Error indicators for the Navier-Stokes equations in stream function and vorticity formulation

This paper deals with a posteriori estimates for the finite element solution of the Stokes problem in stream function and vorticity formulation. For two different discretizations, we propose error indicators and we prove estimates in order to compare them with the local error. In a second step, these results are extended to the Navier-Stokes equations. Received March 25, 1996 / Revised version received April 7, 1997     

Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids

Sol–gel derived poly(oxyethylene)/siloxane organic/inorganic di-ureasil hybrids containing different amounts of methacrylic acid (McOH, CH₂=C(CH₃)COOH)) modified zirconium oxo-clusters (Zr-OMc) were processed as thin films deposited in glassy substrates via spin coating and as transparent and shape controlled monoliths. Channel monomode waveguides and diffraction gratings were UV patterned using the Talbot interferometer and the Lloyd mirror interferometer experimental setups. The time dependence of the diffraction gratings efficiency was studied for hybrids containing different amounts of Zr-OMc. Finally, the number of propagating modes and the refractive index gradient within the waveguide region, determined as a Gaussian section located below the patterned channel, was evaluated and modeled, a maximum index contrast of 2.43 × 10^?5 being estimated.     

New convenient one-step synthesis of 4-arylphthalaz-1 -ones

4-Arylphthalaz-1-ones (2a–e) are prepared by the hitherto unknown reaction of N-aminophthalimide (1) with aromatic hydrocarbons under Friedel-Crafts conditions. The reaction of N-aminophthalimide with Grignard reagents presents another convenient method for the synthesis of 4-alkyl or 4-arylphthalaz-1-ones.     

Synthesis and Structural Characterization and Thermal Properties of a Novel Aza‐aromatic Base Adduct of Cadmium Thenoyltrifluoroacetonate: A precursor for Pure Phase Nano‐sized Cadmium(II) Oxide

A novel aza‐aromatic base adduct of cadmium(II) thenoyltrifluoroacetonate, [Cd(phen)(ttfa)₂] ( 1 ), (phen = 1, 10‐phenanthroline; ttfa = thenoyltrifluoroacetonate) was synthesized and characterized by elemental analysis, IR, ¹H NMR, and ¹³C NMR spectroscopy, thermal analysis as well as X‐ray crystallography. The single‐crystal structure of this complex shows that the coordination number of the Cd²⁺ ions are six with two nitrogen donor atoms from aza‐aromatic base ligands and four oxygen donors from two thenoyltrifluoroacetonate ligands. The supramolecular features in these complexes are directed by weak directional intermolecular interactions. The structure of the title complex was optimized by density functional theory calculations. Calculated structural parameters and IR spectra for the title complex are in agreement with the crystal structure. The CdO nanoparticles were obtained by thermolysis of 1 at 180 °C with oleic acid as a surfactant. The average size of the nanoparticles was estimated by the Scherrer equation with the diameter about 45 nm. The morphology and size of the prepared CdO samples were further observed using SEM.     

Theoretical study on the mechanism and kinetics of atmospheric reactions NH2OH + OOH and NH2CH3 + OOH

Mechanism and kinetics of NH₂OH + OOH and NH₂CH₃ + OOH reactions were studied at the B3LYP and M062X levels of theory using the 6-311++G(3df, 3pd) basis set. The NH₂OH + OOH and NH₂CH₃ + OOH reactions proceed through different paths which lead to different products. Transition state structure and activation energy of each path were calculated. The calculated activation energies of hydrogen abstraction reactions were smaller than 25 kcal/mol and of substitution reactions are in the range of 50–70 kcal/mol. The rate constants were calculated using transition state theory (TST) modified for tunneling effect at 273–2000 K.     

Stereochemistry of new nitrogen containing heterocyclic aldehyde. VI. Novel structural and properties models of uranyl with quinoline azodyes

A novel series of UO2(2+) complexes with 5-(4'-derivatives phenyldiazo)-8-hydroxy-7-quinolinecarboxaldehyde (L1H-L7H), have been prepared. The composition and structure were confirmed by elemental analyses, 'HNMR spectra and IR spectroscopy measurements. Data from the above show that they exist in two isomeric solid forms. The polymeric structure results from intermolecular U=O...U=O interactions. The ligands act as a monobasic bidentate chelating agent coordinating through C=O and OH groups by replacement of a proton from the latter group. The force constant F(U-O) (mdyn A(-1)) and the bond length R(U-O) (A) of the U-O bond were calculated from the IR data and related to the electronic properties of the substituents. The existing literature on the coordination chemistry of these ligands are obscure.     

ESI-MS/MS Analysis of Phenolic Compounds from Aeonium arboreum Leaf Extracts and Evaluation of their Antioxidant and Antimicrobial Activities

Aeonium is a genus of succulents belonging to the Crassulaceae family. Their importance in traditional medicine has stimulated both pharmacological and chemical research. In this study, we optimized extraction, separation, and analytical conditions using a high performance liquid chromatographic method coupled with electrospray ionization mass spectrometry by the negative mode (HPLC-ESI-MS) in order to, for the first time, determine thirty-four compounds from Aeonium arboreum leaves. Twenty-one of them are assigned among which are sixteen flavonoids and five phenolic acids. FRAP, TAC, DPPH, and ABTS^•+ radical scavenging were used to evaluate antioxidant activity. The obtained IC₅₀ values ranged from 0.031 to 0.043 mg.mL⁻¹ for DPPH and between 0.048 and 0.09 mg·mL⁻¹ for ABTS^•+. Antimicrobial activity was also assessed. The obtained minimum inhibitory concentrations (MIC) of these extracts ranged from 12.5 to 50 µg·mL⁻¹ against Micrococcus luteus, Listeria ivanovii, Staphylococcus aureus, Salmonella enterica, Escherichia coli, Pseudomonas aeruginosa, Aspergillus niger, and Fusarium oxysporum, and from 25 to 50 µg·mL⁻¹ against Candida albicans. Therefore, these extracts can be considered as a potential source of biological active compounds.     

Parametric Inference for imperfectly observed Gibbsian fields

Summary This paper presents a maximum likelihood estimation method for imperfectly observed Gibbsian fields on a finite lattice. This method is an adaptation of the algorithm given in Younes [28]. Presentation of the new algorithm is followed by a theorem about the limit of the second derivative of the likelihood when the lattice increases, which is related to convergence of the method. Some practical remarks about the implementation of the procedure are eventually given.     

Capacitated transit assignment with loading priorities

In a transit network involving vehicles with rigid capacities, we advocate the use of strategies for describing consumer behavior. At each boarding node, a user sorts the transit lines in decreasing order of preference, and boards the first vehicle in this list whose residual capacity is nonzero. Since a users position in the queue varies from day to day, the delay experienced is stochastic. This leads to an equilibrium problem where, at a solution, users are assigned to strategies that minimize their expected delay. This situation is formulated as a variational inequality, whose cost mapping is discontinuous and strongly asymmetric, due to the priority of current passengers over incoming users. We prove that the solution set is nonempty and provide numerical results obtained by an efficient solution algorithm.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Fonds pour la formation de chercheurs et laide à la recherche (FCAR).Mathematics Subject Classification (2000):20E28, 20G40, 20C20Accepted: December 20, 2003