Flows for rectangular matrix models

Several new results on the multicritical behavior of rectangular matrix models are presented. We calculate the free energy in the saddle point approximation, and show that at the triple-scaling point, the result is the same as that derived from the recursion formulae. In the triple-scaling limit, we obtain the string equation and a flow equation for arbitrary multicritical points. Parametric solutions are also examined for the limit of almost-square matrix models. This limit is shown to provide an explicit matrix model realization of the scaling equations proposed to describe open-closed string theory.Comment: 13 pages, LaTeX, McGill/93-2

Regiodivergent Late-Stage Pd- or Ru-Catalyzed C-H Bond Functionalization Applied to the Straightforward Synthesis ofN-Methylated Diflufenican Derivatives

International audienceThe late-stage C-H diversification methodology was applied to the preparation of arylated Diflufenican derivatives. Using a palladium catalyst associated with potassium pivalate, a regioselective arylation of the C-H bond flanked by the two fluorine atoms was observed. The reaction tolerated a wide range of useful functional groups on the aryl bromide. Conversely, the use of a ruthenium catalyst allowed to arylate the trifluoromethylbenzene ring of Diflufenican. To the best of our knowledge, these synthetic schemes are the first ones allowing the preparation of such arylated Diflufenican derivatives