本文证明了，任意有限半群均含循环子群。利用此结果，就能容易地导出环论中的一些定理。
In this paper, it is proved that any finite semigroup can contain cycle subgroup, Witn this result, some theorems in ring theory are induced easily.
本文介绍了一个循环差集的存在性定理。
A new existence theorem on cyclic difference sets is introduced in this note.
本文提出两条等价性定理，用来判别不同排列的相位循环是否等价。
Two equivalent theorems are presented which judge whether phase cycles of different arrangements are equivalent.
根据卡诺定理给出了热机的循环效率极大值问题。
Carnot's Theorem discusses the extreme value of the efficiency of heat engines' cycles.
本文探讨用向量运算代替串行FORTRAN的DO循环的基本条件，提出了向量化判别定理以及实现向量化的算法。
Conditions for vectorization of FORTRAN DO-loops are discussed in this paper. Based on these conditions, the decision theorems and the algorithm for vectorization are given.
本文提出并证明了在各向同性强化条件下的安定定理，即在循环载荷作用下，各向同性强化材料的结构，其安定状态总是可以实现的。
Shakedown theorem under isotropic hardening is presented and proved in this paper. Namely, shakedown state is always achievable for structure of isotropic hardening materials under cycling loads.
在证明卡诺定理时，不可逆热机只能作正向循环，不能令其作逆向循环。
While proving Carnot theorem, the irreversible heat engine can only run on forward circulation, but not on the opposite.
本文利用连通循环图及其连通度的有关性质，得到了构造具有最佳连通性的循环网络的定理。
Using the properties of circulant graphs and its connectivity, the theorems about constructing a network with optimal connectedness have been obtained in this paper.
在其终止性可判定理论的基础上，对于给定非终止循环构造出其非终止输入作为反例，使该结果更加完整。
Under his termination-deciding method, a nonterminating input can be further constructed as an counterexample for the given nonterminating loop, which makes the result more complete.
给出了对称对角A-因子循环分块矩阵的概念，讨论了它的一些性质，推广了几个主要定理．。
A concept of symmetric diagonal A-factor block circulant matrices and some of their prop- crtics are given, the main theorems are extended.
利用范德蒙矩阵对循环矩阵的一个定理给出了推广，并得到了广义循环矩阵的几个性质。
The generalization of a theorem for circular matrix is given by using generalized Vandermonde matrix, and several properties of generalized circular matrix are obtained.
本文应用霍夫曼定理、地区差异循环理论、规模经济理论、产业联系理论，对我国的产业结构现状加以分析，进而提出优化我国产业结构的对策思路。
The status of industrial structure in china is analysed with the industrial theories in the article. Furthermore, the suggestion about industrial structure in China is advised, abvised.
本文应用霍夫曼定理、地区差异循环理论、规模经济理论、产业联系理论，对我国的产业结构现状加以分析，进而提出优化我国产业结构的对策思路。
The status of industrial structure in china is analysed with the industrial theories in the article. Furthermore, the suggestion about industrial structure in China is advised, abvised.
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