膜相渗透原位化学聚合法制备PAn/CA复合透膜

采用膜相渗透原位化学聚合法,使苯胺(An)原位化学聚合于醋酸纤维素(CA)基体膜的微孔壁中,得到均匀分布的PAn/CA复合导电透膜.通过研究聚合反应条件对复合透膜的导电性能和CO₂/O₂表观分离性能的影响,获得了制备性能较优的PAn/CA复合导电透膜的适宜条件.结果表明,采用膜相渗透化学原位聚合法制备的PAn/CA复合导电透膜,平均孔径明显变小,孔径分布变窄,具有优于CA基体膜的微孔结构形态.     

Universal Associated Legendre Polynomials and Some Useful Definite Integrals

We first introduce the universal associated Legendre polynomials, which are occurred in studying the non-central fields such as the single ring-shaped potential and then present definite integrals I_A^±(a, τ)=∫_-1⁺¹x^a[P_l'^m'(x)]²/(1±x)^τdx, a=0, 1, 2, 3, 4, 5, 6, τ=1, 2, 3, I_B(b, σ)=∫_-1⁺¹x^b[P_l'^m'(x)]²/(1- x²)^σdx, b=0, 2, 4, 6, 8, σ=1, 2, 3, and I_C^±(c, κ)=∫_-1⁺¹x^c[P_l'^m'(x)]²/[(1-x²)^κ(1±x)]dx, c=0, 1, 2, 3, 4, 5, 6, 7, 8, κ=1, 2. The superindices “±” in I_A^±(a, τ) and I_C^±(c, κ) correspond to those of the factor (1±x) involved in weight functions. The formulas obtained in this work and also those for integer quantum numbers l' and m' are very useful and unavailable in classic handbooks.     

On Integrals Involving Universal Associated Legendre Polynomials and Powers of the Factor (1-x2) and Their Byproducts

The associated Legendre polynomials play an important role in the central fields, but in the case of the non-central field we have to introduce the universal associated Legendre polynomials P_l'^m'(x) when studying the modified Pschl-Teller potential and the single ring-shaped potential. We present the evaluations of the integrals involving the universal associated Legendre polynomials and the factor (1-x²)^-p-1 as well as some important byproducts of this integral which are useful in deriving the matrix elements in spin-orbit interaction. The calculations are obtained systematically using some properties of the generalized hypergeometric series.     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

Hulthén势任意l波束缚态的近似解析解

在任意l波的离心项1/r2用δ2e-δr/(1-e-δr)2近似表达的条件下,对Hulthen势的径向Schrodinger方程作自变量指数变换,使此转化为超几何微分方程,获得了Hulthen势任意l波束缚态的解析解.给出了解析的能谱方程和用超几何多项式表示的归一化的径向波函数,讨论了近似解析解的意义.