几类特殊r-循环阵的逆

本文利用多项式理论给出了几类特殊r-循环阵逆阵的求法.     

基于一个新核函数的半定规划的内点算法的复杂性分析

Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.     

矩阵多项式的求逆

本文对矩阵多项式的求逆给出了一般方法,并针对于每一种方法给出了具体实例.     

多项式向量场空间的维数与基

本文借助于数域P上的n次多项式的齐次分解,证明了线性空间P[X1,X2,…Xn]m的维数等于Cn＋m^n并给出了该空间的一组基;进而得到R^n上次数不超过m的多项式向量场的全体构成的线性空间V的维数等于n·Cn＋m^n。     

关于一个广义Euler多项式的恒等式

用初等的方法研究了一个广义Euler多项式的性质,并得到了一组恒等式.     

Least-squares function-valued Padé-type approximation and its application in solving integral equations

To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polyno- mials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the least-squares function： valued Pad＆type approximation is constructed. Their existence and uniqueness are studied. A recursive computation formula of the least-squares function-valued Padetype approximation is given. In the end, an example is given to show that the method is effective and stable.     

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.