First stereoselective total synthesis of decytospolides A and B

The first synthesis of bioactive decytospolides A and B adopting an oxa-Michael addition as the key step is reported.     

Novel Iodine Reagent System for Regioselective Cleavage of Epoxides to Alcohols

Epoxides are converted regioselectively to corresponding higher substituted alcohols with greater yields using diphosphorus tetraiodide (P₂I₄) as a reducing agent and a catalytic amount of tetraethylammonium bromide at room temperature.     

Perchloric Acid-Catalyzed Synthesis of 9-Aryl Xanthenes-9H-3,6-diol and 1,3,6,8-Tetraol in Water

Efficient syntheses of xanthenes have been described using a catalytic amount of perchloric acid in water. The high temperature and lengthy reaction time normally required for formation of xanthenes derivatives are not necessary when using a catalytic amount of perchloric acid. The method is relatively inexpensive, easily available, nonvolatile, nonexplosive, and thermally robust to catalyze the reaction at 80 °C by simple heating with good to excellent yields. The advantages of the reaction involve simple reaction protocol, simple workup, and improved synthesis in the presence of perchloric acid as catalyst.     

Novel,Mild, and Highly Efficient Method for the Synthesis of 2-Arylbenzothiazoles by the Oxidation of 2-Arylbenzothiazolines with Silicon Lewis Acids

Oxidation of structurally diverse 2-arylbenzothiazolines to give the corresponding 2-arylbenzothiazoles has been carried out in benzene using dimethyldichlorosilane and trimethylchlorosilane. Short reaction times, mild reaction conditions, easy and quick isolation of the products, and excellent yields are the main advantages of this procedure.     

Palladium-catalyzed hydrodehalogenation of aryl halides using paraformaldehyde as the hydride source: high-throughput screening by paper-based colorimetric iodide sensor

Paraformaldehyde was employed as a hydride source in the palladium-catalyzed hydrodehalogenation of aryl iodides and bromides. High throughput screening using a paper-based colorimetric iodide sensor (PBCIS) showed that Pd(OAc)₂ and Cs₂CO₃ were the best catalyst and base, respectively. Aryl iodides and bromides were hydrodehalogenated to produce the reduced arenes using Pd(OAc)₂ and Pd(PPh₃)₄ catalyst. This catalytic system showed good functional group tolerance. In addition, it was found that paraformaldehyde is the hydride source and the reducing agent for the formation of palladium nanoparticles.     

Chebyshev centers and fixed point theorems

Brodskii and Milman proved that there is a point in C(K)$C(K)$, the set of all Chebyshev centers of K, which is fixed by every surjective isometry from K into K whenever K   is a nonempty weakly compact convex subset having normal structure in a Banach space. Motivated by this result, Lim et al. raised the following question namely “does there exist a point in C(K)$C(K)$ which is fixed by every isometry from K into K?”. In fact, Lim et al. proved that “if K is a nonempty weakly compact convex subset of a uniformly convex Banach space, then the Chebyshev center of K is fixed by every isometry T from K into K”. In this paper, we prove that if K   is a nonempty weakly compact convex set having normal structure in a strictly convex Banach space and F$\mathfrak{F}$ is a commuting family of isometry mappings on K   then there exists a point in C(K)$C(K)$ which is fixed by every mapping in F$\mathfrak{F}$.