集合关系

Through the analysis of the second power Cartesian product of natural number set N——N×N and the thirdpower Cartesian product of natural number set N——N×N×N,obtains the conclusion that they all have the bijective relation to natural number set N,it means that the set N×N and the set N×N×N are all countably infinite.

通过对自然数集合N的二次笛卡尔积运算———N×N和三次笛卡尔积运算———N×N×N的详细分析，得出了它们与自然数集合N之间都存在双射关系结论，即集合N×N和集合N×N×N都是可数无穷的。

Firstly a formal syntactic of UML statechart diagrams was given and a series of auxiliary functions to describe the structure features of UML statechart diagrams were presented in which target determinator and source restriction were used to describe the inter-level transitions and open events and close events were used to describe the communication among UML statechart diagrams.

首先给出了UML状态图的形式化语法定义，其中用状态集合、转移集合、事件集合、条件集合、活动集合、对象集合和变量集合，定义了一系列辅助函数描述UML状态图特征，用确定目标状态和受限源状态表示层次关系，用开放事件和封闭事件表示对象之间的消息。

In this article, we first discuss the various algebraic properties of fuzzy sets, and then define a fuzzy digraph by the fuzzy set and the fuzzy relation of the set.

在本文中，我们首先讨论迷离集合的各种代数性质，然后我们利用一个集合的迷离集合与其迷离关系来定义迷离有向图形。

It introduces the basic knowledge and ideas of mathematical logic and classic set theory, including proposition logic and predicate logic, reasoning calculus and theorem proving methods, basic operations and properties of sets and relations, functions of any sets and their properties, the cardinals of infinite sets, and the applications of knowledge and ideas above in computer sciences.

本课程系统介绍数理逻辑与朴素集合论的基础知识，包括：命题逻辑和谓词逻辑、定理的推理演算和机器证明方法，集合和二元关系的基本运算和性质、任意集合中的函数及其性质，无穷集合的基数，以及上述知识在计算机科学中的应用。

Then, using the reasoning matrix between the unit colors and individual colors of the polychromatic sets, the reasoning and generation of geometric tolerance types are achieved.

介绍了各层的意义和各层之间的关系，利用多色集合理论对该模型进行描述，通过多色集合统一颜色和个人颜色的推理关系矩阵，实现了计算机辅助形位公差类型的推理生成，为计算机辅助形位公差类型推理的进一步形式化打下了基础。

A one - to - one correspondence between the points of two geometric figures that is continuous in both directions.

映象一种集合间一一对应关系的规则，一个集合中的每个元素与同一或另一集合中的一个元素相对应

Chapter one is "Introduction". On the basis of summarizing the history of the study of the pictophonetic characters, we suppose some theoretical principle, such as the principle of the correspondence between the form and the meaning of the individual graph of Chinese characters, the principle of the total graphs of Chinese characters being a character-formation system, and the principle of the optimum development of the character -formation system in the history, and som analytic methods, such as the methods of structrue-function analysis, form-position analysis and meaning factor analysis, in the study of the pictophonetic characters. Chapter two is titled"General knwledge of the pictophonetic character." We discuss their origins, nature and some standards of distingnishing them, introduce the knowledge about the editions of SHUO WEN JIE ZI, analyse the functions of the modules of pictophonetic characters in detail, discuss concretely the function of phonetic graphs showing origins and pronunciations, the function of meaning graphs showing meanings and analogies, and the function of distinguishment when the two kinds of graphs are conbined. Chapter three is"The system of meaning graphs of Xiao Zhuan system."After we describe the structure of the meaning graph system, the relations between meaning graphs, the distributions of the function of meaning graphs showing meanings, and the frequency of all this kind of graphs, we get a table of all meaning graphs, a table of the frequency. Chapter four is"The system of phonetic graphs of Xiao Zhuan system."We describe the structure of the phonetic graph system, the relations between phonetic graphs, and between their function showing origins and their function showing pronunciations, and their frequency, then we get ageneral table of phonetic graphs and table of their frequency. Chapter five is "conclusion". We think that systematical methodology is useful in describing and analysing the formation system of Chinese characters. The methodology is adaptable in describing the formation system of modern Chinese characters as well as the historical character systems, adaptable in describing horizontally as well as comparing vertically. Only when we finish the systematical vertical compare on the base of systematical horizontal decription, could we know the true history of the system of Chinese characters, recover the rule of the system's development, and supply the theoretical supports for the scientifical arrangement of modern Chinese characters.

第一部分—绪论，在总结形声字研究历史状况的基础上，提出了研究形声系统的理论原则和分析方法，即汉字个体字符形义统一的思想，汉字字符集合构形系统的思想，汉字构形系统历史演变系统优化的思想等三项理论原则和结构功能分析法，形位分析法，义素分析法等三种分析方法，还扼要地介绍了具体的工作程序和论文的主要内容；第二部分—形声字概述，论述了形声字的来源、性质和鉴别标准，介绍了对《说文解字》正篆形声字说解中的传抄讹误，版本异文，说解错误校勘和考证的经过，详细分析了形声字构件的功能，具体讨论了声符的示源功能与示音功能，义符的示意功能与类化功能以及声符与义符组合中的相互区别功能；第三部分—小篆字系的义符系统，从义符系统的构成、义符间的相互关系，义符示意功能的分布及义符的构字频度等不同侧面，对义符系统进行了全面的描写，产生了义符总表、义符间意义关系总表和义符构字频度总表；第四部分—小篆字系形声字的声符系统，从声符系统的构成、声符间的相互关系，声符的示源功能与示音功能的关系以及声符的构字频度等不同侧面，对声符系统进行了全面描写，产生了声符总表和声符构字频度总表；第五部分—结束语，在全面测查小篆字系形声字的基础上，对研究汉字的方法和现代汉字发展方向的问题提出了一些看法，认为系统论的方法是描写和分析汉字构形系统行之有效的方法，系统论方法，不仅适用于历史上文字系统的描写，也适用于现代汉字构形系统的描写，不仅适用了断代描写，也适用于历史比较，只有在对汉字断代系统描写的基础上进行系统的历史比较，才能认清汉字系统历史演变的真相，揭示汉字系统发展的客观规律，为科学地整理现代汉字提供理论上的依据。

These relations can be viewed either paradigmatically or syntagmatically,and the elaboration on the main sense relations falls into either of the two axes.

对语义关系的讨论可以沿着横组合关系和纵集合关系这两大中心轴来研究。

This kind is based on the computational means of PPV, the means of unlike tradition, can become good proportion to shrink with H gather size put a concern, and this kind of technology also can be in bigger PPV obtains similar result on gather, a few more contented to individuation of aggregate of aleatoric preference webpage computation asks.

这种基于PPV的计算方式，不像传统的方式，能够和H集合大小成良好的比例缩放关系，并且这种技术也可以在更大的PPV集合上取得近似的效果，满足一些对于任意偏好网页集合的个性化计算要求。

In this paper, I have constructed models for local population and metapopulation dynamics. Then by mathematical analysis and numerical simulation, I focus my studies on the relation between the Allee-like effects at the metapopulation level and the Allee effects at the local population level and their impacts on the stability of ecological systems.

在本文中，通过建立局域种群和集合种群的理论模型，把局域种群动态和集合种群动态结合起来，用数学分析和数值模拟分析的方法研究了集合种群水平上的似Allee效应与局域种群的Allee效应之间的关系以及它们对生态学系统稳定性的影响，并对含Allee效应的物种的自然保护提供了理论依据。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。