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special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]).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⁺.     

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).     

Influence diagrams with super value nodes involving imprecise information

The concept of super value nodes was established to allow dynamic programming to be performed within the theory of influence diagrams and to reduce the computational complexity in solving problems by means of influence diagrams. This paper is focused on how influence diagrams with super value nodes are affected by the presence of imprecise information. We analyze how to reduce the complexity when evaluating an influence diagram in this framework by modelling these kinds of nodes and random magnitudes in terms of fuzzy random variables. Finally, an applied example of the theoretical results is developed.     

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).     

A Necklace of Wulff Shapes

In a probabilistic model of a film over a disordered substrate, Monte-Carlo simulations show that the film hangs from peaks of the substrate. The film profile is well approximated by a necklace of Wulff shapes. Such a necklace can be obtained as the infimum of a collection of Wulff shapes resting on the substrate. When the random substrate is given by iid heights with exponential distribution, we prove estimates on the probability density of the resulting peaks, at small density.AMS subject classification: 60K35, 60K37, 82B24, 82B41