等价的

By proving the simulator-based and comparison-based definitions of semantic security both equivalent to the indistinguishability we obtain the equivalence of the two definitions. This conflicts with the conclusion of Watanabe, et al. The reason lies in that in the simulation-based definition they used, the adversary and its simulator are allowed to choose by themselves the auxiliary partial information about the plaintext to be input, which results in that the information chosen by them can be different.

该结论与Watanabe等人的结论相悖，原因在于他们采用的基于模拟器的语义安全性定义中允许敌手及其模拟器自己选择其输入的有关明文的附加部分信息，导致敌手模拟器与敌手选择的可能不同，使得该定义不等价于不可区分性，与公认的结论不符。

Professor Chen Xingshen achievements in order to affirm and encourage the development of our young mathematicians to contribute to the cause of China's Mathematical What he has in-depth introduction to the mathematics outside the field of theoretical physics to become an important tool G introduced geometric structure of the equivalent problem, a 20th century one of the major developments of mathematics, Integral geometry for the generalized basis, access to basic kinematics formulas.

为了肯定陈省身教授的功绩，激励我国中青年数学工作者对发展我国的数学事业做出贡献他引入的东西已深入到数学之外的领域，成为理论物理的重要工具，引进了G 几何的结构，研究其等价问题，成为20世纪后数学的主要发展之一，为广义的积分几何奠定基础，获得基本运动学公式。

And several rough set operation algorithms are also offered in this paper,such as upper approximation set,lower approximation set,intersection, cardinal number and so on.

通过讨论二进制与粗糙集之间的内在联系，提出基于二进制的粗糙集运算理论，并借助二进制的位运算操作，给出粗糙集的上近似集和下近似集、等价类的交、集合的基数的运算算法。

In the mean time we also give out a reduction way for nonlinear generalized system F =0 by use of the special projection mappings Q . Based on these we prove that the qualitative structure near the isolated equilibrium point of regular nonlinear generalized system is qualitatively equivalent with the structure near the equilibriun point of the linearization system of nonlinear generalized system, so we give out a way for qualitative analysis near equilibrium point of nonlinear generalized system.

其次，对一般形式的非线性广义系统F=0，利用特殊选择的投影函数Q，给出了一种归约方法，在此基础上，并证明了正则非线性广义系统问题的孤立平衡点的小邻域的定性结构等价于其线性化后的线性广义系统平衡点的定性结构，从而为非线性广义系统的平衡点的定性分析提供了一条途径。

For simplifying and unifying the defini- tions,and for understanding and mastering the concepts of Lebesgue integral from different angle,it is very significant to study how to define Lebesgue integral,and to prove the equivalence of different defin- tions.

关于L积分理论的研究，特别是关于L积分定义的研究，研究新的定义方法以简化L积分的定义，证明各种定义的等价性以统一L积分的定义，引起了国内外专家学者的广泛关注，并进行了许多深人的研究l一6〕。

We study the recursive structure of the twisted-cube connected network sufficiently, and prove that the twisted-cube connected network is an n regular graph with connectivity n: point out that the twisted-cube connected network is a cube-free network, which is an essential distinction with the hypercube and other variations of the hypercube; prove that the diameter of n dimensional twisted-cube connected network is [ (n+1)/2] , which is almost the half of hypercube's.

首先对其结构的递归性进行充分地研究，证明它是连通度为n的n正则图；指出扭立方体连接网络无立方体子图，这是扭立方体连接网络与超立方体及其其它变种的本质差别；证明了n维扭立方体连接网络的直径为[（n+1）/2]，它几乎是超立方体直径的一半；最后，给出超立方体及其变种的等价定义，并对它们的结构递归性、网络参数和拓扑性质等作了简单的分析、综合和比较。

In chapter5, the serial properties of numerical range of operator polynomial are put firstly. Secondly, the relation between numerical range of operator polynomial and n-numerical range are considered. Thirdly, in the light of matrix norm, matrix singular value, the regions and bounds of numerical range and spectrum of operator polynomial are dicussed carefully.

第五章研究了算子多项式数值域的性质、算子多项式数值域与n-次数值域的关系，特别地利用矩阵范数、矩阵的奇异值、非负矩阵的理论、友矩阵为工具，给出了算子多项式数值域及谱的范围全面刻画，并深刻地研究了算子线性束的正则性的等价条件及谱分布。

Based on the principle of optimality,the search problem is then transformed to an equivalent problem of deterministic distributed parameters system,represented by a second order PDE.

采用分析的方法来研究随机运动目标的最优搜索问题，并将原问题转化为由一个二阶偏微分方程所表示的确定性分布参数系统的等价问题，推导出随机运动目标的最优搜索问题的HJB方程，并证明了该方程的解即是所寻求的最优搜索策略。

The main contributions include:(1) Energy conservation law of Haar wavelets transform is proved to compress data streams.(2) The relation between the coincidence measure and trend of streams is revealed as along with the invariability under parallel shift and the equivalence law over coincidence measure to approximately express data-streams by the wavelet coefficient of the characteristic stream and its energy.(3) Multi-Scales energy decomposition model is proposed to improve the compression precision.(4) The multi-scales compression algorithm and the energy conservation reconstruction algorithm are designed.(5) Extended experiments show that the compression ratio of the new methods is 2~4 times as the traditional method.

主要研究成果包括：(1)证明了Haar小波变换服从能量守恒规律，并用于压缩数据流；(2)揭示了数据流的偶合度与变化趋势的相关性、偶合度的平移不变性及等价规律，采用特征流序列的小波系数和流能量近似表示流的趋势，达到压缩的目的；(3)提出了多尺度能量分解模型，提高了表示精度；(4)设计了多尺度能量分解压缩算法以及多尺度重构算法；(5)在真实数据集上的实验表明，新方法的压缩比是传统小波方法的2～4倍。

For detail,we studied the Incidence Algebra I defined by finite Partially Ordered Set X,and sheaf F based on the topology T_x defined by the partial order;By studying the relation between finite module category mod I and the sheaf category Sh_x A,we proved that they are equivalent.

特别的，对给定的有限偏序集X确定的Incidence代数Ⅰ，及由X的序关系定义的拓扑结构T_X上的层F，通过考查有限模范畴modⅠ与层范畴Sh_XA之间的关系，证明了Incidence代数上的模范畴与层范畴的等价性。

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。