基于函数值的线性有理插值样条的区域控制

将插值曲线约束于给定的区域之内是插值与逼近的一个重要内容.本文讨论了一种带形状参数的线性有理插值样条的区域控制问题.给出将插值曲线约束于给定的折线及抛物线之上、之下或之间的条件.数值实例表明本文给出的条件在曲线设计中是有效的.     

Discrete-time orthogonal spline collocation methods for the nonlinear Schrödinger equation with wave operator

In this paper, discrete-time orthogonal spline collocation schemes are proposed for the nonlinear Schrödinger equation with wave operator. These schemes are constructed by using orthogonal spline collocation approaches combined with finite difference methods. The conservative property, the convergence, and the stability of these methods are theoretically analyzed and also verified by extensive numerical experiments. In addition, some interesting phenomena which require further theoretical analysis are discussed numerically.     

锥方向高阶广义邻近导数及高阶Mond-Weir对偶(英文)

本文引入了集值映射的锥方向的高阶广义邻近导数.应用这种导数,构建了约束的集值优化问题的一种高阶Mond-Weir型对偶,并建立了相应的弱对偶,强对偶和逆对偶性,获得的结果推广了文献中的相应结论.     

用样条逼近Sobolev函数类W_p~1(R)的逼近误差

作者研究了定义在全实轴上的Sobolev函数类W_p~1(R)的逼近问题.以一次样条函数作为逼近工具,给出了p=1和p=∞时的逼近误差.     

Projected subgradient method for non-Lipschitz set-valued mixed variational inequalities

A projected subgradient method for solving a class of set-valued mixed variational inequalities (SMVIs) is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.     

Numerical solution of the Rosenau–KdV–RLW equation by operator splitting techniques based on B‐spline collocation method

In the present study, the operator splitting techniques based on the quintic B‐spline collocation finite element method are presented for calculating the numerical solutions of the Rosenau–KdV–RLW equation. Two test problems having exact solutions have been considered. To demonstrate the efficiency and accuracy of the present methods, the error norms L₂ and L_∞ with the discrete mass Q and energy E conservative properties have been calculated. The results obtained by the method have been compared with the exact solution of each problem and other numerical results in the literature, and also found to be in good agreement with each other. A Fourier stability analysis of each presented method is also investigated.     

Operator splitting for numerical solution of the modified Burgers' equation using finite element method

The aim of this study is to obtain numerical behavior of a one‐dimensional modified Burgers' equation using cubic B‐spline collocation finite element method after splitting the equation with Strang splitting technique. Moreover, the Ext4 and Ext6 methods based on Strang splitting and derived from extrapolation have also been applied to the equation. To observe how good and effective this technique is, we have used the well‐known the error norms L₂ and L_∞ in the literature and compared them with previous studies. In addition, the von Neumann (Fourier series) method has been applied after the nonlinear term has been linearized to investigate the stability of the method.     

带约束条件集值优化问题近似Henig有效解集的连通性

研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理.     

基于联合估计法的债券信用利差期限结构拟合及应用

基于2016~2018年月度数据,通过独立估计的单曲线样条模型和SV 模型、联合估计的多曲线样条模型和SV模型拟合公司债信用利差期限结构,进而对模型拟合效果进行比较,讨论模型在宏观经济预测中的应用,得到以下结论:(1)拟合模型的函数形式是导致理论信用利差期限结构曲线翻折的原因。样条模型和SV模型拟合的信用利差曲线形状完全不同,且模型函数变动引起的误差变动大于曲线变动引起的误差变动。(2)联合估计模型可以修正独立估计模型的人为扭曲形式。多曲线模型的结果更接近实际信用利差,误差波动性明显减小,曲线更为平滑,且联合估计的多曲线样条模型优于独立估计的单曲线样条模型、独立估计的SV 模型和联合估计的SV模型。(3)公司债信用利差期限结构在一定程度上蕴含了市场对未来宏观经济的预期信息,且在短期内预测结果随先行期限延长而改善。因此,宏观经济政策制定者需关注信用利差和期限结构模型拟合研究,重视对信用利差期限结构的深度信息挖掘,从而提高中国宏观政策制定者调控手段的前瞻性和有效性。     

一种低原子序数元素EDX RF的多次导-样条小波解析方法研究

能量色散X射线荧光（EDXRF）光谱分析待测元素的信息主要反映在能谱的特征峰峰位以及特征峰净峰面积中。对于特征峰的准确检测是EDXRF光谱分析的关键。特征X射线之间的能量在低原子序数元素中相差很小,在实际测量过程中由其他一些因素干扰会导致EDXRF光谱中特征峰产生严重重叠,以EDXRF光谱中低序列元素的重叠峰作为研究对象,提出一种四次导数结合三样条小波变换处理低序列元素重叠峰的新方法。通过数学模型模拟重叠峰检测了该方法的可行性,并仿真了实测X荧光光谱数据进行检测得到良好的效果,通过使用了CIT-3000SY X 荧光元素录井仪实测T铅黄铜数据和混合轻元素数据荧光光谱作为验证。首先,介绍导数法以及三样条小波法分解重叠的原理。导数法阶数越高信号越畸形但可以有效提高重峰分离度,而三样条小波变换对低分离度重峰处理较为无力但能有效的保持峰型。通过Tsallis峰信号模拟重叠峰,模拟出3个峰信号,第1个峰和第2个峰的分离度R=0.33,第2个峰和第3个峰的分离度R=0.67,导数处理后信号任仍具有一部分重叠,但是导数处理后不仅保留了信号的峰位值,且出现了分离度变大的现象,而三样条小波对低分离度重叠峰的分解较为无力,但是对于分离度较大的重叠峰具有较好的效果,信号通过四次导增加分离度再进行三样条小波变换,通过调节样条小波分解层次的次数,然后对分解出的高频信号采取适当的系数进行放大,最后进行信号重构。实验实现了对模拟信号的分解。验证了此方法针对重叠峰分解具有可行性。实验采用分解4层的三样条小波变换以及放大6倍的高频信号。然后,处理仿真K元素的重叠光谱,实现了重叠峰的分解,通过仿真实验表明新方法能准确的识别峰位,结果表明只有1%之内的误差,证明了新方法对X荧光光谱重叠峰分解的适用性。最后用此方法对CIT-3000SY X荧光元素录井仪实测T铅黄铜元素数据以及混合轻元素数据X荧光光谱进行处理,实现了对重叠峰的分解,且分解后的峰位误差控制在1%之内,具有较高的准确率。实验结果证明：四次导数结合三样条小波变换能有效分离重叠峰,并且在处理X荧光光谱的重叠峰分解上具有实用性。