There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral dela...By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.展开更多
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 the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a ...In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.展开更多
The parameters are considered as normal random quantities in filtering and prediction, and the observation equations usually are nonlinear ones. The nonlinear equations should be deployed in Taylor抯 formula, adopting...The parameters are considered as normal random quantities in filtering and prediction, and the observation equations usually are nonlinear ones. The nonlinear equations should be deployed in Taylor抯 formula, adopting to first power of term, by linear static filtering and prediction, and transformed into linear equations, and then the tested estimating values and their variances according to some statistical methods such as maximum tested estimation. The formulas of nonlinear static filtering and prediction, adapting to quadratic and cross terms by Taylor抯 progression formula, and the compu-tation formulas were also deduced that filtering the corresponding function nonlinear sig-nals and predicting the signals with nonlinear function. Meanwhile, it is been testified that the formula of static filtering and prediction is a special case of nonlinear filtering formulas.展开更多
The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infinitec...The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infiniteconservation laws of the GNNV equation are obtained directly,without too much trick like Hirota’s bilinear method.展开更多
In 1998, Maschietti constructed several cyclic difference sets from monomial hyperovals. R. Evans, H.D.L. Holloman, C. Krattnthaler and Qing Xiang gave an algebraic proof of the two autocorrelation property of the rel...In 1998, Maschietti constructed several cyclic difference sets from monomial hyperovals. R. Evans, H.D.L. Holloman, C. Krattnthaler and Qing Xiang gave an algebraic proof of the two autocorrelation property of the related binary sequence. In this paper, we show that hyperovals are very closely related to two-to-one maps, and then we proceed to generalize Maschietti＇s result.展开更多
We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for...We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for d=2.The proof for smoothness is based on elementary calculations on the pushforwards of specific quadratic differentials,following Thurston and Epstein,while the proof for irreducibility is a simplified version of Lau-Schleicher’s proof by using elementary arithmetic properties of kneading sequence instead of internal addresses.展开更多
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
文摘By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.
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.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,61021004,10735030Shanghai Leading Academic Discipline Project under Grant No.B412Program for Changjiang Scholars and Innovative Research Team in University(IRT0734)
文摘In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.
文摘The parameters are considered as normal random quantities in filtering and prediction, and the observation equations usually are nonlinear ones. The nonlinear equations should be deployed in Taylor抯 formula, adopting to first power of term, by linear static filtering and prediction, and transformed into linear equations, and then the tested estimating values and their variances according to some statistical methods such as maximum tested estimation. The formulas of nonlinear static filtering and prediction, adapting to quadratic and cross terms by Taylor抯 progression formula, and the compu-tation formulas were also deduced that filtering the corresponding function nonlinear sig-nals and predicting the signals with nonlinear function. Meanwhile, it is been testified that the formula of static filtering and prediction is a special case of nonlinear filtering formulas.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10735030,11075055,61021004,90718041,Shanghai Leading Academic Discipline Project (No. B412)Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)
文摘The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infiniteconservation laws of the GNNV equation are obtained directly,without too much trick like Hirota’s bilinear method.
文摘In 1998, Maschietti constructed several cyclic difference sets from monomial hyperovals. R. Evans, H.D.L. Holloman, C. Krattnthaler and Qing Xiang gave an algebraic proof of the two autocorrelation property of the related binary sequence. In this paper, we show that hyperovals are very closely related to two-to-one maps, and then we proceed to generalize Maschietti＇s result.
基金supported by National Natural Science Foundation of China (Grant No. 11101402)
文摘We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for d=2.The proof for smoothness is based on elementary calculations on the pushforwards of specific quadratic differentials,following Thurston and Epstein,while the proof for irreducibility is a simplified version of Lau-Schleicher’s proof by using elementary arithmetic properties of kneading sequence instead of internal addresses.
