In this paper, we first give an intersection theory for moduli problems for nonlinear elliptic operators with certain precompact space of solutions in differential geometry. Then we apply the theory to constructing Gromov-Witten invariants for general symplectic manifolds.

We analyse three nite diierence approximations of the nonlinear Klein{Gordon equation and show that they are directly related to symplectic mappings. Two of the schemes, the Perring{Skyrme and Ablowitz{Kruskal{Ladik, are long established and the third is a new, higher order accurate scheme. We test the schemes on travelling wave and periodic breather problems over long time intervals, and compa...

by Zheng Wen, M.S. Washington State University August 2007 Co-Chairs: Ali Saberi and Sandip Roy This thesis is motivated by the need to better understand the analysis and control of linear systems subject to constraints. We contribute to this field by pursuing research on two specific topics: 1) the external stability of linear systems subject to actuator saturation, and 2) the security of Comm...

We apply a flexible numerical integrator to the simulation of adiabatic quantum computation with nonlinear paths. We find that a nonlinear path may significantly improve the performance of adiabatic algorithms versus the conventional straight-line interpolations. The employed integrator is suitable for solving the time-dependent Schrödinger equation for any qubit Hamiltonian. Its flexible stora...

For many physical systems like vehicles, acceleration can be easily measured for the respective states. However, the outputs are usually affected by stochastic noise disturbance. The mentioned systems are often sensitive to noise and structural uncertainties. Furthermore, it is very difficult to estimate the multiple integrals of the signal, acceleration to velocity and velocity to position. In...

This paper develops a methodology for recursive construction of optimal and nearoptimal controllers for strict-feedback stochastic nonlinear systems under a risk-sensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers obtained guarantee any desired achievable level of long-term average cost for a given risk-sensitivity paramet...

Sigma-delta (Σ∆) modulators are widely used for analogue-to-digital and digital-to-analogue conversion in both discrete-time and continuous-time implementations [1]. A Σ∆ modulator is an example of a nonlinear system, the nonlinearity being introduced by the presence of the quantiser. In [2] we applied results of our work on driven interval shifts to explain the steady-state dynamics of the fir...

Robust nonlinear controller design with constraint on the poles' location of the linear part of closed-loop system is proposed. The design method is based on the integrator backstepping procedure and linear constrained ∞ H for nonlinear strictfeedback systems with disturbance also in strict-feedback form. The resulted closedloop system will be globally stable, while both local robustness and de...