In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm ...In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm for the variational model.Some numerical results are presented to illustrate the efficiency of the展开更多
We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems a...We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton’s principle.Secondly,the definitions of Mei symmetry on time scales are given and its criterions are deduced.Finally,Mei’s symmetry theorems for time scales nonshifted holonomic conservative systems,time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved,and new conserved quantities of above systems are obtained.Results are illustrated with two examples.展开更多
In this paper,an optimal switch-time control problem is solved for a class of impulsive switched autonomous systems.The considered systems jump at the switching times,and the sequence of active subsystems is pre-speci...In this paper,an optimal switch-time control problem is solved for a class of impulsive switched autonomous systems.The considered systems jump at the switching times,and the sequence of active subsystems is pre-specified.The control variables consist of the impulse times and a set of scalars which determine the jump amplitudes.Moreover,the subsystems do not require a refractory period,which can bring more generality.Using the calculus of variation,the partial derivatives of the cost with respect to the control variables are derived,based on which the optimality conditions are given.Meanwhile,the obtained formulas can be used in some gradient descent algorithms to locate the optimal control variables.Finally,the viability of the proposed method is illustrated through two numerical examples.展开更多
The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variation...The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variational problem defined on Ck(Ω), in which the base functions are polynomials and the computation of problems is transferred to compute the coefficients of the base functions. The theoretical treatment and some simple examples are provided for understanding the modification procedure of the methods. A modified least square method on difference scheme is introduced with a general matrix form of dynamical systems. We emphasize the simplicity of the algorithm and only use Euler algorithm to compute initial value problems of ODEs. A better algorithm is needed to reduce the stiffness of ODEs.展开更多
基金supported by the National Natural Science Foundation of China(11101218)Natural Science Fouadation for Colleges and Universities in Jangsu Province(11KJB110009)the Scientific Research Foundation of NUPT(NY209025)
文摘In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm for the variational model.Some numerical results are presented to illustrate the efficiency of the
基金supported by the National Natural Science Foundation of China(Grants 11972241 and 11572212)the Natural Science Foundation of Jiangsu Province of China(Grant BK20191454).
文摘We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton’s principle.Secondly,the definitions of Mei symmetry on time scales are given and its criterions are deduced.Finally,Mei’s symmetry theorems for time scales nonshifted holonomic conservative systems,time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved,and new conserved quantities of above systems are obtained.Results are illustrated with two examples.
基金supported by the National Natural Science Foundation of China under[Grant 61803238 and Grant 61873151].
文摘In this paper,an optimal switch-time control problem is solved for a class of impulsive switched autonomous systems.The considered systems jump at the switching times,and the sequence of active subsystems is pre-specified.The control variables consist of the impulse times and a set of scalars which determine the jump amplitudes.Moreover,the subsystems do not require a refractory period,which can bring more generality.Using the calculus of variation,the partial derivatives of the cost with respect to the control variables are derived,based on which the optimality conditions are given.Meanwhile,the obtained formulas can be used in some gradient descent algorithms to locate the optimal control variables.Finally,the viability of the proposed method is illustrated through two numerical examples.
文摘The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variational problem defined on Ck(Ω), in which the base functions are polynomials and the computation of problems is transferred to compute the coefficients of the base functions. The theoretical treatment and some simple examples are provided for understanding the modification procedure of the methods. A modified least square method on difference scheme is introduced with a general matrix form of dynamical systems. We emphasize the simplicity of the algorithm and only use Euler algorithm to compute initial value problems of ODEs. A better algorithm is needed to reduce the stiffness of ODEs.
