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
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,