Gradient Maximum Principle for Minima

We state a maximum principle for the gradient of the minima of integral functionals

Positronium Spin-Conversion Reactions Promoted by 3d Complexes in Highand Low-Spin States

Continuing in our work on the correlations between the rate constants, k _CR, of the ortho into para-positronium conversion reactions, CR, promoted by complexes of various 3d ions and the metal electron delocalization caused by the ligands, the relationship between the parameters of the correlation lines pertinent to highand low-spin complexes of Cr^II, Mn^II, and Co^II ions was ascertained. Moreover, it was experimentally verified, for the first time, that the statistical probability of the CR promoted by paramagnetic compounds with S = 1/2 is three times larger than that of the CR caused by compounds with S > 1/2.     

The pivotal role of symmetry in the ruthenium-catalyzed ring-closing metathesis of olefins

The synthesis of Ru-based precatalysts with N-heterocyclic carbene (NHC) ligands bearing syn- and anti-methyl groups on the NHC backbone and aryl N-substituents with differing steric bulk was carried out. The catalytic behavior of the monophospine Ru precatalysts (7a, 7b, 8a, and 8b) was compared to the corresponding family of phosphine-free catalysts (9a, 9b, 10a and 10b) in the ring-closing metathesis (RCM) of olefins. These catalysts showed high efficiency in RCM reactions and the syn-isomers 7a and 9a, in particular, proved to be among the most active catalysts in the formation of tetrasubstituted olefins through RCM. DFT studies on the entire RCM catalytic cycle of hindered olefins were performed to rationalize the different behaviors of catalysts with syn- and anti-methyl groups on the NHC backbone. Theoretical results not only disclosed how NHC symmetry influences the overall activity of the catalyst, but also gave relevant and more general indications on the crucial steps of the RCM of olefins.     

Copolymerization of ethylene with cyclopentene or 2‐butene with half titanocenes‐based catalysts

Half titanocenes (CpCH₂CH₂O)TiCl₂ (1), (CpCH₂CH₂OCH₃)TiCl₃ (2), and CpTiCl₃ (3), activated by methylaluminoxane (MAO) were tested in copolymerization of ethylene with internal olefins such as cyclopentene. All the catalysts were able to give incorporation of cyclopentene in polyethylene matrix. ¹³C NMR analysis of obtained copolymers showed that the catalytic systems have low regiospecificity. In fact, in ethylene–cyclopentene copolymers, cyclic olefin inserts with both 1,2 and 1,3‐enchainment. X‐ray powder diffraction analysis of these copolymers confirmed that 1,2 inserted cyclopentene units are excluded from crystalline phase, whereas 1,3‐cyclopentene units are included, giving rise to expansion of unit cell of crystalline polyethylene. Titanium‐based catalysts were investigated also in the copolymerization of ethylene with E and Z‐2‐butene. Only complex (1) was able to give copolymers and ¹³C NMR analysis of products showed 2‐3, 1‐3, and 1‐2 insertion of 2‐butene. Differential scanning calorimetry analysis displayed that ethylene–cyclopentene, as well as ethylene‐2‐butene, copolymers are crystalline and their melting point decreases by increasing the comonomer content. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4725–4733, 2008     

Microstructural and thermal characterization of neolithic ceramics

The aim of this research was to characterize some Neolithic ceramic finds collected during an excavation carried out at Lugo di Grezzana (Verona, Italy). Pottery shards with different paste and tempers were analyzed to better understand the manufacturing and firing technologies used for their production. Another task of the study was to determine whether highly refined artefacts, found in the site and resembling figulina-type ceramics, were of local production or imported from other places in the north of Italy, where the production of this sort of product has already been unambiguously assessed. Several results emerged from this investigation, providing indications on the finds from this Neolithic settlement and, therefore, on the technological expertise achieved by the primitive community. Moreover, a comparative study carried out on refined ceramic products found in Lugo and genuine figulina items from other northern Italian sites suggests that no trading exchange and commercial routes existed among those primitive communities.     

Lipschitz regularity for minima without strict convexity of the Lagrangian

We give, in a non-smooth setting, some conditions under which (some of) the minimizers of among the functions in W^1,1(Ω) that lie between two Lipschitz functions are Lipschitz. We weaken the usual strict convexity assumption in showing that, if just the faces of the epigraph of a convex function are bounded and the boundary datum u₀ satisfies a generalization of the Bounded Slope Condition introduced by A. Cellina then the minima of on , whenever they exist, are Lipschitz. A relaxation result follows.     

Lipschitz regularity of the minimizers of autonomous integral functionals with discontinuous non-convex integrands of slow growth

Let be a Borelian function and let (P) be the problem of minimizing