All Results

Subjects: Management Science >> Science ology and Management

本文从学理层面指出科研诚信量化评价制度的形成根源来自路径依赖和制度锁定，并深入论证了科研诚信的度量困难、实践悖论与非理性风险。研究对于补充科学政策学理论、建构科研诚信外部规范学理基础，优化科研诚信外部规范的技术进路具有重要的现实参考意义。 |

Subjects: Management Science >> Science ology and Management

“科研诚信内部规范”和“科研诚信外部规范”的范式区分，为正确定义政府在科学事业管理中的未来角色提供了学理分析进路。本文基于经济学、法学、社会学、管理学等基本规律，从学理层面和科学制度化视角反思“科研诚信内部规范”的合理性及其失灵原因，指明了政府在科研诚信建设及科研体制改革中的“放、管、服”内容与边界。研究对于完善科学政策学，促进思想界、学术界参与“科研诚信外部规范”相关理论和技术的批判完善与前瞻性建构具基础性奠基意义。 |

Copositivity for 3rd order symmetric tensors and applications

刘佳蕊; 宋义生Subjects: Mathematics >> Mathematical Physics

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 4th order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity of 3th order 2 dimensional (3 dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th order tensors, the analytically sufficient conditions of copositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for $\mathbb{Z}_3$ scalar dark matter. |

submitted time
2019-11-23
Hits*19800*，
Downloads*1181*，
Comment
*0*

Analytical expressions of copositivity for 4th order symmetric tensors and applications

宋义生; 祁力群Subjects: Mathematics >> Control and Optimization.

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 copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are 4th order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of 4th order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for 4th order 2 dimensional symmetric tensors. For 4th order 3 dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) cpositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for 4th order 2 dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for 4th order 2 dimensional symmetric tensors. Finally, we apply these results to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson. |

submitted time
2019-08-30
Hits*16679*，
Downloads*1040*，
Comment
*0*

Upper bounds for Z$_1$-eigenvalues of generalized Hilbert tensors

孟娟; 宋义生Subjects: Mathematics >> Mathematics （General）

In this paper, we introduce the concept of Z$_1$-eigenvalue to infinite dimensional generalized Hilbert tensors (hypermatrix) $\mathcal{H}_\lambda^{\infty}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}})$, $$ \mathcal{H}_{i_{1}i_{2}\cdots i_{m}}=\frac{1}{i_{1}+i_{2}+\cdots i_{m}+\lambda},\ \lambda\in \mathbb{R}\setminus\mathbb{Z}^-;\ i_{1},i_{2},\cdots,i_{m}=0,1,2,\cdots,n,\cdots, $$ and proved that its $Z_1$-spectral radius is not larger than $\pi$ for $\lambda>\frac{1}{2}$, and is at most $\frac{\pi}{\sin{\lambda\pi}}$ for $\frac{1}{2}\geq \lambda>0$. Besides, the upper bound of $Z_1$-spectral radius of an $m$th-order $n$-dimensional generalized Hilbert tensor $\mathcal{H}_\lambda^n$ is obtained also, and such a bound only depends on $n$ and $\lambda$. |

submitted time
2017-12-12
Hits*6640*，
Downloads*1478*，
Comment
*0*

[1 Pages/ 5 Totals]