| 线性空间中函数的单位分解性 |
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| 引用本文： | 罗炯兴,刘焕文.线性空间中函数的单位分解性[J].西昌学院学报(自然科学版),2018,32(3):51-56. |
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| 作者姓名： | 罗炯兴 刘焕文 |
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| 作者单位： | 西昌学院少数民族预科教育学院;浙江海洋大学船舶与机电工程学院 |
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| 基金项目： | 2014年广西自然科学基金：缓坡类方程的准确解析解及在近海工程中的应用(2014GXNSFAA118322)。 |
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| 摘 要： | 利用微分流形研究了实数域R上的n维线性空间X的连续函数,指出在线性空间X中存在满足单位分解的一簇光滑函数,并得到了线性空间X中函数的一个单位分解定理;另外,在二维线性空间X中应用单位分解定理,指出了存在定义在任意开凸体A上,满足单位分解性的3个连续函数,这样将线性空间与微分流形相结合,为研究线性空间的函数分解问题及相关问题提出了一种新方法。
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| 关 键 词： | 线性空间 微分流形 单位分解性 开凸体 |
On the Unit Decomposition of Functions in the Linear Space |
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| LUO Jiong-xing,LIU Huan-wen.On the Unit Decomposition of Functions in the Linear Space[J].Journal of Xichang College,2018,32(3):51-56. |
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| Authors: | LUO Jiong-xing LIU Huan-wen |
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| Institution: | 1. School of Preparatory Education for Minorities, Xichang University, Xichang, Sichuan 615000, China;
2. School of Naval Architecture and Mechanical Engineering, Zhejiang Ocean University, Zhoushan, Zhejiang
316022, China |
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| Abstract: | Using the knowledge of differential manifold, the linear space with the dimension of n on the real number
field was researched. In linear space , the existence about a cluster of smooth functions satisfying
the unit decomposition were pointed out, and a unit decomposition theorem was established. In addition, applying the
unit decomposition theorem in the linear space with the dimension of 2, the existence was shown that the three
continuous functions satisfying the unit decomposition were defined in arbitrary open convex body . The linear space
was combined with differential manifold, and a new method was showed to research decomposition and related
problem of functions in the general linear space. |
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| Keywords: | linear space differential manifold unit decomposition open convex body |
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