广义Laplace-Stieltjes变换的准确零(R)级

本文对广义Ｌａｐｌａｃｅ－Ｓｔｉｅｌｔｊｅｓ变换确定的解析函数引进了准确零（Ｒ）级的概念，得到了这样的函数有准确零（Ｒ）级的两个充要条件．其结果类似于指数级数     

分形油藏中非牛顿松弛粘弹性液体广义流动分析

将分形引入渗流力学,建立了分形油藏具有松弛特性的粘弹性液体的不稳定渗流模型;利用双参数（ ｄｆ ,ｄｓ） 刻画分形油藏的分形特性,利用四参数（ｄｆ,ｄｓ ,λｖ ,λｐ） 描述粘弹性液的广义流动特征;提出了广义的正交变换,并利用Ｌａｐｌａｃｅ＿Ｗｅｂｅｒ 变换,拉氏＿正交变换给出了无限大地层和有界地层的精确解和渐近解;通过拉氏数值反演和渐近解分析了分形油藏粘弹性液体流动特征·　探讨了改变分形参数时压力变化规律·     

对称反对称多重尺度函数的构造

１　多重小波的定义和双尺度相似变换 作为一种分析工具,小波已经运用在各种领域,并取得了显著的成果．近年来,多重小波成为小波研究的热点．Ｉ．Ｄａｕｂｅｃｈｉｅｓ［１］已经证明,对单重小波,除Ｈａｒｒ基外不存在对称和反对称的有紧支集的小波正交基．而多重小波则不受这一限制． 利用分形插值的方法,Ｇｅｒｏｎｉｍｏ、Ｈａｒｄｉｎ和 Ｍａｓｓｏｐｕｓｔ［２］等构造出了ＧＨＭ多重小波,相应的多重尺度函数和多重小波函数如图１和图２所示．ＧＨＭ多重小波的两个尺度函数都是对称的,相应的小波函数则一个对称另一个反对称;…     

Cgau小波变换像空间中的等距变换与反演公式

在以再生核Hilbert空间为连续小波变换像空间的基础上,针对Cgau小波(复数形式的Gauss小波),给出了其小波变换像空间的再生核的具体表达式.当固定尺度因子时,利用再生核空间理论,对Cgau小波变换像空间做了具体描述,分别给出了Cgau小波变换像空间中的等距变换和反演公式,这为进一步研究一般的小波变换像空间提供了理论基础.     

小波尺度函数计算的广义高斯积分法及其应用

对于小波尺度函数变换的分解系数的积分运算建立了以尺度函数为权的广义高斯积分方法的运算格式．借助于样条函数,证明了其广义高斯积分随小波分解水平（resolutionlevel）指标的上升而收敛．在此基础上给出了以小波尺度函数变换重构或逼近任一函数的显式解析式,并对具有函数算子、微分或积分算子的运算给出了变换规则．这对于求解复杂非线性方程（组）是一种强有力的工具．最后给出了用该文方法求解非线性二点边值问题的算例．     

Cgau小波变换像空间中的等距变换与反演公式

在以再生核Hilbert空间为连续小波变换像空间的基础上,针对Cgau小波(复数形式的Gauss小波),给出了其小波变换像空间的再生核的具体表达式.当固定尺度因子时,利用再生核空间理论,对Cgau小波变换像空间做了具体描述,分别给出了Cgau小波变换像空间中的等距变换和反演公式,这为进一步研究一般的小波变换像空间提供了理论基础.     

Gauss小波变换像空间的描述

在连续小波变换像空间是再生核Hilbert空间的基础上,针对经常用于边界检测并且使用效果非常好的Gauss小波,给出了其小波变换像空间的再生核具体表达式.并且当固定尺度因子和固定平移因子时,利用再生核空间理论,对Gauss小波变换像空间做了具体描述,分别给出了Gauss小波变换像空间中的等距恒等式和反演公式,这为进一步研究一般的小波变换像空间提供了理论基础.     

在右半平面收敛的Laplace-Stieltjes变换的增长性

本文研究了在右平面收敛的Ｌａｐｌａｃｅ－Ｓｔｉｅｌｔｊｅｓ变换的增长性,得到了与指数级数类似的结果     

向量值Laplace变换与右连续积分半群

该文利用向量值Ｌａｐｌａｃｅ变换给出一类向量值函数的表示，并将它应用于Ｂａｎａｃｈ空间的Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的刻划，引进了右连续积分半群，证明了一类非稠定且指数增长的算子对应的Ｃａｕｃｈｙ问题是适定的．     

紧支撑正交对称和反对称小波的构造

１．引言 近年来,人们分别从数学和信号的观点对正交小波进行了广泛的研究．尤其是２尺度小波,它克服了短时 Ｆｏｕｒｉｅｒ变换的一些缺陷．目前最常用的 ２尺度小波是 Ｄａｕｂｅｃｈｉｅｓ 小波,但 ２尺度小波也存在一些问题：如 Ｄａｕｂｅｃｈｉｅｓ［２］已证明了除 Ｈａａｒ小波外不存在既正交又对称的紧支撑 ２尺度小波．因此人们提出了 ａ尺度小波理论［３］－［６］,文献［４］－［６］对 ４尺度小波迸行研究．本文的目的是研究４尺度因子时紧支撑正交对称和反对称小波的构造方法．并指出对同一紧支撑正交对称尺度函数而言,…     

基于直接数值积分的Laplace逆变换方法的比较研究

为了探讨各种数值积分方法,如梯形公式、Simpson法、Gauss积分方法和振荡函数积分方法等,在数值Laplace逆变换中的应用效果,本文进行了基于各种离散数值积分公式的Laplace逆变换方法的比较研究,涉及到24种方法,针对Davies和Martin的16个考题,给出了数值比较结果,得出了一些新的结论。     

Numerical Inversion of the Mellin Transform

A method is described for the numerical inversion of the Mellintransform, without reduction of the problem to the inversionof the Laplace transform. The expansion of the original function(t) in a series of orthogonal Laguerre functions is used andthe coefficients of this expansion are obtained by means ofa collocation on the real axis of the transformed plane. Theperformance of the method is illustrated by the inversion offive test functions.     

指数型Radon变换的一些结果

该论文主要研究在平面情形下指数型 Radon 变换的连续性,得到了它的近似反演公式，并对近似反演的数值解法加以改进.借助一些技巧,该文从理论上还建立了精确反演公式，从而推广了古典 Radon 变换的相应结果.     

ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

A software package for numerical inversion of Laplace transforms computable everywhere on the real axis is described. Besides the function to invert the user has only to provide the numerical value (even if it is an approximate value) of the abscissa of convergence and the accuracy required for the inverse function. The software provides a controlled accuracy, i.e. it dynamically computes the so-called maximum attainable accuracy such that numerical results are provided within the greatest value between the user’s required accuracy and the maximum attainable accuracy. This is done because the intrinsic ill posedness of the real inversion problem sometime may prevent to reach the desired accuracy. The method implemented is based on a Laguerre polynomial series expansion of the inverse function and belongs to the class of polynomial-type methods of inversion of the Laplace transform, formally characterized as Collocation methods (C-methods).     

The use of partition polynomial series in Laplace inversion of composite functions with applications in fractional calculus

This paper presents an analytical method towards Laplace transform inversion of composite functions with the aid of Bell polynomial series. The presented results are used to derive the exact solution of fractional distributed order relaxation processes as well as time‐domain impulse response of fractional distributed order operators in new series forms. Evaluation of the obtained series expansions through computer simulations is also given. The results are then used to present novel series expansions for some special functions, including the one‐parameter Mittag‐Leffler function. It is shown that truncating these series expansions when combined with using potential partition polynomials provides efficient approximations for these functions. At the end, the results are shown to be also useful in studying asymptotical behavior of partial Bell polynomials. Numerical simulations as well as analytical examples are provided to verify the results of this paper.     

Cooling of a cylindrical container blasted into the rock

An upright cylindrical container blasted into the rock is filled instantaneously with a warm liquid. Heat is transferred from the liquid into the surrounding rock and the open air. The temperature of the liquid and the surrounding rock is determined as a function of time.The differential equation and the auxiliary conditions of the transient heat conduction problem are Laplace transformed, the subsidiary equations are solved by two-dimensional relaxation, and the resulting temperature is obtained by means of numerical inversion of the Laplace transform.The results are presented numerically and graphically.     

Inverse two-sided Laplace transform for probability density functions

We present a method for the numerical inversion of two-sided Laplace transform of a probability density function. The method assumes the knowledge of the first M derivatives at the origin of the function to be antitransformed. The approximate analytical form is obtained by resorting to maximum entropy principle. Both entropy and L₁-norm convergence are proved. Some numerical examples are illustrated.     

变荷载下半透水边界成层地基的一维固结

在Terzaghi一维固结理论假设基础上,研究分析了半透水边界的层状饱和土在变荷载作用下有效应力比的变化规律．利用Laplace变换,得到了随时间任意变化荷载作用下的解答,并结合Laplace逆变换方法,对几种常见变荷载作用下的情况进行了讨论,得到了一些有益的结论．通常所研究的透水或不透水边界条件只是该文的特例．和平均指标法相比,该文所给方法计算的土体有效应力变化规律更精确．     

Classroom Note: Fourier Method for Laplace Transform Inversion

A method is described for inverting the Laplace transform. The performance of the Fourier method is illustrated by the inversion of the test functions available in the literature. Results are shown in the tables.