Wavelet-Based Estimation for Univariate Stable Laws

Stable distributions are characterized by four parameters which can be estimated via a number of methods, and although approximate maximum likelihood estimation techniques have been proposed, they are computationally intensive and difficult to implement. This article describes a fast, wavelet-based, regression-type method for estimating the parameters of a stable distribution. Fourier domain representations, combined with a wavelet multiresolution approach, are shown to be effective and highly efficient tools for inference in stable law families. Our procedures are illustrated and compared with other estimation methods using simulated data, and an application to a real data example is explored. One novel aspect of this work is that here wavelets are being used to solve a parametric problem, rather than a nonparametric one, which is the more typical context in wavelet applications.     

The isomorphism problem for toral relatively hyperbolic groups

We provide a solution to the isomorphism problem for torsion-free relatively hyperbolic groups with abelian parabolics. As special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]). We also give a solution to the homeomorphism problem for finite volume hyperbolic n-manifolds, for n≥3. In the course of the proof of the main result, we prove that a particular JSJ decomposition of a freely indecomposable torsion-free relatively hyperbolic group with abelian parabolics is algorithmically constructible.     

Preparation of a chromatographic solid support on the basis of perlite and separation of uranium on a TBP-loaded perlite column

The possibilities of preparing a packing for reversed phase column chromatography from Menderes' perlite were studied. Its physical and chemical characteristics were compared with other solid supports prepared from rocks, such as perlite and volcanic slags. A series of chemical treatments were applied to improve the mechanical and chemical properties of perlite. The experimental work covers the strong acid treatment, the strong base treatment and the silanization with DMCS. The raw perlite containing 70–73% SiO₂ was treated with NaOH to make soluble silicates and to increase it. Thus the surface and mechanical characters of the modified perlite were determined. The mean surface OH group density and the specific surface area were 3.2 μmol/m² and 9.2 m²/g, respectively. The modified perlite was silanized and hydrophized to load organic complexing agents. The TBP was fixed successfully on perlite up to 20% w/w. The packing prepared was used to study the chromatographic behavior of UO₂ ²⁺ Fe³⁺.     

A novel concept for optoelectronic nanotransistor design

Considering the new features and particular quantum properties of nanooptoelectronics components, the revision of the traditional analytical approach to model analytically is made indispensable. A novel approach leads to take into account quasi-virtual electrons trapped in nanometric space cells with high discontinuities of potential. Another strong difficulty to overcome is existing: the strong difference of scales between the wavelength of the focusing laser spot size (currently close to the micrometer range) and the nanostructures sizes (close to the nanometer range). A recent breakthrough in the studies of diffraction limits affords the possibility to produce a subwavelength light source with high transmission through arrays in metallic screen. Thanks to some recent works [T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Extraordinary optical transmission through subwavelength hole arrays, Nature 391 (1998) 667-669. A. Degiron, T.W. Ebbesen, The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures, J. Opt. A: Pure Appl. Opt. (2005) S90-S96. J. Xu, T. Xu, J. Wang, Q. Tian, Design tips of nanoapertures with strong field enhancement and proposal of novel L-shaped aperture, Opt. Eng. 44(1) (2005)], we intend to consider the physical possibility of applications involving a violation of the Bethe diffraction law. With the aim to implement the generation of a photon-plasmon-polariton (SPPs) interaction [J. Xu, T. Xu, J. Wang, Q. Tian, Design tips of nanoapertures with strong field enhancement and proposal of novel L-shaped aperture, Opt. Eng. 44(1) (2005). J.-F. Eloy, Mise en évidence d’une anisotropie d’absorption multiphotonique dans des monocristaux organiques ‘HMX et RDX) et approche théorique, Réactivité et cinétique réactionnelle, Ann. Chim. Fr. 16 (1991) 1-39] liable to the physical conditions to generate this particular electromagnetic phenomenon, we conceived of a particular layout. This optoelectronics component is equipped with subwavelength apertures (typically 100 nm of diameter) bored in a metallic (Ag or Cr) thin film screen to reduce drastically the focused laser beam spot in order to illuminate the photoconducting gap between two nanotubes (e.g. polycarbon walls).To master the main theoretical and technological difficulties, a new optoelectronic concept of nanotransistor is proposed. This system involves a metal-oxide-semiconductor field effect transistor (MOSFET) augmented with a nanoscale cell consisting of a ‘Coulombian box’ controlled by a laser photoconducting switch. In order to preserve the different electronic functions such as the potential barriers, the implementation of semirefractors [J.-F. Eloy, M.Y. Depeyrot, Nanometer range: a new theoretical challenge for microelectronics and optoelectronics, Microelectron. J. 37(7) (2006) 630-634] such as polycrystal diamond monolayers is commendable.     

Analyse numérique de la supraconductivité

Motivated by the superconductivity, we are interested in the fundamental state of the Schorödinger operator with magnetic field. In this paper, we propose a numerical approach based on the finite elements method to determine the bottom of the spectrum of this operator in general domains. We improve the numerical results by using mesh-refinement techniques based on a posteriori error estimators developed elsewhere. We also look at the monotonicity of the bottom of the spectrum in an angular sector according to the angle to complement the theorical study of Bonnaillie (C. R. Acad. Sci. Paris, Ser. I 336 (2) (2003) 135–140). To cite this article: F. Alouges, V. Bonnaillie, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Time-harmonic acoustic propagation in the presence of a shear flow

This work deals with the numerical simulation, by means of a finite element method, of the time-harmonic propagation of acoustic waves in a moving fluid, using the Galbrun equation instead of the classical linearized Euler equations. This work extends a previous study in the case of a uniform flow to the case of a shear flow. The additional difficulty comes from the interaction between the propagation of acoustic waves and the convection of vortices by the fluid. We have developed a numerical method based on the regularization of the equation which takes these two phenomena into account. Since it leads to a partially full matrix, we use an iterative algorithm to solve the linear system.     

Clustering via minimum volume ellipsoids

We propose minimum volume ellipsoids (MVE) clustering as an alternative clustering technique to k-means for data clusters with ellipsoidal shapes and explore its value and practicality. MVE clustering allocates data points into clusters in a way that minimizes the geometric mean of the volumes of each cluster’s covering ellipsoids. Motivations for this approach include its scale-invariance, its ability to handle asymmetric and unequal clusters, and our ability to formulate it as a mixed-integer semidefinite programming problem that can be solved to global optimality. We present some preliminary empirical results that illustrate MVE clustering as an appropriate method for clustering data from mixtures of “ellipsoidal” distributions and compare its performance with the k-means clustering algorithm as well as the MCLUST algorithm (which is based on a maximum likelihood EM algorithm) available in the statistical package R. Research of the first author was supported in part by a Discovery Grant from NSERC and a research grant from Faculty of Mathematics, University of Waterloo. Research of the second author was supported in part by a Discovery Grant from NSERC and a PREA from Ontario, Canada.     

Measuring stress intensity factors with a camera: Integrated digital image correlation (I-DIC)Mesure de facteurs d'intensité des contraintes avec une caméra : corrélation d'images numériques intégrée (CINI)

A novel ‘integrated’ approach coupling image correlation and elastic displacement field identification provides a powerful and accurate tool to evaluate mode I and II stress intensity factors. This technique is applied to silicon carbide subjected to a sandwiched three-point bend test, using digital pictures obtained in optical microscopy where the pixel physical scale is about 2 μm. A crack whose maximum opening is 500 nm can be detected and its geometry identified. The toughness is determined well within a 10%uncertainty. To cite this article: F. Hild, S. Roux, C. R. Mecanique 334 (2006).