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| 研究生： |
劉軒亦 LIU, XUAN-YI |
|---|---|
| 論文名稱： |
具有延遲時間的分支費波納契數列 k-Delayed Branching Fibonacci Sequences |
| 指導教授： |
洪芷漪
Hong, Jyy-I |
| 口試委員: |
洪芷漪
Hong, Jyy-I 陳隆奇 Chen, Lung-Chi 顏如儀 Yen, Ju-Yi |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2024 |
| 畢業學年度： | 112 |
| 語文別： | 中文 |
| 論文頁數： | 34 |
| 中文關鍵詞： | 具延遲時間的費波納契數列 、費波納契數列 、分支過程 |
| 外文關鍵詞： | K-delayed Fibonacci sequences, Fibonacci sequences, Branching process |
| 相關次數： | 點閱：47 下載：20 |
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考慮一個延遲時間為 k 且每次生產數為服從同一分布的獨立隨機變數的分支費波那契數列，在本文中我們討論在時間趨近於無窮大時，兔子的總對數會成指數成長且相鄰兩代間個數的比值會趨近於定值，而此定值滿足某一由兔子總對數所對應的疊代式所產生的方程式。
Consider a branching Fibonacci sequence with delayed time k time units and a random production quantity each time. In this article, we discuss that, when time approaches infinity, the ratio of the numbers of pairs of rabbits between two successive time points will approach a constant value.
致謝 i
中文摘要 ii
Abstract iii
Contents 0
Chapter 1 Introduction 1
1.1 Fibonacci sequence 1
1.2 Galton-Watson branching process 3
1.3 Fibonacci branching process 7
Chapter 2 k-Delayed Branching Fibonacci Sequences 10
2.1 The setting for k-delayed branching Fibonacci sequences 10
2.2 Properties of the key equation 12
2.3 Main result on k-delayed brancging Fibonacci sequences 15
2.4 Proof of Theorem2.3.1 16
Chapter 3 Conclusion 27
Appendix A 29
Appendix B 32
Bibliography 34
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[2] A. F. Horadam. A Generalized Fibonacci Sequence. Amer. Math. Monthly 68 (1961), 455-459.
[3] M. Feinberg. Fifonacci-Tribonacci. Fibonacci Quarterly 1.3 (1963), 71-74.
[4] C. C. Yalarigi. Properties of the Tribonacci Numbers. Fibonacci Quarterly 15.3 (1977), 193-200.
[5] M. E. Waddill. The Tetranacci Sequence and Its Generalizations. Fibonacci Quarterly 30.1 (1992), 9-20.
[6] S. Falcon and A. Plaza. On the Fibonacci k-numbers. Chaos, Solitons & Fractols, 32(5) (2007), 1615-1624.
[7] S. Falcon. Generalized -Fibonacci Numbers. Gen. Math. Notes, vol.25, No.2.(2014),148-158.
[8] C. C. Heyde. On a probabilistic analogue of the Fibonacci sequence. J. Appl. Prob.17. (1980). 1079-1082.
[9] C. C. Heyde. On Fibonacci (or lagged Bienaymé-Galton-Watson) branching processes. J. Appl. Prob.18. (1981). 583-591.
[10] J. B. MacQueen. A linear extension of the martingale convergence theorem. The Annals of Probability, vol.1, No.2. (1973). 263-271.
