Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

基于SWT方法的钢绞线索微动疲劳特性分析

为得到钢绞线索丝间接触区的应力场分布并预测微动疲劳裂纹萌生位置和微动疲劳寿命，本文利用参数化方法建立了精细化的钢绞线拉索有限元模型，包括整索模型和不同层丝间接触区域的局部精细化子模型．分析了钢绞线索在两种交变荷载工况下的应力场变化情况，并基于多轴疲劳SWT(Smith-Watson-Topper)临界平面法进行了疲劳特性分析和疲劳寿命预测．主要结论如下：钢绞线索内接触区边缘处的微动幅值较大，中心处几乎没有相对滑动，微动疲劳的初始裂纹萌生点位于接触区域边缘；经不同区域子模型分析比较，在轴向循环荷载作用下，外层钢丝的接触区域比内层钢丝更易发生微动疲劳损伤；在横向位移循环荷载作用下，同层钢丝因位置角度不同而产生了较大的疲劳特性差异，且相比轴向循环拉伸，该工况下最不利单丝的微动疲劳寿命更低；与非接触区域相比，接触区的疲劳寿命大幅降低，微动现象对钢绞线索的抗疲劳性能有明显降低作用．     

航空导管弯曲试验的疲劳裂纹萌生寿命

飞行器液压导管受接头和卡箍等约束，在使用的振动环境中，会因弯曲应力而导致破裂，影响到飞行安全．本文对飞行器液压系统通用的不锈钢导管的裂纹萌生寿命进行了试验研究．首先在对8 mm、12 mm 无缺陷导管和含U 型缺口8 mm 导管的疲劳试验和有限元分析的基础上，得到了导管的最大拉应变-裂纹萌生寿命数据．然后采用基于强度极限和弹性模量估算法的Manson-Coffin 公式来预测导管裂纹萌生寿命．最后引入加载类型修正系数、表面质量修正系数、试样尺寸修正系数、应力集中敏感系数和有效应力集中系数，使修正后的公式对三种类型的导管均有较好的裂纹萌生寿命预测精度．     

Study of blood collection and sample preparation for analysis of vitamin D and its metabolites by liquid chromatography–tandem mass spectrometry

The analysis of vitamin D status, with special emphasis on 25-hydroxyvitamin D and 1,25-dihydroxyvitamin D, is gaining interest in clinical studies due to the classical and non-classical effects attributed to this prohormone. In this research, the influence of the two steps preceding determination (viz. sample collection and preparation) on the quantitative analysis of vitamin D and its more important metabolites has been studied. Two preparation approaches, deproteination and solid-phase extraction (SPE), have been evaluated in terms of sensitivity to delimit their application, thus establishing that detection of 1,25-dihydroxyvitamin D cannot be addressed by protein precipitation. Concerning sample collection, serum and plasma reported high accuracy (above 83.3%) for vitamin D and metabolites, while precision, expressed as relative standard deviation, was below 12.9% for all analytes in both samples. Statistical analysis revealed that serum and plasma provided similar physiological levels for vitamin D₃, 24,25-dihydroxyvitamin D₃ and 25-hydroxyvitamin D₃, while significantly different levels were obtained for 1,25-dihydroxyvitamin D₃, always higher in plasma than in serum. Sample collection and treatment have proved to be significant in the analysis of vitamin D and its relevant metabolites.     

一种轿车车轮应力状态测量与分析方法

基于台架应变测试试验方法,研究轿车车轮在疲劳试验中的应力状态。结果表明:车轮的径向疲劳试验时,轮胎会对车轮的载荷产生较大的影响,轮胎与转鼓的挤压变形以及正反转动都会对车轮的应力状态产生影响;车轮径向疲劳试验时,最大应变出现在轮辋与轮胎接触位置沿车轮圆周方向,而在靠近轮心位置的应变较小;车轮弯曲疲劳试验时,最大应变出现在轮辐靠近轮心的位置,最大应变出现在轮辐的长度方向;不同的载荷对车轮应变的变化规律并没有影响,但是会对最大和最小峰值产生影响。     

一种经验型疲劳小裂纹扩展模型

金属材料疲劳寿命由裂纹萌生和裂纹扩展寿命两部分组成，其中对于萌生寿命中的小裂纹分析是精确描述裂纹萌生寿命的关键．而小裂纹在扩展过程中由于尺寸相对较小，导致传统线弹性断裂力学预测方法失效，需要对其进行改进，考虑裂纹尖端塑性区引起的残余压应力对小裂纹扩展速度的影响．本文针对此问题进行了初步分析，通过对塑性区引起的残余应力的量化，结合小裂纹门槛值特性，提出了一种经验型修正的小裂纹扩展模型，用于定量预测裂纹的萌生寿命．使用铝合金6082-T6缺口试样进行了疲劳实验，并与理论结果进行了对比，验证了所提模型的有效性．     

An interview with Sam C. Saunders

Sam C. Saunders, the son of Elizabeth Cundiff and Winston E. Saunders, was born in Richland, OR, on February 24, 1931. The family moved to La Grande, OR, in 1944, where Sam completed high school and two years at Eastern Oregon College. He then received the BSc degree in Mathematics from the University of Oregon, Eugene, OR, in 1952, and he attended the University of Washington, Seattle, WA, receiving a PhD degree under Z. W. Birnbaum. After graduating, he accepted employment at the Boeing Company in its Mathematical Services Unit and, in 1972, a position as a Full Professor at Washington State University, Pullman, WA, from which he retired in 1996.     

Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

过载作用下聚乙烯疲劳裂纹扩展行为研究

论文针对中密度聚乙烯材料(MDPE)，采用平板试样进行了I型疲劳裂纹扩展和单次过载下裂纹扩展试验．发现与金属材料类似，单次拉伸过载对聚乙烯(PE)的疲劳裂纹扩展有明显的迟滞作用，降低了裂纹扩展速率．试验还通过变载荷刻线法获取疲劳裂纹扩展前缘的实际形貌和变化规律，对常规变载荷刻线方法进行了调整和验证，其修正方法对高分子材料的疲劳裂纹扩展前缘刻线具有较好的效果．通过观察发现含楔形塑性区的裂尖钝化是裂纹迟滞的主要原因．过载引入的塑性区内残余应力对裂纹迟滞也起了重要作用．论文利用Dugdale模型计算了塑性区尺寸，使用基于残余应力的Wheeler模型对过载迟滞进行了很好的拟合．     

吊车荷载作用下钢结构吊车梁的疲劳可靠寿命评估

从Miner累积损伤的定义出发，视累积损伤为随机过程，临界损伤为随机变量，基于疲劳动态可靠性理论，提出了在役钢结构吊车梁疲劳剩余寿命的可靠寿命评估法。之后与现行《钢结构检测评定与加固技术规程》(YB9257-96)中安全期限寿命评估法进行了分析比较，说明了安全寿命评估方法的概率意义。算例分析结果表明，本文提出的可靠寿命评估方法更加合理。