随机变量的一种顺序及其应用

本文对分布于有限区间上的随机变量给出了一种顺序，并给出了其在实际中的一种应用．     

《概率论与数理统计》中有关独立性一反例的深入分析

独立性是《概率论与数理统计》是的一个非常重要的概念.教学中在说明随机变量函数独立性时会涉及许多反例.本文就有关随机变量函数独立性的一个反例作了进一步的推广分析.     

‖S_n‖超越ε(nlgn)~(1/2)的次数、最大程度和最后时刻的矩的讨论

设{X_n,n≥1}是i.i.d.的B值随机变量序列,本文讨论了‖S_(?)‖超越ε(nlgn)~(1/2)的次数L(ε)、最大程度N(ε)和最后时刻H(ε)关于某一类特定的函数φ(t)的某种形式的矩同相应的尾概率级数收敛性之间的关系,得到了若干等价性命题.     

二维连续型随机变量函数的分布密度的计算

二维连续型随机变量函数的密度函数的计算既是概率论教学中的一个重点,又是一个难点.本文介绍了一般二维连续型随机变量函数的分布密度的计算方法,并给出了一个新的方法——密度函数转化法.     

相依随机变量和的极限理论

本文对各种混合r.w.序列及相伴r.w.序列的有关结果作一概略介绍。     

对数似然比与离散随机变量序列强极限定理的一种分析方法

本文引进对数似然比作为任意离散随机变量序列相依性的一种度量，并通过限制似然比给出样本空间的某种子集，在这种子集上得到了离散随机变量序列的一类强极限定理，它包含若干经典强大数定律为其特例．在证明中本文提出了证明强极限定理的一种分析方法，其要点是将关于单调函数可微性的定理应用于几乎处处收敛的研究．     

负相依随机变量之和的概率大偏差不等式

本文建立了负相依随机变量序列的概率大偏差不等式，并推广了以往文献的结果．     

用积分变换法求连续型随机变量函数的密度函数

设X是一个连续型随机变量,其密度函数为px(x),g(x)是一个连续函数,给出了用积分变换求随机变量X的函数9(X)的密度函数的一个方法.该方法比传统的方法更简单.     

具有不同分布NA随机变量列的强大数律及应用

给出了具有不同分布的NA随机变量列满足的若干强大数律;作为应用,不仅将独立随机变量的一类强极限定理完整的推广到NA随机变量情形,而且关于NA随机变量的一些已有结果可以作为推论得出.     

随机变量相等的一个充要条件

本文证得分布于有限区间上的随机变量相等的充要条件为其各阶原点矩相等．     

驾驶者行为选择对十字路口通行能力的影响

考虑通过十字路口时左转车辆和直行车辆发生路权冲突时的不同驾驶者行为,将驾驶者分为跟随型驾驶者和谦让型驾驶者,并建立了左转车辆通过十字路口的模型,研究不同的驾驶者行为选择对十字路口通行能力的影响。结果表明,随着交通流量逐渐增加,驾驶者的行为越趋向于跟随时,十字路口的通行能力将会急剧降低;而当驾驶者的行为趋向于谦让时,十字路口的通行能力甚至优于有交警指挥的情形。该结果很好地解释了在行车高峰期中国十字路口堵塞的原因,即驾驶者的行为选择,可以通过改变驾驶者的行为选择和在交通流量达到一定的饱和度时派出交警来改善十字路口的通行能力。     

基于上限理论的孔隙水压力作用下隧道洞口段含裂缝仰坡稳定性分析

研究了孔隙水压力作用下隧道洞口段含裂缝仰坡的稳定性。采用极限分析上限法,构建了坡顶含竖向裂缝的对数螺旋转动破坏机制,推导了可反映边坡临界坡高的稳定系数计算公式,将计算结果与未考虑孔隙水压力作用下的含裂缝边坡稳定性极限分析结果进行对比,验证了所提研究方法的合理性。通过算例分析,研究了坡顶裂缝最不利位置分布及仰坡整体安全系数。结果表明:坡顶裂缝开裂深度、土体内摩擦角、坡角越大及水位分布越浅,裂缝位置越靠近坡顶边缘处;孔隙水压力系数、坡顶裂缝开裂深度越大,仰坡稳定性系数越小;坡顶裂缝越深、孔隙水压力系数越大、边坡越陡,越不利于仰坡稳定;而坡内水位分布越低,越有利于仰坡稳定。     

Effect of contact stiffness modulation in contact-mode AFM under subharmonic excitation

We report on the effect of fast contact stiffness modulation on frequency response to 2:1 subharmonic resonance in contact-mode atomic force microscopy. The model of the contact-mode dynamic between the tip of the microbeam and the moving surface consists of a lumped single degree of freedom Hertzian contact oscillator. Perturbation methods are applied to obtain the frequency response of the slow dynamic of the system. We focus on the effect of the amplitude and the frequency of the modulation on the nonlinear characteristic of the contact stiffness, the jump phenomenon and the shift in the frequency response of the subharmonic. We also show the effect of the contact stiffness modulation on the interval of the unstable trivial solution which is directly correlated to the depth of the jump. The obtained results can directly influence the material properties and the loss of contact between the tip and the sample.     

废弃食品回流再造问题的产品价格分析

针对废弃食品回流再造的食品安全问题,建立相关利益主体包括食品制造商、废弃食品收购者在各自独立以及作为利益共同体的不同条件下的优化模型,分析新生产食品价格和回流再造食品价格以及相应的利润、影响因素.结果表明:作为同一利益主体,生产制造昂贵食品对食品制造商获利不利,而回流再造成本越低,对食品制造商通过回流再造获利是有利的;若食品制造商和收购者各自独立决定价格,收购者进行回流再造的行为会干扰当前食品零售市场;由于回流再造食品的价格比较优势,在信息不对称时消费者会倾向选择回流再造食品.     

Local defect modelling and nonlinear dynamic analysis for the inter-shaft bearing in a dual-rotor system

This paper presents a force model for the inter-shaft bearing with a local defect on the surface of the outer race or the inner race, and the nonlinear dynamic characteristics of a dual-rotor system affected by the local defect are investigated. A simplified dual-rotor system is presented with the consideration of the inter-shaft bearing's nonlinearities such as the Hertzian contact force and the radial clearance. The local defect is considered as a regular dent with a constant depth, thus the radial clearance will increase when rolling elements go through the range of the local defect. The motion equations of the system with eight degrees of freedom are formulated by using the Lagrange's equation. The nonlinear vibration responses of the dual-rotor system affected by the local defect are obtained using numerical method. The results show that there exist four abnormal resonances on the amplitude frequency curves of the system due to the effect of the local defect, apart from the couple of primary resonances excited by the unbalance excitations of the two rotors. With the aid of the characteristic defect frequency analysis, it is revealed that one pair of the abnormal resonances are excited by the characteristic defect frequency, and the other pair of the abnormal resonances are excited by the combination frequency. Furthermore, a comprehensive parametric analysis is carried out to give an insight into the nonlinear resonant response characteristics affected by parameters such as the depth and the span of the defect, the rotation speed ratio, the unbalances of two rotors, the stiffness and the damping of the linear elastic spring, and the radial clearance, the stiffness and the roller number of the inter-shaft bearing. The results show that the vibration amplitudes for the abnormal resonances are mainly determined by the depth and the span of the defect, while the resonant frequencies for the abnormal resonances are mainly influenced by the rotation speed ratio and the roller number of the inter-shaft bearing. However, the rotors’ unbalances mainly affect the corresponding primary resonance rather than the abnormal resonances. The obtained results will contribute to a better understanding of the nonlinear resonant response characteristics of dual-rotor systems with a local defect on the inter-shaft bearing, which are helpful for the fault diagnostics of the inter-shaft bearing in a dual-rotor system.     

考虑质押物损耗的存货质押融资合约设计

研究易损耗物品质押融资中金融机构与第三方物流服务供应商(Third Party Logistics Service Provider, 3PLs)的合约设计问题。在存货被质押期间,3PLs的监管付出程度会对金融机构的期望收益产生影响。因此,金融机构应赋予3PLs一份激励合约,以刺激3PLs提高监管努力水平。考虑存货在质押期间发生损耗的基础上,建立金融机构与3PLs进行合作的期望收益函数,分析金融机构与3PLs采用委托监管、共同经营及统一授信等模式时的固定支付与激励系数特征,推导每种模式下3PLs的最优监管努力水平。通过数值算例对三种模式下的期望收益水平进行比较,并考察损耗率、努力成本系数和价值变现系数变动对决策变量的影响。结果表明:价值变现系数存在一个临界值,当价值变现系数小于该临界值时,统一授信模式的总期望收益最大;而当价值变现系数大于该临界值时,委托监管模式的总期望收益最大。     

一种便于摄动分析的编队飞行卫星相对运动的描述

定义了一组参数来描述卫星编队飞行的相对运动,称为相对轨道要素．利用它可以方便地分析摄动对相对轨道构形的影响以及卫星编队队形的几何特点．首先,对相对轨道要素给予了详细的推导,指出当主星偏心率为小量时,在主星轨道坐标系中相对轨道是一椭圆柱和一平面相交所得的交线,用描述该椭圆柱和平面的参数即可确定相对轨道构形,进而提出了相对轨道要素．其次,利用相对轨道要素对相对轨道进行地球扁率摄动分析,指出相对轨道构形的变化由两部分组成:一是椭圆柱的漂移导致相对轨道中心的漂移,二是平面法线的章动和进动引起相对轨道平面转动,同时还给出了地球扁率摄动下相对轨道构形漂移率及转动率的解析公式．最后,针对J2摄动分析了卫星编队相对轨道构形的变化以及相对轨道构形的漂移量和转动量．     

On the convergence of the vortex loop method with regularization for the Neumann boundary value problem on a plane screen

We consider a linear integral equation with a supersingular integral treated in the sense of the Hadamard finite value, which arises in the solution of the Neumann boundary value problem for the Laplace equation with the representation of the solution in the form of a doublelayer potential. We consider the case in which the exterior boundary value problem is solved outside a plane surface (a screen). For the integral operator in the above-mentioned equation, we suggest quadrature formulas of the vortex loop method with regularization, which provide its approximation on the entire surface when using an unstructured partition. In the problem in question, the derivative of the unknown density of the double-layer potential, as well as the errors of quadrature formulas, has singularities in a neighborhood of the screen edge. We construct a numerical scheme for the integral equation on the basis of the suggested quadrature formulas and prove an estimate for the norm of the inverse matrix of the resulting system of linear equations and the uniform convergence of the numerical solutions to the exact solution of the supersingular integral equation on the grid.