基于连续细节层次的地表模型实时绘制算法

研究地表模型的实时绘制,提高绘制速度及可信度。采用点到平均平面的误差度量和基于渐进网格的动态简化方法,使简化可随视点参数而动态变化。     

K-Fuzzy赋范空间与WF-Fuzzy赋范空间

研究了Ｋ－ｆｕｚｚｙ赋范空间与ＷＦ－ｆｕｚｚｙ赋范空间之间的关系,证明了Ｈａｕｓｄｏｒｆｆ的Ｋ－ｆｕｚｚｙ赋范空间与ＷＦ－ｆｕｚｚｙ赋范空间本质上是一致的。     

一致光滑Banach空间中一类非线性映象的迭代过程

在周海云等人的基础上继续研究挠动的Ｉｓｈｉｋａｗａ迭代过程的收敛性,所得结果统一和推广了近期一些相关结果。     

混合范数空间与面积积分

研究了混合范数空间Ｈ（ｐ,ｑ,α）中解析函数ｆ的面积积分Ａｒ（ｆ）和Ａｒ（ｔ,θ,ｆ）的增长性,对ｐ的不同取值,分别用Ａｒ（ｆ）和Ａｒ（ｔ,θ,ｆ）给出了ｆ∈Ｈ（ｐ,ｑ,α）的充分条件和必要条件。对Ｄ上的面积平均ｊ叶函数族,给出了充要条件。结果推广了Ｆ．Ｈｏｌｌａｎｄ,Ｊ．Ｂ．Ｔｗｏｍｅｙ和Ｓ．Ｙａｍａｓｈｉｔａ的主要结论。     

光子与弱引力场

使用几何光学的方法研究光跟引力场之间的相互作用,得到了在引力场中光的速度,从一个新的角度讨论了ReissnerNordström度规中光的偏折和雷达波延迟,从而验证了广义相对论.另外,几何光学的方法新颖简洁,在其他研究领域也有应用前景.最近讨论非常热烈的课题——强光在等离子体中传播的几何光学及度规光学问题——原则上是可以应用本文提供的新方法.     

模度量空间下的不动点定理

推广了模度量空间，针对一类被称之为Chatterjea映射，在适当的条件下，建立了映射T具有不动点的存在性和唯一性结果．     

双曲空间中混合型迭代的△-收敛定理

最近,文献(Fixed Point Theory and Applications,2013,122(1):1687-1812.)在CAT(0)空间中研究了一迭代方案的△-收敛性.受他们的启发,在双曲空间的框架下,介绍了一种新的迭代方案,并在一定条件下,证明了△-收敛定理,结果改进和推广了近期一些文献的相应结果.     

Linear structures,causal sets and topology

Causal set theory and the theory of linear structures (which has recently been developed by Tim Maudlin as an alternative to standard topology) share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin׳s more general framework and I characterise what Maudlin׳s topological concepts boil down to when applied to discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of causal sets that can be described in Maudlin׳s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin׳s theory. The value of this theory depends crucially on whether it is true that (a) its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and (b) it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On one hand, my theorems support (a). The theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine (b). Standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin׳s framework. This fact poses a challenge for the proponents of Maudlin׳s theory to prove it fruitful.     

R6中的Laguerre等参超曲面的分类

若超曲面的Laguerre形式为零且Laguerre第二基本形式的特征值(称为Laguerre主曲率)为常数,则称超曲面为Laguerre等参超曲面. 对$\mathbb{R}^{6}$中的Laguerre等参超曲面进行了研究,得到了分类定理.     

非阿基米德2-赋范空间的等距问题

推广了Mazur-Ulam定理和Aleksbndrov 问题到非阿基米德2-赋范空间。 证明了两个非阿基米德空间的任何2-等距是仿射的;一个单位距离保持映射是2-等距当且仅当它保持零距离。