Quadrature for meshless Nitsche's method

In this article, we study effect of numerical integration on Galerkin meshless method (GMM), applied to approximate solutions of elliptic partial differential equations with essential boundary conditions (EBC). It is well‐known that it is difficult to impose the EBC on the standard approximation space used in GMM. We have used the Nitsche's approach, which was introduced in context of finite element method, to impose the EBC. We refer to this approach as the meshless Nitsche's method (MNM). We require that the numerical integration rule satisfies (a) a “discrete Green's identity” on polynomial spaces, and (b) a “conforming condition” involving the additional integration terms introduced by the Nitsche's approach. Based on such numerical integration rules, we have obtained a convergence result for MNM with numerical integration, where the shape functions reproduce polynomials of degree k ≥ 1. Though we have presented the analysis for the nonsymmetric MNM, the analysis could be extended to the symmetric MNM similarly. Numerical results have been presented to illuminate the theoretical results and to demonstrate the efficiency of the algorithms.Copyright © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 265–288, 2014     

Applications of hypergeometric summation theorems of kummer and dixon involving double series

Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.     

Red and blue shifted hydridic bonds

By performing MP2/aug‐cc‐pVTZ ab initio calculations for a large set of dimer systems possessing a R? H hydridic bond involved in diverse types of intermolecular interactions (dihydrogen bonds, hydride halogen bonds, hydride hydrogen bonds, and charge‐assisted hydride hydrogen bonds), we show that this is rather an elongation than a shortening that a hydride bond undergoes on interaction. Contrary to what might have been expected on the basis of studies in uniform electric field, this elongation is accompanied by a blue instead of red shift of the R? H stretching vibration frequency. We propose that the “additional” elongation of the R? H hydridic bond results from the significant charge outflow from the sigma bonding orbital of R? H that weakens this bond. The more standard red shift obtained for stronger complexes is explained by means of the Hermansson's formula and the particularly strong electric field produced by the H‐acceptor molecule. © 2014 Wiley Periodicals, Inc.     

Heaviside公式的一种改进

针对一般积分变换教材中Heaviside公式的形式不容易被记忆和理解的情况,运用复变函数的相关知识对Heaviside公式的形式做进一步改进和说明.     

A hybrid mean value related to the Dedekind sums and Kloosterman sums

The main purpose of this paper is to use the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.     

一类直线上自相似集的相似压缩不动点的分布

先构造了一类直线上的自相似集,研究了它的相似压缩不动点的坐标公式.作为推论我们给出了三分Cantor集相似压缩不动点的坐标公式,从而首次发现了它的相似压缩不动点的分布规律.     

On the theory of periodic solution for some nondensely nonautonomous delayed partial differential equations

We first study the Massera problem for the existence of a τ?periodic solution for some nondensely defined partial differential equation, where the autonomous linear part satisfies the Hille‐Yosida condition and the delayed nonlinear part satisfies a locally Lipschitz condition. Second, inspired by an existing study, we prove in the dichotomic case, for τ=1, the existence‐uniqueness and conditional stability of the periodic solution. Moreover, we show the existence of a local stable manifold around such solution. Our theoretical results are finally illustrated by an application.     

Development of fluorescence imaging-based assay for screening cardioprotective compounds from medicinal plants

Medicinal plants have been widely recognized as a renewable resource for the discovery of novel leads and drug. In this study, an approach for screening and identification compounds with cardioprotective activity from medicinal plant extracts by cellular-fluorescence imaging technique was developed. It is a cell-based assay for measuring mitochondrial membrane potential changes in H9c2 cardiac muscle cells exposed to H₂O₂ by using a fluorescence automatic microscopy screening platform. Rhodamine 123 was used as the fluorescent dye to indicate the change of mitochondrial membrane potential. The sensitivity and linear range of the proposed approach were evaluated and validated using vitamin C, an antioxidative compound. The method was applied to screen active components with potent cardioprotective effects from a traditional Chinese formula. The potential cardioprotective components were identified by liquid chromatography coupled with mass spectrometry (LC/MS). Moreover, the utility of the proposed approach was further validated by three compounds (salvianolic acid B, protocatechuic aldehyde, and tanshinone II A) identified from the formula which showed cardioprotective effects in a dose-dependent manner. These applications suggested that the proposed rapid and sensitive screening approach offers an efficient way to discover active components or compounds from medicinal plants.     

基于拆分思想的酸碱滴定误差公式简便推导

提出了一种酸碱滴定误差公式推导的新方法。该方法利用拆分思想即可方便地导出酸碱滴定误差公式,避免了现行教材中利用物料平衡方程(MBE)和电荷平衡方程(CBE)联立推导该公式的繁琐,便于学生理解和掌握。