Aggregate expenditure elasticity for transport and communication in Australia

For the purpose of estimating Engel elasticity, one needs to find the best functional form among various alternatives. In this paper, a new function, which is called the double semi-log Engel function turns out to be the best functional form for the transport and communication items in Australia on the basis of the distance function (D²) criterion, and the non-nested hypothesis testing procedure. This function is then used to estimate total expenditure elasticity, and the percentage change in consumer demand due to changes in total expenditure and total expenditure inequalities; using the 1975–76 Household Expenditure Survey data. The results of the analyses demonstrate that transport and communication is a necessary item in Australia on the basis of two criteria, viz., its elasticity is not significantly greater than unity, and the percentage change in demand increases with a decrease of the total expenditure inequality [emphasised by Iyengar (I960)]. Policy implication of the analyses has also been discussed.     

On a link-based day-to-day traffic assignment model

In this paper, we perform a rigorous analysis on a link-based day-to-day traffic assignment model recently proposed in He et al. (2010). Several properties, including the invariance set and the constrained stability, of this dynamical process are established. An extension of the model to the asymmetric case is investigated and the stability result is also established under slightly more restrictive assumptions. Numerical experiments are conducted to demonstrate the findings.     

带转向延误的非对称多模式用户平衡模型及算法

为了在网络建模中更精确地反映交通网络和出行行为的复杂特征,从多模式用户平衡原理出发,综合考虑多模式和转向延误因素以及不同模式、路段和转向之间的非对称作用,利用变分不等式理论建立了带转向延误的非对称多模式用户平衡模型,并在精简对角化算法的框架内设计了求解算法。该模型集成了交通网络的诸多特征,且能直接刻画转向延误与转向流量之间的互动关系,避免了传统扩展网络法的缺陷。算例表明:该模型及其算法对问题的描述与求解是有效的。     

三阶非线性边值问题的奇摄动

利用微分不等式技巧和Volterra型积分算子，研究了一类三阶非线性奇摄动边值问题解的存在和渐近估计。     

Nonlinear feedforward–feedback control of clutch-to-clutch shift technique

To improve the shift quality of the vehicle with clutch-to-clutch gear shifts, a nonlinear feedforward–feedback control scheme is proposed for clutch slip control during the shift inertia phase. The feedforward control is designed based on flatness in consideration of the system nonlinearities, and the linear feedback control is given to accommodate the model errors and the disturbances. Lookup tables, which are widely used to represent complex nonlinear characteristics of powertrain systems, appear in their original form in the designed feedforward controller, while the linear feedback controller is calculated through linear matrix inequalities such that the control system is robust against the parameter uncertainties. Finally, the designed controller is tested on an AMESim powertrain simulation model, which contains a time-variant model of clutch actuators.     

抽象广义双拟变分不等式的推广

笔者研究了文 [1]、[2 ]中引入的抽象广义双拟变分不等式解的存在性问题 .我们的结果统一、改进和发展了有关变分不等式问题的许多最新结果 .     

Non-fragile multi-objective static output feedback control of vehicle active suspension with time-delay

This paper presents an approach to design a delay-dependent non-fragile H_∞/L₂–L_∞ static output feedback (SOF) controller for active suspension with input time-delay. The control problem of quarter-car active suspension with actuator time-delay is formulated to a H_∞/L₂–L_∞ control problem. By employing a delay-dependent Lyapunov function, new existence conditions of delay-dependent non-fragile SOF H_∞ controller and L₂–L_∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities (BMIs). Then, a procedure based on linear matrix inequality optimisation and a hybrid algorithm of the particle swarm optimisation and differential evolution is used to solve an optimisation problem with BMI constraints. Design and simulation results of non-fragile H_∞/L₂–L_∞ controller for active suspension show that the designed controller not only can achieve the optimal performance and stability of the closed-loop system in spite of the existence of the actuator time-delay, but also has significantly improved the non-fragility characteristics over controller perturbations.     

奇摄动三阶非线性边值问题

利用微分不等式技巧和Volterra型积分算子，研究了三阶非线性奇摄动边值问题εx^(3)=f(t,x,x′,w(ε）x^(3)，ε），g（x′（0），x″（0）=0，x（1）=A，x′（1）=B的存在性及渐近估计。     

锐角三角形的一个不等式链

应用重要的R-r-s方法,证明了有关锐角三角形的中线、高线与旁切圆半径的不等式链:设锐角ΔABC的三条中线,三条高线与旁切圆半径分别为ma,mb,mc;ha,hb,hc和ra,rb,rc,则成立不等式:maha mbhb mchc≥wbwc wcwa wawb≥hara hbrb hcrc.提出并应用计算机验证了三个有关的猜想.     

不等式证明中的概率方法

在分析数学中有些不等式的证明往往比较复杂，而且具体的直观含义也比较抽象．如果能够建立起适当的概率模型，赋以一些随机事件或随机变量的具体含义，再利用概率论的理论加以证明，则常常能使证明过程得到简化．同时还可以为抽象的数学问题提供具体的概率背景，沟通各数学分支之间的联系．文中在分析数学的几个重要不等式的证明之中引进了概率方法，取得较好的效果。