A Note on Caterpillar-Embeddings with No Two Parallel Edges

Let G be a set of n points in general position (i.e., no three points are on a line) in the plane, and let C be a caterpillar on n vertices. We show that one can always find a rectilinear embedding of C in the plane such that the vertices of C are the points of G and no two edges of C go to parallel segments. This proves a conjecture of Robert E. Jamison.     

A robust and efficient adaptive reweighted estimator of multivariate location and scatter

This article proposes a reweighted estimator of multivariate location and scatter, with weights adaptively computed from the data. Its breakdown point and asymptotic behavior under elliptical distributions are established. This adaptive estimator is able to attain simultaneously the maximum possible breakdown point for affine equivariant estimators and full asymptotic efficiency at the multivariate normal distribution. For the special case of hard-rejection weights and the MCD as initial estimator, it is shown to be more efficient than its non-adaptive counterpart for a broad range of heavy-tailed elliptical distributions. A Monte Carlo study shows that the adaptive estimator is as robust as its non-adaptive relative for several types of bias-inducing contaminations, while it is remarkably more efficient under normality for sample sizes as small as 200.     

Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.     

Derivation of the k–ε model for locally homogeneous turbulence by homogenization techniques

We derive the incompressible and compressible k–ε model for locally homogeneous turbulence. The model is rigorously derived on formal mathematical grounds using the MPP modelling technique. This lets us calculate by either analytical or numerical means the closure constants of the model. To cite this article: T. Chacón Rebollo, D. Franco Coronil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Projectivep-algebras

Presented by R. Freese.     

Canonical methods for Hamiltonian systems: numerical experiments

A Hamiltonian system possesses dynamics (e.g. preservation of volume in phase space and symplectic structure) that call for special numerical integrators, namely canonical methods. Recent research on this aspect have shown that canonical numerical integrators may be needed for Hamiltonian systems. In this paper, we focus on numerical experiments that compare canonical and non-canonical numerical integrators. Test problems are taken from different areas in physical sciences. These experiments help to buttress the claims that canonical numerical integrators give results that mimic the qualitative behavior of the original system and that canonical numerical integrators are suitable for long time integrations. Our experiments indicate that higher-order canonical methods allow for larger timestep than lower-order canonical methods.     

Topochemically Controlled Redox Reactions in the System In/Sn/Cl

The difference in reactivity of the two modifications of InCl in solid state reactions with SnCl₂ is discussed. It is explained on the basis of semi‐empirical and ab initio calculations giving the density of states diagrams of InCl and the energies of possible disproportionation reactions. Their general features are discussed on the basis of a simple bonding picture for open‐packed structures involving inert pair elements. A detailed analysis of the DOS distribution allows to pinpoint the observed redox instability to a specific structural feature of α‐InCl.     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25