Diviseurs Des Nombres Ellipséphiques

Les propriétés multiplicatives des nombres ellipséphiques peuvent être obtenues à l’aide des moments de la série génératrice de cette suite. Nous donnons des estimations précises pour les grands moments par deux méthodes distinctes: l’une combinatoire fournit un résultat précis dans le cas réputé le plus difficile des nombres n’utilisant que les 0 et les 1; la seconde purement analytique fournit un résultat sans condition sur les chiffres.

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Molecular assemblies from imidazolyl-containing haloalkenes and haloalkynes: competition between halogen and hydrogen bonding

The structural characterization of molecular assemblies constructed from imidazolyl-containing haloalkenes and haloalkynes is reported. 1-(3-Iodopropargyl)imidazole (2) and 1-(2,3,3-triiodoallyl)imidazole (5) were synthesized from 1-propargylimidazole (1). In the solid state, these wholly organic modules self-assemble through N...I halogen-bonding interactions, thus giving rise to polymeric chains. The N...I interaction observed in 2 (d(N...I)=2.717 A, angle-spherical C(sp)-I...N=175.8 degrees) is quite strong relative to previously reported data. The N...I interaction in 5 (d(N...I)=2.901 A, angle-spherical C(sp2)-I...N=173.6 degrees) is weaker, in accordance with the order C(sp)-X<--base>C(sp2)-X<--base. Compound 5 was found to give a 1:1 cocrystal 4 with morpholinium iodide (6). In the X-ray crystal studies of 4, N...I halogen-bonding interactions similar to those observed in 5 were shown not to be present, as the arrangement of the molecules is governed by two interwoven hydrogen-bonding networks. The first network involves N-H...O interactions between nearby morpholinium cations, and the second network is based on N-H...N hydrogen bonding between morpholinium cations and imidazolyl groups. Both hydrogen-bonding schemes are charge-assisted. Halogen bonding is not completely wiped out, however, as the triiodoalkene fragment forms a halogen bond with an iodide anion in its vicinity (d(I...I)=3.470 A, angle-spherical C(sp2)-I...I=170.7 degrees). X-ray crystal studies of 6 show a completely different arrangement from that observed in 4, namely, N-H...O interactions are not present. In crystalline 6, morpholinium cations are interconnected through C-H...O bridges (d(H...O)=2.521 and 2.676 A), and the NH2+ groups interact with nearby iodide anions (d(H...I)=2.633 and 2.698 A).     

Stereoselective synthesis of P-chirogenic dibenzophosphole-boranes via aryne intermediates

A new aryne-mediated tandem cross-coupling/P-cyclization sequence starting from tertiary phosphine-boranes and 1,2-dibromobenzenes is reported. P-chirogenic dibenzophospholes become accessible in a regio-, chemo-, and diastereoselective way.     

C-O and C-C bond formation in the cyclisation of gem-(dialkoxymethyl)-1,6-dienes catalysed by tin(IV) triflimidate at room temperature

We described herein a Sn(NTf₂)₄-catalysed cyclisation of gem-(dialkoxymethyl)-1,6-dienes and derivatives where cyclohexane or tetrahydrofuran rings are formed following either a 6-enexo-endo-trig process or a 5-exo-trig process, respectively, depending on substitution patterns. The latter process features an unusual dealkylative ether cyclisation, triggered by the strong Lewis acid character of the tin(IV) triflimidate catalyst.     

Understanding the Reshaping of Fluorinated Polyester Vitrimers by Kinetic and DFT Studies of the Transesterification Reaction

Vitrimers are a third class of polymers gathering the mechanical properties and solvent resistance of 3D thermosets and the reprocessability of thermoplastics. This unique behaviour is due to the triggering of certain covalent exchange reactions that allow the network to rearrange upon application of a stimulus. The constitutive feature of vitrimers is the adoption of a glass-like viscosity during the rearrangement of the network, often due to an associative mechanism for the exchange reaction. Transesterification networks are one of the most studied type of vitrimers that usually require the incorporation of a catalyst, implying the associated drawbacks. Following up on a recent report on catalyst-free transesterification vitrimers in which the ester functions are particularly reactive thanks to the presence of fluorine atoms in α- or β-position, parallel DFT calculations and an experimental kinetic study on model molecules are presented in order to quantitatively assess the effect of neighbouring fluorinated groups on the transesterification reaction rate.     

Development of a compact alpha and beta camera for dismantlement applications

Journal of Radioanalytical and Nuclear Chemistry - A new method has been developed to image surface contamination on-site by short range radiation emitters (such as alpha or beta particle...     

Novel Foaming-Agent Free Insulating Geopolymer Based on Industrial Fly Ash and Rice Husk

This study highlights the synthesis of a new thermal insulating geopolymer based on the alkaline activation of fly ashes. A porous geopolymer material can be prepared without the addition of a foaming agent, using high ratio solution/ashes (activating solutions used are water, sodium or potassium hydroxide). In order to increase the porosity of the material and to make it more ecological, rice husks are incorporated into the formulation. The geopolymer materials were prepared at room temperature and dried at moderate temperature (105 °C) by a simple procedure. The microstructural characteristics of these new porous geopolymers were assessed by optical microscopy, X-ray diffraction (XRD), thermogravimetric analysis (TGA) and X-ray fluorescence (XRF). Infrared spectroscopy (FTIR) was used to confirm the geopolymerisation. The effect of the ratio solution/ashes and the percentage of the rice husk addition on thermal and mechanical analysis was evaluated. An insulating material for a solution/ashes ratio of 0.9 and a rice husk content of 15% having a λ value of 0.087 W/(m·K), a porosity of 61.4% and an Rc value of 0.1 MPa was successfully prepared.