Facile Oxidative Rearrangements Using Hypervalent Iodine Reagents

Aromatic substituents migrate in a novel oxidative cyclization mediated by iodine(III) reagents. 4-Arylbut-3-enoic acids are cyclized and rearranged to 4-arylfuran-2(5H)-ones by hypervalent iodine compounds in good to excellent yields under mild reaction conditions. Other ring sizes are also accessible. The mechanism of the reaction is described in detail, and calculations highlight the cationic nature of the intermediates in the rearrangement. The fast access to heavily substituted furanones is used for the synthesis of biologically active derivatives.     

Traveling Salesman Problem with Clustering

In the original traveling salesman problem, the traveling salesman has the task to find the shortest closed tour through a proposed set of nodes, touching each node exactly once and returning to the initial node at the end. For the sake of the tour length to be minimized, nodes close to each other might not be visited one after the other but separated in the tour. However, for some practical applications, it is useful to group nodes to clusters, such that all nodes of a cluster are visited contiguously. Here we present an approach which leads to an automatic clustering with a clustering parameter governing the sizes of the clusters.