A three‐dimensional CdII coordination framework: poly[di‐μ2‐aqua‐{μ2‐1,4‐bis[(1H‐1,2,4‐triazol‐1‐yl)methyl]benzene‐κ2N4:N4′}di‐μ3‐terephthalato‐κ3O:O′:O′′‐dicadmium(II)]

The title Cd^II coordination polymer, [Cd(C₁₀H₈O₄)(C₁₂H₁₂N₆)_0.5(H₂O)]_n, has been obtained by the hydrothermal method and studied by single‐crystal X‐ray diffraction, elemental analysis, thermogravimetric analysis, IR spectroscopy and fluorescence spectroscopy. The compound forms a novel three‐dimensional framework with 3,8‐connected three‐dimensional binodal {4.5²}₂{4².5¹⁰.6¹².7.8³} topology. An investigation of its photoluminescence properties shows that the compound exhibits a strong fluorescence emission in the solid state at room temperature.     

Unexpected Room‐Temperature Ferromagnetism in Nanostructured Bi2Te3

There is an urgent need for the development in the field of the magnetism of topological insulators, owing to the necessity for the realization of the quantum anomalous Hall effect. Herein, we discuss experimentally fabricated nanostructured hierarchical architectures of the topological insulator Bi₂Te₃ without the introduction of any exotic magnetic dopants, in which intriguing room‐temperature ferromagnetism was identified. First‐principles calculations demonstrated that the intrinsic point defect with respect to the antisite Te site is responsible for the creation of a magnetic moment. Such a mechanism, which is different from that of a vacancy defect, provides new insights into the origins of magnetism. Our findings may pave the way for developing future Bi₂Te₃‐based dissipationless spintronics and fault‐tolerant quantum computation.     

基于支座反力影响线曲率差分的等截面连续梁损伤识别方法

为了实现仅采用损伤状态信息对等截面连续梁进行损伤识别,通过推导三跨不等跨连续梁在移动荷载作用下的支座反力影响线,发现支座反力影响线求曲率并作差分后的曲线在损伤位置会发生突变,基于该现象提出了一种损伤定位方法,进一步建立了损伤程度计算方法,可对损伤程度进行较精确的定量。通过一三跨连续梁和一四跨连续梁工程实例的仿真分析,证明了支座反力影响线曲率差分指标损伤定位和相应的损伤程度定量方法对等截面连续梁损伤识别具有可行性。     

高斯涡旋光束的傍轴度

按单色光束傍轴度的定义,对高斯涡旋光束的傍轴度进行了研究.使用角谱表示法推导出高斯涡旋光束傍轴度的解析公式,用此研究了傍轴度和高斯涡旋光束参数之间的关系.结果表明,随背景高斯光束束腰宽度和光涡旋离轴参数的增加及随光涡旋拓扑电荷的减少,高斯涡旋光束的傍轴度增加.对所得结果用傍轴度与远场发散角间的关系做了物理解释.     

无约束优化的一个充分下降共轭梯度算法

在修正PRP共轭梯度法的基础上,提出了求解无约束优化问题的一个充分下降共轭梯度算法,证明了算法在Wolfe线搜索下全局收敛,并用数值实验表明该算法具有较好的数值结果.     

数学分析中若干具有共性理论的问题

探讨数学分析中若干具有共性理论的问题,并重点阐述数学分析中若干关于一致问题与Cauchy定理的教学探索和实践.     

基于统一价格拍卖的初始排污权分配方法

针对初始排污权总量分配的实际问题,基于统一价格拍卖的思想提出了一种具有激励性的可变总量的分配方法,分别给出了排污企业对称和排污企业非对称两种情形下的线性均衡报价策略,并证明了该方法的可行性和有效性,从而为建设排污权分配和交易制度提供了理论依据和方法参考.     

对流扩散方程特征线双线性元的一致估计

利用双线性元的积分恒等式,给出了二维非定常对流占优扩散方程的特征线有限元解和真解的一致误差估计,并利用插值后处理算子给出了有限元解梯度的一致超收敛估计,即上述误差与ε无关,而仅与右端f和初值u_0有关.     

梯度下降法在沉积物粒度分布拟合中的应用

结合实测数据,以三个对数正态分布函数的和函数为拟合函数,以梯度下降法为主要方法,对沉积物粒度分布进行了数据拟合,通过数值实验我们发现:利用梯度下降法可以有效地优化分布函数的各参数,实现拟合残差的稳步持续减小,具有良好的可操作性,拟合效果是令人满意的,它为我们进行数据拟合提供了一条新的思路,同时此方法也可以推广到解决其他极值问题.     

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A DISCRETE TIME NON-AUTONOMOUS COMPETING SYSTEM WITH FEEDBACK CONTROLS

In this paper,a class of discrete time non-autonomous competing system with feedback controls is considered. With the help of differential equations with piecewise constant arguments,we first propose a discrete model of a continuous non-autonomous competing system with feedback controls. Then,using the coincidence degree and the related continuation theorem as well as some priori estimations,a suficient condition for the existence of positive solutions to difference equations is obtained.