与给定矩阵A的可交换子环C(A)的一些探讨

收集整理现在常用的高等代数与线性代数材料中与给定矩阵A可交换的矩阵所构成的全矩阵空间Pn×n的子空间C(A)的习题,指出CA的交换性及用A的多项式表示问题同C(A)的维数与n有密切关系,得到n(n叟3)阶幂等矩阵A或对合矩阵A的CA都是不可交换的结论。     

Mathematica在中学数学教学及建模中的应用

在中学数学教学实践中介绍数学软件Mathematica的知识及其应用,可以丰富中学数学教学内容,激发学生学习数学的兴趣,帮助学生提高对数学的理解能力、动手能力,同时对培养学生的科研实践能力也具有现实意义.     

基于矩阵的特征多项式与最小多项式相关的探讨

特征多项式是多项式和线性代数联系的纽带,是高等代数学习中重点和难点。从矩阵的特征多项式与最小多项式的定义出发,基于它们的最基本性质,对两者之间的关系进行了分析探讨并得到了一些有益的结论。     

Influence of regression model and initial intensity of an incremental test on the relationship between the lactate threshold estimated by the maximal-deviation method and running performance

Abstract

This study investigated the influence of the regression model and initial intensity during an incremental test on the relationship between the lactate threshold estimated by the maximal-deviation method and performance in elite-standard runners. Twenty-three well-trained runners completed a discontinuous incremental running test on a treadmill. Speed started at 9 km · h^?1 and increased by 1.5 km · h^?1 every 4 min until exhaustion, with a minute of recovery for blood collection. Lactate–speed data were fitted by exponential and polynomial models. The lactate threshold was determined for both models, using all the co-ordinates, excluding the first and excluding the first and second points. The exponential lactate threshold was greater than the polynomial equivalent in any co-ordinate condition (P < 0.001). For both models, the lactate threshold was lower when all co-ordinates were used than when the first and the first and second points were excluded (P < 0.001). 10-km race pace was correlated with both the exponential and polynomial lactate thresholds for all the co-ordinate conditions (r ≥ 0.75, P < 0.001 and r ≥ 0.56, P < 0.05, respectively). The results suggest that the exponential lactate threshold should be used instead of the polynomial equivalent since it is more strongly associated with performance and is independent of the initial intensity of the test.     

Smarandache对偶函数的一个猜想

对于正整数n，设S^*(n)是，n的Smarandache对偶函数．该文证实了有关S^*(n)的一个猜想．     

互素多项式在线性变换下的维数特征

给出了一类线性变换多项式的维数特征定理,并通过将该定理应用于矩阵多项式的秩问题,获得或推广了现行相关文献中的许多结果。     

样条函数δ~nX_+~(n-1)的两个重要性质的一个证明

本文采用特殊的组合式证明了样条函数δnX+n-1当n≥3时都具有的两个重要性质：（1）■时，■时，δnX+n-1为恒大于零的偶函数，且δnX+n-1在（－nw，0）单调增加，在（0，nw）单调减少。     

关于简单线性恶化问题的平行机排序的一个全多项式逼近算法

In this paper, a parallel machine scheduling problem was considered , where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time approximation scheme for the problem of scheduling n deteriorating jobs on two identical machines was worked out. Furthermore, the result was generalized to the case of a fixed number of machines.     

用广义特征矩阵寻找若当链的方法

定义了复数域上方阵的广义特征矩阵，它们可通过解线性方程组求出。利用它们可求出A的若当链，从而给出了一种求A的过渡矩阵的方法。     

关于阶乘多项式

本文概括叙述阶乘多项式的某些性质,推导了阶乘多项式差分的Telescopeing Sums和Summation by Parts公式,并给出在解差分方程、级数求和及概率论中的应用实例。