ON THE NUMBER OF SOLUTIONS OF AN ALGEBRAIC EQUATION ON THE CURVE y = e + sin x, x > 0, AND A CONSEQUENCE FOR O-MINIMAL STRUCTURES
ON THE NUMBER OF SOLUTIONS OF AN ALGEBRAIC EQUATION ON THE CURVE y = e + sin x, x > 0, AND A CONSEQUENCE FOR O-MINIMAL STRUCTURES
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论曲线 y = e sin x, x > 0 上代数方程的解数以及 O-极小结构的结果
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. Parusiński
中科院分区：
文献类型：
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作者：
K. Kurdyka;A. Parusiński
.证明了任意d次多项式P（x，y）在曲线y = ex + sin（x）（x > 0）上至多有2（d + 2）12个零点.因此，我们推出的存在一个统一的界限的多项式的零点的数目固定次数的解析曲线上并不意味着该曲线属于一个O-最小结构。
. We prove that every polynomial P ( x,y ) of degree d has at most 2( d + 2) 12 zeros on the curve y = e x + sin( x ) , x > 0. As a consequence we deduce that the existence of a uniform bound for the number of zeros of polynomials of a fixed degree on an analytic curve does not imply that this curve belongs to an o-minimal structure.