Total curvatures of geodesic spheres associated to quadratic curvature invariants

Total scalar curvatures of geodesic spheres obtained by integrating the second-order scalar invariants of the curvature tensor are investigated. The first terms in their power-series expansions are derived and these results are used to characterize the two-point homogeneous spaces among Riemannian manifolds with adapted holonomy. Dedicated to Professor L. VanheckeMathematics Subject Classification (2000) 53C25, 53C30     

A rigid subspace of the real line whose square is a homogeneous subspace of the plane

Working in ZFC, we give an example as indicated in the title.

     

Randomization of Q_p spaces on the unit ball of C~n

In this paper, we study the random power series of several complex variables, and give some sufficient conditions for random power series to belong to Qp and Qp,0 spaces by means of their characterizations of Carleson measure. Moreover, we show that such conditions are best possible in some sense.     

On the riemann zeta-function and the divisor problem II

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If E ^*(t)=E(t)-2πΔ^*(t/2π) with , then we obtain

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.     

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。     

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。     

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。     

输流粘弹性曲管的稳定性分析

根据变质量弹性系统Hamilton原理,用变分法建立了输流粘弹性曲管的运动微分方程,并用归一化幂级数法导出了输流粘弹性曲管的复特征方程组．以两端固支Kelvin-Voigt模型粘弹性输流圆管为例,分析了无量纲延滞时间和质量比对输流管道无量纲复频率和无量纲流速之间的变化关系的影响．在无量纲延滞时间较大时,粘弹性输流圆管的特点是它的第1、2、3阶模态不再耦合,而是在第1、第2阶上先发散失稳,然后在1阶模态上再发生单一模态颤振．     

障碍平方期权的定价

本讨论了一种变异期权——收益结构为平方的障碍期权，在股票价格服从几何布朗运动的模型下，由带单侧吸收壁的布朗运动的密度和分布函数得到连续障碍平方期权的定价公式．