有关中值定理的探究性教学

通过对中值定理教学思路的设计,给出探究性教学方法的一个实例,即通过导数概念的物理意义导出Lagrange中值定理,经特殊化后推出Rolle定理,再经化归思想给出Lagrange定理的证明,最后推广得到Cauchy中值定理,并借助类比或化归思想分别给出Cauchy定理的证明．     

柯西中值定理的逆问题及渐进性

讨论了柯西中值定理的逆问题,并将柯西中值定理"中间点"的渐进性在高阶柯西中值定理中作了推广,得到了一般性的结论.     

一类高阶超双曲型方程的中量定理及其逆定理

Asgeirsson中量定理表明超双曲型方程的Cauchy问题一般是不适应的,对Asgeirsson中量定理的推广就有重要意义,目前关于高阶方程解的中量只有初步探讨,尚未得到具体结果,本文直接利用Asgeisson中量定理结果和积分,微分的性质与关系,得到了高阶方程解的中量满足广义双轴对称位势方程,同时还证明了其逆定理,利用关于广义双轴对称位势方程正则解的表达式及雅可比多项式的特殊性质,得到了高阶方程解的中量公式,从而使得关于解的拓展性和适定性的讨论将有可能。     

On a Cochrane Sum and Its Hybrid Mean Value Formula

The main purpose of this paper is to use a mean value theorem of Dirichlet L-functions to study the asymptotic property of a hybrid mean value of a Cochrane sum and to give an interesting mean value formula.     

关于Hardy和的混合均值公式

本文的目的是利用Dirichlet L-函数的均值定理研究类似于Dedekind和的和与Ramanujao和的混合均值的分布性质，并给出一个较为精确的渐近公式及一个有趣的恒等式．     

A hybrid mean value related to certain hardy sums and Kloosterman sums

The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.     

On a Cochrane sum and its hybrid mean value formula (II)

The main purpose of this paper is using a mean value theorem of Dirichlet L-functions to study the asymptotic property of a hybrid mean value of a Cochrane sum, and give an interesting mean value formula.     

积分第一中值定理的推广

将积分第一中值定理中的连续性条件减弱为有介值性,建立了具有介值性质的可积函数的积分第一中值定理的推广形式.     

On a Generalized Cochrane Sum and Its Hybrid Mean Value Formula

The main purpose of this paper is to use a mean value theorem of Dirichlet L-functions to study the asymptotic property of a hybrid mean value of a generalized Cochrane sum, and give an interesting mean value formula.2000 Mathematics Subject Classification: Primary—11F20; Secondary—11F99     

A hybrid mean value formula involving Kloosterman sums and Hurwitz zeta-function

The main purpose of this paper is using the mean value theorem of Dirichlet L-function and the estimates for character sums to study the asymptotic properties of a hybrid mean value of Kloosterman sums with the weight of Hurwitz zeta-function and the Cochrane sums, and give an interesting mean value formula for it.