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)
.
The Ordered Multiplicity Inverse Eigenvalue Sequence Problem, Powers Of Graphs, And More!
Người báo cáo: Franklin H. J. Kenter (U.S. Naval Academy)
Time: 9:30 -- 11: 00, October 01, 2025
Venue: Room 612, A6, Institute of Mathematics-VAST
Abstract: Given a matrix pattern, one may ask: "What sets of eigenvalues are possible over all such matrices?'' This problem is very hard! A mild relaxation of this question considers the multiplicity sequence instead of the exact eigenvalues themselves. For instance, ``Given an $n times n$ matrix pattern and an ordered partition $(m_1, ldots, m_q)$ of $n$, is there a matrix with that pattern where the $i$-th distinct eigenvalue has multiplicity $m_i$?'' This is known as the ``ordered multiplicity inverse eigenvalue sequence problem''. Recent work has solved this problem for all symmetric matrix patterns up to size $6 times 6$.
In this talk, we develop methods using combinatorial optimization on networks to approach this otherwise linear-algebraic problem. We apply many different ``zero forcing'' techniques to simultaneously bound on sums of various multiplicities. Not only can we verify the result above in a more straight-forward manner, but we apply our techniques to more domains including skew-symmetric matrices, nonnegative matrices, among others. This is joint work with Jephian C.-H. Lin (National Sun Yat-sen University, Taiwan).