n × n 上三角算子矩阵的单值扩张性以及应用*

设X_i是无穷维复Banach空间, L(X_j,X_i)是X_j到X_i上的有界线性算子全体.考虑 n × n 上三角算子矩阵T=(T_ij)_1≤j≤n, 其中T_ij L(X_j,X_i),1≤j≤n; T_ij=0, i>j.本文研究了T的单值扩张性, 通过考察集合S(T)={λ∈C}: T在点λ没有SVEP},证明了S(T)在i=1 ? nS(T_i)中退化,进而给出等式S(T)=i=1 ? n S(T_i)成立的条件. 同时, 考察了T的单值扩张性扰动,得到了S(T)保持对角稳定时T_i所需的条件并予以证明, 同时举例说明这些条件的合理性.最后, 给出单值扩张性关于谱σ(T)和局部谱σT (x)的应用, 得到了谱扰动和局部谱扰动不变的新条件.     

符号圈拼接图的零度

令$\eta(\Gamma)$和$c(\Gamma)$是符号图$\Gamma$的零度和基本圈数. 一个符号圈拼接图是指每个块都是圈的连通符号图. 本文证明了对任意符号拼接图$\eta(\Gamma)\le c(\Gamma)+1$成立, 并且刻画了等号成立的极图, 推广了王登银等人(2022)在简单圈拼接图上的结果. 此外, 我们证明了任意的符号拼接图$\eta(\Gamma)\neq c(\Gamma)$, 给出了满足$\eta(\Gamma)=c(\Gamma)-1$的符号拼接图的一些性质并刻画处$\eta(\Gamma)=c(\Gamma)-1$的二部符号拼接图.     

基于摇臂——转向架结构月球车的越障能力判断准则

对轮式移动系统进行越障分析时,常以垂直越障作为评价标准.但是,月球车在凹凸不平的月面上行驶时,垂直越障模型不具有一般性.为此,本文对基于摇臂-转向架结构月球车在任意路面的越障进行了研究.一般情况下,由于任意路面越障模型相对复杂,可以建立的独立平衡方程数目少于未知变量数,因此无法得到越障能力与路面参数的函数关系式.针对上述问题,文中将最大有效牵引力假设引入越障模型中,得到了一种任意路面越障能力的判断准则.通过算例分析,表明了所提方法的有效性.     

SrMoO_4∶Sm~(3+),Na~+红色荧光粉的形貌调控和发光性能

以Sm~(3+)为激活剂,Na~+为电荷补偿剂,柠檬酸为配位剂,乙二醇作为辅助配位剂,采用溶胶-凝胶法合成前驱体,然后在800℃下焙烧,成功制备了一系列SrMoO_4∶Sm~(3+),Na~+红色荧光粉。用X射线衍射仪、扫描电镜、荧光光谱和傅里叶变换红外光谱等手段对样品的物相、形貌、组成、发光性能和量子效率等进行测试和表征。分析结果表明:制备的SrMoO_4∶Sm~(3+),Na~+荧光粉均为四方晶系结构,掺杂离子的加入对基质晶体结构影响不大。在403 nm近紫外光激发下,产物有4个发射峰,分别位于563、600、647和707 nm处,归属于~5G_(5/2)→~6HJ(J=5/2,7/2,9/2,11/2)的电子跃迁,其中位于647 nm处的主发射峰的相对发光强度最大。当Sm~(3+)的掺杂物质的量分数为1%~3%时,发光强度最好,当浓度超过1%~3%时,会发生荧光猝灭。对实验数据进行分析,确定荧光猝灭机理是由于钐离子间交换作用引起的,并计算了能量传递的临界距离为1.77~2.56 nm。此外,还详细研究了乙二醇对SrMoO_4∶Sm~(3+),Na~+荧光粉形貌的影响,研究结果表明:乙二醇加入量为5 m L时,产物形貌均匀,呈球形或椭球形;且分散性较好;荧光强度最大。     

两个dpa类配体的铜(Ⅱ)配合物的合成、结构、核酸酶活性及细胞毒性

以dpa衍生配体4-methyl-N,N-bis（pyridin-2-ylmethyl）aniline（L）合成2个单核铜配合物[CuL（NO₃）₂]（1）和[CuL（OAc）（H₂O）]ClO₄（2）,并对其进行了表征。单晶结构显示,配合物1中的Cu中心可以描述为畸变的五角双锥构型,而2的Cu中心为畸变的八面体构型。运用电子吸收和发射光谱法研究了配合物与CT-DNA的键合作用,结果表明2个配合物与DNA的相互作用均为部分插入模式。通过改变浓度、时间进一步检测配合物切割DNA的能力,以及验证其切割机理,结果表明在外界诱导剂存在下,2个配合物均表现出强的切割DNA的能力,其作用机理为氧化切割机理,其中活性氧可能为·OH和¹O₂。利用MTT法测定了配合物对体外HeLa、HepG-2和SGC-7901肿瘤细胞增殖的抑制能力。     

Edge agreement of second-order multi-agent system with dynamic quantization via the directed edge Laplacian

This work explores the edge agreement problem of second-order multi-agent systems with dynamic quantization under directed communication. To begin with, by virtue of the directed edge Laplacian, we propose a model reduction representation of the closed-loop multi-agent system depending on the spanning tree subgraph. Considering the limitations of the finite bandwidth channels, the quantization effects of second-order multi-agent systems under directed graph are considered. The static quantizers generally contain a fixed quantization interval and infinite quantization level, which are, to some extent, inefficient and impractical. To further reduce the bit depth (number of bits available) and to obtain better precision, the dynamic quantized communication strategy referring to zooming in-zooming out scheme is required. Based on the reduced model associated with the essential edge Laplacian, the asymptotic stability of second-order multi-agent systems under dynamic quantized effects with only finite quantization level can be guaranteed. Finally, the simulation of altitude alignment of micro air vehicles is provided to verify the theoretical results.     

集值映射多目标半定规划问题的epsilon-弱有效性

对于集值映射多目标半定规划问题, 在近似锥-次类凸的框架下, 建立了含矩阵和向量的择一性定理, 给出了问题的epsilon-弱有效解的epsilon-Lagrange乘子定理及标量化定理和epsilon-弱鞍点定理．     

Calculus of directional coderivatives and normal cones in Asplund spaces

We study the directional Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings in Asplund spaces and establish extensive calculus results on these constructions under various operations of sets and mappings. We also develop calculus of the directional sequential normal compactness both in general Banach spaces and in Asplund spaces.     

Some inequalities for the Bell numbers

In this paper, we present derivatives of the generating functions for the Bell numbers by induction and by the Faà di Bruno formula, recover an explicit formula in terms of the Stirling numbers of the second kind, find the (logarithmically) absolute and complete monotonicity of the generating functions, and construct some inequalities for the Bell numbers. From these inequalities, we derive the logarithmic convexity of the sequence of the Bell numbers.