On the Patterson–Sullivan Measure for Geometrically Finite Groups Acting on Complex or Quaternionic Hyperbolic Space

The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry.     

Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes

Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear fluxes in such a way that the discrete operator inherits the key properties of the continuous one. Furthermore, it is well adapted to very general meshes including the case of nonconformal locally refined meshes. We show that the approximate solution exists and is unique, which is not obvious since the scheme is nonlinear. We prove that, for general W^?1,p′(Ω) source term and W^1‐(1/p),p(?Ω) boundary data, the approximate solution and its discrete gradient converge strongly towards the exact solution and its gradient, respectively, in appropriate Lebesgue spaces. Finally, error estimates are given in the case where the solution is assumed to be in W^2,p(Ω). Numerical examples are given, including those on locally refined meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Study of the spontaneous formation of organic layers on carbon and metal surfaces from diazonium salts

This study investigates the spontaneous grafting of different para-substituted phenyl groups on carbon and metallic surfaces from diazonium salts solutions. Glassy carbon, nickel, zinc and iron plates were allowed to react with an acetonitrile solution of aryldiazonium tetrafluoroborate salt by simple dipping. The surfaces were characterized before and after their immersion by XPS and AFM to evidence the formation of a coating on the different materials. The results are indicative of the presence of substituted phenyl groups on all the investigated surfaces. This study also aims at correlating grafting efficiency with metal reactivities and diazonium salt electronic properties by means of AFM and FT-IRRAS. For this purpose, zinc and nickel were chosen due to their opposite reducing properties and two diazonium salts were selected with electron-donor or -withdrawing para-substituents. The results tend to indicate that redox properties of both partners (diazonium + metal) are of prime importance for grafting to occur.     

Points rationnels sur les espaces homogenes et leurs compactifications

Let k be a perfect field and G an algebraic group defined over k. Let X be a homogeneous space of G. We show the following: if there exists a k-variety which is birational to X and which has a smooth k-rational point, then X also has a k-rational point (Theorem 5.7).     

An investigation of the role of the disparate redox states of the tetrathiafulvalene unit in modulating hydrogen bonding interactions in solution

We have investigated the electrochemically controlled hydrogen bonding interactions between tetrathiafulvalene host 3 and guests 4 or 5. Stabilisation of the 3⁺ state is dependent upon the nature of the guest species, whereas both guests prevent precipitation of the electrochemically generated 3²⁺ species at the working electrode via hydrogen bonded molecular recognition processes.     

Formal orthogonal polynomials revisited. Applications

From some results concerning the formal orthogonal polynomials, already proved in [5], we develop new properties of generalized adjacent polynomials which correspond to a change in the weight function. A new structure of the singular blocks is given. These results have a direct application to Lanczos methods, theG and -algorithms.     

Determination of thallium in natural waters by anodic stripping voltammetry

Thallium was determined in natural waters by anodic stripping voltammetry at a hanging mercury drop electrode, in acetate buffer pH 4.6+EDTA, after preconcentration and separation on an anion exhange resin. For Pacific Ocean surface waters a mean value of 13.0±1.4 ng Tl l^?1 was found, while for freshwater samples the value was 3.7±1.0 ng Tl l^?1. Thermodynamic considerations of thallium speciation predict that both in seawater and freshwater thallium exists primarily in the trivalent state. This was confirmed by experiment.     

Iron-catalyzed homo-coupling of simple and functionalized arylmagnesium reagents

Iron-catalyzed homo-coupling of simple and functionalized arylmagnesium reagents is described. The reaction is highly chemoselective (CN, COOEt and NO(2) groups are tolerated). The procedure was used to perform intramolecular couplings. This cyclization reaction is the key step of the total synthesis of the N-methylcrinasiadine.     

Cationic lanthanide complexes of neutral tripodal N,O ligands: enthalpy versus entropy-driven podate formation in water

The cationic lanthanide complexes of two neutral tripodal N,O ligands, tpa (tris[(2-pyridyl)methyl]amine) and tpaam (tris[6-((2-N,N-diethylcarbamoyl)pyridyl)methyl]amine) are studied in water. The analysis of the proton lanthanide induced NMR shifts indicate that there is no abrupt structural change in the middle of the rare-earth series. Unexpectedly, the formation constant values of the lanthanide podates of tpaam and tpa in D2O at 298 K are similar, suggesting that the addition of the three amide groups to the ligand tpa does not lead to any increase in stability of the lanthanide complexes of tpaam in respect to tpa, even though the amide groups are coordinated to the metal in aqueous solution. The measurement of the enthalpy and entropy changes of the complexation reactions shows that the two similar ligands tpa and tpaam have different driving forces for lanthanide complexation. Indeed, the formation of tpa podates benefits from an exothermic enthalpy change associated with a small entropy change, whereas the complexation reaction with tpaam is clearly entropy-driven though opposed by a positive enthalpy change. The hydration states of the europium complexes were measured by luminescence and show the coordination of 4-5 water ligands in [Eu(tpa)]3+ whereas there are only 2 in [Eu(tpaam)]3+. Therefore the heptadentate ligand tpaam releases the translational entropy of more water molecules than does the tetradentate ligand tpa.     

Pyridylmagnesiates: generation by bromine–metal exchange and enantioselective addition to aldehydes

Butyl and dibutylmagnesiates incorporating chiral ligands have been prepared and their reactivity studied. The reagents were efficient to promote the clean bromine–magnesium exchange of azinyl bromides at room temperature and subsequent reaction with aldehydes affording pyridylcarbinols. (R,R)-TADDOL-based dibutylmagnesiate was the best reagent leading to acceptable to good enantioselectivities, depending on the substrate and on the aldehyde substitution. This is the first example of enantioselective addition of in situ generated pyridylmagnesiate to carbonyl electrophiles.