Selective conversion of {Mo132} Keplerate ion into 4-electron reduced crown-capped Keggin derivative [Te5Mo15O57](8-). A key intermediate to single-phase M1 multielement MoVTeO light-alkanes oxidation catalyst

{Mo(132)} Keplerate anion reacts with tellurites to give a soluble precursor to produce in hydrothermal conditions single-phase M1 MoVTeO light-alkanes oxidation catalyst. Characterization of this Te-containing intermediate by single-crystal X-ray diffraction, (125)Te NMR, UV-visible and redox titration reveals a molybdotellurite anion as a crown-capped Keggin derivative.     

Rotation Numbers of Discontinuous Orientation-Preserving Circle Maps

We extend a few well-known results about orientation preserving homeomorphisms of the circle to orientation preserving circle maps, allowing even an infinite number of discontinuities. We define a set-valued map associated to the lift by filling the gaps in the graph, that shares many properties with continuous functions. Using elementary set-valued analysis, we prove existence and uniqueness of the rotation number, periodic limit orbit in the case when the latter is rational, and Cantor structure of the unique limit set when the rotation number is irrational. Moreover, the rotation number is found to be continuous with respect to the set-valued extension if we endow the space of such maps with the Haussdorff topology on the graph. For increasing continuous families of such maps, the set of parameter values where the rotation number is irrational is a Cantor set (up to a countable number of points).     

Convergence of the wave equation damped on the interior to the one damped on the boundary

In this paper, we study the convergence of the wave equation with variable internal damping term γn(x)ut to the wave equation with boundary damping γ(x)⊗δx∈∂Ωut when (γn(x)) converges to γ(x)⊗δx∈∂Ω in the sense of distributions. When the domain Ω in which these equations are defined is an interval in R, we show that, under natural hypotheses, the compact global attractor of the wave equation damped on the interior converges in X=H¹(Ω)×L²(Ω) to the one of the wave equation damped on the boundary, and that the dynamics on these attractors are equivalent. We also prove, in the higher-dimensional case, that the attractors are lower-semicontinuous in X and upper-semicontinuous in H1−ε(Ω)×H−ε(Ω).     

Micellar Solubilization of Proteins in Aprotic Solvents and their Spectroscopic Characterisation

The quaternary ammonium salt methyl-trioctylammonium chloride enables the transfer of α-chymotrypsin, trypsin, pepsin and glucagone from water to cyclohexane. Reversed micelles, whose polar core solubilizes both protein and water, are probably formed in the apolar phase. The influence of various parameters on the phase transfer (concentration, pH, solvent, temperature, etc.) has been investigated. Absorption, fluorescence and circular dichroism studies of the biopolymers in the cyclohexane system have been carried out. For trypsin and chymotrypsin, the CD. signal in the 200 nm region is very similar in water and in cyclohexane, which suggests that the polypeptide folding is not substantially different in the two phases. The fluorescence quantum yield is always much larger in the cyclohexane phase than in water. The longer wavelength region of the UV. absorption spectrum is slightly red-shifted relative to water, and a band at 225 nm, probably arising from the aromatic chromophore, is apparent in the organic phase. Reasons for these spectral perturbations are discussed. The enzymes transferred from water into cyclohexane phases can be continuously retransferred into a second water phase. The possible relevance of this ‘double transfer’ as a model for the vectorial transport of biopolymers or a separation technique is discussed.     

Relation between the Grüneisen ratio and the pressure dependence of Poisson's ratio for metals

The Grüneisen ratio of crystalline solids is shown to be dependent on a parameter n whose values are characteristic of each solid, and can be determined by two independent ways: from experimental shock data and from the pressure derivative of Poisson's ratio. The determinations are made for several metals, using data on the pressure derivatives of polycrystalline elastic moduli or of the second order elastic constants measured on single crystals, and giving the pressure derivatives of Poisson's ratio by means of the Voigt-Reuss-Hill averaging procedure. The values of the parameter n deduced from shock data are found to be in good agreement with those deduced from the pressure derivatives of Poisson's ratio. Positive and negative values of parameter n correspond respectively to increasing and decreasing Poisson's ratio with increasing pressure. Discussion of the results is made using the linear and the quadratic relationships between shock velocity and particle velocity. It is shown that shock wave data cannot yield directly an accurate estimation of the derivative of the initial slope of the Hugoniot.     

Laminar currents in ℙ<Superscript>2</Superscript>

 In this paper we study laminar currents in ℙ². Given a sequence of irreducible algebraic curves (C _n ) converging in the sense of currents to T, we find geometric conditions on the curves ensuring that the limit current T is laminar. This criterion is then applied to meromorphic dynamical systems in ℙ², and laminarity of the dynamical ``Green' current is obtained for a wide class of meromorphic self maps of ℙ², as well as for all bimeromorphic maps of projective surfaces. Received: 24 September 2001 / Published online: 10 February 2003 Mathematics Subject Classification (2000): 32U40, 37Fxx, 32H50     

On the dynamics near infinity of some polynomial mappings in

We construct the Green current for a random iteration of horizontal-like mappings in . This is applied to the study of a polynomial map with the following properties: i. infinity is f-attracting; ii. f contracts the line at infinity to a point not in the indeterminacy set. We study for such mappings the escape rates near infinity, i.e. the set of possible values of the function We show in particular that the set of possible values can contain an interval. On the other hand the Green current T of f can be decomposed into pieces associated to an itinerary defined by the indeterminacy points. This allows us to prove that exists ||T||-a.e. and we give its value in terms of explicit quantities depending on f.     

Orienting the Demixion of a Diblock‐copolymer Using 193 nm Interferometric Lithography for the Controlled Deposition of Nanoparticles

DUV interferometric lithography and diblock copolymer self‐organization have successfully been combined to provide a simple and highly collective nanopatterning technique enabling the organization of nanoparticles over several orders of magnitude, from nanometre to millimetre. The nanostructural changes at the surface of the polymer film after thermal annealing have been monitored by AFM and the process parameters optimized for obtaining a long‐range organization of the lamellar domains. In particular, the impact of the annealing conditions and geometric parameters of the substrate patterns have been investigated. The nanopatterns resulting from the lamellar demixion of (PS‐b‐MMA) were used for a controlled deposition of nanoparticles. The affinity of the hydrophobic particles for the PS block was demonstrated, opening new doors towards the preparation of high‐density arrays of nanoparticles with potential applications in data storage.

     

Tetranuclear polybipyridyl complexes of Ru(II) and Mn(II), their electro- and photo-induced transformation into di-mu-oxo Mn(III)Mn(IV) hexanuclear complexes

Three heterotetranuclear complexes, [{Ru(II)(bpy)(2)(L(n))}(3)Mn(II)](8+) (bpy = 2,2'-bipyridine, n = 2, 4, 6), in which a Mn(II)-tris-bipyridine-like centre is covalently linked to three Ru(II)-tris-bipyridine-like moieties using bridging bis-bipyridine L(n) ligands, have been synthesised and characterised. The electrochemical, photophysical and photochemical properties of these complexes have been investigated in CH(3)CN. The cyclic voltammograms of the three complexes exhibit two successive very close one-electron metal-centred oxidation processes in the positive potential region. The first, which is irreversible, corresponds to the Mn(II)/Mn(III) redox system (E(pa) approximately 0.82 V vs Ag/Ag(+) 0.01 M in CH(3)CN-0.1 M Bu(4)NClO(4)), whereas the second which is, reversible, is associated with the Ru(II)/Ru(III) redox couple (E(1/2) approximately 0.91 V). In the negative potential region, three successive reversible four electron systems are observed, corresponding to ligand-based reduction processes. The three stable dimeric oxidized forms of the complexes, [Mn(2)(III,IV)O(2){Ru(II)(bpy)(2)(L(n))}(4)](11+), [Mn(2)(IV,IV)O(2){Ru(II)(bpy)(2)(L(n))}(4)](12+) and [Mn(2)(IV,IV)O(2){Ru(III)(bpy)(2)(L(n))}(4)](16+) are obtained in fairly good yields by sequential electrolyses after consumption of respectively 1.5, 0.5 and 3 electrons per molecule of initial tetranuclear complexes. The formation of the di-micro-oxo binuclear complexes are the result of the instability of the {[Ru(II)(bpy)(2)(L(n))](3)Mn(III)}(9+) species, which react with residual water, via a disproportionation reaction and the release of one ligand, [Ru(II)(bpy)(2)(L(n))](2+). A quantitative yield can be obtained for these reactions if the electrochemical oxidations are performed in the presence of an added external base like 2,6-dimethylpyridine. Photophysical properties of these compounds have been investigated showing that the luminescence of the Ru(II)-tris-bipyridine-like moieties is little affected by the presence of manganese within the tetranuclear complexes. A slight quenching of the excited states of the ruthenium moieties, which occurs by an intramolecular process, has been observed. Measurements made at low concentration (<1 x 10(-5) M) indicate that some decoordination of Mn(2+) arises in 1a-c. These measurements allow the calculation of the association constants for these complexes. Finally, photoinduced oxidation of the tetranuclear complexes has been performed by continuous photolysis experiments in the presence of a large excess of a diazonium salt, acting as a sacrificial oxidant. The three successive oxidation processes, Mn(II)--> Mn(III)Mn(IV), Mn(III)Mn(IV)--> Mn(IV)Mn(IV) and Ru(II)--> Ru(III) are thus obtained, the addition of 2,6-dimethylpyridine in the medium giving an essentially quantitative yield for the two first photo-induced oxidation steps as found for electrochemical oxidation.