Solutions nulles d'opérateurs aux dérivées partielles à plusieurs variables fuchsiennes

Taking the concept of operator with several Fuchsian variables of N.S. Madi (Ann. Mat. Pura Appl. (4) 163 (1993) 1–15), the results of K. Igari (J. Math. Kyoto Univ. 25 (1985) 341–355) are extended in this Note to show the existence of null-solutions for some of these operators. To cite this article: M. Belarbi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Ersatz Commutant Lifting with Test Functions

This note presents a commutant lifting theorem (CLT) with initial data a finite set of (test) functions and a compatible reproducing kernel k on a set X. This covers the CLT of Ball, Li, Timotin, and Trent [9] for the polydisc, but in general no analyticity is required, rather statements and proofs use the language and techniques of reproducing kernel Hilbert spaces. Uniqueness of the de Branges–Rovnyak construction like found in Agler [1] and Ambrozie, Englis, and Müller [5] and an abstract Beurling Theorem in the present context are of independent interest. Received: October 12, 2006. Accepted: May 8, 2007.     

Hydration of a Na(+)-montmorillonite studied by thermally stimulated depolarization current

Thermally stimulated depolarization current (TSDC) technique is a powerful tool for probing dipole re-orientational motions in condensed matter. In the case of cation-exchangeable aluminosilicates, it allows the assessment of the potential barrier related to the hopping mechanism of cations and, consequently, the measurement of its evolution when molecules, i.e. water, are adsorbed and interact with the cations embedded in the solid framework. Then, using suitable models based on thermodynamics, the analysis of TSDC signals obtained at various hydration states provides insights about the surface properties of the studied solid and the mechanism of adsorption at the cationic site. In this work, TSDC is used to study the first stage, i.e. when the number of adsorbed molecules is below the occurrence of the water monolayer, of water adsorption in a Na(+)-montmorillonite from Mostaganem (Algeria). It is shown that the hydration process follows two stages. Using the "chemical force" concept it can then be concluded that when the number of adsorbed water molecules per cation is lower than 2, cation-water interaction dominates the energetics of adsorption, whereas at higher water loading the water "chemical force" is also involved into water-water and/or water-clay framework interactions. The number of water molecules for the monohydrated state is found to be about 7.     

Synthesis of palladium-bidentate complex and its application in Sonogashira and Suzuki coupling reactions

A new palladium-bidentate complex [m-C₆H₄(CH₂ImMe)₂(PdCl₂)] (III) was prepared in two steps. In the first step, [m-C₆H₄(CH₂ImMeAgCl)₂] (II) (Im = imidazole moiety) was obtained by reacting imidazolium salt [m-C₆H₄(CH₂ImMe)₂]Cl₂ (I) (prepared by quaternisation of Nmethylimidazole with 1,3-bis(chloromethyl)benzene) and Ag₂O in CH₂Cl₂. In the next step, treatment of (II) with Pd(CH₃CN)₂Cl₂ afforded complex III which was evaluated for its catalytic activity for C-C bond-formation reactions by examining the coupling reaction of 3-iodoanisole with phenylacetylene in the Sonogashira reaction. In addition, 3-methoxybiphenyls were obtained with good to excellent yields by Suzuki coupling reactions of 3-iodoanisole with phenylboronic acids or phenylborates salts in the presence of this complex.     

Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times

In this paper, the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is proved under the mixed generalized Lipschitz and Carathéodory's conditions.     

Local tunneling barrier height observations of NiAl(1 1 0)

Local work functions at individual atoms on a compound metal surface have been experimentally examined. The simultaneously obtained STM and local tunneling barrier height (LBH) images of NiAl(1 1 0) show that LBH at geometrically lower Ni sites is much higher than that at geometrically higher Al sites, indicating that each individual atom on the NiAl(1 1 0) surface has a specific potential barrier for relevant electrons.     

Interference of verbal labels in color categorical perception

Previous studies demonstrated that color categorical perception (CP; better cross-category than within-category discrimination) was reduced by verbal interference, suggesting that CP is mediated by verbal labeling. Here, we examined chromatic generality and experience-dependency of verbal interference in CP using the Stroop effect. We employed a simultaneous two-alternative forced choice discrimination task. Congruent or incongruent words were presented prior to discrimination. In experiment 1, incongruent color names reduced CP regardless of color boundary pairs. Next, we used noncolor words that seemed to be associated with color through experience. The results showed that the tested noncolor words did not modify CP (experiment 2). However, combined presentation of color and shape produced Stroop interference (experiment 3). Our finding suggests that familiarity or mastery of categorized information through experience may be evaluated by verbal interference.     

Mode multiplexing in optical frequency mixers

Asymmetric Y junctions allow the development of a new class of optical frequency mixers that utilize higher-order waveguide modes for signal processing. We measure high-contrast (>30 dB) mode sorting in asymmetric Y junctions by use of a novel technique: efficient TM00, TM10, and TM20 mode mixing in a periodically poled lithium niobate waveguide. We also demonstrate an odd-to-even mode wavelength converter capable of spectral inversion without offset or bidirectional wavelength conversion.     

One-pot synthesis to engineer a Co-KIT-6 catalyst for the ring opening of methylcyclopentane

Co-KIT-6 mesoporous materials with Ia3d symmetry and Si/Co ratios of 50, 25, and 10 were prepared using hydrothermal one-pot synthesis. The Co-KIT-6 mesoporous materials were characterized by X-ray diffraction, N₂ adsorption–desorption isotherms, scanning electron microscopy, transmission electron microscopy, Fourier transform infrared, and X-ray photoelectron spectroscopy. The physicochemical characterization results show that all of the samples have well-ordered cubic mesostructures and that the structural integrity is preserved for n_Si/n_Co ratios as high as 10. It was found that most of the cobalt ions exist as isolated framework species, but for Co-KIT-6 with an n_Si/n_Co ratio of 10, the presence of extra-framework species/small cobalt oxide clusters cannot be excluded. The ability of these catalysts was tested by examining the conversion of the reaction of methylcyclopentane with hydrogen at atmospheric pressure and temperatures between 200 and 450 °C. The catalytic results show that their catalytic activity increases significantly with increasing cobalt content. The active sites, tetrahedrally coordinated Co and isolated atomic Co sites, were responsible for the endocyclic CC bond rupture between substituted secondary–tertiary carbon atoms, whereas the small clusters serve as active sites for the successive CC bond rupture. The ring-opening selectivity can be improved by increasing the density of isolated cobalt atom sites at low reaction temperatures.     

Superparamagnetic iron oxide-enhanced MR imaging for early and late radiation-induced hepatic injuries

Superparamagnetic iron oxide (SPIO)-enhanced MRI was performed in twenty-one patients undergoing proton-beam radiotherapy for hepatocellular carcinomas. Patients were divided into two groups: early and late phase hepatic injuries. Each group was investigated 3 to 9 weeks and 4 to 65 months after the start of irradiation, respectively. T(1)-weighted, T(2)-weighted, and T(2)*-weighted images were obtained before and after SPIO administration. In all postcontrast sequences in the early phase, irradiated livers demonstrated relatively higher intensity than nonirradiated livers and the radiation-to-liver contrast-to-noise ratio (C/N) was improved. Postcontrast T(2)*-weighted images showed the highest C/N. In the late phase, the irradiated areas showed high intensity on T(2)-weighted images and low intensity on T(1)-weighted images without SPIO, while high intensity on T(1)-weighted images with SPIO. The C/N increased with SPIO in all sequences and postcontrast T(2)-weighted images showed the highest C/N in the late phase. SPIO-enhanced MRI is useful to evaluate this entity both in the early and late phase of clinical studies.