We consider sign-changing solutions of the Dirichlet problem u′′ +λ f (u) = 0, 0 < x < 1, u(0) = u(1) = 0 , with n 0 interior roots. We give a necessary and sufficient condition that a turn occurs at the solution (λ ,u(x)) , depending only on the maximum value of the solution u(x) . If a turn does occur, we give another formula allowing to compute the direction of the turn. Our results generali...

Abstract In the Photon Factory 2.5 GeV electron storage ring at KEK, the upgrade project of its straight sections is underway. In the project, we improve the beam-position monitors (BPMs) and the global orbit feedback system. New BPMs are designed and installed in the straight sections and the orbit stabilization system is improved. The effect RF phase modulation to the beam position fluctuatio...

Title of Document: LONGITUDINAL SPACE-CHARGE WAVES INDUCED BY ENERGY MODULATIONS Brian L. Beaudoin, Master of Science, 2008 Directed By: Professor Patrick G. O’Shea and Professor Rami A. Kishek Department of Electrical and Computer Engineering High intensity beams that are space-charge dominated are important for applications such as free electron lasers that require high intensity and low emit...

The turn-by-turn directions provided in existing navigation applications are exclusively derived from underlying road network topology information, i.e., the connectivity of edges to each other. Therefore, the turn-by-turn directions are simplified as metric translation of physical world (e.g. distance/time to turn) to spoken language. Such translation that ignores human cognition of the geogra...

Mimetics of secondary structure elements are one promising approach in the design of protein-protein interaction inhibitors, since secondary structure elements are very important recognition motifs in protein-protein interfaces. In helices and turns, the protein backbone provides a scaffold to present the sidechains in the correct orientation for the three-dimensional interaction motif. For bot...