相关系数矩阵与多元线性相关分析

相关系数指度量两个随机变量间线性关系的无量纲指标,在研究了相关系数矩阵性质及其与多元随机变量线性相关性之间关系的基础上,提出多元线性相关系数的定义,用于衡量多个变鼋间线性相关强弱的无量纲指标.分析表明,所提多元线性相关系数能够较全面地反映变量间的线性相关强度.     

交换半环上矩阵行列式的性质

本文主要研究了交换半环上矩阵乘积行列式的性质。讨论了行列式的乘积与乘积的行列式间的关系,并进一步给出了伴随阵的乘积与乘积的伴随阵之间的关系。     

若干矩阵Γ分布的相关分布

本文研究了与矩阵Γ分布相关的若干分布的密度函数,利用矩阵Γ分布的特征函数和它的Bartlett分解等方法,获得了与矩阵Γ分布相关的几个分布的密度函数解析表达式,它们包括Γ分布随机矩阵的子矩阵、行列式、迹和特征根的分布密度,进一步还得到了相关系数矩阵的分布密度函数形式.     

若干矩阵Г分布的相关分布

本文研究了与矩阵Г分布相关的若干分布的密度函数，利用矩阵Г分布的特征函数和它的Bartlett分解等方法，获得了与矩阵Г分布相关的几个分布的密度函数解析表达式，它们包括Г分布随机矩阵的子矩阵、行列式、迹和特征根的分布密度，进一步还得到了相关系数矩阵的分布密度函数形式．     

局部环上幂等矩阵线性组合广义逆之间的关系

设R是2为单位的局部环.研究了R上三个两两可换的n阶非零幂等矩阵的线性组合广义逆之间的包含关系,确定了R上一类特殊矩阵广义逆的列表算法.利用这种列表算法和相关的矩阵理论,得到了这些矩阵线性组合广义逆之间的包含关系的充要条件,推广了矩阵自反广义逆的逆反律的相关结果.     

“杨辉三角”中某些矩阵及其行列式的讨论

“杨辉三角”中某些矩阵及其行列式的讨论张之正，刘麦学（河南洛阳师范专科学校数学系４７１０２２）近来，许多作者对杨辉三角中的矩阵和行列式进行了讨论（如［１］─［５］），文［６］还给出了一类矩阵的逆矩阵的求法．本短文对这些矩阵及行列式做进一步的探讨．杨辉...     

具有带状系数矩阵的无限维线性规划的解法

研究一类每个约束条件有两个变量且每个变量出现在两个约束条件中的无限维线性规划.引入松弛变量后,得到约束方程组的系数矩阵为无限阶带状矩阵,用它的左逆以及属于零的特征向量可以表示这类问题的最优解.获得目标函数值收敛的一个充分条件.     

广义正定矩阵的进一步研究

基于正定矩阵的几个定义,首先给出了广义正定矩阵的一些新性质,其次研究了广义正定矩阵与H-矩阵、M-矩阵的关系,推广和改进了文献中的有关行列式不等式.     

关于Mina矩阵及其相关行列式恒等式的一些注释

本文通过对所谓的Mina矩阵$\mathbf{D}^{n}_x(f^{a_k}(x))$建立的LU分解,不仅得到Mina行列式恒等式的一个初等证明,而且还给出了Mina矩阵的逆矩阵. 进一步地,通过建立在拉格朗日插值公式上的矩阵分解,本文给出了Mina型矩阵的两个新的行列式恒等式.     

奇异多元正态随机向量的新定义及与其他定义的等价性

通过对奇异协方差阵的行列式重新定义及广义逆矩阵的概念,给出了奇异多元正态随机向量的新定义,并讨论了与其他定义之间的等价关系.     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the comparison between the APV and the NPV computed via the WACC

The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

On the Gap in the Spectrum of the Translations

The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m₁ there is no gap in the spectrum which is larger than 2m₁. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables.     

From the subalgebras of the square to the discriminator

Presented by A. F. Pixley.     

On the dependence of the growth rate on the length of the defining relator

Let { } be a sequence of finitely presented groups with generating setA={a1, …, am}, and letRk be the symmetrized set of words over the alphabetA∪A−1 obtained from the defining words and their inverses by all cyclic shifts. We shall assume that the words inRk are cyclically irreducible, and their lengths tend to ∞ ask increases. In the paper, it is proved that ifRk satisfies the small cancellation conditionC'(1/6) and the number of relators increases not very rapidly with increasingk, then the growth rate ψ(Gk) tends to 2m−1 ask→∞. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 611–617, April, 1999.