(3,3,1,1)层次B样条与分级T网格上多项式样条的相互转换

1引言 B样条在计算机图形学和几何建模等领域有着广泛的应用[3,8].在应用过程中,通常都需要对得到的模型进行修改以到达更好的效果.对于B样条曲线,利用节点插入算法可以有效地进行局部修改.     

强磁场中氢负离子的基态与低激发态

在球坐标系下采用组态相互作用方法,计算了磁场中氢负离子基态与低激发态的能量和结合能.在径向采用高阶B-spline基组,有效地处理了电子关联;角向采用超球谐函数基组,简化了矩阵元角度部分的计算,使计算效率得到了大幅度的提高.用上述方法计算的磁场中氢负离子基态与低激发态能量的高精度结果与已有理论和计算数据作了详细的比较.结果表明,此方法适用于磁场为β=0.000 1~1.0（此处β=1.0时,对应磁场为4.710 8×105T）范围内的精确计算.     

B-Spline Gaussian Collocation Software for Two-Dimensional Parabolic PDEs

In this paper we describe new B-spline Gaussian collocation software for solving two-dimensional parabolic partial differential equations (PDEs) defined over a rectangular region. The numerical solution is represented as a bi-variate piecewise polynomial (using a tensor product B-spline basis) with time-dependent unknown coefficients. These coefficients are determined by imposing collocation conditions: the numerical solution is required to satisfy the PDE and boundary conditions at images of the Gauss points mapped onto certain subregions of the spatial domain. This leads to a large system of time-dependent differential algebraic equations (DAEs) which is solved using the DAE solver, DASPK. We provide numerical results in which we use the new software, called BACOL2D, to solve three test problems.     

Statistics and Correlation Properties of Diamagnetic High Rydberg Hydrogen Atom

The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done some statistics analysis about the high Rydberg energy levels. The nearest-neighbor energy spacing distribution and the 3-statistics have been shown about diamagnetic Rydberg hydrogen atom with the magnetic field being 0.6 T and 6 T. The phenomena of multiply crossing, multiply anti-crossing, and the mixed of crossing and anti-crossing of energy levels have appeared in this paper. For both cases, in range of lower energy, the energy 1evel statistics properties close to Poisson distribution. With the increasing of the energy, the energy level statistics properties are away to Poisson distribution and tend to Wigner distribution step by step.     

Positions and Widths of Anticrossings for Potassium Rydberg Stark States

The B-spline expansion technique is applied to study the anticrossings for potassium Rydberg states in a static electric field. The results of our calculation indicate that the antierossings are caused mainly by the core interaction or by the fine structure interaction. Our results for the positions and the widths of the anticrossings are in good agreement with experimental data.     

利用B-splines特性计算PbS量子点中的激子基态能量的量子尺寸效应

利用B-splines特性构建量子点中激子的波函数,计算PbS量子点中激子的基态能量E_g的量子尺寸效应,并将计算结果与实验结果及其他理论计算结果进行比较;利用B-splines技术计算的激子的基态能量在整个区域与实验完全符合,同时计算了有效质量和势垒高度对基态能量E_g的量子尺寸效应的影响.     

An approximated principal component prediction model for continuous-time stochastic processes

In this paper, a linear model for forecasting a continuous-time stochastic process in a future interval in terms of its evolution in a past interval is developed. This model is based on linear regression of the principal components in the future against the principal components in the past. In order to approximate the principal factors from discrete observations of a set of regular sample paths, cubic spline interpolation is used. An application for forecasting tourism evolution in Granada is also included. © 1997 by John Wiley & Sons, Ltd.     

Piecewise polynomial,positive definite and compactly supported radial functions of minimal degree

We construct a new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support. For given smoothness and space dimension it is proved that they are of minimal degree and unique up to a constant factor. Finally, we establish connections between already known functions of this kind.     

On the numerical solution of the generalized Prandtl equation using variation-diminishing splines

Convergence results are proved for Cauchy principal value integrals of the Schoenberg variation-diminishing splines and its first derivative. The use of such splines in the numerical solution of the Prandtl and generalized Prandtl integral equations is proposed. A Nyström-type method and a modified Nyström method are used and compared computationally.     

Wavelets and molecular structure

Summary The wavelet method offers possibilities for display, editing, and topological comparison of proteins at a user-specified level of detail. Wavelets are a mathematical tool that first found application in signal processing. The multiresolution analysis of a signal via wavelets provides a hierarchical series of best lower-resolution approximations. B-spline ribbons model the protein fold, with one control point per residue. Wavelet analysis sets limits on the information required to define the winding of the backbone through space, suggesting a recognizable fold is generated from a number of points equal to 1/4 or less the number of residues. Wavelets applied to surfaces and volumes show promise in structure-based drug design.This paper is based on a presentation given at the 14th Molecular Graphics and Modelling Society Conference, held in Cairns, Australia, August 27–September 1, 1995.