Non-standard asymptotics in an inhomogeneous gamma process

Nonhomogeneous Poisson process (NHPP) is a commonly used stochastic model that is utilized to describe the pattern of repeated occurrence of certain events or conditions. Aninhomogeneous gamma process evolves as a generalization to NHPP, where the observed failure epochs correspond to every successive κ-th event of the underlying Poisson process, κ being an unknown parameter to be estimated from the data. This article focuses on a special class of inhomogeneous gamma process, calledmodulated power law process (MPLP) that assumes the Weibull form of the intensity function. The traditional power law process is a popular stochastic formulation of certain empirical relationships between the time to failure and the cumulative number of failures, often observed in industrial experiments. The MPLP retains this underlying physical basis and provides a more flexible modeling environment potentially leading to a better fit to the failure data at hand. In this paper, we investigate inference issues related to MPLP. The maximum likelihood estimators (MLE’s) of the model parameters are not in closed form and enjoy the curious property that they are asymptotically normal with a singular variance-covariance matrix. Consequently, the derivation of the large-sample results requires non-standard modifications of the usual arguments. We also propose a set of simple closed-form estimators that are asymptotically equivalent to the MLE’s. Extensive simulation results are carried out to supplement the theoretical findings. Finally, we implement our inference results to a failure dataset arising from a repairable system.     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

不同硬化指数的幂次硬化结合材料的界面端奇异性分析

从位移匹配的观点出发,本文认为对任意结合角度的幂次硬化材料界面端弹塑性问题,如果两种材料的硬化指数不相同,则应力场的奇异次数应由硬化指数较高一方材料的材料性质和几何形状决定。进一步分析表明,奇异次数只与该材料的硬化指数n及界面端角度有关,与比例常数α等其它材料常数无关。通过边界元数值计算对上述结论进行了验证,并且发现随着硬化指数的提高,应力奇异次数降低。     

Bifurcations in Nonlinear Discontinuous Systems

This paper treats bifurcations of periodic solutions indiscontinuous systems of the Filippov type. Furthermore, bifurcations offixed points in non-smooth continuous systems are addressed. Filippov'stheory for the definition of solutions of discontinuous systems issurveyed and jumps in fundamental solution matrices are discussed. It isshown how jumps in the fundamental solution matrix lead to jumps of theFloquet multipliers of periodic solutions. The Floquet multipliers canjump through the unit circle causing discontinuous bifurcations.Numerical examples are treated which show various discontinuousbifurcations. Also infinitely unstable periodic solutions are addressed.     

线弹性幂强化材料平面杆系弹塑性分析的数值解

各杆任意铰接在一个刚体上的平面杆系是一种比较复杂的杆系结构,某些其它类型的平面杆系常常可以看作是它的特例。本文将材料的本构关系描述为线性幂强化形式,推导出了该类平面杆系结构弹塑性分析的普遍表达式,编制了通用程序,使这一类问题有了一个通用的解题方法。     

地理信息系统GIS支持下的城市地质环境评价

以 GIS为支撑工具 ,对城市地质环境空间数据库的建立方法、城市建设用地类型的初步划分及城市建设用地与地质环境的协调性评价模型作了分析 ,并选取典型实例进行剖析 ,结果表明 GIS是城市地质环境研究的有效工具。     

风载对筒形高耸建筑物定向爆破倾倒过程影响的研究

对烟筒、水塔定向爆破的切口处进行了受力分析,着重考虑风载作用对倾倒力学条件的改变及对倾倒方向的影响,分析了转角、风载、切口大小之间的变化规律,并根据几个实例进行计算和分析。研究结果表明,风载对筒形高耸建筑物爆破倾倒方向有显著影响,风载增大时,偏转角呈线性增加,同时改变了中心轴的位置。计算时应根据建筑物的形状具体计算。     

彩票发行方案的合理性评价

本文根据目前常见的彩票销售规则及相应的奖金设置方案，综合分析了高项奖奖金额和低项奖中奖率对彩民的吸引力等因素，将发行方案的合理性问题归结为发行方案对彩民的吸引力上，引入了表示彩民心理趋向的偏好系数，构造了吸引力函数，同时综合考虑了封顶值等因素，对现行常见的29种彩票发行方案进行了综合评价。     

一种可用于生产效率评价的灰靶评估算法

本文在分析和比较了DEA和灰靶评估两种方法之后，给出一种可用于生产效率评价的灰靶评估算法。该算法由于运用了DEA方法中的“生产效率”概念，弥补了灰靶评估算法不能对不同的被评价单元进行效率评价的不足，从而拓宽了灰靶评估算法的应用背景。文章最后给出实例分析。     

辛映射与Hamilton控制系统

给定等价辛流形 ,即辛同态或形变等价的辛流形 ,研究了建立在这些辛流形上的Hamilton控制系统之间的一些性质的联系 ,诸如 (局部 )能观测性 ,强可接近性 ,(拟 )极小性等 .而且 ,利用Cort啨ｓ介绍的 (弱 )外等价系统的概念 ,给出使得两个Hamilton控制系统是辛同态的一个充分条件