等价的

Nyang and Song proposed a digital signature scheme based on quadratic residue problem.

对Shimada公钥密码体制进行推广，提出一种新的密码体制，这种新的公钥密码体制的安全性建立在一般形式的素因子分解问题之上，攻击这种新的密码体制等价于对一般形式的大整数进行素因子分解，并设计一种新的数字签名方案和新的认证加密方案。

First, we have proved that the constraint of local constant gradient angles is equivalent to the minimization of total variation. Based on this, a stronger continuity constraint of gradient angle is presented. The interpolation formula (a 3-degree-PDE) derived from the constraint can ensure the continuity of level lines and reduce the width of edges. The contrast invariant of the regularizer of the formula is also proved.

首先证明了局部恒定的梯度角约束插值等价于总变分最小化；在此基础上，提出一个具有更强连续性的梯度角约束，由这个约束条件导出的三阶偏微分方程使插值的图像既可以保证水平线方向的连续性，又减小图像边缘的宽度；最后证明了插值方程中正则项的对比不变性。

In the paper the separate theorem of convex set with weak topology σ(L ∞,L 1) is proved, and the topological characterization about No Free Lunch with Vanishing Risk Condition is given, from it, the equivalency between exist of equivalent martingale measures and NFLVR is proved, this is the first fundamental theorem of asset pricing.

资产定价的第一基本定理是数量金融学中核心的定理之一，本文证明了在 L∞的弱*拓扑σ(L∞，L1)中的凸集分离定理，并在此定理的基础上给出了没有无风险免费午餐的拓扑描述，证明了市场公平性与没有无风险免费午餐条件的等价性，从而重新证明了资产定价的第一基本定理。

The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality.

首先证明了所构造泛函的强制性，从而证明了所构造的等价变分不等式解的惟一性，并根据椭圆型变分不等式解存在的充分条件论证了弹塑性接触问题解的存在性，为该问题的变分极值原理的建立莫定了数学理论基础。

This paper has obtained following three results about the new scheme:(1) The hardness of recovering the private key from the public key is based on the hardness of the shortest vector problems of several lattices;(2) The hardness of forging a signature is equivalent to the hardness of the closest vector problem of some lattice;(3) Each signature will leak information on the private key,but the final shape of the unlimited leakage is just a group of complicated non-linear equations.

文中给出新方案的3个结果：(1)由公钥恢复出私钥的困难性基于若干格上的最小向量问题；(2)由公钥伪造签名的困难性等价于某个格上的最近向量问题；(3)每个签名值仍然会泄露私钥的一些信息，但无限制泄露的最终形式只是关于私钥的一组复杂的非线性方程。

The notion of weak fuzzy similarity relations,a generalization of fuzzy similarity relations,is used to represent indiscernibility of elements.

为此提出用模糊相似关系和弱模糊相似关系的概念来代替等价关系，同时引入了弱模糊相似关系的相似度概念和相似类概念，定义了基于弱模糊相似关系的广义粗糙集及标准的广义粗糙集上下近似；研究了两对上下近似算子的性质，讨论了3种粗糙隶属函数的性质并验证了它们的性质。

This paper describes a new algorithm of image enhancement of impulse noise based on PCNN time matrix and rough sets indiscernibility relation. For noisy gray images, the results of computer simulations show that the image noise can be reduced efficiently and the image becomes clear and the target details of the image can be enhanced better by using this algorithm. In addition, the effects of this algorithm are better than usual image enhancement algorithm.

基于粗集理论中的不可分辨关系的等价概念及PCNN赋时矩阵，提出了一种含有脉冲噪声的图像增强算法，计算机仿真结果表明，对被噪声污染的灰度图像，用基于PCNN与粗集理论相结合的图像增强算法处理后，图像噪声得到有效抑制，画面更清晰，图像中目标的细节也得到了很好的增强，其结果优于常规方法。

Considering the restricted relationships of time, classroom, teacher and class, PCA compartmentalizes the different equivalents and processes one off scanned courses by the levels of their precedence, avoiding conflicts adjustment. The PCA system can fulfill the processing course plan in several minutes, even the condition. The application of this system which has been used for two years demonstrates the effectiveness of the system and the high efficiency of its related algorithm.

根据时间、教室、教师和班级的约束关系，进行等价类划分，依据所设定的优先级次序进行一次性扫描排课，尽量回避对冲突的调整工作，并在此基础上实现了一个课程调度系统，既适应学分制排课要求或满足教师提出较苛刻的上课条件要求，也能在几分钟内做出排课计划。2年的使用实践表明了该系统的有效性和相关算法的高效性。

A virus is a unit of infectious genetic material smaller than any bacteria and embodying properties placing it on the borderline between life and non-life. The vast majority of the virus capsid protein assembled into icosahedral symmetry of the structure. Caspar-Klug Theory has become a fundamental concept for the classification of icosahedral viral capsids based on the principle of quasi-equivalence.

二：病毒是比任何细菌都小的感染性遗传物质，介于生命与非生命之间的一类无细胞结构的生物，绝大多数病毒的衣壳蛋白装配成二十面体对称的结构，&准等价&原理是解决严格遵从二十面体对称性的病毒衣壳几何特征的有效而成熟的方法。

Stability of solutions of the cavitated bifurcation equation is discussed in each region by using the minimal potential principle, and the catastrophic phenomenon of cavity formation is explained. 2. In Chapter 4, problems of cavitated bifurcation for two spheres, which are composed of two different kinds of imperfect compressible hyper-elastic materials, were examined, respectively. The parametric analytic solutions of the radially deformed function and the parametric cavitated bifurcation solutions are all obtained for the two spheres.

利用奇点理论给出了空穴分岔方程在分岔点的等价正规形，将缺陷参数分成若干个区域，证明了当缺陷参数属于某些区域时，具有缺陷的超弹性材料球体发生空穴分岔时的临界载荷比无缺陷的小；并利用最小势能原理讨论了空穴分岔方程的解在各个参数区域内的稳定性，解释了空穴生成的突变现象。

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。