Un théorème de convergence presque-sŭre pour des familles subordonnées à un semi groupe discret

LetP be a positive contraction ofL ¹, we say that a sequence (Q _n ) _n of positive operators is subordinated toP if $$Q_0 = Id, \forall n \in \mathbb{N} Q_n P \geqslant Q_{n + 1} .$$ Let (Q _n,k ) be a double sequence of operators such that for each integerk the sequence (Q _n,k ) _n is subordinated toP. We prove a result of almost everywhere convergence for the quotientsW ^k f/W _k g, whereW ^k f=∑ _n=0 ^∞ Q _n,k f.     

Zirconocene-mediated route to enantiopure 9-oxabicyclononanes functionalized on both carbon bridges

[reaction: see text] A zirconocene-mediated ring contraction of 4-vinylfuranosides generated either from d-arabinose or d-glucose is followed by sequential oxidation to the ketone and alkynyl Grignard addition. The resulting cis-cyclobutanediols are subjected in turn to thermal rearrangement and intramolecular oxymercuration-demercuration. The regiochemistry of the final ring closure is controlled by the nature of R.     

Giant vesicles formed by gentle hydration and electroformation: a comparison by fluorescence microscopy

Giant unilamellar vesicles (diameter of a few tens of micrometers) are commonly produced by hydration of a dried lipidic film. After addition of the aqueous solution, two major protocols are used: (i) the gentle hydration method where the vesicles spontaneously form and (ii) the electroformation method where an ac electric field is applied. Electroformation is known to improve the rate of unilamellarity of the vesicles though it imposes more restricting conditions for the lipidic composition of the vesicles. Here we further characterize these methods by using fluorescence microscopy. It enables not only a sensitive detection of the defects but also an evaluation of the quantity of lipids in these defects. A classification of the defects is proposed and statistics of their relative importance in regard to both methods and lipid composition are presented: it shows for example that 80% of the vesicles obtained by electroformation from 98% 1,2-dioleoyl-sn-glycero-3-phosphocholine are devoid of significant defects against only 40% of the vesicles with the gentle hydration method. It is also shown that the presence of too many negatively charged lipids does not favor the formation of unilamellar vesicles with both methods. For the gentle hydration, we checked if the negatively charged lipids were inserted in the vesicles membrane in the same proportion as that of the lipid mixture from which they are formed. The constant incorporation of a negatively charged labeled lipid despite an increasing presence of negatively charged 1,2-dioleoyl-sn-glycero-3-[phospho-l-serine] tends to confirm that the composition of vesicles is indeed close to that of the initial mixture.     

Design and synthesis of push-pull chromophores for second-order nonlinear optics derived from rigidified thiophene-based pi-conjugating spacers.

Two series of push-pull chromophores built around thiophene-based pi-conjugating spacers rigidified either by covalent bonds or by noncovalent intramolecular interactions have been synthesized and characterized by UV-vis spectroscopy, electric field induced second harmonic generation (EFISH) and differential scanning calorimetry. Comparison of the linear and second-order nonlinear optical properties of chromophores based on a covalently bridged dithienylethylene (DTE) spacer with those of their analogues based on open chain DTE shows that the rigidification of the spacer produces a considerable bathochromic shift of the absorption maximum together with a dramatic enhancement of the molecular quadratic hyperpolarizability (mu beta) which reaches values among the highest reported so far. A second series of NLO-phores has been derived from a 2,2'-bi(3,4-ethylenedioxythiophene) (BEDOT) pi-conjugating spacer. As indicated by X-ray and UV-vis data, rigidification of the spacer originates in that case, from noncovalent intramolecular interactions between sulfur and oxygen atoms. Again, comparison with the parent compounds based on an unsubstituted bithiophene spacer reveals a marked red shift of the absorption maximum and a large enhancement of mu beta. In an attempt to distinguish the contribution of the electronic and geometrical effects of the ethylenedioxy group, a third series of NLO-phores based on 3,4-ethylenedioxythiophene (EDOT) and 3,4-dihexyloxythiophene spacers has been synthesized. Comparison with compounds based on unsubstituted thiophene shows that, despite a red shift of lambda(max), introduction of alkoxy groups leads to a decrease of mu beta. Theoretical calculations indicate that this effect results from a decrease of the dipole moment (mu) caused by the auxiliary electron-donor alkoxy groups on the thiophene ring. In contrast, replacement of BT by BEDOT produces an increase of mu, which associated with the noncovalent rigidification of the BT system accounts for the observed enhancement of mu beta.     

Mn(approximately)2.4Mo6O9: first example of empty twin chains of edge-sharing M6 octahedra in transition metal cluster chemistry

The novel ternary reduced molybdenum oxide Mn(approximately)(2.4)Mo(6)O(9) has been synthesized by solid-state reaction at 1400 degrees C for 96 h in sealed molybdenum crucibles. Electron diffraction studies showed that Mn(approximately)(2.4)Mo(6)O(9) presents a complex crystal structure with a 3d incommensurate modulation. The average crystal structure was determined on a single-crystal by X-ray diffraction in the orthorhombic space group Pnma with the following lattice parameters: a = 16.4824(2) A, b = 2.8273(2) A, c = 17.3283(2) A, Z = 4. The Mo network consists of empty twin chains of trans-edge-sharing octahedra that occur for the first time in a solid-state compound. The Mo-Mo distances within the chains range from 2.62 to 2.92 A, and the Mo-O distances from 1.99 to 2.17 A as usually observed in the reduced molybdenum oxides. Single-crystal resistivity measurements show that Mn(approximately)(2.4)Mo(6)O(9) is metallic between 4.2 and 300 K. The magnetic susceptibility data indicate paramagnetic behavior due to the Mn(2+) moment at high temperatures with a weak ferromagnetic behavior below 80 K.     

A novel layered oxysulfide intergrowth compound Sr4Mn2Cu5O4S5 containing a fragment of the alpha-Cu2S antifluorite structure

Sr4Mn2Cu5O4S5 contains manganese oxide sheets separated by unusual antifluorite-type Cu3S3 layers in which copper(I) ions are distributed over three- and four-coordinates sites in a similar fashion to in alpha-Cu2-xS and suggestive of high two-dimensional copper ion mobility.     

Development of a multiplexed microbioreactor system for high-throughput bioprocessing

A multiplexed microbioreactor system for parallel operation of multiple microbial fermentation is described. The system includes miniature motors for magnetic stirring of the microbioreactors and optics to monitor the fermentation parameters optical density (OD), dissolved oxygen (DO), and pH, in-situ and in real time. The microbioreactors are fabricated out of poly(methylmethacrylate)(PMMA) and poly(dimethylsiloxane)(PDMS), and have a working volume of 150 microl. Oxygenation of the cells occurs through a thin PDMS membrane at the top of the reactor chamber. Stirring is achieved with a magnetic spin bar in the reactor chamber. Parallel microbial fermentations with Escherichia coli are carried out in four stirred microbioreactors and demonstrate the reproducible performance of the multiplexed system. The profiles for OD, DO, and pH compare favourably to fermentations performed in bioreactor systems with multiple bench-scale reactors. Finally, the multiplexed system is used to compare two different reactor designs, demonstrating that the reproducibility of the system permits the quantification of microbioreactor performance.     

Efficient synthesis of bromocyclopenta[b] indoles via a bromination ‐ reduction sequence

Substituted cyclopenta[b]indoles are selectively brominated in good yields with excess pyridine ‐ Br₂ charge‐transfer complex (PyBr₂) in a one‐pot reaction to provide 5 and/or 7‐bromoindoles. The mechanism involves the formation of an adduct (addition of bromine on the central double bond) which is subsequently reduced in situ with Zn and AcOH. A variety of functional groups in the cyclopentyl and the benzenoid rings are tolerated.