The general theorems of the complete convergences for sums of - - mixing random fields are obtained under some suitable conditions . and the equivalent relationship between rates of complete convergence and moment condition is obtained 在一些适当的条件下，获得了较为一般的~ - -混合随机场的部分和的完全收敛性定理，并得到了完全收敛速度与矩条件之间的等价关系。
The auto - spectrum is attached to linear phase , the amplitude - frequency drawing is got according to the arithmetic of bi - spectrum , then the equivalent is educed , the conversion relation is attained 该方法通过对自谱添加线性相位，根据双谱的数值估计算法计算获得双谱在三维空间的幅频图，通过推导双谱与自谱估计算法之间的等价关系以及所得的幅频图来实现两者之间的相互转换。
By making use of the advantage of characterizing granularity of partial granulation , different from the single equivalence relation in the classical rough set theory , this algorithm can study one decision table from different angles and different hierarchies 该算法利用了偏序粒在粒度表达上的优势,区别于经典粗糙集理论中采用的单一等价关系,对同一决策表从不同的角度和多个层次来研究。
By making use of the advantage of characterizing granularity of partial granulation , different from die single equivalence relation in the classical rough set theory , this algorithm can study one decision table from different angles and different hierarchies 该算法利用了偏序粒在粒度表达上的优势，区别于经典粗糙集理论中采用的单一等价关系，对同一决策表从不同的角度和多个层次来研究。
This paper discusses the application of the characteristic that the fuzzy equivalent relationship equates the normalized distance of the x quotient space in the theoretical model of fuzzy quotient space , and advances the algorithm of text clustering in the fuzzy quotient space 讨论了在模糊商空间理论模型中模糊等价关系与x商空间的归一化距离等同这一特征在文本聚类搜索中的应用,并提出了模糊商空间下文本聚类的算法。
Spatial data model is formalized according to partial order relationship , equivalence relationship and simplicial complex theory . a formalizing two - tuple ( m , f ) multi - resolution spatial data model is presented . based on the jarno peschie algorithms , an improved algorithm of road network map generalization is developed 应用偏序关系、等价关系和单纯复形理论，初步研究了多分辨率空间数据模型形式化表达方法，提出了一个二元组形式化多分辨率空间数据模型。
In chapter one , we investigate the complete convergence for sums of non - indentically distributed na random variable sequences . we obtain a more general complete convergence than the result appeared in literature . and we obtain the equivelent relationship between rates of complete convergence and moment condition 第一章，讨论了不同分布na随机变量序列加权和的完全收敛性，获得了较已有结果更为一般的完全收敛性，并得到了完全收敛速度与矩条件之间的等价关系。
All the contents are developed around a set of scaling laws taking the form of exponentials which relate to almost all the issues of complexity including fractals , chaos , strange attractors , localization , and symmetry breaking , etc . the main work can be summarized as follows : starting from the law of allmetric growth three fractal dimensions in a broad sense are derived , and according to these dimensions , geographical space is divided into three levels , i . e . , real space , phase space , and order space , each of which corresponds to a kind of dimension . based on the idea of spatial disaggregation and using the rmi ( relationship - mapping - reversion ) principle , the urban system is formulated as three scaling laws of the three spaces , including number law , size law , and area law , which can be transformed into a set of power laws such as allometric law and zipf ’ s law associated with fractal structure 从异速生长律的纵向、横向和切向三个角度将地理空间划分为实空间、相空间和序空间,分别对应于空间系列、时间序列和等级序列三个层面,每个层面的测度各有自己的空间维度。基于“空间循环细分-等级体系-网络结构”的数理等价关系,利用rmi (关系-映射-反演)原则,成功地实现了城市系统宏观模型的理论抽象,将空间复杂性问题表征为简单的指数式标度定律(包括数量律、规模律和尺度律) ,这一组标度律可以与一组幂次定律(包括具有分形性质的规模-数目律、异速生长定律和三参数zipf定律)互为变换。
In section 4 , knowledge sets , and knowledge equivalent relation sets and knowledge class sets are defined respectively on knowledge , equivalent relation and class parts . the connection of union - intersection lattice and fine lattice of them is researched , and the combination of rough sets and lattice is achieved 第4节，在知识、等价关系和分类三个层面上定义了知识集、知识等价关系集、知识分类集，研究了其上的并交格和精细格的性质和相互关系，得出了粗糙集与格的复合关系。
3 the concept of equivalence matrix , which expresses equivalence relation in rough set information system , is introduced ; the relations between equivalence matrix and equivalence classes are discussed . the algorithms for data cleaning and rules extraction in knowledge system based on matrix computation are proposed and their complexity of computation is analyzed 3 、在等价矩阵概念的基础上，分析了粗糙集知识系统中等价划分与等价摘要矩阵的关系，采用等价矩阵来表示粗糙集的等价关系，提出了一种对数据库知识系统进行数据清洗以及从中提取决策规则的矩阵算法，分析了该算法的计算复杂性。
