School of Mathematics Faculty Publications
http://hdl.handle.net/1853/26891
Pre-prints by faculty members in the School of Mathematics2022-08-12T09:47:20ZOn a transformation of Bohl and its discrete analogue
http://hdl.handle.net/1853/48752
On a transformation of Bohl and its discrete analogue
Harrell, Evans M., II; Wong, Manwah Lilian
Fritz Gesztesy’s varied and prolific career has produced many transformational contributions to the spectral theory of one-dimensional Schrödinger equations. He has often done this by revisiting the insights of great mathematical analysts of the past, connecting them in new ways, and reinventing them in a thoroughly modern context. In this short note we recall and relate some classic transformations that figure among Fritz Gestesy’s favorite tools of spectral theory, and indeed thereby make connections among some of his favorite scholars of the past, Bohl, Darboux, and Green. After doing this in the context of one-dimensional Schrödinger equations on the line, we obtain some novel analogues for discrete one-dimensional Schrödinger equations.
First published in Proceedings of Symposia in Pure Mathematics in Volume 87, 2013, published by the American Mathematical Society.; DOI: 10.1090/pspum/087/01433
2013-01-01T00:00:00ZHarrell, Evans M., IIWong, Manwah LilianFritz Gesztesy’s varied and prolific career has produced many transformational contributions to the spectral theory of one-dimensional Schrödinger equations. He has often done this by revisiting the insights of great mathematical analysts of the past, connecting them in new ways, and reinventing them in a thoroughly modern context. In this short note we recall and relate some classic transformations that figure among Fritz Gestesy’s favorite tools of spectral theory, and indeed thereby make connections among some of his favorite scholars of the past, Bohl, Darboux, and Green. After doing this in the context of one-dimensional Schrödinger equations on the line, we obtain some novel analogues for discrete one-dimensional Schrödinger equations.Asymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence
http://hdl.handle.net/1853/31312
Asymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence
Shen, Wenxian; Yi, Yingfei
2009-12-07T00:00:00ZShen, WenxianYi, YingfeiDynamics of Almost Periodic Scalar Parabolic Equations
http://hdl.handle.net/1853/31311
Dynamics of Almost Periodic Scalar Parabolic Equations
Shen, Wenxian; Yi, Yingfei
2009-12-07T00:00:00ZShen, WenxianYi, YingfeiRandom Restarts in Global Optimization
http://hdl.handle.net/1853/31310
Random Restarts in Global Optimization
Hu, X.; Shonkwiler, R.; Spruill, M. C.
In this article we study stochastic multistart methods for global optimization, which combine local search with random initialization, and their parallel implementations. It is shown that in a minimax sense the optimal restart distribution is uniform. We further
establish the rate of decrease of the ensemble probability that the global minimum has not been found by the nth iteration. Turning to parallelization issues, we show that under independent identical processing (iip), exponential speedup in the time to hit the goal bin normally results. Our numerical studies are in close agreement with these finndings.
2009-12-07T00:00:00ZHu, X.Shonkwiler, R.Spruill, M. C.In this article we study stochastic multistart methods for global optimization, which combine local search with random initialization, and their parallel implementations. It is shown that in a minimax sense the optimal restart distribution is uniform. We further
establish the rate of decrease of the ensemble probability that the global minimum has not been found by the nth iteration. Turning to parallelization issues, we show that under independent identical processing (iip), exponential speedup in the time to hit the goal bin normally results. Our numerical studies are in close agreement with these finndings.