簡易檢索 / 詳目顯示
| 研究生： |
楊明訓 Yang, Ming-Xun |
|---|---|
| 論文名稱： |
基於調和多項式的重力透鏡成像數之研究 A Study of the Number of Gravitationally Lensed Images Based on Harmonic Polynomials |
| 指導教授： |
鄭志豪
Teh, Jyh-Haur |
| 口試委員: |
黃明傑
Huang, Min-Jei 朱家杰 Chu, Chia-Chieh |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2017 |
| 畢業學年度： | 105 |
| 語文別： | 中文 |
| 論文頁數： | 32 |
| 中文關鍵詞： | 調和多項式 、調和有理函數 、重力透鏡 |
| 外文關鍵詞： | harmonic polynomial, harmonic rational function, gravitational lensing |
| 相關次數： | 點閱：61 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本文探討形式如 $p(z)-\overline{z}$ 與 $r(z)-\overline{z}$ 兩調和函數的零點個數之上界，其中 $p$ 為多項式、$r$ 為有理函數。該結果有一個令人訝異的應用，是給出了在某個天文模型中重力透鏡成像數的上界。
In this thesis, we study bounds for zeros of harmonic functions $p(z)-\overline{z}$ and $r(z)-\overline{z}$, where $p$ is a polynomial and $r$ is a rational function. A surprising applications of results obtained in this study is that we are able to bound the number of gravitational lensed images in some astronomical models.
[1] L. Carleson, T. W. Gamelin. 1993. Complex Dynamics, Springer-Verlag, New York.
[2] P. Duren, W. Hengartner, R. S. Langesen. 1996. The argument principle for harmonic functions, The American mathematical monthly 103.5: 411–415.
[3] O. Forster. 1981. Lectures on Riemann surfaces, Graduate Texts in Mathematics (Vol. 81), Springer Science & Business Media-Verlag, New York.
[4] D. Khavinson, G. Neumann. 2006. On the Number of Zeros of certain Rational Harmonic Functions, Proceedings of the American Mathematical Society 134.4: 1077–1085.
[5] D. Khavinson, G. Świątek. 2003. On the Number of Zeros of Certain Harmonic Polynomials, Proceedings of the American Mathematical Society 131.2: 409–414.
[6] M. Meneghetti. 2007. Introduction to gravitational lensing, Lecture scripts.
[7] T. J. Suffridge, J. W. Thompson. 2000. Local behavior of harmonic mappings. Complex Variables, Theory and Application 41: 63–80.
[8] J. H. Teh. 2007. Complexification of real cycles and Lawson Suspension Theorem, Journal of London Mathematical Society 75: 463–478.
[9] A. S. Wilmshurst, Complex harmonic mappings and the valence of harmonic polynomials, Ph.D. thesis, University of York, 1994.
[10] A. S. Wilmshurst, 1998. The valence of harmonic polynomials, Proceedings of the American Mathematical Society: 2077–2081.
[11] H. J. Witt. 1990. Investigation of high amplification events in light curves of gravitationally lensed quasars, Astronomy and Astrophysics 236: 311–322.