政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/51470

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/51470

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题名:	熱帶亞純函數及其在差分方程之應用 Tropical Meromorphic Functions and Their Application on Difference Equations
作者:	陳亮 Chen, Liang
贡献者:	蔡炎龍 Tsai, Yen Lung 陳亮 Chen, Liang
关键词:	熱帶幾何熱帶多項式熱帶亞純函數熱帶週期函數 tropical geometry tropical polynomial tropical meromorphic function tropical periodic function
日期:	2010
上传时间:	2011-10-05 16:18:29 (UTC+8)
摘要:	在這篇論文中，一個熱帶亞純函數(tropical meromorphic function)若給定有限個零根(roots)與極點(poles)還有它們的重數(multiplicities)，我們證明了這個熱帶亞純函數的存在與唯一性。另外，一個熱帶週期函數(tropical periodic function)若給定一個週期區間內的有限個零根與極點還有它們的重數，我們也找到了這個熱帶週期函數的一個簡單表達式。接著，給定一個一階線性差分方程(first-order linear difference equation)，我們討論了各種情況下的所有熱帶亞純函數解的表達式。最後，對於連續函數我們提供了一個它的熱帶近似函數，希望對於解差分方程的熱帶亞純函數解時能有所助益。 In this thesis, we find the formula of tropical meromorphic function by giving finite number of roots and poles (with multiplicities). We also find a simple formula for tropical periodic function by giving finite number of roots and poles (with multiplicities) during a period [0,T). We then discuss all cases of the tropical meromorphic solution functions of first-order linear difference equation. At last, we provide a tropical approximated function of a given continuous function. We hope it is helpful in solving the tropical meromorphic solution functions of a given difference equation.
參考文獻:	Bibliography [1] Nathan Grigg. Factorization of tropical polynomials in one and several variables. Honor`s thesis,Brigham Young University, 2007. [2] Nathan Grigg and Nathan Manwaring. An elementary proof of the fundamental theorem of tropical algebra. arXiv:math.CO/0707.2591, 2008. [3] Rodney G. Halburd and Neil J. Southall. Tropical nevanlinna theory and ultradiscrete equations. Int. Math. Res. Not. IMRN, (5):887{911, 2009. [4] Ilpo Laine and Kazuya Tohge. Tropical nevanlinna theory and second main theorem. ArXiv e-prints, October 2009. [5] Diane Maclagan and Bernd Sturmfels. Introduction to tropical geometry. 2009. [6] Jurgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. First steps in tropical geometry. ArXiv e-prints:math/0306366, 2003. [7] David Speyer and Bernd Sturmfels. Tropical mathematics. ArXiv e-prints:math/0408099, 2004. [8] Yen-Lung Tsai. Working with tropical meromorphic functions of one variable. ArXiv e-prints, January 2011.
描述:	碩士國立政治大學應用數學研究所 97751005 99
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0097751005
数据类型:	thesis
显示于类别:	[應用數學系] 學位論文

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