Comportement asymptotique des solutions d'un système elliptique conservatif non linéaire

Let M be a compact riemannian manifold; in a previous article we show that every non- negative solution of u_tt + Δ_g u=f(u) on M ×R ⁺, satisfying Dirichlet or Neumann boundary conditions, converges to a (stationary) solution Φ of Δ_g Φ=f(Φ) with exponential decay of ∥u - Φ∥c²(M), if we assume that f behaves like r? r^p - λr. We extend this result to a system in the following form $$\left\{ {\begin{array}{*{20}c} {u_{tt} + \Delta _g u + \alpha u - G_x (u,\upsilon ) = 0,} \\ {u_{tt} + \Delta _g \upsilon + \beta \upsilon - G_x (u,\upsilon ) = 0,} \\ \end{array} } \right.$$ . where G satisfies some growth and convexity properties.     

Theoretical and electrochemical studies on organometallic symmetrical schiff base complexes of Zn(II), Cu(II), Ni(II) and Co(II)

The electronic communication between two redox centres through a Schiff base complex has been investigated in a series of ethylenediimine-bis(1-ferrocenyl-1,3-butanedionate) complexes of Zn(II) 1, Cu(II) 2, Ni(II) 3 and Co(II) 4. Cyclic voltammetry experiments of 1 and 2 exhibit a unique two-electron reversible oxidation wave, whereas in the case of 3 and 4 two and three one-electron oxidation processes are, respectively, observed. These results suggest some electronic interaction between the iron atoms of the ferrocenyl groups. DFT calculations carried out on model complexes show that for all the studied compounds the removal of the first two electrons corresponds to the oxidation processes of the iron centres in the weakly coupled ferrocenyl termini. The electronic communication between the two iron centres increases on going from 1 to 4. Finally, a re-indexation of the bands observed in the UV-Visible spectra has been carried out using TDDFT calculations.     

On the Zero-Temperature Limit of Gibbs States

We exhibit Lipschitz (and hence Hölder) potentials on the full shift ${\{0,1\}^{\mathbb{N}}}We exhibit Lipschitz (and hence H?lder) potentials on the full shift {0,1}^\mathbbN{\{0,1\}^{\mathbb{N}}} such that the associated Gibbs measures fail to converge as the temperature goes to zero. Thus there are “exponentially decaying” interactions on the configuration space {0,1}^{\mathbb Z}{\{0,1\}^{\mathbb Z}} for which the zero-temperature limit of the associated Gibbs measures does not exist. In higher dimension, namely on the configuration space {0,1}^\mathbbZd{\{0,1\}^{\mathbb{Z}^{d}}}, d ≥ 3, we show that this non-convergence behavior can occur for the equilibrium states of finite-range interactions, that is, for locally constant potentials.     

A Tetrairon Dication Featuring Tetraethynylbenzene Bridging Ligand: A Molecular Prototype of Quantum Dot Cellular Automata

The unprecedented tetrairon dication [{Cp*(dppe)FeC≡C-}₄-μ-(1,2,4,5-C₆H₂)](PF₆)₂ ( 1 ) was obtained through a sequence of three reactions from 1,2,4,5-tetraethynylbenzene, Cp*(dppe)FeCl (Cp*=C₅Me₅, dppe=1,2-bis(diphenylphosphino)-ethane), KOtBu, and ferrocenium hexafluorophosphate. The cyclic voltammogram of the target molecule, isolated in 77 % yield, exhibits four well separated and reversible redox events showing that 1 is thermodynamically stable with respect to disproportionation (Kc>10⁶). The tetranuclear dication 1 was characterized by XRD on single crystal, IR and NMR spectroscopies and Mössbauer spectrometry. The experimental data show that 1 behaves as a class II mixed-valence complex with the positive charges preferentially disposed on antipodal positions. This new molecule can be regarded as a potential molecular prototype of quantum dot cellular automata.     

Assembly of the c19-c29 aliphatic segment of rifamycin s from d-glucose by the chiron approach

We describe a stereocontrolled method for the construction of the aliphatic chain of rifamycin S, based on a strategy that utilizes carbohydrates as optically active precursors.     

Novel tert-butyl-tris(3-hydrocarbylpyrazol-1-yl)borate ligands: synthesis, spectroscopic studies, and coordination chemistry

The lithium (1) and thallium (2) salts of five new tert-butyl-tris(3-hydrocarbylpyrazol-1-yl)borate ligands [t-BuTp(R)]- (R = H, a; Me, b; i-Pr, c; t-Bu, d; Ph, e) have been synthesized and characterized. Because of steric congestion at B, the reaction between t-BuBH3Li x 0.5 Et2O and excess 2,5-dimethylpyrazole Hpz(Me2) afforded the bis-pz(Me2) derivative, Tl[t-BuBH(3,5-Me2pz)2] (3) after metathesis with TlNO3. The compounds were characterized by elemental analysis and NMR spectroscopy. The Li salts 1a and 1c exhibit fluxional behavior on the NMR time scale in solution at room temperature. The solid-state 7Li and 11B NMR spectra of 1c suggest that this salt exists as a mixture of axial and equatorial isomers. The partial hydrolysis of 1d afforded the dimeric Li complex {Li[t-BuB(pz(t-Bu))2(mu-OH)]}2 (4). The crystal structure of 4 shows two Li cations encapsulated by the heteroscorpionate [t-BuB(OH)(3-t-Bupz)2]- ligands. A salt elimination reaction between FeCl2(THF)1.5 and 2 equiv of Li[t-BuTp(R)] (R = H, Me) followed by an in situ one-electron oxidation produced good yields of the homoleptic, paramagnetic low-spin iron(III) complexes [Fe(t-BuTp)2]PF6 (5) and [Fe(t-BuTp(Me))2]PF6 (6) that were characterized by elemental analyses, magnetic susceptibility measurements in solution and the solid phase, 1H NMR, high-resolution mass spectrometry, M?ssbauer spectroscopy, and single-crystal X-ray diffraction. The crystals are composed of discrete molecular units with the central Fe(III) ion in an almost perfectly octahedral coordination to six nitrogen atoms. Compound 5 has the shortest Fe-N bond lengths ever reported for [Fe(RTp(R)')2]+-type compounds.     

A synthesis of the marine antibiotic (-)-malyngolide from D-glucose

(-)_Malyngolide, an antibiotic from the marine blue-green alga Lyngbya majuscula, was synthesized in about 30% yield from ethyl 4,6-0-benzylidene-2-deoxy-α-D-erythro-hexopyranosid-3-ulose, a chiral synthon easily derived from commercially available methyl α-D-glucopyranoside.     

Tilings of the plane and Thurston semi-norm

We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional simplex. This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact \(3\) -manifolds.     

(5S)-Hydroxymethyl-δ-Valerolactone: A Useful Intermediate for Leucotrienes B Synthesis

Abstract

LTB₄ 11, a member of the arachidonic acid cascade has been identified by Borgeat and Samuelsson¹. LTB₄ is a potent chemotactic factor and it is now considered as the chemical mediator implicated in inflammatory processes.