等价的

The argument principle of the method of proof by contradiction is base on equivalent relation of dual propositions.

反证法是利用对偶命题等价的原理进行论证。

All of the above statements are now easily seen to be equivalent.

所有上述陈述都是等价的。

Further more, we get the necessary and sufficient conditions for the two-dimensional discrete system, where the permanence and extinction of the system are decided and only decided by the relationship of the non-delay coefficients in the system. Further, we for the first time find the equivalent permanence and extinction between the two-dimensional discrete Lotka-Volterra and its corresponding continuous system.

进一步，本得到了此类离散系统二维自治情形下，其持续生存和灭绝分别等价于系统非时滞系数构成的相应不等式；通过比较本文中二维自治Lotka-Volterra竞争系统的连续和离散两种情形的有关结论，首次发现这两类系统具有等价的持续生存和灭绝性质，建立了这两类系统之间的联系。

At length 50, we got 3 inequivalent extremal self-dual [50,25,10] codes.

将这个性质用在寻找长度为66的自对偶码，我们得到至少五十个对应於w2互不等价的极端自对偶[66，33，12]码与一个对应於w1，β=32的极端自对偶[66，33，12]码；用在寻找长度为50的自对偶码上，我们得到三个互不等价的极端自对偶[50，25，10]码。

Adopting generalized Jordan block and algebra equivalence transform method, all of the transfer functions at different load points can be transformed to state-space description with time variable. The steady robustness of three different mode of control systems were researched by mathematic analysis. It shows that: for the high order inertia controlled object with the characteristic of nonlinear and time-variable that described by the set of transfer functions, the Luenberger function observer established according to its any algebra equivalence state-space description, if some conditions can be met, there would be a matrix of T with n′n satisfied the Sylvester matrix equation TA- FT=GC.

采用广义约当块及代数等价变换方法，可将分段的传递函数描述转换为变参数的状态空间描述，对3种典型控制系统的稳定鲁棒性所进行的理论研究表明，对同一组传递函数描述的具有非线性和时变特性的高阶惯性受控对象，依据其任一代数等价的状态空间描述所构建的Luenberger函数观测器，在满足一定的条件时，存在n′n解阵T满足Sylvester矩阵方程TA- FT=GC。

The forth algorithm is the same as the third one with an addition of finite termination criteria. Although the latter two algorithms have only linear rate of convergence, they are especially suitable for large-scale and sparse problems, with features of simple formula, small storage, sparsity preservation and easy implementation.

前者借助NCP函数把互补问题转化为等价的非光滑方程组，再用带参数的光滑方程组近似这些非光滑方程组，最后用牛顿型方法求解所得到的光滑方程组，希望通过光滑参数趋于零得到原来互补问题的解；后者基于等价不动点格式，构造了一个光滑迭代算法和一个具有有限终止性质的算法，虽然这种迭代算法仅有线性收敛速度，但由于其格式简单、存储量小、保稀疏性、非常易于计算机实现等特点，故较适用于求解大规模稀疏问题。

The traditional query tree optimization methods,parallel database optimization methods based on left linear trees and right linear trees,bushy trees,and operation of the forest,have their own pros and cons,they have been more in-depth and maturity of the study.The query optimization method based on multiple weighted tree has studied its model of parallel query plan,its complexity model of parallel query plan and query optimization algorithms.The semantic query method transforms an inquiry into one or several semantic equivalence inquiries then has to find and implement a strategy to achieve a better query.Agent-based parallel database query optimization using Multi-Agent technology to automatically search the integrity constraint conditions which are related to the determined query,there for,the efficiency between several relations' joins has been greatly improved.The parallel optimization algorithm,based on genetic algorithm which is suitable for multi-joins of cluster environment,has deeply studied the relations storage options,multi-joins query optimization and query processing and other key technologies based on cluster parallel database.

传统的查询树优化方法，即基于左线性树、右线性树、浓密树、操作森林的并行数据库查询优化方法，各有优劣，对其的研究比较深入、成熟；基于多重加权树的查询优化方法，研究了其并行查询计划模型、并行查询计划的复杂性模型和查询优化算法；语义查询优化方法将一个查询变换成一个或数个语义等价的查询，进而寻找并执行这些等价查询中具有较好实现策略的一个；基于Agent的并行数据库查询优化采用Multi-Agent技术自动查找与给定查询有关的完整性约束条件，使得多个关系间连接操作的效率得到很大的提高；基于遗传算法的并行优化算法，深入研究了基于机群并行数据库中关系存储的选择、多连接查询优化和查询处理等关键技术。

As an application of continuous wavelet transform,we discuss the relationsbetween some differemtial equaltions and the integral equations by using thecontinuous wavelet transform in 〓,vector function space andabstract function space respectively;prove that they are equivalent not only in theweak topology but also in the strong topology.

作为连续小波变换的应用，分别利用〓上的，多元函数空间上的，向量函数空间上的和抽象函数空间上的连续小波变换分别得到了某些线性微分方程，某些线性偏微分方程，某些向量线性微分方程和某些抽象函数的微分方程分别等价于其相应的积分方程，证明了它们不仅在弱收敛意义下而且在范数收敛意义下是等价的。

By simulating and spitting of the line atδ145, we were able to show five isotropic components at δ134.6,δ139.6,δ145.1,δ147.9 and δ149.1, and the numbers the inequivalent sp2 carbons neatly dovetailed with the integral areas of the every line.

我们利用拟合分峰的方法得出了这五个不等价的碳原子的峰的位置，分别位于δ134.6、δ139.6、δ145.1、δ147.9 以及δ149.1，这五个不等价的碳原子数目上的比例关系和核磁共振曲线的积分面积吻合。

Operations are given and testified in this paper. The research methods of intrinsical linear nonholonomic dynamics are similar to those of holonomic dynamics.The rationality and equivalence of Chetaev model and Vacco model in the intrinsical linear nonholonomic system are testified from the mathematic and mechanical aspects. The essential reason is the nonlinear property of intrinsical nonlinear nonholonomic constrain that bring on Chetaev model and Vacco model inequivalent. Chetaev model is a linear approximate method in intrinsical nonlinear nonholonomic system. Vacco dynamical equations are not satisfied to the ideal constraint force conditions, but it gives a significative ponderation on the realizations of intrinsical nonlinear nonholonomic constrain.

本文比较研究了一般非完整系统的Chetaev模型和Vacco模型，首次从力学和数学的角度论证了这两种模型在完整系统和本质线性非完整系统中的合理性和等价性；同时给出了在本质非线性非完整系统中，Chetaev模型和Vacco模型不等价的根本原因，是由本质非线性非完整约束的不确定性非线性本质所导致的；指出在本质非线性非完整系统中，Chetaev模型是一种线性近似的结果，Vacco动力学方程虽然不满足约束力的理想性质，但是为我们研究本质非线性非完整约束的物理实现提供了有益的思考。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。