扁球壳在均布压力与均匀温度场联合作用下的屈曲

根据扁壳几何非线性理论,推导了均布压力与均匀温度场联合作用下的扁球壳的位移型几何非线性控制方程.考虑夹紧边界条件,采用打靶法得到了扁球壳轴对称弯曲与屈曲的数值结果.讨论了壳体几何参数对平衡路径、临界荷载的影响.给出了壳体临界几何参数.当几何参数大于临界几何参数时,上、下临界荷载都随几何参数增加而增加.给定几何参数时,考察了不同均匀温度场对壳体上、下临界荷载、临界几何参数以及平衡构型的影响.均匀升温会使上临界荷载显著增加,会使下临界荷载略有减小.均匀变温会使临界几何参数改变.     

指数族下参数双边检验的p-值

在单参数指数族下,对参数的双侧检验问题给出了一致最优检验或一致最优无偏检验的p-值;在多参数指数族下,对单个参数双侧检验问题给出了一致最优无偏检验的p-值.在正态总体下,给出了几个计算上述p-值的例子.     

扁球壳在热-机械荷载作用下的稳定性分析

基于扁壳几何非线性理论,应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件,运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时,上临界荷载随几何参数的增加单调增加,下临界荷载在很小范围内随几何参数的增加而增加,之后随几何参数的增加而减小.给定几何参数时,考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加,使下临界荷载和临界几何参数显著减小.     

离散参数集值序下鞅的Riesz分解及收敛性

本文研究了离散参数集值序下鞅的Riesz分解及收敛性.利用集值序关系及集值鞅方法,给出了离散参数集值序下鞅的Riesz分解的存在性及唯一性定理.并获得离散参数集值序下鞅的收敛性定理.     

Weibull分布步进应力加速寿命试验的Bayes估计

本文研究了定时和定数截尾情形CE模型下Weibull分布场合步进应力加速寿命试验的Bayes估计.利用加速系数和加速方程将各种加速应力水平下的尺度参数换算为正常应力水平下的尺度参数,从而获得含正常应力下尺度参数的似然函数.在参数先验的选取时,尺度参数和加速系数分别取共轭先验和无信息先验,当形状参数m<1和m>1时分别取Beta分布和Gamma分布作为其先验.在平方损失下,利用Gibbs抽样和切片抽样给出了该模型参数的Bayes估计.最后,通过Monte Carlo模拟表明该Bayes估计是有效的.     

纵向数据下半参数回归模型的统计分析

对于纵向数据下半参数回归模型,基于广义估计方程和一般权函数方法构造了模型中参数分量和非参数分量的估计.在适当的条件下证明了参数估计量具有渐近正态性,并得到了非参数回归函数估计量的最优收敛速度.通过模拟研究说明了所提出的估计量在有限样本下的精确性.     

定数截尾两参数指数——威布尔分布形状参数的Bayes估计

在不同的损失函数下,本文研究了两参数指数—威布尔分布(EWD)形状参数的Bayes估计问题.基于定数截尾试验,当其中一个形状参数α已知时,给出了另一个形状参数θ在三种不同损失函数下的Bayes估计表达式,并求得了可靠度函数的Bayes点估计.最后运用随机模拟方法,将Bayes估计和极大似然估计进行了比较.结果表明,LINEX损失下Bayes估计的精度比极大似然估计高.     

NA样本下随机设计的半参数回归模型的弱相合性

本文研究了误差为NA序列下随机设计的半参数回归模型的问题.利用权函数和最小二乘估计的方法给出了参数、非参数及误差方差的估计,在较弱的条件下获得了它们的弱相合性结果.     

固定设计下非参数回归模型估计的渐近性质

考虑固定设计下具有非参数AR(1)的非参数回归模型,综合最小二乘和非参数核估计法,定义了非参数函数的估计量,在适当的条件下,研究了它们的渐近性质.     

一类连续型单参数指数族参数的经验Bayes检验问题

讨论了独立同分布样本情形下一类连续型单参数指数族参数的经验Bayes(EB)单侧检验问题.利用密度函数的递归核估计构造了参数的EB检验函数.在适当的条件下,证明了所提出的EB检验函数的渐近最优性,并获得了其收敛速度.最后,给出了一个满足文中主要结果的例子.     

The Hill estimators under power normalization

By using the link between the affine and the power norming, eight Hill estimators under power normalization for the tail index (the non-zero extreme value index) are suggested. Moreover, more compact and adaptive four Hill estimators under power normalization are derived based on the generalized Pareto distributions under power normalization. Two classes of harmonic t-Hill estimators under power normalization are also suggested. A comprehensive simulation study using the R-package shows that all the suggested estimators under power normalization work well, but in all cases the Hill estimators under power normalization based on Pareto distributions under power normalization are better. The two models under linear and power normalization for extreme value analysis are applied with comparison on a real data set of two pollutants, Sulphur Dioxide and Particulate Matter.     

Interactions between investment timing and management effort under asymmetric information: Costs and benefits of privatized firms

In this paper, we examine the interactions between investment timing and management effort in the presence of asymmetric information between the owner and the manager where the manager has an informational advantage. We find that investment timing is later under asymmetric information than under full information, implying a decrease in the value of equity option. However, in order to minimize any distortion under underinvestment, management effort is greater under asymmetric information than under full information. We show that there are trade-offs in the efficiencies of investment timing and management effort under asymmetric information. These results fit well with the findings of past empirical studies concerning the costs and benefits of privatized firms.     

On estimation in multivariate linear calibration with elliptical errors

The estimation problem in multivariate linear calibration with elliptical errors is considered under a loss function which can be derived from the Kullback-Leibler distance. First, we discuss the problem under normal errors and give unbiased estimate of risk of an alternative estimator by means of the Stein and Stein-Haff identities for multivariate normal distribution. From the unbiased estimate of risk, it is shown that a shrinkage estimator improves on the classical estimator under the loss function. Furthermore, from the extended Stein and Stein-Haff identities for our elliptically contoured distribution, the above result under normal errors is extended to the estimation problem under elliptical errors. We show that the shrinkage estimator obtained under normal models is better than the classical estimator under elliptical errors with the above loss function and hence we establish the robustness of the above shrinkage estimator.     

Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators北大核心CSCD

Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Enlarged filtrations and indistinguishable processes

Abstract

We study modification properties of stochastic processes under different probability measures in an initially enlarged filtration setup. For this purpose, we consider several pure-jump Lévy processes under two equivalent probability measures and derive the associated martingale compensators with respect to different enlarged filtrations. As our main result, we prove that the obtained martingale processes under different probability measures in our enlarged filtration approach are indistinguishable. In addition, we provide a condition under which the pure-jump result can be carried over to the Brownian motion case. In this context, we show how indistinguishable Brownian motions under different probability measures can be constructed in an enlarged filtration framework. We finally apply our theoretical results to precipitation derivatives pricing under weather forecasts.     

线性等式约束下基本线性模型最佳线性无偏预测值的一些评论

In this paper, we give the representation of the best linear unbiased predictor(BLUP)of the new observations under M_r_f. Through the representation, we give necessary and sufficient conditions that the estimators, OLSEs(ordinary least squares estimators) and BLUEs(best linear unbiased estimators), under M_f and M_r_f, and the predictor, BLUP, under M_f continue to be the BLUP under M_r_f, respectively.     

一类带扩散项的HIV模型的平衡解的稳定性分析

研究了一类齐次Neumann边界条件下带扩散项的HIV模型.运用赫尔维茨判定定理得出正常数平衡解在一定条件下的局部渐近稳定性;当游离病毒达到一定量时,通过构造Lyapunov函数得出正常数平衡解全局稳定的条件.     

相依数据下一般函数核估计的一致收敛速度

不论数据是独立的还是相依的,在非参数和半参数模型中,都涉及到对未知均值函数或者对某函数的未知条件期望的估计.本文针对这一问题,在比较弱的条件下,给出在数据是α-混合相依时一般函数的条件数学期望的估计,并讨论了它的一致收敛速度.     

逆向选择下的委托—代理模型分析

分别讨论了在对称信息和逆向选择下,保险代理人的类型是离散和连续情形时激励合同设计问题,得出如下主要结论:保险人在对称信息和逆向选择下要求最高效率的代理人的努力水平相同,且在逆向选择下的支付更多,然而对其他类型的代理人而言,在逆向选择下要求的努力水平和所支付比在对称信息条件下都要少些.     

Geometric Models for Quasicrystals II. Local Rules Under Isometries

The atomic structures of quasicrystalline materials exhibit long range order under translations. It is believed that such materials have atomic structures which approximately obey local rules restricting the location of nearby atoms. These local constraints are typically invariant under rotations, and it is of interest to establish conditions under which such local rules can nevertheless enforce order under translations in any structure that satisfies them. A set of local rules in is a finite collection of discrete sets {Y _i } containing 0, each of which is contained in the ball of radius ρ around 0 in . A set X satisfies the local rules under isometries if the ρ -neighborhood of each is isometric to an element of . This paper gives sufficient conditions on a set of local rules such that if X satisfies under isometries, then X has a weak long-range order under translations, in the sense that X is a Delone set of finite type. A set X is a Delone set of finite type if it is a Delone set whose interpoint distance set X-X is a discrete closed set. We show for each minimal Delone set of finite type X that there exists a set of local rules such that X satisfies under isometries and all other Y that satisfy under isometries are Delone sets of finite type. A set of perfect local rules (under isometries or under translations, respectively) is a set of local rules such that all structures X that satisfy are in the same local isomorphism class (under isometries or under translations, respectively). If a Delone set of finite type has a set of perfect local rules under translations, then it has a set of perfect local rules under isometries, and conversely. Received February 14, 1997, and in revised form February 14, 1998, February 19, 1998, and March 5, 1998.