A regularity result for critical points of conformally invariant functionals

Let be an open set inR ² andI be a conformally invariant functional defined onH ¹(,R ^d ). Letu be a critical point ofI. We show that, ifu is apriori assumed to be bounded, thenu is smooth in , up to (ifu _| is smooth). This is a partial (positive) answer to a conjecture of S. Hildebrandt [13]. As an application, we establish a regularity result for weak solutions to the equation of surfaces of prescribed mean curvature in a three-dimensional compact riemannian manifold.     

Electrochemical mass spectrometric studies on 1-cyclopropyl-4-phenyl-1,2,3,6-tetrahydropyridine

Mechanistic studies on chemical and biological one-electron oxidations of cyclic tertiary allylamines are being pursued with the aid of an electrochemical-electrospray ionization mass spectrometric based assay. The results of previous studies on the electrochemical oxidation of 1-cyclopropyl-4-phenyl-1,2,3,6-tetrahydropyridine have documented a two-electron oxidative N-decyclopropylation pathway. The present paper describes the characterization of a second pathway involving an overall four-electron oxidation of this cyclopropylamine. The results document more completely the fate of cyclopropylaminyl radical cations that are thought to be intermediates in enzyme-catalyzed oxidations of aminyl substrates and that may lead to chemically reactive metabolites.     

Analysis of cocaine and its principal metabolites in waste and surface water using solid-phase extraction and liquid chromatography–ion trap tandem mass spectrometry

A validated method based on solid-phase extraction (SPE) and liquid chromatography-ion trap tandem mass spectrometry (LC-MS/MS) is described for the determination of cocaine (COC) and its principal metabolites, benzoylecgonine (BE) and ecgonine methyl ester (EME), in waste and surface water. Several SPE adsorbents were investigated and the highest recoveries (95.7 +/- 5.5, 91.8 +/- 2.2 and 72.5 +/- 5.3% for COC, BE and EME, respectively) were obtained for OASIS HLB(R) cartridges (6 mL/500 mg) using 100 mL of waste water or 500 mL of surface water. Extracts were analysed by reversed-phase (RP) or hydrophilic interaction (HILIC) LC-MS/MS in positive ion mode with multiple reactions monitoring (MRM); the latter is the first reported application of the HILIC technique for drugs of abuse in water samples. Corresponding deuterated internal standards were used for quantification. The method limits of quantification (LOQs) for COC and BE were 4 and 2 ng L(-1), respectively, when RPLC was used and 1, 0.5 and 20 ng L(-1) for COC, BE and EME, respectively, with the HILIC setup. For COC and BE, the LOQs were below the concentrations measured in real water samples. Stability tests were conducted to establish the optimal conditions for sample storage (pH, temperature and time). The degradation of COC was minimal at -20 degrees C and pH = 2, but it was substantial at +20 degrees C and pH = 6. The validated method was applied to a set of waste and surface water samples collected in Belgium.     

A model for the calculation of noise transmission inside dwellings: application to aircraft noise

A numerical model of sound transmission inside dwellings has been developed. It is based on a decoupled method mixing integral, modal and geometric approaches. Kropp's formulation has been adapted to take balconies into account. Architectural effects such as projected roofs or nearby buildings have been analysed. Sound transmission is strongly affected by the angle of incidence of incoming waves. The proposed approach makes use of velocity fields on windows either computed or measured with a laser vibrometer. Comparisons between computations and measurements are reported.     

Experimental and modeling study of Newtonian and non-Newtonian fluid flow in pore network micromodels

The in situ rheology of polymeric solutions has been studied experimentally in etched silicon micromodels which are idealizations of porous media. The rectangular channels in these etched networks have dimensions typical of pore sizes in sandstone rocks. Pressure drop/flow rate relations have been measured for water and non-Newtonian hydrolyzed-polyacrylamide (HPAM) solutions in both individual straight rectangular capillaries and in networks of such capillaries. Results from these experiments have been analyzed using pore-scale network modeling incorporating the non-Newtonian fluid mechanics of a Carreau fluid. Quantitative agreement is seen between the experiments and the network calculations in the Newtonian and shear-thinning flow regions demonstrating that the 'shift factor,'alpha, can be calculated a priori. Shear-thickening behavior was observed at higher flow rates in the micromodel experiments as a result of elastic effects becoming important and this remains to be incorporated in the network model.     

One-dimensional uranium-organic coordination polymers: crystal and electronic structures of uranyl-diacetohydroxamate

The structure of the uranyl-diacetohydroxamate compound, UO(2)(C(2)NO(2)H(4))(2), was elucidated using a combination of single crystal X-ray diffraction measurements and all-electron scalar relativistic density functional calculations. This polymeric compound crystallizes in the C2/c space group (IT No. 15; a = 12.8386(13) ?, b = 7.5661(7) ?, c = 8.9299(9) ?, β = 103.185(2) °; Z = 4), with main-chain repeating units featuring a bidentate structure analogous to that frequently found for d-block as well as lanthanide metal ions. Density functional analysis reveals that this compound is a semiconductor, with a direct band gap of 1.1 eV.     

Magnetic Bistability of Individual Single‐Molecule Magnets Grafted on Single‐Wall Carbon Nanotubes

A POM to remember : Hexanuclear Fe^III polyoxometalate (POM) single‐molecule magnets (see structure) can be noncovalently assembled on the surface of single‐wall carbon nanotubes. Complementary characterization techniques (see TEM image and magnetic hysteresis loops) demonstrate the integrity and bistability of the individual molecules, which could be used to construct single‐molecule memory devices.

     

On the well-posed coupling between free fluid and porous viscous flows

We present a well-posed model for the Stokes/Brinkman problem with a family of jump embedded boundary conditions (J.E.B.C.) on an immersed interface with weak regularity assumptions. It arises from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface $\Sigma$ separating the fluid and porous domains. These conditions are well chosen to get the coercivity of the operator. Then, the general framework allows us to prove new results on the global solvability of some models with physically relevant stress or velocity jump boundary conditions for the momentum transport at a fluid–porous interface. The Stokes/Brinkman problem with Ochoa-Tapia and Whitaker (1995) [9], [10] interface conditions and the Stokes/Darcy problem with Beavers and Joseph (1967) [13] conditions are both proved to be well-posed, by an asymptotic analysis. Up to now, only the Stokes/Darcy problem with Saffman (1971) [15] approximate interface conditions with negligible tangential porous velocity was known to be well-posed.