论文标题
三维对称张量的共同积极性
Copositivity of Three-Dimensional Symmetric Tensors
论文作者
论文摘要
在本文中，我们寻求可以分析可检查的必要条件，以实现三维对称张量的共同阳性。我们首先表明，对于一般的三阶三维对称张量，这意味着解决四分之一方程和一些二次方程。所有这些都可以通过分析解决。因此，我们提出了一种分析方法来检查三阶三维对称张量的三阶的共阳性。然后，我们考虑了$ \ mathbb {z} _3 $标量暗物质的真空稳定性模型。这是一个特殊的第四阶三维对称张量。我们表明，通过使用Ulrich和Watson在1994年给出的结果，可以给出分析表达的该模型的必要条件。
In this paper, we seek analytically checkable necessary and sufficient condition for copositivity of a three-dimensional symmetric tensor. We first show that for a general third order three-dimensional symmetric tensor, this means to solve a quartic equation and some quadratic equations. All of them can be solved analytically. Thus, we present an analytical way to check copositivity of a third order three dimensional symmetric tensor. Then, we consider a model of vacuum stability for $\mathbb{Z}_3$ scalar dark matter. This is a special fourth order three-dimensional symmetric tensor. We show that an analytically expressed necessary and sufficient condition for this model bounded from below can be given, by using a result given by Ulrich and Watson in 1994.
