Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary valu...Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary value problem and variational equations, then replaced the complex resistivity of the model with the Cole-Cole model's parameters under ignoring the EM effect. Through solving the last linear equations, electric potentials of all the model's points were obtained. With changing model's parameters, the authors got different curves of the Fs and phases. According to the results of the simulation, the algorithm is proved to be correct and adaptable.展开更多
Many systems of fuzzy linear equations do not have solutions when the solution concept is based on α cuts and interval arithmetic. In this paper,we establish the relations between the systems of fuzzy linear equation...Many systems of fuzzy linear equations do not have solutions when the solution concept is based on α cuts and interval arithmetic. In this paper,we establish the relations between the systems of fuzzy linear equations and the possibilistic linear programming problems and present an alternative method of solving the systems of fuzzy linear equations.展开更多
In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Fie...In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.展开更多
A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. T...A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.展开更多
This study presented the application of partial least squares regression （PLSR） in estimating daily pan evaporation by utilizing the unique feature of PLSR in eliminating collinearity issues in predictor variables. ...This study presented the application of partial least squares regression （PLSR） in estimating daily pan evaporation by utilizing the unique feature of PLSR in eliminating collinearity issues in predictor variables. The climate variables and daily pan evaporation data measured at two weather stations located near Elephant Butte Reservoir, New Mexico, USA and a weather station located in Shanshan County, Xinjiang, China were used in the study. The nonlinear relationship between climate variables and daily pan evaporation was successfully modeled using PLSR approach by solving collinearity that exists in the climate variables. The modeling results were compared to artificial neural networks （ANN） models with the same input variables. The resuits showed that the nonlinear equations developed using PLSR has similar performance with complex ANN approach for the study sites. The modeling process was straightforward and the equations were simpler and more explicit than the ANN black-box models.展开更多
In this paper, an exponential method is presented for the approximate solutions of the HIV infection model of CD4＋T. The method is based on exponential polynomi- als and collocation points. This model problem corresp...In this paper, an exponential method is presented for the approximate solutions of the HIV infection model of CD4＋T. The method is based on exponential polynomi- als and collocation points. This model problem corresponds to a system of nonlinear ordinary differential equations. Matrix relations are constructed for the exponential functions. By aid of these matrix relations and the collocation points, the proposed technique transforms the model problem into a system of nonlinear algebraic equations. By solving the system of the algebraic equations, the unknown coefficients are com- puted and thus the approximate solutions are obtained. The applications of the method for the considered problem are given and the comparisons are made with the other methods.展开更多
基金Project supported by the National Key Technology R &D Program(2006BAB01A07)
文摘Using the finite element method and Cole-Cole model for dual-frequency IP method to research numerical simulation, the authors introduced the fundamental principle of the dual-frequency IP method and the boundary value problem and variational equations, then replaced the complex resistivity of the model with the Cole-Cole model's parameters under ignoring the EM effect. Through solving the last linear equations, electric potentials of all the model's points were obtained. With changing model's parameters, the authors got different curves of the Fs and phases. According to the results of the simulation, the algorithm is proved to be correct and adaptable.
文摘Many systems of fuzzy linear equations do not have solutions when the solution concept is based on α cuts and interval arithmetic. In this paper,we establish the relations between the systems of fuzzy linear equations and the possibilistic linear programming problems and present an alternative method of solving the systems of fuzzy linear equations.
文摘In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.
基金supported by National Natural Science Foundation of China (Grant No.10901027)
文摘A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.
基金supported in part by the National Natural Science Founda-tion of China (Grant Nos.51069017,41071026)their sincere appreciation of the reviewers’ valuable suggestions and comments in improving the quality of this paper
文摘This study presented the application of partial least squares regression （PLSR） in estimating daily pan evaporation by utilizing the unique feature of PLSR in eliminating collinearity issues in predictor variables. The climate variables and daily pan evaporation data measured at two weather stations located near Elephant Butte Reservoir, New Mexico, USA and a weather station located in Shanshan County, Xinjiang, China were used in the study. The nonlinear relationship between climate variables and daily pan evaporation was successfully modeled using PLSR approach by solving collinearity that exists in the climate variables. The modeling results were compared to artificial neural networks （ANN） models with the same input variables. The resuits showed that the nonlinear equations developed using PLSR has similar performance with complex ANN approach for the study sites. The modeling process was straightforward and the equations were simpler and more explicit than the ANN black-box models.
文摘In this paper, an exponential method is presented for the approximate solutions of the HIV infection model of CD4＋T. The method is based on exponential polynomi- als and collocation points. This model problem corresponds to a system of nonlinear ordinary differential equations. Matrix relations are constructed for the exponential functions. By aid of these matrix relations and the collocation points, the proposed technique transforms the model problem into a system of nonlinear algebraic equations. By solving the system of the algebraic equations, the unknown coefficients are com- puted and thus the approximate solutions are obtained. The applications of the method for the considered problem are given and the comparisons are made with the other methods.
