Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions phi(lambda) is obtained for all lambda is an element of alpha(C)*. As a consequence, estimates for phi(lambda) away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The L-P-theory for the hypergeometric Fourier transform is developed for 0 < p < 2. In particular, an inversion formula is proved when 1 <= p < 2. (C) 2013 Elsevier Inc. All rights reserved.

In Vivo Genotoxicity Assessment of Titanium Dioxide Nanoparticles by Allium cepa Root Tip Assay at High Exposure Concentrations

The industrial production and commercial applications of titanium dioxide nanoparticles have increased considerably in recent times, which has increased the probability of environmental contamination with these agents and their adverse effects on living systems. This study was designed to assess the genotoxicity potential of TiO2 NPs at high exposure concentrations, its bio-uptake, and the oxidative stress it generated, a recognised cause of genotoxicity. Allium cepa root tips were treated with TiO2 NP dispersions at four different concentrations (12.5, 25, 50, 100 mu g/mL). A dose dependant decrease in the mitotic index (69 to 21) and an increase in the number of distinctive chromosomal aberrations were observed. Optical, fluorescence and confocal laser scanning microscopy revealed chromosomal aberrations, including chromosomal breaks and sticky, multipolar, and laggard chromosomes, and micronucleus formation. The chromosomal aberrations and DNA damage were also validated by the comet assay. The bio-uptake of TiO2 in particulate form was the key cause of reactive oxygen species generation, which in turn was probably the cause of the DNA aberrations and genotoxicity observed in this study.

LDPC Code Designs Based on root I Matrices

LDPC codes can be constructed by tiling permutation matrices that belong to the square root of identity type and similar algebraic structures. We investigate into the properties of such codes. We also present code structures that are amenable for efficient encoding.