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。     

偏序半群的n素理想、偏序同态与商序同态

通过可换偏序半群的素理想和n素理想,刻画了偏序半群的偏序同态与商序同态的一些重要性质,并得到了一些重要的结论。     

带p(x)-双调和算子的Kirchhoff型问题解的存在性

研究了一类带p(x)-双调和算子的Kirchhoff型问题解的存在性,利用临界点定理,得到问题至少存在一个非平凡弱解的充分条件.     

关于序Γ－半群的广义直觉模糊子集

笔者主要研究了序Γ－半群的广义第一（二）直觉模糊左（右、内禀）理想的若干性质，推广了若干已知结果。     

弱相容映象的公共不动点定理

在完备度量空间中,证明了弱相容自映象的公共不动点的存在性和唯一性,改进和推广了文献[1]中的定理3.3及度量空间中的一些已知结果.     

改进的加权调和平均算子及其在多属性决策中应用

在加权调和平均（WHA）算子的基础上,提出了信息数据集结的有序加权调和平均（OWHA）算子和组合加权调和平均（CWHA）算子,探讨了它们的一些性质关系,给出了OWHA算子和CWHA算子应用于多属性决策的方法,最后通过实例分析表明该决策方法是有效和可行的.     

非线性优化的广义投影变尺度算法及超线性收敛性

结合罚函数法的思想,提出一种初始点任意的广义投影变尺度算法求解非线性等式和不等式约束优化问题,克服了Maratos效应的校正方向自动产生显式表达式,并在适当的条件下证明了算法是全局收敛的,且具有超线性收敛性.实验结果表明算法有效.