No abstract

No abstract

We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms (MCFs) which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and the MCF are not known analytically. We solve numerically using a modified Hejhal and Then algorithm, which is suitable to compute eigenvalues for a surface with more than one cusp. We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica.

No abstract

Ceria (CeO2) is an important material mainly for microelectronic and fuel-cell applications due to having high dielectric constant and good catalytic properties. The first principle and experimental investigations were carried out to study the effect of Zn incorporation on the electronic and optical response of CeO2. Density of states spectra depict the prominent hybridization of Ce-f and O-p states while band structure reveals the decrease in bandgap with the incorporation of metallic Zn content in ceria structure. X-ray diffraction analysis detects the crystalline traces of CeO2 in pristine and doped thin films. Field emission scanning electron micrographs and energy dispersive X-ray spectra of synthesized thin films present the uniform distribution of grains with clear grain boundaries with expected elemental contents. The experimental observations comparatively follow the trend of simulation curves. Optical studies demonstrate a clear increment in absorption coefficient, optical conductivity, and real epsilon with Zn incorporation in ceria which makes these compositions favorable for applications in modern electronic devices.