Hamilton算子和Laplace算子间的一个积分公式

本文给出了Hamilton算子和Laplace算子间的一个积分公式,并指出文献[1]中的一个错误.     

Approximations for optimal Laplace transform inversion

A function (p) of the Laplace transform operatorp is approximated by a finite linear combination of functions (p+ _r ), where (p) is a specific function ofp having a known analytic inverse (t), and is chosen in accordance with various considerations. Then parameters _r ,r=1, 2,...,n, and then corresponding coefficientsA _r of the (p + _r ) are determined by a least-square procedure. Then, the corresponding approximation to the inversef(t) of (p) is given by analytic inversion of _r=1 ⁿ A _r (p+ _r ). The method represents a generalization of a method of best rational function approximation due to the author [which corresponds to the particular choice (t)1], but is capable of yielding considerably greater accuracy for givenn.The computations for this paper were carried out on the CDC-6600 computer at the Computation Center of Tel-Aviv University. The author is grateful to Dr. H. Jarosch of the Weizmann Institute of Science Computer Center for use of their Powell minimization subroutine (Ref. 1).     

Laplace Transform of Temperate Holomorphic Functions

Let V be n-dimensional complex vector space. The aim of this paper is to give an elementary proof of the isomorphism O ^t _V ^{^}[n] O ^t _V*, which quantizes the Fourier–Sato transform of the conic sheaf O ^t _V of temperate holomorphic functions     

On representations,inversions, and approximations of laplace transforms in banach spaces

The paper extend's some of the basic results of classical Laplace transform theory to the Laplace transform of bounded Bochner integrable functions and the Laplace-Stieltjes transform of Lipschitz continuous functions with values in a Banach space.     

The Laplace transform of the digamma function: An integral due to Glasser, Manna and Oloa

The definite integral

is related to the Laplace transform of the digamma function

by when . Certain analytic expressions for in the complementary range, , are also provided.

     

Non-stationary waiting times in a closed exponential tandem queue

A closed exponential tandem queue in which every customer has to be served by two servers is considered. Given the numbers of customers lined up at each of the two servers, we derive the probability distributions of the waiting time of any customer until his second service is completed, and of the total busy time of the system.     

Henstock-Kurzweil 可积函数的Laplace 变换的反演定理

该文建立了Henstock-Kurzweil 可积函数的 Laplace变换, 讨论了其基本性质及解析性质, 得到Henstock-Kurzweil可积意义下的反演公式, 并给出反例说明这一结果不能改进     

Real inversion formulas with rates of convergence

Some classical real inversion formulas, such as those concerning Fourier, Laplace and Stieltjes transforms, are unified in a way which allows us to give rates of convergence. As illustration, the case of the Fourier transform is considered. This revised version was published online in June 2006 with corrections to the Cover Date.     

Acceleration of the convergence of the Laguerre series in the problem of inverting the Laplace transform

When the Laplace transform is inverted numerically, the original function is sought in the form of a series in the Laguerre polynomials. To accelerate the convergence of this series, the Euler-Knopp method is used. The techniques for selecting the optimal value of the parameter of the transform on the real axis and in the complex plane are proposed.     

The h-Laplace and q-Laplace transforms

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the particular concepts of the h-Laplace and q-Laplace transforms. The convolution and inversion problems for these transforms are considered in some detail.     

一类索赔相关且带干扰的风险模型

该文讨论了索赔时间间隔与索赔量相关且带干扰的风险模型. 借助拉普拉斯变换研究了此模型的破产时刻、破产前瞬间盈余及破产时赤字三者的联合分布,得到了此联合分布拉普拉斯变换的一个分析表达式并讨论了当初始盈余值趋于无穷大时,此联合分布的渐近表达式.     

A comparison of two equivalent solutions of the diffusion equation

Plane radial flow of water in a closed aquifer towards a circular well or heat flow through a homogeneous conducting solid from a circular hole to infinity are well known problems that were solved long ago. The solution is expressed in terms of an integral of ordinary Bessel functions. A new solution, which is expressed in terms of an integral of modified Bessel functions, is derived by means of Laplace transformation instead of integration of Green's function. One particular choice of the Bromwich contour in the invers transformation, which appears unnecessarily complicated, gives a solution the integral of which converges much more rapidly than the corresponding integral that is given in the literature. In contrast with the classical solution, the new one gives an explicit expression for the transient part. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 657–671, 1999     

Shehu Transform: Extension to Distributions and Measures

This paper improves the computational aspect of the Shehu transform. An inversion formula is given. Finally the Shehu transform is extended to distributions and measures.