A class of singularly perturbed,nonlinear, fixed-endpoint control problems

Singular perturbation techniques are applied to a class of nonlinear, fixed-endpoint control problems to decompose the full-order problem into three lower-order problems, namely, the reduced problem and the left and right boundary-layer problems. The boundary-layer problems are linear-quadratic and, contrary to previous singular perturbation works, the reduced problem has a simple formulation. The solutions of these lower-order problems are combined to yield an approximate solution to the full nonlinear problem. Based on the properties of the lower-order problems, the full problem is shown to possess an asymptotic series solution.This work was supported in part by the National Science Foundation under Grant No. ENG-47-20091 and in part by the US Air Force under Grant No. AFOSR-73-2570.The author acknowledges the helpful suggestions of Professor P. V. Kokotovic, University of Illinois, Urbana, Illinois.     

Dual function catalysts. Dehydrogenation and asymmetric intramolecular Diels-Alder cycloaddition of N-hydroxy formate esters and hydroxamic acids: evidence for a ruthenium-acylnitroso intermediate

The chiral ruthenium salen complex, 13b, functions as an efficient catalyst for the sequential oxidation and asymmetric Diels-Alder cycloaddition of hydroxamic acids and N-hydroxy formate esters. This result provides evidence for the formation of a ruthenium-nitroso formate (acyl nitroso) intermediate. The Diels-Alder precursors are prepared from simple building blocks, and the cycloadducts, bridged oxazinolactams, can serve as useful intermediates in organic synthesis.     

On the transition from supercritical to subcritical Hopf bifurcations

By using the method of averaging, we give a complete Hopf bifurcation diagram when the differential equation has more than one parameter. The method is applied to a system of parabolic equations with nonlinear coupling on the boundary. This set of equations is a mathematical model which describes the normalized concentrations of substances in a solution produced by two enzymes.     

Laser cavity dumping using optical bistability

In this paper we present a scheme for passive cavity dumping of a laser. The basic idea is to replace one of the laser mirrors with an optically bistable element. The cases of operation with absorptive and dispersive bistable elements are analyzed.