We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main...We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.展开更多
In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
Analytical solutions for contaminant transport are widely used for both theoretical and practical purposes.However,many existing solutions are obtained subject to an initial condition of zero concentration,which is of...Analytical solutions for contaminant transport are widely used for both theoretical and practical purposes.However,many existing solutions are obtained subject to an initial condition of zero concentration,which is often unrealistic in many practical cases.This article proposed a stepwise superposition approximation approach to solve the non-zero initial concentration problem for first-type and third-type boundary conditions by using the existing zero initial concentration solution.Theoretical examples showed that the approach was highly efficient if a proper superposition scheme with relative concentration increments was constructed.The key parameter that controlled the convergence speed was the time increment（△t） multiplied by the rate constant（λ）.The approach served also as an alternative way to make a convenient concentration calculation even if the non-zero initial concentration solution of a problem was known.展开更多
This paper gives the rank of matrix and equalities and inequalities of the difference number of non-zero eigenvalue, and discuss the equivalent description of multi angle of equalities for upper and lower bounds of th...This paper gives the rank of matrix and equalities and inequalities of the difference number of non-zero eigenvalue, and discuss the equivalent description of multi angle of equalities for upper and lower bounds of the inequality.展开更多
There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin partic...There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin particle and other spin particles. This paper shows: in Spin Topological Space, STS [1], the third component of zero spin particle possesses non-zero eigenvalues besides original zero value, this leads to a miraculous spin interaction phenomenon between zero spin particle and other spin particles. In STS, zero spin particle could "dissolve other spin particles", degrade the values of their Casimir operator, and decay these spin particles into other forms of spin particle.展开更多
Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, ...Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, have been used to control this kind of system, but there are some deficiencie s in those methods: some need accurate and some need complicated operation and e tc. In recent years, in need of controlling the industrial robots, aiming at com pletely tracking the ideal input for the controlled subject with repetitive character, a new research area, ILC (iterative learning control), has been devel oped in the control technology and theory. The iterative learning control method can make the controlled subject operate as desired in a definite time span, merely making use of the prior control experie nce of the system and searching for the desired control signal according to the practical and desired output signal. The process of searching is equal to that o f learning, during which we only need to measure the output signal to amend the control signal, not like the adaptive control strategy, which on line assesses t he complex parameters of the system. Besides, since the iterative learning contr ol relies little on the prior message of the subject, it has been well used in a lot of areas, especially the dynamic systems with strong non-linear coupling a nd high repetitive position precision and the control system with batch producti on. Since robot manipulator has the above-mentioned character, ILC can be very well used in robot manipulator. In the ILC, since the operation always begins with a certain initial state, init ial condition has been required in almost all convergence verification. Therefor e, in designing the controller, the initial state has to be restricted with some condition to guarantee the convergence of the algorithm. The settle of initial condition problem has long been pursued in the ILC. There are commonly two kinds of initial condition problems: one is zero initial error problem, another is non-zero initial error problem. In practice, the repe titive operation will invariably produce excursion of the iterative initial stat e from the desired initial state. As a result, the research on the second in itial problem has more practical meaning. In this paper, for the non-zero initial error problem, one novel robust ILC alg orithms, respectively combining PD type iterative learning control algorithm wit h the robust feedback control algorithm, has been presented. This novel robust ILC algorithm contain two parts: feedforward ILC algorithm and robust feedback algorithm, which can be used to restrain disturbance from param eter variation, mechanical nonlinearities and unmodeled dynamics and to achieve good performance as well. The feedforward ILC algorithm can be used to improve the tracking error and perf ormance of the system through iteratively learning from the previous operation, thus performing the tracking task very fast. The robust feedback algorithm could mainly be applied to make the real output of the system not deviate too much fr om the desired tracking trajectory, and guarantee the system’s robustness w hen there are exterior noises and variations of the system parameter. In this paper, in order to analyze the convergence of the algorithm, Lyapunov st ability theory has been used through properly selecting the Lyapunov function. T he result of the verification shows the feasibility of the novel robust iterativ e learning control in theory. Finally, aiming at the two-freedom rate robot, simulation has been made with th e MATLAB software. Furthermore, two groups of parameters are selected to validat e the robustness of the algorithm.展开更多
针对受非零均值高斯噪声干扰的双率Hammerstein输出误差系统,提出一种基于偏差补偿的递推最小二乘(bias compensation based recursive least squares,BCRLS)辨识算法。首先,利用多项式变换技术将目标系统转换为可直接采用双率采样数据...针对受非零均值高斯噪声干扰的双率Hammerstein输出误差系统,提出一种基于偏差补偿的递推最小二乘(bias compensation based recursive least squares,BCRLS)辨识算法。首先,利用多项式变换技术将目标系统转换为可直接采用双率采样数据进行辨识的模型,并利用递推最小二乘(recursive least squares,RLS)算法进行辨识。其次,为了对RLS算法给出的有偏参数估计进行有效补偿,在偏差补偿原理的基础上,通过引入非奇异矩阵和扩展信息向量求解偏差项中的参数,推导得到BCRLS辨识算法。最后,通过数值仿真实验表明,BCRLS算法能够获得双率Hammerstein输出误差系统的无偏参数估计;且具有较强的鲁棒性,其辨识精度不容易受到噪声均值和方差变化的影响。展开更多
Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected...Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected 2n-manifolds M and L, n > 1. A corollary is that each (n ? 1)-connected 2n-manifold admits selfmaps of degree larger than 1, n > 1. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree k map from a closed orientable 4-manifold M to a closed simply connected 4-manifold L in terms of their intersection forms; in particular, there is a map f : M → L of degree 1 if and only if the intersection form of L is isomorphic to a direct summand of that of M.展开更多
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.
基金Foundation item： Supported by the Sichuan Educational Comittee Science Foundation for Youths（08ZB002） Supported by the National Secience Foundation of Yibin University（2008Z02）
文摘In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
基金supported by the National Natural Science Foundation of China (No. 40872151)the Key Project in the National Science and Technology Pillar Program of China (No. 2006BAC06B05)
文摘Analytical solutions for contaminant transport are widely used for both theoretical and practical purposes.However,many existing solutions are obtained subject to an initial condition of zero concentration,which is often unrealistic in many practical cases.This article proposed a stepwise superposition approximation approach to solve the non-zero initial concentration problem for first-type and third-type boundary conditions by using the existing zero initial concentration solution.Theoretical examples showed that the approach was highly efficient if a proper superposition scheme with relative concentration increments was constructed.The key parameter that controlled the convergence speed was the time increment（△t） multiplied by the rate constant（λ）.The approach served also as an alternative way to make a convenient concentration calculation even if the non-zero initial concentration solution of a problem was known.
文摘This paper gives the rank of matrix and equalities and inequalities of the difference number of non-zero eigenvalue, and discuss the equivalent description of multi angle of equalities for upper and lower bounds of the inequality.
文摘There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin particle and other spin particles. This paper shows: in Spin Topological Space, STS [1], the third component of zero spin particle possesses non-zero eigenvalues besides original zero value, this leads to a miraculous spin interaction phenomenon between zero spin particle and other spin particles. In STS, zero spin particle could "dissolve other spin particles", degrade the values of their Casimir operator, and decay these spin particles into other forms of spin particle.
文摘Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, have been used to control this kind of system, but there are some deficiencie s in those methods: some need accurate and some need complicated operation and e tc. In recent years, in need of controlling the industrial robots, aiming at com pletely tracking the ideal input for the controlled subject with repetitive character, a new research area, ILC (iterative learning control), has been devel oped in the control technology and theory. The iterative learning control method can make the controlled subject operate as desired in a definite time span, merely making use of the prior control experie nce of the system and searching for the desired control signal according to the practical and desired output signal. The process of searching is equal to that o f learning, during which we only need to measure the output signal to amend the control signal, not like the adaptive control strategy, which on line assesses t he complex parameters of the system. Besides, since the iterative learning contr ol relies little on the prior message of the subject, it has been well used in a lot of areas, especially the dynamic systems with strong non-linear coupling a nd high repetitive position precision and the control system with batch producti on. Since robot manipulator has the above-mentioned character, ILC can be very well used in robot manipulator. In the ILC, since the operation always begins with a certain initial state, init ial condition has been required in almost all convergence verification. Therefor e, in designing the controller, the initial state has to be restricted with some condition to guarantee the convergence of the algorithm. The settle of initial condition problem has long been pursued in the ILC. There are commonly two kinds of initial condition problems: one is zero initial error problem, another is non-zero initial error problem. In practice, the repe titive operation will invariably produce excursion of the iterative initial stat e from the desired initial state. As a result, the research on the second in itial problem has more practical meaning. In this paper, for the non-zero initial error problem, one novel robust ILC alg orithms, respectively combining PD type iterative learning control algorithm wit h the robust feedback control algorithm, has been presented. This novel robust ILC algorithm contain two parts: feedforward ILC algorithm and robust feedback algorithm, which can be used to restrain disturbance from param eter variation, mechanical nonlinearities and unmodeled dynamics and to achieve good performance as well. The feedforward ILC algorithm can be used to improve the tracking error and perf ormance of the system through iteratively learning from the previous operation, thus performing the tracking task very fast. The robust feedback algorithm could mainly be applied to make the real output of the system not deviate too much fr om the desired tracking trajectory, and guarantee the system’s robustness w hen there are exterior noises and variations of the system parameter. In this paper, in order to analyze the convergence of the algorithm, Lyapunov st ability theory has been used through properly selecting the Lyapunov function. T he result of the verification shows the feasibility of the novel robust iterativ e learning control in theory. Finally, aiming at the two-freedom rate robot, simulation has been made with th e MATLAB software. Furthermore, two groups of parameters are selected to validat e the robustness of the algorithm.
文摘针对受非零均值高斯噪声干扰的双率Hammerstein输出误差系统,提出一种基于偏差补偿的递推最小二乘(bias compensation based recursive least squares,BCRLS)辨识算法。首先,利用多项式变换技术将目标系统转换为可直接采用双率采样数据进行辨识的模型,并利用递推最小二乘(recursive least squares,RLS)算法进行辨识。其次,为了对RLS算法给出的有偏参数估计进行有效补偿,在偏差补偿原理的基础上,通过引入非奇异矩阵和扩展信息向量求解偏差项中的参数,推导得到BCRLS辨识算法。最后,通过数值仿真实验表明,BCRLS算法能够获得双率Hammerstein输出误差系统的无偏参数估计;且具有较强的鲁棒性,其辨识精度不容易受到噪声均值和方差变化的影响。
文摘Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected 2n-manifolds M and L, n > 1. A corollary is that each (n ? 1)-connected 2n-manifold admits selfmaps of degree larger than 1, n > 1. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree k map from a closed orientable 4-manifold M to a closed simply connected 4-manifold L in terms of their intersection forms; in particular, there is a map f : M → L of degree 1 if and only if the intersection form of L is isomorphic to a direct summand of that of M.
