arXiv subjects
Publications and source records attributed to Sheng Qin.
Jin and Rubinstein asked whether the fixed-level equivariant Tian's alpha invariant equals the fixed-level equivariant global log canonical threshold, and proved this equality for toric varieties. In this paper we provide a positive answer to Jin and Rubinstein's question in full generality. The main result of this paper was obtained by Chatgpt 5.5 pro, and the Danus system based on the Rethlas system.
We prove Shokurov's global index conjecture for foliations in dimension at most three. This answers a question of the first author, Meng, and Xie in dimension three. The main result of this paper is partially obtained by generative AI, particularly the Rethlas system.
We show that the total Cartier index of varieties with rational singularities in a bounded family is bounded. This solves a problem of Han and Jiang. The overall structure of the proof, which treats the surface case and the higher-dimensional case separately, was originated by generative AI, particularly the Rethlas system, and was substantially corrected and elaborated by hand.
This paper focuses on the active flow control (AFC) of the flow over a circular cylinder with synthetic jets through deep reinforcement learning (DRL) by implementing a reward function based on dynamic mode decomposition (DMD). As a main factor that affects the DRL model, the reward is determined by the information extracted from flow field by performing DMD on measurements through simulation. With the data-driven reward, the DRL model is able to learn the AFC policy through the more global information of the field, and instructs the mass flow rate of the synthetic jets. As a result of this type of AFC, the vortex street is stabilized with a reduction of approximately 8% in drag and an improvement of approximately 109% in recirculation area. Furthermore, the configuration of the flow modified by the AFC is studied with DMD on the velocity measurement of the complete flow field.