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Communications on Applied Mathematics and Computation 2021年第1期3卷 1-40页

作者： Le Zhao Can Li Fengqun Zhao Department of Applied Mathematics Xi’an University of TechnologyXi’an 710054China

The tempered fractional calculus has been successfully applied for depicting the time evolution of a system describing non-Markovian diffusion *** related governing equations are a series of partial differential equations with tempered fractional *** the polynomial interpolation technique,in this paper,we present three efficient numerical formulas,namely the tempered L1 formula,the tempered L1-2 formula,and the tempered L2-1_(σ)formula,to approximate the Caputo-tempered fractional derivative of orderα∈(0,1).The truncation error of the tempered L1 formula is of order 2-α,and the tempered L1-2 formula and L2-1_(σ)formula are of order 3-α.As an application,we construct implicit schemes and implicit ADI schemes for one-dimensional and two-dimensional time-tempered fractional diffusion equations,***,the unconditional stability and convergence of two developed difference schemes with tempered L1 and L2-1_(σ)formulas are proved by the Fourier analysis ***,we provide several numerical examples to demonstrate the correctness and effectiveness of the theoretical analysis.

关键词： Caputo-tempered fractional derivative polynomial interpolation Implicit ADI schemes Stability

Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

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Chinese Physics B 2006年第1期15卷 143-148页

作者：肖金标张明德孙小菡 Laboratory of Photonics and Optical Communications Electronic Engineering Department Southeast University Nanjing 210096 China

Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.

关键词： polynomial interpolation finite difference full vectorial mode solver optical waveguides,photonic integrated circuits

An Easy-implemented Optimization Method of Trajectory Planning Based on polynomial interpolation

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An Easy-implemented Optimization Method of Trajectory Planni...

THE ELLIPTIC TYPE NODE CONFIGURATION AND interpolation IN R^2

第40届中国控制会议

作者： Guangrong Chen Ming Ma Sheng Guo Bowen Hou Junzheng Wang Robotics Research Center Beijing Jiaotong University Beijing Engineering and Technology Research Center of Rail Transit Line Safety and Disaster Prevention State Key Laboratory of Intelligent Control and Decision of Complex Systems School of AutomationBeijing Institute of Technology

Firstly,the forward kinematics and inverse kinematics of a five axis manipulator are ***,an easyimplemented optimization method of trajectory planning based on seventh order polynomial interpolation is *** proposed optimization method can capture the time optimal trajectory,while the actuators specifications including speed,acceleration of motor can be guaranteed as ***,simulation results validate the effectiveness and efficiency of proposed optimization *** research provides an insight for the application of trajectory optimization on the controller with low computing capability and real-time requirement.

关键词： Trajectory planning Optimization method polynomial interpolation Manipulator

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Journal of Computational Mathematics 1998年第3期16卷 257-266页

作者： Ping Zhu (Ji’an Teachers College, Ji’an 543009, Jiangxi, China) 吉安师范专科学校江西吉安 343009

In this paper, we have obtained an expression of the bivariate Vandermonde determinant for the Elliptic Type Node Configuration in R-2, and discussed the possibility of the corresponding multivariate Lagrange, Hermite... 详细信息

关键词： multivariate interpolation polynomial interpolation Birkhoff interpolation node configuration

Error Bounds of Two Smoothing Approximations for Semi-infinite Minimax Problems

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Acta Mathematicae Applicatae Sinica 2009年第4期25卷 685-696页

作者： Hong-xia Yin Department of Mathematics and Statistics Minnesota State University Mankato 273 Wissink Hall Mankato MN 56001 USA

In the paper we investigate smoothing method for solving semi-infinite minimax problems. Not like most of the literature in semi-infinite minimax problems which are concerned with the continuous time version（i.e., the one dimensional semi-infinite minimax problems）, the primary focus of this paper is on multi- dimensional semi-infinite minimax problems. The global error bounds of two smoothing approximations for the objective function are given and compared. It is proved that the smoothing approximation given in this paper can provide a better error bound than the existing one in literature.

关键词： Semi-infinite minimax problem smoothing method aggregate function error bound polynomial interpolation

Mode analysis of structures using the Fourier p-element method

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Earthquake Engineering and Engineering Vibration 2003年第2期2卷 315-318页

作者：吴国荣钟伟芳 Department of Mechanics Huazhong University of Science and TechnologyWuhan 430074China Post doctor Department of Mechanics Huazhong University of Science and TechnologyWuhan 430074China Professor

The Fourier p-element method is an improvement to the finite element method,and is particularly suitable for vibration analysis due to the well-behaved Fourier *** this paper,an iteration procedure is presented for solving the resulting nonlinear eigenvalue *** types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration,the plate in-plane vibration and annular plate flexural vibration modes,respectively. The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation,especially for higher mode analysis.

关键词： vibration mode analysis eigenvalue problem FEM dynamic condensation Fourier series polynomial interpolation

Subpixel accuracy for extracting groove center based on corner detection

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China Welding 2006年第3期15卷 59-63页

作者：刘苏宜王国荣石永华 College of Mechanical Engineering South China University of Technology

Subpixel accuracy for V-groove center in robot welding is researched and a software measure to increase the accuracy of seam tracking by laser is presented. LOG （ Laplacian of Gaussian ） operator is adopted to detect image edge. Vgroove center is extracted by corner detection of extremum curvature. Subpixel position is obtained by Lagarange polynomial interpolation algorithm. Experiment results show that the method is brief and applied, and is sufficient for the real time of robot welding by laser sensors.

关键词： edge detection LOG operator corner detection subpixel polynomial interpolation

FUNCTIONS APPROXIMATED BY ANY SEQUENCE OF interpolation polynomialS

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Analysis in Theory and Applications 2010年第1期26卷 7-12页

作者： Kazuaki Kitahara Kwansei Gakuin University Japan

In this note, we seek for functions f which are approximated by the sequence of interpolation polynomials of f obtained by any prescribed system of nodes.

关键词： polynomial interpolation nodes Runge's example

AN IMPROVED(k,m)-DOT1n SCHEME FOR ARBITRARY K

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AN IMPROVED(k,m)-DOT1n SCHEME FOR ARBITRARY K

Simulation Control of Concrete Pump Truck Boom Based on PSO and Adaptive Robust PD

2009中国宁波国际计算机科学与技术学术大会

作者： Juan Xie Yanqin Zhu Xizhao Luo School of Computer Science and Technology Soochow University Jiangsu Provincial Key Lab of Computer Information Processing Technology

In(k,m)-DOTScheme,the sender’s privacy can not be guaranteed,even if the protocol itself is security,if we can not ensure that a receiver gets information from at most k *** Naor and Pinkas’ s scheme,they give two solutions that are applicable for the case k>m/2,in Nikov et al.’s scheme,they avoid this problem by means of implementing a m-out-of-m access *** this paper,we put forward a settlement for arbitrary k,in which the receiver only can choose k servers to interactive and solve the problem getting the desired security.

关键词： Distributed Oblivious Transfer polynomial interpolation Privacy Preserving

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Simulation Control of Concrete Pump Truck Boom Based on PSO ...