly r occurrences of the pattern 1324 and derive functional equations for this general case as well as for the pattern avoidance (r = 0) case. The functional equations lead to a new algorithm for enumerating length n permutations that avoid 1324. This approach is used to enumerate the 1324-avoiders up to n = 31. We also extend those f...

A cyclotriveratrylene-based molecular cage forms hemicarceplexes that significantly increase the solubility of commercially available Sc3N@C80 in CDCl3. When incarcerated within the molecular cage, the two structural isomers of this metallofullerene, Sc3N@D5h-C80 and Sc3N@Ih-C80, displayed characteristic signals in both (1)H and (13)C NMR spectra, allowing direct identification of each isomer w...

We consider permutations that avoid the pattern 1324. By studying the generating tree for such permutations, we obtain a recurrence formula for their number. A computer program provides data for the number of 1324-avoiding permutations of length up to 20.

Hepatic injury is associated with a defective intestinal barrier and increased hepatic exposure to bacterial products. Here we report that the intestinal bacterial microflora and a functional Toll-like receptor 4 (TLR4), but not TLR2, are required for hepatic fibrogenesis. Using Tlr4-chimeric mice and in vivo lipopolysaccharide (LPS) challenge, we demonstrate that quiescent hepatic stellate cel...

(xi − xj) . The patterns appear in geometry, characterizing some families of Schubert varieties. Schubert varieties are indexed by permutations, and the varieties which are non singular are those whose indexing permutation does not contain the pattern 2143 nor the pattern 1324. In [2], Cortez has described geometrical properties of Schubert varieties for permutations avoiding the patterns 1324 ...