凸点

This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included.

通过Hilbert空间中的Riesz表示定理，首先将变分不等式问题的迭代过程转化为一种不动点形式，再利用Schauder不动点定理构造了一个高效率的数值证明过程，即通过数值计算产生一个包含近似解的有界闭凸子集。

Of if is concave up on one side of and concave down on the other side.

点，如果在点的一侧是凹的，而在的另一侧是凸的。

First,the convex hull points of the characteristic region such as eyes,mouth etc. are confirmed,and,the integral contour points are obtained by fitting the curve.Then,the coordinate of the contour and the corresponding points of the adapted facial model are transformed to a new coordinate.At last,the model is adjusted in the new coordinate to get a good adaptation between the human facial model and human face image by revising the corresponding detail data in the model.

首先，对检测出的眼睛、嘴巴等特征区域，确定出其外凸包点集，通过曲线拟合得出其完整外轮廓，然后对此轮廓点以及已经粗调的对应模型点进行坐标转换，在转换后的坐标系中，对模型中相应的细节数据进行修改，实现模型和人脸图像的配准。

This paper proves that every probabilistic contraction map from E to E has a unique fixed point, where E is a complete and uniformly local semi-convex probabilistic normed spacer and obtains a fixed point theorem in metric linear spaces.

摘要证明了完备的一致局部半凸概率赋范空间上的概率压缩映象必有唯一不动点，得到了一类度量线性空间中关于伪范数族一致压缩映象的不动点定理。

By using the partition theorem of unity, a continuous selection theorem for a multimap from a compact Hausdorff topological space to a finitely continuous topological spaces (simply, FC-spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaces and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given.

利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间的集值映射的连续选择定理，并从该结果和Tychonoff不动点定理，得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理，对文献中的相应结果进行了改进和一般化。

Firstly, the generalization of Fan-Ha section theorem and a general vector variational inequality without convexity assumption and minimax theorem of vector-valued function are obtained. Then, the quasi-montone vector variational inequality problem is concerned. Cx-quasi-monotone operator is defined in topological vector space, inner point of a closed convex set K is introduced, the relation between inner point and relative algebraic interior point is given, an existence result for quasi-monotone vector variational inequality is obtained.

第三章主要研究了向量变分不等式和极小极大定理(来源：3282AB83C论文网www.abclunwen.com)，建立了广义的Fan-Ha截口定理、新的向量变分不等式与极小极大定理，并在拓扑向量空间中定义了C_x-拟单调算子，引入了闭凸集K的inner点，给出了inner点与相对代数内点的关系，利用innK_c代替K的拓扑内部，建立了新的拟单调向量变分不等式。

If P is a convex lattice polygon, and its pair-wise disjoint family of translates are also lattice polygons, whose union contains every lattice point, it is called a TLP .

若P为凸格点多边形，其内部边界不交平移覆盖平面格点集，则称之为可平移格点多边形TLP。记顶点数为v的TLP的内格点数的下确界为i ，得出i(5)=i(6)=1，i(7)=i(8)=4。

Then, the notion of ordered target triangle was defined. It quickly found ordered target triangles and generated the non-ray Voronoi diagram. Considering the characteristics of convex hull, a ray Voronoi diagram was generated by three infinite points.

然后又定义了有序目标三角形的概念，该算法能迅速查找点的有序目标三角形，生成无射线的Voronoi图；考虑凸壳上点的特性，借助三个无穷点生成带射线的Voronoi图。

Hence the study of geometric properties, which include the distribution of singular and inflection points and the convexity of parametric curves, is the key for designer to control the curves shape.

在计算机辅助几何设计的光顺曲线造型中，不希望曲线带有二重结点、尖点及多余拐点，因此对参数曲线的几何性质(包括奇、拐点分布及凸性等)的研究是控制其曲线形状的关键。

The algorithm makes the discrete points sort in scan manner, and secondly it constructs convex hull and triangulates the sorted points by the optimal convex hull technology which is proved by the author, and optimizes triangles utilizing topological structures of directed edges.

该算法对离散点进行扫描线方式排序，利用最优凸壳技术进行凸壳的生成和三角网联结，最后利用有向边的拓扑结构进行三角网优化。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。