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The asymptoticbehavior of two ecological systems and the unconditionally stability and oscillations in kinds of 4-order delay difference equations are investigated by using analysis method, constructing Lyapunovfunctions, the logarithmic norm, charateristic roots theory and the bifurcation theory. Here, theasymptotic properity includes the uniform persistence, the global attractability of the solutions,the asymptotic stability of the positive solution local or global and the oscillations of solutions.

本文利用定性分析的方法、比较原理、特征值分析法、对数范数、构造Lyapunov函数及分支理论等方法和理论,研究了两类生态模型解的渐近性及一类四阶时滞微分方程解的无条件稳定性,其中包含模型的一致持久生存性、正平衡态的全局吸引性、局部和全局渐近性以及解的振动性等问题。

In chapter 3, the author considers that approximate value of Bessel fuctions and transcendental equations are main ob stacle to realize computer simulation for isolated well principle. The character of Bessel functions are studied, new approximate values of Bessel function are set forth.

第3章中,针对"割离井法"微机实现的难点——贝塞尔函数的渐近计算和超越方程的合理求解,研究了贝塞尔函数的性质,提出了新的贝塞尔函数的渐近式,并采用ZEROIN法完成了超越方程的求解,最后编制出新的"割离井法"计算程序。

For PDEs with small parameters, a scheme is AP if it possesses the discreteanalogy of the continuous asymptotic limit as the small parameter goes to zero.

对于含有小参数的偏微分方程,所谓一个算法是渐近保持的指的是,当相应的数值离散在小参数趋于零的时候,仍然是渐近极限的合理数值离散。

What differ from that of the researchers in the past is the consideration of the direction of Hopf bifurcation with Dirichlet boundary condition , that is, the conditions when the Hopf bifurcation periodic solutions are orbitally asymptotically stable with asymptotic phase.Our basic idea come from the results given by Tang[30]. We adopt the method used by Hassard in the Hopf bifurcation theorem in [24], which is to judge the existence and the direction of Hopf bifurcation, and the stability of the Hopf bifurcation periodic solutions.

与以前的研究者不同的是,本文不仅讨论了在Dirichlet边界条件下系统的Hopf分支在以扩散系数为分支参数的情况下的存在性和分支周期解的空间非齐次性,而且更多的关注了系统在Dirichlet边界条件下Hopf分支解的稳定性及Hopf分支的方向,也即系统定态解在何种条件下,当分支参数如何变化时产生Hopf分支且分支周期解是带渐近位相轨道渐近稳定的。

At the same time, the practical implementation of evolutionary algorithm is given in order that evolutionary algorithm is introduced into vector quantizer. In the fourth section the asymptotic theory of vector quantization is studied. Then the partial distortion theorem that when codebook size is large enough, each region of the partition makes an equal contribution to the distortion for an optimal quantizer, which is the key part of vector quantizer is obtained. Finally, the competitive learning algorithm based on the partial distortion theorem is proposed, which introduces the subdistortion of each region into the distortion measure to assure that the subdistortion of each region approximately equals to each other.

第四章详细研究矢量量化的渐近理论,然后得出了矢量量化器设计的核心部分——部分失真定理,当码本尺寸足够大且输出矢量的渐近概率密度与输入矢量的概率密度的幂成比例时,最优量化器划分的各个区域对该量化器的平均误差产生相同的影响,最后提出基于部分失真定理的竞争学习算法,它通过在误差测度中,引入与各区域相关的子误差以保证各区域的子误差近似相等,该算法实现较为简单,在一定程度上确保全局最优。

Firstly, we consider SIQR epidemical models with continuous and pulse vaccinations; the reproduction numbers have been obtained for those models; by using Dulac function, we prove the global stabilities of equilibrium of SIQR model with continuous vaccination. In the SIQR epidemical models with pulse vaccinations, we have also discussed the existence of the infection-free periodic solution, the global stabilities of the infection-free periodic solutions, and the effectiveness of pulse vaccination and continuous vaccination policies has been compared for the two models.

文中首先考虑具有连续免疫接种和脉冲免疫接种的SIQR传染病模型,分别获得了它们各自的基本再生数;利用Dulac函数方法证明了具有连续免疫接种的SIQR模型无病平衡点的全局渐近稳定性;在脉冲免疫接种下SIQR传染病模型里,讨论了无病周期解的存在性,证明了该周期解的全局渐近稳定性,并且对连续和脉冲接种下的SIQR传染病模型的接种效率进行了比较。

Combining NA samples the EB estimation with convergence rates is also obtained; Thirdly, for one-parameter exponential distribution family, we give the parameters' EB estimator that is admissible and asymptotically optimal with convergence rates. Finally, Bayesian and hierarchical Bayesian approaches are applied to analyze the reliability performances for series system with cold standby units and the numerical simulation results show that multiple Bayes estimator is superior to Bayes estimator.

其次,针对一类双边截断分布族,在非对称linex损失下构造了经验Bayes决策函数,建立了它的收敛速度,给出了渐近最优的证明;并结合NA样本研究了参数的经验Bayes估计及其收敛速度;接着给出了指数族参数的经验Bayes估计,证明了它是渐近最优的,也是可容许的,同时也获得了该EB估计的收敛速度;最后,运用Bayes与多层Bayes方法研究了具有冷贮备部件串联系统的可靠性指标的估计,并给出了数值模拟结果,结果表明多层Bayes估计优于Bayes估计。

In chapter 1, regression models with censored data, LSE for censored regression models and LAD estimation for models with fixed censoring point are introduced. Then, we state our main results for LAD estimator of nonlinear regression models with randomly censored data, including consistency, boundedness in probability and asymptotic normality. The proofs of our main theorems are given in detail. In chapter 2, we state the main difficulty of obtaining numerical solution for censored LAD estimation, and recall the history of studies on this problem including some anterior algorithms.

在第一章,首先介绍删失线性回归模型的基本概念和性质,并对已有的估计方法,如最小二乘估计、固定点删失的最小一乘估计等做了简单的回顾;然后,把固定点删失线性回归模型的最小一乘估计方法推广到了随机删失、非线性模型的情形,并得到了估计量的一些渐近性质,如相合性、渐近正态性等;最后,给出主要结果的详细证明过程。

The design of output feedback H(subscript ∞) controllers is discussed for nonlinear discrete singular systems. First of all, by means of generalized Lyapunov function and linear matrix inequalities, zero solution E-asymptotically stable is studied for the system, a sufficient condition is given such that the system is zero solution E-asymptotically stable and a H(subscript ∞) norm constraint. And the output feedback H(subscript ∞) controller is designed to guarantee the performance of the resulting closed-loop system.

主要对非线性离散广义系统的输出反馈H控制器的设计问题进行讨论,首先利用广义Lyapunov函数和线性矩阵不等式,对系统的零解E-渐近稳定性问题进行分析,在此条件基础上给出系统零解E-渐近稳定且具有H范数约束的充分条件,然后设计系统的输出反馈H控制器,使得闭环系统具有同样的性能。

Based on the dynamical system of a tuberculosis spread m odel, the dynamical behavior of a tuberculosis spread model with constant immigr ation was discussed, and the local and global asymptotic stability of the endemi c equilibrium on this model is studied by using Hurwitz criterion and multiple m atrix theory. Sufficient conditions for the local and global asymptotically stab ility of the endemic equilibrium on this model are obtained.

在结核病传播的数学模型的动力学系统基础上,利用 Hurwitz 判据和复合矩阵理论,讨论了具有常数移入的结核病传播的数学模型的动力学性质,研究了具有常数移入的结核病模型的地方病平衡点的局部和全局渐近稳定性,得到了具有常数移入的结核病模型的地方病平衡点是局部和全局渐近稳定的充分条件。

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