Crystal structures of high-T c oxides

A comprehensive review of structure work on high-T _c oxides as reported during the years 1987 and 1988 is given. Thirteen structures are refined from X-ray single-crystal and/or neutron powder diffraction data:I. (Ba_1–x ,K _x )BiO₃ (T _c =30 K),II. (La_2–x , Sr _x )CuO₄ (T _c =40 K),III. (Nd, Ce, Sr)₂CuO₄ (T _c =28 K),IV. (Nd_2–x , Ce _x )CuO₄ (T _c =24 K),V. YBa₂Cu₃O₇ (T _c =90 K),VI. YBa₂Cu₄O₈ (T _c =80 K),VII. Y₂Ba₄Cu₇O₁₄ (T _c =40 K),VIII. Pb₂Sr₂NdCu₃O₈ (T _c =70 K),IX. TlBa₂CaCu₂O₇ (T _c =103 K),X. TlBa₂Ca₂Cu₃O₉ (T _c =120 K),XI. Tl₂Ba₂CuO₆ (T _c =90 K),XII. Tl₂Ba₂CaCu₂O₈ (T _c =112 K),XIII. Tl₂Ba₂Ca₂Cu₃O₁₀ (T _c =125 K). Except forI (perovskite type),II (K₂NiF₄ type) andIV (Nd₂CuO₄ type) they represent new structure types. Structure data, bond distances, structure drawings and calculated X-ray powder diffraction patterns are given for each compound. Structural features and correlations with superconductivity are discussed. The review contains 301 citations.     

Rigidity Result for Certain Three-Dimensional Singular Spaces and Their Fundamental Groups

In this paper, we introduce a particularly nice family of locally CAT(−1) spaces, which we call hyperbolic P-manifolds. For X³ a simple, thick hyperbolic P-manifold of dimension 3, we show that certain subsets of the boundary at infinity of the universal cover of X³ are characterized topologically. Straightforward consequences include a version of Mostow rigidity, as well as quasi-isometry rigidity for these spaces.     

Small covering designs by branch-and-cut

 A Branch-and-Cut algorithm for finding covering designs is presented. Its originality resides in the use of isomorphism pruning of the enumeration tree. A proof that no 4-(10, 5, 1)-covering design with less than 51 sets exists is obtained together with all non isomorphic 4-(10, 5, 1)-covering designs with 51 sets. Received: August 16, 2000 / Accepted: July 18, 2001 Published online: September 5, 2002     

Intramolekulare Cycloadditionen Mit Azomethin-Yliden: Synthese und NMR-Untersuchungen einiger Paracyclophan-Derivate vom Makrolid-Typ

Intramolecular Cycloaddition Reactions with Azomethine Ylides: Synthesis and NMR Investigations of Some Macrolide-Type Paracyclophanes Several aziridine derivatives bearing a para-substituted phenyl group have been prepared as precursors of azomethine ylides for intramolecular 1,3-dipolar cycloadditions. Upon heating in refluxing toluene, the expected reactions take place resulting in the regioselective formations of the pairs of diastereoisomers 14 / 15 and 16 / 17 , respectively. As indicated by the sharply decreasing yield in the a -series (< 5%), a useful application of this method for preparing paracyclophane compounds is restricted to derivatives with more than 11 bridging atoms. The results of detailed ¹H- and ¹³C-NMR investigations with the pyrrolidino-annulated cyclophanes are discussed with respect to the configuration at the five-membered heterocycles and to the conformational flexibility of the bridges.     

Rang maximal pourT_{P^n }

Letk be an algebraically closed field,P ⁿ the n-dimensional projective space overk andT _P ⁿ the tangent vector bundle ofP ⁿ . In this paper I prove the following result: for every integerl, for every non-negative integers, ifZ _s is the union ofs points in sufficiently general position inP ⁿ , then the restriction mapH ⁰(P ⁿ ,T _P ⁿ (l)) →H ⁰(Z _s,T _P ⁿ (l)_{|z s} ) has maximal rank. This result implies that the last non-trivial term of the minimal free resolution of the homogeneous ideal ofZ _s is the conjectured one by the Minimal Resolution Conjecture of Anna Lorenzini (cf. [Lo]).     

Averaging regularity results for PDEs under transversality assumptions

Let u = u(x,y) and f = f(x,y) be two functions related by a PDE P(x,y,D_x,D_y)u = f; the regularity of the y-average ∫ u(x,·)dy as a function of x is investigated knowing that of u and f. Our method consists in reducing P to a microlocal normal form under a natural transversality assumption. The 2-microlocal regularity of u is also determined knowing that of f. These results are then applied to a homogenization problem. This article generalizes the results of [16] and [12] on velocity averaging and homogenization for kinetic equations.     

Bonding Analysis of Square-Antiprismatic and Fused Square-Antiprismatic Copper(I)-Selenium Clusters

The electronic structure of the Cu_2(4n+2)Se_4n+2(PH₃)₈ (n = 1–4) D _4h series of model clusters has been analyzed by means of density functional theory calculations. The fused square antiprismatic structure of the metal framework is found to be always preferred over the fused cuboctahedral one because it reinforces the Cu-P bonds. Thus, the presence of the terminal phosphine ligands tends to strengthen the Cu...Cu (d¹⁰...d¹⁰) bonding by mixing bonding combinations of the vacant Cu 4s and 4p orbitals into the occupied 3d combinations. The calculations indicate that the compounds corresponding to n = 3 and 4 should be easily two-electron-reduced, leading to stable dianionic species.     

1,3-Dipolar cycloaddition reaction of bipyridinium ylides with the propynamido-β-cyclodextrin. A regiospecific synthesis of a new class of fluorescent β-cyclodextrins

The 1,3-dipolar cycloaddition reaction of bipyridinium ylides with the electron deficient propynamido-β-cyclodextrin was studied. This reaction resulted in the regiospecific formation of a new class of fluorescent β-cyclodextrins. The new fluorophore systems were characterized spectroscopically by their absorption and emission maxima and their quantum yields.     

Transformation aux rayons X sur un espace symétrique

An inversion formula is proved for the X-ray transform on a Riemannian symmetric space of the non-compact type, by means of the shifted dual Radon transform. To cite this article: F. Rouvière, C. R. Acad. Sci. Paris, Ser. I 342 (2006).