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.     

Impact of the industry on franchise chain efficiency: a meta-DEA and context-dependent DEA approach

A meta-DEA (Data Envelopment Analysis) approach is used to analyse the impact of the industry in which the franchisor operates its business on its chain efficiency by comparing chain efficiency between and across industries (retail versus services). To provide realistic short-term and long-term objectives to inefficient chains, a level-by-level benchmarking path is developed with the context-dependent DEA approach. Furthermore, the joint implementation of both approaches enables an identification of chains for which the industry influences their efficiency, an evaluation of the efficiency share that results from industry-specific factors rather than factors common to the franchise sector as a whole, and the characterization of an implementable and achievable benchmarking defining level-by-level improvements of chain efficiency and taking into account chain characteristics. Such an analysis can help franchisors to define their future strategic and managerial orientations.     

Norm Estimates for Weighted Composition Operators on Spaces of Holomorphic Functions

This paper shows that the boundedness of a weighted composition operator on the Hardy–Hilbert space on the disc or half-plane implies its boundedness on a class of related spaces, including weighted Bergman spaces. The methods used involve the study of lower-triangular and causal operators.     

Preparation of a polyacrylonitrile/multi-walled carbon nanotubes composite by surface-initiated atom transfer radical polymerization on a stainless steel wire for solid-phase microextraction

We report on the fabrication and performances of a solid-phase microextraction (SPME) fiber based on a stainless steel wire coated with a covalently attached polyacrylonitrile (PAN)/multi-walled carbon nanotubes (MWCNTs) composite. This new coating is obtained by atom transfer radical polymerization (ATRP) of acrylonitrile mixed with MWCNTs. ATRP is initiated from 11-(2-bromo-2-methylpropionyloxy)-undecyl-phosphonic acid molecules grafted on the wire surface via the phosphonic acid group. The extraction performances of the fibers are assessed on different classes of compounds (polar, non-polar, aromatic, etc.) from water solutions by headspace extraction. The optimization of the parameters affecting the extraction efficiency of the target compounds was studied as well as the reproducibility and the repeatability of the fiber. The fibers sustain more than 200 extractions during which they remain chemically stable and maintain good performances (detection limits lower than 2 μg/l, repeatability, etc.). Considering their robustness together with their easy and inexpensive fabrication, these fibers could constitute promising alternatives to existing products.     

Microwave-assisted synthesis of α-ethoxycarbamates

An efficient and reproducible synthesis of various α-ethoxycarbamates is described via a microwave heating mode. Compared to the thermal process, the microwave dielectric heating induces a dramatic reduction of the reaction time and the improvement of the yields. The reaction is general since applicable to aromatic and aliphatic aldehydes with various primary amines. Several examples involving chiral aldehydes have also been considered.     

Enantioselective hydrogenation of indoles derivatives catalyzed by Walphos/rhodium complexes

The enantioselective hydrogenation of indole esters has been carried out efficiently in the presence of a rhodium catalyst modified by Walphos-type chiral ligands. The addition of a base can be beneficial in some catalytic conditions.     

Purcell enhancement of spontaneous emission from quantum cascades inside mirror-grating metal cavities at THz frequencies

Quantum cascade devices processed into double metal cavities with subwavelength thickness and a grating on top are studied at terahertz frequencies. The power extracted from the devices as a function of the device thickness and the grating period is analyzed owing to electrodynamical modeling of dipole emission based on a modal method in multilayer systems. The experimental data thus reveal a strong Purcell enhancement, with Purcell factors up to approximately 50.     

Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group

It was proved by Bahouri et al. [9] that the Schrödinger equation on the Heisenberg group $\mathbb{H}^d,$ involving the sublaplacian, is an example of a totally non-dispersive evolution equation: for this reason global dispersive estimates cannot hold. This paper aims at establishing local dispersive estimates on $\mathbb{H}^d$ for the linear Schrödinger equation, by a refined study of the Schrödinger kernel $S_t$ on $\mathbb{H}^d.$ The sharpness of these estimates is discussed through several examples. Our approach, based on the explicit formula of the heat kernel on $\mathbb{H}^d$ derived by Gaveau [19], is achieved by combining complex analysis and Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel $S_t$ concentrates on quantized horizontal hyperplanes of $\mathbb{H}^d.$