Relationship between the component synthesis order of zinc ferrite–titania nanocomposites and their performances as visible light-driven photocatalysts for relevant organic pollutant degradation

The main objective of this work was to investigate the influence of the order of component synthesis of zinc ferrite–titania nanocomposites on their structural, morphologic, textural, light absorption properties, and performances as photocatalysts. In this respect, nanocomposite materials with 10ZnFe₂O₄90TiO₂ (wt %) composition were prepared via a two-step synthesis procedure by alternating the order of the component addition during the preparation protocol and characterized by X-ray diffraction, transmission electron microscopy, energy dispersive X-ray, small-angle X-ray scattering, nitrogen sorption, and UV–vis diffuse reflectance spectroscopy. The photocatalytic activity of nanocomposites was evaluated on Rhodamine 6G degradation under visible light illumination. The photocatalytic performances of nanocomposites were clearly superior to the classical TiO₂. Nevertheless, preparing titania in the presence of a presynthesized zinc ferrite led to superior characteristics in terms of band gap value, specific surface area, and grain sizes crucial for the enhancement of the photocatalytic performances.     

Observation of two N2‐isobutyrylguanine tautomers by NMR spectroscopy

N₂‐Isobutyrylguanine was prepared by treatment of guanine with isobutyryl chloride. Two tautomers, 1,7‐dihydro‐2‐(isobutyroyl)amino‐6H‐purin‐6‐one and 1,9‐dihydro‐2‐(isobutyroyl)amino‐6H‐purin‐6‐one, were identified in almost 1 : 1 ratio in dichloromethane–dimethyl sulfoxide (1 : 1 v/v) by NMR spectroscopy. By using the selective‐inversion experiments, enthalpy, entropy, and free energy for activation were determined. This work represents the first report of guanine tautomers observed directly by NMR spectroscopy. Copyright © 2012 John Wiley & Sons, Ltd.     

A diagrammatic equation for oriented planar graphs

In this paper we derive a diagrammatic equation for the planar sector of square non-Hermitian random matrix models. Our fundamental equation is first obtained by a graph counting argument (inspired by the Polchinski equation in quantum field theory) and subsequently derived independently by a precise saddle point analysis of the corresponding random matrix integral. We solve the equation perturbatively for a generic model and conclude by exhibiting two duality properties of the perturbative solution.     

Topological Graph Polynomials in Colored Group Field Theory

In this paper, we analyze the open Feynman graphs of the Colored Group Field Theory introduced in Gurau (Colored group field theory, arXiv:0907.2582 [hep-th]). We define the boundary graph ${\mathcal{G}_{\partial}}In this paper, we analyze the open Feynman graphs of the Colored Group Field Theory introduced in Gurau (Colored group field theory, arXiv:0907.2582 [hep-th]). We define the boundary graph G_?{\mathcal{G}_{\partial}} of an open graph G{\mathcal{G}} and prove it is a cellular complex. Using this structure we generalize the topological (Bollobás–Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension.     

Compact eye-safe laser sources based on OPOs with KTP or PPKTP crystals

We report on compact eye-safe nanosecond laser sources emitting in the 1.5 μm wavelength range based on non-critically phase-matched parametric interaction in optical parametric oscillators (OPOs) with KTP and periodically poled KTP (PPKTP) crystals, pumped by the fundamental frequency of Nd:YAG lasers. As much as 250 μJ signal pulse energy at 1.5 μm wavelength, 6.5 ns FWHM pulse-width, has been obtained in a PPKTP-OPO, extracavity pumped by a Nd:YAG microlaser oscillator–amplifier at 650 μJ pump pulse energy, 8 ns pulse-width. A single signal pulse of 2.7-mJ output energy at 1.57 μm wavelength, less than 5 ns pulse-width, was generated in a KTP-OPO, intracavity pumped by a passively Q-switched Nd:YAG laser.     

Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the Kortweg-de vries hierarchy

We show that unstable fingering patterns of two-dimensional flows of viscous fluids with open boundary are described by a dispersionless limit of the Korteweg-de Vries hierarchy. In this framework, the fingering instability is linked to a known instability leading to regularized shock solutions for nonlinear waves, in dispersive media. The integrable structure of the flow suggests a dispersive regularization of the finite-time singularities.     

Skein modules and the noncommutative torus

We prove that the Kauffman bracket skein algebra of the cylinder over a torus is a canonical subalgebra of the noncommutative torus. The proof is based on Chebyshev polynomials. As an application, we describe the structure of the Kauffman bracket skein module of a solid torus as a module over the algebra of the cylinder over a torus, and recover a result of Hoste and Przytycki about the skein module of a lens space. We establish simple formulas for Jones-Wenzl idempotents in the skein algebra of a cylinder over a torus, and give a straightforward computation of the -th colored Kauffman bracket of a torus knot, evaluated in the plane or in an annulus.