An organometallic RhIII complex with a distorted octahedral structure: (acetonitrile‐κN)dimethyl(1,4,7‐trimethyl‐1,4,7‐triazacyclononane‐κ3N,N′,N′′)rhodium(III) tetraphenylborate

In the title compound, [Rh(CH₃)₂(C₂H₃N)(C₉H₂₁N₃)](C₂₄H₂₀B), the geometry around the Rh^III centre is distorted octahedral, with elongated Rh—N bonds trans to the metal‐bonded methyl groups. The metal‐containing cations are located in channels formed by an anionic supramolecular mesh, in which aromatic π–π interactions between anionic [B(Ph)₄]^? units play a major role.     

Explicit limits for nonperiodic homogenization and reduction of dimensionLimites explicites pour l'homogénéisation non-périodique et la réduction de dimension

The aim of this Note is to give explicit limit expressions, for diffusion equations involving a small parameter ε, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials. To cite this article: B. Gustafsson, J. Mossino, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 977–982.     

Dynamics of the periodic type-K competitive Kolmogorov systems

For time-periodic dissipative and irreducible type-K competitive Kolmogorov systems, it is proved that there is a canonically defined countable family F of unordered, disjoint invariant sets with the property that, for every persistent trajectory whose ω-limit set is not a cycle, there exists a unique trajectory in some element of F such that these two trajectories are asymptotic and the corresponding points in these two trajectories are K-related.     

Crystal structure and magnetic properties of two new cobalt selenite halides: Co5(SeO3)4X2 (X=Cl, Br)

Two new isostructural cobalt selenite halides Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂ have been synthesized. They crystallize in the triclinic system space group P−1 with the following lattice parameters for Co₅(SeO₃)₄Cl₂: a=6.4935(8) Å, b=7.7288(8) Å, c=7.7443(10) Å, α=66.051(11)°, β=73.610(11)°, γ=81.268(9)°, and Z=1. The crystal structures were solved from single-crystal X-ray data, R1=3.73 and 4.03 for Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂, respectively. The new compounds are isostructural to Ni₅(SeO₃)₄Br₂.Magnetic susceptibility measurements on oriented single-crystalline samples show anisotropic response in a broad temperature range. The anisotropic susceptibility is quantitatively interpreted within the zero-field splitting schemes for Co²⁺ and Ni²⁺ ions. Sharp low-temperature susceptibility features, at T_N=18 and 20 K for Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂, respectively, are ascribed to antiferromagnetic ordering in a minority magnetic subsystem. In isostructural Ni₅(SeO₃)₄Br₂ magnetically ordered subsystem represents a majority fraction (T_N=46 K). Nevertheless, anisotropic susceptibility of Ni₅(SeO₃)₄Br₂ is dominated at low temperatures by a minority fraction, subject to single-ion anisotropy effects and increasing population of S_z=0 (singlet) ground state of octahedrally coordinated Ni²⁺.     

Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators A_j on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.     

Corrigendum to “EuBaFe2O5+w: Valence mixing and charge ordering are two separate cooperative phenomena” [J. Solid State Chem. 180 (2007) 148-157]

An error in the expression for the Fe²⁺, Fe³⁺ valence-mixing probability in RBaFe₂O_5+w is acknowledged and correct formula is derived. The new formula slightly improves the least-squares fit to the experimental concentrations of the Mössbauer component Fe^2.5+ as a function of the oxygen-nonstoichiometry parameter w for R=Eu.     

Pure-silica optical waveguides, fiber couplers, and high-aspect ratio submicrometer channels for electrokinetic separation devices

A new fabrication procedure for integration of ultraviolet transparent pure-silica planar waveguides, fiber couplers and high-aspect ratio submicrometer channels is presented. Only a single photolithographic mask step is required. The channels are 80-90 microm deep and the width can be reduced to about 0.5 microm, corresponding to a height-to-width ratio of more than 150. The core of the waveguides consists of pure silicon dioxide, which is favorable over doped silica, due to the absence of absorption centers associated with the dopants. This furthermore improves the long-term stability of the waveguides, because of an increased radiation resistance of the glass. The propagation loss decreases from 1.0 dB/cm at 200 nm to 0.2 dB/cm at 800 nm, which, to our knowledge, is the lowest propagation loss reported for integrated planar waveguides in the ultraviolet wavelength region to date. The effective optical path length is 1.2 mm for an absorbance cell with a nominal length of 1.0 mm, indicating effective suppression of stray light. The limit of detection for paracetamol when present in the entire channel network was determined to 3 microg/mL. Finally, the applicability of the fabricated devices for capillary electrophoresis was evaluated by separation of caffein, paracetamol and ketoprofone using absorbance detection at 254 nm.     

Crosslinked polystyrene with improved mechanical properties

The synthesis of some divinyl monomers—bis(vinylphenyl)ethane ( 2 ), bis(vinylbenzyloxy)hexane ( 3a ), and bis(vinylbenzyloxy)dodecane ( 3b ) is reported. Copolymers of the new monomers and styrene were evaluated as an alternative to divinylbenzene-crosslinked polymers for use as matrices and absorbents. The mechanical properties and the amount of residual double bonds in the copolymers were compared. It was found that the new copolymers, unlike the divinylbenzene-crosslinked polymers, retained their mechanical strength even at high crosslinking degrees. Stress at break values of 79, 68, and 18 N/mm² were found for the polymers crosslinked with 20 mol % of 3a, 2 , and divinylbenzene; 5, 25 and 45% of the divinyl units in these polymers were left as pendant double bonds. Porous styrene– 2 copolymers were synthesized and shown to have lower surface areas than the corresponding divinylbenzene-crosslinked polymers. The pore size distribution showed that this was due to the absence of the smallest pores which are found in the divinylbenzene-crosslinked polymers in between heavily crosslinked nodules. © 1993 John Wiley & Sons, Inc.     

Independent component analysis yields chemically interpretable latent variables in multivariate regression

This work shows that independent component analysis (ICA) can be used to obtain statistically independent and, therefore, chemically interpretable latent variables (LVs) in multivariate regression. Two novel algorithms based on ICA are introduced and compared with two classical methods on simulated data: principal component regression and partial least-squares regression. All methods compared yield accurate predictions, but only those based on ICA yield LVs that are chemically interpretable. Practical limitations of ICA-based regression with respect to the underlying assumptions, sample size, and measurement noise are discussed and illustrated by means of simulations.     

Microwave-enhanced carbonylative generation of indanones and 3-acylaminoindanones

The development of microwave-accelerated protocols for palladium(0)-catalyzed carbonylative cyclization of unsaturated aryl bromides and chlorides is described. By employing o-bromostyryl derivatives lacking substituents on the vinylic bond, molybdenum hexacarbonyl-mediated in situ carbonylation delivered a set of indan-1-one products in high yield after only 20 min of heating. Without the addition of the tri-tert-butylphosphine releasing Fu-salt ((t-Bu)(3)PHBF(4)), only incomplete conversions of sluggish o-styryl bromides and chlorides were realized. Internal and chemoselective palladium(0)-catalyzed Heck arylations of enamides afforded suitable starting materials for subsequent rapid ring-closing reactions. Microwave-heated intramolecular in situ carbonylation of these electron-rich and sterically congested olefins conveniently afforded eight functionalized 3-acylaminoindanone derivatives in a novel synthetic process. Attempted carbonylative annulation of electron-poor o-bromocinnamic acid derivatives furnished only the corresponding lactones via a competing hydroxycarbonylation-Michael addition reaction sequence.