Related papers: Copositivity for 3rd order symmetric tensors and a…
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…
In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking…
This paper focuses on the strict copositivity analysis of 4th-order 3-dimensional symmetric tensors. A necessary and sufficient condition is provided for the strict copositivity of a fourth-order symmetric tensor. Subsequently, building…
In this paper, we mainly dicuss the non-negativity conditions for quartic homogeneous polynomials with 3 variables, which is the analytic conditions of copositivity of a class of 4th order 3-dimensional symmetric tensors. For a 4th order…
In this article, we mainly give the strictly copositive conditions of a special class of third order three dimensional symmetric tensors. More specifically, by means of the polynomial decomposition method, the analytic sufficient and…
The mathematical model of multiple microscopic particles potentials corresponds to a fourth order symmetric tensor with a particular structure in particle physics. In this paper, we mainly dedicate to the study of copositivity for a class…
For a 4th order 3-dimensional symmetric tensor with its some entries $1$ or $-1$, we show the analytic sufficient and necessary conditions of its positive definiteness. By applying these conclusions, several strict inequalities is bulit for…
In this paper, it is proved that (strict) copositivity of a symmetric tensor $\mathcal{A}$ is equivalent to the fact that every principal sub-tensor of $\mathcal{A}$ has no a (non-positive) negative $H^{++}$-eigenvalue. The necessary and…
For a 4th order 3-dimensional cyclic symmetric tensor, a sufficient and necessary condition is bulit for its positive semi-definiteness. A sufficient and necessary condition of positive definiteness is showed for a 4th order $n$-dimensional…
A scalar potential of the form $\lambda_{ab} \phi_a^2 \phi_b^2$ is bounded from below if its matrix of quartic couplings $\lambda_{ab}$ is copositive -- positive on non-negative vectors. Scalar potentials of this form occur naturally for…
A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositive tensors have found important applications in polynomial optimization and tensor complementarity…
In this paper, we consider higher order paired symmetric tensors and strongly paired symmetric tensors. Elasticity tensors and higher order elasticity tensors in solid mechanics are strongly paired symmetric tensors. A (strongly) paired…
Copositivity of tensors plays an important role in vacuum stability of a general scalar potential, polynomial optimization, tensor complementarity problem and tensor generalized eigenvalue complementarity problem. In this paper, we propose…
We find analytical vacuum stability or bounded below conditions for general scalar potentials of a few fields. After a brief review of copositivity we go beyond it. We discuss the vacuum stability conditions of the general potential of two…
Octupolar tensors are third order, completely symmetric and traceless tensors. Whereas in 2D an octupolar tensor has the same symmetries as an equilateral triangle and can ultimately be identified with a vector in the plane, the symmetries…
By applying the concepts of copositivity and using the gauge orbit spaces on the scalar potential, we derive analytic necessary and sufficient conditions which guarantee the boundedness of the scalar potential in all the directions in the…
We derive analytic necessary and sufficient conditions for the vacuum stability of the left-right symmetric model by using the concepts of copositivity and gauge orbit spaces. We also derive the conditions sufficient for successful symmetry…
By applying copositivity criterion to the scalar potential of the economical $3-3-1$ model, we derive necessary and sufficient bounded-from-below conditions at tree level. Although these are a large number of intricate inequalities for the…
In this paper, we give a necessary and sufficient condition for an even order three dimensional strongly symmetric circulant tensor to be positive semi-definite. In some cases, we show that this condition is also sufficient for this tensor…
It is well-known that a symmetric matrix with its entries $\pm1$ is not positive definite. But this is not ture for symmetric tensors (hyper-matrix). In this paper, we mainly dicuss the positive (semi-)definiteness criterion of a class of…