On a functional equation generalizing the class of semistable distributions

With ?(p),p≥0 the Laplace-Stieltjes transform of some infinitely divisible probability distribution, we consider the solutions to the functional equation ?(p-e ^?pβΠ _i=1 ^m ?^γi (c _i p) for somem≥1,c _i>0, γ _i >0,i=1., …,m, β ε ®. We supply its complete solutions in terms of semistable distributions (the ones obtained whenm=1). We then show how to obtain these solutions as limit laws (r → ∞) of normalized Poisson sums of iid samples when the Poisson intensity λ(r) grows geometrically withr.     

On the physical relevance of max- and log-max-selfsimilar distributions

This work emphasizes the special role played by max-semistable and log-max-semistable distributions as relevant statistical models of various observable and “internal” variables in Physics. Some of their remarkable properties (chiefly self-similarity) are displayed in some detail. One of their characteristic features is a log-periodic variation of the scale parameter which appears in the stable extreme value distributions. Received 29 November 1999 and Received in final form 24 March 2000     

Elaboration and characterization of TiO2 nanoparticles incorporated in SiO2 host matrix

Nanometer-scale TiO₂ particles have been synthesized by sol-gel method. It was incorporated in a glass-based silica aerogel. The composite was characterized by various techniques such as particle size analysis, scanning electron microscopy (SEM), atomic force microscopy (AFM), transmission electron microscopy (TEM), X-ray diffraction (XRD), infrared spectroscopy (IR) and photoluminescence (PL). The bulk glass presents a strong luminescence at wavelengths ranging from 750 to 950 nm. This PL was attributed to various non-bridging oxygen hole centers (NBOHCs) defects resulting from thermal treatment and crystallization of TiO₂ at the interface between titania nanoparticles and silica host matrix.     

On orthogonal polynomials with respect to the form -(x - c)S'

Summary A form (linear functional) $u$ is called regular if we can associate with it a sequence of monic orthogonal polynomials. On certain regularity conditions, the product of a non regular form by a polynomial can be regular. The purpose of this work is to establish regularity conditions of the form $-(x-c){\mathbf S}',$ where ${\mathbf S}$ is a classical (Bessel, Jacobi). We give the second-order recurrence relations and structure relations of its corresponding orthogonal polynomial sequence. We conclude with an example as an illustration.     

Electrical conductivity and complex impedance analysis of 20% Ti-doped La0.7Sr0.3MnO3 perovskite

The electrical conductance of 20% Ti-doped La_0.7Sr_0.3MnO₃ (LSMO) was measured using admittance spectroscopy over a wide temperature and frequency ranges. The impedance plane plot shows semicircle arcs at different temperatures and an electrical equivalent circuit has been proposed to explain the impedance results. Activation energy inferred from conductance spectrum matches very well with the value estimated from relaxation time indicating that relaxation process and conductivity have the same origin. The electrical conductance of La_0.7Sr_0.3Mn_0.8Ti_0.2O₃ is found to be dependent on temperature and frequency. Also, the electronic conduction appears to be dominated by thermally activated hopping of small polaron (SPH) at high temperatures and by variable range hopping (VRH) at low temperatures.     

Sol–gel synthesis and luminescent properties of SiO2/Zn2SiO4 and SiO2/Zn2SiO4:V composite materials

Undoped and vanadium-doped Zn₂SiO₄ particles embedded in silica host matrix were prepared by a simple solid-phase reaction after the incorporation of ZnO and ZnO:V nanoparticles, respectively, in silica monolith using the sol–gel method with supercritical drying of ethyl alcohol in two steps. After supercritical drying and annealing in the temperature range between 1423 and 1473 K in an air atmosphere, the photoluminescence (PL) measurements show a band centered at about 760 nm in the case of non-doped Zn₂SiO₄ which is attributed to energy transfer from Zn₂SiO₄ particles to NBOHs interface defects. In the case of vanadium doped Zn₂SiO₄, the PL reveals a band centered at about 540 nm attributed to the vanadium in the interfaces between Zn₂SiO₄ particles and SiO₂ host matrix. Photoluminescence excitation (PLE) measurements show different origins of the emission bands. The PLE band (～240–350 nm) may be understood as an energy transfer process from O^2? to V⁵⁺ which occurs intrinsically in the vanadyl group.     

Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations

We consider a jump-type Cox–Ingersoll–Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak consistency and asymptotic normality, and, under an additional moment assumption, strong consistency as well. In the supercritical case, we prove strong consistency and mixed normal (but non-normal) asymptotic behavior, while in the critical case, weak consistency and non-standard asymptotic behavior are described. We specialize our results to so-called basic affine jump–diffusions as well. Concerning the asymptotic behavior of the MLE in the supercritical case, we derive a stochastic representation of the limiting mixed normal distribution, where the almost sure limit of an appropriately scaled jump-type supercritical CIR process comes into play. This is a new phenomenon, compared to the critical case, where a diffusion-type critical CIR process plays a role.     

Preparation and characterization of n-type conductive (Al, Co) co-doped ZnO thin films deposited by sputtering from aerogel nanopowders

Highly transparent, n-type conducting ZnO thin films were obtained by low temperature magnetron sputtering of (Co, Al) co-doped ZnO nanocrystalline aerogels. The nanoparticles of ∼30 nm size were synthesized by a sol-gel method using supercritical drying in ethyl alcohol. The structural, optical and electrical properties of the films were investigated. The ZnO films were polycrystalline textured, preferentially oriented with the (0 0 2) crystallographic direction normal to the film plane. The films show within the visible wavelength region an optical transmittance of more than 90% and a low electrical resistivity of 3.5 × 10⁻⁴ Ω cm at room temperature.