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.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

Zur Bestimmung des St?rkegehaltes in der Gerste und in anderen Getreidearten

Ohne Zusammenfassung     

Complexation of Al(III) by 8-Hydroxyquinoline and Drastic Fluorescence Enhancement in Reverse Micelles

Complexation of Al^IIIby 8-hydroxyquinoline and fluorescence behavior of the quinolinate(s) were studied in reverse micellar systems at low water content, and compared to aqueous media. Two surfactants were used: one was cationic (CTAC: cetyltrimethylammonium chloride) and the other was anionic (AOT: sodium bis(2-ethylhexyl)sulfosuccinate). The results obtained in the CTAC/dichloromethane system (W= [H₂O]/[surfactant] = 0.9) showed that complexation occurred very likely in the oil phase and no micellar effect was observed. On the contrary, in the presence of AOT, specific micellar effects were observed due to the presence of the anionic polar heads: stabilization of the positively charged 1:1 and 1:2 chelates, at the expense of the neutral water-insoluble 1:3 chelate which is formed in aqueous solutions under similar conditions;drastic fluorescence enhancement factorsof 120 and 100 in AOT/heptane (W= 1.5) and AOT/dichloromethane (W= 1.6), respectively. Such factors have never been reported so far in either hydroorganic or direct micellar systems. In return, the length of time for the production of the complex(es) is increased because of the microheterogeneity of the medium and the small sizes of the water pools.     

Inclusion complexes of trivalent lutetium cations with an acidic derivative of per(3,6-anhydro)-alpha-cyclodextrin

The cyclodextrin derivative (hexakis (2-O-carboxymethyl-3,6-anhydro)-alpha-cyclodextrin) forms mono- and bimetallic complexes with lutetium(III) in aqueous solution; the X-ray structure of the binuclear complex [Lu2(ACX)(H2O)2] is the first example of a lanthanide-cyclodextrin inclusion complex.     

Glycoconjugate libraries accessed by multicomponent reactions

Glycobiology opens a wide field for new therapeutic approaches. However, the complexity and unavailability of various carbohydrate test compounds has excluded this class of natural products from modern screening systems. Alternatively, glycomimetics are considered to be more drug-like candidates for development. By means of multicomponent condensations (MCCs) utilizing suitable carbohydrate synthons, rapid and effective access to glycoconjugate libraries can be obtained. The flexibility of MCCs allows the assembly of diverse carbohydrate containing libraries. It may be assumed that MCCs containing carbohydrate moieties will play an important role in glycomimetic chemistry and biology.     

Synthesis and properties of water-soluble gold colloids covalently derivatized with neutral polymer monolayers

Citrate-capped gold nanoparticles as well as planar gold surfaces can be efficiently grafted with a covalently attached polymer monolayer a few nanometers thick, by simple contact of the metal surface with dilute aqueous solutions of hydrophilic polymers that are end-capped with disulfide moieties, as shown by UV/vis absorption, dynamic light scattering, and surface plasmon resonance studies. The hydrophilic polymer-coated gold colloids can be freeze-dried and stored as powders that can be subsequently dissolved to yield stable aqueous dispersions, even at very large concentrations. They allow for applying filtrations, gel permeation chromatography, or centrifugation. They do not suffer from undesirable nonspecific adsorption of proteins while allowing the diffusion of small species within the hydrogel surface coating. In addition, specific properties of the original hydrophilic polymers are retained such as a lower critical solution temperature. The latter feature could be useful to enhance optical responses of functionalized gold surfaces toward interaction with various substrates.     

Stereoselective Syntheses of Tetrahydroesterastin-β -Lactam Analogues

A total synthesis of the optically active tetrahydroesterastin β -lactam analogue 2 using Miller's hydroxamate approach is described (Scheme 2). Significant modification of published procedures has resulted in a short and facile stereospecific preparation of the N-[(benzyloxycarbonyl)methyl]-β -lactam 17 starting from the readily available D -serine. This material served as intermediate for the preparation of a variety of N-[(benzyloxycarbonyl)methyl]tetrahydroesterastin β-lactam analogues (Scheme 5).     

Electronic relaxation of paramagnetic metal ions and NMR relaxivity in solution: critical analysis of various approaches and application to a Gd(III)-based contrast agent

The time correlation functions (TCFs) G(alphaalpha(t)[triple bond](Salpha(t)Salpha(0)) (alpha = x,y,z) of the electronic spin components of a complexed paramagnetic metal ion give information about the time fluctuations of its zero-field splitting (ZFS) Hamiltonian due to the random dynamics of the coordination polyhedron. These TCFs reflect the electronic spin relaxation which plays an essential role in the inner- and outer-sphere paramagnetic relaxation enhancements of the various nuclear spins in solution. When a static ZFS Hamiltonian is allowed by symmetry, its modulation by the random rotational motion of the complex has a great influence on the TCFs. We discuss several attempts to describe this mechanism and show that subtle mathematical pitfalls should be avoided in order to obtain a theoretical framework, within which reliable adjustable parameters can be fitted through the interpretation of nuclear-magnetic relaxation dispersion experimental results. We underline the advantage of the numerical simulation of the TCFs, which avoids the above difficulties and allows one to include the effect of the transient ZFS for all the relative magnitudes of the various terms in the electron-spin Hamiltonian and arbitrary correlation times. This method is applied for various values of the magnetic field taken to be along the z direction. At low field, contrary to previous theoretical expectations, if the transient ZFS has negligible influence, the longitudinal TCF GII(t) [triple bond] G(zz)(t) has a monoexponential decay with an electronic relaxation time T1e different from 1/(2D(r)), D(r) being the rotational diffusion coefficient of the complex. At intermediate and high field, the simulation results show that GII (t) still has a monoexponential decay with a characteristic time T1e, which is surprisingly well approximated by a simple analytical expression derived from the Redfield perturbation approximation of the time-independent Zeeman Hamiltonian, even in the case of a strong ZFS where this approximation is expected to fail. These results are illustrated for spins S = 1, 3/2, and 5/2 in axial and rhombic symmetries. Finally, the simulation method is applied to the reinterpretation of the water-proton relaxivity profile due to P760-Gd(III), an efficient blood pool contrast agent for magnetic-resonance imaging.