MULTIFRACTAL FORMALISMS：BOXED VERSUS CENTERED INTERVALS

There are mainly two approaches to the multifractal analysis of measures. The first one, which is used in applications and in studying problems arising from dynamical systems, uses a hierarchy of boxes. The second one, which is more satisfactory from the viewpoint of geometric measure theory, uses more intrinsicconcepts. This article is an account of a work by J. Barral, F. Ben Nasr, and J. Peyriere [3] which pro-vides a bridge between these two theories.     

Symmetric Groups and Lattices

This paper deals with various problems in lattice theory involving local extrema. In particular, we construct infinite series of highly symmetric spherical 3-designs which include some of the examples constructed in [9] in dimensions 5 and 7. We also construct new types of dual-extreme lattices.Received June 29, 2002; in final form January 14, 2003 Published online May 16, 2003     

Local self-similarity and the Hausdorff dimension

Let X be a locally self-similar stochastic process of index 0<H<1 whose sample paths are a.s. C^H?ε for all ε>0. Then the Hausdorff dimension of the graph of X is a.s. 2?H. To cite this article: A. Benassi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Approximation of multi-scale elliptic problems using patches of finite elements

In this paper we present a method to solve numerically elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. It resembles the FAC method (see Math. Comp. 46 (174) (1986) 439–456) and its convergence is obtained by a domain decomposition technique (see Math. Comp. 57 (195) (1991) 1–21). However it is of much more flexible use in comparison to the latter. To cite this article: R. Glowinski et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Contribution a L'etude de melanges susceptibles de former des microemulsions selon leurs compositions,par la definition de leurs comportements dielectriques a 9,455 GHz

The dielectric studies of four components mixtures are rarely made on a great deal of concentrations. The authors propose a dielectric behavior study of mixtures made with toluene-water-butanol-SDS, from specific mappings of permittivities which are plotted on pseudo ternary diagrams at 9.455 GHz. They draw different conclusions to know how at 9.455 GHz the variations of real and imaginary parts of permittivity involve the concentration of each component and the structure of the mixture.These conclusions will be perfected by studies made at other frequencies and by spectral analysis of each mixture.     

Universality and self-similarity in the bifurcations of circle maps

The bifurcation structure in a two-parameter family of circle maps is considered. These maps have a (topological) degree that may be different from one. A generalization of the rotation number is given and symmetries of the bifurcations in parameter space are described. Continuity arguments are used to establish the existence of periodic orbits. By plotting the locus of parameter values associated with superstable cycles, self-similar bifurcations are found. These bifurcations are a generalization of the familiar period-doubling cascade in maps with one extrema, to two-parameter maps with two extrema. Finally, a scheme for the global organization of bifurcation in these maps is proposed.     

Multivariate analysis of hyperspectral hard X‐ray images

This article describes methods to analyse and process hyperspectral hard X‐ray imaging data. We focus on the use of multivariate techniques that exploit the spectral information to make informed decisions on the material content within each pixel of an X‐ray image. These analysis methods have the ability to auto‐segment data without prior knowledge of the sample composition or structure, and are particularly useful for studying completely unknown, diluted or complex specimens. We demonstrate the methods on a variety of hard X‐ray images including X‐ray fluorescence and absorption data recorded using a hard X‐ray imaging spectrometer. The multivariate methods described are very powerful with the ability to segment, distinguish and, in some cases, identify different materials within a single X‐ray image. Potential uses of hyperspectral X‐ray imaging are discussed varying from materials science to industrial or security applications. Copyright © 2013 John Wiley & Sons, Ltd.     

MR detection of mechanical vibrations using a radiofrequency field gradient

A new method for NMR characterization of mechanical waves, based upon radiofrequency field gradient for motion encoding, is proposed. A binomial B1 gradient excitation scheme was used to visualize the mobile spins undergoing a periodic transverse mechanical excitation. A simple model was designed to simulate the NMR signal as a function of the wave frequency excitation and the periodicity of the NMR pulse sequence. The preliminary results were obtained on a gel phantom at low vibration frequencies (0-200 Hz) by using a ladder-shaped coil generating a nearly constant RF field gradient along a specific known direction. For very small displacements and/or B1 gradients, the NMR signal measured on a gel phantom was proportional to the vibration amplitude and the pulse sequence was shown to be selective with respect to the vibration frequency. A good estimation of the direction of vibrations was obtained by varying the angle between the motion direction and the B1 gradient. The method and its use in parallel to more conventional MR elastography techniques are discussed. The presented approach might be of interest for noninvasive investigation of elastic properties of soft tissues and other materials.