度量空间

Figure associated with the metric space subdominant hierarchical tree on the impact of the study given the equity portfolio in the stock prices of several series of economic factors the quantity and nature of the provision of useful information.

与图相关联的亚超度量空间上的分层树为研究影响给定股票组合的股价对数序列的经济因素的数量和性质提供了有用的信息。

Chapter 3, in the above system, gives out the definitions of topological new transitivity, topological transitivity, topological strong transitivity and topological conjugate of a sequence of maps, studies basic properties of the above topological conjugate, and obtains some main results, proves topological new transitivity and topological transitivity are equivalent u-under a compact metric space, a sequence of full maps and interchangeable with each other, and that some conclusions associated with topological conjugate.

第三章，在上述系统中给出了一列映射的拓扑新传递、拓扑传递、拓扑强传递和拓扑共轭的定义；研究了一列映射的拓扑共轭的基本性质，得到了一些主要结果；证明了在底空间是紧致度量空间、一列映射是满映射并且两两可交换的条件下拓扑新传递和拓扑传递是等价的；还证明了几个与拓扑共轭相关的结论。

This method bases on distance transformation in Euclidean metric with the computational complexity of O(2+kn,and is the same with non-Euclidean metric space.

基于欧氏空间中离散点集的2阶V图距离变换原理，论述了栅格形式下离散点集和一般点集图形的2阶V图生成的方法，确定了它的时间复杂性为O(2+kn，适用于欧氏及非欧度量空间的自然图形2阶V图构造。

In Chapter One,we find the relationship between strong open set condition , Hausdorff dimension,the positivity of the Hausdorff measure and β space of graph-directed self-similar sets in complete metric spaces.

在第一章中，我们讨论了在度量空间中，图定向自相似集的强开集条件、Hausdorff维数，正的Hausdorff测度和β空间之间的关系。

Three counter-examples of topological space are proposed in this study: There are two metric spaces, X and Y, in which and are isometric, whileand are not isometric; Non-metric tight regular space is a counter-example of the separation of topological space; No non-zero continuous linear functionals of the linear topological space is a counter-example of linear topological space.

这里给出三个反例，存在两个度量空间X与Y，使X^2与Y^2等距而X与Y并不等距是拓扑空间中的反例；存在不可度量化的紧的完全正规空间是拓扑空间分离性的反例；不存在非零连续线性泛函的线性拓扑空间是线性拓扑空间的反例。

In this paper, the Lipschitz condition in calculus is generalized into metric space.

将数学分析中的Lipschitz条件在实数空间上的应用推广到度量空间上。

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

In this dissertation, we investigate the theory of fuzzy number space and fuzzy metric space, the main works of t...

本文研究了模糊数空间和模糊度量空间的有关理论，主要内容如下

Some important properties of L-topological spaces, induced topological spaces, fuzzy real lines and fuzzy metric spaces in topology on lattices are obtained.

在格上拓扑中，对L-拓扑空间、诱导拓扑空间、fuzzy 实直线和fuzzy度量空间等的性质研究，得到了一系列重要的结果。

By properties of a real function, fixed points problem on two complete metric spaces are discussed.The result generalizes corresponding result of Fisher.Moreover, this result provides a general convergence rate estimate. Meanwhile, we discuss the existence of fixed point on two normed linear spaces under the condition of weak topology, and we obtain a new fixed point theorem.

利用实函数性质，讨论了两个不同度量空间中两个映象乘积的不动点问题，推广了Fisher的主要结果，并给了出逼近不动点的敛速估计；同时，在弱拓扑的意义下，利用分析的方法，讨论了赋范空间中有关映象不动点的存在性，得到一个新的不动点定理。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。