Real Principal Value Integrals

 We study principal value integrals of multi-valued differential forms on compact spaces, as introduced by Langlands. Using resolutions of singularities we extend Langlands definition to the case in which the differential form may have no normal crossings. We show by an example that for non-compact spaces the principal value integral associated to a compactification may depend on the compactification. Principal value integrals appear as residues of poles of distributions and as coefficients of asymptotic expansions of oscillating integrals and fibre integrals. (Received 11 November 1999)     

Fast Integration for Cauchy Principal Value Integrals of Oscillatory Kind

In this paper we give a simple, but high order and rapid convergence method for computing the Cauchy principal value integrals of the form $\int_{-1}^{1}e^{i\omega x}\frac{f(x)}{x-\tau}dx$ and its error bounds, where f(x) is a given smooth function, ω∈R ⁺ may be large and ?1<τ<1. The proposed method is constructed by approximating $(\frac{f(x)-f(\tau)}{x-\tau})^{(s)}$ by using the special Hermite interpolation polynomial, which is a Taylor series. The validity of the method has been demonstrated by the results of several numerical experiments and the comparisons with other methods.     

A Note on Quadrature Formulae for Cauchy Principal Value Integrals

The quadrature formulae of Chawla & Jayarajan (1975) havebeen extended in a simple manner for the numerical evaluationof the weighted Cauchy principal value integrals where , ß > –1 and a (–1, 1). The presentquadrature formulae give better approximate values for Cauchyprincipal value integrals than those in Chawla & Kumar (1979),and may also be used for the numerical evaluation of properintegrals      

Error Estimates for Three Methods of Evaluating Cauchy Principal Value Integrals

In this paper, we give error expressions for the subtractionof the singularity method, the method of symmetric pairing anda method of L. M. Delves in the evaluation of the PrincipalValue of the improper integral The error form for the subtraction of the singularity methodis used to deduce the important property that the numericalmethod for the value of the improper integral remains stableas the value of x approaches either of the end-point valuesa and b.     

一类亚纯函数的广义积分及其Cauchy主值

利用函数zp(-1相似文献   

应用留数定理计算一类实积分

应用留数定理,通过构造被积函数,将一类实积分的计算问题转化为求留数的计算,得到求此类问题的一种解法.     

积分第二中值定理“中间点”的渐近性

给出了在各种情况下积分第二中值定理“中间点”的渐近性的几个结论 ,相信在积分学中有着很重要的作用 .     

积分中值定理的推广及其应用

给出了积分中值定理的一个推广,讨论了推广的积分中值定理中间值的渐近性.     

关于积分中值定理的一个注记

研究当积分区间长度趋于无穷时 ,积分中值定理中间点的渐近性质     

关于积分中值定理的一个结论(英文)

文 [1 ],[2 ]研究了当积分区间长度趋于零时 ,积分中值定理中间点的渐近性质 ,本文研究当积分区间长度趋于无穷时 ,积分中值定理中间点的渐近性质 .     

改进的积分第一中值定理的应用

提供若干实例用以说明积分第一中值定理中的中值点ε∈[a，b]加强为ε∈（a，b）后所带来的好处．     

关于积分中值定理的一个一般性结果

本文旨在研究积分中值定理中间点当区间长度趋于零时的渐近性质 ,得到一个具有一般性的新结果     

积分中值定理中值研究的进一步结果

继续杨彩萍、贾云暖等人对积分中值定理的中值当区间长度趋于零时的渐近性研究,这里又得到系列新结果.     

积分第二中值定理的中间点ξ的渐近性质

讨论积分第一和第二中值定理的中间点ξ的渐近性质的一般结果,主要证明积分第二中值定理的中间点在弱条件下的渐近性质.     

积分第一中值定理中值点渐近性

本文从积分第一中值定理出发,在实分析中介绍积分第一中值定理在不同条件下中值点的渐近·I~f＊-I题．     

对称性在重积分及曲面积分中的应用

在积分区域具有某种对称性时,给出重积分及曲面积分所具有的相应性质,并通过例题给出这些性质在重积分及曲线、曲面积分中的应用方法.     

Real Hypersurfaces with Two Principal Curvatures in Complex Projective and Hyperbolic Planes

We find the first examples of real hypersurfaces with two nonconstant principal curvatures in complex projective and hyperbolic planes, and we classify them. It turns out that each such hypersurface is foliated by equidistant Lagrangian flat surfaces with parallel mean curvature or, equivalently, by principal orbits of a cohomogeneity two polar action.     

积分中值定理逆问题及其渐近性

本文讨论积分中值定理的逆问题及逆问题的渐近性     

积分第二中值定理的中值点的近似计算

研究了积分第二中值定理的中值点的近似计算,利用连续函数的零点定理,设计了一个求积分第二中值定理的近似中值点的非线性优化方法,为抽象的积分第二中值定理的可视化问题提供了一种实现方案和算法.最后给出了两个实例的Matlab图示.     

简化形式的积分中值定理另一种表述

阐述了简化形式的积分中值定理中f(x)不要求连续的情况下成立的条件.即"设函数f(x)在闭区间[a,b]上可积,同时f(x)在[a,b]上有原函数,则存在ξ∈(a,b),使∫ from x=a to b f(x)dx=f(ξ)(b-a)成立",并且给出了简洁的证明.