Rn上无奇点C1流的强极限跟踪性

本文证明了R 上无奇点C1流的双曲集附近具有强极限跟踪性.     

完全与截尾样本时回归函数的核估计

本文得到了完全与截尾样本时回归函数核估计的强相合性．接着，构造了截尾样本的改良核估计，在Ｅ｜Ｙ｜＜∞下，得到了其强相合性．     

具有跟踪性质的连续半流

在这篇论文中，我们给出了连续半流的跟踪性质与其逆极限的跟踪性质之间的一些等价条件，并且做为应用，我们证明了具有强跟踪性质的连续半流在其游荡集上的限制也具有强跟踪性质以及连续半流的谱分解定理。     

伪轨和拓扑压

本文证明了紧度量空间上连续自映射的拓扑压可分别用分离的伪轨集及分离的周期协轨集予以描述．作为应用，得到了具有跟踪性的可扩系统的拓扑压与其周期点之间的明确关系式．     

弱误差结构下非参数,半参数回归模型

在弱误差结构下，该文获得了一类非参数模型回归函数估计量的强一致相合性，进而获得了一类半参数模型的参数分量估计的强相合性．     

伪轨跟踪与伪移位不变集

本文证明了对于具有伪轨跟踪性质的紧致度量空间上的连续满射ｆ，存在某个正整数ｎ，有相对于ｆｎ的伪移位不变集的充要条件是存在非回归点的链回归点，或是存在非几乎周期点的回归点     

Rn上无奇点C1流的强极限跟踪性

本文证明了Rⁿ上无奇点C¹流的双曲集附近具有强极限跟踪性。     

跟踪雷达测量误差的统计模型(Ⅰ):模型的建立

本文提出以如下具有慢时变万差的线性回归－自回归混合模型用于描述跟踪雷达测量误差的变化规律，并提出了模型个数的估计方法．数值例子表明，本文提出的模型能较好地拟合跟踪雷达误差数据．     

强S—Lindelof空间

利用强半开集定义了强S-Lindelof可数性的概念,讨论了其基本性质．证明了强S-Lindelof性对强半闭子集是遗传的,具有强半同胚不变性等,并给出了强S-Lindelof空间的一些应用．     

m（n）相依样本k近邻回归函数估计的一致强相合性

对一大类非参数回归函数，基于m（n）相依样本构造了回归函数的近邻估计并在合适的条件下获得了估计的一致强相合性及收敛速度．     

关于满足弱开集条件的自相似测度的局部维数的注记

对于自相似集合,已知开集条件与强开集条件是等价的,我们讨论了强开集条件的基些性质,并给出了自似测度局部维数研究的一个应用。     

Strong Minkowski Separation and Co-Drop Property

In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.     

动力系统在链回复集上的拓扑稳定性

本文证明, 紧度量空间上的同胚, 若在链回复集上可扩且具有伪轨跟踪性, 则是链拓扑稳定的.     

关于奇强协调图的一些结果

对于一个(p,q)-图G,如果存在一个单射f:V(G)→{0,1,…,2q-1},使得边标号集合{f(uv)|uv∈E(G)}={1,3,5,…,2q-1},其中边标号为f(uv)=f(u)+f(v),那么称G是奇强协调图,并称f是G的一个奇强协调标号.通过研究若干奇强协调图,得出一些奇强协调图的性质.     

不分明化拓扑中强紧性

在不分明化拓扑空间中,从pre-开集出发引入了强紧性的概念,并且给出了它的一些性质.这些概念的结合有助于我们对不分明化拓扑的研究.     

Interiors of sets of vector fields with shadowing corresponding to certain classes of reparameterizations

The structure of the C ¹-interiors of sets of vector fields with various forms of the shadowing property is studied. The fundamental difference between the problem under consideration and its counterpart for discrete dynamical systems generated by diffeomorphisms is the reparameterization of shadowing orbits. Depending on the type of reparameterization, Lipschitz and oriented shadowing properties are distinguished. As is known, structurally stable vector fields have the Lipschitz shadowing property. Let X be a vector field, and let p and q be its points of rest or closed orbits. Suppose that the stable manifold of p and the unstable manifold of q have a nontransversal intersection point. It is shown that, in this case, the vector field X does not have the Lipschitz shadowing property. If one of the orbits p and q is closed, then X does not have the oriented shadowing property. These assertions imply that the C ¹-interior of the set of vector fields with the Lipschitz shadowing property coincides with the set of structurally stable vector fields. If the dimension of the manifold under consideration is at most 3, then a similar result is valid for the oriented shadowing property. We study the structure of the C ¹-interiors of sets of vector fields with various forms of the shadowing property. It is shown that, in the case of the Lipschitz shadowing property, it coincides with the set of structurally stable systems. For manifolds of dimension at most 3, a similar result is valid for the oriented shadowing property.     

Shadowing and Inverse Shadowing for C^1 Endomorphisms

In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also ＂uniform＂ with respect to C^1 perturbation.     

强S-仿紧空间

在一般拓扑空间中给出了强S-仿紧空间的概念,研究了它的性质并给出了Hausdorff空间下它的等价刻画,同时讨论了它的相对性质.