求解一维定常对流扩散反应方程的混合型紧致差分格式

借助显式紧致格式和隐式紧致格式的思想,基于截断误差余项修正,并结合原方程本身,构造出了一种求解一维定常对流扩散反应方程的高精度混合型紧致差分格式.格式仅用到三个点上的未知函数值及一阶导数值,而一阶导数值利用四阶Pade格式进行计算,格式整体具有四阶精度.数值实验结果验证了格式的精确性和可靠性.     

Speciation of Arsenic in Drinking Water by Dispersive Liquid–Liquid Microextraction,Graphite Furnace Atomic Absorption Spectrometry,and Orthogonal Array Design

Orthogonal array design was used to optimize arsenic speciation in drinking water in contact with materials by dispersive liquid–liquid microextraction followed by graphite furnace atomic absorption spectrometry. Arsenic speciation was achieved by the formation of an arsenic(III) hydrophobic complex with a new chelating agent, 1,2,6-hexanetriol trithioglycolate, at neutral pH. The complex was extracted into the organic phase, while arsenic(V) remained in aqueous solution. The concentration of As(V) was determined by subtracting As(III) from the total arsenic following the reduction of As(V) to As(III) by L-cysteine. Orthogonal array design with OA₁₆ (44) and OA₉ (33) matrices was used to optimize the efficiency of dispersive liquid–liquid microextraction and the reduction of As(V) to As(III), respectively. Under the optimal conditions, the detection limit was 0.03?µg?L^?1 for As(III) and the relative standard deviation was 5.9% with an enhancement factor of 87. The calibration curve was linear from 0.19 to 3.0?µg?L^?1 with a correlation coefficient of 0.9996. The developed method was used for arsenic speciation in solutions of drinking water that contacted materials. The recoveries of fortified samples were in an acceptable range from 92.0 to 113.3%.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

On null sequences for Banach operator ideals,trace duality and approximation properties

Let be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of ‐null sequences of Carl and Stephani on X , , from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when is right‐accessible for , behaves much alike . When this is the case we give a geometric tensor product representation of . On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of . We apply our results to study some problems related with the ‐approximation property giving a trace condition which is used to solve the remaining case () of a problem posed by Kim (2015). Namely, we prove that if a dual space has the ‐approximation property then the space has the ‐approximation property.     

Mixed two‐grid finite difference methods for solving one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations

The aim of this paper is to propose mixed two‐grid finite difference methods to obtain the numerical solution of the one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations. The finite difference equations at all interior grid points form a large‐sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The proposed method is based on applying a family of finite difference methods for discretizing the spatial and time derivatives. The obtained system has been solved by two‐grid method, where the two‐grid method is used for solving the large‐sparse linear systems. Also, in the proposed method, the spectral radius with local Fourier analysis is calculated for different values of h and Δt. The numerical examples show the efficiency of this algorithm for solving the one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact separation theorem for closed sets in Asplund spaces

In this paper, in terms of the Fréchet normal cone, we establish exact separation results for finitely many disjoint closed sets in an Asplund space, which supplement the extremal principle and some fuzzy separation theorems. As an application, we provide a new optimality condition for a constraint optimization problem in terms of Fréchet subdifferential and Fréchet normal cone.     

Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.     

“蓝瓶子”实验再探究*

利用SPSS 25.0统计软件对“蓝瓶子”实验进行正交实验设计,通过统计学分析得出最佳实验条件。利用氧化还原传感器(ORP)对“蓝瓶子”振荡体系的电极电势变化曲线进行分析,并针对蓝色的产生和消失过程设计3组对比实验深入探究,阐明其反应原理,意在引导学生深刻理解趣味实验现象背后的微观反应本质。     

Confidence intervals and ellipsoids for estimable functions and estimable vectors in models with orthogonal block structure

Sub-models of mixed linear models are considered. The independence of these sub-models leads to sufficient statistics for the parameters relevant for their densities. Using pivot variables, confidence regions are obtained as well hypothesis testing for variance components, estimable functions, and estimable vectors. In addition, to compare the estimators and the models, we present the histograms with the empirical joint densities for positive and negative parts of the estimators. The figures, for the two-dimensional charts, contain the corresponding UMVUE and are all unimodal with the UMVUE near the mode. The nearness of the estimators and the modes validates the presented methodology and allows the safe use of induced densities. A numerical example applied to real data is presented.