再论微分中值定理"中间点"ξ的性质

主要研究拉格朗日中值定理"中间点"ξ的单调性、连续性及可导性问题.     

二类广义Vandermonde行列式的计算

给出了二类广义Vandermonde行列式计算的显式表示式.     

分次环的有限正规扩张

本文研究了群分次环的有限正规分次扩张问题．利用经典环论方法,得到一个群分次环与其有限正规分次扩张环之间关于分次Jacobson根和分次素根的关系,同时,给出了分次情形的Cutting down定理和Lying over定理．     

Banach空间中φ-渐进非扩展映像不动点的迭代构造

在Mann的迭代算法基础上,运用Banach空间中的广义投影,使渐进非扩展映像每次迭代生成的序列都投影到一个闭凸的集合中．并证明了该算法的强收敛性．     

一类三阶非线性伪抛物方程的初边值问题

非线性伪抛物方程由于其来源于一些重要的物理过程而成为研究热点.对于一类三阶非线性伪抛物方程的初边值问题,给出了Hilbert空间中相应的强制不等式,利用同胚理论及推广的反函数定理,得到了非线性方程初边值问题解的大范围存在定理.对于相应的半线性方程给出了初边值问题解的大范围存在性、唯一性定理.     

积分学第一中值定理“中间点”的渐近性研究新进展

对积分学第一中值定理的中间点当区间长度趋于零时的渐近性研究.新得到的结果不仅包含了过去若干已有结果,而且对涉及函数f(x),g(x)要求的条件几乎就是中值定理的,一个为连续,一个为可积不变号.     

基于Bayes方法的诊断模型分析

文中证明了在Bayes框架下,当漂移参数7服从有信息先验时,在相当广泛的统计模型中,数据删除模型(CDM)和均值漂移模型(MSOM)的参数估计不相等,几个数值例子验证了相应的结论.     

Diameter preserving surjections in the geometry of matrices

We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping φ:Γ→Γ^′ between graphs from this class is shown to be an isomorphism provided that the following holds: Any two points of Γ are at a distance equal to the diameter of Γ if, and only if, their images are at a distance equal to the diameter of Γ^′. This result is then applied to the graphs arising from the adjacency relations of spaces of rectangular matrices, spaces of Hermitian matrices, and Grassmann spaces (projective spaces of rectangular matrices).     

A note on the central limit theorem for bipower variation of general functions

In this paper we present a central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in [O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij, N. Shephard, A central limit theorem for realised power and bipower variations of continuous semimartingales, in: From Stochastic Analysis to Mathematical Finance, Festschrift for Albert Shiryaev, Springer, 2006], where the central limit theorem was shown for even functions. We prove an infeasible central limit theorem for general functions and state some assumptions under which a feasible version of our results can be obtained. Finally, we present some examples from the literature to which our theory can be applied.     

Monotone positive solution for three-point boundary value problem

In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied：
x″（t）＋f（t,x（t））=0,0〈t〈1,
x′（0）=0,x（1）＋δx′（η）=0,
where η ∈ （0, 1）, δ∈ [0, ∞）, f ∈ C（[0, 1] × [0, ∞）, [0, ∞））. Under certain growth conditions on the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper.