On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

Electrokinetic characterization of hybrid NOA 81-glass microchips: Application to protein microchip electrophoresis with indirect fluorescence detection

A low-cost and straightforward hybrid NOA (Norland optical adhesive) 81-glass microchip electrophoresis device was designed and developed for protein separation using indirect fluorescence detection. This new microchip was first characterized in terms of surface charge density via electroosmotic mobility measurement and stability over time. A systematic determination of the electroosmotic mobility (μ_eo) over a wide pH range (2–10) and at various ionic strengths (20–50 mM) was developed for the first time via the neutral marker approach in an original simple frontal methodology. The evolution of μ_eo was proved consistent with the silanol and thiol functions arising from the glass and the NOA materials, respectively. The repeatability and reproducibility of the measurements on different microchips (RSD < 14%) and within 15 days (less than 5% decrease) were successfully demonstrated. The microchip was then applied for the efficient electrophoretic separation of proteins in a zonal mode coupled with indirect fluorescence detection, which is, to our knowledge, the first proof of concept of capillary zone electrophoresis in this hybrid microsystem.     

INTERFACIAL FREE ENERGIES,ZETA POTENTIALS AND THROMBORESI STANCE IN BOVINE AND OVINE CAROTID ARTERIES

The physical properties of the intimal surfaces of both natural and artificial arteries are important In the prevention of thrombosis and clotting. It Is expected thati a) the interface between the blood plasma and the intima should be highly negatively charged, to repel negatively charged platelets and other blood constituents, and b) the interfacial free energy at the plasma-intima interface should be as low as possible, to prevent adhesion If the charge barrier is breached. Few measurements of either the zeta potential or the interfacial free energy at the intimal surface can be found in the literature. Zeta potentials of natural and cross-linked bovine carotid intima, and of an expanded Teflon prosthesis were determined by a streaming potential method in 0.9% (w/v) NaC1. Interfacial free energies of both bovine and ovine carotid intima, and of an expanded Teflon prosthesis were also determined by a contact-angle method using water immiscible liquid drops on the intimal surface Immersed in 0.9% (w/v) NaC1.     

Reactivity Studies of Iridium Pyridylidenes [TpMe2Ir(C6H5)2(C(CH)3C(R)NH] (R=H,Me, Ph)

The reactivity of a series of iridium? pyridylidene complexes with the formula [Tp^Me2Ir(C₆H₅)₂(C(CH)₃C(R)N H] ( 1 a – 1 c ) towards a variety of substrates, from small molecules, such as H₂, O₂, carbon oxides, and formaldehyde, to alkenes and alkynes, is described. Most of the observed reactivity is best explained by invoking 16 e^? unsaturated [Tp^Me2Ir(phenyl)(pyridyl)] intermediates, which behave as internal frustrated Lewis pairs (FLPs). H₂ is heterolytically split to give hydride? pyridylidene complexes, whilst CO, CO₂, and H₂C?O provide carbonyl, carbonate, and alkoxide species, respectively. Ethylene and propene form five‐membered metallacycles with an IrCH₂CH(R)N (R=H, Me) motif, whereas, in contrast, acetylene affords four‐membered iridacycles with the IrC(?CH₂)N moiety. C₆H₅(C?O)H and C₆H₅C?CH react with formation of Ir? C₆H₅ and Ir? C?CPh bonds and the concomitant elimination of a molecule of pyridine and benzene, respectively. Finally the reactivity of compounds 1 a – 1 c against O₂ is described. Density functional theory calculations that provide theoretical support for these experimental observations are also reported.     

Synthesis of functionalized 2-alkoxybenzoates, 2-aryloxybenzoates and xanthones based on formal [3+3] cyclocondensations of 3-alkoxy- and 3-aryloxy-1-silyloxy-1,3-butadienes with 3-silyloxy-2-en-1-ones

Functionalized 2-alkoxy- and 2-aryloxybenzoates were prepared by formal [3+3] cyclocondensations of 3-alkoxy- and 3-aryloxy-1-silyloxy-1,3-butadienes with 3-silyloxy-2-en-1-ones. The reaction of 2-aryloxybenzoates with concentrated sulfuric acid resulted in the formation of xanthones.     

X‐ray photoelectron spectroscopic chemical state quantification of mixed nickel metal,oxide and hydroxide systems

Quantitative chemical state X‐ray photoelectron spectroscopic analysis of mixed nickel metal, oxide, hydroxide and oxyhydroxide systems is challenging due to the complexity of the Ni 2p peak shapes resulting from multiplet splitting, shake‐up and plasmon loss structures. Quantification of mixed nickel chemical states and the qualitative determination of low concentrations of Ni(III) species are demonstrated via an approach based on standard spectra from quality reference samples (Ni, NiO, Ni(OH)₂, NiOOH), subtraction of these spectra, and data analysis that integrates information from the Ni 2p spectrum and the O 1s spectra. Quantification of a commercial nickel powder and a thin nickel oxide film grown at 1‐Torr O₂ and 300 °C for 20 min is demonstrated. The effect of uncertain relative sensitivity factors (e.g. Ni 2.67 ± 0.54) is discussed, as is the depth of measurement for thin film analysis based on calculated inelastic mean free paths. Copyright © 2009 John Wiley & Sons, Ltd.     

Global solvability on the torus for certain classes of formally self-adjoint operators

In this paper we prove a necessary and sufficient condition for global solvability on the torus for two classes of formally self-adjoint operators. For the first class of operators we prove that global solvability is equivalent to an algebraic condition involving Liouville vectors and simultaneous approximability. For the second class of operators, when the coefficients are not identically zero, an independence condition on the coefficients is shown to be necessary and sufficient for global solvability. Received: 21 June 1999 / Revised version: 8 May 2000     

Global s-solvability and global s-hypoellipticity for certain perturbations of zero order of systems of constant real vector fields

The main purpose of this paper is to show, in the two-dimensional torus, a necessary and sufficient condition in order to certain perturbations of zero order of a system of constant real vector fields to be globally s-solvable. We are also interested in studying its global s-hypoellipticity. We present connections between these global concepts and a priori estimates. We also present two applications of our results for systems of operators with variable coefficients.