Réseaux quaternioniens et invariant de Venkov

We define an infinite family of even unimodular latticesU _n with minimal norm 4, endowed with a quaternionic structure. We compute their ‘Venkov invariant’, which allows us to identifyU ₃₂ with a previous known lattice, constructed from the Reed-Muller code of length 32.      

Improving product location and order picking activities in a distribution centre

This article examines the effect of different product location strategies on the distance that order pickers must cover to do their job. This distance is an important cost component in warehousing activities. Our empirical study is based on a real industrial setting, in which the products are located on both sides of a conveyor belt. We show that choosing the right product location strategy allows the current picking distance to be reduced more than 10%. We also propose a post-optimization procedure that can further reduce picking distances—up to 20% of the current distances. Through a study of the routing strategy used to dispatch pickers, we demonstrate that solving a simple travelling salesman problem can further reduce distances up to 13%, compared with the distances incurred using a predetermined route. We show that reductions of up to 27% compared to current picking distances are possible if our product location and routing methods are combined.     

Superoxide dismutase-like activity of cobalt(II) complexes based on a sugar platform

A SOD-like activity evaluated by a modified McCord-Fridovich test was evidenced for two Co(II) complexes built from "glycoligands" using a sugar platform derived from d-galactose and D-galactal and functionalized by three 2-picolyl groups.     

Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we consider the characteristic functions of the subsets of R² and their distance functions. The L² norm of the difference of characteristic functions, the L and the W^1,2 norms of the difference of distance functions define interesting topologies, in particular the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with image shapes defined on finite grids of pixels, we restrict our attention to subsets of ² of positive reach in the sense of Federer [16], with smooth boundaries of bounded curvature. For this particular set of shapes we show that the three previous topologies are equivalent. The next problem we consider is that of warping a shape onto another by infinitesimal gradient descent, minimizing the corresponding distance. Because the distance function involves an inf, it is not differentiable with respect to the shape. We propose a family of smooth approximations of the distance function which are continuous with respect to the Hausdorff topology, and hence with respect to the other two topologies. We compute the corresponding Gâteaux derivatives. They define deformation flows that can be used to warp a shape onto another by solving an initial value problem.We show several examples of this warping and prove properties of our approximations that relate to the existence of local minima. We then use this tool to produce computational definitions of the empirical mean and covariance of a set of shape examples. They yield an analog of the notion of principal modes of variation. We illustrate them on a variety of examples.     

Self-organized growth of nanoparticles on a surface patterned by a buried dislocation network

The self-organized growth of Co nanoparticles is achieved at room temperature on an inhomogenously strained Ag(001) surface arising from an underlying square misfit dislocation network of 10 nm periodicity buried at the interface between a 5 nm-thick Ag film and a MgO(001) substrate. This is revealed by in situ grazing-incidence small-angle x-ray scattering. Simulations of the data performed in the distorted wave Born approximation framework demonstrate that the Co clusters grow above the dislocation crossing lines. This is confirmed by molecular dynamic simulations indicating preferential Co adsorption on tensile sites.     

Retarded Green Functions and Modified Dispersion Relations

We analyse a three-field model, which describes a relativistic two-level atom interactingwith a radiation bath. From the one-loop retarded propagators at finite temperature we extract the transition rates and the modifications of the dispersion relations. To further investigate the relationships between propagators and these physical quantities, we analyse a non-equilibrium situation in which an additional atom is present in the bath. Preliminary results indicate that transition rates can still be extracted from the (retarded) propagator. This approach couldtherefore be useful in relating high-frequency (trans-Planckian) dispersion relations to the physical processes occurring at these scales.