The limit of the partial sums process of spatial least squares residuals

We establish a functional central limit theorem for a sequence of least squares residuals of spatial data from a linear regression model. Under mild assumptions on the model we explicitly determine the limit process in the case where the assumed linear model is true. Moreover, in the case where the assumed linear model is not true we explicitly establish the limit process for the localized true regression function under mild conditions. These results can be used to develop non-parametric model checks for linear regression. Our proofs generalize ideas of a univariate geometrical approach due to Bischoff [W. Bischoff, The structure of residual partial sums limit processes of linear regression models, Theory Stoch. Process. 8 (24) (2002) 23–28] which is different to that proposed by MacNeill and Jandhyala [I.B. MacNeill, V.K. Jandhyala, Change-point methods for spatial data, in: G.P. Patil, et al. (Eds.), Multivariate Environmental Statistics. Papers Presented at the 7th International Conference on Multivariate Analysis held at Pennsylvania State University, University Park, PA, USA, May 5–9 1992, in: Ser. Stat. Probab., vol. 6, North-Holland, Amsterdam, 1993, pp. 289–306 (in English)]. Moreover, Xie and MacNeill [L. Xie, I.B. MacNeill, Spatial residual processes and boundary detection, South African Statist. J. 40 (1) (2006) 33–53] established the limit process of set indexed partial sums of regression residuals. In our framework we get that result as an immediate consequence of a result of Alexander and Pyke [K.S. Alexander, R. Pyke, A uniform central limit theorem for set-indexed partial-sum processes with finite variance, Ann. Probab. 14 (1986) 582–597]. The reason for that is that by our geometrical approach we recognize the structure of the limit process: it is a projection of the Brownian sheet onto a certain subspace of the reproducing kernel Hilbert space of the Brownian sheet. Several examples are discussed.     

Gradient type noises II - Systems of stochastic partial differential equations

The present paper is the second and main part of a study of partial differential equations under the influence of noisy perturbations. Existence and uniqueness of function solutions in the mild sense are obtained for a class of deterministic linear and semilinear parabolic boundary initial value problems. If the noise data are random, the results may be seen as a pathwise approach to SPDE's. For typical examples, such as spatially one-dimensional stochastic heat equations with additive or multiplicative perturbations of fractional Brownian type, we recover and extend known results. In addition, we propose to consider partial noises of low order.     

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.     

Transparent conductive graphene films prepared by hydroiodic acid and thermal reduction

Transparent conductive graphene films are fabricated by the transfer printing of graphene aqueous dispersion followed by hydrohalic acids and thermal reduction. Results indicate that the graphene film reduced by hydroiodic acid （HI） reduction combined with thermal treatment shows a higher electrical conductivity than that reduced only by thermal treatment at the same transparency. A film with a sheet resistance of - 2400 D./sq at a transparency over 72% is obtained at a typical wavelength of 550 nm.     

Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting： method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions （the classical Newtonian fluid model） is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.     

基于ANSYS二次开发的板片空间结构的参数化建模

板片空间结构是由轻质、高强的复合板材和薄壁金属骨架或完全由板通过特定方式组合而成的一种新型空间结构体系.为研究适用于设计的理论,需要进行大规模参数化分析,因此需要适用于此分析的可行的建模方法.分析板片空间结构构件的几何拓展规律,将球面坐标系和直角坐标系结合,运用APDL语言,编制相应的建模和分析模块程序,实现了板片空间结构的参数化建模,为对板片空间结构的大规模参数化分析提供工具.并分析了板片空间结构与网壳结构的异同,将两者的建模程序相组合,实现同一程序下的两种结构的自动建模.同时运用本文所提出的建模思路可以实现大部分空间网架结构的参数化建模.     

波纹状银纳米线的制备及其SERS性能研究

首先通过传统的多元醇方法合成了表面光滑的银纳米线,然后利用Fe（NO₃）₃作为刻蚀剂在室温条件下对合成的银纳米线进行刻蚀得到了具有波纹状表面的银纳米线. 通过扫描电镜（SEM）分析表明：银纳米线的表面粗糙程度随着刻蚀剂量的增加而增加,但过量的刻蚀剂又会导致纳米线的断裂甚至形成球状颗粒;当刻蚀剂的量为100 μL时,获得了波纹状表面的银纳米线. 对结晶紫（CV）的表面增强拉曼光谱（SERS）结果表明,这种波纹状银纳米线的拉曼信号强度比表面光滑的银纳米线提高了约5倍,其检测限可低至10^-10 mol/L. 此外,这种优势还可以延伸到敏感性检测10^-9 mol/L的对巯基吡啶（4-Mpy）分子,可以作为一种普适、有效的SERS活性基底.     

Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet

The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations (ODEs) are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles φ, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.     

DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip

An unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTMBF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.