映射

This thesis consists of five chapters. At first, We introduce the study history as well as present situation on KKM theory. Secondly, We discuss the invariability of transfer open valued multimap under the restriction of upper and lower semicontinuity on generalized convex spaces. Then, We obtain new KKM type theorems from the classical KKM theorem by applying upper and lower semicontinuity. We also obtain intersection theorems by applying the KKM type theorems for a multimap from a topological space to another topological space. Further, We obtain Ky-Fan type coincidence theorem by applying known variational results on the KKM type theorems. Finally, We give an application to new theorems.

本文共分五章，首先回顾了KKM理论的研究历史和现状，其次讨论了在一般化凸空间上转移开值映射在上、下半连续映射下的不变性，然后在上、下半连续映射下，以古典的KKM定理为基础得到新的KKM型定理，并利用从一个拓扑空间到另一个拓扑空间的集值映射及KKM型定理得到相交定理，进一步利用已知的KKM型定理的变形结论得到Ky-Fan型重叠定理，最后给出新定理的一个应用。

It is proved that every Lie derivation of nest algebra is the sum of an associative derivation and a general trace. Every Lie isomorphism between nest subalgebras of a factor von Neumann algebra is the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace. Lie invariant subspace of linear mappings on Banach algebras is introduced, and linear maps from nest subalgebra of a factor von Neumann algebra into itself which satisfy the property that the space of derivations is their Lie invariant subspaces are characterized. Simultaneously, it is shown that such maps are Lie derivations modulo the set of scalar multiple of the identity.

得到Lie导子的特征表示，即套代数上的任何一个Lie导子都是内导子与广义迹之和；给出了Lie同构和同构及反同构之间的关系，即因子von Neumann代数中套子代数之间的任何一个Lie同构要么是同构与广义迹之和要么是负反同构与广义迹之和；引入了Banach代数上线性映射的Lie不变子空间，并给出von Neumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一个刻画，同时也表明在模去数乘恒等映射的意义下，以导子空间为Lie不变子空间的线性映射就是Lie导子。

Based on the inverse mapping with linear deformation, the geometric mapping was used to carry out the second element transformation in order to avoid the abnormality of the stiffness matrix and to improve the stability and the convergence of the numerical calculations.

在现有线性变形逆向映射法的基础上，采用几何映射法计算变换单元，避免单元刚度矩阵出现畸形，提高钣金展开有限元逆算法的稳定性和收敛速度，对几何映射法与投影法所计算的变换单元进行了对比，数值计算结果表明用几何映射法计算的初始估算展开料形状更接近于最终的钣金件展开形状。

As CMAC neural network could not be used to approximate the multi-valued mapping of an inverse hysteresis directly, an inverse hysteretic operator was proposed to transform the multi-valued mapping into a one-to-one mapping which could enable neural networks to approximate the behavior of an inverse hysteresis.

由于CMAC神经网络不能够直接逼近滞回逆这种具有记忆性的多映射现象，通过引入一个滞回逆算子，将多映射的滞回逆转换成一一映射，然后运用CMAC神经网络控制器来逼近这个一一映射，从而建立一个基于CMAC神经网络的滞回逆模型。

Base vectors are selected for formulating the nonlinear mapping. An approximate explicit expression is formed by using the Nystrm method for nonlinear mapping which is not available originally. The data in the nonlinear input space is mapped into some linear feature subspace and fisher linear discriminant analysis is computed for the mapped data.

首先提取基向量；然后采用Nystrm方法，以基向量为训练样本，将形式未知的非线性映射近似表达为已知形式的非线性映射，这种近似的非线性映射将变量由非线性的输入空间转换到线性的特征子空间；最后对映射数据进行线性Fisher判别分析。

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。

Two-dimensional texture mappings are summarized in this paper including Catmull algorithm and Blinn algorithm, two-step texture mapping, environment mapping and bump mapping. Moreover, a new method of regional texture mapping based on intermediate surface is presented and a new algorithm is promoted to reduce texture distortion in the process of mapping onto the sphere surface.

在二维纹理方面，本文讨论了适用于参数曲面的Catmull算法与Blinn算法，适用于一般曲面的两步纹理映射技术，现已广为应用的环境纹理映射技术及凸包纹理映射技术，还分析了纹理映射的几种快速反走样技术。

Adopting the method of discontinuity bypass mapping,the Poincare mapping of Jeffcott model near a grazing orbit was estimated as a four-dimensional mapping with square-root compressing or stretching at one direction,from which many chaos motions were found by researching the mapping.

采用不连续穿越映射技术，Jeffcott碰摩转子系统的映射在擦边碰撞附近可以近似为在一个方向上有平方根伸缩的四维映射，本文对此映射的动力学行为进行了研究，而且发现了有大量的混沌现象存在。

In the category Quant,it is proved that quotient object of any object of Quant can be induced by nuclei in the sence of isomorphism, we dicuss the relationships between closed maps and closed filters which is closely related with Gabriel topologies of quantales.

给出了在不同类型的Quantale中c-核映射的刻划以及c-核映射和，r-核映射的等价性。在范畴Quant中，证明了任一对象的商对象在同构的意义下可由核映射诱导。

Optimization; parametric quadratic convex programming; set-valued map; directional derivative; linear stability; solution-set map; parametric linear programming; error bound; subdifferential map; lower locally directionally Lipschitzian; upper locally di-rectionally Lipschitzian; locally directionally Lipschitzian; convex function; quasidiferential; kernelled quasidiferential; quasi-kernel; star-kernel; star-diferential; Penot diferential; subderivative; superderivative; epiderivative; set-valued optimization; set-valued analysis; subdifferential; optimization condition;ε-dual; scalization; generalized subconvexlike-cone;ε-Lagrange multiplier

基础科学，数学，运筹学最优化；集值映射；方向导数；线性稳定；最优解集映射；参数线性规划；参数凸二次规划；误差界；次微分映射；下局部方向Lipschitzian；上局部方向Lipschitzian；局部方向Lipschitzian；凸函数；拟微分；核拟微分；拟核；星核；星微分； Penot-微分；上导数；下导数； Epi-导数；集值优化；集值分析；集值映射的次微分；最优性条件；广义锥次类凸；ε-对偶；数乘；ε-Lagrange乘子

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷