Winograd矩阵乘法算法用于任意阶矩阵时的一种新处理方法

摘要t矩阵乘法StraSsen算法及其变形winograd算法用分而治之的方法把矩阵乘法时间复杂性由传统的D(n。)改进到0(佗kg。n.但是对于奇数阶矩阵,在划分子矩阵时,要作特殊处理才能继续使用此算法.本文提出了一种非等阶“十”字架划分方法,可以最少化填零,最大化性能,使得奇数阶矩阵乘法的时间复杂性更加接近偶数阶矩阵乘法的效果.计算实例显示该方法是有效的.     

矩阵的合同、相似与二次型

矩阵的合同关系、相似关系都是等价关系，它们虽然不同。但又有联系．对称矩阵是这两个知识点的交汇点。即两个实对称矩阵合同当且仅当它们相似．进一步得到二次型可以通过一个正交变换化为标准型。这一理论是高等代数教科书的重要内容。然而．现行的教科书对该理论的证明至少涉及到二次型、线性空间、线性变换和欧氏空间的内容．本文利用欧氏空间的正交性质给出这一理论新的简洁证明。以供教学参考之用。     

用无限阶Toeplitz矩阵求常系数微分方程的级数解

无限阶Toeplitz矩阵的属于0的特征向量可递推地求得,可表示常系数齐次微分方程的解.用它的逆可求得常系数非齐次微分方程的特解.     

2级矩阵的迹

给出了2级矩阵的迹的几个结果,同时给出了若干应用例子.     

Influence of temperature on phosphorescence spectra of Pd-porphine in Shpol’skii matrices

We have studied the temperature dependence of the radiative deactivation of the Pd-porphine triplet states in Shpol’skii matrices in the temperature range 1.2–210 K. A substantial transformation of the phosphorescence spectra is observed as the temperature increases and is due to the inclusion of thermally activated Pd-porphine states in the radiative deactivation processes. The activation energy E_a of these Pd-porphine states is measured in matrices of n-octane and n-nonane. The splitting of the lowest quasidegenerate triplet state ΔE(T₂−T₁) is determined for planar and distorted conformations of the Pd-porphine macrocycle in the n-octane matrix as 40 and 57 cm⁻¹, respectively. The ability to use the temperature dependence of the phosphorescence properties of Pd-porphine to fabricate molecular thermometers for the low-temperature range is analyzed. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 4, pp. 460–464, July–August, 2007.     

高压下某些导电高分子色散关系的研究

利用晶格动力学方法,研究在高压下几种导电高分子具有不同晶格链时的色散关系及其曲线的变化.链间耦合作用的减弱使横波与纵波的ω差值相应增大,且在BZ边界处拉开一个间隙,这是维度作用的结果.     

n维氢原子的散射态

研究了n维氢原子的散射态性质．给出了精确的按“k/2π标度”归一化的散射态的精确解波函数及相移表达式，讨论了相移的解析性质，获得了束缚-连续跃迁矩阵元的解析计算公式．普通氢原子(n=3)散射态的有关结果作为特例包含在本文的一般结论之中． 关键词： n维氢原子 散射态 精确解 相移 束缚-连续跃迁矩阵元     

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).