Kale Oyedeji

A computational method for the determination of the response of a linear system

A number of issues are discussed relating to the analysis of a linear damped oscillator equation with a forcing term where the right side of the equation, g(t), is known only at fixed, equal time intervals. (A particular class of such equations has application to civil earthquake engineering.) It is noted that the equation is not a differential equation because the condition of uniqueness does not obtain. A general computational method is presented for calculating x(t), based on an unconditionally stable finite difference technique. The work generalizes the results given in the recent paper of Ly (1984).

Career of Professor Ronald E. Mickens

Professor Mickens graduated summa cum laude from Fisk University in 1964 with a B.A. degree in Physics and Mathematics. His graduation honors included election to Phi Beta Kappa. Doctoral studies in theoretical Physics were completed in 1968 at Vanderbilt University. For the next 2 years, as a National Science Foundation Postdoctoral Fellow at the Center for Theoretical Physics, the Massachusetts Institute of Technology, he did research on calculating and studying the scattering amplitudes for strongly interacting elementary particles at high energies. In 1970, he returned to Fisk University to teach and do research in Mathematical Physics. Professor Mickens’ major research activities from 1966–1977 were centered on the application of scattering theory to problems in both elementary particle physics and chemical reaction rates. He showed that the chemical equilibrium coefficient could be directly constructed from the general principles of scattering theory. He also applied these techniques to obtain new results for the low temperature behavior of recombination reaction rate functions. In addition, Mickens showed how to generalize the fundamental Pomeranchuk Theorem, which relates various physical properties of particle and anti-particle collisions at very high energies, to complex processes having twoand many-particle final states. During 1977–1981, Professor Mickens began a study of second-order, ordinary differential equations which model nonlinear oscillatory dynamical systems. One of the results from this research was the publication of the book, Nonlinear Oscillations (Cambridge University Press, New York, 1981). Subsequent work in this area led to more than 35 publications related to the analysis and construction of uniformly valid perturbation and global methods to calculate analytical approximations to the solutions of such equations. A major tool used for these investigations was the rewriting of the original second-order ODEs to system form and then studying the behavior of the trajectories in the resulting twodimensional phase-space. In 1981, Professor Mickens was a Visiting Research Fellow at the Joint Institute for Laboratory Astrophysics located in Boulder, CO. There he began a study of difference equations and the instabilities that can arise in the numerical integration of differential