等价的

A simple equivalent definition of original Grzegorczyks hierarchy is presented at first.

首先给出的是原始的Gorzegorczyk分层的一种较为简单的等价定义。

Part 4 (chapter5) The weighted-star partial ordering is defined, some characterizations are given using the weighted inverse, and the relation between the partial ordering with the existing partial ordering of the matrices are discussed.

4利用加权广义逆定义复数域上矩阵的加权*序，给出它们的若干性质和等价刻划，讨论它们与已有的矩阵偏序之间的关系，并推广关于矩阵*序的有关结果。

The plumpness ratio is the bestindicator of full rapeseed.(5) The equivalent diameter is used to estimate the weight of rapeseed, andestablish the special and common model. In the overall, the correlation coefficient ofpredicted and measured values was over 0.99. The accuracy is more than 95%.

5以等价直径估测油菜种子重量，分别建立各品种的专用模型和面向白菜型、甘蓝型油菜的通用模型，两类模型在整体预测方式下的预测值与实测值间的相关系数均在0.99以上，预测精度可达到95％以上。

These knowledge granules are obtained according to equivalence relation in essence, it is possible there exist attributes which contain preference order relation among their values and correlate semantically with other attributes.

这些知识粒子的实质是根据存在于属性值间的等价关系得到的，而事实上可能存在某些属性，其属性值内部存在序关系，与其它某属性间存在语义关系，这样的属性称为标准。

By Monte Carlo simulation of stochastic demand, the hybrid simulation-optimization policy is brought forward to solve the model as well as the principle to select size of the sample. Benders decomposition algorithm and its accelerated technique are presented to solve the deterministic equivalent of primal problem.

利用随机需求的蒙特卡洛仿真，提出仿真一优化相结合的模型求解策略以及样本容量的选择法则，针对原问题的等价确定性问题设计Benders分解算法及其改进技术求解。

This paper introduces and investigates the filter theory of pseudo NM algebra. The notions of filters, generated filters, normal filters and prime filters etc. are defined. Their basic properties are investigated, with the structures of generated filters obtained. We show that prime filters and irreducible filters are equivalent, and that maximum filters must be prime filters. The prime filter theorem of pseudo NM algebra and its some corollaries are established.

引入了伪NM代数的滤子理论，定义了滤子、生成滤子、正规滤子和素滤子等概念，研究了它们的特征性质，给出了生成滤子的结构，证明了在伪NM代数中素滤子与不可约滤子等价以及极大滤子必是素滤子，建立了伪NM代数的素滤子定理及其推论。

At the same time,Security of RSA is based on the difficulty in resolving a large number.The public key and the secret key are functions of a pair of large prime numbers.The difficulty in converting the cipher text into the plaintext through the public key equals to that of resolving the product of two large prime numbers.

RSA 的安全基于大数分解的难度，其公开密钥和私人密钥是一对大素数的函数，从一个公开密钥和密文中恢复出明文的难度等价于分解两个大素数之积。

A notion of design object is proposed,based on which the design information of product is described.The composed relation,version relation,and equivalent relation are used to establish the relation design object.

文中提出了设计对象的概念，以设计对象为基础组织和描述完整的产品设计信息，建立了设计对象之间的组合联系、等价联系以及版本联系，提出了设计对象的层次模型表示方法。

A notion of design object is proposed,based on which the design information of product is described.The composed relation,version relation,and equivalent relation are used to establish the relation design object.A version mechanism is established in the paper for engineering data management.

文中提出了设计对象的概念，以设计对象为基础组织和描述完整的产品设计信息，建立了设计对象之间的组合联系、等价联系以及版本联系，提出了设计对象的层次模型表示方法。

Finally, as a generalization of the group-graded regular ring, the notion of group-graded weakly regular ring is introduced and we discuss it in a new way. In particular, an equivalent condition for the semigroup rings to be weakly regular(T-weakly regular) is given.

将群分次正则环推广到群分次弱正则环；用新的方法研究了环的弱正则性，并得到半群环的弱正则性和T-弱正则性的一个等价刻画。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。