| 一个猜想的微分法证明及推广 |
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| 引用本文： | 薛惠良,汤炳兴.一个猜想的微分法证明及推广[J].常熟理工学院学报,2012(4):41-45. |
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| 作者姓名： | 薛惠良 汤炳兴 |
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| 作者单位： | 1. 常熟市中学,江苏常熟215500
2. 常熟理工学院数学与统计学院,江苏常熟215500 |
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| 摘 要： | 利用排序不等式证明猜想(1)的轮换对称不等式(2);把所给出的命题建模为二元函数,使用二元函数极值的判定定理给出猜想的证明;同时把猜想中的指数从正整数k推广到了实数R~+;当k=1时,对称式(2)就是著名的内斯比特不等式的推广.最后把猜想(1)推广到更一般的情形,得到命题③和④.
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| 关 键 词： | 轮换对称 排序不等式 偏微分 极值定理 内斯比特不等式 推广 |
Proof and Generalization of a Method of Differentiation Hypothesis |
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| XUE Hui-liang,TANG Bing-xing.Proof and Generalization of a Method of Differentiation Hypothesis[J].Journal of Changshu Institute of Technology,2012(4):41-45. |
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| Authors: | XUE Hui-liang TANG Bing-xing |
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| Institution: | 1.Changshu Middle School,Changshu 215500,China;2.School of Mathematics and Statistics,Changshu Institute of Technology,Changshu 215500,China) |
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| Abstract: | Sorting algorithm and inequality is used to testify rotation symmetric inequality(2) of hypothesis(1);the propositions are utilized to model binary function,and the laws of two variable extreme value are used to prove the hypothesis.Meanwhile,the hypothesis spreads exponents from positive integer K to real number R+;When K=1,symmetric expression(2) is the spread of Nesbitt’s inequality.In the end,hypothesis(1) can be generalized to more common conditions,thus concluding proposition ③ and proposition④. |
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| Keywords: | rotational symmetry sorting algorithm and inequality partial differential laws of two variable extreme value Nesbitt’s inequality generalization |
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