Representing products of manifolds by edge-coloured graphs: the boundary case

In this paper we generalize the construction - introduced by Gagliardi and Grasselli in the closed case - of a coloured-graph representing the product of two manifolds, starting by two coloured graphs representing the manifolds themselves, to the boundary case. In particular we study the genus of the graph product of low dimensional manifold ( resp. n-spheres ) with m-disks. Received September 28, 1998; in final form January 5, 2000 / Published online October 11, 2000     

Nombres de Tamagawa des groupes réductifs quasi-connexes

We define Tamagawa numbers for quasi-connected linear algebraic groups. This category of non-connected linear algebraic groups occurs naturally in the stabilization of the Arthur-Selberg trace formula. An expression for their Tamagawa numbers, needed for the stabilization process, is given in term of cohomological invariants generalizing results of Ono, Sansuc, Kottwitz and Kottwitz & Shestad. Received: 7 March 2000     

Phase transition of the principal Dirichlet eigenvalue in a scaled Poissonian potential

We consider d-dimensional Brownian motion in a scaled Poissonian potential and the principal Dirichlet eigenvalue (ground state energy) of the corresponding Schr?dinger operator. The scaling is chosen to be of critical order, i.e. it is determined by the typical size of large holes in the Poissonian cloud. We prove existence of a phase transition in dimensions d≥ 4: There exists a critical scaling constant for the potential. Below this constant the scaled infinite volume limit of the corresponding principal Dirichlet eigenvalue is linear in the scale. On the other hand, for large values of the scaling constant this limit is strictly smaller than the linear bound. For d > 4 we prove that this phase transition does not take place on that scale. Further we show that the analogous picture holds true for the partition sum of the underlying motion process. Received: 10 December 1999 / Revised version: 14 July 2000/?Published online: 15 February 2001     

Approximation inL 2 Sobolev spaces on the 2-sphere by quasi-interpolation

In this article we consider a simple method of radial quasi-interpolation by polynomials on the unit sphere in ℝ³, and present rates of covergence for this method in Sobolev spaces of square integrable functions. We write the discrete Fourier series as a quasi-interpolant and hence obtain convergence rates, in the aforementioned Sobolev spaces, for the discrete Fourier projection. We also discuss some typical practical examples used in the context of spherical wavelets.     

A version of the Jensen–Johnsbråten coding at arbitrary level n≥ 3

We generalize, on higher projective levels, a construction of “incompatible” generic Δ¹ ₃ real singletons given by Jensen and Johnsbr?ten. Received: 3 November 1998 / Revised version: 23 April 2000 / Published online: 3 October 2001     

On the convergence of finite difference schemes for the heat equation with concentrated capacity

Summary. We investigate the convergence of difference schemes for the one-dimensional heat equation when the coefficient at the time derivative (heat capacity) is represents the magnitude of the heat capacity concentrated at the point . An abstract operator method is developed for analyzing this equation. Estimates for the rate of convergence in special discrete energetic Sobolev's norms, compatible with the smoothness of the solution are obtained. Received November 2, 1999 / Revised version received July 24, 2000 / Published online May 4, 2001     

Theory of oxidation/reduction-induced valence transformations of metal ion dopants in oxide crystals mediated by oxide-vacancy diffusion: I. Thermodynamic analysis

We consider theoretically valence transformations of doping metal ions in oxide crystals induced by oxidation and reduction obtained by changes in the ambient oxygen partial pressure. Three types of oxygen vacancies are assumed to mediate transformations: neutral, singly ionized, and doubly ionized. We provide thermodynamic equilibrium analyses, yielding concentration relations among the oxygen vacancy, metal ions, holes and electrons as functions of the ambient oxygen pressure. The results suggest that experimental study of different species concentrations at thermodynamic equilibrium as functions of pressure and temperature should allow assessment of various reversible reaction constants controlling the process. In the Part II companion paper, the kinetic (diffusion) characteristics are considered in detail.     

Facile in situ hydrothermal synthesis of BiVO4/MWCNT nanocomposites as high performance visible-light driven photocatalysts

Visible-light responsive monoclinic BiVO₄/MWCNT nanocomposites were facilely prepared via an in situ hydrothermal method by using sodium dodecyl sulfonate (SDS) as a guiding surfactant. The as-prepared BiVO₄/MWCNT nanocomposites were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), Raman spectroscopy, field emission scanning electron microscopy (FE-SEM), the Fourier transform infrared spectroscopy (FTIR) and UV–vis diffuse reflectance spectroscopy. The results showed that the hydrothermal temperature and adding SDS had significant influence on the morphology and size of BiVO₄. The photocatalytic activities of BiVO₄/MWCNT nanocomposites were investigated by degrading methylene blue (MB) under visible-light irradiation. Remarkable enhancement in photodecomposition of MB was observed with BiVO₄/MWCNT composite compared with bare BiVO₄ particles. This improvement of photocatalytic was attributed to the effective charge transfer from BiVO₄ nanocrystals to MWCNT, which promoted the migration efficiency of photogenerated electron–hole. Furthermore, a possible mechanism for the photocatalytic oxidative degradation was also discussed.     

Europium-doped nanocrystalline Y2O3−La2O3 solid solutions with bixbyite structure

Nanocrystals of Y₂O₃ and La₂O₃ solid solutions were synthesized with a cubic bixbyite structure containing La₂O₃ content of up to 50 mol%. This is comparatively higher than that in bulk materials of the same structure, where La₂O₃ content of only 20 mol% can be obtained. A set of europium-doped (Y_1−xLa_x)₂O₃ (x=0.1, 0.2, 0.3, 0.4) cubic bixbyite solid solutions with crystallites of approximately 10 nm in size was prepared using the polymer complex solution method. Structural analysis was performed using X-ray diffraction measurements, Rietveld full profile refinement, and from Eu³⁺ luminescence emission. The energy levels of the Eu³⁺ ion, second order crystal field parameters, and crystal field strength were obtained for all compositions of solid solutions. We show that the crystal field parameters linearly depend on unit cell parameter and that these dependencies may be considered as part of an overall dependence for the entire sesquioxide family.     

Normal analytic polyhedra in ℂ2 with a noncompact automorphism group

Let P be a bounded analytic polyhedron in ℂ² whose boundary is smooth except for normal crossing singularities. We show that P is a holomorphic quotient of the bidisc, if its automorphism group is noncompact.