Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Synthesis and structural aspects of N-triflylphosphoramides and their calcium salts--highly acidic and effective Brønsted acids

Recently, 1,1′‐bi‐2‐naphthol (BINOL)‐based N‐triflylphosphoramides emerged as a new class of potent Brønsted acid catalysts. In this paper we describe the efficient synthesis of various BINOL‐based N‐triflylphosphoramides and their calcium salts. Furthermore, X‐ray crystal structure analysis combined with energy‐dispersive X‐ray spectroscopy (EDX) measurements confirmed that the synthesised chiral N‐triflylphosphoramides are highly acidic metal‐free catalysts.