Distribution of Resonances and Decay Rate of the Local Energy for the Elastic Wave Equation

We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle with Neumann or Dirichlet boundary conditions. We prove that there exists an exponentially small neighborhood of the real axis free of resonances. Consequently we prove that for regular data, the energy for the elastic wave equation decays at least as fast as the inverse of the logarithm of time. According to Stefanov–Vodev ([SV1, SV2]), our results are optimal in the case of a Neumann boundary condition, even when the obstacle is a ball of ℝ³. The main difference between our case and the case of the scalar Laplacian (see Burq [Bu]) is the phenomenon of Rayleigh surface waves, which are connected to the failure of the Lopatinskii condition. Received: 22 February 2000 / Accepted: 28 June 2000     

Multifractal Formalism for Selfsimilar Functions Expanded in Singular Basis

Selfsimilar functions can be written as the superposition of similar structures, at different scales, generated by a function g. Their expressions look like wavelet decompositions. In the case where g is regular, the multifractal formalism has been proved for the corresponding selfsimilar function, for Hölder exponents smaller than the regularity of g. In this paper, we show, in the case where g is the Schauder function (or the Haar function or a spline-type wavelet), that for larger Hölder exponents, the singularities of g can disturb the Hölder exponents of the associated selfsimilar function, modify the shape of the spectrum of singularities, and finally affect the validity of the multifractal formalism.     

Use of Photothermally Generated Seebeck Voltage for Thermal Characterization of Thermoelectric Materials

A simple and accurate experimental procedure to measure simultaneously the thermal properties (conductivity, diffusivity, and effusivity) of thermoelectric (TE) materials using their Seebeck voltage is proposed. The technique is based on analysis of a periodically oscillating thermoelectric signal generated from a TE material when it is thermally excited using an intensity-modulated laser source. A self-normalization procedure is implemented in the presented method using TE signals generated by changing the laser heating from one side to another of the TE material. Experiments are done on a polyaniline carbon nanohybrid (6.6 wt.% carbon nanotubes), yielding a thermal conductivity of 1.106 ± 0.001 W/m-K. The results are compared with the results from photothermal infrared radiometry experiments.     

Connection relations and bilinear formulas for the classical orthogonal polynomials

Suppose we have an operator T that maps a set of orthogonal polynomials {P_n(x)}_{n = o}^∞ to another set of orthogonal polynomials. We show how such a mapping can be used to derive connection relations as well as bilinear formulas for the pre-images {P_n(x)}_{n = o}^∞. This method is carried out in detail for the Jacobi, Laguerre, and Hahn polynomials.     

Kinetics of adsorption of zinc-ions by doped manganese dioxides

Using⁶⁵Zn-labelled solutions, the kinetics of the specific adsorption of Zn²⁺-ions by doped manganese dioxides was studied, at pH values corresponding to their isoelectric points (IEP's), by γ-ray scintillation counting. The rate of the fast adsorption of Zn²⁺-ions by doped dioxides increased in the series: Li⁺-doped<undoped<Mo(VI)-≈V(V)-doped samples. The uptake of Zn²⁺-ions in about 10 minutes exhibited a similar increase. Compared to the undoped sample, the extent and the rate of adsorption were lower for the samples doped with an ion of valence<4 but were higher for samples doped with ions of valence>4.     

Linear birth and death models and associated Laguerre and Meixner polynomials

We study birth and death processes with linear rates λ_n = n + α + c + 1, μ_{n + 1} = n + c, n 0 and μ₀ is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ₀ = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations.     

Quadratic -exponentials and connection coefficient problems

We establish expansion formulas of -exponential functions in terms of continuous -ultraspherical polynomials, continuous -Hermite polynomials and Askey-Wilson polynomials. The proofs are based on solving connection coefficient problems.

     

Dendrimers with a copper(I) bis(phenanthroline) core: synthesis, electronic properties, and kinetics

The copper(I) bis(chelate) complex Cu(L(0))(2) has been prepared from 2,9-diphenethyl-1,10-phenanthroline and Cu(CH(3)CN)(4)BF(4). Derivative Cu(L(0))(2) has been characterized by NMR, UV-vis spectroscopy, and X-ray crystallography. Interestingly, owing to the presence of the ethylene linker, the interligand pi-pi stacking interactions between the phenyl rings and the phenanthroline subunits in Cu(L(0))(2) do not induce significant distortions of the pseudotetrahedral symmetry around the Cu(I) center in the solid state or in solution. Following the synthesis of Cu(L(0))(2), dendrimers Cu(L(1)(-)(4))(2) with a Cu(I) bis(2,9-diphenethyl-1,10-phenanthroline) core surrounded by Fréchet type dendritic branches have been prepared and the kinetics of their cyanide-assisted demetalation studied. Importantly, the surrounding dendritic wedges have no significant influence on the coordination geometry of the Cu(I) center, as deduced from their absorption spectra. Therefore, the variations of the rate constants only reflect changes resulting from the presence of the dendritic branches. The kinetics of the cyanide-mediated demetalation reaction indeed revealed that cyanide diffusion through the dendritic shell is slightly influenced by the size of the branches. Significant effects were observed in the kinetics when going from the third to the fourth generation and have been ascribed to changes in the lipophilicity around the metallic core as a result of dendritic encapsulation.