The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

浅析“四项负责制”在高校图书馆的实施——以湖北工程学院图书馆为例

分别从"四项负责制"的基本概念入手,阐述了在高校图书馆实施"四项负责制"的基本内容及基本要求,以湖北工程学院图书馆为例,介绍了该馆倡导和推行"四项负责制"的情况,以提高图书馆整体服务质量。     

Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.     

New Develoopment of the Basic Theory of Extenics

In this paper,the new development of three basic theories of Extenics,incluing basic-element theory,extension set theory and extension logic theory ,has been introduced.And the new theoretical frame of Extenics has also been set forth.     

对高校道德实践教育的探讨

文章从道德教育的实践要求、特征、途径等方面，阐述了道德实践在道德教育过程中的地位和作用，并从高校道德教育实际出发，提出了加强道德实践训练的有关措施与方法。     

浅谈功率因数的补偿及其应用

根据我国当前电力系统运行情况，对电网无功功率补偿的必要性及通用补偿方法及其装置进行了具体阐述。     

以人为本的教学理念与高校体育教学

以人为本的教学理念是现代教育影响最大的教育思想之一，它更注重情感教育和创新教育．从教学情境、课程内容、教学方法和学生学习方式人手，本文对以人为本的教学理念与高校体育教学进行了研究．     

关于我区非计算机专业计算机基础教育的几点思考

针对非计算机专业的计算机基础教育是国内正研究的一项重要的课题．在信息技术日新月异，高速发展的今天，意义重大。本是根据计算机基础教育发展的要求并结合自己的教学实践对非计算机专业的计算机基础教育发表一些看法以供大家共同探讨。     

论住宅户型设计

为适应现代人居住观念的变化，结合设计工作的实践，分别就住宅户型设计中的户内空间序列以及起居室、卧室、厨房、卫生间的设计理念、设计原则和有关具体问题进行了探讨。