Photoproduction of iodine with nanoparticulate semiconductors and insulators

The crystal structures of different forms of TiO2 and those of BaTiO3, ZnO, SnO2, WO3, CuO, Fe2O3, Fe3O4, ZrO2 and Al2O3 nanoparticles have been deduced by powder X-ray diffraction. Their optical edges have been obtained by UV-visible diffuse reflectance spectra. The photocatalytic activities of these oxides and also those of SiO2 and SiO2 porous to oxidize iodide ion have been determined and compared. The relationships between the photocatalytic activities of the studied oxides and the illumination time, wavelength of illumination, concentration of iodide ion, airflow rate, photon flux, pH, etc., have been obtained. Use of acetonitrile as medium favors the photogeneration of iodine.     

An approximate moving boundary method for American option pricing

We present a method to solve the free-boundary problem that arises in the pricing of classical American options. Such free-boundary problems arise when one attempts to solve optimal-stopping problems set in continuous time. American option pricing is one of the most popular optimal-stopping problems considered in literature. The method presented in this paper primarily shows how one can leverage on a one factor approximation and the moving boundary approach to construct a solution mechanism. The result is an algorithm that has superior runtimes-accuracy balance to other computational methods that are available to solve the free-boundary problems. Exhaustive comparisons to other pricing methods are provided. We also discuss a variant of the proposed algorithm that allows for the computation of only one option price rather than the entire price function, when the requirement is such.