关于无穷小量乘积的讨论

本文由有限个无穷小量的乘积仍是无穷小量的证明入手 ,给出无穷多个无穷小量的乘积不一定是无穷小量的例子 ,并根据这种方法得到无穷多个无穷大量的和也不一定是无穷大量的结论     

无穷自动机的几个等价命题

本文证明了具有无穷栈符合的实时确定下推自动机与无穷自动机的等价性，并且将有限状态自动机的Ｍｙｈｉｌｌ－Ｎｅｒｏｄｅ定理推广到了无穷自动机和具有无穷栈符号的实时确定下推自动机。     

模糊数无穷乘积

在定义了区间无穷乘积、模糊数无穷乘积及其收敛的基础上 ,利用 [3]中得到的关于模糊级数收敛的某些结论 ,得出模糊数无穷乘积与实数无穷乘积理论类似的结果 ,从而说明本文定义的模糊数无穷乘积确为实数无穷乘积的推广。     

无穷级数与无穷乘积

通过构造新的级数以研究原来级数通项的极限性质,从而得到其敛散性.该方法在精细判别和无穷乘积研究有重要有用.     

再论无穷多个无穷小量的乘积

对文[6]提出的质疑给出回答,表明由于不同的无穷小量趋近于0的速度有快有慢,因此无穷多个无穷小量的乘积∏∞k=1{x_n~(k)}∞n=1,有可能不是无穷小量(其中对每个正整数k,{x_n~(k)}_(n=1)~∞表示极限为0的数列),而验证∏∞k=1{x_n~(k)}∞n=1是否是无穷多个无穷小量的乘积,只需验证对每个正整数k,当n→+∞时,{x_n~(k))_(n=1)~∞是否趋近于0,而无需考虑函数列{{x_n~(k)}_(n=1)~∞}_(k=1)~∞的极限limk→∞x_n~(k)是不是无穷小量.进而,对无穷多个无穷小量的乘积是无穷小量或不是无穷小量给出了一些充分条件,     

常数项无穷乘积的性质及判定法

无穷乘积是研究数串级数的一种方法，在无穷乘积里极限的近似值是由反复乘新的因子形成的．本文主要讨论无穷乘积的性质及收敛的判定法．     

一类无穷矩阵代数的乘法序列连续性

设λ，μ是两个序列空间并有符号弱滑脊性，（λ，μ）是变换λ进入μ的无穷矩阵算子所成的无穷矩阵代数，本文研究了这类代数的强，Mackey、弱乘法序列连续性问题。     

关于等价无穷小量

对等价无穷小量代换问题进行探讨.通过实例说明某文献中的一条定理存在不妥之处,并给出相应修正.结果可拓广等价无穷小量替换方法的使用范围.     

关于无穷线性方程组的相容性

本文研究无穷线性方程组的相容性，采用的方法是Abel群同态的延拓．     

无穷维动力系统

本文简要介绍了无穷维动力系统研究中的一些重要问题。     

Summation of double series using the Euler-Maclaurin sum formula

A certain variation of the Euler-Maclaurin sum formula is used to deduce a corresponding formula, suitable for the summation of finite or infinite double series.     

Poisson Summation Formulas and Inversion Theorems for an Infinite Continuous Legendre Transform

The classical Fourier transform and Fourier series are linked by the Poisson summation formula. The goal of this article is to find an infinite continuous Legendre transform which complements Legendre series in a similar way. To this end, the finite continuous Legendre transform due to Butzer/Stens/Wehrens is extended to an infinite transform. We show that for the new Legendre transform variants of Poissons formula and inversion theorems hold.     

表整数为八个三角数的表法数目

通过留数定理把一个无究乘积展成Laurent级数,利用这个展式可以简单地证明表整数为八个三角数的表法数目公式。     

Ramanujan's “Lost” Notebook VIII: the entire Rogers-Ramanujan function

In the Lost Notebook, Ramanujan presents a truly enigmatic infinite product expansion for the two variable Rogers-Ramanujan series. In this paper, we prove this formula by a careful analysis of the Stieltjes-Wigert polynomials.     

The Euler-Maclaurin sum formula for an inner derivation

An operator form of the Euler-Maclaurin sum formula is obtained, expressing the sum of the Euler-Maclaurin infinite series in an inner derivation as the difference between a summation operator and an inner antiderivation, on a closed subalgebra of a Banach algebra.     

A Function Related to a Lagrange-Bürmann Series

An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.     

A formula for the error of finite sinc interpolation with an even number of nodes

Sinc interpolation is a very efficient infinitely differentiable approximation scheme from equidistant data on the infinite line. We give a formula for the error committed when the function neither decreases rapidly nor is periodic, so that the sinc series must be truncated for practical purposes. To do so, we first complete a previous result for an odd number of points, before deriving a formula for the more involved case of an even number of points.     

A Multivariate Faa di Bruno Formula with Applications

A multivariate Faa di Bruno formula for computing arbitrary partial derivatives of a function composition is presented. It is shown, by way of a general identity, how such derivatives can also be expressed in the form of an infinite series. Applications to stochastic processes and multivariate cumulants are then delineated.

     

Second-order expansion for the maximum of some stationary Gaussian sequences

We prove a second-order approximation formula for the distribution of the largest term among an infinite moving average Gaussian sequence. The second-order correction term depends on the autocovariance function only through the second largest autocovariance. Applications to Gaussian time series are discussed and a simulation study showed a substantial improvement over other approximations to the exact distribution of the maximum.     

Feynman path integrals for polynomially growing potentials

A general class of infinite dimensional oscillatory integrals with polynomially growing phase functions is studied. A representation formula of the Parseval type is proved, as well as a formula giving the integrals in terms of analytically continued absolutely convergent integrals. These results are applied to provide a rigorous Feynman path integral representation for the solution of the time-dependent Schrödinger equation with a quartic anharmonic potential. The Borel summability of the asymptotic expansion of the solution in power series of the coupling constant is also proved.