Hausdorff measures and dimension on

We consider the Hausdorff measures , , defined on with the topology induced by the metric

for all . We study its properties, their relation to the ``Lebesgue measure" defined on by R. Baker in 1991, and the associated Hausdorff dimension. Finally, we give some examples.

     

Antimony dispersion and phase evolution in the Sb2O3-Fe2O3 system

This paper studies the antimony spreading and segregation that occurred along with the oxidation and solid-state reactions in the Fe2O3-Sb2O3 system. XRD, SEM, TG-DSC and particularly XPS were employed for characterizations. Sb2O4 and FeSbO4 are the only new phases detected. The formation of FeSbO4 is a more exothermic but slower reaction than oxidation of Sb2O3. A mechanical grinding of Sb2O3 and Fe2O3 leads to a significant dispersion of Sb2O3 possibly because of its low hardness. Dispersion of reference Sb2O4 in this way is negligible. During the heating of a mixture of Sb2O3 and Fe2O3 with an atomic ratio of Sb/Fe = 0.5 at 200-1000 degrees C in ambient air, the thermal spreading of Sb2O3 onto Fe2O3 increases with increasing temperature until Sb2O3 is oxidized into Sb2O4. The surface atomic ratio of Sb/Fe measured by XPS, R(Sb/Fe), reaches a maximum around 400 degrees C. The complete oxidation of Sb2O3 leads to a decrease in R(Sb/Fe) because of poorer dispersibility of Sb2O4. The formation of FeSbO4 starting at ca. 800 degrees C causes a further decrease in R(Sb/Fe), but the R(Sb/Fe) is still 3.2 times the nominal bulk Sb/Fe ratio when the Sb2O4 is completely transformed into FeSbO4.     

Passive Transport of Ionic Drugs through Membranes with pH-Dependent Fixed Charges

We have studied both theoretically and experimentally the passive transport of ionic drugs through membranes with pH-dependent fixed charge. The system considered constitutes a simplified model for pH-controlled drug delivery through membranes of biochemical and pharmaceutical interest. The theoretical approach employed is based on the Nernst-Planck flux equations and all of the species present in the system (the neutral or ionic drug and the hydrogen and hydroxide ions) have been taken into account together with a Langmuir-type isotherm for the adsorption of the ionic drug onto the membrane surface. The membrane permeabilities of cationic, anionic, and neutral drugs through porous membranes with graft-polymerized weak polyelectrolytes have been measured as a function of the external pH. According to the nature of the grafted polyelectrolyte, the ionized membrane fixed groups can be negative or positive. For the amphoteric membrane, both fixed charge groups are present in the grafted chains. In all cases, the ionization state of the weak polyelectrolyte fixed groups changes with the local pH within the membrane. A comparison of the theoretical results with the experimental data allows one to explain qualitatively the changes of the membrane flux with the external pH and gives new physical insights into the transport problem. Copyright 2000 Academic Press.     

Aqueous biphasic olefin hydroformylation catalyzed by water-soluble rhodium complexes

Catalysis with water-soluble rhodium complexes, RhCl(CO)(TPPMS)₂, [TPPMS = P(C₆H₅)₂(C₆H₄SO₃)] (1), RhCl(CO)(TPPDS)₂, [TPPDS = P(C₆H₅)(C₆H₄SO₃)₂] (2) and RhCl(CO)(TPPTS)₂, [TPPTS = P(C₆H₄SO₃)₃] (3) in hydroformylation of 1-hexene, 2-pentene, 2,3-dimethyl-1-butene, cyclohexene and several mixtures of these olefins have been studied, under moderate reaction conditions (T: 50–150 °C; pCO/pH₂ = 1; total p: 14–68 bar; Substrate/Catalyst: 600/1) in biphasic toluene/water media. The catalytic system shows high activity but low selectivity. The linear and branched oxygenated products obtained are equally useful in naphtha upgrading, as observed in the real El Palito naphtha tried. The catalysts can be recycled several times without significant activity loss.     

Diels-Alder Reactions of 2-Oxazolidinone Dienes in Polar Solvents Using Catalysis or Non-conventional Energy Sources

Summary. The (Z)-N-substituted 4-methylene-5-propylidene-2-oxazolidinone dienes were prepared by a one-step synthesis, starting from 2,3-hexanedione and isocyanates. Diels-Alder cycloadditions of these dienes were carried out in the presence of the dienophiles methyl vinyl ketone, methyl propiolate, and a captodative olefin, under conditions such as solvents of high polarity, Lewis acid catalysis, and non-conventional energy sources. The reactions carried out either with mixtures of H₂O/MeOH or under BF₃·Et₂O catalysis yielded the highest regio- and stereoselectivities. The use of ionic liquids, microwaves, and ultrasound did not significantly increase the selectivity.     

The role of bismuth as promoter in Pd–Bi catalysts for the selective oxidation of glucose to gluconate

Bismuth is a well-established promoter of noble metal-based catalysts for the selective liquid phase oxidation of alcohols, aldehydes and carbohydrates with molecular oxygen. Experiments were carried out to improve the understanding of the promoting role of bismuth in bimetallic Pd–Bi catalysts used for the selective oxidation of glucose to gluconate. In relationship with the fact that these catalysts undergo substantial bismuth leaching under the reaction conditions, particular attention was paid to the possible role played by the soluble fraction of bismuth in the oxidative process. Carbon-supported Pd–Bi/C catalysts characterized by various Bi–Pd compositions (0.33≤Bi/Pd≤3.0,10 wt.%Pd+Bi) were prepared from acetate-type precursors, tested under various experimental conditions and analyzed by X-ray diffractometry and X-ray photoelectron spectroscopy (XPS). Whatever the initial catalyst composition, the surface intensity ratio measured by XPS in used catalysts lies in the range 0.4–0.6, suggesting that the dynamic state of the catalyst involves the association of one Bi and two to three Pd atoms. The leaching process and the promoting effect itself are discussed in line with the formation of Bi–glucose and Bi–gluconate complexes present in solution but also as adsorbed species at the catalyst surface. The performances of a monometallic Pd/C catalyst are significantly improved in the presence of adequate amounts of soluble Bi. The involvement of the soluble fraction of bismuth in the overall mechanistic scheme of glucose oxidative dehydrogenation is suggested. The detrimental effect of large amounts of soluble bismuth is attributed to a too extensive adsorption of Bi–glucose complexes on the surface Pd atoms.     

Theoretical study of the adsorption of H on Si n clusters, (n=3-10)

A recently proposed local Fukui function is used to predict the binding site of atomic hydrogen on silicon clusters. To validate the predictions, an extensive search for the more stable SinH (n=3-10) clusters has been done using a modified genetic algorithm. In all cases, the isomer predicted by the Fukui function is found by the search, but it is not always the most stable one. It is discussed that in the cases where the geometrical structure of the bare silicon cluster suffers a considerable change due to the addition of one hydrogen atom, the situation is more complicated and the relaxation effects should be considered.     

Electrochemical deposition onto self-assembled monolayers: new insights into micro- and nanofabrication

Pattern transfer with high resolution is a frontier topic in the emerging field of nanotechnologies. Electrochemical molding is a possible route for nanopatterning metal, alloys and oxide surfaces with high resolution in a simple and inexpensive way. This method involves electrodeposition onto a conducting master covered by a self-assembled alkanethiolate monolayer (SAMs). This molecular film enables direct surface-relief pattern transfer from the conducting master to the inner face of the electrodeposit, and also allows an easy release of the electrodeposited film due their excellent anti-adherent properties. Replicas of the original conductive master can be also obtained by a simple two-step procedure. SAM quality and stability under electrodeposition conditions combined with the formation of smooth electrodeposits are crucial to obtain high-quality pattern transfer with sub-50 nm resolution.     

Pyridazines. Part 31: synthesis and antiplatelet activity of 4,5-disubstituted-6-phenyl-3(2H)-pyridazinones

This paper describes the synthesis and the antiplatelet activity of a series of 4,5-disubstituted-6-phenyl-3(2H)-pyridazinones. Some of these compounds show a dose-dependent activity and were found to be more active than their 5-substituted analogues.     

Moreau’s decomposition in Banach spaces

Moreau’s decomposition is a powerful nonlinear hilbertian analysis tool that has been used in various areas of optimization and applied mathematics. In this paper, it is extended to reflexive Banach spaces and in the context of generalized proximity measures. This extension unifies and significantly improves upon existing results.