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991.
992.
This paper studies the mode III crack problem of two bonded functionally graded piezoelectric half planes which contain a
crack respectively. These two cracks are located normal to the interface. All the material properties are assumed to vary
along the direction of the crack line. A system of singular integral equations for electrically impermeable and permeable
cracks is derived and solved numerically by using the Gauss–Chebyshev integration formula. The influence of the nonhomogeneous
parameters and the dependence of the crack interactions on the stress and electric displacement intensity factors are investigated. 相似文献
993.
The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results, such as the Bochner-Martinelli formula, the existence theorem of the solutions to the non-homogeneous Cauchy-Riemann equations, and the Hartogs theorem, are generalized from complex analysis in several variables to Clifford analysis in several paravector variables. In particular, the Bochner-Martinelli formula in several paravector variables unifies the corresponding formulas in the theory of one complex variable, several complex variables, and several quaternionic variables with suitable modifications. 相似文献
994.
995.
996.
Qinghui Zhang 《Numerical Methods for Partial Differential Equations》2014,30(1):265-288
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 相似文献
997.
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. 相似文献
998.
999.
Mirosław Jabłoński 《Journal of computational chemistry》2014,35(24):1739-1747
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. 相似文献
1000.
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. 相似文献