具有迁移效应和隔离措施的COVID-19传播模型分析

基于COVID-19传播过程中人口流动的必然性、无症状感染者的普遍性和隔离策略的有效性,该文提出了一类具有迁移效应、无症状感染者、自我防护意识和隔离策略的COVID-19传播动力学模型,利用下一代矩阵方法给出了各类子系统和全系统基本再生数的精确表达式.进一步地,通过采用线性近似理论,构造Lyapunov函数、比较原理等方法,得到了无病平衡点的全局渐近稳定性以及疾病的持久性.最后,数值模拟解释了主要的理论结果以及人口的迁移和隔离对疾病传播的影响.     

停车受限条件下多模式交通网络动态拥挤收费

在一个多起始单终点的交通网络上,本文研究当终点处停车空间不足时,如何通过在路段瓶颈处实施拥挤收费实现系统最优.首先,根据小汽车和公交的出行成本函数,运用凸规划算法求解系统最优条件下网络中各OD最优的小汽车和公交出行量.其次,根据系统最优时的小汽车出行量,计算出为了消除交通瓶颈处车辆排队而实施的动态拥挤收费.再次,根据小汽车和公交车出行成本的均衡条件,计算出各OD对每辆小汽车出行者应缴纳的停车拥挤附加费(或应获取的补贴),收取该费用(或发放补贴)的目的是调节小汽车和公交的出行量使它们在双模式均衡(小汽车与公交车出行模式均衡)条件下分别达到系统最优水平.最后,算例分析了两组OD对的情况,计算出两种泊位供应量下各OD对小汽车最优出行量与小汽车出行的停车拥挤附加费或补贴,并且给出了动态拥挤收费与道路收费的函数曲线.     

无风险利率影响担保市场交易结构的效应研究

担保市场交易结构是参与主体行为的分布格局,取决于担保人、债权人和债务人三方签署担保契约协议的执行结果.无风险利率是调控金融市场的政策工具,但对担保市场交易结构的影响机理和效应的研究被忽视.基于担保人资本结构本文构建担保市场均衡理论模型,推理给出无风险利率变化影响担保市场交易结构的机理假设是:随着无风险利率增高,偿付率高的优质担保人会提高其定价,压缩债务人购买担保获得的收益,但对偿付率低的劣质担保人不会产生影响,造成偿付率高的优质担保人从市场中退出,整体担保市场中优质担保人构成减少,增加担保市场的风险.同时利用我国2007-2016年上市公司提供担保实际数据进行实证检验,结果支持了假设的有效性,为我国有效防范担保市场风险的形成和演化提供了理论和实际依据.     

Zr-xNb-4Sn alloys with low Young’s modulus and magnetic susceptibility for biomedical implants

The microstructure, mechanical and magnetic properties of Zr–x (8, 9, 10, wt.%)Nb–4Sn alloys were investigated to obtain novel Zr-based alloy with low Young’s modulus and magnetic susceptibility for biomedical implants. After homogenization annealing, hot forging and solution annealing, Zr–8Nb–4Sn, Zr–9Nb–4Sn and Zr–10Nb–4Sn alloys were composed of β+α″ phase, β+α″ phase, β+ω phase, respectively. The temperature at which the α" and ω phase were transformed into β phase during the heating process was about 200 ​°C, and the phase transformation temperature decreased with the increase of Nb element. Among all the Zr–x (x ​= ​8,9,10)Nb–4Sn(wt.%) alloys, Zr–9Nb–4Sn alloy had the lowest Young's modulus of 46.6 ​GPa and the low magnetic susceptibility of 1.294 ​× ​10⁻⁶ cm³g⁻¹, which has a good application prospect for biomedical applications.     

不同阶次下分数阶SIR传染病模型的稳定性分析

建立一类考虑Logistic增长与饱和传染率的不同阶次分数阶时滞传染病模型. 首先, 利用Jacobi矩阵和特征根轨迹法, 分析该模型的局部稳定性, 并给出基本再生数; 其次, 选取分岔参数作为时滞, 给出地方病平衡点发生Hopf分岔的充分条件； 最后, 利用数值仿真验证理论分析的正确性. 研究结果表明, 分数阶次的改变会影响系统的稳定性.     

基于分布式算法的含微电网电力供应侧市场均衡分析

考虑微电网参与配电侧电力市场投标竞争,并引入一个中间商来实现日前批发市场与配电侧电力市场之间的电力交易.基于该市场交易架构,建立了微电网参与投标竞争的电力市场供应函数均衡模型.然后将该均衡模型转化为凸优化问题,在理论上证明了解的存在性和唯一性,并考虑到实际电力市场中信息的不对称性,采用分布式优化算法进行求解.最后通过算例验证了该均衡模型和求解方法的有效性,表明在微电网参与的配电侧电力市场和日前批发市场之间引入中间商,会平滑日前批发市场电价的激烈变化,缓解市场力滥用行为,有助于整个电力市场的高效平稳运行.     

Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence

In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in full generality – i.e. without making any assumptions about the system׳s dynamics or the nature of the interactions between its components – that the equilibrium macro-region is the largest macro-region. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another – again fully general – theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor (such as ergodicity or typicality), the focus should be on finding triplets of macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem.     

GPS载体姿态测量技术研究

本文首先介绍了ＧＰＳ姿态测量技术的原理,包括坐标转换、相位干涉等,并在此基础上重点讨论了基线矢量解算过程中存在的相位模糊问题。在低精度基线较短时可采用搜索方法,并推导了模糊空间的大小和搜索检验方法;在高精度基线较长时,可采用多天线辅助解相位模糊,并推导了为满足给定的整周模糊错误概率和一定精度要求时,所需的相邻基线长度比及所需的天线阵元总数,同时给出了实例。本文的研究对ＧＰＳ姿态测量的工程应用具有一定的参考价值。     

An M/G/1 Queueing System with Delay Server Vacations

ＡｎＭ／Ｇ／１ＱｕｅｕｅｉｎｇＳｙｓｔｅｍｗｉｔｈＤｅｌａｙＳｅｒｖｅｒＶａｃａｔｉｏｎｓ⒇ＴＡＮＧＹｉｎｇｈｕｉＴＡＮＧＸｉａｏｗｏ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈ．,Ｍａｎａｇｅｍｅｎｔｃｏｌｅｇｅ,Ｕｎｉｖｅｒ．ｏｆＥｌｅｃｔｒ...     

钴与噻唑偶氮间苯二胺类试剂配合物溶液平衡的研究

以２－（４,５－二甲基－２－噻唑偶氮）－５－二甲氨基苯胺为代表,应用分光光度法研究了噻唑偶氮间苯二胺类试剂与钴配合物的溶液平衡．结果表明,该配合物在溶液中存在着四种质子化型体ＣｏＲ２Ｈ３＋３,ＣｏＲ２Ｈ２＋２,ＣｏＲ２Ｈ＋和ＣｏＲ２,它们之间存在着三级离解平衡,测定其离解常数分别为ｐＫａ１＝－４．６４,ｐＫａ２＝０．６８,ｐＫａ３＝４．６２．其中ＣｏＲ２Ｈ２＋２具有较高的摩尔吸光系数,且能在较宽的酸度范围内存在,是适宜于分析应用的型体