Sur les graphes 2-reconstructibles

Let k be an integer (k?1) and G=(V,E) a graph with more than k vertices, a graph G′=(V,E′) is a k-reconstruction of G if, for any subset W of V with k elements, the subgraphs G(W) and G′(W) induced by W are isomorphic. The graph G is k-reconstructible when each k-reconstruction of G is isomorphic to G. Lopez (Z. Math. Logik Grundlag. Math. 24 (1978) 303–317) proved that any graph is 6-reconstructible. For k=3,4 and 5, the k-reconstructible graphs were studied in Boudabbous and Lopez (Eur. J. Combin. 23 (2002) 507–522; C. R. Acad. Sci. Paris, Sér. I 329 (1999) 845–848). In this Note, we introduce a permutations group allowing for the interpretation of the 2-reconstructibility and we characterize the graphs which are embedded in a 2-reconstructible graph. To cite this article: A. Boussairi, A. Chaichaa, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

A new sorbent for europium nitrate extraction: phosphonic acid grafted on polystyrene resin

A new chelating polymeric sorbent has been developed using polystyrene resin grafted with phosphonic acid. After characterization by FTIR and elementary analysis, the new resin has been investigated in liquid–solid extraction of europium(III). The results indicated that phosphonic resin could adsorb Eu(III) ion effectively from aqueous solution. The adsorption was strongly dependent on pH of the medium with enhanced adsorption as the pH value of 6.5. The influence of other analytical parameters including contact time, amount of resin, metal ion concentration, and ionic strength were investigated. The maximum uptake capacity of Eu(III) ions was 122.6 mg/g grafted resin at ambient temperature, at an initial pH value of 6.50. The overall adsorption process was best described by pseudo first-order kinetic. When Freundlich and Langmuir isotherms were tested, the latter had a better fit with the experimental data. Furthermore, Eu(III) could be eluted by using 1.0 mol/L H₂SO₄ solution and the grafted resin could be regenerated and reused.     

Optimization,Convex and Variational Analysis – Volume II

Set-Valued and Variational Analysis -     

Efficient computation of non-isothermal highly viscous incompressible flow

We consider the numerical solution of the non–isothermal incompressible Navier–Stokes equations using a discrete projection method. The computation of velocity and temperature subproblems is carried out on different meshes chosen with respect to the physical behavior of these quantities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rheological modeling of the diffusion process and the interphase of symmetrical bilayers based on PVDF and PMMA with varying molecular weights

The diffusion process in the molten state at a polymer/polymer interface of symmetrical and model bilayers has been investigated using a small-amplitude oscillatory shear measurement. The polymers employed in this study were poly (vinylidene fluoride) (PVDF) and poly (methyl methacrylate) (PMMA) of varying molecular weights and polydispersities. The measurements were conducted in the linear viscoelastic regime (small deformations) so as to decouple the effect of flow from the diffusion. The focus of this paper has been to investigate the effects of healing time, angular frequency (ω), temperature, and molecular weight on the inter-diffusion and the triggered interphase between the neighboring layers. The kinetics of diffusion, based on the evolution of the apparent diffusion coefficient (D _a) versus the healing time, was experimentally obtained. The transition from the non-Fickian to the normal Fickian region for the inter-diffusion at the interface was clearly observed, qualitatively consistent with the reptation model, but it occurred at a critical time greater than the reptation time (τ _rep). In non-Fickian region, effects of frequency and temperature were studied with regard to the ratio of the apparent diffusion coefficient to the self-diffusion coefficient (D _a/D _s). The D _s determined in the Fickian region was found to be consistent with Graessley’s model as well as with the literatures. And the dependence of the D_s on the frequency agreed well with the Doi–Edwards theory, in particular, scaling as $D_{\rm s} \sim \omega^{1/2}$ at ω?>?1/τ _e and $D_{\rm s} \sim \omega^{0}$ at ω?<?1/τ _rep. Our experimental results also confirmed that the dependence of the D _s on the temperature for PMMA and PVDF can be well described by the Arrhenius law. Moreover, blends of PMMAs have been proposed in order to be able to change the $\overline M_\emph{w} $ . The rheological investigations of these corresponding bilayers rendered it possible to monitor the effect of $\overline M_\emph{w} $ on the diffusion process. The obtained results gave $D_{\rm s} \sim \overline M_\emph{w}^{-1}$ , thus corroborating some earlier studies and some experimental results recently reported by Time-Resolved Neutron Reflectivity Measurements. Lastly, the thickness of the interphase and its corresponding viscoelastic properties could be theoretically determined as a function of the healing?time.     

Aryl Radical‐Mediated Alkenylation of Alkyl Halides

The free‐radical alkenylation of a range of alkyl iodides with a vinyldisulfones has been carried out, leading to the desired vinylsulfones in moderate to good yields under mild conditions. The process is initiated by an aryl radical which abstracts the iodine atom from the alkyl iodide to form a C‐centered radical intermediate, the addition of which onto the vinyldisulfone providing the final vinylsulfone. The aryl radical is generated in situ through a single‐electron transfer from an electron donor‐acceptor complex (EDA) formed between a diaryliodonium salt (Ph₂I⁺ PF₆^?) and triethylamine.     

Synthesis of new molecules containing head,spacer, and label moieties

We describe the synthesis and characterization of novel molecules containing head with precise shape, spacer, and label moieties. The protocol is based on a Pd(0)-catalyzed cross-coupling reaction between ethynylphenyl/bromide to obtain a rigid head followed by the attachment of a flexible spacer possessing two reactive functional groups on the termini. The final step consists of forming a covalent bond between spacer and label. In addition, monosubstituted soluble labels were synthesized in good yields.