Exact solution of a vertex model ind dimensions

We consider a class of vertex models describing directed lines on a lattice in arbitraryd dimensions, and solve the model exactly for the Cartesian lattice and in the case that each loop of lines carries a fugacity - 1. Our analysis, which can be carried out for arbitrary lattices, is based on an equivalence of the vertex model with a dimer problem. The dimer problem is, in turn, solved using the method of Pfaffians. It is found that the system is frozen below a critical temperatureT _cwith the critical exponent = (3 –d)/2.     

Self-assembly of highly oriented one-dimensional h-WO3 nanostructures

A new self-assembled and highly oriented one-dimensional single-crystal nanostructure of WO3 with hexagonal form was successfully prepared by a mild, solution-based colloidal approach.     

Radical mediated synthesis of 6-arylphenanthridines via benzotriazole ring-opening

Lithiation of diarylbenzotriazol-1-ylmethanes followed by addition of copper( I ) iodide gave 6-arylphenanthridine derivatives in moderate yields. When the two aryl groups were the same or contained very different electron densities, only one product was obtained. However, when the two aryl groups exhibited electron densities of similar magnitude, two isomers were afforded. According to the substituent effect, we believe that the reactions proceed via radical intermediates formed by copper( I ) iodide.