On the asymptotic behaviour of semigroups for flows in infinite networks

We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic behaviour is quite well understood. However, recently new examples of transport processes emerged where the corresponding semigroup is not strongly continuous. Due to this lack of strong continuity, there are currently only few results on the long-term behaviour of these semigroups. In this paper, we discuss the asymptotic behaviour for a certain class of these transport processes. In particular, it is proved that the solution semigroups behave asymptotically periodic with respect to the operator norm as a consequence of a more general result on the long-term behaviour by positive semigroups containing a multiplication operator. Furthermore, we revisit known results on the asymptotic behaviour of transport processes on infinite networks and prove the asymptotic periodicity of their extensions to the space of bounded measures.Comment: Correction of typos, rewritten introduction, some further simplifications of arguments, strengthened main result -- final versio

Mono- and bi-functional arenethiols as surfactants for gold nanoparticles: synthesis and characterization

Stable gold nanoparticles stabilized by different mono and bi-functional arenethiols, namely, benzylthiol and 1,4-benzenedimethanethiol, have been prepared by using a modified Brust's two-phase synthesis. The size, shape, and crystalline structure of the gold nanoparticles have been determined by high-resolution electron microscopy and full-pattern X-ray powder diffraction analyses. Nanocrystals diameters have been tuned in the range 2 ÷ 9 nm by a proper variation of Au/S molar ratio. The chemical composition of gold nanoparticles and their interaction with thiols have been investigated by X-ray photoelectron spectroscopy. In particular, the formation of networks has been observed with interconnected gold nanoparticles containing 1,4-benzenedimethanethiol as ligand

Polynuclear Gold [Au(I) ]4 , [Au(I) ]8 , and Bimetallic [Au(I) 4 Ag(I) ] Complexes: C-H Functionalization of Carbonyl Compounds and Homogeneous Carbonylation of Amines.

The synthesis of tetranuclear gold complexes, a structurally unprecedented octanuclear complex with a planar [Au(I) 8 ] core, and pentanuclear [Au(I) 4 M(I) ] (M=Cu, Ag) complexes is presented. The linear [Au(I) 4 ] complex undergoes C-H functionalization of carbonyl compounds under mild reaction conditions. In addition, [Au(I) 4 Ag(I) ] catalyzes the carbonylation of primary amines to form ureas under homogeneous conditions with efficiencies higher than those achieved by gold nanoparticles