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1·The article puts forward and sets out clearly algebraic substitution axiom and the principle of duality, which are both universal logic laws.

提出和阐明了两个普遍的逻辑规律——代数替换公理与对偶原理。

2·The dual law in lattice theory is introduced and some concepts and properties relative to it are discussed, while generalizing the concept of duality and the idea of the duality principle.

推广了对偶的概念与对偶原理的思想，在格论中引入了对偶律，并讨论了与之相关的一些概念和性质。

3·The article deals briefly with the ideal element and Duality principle, which includes methods of teaching of the author.

本文简要而概括地介绍了“理想元素”和“对偶原理”，表明了作者在高等几何教学方法上的见解。

4·Duality principle is a powerful tool for the analysis of topological structure of power electronic circuits.

对偶原理是分析电力电子电路拓扑结构的有力工具。

5·In this paper the application of the duality principle to the DC-to-DC switching converters are investigated.

本文研究在直流-直流开关变换器电路中对偶原理的具体应用问题。