Invariant projections and convolution operators

We prove the existence of invariant projections from the Banach space of -pseudomeasures onto with for closed neutral subgroup of a locally compact group . As a main application we obtain that every closed neutral subgroup is a set of -synthesis in and in fact locally -Ditkin in . We also obtain an extension theorem concerning the Fourier algebra.

     

Synthesis,structure and magnetism of homologous series of polycrystalline cobalt alkane mono- and dicarboxylate soaps

Carboxylate-bridged chain complexes of Co(II) (the diaquacobalt(II) mono- and ,-dialkanoates) form two homologous series of layered compounds which have been fully characterised both structurally and magnetically. The crystal structures of two selected members, [Co[CH3(CH2)10COO]2(H2O)2] and [Co[CH3(CH2)18COO]2(H2O)2], have been solved by X-ray powder diffraction and selected-area electron diffraction methods, and refined by the Rietveld technique. Crystal data: monoclinic, P 2(1)/a; a=9.688(1), b=7.5495(9), c=37.281(5) A, =96.70(3) primary, Z=4; and monoclinic, P 2(1)/a; a=9.7260(7), b=7.5477(7), c=57.53(1) A, =94.66(4) primary, Z=4, respectively. Their isomorphous structures contain layers of octahedral diaquacobalt(II) ions bonded to two chemically inequivalent alkanoates, one chelating and one bridging two Co atoms about 6.3 A apart, thus confirming the rare anti-anti conformation mode of the -RCOO groups recently proposed for diaquacobalt(II) ,-dodecanedioate. Extensive magnetic characterisation allowed estimation of the feeble antiferromagnetic coupling, which is weaker in the mono- than in the dialkanoate series.     

Controlling the work function of indium tin oxide: differentiating dipolar from local surface effects

Indium tin oxide (ITO) reacts with tetra(tert-butoxy)tin to give surface bound alkoxytin species. Ligand exchange occurs in these surface bound species by reaction with substituted phenols. The speciation of surface phenoxides was measured in ultrahigh vacuum by X-ray photoelectron spectroscopy, as was the work function for the surface modified ITO. It is shown that the molecular dipole moment of the phenol correlates strongly with the measured ITO work function change; no such correlation exists between the acidity of the phenol and this measured change in work function. Results are consistent therefore with an electrostatic model and not with one involving electronegativities of the ligated phenoxide oxygens.     

The Generalized Multifractional Field: A Nice Tool for the Study of the Generalized Multifractional Brownian Motion

The Generalized Multifractional Brownian Motion (GMBM) is a continuous Gaussian process {X(t)}_{t ? [0,1]}\{X(t)\}_{t\in [0,1]} that extends the classical Fractional Brownian Motion (FBM) and the Multifractional Brownian Motion (MBM) [15, 4, 1, 1]. Its main interest is that, its Hölder regularity can change widely from point to point. In this article we introduce the Generalized Multifractional Field (GMF), a continuous Gaussian field {Y(x,y)}_{(x,y) ? [0,1] ²}\{Y(x,y)\}_{(x,y)\in [0,1]^{\,2}} that satisfies for every tt, X(t)=Y(t,t)X(t)=Y(t,t). Then, we give a wavelet decomposition of YY and using this nice decomposition, we show that YY is b\beta-Hölder in yy, uniformly in xx. Generally speaking this result seems to be quite important for the study of the GMBM. In this article, it will allow us to determine, without any restriction, its pointwise, almost sure, Hölder exponent and to prove that two GMBM's with the same Hölder regularity differ by a "smoother' process.     

The screened polarons

We present a theory of polarons incorporating the screening of the Coulomb interaction, and we apply this theory to the case of anisotropic ionic crystals as the perovskites. We show that the “screened polarons" cannot be treated individually: all the polarons present in the material are coupled via the screening. We also show that, in the frame of this theory of large-scale polarons, the bipolarons are excluded and replaced by pairs of polarons; we propose to associate the pseudogap experimentally observed in perovskites with the binding energy of these pairs. Finally we suggest that the existence of the polarons pairs poses in new terms the problem of a polaronic theory of superconductivity. Received 9 December 1998 and Received in final form 2 March 2000     

Le théorème ergodique pour les opérateurs positifs sur les espaces Lp (1<p<∞) revisitéErgodic theorem for positive operators on Lp-spaces Lp (1<p<∞) revisited

We consider positive linear operators on L_p-spaces (1<p<∞), (A(L_p⁺)?L_p⁺), satisfying the inequality A^m+n<A^m+Aⁿ for all $\text{m,n∈}\text{N}\text{.}$ We describe the structure of these operators (Theorem 1). As a consequence we obtain for all f∈L^p,Aⁿf converges a.e. The last statement contains the theorem of a.e. convergence of Cesaro averages for positive mean bounded operators. To cite this article: A. Brunel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 205–207.     

Stability of divalent europium in an ionic liquid: spectroscopic investigations in 1-methyl-3-butylimidazolium hexafluorophosphate

In this work, devoted to 1-methyl-3-butylimidazolium hexafluorophosphate ionic liquid (BumimPF(6)), the importance of the purity of the solvent for spectroscopic investigations is highlighted. Results from small angle X-ray scattering indicate that the pure solvent exhibits a local organization. Europium(II), which appears to be unusually stable in BumimPF(6), is characterized by spectroscopic techniques (absorption, luminescence). Solvation of Eu(II) in BumimPF(6) and complexation effects in the presence of the crown ether 15C5 solubilized in the ionic liquid are discussed.     

Determination of critical micelle concentration of surfactants using a near-infrared hydrophobicity probe

A near-infrared (NIR) dye has been used for the determination of critical micelle concentrations (CMC) of surfactants. This NIR dye displays significant changes in its absorption spectra dependent on the hydrophobicity of the microenvironment around the dye molecule. The absorption spectra of this NIR dye show two distinct maxima which can be used in determining hydrophobicity. The NIR hydrophobicity probe detects the changes in the microenvironment hydrophobicity accompanying micelle formation. The determined CMC values are in good agreement with values obtained using other techniques. The major advantage of this NIR method lies in the inherently low interference of the NIR spectral region.     

Action du N-bromosuccinimide sur les dioxolannes. Intermediaires réactionnels

1,3-Dioxolan-2-ylium ion intermediates formed by reaction of bromine or NBS on 4-syn-aryl-3,5-dioxa-tricyclo [5.2.1.0^2.6] décanes have been isolated. 2-Succinimido-1,3-dioxolanes have been prepared for the first time.