共形几何

On the other hand,the conformal deformations problem is to find a metric on H2(-1), conformal to g,with the given function K as its Gaussian curvature ,that is,it is important for us to study the solvability of the conformal Gauss curvature equation in geometry analysis.

e~(2u)g，它的高斯曲率函数K满足共形高斯曲率方程Δ_gu+1+Ke~(2u)=0。另一方面，对H~2(-1)上预先给定的一个函数K，共形形变问题-寻找g的共形度量=e~(2u)g使K是的高斯曲率，即共形高斯曲率方程的可解性研究是几何分析中的一个重要问题。

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

Conformal Geometric Algebra is a new tool for geometric representation and computation.

共形几何代数是一个新的几何表示和计算工具。

conformal geometric algebra is a kind of new geometric representation and geometric computation tool, and it has properties of geometric intuitiveness, compactness, high efficiency, unification and elegance.

摘 要：共形几何代数是一种新的几何表示和几何计算工具，它具有直观、简洁、高效、统一、雅致等特性。

Bernstein type theorem; Quaternion Euclidean space; minimal Lagrangian graphs; Twisted special Lagrangian submanifold; twisted normal bundle; Austere submanifolds; Real space form; Complex space form; Hamiltonian minimal submanifold; A Lagrangian submanifold with conformal Maslov form

基础科学，数学，几何、拓扑伯恩斯坦型定理；四元数欧氏空间；极小拉格朗日图；扭曲特殊拉格朗日子流形；扭曲法丛； Austere子流形；实空间形式；复空间形式；哈密尔顿极小子流形；具有共形Maslov形式的拉格朗日子流形

After introducing the basic knowledge of geometric algebra such as outer product,inner product and geometric product,this paper focused on the CGA description and computation with graphic reflection,rotation,translation,rigid body motion and screw motion,and gave the experimental demonstrations.

在简单介绍外积、内积和几何积等基本概念之后，重点论述了共形几何代数在图形反射、旋转、平移等变换和刚体运动、螺旋运动等方面的描述和计算方法，并给出了实验示例。

In the Mathematics Test, three subscores are based on six content areas: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry , plane geometry , and trigonometry.

数学测试部分，共六个方面的内容组成了三个部分的得分：算术、级代数、级代数、何坐标、面几何、角形。

The E optotype on the chart had 3 limbs of equal length. A regular geometric progression of optotype size and distrbution was employed to arrange 11 lines with 4 optotypes on each lines.

采用三划等长的E形视标，视标大小及排列采用均匀的几何增率，每行有4个视标，共11行，每两行视标变化进率为。

So the design method given in this paper avoids the blindness of the design of the antenna, decreases the waste of the antenna fabricates repeatedly. On the other hand, this method takes advantages of the geometrical theory and the nonlinear optimization, so it can be used in a wide region. This leads us a new road to design conformal array in the complex electromagnetic environment.

因此，应用本论文的设计方法，避免了天线设计的盲目性，减少了重复加工的浪费，同时由于整套设计方法利用了几何绕射理论和非线性规化的数学手段，因而具有广泛的通用性，为复杂电磁环境下共形阵的设计走出了一条新路。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。