Characterizations of Riesz spaces with b-property

A Riesz space E is said to have b-property if each subset which is order bounded in E^~~ is order bounded in E. The relationship between b-property and completeness, being a retract and the absolute weak topology |σ|(E^~, E) is studied. Perfect Riesz spaces are characterized in terms of b-property. It is shown that b-property coincides with the Levi property in Dedekind complete Frechet lattices.      

Bergman型空间的加权复合算子

Let g1,g2 be normal functions. For all 0 〈 p,q 〈 ∞, the necessary and sufficient conditions for weighted composition operators Tψ,φ ： A^Pg1 → A^Pg2 to be bounded or compact between Bergman type spaces on the unit ball of C^n are given.     

Topological representation for monadic implication algebras

In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.      

Numerical Schemes for Linear and Non-Linear Enhancement of DW-MRI

We consider the linear and non-linear enhancement of diffusion weighted magnetic resonance images (DW-MRI) to use contextual information in denoising and inferring fiber crossings. We describe the space of DW-MRI images in a moving frame of reference, attached to fiber fragments which allows for convection-diffusion along the fibers. Because of this approach, our method is naturally able to handle crossings in data. We will perform experiments showing the ability of the enhancement to infer information about crossing structures, even in diffusion tensor images (DTI) which are incapable of representing crossings themselves. We will present a novel non-linear enhancement technique which performs better than linear methods in areas around ventricles, thereby eliminating the need for additional preprocessing steps to segment out the ventricles. We pay special attention to the details of implementation of the various numerical schemes.     

基于郭仲衡先生现代张量分析及有限变形理论知识体系的相关研究

作为我国理性力学先驱之一的郭仲衡先生在其所著《张量(理论和应用)》以及《非线性弹性理论》中记述了现代张量分析以及有限变形理论知识体系.本文按有限维Euclid空间上微积分以及一般赋范线性空间上微分学认识相关知识体系的理论框架,相关思想及方法,阐述了有关思想及方法的发展及其应用.本文未涉及现代几何学在连续介质力学中的应用.     

单位球上βP空间到Za型空间的加权Cesàro算子

利用泛函分析多复变的方法,研究了单位球上βP空间到Za空间的加权Cesàro算子的有界性和紧性问题.获得了单位球上βP空间到Za空间的加权Cesàro算子为有界算子和紧算子的充要条件.     

单位球上μ-Bloch空间到Zygmund型空间的加权Cesàro算子

设α>0,g是单位球B上的全纯函数,μ(r)是［0,1）上的正规权函数,利用泛函分析多复变的方法,讨论了单位球上μ-Bloch空间到Zygmund型空间的加权Cesàro算子T_g的有界性和紧性问题.并给出了单位球上μ-Bloch空间到Zygmund型空间的加权Cesàro算子T_g为有界算子和紧算子的充要条件.     

Spaces and moduli spaces of Riemannian metrics

These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness properties. They also discuss several open problems and questions in the field.