教学方法的改革与优化

概述了对教改的认识，以及《高等代数》教学的具体改革过程．形成了便于操作的教改模式：细读-精讲-习作．     

关于矩阵迹结论的一个应用

牛顿恒等式是联系多项式根的幂和与其系数关系的一个重要恒等式.本文利用矩阵迹的结论和凯莱-哈密顿定理,得到了牛顿恒等式证明的一个矩阵方法.     

关于M值随机序列的强极限

利用对数似数比作为任意离散型随机变量相对独立变量偏差的一种随机性度量,采用研究强极根定理的一种新方法一网的微分法(参见[4],[5],给到一一个关于离散型随机变量序列的强极限定理。     

关于1-齐次图的一种分类

本文对满足条件（1）对T中任意一边uv,Di^i＋1（u,v）是团,和条件（2）对某个整数i（1〈i〈d）,ci=1且αi^2=bi,且直径为d,价为k的齐次图T进行了完全分类．     

反粒子与Klein-Gordon方程Ψ函数的物理意义

基于相对论质能关系、Dirac在相对论框架下建立的反粒子理论和CPT定理,给出了Klein-Gordon方程Ψ函数的一种新解释。     

一类高维非线性椭圆型方程正整解的存在性

以Shauder-Tychonoff不动点定理为工具,建立一类高维非线性椭圆型方程△u=f（x,△↓u）u^y（x∈R^n,n≥3,0〈y〈1）正的整体解的存在性定理,并给出了解的有关性质．     

部分泛von Staudt定理的简化证明

运用p-adic赋值理论给出了泛可除Bernoulli数B^An／n的系数τu的p—adic赋值的界,从而给出了泛von Staudt定理中部分同余式的简化证明．     

XMage: An image retrieval method based on partial similarity

XMage is introduced in this paper as a method for partial similarity searching in image databases. Region-based image retrieval is a method of retrieving partially similar images. It has been proposed as a way to accurately process queries in an image database. In region-based image retrieval, region matching is indispensable for computing the partial similarity between two images because the query processing is based upon regions instead of the entire image. A naive method of region matching is a sequential comparison between regions, which causes severe overhead and deteriorates the performance of query processing. In this paper, a new image contents representation, called Condensed eXtended Histogram (CXHistogram), is presented in conjunction with a well-defined distance function CXSim() on the CX-Histogram. The CXSim() is a new image-to-image similarity measure to compute the partial similarity between two images. It achieves the effect of comparing regions of two images by simply comparing the two images. The CXSim() reduces query space by pruning irrelevant images, and it is used as a filtering function before sequential scanning. Extensive experiments were performed on real image data to evaluate XMage. It provides a significant pruning of irrelevant images with no false dismissals. As a consequence, it achieves up to 5.9-fold speed-up in search over the R*-tree search followed by sequential scanning.     

重积分计算中的对称性定理及应用

利用积分区域的对称性和被积函数的奇偶性可以简化二重积分和三重积分的计算,为此,给出基本的、常用的对称性定理,并赋予严格的证明和应用实例.再在此基础上将其推广,使得对称性定理更具有一般性,进而也扩大了它的适用范围.     

分段函数求导问题的多种解法

求分段函数在分段点处的导数，不能直接利用求导公式或求导法则；但是可以借助其它数学工具，如导数极限定理、泰勒公式等等，将问题转化，进而得到求解该问题的多种方法。