Shakespeare’s Brave Women and Brave World--A Topological Study of His Juliet,Portia and Cordelia

Juliet,Portia and Cordelia are three heroines in plays of King Lear,Romeo and Juliet and The Merchant of Venice written by Shakespeare.Although they are endowed with various personalities,the three women have all shown a brave trait in their character,which makes them become the representatives of brave women.Deformation and equivalence are two important terms used to describe the deduction of topological spaces.From a topological perspective,the thesis purports to study and interpret the distinctive and vivid artistic images of Juliet,Portia and Cordelia,finding that their diverse artistic images and similar bravery are in response to the transformation and equivalence in literary metaphorical topological spaces.It helps to explain the reason why Shakespeare had created so many colorful female images.In this sense,this paper provides a new point of view and a new mechanism to interpret Shakespeare’s plays.

STRONG EQUIVALENCES OF APPROXIMATION NUMBERS AND TRACTABILITY OF WEIGHTED ANISOTROPIC SOBOLEV EMBEDDINGS

In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

Relative Strong F Compactness and Relative Ultra-F Compactness in L-topological Spaces

In this paper, two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set. Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given. Some examples are illustrated.

CHAIN RECURRENT POINTS AND TOPOLOGICAL ENTROPY OF A TREE MAP

Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.

The Unitary Group in Its Strong Topology

The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.

On the Equivalence of Implicit Kirk-Type Fixed Point Iteration Schemes for a General Class of Maps

In this paper, a modified implicit Kirk-multistep iteration scheme and a strong convergence result for a general class of maps in a normed linear space was established. It was also shown that the convergence of this iteration scheme is equivalent to the convergency of some other implicit Kirk-type iteration (implicit Kirk-Noor, implicit Kirk-Ishikawa and implicit Kirk-Mann iterations) for the same class of maps. Some numerical examples were considered to show that the equivalence of convergence results to the fixed point is true. The results unify most equivalence results in literature.

A Ubi Sunt Motif of Life Philosophy:Construction of Three Topological Spaces in Shakespeare’s Merchant of Venice

Topology,as a geometrical branch,studies spaces,whose essence lies in its topological equivalence.As far as literary criticism is concerned,the author’s writing purpose can be regarded as an open set in topology,which contains a number of different topological spaces.No matter how these spaces transform,they remain fundamental properties as long as their essence is invariant.From the perspective of topology,Shakespeare constructed three equivalent metaphorical topological spaces:one-pound-flesh agreement,marriage casket“lottery”,and wedding ring trick.The present paper purports to explore how Shakespeare constructed the three equivalent topological spaces to express the theme of literature:the ubi sunt1 motif of life philosophy.

Strongly nonlinear topological phases of cascaded topoelectrical circuits

Circuits provide ideal platforms of topological phases and matter,yet the study of topological circuits in the strongly nonlinear regime,has been lacking.We propose and experimentally demonstrate strongly nonlinear topological phases and transitions in one-dimensional electrical circuits composed of nonlinear capacitors.Nonlinear topological interface modes arise on domain walls of the circuit lattices,whose topological phases are controlled by the amplitudes of nonlinear voltage waves.Experimentally measured topological transition amplitudes are in good agreement with those derived from nonlinear topological band theory.Our prototype paves the way towards flexible metamaterials with amplitude-controlled rich topological phases and is readily extendable to two and three-dimensional systems that allow novel applications.

电动挖掘机落物保护装置拓扑优化设计

针对某型电动挖掘机的乘员防护,提出使用基于等效静态载荷法的拓扑优化方法设计落物保护装置(Falling Object Protective Structures,FOPS)。首先,使用基于位移等效原则的等效静态载荷法,将动态非线性碰撞过程简化为多工况条件下的静态非线性变形过程。随后,提出使用加权系数法,将动态非线性拓扑优化简化为多工况条件下的静态非线性拓扑优化,可显著提高拓扑优化的计算速率和收敛性。最后,基于拓扑优化结果设计FOPS,并按照GB/T 17771—2010进行仿真试验分析。结果表明,新设计的FOPS无须额外加强即可满足乘员落物保护要求,且FOPS的总质量减轻了49.8 kg,这对降低工程机械的采购和使用成本,以及满足节能减排具有积极意义。

基于均匀化拓扑优化的轻质多孔结构等效方法

通过拓扑优化设计得到的孔洞结构,往往不规则,甚至过于复杂、难于加工、多数需要进行二次设计,为了避免二次拓扑优化求解过程复杂、效率低、耗时长,甚至出现不收敛、棋盘格、灰色单元等情况,提出一种基于均匀化拓扑优化的轻质多孔结构等效方法。该方法首先需对研究结构进行初次拓扑优化,提取拓扑优化后的关键性能参数如应变能、最大应力、最大位移等。然后依据上述提取的参数作为后续寻求结构等效的条件。基于能量均匀化方法求解出与拓扑优化后等效的微结构。将等效微结构阵列得到的周期排列结构即为轻质多孔等效结构。最后对拓扑优化结构和轻质多孔等效结构进行有限元分析对比,验证此方法的可行性。结果表明:轻质多孔等效结构与初始拓扑结构相比,其综合性能基本不变,但因轻质多孔结构的规则性使得加工难度大大降低。

分数量子霍尔液体中的几何自由度及类引力子元激发

拓扑在凝聚态物理中的应用始于量子霍尔效应的研究,并逐渐成为现代凝聚态物理的主旋律.其重要性在于它描述物理系统的普适性质.但基于拓扑场论的分数量子霍尔液体宏观描述并非完备.本文从微观角度出发讨论分数量子霍尔液体中的几何自由度及其量子动力学,揭示其基本元激发为自旋为2的类引力子并据有特定手性,着重讨论该手征类引力子的实验探测.

风电富集地区电网动态等值建模

为了满足大规模风电并网下对地区电网进行详细仿真的需求,提出了一种适用于风电并网的地区电网等值方法。与聚焦于主网的传统动态等值不同,风电富集地区电网等值不仅要考察风电在地区电网中密集接入的特点,圈定各个风电场站影响范围,而且还要在边界节点上综合考虑外网的源、荷特性约束。所提方法可在保持稳态、暂态特性一致的前提下对外网进行大规模化简,实现地区电网的等值建模。首先,突破在风电场站接入点仅以短路比等电气强度指标来等效电网的传统方案,提出以节点残压来界定待研究区域与待等值外部区域;其次,考虑地区电网的拓扑约束对地区电网进行进一步化简;再次,考虑在边界节点上以等值同步发电机与复合负荷的组合形式构建外部系统的等值模型;最后,利用所提方法对实际风电富集地区电网进行了验证。仿真结果表明了所提等值方法的有效性。

L-拓扑空间中的SPC-连通性

研究了L-拓扑空间中的SPC-连通性.首先借助强半开集和强半闭集引入SPC-连通性的概念,并研究了SPC-连通性的等价刻画;其次讨论了SPC-连通性的一些性质以及证明了SPC-连通性是拓扑不变性;最后讨论了SPC-连通性与连通性之间的关系,得出:在L-拓扑空间中,SPC-连通一定是连通的,反之不成立,进而丰富和完善了L-拓扑空间中的连通性理论.

耦合排障−吸能的高速列车排障器结构双尺度拓扑优化设计

排障器置于列车前端,先于车体冲击排开轨道上的障碍物。在列车速度或障碍物尺寸发生改变时,排障器结构在刚度和吸能特性上具有不同的设计要求。为了设计一种耦合排障−吸能的结构形式,提出一种整体大刚度(排障)、局部结构降低冲击力(削峰吸能)的双尺度优化设计方法。该方法在以刚度为目标的整体结构初设计中确定变形区间,并在串行路线下完成以引导结构变形为目标的局部结构优化,最终形成新型排障器。研究结果表明:在基于标准EN 15227的静载荷工况下,新型排障器结构的质量降低了7%,同时,结构安全性提升;在冲击刚性墙仿真中,相较于原有排障器,新型排障器的峰值力降低了17.5%,且优化后的缓冲梁结构使排障器中部产生的弯折变形变为压缩变形,有效缓解了排障器后侧对车体结构的挤压现象。

基于等效静态载荷法的多相材料结构动态拓扑优化设计

为了满足多相材料结构动态性能要求,提出一种基于等效静态载荷法的多相材料结构动态拓扑优化设计方法。采用序列固体各向同性料插值模型惩罚刚度矩阵和质量矩阵,以多个动载荷作用的多相材料结构总动态柔顺度最小化为优化目标,以结构质量和成本为约束条件,构建多相材料结构动态拓扑优化模型,利用等效静态载荷法将多相材料结构动态拓扑优化问题转化为多工况下的多相材料结构静态拓扑优化问题,以降低灵敏度分析的复杂程度;采用移动渐近线算法求解多相材料结构动态拓扑优化问题。数值算例结果表明所提方法是有效性的,与传统的拓扑优化方法相比,基于等效静态载荷法的多相材料结构动态拓扑优化求解时间节省了75%,大大提高了计算效率;与单相材料拓扑优化结果相比,多相材料结构动态拓扑优化设计获得的结构具有更好的动态性能。

月球微电网——深空探测综合能源基地

针对月球科研站能源供需特点,提出具有“五强”技术特征、“五高”供应能力的月球数智化高可靠微电网综合能源基地蓝图,明确了以直流为主交流为辅的混合微电网基本形态、以电氢耦合为基本能量转换形式的“电-氢-氧-热-水”综合能源基地的建设愿景,并在地球建立全域、全态、全时数字孪生系统,支撑其安全稳定、高质高效运行。月球微电网综合能源基地建设是一项全局性、复杂性和开创性的系统工程,创新提出兆瓦级月球微电网电源结构、储能形式、网架形态以及系统拓扑结构、运行模式,提出基于月球科研站用能需求的三阶段发展设想,为我国深空探测能源供给提供全套解决方案。基于新质生产力形成的新供给,提出加强前沿技术、颠覆性技术多路径探索和交叉融合,尽早开展月球微电网综合能源基地研究的建议。月球微电网综合能源基地将有力促进地球新型电力系统的建设和发展。

自同构系统的拓扑刚性

研究了可数离散群在紧度量空间étale等价关系上的自同构作用。文章引入了自同构系统上连续强轨道等价的定义,证明了共轭的两个自同构系统一定是连续强轨道等价的,反之,在本质自由和离散群是顺从无挠的条件下,满足刚性条件的两个连续强轨道等价的自同构系统是共轭的。

基于模糊超群构建的Engel群及其性质研究

通过构造满足Engel递减条件的模糊超群(H,。)上最小的等价关系■^(*),使得模糊超群关于等价关系构建的商群(等价类的集合)H/■^(*)是一个Engel群,并通过等价关系的强正则性来刻画该Engel群,最后引入模糊超群的?-部分的概念,确定等价关系?是可传递的充要条件.

堆石料宏细观力学特性离散元分析

堆石料的力学特性直接影响堆石坝工程的设计、施工和运行,对坝体变形及安全有重要影响。基于大石峡混凝土面板堆石坝工程,采用离散单元法(DEM)建立了接近于3BA区堆石料真实颗粒形状的椭球颗粒试样,开展了一系列常规三轴数值试验,研究了3BA区堆石料的宏、细观力学特性。通过不同围压下的宏观应力应变演化曲线,获得堆石料的宏观应力、变形指标。采用平均接触力将接触网络划分为强、弱2个子网络,分析强、弱接触网络的配位数分布与拓扑演化规律。结果表明:割线模量、泊松比、峰值内摩擦角与围压呈线性变化,剪胀角与围压呈非线性变化;颗粒体系内接触的拓扑演化主要发生在弱接触网络,进而影响堆石料的宏观体积变化,强接触网络内的接触保持不变,为堆石料提供稳定的传力通道。研究结果可用于指导实际工程中不同围压下宏观力学指标的选取。