A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations. We apply the new error bound to study sensitivi...A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations. We apply the new error bound to study sensitivity of changing the knots for curve fitting of interest rate term structure by cubic spline.Numerical experiments are given to illustrate the sharpness of this bound.展开更多
Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable app...Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.展开更多
金属橡胶是一种新型材料,文中运用Fourier级数展开和谐波平衡法相结合的方法FHB(the technique of Fourier series expansion combining with harmonic balance method)推导出金属橡胶干摩擦系统在简谐激励下的频响方程,通过数值仿真,...金属橡胶是一种新型材料,文中运用Fourier级数展开和谐波平衡法相结合的方法FHB(the technique of Fourier series expansion combining with harmonic balance method)推导出金属橡胶干摩擦系统在简谐激励下的频响方程,通过数值仿真,比较三次非线性因素和五次非线性因素对金属橡胶干摩擦系统幅频特性的影响,发现对金属橡胶干摩擦系统幅频特性起决定作用的是三次非线性因素,只有五次非线性因素超过1011数量级时才需考虑五次非线性因素的影响,对金属橡胶减振器作动态响应实验,发现减振器的固有频率和传递率幅值都表现出非线性特性。展开更多
基金Funds for Major State The work of the second author is partly supported by the Special Basic Research Projects （2005CB321700）the National Science Foundation of China under grant No. 10571031The work of the third author is partly supported by the National Science Foundation of China under grant No. 10571031.
文摘A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations. We apply the new error bound to study sensitivity of changing the knots for curve fitting of interest rate term structure by cubic spline.Numerical experiments are given to illustrate the sharpness of this bound.
文摘Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.
文摘金属橡胶是一种新型材料,文中运用Fourier级数展开和谐波平衡法相结合的方法FHB(the technique of Fourier series expansion combining with harmonic balance method)推导出金属橡胶干摩擦系统在简谐激励下的频响方程,通过数值仿真,比较三次非线性因素和五次非线性因素对金属橡胶干摩擦系统幅频特性的影响,发现对金属橡胶干摩擦系统幅频特性起决定作用的是三次非线性因素,只有五次非线性因素超过1011数量级时才需考虑五次非线性因素的影响,对金属橡胶减振器作动态响应实验,发现减振器的固有频率和传递率幅值都表现出非线性特性。
基金Supported by the Natural Science Foundation of Gansu Province(1606RJZA038) the Scientific Study Project for Gansu Province Institutes of Higher Learning(2017B-41) the National Statistical Scientific Research Projects(2017LZ41)
