分类： 数学 >> 控制和优化 提交时间： 2023-12-04
摘要： In this paper, we mainly dicuss the analytic conditions of copositivity of a class of 4th order 3-dimensional symmetric tensors. For a 4th order 3-dimensional symmetric tensor with its entries $1$ or $-1$, an analytic necessary and sufficient condition is given for its strict copositivity with the help of the properties of strictly semi-positive tensors. And by means of usual maxi-min theory, a necessary and sufficient condition is established for copositivity of such a tensor also. Applying these conclusions to a general 4th order 3-dimensional symmetric tensor, the analytic conditions are successfully obtained for verifying the (strict) copositivity, and these conditions can be very easily parsed and validated.
分类： 物理学 >> 基本粒子与场物理学 提交时间： 2023-12-04
摘要： In this paper, we present how to calculate the bounded from below or the vacuum stability of scalar potential for a general CP violating two-Higgs-doublet model by using the concepts of co-positivity and the gauge orbit spaces. Meanwhile, the semi-positive definiteness is prove for a class of 4th-order 2-dimensional complex tensor.
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