实分片代数超曲面的连通分支数的上界

doi:10.12341/jssms13266

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (10): 2095-2102.DOI: 10.12341/jssms13266

实分片代数超曲面的连通分支数的上界

赖义生，段德鑫

浙江工商大学统计与数学学院, 杭州 310018

出版日期:2017-10-25 发布日期:2017-12-14

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赖义生，段德鑫. 实分片代数超曲面的连通分支数的上界[J]. 系统科学与数学, 2017, 37(10): 2095-2102.

LAI Yisheng,DUAN Dexin. The Upper Bound of the Number of Connected Components of Real Piecewise Algebraic Hypersurfaces[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(10): 2095-2102.

The Upper Bound of the Number of Connected Components of Real Piecewise Algebraic Hypersurfaces

LAI Yisheng ,DUAN Dexin

School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018

Online:2017-10-25 Published:2017-12-14

多元样条是具有一定光滑度的分片多项式, 具有一定光滑度的分片代数(超)曲面(即多元样条的零点集)是表示或逼近曲面的重要工具. 这篇文章建立了实分片代数超曲面与实分片代数曲线的连通分支数的界.

关键词： 分片多项式, 实分片代数超曲面, 实分片代数曲线, 连通分支.

A multivariate spline is a piecewise polynomial with certain smoothness. Piecewise algebraic (hyper) surfaces with certain smoothness (i.e., the zero set of multivariate splines) are an important tool to represent or approximate surfaces. This paper gives the bounds of the number of connected componects of both real piecewise algebraic hypersurfaces and real piecewise algebraic curves.

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