Rigorous Shadowing of Numerical Solutions of Ordinary Di erential Equations by Containment Wayne Brian Hayes Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2001 An exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow. We present a general-purpose method for proving the existence of nite-time shadows of numerical ODE ...

In a stochastic simulation context, iterative methods of optimization, which perform at each step of their optimization procedure a comparison between two di€erent values of the objective function, need the use of statistical tests in order to properly evaluate and compare the simulation results. However, when the objective function to be optimized is a multicriteria function involving several ...

A comprehensive design procedure based on extremum seeking for minimum power demand formation  ight is presented, the Ž rst with performance guarantees. The procedure involves the design of a new wake robust formation hold autopilot and transformation of the closed-loop aircraft dynamics to a form in which a newly available rigorous design procedure for extremum seeking is applicable. The desi...

To the Editor:—We read with much interest the article by Biki et al. regarding the effect of anesthetic technique and postoperative analgesia on the cancer recurrence rate after open radical prostatectomy. The results suggesting that epidural anesthesia/analgesia lowers the rate of recurrence are certainly intriguing; however, we are concerned with the lack of detailed information presented in ...

Our rigorous path integral is extended to quantum evolution on metricaffine manifolds. 1 Path Integrals on Euclidean Spaces. Consider the evolution operator U [ψ(t, q)] = ψ(t, q), t ≥ t, of the quantum evolution equation on L(R): h̄ i ∂ψ(t, q)/∂t+ f(t, q, h̄ i ∂/∂q)ψ(t, q) = 0. Here the operator f(t, q, h̄ i ∂/∂q) is the standard quantization of a classical timedependent quasi-Hamiltonian f(t, q, ...

The Uni ed Modelling Language (UML) is becoming the de facto industry standard notation for object-oriented analysis and design. In this paper we propose a development process using UML and other notations which supports formal analysis and veri cation, so enabling the notation to be used for highly critical systems. We will illustrate the development process using a small example of a tra c li...