Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

Particle-depletion dynamics in axisymmetric thermocapillary flows

The European Physical Journal Special Topics - The removal of suspended particles from the interior of a thermocapillary liquid bridge via a finite-particle-size effect restricting the particle...