One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some un...One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.展开更多
The main purpose of this work is to find for any non-negative measure, the relations between the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure. As applications, the author obtained the ...The main purpose of this work is to find for any non-negative measure, the relations between the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure. As applications, the author obtained the explicit Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and the Gori-Micchelli weight.展开更多
With a view to obtaining an exact closed form solution to the Schroedinger equation for a variety of hypercentral potentials, we investigate further application of an ansatz. This method is good enough for many kinds ...With a view to obtaining an exact closed form solution to the Schroedinger equation for a variety of hypercentral potentials, we investigate further application of an ansatz. This method is good enough for many kinds of potentials, but in this article it applies to a type of the hypercentral singular potentials V（x） = ax^2 ＋ bx^-4＋ cx^-6 and exponential hypercentral Morse potential U （x） = Uo （ e^-2ax - 2 e^-ax） for three interacting particles. The Morse potential is used for diatomic molecule while this method will be successfully used for many atomic molecules. The three-body potentials are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of Jacobi relative coordinates p, A, and R, in terms of three particle positions r1, r2, and r3. We discuss some results obtained by using harmonic and anharmonic oscillators, however the hypercentral potential can be easily generalized in order to allow a systematic anaiysis, which admits an exact solution of the wave equation. This method is also applied to some other types of three-body, four-body, ..., interacting potentials.展开更多
Accuracy of a simulation strongly depends on the grid quality. Here, quality means orthogonality at the boundaries and quasi-orthogonality within the critical regions, smoothness, bounded aspect ratios and solution ad...Accuracy of a simulation strongly depends on the grid quality. Here, quality means orthogonality at the boundaries and quasi-orthogonality within the critical regions, smoothness, bounded aspect ratios and solution adaptive behaviour. It is not recommended to refine the parts of the domain where the solution shows little variation. It is desired to concentrate grid points and cells in the part of the domain where the solution shows strong gradients or variations. We present a simple, effective and com- putationally efficient approach for quadrilateral mesh adaptation. Several numerical examples are presented for supporting our claim.展开更多
By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function so...By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.展开更多
In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for three nonlinear differential-difference equations are obtained.
Based on the Jacobian matrices relating the input speeds with the output speeds of linkages, a general method, which is used for solving the singularities of planar multi-loop multi-DOF linkages, is presented. The fou...Based on the Jacobian matrices relating the input speeds with the output speeds of linkages, a general method, which is used for solving the singularities of planar multi-loop multi-DOF linkages, is presented. The four kinds of singularities of 2-DOF planar seven-bar linkages used in hybrid actuators are analyzed in detail by this method. Its five kinds of singular positions whose characteristics are discussed respectively are discovered. Three approaches are proposed on how to avoid the singular positions of planar multi-loop multi-DOF linkages. Based on the assemblability of planar single-loop N-bar chains or linkages, the geometry conditions are investigated and discovered to avoid the singular positions of the linkages. In order to versify aforementioned conclusions, a case is given in which the singular curves are plotted and simulated.展开更多
Currently, most visual servoing system must be calibrated, while it is impossible to calibrate cameras and robot models precisely in industrial practice, so a novel dynamic uncalibrated eye-in-hand visual servoing sys...Currently, most visual servoing system must be calibrated, while it is impossible to calibrate cameras and robot models precisely in industrial practice, so a novel dynamic uncalibrated eye-in-hand visual servoing system of tracking a moving target is proposed. The method does not require calibration of camera and robot kinematic models. Vision guided algorithm for tracking dynamic image is developed through minimizing nonlinear objective function. For the large residual has not been approximated in dynamic environment and the change of composite image Jacobian with time increment has not been computed in visual servoing system now,large residuals are dynamic approximated and the change of composite image Jacobian at each iterative step is computed. Simulation results demonstrate the validity of these approaches.展开更多
Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigen...Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigenvalues and the corresponding wave functions expressed in terms of a Jacobi polynomial are also obtained using the parametric generalization of the Nikiforov-Uvarov （NU） method. Under limiting cases our result are in agreement with the existing literature. Our results could be used to study the interactions and binding energies of the central potential for diatomic molecules in the relativistic framework which have many applications in physics and some others related disciplines.展开更多
基金National Natural Science Foundation of China under Grant No.10172056
文摘One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.
文摘The main purpose of this work is to find for any non-negative measure, the relations between the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure. As applications, the author obtained the explicit Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and the Gori-Micchelli weight.
文摘With a view to obtaining an exact closed form solution to the Schroedinger equation for a variety of hypercentral potentials, we investigate further application of an ansatz. This method is good enough for many kinds of potentials, but in this article it applies to a type of the hypercentral singular potentials V（x） = ax^2 ＋ bx^-4＋ cx^-6 and exponential hypercentral Morse potential U （x） = Uo （ e^-2ax - 2 e^-ax） for three interacting particles. The Morse potential is used for diatomic molecule while this method will be successfully used for many atomic molecules. The three-body potentials are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of Jacobi relative coordinates p, A, and R, in terms of three particle positions r1, r2, and r3. We discuss some results obtained by using harmonic and anharmonic oscillators, however the hypercentral potential can be easily generalized in order to allow a systematic anaiysis, which admits an exact solution of the wave equation. This method is also applied to some other types of three-body, four-body, ..., interacting potentials.
文摘Accuracy of a simulation strongly depends on the grid quality. Here, quality means orthogonality at the boundaries and quasi-orthogonality within the critical regions, smoothness, bounded aspect ratios and solution adaptive behaviour. It is not recommended to refine the parts of the domain where the solution shows little variation. It is desired to concentrate grid points and cells in the part of the domain where the solution shows strong gradients or variations. We present a simple, effective and com- putationally efficient approach for quadrilateral mesh adaptation. Several numerical examples are presented for supporting our claim.
基金the State Key Basic Research Program of China under Grant No.2004CB418304
文摘By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.
基金The project supported by National Natural Science Foundation of China under Grant Nos.90511009 and 40305006
文摘In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for three nonlinear differential-difference equations are obtained.
文摘Based on the Jacobian matrices relating the input speeds with the output speeds of linkages, a general method, which is used for solving the singularities of planar multi-loop multi-DOF linkages, is presented. The four kinds of singularities of 2-DOF planar seven-bar linkages used in hybrid actuators are analyzed in detail by this method. Its five kinds of singular positions whose characteristics are discussed respectively are discovered. Three approaches are proposed on how to avoid the singular positions of planar multi-loop multi-DOF linkages. Based on the assemblability of planar single-loop N-bar chains or linkages, the geometry conditions are investigated and discovered to avoid the singular positions of the linkages. In order to versify aforementioned conclusions, a case is given in which the singular curves are plotted and simulated.
文摘Currently, most visual servoing system must be calibrated, while it is impossible to calibrate cameras and robot models precisely in industrial practice, so a novel dynamic uncalibrated eye-in-hand visual servoing system of tracking a moving target is proposed. The method does not require calibration of camera and robot kinematic models. Vision guided algorithm for tracking dynamic image is developed through minimizing nonlinear objective function. For the large residual has not been approximated in dynamic environment and the change of composite image Jacobian with time increment has not been computed in visual servoing system now,large residuals are dynamic approximated and the change of composite image Jacobian at each iterative step is computed. Simulation results demonstrate the validity of these approaches.
文摘Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigenvalues and the corresponding wave functions expressed in terms of a Jacobi polynomial are also obtained using the parametric generalization of the Nikiforov-Uvarov （NU） method. Under limiting cases our result are in agreement with the existing literature. Our results could be used to study the interactions and binding energies of the central potential for diatomic molecules in the relativistic framework which have many applications in physics and some others related disciplines.
