A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Comparative study on Artemisia halodendron Turcz. and its two related plants by GC-MS analysis and protective effect against carbon tetrachloride-induced hepatotoxicity in mice

A rapid method had been used for comparative study on Artemisia halodendron Turcz. and its two related plants by gas phase-mass spectrometry (GC-MS). The comparison of the volatile oils obtained in three plants by GC-MS were similar in 20 compositions. However, n-Hexadecanoic acid (10.40%), Biphenyl (7.867%) and 9,12-Octadecadienoic acid (7.25%) were the predominant in the volatile oils of A. halodendron Turcz., whereas these constituents did not exist in the other two plants. And the study investigated the effect of three plants against CCl₄-induced hepatotoxicity in mice. 70% ethanol extracts of A. halodendron Turcz. showed weaker protective effect than the other two plants. It suggested that they provide a basis for the identification of the A. halodendron Turcz. from the other two plants and the ethanol extract from three plants exerted a protecting effect against hepatotoxicity.     

An Efficient Selective Oxidation of Alcohols with Potassium Permanganate Adsorbed on Aluminum Silicate under Solvent-free Conditions and Shaking

A new procedure for the selective oxidation of alcohols to the corresponding aldehydes and ketones with potassium permanganate supported on aluminum silicate at room temperature under solvent-free conditions and shaking is reported.     

Convex functions, subdifferentiability and renormings

This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces. Supported by NSFC     

Recursive partition and amalgamation with the exponential family: Theory and applications

The theory of tree-growing (RECPAM approach) is developed for outcome variables which are distributed as the canonical exponential family. The general RECPAM approach (consisting of three steps: recursive partition, pruning and amalgamation), is reviewed. This is seen as constructing a partition with maximal information content about a parameter to be predicted, followed by simplification by the elimination of ‘negligible’ information. The measure of information is defined for an exponential family outcome as a deviance difference, and appropriate modifications of pruning and amalgamation rules are discussed. It is further shown how the proposed approach makes it possible to develop tree-growing for situations usually treated by generalized linear models (GLIM). In particular, Poisson and logistic regression can be tree-structured. Moreover, censored survival data can be treated, as in GLIM, by observing a formal equivalence of the likelihood under random censoring and an appropriate Poisson model. Three examples are given of application to Poisson, binary and censored survival data.     

天文斑点成像技术中的噪声影响分析

为进一步说明天文像复原新方法-迭代位移叠加法的性质，对探测器的附加噪声在斑点干涉术、斑点掩模法和迭代位移叠加法中的影响分别进行了分析。结果表明：在斑点掩模法中，复杂的噪声高阶矩统计被引入了重谱的噪声偏差，因此对噪声极为敏感，使数据处理更加复杂化；与斑点掩模法相比，迭代位移叠加法仅涉及对噪声的一阶矩统计平均，所以此新方法的特点是对噪声不敏感，具有图像复原处理过程简单快捷的优越性。     

非傍轴平顶高斯光束M2因子两种定义的比较研究

基于功率密度的二阶矩方法,推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式·研究表明,当w0/λ→0时,远场发散角趋于渐近值θmax=63.435°,与阶数无关·使用非傍轴高斯光束代替傍轴高斯光束作为理想光束,研究了非傍轴FG光束的M2因子,并与传统定义的M2因子作了比较·在非傍轴范畴,非傍轴FG光束的M2因子不仅与阶数N有关,而且与w0/λ有关·按照定义,当w0/λ→0时,非傍轴FG光束的M2因子不等于0,对阶数N=1,2,3时,M2因子分别趋于0.913,0.882和0.886·当N→∞时,M2因子取最小值M2min=0.816·     

Efficient Oxidation of Alcohols with Potassium Permanganate Adsorbed on Aluminum Silicate Reagent

A new reagent, potassium permanganate adsorbed on aluminum silicate, suitable for the oxidation of primary and secondary alcohols to the corresponding carbonyl compounds is described.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved.