渐近的

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。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

The model generalizes the input-output function in transiently chaotic neural network to a class of continuous, differentiable and monotone increasing functions. Secondly we study the uniformly asymptotical stability of equilibrium in the non-autonomous model. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories. In chapter 3, we firstly introduce a specific class of discrete-time neural network models with sinusoidal activation function.

在本文的第二章中，首先介绍了一类具有广义输入输出函数的非自治离散神经网络模型，该模型把瞬时混沌神经网络模型中的输入输出函数推广到了一般的单调递增且连续可微的函数；其次，利用Schauder不动点原理和利用Lyapunov函数逆定理依次证明了模型平衡点的存在性和在时变权值下的一致渐近稳定性；最后，对几个具体的例子进行数值模拟，数值模拟的结果更好地说明了我们的结论。

For the uniformly ergodic Markov processes, which is a classic framwork established by Deuschel-Stroock for studying the LDP for empirical measures, the LDP of f_n~* in the weak topology and the uniform weak*-LDP in the strong topology ||·||_1 for f_n~* are established. Furthermore, we prove that f_n~* is asymptotic optimal in the sense of Bahadur. These results are obtained for the first time in the dependent case. For this generalization from the i.i.d.

在此框架下，我们建立了f_n~*在弱拓扑下的大偏差原理以及在L~1-拓扑下对初始点一致的弱*大偏差原理，另外，我们还证明了f_n~*在Bahadur意义下是渐近最优的，这些结果在相依情形下是全新的，为了做这样本质性的推广，我们需要克服许(来源：ABC论文6d网www.abclunwen.com)多技术上的困难和应用不少特殊的工具，诸如Harnack型不等式，Cramèr型偏差不等式，一致可积算子，线性算子的扰动理论，Bishop-Phelps定理等等(它们都是首次用于处理这样的问题)。

The nature of the acceleration unit-impulse response function of unbounded medium tending to vary linearly is proved by means of asymptotic analysis. Thus, the acceleration unit-impulse response function can be regarded as the summation of a linear function and a residual part which converges to zero. Based on this decomposition, two FE-SBFE coupling procedures are presented based on system realization and truncation integral technique respectively.

本文系统研究了相互作用力-运动关系的位移表达、速度表达和加速度表达，通过比较位移、速度和加速度单位脉冲响应函数的SBFE求解过程，确定采用相互作用力的加速度表达；通过渐近分析证明了无限地基加速度单位脉冲响应函数具有随时间延长而趋于线性变化的性质；利用这一性质将加速度单位脉冲响应函数分解为一个线性函数和一个衰减到零的残余函数的和，以此为起点发展出两种FE-SBFE时域耦合方法：基于系统实现的FE-SBFE时域耦合方法和基于截断卷积的FE-SBFE时域耦合方法。

By using the new method, it relaxes the restriction of the related results in the Pa-per[31],extends the mainly results of the Paper[31], obtains the existence and uniqueness of a positive periodic solution, proves the existence and the uniform asymptotic stability of the almost periodic solutions of the studying model.

通过采用新的方法，减弱了文[31]的相应定理的条件，同时考虑了新的因素，推广了文[31]的结论，得到了所讨论方程的周期解存在的充分条件及其概周期解存在的充分性和一致渐近性。

Since the roots of the characteristic equation of the digital control system must stay inside the unit circle =1 in the z-plane for the overall system to be asymptotically stable,we see that the second-order digital control system can be unstable for large values of T.

由于基层的特征方程的数字控制系统必须留在单位内循环= 1中的Z -飞机的整体系统是渐近稳定的，我们看到，二阶数字控制系统可为大型值不稳定普通应用评委的稳定性试验的特征方程的均衡器。

We obtain the conditions of asymptotical stability of the pest-eradication periodic solution and permanence of the system.

在第四章中，应用天敌助增(即天敌的人工繁殖和释放)的方法，建立了在固定时刻释放天敌的具有一般功能性反应的三种群的食物链模型，并系统地研究了系统在释放天敌这种外在的不连续受迫作用下的动力学性质，得到了害虫根除周期解存在性和渐近稳定性，以及系统持续生存的条件。4。

The CVD is an important index to indicate tree diameterdifferentiating.On basis of dynamic change and tendency of CVDamong trees in stand,three models of square CVD are proposed.i.e.,basic model,stand factor model,and thinning effects model.All threemodels are of mechanism,asymptotic characteristic,and invariance forprojection length.Futhermore,there are compatiability and extremevalues in thinning effects model for thinned and unthinned stands.

直径变动系数是描述林木直径分化的重要指标，根据林木直径变动系数的动态变化和趋势，本文提出了直径变动系数平方动态变化的三个模型：基本模型，与林分因子相关的模型，考虑间伐效应的模型，上述三个模型均具有一定的机理性、渐近性和步长不变性，特别是考虑间伐效应的模型为间伐林分和未间伐林分的相容性模型，它还具有相容性和极值性。

Modeling and stability analysis problem of linear switched system are emphasized in this part and main results include:(1) Through investigation in the projection of 〓 on x, where x denotes continuous state vector, a series of sufficient conditions for stability, asymptotic stability and unstability of linear switched system's equilibrium in the sense of Lyapunov are achieved. And also, a sufficient and necessary condition for state bounded stability of linear switched system is received.(2) For a class of periodical linear switched system whose switching sets are a group of ordinal lines starting from the original point, it's proved that state bounded stability can be defined by the running characteristic in a single period (3) Based on linear switched system, the concept of linear switched system network is put forward. Linear switched system network is a complex network interconnected by many linear switched systems.

这部分着重研究线性切换系统的建模与稳定性分析问题，主要成果包括：（1）通过考察〓在x上的投影，得到线性切换系统的平衡点在Lyapunov意义下稳定、渐近稳定及不稳定的一系列充分条件，并得到了线性切换系统状态有界稳定的一个充要条件；（2）证明了对于一类切换集为从原点出发的一组射线的周期线性切换系统，其状态有界稳定可根据一个周期内的系统运行特性来判定；（3）在线性切换系统的基础上提出了线性切换系统网络的概念，线性切换系统网络是由多个线性切换系统交互作用而形成的复杂网络。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。