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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。

Pattern recognition ; pattern representation ; geometric algebra ; multi-vector

模式识别；模式表示；几何代数；多向量

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。

We also set up a Schur-Weyl duality between certain quantum group and Hecke algebra of type D_n.

我们还建立了某些量子群与D_n型黑克代数之间的Schur-Weyl对偶。

Zhang(1997) further generalized them to central duadic group algebra codes.

张胜元(1997)又进一步推广到中心duadic群代数码。

We point out the correspondences between Lie group, Lie algebra and some keyformulae of Huston-Kane method.

首次指出偏速度与偏角速度构成运动相空间的Lagrange子流形，揭示了偏速度与偏角速度的本质及Huston-Kane方法对动力学问题的变换思路。

In order to satisfy itself to as well as enriches my knowledge with the contemporary science hope, I have not only studied the machine science core curriculum like mechanics, the metal, the process and the material, but also through was the audit method has studied the other curriculum like discrete mathematics, the advanced algebra, the group theory in other and so on.

为了满足自己对与当代科学的渴望以及丰富我的知识，我不仅学习了机械科学的基础课程如机械学、金属、过程与材料，还通过在其他系旁听的方法学习了其他课程如离散数学、高等代数、群论等。

Atlast,we consider the tensor product representation of quantum group Uqslandthe representation of Hecke algebra Hwhich commutes with that of Uqsl.

最后，考虑了量子群Uqsl的张量表示及其与之可换的Hecke代数H的表示。

About the existence of duadic codes, Ward and Zhu(1994) obtained necessary and sufficient conditions for existence of duadic abelian codes, Zhang(1997) gave the existent conditions for such codes by some parameters and obtained necessary and sufficient conditions for existence of central duadic group algebra codes.

对duadic群代数码的存在性问题，Ward和朱烈(1994)解决了域上duadic阿贝尔码存在性；张胜元(1997)年用参数形式给出更具体的判定条件和中心duadic群代数码存在的充分必要条件。

Some applications to special cases,which include the Kantorovich\'s condition and theγ-condition as well as the Smale\'sα-theoryfor maps from a Lie group to its corresponding Lie algebra, are provided.

同时把所得的结果应用于：Kantorovich情形，γ-条件及关于映射f的广义Smaleα理论。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。