强满层L-收敛空间的一个注记

众所周知,强满层L-收敛空间自然是满层L-收敛空间,但反之不成立。给出了满层L-收敛空间成为强满层L-收敛空间的一个充要条件。给出了一种生成满层L-收敛空间的方法,并由此构造了一个从满层L-收敛空间到强满层L-收敛空间的具体的反射。     

值域为坡代数的加权图和模糊图的范畴关系

坡代数是元素的乘法小于等于每个因子的加法幂等的半环。以坡代数为取值域,证明了加权图范畴可以作为余反射子范畴嵌入到模糊图范畴中去;如果坡代数的乘法有单位元,则这种嵌入还具有反射性。     

基于[k]-近邻与局部相似度的稀疏子空间聚类

为了获得结构更加合理的仿射矩阵,提出了一种基于[k]-近邻与局部相似度的稀疏子空间聚类算法。该算法首先计算每个点的[k]-近邻,并对其用[k]-近邻数据点进行线性表示,使仿射矩阵在整体稀疏的情况下保证局部的强线性关系。基于图论知识,利用数据的实际分布情况对仿射矩阵进行约束,使仿射矩阵进一步合理地等价于待进行谱聚类的相似矩阵。在人造数据集、随机生成的子空间数据集、图像数据集以及真实数据集上进行了实验,结果表明该算法是有效的。     

正则FI代数的MP滤子与同构基本定理

正则FI-代数是仅基于蕴涵算子在一般集合上建立的逻辑代数,它是[BR0]-代数和BL-代数的基础逻辑代数。基于经典代数的思想和方法,讨论了正则FI-代数的MP滤子与同构基本定理。引入正则FI-代数中MP滤子的概念,并讨论了其基本性质,给出了正则FI-代数中包含任意子集的最小MP滤子的构造方法;讨论了正则FI-代数的MP滤子和同余关系之间的内在联系;给出了正则FI-代数的同构基本定理。     

L-SLLSC同构L-SSC

对层次满层L-收敛空间引入了强左连续条件,证明了强左连续的层次满层L-收敛空间范畴:可以反射嵌入到层次满层L-收敛空间范畴;恰好可以刻画强满层L-收敛空间范畴。     

A note on locally bounded L-topological vector spaces

In this note, we give a counterexample showing that Theorem 5 in [C.-H. Yan, J.-X. Fang, Locally bounded L-topological vector spaces, Information Sciences 159 (2004) 273-281] is incorrect and offer a modified version of this theorem.     

Extension of continuity of maps between axiomatic locally finite spaces

The paper studies the extension problem of continuous maps between axiomatic locally finite spaces (for short, ALF spaces). Indeed, an ALF space is a topological space satisfying a set of axioms suggested in Kovalevsky [Axiomatic digital topology, J. Math. Imag. Vis. 26 (2006), pp. 41–58; Geometry of Locally Finite Spaces, Monograph, Berlin, 2008]. Further, an ALF space is defined by using a special kind of neighbourhood different from the topological neighbourhood in classical topology so that the continuity of maps between ALF spaces can be defined by preserving the neighbourhood relation (see Definition 10). Therefore, it is necessary to develop the notions of continuity, homeomorphism and local homeomorphism for such spaces by using the neighbourhood relation, which can be applicable in computer science. In the study of a deformation of an ALF space, we can develop a special kind of retract on ALF spaces. By using the retract, we can efficiently deal with the extension of continuous maps between ALF spaces.     

Dimensional properties of graphs and digital spaces

Many applications of digital image processing now deal with three- and higher-dimensional images. One way to represent n-dimensional digital images is to use the specialization graphs of subspaces of the Alexandroff topological space ⁿ (where denotes the integers with the Khalimsky line topology). In this paper the dimension of any such graph is defined in three ways, and the equivalence of the three definitions is established. Two of the definitions have a geometric basis and are closely related to the topological definition of inductive dimension; the third extends the Alexandroff dimension to graphs. Diagrams are given of graphs that are dimensionally correct discrete models of Euclidean spaces, n-dimensional spheres, a projective plane and a torus. New characterizations of n-dimensional (digital) surfaces are presented. Finally, the local structure of the space ⁿ is analyzed, and it is shown that ⁿ is an n-dimensional surface for all n1.     

格的模糊滤子与模糊素滤子的度量

主要研究了模糊代数中格的模糊（素）滤子的度量。首先给出了模糊（素）滤子度的新概念,并利用模糊（素）滤子度讨论了格的模糊子集是模糊（素）滤子的程度。其次,利用格的模糊集的（强）水平集得到了模糊（素）滤子的等价刻画。最后,讨论了任意多个模糊子集的交、直积的模糊（素）滤子度以及格的模糊子集在同态映射下像与原像的模糊（素）滤子度的性质。     

Pawlak近似空间中软集的软上（下）近似

在Pawlak近似空间上首次引入了等效软集的软上下近似的概念,研究了软上下近似的交、并、补代数运算的若干性质。结果令人满意。     

组播树维护策略的研究和实现

在IP组播模型、Overlay Network和Peer-to-Peer等技术的基础上发展而来的应用层组播技术正逐步成为一个流媒体直播的有效解决方案。树形组播方案构造简单,维护开销较小,可扩展性较好,比较适合于大规模的组播应用,但是其可靠性较差。通过比较研究其他P2P算法对节点稳定性和节点距离的衡量策略,对树形拓扑维护策略PeerCast进行改进,设计并实现了一个基于该改进算法的流媒体直播系统。应用表明,该算法能动态适应节点数达数百,节点生存周期较短的组播应用,较大程度上减小节点加入退出对QoS的影响。     

BR0代数的模糊理想与直觉模糊理想

引入BR₀代数的Fuzzy理想与素Fuzzy理想的概念;给出了Fuzzy理想与素Fuzzy理想的等价形式;在（素）Fuzzy理想基础之上又进一步引入了（素）直觉Fuzzy理想,并通过Fuzzy理想找到了它们与（素）理想之间的关系。