کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8902299 | 1631962 | 2018 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Bounds on the number of solutions of polynomial systems and the Betti numbers of real piecewise algebraic hypersurfaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Bounds on the number of solutions of polynomial systems and the Betti numbers of real piecewise algebraic hypersurfaces Bounds on the number of solutions of polynomial systems and the Betti numbers of real piecewise algebraic hypersurfaces](/preview/png/8902299.png)
چکیده انگلیسی
This paper, based on Bihan and Sottile's method which reduces a polynomial system to its Gale dual system and then bounds the number of solutions of this Gale system, proves that a real coefficient polynomial system with n equations and with n variables involving n+k+1 monomials has fewer than 27e53+8890âi=0kâ1(2i(nâ1)+1) positive solutions and 27e103+8890âi=0kâ1(2i(nâ1)+1) non-degenerate non-zero real solutions. This dramatically improves F. Bihan and F. Sottile's bounds of e2+342k2nk and e4+342k2nk respectively. Using the new upper bound for positive solutions, we establish restrictions to the sum of the Betti numbers of real piecewise algebraic hypersurfaces and real piecewise algebraic curves. A new bound on the number of compact components of algebraic hypersurfaces in R>n is also given.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 329, February 2018, Pages 147-163
Journal: Journal of Computational and Applied Mathematics - Volume 329, February 2018, Pages 147-163
نویسندگان
Yisheng Lai, Weiping Du, Dexin Duan, Xiaoke Fang,