Synthesis and structural characterisation of [(Ph3P)AuCo(CO)3(PPh3)]

Summary [(Ph₃P)AuCo(CO)₃(PPh₃)] has been synthesised from [(Ph₃P)AuCo(CO)₄], PPh₃v and Me₃NO in acetonitrile. Its molecular structure, determined by single-crystal x-ray crystallography, consists of an almost linear P-Au-Co-P arrangement in which the Co atom is in a slightly distorted trigonalbipyramidal geometry, with the Au and P atoms occupying the apical sites. The Au-Co bond length of 2.450(1) ? is shorter than that reported for [(Ph₃P)AuCo(CO)₄]. The carbonyl ligands are bent towards the Au atom and the mean Au-Co-C angle is 81(1)°.     

Ionic conductivity in Na+, K+, and Ag+ β″-alumina

This paper presents measurements of the ionic conductivity in single crystals of β″-alumina (0.84 M₂O · 0.67 MgO · 5.2 Al₂O₃, M = Na, K, Ag). Single crystals of sodium β″-alumina were grown from a melt of Na₂O, MgO, and Al₂O₃ at 1660 to 1730°C. Selected crystals were converted to the other isomorphs by ion exchange. The conductivity of sodium β″-alumina varies from 0.18 to 0.01 (ohm · cm)^?1 at 25°C depending upon crystal growth conditions. Potassium β″-alumina has the unusually high room temperature conductivity of 0.13 (ohm · cm)^?1. Silver β″-alumina has a slightly lower conductivity, 4 × 10^?3 (ohm · cm)^?1 at 25°C. The activation energies of sodium and potassium β″-alumina decrease with increasing temperature, while that of silver β″-alumina is constant from ?80 to 450°C.     

Comparison of bundle and classical column generation

When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard. One of them is the bundle method; our aim is to illustrate its differences with Kelley’s method. In the process we review alternative stabilization techniques used in column generation, comparing them from both primal and dual points of view. Numerical comparisons are presented for five applications: cutting stock (which includes bin packing), vertex coloring, capacitated vehicle routing, multi-item lot sizing, and traveling salesman. We also give a sketchy comparison with the volume algorithm. This research has been supported by Inria New Investigation Grant “Convex Optimization and Dantzig-Wolfe Decomposition”.     

Deformable two-dimensional photonic crystal slab for cavity optomechanics

We have designed photonic crystal suspended membranes with optimized optical and mechanical properties for cavity optomechanics. Such resonators sustain vibration modes in the megahertz range with quality factors of a few thousand. Thanks to a two-dimensional square lattice of holes, their reflectivity at normal incidence at 1064?nm reaches values as high as 95%. These two features, combined with the very low mass of the membrane, open the way to the use of such periodic structures as deformable end mirrors in Fabry-Perot cavities for the investigation of cavity optomechanical effects.