標題: 應用逆推網絡在克拉茲猜想的探討
Study 3n+1 Problem in a Backward Iteration Net
作者: 段俊旭
Tuan, Chun-Hsu
張書銘
Chang, Shu-Ming
應用數學系所
關鍵字: 克拉茲猜想;逆推網絡;模擬逆推網絡;3n+1 problem;backward iteration net;simulation backward iteration net
公開日期: 2010
摘要: 本論文主要研究一個有名的數學問題:克拉茲猜想。雖然克拉茲猜想的形式與意義容易被理解,但它仍然尚未被證明。也因為如此,引發了我們對克拉茲猜想的興趣,也希望藉著研究對它有更多的了解。首先,我們會對克拉茲猜想做個簡單的介紹,並且整理一些其他人對克拉茲猜想做的研究。接下來,我們會建構一個特別的圖,也就是逆推網絡,開始我們對克拉茲猜想的研究,同時我們也得到一些逆推網絡的特性。最後,我們嘗試建構一個模擬逆推網絡,去模擬實際的逆推網絡,根據兩者相互比較的數值結果做出分析結論。
3n+1 problem is one of the most famous conjectures in mathematics. It can be easily understood even younger children who just know how to divide by 2 and multiply by 3. However, the 3n+1 problem still can not be proved yet. Therefore, we are so interestedin this problem and hope to understand it completely. First, our study gives a brief introduction of the 3n + 1 problem, and we list some results in many research of the 3n+1 problem. Then, we use a graph, a backward iteration net, to examine the 3n+1 problem and obtain some properties in the backward iteration net. Finally, we simulate the backward iteration net and compare the numerical results with the net.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT079722529
http://hdl.handle.net/11536/45083
Appears in Collections:Thesis


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