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In this chapter, firstly, the definition of rough rings and its properties are given. Then the definition and properties of rough subrings, rough ideals and rough quotient rings are put forward and proved. Finally, homomorphism and isomorphism of rough rings is studied.

在这一章中，首先给出了粗糙环的定义及其性质，其次给出了粗糙子环、粗糙理想、粗糙商环的定义及其性质，最后研究了粗糙环的同态与同构。

Based on the definition of technical work and the application of this term, this thesis discusses the inappropriateness of this definition and the misunderstanding caused by introducing this term into the engineering thermodynamics.

针对技术功定义式方面存在的不足及某些因引用技术功而带来的错误观点，论述了技术功这一概念的不合理性。

This kind of definition is a kind of inchoate definition, namely advertisement of so called character paying fee.

这种定义是早期的一种定义，也就是所谓的付费文字广告。

The definition is usually indented in the definition list.

定义通常在定义列表中缩进显示。

This article in order to study the inevitableness of Rococo's appearance and it's advancement in history of art ,I analyze the background of 18's century in France first in this article.Then,I criticize the wrong definition about the characteristic of Rococo,"erotically"and "frivolous",and try hard to find the hidden causes about this wrong definition.

本文力图重现罗可可艺术出现、发展的时代背景，在此基础上重新审视罗可可艺术崛起的必然性和它在艺术史上的进步性，对以往艺术史家对其"艳情"、"浮华"的定性进行批判，并着重分析这种错误定性背后暗藏的深层原因。

A declaration may have an initializer only if it is also a definition because only a definition allocates storage.

声明初始化可能只有一个定义，因为这也是唯一一个定义分配存储。

If you specify both inline and extern in the function definition, then the definition is used only for inlining. In no case is the function compiled on its own, not even if you refer to its address explicitly.

当一个函数是inline和extern的，这个函数定义只会在调用中展开，而不会被编译，即使你明确引用它的地址。

In chapter three, we first give the definition of quadratic automata (3. 6 definition), then study their invertibility. 3. 10 theorem gives a sufficient and necessary conditions for weak inverse quadratic form finite automata, and a way to find the one whose weak inverse is quadratic form finite automata.

第三章首先构造了二次型有限自动机类（3.6定义），研究其上的可逆性理论。3.10定理给出了弱逆二次型有限自动机的充要条件及弱原逆的求法、3.12定理则给出了弱可逆二次型有限自动机的充要条件及弱逆的求法。

In §1. 2, we gave the definition of the Riemann-Liouville operators of the fractional calculus and the basic properties of these operators. In§1. 3, we introduced the definition of the generalized Mittag- Leffler function E〓 and proved the inverse Laplace transform formula below,〓(1) which was used frequently in this paper.

在§1.2节中，主要介绍了Riemann-Liouville型分数阶微积分算子的基本定义以及主要性质，在§1.3节中则给出了广义Mittag-Leffler函数〓的定义及其基本性质，同时证明了如下Laplace逆变换公式：〓在本文中，公式（1）将被多次引用。

The thesis will introduce, respectively, relevant concepts of residue theorem and its promotion and application in two parts In the basic concepts of chapter II, the definition, classification and relationship between function zero and pole of the isolated singular point are given to lead out relevant definition, theorem and solving method, while the core content of this paper is promotion and application of residue theorem, including calculation of integration by using residues, application in diagonal theorem and argument theorem, application in electromagnetism and theorem promotion and relevant application of extension theorems

本文将从两大部分分别引入和浅析了留数定理的相关概念及其推广和应用在第二章的基本概念部分中，给出了孤立奇点的定义和分类、函数零点与极点的关系，从而引出留数定理的相关定义与定理及其求法而本文的核心内容也就是留数定理的推广和应用，包括运用留数来计算积分、体现在对角定理与辐角定理中的应用、在电磁学中的应用及其定理的推广和推广定理的相关应用

The small blue capacitor has very high chances to go fully shorted compare to electrolytic capacitor which is very rare.

小蓝电容器具有很高的机会去充分地缩短了比较电解电容器，这是非常罕见的。

In the Italian campaigns of 1513 and 1515, when the Swiss won the victories of Novara and Marignan, he acted as army chaplain.

在意大利的运动， 1513年和1515年，当瑞士赢得了胜利，诺瓦拉和marignan ，他担任军队的牧师。