Banach空间中线性发展方程的初值最优控制问题

本文讨论一般 Banach 空间X上发展方程(?)+Ay(t)=0,y(O)=v的初值最优控制问题。通过引入控制函数空间的方法,证明了最优控制的存在性,并给出刻划最优控制的优化系统。本文是[1]Lions.J.L.的结果的一个推广,那里要假定 Banach 空间X是自反的,甚至是 Hilbert 空间。

半序空间的两个不动点定理

本文主要提出了半序空间的两个不动点定理,并予以证明。

基于螺旋理论的多模式移动3-RSR并联机构奇异性分析

针对3-RSR并联机构在运动过程中的奇异位形,提出了一种基于螺旋理论、几何代数法和空间线性几何理论的新方法,对3-RSR并联机构的全姿态多运动模式进行奇异性分析.该方法首先运用螺旋理论求出3-RSR并联机构的完整雅克比矩阵,然后通过代数法和几何作图法表示出机构各分支的反螺旋,再结合空间线性几何理论分析反螺旋相关性,得出固定模式下机构的奇异性图解,由此对全姿态多运动模式进行奇异性分析.结果表明,该方法能够更加简洁、直观地表示出3-RSR并联机构在两种运动模式下的奇异位形,且不需要大量计算,也适用于其他多模式移动并联机构的奇异位形求解.

基于Mathematica的量纲分析及其应用

将量纲分析中的Π定理用线性空间表示,建立一种量纲分析的系统方法,并利用科学计算软件Mathematica 9提供的新功能,使量纲分析变得方便易行.

关于可测集值映射的Egorov定理

本文讨论了取值于可分自反 Banach 空间中可测集值映射序列的 Egorov 型收敛定理,在几种不同拓扑收敛意义下,刻划了可测集值映射序列的几乎处处收敛.

CPT-Frames for Non-Hermitian Hamiltonians

Based on the PT-symmetric quantum theory, the concepts of PT-frame, PT-symmetric operator and CPT-frame on a Hilbert space K and for an operator on K are proposed. It is proved that the spectrum and point spectrum of a PT-symmetric linear operator are both symmetric with respect to the real axis and the eigenvalues of an unbroken PT-symmetric operator are real. For a linear operator H on Cd, it is proved that H has unbroken PT- symmetry if and only if it has d different eigenvalues and the corresponding eigenstates are eigenstates of PT. Given a CPT-frame on K, a new positive inner product on K is induced and called CPT-inner product. Te relationship between the CPT-adjoint and the Dirac adjoint of a densely defined linear operator is derived, and it is proved that an operator which has a bounded CPT-frame is CPT-Hermitian if and only if it is T-symmetric, in that case, it is similar to a Hermitian operator. The existence of an operator C consisting of a CPT-frame is discussed, These concepts and results will serve a mathematical discussion about PT-symmetric quantum mechanics.

Strong Convergence Theorems for Asymptotically Strictly Pseudocontractive Maps in Hilbert Spaces

The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive maps in Hilbert spaces to have strong convergence. Our results extend those of Kim, Xu, Nakajo, Takahashi and many others.

The Moduli Space in the Gauged Linear Sigma Model

This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the authors focus on the description of the moduli.