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.     

5-Spirocyclopropane Isoxazolidines as Versatile Intermediates in Organic Synthesis

The review outlines the various different azaheterocycles available from 5-spirocyclopropane isoxazolidines. These compounds can be regarded as versatile direct precursors of tetrahydro-, dihydropyridone and azetidinone derivatives. The current scope and limitations, and the selectivity aspects of the different processes are discussed therein.     

Solid-state interactions and drug release of teicoplanin in binary combinations with peracetylated α-, β-, and γ-cyclodextrins

Triacetyl α-cyclodextrin, triacetyl β-cyclodextrin and triacetyl γ-cyclodextrin were tested as possible hydrophobic carriers to prolong the release of hydrophilic teicoplanin (TCP). Physical–chemical characterization of individual components, drug-carrier physical mixtures at 0.5, 0.67 and 0.75 mass fraction of carrier, and the respective interaction products by kneading or evaporative crystallization under microwave irradiation was carried out using differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). In vitro drug release in pH 7.4 phosphate buffer at 37 °C was determined by intrinsic dissolution rate (IDR) measurements on non disintegrating compressed discs. Solid-state interactions of TCP with triacetyl α-cyclodextrin by evaporative crystallization and kneading and with triacetyl β-cyclodextrin by evaporative crystallization (probably resulting in carrier amorphization) were demonstrated. The role of carrier hydrophobicity, carrier mass fraction and preparation method of solid drug-carrier combinations on solid-state drug-carrier interactions and slowing down of TCP release was assessed. Modulation of drug release can be achieved using TCP-triacetyl γ-cyclodextrin combinations at 0.5 mass fraction of carrier.     

Effect of core size on the partition of organic solutes in the monolayer of water-soluble nanoparticles: an ESR investigation

ESR spectroscopy has been used to study the interaction of para-pentylbenzyl hydroxyalkyl nitroxide with the monolayer of water-soluble protected gold clusters having a core diameter ranging from 1.6 to 5.3 nm. The solubilization of the nitroxide probe in the more hydrophobic environment of the monolayer strongly depends on the size of the gold core. In particular, the partition equilibrium constant increases as the nanoparticle diameter decreases. These results have been attributed to the different packing of the chains in the monolayer resulting from the different radius of curvature of the investigated nanoparticles. This represents, to the best of our knowledge, the first report demonstrating that the core size of metallic nanoparticles affects the solvating properties of the protective organic monolayer.     

Understanding the role of stereoelectronic effects in determining collagen stability. 2. A quantum mechanical/molecular mechanical study of (Proline-Proline-Glycine)(n) polypeptides

The importance of vicinal and long-range interresidue effects in determining the stability of the collagen triple helix has been investigated by quantum mechanical (QM) and molecular mechanical (MM) computations on suitable model polypeptides, taking into account solvent effects by the polarizable continuum model (PCM). At the QM level, the PII conformation corresponds to an energy minimum for pentapeptide analogues incorporating the sequence Gly-Pro-Pro-Gly, irrespective of the down or up puckering of the pyrrolidine ring. However, our computations indicate that the alternation of down and up prolines characterizing collagen and collagen-like peptides is not due to an intrinsic preference of the Pro-Pro-Gly sequence. This result is confirmed by MM computations of longer polypeptides. Next, MM computations on model triple helices show that a better packing is obtained for specific values of backbone dihedrals, which, in turn, favor the alternation of down and up prolines along each chain.     

Coordination properties of 6-deoxy-6-[1-(2-amino) ethylamino]-β-cyclodextrin and the ability of its copper(II) complex to recognize and separate amino acid enantiomeric pairs

The functionalized cyclodextrin 6-deoxy-6-[1-(2-amino)ethylamino]--cyclodextrin was synthesized, and an NMR, EPR, pH-metric, and calorimetric investigation was carried out in aqueous solution in order to ascertain its behaviour towards protonation and copper(II) complex formation. The thermodynamic parameters of the ternary complex formation with alanine, phenylalanine and tryptophan enantiomeric pairs were also determined (25° C andI=0.1 mol dm^–3). No thermodynamic enantioselectivity was observed in these systems, while a chiral, though poor, discrimination was observed in LEC: c.d. spectra also show enantiomeric stereoselectivity. The results of the present investigation, compared with previously reported results, suggest the occurence of acis-complex trans-complex equilibrium in such systems.     

Chromatographic methods for blood alcohol determination.

This review is focused on the different chromatographic strategies for blood alcohol determination which can be adopted for clinical and/or forensic purposes. Particular attention is paid to gas chromatography and to high-performance liquid chromatography. However, other analytical techniques in common use, such as chemical and enzymic methods, are also briefly presented, together with some, at present unusual or experimental, approaches, such as enzymic reactors and catalytic electrodes, which are suitable for application in column liquid chromatography. Finally, mention is made of the methods for the determination of acetaldehyde, the major ethanol metabolite, and of some proposed markers of chronic alcohol abuse, such as acetaldehyde-protein adducts and carbohydrate-deficient transferrin. In order to give the background of knowledge for the rational choice of an analytical strategy, an updated outline of ethanol metabolism and toxicology is presented, together with basic information for the interpretation of the results. Problems concerning blood sampling and storage are also discussed.     

The EPR study of dialkyl nitroxides as probes to investigate the exchange of solutes between micellar and water phases

An EPR investigation of the kinetics of the exit, k ^-, and entrance, k ⁺, processes in micelles of sodium dodecyl sulfate, hexadecyltrimethylammonium bromide and polyoxyethylene(6)decanol of a family of para-substituted benzyl tert -butyl nitroxides and para-substituted benzyl hydroxyalkyl nitroxides is reported. The inclusion of nitroxide probes in the hydrophobic environment of the micelle gives rise to a reduction of the value of both nitrogen and β-proton splittings, with the result that the resonance fields for the M_I(2H _β ) = ±1lines of the free and included species are significantly different. The rate constants were obtained by analyzing the EPR line shape variations as function of surfactant concentration and temperature. The experimental value of k ⁺ obtained from the study of benzyl tert-butyl nitroxide indicates that the association reaction is very close to being controlled by diffusion. The value of the exit rate, k ^-, instead, depends on the probe hydrocarbon chain length. A comparison of our results with those obtained by luminescence quenching techniques is also reported.     

Thermal behavior of Cu(II)-, Cd(II)-, and Hg(II)-exchanged montmorillonite complexedwith cysteine

The thermal behavior of montmorillonite and organically modified montmorillonite, both treated with heavy metal cations [Cu(II), Cd(II) and Hg(II)], was characterized via thermal analyses (TG, DTG and DTA) combined with evolved species gas mass spectrometry (MS-EGA), and X-ray diffraction at in situ controlled temperature (HTXRD). The reactions involving Cu(II)- and Cd(II)-montmorillonite samples are mostly related to H₂O and OH loss, unlike Hg(II)-montmorillonite, where effects associated to Hg(II) loss are also present. Finally reactions related to dehydration, dehydroxylation and to organic matter decomposition can be observed in montmorillonite samples treated with cysteine.     

Commuting traces of multilinear maps on invertible elements

Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:R^m→R satisfying [G(u,…,u),u]?=?0 for all unit u∈R.