Characterization and Reactivity of the [N,N-Dimethyl(thioformamidyl)]-9-fluorenyl Cation(1)

The 9-[N,N-dimethyl(thioformamidyl)]-9-fluorenyl cation was generated under stable ion conditions and characterized by UV/visible and NMR spectroscopy and methanol trapping reactions. The same cation was generated by laser excitation of the appropriate chloride precursor in 2,2,2-trifluoroethanol, and rate constants for nucleophilic quenching by alcohols and several anions were measured. The quenching data for this and other 9-fluorenyl cations demonstrate that the reactivity decreases for 9-substituents in the order H > carbomethoxy > N,N-dimethyl(thioformamidyl), demonstrating that the thioamidyl group imparts substantial kinetic stabilization to an adjacent cationic center. Both steric and electronic factors are suggested to be important in determining this reactivity order.     

A functional equation of Ih-Ching Hsu

Summary A recent note of Ih-Ching Hsu poses an unsolved problem, to wit, the general solution of the functional equation g(x₁, x₂) + g(₁(x₁), ₂(x₂)) = g(x₁, ₂(x₂)) + g(₁(x₁),x₂), where the _i are given functions. This short paper obtains the general solution. It gives conditions which imply that anycontinuous solution has form g₁(x₁) + g₂(x₂).