应力S(t)为复合χ^2更新过程时结构可靠度渐近正态估计

该文讨论强度为随机变量X,应力为复合χ２ 更新过程｛Y（t）,t∈ ［０,T］｝时结构可靠度的渐近正态性问题．获得在设计基准期［０,T］内结构可靠度表达式和结构可靠度渐近正态估计．     

正态—平稳二项过程模型结构可靠度的最小方差无偏估计

本文讨论强度随机变量Ｘ服从正态分布,应力｛Ｙ（ｔ）,ｔ∈［０,Ｔ］｝为平稳二项随机过程模型结构可靠度的最小方差无偏估计．     

部分线性模型参数分量的L_1模估计的渐近正态性

考虑ｉ．ｉ．ｄ．观测数据（Ｔ１，Ｘ１，Ｙ１），…，（Ｔｎ，Ｘｎ，Ｙｎ），其中Ｔｉ∈［０，１］，ｕｉ为观测误差，β０为未知参数向量，ｇ０为未知函数．本文用分段多项式ｇｎ（ｔ）来逼近ｇ０（ｔ），求解得到β０的估计β和ｇ０的估计ｇｎ，其中ｎ是一个ｍ阶分段多项式类．在一定条件下，本文证明了渐近正态．     

应力为复合χ^2—更新过程时结构可靠度的一致估计

本文讨论强度为随机变量Ｘ,应力为复合χ＾２－更新过程Ｙ（ｔ）的半随机过程可靠性模型的结构可靠度一致估计问题。获得在设计基准期［０,Ｔ］内结构可靠度表达式和结构可靠度的一致估计。     

正态——复合Weibull过程模型结构可行性当量正态设计

本文讨论强度Ｒ－Ｎ（μｎ，σＲ＾２），应力（Ｓ（ｔ），ｔ∈「０，Ｔ」）为复合Ｗｅｉｂｕｌｌ过程模型结构可靠性当量正态设计。获得应力在设计基准期「０，Ｔ」内的最在值概率及统计参数估计；正态－复合Ｗｅｉｂｕｌｌ过程模型结构可靠度和结构可靠性当量正态设计表达式。     

具周期系数的奇阶中立型微分方程的振动与非振动结果

对于奇阶中立型方程［ｘ（ｔ） － ｐｘ（ｔ－ τ）］（ｎ） ＋ ｑ（ｔ）ｘ（ｔ－ σ） ＝ ０,其中ｑ（ｔ） 为τ－周期函数,分别得出了振动与非振动结果,并将所得结果用到方程［ｘ（ｔ） － Ｐ（ｔ）ｘ（ｔ－ τ）］（ｎ） ＋Ｑ（ｔ）ｘ（ｔ－ σ） ＝ ０,其中Ｑ（ｔ） 为渐近周期函数．     

奇阶中立型时滞微分方程解的振动性

１．引言考虑奇阶非线性泛函微分方程［ｘ（ｔ）－ｃｘ（ｔ—(）］（ｎ）＋ｐ（ｔ）ｆ（ｘ（ｔ－σ））＝０（１）对方程（１）我们作如下假设（Ｈ）：（Ｈ１）ｎ＞１是奇整数,ｐ∈Ｃ（（ｔ０,∞）,（ｔ０,∞））;（Ｈ２）τ＞０,σ＞０且０≤ｃ≤１;（Ｈ３）ｆ∈Ｃ（Ｒ,Ｒ）是单调增加,ｘｆ（ｘ）＞０,Ｘ≠０且当｜ｘ｜→∞时有｜ｆ（ｔ）｜→∞．设δ＝ｍａｘ｛τ,σ｝,∈Ｃ（［Ｔ－δ,Ｔ］,Ｒ）．方程（１）在［Ｔ,∞）上的解是指函数ｘ∈Ｃ（［Ｔ,∞）,Ｒ）,使得ｘ（ｔ）＝(（ｔ）,Ｔ－δ≤ｔ≤Ｔ,［ｘ（ｔ）－ｃｘ…     

中立型方程x(t)+cx(t-ㄒ)+ax(t)+bx(t-ㄒ)=0零解渐近稳定的代数判据

本文建立了方程ｘ（ｔ）＋ｃｔ（ｔ－ｔ）＋ａｘ（ｔ）＋ｂｘ（ｔ－ｔ）＝０零解渐近稳定的充要条件,给出了其零解渐近稳定的代数判据,同时纠正了文［２］中出现的错误．     

一阶急式微分方程周期边值问题(英文)

本文我们描述了一个构造性方法．在存在一个上解β及下解α且α≤β情形下,得到两个单调序列一致收敛于如下周期边值问题．ｘ′（ｔ）＝ｆ（ｔ,ｘ（ｔ）,ｘ′（ｔ））,ｔ∈［０,Ｔ］ｘ（０）＝ｘ（Ｔ）,｛的极值解     

积分算子的n-逼近数

本文研究了积分算子ＴＫ：Ｌｑ［０，１］→Ｌｑ［０，１］，（ｑ≥１）当核 Ｋ（ｓ， ｔ）是 Ｓｏｂｏｌｅｖ空间 Ｗｐｒ（［０， １］２）中元素时ｎ－逼近数 ａｎ（ＴＫ： Ｌｑ→ Ｌｑ）的估计，并把这个估计应用于退化核方法解第二类线性Ｆｒｅｄｈｏｌｍ方程（Ｉ一ＴＫ）ｘ＝ｙ时，Ｂａｄｈｖａｌｏｖ［５］意义下最佳误差的讨论中，所得到的最佳误差之估计当ｑ＝１时，最优化了［１０］的结论．     

ASYMPTOTICALLY ISOMETRIC COPIES OF lp (1≤p＜∞) AND c0 IN BANACH SPACES

Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1 ＜ p ＜∞). Then there exists a quotient space of X which is asymptotically isometric to lq (1/p 1/q=1). Complementedasymptotically isometric copies of c0 in K(X, Y) and W(X, Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c0, it has to contain complemented asymptotically isometric copies of c0.     

在伽玛-指数模式下串联结构系统可靠度估计

设结构系统由ｎ个结构性部件串联组成．设部件ｋ的强度Ｘｋ服从指数分布厂Г（λ，１），λ＞０，ｋ＝１，２，…，ｎ；系统应力Ｙ服从Ｇａｍｍａ分布Г（μ，α），μ，α＞０．当α已知，λ，μ未知时，本文给出串联结构系统可靠度ＲＲ的ＭＶＵＥＲＲ和ＭＬＥＲＲ．证明了ＲＲ和ＲＲ都是ＲＲ的相合渐近正态估计．     

应力为复合x~2-更新过程时结构可靠度的一致估计

本文讨论强度为随机变量X,应力为复合x2-更新过程Y（t）的半随机过程可靠性模型的结构可靠度一致估计问题．获得在设计基准期[0,T]内结构可靠度表达式和结构可靠度的一致估计．     

β-范空间中l_β(β<1)的渐进等距Copy问题的研究

我们给出了赋β-范空间X包含lβ(β<1)的一个渐进等距copy的定义,并且得到:若一个β-范空间X包含lβ(β<1)的一个渐进等距copy,则在X的闭有界β-凸子集上的非扩张映射没有不动点.还得到了一个β-范空间包含lβ(β<1)的渐进等距copy的某些充分必要条件.注意:本章所有的β满足β<1.     

相依样本下非参数回归函数递推型核估计的渐近分布

设（Ｘｉ，Ｙｉ）１≤ｉ≤ｎ为来自二元总体（Ｘ，Ｙ）的平稳，φ－混合样本，记ｍ（ｘ）△Ｅ（Ｙ│Ｘ＝ｘ），ｍ（ｘ）的一种递推型核估计为ｍｎ（ｘ）＝ｎ∑ｉ＝１ｈｉ＾－１Ｙｉｋ（（ｘ－Ｘｉ）／ｈｉ）／ｎ∑ｊ＝１ｈ＾－１ｊｋ（ｘ－Ｘｊ）／ｈｊ）。本文在一定的条件下证明了（ｎ／（ｎ∑ｊ＝１ｈ＾－１ｊ）＾１／２）（ｍｎ（ｘ１）－ｍ（ｘ１），ｍｎ（ｘ２）－ｍ（ｘ２），．．．ｍｎ（ｘｒ０）－ｍ（ｘｒ０））′依分布收     

Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments

Stochastic simulations applied to black-box computer experiments are becoming more widely used to evaluate the reliability of systems. Yet, the reliability evaluation or computer experiments involving many replications of simulations can take significant computational resources as simulators become more realistic. To speed up, importance sampling coupled with near-optimal sampling allocation for these experiments is recently proposed to efficiently estimate the probability associated with the stochastic system output. In this study, we establish the central limit theorem for the probability estimator from such procedure and construct an asymptotically valid confidence interval to quantify estimation uncertainty. We apply the proposed approach to a numerical example and present a case study for evaluating the structural reliability of a wind turbine.     

Asymptotically Isometric Copy of lβ (0 ＜β ＜ 1) in Spaces of Bounded Linear Operators

Assume X is a normed space, every x* ∈ S(X*) can reach its norm at some point in B(X), and Y is a β-normed space. If there is a quotient space of Y which is asymptotically isometric to lβ, then L(X, Y) contains an asymptotically isometric copy of lβ. Some sufficient conditions are given under which L(X, Y) fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L(X, Y).     

正态—复合Weibull过程模型结构可靠性当量正态设计

本文讨论强度R～N(μR,σ_R~2),应力为{S(t),t∈[0,T]}为复合Weibull过程模型结构可靠性当量正态设计,获得应力在设计基准期[0,T]内的最大值概率分布及统计参数估计,正态—复合Weibull过程模型结构可靠度和结构可靠性当量正态设计表达式。     

On the estimators of model-based and maximal reliability

Four estimators of the reliability for a composite score based on the factor analysis model and five estimators of the maximal reliability for the composite are presented. When the Wishart maximum likelihood is used for the estimation of the model parameters, it is shown that the five estimators of maximal reliability are the same. Asymptotic cumulants of the estimators and their logarithmic transformations are derived under arbitrary distributions with possible model misspecification. The theoretical results considering model misspecification when a model does not hold are shown to be closer to their simulated values than those neglecting model misspecification. Simulations of the confidence intervals using the normal approximation based on the asymptotically distribution-free theory and the asymptotic expansion by Hall’s method with variable transformation are performed.     

On Asymptotically Isometric Copies of lβ (0 《β《1)

We get the characterizations of the family of all nonnegative,subadditive,β-absolutely homogeneous and continuous functionals defined on X,when the β-normed space X contains an asymptotically isometric copy of lβ.Moreover,it is proved that if a closed bounded β-convex subset K of a β-normed space contains an asymptotically isometric lβ-basis,then K contains a closed β-convex subset C which fails the fixed point property.