向量压缩控制与压缩单调函数

周美秀1, 张小明2, 严文兰3

doi:10.3969/j.issn.1007-2861.2013.02.012

上海大学学报(自然科学版) >

2013 , Vol. 19 >Issue 2: 170 - 175

DOI: https://doi.org/10.3969/j.issn.1007-2861.2013.02.012

数理化科学

向量压缩控制与压缩单调函数

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1. 浙江广播电视大学开放与远程教育研究院, 杭州310030; 2. 浙江广播电视大学海宁学院, 浙江海宁314400; 3. 忠信中学, 广东河源517139

收稿日期: 2012-09-18

网络出版日期: 2013-04-30

基金资助

国家自然科学基金资助项目(10971194); 浙江省教育厅科研计划资助项目(Y201223283); 浙江广播电视大学高层次人才科研基金资助项目(GRJ-08)

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Vector Compression Control and Compression Monotonic Function

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(. Open and Distance Education Research Institure, Zhejiang Radio & Television University, Hangzhou 310030, China; 2. Haining College, Zhejiang Radio & Television University, Haining 314400, Zhejiang, China; 3. Zhongxin High School, Heyuan 517139, Guangdong, China

Received date: 2012-09-18

Online published: 2013-04-30

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摘要

通过定义向量压缩控制与压缩单调函数, 给出压缩单调函数的微分判别定理, 用以克服向量控制和Schur凸凹函数的缺点. 通过实例说明, 向量压缩控制比经典的向量控制要狭窄, 压缩单调增(减)函数比Schur凸(凹)函数范围要广.

关键词： 压缩控制; Schur函数; 向量控制

本文引用格式

周美秀1, 张小明2, 严文兰3 . 向量压缩控制与压缩单调函数[J]. 上海大学学报(自然科学版), 2013 , 19(2) : 170 -175 . DOI: 10.3969/j.issn.1007-2861.2013.02.012

Abstract

This paper defines vector compression control and compression monotonic function, and presents a differential distinguishing theorem of compression monotonic function to overcome the defects of vector control and the Schur convex/concave function. With an example, it is shown that vector compression control is narrower than the classical vector control, and the compression monotonic increase/decrease function is broader than the Schur convex/concave function.

Key words： compression control; Schur function; vector compression

参考文献

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[2] 王伯英. 控制不等式基础[M]. 北京: 北京师范大学出版社, 1990.

[3] Zhang X M, Xi B Y. A new method to prove and find analytic inequalities [J]. Abstract and Applied Analysis, 2010, 12: 89-99.

[4] 张小明, 褚玉明. 解析不等式新论[M]. 哈尔滨: 哈尔滨工业大学出版社, 2008: 217-259.

[5] 张小明. 最值定理与分析不等式[J]. 不等式研究通讯, 2010, 17: 107-138.

[6] Alzer H. Sierpinski’s inequality [J]. J Belgian MathSoc B, 1989, 41: 139-144.

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