Two-parameter differential calculus on the h-superplane

We introduce a noncommutative differential calculus on the two-parameter $h$-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under $GL_{h_1,h_2}(1| 1)$ transformations. We also give a two-parameter deformation of the (1+1)-dimensional phase space algebra.Comment: 14 page

Differential Geometry of the q-plane

Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.Comment: 9 page

Image resolution enhancement using dual-tree complex wavelet transform

In this letter, a complex wavelet-domain image resolution enhancement algorithm based on the estimation of wavelet coefficients is proposed. The method uses a forward and inverse dual-tree complex wavelet transform (DT-CWT) to construct a high-resolution (HR) image from the given low-resolution (LR) image. The HR image is reconstructed from the LR image, together with a set of wavelet coefficients, using the inverse DT-CWT. The set of wavelet coefficients is estimated from the DT-CWT decomposition of the rough estimation of the HR image. Results are presented and discussed on very HR QuickBird data, through comparisons between state-of-the-art resolution enhancement methods

Range separated hybrid exchange-correlation functional analyses of W and/or N(S) (co)doped anatase TiO_2

Electronic properties and atomic structures of W, N, S, W/N, and W/S dopings of anatase TiO_2 have been systematically investigated using the density functional theory (DFT). The exchange and correlation effects have been treated with Heyd, Scuseria and Ernzerhof (HSE) hybrid functional. Mixing traditional semi-local and non-local screened Hartree-Fock (HF) exchange energies, the HSE method corrects the band gap and also improves the description of anion/cation derived gap states. Enhanced charge carrier dynamics, observed for W/N codoped titania, can partly be explained by the passivative modifications of N 2p and W 5d states on its electronic structure. Following this trend we have found an apparent band gap narrowing of 1.03 eV for W/S codoping. This is due to the large dispersion of S 3p states at the valance band (VB) top extending its edge to higher energies and Ti--S--W hybridized states appearing at the bottom of the conduction band (CB). W/S-TiO_2 might show strong visible light response comparable to W/N codoped anatase catalysts.Comment: 8 pages, 5 figures and 3 table