多重

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

Finally, the calculation process of CGR graphic's multi-fractal analysis was studied. the scope of choice of the weight factor and the scale invariance range were discussed, the weight factor can be chosen as ? 15≤q≤50; multi-fractal spectrum and generalized dimension of different sequence were calculated, multi-fractal spectrum and generalized dimension in different scales of different sequences were compared, it was found that multi-fractal spectrum and generalized dimension can show different levels of fractal characteristics of CGR graphics of DNA sequence, which can distinguish more complex structure of sequences.

最后，研究了DNA序列CGR图形的多重分形的计算过程，讨论了权重因子及满足标度不变性的范围选择等问题，得到结论：对CGR图形进行多重分形时权重因子可以选择为-15≤q≤50；计算了不同序列的多重分形谱和广义维数，比较了不同序列不同尺度的多重分形谱和广义维数，发现多重分形谱和广义维数能够表现DNA序列CGR图形的不同层次的分形特征，能够区分更复杂的序列结构。

And then, this dissertation proposed a secret sharing scheme of secure vector space based on quadratic residue.

利用特定条件下计算二次剩余的困难性，恢复秘密时验证各参与者提供的份额的有效性，也=肖清华二杜绝了恶意参与者欺诈的可能性；(2)在秘密共享一多重签名方面，本论文针对数字签名的可跟踪性，以及确认签名是否来自同一个参与者授权子集这两个问题，指出了秘密共享和多重签名各自存在的不足，在此基础上，把两者结合起来，并从门限秘密共享一多重签名、矢量空间秘密共享一多重签名两方面对秘密共享一多重签名技术进行探讨，把 Sunder一Kumar门限秘密共享一多重签名方案推广到更为广泛的矢量空间上，并独立地提出了一个双通道的安全矢量空间秘密共享一多重签名方案。

The result indicated: antibacterial concentration of inner thallus increased progressively with time prolongation when added CCCP with antibacteria, proved that multi-resistance of E.coli in livestock and avian is mediated really by active efflux system; The multi-resistant level have positive correlation with AcrAB transcription and expression level; Quantitive RT-PCR,Western-blotting and fluorescence quantitive PCR can use to detect AcrAB.these results provide theory foundation to detect and study multi-resistance of E.coli in veterinary clinic and have a important scientific significance to develop neotype antibacterials.

结果表明，多重耐药株在有CCCP 存在时，菌体内抗菌药物的浓度随时间的延长而递增，证明畜禽大肠杆菌多重耐药性确实由主动外排系统介导；其多重耐药水平与AcrAB的转录、表达水平呈现正相关；定量RT-PCR、Western-blotting、荧光定量PCR可用于AcrAB水平的检测。这些结果对检测临床大肠杆菌的多重耐药水平、对研究兽医临床大肠杆菌多重耐药机制提供理论依据，对开发新型抗菌药物有重要的科学意义。

However, the multi- identities of artists have still been doubt by many people, and the forepassed concept of occupation has always blocked to understand the artist's multi-identities. Artists' intervene in socialty often be regarded as unmindful of their own works or doing other occupations. The identity of the artists in the "rebuilding in art "activity is one aspect of the identities' multiple. But The activity itself has answered to the suspicions, that is ,as for the society, it is good or not to have this kind of activity.

不过，这种艺术家身份的多重性仍然受到众多人的怀疑，职业焦虑一直阻碍着对艺术家多重身份的理解，艺术家介入社会以后，往往会认为是不务正业，或者是做了其他职业的人做的事，&以艺术重建家园&的艺术家身份的这种多重化还只是身份多重化的一个侧面，但这个活动已经对这样的置疑作了回应，即，对社会而言，我们有这样的活动好呢还是没有这样的活动好？

Chapter 8: We discuss the acceleration of multigrid by Krylov subspace approaches, and recognize the reason for slow convergence of algebraic multigrid methods is that error reduction is significantly less efficient for some very specific error components which may cause a few eigenvalues of the algebraic multigrid iteration matrix to be considerably closer to 1 than all the rest. However, the eigenvectors belonging to the few isolated eigenvalues can be expected to be typically captured after only a few conjugate gradient iterations, which accelerate algebraic multigrid algorithms. Theoretical analysis and numerical results of some practical problems show the iterant recombination accelerates algebraic multigrid convergence.

第八章：先介绍用Krylov子空间迭代法加速一般多重网格方法收敛的基本框架，然后紧紧抓住引起代数多重网格方法收敛减慢的根本原因往往是误差减小对几个特别的误差分量不明显，这导致代数多重网格方法的迭代矩阵的几个特征值接近于1，而共轭梯度方法则能比较典型地捕捉属于孤立特征值的特征向量，从而推导出有效的共轭梯度加速算法和程序实现，不仅从一些具体的实际应用例子的数值结果去验证迭代复合加速收敛的效果，而且还从理论上分析了预处理共轭梯度法加速代数多重网格法收敛的机理。

And the direction query efficiency based on multi-approximate index is compared with that based on taditional external approximation index. 2 The algorithms of nearest neighbor and reverse nearest neighbor about point, line and ploygen based on multi-approximate index are proposed after the virous methods of distance measure are discussed in detail. And the query efficiency of NN and RNN based on multi-approximate index is compared with that based on taditional external approximation index. 3 The basic concept of semi-join and the strategy of distance-direction semi-join are introduced. And the model of distance relationship, direction relationship and the bounding for spatial object are discussed. Then the method is presented about how to implement the query of distance-direction semi-join, and the efficiency of the algorithm based on multi-approximate index is compared with that based on taditional external approximation index.

即：1在方向关系矩阵模型、开域方向模型基础上，讨论了基于多重近似索引下的定性与定量方向检索方法，并通过实验对基于多重近似索引与外部近似索引下的方向检索效率进行了对比分析；2详细讨论了各种距离度量方法，提出了基于多重近似索引下的点、线、面的最邻近查询和反最邻近查询算法，并通过实验对基于多重近似索引与外部近似索引下的最邻近查询和反最邻近查询效率进行比较分析；3介绍了半连接的基本概念，探讨了距离关系、方向关系以及空间对象数量的约束模型，给出了基于多重近似索引下的距离方向半连接实现方法，并通过实验对基于多重近似索引与外部近似索引下的距离方向半连接的效率进行了比较分析。

In this article, a new multigrid method for solving p-Laplacian equations is proposed based on the existing multigrid method: FAS multigrid method and Cascade multigrid method. This method is a combination of Cascade method and a new method named "back" method.

本文主要研究现有的几种求解p-Laplace方程的多重网格方法：FAS多重网格方法和Cascade多重网格法，并在此基础上提出了一种新的求解p-Laplace方程的多重网格方法：Cascade-back方法。

This workfocuses on the fractality and multifractality of the gas-liquid two-phase turbulent jet and theapplied theories of deterministic multifractals,discrete random multifiactals and continuousmultifractals.

本文着眼于探索气液两相湍射流中的分形和多重分形特性，并为此而系统地研究了确定性多重分形理论、离散型随机多重分形理论和连续多重分形理论。

As for the study of isospin in intermediate energy HICs, we've investigated how bothstength and density dependence of symmetry potential affect many measurableobservables, such as the yield, phase-space, and isospin distributions of fragments, as wellas the correlations between Intermediate-Mass-Fragment multiplicity 〓 andCharged-Particle multiplicity 〓 Light-Charged-Particle multiplicity 〓 andNeutron multiplicity 〓. The aim is to find sensitive observables specifically for strengthand density dependence of SP.

在中能重离子碰撞的同位旋研究方面，分别研究了对称势的强度和其密度依赖形式对中能重离子核反应各类碎片产物产额、相空间、及其同位旋的分布，中等质量碎片多重数与带电粒子多重数、轻带电粒子多重数、中子多重数的关联等多种实验观测量的影响，以获取对称势中该两方面的信息，尤其着重于研究如何分别获取有关该两方面的信息的途径。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。