Copper halide clusters and polymers supported by bipodal heteroelemental ligands

The flexible, multi dentate, heteroelemental, dipodal ligands; bis(2pyridylthio)methane, (PyS)₂CH₂ (Py = pyridyl = C₅H₄N), (PymS)₂CH₂, bis(2pyrimidylthio)methane, and bipyrimidyldisulfide, (PymS)₂ (Pym = pyrimidine, C₄H₃N₂), were reacted with a series of copper precursors to determine whether monomeric compounds, cubane clusters or polymeric chains would be obtained. Copper(II) chloride, copper(I) cyanide and copper(I) thiocyanate afforded infinite polymeric chains while copper(I) iodide afforded tetranuclear clusters supported by two ligand molecules. All products were characterized in the solid-state by X-ray crystallography.     

Invariance principle for a class of non stationary processes with long memory

We prove a functional central limit theorem for the partial sums of a class of time varying processes with long memory. To cite this article: A. Philippe et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

The synthesis and characterization of germanium dichloride and dimethyl aluminium chloride derivatives of the 2,2-dipyridylamine ligand

The reactions of germanium dichloride and dimethyl aluminium chloride with 2,2-dipyridylamine (dpa) affords germanium and organo-aluminium complexes. Structural characterization reveals that the preferential coordination site of both germanium and aluminium is within the sterically protected pyridyl, (pyridyl = C₅H₅N = py), pocket. Py₂NGeCl, compound (1), crystallizes in the triclinic space group, P-1, with cell coordinates; a=8.2956(11), b=9.9938(13), c=12.6517(17), α=92.033(2)°, β=92.834(2)°, γ=91.685(2)°. The aluminium complex, Py₂NAlMe₂·Al(Me)Cl, (2), crystallizes in the orthorhombic space group, Pna2(1), with cell parameters: a=13.3707(10), b=10.8706(8), c=16.1306(12). The X-ray analysis of the side products of these reactions, the lithium halide adducts are also reported.     

The projective geometry of Mario Pieri: A legacy of Georg Karl Christian von Staudt

The research of Mario Pieri (1860–1913) can be classified into three main areas: metric differential and algebraic geometry and vector analysis; foundations of geometry and arithmetic; logic and the philosophy of science. In writing this article, I intend to reveal some important aspects of his contributions to the foundations of projective geometry, notably those that emanated from his intensive study of the works of Georg Karl Christian von Staudt (1798–1867). Pieri was the first geometer to successfully establish projective geometry as an independent subject (rigorous mathematical theory), freed from all ties to Euclidean geometry. The path to this achievement began with Staudt, and involved the reformulation of the classical ideas of cross ratio and projectivity in terms of harmonic sets, as well as a critical analysis of the proof of a fundamental theorem that connects these ideas. Included is a brief overview of Pieri's life and work.     

Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials

We develop direct and inverse scattering theory for one-dimensional Schrödinger operators with steplike potentials which are asymptotically close to different finite-gap potentials on different half-axes. We give a complete characterization of the scattering data, which allows unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.     

Ionic liquid-mediated bis[(3-methyldimethoxysilyl)propyl] polypropylene oxide-based polar sol–gel coatings for capillary microextraction

Two ionic liquids (IL), namely, 1-methyl-3-octylimidazolium chloride (MOIC) and trihexyltetradecylphosphonium tetrafluoroborate (TTPT) were used to prepare polar and nonpolar sol–gel coatings for capillary microextraction (CME). Bis[(3-methyldimethoxysilyl)propyl] polypropylene oxide (BMPO), containing sol–gel active terminal methoxysilyl groups and polar propylene oxide repeating units, was used to prepare polar sol–gel hybrid organic–inorganic coatings. Hydroxy-terminated poly(dimethyl-co-diphenylsiloxane) was used as the sol–gel active organic component for nonpolar sol–gel hybrid coatings. Compared to a sol–gel BMPO coating prepared without IL, the sol–gel BMPO coatings prepared with the use of both of these ILs provided more efficient extraction as is evidenced by more pronounced GC peak areas. The MOIC-mediated sol–gel BMPO coating provided larger GC peak areas compared to the TTPT-mediated sol–gel BMPO coating. Scanning electron microscopy results suggested that MOIC provided a more porous morphology of the sol–gel BMPO extraction media compared to that prepared with TTPT. Thus, individual ILs can affect the porosity of sol–gel materials to different degrees. Overall, the sol–gel BMPO coating prepared with the ILs could extract nonpolar to polar analytes directly from aqueous samples. Detection limits were on the order of nanograms per liter (1.9–330.5 ng/L) depending on the analyte class. Furthermore, the MOIC-mediated sol–gel BMPO coating demonstrated high thermal stability (330 °C), solvent resistance, and fast extraction equilibrium (10–15 min) for polar and moderately polar analytes.     

A large data existence result for the stationary Boltzmann equation in a cylindrical geometry

AnL ¹-existence theorem is proved for the nonlinear stationary Boltzmann equation with hard forces and no small velocity truncation—only the Grad angular cut-off-in a setting between two coaxial rotating cylinders when the indata are given on the cylinders.