可计算映射

Based upon all above-mentioned, a mathematical representation for multi-material structures is proposed by means of vector level sets, and the general structure topology optimization can be expressed by a constrained functional minimization problem of a set of level set functions.

同时，还提出了在有效约束切空间上构造的非线性映射技术，以改进向量水平集的演化方向，可提高计算效率2到3倍。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

These algorithms can get very high precise mapping together with high speed of convergence, because the mapping error is able to reach zero and the computational complexity is at order of polynomial.

新算法有很高的精度及较快的运算速度，这是由于映射误差可以为零，其计算复杂性是多项式阶。

The curved grids are generated by using the transfinite interpolation and the so-called multiblock techniques that originally developed for computation fluid dynamics.

该方法结合了多块映射和超限插值技术，这项技术出自计算流体力学，它可使产生的网格网线沿着地下所有界面变化。

In chapter 4, basing theories and methods of scientific visualization, and artificial neural network BP algorithm, we integrate the Visual C++, OpenGL graphics library and Excel VBA technique to develop the program of artificial neural network and to make the BP algorithm visually, this program works can be divided into four parts: Using C language to develop program about BP algorithm; Using Visual C++, develop the GUI Interface, make input parameter visually; Using OpenGL graphic technique to display the training sample point in three dimension; at last using Excel DDE technique display the error graphic tables in Excel system In chapter 5, on the view of engineering application, we establish new method of surface reconstruction basing artificial neural network, develop interface program between module and commercial CAD/CAM system, meantime deeply discuss some key problems, for example, setting up the base plane, using the API technique, cutting and editing surface boundary, and also discuss the more compliant problem: how to intersect surface, at end we finish the work of translation from our surface reconstruction module to commercial CAD/CAM system, then make reverse engineering system basing artificial neural network more useful.

第四章基于科学计算可视化理论，依据人工神经网络BP算法理论模型，综合Visual C++，OpenGL图形库以及Excel VBA等多项软件开发技术，编制了人工神经网络程序，实现了BP算法的可视化映射。具体工作分为四部分：利用C语言实现人工神经网络BP算法；利用VisualC++的GUI技术开发图形用户界面，实现参数设置可视化；利用OpenGL图形技术进行三维映射，显示学习样本及训练样本点；利用微软电子表格DDE动态数据交换技术，在Excel上动态显示学习误差曲线图。第五章从工程应用的角度出发，提出了一种新的基于人工神经网络算法的曲面裁剪重构方法，完成了曲面重建模块与通用CAD/CAM系统的接口设计工作，对其中的若干关键问题进行了深入讨论，例如基平面设定、API技术的应用、边界裁剪等问题，同时，对曲面计算中较为困难的曲面相交问题也进行的专门探讨，最终完成了曲面重建模块向CAD/CAM系统的数据传输工作，使人工神经网络逆向工程系统趋向实用。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。