A transmission problem on a polygonal partition: regularity and shape differentiability

We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of the gradient of solutions in a neighbourhood of the vertexes of the partition. This allows to prove shape differentiability of solutions and to establish an explicit formula for the shape derivative.     

Expanding the Scope of Arylsulfonylacetylenes as Alkynylating Reagents and Mechanistic Insights in the Formation of Csp2?Csp and Csp3?Csp Bonds from Organolithiums

We describe the unexpected behavior of the arylsulfonylacetylenes, which suffer an “anti‐Michael” addition of organolithiums producing their alkynylation under very mild conditions. The broad scope, excellent yields, and simplicity of the experimental procedure are the main features of this methodology. A rational explanation of all these results can be achieved by theoretical calculations, which suggest that the association of the organolithiums to the electrophile is a previous step of their intramolecular attack and is responsible for the unexpected “anti‐Michael” reactions observed for substituted sulfonylacetylenes.     

Syntheses,structure, and reactivity of acyclic enetriyne and enetetrayne derivatives

Sonogashira coupling of buta-1,3-diynylbenzene with ((2-iodophenyl)ethynyl)trimethylsilane and 1,2-diiodobenzene led to the novel enetriyne, 1-ethynyl-2-(phenylbuta-1,3-diynyl)benzene, and enetetrayne, 1,2-bis(phenylbuta-1,3-diynyl)benzene, respectively. Solid state structural and thermal analyses are also described. In solution, 1-ethynyl-2-(phenylbuta-1,3-diynyl)benzene was found to undergo thermal Bergman cyclization to afford 2-(phenylethynyl)naphthalene.