将条件收敛级数重排成发散级数的一方法

关于条件收敛级数的重排有著名的黎曼定理:如果级数条件收敛,则无论预先取怎样的数B(有穷的或者等于±∞),都可以重新排列这级数的各项,使得重排后的级数具有和数B。本文要证明下面的结果: 如果一个级数条件收敛,则舍去零项后一定可以重新排列成一个发散的交错级数。     

关于发散的p-级数的一个发散速度估计

设p∈(0,1),本文研究p-级数∑∞n=1n~(-p)的发散速度估计.通过构造适当的区间套,得到了limn→∞A_(n,p):=C_p∈(p,2~(1-p)-1+p),0C_p-A_(n,p)(1-p)n~(-p),这里,A_(n,p)=n~(1-p)-(1-p)∑k=nk=1k~(-p).进一步,应用数值积分的梯形公式,得到了lim_(n→∞)n~p C(_p-A_(n,p))=(1-p)/2以及C_p-A_(n,p)的二次估计.所得结果改进了文(马书燮,关于发散p-级数的一个不等式[J].大学数学,2013,29(2):147-150.)中的结果.     

正规发散级数

本文推广了维数正规发散的古典概念，将幂级数的一个定理推广到很一般的情况，然后讨论其在各种复函数项级数中的应用．     

级数敛散性的一个判别法则及其应用

给出级数敛散性的一条判别法则．即若{an}单调递减,an〉0（n=1,2,……）,且 lim n→∞ n^m-1 m^n^m-n amn^m/am^n=ρ（其中自然数m≥2）, 则当ρ〈1/m时,∑an收敛,当ρ〉1/m时,∑an发散,由此可推得∞∑n=2 1/nlnn发散.     

基于P级数判敛的正项级数敛散性判别方法

借助由比较判别法导出的引理,证明了一种形式类同比值判别法的新的判别方法。     

一道试题引出的级数收敛性判别法

以命题形式给出证明的一道习题,提供了判断级数收敛与否的一种方法。     

Cauchy凝聚判别法的推广

将Cauchy凝聚判别法进行推广,得到正项级数一个新的判别法.该判别法包含了若干已有的结论,同时也产生了一些新的结论.实例说明了这些结论的有效性.     

有关发散级数的一些探讨

通过对发散级数的探讨,得到了发散级数相加仍然发散的充分条件.同时,考虑了反常积分的相应问题.     

几何级数撷趣

我们知道几何级数为∑n=1∞aq^n-1=a aq aq^2 … aq^n-1…其中首项a≠0,公比为q。当|q|≥1时发散。     

几类级数敛散性的一些探讨

通过对子级数的探讨,得到了一类级数和其子级数的敛散性的判断准则.与此同时,对文[3]的结论进行了推广.     

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.