128 citations · 465 across the 27 of their papers we have counts for
29 papers
New Pareto Z-eigenvalue localization theorems for tensors with applications
Licai Shao, Xingong Shao, Xingong Zhang +1
In this paper, we establish some new localization sets for Pareto Z-eigenvalues of tensor eigenvalue complementarity problems and discuss the relationships among existing ones. As…
Vacuum stability conditions of the general two-Higgs-doublet potential
Yisheng Song
In this paper, we present the novel analytical expressions for the bounded-from-below or the vacuum stability conditions of scalar potential for a general CP violating two-Higgs-do…
A Comprehensive Survey of Few-shot Learning: Evolution, Applications, Challenges, and Opportunities
Yisheng Song, Ting Wang, Subrota K Mondal +1
Few-shot learning (FSL) has emerged as an effective learning method and shows great potential. Despite the recent creative works in tackling FSL tasks, learning valid information r…
Co-positivity of tensors and bounded from below conditions of CP conserving two-Higgs-doublet potential
Yisheng Song
In this paper, the analytic sufficient and necessary conditions are obtained for the CP conserving two-Higgs-doublet potential to be bounded from below by using the co-positivity o…
Copositivity for a class of fourth order symmetric tensors given by scalar dark matter
Yisheng Song, Xudong Li
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, w…
Boundedness from below conditions for a general scalar potential of two real scalars fields and the Higgs boson
Yisheng Song, Liqun Qi
The most general scalar potential of two real scalar fields and a Higgs boson is a quartic homogeneous polynomial about 3 variables, which defines a 4th order 3 dimensional symmetr…
Positivity Conditions for Cubic, Quartic and Quintic Polynomials
Liqun Qi, Yisheng Song, Xinzhen Zhang
We present a necessary and sufficient condition for a cubic polynomial to be positive for all positive reals. We identify the set where the cubic polynomial is nonnegative but not…
Copositivity of Three-Dimensional Symmetric Tensors
Liqun Qi, Yisheng Song, Xinzhen Zhang
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 or…
Copositivity for 3rd order symmetric tensors and applications
Jiarui Liu, Yisheng Song
The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of…
Analytical expressions of copositivity for 4th order symmetric tensors and applications
Yisheng Song, Liqun Qi
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 ar…
Upper bounds for Z-eigenvalues of generalized Hilbert tensors
Juan Meng, Yisheng Song
In this paper, we introduce the concept of Z-eigenvalue to infinite dimensional generalized Hilbert tensors (hypermatrix) $\mathcal{H}_λ^{\infty}=(\mathcal{H}_{i_{1}i_{2}\cdots…
B tensors and tensor complementarity problems
Yisheng Song, Wei Mei
In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the…
Infinite and finite dimensional generalized Hilbert tensors
Wei Mei, Yisheng Song
In this paper, we introduce the concept of an -order -dimensional generalized Hilbert tensor , $$ \mathcal{H}_{i_{1}i_…
Infinite dimensional Hilbert tensors on spaces of analytic functions
Yisheng Song, Liqun Qi
In this paper, the order infinite dimensional Hilbert tensor (hypermatrix) is intrduced to define an -homogeneous operator on the spaces of analytic functions, which is…
Pazy's fixed point theorem with respect to the partial order in uniformly convex Banach spaces
Yisheng Song, Rudong Chen
In this paper, the Pazy's Fixed Point Theorems of monotone nonexpansive mapping are proved in a uniformly convex Banach space with the partial order "". That is,…
Spectral projected gradient methods for generalized tensor eigenvalue complementarity problem
Gaohang Yu, Yisheng Song, Yi Xu +1
This paper looks at the tensor eigenvalue complementarity problem (TEiCP) which arises from the stability analysis of finite dimensional mechanical systems and is closely related t…
An adaptive gradient method for computing generalized tensor eigenpairs
Gaohang Yu, Zefeng Yu, Yi Xu +1
High order tensor arises more and more often in signal processing,data analysis, higher-order statistics, as well as imaging sciences. In this paper, an adaptive gradient (AG) meth…
Eigenvalues and structured properties of P-tensors
Yisheng Song, Liqun Qi
We define two new constants associated with real eigenvalues of a P-tensor. With the help of these two constants, in the case of P-tensors, we establish upper bounds of two importa…
Strictly semi-positive tensors and the boundedness of tensor complementarity problems
Yisheng Song, Liqun Qi
In this paper, we prove that all H(Z)-eigenvalues of each principal sub-tensor of a strictly semi-positive tensor are positive. We define two new constants associated with…
Properties of Solution set of Tensor Complementarity Problem
Yisheng Song, Gaohang Yu
The tensor complementarity problem is a specially structured nonlinear complementarity problem, then it has its particular and nice properties other than ones of the classical nonl…
Tensor Complementarity Problem and Semi-positive Tensors
Yisheng Song, Liqun Qi
The tensor complementarity problem $(\q, \mathcal{A})$ is to $$\mbox{ find } \x \in \mathbb{R}^n\mbox{ such that }\x \geq \0, \q + \mathcal{A}\x^{m-1} \geq \0, \mbox{ and }\x^\top…
Properties of Tensor Complementarity Problem and Some Classes of Structured Tensors
Yisheng Song, Liqun Qi
This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor such that the tensor complementarity problem $(\q, \mathcal{A})$: $$\mbox{ finding…
An Even Order Symmetric B Tensor is Positive Definite
Liqun Qi, Yisheng Song
It is easily checkable if a given tensor is a B tensor, or a B tensor or not. In this paper, we show that a symmetric B tensor can always be decomposed to the sum of a strictly…
Properties of Some Classes of Structured Tensors
Yisheng Song, Liqun Qi
In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured t…