Random Euclidean embeddings in spaces of bounded volume ratio

Let $\text{(}\text{R}{}^{\mathrm{N}}\text{,6·6)}$ be the space $\text{R}{}^{\mathrm{N}}$ equipped with a norm 6·6 whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N×n matrix with N>n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space $\text{(}\text{R}{}^{\mathrm{n}}\text{,|·|)}$ onto its image in $\text{(}\text{R}{}^{\mathrm{N}}\text{,6·6)}$: there exist α,β>0 such that for all $\text{x∈}\text{R}{}^{\mathrm{n}}$, $\text{α}\text{N}\text{|x|?6Γx6?β}\text{N}\text{|x|}$. This solves a conjecture of Schechtman on random embeddings of ?₂ⁿ into ?₁^N. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Integrated fluidic adaptive zoom lens

An integrated fluidic adaptive zoom lens is demonstrated for what is believed to be the first time. A zoom lens was fabricated using an UV lithographic-galvanic-like process involving soft lithography and wafer bonding. The zooming capability of such a lens was achieved by varying the focal length instead of the distance between the lenses. A zoom ratio of greater than 2 was obtained for devices that are 8 mm thick and have a 20-mm lens diameter. Including the 30-mm image distance, the total physical length of the fluidic zoom lens was less than 43 mm. More-compact systems with a higher zoom ratio can be obtained by reduction of the aperture size.     

An analytical and experimental comparison of optimal actuator and error sensor location for vibration attenuation

Feedforward active control of the flexural waves in a single and L-shaped plate has been analytically and experimentally investigated. The plates are simply supported along two parallel edges, and free at the other two ends. Point forces were used to generate the primary and secondary plate excitations. The plate flexural displacement is described by a combination of a travelling wave solution and a modal expansion. The flexural wave coefficients were determined using the boundary conditions, continuity equations at the driving force locations, and continuity equations at the corner junction for the L-shaped plate. The control actuator and error sensor are optimally located in order to achieve the best control performance.     

Photoionization microscopy

We present the first experimental results of a technique called photoionization microscopy. Photoelectrons ejected in threshold photoionization of Xe are detected in a velocity map imaging apparatus, and interferences between various trajectories by which the electron moves from the atom to the detector are observed. The structure of the interference pattern, which contains the transverse component of the electronic wave function, evolves smoothly with the excess energy above the saddle point. The main observed features are interpreted within the framework of the semiclassical approximation.     

Gas-phase carbene radical anions: new mechanistic insights

The gas-phase reactivity of the CHCl*- anion has been investigated with a series of halomethanes (CCl4, CHCl3, CH2Cl2, and CH3Cl) using a FA-SIFT instrument. Results show that this anion primarily reacts via substitution and by proton transfer. In addition, the reactions of CHCl*- with CHCl3 and CH2Cl2 form minor amounts of Cl2*- and Cl-. The isotopic distribution of these two products is consistent with an insertion-elimination mechanism, where the anion inserts into a C-Cl bond to form an unstable intermediate, which eliminates either Cl2*- or Cl- and Cl*. Neutral and cationic carbenes are known to insert into single bonds; however, this is the first observation of such reactivity for carbene anions.     

Carbazole compounds as host materials for triplet emitters in organic light-emitting diodes: polymer hosts for high-efficiency light-emitting diodes

A carbazole homopolymer and carbazole copolymers based on 9,9'-dialkyl-[3,3']-bicarbazolyl, 2,5-diphenyl-[1,3,4]-oxadiazole and 9,9-bis(4-[3,7-dimethyloctyloxy]phenyl)fluorene were synthesized and their electrical and photophysical properties were characterized with respect to their application as host in phosphorescent polymer light-emitting diodes. It is shown that the triplet energy of a polymer depends on the specific connections between its building blocks. Without changing the composition of the polymer, its triplet energy can be increased from 2.3 to 2.6 eV by changing the way in which the different building blocks are coupled together. For poly(9-vinylcarbazole) (PVK), a carbazole polymer often used as host for high-energy triplet emitters in polymer light-emitting diodes, a large hole-injection barrier of about 1 eV exists due to the low-lying HOMO level of PVK. For all carbazole polymers presented here, the HOMO levels are much closer to the Fermi level of a commonly used anode such as ITO and/or a commonly used hole-injection layer such as PEDOT:PSS. This makes high current densities and consequently high luminance levels possible at moderate applied voltages in polymer light-emitting diodes. A double-layer polymer light-emitting diode is constructed comprising a PEDOT:PSS layer as hole-injection layer and a carbazole-oxadiazole copolymer doped with a green triplet emitter as emissive layer that shows an efficacy of 23 cd/A independent of current density and light output.