富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

Parametric inference for multiple repairable systems under dependent competing risks

The focus of this article is on the analysis of repairable systems that are subject to multiple sources of recurrence. The event of interest at the system level is assumed to be caused by the earliest occurrence of a source, thereby conforming to a series system competing risks framework. Parametric inference is carried out under the power law process model that has found significant attention in industrial applications. Dependence among the cause‐specific recurrent processes is induced via a shared frailty structure. The theoretical inference results are implemented to a warranty database for a fleet of automobiles, for which the warranty repair is triggered by the failure of one of many components. Extensive finite‐sample simulation is carried out to supplement the asymptotic findings. Copyright © 2014 John Wiley & Sons, Ltd.     

锰氧化物中氧空位的构建及其催化氧化苯系物作用机制研究进展

作为一种过渡金属氧化物,锰氧化物以其多晶型、储/释氧能力强、蕴含丰富氧物种、结构缺陷可控等优点被广泛应用于苯系物的热催化氧化。其中,具有众多特性的氧空位能有效促进苯系物的完全催化氧化,因而成为各界研究的焦点。我们综述了常见的氧空位构建方法及表征技术,并总结了在苯系物催化氧化过程中,锰氧化物中氧空位的几种重要作用机制对催化活性和抗水性能的积极影响。最后文章对氧空位构建新方法、形成机理、具体过程及其在锰氧化物热催化氧化苯系物领域中的应用进行了总结和展望。     

Measurement of viscoelastic properties for polymers by nanoindentation

A new method has been proposed and verified to measure the viscoelastic properties of polymers by nanoindentation tests. With the mechanical response of load–displacement curves at different loading rates, the parameters of creep compliance and relaxation modulus are calculated through the viscoelastic contact model. Dynamic thermomechanical analysis (DMA) tests are conducted to compare the results by the proposed technique. The results show that the correlation coefficients between DMA tests and the new method are above 0.9 in the entire range, which verified the feasibility of the method. The loading curves fitted by the model are identical to the experimental curves within the discrete points and so it shows that this technique is more suitable for general linear viscoelastic materials. Numerical creep tests are carried out to examine the effectiveness of the proposed method by input the Prony series calculated by the three-element Maxwell model and the viscoelastic contact model. The good agreement shows that the proposed technique can be applied in practice.     

A Hybrid Method Using HAVOK Analysis and Machine Learning for Predicting Chaotic Time Series

The prediction of chaotic time series systems has remained a challenging problem in recent decades. A hybrid method using Hankel Alternative View Of Koopman (HAVOK) analysis and machine learning (HAVOK-ML) is developed to predict chaotic time series. HAVOK-ML simulates the time series by reconstructing a closed linear model so as to achieve the purpose of prediction. It decomposes chaotic dynamics into intermittently forced linear systems by HAVOK analysis and estimates the external intermittently forcing term using machine learning. The prediction performance evaluations confirm that the proposed method has superior forecasting skills compared with existing prediction methods.     

Modules of the Intermediate Series over Not-finitely Graded Lie Algebras W(Γ)

Let W(Γ)be a class of not-finitely graded Lie algebras related to gener-alized Virasoro algebras with basis{Lα,i,C | α ∈ Γ,i ∈ Z+},which satisfies relations[Lα,i,Lβ,j]=(β-α)Lα+β,i+j+(j-i)Lα+β,i+j+1+δα+β,0δi+j,0α3-α/12C and[C,Lα,i]=0.In this paper,W(Γ)-modules of the intermediate series satisfying some conditions are con-structed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.     

用无限阶Toeplitz矩阵求常系数微分方程的级数解

无限阶Toeplitz矩阵的属于0的特征向量可递推地求得,可表示常系数齐次微分方程的解.用它的逆可求得常系数非齐次微分方程的特解.     

有限深水域中三维频域自由面格林函数及其导数的计算方法

三维频域自由面格林函数及其偏导数的数值计算是海洋结构物水动力分析的难点.本文对有限水深格林函数及其偏导数的数值算法作出两点改进:①对原函数的级数表达式进行变形,提出适用于数值计算的形式,解决高频率情况下级数解的计算失真问题;②对Gauss-Laguerre积分法作出改进,解决高频率大水深情况下积分解的数值溢出问题.计算...