An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.     

Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

The fixed point property for multivalued nonexpansive mappings

We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties.     

Rapid determination of acetaminophen in physiological fluids by liquid chromatography using SDS mobile phase and ED detection

Acetaminophen is determined in serum and urine samples by a rapid, sensitive, and precise chromatographic method without any pretreatment step in a C18 column using a pure micellar mobile phase of 0.02M sodium dodecyl sulfate at pH 7. Acetaminophen is eluted in less than 5 min with no interference of the protein band. The use of electrochemical and UV detection is compared. Linearities (r > 0.999), as well as intra- and interday precision, are studied in the validation of the method. Limits of detection (LOD) are also calculated to be 0.56, 0.83, and 0.74 ng/mL in micellar solution, serum, and urine using electrochemical detection. The developed micellar liquid chromatographic method is useful for the quantitation of acetaminophen in serum and urine. Recoveries in the biological matrices are in the 98-107% range and results are compared with those obtained using a reference method. Drug excretion (in urine) and serum distribution are studied in several healthy volunteers, and no interference from metabolites is found. The developed procedure can be applied in routine analyses, toxicology, and therapeutic monitoring.     

Acetoxyphenylketene. Reaction with biacetyl

The generation of acetoxyphenylketene (4) in the cold in the presence of biacetyl yields the single β-lactone $\text{12B}$, which undergoes a novel rearrangement to the tricyclic orthoester lactone $\text{11}$ above 130°.     

Mixtures of sodium dodecyl sulfate/dodecanol at the air/water interface by computer simulations

Molecular dynamics simulations of monolayers of surfactant mixtures at the air/water interface were performed where the binary mixture was composed of sodium dodecyl sulfate (SDS) and dodecanol molecules. At the same ratio of SDS and dodecanol molecules, two monolayer mixtures were prepared. In the first monolayer, all the dodecanol molecules were placed together in the center of the simulation box, whereas in the second monolayer, those molecules were uniformly distributed in the surface area in such a way that they were far from each other. Simulations of both systems indicate that the dodecanol tails in the first monolayer are straighter and more ordered than those in the second monolayer. From the present results, we observed new insights of how the different molecules should array or distribute at the interface in real systems. Finally, studies of the interfacial water around the different surfactants were also analyzed, showing that they are closer to the polar headgroups of dodecanol than to the SDS headgroups.     

Hydrogen peroxide in basic media for whole blood sample dissolution for determination of its lead content by electrothermal atomization atomic absorption spectrometry

Hydrogen peroxide in basic media is proposed as a means for dissolving whole blood samples to be analyzed by electrothermal atomization atomic absorption spectrometry, ET AAS. Approximately 2 g of the whole blood sample were directly weighed in a 150 mL volumetric flask; 3 mL of a NaOH 0.2 mol L⁻¹ solution, two drops of 1-octanol, as an antifoaming agent, and 1 mL of 30% volume hydrogen peroxide were added to the flask to promote oxidation. The solution was then manually shaken and after approximately three minutes of shaking, a clear solution, with no apparent suspended solids or greasy layers, was obtained. Distilled-deionized water was used to complete the volume. Ten μL of the resulting solution along with 10 μL of a solution containing 5000 mg L⁻¹ of NH₄H₂PO₄ and 300 mg L⁻¹ of Mg(NO₃)₂ as a modifier, were injected into transversely heated graphite tubes for lead determination. Both aqueous standards and standard addition calibration curves produced results not significantly different at a 95% confidence limit level. Accuracy of the measurements was assessed by analysis of the IAEA A-13 (concentration of trace and minor elements in freeze dried animal blood) standard reference material containing 0.18 mg L⁻¹ lead on a dry basis and by means of recovery tests. Analysis of the IAEA A-13 standard produced 0.17 ± 0.02 mg L⁻¹ lead on a dry basis; recovery tests afforded values from 95 to 105%. Ten consecutive measurements of a 5 ppb lead solution gave a characteristic mass of 47.2 pg and a (3S) detection limit of 1.77 μg L⁻¹ Pb. Results obtained from analysis of whole blood samples of volunteer donors covered a lead concentration range between 8 and 21 μg L⁻¹ with a mean value of 11.9 ± 4.7 μg L⁻¹.     

Synthesis and stereochemistry of tetrahydroprotoberberine derivatives

A series of 5-hydroxytetrahydroprotoberberines has been prepared from 3-aryltetrahydroisoquinoline derivatives via successive N-alkylation, oxidation and cyclization in acidic media. The relative configurations of the resulting diastereomeric 5-hydroxytetrahydroprotoberberines are reported.