查询词典 algebraically equivalent

Let L and P be Lie color algebras and let M be a graded module over P, the crossed modules which make M as their kernal and P as their cokernal are considered. It is shown that under a suitable equivalent relation, there is a bijection between the set of the equivalent classes CML and the homogeneous components of degree zero of H~3.

从交叉模的定义出发，对于给定的Lie color代数L，P以及阶化P模M，考虑所有以M为核、以P为余核的L的交叉模，在这些交叉模之间定义了一个等价关系，由此得到交叉模的等价类集CML，证明了CML与三维上同调群H~3的零次齐次部分之间存在一一对应，从而可以利用三维上同调群对Lie color代数的交叉模进行分类。

The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given.

并将基于等价关系的粗糙集的模糊熵拓展到基于一般二元关系下粗糙集的广义模糊熵，给出了广义模糊熵的计算公式及等效表示形式。

Results Axioms of equivalent characterization is simplest and which is proved to be equivalent to the Boolean algebra.

结果 得出了Boole代数的等价刻画以及等价刻画中各条公理的独立性。

Based on a summary of main work in the field of analyzing impulse voltage distribution on normal transformer windings by computer over last several years, a new method for building up the equivalent circuit and calculating equivalent parameters of converter transformer is given in this paper. Meanwhile , a new method for calculating inductance parameters is given also .

本文在回顾总结国内外几十年来普通电力变压器波过程计算工作的基础上，从工程实际应用的观点出发，论述了换流变压器与普通的变压器在电磁性能、绝缘结构方面的不同之处，提出了换流变压器绕组波过程的等值电路和等值参数的计算方法，同时给出了一种新的电感参数的计算方法。

Based on analogy and equivalent method, presents an improved equivalent method to transform the capillary tube length and inner diameter.

在类比法和当量法基础上，提出多根毛细管之间长度、内径相互转换的当量方法。

One cartload of the enemy's provisions is equivalent to twenty of one's own, and likewise a single picul of his provender is equivalent to twenty from one's own store.

就地取给粮食一钟，相当于从本国运输二十钟；就地征集饲草一石，相当于从本国运输二十石。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

I We present a characterization of equivalent chain graphs based on local transformations, and give an algorithm to transform one chain graph into an equivalent one.

链图可以含有有向边和无向边，因而能够反映相关关系和因果关系，我们主要讨论了三个问题。

The whole industrial chain and branch chains of circular economy have been planned for Zhenhai chemical park. The branch chains consist of ethane chain, C_1 chain, HC1 chain, H_2chain, NH3 chain and S chain. The concept of equivalent pollutant emission, E, has beenproposed and a reference line based on equivalent pollutant emission has been given and applied to the primary appraisal for Zhenhai chemical park. The whole chain and branch chemical industry chains have been also planned for ZJC group company, which include the industrial chain containing fluorine, the industrial chain of basic chemicals and the industrial chain of petroleum chemical industry.

本文对镇海化学工业区的工业链构建进行了可行性分析；完成了园区工业链的整体规划设计，和包括乙烯工业链、碳一工业链、HCl工业链、H_2工业链、NH_3工业链、S元素工业链在内的6条分链的设计；提出了污染排放当量E_t~′的概念，并将其应用到园区工业链招商的初评，制定了入园参考线；本文在对ZJC集团公司发展现状分析的基础上，根据其物质流和能量流的分析，进行了工业链的总体设计，并对氟化工产业、基础化工产业(包括以合成氨为代表的煤化工、以氯碱生产为代表的盐化工以及硫酸、电石等产业)和石油精细化工产业完成了分链设计，进行了分链的分析，提出了建议。

The witness also told the jury at the Royal Courts of Justice in London that he saw a paparazzo fighting with a member of the public who was trying to stop him taking pictures in the minutes before the emergency services arrived.

他还告诉在伦敦皇家法庭的陪审团，在急救服务到来之前，他当时看见一个狗仔队正和一群阻止他拍照的人打架。

The entire N／C program on a tape is made up of an accumulation of these successive data blocks.

纸带上的整个数控程序由这些连续数据单元连接而成。