Characterization of Laborde-Mulder graphs (extended odd graphs)

The identification of diametrical vertices in the d-dimensional hypercube (d 3) leads to a (0, 2)-graph of degree d on 2^d−1 vertices and of diameter d/2 namely the extended odd graph (or Laborde-Mulder graph) for odd values of d, and the half-cube for even values of d. In this paper we prove that the diameter of a (0, 2)-graph of degree d on 2^d−1 vertices is at least d/2 , and when d is odd the equality holds if and only if the graph is a Laborde-Mulder graph.     

Crystal structure and cation transport properties of the layered monodiphosphates Rb6Bi4(PO4)2(P2O7)3

Single crystals of the new Bi(III) phosphates, Rb₆Bi₄(PO₄)₂(P₂O₇)₃, have been isolated and their structure has been determined by X-ray diffraction techniques. This compound crystallizes in the monoclinic space group P2₁/c with a=9.077(1)Å, b=9.268(2)Å, c=36.418(6)Å, β=95.75(1)° and Z=8. The crystal structure is made up of BiO₅ and BiO₆ polyhedra sharing the corners with PO₄ tetrahedra and P₂O₇ diphosphate groups. The structure can be described as infinite anionic layers with composition [Bi₄(PO₄)₂(P₂O₇)₃]_∞⁶⁻ parallel to the [301] plane, connected via P-O-Bi bridges to form a three-dimensional open framework. This framework delimits tunnels running along [100] and [010] directions, where the rubidium ions reside. This compound exhibits a rubidium ion conduction but with rather low conductivity value at 640 K.     

Total synthesis of (±)-hibiscone B and (±)-acyl hibiscone B

The first total syntheses of the furanosesquiterpenoids hibiscone B and acyl hibiscone B are reported. The chemistry used to prepare hibiscone B solves an important challenge to the synthesis of other members of the furanosesquiterpenoid family of natural products, for which the parent molecule, hibiscone C, has shown promising biological activity.     

Microwave-assisted synthesis of calix[4]resorcinarenes

Microwave-assisted synthesis of calix[4]resorcinarenes by cyclocondensation of various aldehydes and resorcinol catalysed by 12-tungstophosphoric acid type Keggin (H₃PW₁₂O₄₀·13H₂O) or concentrated HCl is described. Excellent isolated yields (up to 90%) were attained within short reaction times (typically, 3-5 min) when the reaction was performed under microwaves irradiation.     

Characterizations of realized homogeneous Besov and Triebel-Lizorkin spaces via differences

Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via difference operators in a certain sense.     

Conformation of N,N′-bis (2,6-dimethylmorpholino), N″-dichloroacetyl phosphoric triamide: CHCl2C(O)NHP(O)[2,6(CH3)2(NC4H6O)]2. NMR and ab initio studies

Using phosphorus pentachloride as a substrate, a new carbacyclamidophosphate, N,N″-bis (2,6-dimethylmorpholino), N″-dichloroacetyl phosphoric triamide (1) has been synthesized and characterized by ¹H, ³¹P and ¹³C NMR, IR spectroscopy and elemental analysis. Due to the presence of methyl disubstituted morpholine rings and the dichloroacetamide group, several conformers can be considered for this molecule. The ³¹P{¹H} NMR spectra for the isomeric mixture of synthesized compound showed four signals with the ratio 67.1; 19.0; 12.2; 1.7, which indicates four independent conformers. The ¹H NMR spectra confirmed these results. The conformational space and the molecular geometry of the molecule in the gaseous phase have been studied using the B3LYP method of approximation, with 6-31G and 6-311++G^** basis sets.     

Étude de la décohésion fibre-matrice dans les arcs composites circulairesA study of fiber debonding in circular composite arches

In the framework of linear elasticity, we consider a composite arch constituted by a matrix and a fiber reinforcing the structure. This arch is clamped at one extremity, while at the other the fibre is subject to either prescribed displacements or forces. By making an asymptotic analysis based on the slenderness and loading parameters, we study by means of an energy criterion the fiber-matrix debonding, resulting from the inextensional displacements of the medium line. We show in particular that for these specific loading types, the debonding occurs brutally and the critical length of initiation is of order 1. To cite this article: K. Madani, C. R. Mecanique 330 (2002) 535–541.     

A new acylated flavonol from the aerial parts of Asteriscus maritimus (L.) Less (Asteraceae)

Phytochemical investigation of the flowering aerial parts of Asteriscus maritimus (L.) Less (Asteraceae) led to the isolation of a new compound: patuletin 7-O-β-D-[(2″′S) 6″(3″′-hydroxy-2″′-methyl-propanoyl)] glucopyranoside, together with five known metabolites; β-sitosterol 2, chlorogenic acid 3, P-hydroxy -methylbenzoate 4, luteolin 5 and protocatechuic acid 6. The structures of the isolated compounds were determined by comprehensive analyses of its 1D and 2D NMR, HRMS and compared with previously known analogues. The ethanolic extract of the flowering aerial parts of A. maritimus was found to be safe (LD₅₀ = 4.6 mg/kg) and possess significant antioxidant and anti-inflammatory activities and this was in accordance with its high phenolic content (107.36 ± 0.051 mg GAE/g extract).