Correlations Among Maximum Likelihood and Weighted/Unweighted Least Squares Estimators in Factor Analysis

The asymptotic correlations among maximum likelihood (ML) and various least squares (LS) estimators in factor analysis are derived. The LS estimators include the unweighted (ULS) and weighted estimators for unstandardized variables and the ULS estimators for standardized variables. The derived formulas cover the cases with restrictions on parameters. Numerical examples with simulations are provided to confirm the accuracy of the formulas and the influence of scales on the asymptotic correlations.

     

On Detection of Improper Solutions in Factor Analysis by the EM Algorithm

Behaviormetrika - Adachi (2013) showed that the EM algorithm for maximum likelihood (ML) factor analysis always gives a proper solution if positive unique variances are used as the initial values....     

Correlations Between Indentation Hardness and Yield Stress in Thermoplastic Polymers

Abstract:  In mechanical testing empirical correlations are often used for estimating yield stress values from hardness values. Such empirical correlations are only valid within particular classes of materials and in the case of polymers they may be dependent on deformation rate, temperature and kind of deformation (tensile or compressive). For a better understanding of these complex correlations, instrumented indentation tests, tensile tests and compressive tests were performed on different semicrystalline and amorphous thermoplastic polymers. Indentation hardness and Martens hardness values were compared with tensile and compressive yield stress. The ratio of hardness values to tensile yield stress depends very strongly on the basic deformation mechanism (crazing, voiding or shear yielding) of the polymers. Therefore, under tensile load there is no general linear relationship between hardness and yield stress. In contrast, in the case of compressive loading hardness and yield stress are much better linearly correlated.     

Asymptotic Solutions for Multilayered Piezoelectric Cylinders under Electromechanical Loads

Based on the three-dimensional (3D) piezoelectricity, we presented asymptotic solutions for multilayered piezoelectric hollow cylinders using the method of perturbation. The material properties in the general formulation are firstly regarded to be heterogeneous through the thickness, and then specified as the layerwise step functions in the cases of multilayered cylinders. The transverse normal load and normal electric displacement are respectively applied on the lateral surfaces of the cylinders. The boundary conditions of cylinders are considered to be simply supported at the two edges. In the formulation the twenty-two basic equations of piezoelectricity are reduced to eight differential equations in terms of eight primary variables of elastic and electric fields. After performing nondimensionalization, asymptotic expansion and successive integration, we finally decompose the 3D problem into a series of 2D problems with the same governing equations for various orders except for the nonhomogeneous terms. In view of the recurrent property, it is illustrated that the present asymptotic solutions can be obtained in a hierarchic manner and asymptotically approach 3D piezoelectricity solutions.     

两自由度强非线性振动系统的渐近解及分岔分析

改进了传统规范形理论,使其适用于研究两自由度强非线性振动系统的渐近响应并进行了相应的分岔分析.通过将待定固有频率法引入规范形求解过程,获得了两自由度立方Duffing-Van der Pol强非线性振动子的规范形及稳态渐近解.参照Hopf分岔定理的形式给出了系统周期解的存在条件,通过算例对比了不同方法所得结果之间的差异,证明了方法的可行性与有效性.最后利用Mathematica编程绘制了一类强非线性振动系统的Lyapunov指数谱,验证了在特定参数值附近具有混沌吸引子.     

Experimental Determination of Correlations Between Spontaneously Formed Vortices in a Superconductor

We have imaged spontaneously created arrays of vortices (magnetic flux quanta), generated in a superconducting film quenched through its transition temperature at rates around 10⁹ K/s. From these images, we calculated the positional correlation functions for two vortices and for 3 vortices. We compared our results with simulations of the time dependent Ginzburg Landau equation in 2D. The results are consistent with the Kibble-Zurek scenario of spontaneous vortex creation. Effects due to fluctuations of the gauge field on the correlation functions are below our experimental resolution.     

求强非线性系统共振解的渐近法

本文通过引入参数变换α=ε/(υ^2 ε),并假设ω0^2=(pv／q)^2 α△，把强非线性系统转化为弱非线性系统，再将解展开为傅氏级数，利用参数待定法可方便地求出强非线性系统的共振解。算例表明近似解与数值解非常接近。     

河津转花灯艺术探析

通过对河津转花灯制作过程的阐述,分析了转花灯艺术渊源于风车制作技术,剪纸的影形文化与古灯楼装饰等多种学科原理,借人力跑动,使其转(赚),寓意花灯时来运转。转花灯艺术有着丰富的文化内涵和经济价值,随着现代的光电技术与新材料的出现,转花灯艺术传承与保护必将出现一个辉煌的前景。     

On Absence of Quantitative Correlations Between Strength and Stiffness in Microcracking Materials

We show, by numerical simulations on crack arrays, that there is no stable quantitative correlation between strength of a brittle microcracking material and its effective elastic stiffness. The reason is that fracture processes are controlled by “details” of microcrack field geometry – such as local clusters of closely spaced cracks – to which the stiffness, being a volume average quantity, is almost insensitive.     

疲劳缺口系数Kf与理论应力集中系数Kt之间的关系

疲劳缺口系数Kf是表征缺口部位疲劳强度降低程度的参量,这一系数在结构抗疲劳设计中经常被使用.一般认为Kf与理论应力集中系数Kt呈线性关系,线性的斜率与不同材料类别(铝合金、钛合金和钢)有关.通过对大量不同材料、不同应力比和不同缺口试样形式的高周疲劳极限的系统分析,发现大多数情况下K f与Kt的呈线性关系,但有些情况下二者不服从线性关系.Kf与Kt的关系除与材料类别有关外还与实验的应力比有关.     

氯化镁介质中氧化铝表面的相互作用力

利用原子力显微镜研究了氯化镁介质中氧化铝表面的相互作用力随盐浓度、ｐＨ的变化规律．在中性条件下;当ＭｇＣｌ_２盐浓度由１０^－５ｍｏｌ／Ｌ增加到１０^－2ｍｏｌ／Ｌ时,长程排斥作用由于双电层压缩,作用范围从一百多纳米减弱到十几纳米,实验测得的双电层厚度的实际值与理论值较好的吻合．保持ＭｇＣｌ_２介质浓度不变;ｐＨ由３．６４变化到９．０９;氧化铝表面的相互作用始终表现为排斥力,与测得的Ｚｅｔａ电位值始终为正值相一致．当ｐＨ＝９．５时,由于镁离子的水合氢氧化物在氧化铝表面的特性吸附,产生了短程非静电徘斥力,首次用原子力显微镜证实了Ｍｇ^２＋特性吸附层的存在,厚度约为５ｎｍ。     

两黏性颗粒间切向阻力的渐近解析解

从分析两黏性颗粒的相对切向运动着手,化二阶变系数非齐次液桥流体压力微分方程为欧拉方程,解得具有相对运动的不等径颗粒间液桥流体压力和切向黏性阻力的渐近解析解,并与Goldman意义上的近似解和其他文献中的数值解进行对比。结果表明:利用这些解析解可直接定义黏性颗粒力学模型,也可分析不同参数条件下液桥流体压力与颗粒间切向阻力的变化规律。     

An Asymptotic Approach to Second-kind Similarity Solutions of the Modified Porous-medium Equation

The problem of a spreading ground-water mound of liquid in a porous medium, situated on an impermeable horizontal solid layer is revisited. The mathematical formulation for this problem is given by the modified porous medium equation. A global condition in form of an energy integral is derived, describing the loss of liquid in the porous medium. This yields the necessary condition that enables the aymptotic derivation of the similarity exponents for the similarity solution of second kind. The method developed here, is further applied to the corresponding dipole problem, when instead of an energy integral another conservation law, the first moment integral, is considered. I dedicate this article to the memory of Julian D. Cole, who has been a great inspiration to me and to the Applied Mathematics community in general for his profound impact on the development of Perturbation Methods.     

浅析两块测温仪表指示值不一致的原因及解决办法

通过实验分析企业实际生产中,同一设备两套测温在均检定合格的情况下出现仪表指示温度不一致的原因,并根据原因从测温源头、测温硬件及测温方法三个方面提出此类情况的解决办法,为相关企业的工作人员有效防止事故,提高产品质量,增加企业效益提供一定参考。     

再制造热喷涂层的残余应力与显微特征的对应关系

利用高效能超音速等离子喷涂(HEPS)、爆炸喷涂(DGS)和高速电孤喷涂(HVAS)三种热喷涂技术制备了不同厚度的Fe-Cr-B-Si和Fe-Cr-B-Si-Mo涂层,利用X射线应力测定仪测定了涂层表面残余应力,并得出表面残余应力与涂层厚度的关系曲线,进一步采用电解剥层法+X射线应力测定法研究了涂层应力沿厚度方向的分布...     

含时滞的半线性反应扩散方程解的L2一致渐近稳定性

采用两个Lyapunov泛函方法研究含时滞的时变半线性反应扩散方程,得到其平凡解L^2一致渐近稳定的充分性判别定理。     

脉冲时滞积分-微分系统解的非振动性和渐近性

讨论了脉冲时滞积分-微分系统解的非振动性和渐近性，得到了时滞积分-微分系统在脉冲扰动下解的非振动性和渐近性的充分条件。     

Complexation between Copper(II) and Glycine in Aqueous Acid Solutions by Window Factor Analysis of Visible Spectra

Window factor analysis (WFA), a self-modeling chemometric technique, is used to extract the concentration profiles of the complexes formed between Cu(II) and glycine (GlyH) during pH titration in the acid region. The visible absorption spectra of aqueous acid solutions, each containing 0.0020 M Cu(II) and 0.500 M glycine, are recorded at various pHs, ranging from 1 to 7. The concentration profiles and the spectral absorptivities of four copper species, Cu(2+), CuGlyH(2+), CuGly(+), and CuGly(2), are obtained. The spectral absorptivities of the complexes are in good agreement with those reported in the literature. The concentration profiles are used to determine the stepwise equilibrium constants of the three complexes. The reason why rank annihilation evolving factor analysis (RAEFA), a precursor technique, was not successful in resolving the spectral data is explained.