Characterization of the surface of positive electrodes for Li-ion batteries using 7Li MAS NMR

The growth and evolution of the interphase, due to contact with the ambient atmosphere or electrolyte, are followed using ⁷Li magic-angle spinning nuclear magnetic resonance (MAS NMR) in the case of two materials amongst the most promising candidates for positive electrodes for lithium batteries: LiFePO₄ and LiMn_0.5Ni_0.5O₂. The use of appropriate experimental conditions to acquire the NMR signal allows observing only the «diamagnetic» lithium species at the surface of the grains of active material. The reaction of LiMn_0.5Ni_0.5O₂ with the ambient atmosphere or LiPF₆ (1 M in Ethylene Carbonated/DiMéthyl Carbonate (EC/DMC)) electrolyte is extremely fast and leads to an important amount of lithium-containing diamagnetic species compared to what can be observed in the case of LiFePO₄. The two studied materials display a completely different surface chemistry in terms of reactivity and/or kinetics of the surface towards electrolyte. Moreover, these results show that MAS NMR is a very promising tool to monitor phenomena taking place at the interface between electrode and electrolyte.     

L'intégration graphique des équations différentielles ordinaires

In the period which precedes the appearance of computers, needs in calculation of the scientists and engineers led to an important development of graphic methods of integration. To contribute to the study of this little known phenomenon, the article presents techniques and instruments used for the graphic integration of ordinary differential equations, and looks for their historic origins by going back to the beginning of calculus: processes of geometric calculation by the polygonal method or the method of radius of curvature, use of tractional motion for the conception of integraphs, reduction to graphic quadratures in finite or infinite number.     

Variations on the Theorem of Birkhoff – von Neumann and Extensions

 The theorem of Birkhoff – von Neumann concerns bistochastic matrices (i.e., matrices with nonnegative real entries such that all row sums and all column sums are equal to one). We consider here real matrices with entries unrestricted in sign and we extend the notion of permutation matrices (integral bistochastic matrices); some generalizations of the theorem are derived by using elementary properties of graph theory. Received: October 10, 2000 Final version received: April 11, 2002     

Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces

It is well known that the complexity of the Delaunay triangulation of $n$ points in $\RR ^d$, i.e., the number of its simplices, can be $\Omega (n^{\lceil {d}/{2}\rceil })$. In particular, in $\RR ^3$, the number of tetrahedra can be quadratic. Put another way, if the points are uniformly distributed in a cube or a ball, the expected complexity of the Delaunay triangulation is only linear. The case of points distributed on a surface is of great practical importance in reverse engineering since most surface reconstruction algorithms first construct the Delaunay triangulation of a set of points measured on a surface. In this paper we bound the complexity of the Delaunay triangulation of points distributed on the boundary of a given polyhedron. Under a mild uniform sampling condition, we provide deterministic asymptotic bounds on the complexity of the three-dimensional Delaunay triangulation of the points when the sampling density increases. More precisely, we show that the complexity is $O(n^{1.8})$ for general polyhedral surfaces and $O(n\sqrt{n})$ for convex polyhedral surfaces. Our proof uses a geometric result of independent interest that states that the medial axis of a surface is well approximated by a subset of the Voronoi vertices of the sample points.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

Further results on the euler and Genocchi numbers

Summary We characterize the ordinary generating functions of the Genocchi and median Genocchi numbers as unique solutions of some functional equations and give a direct algebraic proof of several continued fraction expansions for these functions. New relations between these numbers are also obtained.     

The correlation dimension of the Sierpinski carpet

We compute the correlation dimension of a measure defined on a general Sierpinski carpet. We relate this function to a free energy function associated to a partition composed of ‘nearly squares’ and well fitted to the planar Cantor set. Actually, we prove that these functions are real analytic on , are strictly increasing and are strictly concave (respectively linear in the degenerate case). This is an example of a two-dimensional dynamical system contracting in the two directions with different ratios. We first study measures of Gibbsian type before generalizing to Markovian measures.