一类高振荡积分的新方法

本文对具有形式^b∫_af ( x) e^{iωg ( x)} dx ,ω?1 , 其中g 在求积区间[ a , b ] 出现驻点的高振荡积分提出了一种新的数值方法。数值实验表明该方法当振荡加速时, 求积精度迅速提高。     

一类m阶基数B一样条小波插值的误差估计

主要针对基数B-样条函数及其基本性质，研究一类m阶基数B-样条小波插值的误差估计，获得了关于一类m阶基数B-样条小波插值的误差表示以及该类插值误差关于步长h的若干结果，重点是计算、基数B-样条小波逼近和误差处理，特别，这里所说的基数B-样条函数是指具有等距单重节点的多项式样条函数．     

Viscosity approximation methods with weaMy contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.     

Hilbert空间单调的李普希茨算子的一种逼近方法

给出了Hilbert空间单调的李普希茨算子T的方程x+Tx=h的解的逼近方法。     

退化的广义逆函数值Padé逼近

A new generalized inverse function-valued Padé approximation (GIFPA) was defined. Existence condition of GIFPA was given and its uniqueness theorem was proved. All possible degeneracy cases of GIFPA were discussed and constructed. An example was given to illustrate its application.     

耗散近似下原子的熵压缩

利用量子信息熵理论，研究耗散近似下Jaynes—Cummings模型中原子的熵压缩效应，结果表明：由于耗散的影响，原子压缩的幅度随时间减小，压缩效应随着时间减弱，耗散系数越大，压缩效应减弱越快；场强较大时，由耦合引起的耗散效应增强，压缩效应随时间减弱，当场强较小时可以忽略由环境引起的耗散效应．     

关于L_1最佳逼近的一个注记

本文给出了C[0,1]中的子空间U_n满足A性质的一个必要条件,应用所得结果去否定某U_n具有A性质或构造具有某性质的U_n是方便可行的。     

用无网格法求解非线性混凝土受压柱

基于移动最小二乘近似,用无网格法求解考虑材料非线性的混凝土受压柱,在分析中由于混凝土材料的非线性,利用Newton-Raphson迭代法进行求解,编制了相应的分析程序,对混凝土受压柱进行了数值分析。本文分析结果与解析解和有限元解进行比较,吻合较好。     

关于中心厄米特矩阵的广义反特征值问题

1　Introduction　AmatrixA∈Cn×missaidtobecentrohermitianifA =Jn AJm,andskewcentrohermitianifA =-Jn AJm,where Adenotetheconjugateofthema trixAandJlisthepermutationmatrixoforderlwithonesonthecrossdiagonal(bottomlefttotopright)andzeroselsewhere .ThehermitianToeplitzmatricesformanimportantsubclassofcentrohermi tianmatriceswhichoccurnaturallyindigitalsignalprocessingandotherareas ,seeforinstance[1] andreferencetherein .Thecentrohermitianandrelatedmatricesrecentlyplayanimportantroleinthesolu…     

Rational offset approximation of rational Bézier curves

The problem of parametric speed approximation of a rational curve is raised in this paper. Offset curves are widely used in various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational approximation algorithm of offset curve, which preserves the direction of normal, is presented. Project supported by the National Basic Research Program (973) of China (No. 2002CB312101) and the National Natural Science Foundation of China (Nos. 60373033 and 60333010)