不动点方法

Since 1976, homotopy method has been used to solve fixed point problem in convex set.

长期以来，人们一直利用同伦方法来计算凸集上的Brouwer不动点问题。

The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

In Chapter 1, we use the upper and lower solutions method, the bootstrap technique and the Schauder fixed point theorem to investigate the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems of the following three types:(1) Quasimonotone nondecreasing system;(2) Mixed quasimonotone system;(3) A nonquasimonotone 2-system. The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

In order to eliminate the effect of artifacts in electroencephalograph signals, such as electrocardiogram and electrooculogram, etc., a new ICA method with multi-references is proposed based on the fixed-point algorithm and the ICA algorithm with references.

为消除脑电信号中的心电、眼电等伪差，在已有的不动点算法和带参考信号的独立分量分析算法的基础上，提出了一种多参考信号的独立分量分析方法。

With the method of upper and lower solutions,its associated monotone iterations and the fixed point theorem,the coexistence solutions to a strongly coupled elliptic system are studied.

采用上下解及相应的单调迭代序列的方法，结合Schauder不动点定理，研究带Dirichlet边界条件的两种群的互惠模型强耦合问题共存解。

The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容：第一章研究了该模型正平衡解的性质，可分为三部分：第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件；第二部分利用分歧理论给出了平衡态系统正分歧解的结构，并讨论了局部分歧解的稳定性；第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性，并讨论了参数对解的影响。

In Chapter 5, a scheme of the equilibrium iteration with a constant stiffness matrix is constructed by means of Steffensen's acceleration in the fixed-point iteration.

在第五章，我们利用不动点迭代的Steffensen加速方法构造了一个基于常刚度的平衡迭代格式。

Fixed point iteration method is also a common calculation method of nonlinear equations.

详细说明：不动点迭代方法也是一常用的计算非线性方程组的解法。

In this paper, the almost periodic solution for a class of two-degree-of-freedom nonlinear oscillating systems is studied by using the Leray-Schauder fixed point theorem and the method of Liapunov function.

运用Leray-Schauder不动点定理和Liapunov函数方法，研究了一类两自由度非线性振动系统的概周期解，得到了该振动系统概周期解存在的充分条件。

Calculus can be used to find approximate solutions to equations, in methods such as Newton's method , fixed point iteration , and linear approximation .

积分可以用来寻找近似解方程，在方法，如牛顿法，不动点迭代和线性近似。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。