Negatively Charged Metallacarborane Redox Couples with Both Members Stable to Air

The metallacarborane [3,3′‐Co(1,2‐closo‐C₂B₉H₁₁)₂]^? has been synthesized. This species allows the formation of redox couples in which both partners are negatively charged. The E_1/2 potential can be tuned by adjusting the nature and number of substituents on B and C. The octaiodinated species [3,3′‐Co(1,2‐closo‐C₂B₉H₇I₄)₂]^? is the most favorable, as it is isolatable and stable in air. A DFT study on stability and redox potentials of complexes has been performed.     

The Determination of Protonation Constants of Some Amino Acids and Their Esters by Potentiometry in Different Media

In this study, stoichiometric protonation constants of L-tyrosine, L-cysteine, L-tryptophane, L-lysine, and L-histidine, and their methyl and ethyl esters in water and ethanol–water mixtures of 30, 50, and 70% ethanol (v/v), were determined potentiometrically using a combined pH electrode system calibrated as the concentration of hydrogen ion. Titrations were performed at 25^∘C and the ionic strength of the medium was maintained at 0.10 mol⋅L⁻¹ using sodium chloride. Protonation constants were calculated by using the BEST computer program. The effect of solvent composition on the protonation constants is discussed. The log₁₀ K₂ values of esters generally decreased with increasing ethanol content. However, the log₁₀ K₁ values of the esters of L-tyrosine, L-cysteine, and L-tryptophane were found to increase with increasing ethanol content in contrast those of L-lysine and L-histidine esters.     

Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Vector potential theory on nonsmooth domains in R<Superscript>3</Superscript> and applications to electromagnetic scattering

We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for L^p-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.     

Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.     

Organocatalysis: quantum chemical modeling of nucleophilic addition to α,β‐unsaturated carbonyl compounds

One of the successful transformations within the field of organocatalysis, the organocatalytic asymmetric addition of nitromethane to α,β‐unsaturated aldehydes and ketones, has been studied by quantum chemical modeling. The level of accuracy of the hybrid density functional theory method B3LYP/6‐31G(d) was compared to a high level ab initio benchmark for this reaction. It is concluded that B3LYP/6‐31G(d) performs very well for this reaction type, giving good estimates of critical energies. The reaction between acrolein and nitromethane was studied in detail. The reaction mechanism revealed an intermediate oxazolidin structure, which is currently unknown. Alkyl substitution in various positions on the amine catalyst or α,β‐unsaturated carbonyl compound influences the reactivity in a predictive fashion. The iminium ion, prop‐2‐en‐iminium, is less activated towards nucleophilic attack compared to protonated acrolein. Copyright © 2007 John Wiley & Sons, Ltd.     

Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.