用Laplace变换法求解端点系有集中质量的弹性杆的振动问题

用Laplace变换法求解了一端为齐次边界条件,另一端系有集中质量的弹性杆的纵振动问题,推广了相关文献的结果。     

端面受到空气阻力的弹性杆的振动

研究了一端固定、一端受到空气阻力的弹性杆的振动.建立了受阻力端的近似边界条件.本征振动模式含有阻尼振动特有的指数衰减因子,但不具有分离变量的形式.因为边界条件不属于斯特姆-刘维型,所以关于本征函数的完备性和正交性的一般定理不适用于本问题.用拉普拉斯变换法求解了任意给定初始条件下的振动.     

最弱受约束电子势模型的径向波函数的两类递推关系

应用简单的方法———Laplace变换法来求最弱受约束电子势模型(WBEPM势)的径向Schrdinger方程.通过这种方法使得两阶微分方程变为一阶微分方程,这样可以直接运用积分得到WBEPM势束缚态能量方程和归一化的波函数,所得结果与文献一致.更重要的是用Laplace变换得到径向波函数的两类新的递推关系.这种递推关系是有效主量子数和角量子数之间关系,在计算原子和分子跃迁几率时有着广泛的应用.     

脉冲涡流检测瞬态涡流场的时域解析模型

应用Laplace反变换技术建立脉冲涡流检测瞬态涡流场的时域解析模型.首先,基于电磁波的反射与透射理论,应用截断区域特征函数展开式法建立瞬态涡流场的复频域模型,然后通过求解模型极点及其留数应用部分分式展开法求解复频域模型的Laplace反变换,从而建立阶跃型和指数型电流激励下瞬态涡流场的时域解析模型.所建模型具有实现简单、效率高、模型精度不受吉布斯效应影响等优点.最后应用基于Fourier反变换的探头瞬态感应电压模型对本文所建模型,实验结果验证了本文所建模型的正确性.     

用Laplace变换求Hartmann势的精确解及波函数的递推关系

本文求解了在球坐标下Hartmann势的Schrdinger方程,得到了能量方程和归一化的波函数.用Laplace变换使径向的二阶微分方程退化为一阶微分方程,直接积分后用级数展开,应用Laplace逆变换得出本征函数.讨论了径向本征函数的像函数的递推关系,从而得出径向波函数的递推关系.     

核激子态的瞬时概率分布和非平衡熵

本文用Laplace变换和连分式方法解核反应激子模型概率分布,给出了全部转移概率矩阵元的代数表示式,并计算了受激原子核的分态概率分布和瞬时熵.     

基于拉普拉斯塔型变换的Contourlet变换频谱混叠特性分析

针对Contourlet变换存在频谱混叠的问题,立足于拉普拉斯(Laplace)塔型变换的分析研究,指出了Contourlet变换频谱混叠的根本原因在于Laplace塔型变换中两个低通滤波器不满足Nyquist抽样定律,致使阻带截全频率大于π/2,导致Contourlet变换的频谱混叠.基此.设计了满足Nyquist抽样定律的低通滤波器,提出了一种新型的Contourlet变换,即抗混叠Contourlet变换.抗混叠Contourlet变换有效地抑制了频谱混叠,基函数的空频局域件均明显优于Contourlet.通过对Barbara图像的硬阈值去噪实验研究结果表明,抗混叠Contourlet变换去噪在峰值信噪比(PSNR)上高出Contou[et变换2.3 dB(噪声均方差为30),去噪效果好,同时还有效抑制了Contoulet变换去噪后的"划痕"现象,图像的视觉效果更佳.     

用Laplace变换求一维谐振子势的Schrdinger方程束缚态解

用Laplace变换把二阶一维谐振子的Schr dinger微分方程退化为一阶微分方程,用直接积分法求出一阶微分方程的解.然后用波函数的单值性得到束缚态能谱,用级数展开,再进行Laplace逆变换,得到其本征函数.     

用Laplace变换求一维谐振子势的Schr(o)dinger方程束缚态解

用Laplace变换把二阶一维谐振子的Schrodinger微分方程退化为一阶微分方程,用直接积分法求出一阶微分方程的解．然后用波函数的单值性得到束缚态能谱,用级数展开,再进行Laplace逆变换,得到其本征函数．     

颗粒体系中力分布的标量力网系综模型

建立了便于解析计算的标量力网系综模型研究颗粒体系中的力分布问题.所提出的Laplace变换法有效地解决了复杂约束条件下概率密度函数的积分问题,并给出体系中层数较少时极限分布的表达式.发现一般情况下极限分布为多项式与指数函数的乘积,力分布在接近平均力处取最大值,大于平均力时呈指数减小. 关键词： 静态颗粒体系 力空间 力网系综     

用拉普拉斯变换差分法求解试井分析中的一维渗流问题

结合拉普拉斯变换和有限差分法给出求解试井分析中一维渗流问题的拉普拉斯变换差分法:首先对渗流方程采用拉普拉斯变换消去时间变量得到拉普拉斯空间数学模型,采用有限差分法求解拉普拉斯空间数学模型,最后通过拉普拉斯反演算法得到井底压力或产量.通过与有限差分法结果和解析解对比,拉普拉斯变换差分法比有限差分法计算误差小.虽然单步计算耗时长,但计算任意时刻结果时对空间网格的适应性和不依赖其它时刻计算结果的特性使得拉普拉斯变换差分法在试井分析中有非常好的应用前景.     

依赖于速度的量子受迫非简谐振子的演化

运用积分算子和迭代方法求得了依赖于速度的量子受迫非简谐振子的精确解。给出了非简谐振子坐标和动量算符的时间演化。这些算符被表示成适当泛函的拉普拉斯变换及随后的逆拉普拉斯交换的形式。 关键词：     

Analytical and semi-analytical solutions to flows of two immiscible Maxwell fluids between moving plates

Unsteady flows of two immiscible Maxwell fluids in a rectangular channel bounded by two moving parallel plates are studied. The fluid motion is generated by a time-dependent pressure gradient and by the translational motions of the channel walls in their planes. Analytical solutions for velocity and shear stress fields have been obtained by using the Laplace transform coupled with the finite sine-Fourier transform. These analytical solutions are new in the literature and the method developed in this paper can be generalized to unsteady flows of n-layers of immiscible fluids. By using the Laplace transform and classical method for ordinary differential equations, the second form of the Laplace transforms of velocity and shear stress are determined. For the numerical Laplace inversion, two accuracy numerical algorithms, namely the Talbot algorithm and the improved Talbot algorithm are used.     

Optimal Filtering Applied to the Inversion of the Laplace Transform

Inversion of the Laplace transform, used in the laser scattering measurement of colloidal particle size distributions, presents severe numerical difficulties. In the presence of noise the variance of the inversion integral is infinite, indicating maximum uncertainty in the inversion. This paper applies the method of minimum variance, or “optimal”, filtering to the eigenfunction spectrum of the Laplace transform, giving an inversion which has finite variance. Spectral decomposition using the eigenfunctions of the Laplace transform gives a representation of the noise and desired signals analogous to the Fourier spectrum used in linear system theory. It is possible to obtain a filtered estimate of the unknown linewidth distribution. The requirement that the variance of this filtered estimate is minimum leads to a Wiener-Hopf integral equation defining the optimal filter. The results of this paper provide a basis of comparison of all methods of inversion of the Laplace transform, including the extensive literature of colloidal particle sizing by laser scattering or photon correlation.     

Evolution of a velocity-dependent quantum forced anharmonic oscillator

The exact solution to a velocity-dependent quantum forced anharmonic oscillator is derived by using integral operators and an iteration method. The study is carried out in operational form by use of the creation and annihilation operators of the oscillator. The time development of the displacement and momentum operators of the anharmonic oscillator is given. These operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals.     

Exact solutions of the Klein—Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein-Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.     

On overall behavior of Maxwell mechanical model by the combined Caputo fractional derivative

The primary purpose of this paper is to analyze the overall behavior of fractional Maxwell model. The approach used in our study is known as the combined Caputo fractional derivative with pioneer work: the extension Laplace transform (ELT) which broaden the lower limit of the classical Laplace transform. Through the ELT and the Stehfest method, we obtain the strain response of the fractional Maxwell model with different parameters. It is concluded that the obtained results show the variation trend of strain response in a more accurate way.     

利用Laguerre多项式的数字逆Laplace变换方法

提出一种基于Laguere多项式的自动与半自动数字Laplace逆变换方法。给出参数最优选择判据,提供了程序实现方法,并给出数值算例。     

三维时变等离子体目标的电磁散射特性研究

基于电流密度拉普拉斯变换方法改进的时域有限差分(LTJEC-FDTD)算法, 研究时变等离子体目标的电磁散射特性.由Maxwell方程和等离子体本构方程出发, 利用拉普拉斯变换和拉普拉斯逆变换, 推导出计算三维时变问题的时域有限差分(FDTD)算法的迭代式. 采用模式匹配方法验证了FDTD迭代式的正确性, 并通过计算等离子体球的雷达散射截面(RCS)验证了算法相关边界的正确性. 最后用LTJEC-FDTD算法分析了涂覆时变等离子体的战斧式巡航导弹的RCS. 关键词： 时变等离子体 雷达散射截面 模式匹配方法 时域有限差分方法     

Processing DOSY spectra using the regularized resolvent transform

A new method for processing diffusion ordered spectroscopy (DOSY) data is presented. This method, the regularized resolvent transform (iRRT-the i denoting the adaptation of the method to evaluate the inverse Laplace transform), is better than conventional processing techniques for generating 2D DOSY spectra using data that has poor chemical shift resolution. From the same data, it is possible to use the iRRT to generate 1D subspectra corresponding to different components of the sample mixture; these subspectra compare favorably to 1D spectra of the pure substances. Both the 2D spectra and the 1D subspectra offer a vast improvement over results generated using a conventional processing technique (non-linear least-squares fitting). Consequently, we present the iRRT as a stable and reliable tool for solving the inverse Laplace transform problem present in experiments such as DOSY.