Lagrange插值和Hermite-Fejér插值在Wiener空间下的平均误差

在L_q-范数逼近的意义下,确定了基于Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列在Wiener空间下的p-平均误差的弱渐近阶.从我们的结果可以看出,当2≤q<∞,1≤p<∞时,基于第一类Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列的p-平均误差弱等价于相应的最佳逼近多项式列的p-平均误差.在信息基计算复杂性的意义下,如果可允许信息泛函为计算函数在固定点的值,那么当1≤p,q<∞时,基于第一类Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列在Wiener空间下的p-平均误差弱等价于相应的最小非自适应p-平均信息半径.     

Stokes–Darcy coupling for periodically curved interfaces

We investigate the boundary condition between a free fluid and a porous medium, where the interface between the two is given as a periodically curved structure. Using a coordinate transformation, we can employ methods of periodic homogenisation to derive effective boundary conditions for the transformed system. In the porous medium, the fluid velocity is given by Darcy's law with a non-constant permeability matrix. In tangential direction as well as for the pressure, a jump appears. Its magnitudes can be calculated with the help of a generalised boundary layer function. The results can be interpreted as a generalised law of Beavers and Joseph for curved interfaces.     

利用具有相位跳跃技术的阴影摩尔图测量电子组装元件的热翘曲

Phase-stepping technique is applied to the analysis of fringe patterns of shadow moiré of electronic packages.Sensitivity of the fringe pattern analysis is demonstrated to be significantly increased.Thermally induced warpage of electronic packages is successfully measured in real-time as the sample is driven through a simulated reflow process.The paper discusses the technique of phase stepping,noise filtering and its application to the shadow moiré method.Applications of the technology are presented.     

A ranking model in uncertain, imprecise and multi-experts contexts: The application of evidence theory

We consider ranking problems where the actions are evaluated on a set of ordinal criteria. The evaluation of each alternative with respect to each criterion may be imperfect and is provided by one or several experts. We model each imperfect evaluation as a basic belief assignment (BBA). In order to rank the BBAs characterizing the performances of the actions according to each criterion, a new concept called RBBD and based on the comparison of these BBAs to ideal or nadir BBAs is proposed. This is performed using belief distances that measure the dissimilarity of each BBA to the ideal or nadir BBAs. A model inspired by Xu et al.’s method is also proposed and illustrated by a pedagogical example.     

The evolution of growth morphology and corrosion behavior of electrodeposited Ni–P coatings on alumina borate whisker‐reinforced pure aluminum composite

The Ni–P alloy coatings were obtained on alumina borate whisker‐reinforced pure aluminum composite by electro‐deposition. The initial electro‐deposition behavior of the Ni–P alloys on the composite and pure aluminum was studied, respectively. It was found that the composition and the morphology of materials had a distinct effect on the initial electro‐deposition behavior of the Ni–P alloys. The Ni–P alloy coatings preferred to nucleate at the composite as compared with the pure aluminum. Moreover, the Ni–P particles were prone to deposit at the whisker/Al interface in the composite. The Ni–P coatings were barely depositing upon the surface of whisker during the plating process. As the deposition time increased, the Ni–P particles that were deposited on the surface of the composite grew gradually. These Ni–P particles linked to each other and eventually covered the whisker surface. Moreover, it can be found that the surfaces of the composite were gradually covered by Ni–P coatings and the anticorrosion performance of the coated composite increased remarkably with the increase in the deposition time. When the deposition time is 60 min, only the Ni–P diffraction peak could be detected. In this case, the coated composite had significantly better corrosion resistant, which is attributed to the surface of composite was perfectly covered by the Ni–P coatings. Copyright © 2012 John Wiley & Sons, Ltd.     

Fabrication of two-dimensional colloidal arrays

We report the effective fabrication of two-dimensional (2D) arrays of submicron colloidal particles. These colloidal arrays are produced in thin layers of monodisperse colloid suspensions on flat surfaces of solids such as clean glass or cleaved mica. The process of colloid assembling includes two steps, nucleation and growth, similar to those found in crystallization in solution but each of the steps in detail progresses with different mechanisms. The nucleation process is initiated by a special kind of capillary force acting parallel to the surface. The growth is guided by a laminar flow of water to the crystals, which is driven by water evaporation from 2D arrays. What is distinguishable in the 2D assembling is its active nature governed by the forces and flows, making a contrast to the diffusive mechanism in ordinary crystallization. With this two-step mechanism, a domain of hexagonally packed colloidal array can grow with time. A large and uniform film of particle monolayer is, thus, formed in a short period, from several seconds up to several minutes depending on the conditions controlled.     

非线性椭圆边值问题和极大单调算子的零点

本文利用非线性极大单调算子值域的扰动结论,研究一类与广义p-Laplacian算子相关的、具Neumann边值条件的非线性椭圆方程的解的存在唯一性.同时研究这个唯一解与适当定义的非线性极大单调算子的零点之间的关系.进而设计一种迭代算法强收敛到这个唯一解.本文采用新的构造算子和拆分方程的方法,推广和补充了以往的相关研究工作.     

任意相移阴影叠栅相位解调技术的研究

结合时域和频域干涉图分析方法,提出一种任意相移阴影叠栅条纹图相位解调技术,降低了干涉图在采样过程中对相移量的严格标定要求,补偿了相移阴影叠栅技术固有的相移不匀误差。使用空域技术确定采样干涉图的正交信号,进而得到了采样干涉图的相移量,然后运用任意相移相位提取算法搜索测量相位信息。实验证明此方法简单方便、求解迅速,且优于典型的相移算法,其测量误差的标准差不超过3×10-3 mm,该方法为提高相移阴影叠栅技术的测量精度提供了有效手段。     

带两个形状参数的五次Bézier曲线的扩展

给出了一组含有两个形状参数α,β的六次多项式基函数,是五次Bernstein基函数的扩展,分析了这组基的性质;基于这组基定义了带两个形状参数的多项式曲线,所定义的曲线具有五次Bézier曲线的性质,改变参数α,β的取值,曲线具有更灵活的形状可调性,而且能向上或从两侧逼近控制多边形.另外,经典的五次Bézier曲线和有关文献中带一个形状参数的曲线均是该文所定义曲线的特例.实例表明,定义的曲线为曲线/曲面的设计提供了一种有效的方法.     

An L 2-theory for a class of SPDEs driven by Lévy processes

In this paper we present an L 2-theory for a class of stochastic partial differential equations driven by Lévy processes.The coefficients of the equations are random functions depending on time and space variables,and no smoothness assumption of the coefficients is assumed.