Microwave-assisted synthesis of naphthalenemonoimides and N-desymmetrized naphthalenediimides

Naphthalenemonoimides and N-desymmetrized naphthalenediimides were synthesized using a stepwise microwave-assisted protocol. The steric and electronic properties of aliphatic amines determined the outcome of the reactions, while in the amino acid series their ability to solubilize the naphthalene dianhydride starting material was crucial. Molecular modeling was used to rationalize the observed selectivity.     

Zeta functions that hear the shape of a Riemann surface

To a compact hyperbolic Riemann surface, we associate a finitely summable spectral triple whose underlying topological space is the limit set of a corresponding Schottky group, and whose “Riemannian” aspect (Hilbert space and Dirac operator) encode the boundary action through its Patterson–Sullivan measure. We prove that the ergodic rigidity theorem for this boundary action implies that the zeta functions of the spectral triple suffice to characterize the (anti-)complex isomorphism class of the corresponding Riemann surface. Thus, you can hear the complex analytic shape of a Riemann surface, by listening to a suitable spectral triple.