Qualitative and quantitative investigation of chromium-polluted soils by laser-induced breakdown spectroscopy combined with neural networks analysis

Laser-induced breakdown spectroscopy (LIBS) has been applied to the analysis of three chromium-doped soils. Two chemometric techniques, principal components analysis (PCA) and neural networks analysis (NNA), were used to discriminate the soils on the basis of their LIBS spectra. An excellent rate of correct classification was achieved and a better ability of neural networks to cope with real-world, noisy spectra was demonstrated. Neural networks were then used for measuring chromium concentration in one of the soils. We performed a detailed optimization of the inputs of the network so as to improve its predictive performances and we studied the effect of the presence of matrix-specific information in the inputs examined. Finally the inputs of the network—the spectral intensities—were replaced by the line areas. This provided the best results with a prediction accuracy and precision of about 5% in the determination of chromium concentration and a significant reduction of the data, too. Awarded a poster prize on the occasion of the Euro-Mediterranean Symposium on Laser-induced Breakdown Spectroscopy (EMSLIBS 2005), Aachen, Germany, 6–9 September 2005.     

A 2-basic set of the alternating group

In this note, we construct a 2-basic set of the alternating group \mathfrakA_n{\mathfrak{A}_n}. To do this, we construct a 2-basic set of the symmetric group \mathfrakS_n{\mathfrak{S}_n} with an additional property, such that its restriction to \mathfrakA_n{\mathfrak{A}_n} is a 2-basic set. We adapt here a method developed by Brunat and Gramain (J. Reine Angew. Math., to appear) for the case when the characteristic is odd. One of the main tools is the generalized perfect isometries defined by Külshammer et al. (Invent. Math. 151, 513–552, (2003)).     

Conditions for Global Optimality 2

In this paper bearing the same title as our earlier survey-paper [11] we pursue the goal of characterizing the global solutions of an optimization problem, i.e. getting at necessary and sufficient conditions for a feasible point to be a global minimizer (or maximizer) of the objective function. We emphasize nonconvex optimization problems presenting some specific structures like convex-anticonvex ones or quadratic ones.     

Complex calculators in the classroom: theoretical and practical reflections on teaching pre-calculus

University and older school students following scientific courses now use complex calculators with graphical, numerical and symbolic capabilities. In this context, the design of lessons for 11th grade pre-calculus students was a stimulating challenge.In the design of lessons, emphasising the role of mediation of calculators and the development of schemes of use in an 'instrumental genesis' was productive. Techniques, often discarded in teaching with technology, were viewed as a means to connect task to theories. Teaching techniques of use of a complex calculator in relation with 'traditional' techniques was considered to help students to develop instrumental and paper/pencil schemes, rich in mathematical meanings and to give sense to symbolic calculations as well as graphical and numerical approaches.The paper looks at tasks and techniques to help students to develop an appropriate instrumental genesis for algebra and functions, and to prepare for calculus. It then focuses on the potential of the calculator for connecting enactive representations and theoretical calculus. Finally, it looks at strategies to help students to experiment with symbolic concepts in calculus.This revised version was published online in September 2005 with corrections to the Cover Date.     

Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork that are such that the meshwork's energy is a function F(el)[A(xi)] not of the real microscopic membrane area A, but of a smoothed membrane's area A(xi), which corresponds to the area of the membrane coarse grained at the mesh size xi. We show that the meshwork modifies the membrane tension sigma both below and above the scale xi, inducing a steep crossover of amplitude deltasigma=dF(el)/dA(xi). The predictions of our model account for the fluctuation spectrum of red blood cell membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane areas. We also predict an observable tension jump for membranes decorated with polymer "brushes."     

Crack kinking from an interface crack with initial contact between the crack lips

The authors recently theoretically studied crack kinking and opening from an initially closed crack (without friction) in some homogeneous medium. The same problem, but for an interface crack, is considered here. Comninou has shown that the asymptotic stress field prior to kinking is governed by a single, mode II stress intensity factor (SIF). Using this result, plus a homogeneity property of the problems of elastic fracture mechanics with unilateral contact envisaged, a change of scale, and two reasonable hypotheses, we establish the expression of the SIF at the tip of the small, open crack extension. It is shown that whatever the geometry of the external boundary and the crack and whatever the loading, these SIF depend solely upon the initial (mode II) SIF (in a linear way), the kink angle and Dundurs' parameters α and β. Using this result and Goldstein and Salganik's “principle of local symmetry” to predict the kink angle, one finds that it is independent of the loading but does depend upon Dundurs' parameters α and β. This contrasts with the case of an ordinary (initially closed) crack in some homogeneous medium, for which the kink angle was not only independent of the loading but an absolute constant. However, it is numerically found that the influence of the mismatch of elastic properties upon the kink angle is rather weak.     

Modèle électromagnétique d'objet dissimulé

We model propagation of electromagnetic waves in a medium, which is inhomogeneous with a rough layer, and which hides an object. We first get an effective medium, and then we solve the problem by integral equations.     

Size and sequence and the volume change of protein folding

The application of hydrostatic pressure generally leads to protein unfolding, implying, in accordance with Le Chatelier's principle, that the unfolded state has a smaller molar volume than the folded state. However, the origin of the volume change upon unfolding, ΔV(u), has yet to be determined. We have examined systematically the effects of protein size and sequence on the value of ΔV(u) using as a model system a series of deletion variants of the ankyrin repeat domain of the Notch receptor. The results provide strong evidence in support of the notion that the major contributing factor to pressure effects on proteins is their imperfect internal packing in the folded state. These packing defects appear to be specifically localized in the 3D structure, in contrast to the uniformly distributed effects of temperature and denaturants that depend upon hydration of exposed surface area upon unfolding. Given its local nature, the extent to which pressure globally affects protein structure can inform on the degree of cooperativity and long-range coupling intrinsic to the folded state. We also show that the energetics of the protein's conformations can significantly modulate their volumetric properties, providing further insight into protein stability.