同类双原子链一维量子振动的严格解

以量子力学变换严格求解了同类双原子链的一维量子耦合振动,得出了变换矩以及2N个原子振动的频谱。当N为一大数时,作者求解的频谱与以经典力学推导出的频谱相似,但不完全相同。     

Wick型随机广义Fisher方程的精确解

在Kondratiev分布空间(S)-1中利用Hermite变换和齐次平衡法则导出了Wick型随机广义Fisher方程的Backlund变换,给出了该方程在系数G(t)取不同白噪声泛函条件下的精确解.     

电路方程的一种快速精确解法

本文介绍一种有效的电路方程解析解法。该方法不需要进行复杂的指数矩阵运算,简单有效。     

关于“SAS软件包中Fisher精确检验方法的分析”一文的争鸣意见

本文对ＳＡＳ软件包中精确概率的算法与一般统计学教科书有较大差别的问题提出了个人看法。认为在一般情况下根据ＳＡＳ软件包给出的双尾概率作出双侧检验结论时应取慎重态度     

On the quasi-chemical theory of solutions

The classical canonical partition function for a one-dimensional, two-component system is examined for the case of nearest-neighbor interactions. The quasi-chemical model of solid solutions is found to be a natural consequence of the definition of the partition function when one replaces the normal configurational energy with a configurational free energy. Consequently, the quasi-chemical theory may be viewed as a consequence of the definition of the partition function and not as merely a physically pleasing model.     

两类矩阵环上的短正合列

文章讨论了两类二阶矩阵环上的模及其短正合列,得到环R上的短正合列在两类矩阵环的自然推广形式.     

变系数KdV方程的显示精确解

通过齐次平衡法及可化为Bernoulli方程的四阶常微分方程,求出了变系数KdV方程的精确解及孤立波解.     

变厚度圆柱壳的轴对称弯曲问题

本文详细地研究了厚度h=h_0ξ~的圆柱壳的轴对称弯曲问题.文中通过引入一个位移函数H(ξ),将该问题的方程组化成一个关于H(ξ)的6阶常微分方程,用广义超几何函数给出问题的精确解.     

控制能量受限下随机控制系统精确能控性

讨论了控制能量受限下随机控制系统精确能控性问题.从倒向随机微分方程观点出发,利用矩量论方法得到了判定控制能量受限下随机精确能控性充要条件,并得到容易判定的充分条件和必要条件.     

Newman-Penrose Formalism and Gravitational Impulsive and Shock Waves

Vacuum spacetimes endowed with two commuting spacelike Killing vector fields are considered. Subject to the hypothesis that there exists a shearfree null geodesic congruence orthogonal to the two-surface generated by the two commuting spacelike Killing vector fields,it is shown that, with a specific choice of null tetrad, the Newman-Penrose equations are reduced to an ordinary differential equation of Riccati type. fiom the consideration of this differential equation, exact solutions of the vacuum Einstein field equations with distribution valued Weyl curvature describing the propagation of gravitational impulsive and shock wave of variable polarization are then constructed.