By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x...By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.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
Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency （FF） and a single second harmonic （SH） one by competing...Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency （FF） and a single second harmonic （SH） one by competing X^（2） （quadratic） and X^（3） （cubic） nonlinearities and birefringence. This system shares some of the nice properties of soliton system. On the phase-locked condition; we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.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
In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalit...In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalities.Then a smoothing Newton-like method is proposed for solving the reformulated system,which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.展开更多
By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation th...By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.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
We present an alternative scheme for preparing the superpositions of coherent states along a straight line of a cavity field using degenerate atom-cavity field Raman interaction. In the scheme, a collection of A-type ...We present an alternative scheme for preparing the superpositions of coherent states along a straight line of a cavity field using degenerate atom-cavity field Raman interaction. In the scheme, a collection of A-type three-level atoms is orderly sent through the cavity to interact with the cavity field adjusted by a microwave source connected to it, followed by state-selective measurements. In this way, we can prepare the superpositions of several coherent states along a straight line with arbitrary weighting factors for the cavity field. In the scheme, the coherence of the atom-cavity system may be maintained and the second microwave field is unnecessary, which is prior to the previous scheme.展开更多
A high power and low distortion 1.31 μm AlGaInAs/InP multiquantum well distributed feedback laser diode (MQW DFB LD) with RWG structure has been developed by MOCVD technique. The fiber output power of butterfly packa...A high power and low distortion 1.31 μm AlGaInAs/InP multiquantum well distributed feedback laser diode (MQW DFB LD) with RWG structure has been developed by MOCVD technique. The fiber output power of butterfly packaged module with optic isolator P f is more than 10 mW, threshold current is in the range of (13～20) mA, slope efficiency, E s>0.30 W/A and side mode suppression ratio, R S,M,S >35 dB. The composite second order, O C,S <-61 dBc and composite triple beat, B C,T <-65 dBc are obtained by test frequencies of (45～550) MHz with 60 PAL channels. In the test conditions the carrier to noise ratio, R C,N >51 dB.展开更多
The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The ca...The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The cauchy principle value （CPV） integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the comer problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.展开更多
基金Supported by the Scientific Research Foundation of Henan Provincial Education Com mittee(1999110018)
文摘By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.
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 No.10875106
文摘Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency （FF） and a single second harmonic （SH） one by competing X^（2） （quadratic） and X^（3） （cubic） nonlinearities and birefringence. This system shares some of the nice properties of soliton system. On the phase-locked condition; we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.
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 Guangdong Provincial Zhujiang Scholar Award Project,National Science Foundation of China(10671163,10871031)the National Basic Research Program under the Grant 2005CB321703Scientific Research Fund of Hunan Provincial Education Department(06A069,06C824)
文摘In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalities.Then a smoothing Newton-like method is proposed for solving the reformulated system,which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10735030, 90718041, and 40975038Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)
文摘By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.
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We present an alternative scheme for preparing the superpositions of coherent states along a straight line of a cavity field using degenerate atom-cavity field Raman interaction. In the scheme, a collection of A-type three-level atoms is orderly sent through the cavity to interact with the cavity field adjusted by a microwave source connected to it, followed by state-selective measurements. In this way, we can prepare the superpositions of several coherent states along a straight line with arbitrary weighting factors for the cavity field. In the scheme, the coherence of the atom-cavity system may be maintained and the second microwave field is unnecessary, which is prior to the previous scheme.
文摘A high power and low distortion 1.31 μm AlGaInAs/InP multiquantum well distributed feedback laser diode (MQW DFB LD) with RWG structure has been developed by MOCVD technique. The fiber output power of butterfly packaged module with optic isolator P f is more than 10 mW, threshold current is in the range of (13～20) mA, slope efficiency, E s>0.30 W/A and side mode suppression ratio, R S,M,S >35 dB. The composite second order, O C,S <-61 dBc and composite triple beat, B C,T <-65 dBc are obtained by test frequencies of (45～550) MHz with 60 PAL channels. In the test conditions the carrier to noise ratio, R C,N >51 dB.
基金Foundation item： Supported by the National Natural Science Foundation of China （Grant No.51009038/E091002）.
文摘The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The cauchy principle value （CPV） integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the comer problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.
