A $\Gamma$-convergence result for doubling metric measures and associated perimeters

Abstract. In this paper we study the notion of perimeter associated with doubling metric measures or strongly weights. We prove that the metric perimeter in the sense of L. Ambrosio and M. Miranda jr. coincides with the metric Minkowski content and can be obtained also as a -limit of Modica-Mortola type degenerate integral functionals. Received: 27 August 2001 / Accepted: 29 November 2001 / Published online: 10 June 2002 Investigation supported by University of Bologna, funds for selected research topics and by GNAMPA of INdAM, Italy. The authors are very grateful to Luigi Ambrosio and Francesco Serra Cassano for making their preprints available to them, for listening with patience and for many unvaluable suggestions.     

DFT computational study of the mechanism of allyl halides carbonylation catalyzed by nickel tetracarbonyl

A theoretical investigation at the DFT(B3LYP) level on the carbonylation reaction of allyl bromide catalyzed by nickel tetra-carbonyl Ni(CO)(4) is discussed. The computational results show the following: (i) Three main steps characterize the catalytic cycle: (a) an oxidative addition step, (b) a carbonylation step, and (c) a reductive elimination step where the acyl product is obtained and the catalyst is regenerated. (ii) Both Ni(CO)(3) and Ni(CO)(4) complexes can behave as "active" catalytic species. (iii) The oxidative addition leads to the formation of either eta(3) or eta(1)-allyl nickel complexes, which are involved in a fast equilibrium. (iv) The carbonylation occurs much more easily on the eta(1) than on the eta(3) intermediates.     

Relatively regular ideals in semiprime Banach algebras

Nella prima parte di questo lavoro vengono studiate le relazioni che intercorrono tra il concetto di relativa regolarità in un'algebra non necessariamente unitaria ed alcuni ideali (radicale, zoccolo, prezoccolo) che intervengono nello sviluppo della teoria di Fredholm in algebre di Banach. Nella seconda parte del lavoro viene dimostrato che in certe algebre di BanachA complesse semiprime l'esistenza di un ideale relativamente regolare chiuso implica cheA è unitaria e di dimensione finita.     

A new approach to phosphoserine and phosphothreonine analysis in peptides and proteins: chemical modification,enrichment via solid-phase reversible binding,and analysis by mass spectrometry

beta-Elimination of the phosphate group on phosphoserine and phosphothreonine residues and addition of an alkyldithiol is a useful tool for analysis of the phosphorylation states of proteins and peptides. We have explored the influence of several conditions on the efficiency of this PO(4)(3-) elimination reaction upon addition of propanedithiol. In addition to the described influence of different bases, the solvent composition was also found to have a major effect on the yield of the reaction. In particular, an increase in the percentage of DMSO enhances the conversion rate, whereas a higher amount of protic polar solvents, such as water or isopropanol, induces the opposite effect. We have also developed a protocol for enrichment of the modified peptides, which is based on solid-phase covalent capture/release with a dithiopyridino-resin. The procedure for beta-elimination and isolation of phosphorylated peptides by solid-phase capture/release was developed with commercially available alpha-casein. Enriched peptide fragments were characterized by MALDI-TOF mass spectrometric analysis before and after alkylation with iodoacetamide, which allowed rapid confirmation of the purposely introduced thiol moiety. Sensitivity studies, carried out in order to determine the detection limit, demonstrated that samples could be detected even in the low picomolar range by mass spectrometry. The developed solid-phase enrichment procedure based on reversible covalent binding of the modified peptides is more effective and significantly simpler than methods based on the interaction between biotin and avidin, which require additional steps such as tagging the modified peptides and work-up of the samples prior to the affinity capture step.     

Electron impact mass spectrometry of 3-hydroxy-3,4,5,6-tetrahydro-2H-[1]benzoxocines. A comparison with the behaviour of isomeric 2-hydroxymethyl-2,3,4,5-tetrahydro-[1]-benzoxepines and 1,2-epoxy-5-(2-hydroxyphenyl)pentane

The mass spectrometric behavior of 3-methyl-3-hydroxybenzoxocines has been studied in detail by means of linked scans and mass analyzed ion kinetic energy spectrometry. The structure of the molecular ion and the fragmentation processes are strictly related to the structure of the neutral moieties. The possible isomerization of 3-hydroxy-10-methoxy-3-methyl-3,4,5,6-tetrahydro-2H-[1]benzoxocine to 2-methyl-2-[3-(3′-methoxy-2′-hydroxy)phenyl]pentyloxirane and to 2-hydroxymethyl-9-methoxy-2-methyl-2,3,4,5-tetrahydro[1]benzoxepine is investigated.     

Proton controlled intramolecular communication in dinuclear ruthenium(II) polypyridine complexes

The synthesis and characterization of two dinuclear ruthenium polypyridyl complexes based on the bridging ligands 5,5'-bis(pyridin-2' '-yl)-3,3'-bis(1H-1,2,4-triazole) and 5,5'-bis(pyrazin-2' '-yl)-3,3'-bis(1H-1,2,4-triazole) and of their mononuclear precursors are reported. The dinuclear compounds have been prepared by a Ni(0) catalyzed coupling of a mononuclear ruthenium(II) polypyridyl complex containing a brominated triazole moiety. Electrochemical and photophysical studies indicate that, in these dinuclear complexes, the protonation state of the bridge may be used to tune the intercomponent interaction between the two metal centers and that these species act as proton driven three-way molecular switches that can be read by electrochemical or luminescence techniques.     

Heterodinuclear Ln[bond]Na complexes with an asymmetrical macrocyclic compartmental Schiff base

Heterodinuclear lanthanide(III)-sodium(I) complexes [LnNa(L)(Cl)(2)(CH(3)OH)] (Ln=La[bond]Nd, Sm[bond]Lu), where H(2)L is a [1+1] asymmetric compartmental macrocyclic ligand containing a N(3)O(2) Schiff base and a O(3)O(2) crown-ether-like coordination site, have been prepared and characterized by IR, (1)H, (13)C, and (23)Na NMR spectroscopy, mass spectrometry, and electron microscopy. In the solid state, the lanthanide(III) ions coordinate the Schiff-base N(3)O(2) site, and the sodium ion occupies the O(3)O(2) crownlike cavity, as shown by the X-ray crystal structures of the Nd, Eu, Gd, and Yb derivatives. In these complexes, the lanthanide(III) ion is coordinated by two chlorine atoms in the trans position and by three nitrogen and two negatively charged phenol oxygen atoms of the Schiff base, and the ion is heptacoordinated with a pentagonal bipyramidal geometry. The sodium ion is coordinated by three etheric oxygen atoms and the two phenolic oxygens that act as a bridge. A methanol molecule is also coordinated in the apical position of the resulting pentagonal pyramidal polyhedron. A detailed (1)H and (13)C NMR study was carried out in CD(3)OD for both diamagnetic and paramagnetic heterodinuclear complexes [LnNa(L)(Cl)(2)(CH(3)OH)]. The complexes are also isostructural in solution, and their structures parallel those found in the solid state. Moreover, some significative distances determined in the solid state and in solution are comparable. Finally, the potential use of these complexes as molecular probes for the selective recognition of specific metal ions has been tested. In particular, their ability to act as shift reagents and the selectivity of the O(3)O(2) site towards Li(+), Ca(2+), and K(+) were investigated by (23)Na NMR spectroscopy.