REIDEMEISTER TORSION AND ANALYTIC TORSION OF SPHERES

We provide a simple topological derivation of a formula for the Reidemeister and the analytic torsion of spheres.

An existence theorem for G-structure preserving affine immersions

We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of isometric immersions into products of space forms.

A New Indirect Electrochemical Method for Determination of Ozone in Water Using Multiwalled Carbon Nanotubes

A new electrochemical methodology has been developed for the detection of ozone using multiwalled carbon nanotubes (MWCNT). The method presented here is based on the reaction of ozone with indigo blue dye producing anthranilic acid (ATN). The electrochemical profile of ATN on an electrode of glassy carbon (GC) modified with MWCNT showed an oxidation peak potential at 750 mV vs. Ag/AgCl. An analytical method was developed using differential pulse voltammetry (DPV) to determine ATN in a range of 50-400 nmol L(-1), with a detection limit of 9.7 nmol L(-1). Ozonated water samples were successfully analyzed by GC/MWCNT electrode and the recovery procedure yielded values between of 96.5 and 102.3%.