Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Monte Carlo simulation of spatial distribution of X rays in multifilm targets. III: optimum design as applied to W/Al‐film targets

The brightness of the X‐ray source in a W/Al‐film target used for X‐ray projection microscopy was studied by an approach using the Monte Carlo simulation. Since continuous X rays generated in a thin film have a specific angular distribution of emission, the brightness of the continuous X‐ray source cannot simply be estimated on the assumption that the angular distribution is homogeneous. The newly developed approach using the Monte Carlo simulation enables the evaluation of the effective source size, angular distribution, and brightness of a continuous X‐ray source with sufficient accuracy that it leads to the optimum design of a high‐brightness X‐ray source for uses such as X‐ray projection microscopy. The Monte Carlo calculations were performed for W(Δz)/Al (200 µm)‐film targets with different thicknesses of W film, Δz, under bombardment of 60 kV electrons. The results have suggested an optimum design consisting of a W (2 µm)/Al (200 µm)‐film target as most promising for providing an X‐ray source of higher brightness than the W (5 µm)/Al (200 µm)‐film target, which has already been in practice for X‐ray projection microscopy. Copyright © 2006 John Wiley & Sons, Ltd.     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

A multivariate evolutionary credibility model for mortality improvement rates

The present paper proposes an evolutionary credibility model that describes the joint dynamics of mortality through time in several populations. Instead of modeling the mortality rate levels, the time series of population-specific mortality rate changes, or mortality improvement rates are considered and expressed in terms of correlated time factors, up to an error term. Dynamic random effects ensure the necessary smoothing across time, as well as the learning effect. They also serve to stabilize successive mortality projection outputs, avoiding dramatic changes from one year to the next. Statistical inference is based on maximum likelihood, properly recognizing the random, hidden nature of underlying time factors. Empirical illustrations demonstrate the practical interest of the approach proposed in the present paper.     

“多角度欣赏面心立方晶胞”教学设计*

尝试利用“火花学院”App等在线交互资源,引导学生从立体几何及密置层堆积模型视角,观察、描述、绘制面心立方晶胞的正四面体填隙、正八面体填隙、三视图和沿体对角线投影图像,加深学生对以面心立方晶胞结构为基础的CaF₂→金刚石晶胞、NaCl→钙钛矿晶胞结构的理解;再结合新型材料透明镁铝尖晶石晶体结构的探讨,了解晶体制备中的掺杂改性等常用方法,发展学生的微观探析能力和科学创新意识。     

Jordan operator algebras revisited

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.     

基于ELM算法的羊肉水分含量的快速无损检测

在近红外光谱900-1700nm的波长范围内采集南疆羊肉的光谱数据,来研究水分含量的快速无损检测.为减弱非目标因素对光谱的影响,采用SNV和去趋势法对光谱数据进行预处理.为降低建模的复杂度,去除共线性的影响,采用连续投影算法和相关系数法相结合选取8个特征波长变量,最后使用PLS和ELM算法分别进行建模.实验表明,与采用全光谱波段建模相比,采用特征波长变量建模,PLS和ELM算法的运行时间都大大缩短,并且在运行时间和预测精度上,ELM算法均优于PLS算法.ELM算法采用8个特征波段变量建模,预测精度达到0.9768,均方误差为4.4291e-04,相关系数为0.7603,运行时间可控制在1e-04s之下,这可为研发羊肉水分含量的便携式检测装置提供理论参考.     

An optimal perturbation bound

Cai and Zhang establish separate perturbation bounds for distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60?89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.