Quadratic functions on torsion groups

We investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant construction which assigns, to an integral lattice with a distinguished characteristic form, a quadratic function on a torsion group. When the associated symmetric bilinear pairing is fixed, we construct an affine embedding of a quotient of the set of characteristic forms into the set of all quadratic functions and determine explicitly its cokernel. We determine a suitable class of torsion groups so that quadratic functions defined on them are classified by the stable class of their lift. This refines results due to A.H. Durfee, V. Nikulin, C.T.C. Wall and E. Looijenga -- J. Wahl. Finally, we show that on this class of torsion groups, two quadratic functions are isomorphic if and only if they have equal associated Gauss sums and there is an isomorphism between the associated symmetric bilinear pairings which preserves the "homogeneity defects". This generalizes a classical result due to V. Nikulin. Our results are elementary in nature and motivated by low-dimensional topology.Comment: 15 pages; a few minor modifications (improved writing, lengthened abstract

Quadratic functions and complex spin structures on three-manifolds

We show how the space of complex spin structures of a closed oriented three-manifold embeds naturally into a space of quadratic functions associated to its linking pairing. Besides, we extend the Goussarov-Habiro theory of finite type invariants to the realm of compact oriented three-manifolds equipped with a complex spin structure. Our main result states that two closed oriented three-manifolds endowed with a complex spin structure are undistinguishable by complex spin invariants of degree zero if, and only if, their associated quadratic functions are isomorphic.Comment: 41 pages with 10 figures; lightened version (some independent parts of the first version have been moved to other preprints, referenced as math.AC/0301040 and math.GT/0301041 on this server); examples and questions added; exposition improve

Structural and physical properties of antibacterial Ag-doped nano-hydroxyapatite synthesized at 100°C

Synthesis of nanosized particle of Ag-doped hydroxyapatite with antibacterial properties is in the great interest in the development of new biomedical applications. In this article, we propose a method for synthesized the Ag-doped nanocrystalline hydroxyapatite. A silver-doped nanocrystalline hydroxyapatite was synthesized at 100°C in deionized water. Other phase or impurities were not observed. Silver-doped hydroxyapatite nanoparticles (Ag:HAp) were performed by setting the atomic ratio of Ag/[Ag + Ca] at 20% and [Ca + Ag]/P as 1.67. The X-ray diffraction studies demonstrate that powders made by co-precipitation at 100°C exhibit the apatite characteristics with good crystal structure and no new phase or impurity is found. The scanning electron microscopy (SEM) observations suggest that these materials present a little different morphology, which reveals a homogeneous aspect of the synthesized particles for all samples. The presence of calcium (Ca), phosphor (P), oxygen (O), and silver (Ag) in the Ag:HAp is confirmed by energy dispersive X-ray (EDAX) analysis. FT-IR and FT-Raman spectroscopies revealed that the presence of the various vibrational modes corresponds to phosphates and hydroxyl groups. The strain of Staphylococcus aureus was used to evaluate the antibacterial activity of the Ca10-xAgx(PO4)6(OH)2 (x = 0 and 0.2). In vitro bacterial adhesion study indicated a significant difference between HAp (x = 0) and Ag:HAp (x = 0.2). The Ag:Hap nanopowder showed higher inhibition

Reidemeister-Turaev torsion modulo one of rational homology three-spheres

Given an oriented rational homology 3-sphere M, it is known how to associate to any Spin^c-structure \sigma on M two quadratic functions over the linking pairing. One quadratic function is derived from the reduction modulo 1 of the Reidemeister-Turaev torsion of (M,\sigma), while the other one can be defined using the intersection pairing of an appropriate compact oriented 4-manifold with boundary M. In this paper, using surgery presentations of the manifold M, we prove that those two quadratic functions coincide. Our proof relies on the comparison between two distinct combinatorial descriptions of Spin^c-structures on M Turaev's charges vs Chern vectors.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper22.abs.htm

Synthesis, Structure, and Luminescent Properties of Europium-Doped Hydroxyapatite Nanocrystalline Powders

The luminescent europium-doped hydroxyapatite (Eu:HAp, Ca10−xEux(PO4)6(OH)2) with 0≤x≤0.2 nanocrystalline powders was synthesized by coprecipitation. The structural, morphological, and textural properties were well characterized by X-ray diffraction, scanning electron microscopy, and transmission electron microscopy. The vibrational studies were performed by Fourier transform infrared, Raman, and photoluminescence spectroscopies. The X-ray diffraction analysis revealed that hydroxyapatite is the unique crystalline constituent of all the samples, indicating that Eu has been successfully inserted into the HAp lattice. Eu doping inhibits HAp crystallization, leading to a decrease of the average crystallite size from around 20 nm in the undoped sample to around 7 nm in the sample with the highest Eu concentration. Furthermore, the samples show the characteristic 5D0→7F0 transition observed at 578 nm related to Eu3+ ions distributed on Ca2+ sites of the apatitic structure

Etudes Photophysiques d'un polymère conjugué nanostructuré : du film nanocomposite à la nanofibre

This PhD. Thesis is aimed at the investigation of organic nanomaterials presenting original photophysical properties. We address the consequences of the nanostructuration on the absorbing and emissive properties of poly(p-phenylene vinylene) (PPV), a prototype of a semiconducting conjugated polymer for light emitting diode applications. On one hand, we investigate quasi-two dimensional thin composite films of PPV loaded with carbon nanotubes (CNT). On the other hand, we achieve the synthesis of quasi-one dimensional PPV nanofibers exhibiting optical properties different from those of the bulk, which are possibly related to a near confinement regime of the photoexcited species. The PPV/NTC nanocomposite thin films are prepared by drop casting for several concentrations of the PPV precursor polymer and for increasing CNT loads. The optical properties are strongly modified by these synthesis conditions. The interacting effects between polymer chains and CNT on the photoluminescence properties are discussed. The PPV nanofibers are elaborated by the wetting template method in nanoporous membranes. Depending on the synthesis conditions, we obtain either nanowires or nanotubes. These objects present different emissive characteristics. In PPV nanotubes, the quantum yield is increased and a new long-lived photoluminescence band is observed around 450 nm. We discuss the experimental results with two theoretical approaches : (i) molecular calculations of oligomers in order to find the most probable optical transition energies in short chains ; (ii) a phenomenological model based on the distribution of conjugated segment lengths, allowing a better understanding of both intrachain and interchain interactions.Ce travail de thèse comporte un volet Matériaux qui s'insère dans une thématique Nanomatériaux/ Nanocomposites et un volet propriétés optiques relevant de la Nanophysique. Nous avons adressé les effets de nanostructuration d'un polymère conjugué semi-conducteur sur ses propriétés d'émission optique : le poly(p-phénylène vinylène) (PPV). Deux types de nanostructuration sont mis en oeuvre : l'élaboration de films minces nanocomposites polymère / nanotubes de carbone (NTC) ; l'élaboration de nanofibres. Les films minces nanocomposites PPV/NTC sont préparés par “drop-casting” pour diverses concentrations de NTC et dilutions du précurseur du PPV. Leurs propriétés optiques se trouvent fortement modifiées par ces différents paramètres. L'effet sur la photoluminescence de l'interaction entre chaînes de polymère et les NTC est discuté. Les nanofibres de PPV sont élaborées par une méthode d'imprégnation de membranes nanoporeuses. Selon les conditions de synthèse, deux types de morphologie sont obtenus : nanofils ou nanotubes. Des propriétés de photoluminescence très différentes selon la morphologie nanofil-nanotube sont mises en évidence. Ainsi, pour les nanotubes de PPV, le rendement quantique d'émission est fortement renforcé et une nouvelle bande d'émission proche de 450 nm apparaît, présentant un déclin très lent. L'ensemble des résultats de photoluminescence est interprété et discuté à l'aide d'un travail théorique visant à décrire la structure moléculaire et supramoléculaire de ces nanostructures en terme de distribution de segments conjugués (effets intrachaîne/interchaîne, taille des segments). Il s'appuie sur un modèle phénoménologique et sur des calculs de chimie quantique moléculaire

Tuning the oxidation states of dopants: a strategy for the modulation of material photoluminescence properties

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