SU(2) Chern-Simons theory at genus zero

We present a detailed study of the Schrödinger picture space of states in theSU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae.     

9‐Methyl‐3‐phenyl­diazenyl‐9H‐carbazole: X‐ray and DFT‐calculated structures

The title compound, C₁₉H₁₅N₃, was prepared by condensation of 3‐nitroso­carbazole and aniline with subsequent methyl­ation. The structure is built up of stacks of almost planar mol­ecules. Density functional theory (DFT) calculations predict a completely planar conformation, different from that observed in the crystal lattice. HOMA (harmonic oscillator model of aromaticity) indices, calculated for three aromatic rings, demonstrate the small influence of the azo substituent on π electrons in the carbazole system.     

The effect of fluorine-based plasma treatment on morphology and chemical surface composition of biocompatible silicone elastomer

X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM) have been used to investigate the effect of reactive ion etching (RIE) on poly(methylhydrogensiloxane-co-dimethylsiloxane) surface in fluorine-based plasmas. Polysiloxane layers supported on the standard silicon wafers were etched using SF₆ + O₂ or CF₄ + O₂ plasmas. SEM studies show that the polysiloxane morphology depends on plasma chemical composition strongly. Presence of a columnar layer likely covered with a fluorine rich compound was found on the elastomer surface after the CF₄ + O₂ plasma exposure. After the SF₆ + O₂ or CF₄ + O₂ plasma treatment the polysiloxane surface enriches with fluorine or with fluorine and aluminum, respectively. Different morphologies and surface chemical compositions of the silicone elastomer etched in both plasmas indicate different etching mechanisms.     

Lévy processes and Fourier multipliers

We study Fourier multipliers which result from modulating jumps of Lévy processes. Using the theory of martingale transforms we prove that these operators are bounded in Lp(Rd) for 1<p<∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.     

Parallel and superfast algorithms for Hankel systems of equations

Summary Utilizing kernel structure properties a unified construction of Hankel matrix inversion algorithms is presented. Three types of algorithms are obtained: 1)O(n ²) complexity Levinson type, 2)O (n) parallel complexity Schur-type, and 3)O(n log² n) complexity asymptotically fast ones. All algorithms work without additional assumption (like strong nonsingularity).     

PHOTOCYTOTOXICITY OF CURCUMIN

Curcumin, bis (4-hydroxy-3-methoxyphenyl)-l,6-diene-3,5-dione, is a yellow-orange dye derived from the rhizome of the plant Curcuma longa. Curcumin has demonstrated phototoxicity to several species of bacteria under aerobic conditions (Dahl, T. A., et al. , 1989, Arch. Microbiol. 151 183), denoting photodynamic inactivation. We have now found that curcumin is also phototoxic to mammalian cells, using a rat basophilic leukemia cell model, and that this phototoxicity again requires the presence of oxygen. The spectral and photochemical properties of curcumin vary with environment, resulting in the potential for multiple or alternate pathways for the exertion of photodynamic effects. For example, curcumin photogenerates singlet oxygen and reduced forms of molecular oxygen under several conditions relevant to cellular environments. In addition, we detected carbon-centered radicals, which may lead to oxidation products (see accompanying paper). Such products may be important reactants in curcumin's phototoxicity since singlet oxygen and reduced oxygen species alone could not explain the biological results, such as the relatively long lifetime (t¹²= 27 s) of the toxicant responsible for decreased cell viability.