函数展开

• ( 3 ) by means of expanding the aperture function into a finite sum of complex gaussian functions , the propagation of fgbs through a paraxial optical abcd system with hard - edged aperture is studied , and the approximate closed - form equations of apertured fgbs are obtained for the first time . the results obtained by using the approximate closed - form equation and collins formula are compared , and the condition under which the approximate closed - form equation is applicable is analyzed
  ( 3 )利用光阑函数的复高斯函数展开法对截断平顶高斯光束的传输作了研究，首次得到了截断平顶高斯光束在近轴abcd光学系统中传输时的近似解析传输公式，通过比较用近似传物公式和colhns公式直接数值积分所得的结果，得出了近似公式的适用范围。
• Based on the empirical orthogonal function ( eof ) , the characteristics of large scale variations of precipitation anomaly during rainy season ( from jun to aug ) in south - west china for the period 1961 1995 is analyzed , and the teleconnection distribution charac - teristics between sea surface temperature ( sst ) over india ocean and precipitation during rainy season in south - west china were studied by using the method of cca
  用自然正交函数展开方法对1961 1995年西南汛期( 6 8月)降水大尺度变化特征进行分析，并在此基础上用典型相关分析方法研究了1 8月印度洋海温距平场与西南汛期降水场的遥相关分布特征。
• Upon using an artificial neural network ( ann ) a new short - term climate forecast model with the monthly mean rainfall in june in the north of guangxi as predictand is established making empirical orthogonal functions ( eof ) to the 36 predictors ( 15 ssa predictors , 21 500hpa height predictors ) with over 0 . 05 significant correlation level of previous 500hpa height and sea surface temperature ( sst ) field , and selecting the high relative principal components , at the same time , a new approach of constructing ann learning matrix is developed . predictive capability between the new model ( principal components ann model ) and linear regression model for the same predictors is discussed based on the independent samples and historical samples
  本文通过对广西北部6月平均降水量(预报量)同北半球月平均500hpa高度场和北太平洋月平均海温场进行相关普查，选取了前期36个同预报量相关显著水平达到0 . 05以上的预报因子( 15个海温场预报因子， 21个高度场预报因子) ，并运用自然正交函数展开方法对这36个前期预报因子展开，取其中同预报量相关程度高的主成分，结合人工神经网络技术，提出了一种新的构造人工神经网络学习矩阵的方法，建立了一种新的短期气候预测模型。
• Several typical sites are chosen in this paper in order to investigate the main points of wave function expansion method applied to elastic wave scattering problems . antiplane scattering analytical solution for the alluvial valley of shallow circular - arc cross - section is investigated , which has practical engineering value
  本文选择了几种典型场地，研究了波函数展开法在求解其中局部场地弹性波散射问题时的要点，对更有工程实际意义的浅圆弧型沉积盆地，研究了其出平面散射解析解答的收敛性和精度。
• There were troubles in the continuity of the function and of its - derivative divided by band - mass on the boundary . in the theoretical calculation , the wave function is relative to the physical properties of the impurity greatly , the envelop function f ( x , y ) is expanded in terms of the one - dimensional linear harmonic oscillator function in this paper . it satisfies the continuity of the function and of its - derivative divided by the band - mass , so it improves the precision of the function and binding energy
  与以往工作不同的是，以前选用的x ， y方向电子的包络函数f ( x ， y )是一维有限深量子阱中波函数的乘积，在边界上波函数的连续性和粒子流的守恒条件存在问题；而在理论计算中，波函数的选取与杂质的物理性质有密切关系，本文选取的电子的包络函数是用一维线性谐振子的波函数展开而成的，在边界上能够同时满足波函数的连续性及粒子流( 1 / m ~ * ) f ' ( x , y )的守恒条件，从而使得波函数和束缚能的精确度得到了改进。
• ( 2 ) by the jacobi elliptic function expansion method and computer symbolic systems ( maple , matlab or mathematica ) , many exact periodic solutions of nonlinear wave equations can be obtained and under some conditions , these solutions degenerate solitary wave solutions , shock wave solutions , trigonometric function solutions respectively
  ( 2 )利用jacobi椭圆函数展开法和数学计算软件( maple ， matlab ， mathematica等) ，可以求得一类常系数非线性发展方程的双周期解，这些解能退化成孤立子解、冲击波解、三角函数解。
• This thesis in theory deals with electromagnetic wave scattering by multilayered confocal and non - confocal spheroidal particles illuminated by gaussian beams , in which the main contributions are as follows : 1 . in the case of multilayered confocal spheroidal particles , the scattered fields as well as the fields within each layer are obtained in terms of infinite series with spheroidal vector wave functions by using an appropriate expansion of the incident gaussian beam . by virtue of the boundary conditions , we write the set of equations for determining the unknown expansion coefficients and then solve it
  本文从理论上研究了多层共焦和非共焦椭球粒子对高斯波束的散射，主要成果如下： 1 .我们研究了多层共焦椭球粒子对高斯波束的散射，把入射高斯光，散射场，各层椭球内的电场和磁场用适当的椭球矢量波函数展开，应用电磁场边界条件，写出确定各展开系数的方程组，求出散射场系数，进而求出散射场及散射截面。
• In this thesis , based on related previous references , using the non - fourier law of heat conduction , applying the image method , expand method of wave function , multiple scattering of thermal waves in materials with subsurface defects are investigated . our research works are concretely as following
  本文在分析了国内外相关文献的基础上,基于非傅里叶热传导波动方程,采用镜像方法和波函数展开法,研究了固体介质中亚表面圆柱缺陷和球形缺陷对热波的多重散射问题。
• 2 . we present a solution to the scattering of gaussian beams by a concentric multilayered non - confocal spheroidal particle by taking a concentric two - layered one as an example . because the boundaries of these two layers are connected with two different spheroidal coordinate systems , firstly , the electromagnetic fields between the inner and outer boundaries are expanded in terms of the spheroidal vector wave functions with reference to these two systems , and the electromagnetic fields within the inner boundary with reference to the system for it
  2 .以双层椭球为例，我们提出了一种研究同心非共焦多层椭球粒子散射的方法，首先把两层椭球之间的电磁场用对应于两个椭球坐标系的椭球矢量波函数展开，这两个椭球坐标系分别与两层椭球的边界面相联系，在每层椭球边界面上分别应用边界条件，建立关于各展开系数的方程组。