集合关系

Assume a Lie algebra g has a form B which has all the useful properties of Killingform:bilinearity nondegeneracy,symmetry and invariance.Note that for such a Liealgebra the adjoint representation is equivalent to the coadjoint representation.We callit a symmetric self-dual Lie algebra and the form B an invariant scalar product.

在第一部分的最后一节，我们引进了拟Heisenberg代数的概念，证明了这些李代数均为具有非极大秩的CN李代数，进一步我们还证明了这些CN李代数构成的集合与极大秩幂零李代数构成的集合之间存在着1-1对应关系。

Firstly, we analyze the deficiencies ofexisting ones, extend domains of fuzzy logical operators from the cap product withtwo sets to them with arbitrary (finite, enumerable, or non-enumerable) number ofsets to form two general mappings so as to conform them to the fuzzy conjunctionand infimum, and to fuzzy disjunction and supremum, respectively, and fuzzify theset inclusion of fuzzy sets. Similar to the classical adjunction, the concept of fuzzyadjunction is introduced.

首先分析了原有"模糊形态学"框架的缺陷，进而将模糊合取和模糊析取算子的定义域从两个集合的笛卡儿乘积推广到任意多个集合的笛卡儿乘积，形成两个一般的映射，使得模糊合取与下确界、模糊析取与上确界保持一致，以此将模糊集的包含关系一般化。

The set E may be thought of as a binary relation on set V.

集合 E可看成集合 V上的一个二元关系。

Hence morphisms do not so much map sets into sets, as embody a relationship between some posited domain and codomain.

不象映射一个集合的元素到另外一个集合，它们只是表示域和陪域间的某种关系。

For the model,three sub-models,which are domain knowledge description,concept set and relation set,are realized by combined with the definition of Domain Ontology.

结合领域本体的定义，对数据——知识转换模型从领域知识基本描述、概念集合和关系集合三个角度加以分析，实现了相关的子模型，从而得出了完整的数据——知识转换模型，并基于该模型给出了具体的数据——知识转换文本。

Firstly,the classification of probability rule is analyzed on the base of classic rough set concepts and extended to the equal relation of set in the indefinite system,namely,the upper and lower approximation space of research set is expressed in the form of conditional probability;then,according to the measure of probability rule,the attributes reduction is carried out and the classification rule is extracted by using the related parameters of condition attributes' impend precision from the angle of conditional probability;Finally,the related simulation test result is given and the result shows the classification rules with probability measures is more rational.

首先在经典粗糙集概念的基础上分析概率规则的分类，并将其推广到不确定系统的集合等价关系中，即用条件概率的形式表示研究集合的上下近似空间；然后根据概率规则的测度从条件概率的角度利用条件属性的逼近精度的相关参数进行属性集的约简进而提取分类规则；最后给出了相关的仿真实验结果，结果表明带有概率测度的分类规则更合理。

And a way to find the elements ofthat are conjugate to is proposed. Then we prove that the quotient group is isomorphic to, the symmetric group of order , and is a semidirect product group of with the classical binary simplex code in the linear case. Finally, we generalize a result due to Calderbank et al..

本文刻画了商群与集合的关系，给出了一个确定集合中那些与共轭的元素的方法，还证明了在线性情形下，商群与阶对称群是同构的，而且是与经典单形码的一个半直积，并且推关广了Calderbank等人的一个结果。

Another Nominalist strategy is to collect individuals into sets based on resemblance relations, and then account for qualitative identity and resemblance by appeal to commonalities of set membership.

另一个唯名论策略是，基于相似关系而把殊相个体归入集合，然后诉诸集合成员的公共东西来说明性质的等同和相似。

From the point of view of the set, knowledge is a partition of data set about some relations.

从集合的角度来说，知识就是数据集合在某种关系下的划分。

In this dissertation, a theorem to describe the relationship between the quotient group Aut/H and the set F_f is presented. And a way to find the elements of F_f that are conjugate to f is proposed. Then we prove that the quotient group Aut/H is isomorphic to S_3, the symmetric group of order 3, and H is a semidirect product group of GL_(m/2)(4) with the classical binary simplex code S_m in the linear case.

本文刻画了商群Aut／H与集合F_f的关系，给出了一个确定集合F_f中那些与f共轭的元素的方法，还证明了在线性情形下，商群Aut／H与3阶对称群S_3是同构的，而且H是GL_(m/2)(4)与经典单形码S_m的一个半直积，并且推关广了Calderbank等人的一个结果。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。