5 papers
Optimal Configurations for Mordell's Problem
Xiang Ji, Tiancheng Xu, Wensheng Yu
Mordell's problem asks for the largest product of squared pairwise distances among points in the complex plane with a prescribed sum of squared distances from the origin. When…
Math Foundation Formalization Agent: A General-Purpose Approach to Formalizing Mathematical Foundations
Jiaxin Xie, Guowei Dou, Xiang Ji +1
Mathematical formalization plays an important role in establishing rigorous and machine-verifiable foundations for mathematical reasoning. With the development of large language mo…
An Alternative Proof of the SPR Synthesis Theorem for Polynomial Segments of Arbitrary Order
Zhengtai Xiong, Tiancheng Xu, Xiang Ji +3
For any positive integer n and any two monic real Hurwitz polynomials of degree n, every convex combination of the two is Hurwitz stable if and only if there exists a common numera…
Robust Strictly Positive Real Synthesis for Sixth-Order Interval Polynomial Families
Tiancheng Xu, Guowei Dou, Xiang Ji +2
Every Hurwitz-stable interval family of monic real polynomials of degree six admits a single real numerator of degree six that makes all the associated transfer functions strictly…
LiteSC: Lightweight Semantic Communication for Robust Wireless Telesurgical Video Transmission
Zexin Deng, Zhenhui Yuan, Xiang Ji +2
Reliable laparoscopic video is essential for telesurgery, yet fixed-rate digital transmission can degrade abruptly under poor channel conditions. We propose LiteSC, a lightweight s…