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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/51470


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/51470


    Title: 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
    Authors: 陳亮
    Chen, Liang
    Contributors: 蔡炎龍
    Tsai, Yen Lung
    陳亮
    Chen, Liang
    Keywords: 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
    Date: 2010
    Issue Date: 2011-10-05 16:18:29 (UTC+8)
    Abstract: 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.
    Reference: 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.
    Description: 碩士
    國立政治大學
    應用數學研究所
    97751005
    99
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0097751005
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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