Sensitivity of Functionals with Applications to Engineering Sciences
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Sensitivity of Functionals with Applications to Engineering Sciences Proceedings of a Special Session of the American Mathematical Society Spring Meeting 1983 held in New York
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Editor
Vadim Komkov Department of Mathematics, Winthrop College Rock Hill, SC 29733, USA
AMS Subject Classification (1980): 49H, 73K, 73L ISBN 3-540-13871-4 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13871-4 Springer-Verlag New York Heidelberg Berlin Tokyo
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Introduction This volume contains an enlarged version of some of the talks presented at the American Mathematical Society Spring Meeting in New York City, May of 1983 in a special session on the Sensitivity of Functionals with Applications to Engineering Sciences. All talks were given by invitation. The enlarged versions of the talks given by professors M. Vogel ius and R.V. Kohn, and by A. Fiacco and J. Kyparisis were published elsewhere before the publication of this volume. Only an enlarged abstract exists of Professor W.M. Wonham's presentation. Versions of all other papers presented at that meeting are given in this volume. All of these papers discuss applications of sensitivity theory to design of engineering systems or processes. Applications of sensitivity theory to chemical kinetics are given in the contribution of Professor H. Rabitz. Applications to structural or mechnaical engineering were offered in the papers of V. Komkov; of J.W. Hou, E.J. Haug and R.L. Benedict, A. Diaz, N. Kikuchi and J.E. Taylor, V. Komkov and C. Irwin and P. Pedersen. All of these papers stress the functional analytic approach to optimization and to sensitivity theory for structural and mechanical systems. These contributions attempt to clarify some latest developments in sensitivity theory for engineering systems and also present new theoretical solutions to several important problems. For example, the paper of H. Rabitz presents a new insight into the numerical treatment of chemical kinetics and of quantum scattering theory based on the sensitivity density concept. The paper of P. Pedersen deals with the troublesome aspects of nonselfadjoint problems that arise in structural dynamics, such as the dynamic behavior of the Beck column or Hauger column with both external and internal damping. Influence of these theoretical findings on existing numerical techniques is clearly outlined. Grid modification problems for numerical solutions of structural optimization
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