等价的

Then we prove the one-to-one corresponding relation between 3-coloring of inducing four regular graph and 4-coloring of maximal planar graph and find out the relation between three colors of inducing four regular graph and three dual bi-chromatic subgraph of maximal planar graph.

本文给出了极大平面图的导出四正则图的两种构造方式、等价性及性质，证明了导出四正则图的三着色与原极大平面图四着色的一一对应关系，并且找出了导出四正则图的三种颜色与原极大平面图四着色的三组对偶二色子图之间的关系。

It is proved in theory that with the introduction of item constraints, Eclat+ could greatly improve the efficiency and speed of association rule mining, and the Eclat+ is compared with some other related algorithms.

通常这些规则中仅有很小的一部分是用户所关心的，因此泛泛的挖掘既降低了算法的运行速度也使挖掘结果失去了核心。Zaki提出的 Eclat[4]算法利用垂直的数据库结构，并利用基于前缀的等价关系将搜索空间划

The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book:transformation groups, the geometry of differential equations,geometric structures, the equivalence problem the geometry of elliptic operators, G-structures and contact geometry.

这本书是结构，以便读者可以选择部分文本阅读，还带了一个完整的画面，有些地区的微分几何开始入门级和曲线的部分，在欧氏空间变得更有挑战性，终于到达了高级的主题，形成了最大的一部分书：变换团体、几何的微分方程、几何结构、等价问题的几何形状，G-structures椭圆算子和接触几何。

Due to the inspiration of maximal injective module by professor Wang Ming-yi, in chapter two, we introduce the conception of max-projective modules, discuss its properties, applications: the primitive relations between rings and endomorphism rings, an equivalence that is surrounding strongly V.N. rings.

受汪明义教授引进极大内射模概念的启发，在第二章中我们引进了极大投射模的概念，由此讨论了它的一些性质及其应用：环与自同态环之间的本原性关系；强正则环的一个等价刻划；并在环为交换和非交换的情形下分别应用有限表现模的极大投射性得出了SF环和Von Neumann正则环的关系。

In the first place, on the base of studies concept ascending and attribute dependency, we forward a method to select attribute value partition, which can effectively resolve the problem of minimum faith and minimum support, in order to induct potential knowledge from standard discrete symbolic data, the dissertation studies join operation for generating candidate set and delete operation for deleting redundant equivalence class, and propose an recursion algorithm to realize highly generalization of data.

首先在研究概念爬升方法和Rough集理论中属性隶属度原理的基础上提出了一个划分属性值区间的算法，该算法能够有效的解决最小支持度问题和最小信任度问题。进而为了从已离散化的数据中概括出潜在的规则，研究了生成侯选集的交运算方法和排除冗余等价类的删除方法，然后利用循环推进机制实现对数据的概括。

Notice that the solvng ELP problem is equivalent to determine a nonlinear mapping,using the nature that BP neural networks has the parallelism and the capabilities of intrinsic nonlinear mapping,we propose a methods of using back error propagation of ne...

而求解线性规划问题的许多有效方法如单纯形法，Karmarkar's方法等却无法直接用于推广的线性规划问题的求解，注意到推广的线性规划问题等价于一个非线性映射，利用BP神经网络的本质并行性和高度非线性处理能力，该文提出了一类求解推广的线性规划问题的BP神经网络方法，它具有网络构建简单，求解精度高，计算量小等优点，实验结果表明其高效性。

Then we in-vest gate Seiberg-Witten map, which defines the equivalence relation of the gauge symmetries in different spaces. We also analyse the U gauge electromagnetic field in noncommutative space. Finally we discuss the ambiguities of Seiberg-Witten map, and find although that some part of the ambiguities can be absorbed by gauge transformation and hence negligible, the existence of the matter field makes some other parts difficult to be absorbed by gauge transformation or field redefinition.

然后利用Seiberg-Witten映射，我们研究了不同空间的规范对称性的等价问题，并对非对易空间的电磁场进行了微扰分析，最后我们对Seiberg-Witten映射的松动进行了讨论，研究发现这些松动中的一部分可以由规范变换吸收因而是可以忽略的，由于物质场的存在，另外一部分很难用规范变换和场的重定义吸收。

The basic diagnostic statistics such as Cook distance, generalized leverage and residuals et al. are introduced, and the equivalency of case deletion model and mean-shift outlier model is investigated. Some specific problems, such as local influence analysis and the test for heteroscedasticity are discussed. Finally, numerical examples are given to illustrate our diagnostic methods.

首先，证明了均值漂移模型与数据点删除模型的等价性定理并定义了残差、Cook距离等诊断统计量；其次，研究了异常点的Score检验统计量；第三，研究了该模型的局部影响分析，得到了局部影响分析的曲率度量；第四，研究了该模型的异方差检验问题，得到了检验异方差的Score检验统计量和修正的Score检验统计量；最后，通过实例分析验证了这些诊断方法的有效性。

The two kinds of symmetries in holonomic and non-holonom-ic mechanical systems,i.e.symmetries of differential equations of motion(ab-breviated as SDEM)and symmetries of Noether-type,and interrela-tions among all kinds of symmetries are investigated.The necessary and suffi-cient conditions of SNT to be SDEM are found out.It is pointed out thatSDEM have distinct geometric properties which are equivalent to the geodesiccharacteristic of differential equations of motion and geodesic deviation.

文中研究了完整与非完整力学系统的两类对称性，即运动微分方程的对称性和Noether型对称性，以及各种对称性之间的相互关系，确定了Noether型对称性为运动微分方程对称性的充分必要条件，并指出运动微分方程的对称性具有明确的几何性质，即它等价于运动微分方程的测地性质以及测地偏离性质。

We also introduce and study a new system generalized nonlinear variational inclusions for fuzzy mappings in Hilbert space.

我们利用极大单调映象的预解算子技巧，建立了这类模糊映象的变分包含组与非线性集值映象的不动点问题之间的等价关系，再利用Nadler的不动点定理给出了这类变分包含组的解的存在性定理。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失