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     

Analytical application of emulsions Determination of lead in gasoline by atomic-absorption spectrophotometry

A simple rapid method of determining lead in gasoline by AAS with use of stable emulsions has been developed. The emulsions were stabilized with propan-2-ol or a mixture of ethanol and a surface-active agent. The results obtained showed good reproducibility and accuracy and the method is suitable for routine analysis.     

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.     

Cadmium chronic administration to lactating ewes: reproductive performance, cadmium tissue accumulation and placental transfer

20 lactating ewes were allotted to two groups: 10 subjects received orally 100 mg/day of CdCl2 for 108 consecutive days, and the remaining 10 acted as control. Reproductive performance in ewes and cadmium tissue accumulation, both in ewes and their lambs, were investigated. The results showed that in ewes: 1) the regular cadmium intestinal intake negatively influences all reproductive parameters; 2) cadmium is particularly accumulated in kidney and liver, but also in mammary gland, although at a distinctly lower level; 3) chronic administration does not increase cadmium placental transfer in lactating pregnant subjects.     

Structural investigation of 3,5‐disubstituted isoxazoles by 1H‐nuclear magnetic resonance

HIV‐1 integrase (IN) is a very promising and validated target for the development of therapeutic agents against AIDS. In an effort to design and synthesize biological isosteric analogs of β‐diketoacid‐containing inhibitors of IN, we prepared a series of substituted isoxazole carboxylic acids. Several of these compounds inhibited catalytic activities of purified IN at micromolar concentration range. With an aim to prepare a large number of analogues based on the isoxazole pharmacophore we focused our study on a series of 3,5‐disubstituted isoxazole isomers. For a rapid structural analysis we discovered a convenient ¹H‐nmr method for distinguishing between isomeric structures based on their H‐4 assignments. This “finger print” approach to isomer identification will be useful in combinatorial chemistry settings where a mixture can be further derivatized.     

Enantioseparations of polyhalogenated 4,4’-bipyridines on polysaccharide-based chiral stationary phases and molecular dynamics simulations of selector–selectand interactions

2’-(4-Pyridyl)- and 2’-(4-hydroxyphenyl)-TCIBPs (TCIBP = 3,3’,5,5’-tetrachloro-2-iodo-4,4’-bipyridyl) are chiral compounds that showed interesting inhibition activity against transthyretin fibrillation in vitro. We became interested in their enantioseparation since we noticed that the M-stereoisomer is more effective than the P-enantiomer. Based thereon, we recently reported the enantioseparation of 2’-substituted TCIBP derivatives with amylose-based chiral columns. Following this study, herein we describe the comparative enantioseparation of both 2’-(4-pyridyl)- and 2’-(4-hydroxyphenyl)-TCIBPs on four cellulose phenylcarbamate-based chiral columns aiming to explore the effect of the polymer backbone, as well as the nature and position of substituents on the side groups on the enantioseparability of these compounds. In the frame of this project, the impact of subtle variations of analyte and polysaccharide structures, and mobile phase (MP) polarity on retention and selectivity was evaluated. The effect of temperature on retention and selectivity was also considered, and overall thermodynamic parameters associated with the analyte adsorption onto the CSP surface were derived from van ’t Hoff plots. Interesting cases of enantiomer elution order (EEO) reversal were observed. In particular, the EEO was shown to be dependent on polysaccharide backbone, the elution sequence of the two analytes being P-M and M-P on cellulose and amylose tris(3,5-dimethylphenylcarbamate), respectively. In this regard, a theoretical investigation based on molecular dynamics (MD) simulations was performed by using amylose and cellulose tris(3,5-dimethylphenylcarbamate) nonamers as virtual models of the polysaccharide-based selectors. This exploration at the molecular level shed light on the origin of the enantiodiscrimination processes.     

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.     

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.