查询词典 be equivalent to

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 invention also discloses a relative report sender, which comprises inquirer for inquiring said disperse equivalent chain group; a controller for generating sending command to the sender when there is the disperse equivalent chain group; a sender for sending LSA refresh report at the main disperse chain.

本发明还公开了一种报文发送装置，该装置包括：查询单元，用于在网络设备发送LSA更新报文时查询所述网络设备与其邻居设备间的扩散等价链路组信息；控制单元，用于当查询结果为网络设备与其邻居设备间存在扩散等价链路组时，生成发送命令下发给发送单元；发送单元，用于按照所述发送命令，只在所述扩散等价链路组的主扩散链路上向邻居网络设备发送所述LSA更新报文。

In presented method, the correlated variables are transformed into uncorrelated variables equivalently, and the performance functions in the correlated variables space are transformed into those in the equivalent uncorrelated variables space, in which the reliability sensitivity of the system failure probability with respect to the distribution parameters of the uncorrelated variables can be solved by the moment method for the uncorrelated variables. Finally the equivalent relationship between the correlated variables and the uncorrelated variables, the chain rule for derivative are employed to obtain the reliability sensitivity of the system failure probability with respect to the means of the correlated variables.

在所提的方法中，首先将相关变量空间等效转化为不相关变量空间，并将系统多个失效模式的功能函数转化为不相关变量空间的功能函数，进而利用矩方法得到多模式系统失效概率对不相关变量空间基本分布参数的灵敏度，最后利用相关变量空间与不相关变量空间的等价关系及复合函数求导法则，求得多模式系统失效概率对相关变量空间中变量均值的灵敏度。

According to the entire theory of plastic mechanics,the relationship between equivalent stress and equivalent strain of circular chamber plastic zone in the complex stress state is deduced from nonlinear softening constitutive relation of rock under uniaxial compression.

依据塑性力学全量理论，将岩体单轴压缩的非线性软化本构关系推广，得到复杂应力状态下圆形硐室围岩塑性区的等效应力与等效应变关系；籍以求得应变非线性软化的圆形硐室围岩塑性区半径、弹塑性区应力、应变和位移；进而求得相应情况下的硐室围岩平衡方程、地应力与硐室周边位移关系以及围岩压力方程。

According to that characteristic and based on the differential equation of the deformed surface of the orthotropic plate, with one principal direction size fixed, changing another principal direction size linearly, maintaining elasticity coefficient the same as in the first principal direction and Poisson ratio equal to the geometric mean of two principal Poisson ratios, the original orthogonal plate is equivalent to an isotropic plate. Results obtained show that the deflections of the equivalent isotropic plate are the same as the deflections of the original orthotropic plate at the corresponding points, the forces of the correspondent points have simple relations.

根据这一特性、从正交各向异性板挠曲面的偏微分方程出发，保持一个主方向尺寸不变，另一主方向的尺寸做线性缩放，保持弹性模量与第一主方向相同，泊松比取2个主方向泊松比的几何平均值，将这类正交各向异性板等效为一块各向同性板；通过分析得到：各向同性板任意点的挠度就是原正交各向异性板对应点的挠度，各对应点内力之间存在简单的比例关系，该文的方法将为工程技术人员提供方便，同时可以更加直观的认识正交各向异性板的受力。

The stochastic Bonhoeffer-Van der Pol system is first transformed into an equivalent deterministic system using the Chebyshev polynomial approximation, so that the problem of controlling stochastic chaos is reduced to the problem of controlling deterministic chaos in the equivalent system.

首先运用Chebyshev多项式逼近的方法，将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统，使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题，继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题。数值结果表明，随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似。

Chiropodist/Podiatrist denotes a person with a degree in podiatry, podiatric medicine or podiatric studies or equivalent and is eligible for registration with the United Kingdom Council for Professions Supplementary to Medicine or for applying a license in the United States of America or equivalent.

足病诊疗师指持有足病诊疗学、足病医学或足病学学位或具备同等学历，并符合资格向英国辅助医疗专业管理局注册或在美国申领牌照或具备同等资格的人。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。