On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect
We study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function Δ(x^) to the defining index of refraction n(x). By the limit behaviors in frequency sphere, we prove some results on the invers...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/3838507 |
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| _version_ | 1849407411108970496 |
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| author | Lung-Hui Chen |
| author_facet | Lung-Hui Chen |
| author_sort | Lung-Hui Chen |
| collection | DOAJ |
| description | We study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function Δ(x^) to the defining index of refraction n(x). 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 ∂rΔx^=(1+nrx^)/π. |
| format | Article |
| id | doaj-art-43ec76e982ea4e1fa747ba821089e94b |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-43ec76e982ea4e1fa747ba821089e94b2025-08-20T03:36:06ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/38385073838507On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s EffectLung-Hui Chen0Department of Mathematics, National Chung Cheng University, 168 University Rd., Min-Hsiung, Chia-Yi County 621, TaiwanWe study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function Δ(x^) to the defining index of refraction n(x). 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 ∂rΔx^=(1+nrx^)/π.http://dx.doi.org/10.1155/2017/3838507 |
| spellingShingle | Lung-Hui Chen On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect Advances in Mathematical Physics |
| title | On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect |
| title_full | On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect |
| title_fullStr | On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect |
| title_full_unstemmed | On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect |
| title_short | On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect |
| title_sort | on certain translation invariant properties of interior transmission spectra and their doppler s effect |
| url | http://dx.doi.org/10.1155/2017/3838507 |
| work_keys_str_mv | AT lunghuichen oncertaintranslationinvariantpropertiesofinteriortransmissionspectraandtheirdopplerseffect |