任意区间上连续函数的零点定理

将闭区间上连续函数的零点定理扩展到其它区间上,得到若干个相应区间上连续函数的零点定理,从而使零点定理理论更完善、应用更广泛.     

变质量非完整Vacco动力学系统的积分因子和守恒定理

提出了动力学系统守恒定律构成的一般途径。首先，给出运动微分方程积分因子的定义，详细地研究了守恒量存在的必要条件．其次，建立了变质量非完整Vacco动力学系统的守恒定理及其逆定理．最后，举例说明结果的应用。     

拉格朗日微分中值定理几种不同的证法

拉格朗日(Lagrange)微分中值定理在高等数学中占有重要地位,然而多年来其证明方法单一,为弥补此不足,采用几种不同构造函数的方法证明之.     

泰勒公式在用等价无穷小量替换求极限中的应用

用等价无穷小量替换求极限是一种常用、方便、有效的方法.但寻求等价无穷小量并非易事.本文主要探讨用泰勒公式寻求等价无穷小量及用等价无穷小替换求极限的方法.     

如何构造辅助函数--浅谈中值定理及相关命题的证明

证明微分中值定理及相关命题时，如何构造辅助函数，本作了一些探讨，提出了构造辅助函数的一般思路，对现有教材中的方法提出了不同意见。     

Simple groups with orders 2^a3^b5^cp^d, 2^a3^b7^cp^d and 2^a3^b5^c7^d

This work deals with the power exponent r1 and r2 respectively of the maximal and second-maximal prime factors ofthe order of simple K4-group, and the classification for simple {5,7}′-K4-group G (i.e. ｜G｜ can not be divided by 5 nor by 7 or ｜π(G)｜ = 4 ), simple 5′ -K4-group G (i.e. ｜G｜ can not divided by 5 and ｜π(G)｜ =4) and simple 7′-Ea-group G (i.e. ｜G｜ can notdivided by 7 and ｜π(G)｜ =4). It is derived that r1 =1, 2 and 4, and r2 is not greater than 4. All the simple K4-groups with order 2^a3^b5^cp^d, 2^a3^b7^cp^d and 2^a3^b5^c7^d are obtained.     

关于应用残数定理证明代数恒等式问题的探讨

函数在孤立奇点的残数,函数在无穷远点的残数.利用残数及残数定理可以证明高等代数中的一些恒等式,同时导出拉格朗日插值公式.     

集值映象与随机集值映象的几个不动点定理

在本文中我们得到了关于集值映象与随机集值映象的几个新的不动点定理,扩充了[3]中结果,主要结果是定理1—3与定理6—7     

Robust parameterisation of ages of references in published research

The purpose of this research is to illustrate the use of the gamma distribution to model the ages of references in published research, and to demonstrate that the two gamma distribution parameters characterise a field of research in a manner that is complementary to and more nuanced than the Price Index or mean age of references.Minimum Distance Estimation is shown to produce robust estimates of the gamma distribution parameters because of the insensitivity of the Kolmogorov–Smirnov test in the tails of the distribution.Using a sample of 816 articles from 26 different journals across six subject areas, it is shown that the gamma distribution is at least as good as a lognormal distribution to model the ages of references in research articles.The two gamma distribution parameters indicate the rate of publication of new knowledge within the respective discipline and the citing behaviour in terms of the recency of references. Interpretation of these gamma distribution parameters enables a more nuanced and granular interpretation of the distinctiveness of disciplines, sub-disciplines, formats of publication and the distribution of references within articles than possible using the Price Index, half-life or mean age of references.     

带参数的奇异三阶三点边值问题的正解

本文讨论下述带参数的奇异三阶三点边值问题■其中γ>0是参数且a(t)在t=0和t=1处具有奇性,当f和a满足适当条件时,对一定取值范围内的γ,获得了上述边值问题正解的存在性与不存在性.所用主要工具是Guo-Krasnoselskii不动点定理.