Leibniz algebras constructed by Witt algebras

We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself

Accurate Ellipsometric Measurement of Refractive Index and Thickness of Ultrathin Oxide Film

This work presents some suggestions to improve the accuracy of ellipsometry for determining the refractive indices and thicknesses of ultrathin thermal SiO 2 films on silicon. The effects of substrate optical parameter variations on the ellipsometric measurement were ruled out by conducting the ellipsometric measurements in several different media instead of air. An improved ellipsometer adjustment procedure was developed to minimize the error for ⌿ and ⌬ angle measurement and to check the anisotropy of the sample. To extract the thickness and refractive index of ultrathin dielectric film from the light polarization parameters, an optimization technique with fluctuation of substrate parameter taken into account was proposed. Our results show that the refractive indices of ultrathin ͑2.1-8 nm͒ thermal oxide films prepared by several different methods fall in the range of 1.475 ± 0.003