Metallocene ion pairs: A direct insight into the reaction equilibria and polymerization by 13C NMR spectroscopy

The reaction equilibria of Cp₂Ti¹³CH₃Cl and Cp₂Ti(CH₃)₂ with AlMe₃ (TMA) and/or methylaluminoxane (MAO) have been investigated by ¹³C NMR. Several adducts have been identified. A study of the ¹³C 90% enriched ethylene polymerization in an NMR tube in the presence of the above catalytic systems, in the most experimentally significant conditions, and a comparison of the NMR data with the catalytic activity have been made as well. It has been shown that: i) some species are side products, inactive for addition ethylene polymerization; ii) active cation-like species such as Cp₂TiMe⁺Cl·[AlMeO]_n- and Cp₂TiMe⁺Me·[AlMeO]_n- are formed in titanocene-MAO systems. Concerning the role of AlMe₃, contained in MAO solutions, it has been shown that: a) AlMe₃ is mainly bound to MAO; b) if some “free” AlMe₃ exists in solution it is not the actual cocatalyst in the metallocene-MAO based catalytic systems; c) the amount of AlMe₃ influences either active or inactive species.     

The notion of observable and the moment problem for $$*$$∗-algebras and their GNS representations

Letters in Mathematical Physics - We address some usually overlooked issues concerning the use of $$*$$-algebras in quantum theory and their physical interpretation. If $${\mathfrak {A}}$$ is a...     

On equilibrium solutions of diffusion equations with nonlinear boundary conditions

The existence or the nonexistence of nonconstant stable equilibrium solutions for a diffusion equation with nonlinear Neumann boundary conditions is studied. We prove the nonexistence of nonconstant stable equilibria when the nonlinearity has a small Lipschitz constant or a second derivative of constant sign or either when the domain is a ball. We construct an example of existence for a connected domain with several disconnected boundary components.This work is partially supported by the project PB91-0497-C02-02 of the DGICYT (Spain).     

The topology of two-dimensional real algebraic varieties

Sunto È noto che ogni spazio analitico reale è localmente omeomorfo al cono su un poliedro con caratteristica di Eulero-Poincaré pari. Si dimostra che questa condizione è anche sufficiente affinchè un poliedro (compatto) di dimensione due P sia omeomorfo ad una varietà algebrica reale affine P. Segue inoltre dalla costruzione che la P ottenuta ha, in un certo senso, un insieme di singolarità algebriche minimale, compatibilmente con la topologia di P.

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The authors are members of the G.N.S.A.G.A.     

Lepton spectrum in semileptonic b-decay

We present some results from the computation of the charged lepton energy distribution in the decay b → c + $\text{l}$^? + $\text{ν}$ taking into account first order QCD corrections.