Copper-catalyzed functionalization of enynes

The copper-catalyzed functionalization of enyne derivatives has recently emerged as a powerful approach in contemporary synthesis. Enynes are versatile and readily accessible substrates that can undergo a variety of reactions to yield densely functionalized, enantioenriched products. In this perspective, we review copper-catalyzed transformations of enynes, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations. Particular attention is given to the regiodivergent functionalization of 1,3-enynes, and the current mechanistic understanding of such processes.

The copper-catalyzed functionalization of enynes is a powerful approach to yield densely functionalized products. This review covers various transformations, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations.     

A universal Cauchy functional equation over the positive reals

The functional equation af(xy)+bf(x)f(y)+cf(x+y)+d(f(x)+f(y))=0 whose shape contains all the four well-known forms of Cauchy's functional equation is solved for solutions which are functions having the positive reals as their domain. This complements an earlier work of Dhombres in 1988 where the same functional equation was solved for solutions whose domains contain zero, which leaves out the logarithmic function. Here not only the logarithmic function is recovered but the analysis is entirely different and is based on solving appropriate difference equations.