ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING

The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.     

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

从自模式曲线分辨到渐进类因子分析法

本文对自模式曲线分辨法的发展作了简要回顾，其中特别对近来来迅速发展的一类用于色谱波谱联用仪产生的二维分析数据的渐进类分析法作了详尽的讨论。这些新化学计量学方法的涌现，对复杂的未知分析体系的定性定量分析，将带来深刻的变化。     

插值矩阵法分析正交各向异性板切口应力奇异性

基于切口尖端附近区域位移场渐近展开,提出了分析正交各向异性复合材料板切口奇异性的新方法.将位移场的渐近展开式的典型项代入弹性板的基本方程,得到关于正交各向异性板切口奇异性指数的一组非线性常微分方程的特征值问题;再采用变量代换法,将非线性特征问题转化为线性特征问题,用插值矩阵法求解获得的正交各向异性板切口若干阶应力奇异性指数和相应特征函数.该法可由相应的特征角函数对板切口的平面应力和反平面奇异特征值加以区分,并将计算结果与现有结果对照,表明了该文方法的有效性.     

单幅圆条纹相位展开光刻对准研究

针对光刻对准中产生的单幅封闭干涉条纹经相位解析后获得的包裹相位,提出在极坐标系对其进行相位展开进而获得对准偏移量的方法.该方法首先将对准过程中两圆光栅相对移动产生条纹的相位分布从直角坐标系转换到极坐标系;其次分析在极坐标系下对准偏移量与相位参量的关系;最后通过取不同径向半径获得初始相位振幅与相位延迟进而求取对准偏移量.数值模拟与实验验证该方法的可行性并与传统的最小二乘与路径跟踪相位展开方法进行了对比分析.结果表明该方法对包裹相位进行展开进而达到几十纳米量级的高准确度对准,具有很强的适应性.     

(2+1)维色散长波方程的变量分离解

应用改进的G'/G展开法和变量分离法,构造出(2+1)维色散长波方程的变量分离解,根据得到的孤立波解,构造出dromion解,使方程的解变得更加丰富.     

一类五阶非线性波方程的新精确解

通过利用新的G展开法,并借助Mathematica计算软件,研究了一类五阶非线性波方程的精确解,获得了方程的含有多个任意参数的新的显式行波解,分别为三角函数解、双曲函数解、指数函数解,扩大了该类方程的解的范围.     

巧记展开图 妙解中考题——正方体的表面展开图归纳与应用

正方体表面展开图是初中数学的一个重要内容,同学们对于这部分知识的学习很有兴趣,这个知识点也是中考的一个热点,常以选择题和填空题的形式出现,偶尔也以解答题的形式出现.同学们在学习这部分内容时往往会感到比较杂乱,下面我用数字的形式归纳,并举