在奇次Legendre多项式零点上的（0，2）*插值

设Ｐ_ｎ表示ｎ次Ｌｅｓｅｎｄｒｅ多项式，本文考虑多项式（１－ｘ²）Ｐ_ｎ．（ｘ）／ｘ（ｎ为奇数）零点上的（０，２）^*插值问题，得到了这种插值的正则性，显式表达式及收敛性．     

关于素变数丢番图方程组与不等式组（英文）

本文研究了和素数有关的方程组和不等式组，通过更细致的指数和估计，我们改进了以前的结果。     

Uniform Asymptotic Expansions for Meixner Polynomials

Meixner polynomials m _n (x;β,c) form a postive-definite orthogonal system on the positive real line x > 0 with respect to a distribution step function whose jumps are Unlike classical orthogonal polynomials, they do not satisfy a second-order linear differential equation. In this paper, we derive two infinite asymptotic expansions for m _n (nα;β,c) as . One holds uniformly for , and the other holds uniformly for , where a and b are two small positive quantities. Both expansions involve the parabolic cylinder function and its derivative. Our results include all five asymptotic formulas recently given by W. M. Y. Goh as special cases. April 16, 1996. Date revised: October 30, 1996.     

Neighborhood assignments and cardinal functions: a unified approach to metrization and uniformity

We use neighborhood assignments and cardinal functions to give a unified approach to metrizability and uniformity. This leads to a number of characterizations of m(X), the metrizability degree of X, u(X), the uniform weight of X, and w(X), the weight of X. For X normal (and regular), m(X) = u(X); it is unknown whether this result extends to completely regular spaces.     

R（0，θ）分布族参数的矩估计与最大似然估计

本文讨论了均匀分布族｛Ｒ（０，θ），θ＞０｝中参数θ的矩估计及最大似然估计的效率及相合性，结果表明θ修正后的最大似然估计要优于θ的矩估计。     

远红外契伦柯夫FEL的动力学理论

契伦柯夫自由电子激光可以产生远红外相干受激辐射。本文建立了契伦柯夫自由电子激光的动力学理论并详细研究了初始信号频率,电子束电压和束—介质膜间隙对器件性能的影响。与自由电子激光,回旋自谐振脉塞比较,指出了短波契伦柯夫自由电子激光的几个显著特点。     

A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS

The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.     

Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups

In this paper, we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in Hilbert spaces by the hybrid method in the mathematical programming.     

一类非线性Schr dinger方程的高精度守恒数值格式

1引言本文讨论下面非线性Schr(?)dinger方程(NLS)方程的初边值问题:i(?)u/(?)t (?)~2u/(?)x~2 2|u~2|u=0,(1) u(x_l,t)=u(x_r,t)=0,t>0,(2) u(x,0)=u_0(x),x_l≤x≤x_r,(3)其中u(x,t)是复值函数,u_0(x)为已知的复值函数,i~2=-1.该问题有着如下的电荷与能量守恒关系:     

新组合型的三角插值多项式

将被插函数进行组合平均,构造一个新组合型的三角插值多项式Cn(f;t,x),使得它在全轴上一致收敛到每个以2π为周期的连续函数,且对Cj2π连续函数类的逼近阶达到最佳,这里0jt,t为任给的奇自然数.