Asymptotic Approximations of Jacobi Polynomials and Their Zeros with Error Bounds

IntroductionUniform asymptotic expansions and error boundsof the (α,β>- 1 ) two- term approximations of theJacobi polynomials P(α,β)n ( cosθ) were obtained[1] .Their result wassin θ2α cosθ2βP(α,β)n ( cosθ) =Γ( n +α + 1 )n!θsinθ1/ 2 Jα( Nθ)Nα +θB0 (θ) Jα+1( Nθ)Nα+1+σ2 ,|σ2 |≤ E2 θ2 +αN -2 ,　 0≤θ≤ π2 ,where E2 is a construct.Baratella and Gatteschiused the first two terms of this expansion[2 ] toconstructa more accurate one- term approximation:x(θ)x′(θ)…     

旋转变换理论及其在平面度误差评定中的应用

将旋转变换理论应用于平面度误差评定中，通过实例证明了其可行性。     

A carbon- and oxygen-isotope record of recent environ- mental change from Qinghai Lake, NE Tibetan Plateau

An understanding of natural climatic variability is essential for evaluating anthropogenic impacts on recent and future climate[1—3]. Due to the lack of lengthy instrumental records, such an understanding must be gained from natural archives of climate change. Palaeolimnological indicators of past lake levels may provide a sensitive record of changes in effective precipitation in closed basins. This approach is particularly relevant on the Tibetan Plateau, where instrumental records are very…     

Climatic significance of stable carbon isotope in tree rings of Abies spectabibis in southeastern Tibet

The annually cross-dated stable carbon isotope of tree-ring a-cellulose of Abies spectabibis collected from the southeastern Tibetan Plateau is used to examine its rela-tionship with climatic parameters. The residual D13C series in treerings is constructed after removing the effects of age trend and rising CO2. We found a close relationship between D13C in tree rings and the relative humidity of September—November of the previous year measured at the nearby Ny-ingchi Meteorological Station, albeit a strong 搇agged effect? Thus we developed a transfer function to reconstruct the autumn relative humidity for the Nyingchi region, which explained 37.9% of the total variance (p < 0.001). Our results suggest a high frequency and moderate amplitude variance of the relative humidity before 1800, and the variance re-versed afterwards.     

关于常微分方程初值问题数值解误差的探讨

引用B样条插值函数讨论了一阶常微分方程初值问题的数值解 ,给出一个隐式近似求解公式 ,并得到此公式的局部截断误差为O(h5) ,整体截断误差为O(h4 ) .在此基础上又给出了一个校正显式求解公式 ,其局部截断误差为O(h4 ) .     

具有Neumann边界及临界Sobolev指数的半线性抛物方程

主要运用能量方法及稳定集和不稳定集的观点,研究一类半线性抛物方程的整体解和局部解的存在性及爆破问题.这里Ω是RN(N≥3)上的光滑有界区域,2 是临界Sobolev指数.     

基于普通编码器的高精度位置检测方法

根据普通增量式光电编码器测量转角位置的原理，分析了量化误差的形成原因和编码器脉宽制造误差对测量精度的影响，提出了新的信号处理算法——脉冲细分法，利用该方法减小了量化误差．同时标定出编码器的脉宽系数井以它作为脉宽制造误差的补偿参数，消除对位置测量造成的影响，最终提高了系统的测量精度．     

船舶驾驶失效搁浅概率的混合事件树分析

针对传统事件树不能分析和考虑人因错误为主的基本事件的发生概率及其敏感性和不确定性这一问题，通过引入模糊错误率及模糊错误概率的概念，将传统事件树中人因错误为主的基本事件的发生概率用模糊错误率表示，非人因错误为主的基本事件的发生概率用模糊概率表示。采用混合事件树方法得到了船舶驾驶失效引起的搁浅的模糊概率，定义了模糊敏感性和不确定性因子并对其进行了分析，制定了减小船舶搁浅事故发生概率的相关措施。计算结果表明，本文提出的方法在处理包含人因错误为主的事件的船舶搁浅概率计算问题时是有效的。     

增长曲线模型误差方差的非齐次二次型可容许估计

对于增长曲线模型Y=ABC+εEε=0,cov(vecε)=σ2(Ip Gn),在二次损失函数下,研究了误差方差的非齐次二次型估计的容许性.在矩阵A行满秩而矩阵C列满秩时,得到了非齐次估计可容许的充要条件.     

带重尾分布的高速网络交通过程

考虑网络交通模型包括了无穷个顾客一个服务台 ,顾客的初始到来是依泊松过程来到服务台 ,顾客的到达间隔服从重尾分布。将传送周期长度的概率数量指标从 1 <α<2推广到 α>1 ,获得了网输入交通过程收敛到斜平稳列维过程。