An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.     

变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性与守恒量

研究了变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性和守恒量.在群的无限小变换下,定义了变质量Chetaev型非完整系统Appell方程Mei对称性和共形不变性,给出了该系统Mei对称性的共形不变性确定方程,并推导出系统相应的守恒量表达式.最后,给出了应用算例.     

微重力下变内角毛细驱动流研究

本文研究了在满足Concus-Finn条件时,微重力环境下内角沿容器轴线变化时的毛细驱动流问题,建立了变内角的毛细流动控制方程,获得了变内角流动的近似解析解,并与FLOW-3D软件的数值模拟结果进行了对比验证. 计算结果表明,随着时间的增大,近似解析解与数值解的相对误差越来越小,在6 s以后,相对误差不超过5%. 论文研究了不同结构参数对内角毛细流动的影响规律,得出液体前缘位置和液面高度均随内角、接触角、内角斜率和内角幂指数的增大而减小的结论. 在不同时刻,液体的液面高度随着时间的增大而增大,但在初始时刻存在一个常高度,该高度不随时间的变化而变化. 在空间流体管理时,可以根据本文的工作进行容器设计和选择适合的溶液. 关键词： 变内角 毛细驱动流 近似解析解 前缘位置     

Predicting bank loan recovery rates with a mixed continuous‐discrete model

To represent the high concentration of recovery rates at the boundaries, we propose to consider the recovery rate as a mixed random variable, obtained as the mixture of a Bernoulli random variable and a beta random variable. We suggest to estimate the mixture weights and the Bernoulli parameter by two logistic regression models. For the recovery rates belonging to the interval (0,1), we model, jointly, the mean and the dispersion by using two link functions, so we propose the joint beta regression model that accommodates skewness and heteroscedastic errors. This methodological proposal is applied to a comprehensive survey on loan recovery process of Italian banks. In the regression model, we include some macroeconomic variables because they are relevant to explain the recovery rate and allow to estimate it in downturn conditions, as Basel II requires. Copyright © 2012 John Wiley & Sons, Ltd.     

Local Lipschitz-α Mappings and Applications to Sublinear Expectations

The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α operators and local Lipschitz functions. Some applications to the theory of sublinear expectation spaces are given.     

Semiparametric estimation of average treatment effect through a random coefficient dummy endogenous variable model

This paper provides an estimation procedure for average treatment effect through a random coefficient dummy endogenous variable model. A leading example of the model is estimating the effect of a training program on earnings. The model is composed of two equations: an outcome equation and a decision equation. Given the linear restriction in outcome and decision equations, Chen (1999) provided a distribution-free estimation procedure under conditional symmetric error distributions. In this paper we extend Chen’s estimator by relaxing the linear index into a nonparametric function, which greatly reduces the risk of model misspecification. A two-step approach is proposed: the first step uses a nonparametric regression estimator for the decision variable, and the second step uses an instrumental variables approach to estimate average treatment effect in the outcome equation. The proposed estimator is shown to be consistent and asymptotically normally distributed. Furthermore, we investigate the finite performance of our estimator by a Monte Carlo study and also use our estimator to study the return of college education in different periods of China. The estimates seem more reasonable than those of other commonly used estimators.     

高超声速飞行器纵向动力系统平衡态集的拓扑结构研究

以高超声速飞行器纵向运动的空气动力学模型和结构动力学模型为依据,采用数值分析的方法,研究了高超声速飞行器动力系统平衡点集的拓扑结构.首先根据高超声速飞行器在巡航阶段的飞行边界的限制条件得到在给定的飞行高度和马赫数下的平衡点集,由此近似估算出了高超声速飞行器的飞行包线.然后根据得到的平衡点集,分别研究了高超声速飞行器的迎角、升降舵偏角和发动机的燃料当量比与飞行马赫数和高度的关系,并进行了数值拟合,在此基础上分别描绘了以上三个拟合关系式的曲面关系图。     

一类随机适应序列的强收敛性

本文利用对随机变量进行截尾的方法和非负鞅的性质,证明了一类随机变量序列的强收敛性.     

Integrability and soliton-like solutions for the coupled higher-order nonlinear Schrödinger equations with variable coefficients in inhomogeneous optical fibers

Under investigation in this paper are the coupled higher-order nonlinear Schrödinger equations with variable coefficients, which represent the propagation of femtosecond soliton pulses comprising of two fields with the left and right polarization in the inhomogeneous optical fiber media. Infinitely-many conservation laws are obtained based on the Lax pair. Via the Hirota method and symbolic computation, bilinear forms, bilinear Bäcklund transformations, one- and two-soliton-like solutions are also derived. With different coefficients, bell-shaped, periodic-changing, quadratic-varying, exponential-decreasing and exponential-increasing soliton-like profiles are seen, to describe the propagation and interactions of the femtosecond soliton pulses. Head-on and overtaking elastic interactions are shown, which are decided by the directions of the velocities. We also get the bound states with periodic attraction and repulsion between two solitons.     

基于加总和乘积的方差分解法及其应用

研究了加总式和乘积式的方差分解问题,证明了在因变量等于各自变量之和的条件下,因变量方差等于各自变量与因变量的协方差之和;在因变量等于各自变量之乘积的条件下,因变量对数值的方差等于各自变量对数值与因变量对数值的协方差之和．以中国31个省份2005－2012年的居民人均收入及其影响因素的统计数据资料为例,说明了加总式和乘积式的方差分解法的具体应用．