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Veljan-Korchmaros型不等式的稳定性
  • ISSN号：1000-8314
  • 期刊名称：《数学年刊：A辑》
  • 时间：0
  • 分类：O178[理学—数学;理学—基础数学]
  • 作者机构：[1]河西学院数学系,甘肃张掖734000
  • 相关基金：国家自然科学基金（No.10671117）和甘肃省教育厅科研基金（No.0709-03）资助的项目.
作者： 马统一[1]
关键词： EUCLIDEAN空间, 单形, 体积, 棱长, 超球, Veljan—Korchmaros不等式, 稳定性, Euclidean space, Simplex, Volume, Edge-lengh, Hypersphere,Veljan-Korchmaros inequality, Stability
中文摘要：

关于Euclidean空间E^n（n≥2）中单形的几何不等式,由于支撑函数或径向函数的表达式很难找到,因此一般很难用Hausdorff度量或径向度量来度量两个单形的＂偏差＂,使得涉及单形的几何不等式的稳定性的研究比较困难.利用单形棱长在确定单形时起决定性作用这一事实,引进了两个单形＂偏正＂度量的概念,从而较好地解决了单形偏正度量的问题,并建立了著名的Veljan-Korchmaros不等式的稳定性版本.作为推论,还导出了一系列Veljan-Korchmaros型不等式的稳定性版本.

英文摘要：

It is very difficult to find the formula of support function or radial function of simplices in Euclidean space E~n（n≥2）,therefore the deviation metric of two simplices is difficult to realize by Hausdorff metric or radial metric.The study of stability of geometric inequalities of simplices is also difficult.In this paper,the problem of the deviation regular metric is solved by introducing the definition of the deviation regular metric of two sim- plices.The definition based on the fact that edge lengthes of simplex plays an important affect when someone define the simplex. Moreover, stability version of well-known Veljan- Korchmaros inequality is established. As application, some stability versions of a series of Veljan-Korchmaros models inequalities are established.

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期刊信息
  • 《数学年刊：A辑》
  • 中国科技核心期刊
  • 主管单位:国家教育部
  • 主办单位:复旦大学
  • 主编：李大潜
  • 地址：上海市长乐路746号
  • 邮编：200040
  • 邮箱：edcam@fudan.edu.cn
  • 电话：021-65642338
  • 国际标准刊号：ISSN：1000-8314
  • 国内统一刊号：ISSN：31-1328/O1
  • 邮发代号:4-298
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:4264