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.     

Error estimate for a stabilised domain decomposition method with nonmatching grids

Summary. In this paper, we analyse a stabilisation technique for the so-called three-field formulation for nonoverlapping domain decomposition methods. The stabilisation is based on boundary bubble functions in each subdomain which are then eliminated by static condensation. The discretisation grids in the subdomains can be chosen independently as well as the grid for the final interface problem. We present the analysis of the method and we construct a set of bubble functions which guarantees the optimal rate of convergence. Received May 12, 1998 / Revised version received November 21, 2000 / Published online June 7, 2001     

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.     

Single electron traps at the surface of polycrystalline MgO: assignment of the main trapping sites

Paramagnetic centers at the surface of ionic oxides in the form of trapped electrons can be generated by exposure of the material to alkali metal or hydrogen atoms or of molecular hydrogen under UV irradiation. For many years, it has been assumed that the resulting paramagnetic centers consist of oxygen vacancies filled by one electron. High-resolution electron spin resonance spectra and ab initio quantum chemical calculations show that the paramagnetic centers consist of (H(+))(e(-)) electron pairs formed at morphological irregularities of the surface. At least three different kinds of (H(+))(e(-)) centers, [A], [B], and [C], have been identified with abundances of 80%, 10%, and 8%, respectively. In this work, we compare a wide set of measured and computed g-factors and hyperfine coupling constants of the unpaired electron with the surrounding (25)Mg, (17)O, and (1)H nuclei and we propose a general assignment of the centers. (H(+))(e(-)) pairs formed at Mg(4c) ions at steps and edges account for species [A], centers formed at Mg(4c) ions at reverse corners correspond to species [B], and species [C] originates from (H(+))(e(-)) pairs formed at Mg(3c) ions at corners and kinks.     

Unicité du plongement d'une mesure de probabilité dans un semi-groupe de convolution gaussien. Cas non-abélien

Sans résumé     

M(R-dmet)2] bis(1,2-dithiolenes): a promising new class intermediate between [M(dmit)2] and [M(R,R'-timdt)2] (M = Ni, Pd, Pt)

We report the first examples of metal dithiolenes belonging to the class [M(R-dmet)(2)] [R-dmet = formally monoreduced N-substituted thiazolidine-2,4,5-trithione; R = Et, M = Ni (1), Pd (2), Pt (3)]. A comparative spectroscopic, electrochemical, and density functional theory theoretical investigation indicates that [M(R-dmet)(2)] complexes show features intermediate between those of the dithiolenes belonging to the previously reported classes [M(R,R'-timdt)(2)] and [M(dmit)(2)] (R,R'-timdt = formally monoreduced N,N'-disubstituted imidazolidine-2,4,5-trithione; dmit = 2-thioxo-1,3-dithiole-4,5-dithiolato). UV-vis-near-IR spectroscopy and cyclic voltammetry/differential pulsed voltammetry measurements performed on 1 and 3 proved that the new dithiolenes are stable as neutral, monoanionic, and bianionic species and feature a near-IR electrochromic absorption falling at about 1000 and 1250 nm for neutral and monoanionic species, respectively.     

Synthesis and coordination properties of new macrocyclic ligands: equilibrium studies and crystal structures

The synthesis and characterization of two new macrocyclic ligands, the bis-macrocyclic compound 2,6-bis(1,4,13-triaza-7,10-dioxacyclopentadec-1-ylmethyl)phenol (L) and 38-methoxy-1,4,13,16,19,28-hexaaza-7,10,22,25-tetraoxatricyclo[14.14.7.1(32,36)]octatriconta-32,34,Delta(36,38)-triene (L1) are reported. Equilibrium studies of basicity and coordination properties toward metal ions such as Cu(II), Zn(II), Cd(II) and Pb(II) were performed for ligand by potentiometric measurements in aqueous solution (298.1 +/- 0.1 K, I= 0.15 mol dm(-3)). L behaves as a hexaprotic base (logK(1)= 10.93, logK(2)= 9.70, logK(3)= 8.79, logK(4)= 8.05, logK(5)= 6.83, logK(6)= 2.55). All metal ions form stable mono- and dinuclear complexes: logK(MLH(-1))= 25.61 for Cu(II), 15.37 for Zn(II), 12.58 for Cd(II) and 13.79 for Pb(II); logK(M(2)LH(-1))= 31.61 for Cu(II), 23.38 for Zn(II), 24.49 for Cd(II) and 23.68 for Pb(II). All these dinuclear species show a great tendency to add the OH(-) group: the equilibrium constant for the addition reaction was found to be logK(M(2)LH(-1)OH)= 4.77 for Cu(II), 5.66 for Zn(II), 2.8 for Cd(II) and 3.18 for Pb(II). In the case of Ni(II), kinetic inertness prevents the possibility of solution studies. The dinuclear solid adducts [Ni(2)H(-1)L(N(3))(3)].EtOH and [Cu(2)H(-1)L(N(3))](ClO(4))(2) were characterized by X-ray analysis.     

Some exact equivalents for the Brownian motion in Hölder norm

Summary Some exact equivalents of small probabilities are given for the Wiener measure on spaces of Hölder paths. It turns out that most of them are easier to derive than their counterparts in the uniform norm because of a classical result of Z. Ciesielski which makes the Brownian motion on these spaces easy to handle. In particular we study the equivalents of the probability of B in a fixed ball, ofB in a small ball and we give applications to the speed of clustering in Strassen law.     

Cluster and periodic DFT calculations of MgO/Pd(CO) and MgO/Pd(CO)(2) surface complexes

The bonding and vibrational properties of Pd(CO) and Pd(CO)(2) complexes formed at the (100) surface of MgO have been investigated using the gradient-corrected DFT approach and have been compared to the results of infrared and thermal desorption experiments performed on ultrathin MgO films. Two complementary approaches have been used for the calculation of the electronic properties: the embedded cluster method using localized atomic orbital basis sets and supercell periodic calculations using plane waves. The results show that the two methods provide very similar answers, provided that sufficiently large supercells are used. Various regular and defect adsorption sites for the Pd(CO) and Pd(CO)(2) have been considered: terraces, steps, neutral and charged oxygen vacancies (F and F(+) centers), and divacancies. From the comparison of the computed and experimental results, it is concluded that the most likely site where the Pd atoms are stabilized and where carbonyl complexes are formed are the F(+) centers, paramagnetic defects consisting of a single electron trapped in an anion vacancy.