196 citations · 200 across the 4 of their papers we have counts for
4 papers · 1 filter
Examples on the sharpness of an inequality about multiplicities over hyperfields
Ziqi Liu
In this paper, the author introduces hyperfields and give some facts about the roots and multiplicities of polynomials over hyperfield based on \cite{2} and \cite{3}. Then he tests…
Examples on a Conjecture about Makar-Limanov Invariants of Affine Unique Factorization Domains
Ziqi Liu
The author introduces a conjecture about Makar-Limanov invariants of affine unique factorization domains over a field of characteristic zero. Then the author finds that the conject…
Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
Ziqi Liu, Wei Cai, Zhi-Qin John Xu
In this paper, we propose multi-scale deep neural networks (MscaleDNNs) using the idea of radial scaling in frequency domain and activation functions with compact support. The radi…
Finite Hyperfields of Order
Ziqi Liu
In this paper, the author introduces the concept and basic properties of finite (commutative) hyperfields. Also, the author shows that, up to isomorphism, there are exactly 2 hyper…