广义交替近似梯度算法的线性收敛分析

针对两个可分凸函数的和在线性约束下的极小化问题,在交替方向法的框架下,提出广义的交替近似梯度算法.在一定的条件下,该算法具有全局及线性收敛性.数值实验表明该算法有好的数值表现.     

更正说明

正本刊第二期"计算机时代千年算盘如何再拨响"作者张德和一文,第五页右侧下数第三行:"珠算要避免被淘汰的命运,唯有发展珠心算教育,并与数学融合开发儿童智力。这应该成为计算机时代,珠算传承首选的发展方向",原文应是"但相当部分珠算界以至外界人士认为在计算机时代,珠算要     

一堂高三解析几何复习课的教学设计与反思

<正>在距离高考还有100天之际,笔者所带的班有一位学生来找笔者谈心,他说:"老师,复习了那么长时间的解析几何,做了那么多解析几何试题,但是我现在还是很恐惧解析几何,模拟卷的解析几何题我都逼着自己尝试着做,有时会做,有时一点思路都没有,我该怎么办?"听了这位学生的话,笔者陷入了沉思:在解析几何的复习过程中,教师该如何带领学生在制高点获得突破?带着这个问题,笔者精心准备了第二天上课的内容:解析几何中的最值问题.     

平行六边形区域上的快速离散傅立叶变换

In this paper, we propose a fast algorithm for computing the DGFT (Discrete Generalized Fourier Transforms) on hexagon domains [6], based on the geometric properties of the domain. Our fast algorithm (FDGFT) reduces the computation complexity of DGFT from O(N4) to O(N2 log N). In particulary, for N =2^P23^P34^P45^P56^P6, the floating point computation working amount equals to(17/2P2 16p3 135/8p4 2424/25p5 201/2P6)3N^2. Numerical examples are given to access our analysis.     

微分方程解的存在区间的确定

从六个方面说明了确定一阶微分方程解的存在区间的方法.     

Fe48Co52 Alloy Nanowire Arrays： Effects of Magnetic Field Annealing

The effects of magnetic field annealing on the properties of Fe48Co52 alloy nanowire arrays with various interwire distances （Di=30-60 nm） and wire diameters （Dw=22-46 nm） were investigated in detail. It was found that the array＇s best annealing temperature and crys- talline structure did not show any apparent dependence on the treatment of applying a 3 kOe magnetic field along the wire during the annealing process. For arrays with small Dw or with large Di, the treatment of magnetic field annealing also had no obvious influence on their magnetic performances. However, such a magnetic field annealing constrained the shift of the easy magnetization direction and improved the coercivity and the squareness obviously for arrays with large Dw or with small Di. The difference in the intensity of the effective anisotropic field within the arrays was believed to be responsible for this different variation of the array＇s magnetic properties after magnetic field annealing.     

“曲线运动”的速度方向演示实验缺陷及改进

曲线运动的速度方向是高一物理"曲线运动"一节的教学难点,教材试图通过"砂轮"和"转伞"的实例加以说明.可是很多学生没见过用砂轮磨刀具时形成的火星是何形状,课堂上演示此实验,既不现实,也不安全.     

多孔介质中两相可压缩混溶流体驱动问题的交替方向法

多孔介质中二相可压缩流体驱动问题可以由一组非线性方程组来描述,它包含一个压力方程和一个浓度方程.文中对压力方程提出了稳定化校正格式,对浓度方程提出了二阶迎风交替方向差分格式,并结合双线性插值,给出了最优的L~2估计.结果表明该格式有一定的理论意义和实际应用价值.     

Magnetoabsorption spectra of magnetoexciton transitions in GaAs/Ga0.7Al0.3As quantum wells

The internal transitions and absorption spectra of confined magnetoexcitons in GaAs/Ga0.TA10.aAs quan- tum wells have been theoretically investigated under magnetic fields along the growth direction of the semiconductor heterostructure. The magnetoexciton states are obtained within the effective-mass ap- proximation by using a variational procedure. The trial exciton-envelope wavefunctions are described as hydrogeniclike polynomial functions. The internal transition energies are investigated by studying the allowed magnetoexcitonic transitions using terahertz radiation circularly polarized in the plane of the quantum well. The intraexcitonic magnetoabsorption to 2p^± like magnetoexciton states as functions of the coefficients are obtained for transitions from 1s-like applied magnetic field.     

Networks Emerging from the Competition of Pullulation and Decrepitude

In real-world network evolution, the aging effect is universal. We propose a microscopic model for aging networks,which suggests that the activity of a vertex is the result of the competition of two factors: pullulatlon and decrepitude. By incorporating the pullulation factor into previous models of aging networks, both the global and individual aging effect curves in our model are single peaked, which agrees with the empirical data well. This model can generate networks with scale-free degree distribution, large clustering coefficient and small average distance when the decrepitude intensity is small and the network size not very large. The results of our model show that pullulation may be one of the most important factors affecting the structure and function of aging networks and should not be neglected at all.