Corps euclidiens,unités exceptionnelles et courbes elliptiques

Lenstra [Invent. Math.36 (1977), 237–254] has proved that a number field possessing sequences of integers whose differences are units, having a big enough length with respect to the discriminant of the field, is Euclidean. In this paper, we use this result to construct some new Euclidean fields; suitable sequences are obtained by using points of finite order on some elliptic curves.     

Solubility of Triethylamine in Tetraethylammonium Chloride Aqueous Solutions from 20 to 35°C

Solubilities of triethylamine in aqueous tetraethylammonium chloride solutions were measured at 20, 25, and 35°C. The molalities in Et₄NCl of the aqueous solvents ranged from 0.03 to 1 mol-kg^–1. The data were evaluated from density measurements using a vibrating-tube densimeter. At each temperature, least-squares method was used to fit experimental density data points to double polynomial equations of various degrees. Triethylamine molalities of the saturated aqueous phases were estimated by extrapolation from those equations. Experimental data were interpreted in terms of hydrophobic and electrostatic perturbed domains in the hydration shells of the noneleceory and of the cation of the salt, as a function of temperature and salt concentration. The conclusions obtained are consistent with previous volumetric studies.     

The Legacy of Raimond Castaing

 In April 1998 Raimond Castaing left the world of electrons, of ions and others particles, his wife and his family, his numerous students, for the world of stars. Raimond Castaing (Fig. 1) had a very strong personality. No one will forget their first meeting with him and all his students remember how brilliant he was as a teacher. A lot of anecdotes about his famous hot temper are still circulating among his friends and his former students. But in this paper, we would like to evoke Castaing’s memory through his achievements in Instrumental Physics, from the time of his doctoral thesis to later developments with his students, which were all centred on the imaging of the microstructures of materials and their quantitative chemical analysis.     

Expeditive synthesis of homochiral fused tri- and tetrazoles-piperazines from β-amino alcohols

N-Cyanomethyl and N-propargyl β-amino alcohols are chlorinated with SOCl₂ and treated with NaN₃ in DMSO. A substitution/cycloaddition process affords in good yields, with high diastereoselectivity and a regioselectivity depending on the substitution pattern of the starting amino alcohol, fused tri- and tetrazoles-piperazines. These heterocycles were further lithiated with n-BuLi at the benzylic position and reacted diastereoselectively with a range of electrophiles.     

Rapid method for the isolation of the mature collagen cross-links, hydroxylysylpyridinoline and lysylpyridinoline

Hydroxylysylpyridinoline (HP) and lysylpyridinoline (LP) are two non-reducible cross-links of mature collagen which are formed by a sequence of post-translational modifications. HP is a derivative of three residues of hydroxylysine and is present in almost all mature tissues (e.g., tendons, vessel walls, cartilage, teeth and bone). LP is a derivative of two residues of hydroxylysine and one residue of lysine and is present only in dentine and bone. Neither cross-link is found in normal human skin. HP and LP were purified from commercially available bone gelatine (“ossein hydrolysate”) by preparative reversed-phase HPLC and the degree of purity was verified by amino acid determination ( > 98% dry mass). Hydroxylysylpyridinoline and lysylpyridinoline are promising markers in urine of collagen resorption because their levels in urine should reflect only the breakdown of collagen fibres of skeletal tissues. The two components were used as external standards and the determination of HP and LP in urine provides a good means for the specific evaluation of pathological conditions associated with increased bone resorption, e.g., high turnover post-menopausal osteoporosis.     

Theoretical Study of the Distortion from Regular Tetrahedral Structure of M(NH2)4 Complexes

Theoretical study on tetrakis-amido complexes (M(NR₂)₄, M = Ti, V, Cr, and Mo; R = H, Me) is presented. At first a rough investigation of the potential energy surface indicates that all stationary points are of S ₄ or D ₂ symmetry depending on the coupled rotations of the NR₂ groups. Qualitative correlation diagrams are calculated within S ₄ or D ₂ symmetry constraint between two limiting structures of D ₂ d symmetry. DFT (B3LYP) calculations on these two paths are presented for unsubstituted complexes (R = H) and the various minima are optimized and characterized. These results are discussed in the light of the correlation diagrams. Finally, optimization of the different minima has been performed on substituted species (R = Me) and the theoretical results are shown to be in good agreement with the experimental structural determination when available.     

X-ray crystal structures of three nonbenzodiazepinic ligands for the benzodiazepine receptor sites: SR95926, CMW1842, and L16317:nab initio MO study of the electronic properties

The crystal structures ofp-methoxyphenyl-3-triazolo [4,3-a] isoquinoline (SR95926),p-methoxyphenyl-3-triazolophtalazine (CMW1842), andp-methoxyphenyl-3-N-dimethoxyethylamino-6-triazolophtalazine (L16317) have been solved by direct methods from single-crystal X-ray diffraction data, and refined by full-matrix least squares. SR95926: monoclinic,P2₁/n,a=20.950(3),b=6.769(1),c=9.465(2) Å,=100.90(1)°. CMW1842: triclinic,P¯1,a=8.784(1),b=9.160(4),c=8.555(1) Å,=99.10(2),=93.90(1), =106.77(1)°. L16317: monoclinic,P2₁/_n,a=20.124(3),b=9.586(1),c=10.788(1) Å,=91.91(1)°. FinalR factors are 0.034, 0.037, and 0.053, respectively. Experimental geometries were used to perform STO-3Gab initio molecular-orbital calculations. A relationship between the electronic pattern within the molecules and the affinity of the benzodiazepine receptor sites is pointed out.     

A grothendieck factorization theorem on 2-convex schatten spaces

We prove that for every bounded linear operatorT:C ^2p →H(1≤p<∞,H is a Hilbert space,C ^{2 p} p is the Schatten space) there exists a continuous linear formf onC ^p such thatf≥0, ‖f‖(C _C ^p)*=1 and $$\forall x \in C^{2p} , \left\| {T(x)} \right\| \leqslant 2\sqrt 2 \left\| T \right\|< f\frac{{x * x + xx*}}{2} > 1/2$$ . Forp=∞ this non-commutative analogue of Grothendieck’s theorem was first proved by G. Pisier. In the above statement the Schatten spaceC ^2p can be replaced byE _E ² whereE ⁽²⁾ is the 2-convexification of the symmetric sequence spaceE, andf is a continuous linear form onC _E. The statement can also be extended toL _E{(su2)}(M, τ) whereM is a Von Neumann algebra,τ a trace onM, E a symmetric function space.