Proof of the fundamental gap conjecture Ben Andrews,Julie Clutterbuck Full-Text Cite this paper Add to My Lib Abstract: We prove the Fundamental Gap Conjecture, which states that the difference between the first two Dirichlet eigenvalues (the spectral gap) of a Schr\"odinger operator with con...
This is a brief survey of recent results culminating in the proof of the fundamental gap conjecture by Andrews and Clutterbuck [1]. Recalling the Bakry-Émery geometry and laplacian, we present our joint results with Z. Lu [14] which demonstrate an intimate connection between the first non-...
Fuzhou Gong, Huaiqian Li, Dejun Luo, A probabilistic proof of the fundamental gap con- jecture via the coupling by reflection. arXiv:1303.2459v1.F.Z. Gong, H.Q. Li, D.J. Luo. A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection. To appear in ...
We show that there are at most five slopes on \partial M whose associated Dehn fillings have either a finite or an infinite cyclic fundamental group. Furthermore, the distance between two slopes yielding such manifolds is no more than three, and there is at most one pair of slopes which ...
This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence proof—by focusing on the role of radiation in the emerging theory. We argue that the radiation problem played a key role in early quantum mechanics,...
A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection (vol 44, pg 423, 2016) Fuzhou Gong, Huaiqian Li and Dejun Luo, The fundamental gap conjecture: a probabilistic approach via the coupling by reflection. http://arxiv.org/abs/1303.2459.Fuzhou Gong, Huaiqian...
Proof assistants have also been used to verify advanced results in mathematics, such as the Odd Order Theorem, using Coq [12], and the proof of the Kepler conjecture, using HOL-Light and Isabelle [14]. Meanwhile, on the other side of the great chasm between theory and practice, software ...
reveal the gap between embodied learning theory and using theory to design effective learning environments aimed at promoting science, technology, engineering, and mathematics learning. Generally, learning theories under-constrain designs of effective instruction and learning environments, which fundamentally ...
Fuzhou Gong, Huaiqian Li, Dejun Luo, A probabilistic proof of the fundamental gap con- jecture via the coupling by reflection. arXiv:1303.2459v1.Fu-Zhou Gong, Huaiqian Li and Dejun Luo, A probabilistic proof of the fundamental gap conjecture via the coupling by reflection. arXiv:1303.2459...