Kernel Characterization of an Interval Function

This paper proposes a set-membership approach to characterize the kernel of an interval-valued function. In the context of a bounded-error estimation, this formulation makes it possible to embed all uncertainties of the problem inside the interval function and thus to avoid bisections with respect to all these uncertainties. To illustrate the principle of the approach, two testcases taken from robotics will be presented. The first testcase deals with the characterization of all loops of a mobile robot from proprioceptive measurements only. The second testcase is the localization of a robot from range-only measurements.     

Solid state and solution 43Ca NMR of calcium peroxides involved in the disproportionation of hydrogen peroxide by calcium hydroxide

In order to get some insight into the mechanism of the disproportionation of hydrogen peroxide catalyzed by calcium hydroxide, 43Ca NMR spectra of enriched samples of calcium peroxides and of their precursors have been studied in both solution and solid state. This study demonstrates that no well-defined peroxidized calcium species are formed in solution, showing that the catalytic role of calcium is likely restricted to the solid state. Most of the calcium compounds that could be involved in the catalytic process have been investigated with solid state NMR. The shift and quadrupolar parameters of Ca(OH)2, CaO2.8H2O and CaO2.2H2O2 are reported for the first time. These parameters are different enough to allow the quantitative analysis of a complex mixture of these compounds by NMR.     

Polar phase hydroformylation: the dramatic effect of water on mono- and dirhodium catalysts

The addition of 30% water (by volume) to acetone creates a remarkably effective polar phase solvent system for a dicationic dirhodium tetraphosphine hydroformylation catalyst. The initial turnover frequency (TOF) increases by 265% (to 73 min-1) for the hydroformylation of 1-hexene relative to the initial TOF in pure acetone (20 min-1). The aldehyde linear to branched (L:B) ratio increases to 33:1, and alkene isomerization and hydrogenation side reactions are essentially eliminated. Comparisons with monometallic rhodium catalysts based on PPh3, Bisbi, Naphos, and Xantphos ligands demonstrate that this polar-phase bimetallic catalyst is one of the fastest and most selective hydroformylation systems known under these mild conditions (90 degrees C, 6.2 bar H2/CO). The monometallic catalysts also show rate enhancements (although considerably smaller) in water-acetone, but Rh-Xantphos does show a large increase of 115%, with considerably reduced alkene isomerization side reactions. The dramatic effect of water on the dirhodium catalyst system is believed to be due to simple inhibition of the fragmentation of the catalytically active species into inactive mono- and bimetallic complexes.     

Supershell structure in alkali metal nanowires

Nanowires are formed by indenting and subsequently retracting two pieces of sodium metal. Their cross section gradually reduces upon retraction and the diameters can be obtained from the conductance. In previous work we have demonstrated that when one constructs a histogram of diameters from large numbers of indentation-retraction cycles such histograms show a periodic pattern of stable nanowire diameters due to shell structure in the conductance modes. Here, we report the observation of a modulation of this periodic pattern, in agreement with predictions of a supershell structure.     

Oscillatory instabilities of standing waves in one-dimensional nonlinear lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal 0,pi. Incommensurate analytic SWs with |Q|>pi/2 may however appear as "quasistable," as their instability growth rate is of higher order.     

Sur le nombre de points rationnels des variétés abéliennes et des Jacobiennes sur les corps finis

We give upper and lower bounds for the number of points on abelian and Jacobian varieties over finite fields. We also determine the values for the maximum and minimum number of points on Jacobian surfaces on a given finite field.     

A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

This paper presents a dynamic behaviour study of non-linear friction systems subject to uncertain friction laws. The main aspects are the analysis of the stability and the associated non-linear amplitude around the steady-state equilibrium. As friction systems are highly sensitive to the dispersion of friction laws, it is necessary to take into account the uncertainty of the friction coefficient to obtain stability intervals and to estimate the extreme magnitudes of oscillations. Intrusive and non-intrusive methods based on the polynomial chaos theory are proposed to tackle these problems. The efficiency of these methods is investigated in a two degree of freedom system representing a drum brake system. The proposed methods prove to be interesting alternatives to the classic methods such as parametric studies and Monte Carlo based techniques.