Mathematical Large Language Models (LLMs) have demonstrated strong problem-solving capabilities, but their reasoning ability is often constrained by pattern recognition rather than true conceptual ...

Inspired by the pedagogical method of "proof by counterexamples" widely used in human mathematics education, our work aims to enhance Large Language Models’ (LLMs) ability to conduct mathematical ...

Abstract: Learning-based methods have gained popularity for training candidate Control Barrier Functions (CBFs) to satisfy the CBF conditions on a finite set of sampled states. However, since the CBF ...

This is a preview. Log in through your library . Abstract We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the ...

Abstract: Polynomial Lyapunov function $\mathcal{V}({\mathbf{x}})$ provides mathematically rigorous that converts stability analysis into efficiently solvable optimization problem. Traditional ...