映照

In this paper, the author estimated the module of quasiconformal mapping in curved fan, by the expression of local maximal dilatation function of quasiconformal mapping, Riemann′ s existence theorem and extremal length method, the author obtained a result of moduler deviation on curved fan.

本文对曲边扇形内的拟共形映照的模进行估计。借助拟共形映照的局部最大伸张函数来表达，利用黎曼存在定理和极值长度方法，得到关于曲边扇形的一个模偏差定理。

In this chapter, we obtain the following conclusion: Let f=h+〓 be a univalent orientation-preserving harmonic mapping defined on the unit disk U such that f is convex in a direction and real on the real axis, and satisfies the normalization f (0)=0 and 〓, then f is typically real.

在这一章中，我们证明了如下事实：对于单位圆U上的单叶调和映照f=h+〓，如果它满足条件〓，且在其映照下单位圆的像域是一个方向凸的，则它必定是典型实照映射。

In this thesis, we study some classes of holomorphic mappings in several complex variables, and obtain the estimations of some order item coefficients of homogeneous expansion for starlike mappings, close-to-starlike mappings and spirallike mappings relative to A .

本文对多复变数的几类全纯映照族进行研究，给出了星形映照，近星映照与相对于A的螺形映照的齐次展开式的估计。

In this paper,we have studied the modulus and quasiconformal mappings,obtained several conditions for that a homeomorphism is a quasiconformal mapping.

本文研究了模和拟共形映照，得到了一个同胚为拟共形映照的若干条件。

In this project, we have mainly researched the complex-anlyticity,constancy and stability of pluriharmonic maps to complex grassmannian manifolds;the characterization and isotropicity of pluriharmonic maps with finite uniton number;the regularity, singularty and Liouville theorem of harmonic maps.

本课题着重研究到复Grassmann流形多重调和映照的复分析、常值性及稳定性之间的关系；具有有限uniton数的多重调和映照的特征与迷向性；调和映照的正则性、奇异性及Liouville定理。

Keywords: harmonic map;pluriharmonic maps; submanifold

中文关键词：调和映照；多重调和映照；子流形

In this paper, we give explicit constructions and formulations for harmonic maps from R1,1 into classical real semisimple Lie groups by using Darboux transformation. We also discuss pluriharmonic maps from complex manifoldsinto symmetric spaces and Willmore surfaces in Sn. By converting geometric conditions satisfied by these maps into integrable systems, and using the the-ory of integrable systems, we give explicit constructions for pluriharmonic maps from complex manifolds into symmetric spaces and the Willmore surfaces in Sn respectively. Finally, we classify hypersurfaces in Sn+1 with three distinct prin-ciple curvatures and zero Mobius form using the theory of Mobius geometry. The paper consists of four chapters.

本文首先利用Darboux变换的方法给出了从Lorentz平面R~(1，1)到经典实半单Lie群的调和映照的具体构造，并给出其显式表示；其次研究了复流形到对称空间的多重调和映照及球空间S~n中Willmore曲面，将这些映照所满足的几何条件转化为可积系统，然后利用可积系统理论分别给出复流形到对称空间的多重调和映照与S~n中Willmore曲面的构造；最后利用Mōbius几何的理论给出S~(n+1)中具有三个不同主曲率且Mōbius形式为零的超曲面的分类。

Geometry quality for these mappings can be obtained from these inqualities,and some sufficiency conditions for starlike mappings and spirallike mappings are given.

本文建立了多复变数单位球上全纯映照的一些偏微分不等式，由此可映照本身的一些几何性质，并得到星形映照和螺形映照的充分判别条件。

Geometry quality for these mappings can be obtained from these inqualities, and some sufficiency conditions for starlike mappings and spirallike mappings are given.

由此导出全纯映照本身的一些几何性质，并得到星形映照和螺形映照的充分判别条件。

When the viewpoint is changing quickly, the rendering algorithm ignores some details of the diffuse component, otherwise the scene is rendered more precisely. The Specula highlight is dependent of the viewpoint, it must be processed in real time. We present an algorithm to get rid of the area that does not contain specula highlight quickly and calculate only the area that contains the specula highlight. In order to calculate the specula reflection and refraction component, we presented a new raytracing algorithm based on the environment map transformation. The environment maps are constructed at the sample points of the scene in the preprocessing phase. We add depth information in the environment maps and generate the exact reflection and refraction intensity with the transformation of a few pixels.

对于表面光亮度漫射分量，由于它与视点无关，可以把面片按照光照细节的分布预剖分成层次结构，然后在实时漫游时根据场景变化的快慢决定绘制的细致程度；对于镜面高光分量，由于它与视点有关，必须实时处理，我们提出了一种快速高光裁剪算法，通过简单测试，去除那些不包含高光的区域，只处理包含高光的区域；对于镜面反射分量和折射分量，我们提出了一种基于环境映照变换的快速光线跟踪算法，预先在场景的离散采样点处建立环境映照，然后根据入射点的位置，把邻近采样点处的环境映照上相关象素处的可见点变换过来，求取反射分量和折射分量。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。