从几何的角度看微分中值定理

从平面几何中曲线之间的相切关系不依赖于坐标轴的选取这一基本事实去看数学分析中Rolle中值定理、Lagrange中值定理以及Cauchy中值定理.     

探究两圆方程之差的意义

<正>我们都知道:若⊙C1:x2+y2+Dx+Ey+F=0与⊙C2:x2+y2+D′x+E′y+F′=0相交于M、N两点,则直线l:(D-D′)x+(E-E′)y+(FF′)=0(即两圆方程之差)表示⊙C1与⊙C2的公共弦MN的方程.自然而然,我们不禁要问,不同心的⊙C1与⊙C2在外离、内含、内切及外切的情况下,它们的方程之差(D-D′)x+(E-E′)y+(F-     

具p-Laplace算子的分数阶微分方程边值问题的正解

考虑具有p-Laplace算子的分数阶泛函微分方程边值问题,利用锥上的不动点定理,得到了其正解及多个正解存在的充分条件,所得结果推广了已有的结论,并举例说明了结论的适用性.     

关于树上连续状态马氏泛函的一类强偏差定理

强偏差定理一直是国际概率论界研究的中心课题之一.通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,给出了一类特殊非齐次树上连续状态马氏泛函的若干强偏差定理.     

拓扑线性空间中的Drop定理

本文在拓扑线性空间中建立了一般的Ｄｒｏｐ定理并证明新的Ｄｒｏｐ定理与拓扑线性空间中的一个Ｅｋｅｌａｎｄ变分原理型的结果等价．此外,还给出了一个无异Ｄｒｏｐ情形下的Ｄｒｏｐ定理。     

复Banach空间与平衡域上的双全纯凸映射的增长性定理

本文将利用从属原理给出双全纯凸映射的精确增长性定理．     

I.J.Matrix定理的进一步推广

文献 [1]— [5 ]连续讨论了 I.J.Matrix定理的一些推广及应用 ,特别是文 [5 ]利用高阶微分的知识简明地给出了一个推广 ,本文给出其进一步的推广 .设 a0 ,a1 ,… ,an 是 n 1个互不相同且不为零的数 ,f ( x)是次数为 m的多项式 ,文 [5 ]讨论的是m相似文献   

Weighted pseudo almost periodic solutions of N-th order neutral differential equations with piecewise constant arguments

In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.     

On the Well-Posedness of Determination of Two Coefficients in a Fractional Integrodifferential Equation

The authors study an inverse problem for a fractional integrodifferential equation, which aims to determine simultaneously two time varying coefficients, a kernel function and a source function, from the additional integral overdetermination condition. By using the fixed point theorem in suitable Sobolev space, the global existence and uniqueness results of this inverse problem are obtained.     

Moderate deviations and central limit theorem for small perturbation Wishart processes

Let X^ε be a small perturbation Wishart process with values in the set of positive definite matrices of size m, i.e., the process X^ε is the solution of stochastic differential equation with non-Lipschitz diffusion coefficient： dXt^ε = √εXt^εtdBt＇ ＋ dBt＇√εXt^ε ＋ ρImdt, X0 = x, where B is an rn x m matrix valued Brownian motion and B＇ denotes the transpose of the matrix B. In this paper, we prove that { （Xt^ε-Xt^0）/√εh^2（ε）,ε 〉 0} satisfies a large deviation principle, and （Xt^ε - Xt^0）/√ε converges to a Gaussian process, where h（ε） → ＋∞ and √ε h（ε） →0 as ε →0. A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^ε are also obtained by the delta method.