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Advances in Mathematical Physics
Volume 2017, Article ID 3838507, 9 pages
https://doi.org/10.1155/2017/3838507
Research Article

On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect

Department of Mathematics, National Chung Cheng University, 168 University Rd., Min-Hsiung, Chia-Yi County 621, Taiwan

Correspondence should be addressed to Lung-Hui Chen; moc.liamg@nehciuhgnul.rm

Received 9 February 2017; Accepted 26 April 2017; Published 21 May 2017

Academic Editor: Hagen Neidhardt

Copyright © 2017 Lung-Hui Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function to the defining index of refraction . By the limit behaviors in frequency sphere, we prove some results on the inverse uniqueness of index of refraction. In physics, Doppler’s effect connects the variation of the frequency/eigenvalue and the motion velocity/variation of position variable. In this paper, we proved the functional derivative