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TETRAHEDRAL C^m INTERPOLATION BY rational functions

Journal of Computational Mathematics 2001年第2期19卷 131-138页

作者： Guo-liang Xu Chuan I Chu Wei-min Xue State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics an d Systems SciencesChinese Academy of SciencesBeijing 100080China Department of Mathematics Hong Kong Baptist UniversityKowloonHong Kong

A general local C-m(m greater than or equal to 0) tetrahedral interpolation scheme by polynomials of degree 4m + 1 plus low order rational functions from the given data is proposed. The scheme can have either 4m + 1 order algebraic precision if C-2m data at vertices and C-m data on faces are given or k + E[k/3] + 1 order algebraic precision if C-k (k less than or equal to 2m) data are given at vertices. The resulted interpolant and its partial derivatives of up to order m are polynomials on the boundaries of the tetrahedra.

关键词： C-m interpolation rational functions tetrahedra

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Copositive approximation by rational functions with prescribed numerator degree

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Applied Mathematics(A Journal of Chinese Universities) 2009年第4期24卷 411-416页

作者： YU Dan-sheng ZHOU Song-ping Department of Mathematics Hangzhou Normal University Hangzhou 310036 China Department of Mathematics Statistic and Computer Science St. Francis Xaiver University Antigonish Nova Scotia Canada B2G 2W5 Institute of Mathematics Zhejiang Sci-Tech University Hangzhou 310028 China

The paper proves that, if f（x） ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in （-1, 1）,then there exists a real rational function r（x） ∈ Rn^（2μ-1）l which is eopositive with f（x）, such that the following Jackson type estimate ｜｜f-r｜｜p≤Cδl^2μωφ（f,1/n）p holds, where μ is a natural number ≥3/2＋1/p, and Cδ is a positive constant depending only on δ.

关键词： copositive approximation rational functions approximation rate

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Some Recent Advances on SpectralMethods for Unbounded Domains

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Communications in Computational Physics 2009年第2期5卷 195-241页

作者： Jie Shen Li-Lian Wang Department of Mathematics Purdue UniversityWest LafayetteIN47907USA Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological University637616Singapore

We present in this paper a unified framework for analyzing the spectral methods in unbounded domains using mapped Jacobi,Laguerre and Hermite functions.A detailed comparison of the convergence rates of these spectral methods for solutions with typical decay behaviors is carried out,both theoretically and computationally.A brief review on some of the recent advances in the spectral methods for unbounded domains is also presented.

关键词： Spectral method unbounded domain orthogonal polynomials rational functions Hermite functions Laguerre functions

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A new method of frequency-dependent network equivalence for power system

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Science China(Technological Sciences) 2012年第7期55卷 1894-1907页

作者： LIN JiKeng YAN YiPeng PU TianJiao LUO ShanShan LIU Tao ZHENG WeiHong WANG XuDong Key Laboratory of Power System Simulation and Control of Ministry of Education(Tianjin University) Tianjin 300072China China Electric-Power Research institute Beijing 100192China Schneider Electric Co. Ltd(China)Shanghai BranchShanghai 200000China Tianjin Electrieal Power Corperation Tianjin 300010China

Electromagnetic transient simulation for large-scale power system is a time-consuming problem.A new frequency-dependent equivalence method is presented in the paper,which might significantly accelerate power system electromagnetic transient *** the method,an effective algorithm is designed to directly transfer the port admittance determinant of external system's mixing matrix into admittance rational function;and the step-by-step strategy for the equivalence of actual large system is put forward,which further reduces the calculation quantities ***,the study of multiple real root pole characteristics of admittance transfer function of two-port network is performed and a proposition is *** on the proposition and residue theorem,the equivalence system for external system corresponding to the admittance rational function is *** computation complexity of the step-by-step equivalence method is about o(┌n/np×T┐)(┌┐ is upper integral operation,n is the total buses number of external system,N P is the total buses number of single step equivalence network,T is single step equivalence time),which indicates that the computation complexity of the method proposed has nearly linear relationship with the buses number of external system,and the method proposed has satisfactory computation *** the mixing matrix of external system includes all the information of external system,therefore,port admittance rational function derived from it can reflect its full frequency characteristic and the equivalence network achieved has high equivalence ***,since the port rational function is gained at the condition of the external system without source,which equals stable passive network,it could not show any unstable pole and need not extra measure to make the equivalence system *** test results of the samples and comparison with other methods demonstrate that the new method proposed is valid and effective.

关键词： equivalence method electromagnetic transient simulation frequency-dependent rational functions mixing matrix

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A Complete Field of Meromorphic Function

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Advances in Pure Mathematics 2021年第2期11卷 138-148页

作者： Elhadi E. E. Dalam Ahmed M. Ibrahim Department of Mathematics College of Arts and Science Al Baha University Al Mandag KSA

In any completely close complex field C, generalized transcendental meromorphic functions may have some new properties. It is well known that a meromorphic function of characteristic zero is a rational function. This paper introduced some mathematical properties of the transcendental meromorphic function, which is generalized to the meromorphic function by multiplying and differentiating the generalized meromorphic function. The analysis shows that the difference between any non-zero constant and the derivative of the general meromorphic function has an infinite zero. In addition, for any natural number n, there are no practically exceptional values for the multiplication of the general meromorphic function and its derivative to the power of n.

关键词： Meromorphic functions Unit Disk rational functions

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