On the solution of Maxwell's equations in polygonal domains

This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H² when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H², and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd.     

Corner spontaneous magnetization

Details are given of a new method allowing an exact calculation of the spontaneous magnetization in the corner as well as along the edge at an arbitrary distance of the corner for a rectangular planar Ising ferromagnet.     

On a fast direct elliptic solver by a modified Fourier method

We describe high order numerical algorithms for the solution of second order elliptic equations in rectangular domains. These algorithms are based on the Fourier method in combination with a subtraction procedure. The singularities at the corner points, arising due to non-smoothness of the boundaries, are treated explicitly using properly constructed singular corner functions. The present algorithm is a generalization of the Fast Poisson Solver developed in our previous paper. This revised version was published online in August 2006 with corrections to the Cover Date.     

关于“级别婚”的数学分析

介绍了19世纪存在于澳大利亚土著中的一种婚姻形式—级别婚,从群论的角度说明级别婚的三种主要形式都对应于一个对称群,从而可以用几何方法形象的表示这种婚姻形式;进而,从对称的观点说明婚姻形式从简单到复杂的演化过程,代数上对应于对称群阶数的增加,几何上则对应于对称性的加强.     

Inter- and intramolecular potential for the N-formylglycinamide-water system. A comparison between theoretical modeling and empirical force fields

An intramolecular NEMO potential is presented for the N-formylglycinamide molecule together with an intermolecular potential for the N-formylglycinamide-water system. The intramolecular N-formylglycinamide potential can be used as a building block for the backbone of polypeptides and proteins. Two intramolecular minima have been obtained. One, denoted as C5, is stabilized by a hydrogen bonded five member ring, and the other, denoted as C7, corresponds to a seven membered ring. The interaction between one water molecule and the N-formylglycinamide system is also studied and compared with Hartree-Fock SCF calculations and with the results obtained for some of the more commonly used force fields. The agreement between the NEMO and SCF energies for the complexes is in general superior to that of the other force fields. In the C7 region the surfaces obtained from the intramolecular part of the commonly used force fields are too flat compared to the NEMO potential and the ab initio calculations. We further analyze the possibility of using a charge distribution obtained from one conformation to describe the charge distribution of other conformations. We have found that the use of polarizabilities and generic dipoles can model most of the changes in charge density due to the different geometry of the new conformations, but that one can expect additional errors in the interaction energies that are of the order of 1 kcal/mol.     

Rumer's transformation,in biology,as the negation,in classical logic

In this article, we make a connection between the Rumer transformation, used in the study of the genetic code‐doublets, and the negation of classic logic. A unified classification is given, relying on two Klein's 4‐groups describing the symmetries of the 16 doublets of nitrogenous bases and those of the 16 binary connectives of classic logic, both groups being subgroups of a larger noncommutative group with eight elements we identify as the dihedral group D₄. Also, some connections with other works are briefly considered. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

四角点简支双稳态层合板振动特性研究

双稳态层合板作为一种柔性可变体结构,为实现振动状态下的构型调控,将对其开展固有振动特性的研究.本文以四角点简支约束的矩形非对称铺设双稳态板作为研究对象,运用最小势能原理、一阶剪切变形理论、以及冯卡门几何非线性位移应变关系,得到双稳态板的两种稳态构型.首次给出了适合于四点简支的6参数构型函数与17参数构型函数,研究对比发现对于稳态构型采用17参数的构型函数结果相对更精确;对于应用线性位移应变关系的基于任一稳态构型下振动固有特性而言,这两种构型函数得到的结果基频相差2%,其它阶次频率相差也不大.随后采用6参数构型函数得到的稳态构型研究了几何尺寸、铺层数分别对两种稳态构型固有振动特性的影响.本研究对于进一步研究该类结构动态跳变机理具有重要意义.     

三面角反射器的高频电磁散射分析

几何光学/区域投影(Geometrical Optics/Area Projection, GO/AP)法是一种综合利用GO和AP进行电大尺寸目标单站雷达散射截面积(Radar Cross Section, RCS)预估的高频混合算法.文章推导建立了利用GO/AP法进行RCS预估的通用流程, 计算出不同入射方向下三角形三面角反射RCS的完整表达式; 将其与RCS最大值的经验公式以及FEKO软件的仿真结果进行对比, 验证了GO/AP法的可行性; 在边界入射方向对GO/AP算法进行改进, 进一步拓宽了GO/AP法对观察角的适应范围.     

对地面弱小目标的检测算法的研究

在研究地面弱小目标时,由于环境、人为误差及成像系统本身的影响,摄像机拍摄的视频会出现画面抖动比较厉害、成像质量差的现象。因此,需要对图像序列进行运动补偿。为实现对地面弱小目标的检测,提出了一种基于Harris角点检测的对地面弱小目标的检测算法。该算法利用了残差图中的灰度信息及残差图序列,在时间上具有连续性,算法的稳定性高,精度较高,实时性好。能够很好地剔除残差图中的虚警点,在较高精度下大大提高了对于地面弱小目标检测的水平。     

修正二面角散射模型的改进四分量分解

提出了一种面向极化合成孔径雷达数据的改进四分量分解方法.针对极化分解中体散射过高估计问题,改进极化分解使用分布二面角散射模型替代四分量分解原相干偶次散射模型,并引入归一化圆相关系数以实现分解.将改进极化分解运用到奥伯法芬霍芬(Oberpfaffenhofen)地区的实验合成孔径雷达(Experimental Synthetic Aperture Radar,ESAR)的全极化机载L波段数据和北京地区的先进陆地观测卫星L波段相控阵合成孔径雷达(the Phased Array Lband SAR sensor of Advanced Land Observing Satellite,ALOS PALSAR)的全极化星载数据,通过负功率像素、地物散射分量的对比,以及分解结果和光学图像的比对三个方面说明了改进极化分解的有效性.改进极化分解能够有效降低体散射分量,减少负功率像素个数,以及正确获得45°建筑的散射机制.