Optimal convex hull algorithms on enhanced meshes

In this paper we propose time-optimal convex hull algorithms for two classes of enhanced meshes. Our first algorithm computes the convex hull of an arbitrary set ofn points in the plane inO (logn) time on a mesh with multiple broadcasting of sizen×n. The second algorithm shows that the same problem can be solved inO (1) time on a reconfigurable mesh of sizen×n. Both algorithms achieve time lower bounds for their respective model of computation.This work was supported by NASA under grant NCCI-99.Additional support by the National Science Foundation under grant CCR-8909996 is gratefully acknowledged.     

The star chromatic number of a graph

We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.     

On upper records in sequences of non-identically distributed random variables

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 194, pp. 124–133, 1992.     

Intercomparison between ozone-broadening parameters retrieved from millimetre-wave measurements by using different techniques

For atmospheric purposes, the N₂- and O₂-, or Air-broadenings of selected transitions of ozone have been investigated in the 195-300 K temperature range. More precisely, the following 13 transitions in the 280-345 GHz frequency range have been studied: the 2_2,0 ← 2_1,1 (279.5 GHz), 24_2,22 ← 24_1,23 (286.2 GHz), 3_2,2 ← 3_1,3 (286.3 GHz), 5_2,4 ← 5_1,5 (293.2 GHz), 13_4,10 ← 14_3,11 (300.7 GHz), 14_0,14 ← 13_1,13 (301.8 GHz), 7_2,6 ← 7_1,7 (303.2 GHz), 26_2,24 ← 26_1,25 (315.9 GHz), 5_3,3 ← 6_2,4 (317.2 GHz), 20_1,19 ← 20_0,20 (320.0 GHz), 26_6,20 ← 27_5,23 (343.2 GHz), 26_2,24 ← 25_3,23 (343.2 GHz), and 4_3,1 ← 5_2,4 (343.5 GHz) lines. Systematic errors are known to be the principal error source and recent intercomparisons of line-broadening coefficients showed differences up to 20%, thus a large effort in minimizing systematic error sources has been taken and cross check measurements with different techniques have been carried out. The conclusion of the intercomparison performed indicates an excellent agreement of the results and that an uncertainty less than 3%, which also takes into account the systematic errors, can be claimed for the line-broadening parameters.     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007     

Conditions d'optimalité du second ordre nécessaires ou suffisantes pour les problèmes de commande optimale avec une contrainte sur l'état et une commande scalaires

This Note deals with optimal control problems with only one control variable and one state constraint, of arbitrary order. We consider the case of finitely many boundary arcs and touch times. We obtain a no-gap theory of second-order conditions, allowing us to characterize second-order quadratic growth. To cite this article: J.F. Bonnans, A. Hermant, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Generation of 0.2-TW 5.5-fs optical pulses at 1 kHz using a differentially pumped hollow-fiber chirped-mirror compressor

Optical pulses with 1.1-mJ energy and 5.5-fs duration have been generated at 1-kHz repetition rate from a chirped pulse amplification Ti:Sapphire laser incorporating a differentially pumped hollow-fiber chirped-mirror compressor. The effects of self-focusing and multi-photon ionization during the beam propagation were minimized by differentially pumping the hollow fiber filled with neon. The spectral broadening at the hollow-fiber compressor was optimized by adjusting gas pressure, laser intensity, and laser chirp, covering from 540 nm to 950 nm. PACS 42.65.Jx; 42.65.Re