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A Jacobi Spectral Collocation Scheme Based on Operational Matrix for Time-fractional Modified Korteweg-de Vries Equations

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Computer Modeling in Engineering & Sciences 2015年第3期104卷 185-209页

作者： A.H.Bhrawy E.H.Doha S.S.Ezz-Eldien M.A.Abdelkawy Department of Mathematics Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt Department of Mathematics Faculty of ScienceCairo UniversityGizaEgypt Department of Mathematics Faculty of ScienceAssiut UniversityNew Valley BranchEl-Kharja 72511Egypt

In this paper,a high accurate numerical approach is investigated for solving the time-fractional linear and nonlinear Korteweg-de Vries(KdV)*** equations are the most appropriate and desirable definition for physical *** spectral collocation method and the operational matrix of fractional derivatives are used together with the help of the Gauss-quadrature formula in order to reduce such problem into a problem consists of solving a system of algebraic equations which greatly simplifying the *** approach is based on the shifted Jacobi polynomials and the fractional derivative is described in the sense of *** addition,the presented approach is applied also to solve the timefractional modified KdV *** testing the accuracy,validity and applicability of the developed numerical approach,we apply it to provide high accurate approximate solutions for four test problems.

关键词： KdV equation Jacobi polynomials Operational matrix Gauss quadrature Collocation spectral method Caputo derivative

Lie algebras determined by finite valued Auslander-Reiten quivers

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Science China Mathematics 1997年第7期40卷 714-724页

作者：张顺华 Department of Mathematics Shandong UniversityJinan 250100China

Let r denote a connected valued Auslander-Reiten quiver,let (Γ) denote the free abelian group generated by the vertex set Γ0 and let Γ be the universal cover of Γ with fundamental group *** is proved that when Γ is a finite connected valued Auslander-Reiten quiver,(Γ) is a Lie subalgebra of (Γ) and is just the "rbit" Lie algebra (Γ)/G,where (Γ)1 is the degenerate Hall algebra of Γ and (Γ)/G is the "orbit" Lie algebra induced by Γ.

关键词： Hall algebras Hall polynomials degenerate Hall algebras universal covers Galois covers.

On Mean Values of Character Sums

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Acta Mathematica Sinica,English Series 2006年第2期22卷 561-570页

作者： Zai Zhao MENG School of Mathematical Sciences Peking University

We use the resultant of two polynomials to discuss the roots of congruences, and then we improve the result of Burgess on the mean values of character sums in the case r = 3. Finally, we give a new estimate for the me... 详细信息

关键词： Resultant polynomials Character

On the Quasi-Periodic Wave Solutions and Asymptotic Analysis to a(3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

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Communications in Theoretical Physics 2014年第8期61卷 245-258页

作者：田守富马潘丽 Department of Mathematics China University of Mining and TechnologyXuzhou Center of Nonlinear Equations China University of Mining and TechnologyXuzhou

In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic *** two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.

关键词： a(3+1)-dimensional generalized Kadomtsev–Petviashvili equation Bell’s polynomials Riemann theta function soliton solution periodic wave solution

3D Image Synthesis for B-Reps Objects

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Journal of Computer Science & Technology 1991年第2期6卷 113-120页

作者：黄正东彭群生梁友栋 CAD/CAM Center Zhejiang UniversityHangzhou 310027

This paper presents a new algorithm for generating 3D images of B-reps objects with trimmed surface *** 3D image is a discrete voxel-map representation within a Cubic Frame Buffer(CFB). The definition of 3D images for curve,surface and solid object are introduced which imply the connectivity and fidelity *** Forward Differencing matrix(AFD-matrix)for 1D-3D manifolds in 3D space is *** setting rules to update the AFD-matrix,the forward difference direction and stepwise can be ***,an efficient algorithm is presented based on the AFD-matrix concept for converting the object in 3D space to 3D image in 3D discrete space.

关键词： Mathematical Techniques Matrix Algebra Mathematical Techniques polynomials Surfaces

Efficient Orbit Propagation of Orbital Elements Using Modified Chebyshev Picard Iteration Method

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Computer Modeling in Engineering & Sciences 2016年第1期111卷 65-81页

作者： J.L.Read A.Bani Younes J.L.Junkins Graduate Research Assistant Texas A&M UniversityCollege StationTXUSA. Assistant Professor Khalifa UniversityAbu DhabiUAE. Distinguished Professor Texas A&M UniversityCollege StationTXUSA.

This paper focuses on propagating perturbed two-body motion using orbital elements combined with a novel integration *** previous studies show that Modified Chebyshev Picard Iteration(MCPI)is a powerful tool used to propagate position and velocity,the present results show that using orbital elements to propagate the state vector reduces the number of MCPI iterations and nodes required,which is especially useful for reducing the computation time when including computationally-intensive calculations such as Spherical Harmonic gravity,and it also converges for>5.5x as many revolutions using a single segment when compared with cartesian *** for the Classical Orbital Elements and the Modified Equinoctial Orbital Elements(the latter provides singularity-free solutions)show that state propagation using these variables is inherently well-suited to the propagation method *** benefits are achieved using a segmentation scheme,while future expansion to the two-point boundary value problem is expected to increase the domain of convergence compared with the cartesian *** is an iterative numerical method used to solve linear and nonlinear,ordinary differential equations(ODEs).It is a fusion of orthogonal Chebyshev function approximation with Picard iteration that approximates a long-arc trajectory at every *** studies have shown that it outperforms the state of the practice numerical integrators of ODEs in a serial computing environment;since MCPI is inherently massively parallelizable,this capability is expected to increase the computational efficiency of the method presented.

关键词： Propagation Integration Orbital Mechanics Classical Elements Modified Equinoctial Chebyshev Picard Iteration MCPI polynomials Initial Value Problem IVP.

A POSITIVE AND MONOTONE NUMERICAL SCHEME FOR VOLTERRA-RENEWAL EQUATIONS WITH SPACE FLUXES

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Journal of Computational Mathematics 2019年第1期37卷 33-47页

作者： Mario Annunziato Eleonora Messina Dipartimento di Matematica Universita degli Studi di Salerno Via G.Paolo II 132.84084 Fisciano (SA)Italy Dipartimento di Matematica e Applicazioni "R.Caccioppoli" Universita degli Studi di Napoli "Federico II"Via CintiaMonte S.Angelo80126 NapoliItaly

We study a numerical method for solving a system of Volterra-renewal integral equations with space fluxes,that represents the Chapman-Kohnogorov equation for a class of piecewise deterministic stochastic *** solution of this equation is related to the time dependent distribution function of the stochastic process and it is a non-negative and non-decreasing function of the *** on the Bernstein polynomials,we build up and prove a non-negative and non-decreasing numerical method to solve that equation, with quadratic convergence order in space.

关键词： Volterra renewal Piecewise deterministic process Monotone positive numerical scheme Bernstein polynomials

Processing Polynomial Algebraic Problems by Using SAC-2/ALDES

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Journal of Computer Science & Technology 1991年第2期6卷 195-200页

作者：刘卓军 Institute of Systems Science Academia SinicaBeijing 100080

This paper discusses the portability of SAC-2/ALDES and reviews some applications in polynomial ***,we indicate that the concept of the safety variable in the SAC-2/ALDES is not ***,for example,we used safety variable... 详细信息

关键词： Computer Programming Languages Mathematical Techniques polynomials

PGOPO Approach to Design Linear Servomechanism of Time-Varying Systems with Time-Delay

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Chinese Journal of Aeronautics 2001年第2期14卷 88-93页

作者：吴斌程鹏钟宜生 Dept. of Automatic Control Tsinghua University Beijing University of Aeronautics Astronautics

Based on a new linear, continuous and bounded operator (PGOPO), a more effective approach and optimal control algorithm than by the block-pulse functions and Walsh functions to design the linear servomechanism of time-varying systems with time-delay is proposed in the paper. By means of the operator, the differential equation is transferred to a more explicit algebraic form which is much easier than the numerical integration of nonlinear TPBVP derived from Pantryagin's maximum principle method. Furthermore, the method is established strictly based on the theory of convergence in the mean square and it is convenient and simple in computation. So the method can be applied to industry control and aeronautics and astronautics field which is frequently mixed with time varying and time delay. Some illustrative numerical examples are interpreted to support the technique.

关键词： Algorithms Convergence of numerical methods Differential equations Mathematical operators polynomials Time varying systems Walsh transforms