Packing two disks into a polygonal environment

We consider the following problem. Given a polygon P, possibly with holes, and having n vertices, compute a pair of equal radius disks that do not intersect each other, are contained in P, and whose radius is maximized. Our main result is a simple randomized algorithm whose expected running time, on any input, is O(nlogn). This is optimal in the algebraic decision tree model of computation.     

The number of commutative semigroups of order N

An explicit upper bound is given for the number of commutative semigroups withn elements.     

Computing Finite Semigroups, I: The First Row

New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen existing algorithms for the computation of finite semigroups. The results in this first part describe the first row of the multiplication table in detail and provide a numerical profile with which it can be compared to other rows.     

Du discret au continu pour des modèles de réseaux aléatoires d'atomes

We study in this Note the continuum (macroscopic) limit for some atomistic models for crystals. The purpose is to derive densities of mechanical energies from microscopic models. In contrast to the setting of a previous study, where the microscopic structure was assumed to be periodic, it is modelled here by a stochastic lattice, which enjoys some stationarity and ergodicity properties, following notions previously introduced elsewhere. To cite this article: X. Blanc et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Scattering from infinite rough tubular surfaces

We study the Helmholtz equation in the exterior of an infinite perturbed cylinder with a Dirichlet boundary condition. Existence and uniqueness of solutions are established using the variational technique introduced (SIAM J. Math. Anal. 2005; 37 (2):598–618). We also provide stability estimates with explicit dependence of the constants in terms of the frequency and the perturbed cylinder thickness. Copyright © 2006 John Wiley & Sons, Ltd.     

Toward phenanthridin-2-ylidene: electrophilicity versus acidity in planar-constrained C-aryl iminium salts

A phenanthridinium salt was prepared in four steps, including an intramolecular CH-arylation and a hydride abstraction reaction. Treatment with sterically demanding bases does not lead to the corresponding carbene, but rather to addition products: the planar-constrained geometry significantly enhances the electrophilicity over the acidity of C-aryl iminium salts.     

Alternative syntheses of the D2d symmetric 1,3,5,7-tetraiodotricyclo[3.3.0.0]octane

Three alternative syntheses of 1,3,5,7-tetraiodotricyclo[3.3.0.0^3,7]octane are described. Reaction of this tetraiodide with sodium amalgam in the presence of dienes or with molten sodium in boiling 1,4-dioxane in the absence of trapping agents led to very complex mixtures of products, presumably due to competitive 1,2- and 1,3-deiodination reactions.     

Ehrenfest's theorem reinterpreted and extended with Wigner's function

For a wave packet evolving quantum mechanically, the rates of change of the expectations and uncertainties of the position and momentum are exactly the same as if Wigner's function instantaneously obeyed a classical Liouville equation (whatever the Hamiltonian). This extension of Ehrenfest's theorem should be useful for dealing with the evolution and manipulation of quantum states.     

InAs/GaSb/AlSb resonant tunneling spin device concepts

We discuss device concepts for creating spin-polarized current sources without external magnetic fields, using non-magnetic 6.1 Å semiconductor resonant tunneling structures. Spin filters, spin pumps, and spin transistors that exploit structural and bulk inversion asymmetries will be examined.     

Monte Carlo Simulation of Electron Transport and X-Ray Generation. II. Radiative Processes and Examples in Electron Probe Microanalysis

Theoretical models for Monte Carlo simulation of radiative processes, i.e. bremsstrahlung and characteristic x-ray emission, are presented. Possible strategies for simulating electron transport are briefly described. For mechanisms involving energy loss and angular deflections, difficulties for strict implementation of accurate numerical differential cross sections still remain due to the strong correlations between these variables. Practical solutions for the case of inelastic collisions and bremsstrahlung emission are described. Comparisons of simulation results with experimental data for several problems of interest in electron probe microanalysis are presented.