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排序方式: 共有91条查询结果,搜索用时 31 毫秒
21.
在球坐标下采用基组展开方法计算了均匀磁场中的氢原子高Rydberg态能谱和振子强度谱.径向和角向均采用高阶B样条基组. 径向采用B样条基组能很好地描述束缚态与连续态的耦合;角向采用B样条基组有效地减少了基组维数,计算效率得到大幅度提高. 用上述方法计算了磁场中氢原子Rydberg态-40cm-1到零场电离阈的高精度抗磁谱并与已有理论和实验结果作了比较. 该方法适用于低于离化阈的所有能区的精确谱计算并易于推广到非氢原子、交叉场中的原子以及高于离化阈的正能区光谱的计算.
关键词:
氢原子
B样条基组
能谱
振子强度谱 相似文献
22.
A B-spline approach for empirical mode decompositions 总被引:16,自引:0,他引:16
Qiuhui Chen Norden Huang Sherman Riemenschneider Yuesheng Xu 《Advances in Computational Mathematics》2006,24(1-4):171-195
We propose an alternative B-spline approach for empirical mode decompositions for nonlinear and nonstationary signals. Motivated
by this new approach, we derive recursive formulas of the Hilbert transform of B-splines and discuss Euler splines as spline
intrinsic mode functions in the decomposition. We also develop the Bedrosian identity for signals having vanishing moments.
We present numerical implementations of the B-spline algorithm for an earthquake signal and compare the numerical performance
of this approach with that given by the standard empirical mode decomposition. Finally, we discuss several open mathematical
problems related to the empirical mode decomposition.
Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday with friendship and esteem
Mathematics subject classification (2000) 94A12.
Supported in part by National Aeronautics and Space Administration under grant NAG5-5364, and National Science Foundation
under grants NSF0314742 and NSF0312113.
Yuesheng Xu: Corresponding author. Supported in part by Natural Science Foundation of China under grant 10371122. 相似文献
23.
Extending a recent result of Ulrich Reif on cardinal polynomial B-splines, we show that the cardinal Chebyshev B-spline basis
associated with a linear differential operator with constant real coefficients is orthonormal with respect to a unique weighted
Sobolev-type inner product. 相似文献
24.
Continuity of the derivatives of the main variable is an important feature to obtain an accurate representation of moving boundaries with discrete numerical methods, since the value and direction of the velocity are normally used to relocate the nodal points in a time-marching scheme. A recently developed formulation of the boundary element method using cubic B-splines provides up to C2 continuity between adjacent elements. This formulation is applied in this work to saltwater intrusion problems in confined, leaky and unconfined aquifers. 相似文献
25.
Marie-Laurence Mazure 《Advances in Computational Mathematics》2001,14(2):129-156
For polynomial splines as well as for Chebyshev splines, it is known that total positivity of the connection matrices is sufficient to obtain B-spline bases. In this paper we give a necessary and sufficient condition for the existence of B-bases (or, equivalently, of blossoms) for splines with connection matrices and with sections in different four-dimensional extended Chebyshev spaces. 相似文献
26.
27.
A note on fast Fourier transforms for nonequispaced grids 总被引:1,自引:0,他引:1
Gabriele Steidl 《Advances in Computational Mathematics》1998,9(3-4):337-352
In this paper, we are concerned with fast Fourier transforms for nonequispaced grids. We propose a general efficient method
for the fast evaluation of trigonometric polynomials at nonequispaced nodes based on the approximation of the polynomials
by special linear combinations of translates of suitable functions ϕ. We derive estimates for the approximation error. In particular, we improve the estimates given by Dutt and Rokhlin [7].
As a practical consequence, we obtain a criterion for the choice of the parameters involved in the fast transforms.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
28.
T. N. T. Goodman C. A. Micchelli G. Rodriguez S. Seatzu 《BIT Numerical Mathematics》1995,35(2):233-257
Cholesky factorization of bi-infinite and semi-infinite matrices is studied and in particular the following is proved. If a bi-infinite matrixA has a Cholesky factorization whose lower triangular factorL and its lower triangular inverse decay exponentially away from the diagonal, then the semi-infinite truncation ofA has a lower triangular Cholesky factor whose elements approach those ofL exponentially. This result is then applied to studying the asymptotic behavior of splines obtained by orthogonalizing a large finite set of B-splines, in particular identifying the limiting profile when the knots are equally spaced.The first and second authors were partially supported by Nato Grant #920209, the second author also by the Alexander von Humboldt Foundation, and the last two authors by the Italian Ministry of University and Scientific and Technological Research. 相似文献
29.
It is proved that, among all nonnegative bases of its space, the B-spline basis is optimally stable for evaluating spline functions.
30.
变量选择有助于简化模型,提高估计和预测的精度,但目前鲜有涉及面板半参数空间自回归模型变量选择的研究。本文在ALASSO的基础上提出了SSAR-ALASSO法,该法的核心在于惩罚函数的选择和目标函数的构建。SSAR-ALASSO在变量和参数的对应关系、惩罚函数的选择、特殊参数的取值区间以及适用模型等方面与ALASSO存在差异。模拟结果显示,SSAR-ALASSO法在变量选择的准确性和参数估计的精度两方面均表现良好,随着样本容量的增加表现效果更佳。本文在碳排放量影响因素实证中采用SSAR-ALASSO法对STIRPAT模型进行变量选择。研究结果表明人均财富、技术水平、产业结构、所有制结构和产业集聚显著影响碳排放量,城市化、对外开放、能源价格和环境政策对碳排放量无显著影响。 相似文献