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     

Effect of cyclodextrins on physico-chemical and release properties of Eudragit RS 100 microparticles containing glutathione

The objective of this work was to develop a novel microparticulate system based on the mucoadhesive polymer Eudragit-RS 100 and cyclodextrins (CDs), potentially useful for the oral administration of Glutathione (γ–glutamylcysteinylglycine, GSH). For this purpose, an oil-in-oil (O/O) emulsion-solvent evaporation method was used for the preparation of microparticles (MPs) containing GSH alone or together with one of the following CDs: α-, β-, γ-, methyl-β-(Me-β-), hydroxypropyl-β-(HP-β-) or sulfobutylether-β-cyclodextrin (SBE_7m-β-CD). MPs were obtained by emulsifying a mixture of Eudragit RS 100, GSH, CD and magnesium stearate in acetone or acetonitrile with a mixture of liquid paraffin and Span 80. Size, encapsulation efficiency, and drug release of the prepared MPs were evaluated. The results clearly indicated that all the examined properties were dependent on the water-miscible solvents and CD used. In particular, MPs prepared by using acetone or acetonitrile showed different size distributions with mean diameters in the ranges 82–350 and 15–22 μm, respectively. Moreover, encapsulation efficiency values were found to be high in all cases (71–99%) and was significantly affected by the CD type. The GSH release rates were evaluated employing dissolution media with different pH values (1.2, 6.8 and 7.4) and the following rank order was obtained for MPs prepared using acetone: MPs incorporating Me-β-CD > MPs without CD > MPs incorporating the remaining CDs. On the other hand, MPs prepared using acetonitrile gave the highest GSH release rate. Finally, stability of GSH encapsulated in MPs containing HP-β-CD to enzymatic attack by pepsin A, α-chymotrypsin, and γ-glutamyltranspeptidase was also investigated.     

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.     

The infrared spectra of complexes with planar dithiooxamides X. The Cu(LH2)2X1 complexes

In this article, the preparation, X-ray powder results and vibrational properties of a new type of complex with planar dithiooxamides are discussed. In acetonitrile, Cu(I) can form complexes with the formula Cu(LH₂)₂X₁ (X = Cl, Br) where LH₂ is an N,N'-disubstituted dithiooxamide. Complexes with N,N'-dimethyldithiooxamide and N,N'-diethyldithiooxamide have been prepared. A thorough vibrational analysis with infrared and Raman techniques was performed, assisted by H/D and ⁶³Cu/⁶⁵Cu isotope substitution. The vibrational study indicates the presence of an inversion centre in the structure. This leads to the proposal of a very unusual six-coordinate structure for these compounds, with the two dithiooxamide ligands, having S-cis conformation, coordinated to the same copper and with the halogens bridged between two different copper atoms. Confirmation of this result was attempted by X-ray analysis, but although several methods were tried to obtain crystals, only powder X-ray data could be obtained, which could not give a definitive answer. Since such six-coordinate Cu(I) has never been described before, a less rigourous interpretation of the vibrational data was followed, leading to a square-pyramidal five-coordinate structure, with a rather weak bond between Cu(I) and a terminal halogen. The latter structure, with the data available up to now, seems a bit more likely, since five-coordination for Cu(I) has already been described.     

Disorder effects in Mn12–acetate at 83 K

The structure of hexadeca‐μ‐acetato‐tetra­aqua­dodeca‐μ₃‐oxo‐dodecamanganese bis(acetic acid) tetrahydrate, [Mn₁₂O₁₂(CH₃COO)₁₆(H₂O)₄]·2CH₃COOH·4H₂O, known as Mn₁₂–acetate, has been determined at 83 (2) K by X‐ray diffraction methods. The fourfold (S₄) molecular symmetry is disrupted by a strong hydrogen‐bonding interaction with the disordered acetic acid mol­ecule of solvation, which displaces one of the acetate ligands in the cluster. Up to six Mn₁₂ isomers are potentially present in the crystal lattice, which differ in the number and arrangement of hydrogen‐bonded acetic acid mol­ecules. These results considerably improve the structural information available on this molecular nanomagnet, which was first synthesized and characterized by Lis [Acta Cryst. (1980), B 36 , 2042–2046].     

Site-specific ligation of anthracene-1,8-dicarboxylates to an Mn12 core: a route to the controlled functionalisation of single-molecule magnets

A novel single-molecule magnet of the Mn12 family, [Mn12O12(O2CC6H5)8(L)4(H2O)4].8CH2Cl2, has been synthesised by site-specific ligand exchange using a tailor-made dicarboxylate (L2-), which leads to selective occupation of axial binding sites.     

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.