A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identifica...A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.展开更多
In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable non...In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate Adomian polynomials. Next we compare the results by the Adomian decomposition method using the classic Adomian polynomials with the results by the Rach-Adomian-Meyers modified decomposition method incorporating the degenerate Adomian polynomials, which itself has been shown to be a confluence of the Adomian decomposition method and the power series method. Convergence acceleration techniques including the diagonal Pade approximants are considered, and new numeric algorithms for the multistage decomposition are deduced using the degenerate Adomian polynomials. Our new technique provides a significant advantage for automated calculations when computing the power series form of the solution for nonlinear ordinary differential equations. Several expository examples are investigated to demonstrate its reliability and efficiency.展开更多
Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding...Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that q^s can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis （NB） or Optimal Normal Basis （ONB） is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about 42% to 74% less than φ-ary method. For some elliptic curves, our algorithm is also taster than Mǖller＇s algorithm. In addition, an effective algorithm is provided for finding such integer s.展开更多
Linear dispersion relation for linear wave and a Kadomtsev-Petviashvili (KP) equation for nonlinearwave are given for the unmagnetized two-ion-temperature cold dusty plasma with many different dust grain species.The n...Linear dispersion relation for linear wave and a Kadomtsev-Petviashvili (KP) equation for nonlinearwave are given for the unmagnetized two-ion-temperature cold dusty plasma with many different dust grain species.The numerical results of variations of linear dispersion with respect to the different dust size distribution are given.Moreover,how the amplitude,width,and propagation velocity of solitary wave vary vs different dust size distribution isalso studied numerically in this paper.展开更多
As a continuing investigation of an earlier work that establishes the cofiinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness...As a continuing investigation of an earlier work that establishes the cofiinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness up to the first order post-Newtonian approximation. With the help of observed bounds on the scalar field in the Solar System, we show that the seventh-order polynomial equation determining the distance ratio among the three masses has either one or three positive roots. However, in the case with three positive roots, it is found that two positive roots break down the slow-motion condition for the post-Newtonian approximation so that only one positive root is physically valid. The resulting uniqueness suggests that the locations of the three masses are very close to their Newtonian positions with post-Newtonian corrections of general relativity and the scalar field. We also prove that, in the framework of the scalar-tensor theory, the angular velocity of the collinear configuration is always less than the Newtonian one when all other parameters are fixed. These results are valid only for three-body systems where upper-bounds on the scalar field are compatible with those of the Solar System.展开更多
In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of un...In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.展开更多
The paper is devoted to the analysis of certain dynamical properties of a family of iterative Newton type methods used to find roots of non-linear equations. We present a procedure for constructing polynomials in such...The paper is devoted to the analysis of certain dynamical properties of a family of iterative Newton type methods used to find roots of non-linear equations. We present a procedure for constructing polynomials in such a way that superattracting cycles of any prescribed length occur when these iterative methods are applied. This paper completes the study begun in Amat, Bermúclez, Busquier, et al., (2009).展开更多
基金Support by China 973 Project (No. 2002CB312200).
文摘A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.
文摘In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate Adomian polynomials. Next we compare the results by the Adomian decomposition method using the classic Adomian polynomials with the results by the Rach-Adomian-Meyers modified decomposition method incorporating the degenerate Adomian polynomials, which itself has been shown to be a confluence of the Adomian decomposition method and the power series method. Convergence acceleration techniques including the diagonal Pade approximants are considered, and new numeric algorithms for the multistage decomposition are deduced using the degenerate Adomian polynomials. Our new technique provides a significant advantage for automated calculations when computing the power series form of the solution for nonlinear ordinary differential equations. Several expository examples are investigated to demonstrate its reliability and efficiency.
基金Supported by the National 973 High Technology Projects (No. G1998030420)
文摘Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that q^s can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis （NB） or Optimal Normal Basis （ONB） is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about 42% to 74% less than φ-ary method. For some elliptic curves, our algorithm is also taster than Mǖller＇s algorithm. In addition, an effective algorithm is provided for finding such integer s.
基金Supported by the National Natural Science Foundation of China under Grant No.10875082the Natural Science Foundation of Gansu Province under Grant No.3ZS061-A25-013the Natural Science Foundation of Northwest Normal University under Grant No.NWNUKJCXGC-03-17,03-48
文摘Linear dispersion relation for linear wave and a Kadomtsev-Petviashvili (KP) equation for nonlinearwave are given for the unmagnetized two-ion-temperature cold dusty plasma with many different dust grain species.The numerical results of variations of linear dispersion with respect to the different dust size distribution are given.Moreover,how the amplitude,width,and propagation velocity of solitary wave vary vs different dust size distribution isalso studied numerically in this paper.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11573015 and J1210039the Innovation Training Project for Undergraduates of Nanjing University,China
文摘As a continuing investigation of an earlier work that establishes the cofiinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness up to the first order post-Newtonian approximation. With the help of observed bounds on the scalar field in the Solar System, we show that the seventh-order polynomial equation determining the distance ratio among the three masses has either one or three positive roots. However, in the case with three positive roots, it is found that two positive roots break down the slow-motion condition for the post-Newtonian approximation so that only one positive root is physically valid. The resulting uniqueness suggests that the locations of the three masses are very close to their Newtonian positions with post-Newtonian corrections of general relativity and the scalar field. We also prove that, in the framework of the scalar-tensor theory, the angular velocity of the collinear configuration is always less than the Newtonian one when all other parameters are fixed. These results are valid only for three-body systems where upper-bounds on the scalar field are compatible with those of the Solar System.
文摘In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.
基金supported in part by Spanish Grants MTM2007-62945Fondecyt Grant 1095025, Chile
文摘The paper is devoted to the analysis of certain dynamical properties of a family of iterative Newton type methods used to find roots of non-linear equations. We present a procedure for constructing polynomials in such a way that superattracting cycles of any prescribed length occur when these iterative methods are applied. This paper completes the study begun in Amat, Bermúclez, Busquier, et al., (2009).
