有限维算子

In this thesis, we discuss some algorithms for giving the zeros of maximal monotone operator in a Hilbert space and the alternating direction method for the variational inequalities.

本论文主要讨论了求解Hilbert空间上极大单调算子的零点的数值算法以及有限维空间上的变分不等式的交替方向方法。

The finite dimension approximating solution for initial-boundary value problem of coupling nonlinear system of hyperbolic equation is constructed by orthogonal basis of characteristic value sequence of the Laplace operator in the Dirichlet boundary conditions.

以Laplace算子在Dirichlet条件下的特徵值序列为正交基底构造耦合非线性双曲型方程组初边值问题的有限维近似逼近解，证明该逼近解的一致收敛性。

It has been prepared for the investigation of inexact quasi-newton method for operator equations in infinite dimensional space.

文献[1]对有限维空间中非线性方程组的不精确拟牛顿法的收敛性进行了研究，为无穷维空间上的算子方程的不精确拟牛顿法的研究作好了准备。

This thesis carries on research to a class of nonlinear Schrodinger Equation with wave operator of initial value periodic problem.

本文针对一维带波动算子的Schrodinger方程周期初值问题进行数值研究，对上述方程首先构造了守恒的半离散格式，然后将p次Hermite插值方法与有限差分方法相结合构造了差分正交样条配置格式，并证明这两个格式均为稳定和收敛的格式。

In this paper, we use this numerical method and adopt operator splitting method to simulate the conduction model of action potential in two-dimensional cardiac ventricle tissue,the conduction model of the action potential in two-dimensional cardiac ventricle tissue is denoted by one reaction-diffusion equation with a series of ODE describing ionic channels of cell, at the same time,we adopt the compact alternate direct implicit difference method to simulate that model,compar-ing these value results,get some conlusions.

本文中，我们利用摄动有限差分方法和算子分裂思想去模拟二维心室肌中动作电位的传导模型，该模型由一个描述细胞离子通道的常微分方程组和一个反应扩散方程组成。

The notion of - resolvent operator of set-valued mappings is introduced.

利用η-预解算子在有限维空间中探讨了集值混合拟类变分不等式问题和广义集值变分包含问题存在唯一解的条件；利用分析的方法在实Hilbert空间中讨论了集值混合拟类变分不等式问题解集的非空性。

The research is carried on from four aspects. One is, based on answering the above open problem on a finite dimensional Euclidean space by means of partially ordered theory, to research the existence of solutions, global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable-parameter three-step iterative algorithms for generalized set-valued variational inclusion problems by using - resolvent operator of set-valued mapping.Two is to consider the convexity, closedness and boundedness of the solution set of general set-valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory. Three is to discuss directly the existence of solutions by using analytical methods for set-valued mixed quasi-variational-like inequalities and suggest a class of direct variable-parameter three-stepiterative algorithms for solving generalized set-valued variational inclusions.

研究分有三个方面：一是借助于偏序理论在有限维欧氏空间中解决了上述公开问题，在此基础上利用集值映射的η-预解算子，研究了广义集值变分包含问题解的存在性、逼近解的全局误差界、参数唯一解的灵敏性，并提出了一类变参数三步迭代算法；二是借助于图收敛理论研究了一般集值变分包含问题解集的凸性、闭性和有界性以及参数解集的灵敏性；三是用分析的方法直接讨论了集值混合拟类变分不等式问题解的存在性并提出了一类求解广义集值变分包含问题的直接变参数三步迭代算法。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

Thesame rank Lipschitz continuous development of single-valued mappings is proven by means of partially ordered theory on finite dimensional Euclidean spaces.

借助于冲一预解算子研究了有限维欧氏空间中的集值混合类变分不等式问题和广义集值变分包含问题的全局误差界。

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。