Some combinatorial properties of the Hurwitz series ring

We study some properties and perspectives of the Hurwitz series ring \(H_R[[t]]\), for an integral domain R, with multiplicative identity and zero characteristic. Specifically, we provide a closed form for the invertible elements by means of the complete ordinary Bell polynomials, we highlight some connections with well–known transforms of sequences, and we see that the Stirling transforms are automorphisms of \(H_R[[t]]\). Moreover, we focus the attention on some special subgroups studying their properties. Finally, we introduce a new transform of sequences that allows to see one of this subgroup as an ultrametric dynamic space.     

Heterogeneous Ziegler-Natta catalysts: On going progress for the polyolefin industry

A great deal of research and development efforts in Ziegler Natta catalysis has been put within the last ten years into the polyolefin industry. The exploitation of new catalysts, the introduction and consolidation of advanced polymerization process technologies and, finally, the development of a broader range and of a better tailoring of product grades, have made the polyolefin market an expression of a young, dynamic, technology-driven industry. In this context heterogeneous catalysts have played a key role. Many drawbacks of the catalysts of the previous generation have been overcome. However some problems have still to be solved in order to both further improve catalyst performance and reduce the residual areas of empiricism in catalyst design and manufacture.