Tin tức nổi bật
Hội thảo sắp diễn ra
27/09/25, Hội nghị, hội thảo:
Gặp gỡ Toán học 2025 - Hội thảo Khoa học các nhà nghiên cứu trẻ"
06/11/25, Hội nghị, hội thảo:
Lectures on selected areas in Pure Mathematics
24/11/25, Hội nghị, hội thảo:
Hội nghị toàn quốc lần thứ VII “Xác suất - Thống kê: Nghiên cứu, ứng dụng và giảng dạy”
Xuất bản mới
Nguyễn Hữu Sáu,
Piyapong Niamsup,
Vũ Ngọc Phát,
Linear Programming Approach to Constrained Stabilization of Positive Differential-Difference Equations With Unbounded Delay,
Optimal Control Applications and Methods, 2025; 46:2581--2594
(SCI-E, Scopus)
.
Đỗ Hoàng Sơn,
Vũ Đức Việt,
Quantitative stability for the complex Monge-Ampère equations II,
Calculus of Variations and Partial Differential Equations 64 (2025), no. 8, Paper No. 269
(SCI-E, Scopus)
.
Giang Trung Hiếu,
Existence and uniqueness results for a nonlinear Budiansky-Sanders shell model,
Journal of Engineering Mathematics, Volume 151, article number 5, (2025)
(SCI-E, Scopus)
.
Deciding non-negativity of generic polynomials based on Sturm’s theorem
Người báo cáo: Vũ Trung Hiếu (University of Tokyo, Japan)
Date: 14:00-15:00, 02 October 2025
Venue: Room 301, A5, Institute of Mathematics
Abstract: We address the problem of deciding the non-negativity of a real polynomial $f$. To this end, we employ the critical value polynomial $varphi_f,$ whose roots are the complex critical values of $f$. First, we show that, under a genericity assumption, this decision problem reduces to determining whether $varphi_f$ has only non-negative roots. This reduction allows us to apply Sturm’s theorem to resolve the problem. Second, we propose a symbolic algorithm for deciding non-negativity and analyze its bit complexity in the case where the input polynomial has rational coefficients. The talk is based on joint work with Nguyen Hong Duc and Akiko Takeda