Quasipatterns versus superlattices resulting from the superposition of two hexagonal patterns

We present a short review of the experimental observations and mechanisms related to the generation of quasipatterns and superlattices by the Faraday instability with two-frequency forcing. We show how two-frequency forcing makes possible triad interactions that generate hexagonal patterns, twelvefold quasipatterns or superlattices that consist of two hexagonal patterns rotated by an angle α relative to each other. We then consider which patterns could be observed when α does not belong to the set of prescribed values that give rise to periodic superlattices. Using the Swift–Hohenberg equation as a model, we find that quasipattern solutions exist for nearly all values of α. However, these quasipatterns have not been observed in experiments with the Faraday instability for $\alpha \ne \mathrm{\pi }/6$. We discuss possible reasons and mention a simpler framework that could give some hint about this problem.     

关于薛定谔算子的极点散射: 基于狄利克雷级数的视角

本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论.     

The differentiation operator in the space of uniformly convergent Dirichlet series

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half-planes for each . The properties of the formal inverse of the differentiation are also investigated.     

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.     

Influence of sputter power on structural and electrical properties of TiO2 films for Al/TiO2/Si gate capacitors

Titanium dioxide (TiO₂) thin films were deposited onto p‐Si substrates held at room temperature by reactive Direct Current (DC) magnetron sputtering at various sputter powers in the range 80–200 W. The as‐deposited TiO₂ films were annealed at a temperature of 1023 K. The post‐annealed films were characterized for crystallographic structure, chemical binding configuration, surface morphology and optical absorption. The electrical and dielectric properties of Al/TiO₂/p‐Si structure were determined from the capacitance–voltage and current–voltage characteristics. X‐ray diffraction studies confirmed that the as‐deposited films were amorphous in nature. After post‐annealing at 1023 K, the films formed at lower powers exhibited anatase phase, where as those deposited at sputter powers > 160 W showed the mixed anatase and rutile phases of TiO₂. The surface morphology of the films varied significantly with the increase of sputter power. The electrical and dielectric properties on the air‐annealed Al/TiO₂/p‐Si structures were studied. The effect of sputter power on the electrical and dielectric characteristics of the structure of Al/TiO₂/p‐Si (metal‐insulator‐semiconductor) was systematically investigated. 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.