| 哲学观下的数学反演思想及其发展 |
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| 引用本文： | 刘建忠,刘心蓉.哲学观下的数学反演思想及其发展[J].昆明师范高等专科学校学报,2012(5):39-45. |
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| 作者姓名： | 刘建忠 刘心蓉 |
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| 作者单位： | [1]云南省软件工程重点实验室,云南昆明650091 [2]云南昆船设计研究院,云南昆明650051 [3]北京语言大学,北京100083 |
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| 摘 要： | 数学反演思想的哲学基础是辩证法的对立统一规律，不同的反演思想反映了对立统一规律中的两个对立面的不同变化形态。在讨论反演变换、级数反演、反问题理论、关系映射反演方法和反演集合理论的思想差异和相互关系的基础上指出：关系映射反演方法思想包含级数反演思想，级数反演思想包含反演变换思想，在有限集上关系映射反演方法和反问题理论可统一为反演集合理论。同时举例说明了反演集合理论在反问题理论（联合反演）中的应用。
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| 关 键 词： | 辩证法 对立统一规律 反演思想 反演集合 关系映射反演方法 反演理论 级数反演 反演变换 |
Inversion Thoughts in Mathematics and Its Development under the Philosophical Concept |
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| LIU Jian-zhong,LIU Xin-rong.Inversion Thoughts in Mathematics and Its Development under the Philosophical Concept[J].Journal of Kunming Teachers College,2012(5):39-45. |
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| Authors: | LIU Jian-zhong LIU Xin-rong |
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| Institution: | 1. Key Laboratory in Software Engineering of Yunnan Province, Yunnan Kunming 650091, China; 2. Kunming Shipbuilding Design ＆ Research Institute,Yunnan Kunming 650051, China; 3. Beijing Language and Culture University, Beijing 100083, China) |
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| Abstract: | In this thesis, the author thinks that the philosophical basis for inversion thoughts in mathematics is the law of the unity of opposites within the dialectics. The ideological differentiae and mutual relations are discussed in this thesis among the inversion transformation, the series reversion, the inverse problem theory, the method of relation mapping inversion, and the inversion set theory. The author points out that method of relation mapping inversion comprises series reversion, while series reversion includes inversion transformation, and therefore, method of relation mapping inversion and inverse problem theory could be unified into inversion set theory within finite set. The author also illustrates the applications of inversion set theory in the inverse problem theory （joint inversion）. |
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| Keywords: | dialectics the law of the unity of opposites inversion thoughts inversion set theory method of relation mapping inversion inverse problem theory series reversion inversion transformation |
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