无界集值上鞅的Riesz逼近

研究了弱紧凸集值上鞅及无界集值上鞅的Ｒｉｅｓｚ逼近，以及鞅型集序列的若干收敛定理．     

一类算子的固有值与固有元存在性定理

利用Petryshyn W V(1972)中所定义的1-集压缩映象拓扑度的一些基本性质以及半闭1-集压缩映象的诸多性质讨论Banach空间中一类算子的固有值与固有元的存在性问题。当算子满足一些较弱的条件时,可以保证至少存在一个大于1的固有值以及在其定义域的边界上存在对应的固有元。这些结     

Topological aspect of Chern--Simons p-branes

By generalizing the topological current of Abelian Chern--Simons (CS) vortices, we present a topological tensor current of CS p-branes based on the \phi -mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field \phi(x), and the topological structure of CS p-branes is characterized by the winding number of the \phi-mappings. Furthermore, the Nambu--Goto action and the equation of motion for multi CS p-branes are obtained.     

基于拓扑优化和深度学习的新型结构生成方法

计算机辅助设计已广泛应用于结构计算和分析,但如何利用计算机智能生成最佳的新型结构还面临巨大挑战。针对这一问题,提出了一种基于拓扑优化和深度学习的新型结构智能生成方法。该方法首先通过结构拓扑优化分析获得不同参数下的优化结果制作训练集图片,并将训练集标签定义为相应的工况类型,然后应用最小二乘生成对抗网络(LSGAN)深度学习算法进行训练并生成大量的新型结构,最后建立评价指标和评估体系对生成的模型进行评价比较,根据需求选择最佳结构设计方案。结合一个铸钢支座节点底板设计的工程案例,详细阐述了上述方法的应用过程,并借助三维重构技术和增材制造技术实现结构模型的一体化制造。研究结果表明,基于拓扑优化和深度学习的新型结构智能生成方法不仅可以自动生成新的结构,而且可以进一步优化结构的材料用量和力学性能。     

具有星形拓扑结构的捕光分子

合成了单体甲基丙烯酸-2-(9,9-二乙基)芴甲酯(FMMA)作为捕光天线分子,通过原子转移自由基聚合方法(ATRP)合成了以β-环糊精(β-CD)为核的21臂星形发光聚合物β-CD-g-(PFMMA-b-PDMAEMA)21作为捕光聚合物.通过氢核磁共振谱、基质辅助激光解析电离飞行时间质谱和凝胶渗透色谱对其结构进行了表征.将其与能量受体分子蒽包合,通过紫外-荧光测试检测到了两者的能量传递现象,成功证明了基于主客体包合作用的星形拓扑分子捕捉和传递能量的过程,在光敏器件、太阳能电池和有机发光二极管等领域内具有潜在的应用价值.     

Relation between Airy beams and triple-cusp beams

Airy beams and triple-cusp beams are two kinds of accelerating beams. The propagation characteristics and internal topological structures of accelerating Airy beams are well understood because of the developed mathematical theory about Airy function. However, limited information is available about the optical characteristics of accelerating triple-cusp beams. In this work, the relationship between Airy beams and triple-cusp beams is examined theoretically and experimentally. Results reveal some important optical characteristics of triple-cusp beams based on the optical characteristics of Airy beams. These findings are expected to provide a foundation for future applications of triple-cusp beams.     

多种类表面活性剂临界胶束浓度定量构效关系

表面活性剂的临界胶束浓度(CMC)是个非常重要的物质特性参数, CMC在研究表面活性剂的工业应用和生物利用方面发挥着关键作用. 本工作提出了一个新的拓扑指数—扩展距离矩阵, 建立了一个稳定的构效关系模型, 并对175种表面活性剂的临界胶束浓度进行了计算预测. 结果表明, 基于新的拓扑指数建立的构效关系模型计算临界胶束浓度能给出稳定可靠的预测结果, 其预测结果相关性系数R²(training set)=0.9295, 相对标准偏差ARD(training set)=8.20%, R²(testing set)=0.9257, ARD(testing set)=6.76%. 与文献中模型预测结果的对比表明, 本工作在稳定性和可靠性上均有显著改善.     

靶向抑制DNA拓扑异构酶的抗肿瘤药物研究

DNA拓扑异构酶是真核细胞和原核细胞中的一种基本酶,广泛存在于细胞核中,对DNA的转录、复制以及基因表达过程中的DNA拓扑结构的改变起着重要的作用。研究发现DNA拓扑异构酶在肿瘤组织中高度表达,许多抗肿瘤药物的作用机制与抑制拓扑异构酶有关,目前拓扑异构酶已成为筛选抗肿瘤药物的重要靶点。     

A Dinuclear Cu(Ⅱ)-based Coordination Framework with Two-fold Interpenetrated 3D pcu Topology Displaying Catalytic Activity

A new Cu(Ⅱ) coordination polymer, [Cu2(mip)2(bmix)]n(bmix = 1,4-bis(2-methylimidazole-1-ylmethyl)benzene, H2 mip = 5-methylisophthalic acid), has been hydrothermally synthesized and characterized by elemental analyses, IR, TGA and single-crystal X-ray diffraction. The title compound belongs to the triclinic system, space group P1 with a = 9.435(5), b = 12.241(6), c = 13.666(6), β = 94.396(8)o, V = 1565.5(13) 3, Z = 2, C34H30Cu2N4O8, Mr = 749.70, Dc = 1.590 g/cm3, μ = 1.419 mm-1 and F(000) = 768. The title metal-organic coordination polymer exhibits the first two-fold interpenetrated pcu topological structure assembled by two types of dinuclear copper(Ⅱ) clusters and a flexible bis(imidazole)-based ligand. In addition, the fluorescence and catalytic performances of the complex for the degradation of Congo red azo dye in Fenton-like process were presented.