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     

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.     

Simplex optimization procedure for evaluating equivalence points in sigmoidal and segmented titration curves

The use of the simplex procedure as a non-linear least-squares curve-fitting method is proposed for evaluation of equivalence points in sigmoidal and segmented titration curves. The application of this procedure to theoretical curves affected by different amounts of random noise indicates its effectiveness and accuracy for locating the correct end-point in titrations characterized by very low reaction constants. The relevant results are compared with those obtained by other regression methods as well as by the first-derivative and Gran approaches.     

Soft agonist receptor interactions: Theoretical and experimental simulation of the active site of the receptor of sweet molecules

The structure-activity relationship of sweet molecules is chosen as an example to illustrate a mechanistic approach of soft agonist-receptor interactions. It is shown that an essentially geometric model of the receptor site can explain the activity of most sweet molecules, both rigid and flexible. The relevant conformations of flexible molecules in solution are extracted from a combination of NMR data and of energy calculations. A possible experimental simulation of the receptor environment in solution is illustrated by the complex of a dipeptide sweetener with a crown-ether.     

Cassava flour wastewater as a substrate for biosurfactant production

Five cassava flour wastewater (manipueira) preparations were tested as culture media for biosurfactant production by a wild-type Bacillus sp. isolate. No-solids (F), no-solids diluted (F/2), natural (I), natural diluted (I/2), and decanted (IPS) were the tested manipueira media. The microorganism was able to grow and to produce biosurfactant on all manipueira preparations. The media whose solids were removed (F and F/2) showed better results than preparations with the presence of solids (I, I/2, and IPS). No-solids medium (F) showed a surface tension of 26,59 mN/m and reciprocal of critical micelle concentration of over 100 and was selected as a potential substrate for biosurfactant production.     

Mechanism of formation of organic carbonates from aliphatic alcohols and carbon dioxide under mild conditions promoted by carbodiimides. DFT calculation and experimental study

Dicyclohexylcarbodiimide (CyN=C=NCy, DCC) promotes the facile formation of organic carbonates from aliphatic alcohols and carbon dioxide at temperatures as low as 310 K and moderate pressure of CO2 (from 0.1 MPa) with an acceptable rate. The conversion yield of DCC is quantitative, and the reaction has a very high selectivity toward carbonates at 330 K; increasing the temperature increases the conversion rate, but lowers the selectivity. A detailed study has allowed us to isolate or identify the intermediates formed in the reaction of an alcohol with DCC in the presence or absence of carbon dioxide. The first step is the addition of alcohol to the cumulene (a known reaction) with formation of an O-alkyl isourea [RHNC(OR')=NR] that may interact with a second alcohol molecule via H-bond (a reaction never described thus far). Such an adduct can be detected by NMR. In alcohol, in absence of CO2, it converts into a carbamate and a secondary amine, while in the presence of CO2, the dialkyl carbonate, (RO)2CO, is formed together with urea [CyHN-CO-NHCy]. The reaction has been tested with various aliphatic alcohols such as methanol, ethanol, and allyl alcohol. It results in being a convenient route to the synthesis of diallyl carbonate, in particular. O-Methyl-N,N'-dicyclohexyl isourea also reacts with phenol in the presence of CO2 to directly afford for the very first time a mixed aliphatic-aromatic carbonate, (MeO)(PhO)CO. A DFT study has allowed us to estimate the energy of each intermediate and the relevant kinetic barriers in the described reactions, providing reasonable mechanistic details. Calculated data match very well the experimental results. The driving force of the reaction is the conversion of carbodiimide into the relevant urea, which is some 35 kcal/mol downhill with respect to the parent compound. The best operative conditions have been defined for achieving a quantitative yield of carbonate from carbodiimide. The role of temperature, pressure, and catalysts (Lewis acids and bases) has been established. As the urea can be reconverted into DCC, the reaction described in this article may further be developed for application to the synthesis of organic carbonates under selective and mild conditions.     

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.