Moduli of abelian varieties and p-divisible groups

Lecture notes at a conference on Arithmetic Geometry, Goettingen, July/August 2006: Density of ordinary Hecke orbits and a conjecture by Grothendieck on deformations of p-divisible groups.Comment: 92 page

A multi-band semiclassical model for surface hopping quantum dynamics

In the paper we derive a semiclassical model for surface hopping allowing quantum dynamical non-adiabatic transition between different potential energy surfaces in which cases the classical Born-Oppenheimer approximation breaks down. The model is derived using the Wigner transform and Weyl quantization, and the central idea is to evolve the entire Wigner matrix rather than just the diagonal entries as was done previously in the adiabatic case. The off-diagonal entries of the Wigner matrix suitably describe the non-adiabatic transition, such as the Berry connection, for avoided crossings. We study the numerical approximation issues of the model, and then conduct numerical experiments to validate the model.Comment: 29 pages, 10 figure

Employing Psychoacoustic Model for Digital Audio Watermarking

This thesis discusses about digital audio watermarking by employing psychoacoustic model to make the watermarked signal inaudible to the audience. Due to the digital media data able to distribute easily without losing of data information, thus the intellectual property of musical creators and distributor may affected by this kind of circumstance . To prevent this, we propose the usage of spread spectrum technique and psychoacoustic model for embedding process, zero-forcing equalization and detection and wiener filtering for extracting process. Three samples of audio signal have been chosen for this experiment which are categorized as quiet, moderate, and noise state signal. The findings shows that our watermarking scheme achieved the intended purposes which are to test digital audio watermarking by employing psychoacoustic model, to embed different length of messages to test on accuracy of extracted data and to study the suitability on using hash function for verification of modification attacks