| “杜西结论”的推广 |
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| 引用本文： | 孙茂荣,陈绍示.“杜西结论”的推广[J].安徽大学学报(自然科学版),2011,35(5):32-36. |
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| 作者姓名： | 孙茂荣 陈绍示 |
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| 作者单位： | 江苏大学理学院,江苏镇江,212013 |
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| 基金项目： | 国家自然科学基金资助项目(51079064) |
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| 摘 要： | 研究和推广"杜西结论",设α∈φn={(a1,a2,…,an)|ai∈N,i=1,2,…,n},定义杜西变换:D(α)=(|a1-a2|,|a2-a3|,…,|an-a1|),利用离散动力系统的分析方法,研究更一般的问题,得出结论:n(n=2k,(k=1,2,…))个自然数形成一个环形,再进行相邻两数大数减小数,则在有限步内n个数必都变为零,即对任意α∈φn,当n=2k,(k=1,2,…)时,存在m∈N,有Dm(α)=θ,并得出几个相关的结论.
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| 关 键 词： | 杜西结论 杜西问题 离散动力系统 循环移位变换 布尔向量 |
On the extension of the Duthe's conclusion |
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| SUN Mao-rong,CHEN Shao-shi.On the extension of the Duthe's conclusion[J].Journal of Anhui University(Natural Sciences),2011,35(5):32-36. |
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| Authors: | SUN Mao-rong CHEN Shao-shi |
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| Institution: | (Department of Mathematic,Jiangsu University,Zhenjiang 212013,China) |
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| Abstract: | Supposed α∈φn={(a1,a2,…,an)|ai∈N,i=1,2,…,n},in the φn,definited an operator D,called Duthe operator,with the following property:D(α)=(|a1-a2|,|a2-a3|,…,|an-a1|).Thereby using discrete dynamic system,we got a general conclusion,which extended the "Duthe's Conclusion"to the 2k-space,as following:for any α∈φn,where n=2k,(k=1,2,…),then existed m∈N,we had Dm(α)=θ.We also got some relative conclusions in the paper. |
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| Keywords: | Duthe's conclusion Duthe's problem discrete dynamic system circulant shift transformation boolean vector |
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