用B样条函数计算氢分子离子的能级和波函数

采用B样条函数展开方法数值求解了氢分子离子的定态薛定谔方程,计算了不同核间距时氢分子离子的基态和第一激发态的能级,结果表明,将氢分子离子的核位置作为B样条函数的节点,即使对较大的核间距,基态和第一激发态的能级值仍可达到很高的精度,所得基态径向波函数与用GAUSSIAN化学软件计算的结果符合得很好.     

里德堡钠原子抗磁谱的模型势计算

用B样条基组展开方法结合模型势计算了里德堡钠原子抗磁谱和相应的振子强度谱.径向和角向均采用高阶B样条基组.计算结果与已有的R-矩阵和多通道量子亏损理论相结合(R-matrix MQDT)法及其他理论计算结果作了比较,几种理论结果在我们所研究的能区内符合得非常好.本文方法较R-ma-trix MQDT法简单,易于推广到交叉电磁场中里德堡原子的精确谱的计算中.     

Calculation of the hyperfine structure constants in 85Rb and 133Cs

For heavy atoms or ions, such as, Rb and Cs et al., relativistic effect must be considered in the calculation. In this paper, the relativistic many-body perturbation theory is used to solve the Dirac equation. And the zeroth-order hyperfine constants are evaluated with Dirac-Fock wave function. The finite basis sets of dirac equation are constructed by B-splines. With the finite basis sets the core polarization and the correlation diagrams are calculated. The hyperfine structure constants of the 5S1/2 and 6S1/2 states of 85Rb as well as the 6S1/2 and 7S1/2 states of 133Cs are evaluated.     

Totally positive functions through nonstationary subdivision schemes

In this paper a new class of nonstationary subdivision schemes is proposed to construct functions having all the main properties of B-splines, namely compact support, central symmetry and total positivity. We show that the constructed nonstationary subdivision schemes are asympotically equivalent to the stationary subdivision scheme associated with a B-spline of suitable degree, but the resulting limit function has smaller support than the B-spline although keeping its regularity.     

一个新的时间序列的插值模型

在这篇文章里,通过使用二次B样条,给出了一个用于数据挖掘的新的插值法方法,给出了时间序列的局部插值模型,插值曲线是C1连续的,该方法具有不需要解线性方程组的优点,应用上海股票指数进行了数值实验,实验性结果表明方法是有效的.     

边界奇异微分方程的区间样条小波求解

本文基于提升格式的第 2代小波构造方法 ,建立了区间上的三次B样条小波 ,并用于求解有边界奇异性的微分方程 .由于区间小波的边界特性 ,该方法避免了由小波基引起的振荡 .模拟计算结果验证了所提方法     

混合体积、对数凹序列和B样条函数

本文主要通过样条函数方法研究与之相关的离散几何学和组合学问题.在离散几何学方面主要考虑超立方体切面(cube slicing)体积和混合体(mixed volume)的样条表示,利用B样条函数的几何解释,将超立方体切面问题转化为与之等价的样条函数问题,分别给出Laplace和P′olya关于超立方体切面定理的样条证明,将样条函数与混合体积联系起来,给出一类混合体积的样条解释.利用这种解释可以得到一类具有对数凹性质的组合序列,从而部分地回答了Schmidt和Simion所提出的关于混合体积的公开问题.在组合数学方面主要考虑多种组合多项式与样条函数的关联以及组合序列对数凹性质的样条方法研究.本文借助丰富的样条函数理论,不但验证了离散几何学和组合数学中很多现有的结果,而且得到了一系列离散数学对象的新性质,建立了离散数学问题与具有连续性特质的样条函数之间的内在联系.     

利率期限结构的B-样条校准法

瞬时远期利率曲线是利率期限结构的重要表现形式.本文介绍了如何应用B样条方法及序列二次规划算法,根据市场利率产品的报价,快速准确地拟合出远期利率曲线.不同于常用的Bootstrapping方法,我们的方法所产生的曲线满足利率期限结构所要求具有的光滑性.最后作为一个实际应用,本文使用欧元市场数据说明了我们方法的具体应用.     

Scattered data reconstruction by regularization in B-spline and associated wavelet spaces

The problem of fitting a nice curve or surface to scattered, possibly noisy, data arises in many applications in science and engineering. In this paper we solve the problem using a standard regularized least square framework in an approximation space spanned by the shifts and dilates of a single compactly supported function . We first provide an error analysis to our approach which, roughly speaking, states that the error between the exact (probably unknown) data function and the obtained fitting function is small whenever the scattered samples have a high sampling density and a low noise level. We then give a computational formulation in the univariate case when is a uniform B-spline and in the bivariate case when is the tensor product of uniform B-splines. Though sparse, the arising system of linear equations is ill-conditioned; however, when written in terms of a short support wavelet basis with a well-chosen normalization, the resulting system, which is symmetric positive definite, appears to be well-conditioned, as evidenced by the fast convergence of the conjugate gradient iteration. Finally, our method is compared with the classical cubic/thin-plate smoothing spline methods via numerical experiments, where it is seen that the quality of the obtained fitting function is very much equivalent to that of the classical methods, but our method offers advantages in terms of numerical efficiency. We expect that our method remains numerically feasible even when the number of samples in the given data is very large.     

Numerical exploration of population transfer of Rydberg-atom by single frequency-chirped laser pulse

This paper has calculated that Rydberg atoms can be transferred to states of lower principal quantum number by exposing them to a frequency chirped microwave pulse. The atoms experience the consequence： 70p-69s-68p-67s-66p by a constant amplitude field in the adopted model. This study shows that the complete population transfer is related to the chirp rate and the carrier frequency.