Dependence Properties of Multivariate Mixture Distributions and Their Applications

Consider a multivariate mixture model where the random variables X ₁, ..., X _n given (₁, ..., _n ), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X _i 's. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models.     

基于光谱分析的重载车辆变速箱可靠性评估方法研究

润滑油光谱分析是变速箱磨损状态监测的重要手段。以某重载车辆变速箱台架试验中润滑油原子发射光谱分析得到的元素成分含量检测数据为基础,通过相关性分析和磨损机理分析确定了能够反映整机磨损状态和失效特点的金属元素,并对补油、换油后的光谱检测数据进行了修正,将变速箱试验过程中特征金属元素的含量随试验时间的变化规律表示为线性函数的形式。然后,综合考虑检测数据的时序规律与离散性,利用不同时刻光谱检测数据的正态分布均值和标准差进行变速箱可靠性评估,进一步讨论了失效阈值对可靠性评估结果的影响。研究表明,重载车辆变速箱润滑油中的Cu元素浓度与其他金属元素浓度的相关性较高、绝对值较大,既能够反映变速箱整体磨损状态,又便于检测,利用多个试验样本的润滑油Cu元素浓度光谱检测时序数据,可以对重载车辆变速箱进行可靠性评估;若失效阈值取定值,则失效阈值越大,同一时刻变速箱的可靠度越高;若失效阈值取随机分布,则失效阈值的离散度越大,可靠度随时间延长而降低的趋势越缓慢。当可靠度R大于0.9时,失效阈值的均值对可靠性评估结果的影响十分显著,同一时刻变速箱的可靠度随失效阈值标准差的增大而降低。将光谱分析与概率统计学结合进行变速箱可靠性评估方法研究,扩展了光谱分析技术的应用范围,具有创新性。     

关于Hopfield-型神经网络收敛性和求能量函数极小解的可靠性的研究

本文在徐宗本等1996年的论文的基础上进一步完善了Hopfield-型神经网络的收敛性定理;根据徐宗本等1996年的论文中由能量函数的极小解与网络的稳定点之间的关系而提出的三类能量函数(正则性,正常性和完备性能量函数),本文提出了两类具有完备性的Hopfield-型网络.     

探究性教学情景下的大学物理课堂评估策略

为了评估大学物理探究性教学情景下的学生综合素质,本文作者研究课堂评估法在探究性课题教学过程中各阶段的实施策略,并进行相应教学实验,得出针对大学物理探究性教学情景下的课堂评估实施原则、方式、标准.实践表明课堂评估法与探究性教学实现了有机融合,促进了学生综合素质的提高,是一种行之有效的评估学生综合素质的教学评价方法.     

Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays

Let {(ξni, ηni), 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as(S_1, ρ_n S_1 +(1-ρ_n~2S_2)~(1/2)), ρn∈(0, 1), where(S1, S2) is a bivariate spherical random vector. For the distribution function of radius (S_1~2+ S_2~2)~(1/2) belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of ρn to 1 is given. In this paper,under the refinement of the rate of convergence of ρn to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.     

An algebraic translation task solved by grade 7–9 students

In this study, the author examined student attempts to translate a verbal problem into an algebraic statement relating two variables, after they had solved an arithmetic question from the same problem. A total of 645 students from New England (U.S.A.) answered the problem on a mathematics assessment administered at the beginning of the school year. Among students who could solve the arithmetic part of the problem, the use of variables in the correct conventional notation appeared from grade 7 and continuously increased through grade 9. These results suggest that there is a relationship between students’ arithmetic understanding and translating verbal problems into algebraic statements relating two variables.     

Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a professional development program, Learning to Use Formative Assessment in Mathematics with the Assessment Work Sample Method (AWSM) to build middle school math teachers' understanding of the characteristics of high‐quality formative assessment processes and increases their ability to use them in their classrooms. AWSM proved to be feasible to implement in the middle school setting. It improved teachers' practice of formative assessment, especially in their feedback practices, regardless of their pedagogical content knowledge at entry. Results from focus groups suggested that teachers were better able to implement ungraded practice and student self‐ and peer‐assessment after AWSM, and that students were more willing to engage in complex problem solving.     

Evaluation of Transparent Optical Network Performance in Presence of Incoherent Homodyne Crosstalk

A simple method to evaluate the performance of transparent optical networks (TON) that takes into account the incoherent homodyne crosstalk, signal distortion, inter-symbol interference (ISI), amplified spontaneous emission (ASE) noise, and arbitrary optical and electrical filters is proposed. This method combines the effect of the incoherent homodyne crosstalk with an exhaustive Gaussian approximation for the influence of ASE noise, signal distortion, and ISI. It is shown that the incoherent homodyne crosstalk penalty depends on the ASE noise accumulated in the TON, ISI, and extinction ratio. The proposed method estimates are compared with experimental results published by other authors. Good agreement is observed for one, two, and four incoherent homodyne crosstalk signals, revealing that the proposed method provides accurate estimates even when the methods based on a Gaussian approximation for the incoherent homodyne crosstalk fail. The proposed method is used to assess the performance of a TON composed by optical add-drop multiplexers based on arrayed waveguide gratings. Results reveal that incoherent homodyne crosstalk, ASE noise, and ISI impair the TON performance and, therefore, none can be neglected in the TON design.     

人工调控微结构压电驻极体的热稳定性和电荷动态特性

利用表面带有周期性结构的硬质模板,通过冷压工艺将周期结构图案复制到多孔聚四氟乙烯(PTFE)薄膜表面,再经过热黏合工艺与致密氟化乙丙烯共聚物(FEP)薄膜复合,制备出了高度有序的微孔结构复合膜,并用电晕充电的方法对复合膜进行极化处理,最终获得氟聚合物复合膜压电驻极体.借助对这类复合膜压电驻极体介电谐振谱的测量,得到了材料的杨氏模量.并利用等温热老化工艺对它们的压电系数d33的热稳定性进行了考察.最后通过短路热刺激放电谱的测量和分析,讨论了该复合膜在热老化处理后的电荷动态 关键词： 有序结构 压电驻极体 压电性 电荷动态特性     

Multivariate risk models under heavy‐tailed risks

In this paper, we consider four common types of ruin probabilities for a discrete‐time multivariate risk model, where the insurer is assumed to be exposed to a vector of net losses resulting from a number of business lines over each period. By assuming a large initial capital for the risk model and regularly varying distributions for the net losses, we establish some interesting asymptotic estimates for ruin probabilities in terms of the upper tail dependence function of the net loss vector. Our results insightfully characterize how the dependence structure among the individual net losses affect the ruin probabilities in an asymptotic sense, and more importantly, from our main results, explicit asymptotic estimates for those ruin probabilities can be obtained via specifying a copula for the net loss vectors. Copyright © 2013 John Wiley & Sons, Ltd.