稳定收敛

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

The finite difference approximation for this equation is presented.The stability and convergence of the finite difference approximation are analyzed.

并证明了显式格式条件稳定和条件收敛，而隐式格式则是无条件稳定和无条件收敛。

Based on contraction mapping theorem of analysis mathematics, the non-steady flow mathematical model of mine ventilation network was analyzed.

利用分析数学的压缩映射原理，对矿井通风网络非稳定流动数学模型进行了分析，得出了数学模型数值解收敛的条件，确定了以惯性系数排序选择最小生成树的回路选择方案，为矿井通风网络非稳定流动数学模型数值解的收敛性提供了理论依据。

When we analyse rigid body with the theory of limit equilibrium, we do not obtain always reasonable maximal principle in physics, and the maximal value is the result of soil plasticity deformation.(2) Thoroughly commenting the typical method of slices from their satisfid equilibrium conditions, calculational parameter and their convergence, the thesis sortes the methods into four kinds. The first satisfies all kinds of equilibrium conditions, can obtain interslice force and the factor of safety.

2从满足的平衡条件、求解的参数及其解收敛性等，分析了各种常用极限平衡条分法，将其分为四类，第一类方法既满足力的平衡，也满足力矩平衡，能获得条间力和稳定系数的收敛解；第二类方法只满足一个方向力的平衡和力矩平衡，只能求得稳定系数；第三类方法既满足力的平衡，也满足力矩平衡，但不是严格的静定问题，解的收敛性差；第四类方法满足两个方向力的平衡，不满足力矩平衡，可求得稳定系数和条间力的大小，不能求得条间力方向。

In neural networks learning, the Sigmoid function is improved and the stability conditions of backpropagation algorithm is analyzed theoretically.

在神经网络学习中，改进了前向神经网络中Sigmoid作用函数表达式，并在理论上分析了反向传播修正权值的迭代算法稳定收敛的充分条件。

In this model, we discuss the effect of tax policy on economic growth on the condition of market competitive equilibrium. Two chief conclusions are drawn: firstly, when the government has carried out steady tax policies, for consumers there exists unique optimal capital stock path along which economy can grow sostenuto and steadily; when the tax path given by the government converge to some constant tax rate, there still exists one capital stock path which can make the whole economy grow gradually and converge evenly to the optimal state.

在该模型中，我们讨论了在市场均衡条件下，税收政策对经济增长的影响，得到两个主要结论：一、当政府实行稳定的税收政策时，消费者存在着唯一的最优资本存量路径，沿着此路径经济能够持续平稳并且最优地增长；当政府给定的税收路径不稳定但能收敛到某个常值税收率时，此时也存在一条资本存量路径，它能使整个经济渐近平稳地增长，并且最终收敛到最优状态。

It is proved theoretically that CA-PSO is endowed with stable convergence under given conditions.

理论证明，在一定条件下，CA-PSO具有稳定收敛性。

The simulation results show that the scheme is more stable in convergence, insensitive to threshold parameters, less on loss and advantageous to the new agent to join the network during emergence of virtual community.

实验表明，该方法具有评价结果稳定收敛，对门限参数敏感度低，虚拟社区形成过程中损失小，有利于新加入节点融入网络的优点。

The stability of the improved Elman neural networks is proved in the sense of Lyapunov stability theory. The optimal adaptive learning rates are obtained, which can guarantee the stable convergence of the improved Elman networks.

在Lyapunov稳定性意义下分别给出了改进网络的稳定性证明，得到了保证网络稳定收敛的最佳自适应学习速率。

In Chapter 4, image space reconstruction algorithm and regression ICA are employed to construct a new algorithm for the estimation of overcomplete ICA and the stability and convergence conditions are also analyzed.

在第四章，我们把回归ICA以及盲信号分离中图像重构方法应用于ICA，从而获得一个新的欠定ICA算法，论文还分析了所提出算法的稳定收敛条件。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。