生灭链和生灭过程的观测与统计

本文证明了具有反射壁的生灭链（生灭过程）在一个反射壁的击中时分布能够完全唯一决定整个生灭链（生灭过程）。并将该结果应用到了生物学上细胞膜离子单通道门控动力学分析，产生了与实验一致的结果。     

确定环形Markov链的Q-矩阵

给出了Markov链中任一状态集的逗留时间或击中时间的分布(混合指数分布),以及其分布的各阶微分与Q-矩阵之间的约束方程组.利用该约束关系及环形链结构的先验信息,采用Markov链反演方法证明了:对于有限状态环形Markov链,其Q-矩阵能由其中任意两个相邻状态的逗留时间和击中时间分布唯一决定,并给出了相应的算法.     

HPM视角下数学核心素养的教学研究——以“数系的扩充”教学为例

<正>一、研究背景(一)地位和作用复数是中学数学中一个抽象的数学概念,是中学数学学习中不可或缺的一部分.引进虚数,把实数集扩充到复数集,虽然是数学本身的需要,但也只有当复数表示平面上的点这一几何解释出现之后,在解决实际问题中才得到广泛的应用,复数才被人们承认并巩固了下来.复数作为一种新的数学语言,也为我们今后用代数方法解决几何问题提供了新的工具和方法,给数学领域带来了观念性的更新.     

基于HPM的高中数学概念课教学设计与应用研究——以“函数的概念”教学为例

从数学史的角度看,函数概念经历了“萌芽”“解析定义”“对应定义”“集合定义”四个时期.本文中通过若干情境,结合数学史对函数概念的教学进行了重构,加强函数概念发展史内容的渗透,促使学生更好地掌握所学内容,提升学生的人文情怀,提高学生数学核心素养.     

OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE

This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance(CEV) model.Assume that the insurer’s surplus process follows a jump-diffusion process,the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model.The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims.The objective of the insurer is to maximize the expected exponential utility of terminal wealth.This optimization problem is studied in two cases depending on the diffusion term’s explanation.In all cases,by using techniques of stochastic control theory,closed-form expressions for the value functions and optimal strategies are obtained.     

MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS

We consider how to identify the transition rates of ion channels with the underlying scheme which is kinetically modelled as time-homogeneous Markov chain.A Markov chain inversion approach is developed to perform a difficult inversion to identify the transition rates from the parameters characterizing the lifetime distributions at a small number of states,although it is straightforward to derive the lifetime distribution.The general explicit equations relating the parameters of the lifetime distribution to the transition rates are derived and transition rates are then obtained as roots to this system of equations.The concrete solutions are proposed to the basic and regular schemes such as linear,star-graph branch and loop.Useful conclusions and solutions to realistic schemes are also included to show its efficiency.     

非时齐复合泊松过程下对偶风险模型的破产特征量研究

将经典的对偶风险模型中的收益到达过程推广为非时齐的泊松过程.运用经典方法和时变方法,计算了该模型下的破产概率,并定义了时变后相应模型的广义期望折罚函数,验证了时变方法对非时齐泊松风险模型的有效性,最后又考虑了该模型在带壁分红策略下的情形,当单次索赔额服从指数分布时,得到了它的期望折罚函数以及期望折现分红函数.     

带干扰的复合负二项过程下的双险种负风险模型

本文研究了带干扰的索赔过程为复合负二项过程的双险种负风险和模型.用两种不同的方法得到了该模型的最终破产概率,还得到了Lundberg不等式,推广了经典负风险模型.     

温度滴定法测定脱硫石膏中的硫酸盐

采用温度滴定法测定脱硫石膏中的硫酸盐含量。石膏样品中加入盐酸(1+1)溶液,加热微沸10 min,冷却至室温后,在温度滴定仪上,以氯化钡溶液滴定至终点。在优化的试验条件下,对硫酸盐含量在72.8%~93.6%的石膏样品进行测试,测定值的相对标准偏差(n=5)在0.30%~0.95%之间,与标准方法测定值相吻合。方法的加标回收率在96.8%~102%之间。