Precise large deviations for a customer-based individual risk model

In this paper,we propose a customer-based individual risk model,in which potential claims by customers are described as i.i.d.heavy-tailed random variables,but different insurance policy holders are allowed to have different probabilities to make actual claims.Some precise large deviation results for the prospective-loss process are derived under certain mild assumptions,with emphasis on the case of heavy-tailed distribution function class ERV(extended regular variation).Lundberg type limiting results on the finite time ruin probabilities are also investigated.     

束靶耦合传感器光学及机械设计

利用共轭原理设计了用于惯性约束聚变的束靶耦合传感器,不仅解决高精度打靶,同时避免模拟准直光在瞄准过程中直接辐照实验靶。根据束靶耦合传感器的设计功能和工作原理,进行系统的光学设计和机械结构设计,通过成像实验采集的图像光学分辨力达到6 m,束靶耦合精度8.8 m。该束靶耦合传感器已经成功应用于神光-Ⅲ原型装置,通过针孔相机采集的四孔CH靶图像,统计计算得到装置的打靶精度优于25 m,满足设计打靶的束靶耦合精度的指标。     

Precise large deviations for generalized dependent compound renewal risk model with consistent variation

We investigate the precise large deviations of random sums of negatively dependent random variables with consistently varying tails. We find out the asymptotic behavior of precise large deviations of random sums is insensitive to the negative dependence. We also consider the generalized dependent compound renewal risk model with consistent variation, which including premium process and claim process, and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.     

Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory

Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube (SWCNT) subjected to a harmonic load is investigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.     

Improved precise integration method for differential Riccati equation

An improved precise integration method(IPIM) for solving the differential Riccati equation(DRE) is presented.The solution to the DRE is connected with the exponential of a Hamiltonian matrix,and the precise integration method(PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix.The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE.Based on the error analysis,the criterion for choosing two parameters of the PIM is given.Three kinds of IPIMs for solving the DRE are proposed.The numerical examples show that the IPIM is stable and gives the machine accuracy solutions.     

多层地基条带基础动力刚度矩阵的精细积分算法

提出应用精细积分算法计算多层地基的动力刚度问题. 精细积分是计算层状介质中波传播的高效而精确的数值方法. 利用傅里叶积分变换将层状地基的波动方程转换为频率-波数域内的两点边值问题的常微分方程组, 运用精细积分方法求解格林函数, 最后再将得到的频率-波数域内地基表面的动力刚度矩阵转换到频率-空间域内, 进而得到刚性条带基础频率域的动力柔度或刚度矩阵. 所建议的精细积分算法, 可以避免一般传递矩阵计算中的指数溢出问题, 对各种情况有广泛的适应性, 计算稳定, 在高频段可以保障收敛性, 并能达到较高的计算精度.      

时域自适应算法求解弹性地基薄板的动力问题

为更精确地求解弹性地基薄板的动力响应,发展了一种分段时域自适应算法,通过变量在离散时段内的展开,将时空耦合的初边值问题转化为一系列递推的基于有限元(FEM)的空间问题求解,通过自适应计算保持稳定的计算精度。数值算例表明:本文解与解析解相比最大相对误差不超过3.59%;当步长较大时四阶Runge-Kutta法和Newmark法均失效,本文所提算法仍可得到满意的计算结果。     

U-统计量的一些强极限定理的精确渐近性

设{Xn;n≥1}是一列i.i.d.随机变量序列,Un是以对称函数h(x,y)为核函数的U-统计量.记Un=2n(n-1) 1≤i相似文献   

刚性杆-弹簧摆模型复杂动力学特性的数值仿真

建立一种刚性杆-弹簧摆刚柔耦合强非线性动力学系统模型,给出了无量纲的动力学微分方程．该模型同时存在小幅度快速振荡和大范围慢速摆动的快、慢双时间尺度变量．针对工程中此类系统数值求解容易产生的刚性问题,采用一种三次Hermite插值精细积分法进行数值计算．将频率比、摆长比和初始摆角作为控制参数,研究刚性杆-弹簧摆刚柔耦合系统快、慢变量的复杂动力学行为．通过数值仿真分析,发现系统在不同的控制参数组合下呈现出混沌运动状态,并给出了与系统运动状态相关的控制参数范围,为复杂的刚柔耦合多体系统的设计与数值分析提供了参考．     

肽超分子自组装:结构调控和功能化

生物分子自组装对生物体有重要意义,利用生物分子构筑具有功能性的有序组装体一直是人们关注的焦点.肽分子是一类重要的组装基元,肽的超分子自组装可形成多种纳米或微米尺度的结构,并可应用于能源、医药等领域.如何实现肽自组装结构的精准调控以及精准调控肽自组装实现功能化,是目前该领域面临的新挑战.肽的自组装是基于非共价键力的协同作用实现的,通过各种因素调节这些非共价键力的作用,是实现自组装结构调控和功能化的关键.虽然自组装结构调控可以通过改变外部环境调控,但是通过精确分子设计、组装基元分子间的相互作用调控可以更好地实现结构的精准调控;并有利于进一步通过引入功能性分子作为组装基元,实现自组装体的功能化.本文将针对肽自组装体的结构调控以及功能化两个方面对相关研究进行综述.