Magnetic-Field-Dependent Electronic Relaxation of Gd3+ in Aqueous Solutions of the Complexes [Gd(H2O)8]3+, [Gd(propane-1,3-diamine-N,N,N′,N′-tetraacetate)(H2O)2]−, and [Gd(N,N′-bis[(N-methylcarbamoyl)methyl]-3-azapentane-1,5-diamine-3,N,N′-triacetate)(H2O)] of interest in magnetic-resonance imaging

EPR Spectra have been measured for aqueous solutions of a series of Gd³⁺ complexes at variable temperature and a range of magnetic fields; S-band (0.14 T), X-band (0.34 T), Q-band (1.2 T), and 2-mm-band (5.0 T). The major contribution to the observed line widths is magnetic-field-dependent and is interpreted as being due to the modulation of the zero-field splitting produced by distortion of the complexes from perfect symmetry. The transverse and longitudinal relaxation matrices for an ⁸S ion with such an interaction have been calculated using Redfield theory with vector-coupling methods, and diagonalised numerically to obtain relaxation rates and intensities for the degenerate transitions which contribute to the multiplet. The observed line width, which is inversely proportional to the magnetic field at low temperatures, is best described by the intensity-weighted mean transverse relaxation time for the four transitions with non-zero intensity. A least-squares fit of the data yields the square of the zero-field splitting tensor, Δ², and a correlation time, τ_v, with activation energy, E_v. The physical significance of these parameters and the extent of validity of the theoretical approach are considered. The parameters are used to predict the magnetic-field dependence of the longitudinal and transverse electronic relaxation times, which are discussed in the context of their relevance to ¹H-NMR relaxivity.     

Mesures de Monge-Ampère et mesures pluriharmoniques

Sans résumé     

K-Dependence and temperature dependence of N2-, H2-, and He-broadening coefficients for the J = 12-11 transition of acetonitrile CH3CN located near 220.7 GHz

Extensive experiments on the K = 3 component of the J = 12-11 rotational transition of acetonitrile CH₃C¹⁴N, located near 220.7 GHz, were performed at different temperatures in the range 235-350 K. They allow determining the N₂-, H₂-, and He-broadening coefficients, as well as their temperature dependences. More specific measurements on all the K-components of the involved transition perturbed by N₂ at 303 K allow to point out a clear decreasing of the broadening coefficient with increasing K. Narrowing effects are clearly observed, and experimental lines were analysed both with Voigt and speed dependent Voigt profiles; but no exhaustive lineshape study was carried out. All the experimental parameters are compared with results derived from a semiclassical calculation of collisional interactions, including electrostatic, induction, and dispersion energy contributions.     

Remarks on global approximate controllability for the 2-D Navier–Stokes system with Dirichlet boundary conditions

This Note deals with the two-dimensional Navier–Stokes system. In this context, we prove a result concerning its global approximate controllability by means of boundary controls. To cite this article: S. Guerrero et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Algebraically flat or projective algebras

We define and study algebraically flat algebras in order to have a better understanding of algebraically projective algebras of finite type (the projective algebras of literature). A close examination of the differential properties of these algebras leads to our main structure theorem. As a corollary, we get that an algebraically projective algebra of finite type over a field is either a polynomial ring or the affine algebra of a complete intersection.     

RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

Transition-metal-templated synthesis of rotaxanes and catenanes: From small molecules to polymers

This article provides an overview of the fundamental principles of the synthesis of metallocatenanes and metallorotaxanes. It also describes the synthesis and properties of electronic conducting polymers—polypyrrole and polythiophene—built around metallocatenanes and metallorotaxanes. The particular properties of this new class of polymers, including the possibility of transmetallation reactions being performed with them and the observation of electronic coupling between the metal centers and the conducting matrix, are discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3470–3477, 2003