| Estimation of the Bezout number for piecewise algebraic curve |
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| 作者姓名： | 王仁宏 许志强 |
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| 作者单位： | Institute of Mathematical Sciences，Dalian University of Technology Dalian 116024，China Correspondence should be addressed to Xu Zhiqiang，Institute of Mathematical Sciences，Dalian University of Technology Dalian 116024，China Correspondence should be addressed to Xu Zhiqiang |
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| 摘 要： | A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper.a coniecture on trianguation is confirmed The relation between the piecewise linear algebraiccurve and four-color conjecture is also presented.By Morgan-Scott triangulation, we will show the instabilityof Bezout number of piecewise algebraic curves. By using the combinatorial optimization method,an upper
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Estimation of the Bezout number for piecewise algebraic curve |
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| WANG Renhong & XU Zhiqiang
Institute of Mathematical Sciences,Dalian University of Technology,Dalian ,China Correspondence should be addressed to Xu Zhiqiang.Estimation of the Bezout number for piecewise algebraic curve[J].Science in China(Mathematics),2003,46(5):710-717. |
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| Authors: | WANG Renhong & XU Zhiqiang
Institute of Mathematical Sciences Dalian University of Technology Dalian China Correspondence should be addressed to Xu Zhiqiang |
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| Institution: | Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China |
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| Abstract: | A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, a conjecture on triangulation is confirmed. The relation between the piecewise linear algebraic curve and four-color conjecture is also presented. By Morgan-Scott triangulation, we will show the instability of Bezout number of piecewise algebraic curves. By using the combinatorial optimization method, an upper bound of the Bezout number defined as the maximum finite number of intersection points of two piecewise algebraic curves is presented. |
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| Keywords: | piecewise algebraic curve bezout theorem triangulation bivariate splines |
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