Existence of black hole solutions for the Einstein-Yang/Mills equations

This paper provides a rigorous proof of the existence of an infinite number of black hole solutions to the Einstein-Yang/Mills equations with gauge groupSU(2), for any event horizon. It is also demonstrated that the ADM mass of each solutions is finite, and that the corresponding Einstein metric tends to the associated Schwarzschild metric at a rate 1/r ², asr tends to infinity.Research supported in part by the NSF, Contract No. DMS-89-05205Research supported in part by the DE, Contract No. De-FG 02-88 EF 25065     

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.     

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).     

The effect of gamma irradiation and shelf aging in air on the oxidation of ultra-high molecular weight polyethylene

This study has investigated the effect of shelf aging, for up to one year in air, on the properties of gamma-irradiated ultra-high molecular weight polyethylene (UHMWPE). A variety of techniques were used to characterize the properties of treated samples. Differential scanning calorimetery (DSC) was used to characterize the morphology. The extent of cross-linking in a polymer network was detected by swelling measurements. The durometer hardness test was used to measure the relative hardness of this material, and changes in density were also measured. Results from all these measurements were combined to explain the changes in the microstructure of the aged, irradiated UHMWPE. This study shows that crystallinity is increased with radiation dose and with aging due to chain scission, which leads to a reduction in the molecular weight of the material. This allows the chains to rearrange to form crystalline regions. Positron annihilation lifetime spectroscopy confirms these conclusions. Fractional free volumes have been deduced from lifetime parameters, which correlate with the data obtained by the other techniques.     

Influence of octupole interactions on the behavior of negative-parity states at low spins

The energies of negative-parity levels based on two-particle states exhibit a nonlinear behavior at low spins versus the core-rotation energy because the alignment process has not yet been completed for them. This behavior of negative-parity levels in the low-spin region is satisfactorily described upon the inclusion of octupole-octupole interactions. This is demonstrated within the rotational model involving the Coriolis mixing of states for the even-even isotopes ^162–168Hf.     

Propagation of a focused light beam in a circuital system of tunnel-coupled waveguides

The propagation of a pencil beam in a circuital system of tunnel-coupled waveguides is considered. It is shown that the beam periodically focuses into a point when moving along the trajectory. A maximal number of waveguides supporting the propagation of the beam can be estimated in simple terms. The cross-sectional area of the waveguides can be subdivided into three zone with the beam pulsing only in the central one.