可逼近性

By using the interpolation mechanism of fuzzy system, an approach of building the series of fuzzy systems, which can uniformly approximate any continuous function on a compact domain to any accuracy, is given, and then the universal approximation theorem is generally proved.

利用模糊系统的插值模型来代替被控对象的真实模型，设计了一个自适应模糊控制策略；为保证系统的全局稳定性，增加了一个补偿控制律，它是根据模糊系统的逼近误差估计量来设计的，因此这里系统跟踪误差的收敛性不依赖于模型最小误差的平方可积性[70，71]。

On the basis of analysis and comparison of their strengths and weaknesses, each method can find its applied occasion. With energy method, we can conveniently control the precision of the objective surface and add boundary constraints for preserving the models global geometric continuity, but this method is very time-consuming.

其中基于能量原理的光顺方法能够方便地控制目标曲面的精度和边界条件，从而能够实现曲面模型的全局连续性，但是能量法的运算速度还有待提高；刚度调整法实现简单，但是生成的曲面的可编辑性较差；小波分解方法计算速度很快，能够有效地实现数据压缩，但是其逼近误差和边界条件却难于控制。

In order to overcome shortcomings that the circular arc and ellipse could not be accurately represented by CE-Bézier curves, this method used the continuity condition of CE-Bézier curves and C-Bézier curves to resolve the representation of circular arc and ellipse in CE-Bézier curve modeling.

该方法首先构造了一种具有优良形状可调性和更好逼近性的带3个形状参数α，β，γ的三次扩展Bézier曲线(CE-Bézier曲线)；并针对CE-Bézier曲线无法精确表示圆弧和椭圆弧等二次曲线的缺点，利用CE-Bézier曲线与C-Bézier曲线间的拼接技术，解决了CE-Bézier曲线造型中圆弧和椭圆弧的表示问题。

We study the relations among MS, QMDS, RBVS, AMDS, GBVS and NBVS. Finally. we improve some classic results in Fourier analysis such as uniform convergence, L~1 convergence, L~p-integrability, strong approximation of continuous functions et al., by applying this new condition.

我们研究了MS，QMDS，RBVS，AMDS，GBVS和NBVS等不同数列之间的关系，在此基础上，我们给出了NBV条件在研究三角级数的一致收敛性、L~1收敛性、L~p可积性、连续函数的强逼近等Fourier分析经典问题上的应用，对一些经典的结论作了推广。

The well-known spectrum assignment problem are discuussed and a general proofs for it and its generalization are gived. 3. The general conditions of invertible completions of operator pairs are acquired.

作为研究基础，引入了算子对可控性与可容许性指标及算子ε-限制，并利用算子闭值域特性、值域逼近及空间的不同分解，获得了算子谱配置问题及广义的算子谱配置问题一般性证明。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

Chapter 4 -rotundity and nearly strict convexity of quotient spaces. It is proved that ifis a -rotund or nearly strict convex Banach space andis a closed and proximinal subspace of, then the quotient spaceis also -rotund or nearly strict convex.

第四章 商空间的-严格凸性和近严格凸性：本章证明了若是Banach空间的任意可逼近子空间，则商空间对原空间的-严格凸性和近严格凸性都具有遗传性。

Based on the sizeof the set of perturbed minimal points in the variational principle, the differentiability of lower semicontinuous functions is examined by means of approximation of the infconvolution sequence.

摘要通过函数的下卷积函数列的逼近方法，在变分原理中从扰动最小值点集的"大小"入手，研究了下半连续函数的可微性。

The curve, to be calledλ-Bezier curve not only inherits themost properties of n-degree Bezier curve, such as endpoints properties, symmetry,convex hull property, geometric invariability, affine invariance, convex-preservingproperty, variation diminishing property and so on, but also can be adjusted inshape by changing the value ofλwithout changement of control points.

曲线不仅具有n次Bézier曲线的特性：如端点插值、端边相切、凸包性、变差缩减性、保凸性等，而且具有形状的可调性：在控制顶点不变的情况下，随着参数不同，可产生不同逼近控制多边形的曲线。

This thesis focuses on studying the matrix equa-tion problem systematically, and proposed an abstract algorithm of solving the matrixequation with constraints, and established a strict convergence theory. Using this algo-rithm, we can solve the sets of matrix equation satisfying some constraint conditions,such as symmetric, antisymmetric, centrosymmetric, centroskew symmetric, re?exive,antire?exive, bisymmetric, symmetric and antipersymmetric, symmetric orthogonalsymmetric, symmetric orthogonal antisymmetric, Hermite generalized Hamilton ma-trix;So we can solve the problem with this algorithm, if the set of constrain matrixcan make a subspace in matrix space, and this algorithm also can solve the optimalapproximation and least squares problem. So this abstract algorithm has universal andimportant practical value.

本篇硕士论文系统地研究了此类问题，并找到了求解约束矩阵问题的抽象算法，并建立严格的收敛性理论，利用这一算法可求解约束条件为对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵，对称正交对称矩阵、对称正交反对称矩阵、双中心矩阵、Hermite广义Hamilton矩阵等；可以说只要约束矩阵集合在矩阵空间中构成子空间，都可以考虑用此算法求解，而且这一算法还能把矩阵方程解及其最佳逼近，最小二乘解及其最佳逼近统一处理，因此本文算法有普适性和重要的实用价值。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新