区间直觉犹豫模糊集的两种相似测度及其在模式识别中的应用

模糊集的相似测度是模糊集理论的重要组成部分之一,有着广泛的应用.首先给出了基于隶属度、非隶属度和犹豫度的区间直觉犹豫模糊集的标准海明距离、标准欧氏距离、广义标准海明距离公式以及它们的加权距离公式.然后提出了基于距离的区间直觉犹豫模糊集相似测度和区间直觉犹豫模糊集的余弦相似度,并给出了公理化证明.两种相似测度均包含了区间直觉犹豫模糊集的隶属度、非隶属度和犹豫度.最后将这两种相似测度应用到基于区间直觉犹豫模糊信息的模式识别中.     

基于TOPSIS模型的机场网络节点重要度评估

在机场网络中单个机场节点的失效往往会对其他的节点产生影响,特别是关键节点的失效会波及整个网络.准确客观的识别重要节点机场关乎整个机场网络的安全运营.本文分析了机场网络拓扑特性中的度、集聚系数和接近度指标,考虑了机场旅客吞吐量和所在城市人口等交通经济特性指标,使用熵权法确定权重的基础上,应用TOPSIS法构建综合评价体系模型,最后以华东地区机场网络为例进行节点重要度排序.结果表明与单一指标的评估结果相比,该方法更加全面客观的确定不同属性指标的权重,避免了不同指标取值的差异性,使评价更加全面,更符合机场网络实际运营情况.     

由具体数学向形式数学的第一次转折——“正数和负数”课堂教学实录及解析

基于“四度六步”教学法的理论基础与实践架构,采用“温故—引新—探究—变式—尝试—提升”六步教学模式,设计“正数和负数”一课,创造“有温度、有梯度、有深度、有宽度”的四度精彩课堂.     

给定度序列图的覆盖成本和反向覆盖成本的研究

具有n个顶点且度序列为(m,2,…,2,1,…,1)(1的重数为m)的连通图不止一个(这些图均为树),而每个树对应唯一一个段序列(l₁,l₂,…,l_m).通过对任意一树移动最长段的悬挂点到最短段悬挂点的方式得到另一树,比较前后两树的覆盖成本和反向覆盖成本,给出了具有最小覆盖成本和反向覆盖成本的极树,并且进一步给出了取得最小覆盖成本和反向覆盖成本的顶点.     

石墨烯负载的氧配位钴单原子稳定金属锂负极

Lithium (Li)-based batteries are the dominant energy source for consumer electronics, grid storage, and electrified transportation. However, the development of batteries based on graphite anodes is hindered by their limited energy density. With its ultrahigh theoretical capacity (3860 mAh∙g⁻¹), low redox potential (−3.04 V), and satisfactorily low density (0.54 g∙cm⁻³), Li metal is the most promising anode for next-generation high-energy-density batteries. Unfortunately, the limited cycling life and safety issues raised by dendrite growth, unstable solid electrolyte interphase, and "dead Li" have inhibited their practical use. An effective strategy is to develop a suitable lithiophilic matrix for regulating initial Li nucleation behavior and controlling subsequent Li growth. Herein, single-atom cobalt coordinated to oxygen sites on graphene (Co-O-G SA) is demonstrated as a Li plating substrate to efficiently regulate Li metal nucleation and growth. Owing to its dense and more uniform lithiophilic sites than single-atom cobalt coordinated to nitrogen sites on graphene (Co-N-G SA), high electronic conductivity, and high specific surface area (519 m²∙g⁻¹), Co-O-G SA could significantly reduce the local current density and promote the reversibility of Li plating and stripping. As a result, the Co-O-G SA based Li anodes exhibited a high Coulombic efficiency of 99.9% at a current density of 1 mA∙cm⁻² with a capacity of 1 mAh∙cm⁻², and excellent rate capability (high current density of 8 mA∙cm⁻²). Even at a high plating capacity of 6 mAh∙cm⁻², the Co-O-G SA electrode could stably cycle for an ultralong lifespan of 1300 h. In the symmetric battery, the Co-O-G SA based Li anode (Co-O-G SA/Li) possessed a stable voltage profile of 18 mV for 780 h at 1 mA∙cm⁻², and even at a high current density of 3 mA∙cm⁻², its overpotential maintained a small hysteresis of approximately 24 mV for > 550 h. Density functional theory calculations showed that the surface of Co-O-G SA had a stronger interaction with Li atoms with a larger binding energy, −3.1 eV, than that of Co-N-G SA (−2.5 eV), leading to a uniform distribution of metallic Li on the Co-O-G SA surface. More importantly, when matched with a sulfur cathode, the resulting Co-O-G SA/lithium sulfur full batteries exhibited a high capacity of 1002 mAh∙g⁻¹, improved kinetics with a small polarization of 191 mV, and an ultralow capacity decay rate of 0.036% per cycle for 1000 cycles at 0.5C (1C = 1675 mA∙g⁻¹) with a steady Coulombic efficiency of nearly 100%. Therefore, this work provides novel insights into the coordination environment of single atoms for the chemistry of Li metal anodes for high-energy-density batteries.     

一元溶剂体系β-HMX球形化结晶形貌的分子动力学模拟

奥克托金(β-HMX)晶体形貌在很大程度上影响其安定性能、流散性和能量输出,其中溶剂对晶习的影响起着很关键的作用,因此研究溶剂对β-HMX结晶形貌影响的微观机理具有很重要的意义.运用分子动力学方法计算了五种溶剂作用下β-HMX五个重要的晶面层与溶剂层的相互作用能,对附着能进行了修正,预测了不同溶剂作用下β-HMX的晶体形貌.结果表明,β-HMX重要晶面与五种溶剂都呈吸引作用,五种溶剂都会对晶面的附着能产生很大影响,抑制晶面的生长速率,除N-甲基吡咯烷酮(NMP)外,其余四种溶剂作用下(020)面的相对生长速率都是最快的,在晶体的最终形貌中消失.二甲基亚砜(DMSO)溶剂作用下的晶体形貌相对比较好, N,N-二甲基甲酰胺(DMF)、环己酮(CH)和NMP溶剂作用下的晶体形貌次之,γ-丁内酯(GBL)溶剂作用下的晶体形貌球形度最差.     

石油产品酸值测定仪校准方法

通过分析石油产品酸值测定仪工作原理,参考相应的国家技术规范,建立石油产品酸值测定仪的校准方法。使用酸值(以KOH计)为(0.11±0.03) mg/g的酸值标准物质对以颜色指示剂法为原理的石油产品酸值测定仪进行校准,设定校准项目:示值误差为–0.01 mg/g;重复性为0.02 mg/g。对石油产品酸值测定仪示值误差测量结果的不确定度进行评定,扩展不确定度为0.04 mg/g(k=2)。该校准方法计量特性满足校准要求,可用于评价石油产品酸值测定仪的性能。     

GGA+U法研究稀土(La、Ce、Pr、Nd)掺杂对ZnO电子结构和光学性质的影响

基于GGA+U的第一性原理方法,分析了La、Ce、Pr、Nd四种元素掺杂的ZnO结构,对晶体的结构、电子结构和光学性质进行了对比分析.由键布局分析可知,掺杂体系Zn-O键共价性的强弱与杂质掺入原子的序数成正比.掺杂后体系的类型仍为直接跃迁,能级整体下移;随着Pr、Nd掺入,出现了杂质能级,这是由稀土元素的4f电子态所导致.在光学性质方面,掺杂体系的吸收系数、静介电常数都比纯ZnO的高,体系的吸收边都向低能方向移动,其中Zn7LaO8的红移程度最高、静介电常数最大,说明其光催化能力和极化能力都最强.