The alternating-direction iterative method for saddle point problems

In the paper, a new alternating-direction iterative method is proposed based on matrix splittings for solving saddle point problems. The convergence analysis for the new method is given. When the better values of parameters are employed, the proposed method has faster convergence rate and less time cost than the Uzawa algorithm with the optimal parameter and the Hermitian and skew-Hermitian splitting iterative method. Numerical examples further show the effectiveness of the method.     

基于三次样条插值的艾滋病治疗模型

基于数学建模提供的艾滋病治疗方案中的实验数据,依据病人的初始CD4状态,将实验数据分类筛选,采用一维三次样条插值法描绘各类病人服药时间与病情的关系图形,进而由图形确定最佳治疗终止时间;并建立了CD4与时间的函数关系模型,借助于性价比函数进行疗效、价格的综合比较分析,此模型解法对最佳治疗方案的选择提供了有力依据.     

Combined Influence of Off-diagonal System Tensors and Potential Valley Returning of Optimal Path

The two-dimensional barrier passage is studied in the framework of Langevin statistical reactive dynamics. The optimal incident angle for a particle diffusing in the dissipative non-orthogonal environment with various strengths of coupling between the two degrees of freedom is systematically calculated. The optimal diffusion path of the particle in a non-Ohmic damping system is revealed to have a probability to return to the potential valley under the combined influence of the off-diagonal system tensors.     

Multi-mesh Adaptive Finite Element Algorithms for Constrained Optimal Control Problems Governed By Semi-Linear Parabolic Equations

In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and efficient multi-mesh adaptive finite element algorithms for the optimal control problems. Some numerical experiments are presented to illustrate the theoretical results.     

Effect of Four-Wave Mixing on Optimal Placement of Optical Amplifier in WDM Star Networks

In this article, the effect of four-wave mixing (FWM) and amplified spontaneous emission (ASE) noise on WDM optical star networks has been investigated. Analysis for the evaluation of probability of error has been carried out (a) when only FWM is present and (b) when both FWM and ASE noise are present. Numerical results are presented in the graphical and tabular forms for the practical values of parameters. Finally, optimal location of the amplifier in the network has been identified as being before the star coupler preceding the receiver.     

Three Control Methods for Time-Dependent Fluid Flow

We summarize some of the recent developments in the field of optimal and suboptimal control strategies for time-dependent incompressible Navier–Stokes equations. Besides the Newton method,reduced order modeling (ROM) and receding horizon control strategies are described. All approaches are applied to compute controls for the unsteady flow around a cylinder in two spatial dimensions. This revised version was published online in July 2006 with corrections to the Cover Date.     

A review of mathematical models in economic environmental problems

The paper presents a review of mathematical models used in economic analysis of environmental problems. This area of research combines macroeconomic models of growth, as dependent on capital, labour, resources, etc., with environmental models describing such phenomena like natural resources exhaustion or pollution accumulation and degradation. In simpler cases the models can be treated analytically and the utility function can be optimized using, e.g., such tools as the maximum principle. In more complicated cases calculation of the optimal environmental policies requires a computer solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

线性子空间上求解AX=B的最小二乘问题的迭代算法

应用共轭梯度方法和线性投影算子,给出迭代算法求解了线性矩阵方程AX=B在任意线性子空间上的最小二乘解问题.在不考虑舍入误差的情况下,可以证明,所给迭代算法经过有限步迭代可得到矩阵方程AX=B的最小二乘解、极小范数最小二乘解及其最佳逼近.文中的数值例子证实了该算法的有效性.     

Data analysis for accelerated life tests via Weibull-gamma frailty regression models

In this article, we study data analysis methods for accelerated life test (ALT) with blocking. Unlike the previous assumption of normal distribution for random block effects, we advocate the use of Weibull regression model with gamma random effects for making statistical inference of ALT data. To estimate the unknown parameters in the proposed model, maximum likelihood estimation and Bayesian estimation methods are provided. We illustrate the proposed methods using real data examples and simulation examples. Numerical results suggest that distribution of random effects has minimal impact on the estimation of fixed effects in the Weibull regression models. Furthermore, to demonstrate the advantage of our proposed model, we also provide methods to compare ALT plans and thus identify the optimal ALT plans.     

基于运动稳定性轧管机主机头模糊优化设计

为提高轧管机主机头的运动稳定性,改善钢管的轧制质量,本文在对轧管机主机头的结构及运动状态分析的基础上,推导出主机头的运动加速度解析式,并以此为基础,建立模糊优化的数学模型。文中分别以各构件长度尺寸为设计变量,进行单变量模糊优化设计,求得各构件长度的最优取值区间,使主机头的运动稳定性得到较大的提高。本文建立的数学模型对提高轧管机的稳定性及进行优化设计提供了依据,所得出的结论为轧管机的整体优化奠定了研究基础。