两条代数曲线之间Hausdorff距离有限性的刻画
Characterizing the finiteness of the Hausdorff distance between two algebraic curves
摘要：
本文给出了$n$维空间（参数定义或隐式定义）中两条给定代数曲线之间Hausdorff距离为有限的一个刻划.该特征与两条曲线的渐近性态有关，且易于检验。更精确地说，两条曲线$\cal C$和$\overline{\cal C}$之间的Hausdorff距离是有限的，当且仅当对于$\cal C$的每个无穷大分支，存在$\overline{\cal C}$的无穷大分支，使得在相应的级数中具有正指数的项是相同的，并且是π。
英文摘要：
In this paper, we present a characterization for the Hausdorff distance between two given algebraic curves in the $n$-dimensional space (parametrically or implicitly defined) to be finite. The characterization is related with the asymptotic behavior of the two curves and it can be easily checked. More precisely, the Hausdorff distance between two curves $\cal C$ and $\overline{\cal C}$ is finite if and only if for each infinity branch of $\cal C$ there exists an infinity branch of $\overline{\cal C}$ such that the terms with positive exponent in the corresponding series are the same, and reciprocally.
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