On the full Kostant-Toda system and the discrete Korteweg-de Vries equations

The relation between the solutions of the full Kostant–Toda lattice and the discrete Korteweg–de Vries equation is analyzed. A method for constructing solutions of these systems is given. As a consequence of the matricial interpretation of this method, the transform of Darboux is extended for general Hessenberg banded matrices

Stern-Gerlach Entanglement in Spinor Bose-Einstein Condensates

Entanglement of spin and position variables produced by spatially inhomogeneous magnetic fields of Stern-Gerlach type acting on spinor Bose-Einstein condensates may lead to interference effects at the level of one-boson densities. A model is worked out for these effects which is amenable to analytical calculation for gaussian shaped condensates. The resulting interference effects are sensitive to the spin polarization properties of the condensate.Comment: 9 pages, 2 figure

A Platinum molecular complex immobilised on the surface of graphene as active catalyst in alkyne hydrosilylation

Abstract A platinum complex bearing a N‐heterocyclic carbene (NHC) ligand functionalised with a pyrene‐tag is immobilised onto the surface of reduced graphene oxide (rGO). The hybrid material composed of an organometallic complex and a graphene derivative is ready available in a single‐step process under mild reaction conditions. This methodology preserves the inherent properties of the active catalytic centre and the support. The platinum hybrid material is an efficient catalyst in hydrosilylation of alkynes and can be recycled and reused for ten runs without significant loss of activity due to its high stability. Interestingly, the catalytic properties of the platinum complex are enhanced after immobilisation onto graphene. The influence of graphene in hydrosilylation of alkynes is discussed