维数理论

Chaper 3 is general description of ADA encryption. Chapter 4 deals with the transform domain encryption. Includes the element of perfect and quasi-perfect transform domain encryption, and presents two type new schemes. Chapter 5 deals with asynchronous ADA encryption. Extends the general theory and model of asynchronous ADA scrambling, and introduces two type phase-distortion-free a synchronous ADA schemes. Chapter 6 is about new direction of ADA encryption. Includes TASI scrambling, transform domain dummy insertion scrambling, noise coving scrambling and other multi-dimension ADA scrambling, and proposes an adaptive dummy spectrum insertion asynchronous scrambling and a new adaptive noise-coving DFT scrambling algorithm. Chapter 7 is on permutation key. presents part results on permutation features, selecting criterion and constructing method. Chapter 8 introduces the hard and software design of a common ADA encryption/decryption system, and presents the experimental results on several proposed ADA encryption schemes.

第一章为绪论；第二章为语声信号、及其处理基础；第三章为模数模加密的一般描述；第四章为变换域加密研究，包括变换域加密机理，变换域完善与准完善保密研究，提出两种新的变换域加密方案；第五章为异步模数模加密研究，扩充了异步模数模加密的一般理论，介绍了两种新的无相位失真异步加密方案的原理与实现方法；第六章对模数模加密新方向：TASI应用途径、变换域伪谱插空置乱、噪声掩盖、多维置乱加密的原理和方法进行介绍，提出了自适应伪频插空异步模数模置乱算法与自适应DFT系数噪声掩盖置乱新算法；第七章为置换密钥性质、筛选准则以及构造方法研究的部分结果；第八章介绍了通用模数模加/解密实验系统的硬件、软件研制概况，并给出了几种加密方法的实验结果。

This paper analyzes the property of FNT, the characteristics of Kernel Matrixes and the relationship between Kernel Matrixes of two-dimensional Fermat number transform whose modulus are odd prime and image data, and presents and proves the deduction of the theorem which demonstrates the relationship among different transform matrixes corresponding to different roots of unity under the same odd prime modulus of FNT, and reveals the essence of FNT whose modulus are odd prime.

分析二维Fermat数变换性质、正反变换核的特点、二维模为奇素数的二维Fermat数变换正反变换核以及与图像数据的关系，提出了不同单位根对应变换矩阵间的关系定理的推论，证明了该推论中模为奇素数的二维Fermat数变换的不同单位根对应的变换矩阵之间的关系，揭示了模为奇素数的二维Fermat数变换的本质，在构造离散图象数据Fermat数变换时为单位根的选择奠定了理论基础。

Key words:the three dimensional contact problem with friction;nonlinearcomplementary;nonsmooth equations;generalized derivative;nonsmoothmethod;convergence analysis

给出了三维摩擦接触问题的一个非光滑混合不动点模型及算法，这种算法无须求导数，没有引进任何额外变量，并且可视为一种三维摩擦接触问题的迭代法，利用非光滑分析和不动点理论对算法做了分析，给出了算法的不动点理论背景及算法的理论分析，为模型解的存在性及算法收敛性提供分析依据，最后给出了相应的数值算例。

The strongly nonlinear pore structures of pulverized coals can be described by the fractal theory. The pore fractal dimensions of 10 pulverized coals, which are in the range of 2.572~2.722, were analyzed on a N2 adsorption porometer. The apparent viscosities of coal water slurries were measured on a Haake rotary viscometer.

用分形理论能描述具有强烈非线性特征的煤粉孔隙结构，利用氮吸附仪分析得到10种煤样的孔隙分形维数为2.572~2.722，利用Haake黏度计测量水煤浆黏度，讨论了孔隙分形、水分、氧量和可磨性指数等对水煤浆性质的影响规律，得到相关的拟合经验公式。

By means of reductional operation, reduces the attribute dimensionality, summarize of the knowledge rule which is suitable for the policy-making support, is one of important applications of the rough set theory.

通过约简操作，降低属性维数，总结出适于决策支持的知识规则，是粗糙集理论的重要应用之一。

These results in the chapter two are on the basis of theocratical analysis and numerical simulations such as condition for SNB and Hopf bifurcation, bifurcation diagram, trajectories, Lyapunov exponent, Floquet multipliers, dimension of attractor and so on.

本章的结论是根据理论分析和数值模拟的结果，这包括给出SNB和Hopf分支条件，分支图，轨线模拟，Floquet乘子的计算，Lyapunov指数和吸引子的维数的计算等。

New insight in examining the utility and the limitation of the method have been provided by using the basic theory of fractals.

1利用分维数的基本理论得到了关于欧拉方法的适用性和局限性的新认识。

Moreover, the SALS images were digitally analyzed by means of Debye-Bueche and Mie scattering theory to obtain corresponding structure parameters describing the morphology, e.g., correlation distance ac, integral constant Q and fractal dimension Dc as well as the relationship between these parameters with blend composition, blending time and content of the compatibilizer.

根据Debye-Bueche和Mie散射理论，利用光散射处理软件对光散射在线采集数据进行了分析并得出表征合金体系相结构的参数：相关距离ac、积分不变量Q、分形维数Dc等并分析了各结构参数与体系组成、共混时间及相容剂含量的关系。

5By introducing the fractal theory to analyze logging curve's characteristics, the Rescaled Range Analysis method is used to calculate the fractal dimension on acoustic transit time, resistivity, natural gamma, spontaneous potential.

将分形理论引入到对测井曲线的特性分析之中，利用R/S分析方法对声波、电阻率、自然伽马和自然电位进行分维数计算，将计算结果与不同的水淹级别相联系，利用模糊综合评判方法对水淹层分级。

The fractal theory was used to build fractal microfibril in wood cell wall,and fractal dimension of fractal microfibril layer S1 and layer S2 were calculates,then wood fiber frame with nanometer scale was pointed out.

利用分形理论构建了木材细胞壁中的分形木质纤维，并计算了分形木质纤维 S1层和S2层的扭曲分形维数，指出木材中具有纳米尺度的纤维结构；同时，以木材液化和纳米纺丝技术为基础，提出了木材苯酚液化产物制备碳素纤维材料的构思和技术路线，为解决木材纳米、微米材料的制备提出了新思路。

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。