点集拓扑理论在拓扑关系描述中的应用

在R∧n中两个n维面状空间目标之间,可以根据4元交拓扑不变量的空与非空取值情况区分8种拓扑关系,但仅用4元交模型不能区分一些拓扑不同胚的空间目标之间的拓扑关系,在Egen-hofer等人提出的目标之间非空交的维数和分离数的基础上增加两目差的分离数及目标间相交边界和相交内部的度量尺度,使空间目标之间拓扑关系的描述更为完善。     

论GIS空间关系描述中存在的几个基本问题

首先剖析了空间关系描述中"空间"的概念,论述了拓扑关系具有与实体位置本身无关的特性,进而阐述了空间实体的拓扑表达,分析了拓扑空间描述存在的不足,以及与地理环境、地理空间认知的相关性,提出了纳入度量特性的拓扑空间关系描述的方法。     

拓扑关系与性质及其在空间推理中的应用

首先根据笔者以前的研究成果,给出了两个空间实体之间完备、唯一的拓扑关系形式化表达,进而论述了它们之间存在的性质。从这些性质出发,得出了相互间空间关系复合的结果。空间推理从广义上而言,是指从已知信息推导未知信息的理论和方法,据其使用的理论基础,可以分为代数推理和逻辑推理,空间复合的结果可以直接用于代数推理,又可以作为前提条件用于逻辑推理。     

上下文感知计算中的时序表示与推理方法研究

分析了基于本体论的上下文建模方法,对现有上下文本体进行了分类和比较,并针对其在时序表示方面存在的问题,提出了基于资源描述框架(RDF)具体化的上下文时序信息表示方法,扩展了上下文本体的描述能力.同时针对上下文感知中的时序推理问题,提出了一个持续时间推理算法;另外还通过整合Allen区间代数和本体推理实现了时序关系推理.最后通过实验验证了上述两种时序推理方法的效率.     

Vietoris拓扑空间中的一些紧致性质

研究了Vietoris拓扑空间F0(X)中的一些紧致性质与拓扑空间X中紧致性质的关系,证明了（1）F（U^-1,…U^-n)在Vietoris拓扑空间F0（X)强紧致的充要条件是对每个i∈｛1,…,n｝,U^ni在拓扑空间X中是紧致的：（2）如果F（X）是Vietoris拓扑空间F0（X）中的闭子集,那么X是局部紧的充要条件是F（X）是Vietoris拓扑空间F0（X）中的局部紧致子空间。     

基于Voronoi区的GIS中方向关系的描述与计算

方向关系在地理信息系统(GIS)中占据着十分重要的地位,由于它的模糊性和依赖空间实体形状的特性,使得它的形式化描述和判断比较困难。本文在三角形模型(CDR)方法的基础上,利用最小矩形(MBR)四边的Voronoi多边形及其边界,形式化描述了方向关系,进而将方向关系分为主方向关系和次方向关系,并分别给出了两者利用MBR四边Voronoi多边形及其边界判断的算法。     

GIS空间拓扑关系概率描述

重点研究二维空间中不确定目标间的拓扑关系的判定。利用概率论与数理统计的方法计算出某随机点落在另一随机点的左边或右边的概率,并根据概率值的大小定量判定出两随机点间的拓扑关系。     

集值映射空间的度量化

本文研究拓扑空间到一致空间上点紧致的连续集值映射空间在紧开拓扑、一致收敛拓扑、紧致处一致收敛拓扑和度量拓扑等之下它们之间的关系,利用诱导映射和嵌入的方法给出了拓扑空间到实直线上点紧致的连续集值映射空间可度量化的若干等价条件。这些结论将单值连续映射空间上的可度量化结果推广到了点紧致的连续集值映射空间上。     

多工况应力约束下的拓扑优化格栅

提出一种多工况应力约束下格栅结构的拓扑优化方法。优化目标结构是由无限细无限密的梁(或肋)构成的类格栅连续体(或加肋板)。采用正交异性增强复合材料模型模拟该类格栅连续体(或加肋板)的本构关系。以梁在结点处的密度和方向作为设计变量。根据有限元分析结果,采用满应力准则法优化各单工况下材料分布。按照多工况下材料的方向刚度与各单工况下材料的方向刚度最大值的差值最小为原则建立多工况下梁(或肋)的拓扑优化分布。经过少量迭代就可以建立优化的材料连续分布场。最后以3个算例演示拓扑优化的过程,并给出结点处梁的密度和方向分布。     

三维连续体结构仿生拓扑优化新方法

Wolff法则是指骨骼通过重建/生长,保证骨小梁方向趋于与主应力方向一致以不断地适应它的力学环境。根据Wolff法则,建立了一种新的拓扑优化的准则法。该方法的基本思想是:(1)将待优化的结构看作是一块遵从Wolff法则生长的骨骼,骨骼的重建过程作为三维连续体结构寻找最优拓扑的过程;(2)用构造张量描述正交各向异性材料的弹性本构;(3)重建规律为结构中材料的更新规律。通过引入参考应变区间,材料更新规律可解释为:设计域内一点处主应变的绝对值不在该区间时,该点处构造张量出现变化;否则,构造张量不变化,该点处于生长平衡状态。(4)当设计域内所有点都处于生长平衡状态时,结构拓扑优化结束。采用各向同性本构模型,即令二阶构造张量与二阶单位张量成比例,分析三维结构拓扑优化。实例进一步验证基于Wolf法则的连续体结构优化方法的正确性和可行性。     

材料拓扑空间及其一些性质(英文)

根据灰关系理论和点集拓扑学原理 ,提出了材料拓扑空间概念并论证了它的一些性质     

Synthesis and characterization of 3D topological insulators: a case TlBi(S1?xSex)2

In this article, practical methods for synthesizing Tl-based ternary III-V-VI₂ chalcogenide TlBi(SSe_x)₂ are described in detail, along with characterization by x-ray diffraction and charge transport properties. The TlBi(SSe_x)₂ system is interesting because it shows a topological phase transition, where a topologically nontrivial phase changes to a trivial phase without changing the crystal structure qualitatively. In addition, Dirac semimetals whose bulk band structure shows a Dirac-like dispersion are considered to exist near the topological phase transition. The technique shown here is also generally applicable for other chalcogenide topological insulators, and will be useful for studying topological insulators and related materials.     

Criteria for Realizing Room-Temperature Electrical Transport Applications of Topological Materials

The unusual electronic states found in topological materials can enable a new generation of devices and technologies, yet a long-standing challenge has been finding materials without deleterious parallel bulk conduction. This can arise either from defects or thermally activated carriers. Here, the criteria that materials need to meet to realize transport properties dominated by the topological states, a necessity for a topological device, are clarified. This is demonstrated for 3D topological insulators, 3D Dirac materials, and 1D quantum anomalous Hall insulators, though this can be applied to similar systems. The key parameters are electronic bandgap, dielectric constant, and carrier effective mass, which dictate under what circumstances (defect density, temperature, etc.) the unwanted bulk state will conduct in parallel to the topological states. As these are fundamentally determined by the basic atomic properties, simple chemical arguments can be used to navigate the phase space to ultimately find improved materials. This will enable rapid identification of new systems with improved properties, which is crucial to designing new material systems and push a new generation of topological technologies.     

Topological modeling of 1-Pentagon carbon nanocones – topological efficiency and magic sizes

In this article topological modeling techniques have been applied to the study of one pentagon carbon nanocones (apical angle 19°) to derive important results about preferred sizes and chemical reactivity. This theoretical model looks to the nanocone just like a 3-connected graph and considers the topological efficiency (or topological roundness) of such a system as the long-range topological potential whose local minima correspond to magic sizes of the nanocone with high probability of formation. This study moreover shows that topology alone can determine a migration of the stable regions of the nanocone along the nanocone itself, leaving in such a way the apical pentagon in a topologically reactive status. This study expands and systematizes previous works on the same subject.     

Some properties of topological pressure of a semigroup of continuous maps

Based on the work of Ma and Wu,[9 Ma D, Wu M. Topological pressure and topological entropy of a semigroup of maps. Discrete Contin Dyn Syst. 2011;31:545–557.[Crossref], [Web of Science ®] , [Google Scholar]] some equivalent definitions of topological pressure of a semigroup of continuous maps are given and several of their basic properties are provided by using separated sets and spanning sets. We also answer an open problem of Bi? and Urbański.[19 Bi? A, Urbański M. Some remarks on topological entropy of a semigroup of continuous maps. Cubo. 2006;8:63–71. [Google Scholar]] That is, letting f_i, i = 2, … , k, be homeomorphisms acting on a compact metric space, G₁ = {id_X, f₂, … , f_k}, G^{? 1}₁ = {id_X, f^{? 1}₂, …, f_k^{? 1}} and letting G and G^?1 denote the semigroups generated by G₁ and G^{? 1}₁, respectively, we give an example showing that the topological entropy of G does not equal the topological entropy of G^?1.     

物件自动定向原理与方法

对物件的定向原理及方法进行研究,表明决定物件定向的关键因素是定向概率,同时讨论了物件定向的主要方法以及影响定向的其他一些因素。     

基于可拓符号学和眼动实验的黄梅挑花再设计研究

目的 针对传统文化符号再设计过程中,显隐性因子提取与表征存在模糊主观问题,提出一种基于可拓符号学和眼动实验的显隐性文化特征提取与应用的研究方法。方法 以黄梅挑花为例,在可拓符号学的基础上融入眼动实验,首先,利用爬虫技术提取黄梅挑花文化特征词(隐性因子),并进行可拓语义评估得到其可拓区间值;其次,运用眼动实验提取挑花纹样特征(显性因子),结合隐性因子可拓区间值进行综合图解语义评估;最后,将图案元素进行可拓变换设计。结果 变换结果在服饰纹样图案设计中得到合理应用。结论 研究表明:运用该方法可修正传统的依据从业经验及主观思维表征文化特征存在的偏差,能客观、科学地提取显隐性因子并作为设计因素,有助于更好地表达文创产品的文化内涵。     

Quantum Topological Boundary States in Quasi‐Crystals

Topological phases play a novel and fundamental role in matter and display extraordinary robustness to smooth changes in material parameters or disorder. A crossover between topological material and quantum information may lead to inherent fault‐tolerant quantum simulations and quantum computing. Quantum features may be preserved by being encoded among topological structures of physical evolution systems. This requires stimulation, manipulation, and observation of topological phenomena at the single quantum particle level, which has not, however, yet been realized. It is asked whether the quantum features of single photons can be preserved in topological structures. The boundary states are experimentally observed at the genuine single‐photon level and the performance of the topological phase is demonstrated to protect the quantum features against diffusion‐induced decoherence in coupled waveguides and noise decoherence from the ambient environment. Compatibility between macroscopic topological states and microscopic single photons in the ambient environment is thus confirmed, leading to a new avenue to “quantum topological photonics” and providing more new possibilities for quantum materials and quantum technologies.