一类比例保险模型的破产概率问题

研究了比例再保险的破产概率问题,推广了Gramer-Lundberg经典模型的有关结果,并证明了基于比例模型合保问题最低保费的一个结果。     

一类非线性方程解的存在和唯一性及在图像中的应用

本文我们给出一个修正的非线性扩散方程模型，与Cotte Lions和Morel的模型相比该模型有许多实质上的优点。主要的想法是把原来去噪声部分：卷积Gauss过程替代为解一个有界区域上的线性抛物方程问题，因此避开了对初始数值如何全平面延拓的问题。我们从数学上的证明该问题解的存在性和适定性，同时给出对矩形域情况的解的级数形式。最后我们给基于本模型的数值计算差分模型，并且给出几个具体图像在该模型下处理结果。     

多元Lanchester方程在装备战损量预计中的应用

在战时装备保障中,装备战损量预计是一难点问题.本文从分析影响装备战损的因素出发,采用多元Lanchester方程寻求解决方案.提出了基于指数多元Lanchester方程的装备战损量预计模型和模型中毁伤系数的确定方法.据此,建立了一种新的装备战损量预计方法,并举例验证.该方法较好的满足了未来信息化条件下作战装备保障的需要,具有重要的参考价值.     

带色散项的周期可积Hunter-Saxton方程的波的破裂

本文考虑一个带色散项的可积Hunter-Saxton方程的周期柯西问题.首先,我们得出该模型的强解的一个精确的爆破机制.其次,利用守恒量和特征方法,分别建立了有限时间内强解的爆破发生的充分条件.最后,给出了强解的爆破率.     

2011年研究生建模竞赛B题的评阅综述

本题从一项科研项目中提炼、并结合目前成为关注热点的隐身技术而设计,侧重于数学建模.结合题中的2个问题,可以抽象出3个平时比较少见的数学模型:几何模型,反射投影模型和积分方程模型.在竞赛中,前2个模型都有部分同学正确地得出,可惜的是,问题2所要求的积分方程模型,在近500份答卷,却无人得出,甚为遗憾.问题2属于一个需要同时确定数个彼此关联影响的函数的问题,处理这样问题的基本方法是建立以这些函数为变量的方程组,在这里由于确定相互影响的定量关系必须用积分,所以最终得出的是一个积分方程组.微分积分是大学数学中最基本最重要的概念和方法,由此不难看出,我们的基础教育中的弊病与问题,这需要引起有识之士们的反思.     

波动方程的差分反演模型

为了反演波动方程的系数函数,利用差分离散及扰动假设,推导出一个适合迭代的数值模型．解决了以往方法中正反演模型数值精度不一致问题,以及由此带来的一系列问题．经数值模拟计算说明,该方法是可行的和有效的．     

确定非线性椭圆方程系数的反问题

文[6]、[7]分别研究了两个自变量确定椭圆方程第一和第三边值问题系数的反问题,文[8]考虑非线性的超定边值条件,证明反问题按最大模和L_2模下均是适定的.文[1]研究确定线性椭圆方程系数的反问题,但对线性方程采用迭代法证明反问题解的存在性时,证明不够完善.本文将采用Banach空间中的Schauder不动点原理来证明此问题. Ω和D分别是R~n和R~(n 1)中的有界域,(x,y)=(x_1,…,x_n,y),(y)是D中的点,x∈Ω,y有时记作x_(n 1).(?)Ω和分别是Ω和D的光滑边界.γ(或γ_i,i=1,…,N)是D中的n维超曲面,且设在R~n中的投影复盖Ω.     

F检验和信度系数a

一次测验之后，可以把检验分数表为关于因子A（代表人）和因子B（代表题目）的两向分类模型。对这个模型，我们感兴趣的一个问题是：因子A效应之间的差异是否显著，用F－检验可以对此进行检验。在测验理论中考虑的另一个问题是：测验分数是否反映出考生的真实水平，通常用信度系数a作为可靠性的一种度量。对同一个考生样本来说。因子A的F－检验与a系数之间存在函数关系。根据这一关系可以进一步认识这两个不同统计量的作用。     

半线性奇系数临界双调和方程的Dirichlet问题

主要探讨了两类半线性双调和Dirichlet问题：奇系数次临界问题和临界但带较弱奇性问题 ，得出了在临界维数和正常维数不同情况下都至少有一个正解的结论. 同时也研究了临界维数的消失问题，比较了奇系数与较弱奇性不同情况下临界维数的变化，得出奇性越大临界维数越少的结论.      

非稳态奇异系数方程的有限元方法

如果求解区域与数据都满足轴对称条件,利用柱坐标变换可将三维Poisson方程-△u=f的第一边值问题化为具有奇异系数的二维稳态问题     

Optimal reinsurance under dynamic VaR constraint

This paper deals with the optimal reinsurance strategy from an insurer’s point of view. Our objective is to find the optimal policy that maximises the insurer’s survival probability. To meet the requirement of regulators and provide a tool to risk management, we introduce the dynamic version of Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR) and worst-case CVaR (wcCVaR) constraints in diffusion model and the risk measure limit is proportional to company’s surplus in hand. In the dynamic setting, a CVaR/wcCVaR constraint is equivalent to a VaR constraint under a higher confidence level. Applying dynamic programming technique, we obtain closed form expressions of the optimal reinsurance strategies and corresponding survival probabilities under both proportional and excess-of-loss reinsurance. Several numerical examples are provided to illustrate the impact caused by dynamic VaR/CVaR/wcCVaR limit in both types of reinsurance policy.     

Lattice Boltzmann equation model for multi-component multi-phase flow with high density ratios

Multi-component multi-phase (MCMP) flows are very common in engineering or industrial problems, as well as in nature. Because the lattice Boltzmann equation (LBE) model is based on microscopic models and mesoscopic kinetic equations, it offers many advantages for the study of multi-component or multi-phase flow problems. While the original formulation of Shan and Chen’s (SC) model can incorporate some MCMP flow scenarios, the density ratio of the different components is greatly restricted to less than approximately 2.0. This obviously limits the applications of this MCMP LBE model. Hence, based on the original SC MCMP model and the improvements in the single-component multi-phase (SCMP) flow model reported by Yuan and Schaefer, we have developed a new model that can simulate a MCMP system with a high density ratio.     

Dependence structure between LIBOR rates by copula method

This paper discusses the correlation structure between London Interbank Offered Rates (LIBOR) by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela (1997) and find out that the copula function between two LIBOR rates can be expressed as a sum of an infinite series, where the main term is a distribution function with Gaussian copula. Partial differential equation method is used for deriving the copula expansion. Numerical results show that the copula of the LIBOR rates and Gaussian copula are very close in the central region and differ in the tail, and the Gaussian copula approximation to the copula function between the LIBOR rates provides satisfying results in the normal situation.     

对白化方程优化的一类新信息灰色GM(1,1)模型研究

通过对一类灰色GM(1,1)模型中的白化方程进行优化,同时利用灰色系统理论中的新信息原理,得到了一种改进的灰色GM(1,1)模型.最后,实例分析结果表明,该改进模型具有更高的预测精度和实用性.     

隐变量交互作用分析建模及其在SAS上的实现

探讨隐变量交互作用分析的建模方法及其在SA S软件上的实现;首先阐述隐变量交互作用分析建模的原理,通过拟合一个隐变量交互作用分析示例,对加入交互作用项的统计分析结果与无交互作用项的统计分析结果进行对比;示例中交互作用项引起的变异在结果变量的总变异中占到79.20%.在应用结构方程模型分析隐变量产生的效应时,有时候不进行隐变量交互作用的分析可能会产生偏倚.     

具有相位阻尼的Milburn主方程控制的双光子JC模型

该文利用超算子技术求出了相位阻尼下非共振双光子JC模型主方程的解析解，研究了其相位阻尼对光子数分布振荡，原子数反转与恢复和亚泊松光子分布等非经典效应的影响。研究表明：相位阻尼能抑制原子反转与恢复和腔场的非经典效应。     

Identification of the unknown diffusion coefficient in a linear parabolic equation by the semigroup approach

In this article, we study the semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(x) in the linear parabolic equation ut(x,t)=(k(x)uxx(x,t)), with Dirichlet boundary conditions u(0,t)=ψ₀, u(1,t)=ψ₁. Main goal of this study is to investigate the distinguishability of the input-output mappings Φ[⋅]:K→C¹[0,T], Ψ[⋅]:K→C¹[0,T] via semigroup theory. In this paper, we show that if the null space of the semigroup T(t) consists of only zero function, then the input-output mappings Φ[⋅] and Ψ[⋅] have the distinguishability property. Moreover, the values k(0) and k(1) of the unknown diffusion coefficient k(x) at x=0 and x=1, respectively, can be determined explicitly by making use of measured output data (boundary observations) f(t):=k(0)ux(0,t) or/and h(t):=k(1)ux(1,t). In addition to these, the values k^′(0) and k^′(1) of the unknown coefficient k(x) at x=0 and x=1, respectively, are also determined via the input data. Furthermore, it is shown that measured output dataf(t) and h(t) can be determined analytically, by an integral representation. Hence the input-output mappings Φ[⋅]:K→C¹[0,T], Ψ[⋅]:K→C¹[0,T] are given explicitly in terms of the semigroup. Finally by using all these results, we construct the local representations of the unknown coefficient k(x) at the end points x=0 and x=1.     

SEM Modeling with Singular Moment Matrices Part I: ML-Estimation of Time Series

A structural equation model (SEM) with deterministic intercepts is introduced. The Gaussian likelihood function does not contain determinants of sample moment matrices and is thus well-defined for only one statistical unit. The SEM is applied to the dynamic state space model and compared with the Kalman filter (KF) approach. The likelihood of both methods are shown to be equivalent, but for long time series numerical problems occur in the SEM approach, which are traced to the inversion of the latent state covariance matrix. Both approaches are compared on several aspects. The SEM approach is now open for idiographic (N = 1) analysis and estimation of panel data with correlated units.     

ConvexLAR: An Extension of Least Angle Regression

The least angle regression (LAR) was proposed by Efron, Hastie, Johnstone and Tibshirani in the year 2004 for continuous model selection in linear regression. It is motivated by a geometric argument and tracks a path along which the predictors enter successively and the active predictors always maintain the same absolute correlation (angle) with the residual vector. Although it gains popularity quickly, its extensions seem rare compared to the penalty methods. In this expository article, we show that the powerful geometric idea of LAR can be generalized in a fruitful way. We propose a ConvexLAR algorithm that works for any convex loss function and naturally extends to group selection and data adaptive variable selection. After simple modification, it also yields new exact path algorithms for certain penalty methods such as a convex loss function with lasso or group lasso penalty. Variable selection in recurrent event and panel count data analysis, Ada-Boost, and Gaussian graphical model is reconsidered from the ConvexLAR angle. Supplementary materials for this article are available online.     

一种改进的四阶偏微分方程图像去噪模型

针对四阶偏微分方程图像去噪模型对图像平滑区域处理造成不平整现象,以及无法去除椒盐噪声的问题.首先对含噪图像进行高斯滤波,然后通过修改扩散系数得到一个改进的四阶偏微分方程图像去噪模型.MATLAB仿真结果表明:新模型与原四阶偏微分方程去噪模型相比,其去噪图像不仅视觉效果好;而且峰值信噪比也高;另外,新模型还能有效去除椒盐噪声.