The plus construction, Postnikov towers and universal central module extensions

Given a connected spaceX, we consider the effect of Quillen’s plus construction on the homotopy groups ofX in terms of its Postnikov decomposition. Specifically, using universal properties of the fibration sequenceAX→X→X ⁺, we explain the contribution of π _n X to π _n X ⁺, π _n+1 X ⁺ and π _n AX, π _n+1 AX explicitly in terms of the low dimensional homology of π _n X regarded as a module over π₁ X. Key ingredients developed here for this purpose are universal II-central fibrations and a theory of universal central extensions of modules, analogous to universal central extensions of perfect groups. Research partially supported by NSERC of Canada.     

Decay of neutron-rich Ga isotopes near N = 50 at PARRNe

The PARRNe facility has been used to produce neutron-rich isotopes ^83,84Gaby the ISOL method. Their decay has been studied, and β-γ coincidence and γ-γ coincidence data were collected as a function of time. The first two excited levels in ⁸³Ge and the first excited level in ⁸⁴Ge have been measured for the first time.     

Du discret au continu pour des modèles de réseaux aléatoires d'atomes

We study in this Note the continuum (macroscopic) limit for some atomistic models for crystals. The purpose is to derive densities of mechanical energies from microscopic models. In contrast to the setting of a previous study, where the microscopic structure was assumed to be periodic, it is modelled here by a stochastic lattice, which enjoys some stationarity and ergodicity properties, following notions previously introduced elsewhere. To cite this article: X. Blanc et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Computation of Autocorrelations of Interdeparture Times by Numerical Transform Inversion

The generating function of the autocorrelations of the interdeparture times in stationary M/G/1 and GI/M/1 systems involves the probability generating function of the number of customers served in a busy period. The latter function is implicitly determined as a solution to a functional equation. Standard methods for the numerical inversion of generating functions require the values of these functions at many complex arguments. A recently discovered substitution method for contour integrals allows the numerical inversion of implicitly determined generating functions without the numerical solution of the functional equations.     

The ALTO project at IPN-Orsay

The availability of both a tandem deuteron beam and a linac electron beam, the latter converted into Bremsstrahlung, at the new ALTO facility at IPN-Orsay offers a unique opportunity to compare the performance of a laser ion guide under different regimes. The ALTO accelerator has delivered its first electron beam at the end of 2005 and a design for a gas-cell prototype is being studied.     

Nouvelle méthode de dosage automatique de substances oxydantes ou réductrices par potentiométrie différentielle : Partie I. Étude théorique

A new method is proposed for routine determinations of oxidizable and reducible substances. A mathematical development and criticism of the method of Schierjott has led to a fundamental modification of the earlier experimental conditions (ratio of the oxidized/reduced forms of the reagent at the start and end of the redox reaction). This improvement allows a considerable increase in the sensitivity of the method and is particularly advantageous for the determination of substances of low reactivity, e.g. carbohydrates. Other advantages are a reduction in the quantity and thus cost of the necessary reagent, and a decreased risk of precipitation of the substances involved. The mathematical treatment of the proposed version allows a rigorous theoretical comparison of the two methods. An evaluation of the quality of the approximations introduced into both methods is also proposed, based on the calculation of the deviation (absolute and relative differences) of approximated values from theoretical values. The final part of the work deals with optimization of the different principal parameters, i.e. concentration of the reagent, temperature and reaction time.     

Rational incorporation of defects within metal–organic frameworks generates highly active electrocatalytic sites

The allure of metal–organic frameworks (MOFs) in heterogeneous electrocatalysis is that catalytically active sites may be designed a priori with an unparalleled degree of control. An emerging strategy to generate coordinatively-unsaturated active sites is through the use of organic linkers that lack a functional group that would usually bind with the metal nodes. To execute this strategy, we synthesize a model MOF, Ni-MOF-74 and incorporate a fraction of 2-hydroxyterephthalic acid in place of 2,5-dihydroxyterephthalic acid. The defective MOF, Ni-MOF-74D, is evaluated vs. the nominally defect-free Ni-MOF-74 with a host of ex situ and in situ spectroscopic and electroanalytical techniques, using the oxidation of hydroxymethylfurtural (HMF) as a model reaction. The data indicates that Ni-MOF-74D features a set of 4-coordinate Ni–O₄ sites that exhibit unique vibrational signatures, redox potentials, binding motifs to HMF, and consequently superior electrocatalytic activity relative to the original Ni-MOF-74 MOF, being able to convert HMF to the desired 2,5-furandicarboxylic acid at 95% yield and 80% faradaic efficiency. Furthermore, having such rationally well-defined catalytic sites coupled with in situ Raman and infrared spectroelectrochemical measurements enabled the deduction of the reaction mechanism in which co-adsorbed *OH functions as a proton acceptor in the alcohol oxidation step and carries implications for catalyst design for heterogeneous electrosynthetic reactions en route to the electrification of the chemical industry.

The allure of metal–organic frameworks (MOFs) in heterogeneous electrocatalysis is that catalytically active sites may be designed a priori with an unparalleled degree of control.     

Synthesis and crystal chemistry of NH3(MoO3)3

NH₃(MoO₃)₃ crystallizes with hexagonal symmetry, space group $\text{P6}{}_3\text{m}$, lattice constants a = 10.568 Å, c = 3.726 Å, and Z = 2. The crystal structure has been determined by Patterson synthesis and refined assuming isotropic temperature factors to a final conventional R value of 0.085. The structure shows a three-dimensional arrangement built up of double chains of distorted MoO₆ octahedra, parallel to the [001] direction. The octahedral double chains are linked among each other through common oxygen atoms. In addition to the shared oxygen atoms, each molybdenum is coordinated to one terminal oxygen. MoO distances range from 1.645 to 2.378 Å and OMoO angles from 74.3 to 114.3°. These results are consistent with the fact that molybdenum in high-valence states shows octahedral coordination with terminal oxygens.     

19F NMR chemical shifts of n-F-alkyl compounds

The examination of ¹⁹F chemical shifts for ca. 650 F-alkylated compounds of general formula CF₃(CF₂)_nCF₂X led to the following conclusions: the CF₂ groups α to X are very sensitive to the nature of X, and are spread over a range of 85 ppm. The effect of the length of the F-alkyl chain decreases rapidly, so that δCF₂(α) can already be considered as characteristic of X for n = 1 or 2 for most practical purposes. Solvent effects (in 9 different solvents having ε = 1.8 to 52.1) were found to be rather small except for the F-alkyl iodides. A chart which indicates the domain in which the CF₂(α) resonance signal is to be expected is given for 42 different series of F-alkylated compounds; it is expected to provide the synthetic chemist with a useful tool for the identification and characterization of such compounds.     

Simultaneous off-shell excitation of He 23 S by an electron and one or more photons

We report data on the excitation of the 2³ S metastable state in helium by electrons in the presence of an intense laser field. The metastable signal is detected when the electron energy is insufficient to excite this state by itself. The additional energy comes from a pulsed CO₂ laser developing peak intensities in the interaction region in the 10⁸ W× cm^?2 range and requires the absorption of one or more photons. This process involves the active participation of all three bodies: the electron, the photon and the target atom. These data represent the first observation of this process when more than one photon is required.