A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives

In this paper, we develop a new discontinuous Galerkin (DG) finite element method for solving time dependent partial differential equations (PDEs) with higher order spatial derivatives. Unlike the traditional local discontinuous Galerkin (LDG) method, the method in this paper can be applied without introducing any auxiliary variables or rewriting the original equation into a larger system. Stability is ensured by a careful choice of interface numerical fluxes. The method can be designed for quite general nonlinear PDEs and we prove stability and give error estimates for a few representative classes of PDEs up to fifth order. Numerical examples show that our scheme attains the optimal -th order of accuracy when using piecewise -th degree polynomials, under the condition that is greater than or equal to the order of the equation.

     

Gram-Charlier展开在动态金融高阶矩建模中的近似误差

Gram-Charlier展开(GCE)在动态条件高阶矩GARCH模型中得到了广泛应用。相比于常见的分布,GCE的高阶矩形式更加直观,能更直接地刻画条件高阶矩的动态特征。此展开函数并不非负,在实际应用时需要平方并归一化,但已有文献大多忽略此处理后高阶矩所发生的变化。本文研究了平方处理方法对展开函数高阶矩的影响,推导了正确的高阶矩形式。实证研究表明,用原始参数作为近似高阶矩会产生显著偏误,在VaR预测时会严重低估风险。     

Reduction and transformation formulas for the Appell and related functions in two variables

In many seemingly diverse areas of applications, reduction, summation, and transformation formulas for various families of hypergeometric functions in one, two, and more variables are potentially useful, especially in situations when these hypergeometric functions are involved in solutions of mathematical, physical, and engineering problems that can be modeled by (for example) ordinary and partial differential equations. The main object of this article is to investigate a number of reductions and transformations for the Appell functions F₁,F₂,F₃, and F₄ in two variables and the corresponding (substantially more general) double‐series identities. In particular, we observe that a certain reduction formula for the Appell function F₃ derived recently by Prajapati et al., together with other related results, were obtained more than four decades earlier by Srivastava. We give a new simple derivation of the previously mentioned Srivastava's formula 12 . We also present a brief account of several other related results that are closely associated with the Appell and other higher‐order hypergeometric functions in two variables. Copyright © 2017 John Wiley & Sons, Ltd.     

CuZnAl/碳纤维复合材料催化合成气制备低碳醇

采用共沉淀法制备CuZnAl类水滑石,将其担载于活化碳纤维(ACFs)表面,通过焙烧还原合成功能化复合催化剂(CuZnAl/ACFs)。借助XRD、FT-IR及N2吸附-脱附等方法对该复合物进行表征,并将其应用于合成气制备低碳醇的反应中,进行活性评价。结果表明,复合催化剂中活性组分在碳纤维表面均匀分散,碳纤维表面催化剂的颗粒尺寸减小,比表面积增大。ACFs的导电性加速醇合成过程中的电子传递,促进反应进行,因而CO转化率的提高(最高可达47%)。同时,ACFs提高催化剂表面ZnO的分散度,从而促进Cu与ZnO形成金属氧化物界面。这有利于低碳醇的生成,因而使C2以上醇的选择性高达39%。     

Experimental and Theoretical Investigations of the Existence of CuII,CuIII, and CuIV in Copper Corrolato Complexes

The most common oxidation states of copper in stable complexes are +I and +II. Cu^III complexes are often considered as intermediates in biological and homogeneous catalysis. More recently, Cu^IV species have been postulated as possible intermediates in oxidation catalysis. Despite the importance of these higher oxidation states of copper, spectroscopic data for these oxidation states remain scarce, with such information on Cu^IV complexes being non‐existent. We herein present the synthesis and characterization of three copper corrolato complexes. A combination of electrochemistry, UV/Vis/NIR/EPR spectroelectrochemistry, XANES measurements, and DFT calculations points to existence of three distinct redox states in these molecules for which the oxidation states +II, +III, and +IV can be invoked for the copper centers. The present results thus represent the first spectroscopic and theoretical investigation of a Cu^IV species, and describe a redox series where Cu^II, Cu^III, and Cu^IV are discussed within the same molecular platform.     

淀粉基高吸水树脂微波合成及其性能的综合实验教学设计*

为了达成工程认证教育的培养要求,设计了“淀粉基高吸水树脂微波合成及其性能”综合实验。实验包括淀粉基高吸水树脂的微波辅助合成、结构表征及产品性能测定等内容;要求学生查阅文献,了解各种制备工艺并设计实验方案,掌握衰减全反射傅里叶红外光谱与X射线衍射等表征技术及树脂溶胀性能测定技术,分析实验数据。另外,设计了融合过程考核与结果考核的考核体系,通过实验设计、实验操作与数据分析等环节全面考核学生的综合实验能力。该实验教学方案不仅提高教学质量,还激发学生实验兴趣,培养其创新思维与应用实践能力。     

Laguerre Tau Methods for Solving Higher-Order Ordinary Differential Equations

In this paper, we present two numerical methods for solving higher-order differential equations using the Laguerre Tau method. These methods generate linear systems, which can be solved by Gauss elimination with maximal partial pivoting strategy. Results of some numerical experiments and theoretical analysis are presented.     

强厚度叠层板的一种高阶单元

提出一种新的八节点平板元用于分析复合材料叠层厚板的静力问题,板的位移场在板面内采用抛物线型插值,而在板厚方向采用Maclaurin级数展开,使得厚度方向的插值为任意阶多项式,相当于厚板中的高阶理论,取不同的级数项数,可得到不同精度的解。该单元满足C^0连续条件,不需增加新的网络,也不需增加新的输入数据,只要增加多项式级数的项数,便可得到较高精度的解。文中研究了算法的收敛性及计算精度,并与已有结果作了比较。     

Generalized Higher-Order Algebraic Differential Equations with Admissible Algebroid Solutions

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　ＩｎｔｈｉｓｐａｐｅｒｗｅｕｓｅｔｈｅｓｔａｎｄａｒｄｎｏｔａｔｉｏｎｓｏｆｔｈｅＮｅｖａｎｌｉｎｎａｔｈｅｏｒｙｏｆｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｓｏｒａｌｇｅｂｒｏｉｄｆｕｎｃｔｉｏｎｓ.Ｆｏｒｒｅｆｅｒｅｎｃｅｓｅｅｅ.ｇ.[1 ] .　Ｃｏｎｓｉｄｅｒｔｈｅｇｅｎｅｒａｌｉｚｅｄｈｉｇｈｅｒ ｏｒｄｅｒａｌｇｅｂｒａｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎΩ1(ｚ,ｗ)Ω2 (ｚ,ｗ) =Ｐ(ｚ,ｗ)Ｑ(ｚ,ｗ) , ( 1 )ｗｈｅｒｅΩ1(ｚ,ｗ) =∑…