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A Convergence Theorem for a Kind of Composite power series expansions

Journal of Mathematical Research and Exposition 2008年第4期28卷 850-854页

作者： HSU Leetsch Charles 徐沥泉 Department of Mathematics Dalian University of Technology Wuxi Education Research Center

Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a ... 详细信息

关键词： power series expansion Faa` di Bruno’s formula convergence theorem.

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Note on Barenblatt power series solution to Boussinesq equation

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Applied Mathematics and Mechanics(English Edition) 2007年第6期28卷 823-828页

作者：宋志尧李凌 David Lockington State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Ocean CollegeHohai UniversityNanjing 210098P. R. China Center for Eco-environmental Modelling Hohai UniversityNanjing 210098P. R. China Key Laboratory of Virtual Geographic Environment (Ministry of Education) Nanjing Normal UniversityNanjing 210097P. R. China School of Engineering The University of QueenslandQld 4072Australia

To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.

关键词： power series expansion similarity solution recurrent formula convergence

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TWO PRIVACY-PRESERVING PROTOCOLS FOR POINT-CURVE RELATION

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Journal of Electronics(China) 2012年第5期29卷 422-430页

作者： Liu Liang Wu Chunying Li Shundong School of Computer Science Shaanxi Normal University Computer Department of Qinghai Normal University

Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is essential and critical. In this paper, we have solved two problems regarding to how to determine the position relation between points and curves without revealing any private information. Two protocols have been proposed in order to solve the problems in different conditions. In addition, some building blocks have been developed, such as scalar product protocol, so that we can take advantage of them to settle the privacy-preserving computational geometry problems which are a kind of special secure multi-party computation problems. Moreover, oblivious transfer and power series expansion serve as significant parts in our protocols. Analyses and proofs have also been given to argue our conclusion.

关键词： Secure multiparty computation Privacy-preserving Point-curve relation power series expansion

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A New Research On Bivariate Quadratic Padé Approximation

A New Research On Bivariate Quadratic Padé Approximation

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2010 International Conference on Computer and Communication Technologies in Agriculture Engineering (CCTAE 2010)

作者： Li Jin Department of Mathematics Dalian Jiaotong University 116028 China

This paper analyses the local behavior of the offdiagonal bivariate quadratic Pade’ approximation to a bivariate function which has a given power series expansion about the *** is shown that the off-diagonal bivariate quadratic Hermite-Pade’ form always defines a bivariate quadratic function and that this function is analytic in a neighbourhood of the origin.

关键词： bivariate quadratic Pade’ approximation bivariate quadratic function power series expansion

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A NEW TRAPPED MODE CAUSED BY LOCAL DEFECT OR THERMAL INHOMOGENEITY

A NEW TRAPPED MODE CAUSED BY LOCAL DEFECT OR THERMAL INHOMOG...

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2013全国压电和声波理论及器件技术研讨会

作者： Peng LI Feng JIN State Key Laboratory for Strength and Vibration of Mechanical Structures School of AerospaceXi’an Jiaotong University

The trapped modes,widely used in resonators,filters,quartz crystal microbalance,and other wave devices,are usually excited by attaching a partially mass layer or electrode on the surface of a plate.A new thickness-twist trapped mode in a transversely piezoelectric plate with a defect or local inhomogeneous temperature in it has been obtained by using of power series expansion *** results obtained indicate that trapped modes exist in such a damaged or thermal plate,which can not be observed when the plate is *** finding of energy trapping phenomenon provides a new style for the excitation of trapped waves.

关键词： Thickness-twist waves Piezoelectric damage Energy trapping power series expansion

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