K-g-框架扰动的稳定性

在Hilbert空间中定义了K-g-框架,研究了Hilbert空间中K-g-框架扰动的稳定性,利用分析与框架理论上的方法和技巧,得到了K-g-框架满足扰动稳定性的一些充分条件,所得的结论推广了g-框架扰动稳定性的相关结果.  

酉空间中一类子空间的排列问题与具有纠错能力的d~z-析取矩阵

Pooling设计在实践中有着广泛的应用,它的数学模型是d~z-析取矩阵.本文利用酉空间的一类子空间构做了一类新的d~z-析取矩阵.为了讨论此设计的纠错能力,重点研究了酉空间中的一类子空间的排列问题,即对于酉空间F_q~2~((n))上的一个给定的(m,s)型子空间C和一个整数d,找到C的d个(m-1,s-1)型子空间H_1,H_2,…,H_d,使得包含在H_1∪H_2∪…∪H_d中的(r,s-4)型子空间的个数最多,并确定这个数的上界.然后应用此结果,给出了d~z-析取矩阵中反映纠错能力的z值的紧界.  

贫信息背景下朱兰质量成本灰色GM(1,1)测算模型

朱兰曲线将质量总成本表示为质量投入与直接质量损失的合成.针对不同质量水平下的质量成本变化趋势,建立保证成本和故障成本的正负指数模型来确定最佳质量成本.灰色均值GM(1,1)测算模型可以同时克服“少数据”“贫信息”的缺陷,更加精确地拟合质量成本的变动趋势.与指数函数模型模拟效果进行对比,结果表明灰色系统理论系列模型具有较高的预测精度,将指数函数模型和灰色GM(1,1)模型结合起来可以为企业提高质量管理水平尤其是质量成本管理提供依据和指导.  

A numerical method for solving the nonlinear fermi–pasta–ulam problem

An effective finite difference scheme for solving the nonlinear Fermi–Pasta–Ulam (FPU) problem is derived. The most important feature of the scheme inherits energy conservation property from the nonlinear FPU problem. The unique solvability and the convergence of the difference scheme are proved by the energy method. The convergence order is in the maximum norm, where τ is the temporal grid size and h is the spatial grid size, respectively. In addition, the stability of the difference scheme is obtained. Numerical results are presented to support the theoretical analysis and verify numerically the energy conservation property.© 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 187‐209, 2014  

A three‐level linearized finite difference scheme for the camassa–holm equation

The Camassa–Holm (CH) system is a strong nonlinear third‐order evolution equation. So far, the numerical methods for solving this problem are only a few. This article deals with the finite difference solution to the CH equation. A three‐level linearized finite difference scheme is derived. The scheme is proved to be conservative, uniquely solvable, and conditionally second‐order convergent in both time and space in the discrete L_∞ norm. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 451–471, 2014